Subgroups — #28292707

Order 13568.

9494 conjugacy classes of subgroups.

The subgroup lattice has 1484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288872	C₂	1	2	yes	maximal, complemented
2	#20288870	C₂	1	3	yes	maximal, complemented
3	#20288869	C₂	1	3	yes	maximal, complemented
4	#20288868	C₂	1	6	yes	maximal, complemented
5	#20288867	C₂	1	3	yes	maximal, complemented
6	#20288866	C₂	1	6	yes	maximal, complemented
7	#20288401	C₂	1	6	yes	maximal, complemented
8	#20288399	C₂	1	6	yes	maximal, complemented
9	#20288397	C₂	1	6	yes	maximal, complemented
10	#20288349	C₂	1	3	yes	maximal, complemented
11	#20288347	C₂	1	3	yes	maximal, complemented
12	#20288345	C₂	1	6	yes	maximal, complemented
13	#20288343	C₂	1	6	yes	maximal, complemented
14	C₂×#120×D₅₃	C₂	1	3	yes	maximal, complemented
15	C₅₃×#3532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#13133263	C₂²	1	3	yes	complemented
18	C₂×#13133262	C₂²	1	3	yes	complemented
19	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
20	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
21	#16811366	C₂²	1	1	yes	characteristic, complemented
22	#16811366	C₂²	1	3	yes	complemented
23	#16811365	C₂²	1	3	yes	complemented
24	#16811364	C₂²	1	2	yes	complemented
25	#16811363	C₂²	1	3	yes	complemented
26	#16811362	C₂²	1	3	yes	complemented
27	#16811362	C₂²	1	6	yes	complemented
28	#16811361	C₂²	1	6	yes	complemented
29	#16811360	C₂²	1	1	yes	characteristic, complemented
30	#16811304	C₂²	1	3	yes	complemented
31	#16811303	C₂²	1	3	yes	complemented
32	#16811303	C₂²	1	6	yes	complemented
33	#16811302	C₂²	1	6	yes	complemented
34	#16811301	C₂²	1	3	yes	complemented
35	#16811301	C₂²	1	6	yes	complemented
36	#16811300	C₂²	1	6	yes	complemented
37	#16811299	C₂²	1	6	yes	complemented
38	#16811298	C₂²	1	6	yes	complemented
39	#16811298	C₂²	1	6	yes	complemented
40	#16811298	C₂²	1	6	yes	complemented
41	#16811297	C₂²	1	6	yes	complemented
42	#16811296	C₂²	1	6	yes	complemented
43	#16811270	C₂²	1	6	yes	complemented
44	#16811270	C₂²	1	6	yes	complemented
45	#16811270	C₂²	1	6	yes	complemented
46	#16811269	C₂²	1	6	yes	complemented
47	#16811268	C₂²	1	6	yes	complemented
48	#16811267	C₂²	1	6	yes	complemented
49	#16811266	C₂²	1	6	yes	complemented
50	#16811266	C₂²	1	6	yes	complemented
51	#16811266	C₂²	1	6	yes	complemented
52	#16811265	C₂²	1	6	yes	complemented
53	#16811265	C₂²	1	6	yes	complemented
54	#16811265	C₂²	1	6	yes	complemented
55	#16811265	C₂²	1	6	yes	complemented
56	#16811264	C₂²	1	6	yes	complemented
57	#16811263	C₂²	1	6	yes	complemented
58	#16811263	C₂²	1	6	yes	complemented
59	#16811262	C₂²	1	6	yes	complemented
60	#16811262	C₂²	1	6	yes	complemented
61	#16811262	C₂²	1	6	yes	complemented
62	#16811262	C₂²	1	6	yes	complemented
63	#16811261	C₂²	1	6	yes	complemented
64	#16811260	C₂²	1	6	yes	complemented
65	#16811260	C₂²	1	6	yes	complemented
66	D₄×D₂₁₂	C₂²	1	6	yes	complemented
67	#16811258	C₂²	1	6	yes	complemented
68	#16811258	C₂²	1	3	yes	complemented
69	#16811257	C₂²	1	6	yes	complemented
70	#16811257	C₂²	1	6	yes	complemented
71	#16811257	C₂²	1	6	yes	complemented
72	#16811257	C₂²	1	6	yes	complemented
73	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
74	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
75	#16811255	C₂²	1	3	yes	complemented
76	#16811255	C₂²	1	6	yes	complemented
77	#16811255	C₂²	1	3	yes	complemented
78	#16811255	C₂²	1	6	yes	complemented
79	#16811248	C₂²	1	6	yes	complemented
80	#16811212	C₂²	1	6	yes	complemented
81	#16811212	C₂²	1	6	yes	complemented
82	#16811211	C₂²	1	6	yes	complemented
83	#16811209	C₂²	1	6	yes	complemented
84	#16811209	C₂²	1	6	yes	complemented
85	#16811208	C₂²	1	6	yes	complemented
86	#16811208	C₂²	1	6	yes	complemented
87	#16811207	C₂²	1	6	yes	complemented
88	#16811207	C₂²	1	6	yes	complemented
89	#16811205	C₂²	1	6	yes	complemented
90	#16811205	C₂²	1	6	yes	complemented
91	#16811191	C₂²	1	6	yes	complemented
92	#16811190	C₂²	1	3	yes	complemented
93	#16811189	C₂²	1	6	yes	complemented
94	#16811189	C₂²	1	6	yes	complemented
95	#16811188	C₂²	1	6	yes	complemented
96	#16811186	C₂²	1	6	yes	complemented
97	#16811184	C₂²	1	6	yes	complemented
98	#16811184	C₂²	1	6	yes	complemented
99	#16811183	C₂²	1	6	yes	complemented
100	#16811183	C₂²	1	6	yes	complemented
101	#16811183	C₂²	1	6	yes	complemented
102	#16811182	C₂²	1	3	yes	complemented
103	#16811181	C₂²	1	6	yes	complemented
104	#16811181	C₂²	1	6	yes	complemented
105	#16811181	C₂²	1	6	yes	complemented
106	#16811136	C₂²	1	6	yes	complemented
107	#16811135	C₂²	1	3	yes	complemented
108	#16811133	C₂²	1	6	yes	complemented
109	#16811132	C₂²	1	6	yes	complemented
110	#16811132	C₂²	1	6	yes	complemented
111	#16811131	C₂²	1	6	yes	complemented
112	#16811130	C₂²	1	3	yes	complemented
113	C₂×#13133187	C₂²	1	6	yes	complemented
114	C₂×#13133187	C₂²	1	3	yes	complemented
115	C₂×#13133187	C₂²	1	3	yes	complemented
116	C₂×#13133186	C₂²	1	3	yes	complemented
117	C₂×#13133185	C₂²	1	6	yes	complemented
118	C₂×#13133185	C₂²	1	3	yes	complemented
119	C₂×#13133185	C₂²	1	3	yes	complemented
120	#120×D₅₃	C₂²	1	6	yes	complemented
121	#120×D₅₃	C₂²	1	6	yes	complemented
122	#120×D₅₃	C₂²	1	6	yes	complemented
123	#120×D₅₃	C₂²	1	6	yes	complemented
124	#120×D₅₃	C₂²	1	6	yes	complemented
125	#120×D₅₃	C₂²	1	6	yes	complemented
126	#120×D₅₃	C₂²	1	6	yes	complemented
127	#120×D₅₃	C₂²	1	6	yes	complemented
128	#120×D₅₃	C₂²	1	6	yes	complemented
129	#16811097	C₂²	1	3	yes	complemented
130	#16811096	C₂²	1	3	yes	complemented
131	#16811095	C₂²	1	6	yes	complemented
132	#16811095	C₂²	1	6	yes	complemented
133	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
134	C₂×C₂²⋊C₄×D₅₃	C₂²	1	3	yes	complemented
135	C₅₃×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#560	C₂²	1	3	yes	complemented
137	C₅₃×#551	C₂²	1	3	yes	complemented
138	C₅₃×#546	C₂²	1	6	yes	complemented
139	D₄²×C₅₃	C₂²	1	3	yes	complemented
140	C₅₃×#538	C₂²	1	6	yes	complemented
141	C₅₃×#535	C₂²	1	3	yes	complemented
142	C₅₃×#534	C₂²	1	3	yes	complemented
143	C₂×#120×C₅₃	C₂²	1	3	yes	complemented
144	C₂⁴×D₅₃	—	4	12	no	—
145	C₂⁴×D₅₃	C₂³	1	3	yes	—
146	C₂⁴×D₅₃	C₂³	1	6	yes	—
147	C₂⁴×D₅₃	C₂³	1	2	yes	—
148	C₂⁴×D₅₃	C₂³	1	3	yes	—
149	C₂⁴×D₅₃	C₂³	1	3	yes	complemented
150	#13133263	—	4	12	no	—
151	#13133262	—	4	12	no	—
152	C₂×#11719949	C₂³	1	6	yes	complemented
153	C₂×#11719945	C₂³	1	6	yes	complemented
154	C₂×#11719945	C₂³	1	6	yes	complemented
155	C₂×#11719945	C₂³	1	3	yes	complemented
156	C₂×#11719947	C₂³	1	6	yes	complemented
157	C₂×#11719947	C₂³	1	6	yes	complemented
158	C₂²×D₂₁₂	C₂³	1	3	yes	—
159	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
160	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
161	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	—
162	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
163	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	complemented
164	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
165	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
166	C₂²×C₂²⋊D₅₃	C₂³	1	3	yes	complemented
167	C₂×D₄×D₅₃	—	4	12	no	—
168	C₂×D₄×D₅₃	—	4	24	no	—
169	C₂×D₄×D₅₃	C₂³	1	6	yes	—
170	C₂×D₄×D₅₃	C₂³	1	6	yes	—
171	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
172	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
173	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
174	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
175	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
176	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
177	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
178	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
179	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
180	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
181	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
182	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
183	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
184	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
185	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
186	#13133214	C₂³	1	2	yes	complemented
187	#13133213	C₂³	1	6	yes	complemented
188	#13133213	C₂³	1	6	yes	complemented
189	#13133213	C₂³	1	3	yes	complemented
190	#13133213	C₂³	1	3	yes	complemented
191	#13133212	C₂³	1	6	yes	complemented
192	#13133212	C₂³	1	6	yes	complemented
193	#13133211	C₂³	1	2	yes	complemented
194	#13133211	C₂³	1	2	yes	complemented
195	#13133210	C₂³	1	6	yes	complemented
196	#13133210	C₂³	1	6	yes	complemented
197	#13133210	C₂³	1	6	yes	complemented
198	#13133210	C₂³	1	6	yes	complemented
199	#13133206	C₂³	1	6	yes	complemented
200	#13133205	C₂³	1	6	yes	complemented
201	#13133204	C₂³	1	6	yes	complemented
202	#13133204	C₂³	1	3	yes	complemented
203	#13133204	C₂³	1	3	yes	complemented
204	#13133203	C₂³	1	6	yes	complemented
205	#13133203	C₂³	1	6	yes	complemented
206	#13133203	C₂³	1	6	yes	complemented
207	#13133203	C₂³	1	6	yes	complemented
208	#13133203	C₂³	1	6	yes	complemented
209	#13133203	C₂³	1	6	yes	complemented
210	#13133202	C₂³	1	6	yes	complemented
211	#13133202	C₂³	1	6	yes	complemented
212	#13133202	C₂³	1	6	yes	complemented
213	#13133202	C₂³	1	6	yes	complemented
214	#13133202	C₂³	1	6	yes	complemented
215	#13133202	C₂³	1	6	yes	complemented
216	#13133201	C₂³	1	6	yes	complemented
217	#13133201	C₂³	1	6	yes	complemented
218	#13133200	C₂³	1	6	yes	complemented
219	#13133200	C₂³	1	6	yes	complemented
220	#13133199	C₂³	1	6	yes	complemented
221	#13133199	C₂³	1	6	yes	complemented
222	#13133199	C₂³	1	6	yes	complemented
223	#13133199	C₂³	1	6	yes	complemented
224	#13133199	C₂³	1	6	yes	complemented
225	#13133199	C₂³	1	6	yes	complemented
226	#13133199	C₂³	1	6	yes	complemented
227	#13133199	C₂³	1	6	yes	complemented
228	#13133198	C₂³	1	6	yes	complemented
229	#13133198	C₂³	1	6	yes	complemented
230	#13133198	C₂³	1	3	yes	complemented
231	#13133198	C₂³	1	3	yes	complemented
232	#13133197	C₂³	1	6	yes	complemented
233	#13133197	C₂³	1	6	yes	complemented
234	#13133196	C₂³	1	6	yes	complemented
235	#13133195	C₂³	1	6	yes	complemented
236	#13133195	C₂³	1	6	yes	complemented
237	#13133195	C₂³	1	6	yes	complemented
238	#13133195	C₂³	1	6	yes	complemented
239	#13133194	C₂³	1	6	yes	complemented
240	#13133194	C₂³	1	6	yes	complemented
241	#13133193	C₂³	1	6	yes	complemented
242	#13133193	C₂³	1	6	yes	complemented
243	#13133192	C₂³	1	6	yes	complemented
244	#13133192	C₂³	1	6	yes	complemented
245	#13133192	C₂³	1	6	yes	complemented
246	#13133192	C₂³	1	6	yes	complemented
247	#13133191	C₂³	1	6	yes	complemented
248	#13133191	C₂³	1	6	yes	complemented
249	#13133191	C₂³	1	6	yes	complemented
250	#13133190	C₂³	1	6	yes	complemented
251	#13133190	C₂³	1	6	yes	complemented
252	#13133190	C₂³	1	6	yes	complemented
253	#13133190	C₂³	1	6	yes	complemented
254	#13133190	C₂³	1	6	yes	complemented
255	#13133190	C₂³	1	6	yes	complemented
256	#13133190	C₂³	1	6	yes	complemented
257	#13133190	C₂³	1	6	yes	complemented
258	#13133190	C₂³	1	6	yes	complemented
259	#13133190	C₂³	1	6	yes	complemented
260	#13133189	C₂³	1	6	yes	complemented
261	#13133189	C₂³	1	6	yes	complemented
262	#13133189	C₂³	1	6	yes	complemented
263	#13133189	C₂³	1	6	yes	complemented
264	#13133189	C₂³	1	6	yes	complemented
265	#13133189	C₂³	1	6	yes	complemented
266	#13133189	C₂³	1	6	yes	complemented
267	#13133189	C₂³	1	6	yes	complemented
268	#13133188	C₂³	1	6	yes	complemented
269	#13133188	C₂³	1	6	yes	complemented
270	#13133188	C₂³	1	6	yes	complemented
271	#13133188	C₂³	1	6	yes	complemented
272	#13133188	C₂³	1	6	yes	complemented
273	#13133188	C₂³	1	6	yes	complemented
274	#13133187	C₂³	1	6	yes	—
275	#13133187	C₂³	1	6	yes	—
276	#13133187	C₂³	1	6	yes	—
277	#13133187	C₂³	1	6	yes	—
278	#13133187	C₂³	1	6	yes	—
279	#13133187	C₂³	1	6	yes	complemented
280	#13133187	C₂³	1	6	yes	complemented
281	#13133187	C₂³	1	6	yes	complemented
282	#13133187	C₂³	1	6	yes	complemented
283	#13133187	C₂³	1	6	yes	complemented
284	#13133187	C₂³	1	6	yes	complemented
285	#13133187	C₂³	1	6	yes	complemented
286	#13133187	C₂³	1	6	yes	complemented
287	#13133187	C₂³	1	6	yes	complemented
288	#13133187	C₂³	1	6	yes	complemented
289	#13133187	C₂³	1	6	yes	complemented
290	#13133187	C₂³	1	6	yes	complemented
291	#13133187	C₂³	1	6	yes	complemented
292	#13133186	C₂³	1	6	yes	—
293	#13133186	C₂³	1	6	yes	complemented
294	#13133186	C₂³	1	6	yes	complemented
295	#13133186	C₂³	1	6	yes	complemented
296	#13133186	C₂³	1	2	yes	complemented
297	#13133186	C₂³	1	6	yes	complemented
298	#13133185	C₂³	1	6	yes	—
299	#13133185	C₂³	1	3	yes	—
300	#13133185	C₂³	1	6	yes	—
301	#13133185	C₂³	1	6	yes	—
302	#13133185	C₂³	1	3	yes	—
303	#13133185	C₂³	1	6	yes	—
304	#13133185	C₂³	1	3	yes	complemented
305	#13133185	C₂³	1	3	yes	complemented
306	#13133185	C₂³	1	6	yes	complemented
307	#13133185	C₂³	1	6	yes	complemented
308	#13133185	C₂³	1	6	yes	complemented
309	#13133185	C₂³	1	6	yes	complemented
310	#13133185	C₂³	1	6	yes	complemented
311	#13133185	C₂³	1	6	yes	complemented
312	#13133185	C₂³	1	3	yes	complemented
313	#13133185	C₂³	1	3	yes	complemented
314	#13133185	C₂³	1	6	yes	complemented
315	#13133185	C₂³	1	6	yes	complemented
316	#13133185	C₂³	1	6	yes	complemented
317	#13133185	C₂³	1	6	yes	complemented
318	#13133185	C₂³	1	6	yes	complemented
319	#13133185	C₂³	1	6	yes	complemented
320	C₄×D₂₁₂	C₂³	1	6	yes	complemented
321	C₄×D₂₁₂	C₂³	1	6	yes	complemented
322	C₄×D₂₁₂	C₂³	1	6	yes	complemented
323	C₄×D₂₁₂	C₂³	1	6	yes	complemented
324	D₄×Dic₅₃	C₂³	1	6	yes	complemented
325	D₄×Dic₅₃	C₂³	1	6	yes	complemented
326	#13133179	C₂³	1	6	yes	complemented
327	#13133179	C₂³	1	6	yes	complemented
328	#13133179	C₂³	1	6	yes	complemented
329	#13133179	C₂³	1	6	yes	complemented
330	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
331	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
332	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
333	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
334	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
335	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
336	#13133177	C₂³	1	6	yes	complemented
337	#13133177	C₂³	1	6	yes	complemented
338	#13133177	C₂³	1	6	yes	complemented
339	#13133177	C₂³	1	6	yes	complemented
340	#13133177	C₂³	1	6	yes	complemented
341	#13133177	C₂³	1	6	yes	complemented
342	#13133176	C₂³	1	3	yes	complemented
343	#13133175	C₂³	1	6	yes	complemented
344	#13133175	C₂³	1	6	yes	complemented
345	#13133174	C₂³	1	6	yes	complemented
346	#13133174	C₂³	1	6	yes	complemented
347	#13133173	C₂³	1	6	yes	complemented
348	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	complemented
349	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	complemented
350	C₂×C₂²⋊Dic₅₃	C₂³	1	3	yes	complemented
351	C₂×#11719921	C₂³	1	6	yes	—
352	C₂×#11719921	C₂³	1	6	yes	complemented
353	C₂×#11719921	C₂³	1	6	yes	complemented
354	C₂×#11719921	C₂³	1	6	yes	complemented
355	C₂×#11719921	C₂³	1	6	yes	complemented
356	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
357	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
358	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
359	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
360	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
361	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
362	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
363	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
364	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
365	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
366	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
367	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
368	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
369	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
370	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
371	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
373	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
374	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
375	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
376	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
377	#127×C₅₃	C₂³	1	3	yes	complemented
378	#126×C₅₃	C₂³	1	2	yes	complemented
379	#126×C₅₃	C₂³	1	6	yes	complemented
380	#124×C₅₃	C₂³	1	3	yes	complemented
381	#124×C₅₃	C₂³	1	3	yes	complemented
382	#124×C₅₃	C₂³	1	6	yes	complemented
383	#123×C₅₃	C₂³	1	6	yes	complemented
384	#123×C₅₃	C₂³	1	3	yes	complemented
385	#123×C₅₃	C₂³	1	3	yes	complemented
386	#123×C₅₃	C₂³	1	6	yes	complemented
387	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
388	#121×C₅₃	C₂³	1	6	yes	complemented
389	#121×C₅₃	C₂³	1	6	yes	complemented
390	#121×C₅₃	C₂³	1	6	yes	complemented
391	#121×C₅₃	C₂³	1	6	yes	complemented
392	#121×C₅₃	C₂³	1	6	yes	complemented
393	#120×C₅₃	C₂³	1	3	yes	—
394	#120×C₅₃	C₂³	1	3	yes	—
395	#120×C₅₃	C₂³	1	6	yes	complemented
396	#120×C₅₃	C₂³	1	6	yes	complemented
397	#120×C₅₃	C₂³	1	3	yes	complemented
398	#120×C₅₃	C₂³	1	3	yes	complemented
399	#120×C₅₃	C₂³	1	1	yes	characteristic, complemented
400	#120×C₅₃	C₂³	1	3	yes	complemented
401	#120×C₅₃	C₂³	1	6	yes	complemented
402	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
403	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
404	#117×C₅₃	C₂³	1	3	yes	complemented
405	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	complemented
406	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	complemented
407	C₂×C₂²⋊C₄×C₅₃	C₂³	1	3	yes	complemented
408	C₂⁴×C₅₃	—	4	6	no	—
409	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
410	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
411	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
412	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic, complemented
414	C₂³×D₅₃	—	2	12	no	—
415	C₂³×D₅₃	—	2	24	no	—
416	C₂³×D₅₃	—	4	12	no	—
417	C₂³×D₅₃	—	4	12	no	—
418	C₂³×D₅₃	—	4	12	no	—
419	C₂³×D₅₃	—	4	12	no	—
420	C₂³×D₅₃	—	4	12	no	—
421	C₂³×D₅₃	—	4	12	no	—
422	C₂³×D₅₃	—	4	6	no	—
423	C₂³×D₅₃	—	4	6	no	—
424	C₂³×D₅₃	—	4	64	no	—
425	C₂³×D₅₃	C₂⁴	1	3	yes	—
426	C₂³×D₅₃	C₂⁴	1	6	yes	—
427	C₂³×D₅₃	C₂⁴	1	3	yes	—
428	C₂³×D₅₃	C₂⁴	1	6	yes	—
429	C₂³×D₅₃	C₂⁴	1	6	yes	—
430	C₂³×D₅₃	C₂⁴	1	3	yes	—
431	C₂³×D₅₃	C₂⁴	1	6	yes	—
432	C₂³×D₅₃	C₂⁴	1	6	yes	—
433	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
434	C₂³×D₅₃	C₂⁴	1	3	yes	—
435	C₂³×D₅₃	C₂⁴	1	3	yes	complemented
436	#41×C₅₃	—	4	6	no	—
437	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	complemented
438	C₂×D₄×C₅₃	—	4	6	no	—
439	C₂×D₄×C₅₃	—	4	12	no	—
440	C₂×D₄×C₅₃	—	4	6	no	—
441	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
442	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
443	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
444	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
445	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
446	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
447	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
448	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
449	C₂×D₄×C₅₃	C₂⁴	1	3	yes	complemented
450	C₂×D₄×C₅₃	C₂⁴	1	6	yes	complemented
451	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
452	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
453	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	complemented
454	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	complemented
455	C₂×C₂²⋊D₅₃	—	2	12	no	—
456	C₂×C₂²⋊D₅₃	—	4	6	no	—
457	C₂×C₂²⋊D₅₃	—	4	12	no	—
458	C₂×C₂²⋊D₅₃	—	4	12	no	—
459	C₂×C₂²⋊D₅₃	—	4	12	no	—
460	C₂×C₂²⋊D₅₃	—	4	6	no	—
461	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
462	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
463	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
464	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
465	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
466	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
467	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
468	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
469	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
470	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
471	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
472	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
473	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	complemented
474	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	complemented
475	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	complemented
476	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
477	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
478	C₂²×Dic₅₃	C₂⁴	1	3	yes	complemented
479	C₂²×Dic₅₃	C₂⁴	1	6	yes	complemented
480	#11719949	—	4	12	no	—
481	#11719947	—	4	12	no	—
482	#11719947	—	4	12	no	—
483	D₄×D₅₃	—	2	24	no	—
484	D₄×D₅₃	—	2	24	no	—
485	D₄×D₅₃	—	4	12	no	—
486	D₄×D₅₃	—	4	12	no	—
487	D₄×D₅₃	—	4	12	no	—
488	D₄×D₅₃	—	4	12	no	—
489	D₄×D₅₃	—	4	12	no	—
490	D₄×D₅₃	—	4	12	no	—
491	D₄×D₅₃	—	4	12	no	—
492	D₄×D₅₃	—	4	12	no	—
493	D₄×D₅₃	—	4	12	no	—
494	D₄×D₅₃	—	4	12	no	—
495	D₄×D₅₃	—	4	12	no	—
496	D₄×D₅₃	—	4	12	no	—
497	D₄×D₅₃	—	4	12	no	—
498	#11719945	—	4	12	no	—
499	#11719945	—	4	12	no	—
500	#11719945	—	4	6	no	—
501	C₂×D₂₁₂	—	2	12	no	—
502	C₂×D₂₁₂	—	4	12	no	—
503	C₂×D₂₁₂	—	4	12	no	—
504	C₂×D₂₁₂	C₂⁴	1	6	yes	—
505	C₂×D₂₁₂	C₂⁴	1	6	yes	—
506	C₂×D₂₁₂	C₂⁴	1	6	yes	—
507	C₂×D₂₁₂	C₂⁴	1	6	yes	—
508	C₂×D₂₁₂	C₂⁴	1	6	yes	—
509	C₂×D₂₁₂	C₂⁴	1	6	yes	—
510	C₂×D₂₁₂	C₂⁴	1	6	yes	complemented
511	C₂×D₂₁₂	C₂⁴	1	3	yes	complemented
512	C₂×C₄×D₅₃	—	4	12	no	—
513	C₂×C₄×D₅₃	—	4	6	no	—
514	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
515	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
516	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
517	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
518	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
519	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
520	C₂×C₄×D₅₃	C₂⁴	1	6	yes	complemented
521	C₂×C₄×D₅₃	C₂⁴	1	6	yes	complemented
522	C₂×C₄×D₅₃	C₂⁴	1	6	yes	complemented
523	C₂×Dic₁₀₆	C₂⁴	1	3	yes	complemented
524	C₂×Dic₁₀₆	C₂⁴	1	6	yes	complemented
525	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	complemented
526	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	complemented
527	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	complemented
528	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
529	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
530	C₂²⋊C₄×C₅₃	C₂⁴	1	3	yes	—
531	C₂²⋊C₄×C₅₃	C₂⁴	1	3	yes	—
532	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
533	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
534	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
535	C₂²⋊C₄×C₅₃	C₂⁴	1	3	yes	complemented
536	C₂²⋊C₄×C₅₃	C₂⁴	1	3	yes	complemented
537	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	complemented
538	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	complemented
539	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic, complemented
540	C₄²×C₅₃	C₂⁴	1	3	yes	complemented
541	C₄²×C₅₃	C₂⁴	1	2	yes	complemented
542	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
543	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
544	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
545	C₂²⋊Dic₅₃	C₂⁴	1	3	yes	—
546	C₂²⋊Dic₅₃	C₂⁴	1	3	yes	—
547	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
548	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
549	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	complemented
550	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	complemented
551	C₂²⋊Dic₅₃	C₂⁴	1	3	yes	complemented
552	C₂²⋊Dic₅₃	C₂⁴	1	3	yes	complemented
553	#11719921	C₂⁴	1	6	yes	—
554	#11719921	C₂⁴	1	6	yes	—
555	#11719921	C₂⁴	1	6	yes	—
556	#11719921	C₂⁴	1	6	yes	—
557	#11719921	C₂⁴	1	6	yes	—
558	#11719921	C₂⁴	1	6	yes	—
559	#11719921	C₂⁴	1	6	yes	—
560	#11719921	C₂⁴	1	6	yes	—
561	#11719921	C₂⁴	1	6	yes	—
562	#11719921	C₂⁴	1	6	yes	—
563	#11719921	C₂⁴	1	6	yes	—
564	#11719921	C₂⁴	1	6	yes	—
565	#11719921	C₂⁴	1	6	yes	complemented
566	#11719921	C₂⁴	1	6	yes	complemented
567	#11719921	C₂⁴	1	6	yes	complemented
568	#11719921	C₂⁴	1	6	yes	complemented
569	#11719921	C₂⁴	1	6	yes	complemented
570	#11719921	C₂⁴	1	6	yes	complemented
571	C₄⋊Dic₅₃	C₂⁴	1	6	yes	complemented
572	C₄⋊Dic₅₃	C₂⁴	1	6	yes	complemented
573	C₄⋊Dic₅₃	C₂⁴	1	6	yes	complemented
574	#11719919	C₂⁴	1	6	yes	complemented
575	#11719919	C₂⁴	1	6	yes	complemented
576	#11719919	C₂⁴	1	6	yes	complemented
577	#11719919	C₂⁴	1	6	yes	complemented
578	#11719919	C₂⁴	1	6	yes	complemented
579	#11719919	C₂⁴	1	6	yes	complemented
580	C₄×Dic₅₃	C₂⁴	1	3	yes	complemented
581	C₄×Dic₅₃	C₂⁴	1	6	yes	complemented
582	C₄×Dic₅₃	C₂⁴	1	6	yes	complemented
583	C₄×Dic₅₃	C₂⁴	1	3	yes	complemented
584	C₂³×C₅₃	—	2	12	no	—
585	C₂³×C₅₃	—	2	6	no	—
586	C₂³×C₅₃	—	2	6	no	—
587	C₂³×C₅₃	—	4	3	no	—
588	C₂³×C₅₃	—	4	6	no	—
589	C₂³×C₅₃	—	4	3	no	—
590	C₂³×C₅₃	—	4	6	no	—
591	C₂³×C₅₃	—	4	3	no	—
592	C₂³×C₅₃	—	4	16	no	—
593	C₂³×C₅₃	C₂⁵	1	3	yes	—
594	C₂³×C₅₃	C₂⁵	1	3	yes	—
595	C₂³×C₅₃	C₂⁵	1	3	yes	—
596	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
597	C₂³×C₅₃	C₂⁵	1	3	yes	—
598	C₂²×D₅₃	—	2	6	no	—
599	C₂²×D₅₃	—	2	12	no	—
600	C₂²×D₅₃	—	2	12	no	—
601	C₂²×D₅₃	—	2	6	no	—
602	C₂²×D₅₃	—	2	12	no	—
603	C₂²×D₅₃	—	2	12	no	—
604	C₂²×D₅₃	—	2	12	no	—
605	C₂²×D₅₃	—	2	12	no	—
606	C₂²×D₅₃	—	2	12	no	—
607	C₂²×D₅₃	—	2	12	no	—
608	C₂²×D₅₃	—	2	12	no	—
609	C₂²×D₅₃	—	4	6	no	—
610	C₂²×D₅₃	—	4	6	no	—
611	C₂²×D₅₃	—	4	3	no	—
612	C₂²×D₅₃	—	4	6	no	—
613	C₂²×D₅₃	—	4	6	no	—
614	C₂²×D₅₃	—	4	6	no	—
615	C₂²×D₅₃	—	4	3	no	—
616	C₂²×D₅₃	—	4	6	no	—
617	C₂²×D₅₃	—	4	6	no	—
618	C₂²×D₅₃	—	4	6	no	—
619	C₂²×D₅₃	—	4	6	no	—
620	C₂²×D₅₃	—	4	6	no	—
621	C₂²×D₅₃	—	4	6	no	—
622	C₂²×D₅₃	—	4	3	no	—
623	C₂²×D₅₃	—	4	48	no	—
624	C₂²×D₅₃	—	4	96	no	—
625	C₂²×D₅₃	—	4	32	no	—
626	C₂²×D₅₃	—	4	48	no	—
627	C₂²×D₅₃	—	8	24	no	—
628	C₂²×D₅₃	H(5,𝔽₂)	1	12	yes	complemented
629	C₂²×D₅₃	C₂⁵	1	6	yes	—
630	C₂²×D₅₃	C₂⁵	1	2	yes	—
631	C₂²×D₅₃	C₂⁵	1	6	yes	—
632	Q₈×C₅₃	—	4	3	no	—
633	D₄×C₅₃	—	2	12	no	—
634	D₄×C₅₃	—	2	12	no	—
635	D₄×C₅₃	—	4	6	no	—
636	D₄×C₅₃	—	4	3	no	—
637	D₄×C₅₃	—	4	3	no	—
638	D₄×C₅₃	—	4	6	no	—
639	D₄×C₅₃	—	4	3	no	—
640	D₄×C₅₃	—	4	3	no	—
641	D₄×C₅₃	—	4	3	no	—
642	D₄×C₅₃	—	4	6	no	—
643	C₂×C₄×C₅₃	—	2	6	no	—
644	C₂×C₄×C₅₃	—	4	6	no	—
645	C₂×C₄×C₅₃	—	4	6	no	—
646	C₂×C₄×C₅₃	—	4	3	no	—
647	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
648	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
649	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
650	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
651	C₂²⋊D₅₃	—	2	12	no	—
652	C₂²⋊D₅₃	—	2	12	no	—
653	C₂²⋊D₅₃	—	2	12	no	—
654	C₂²⋊D₅₃	—	2	12	no	—
655	C₂²⋊D₅₃	—	2	12	no	—
656	C₂²⋊D₅₃	—	2	12	no	—
657	C₂²⋊D₅₃	—	4	6	no	—
658	C₂²⋊D₅₃	—	4	6	no	—
659	C₂²⋊D₅₃	—	4	6	no	—
660	C₂²⋊D₅₃	—	4	6	no	—
661	C₂²⋊D₅₃	—	4	6	no	—
662	C₂²⋊D₅₃	—	4	6	no	—
663	C₂²⋊D₅₃	—	4	6	no	—
664	C₂²⋊D₅₃	—	4	6	no	—
665	C₂²⋊D₅₃	—	4	6	no	—
666	C₂×Dic₅₃	—	2	6	no	—
667	C₂×Dic₅₃	—	4	6	no	—
668	C₂×Dic₅₃	—	4	3	no	—
669	C₂×Dic₅₃	—	4	6	no	—
670	C₂×Dic₅₃	C₂⁵	1	6	yes	—
671	C₂×Dic₅₃	C₂⁵	1	6	yes	—
672	C₂×Dic₅₃	C₂⁵	1	6	yes	—
673	D₂₁₂	—	2	12	no	—
674	D₂₁₂	—	2	12	no	—
675	D₂₁₂	—	2	12	no	—
676	D₂₁₂	—	2	12	no	—
677	D₂₁₂	—	4	3	no	—
678	D₂₁₂	—	4	6	no	—
679	D₂₁₂	—	4	6	no	—
680	D₂₁₂	—	4	6	no	—
681	C₄×D₅₃	—	2	12	no	—
682	C₄×D₅₃	—	2	12	no	—
683	C₄×D₅₃	—	4	6	no	—
684	C₄×D₅₃	—	4	6	no	—
685	C₄×D₅₃	—	4	6	no	—
686	C₄×D₅₃	—	4	6	no	—
687	C₄×D₅₃	—	4	6	no	—
688	C₄×D₅₃	—	4	6	no	—
689	C₄×D₅₃	—	4	6	no	—
690	Dic₁₀₆	—	4	3	no	—
691	Dic₁₀₆	—	4	6	no	—
692	#62817	—	53	1	no	maximal, Sylow
693	C₂²×C₅₃	—	2	6	no	—
694	C₂²×C₅₃	—	2	3	no	—
695	C₂²×C₅₃	—	2	6	no	—
696	C₂²×C₅₃	—	2	3	no	—
697	C₂²×C₅₃	—	2	6	no	—
698	C₂²×C₅₃	—	2	3	no	—
699	C₂²×C₅₃	—	2	6	no	—
700	C₂²×C₅₃	—	2	3	no	—
701	C₂²×C₅₃	—	4	12	no	—
702	C₂²×C₅₃	—	4	12	no	—
703	C₂²×C₅₃	—	4	4	no	—
704	C₂²×C₅₃	—	8	6	no	—
705	C₂²×C₅₃	—	16	1	no	—
706	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	6	yes	—
707	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
708	C₂×D₅₃	—	2	24	no	—
709	C₂×D₅₃	—	2	6	no	—
710	C₂×D₅₃	—	2	6	no	—
711	C₂×D₅₃	—	2	6	no	—
712	C₂×D₅₃	—	2	6	no	—
713	C₂×D₅₃	—	2	6	no	—
714	C₂×D₅₃	—	2	6	no	—
715	C₂×D₅₃	—	4	12	no	—
716	C₂×D₅₃	—	4	12	no	—
717	C₂×D₅₃	—	4	24	no	—
718	C₂×D₅₃	—	4	24	no	—
719	C₂×D₅₃	—	4	24	no	—
720	C₂×D₅₃	—	4	4	no	—
721	C₂×D₅₃	—	8	12	no	—
722	C₂×D₅₃	—	8	12	no	—
723	C₂×D₅₃	—	8	6	no	—
724	C₂×D₅₃	—	16	3	no	—
725	C₂×D₅₃	C₂×H(5,𝔽₂)	1	12	yes	—
726	C₄×C₅₃	—	2	6	no	—
727	C₄×C₅₃	—	2	3	no	—
728	C₄×C₅₃	—	2	6	no	—
729	C₄×C₅₃	—	2	3	no	—
730	Dic₅₃	—	2	6	no	—
731	Dic₅₃	—	2	6	no	—
732	Dic₅₃	—	2	6	no	—
733	#3532	—	53	2	no	—
734	#3532	—	53	6	no	—
735	#3532	—	53	6	no	—
736	#3532	—	53	3	no	—
737	#3532	—	53	3	no	—
738	#3532	—	53	3	no	—
739	#3532	D₅₃	1	1	yes	characteristic, complemented
740	#3490	—	53	6	no	—
741	#3490	—	53	6	no	—
742	#3490	—	53	6	no	—
743	#3484	—	53	6	no	—
744	#3484	—	53	6	no	—
745	#3484	—	53	3	no	—
746	#3484	—	53	3	no	—
747	C₂²×#120	—	53	3	no	—
748	C₂×C₅₃	—	2	6	no	—
749	C₂×C₅₃	—	4	1	no	—
750	C₂×C₅₃	—	4	3	no	—
751	C₂×C₅₃	—	4	3	no	—
752	C₂×C₅₃	—	4	3	no	—
753	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	3	yes	—
754	D₅₃	—	2	12	no	—
755	D₅₃	—	4	2	no	—
756	D₅₃	—	4	6	no	—
757	C₂⁶	—	53	1	no	—
758	C₂×H(5,𝔽₂)	—	53	3	no	—
759	C₂×H(5,𝔽₂)	—	53	3	no	—
760	C₂³×D₄	—	53	3	no	—
761	C₂³×D₄	—	53	6	no	—
762	H(3,𝔽₄)	—	53	3	no	—
763	H(3,𝔽₄)	—	53	3	no	—
764	H(3,𝔽₄)	—	53	1	no	—
765	H(3,𝔽₄)	C₂×D₅₃	1	1	yes	characteristic, complemented
766	#560	—	53	1	no	—
767	#560	—	53	2	no	—
768	#560	—	53	3	no	—
769	#560	—	53	6	no	—
770	#560	—	53	6	no	—
771	#560	—	53	3	no	—
772	#560	C₂×D₅₃	1	3	yes	complemented
773	#551	—	53	6	no	—
774	#551	—	53	6	no	—
775	#551	—	53	6	no	—
776	#551	—	53	6	no	—
777	#551	—	53	3	no	—
778	#551	—	53	6	no	—
779	#551	—	53	6	no	—
780	#551	—	53	3	no	—
781	#551	—	53	6	no	—
782	#551	—	53	3	no	—
783	#551	—	53	6	no	—
784	#551	—	53	6	no	—
785	#551	—	53	6	no	—
786	#551	C₂×D₅₃	1	3	yes	complemented
787	#546	—	53	6	no	—
788	#546	—	53	6	no	—
789	#546	—	53	6	no	—
790	#546	—	53	6	no	—
791	#546	—	53	6	no	—
792	#546	—	53	6	no	—
793	#546	—	53	6	no	—
794	#546	—	53	6	no	—
795	#546	—	53	6	no	—
796	#546	—	53	6	no	—
797	#546	—	53	6	no	—
798	#546	—	53	6	no	—
799	#546	—	53	6	no	—
800	#546	—	53	6	no	—
801	#546	—	53	6	no	—
802	#546	—	53	6	no	—
803	#546	—	53	6	no	—
804	#546	—	53	6	no	—
805	#546	—	53	6	no	—
806	#546	—	53	6	no	—
807	#546	—	53	6	no	—
808	#546	—	53	6	no	—
809	#546	—	53	6	no	—
810	#546	C₂×D₅₃	1	6	yes	complemented
811	D₄²	—	53	6	no	—
812	D₄²	—	53	6	no	—
813	D₄²	—	53	6	no	—
814	D₄²	—	53	3	no	—
815	D₄²	—	53	6	no	—
816	D₄²	—	53	6	no	—
817	D₄²	—	53	6	no	—
818	D₄²	—	53	6	no	—
819	D₄²	—	53	3	no	—
820	D₄²	—	53	6	no	—
821	D₄²	—	53	6	no	—
822	D₄²	—	53	3	no	—
823	D₄²	—	53	6	no	—
824	D₄²	C₂×D₅₃	1	3	yes	complemented
825	#543	—	53	6	no	—
826	#538	—	53	6	no	—
827	#538	—	53	6	no	—
828	#538	—	53	6	no	—
829	#538	—	53	6	no	—
830	#538	—	53	6	no	—
831	#538	—	53	6	no	—
832	#538	—	53	6	no	—
833	#538	—	53	6	no	—
834	#538	—	53	6	no	—
835	#538	—	53	6	no	—
836	#538	—	53	6	no	—
837	#538	C₂×D₅₃	1	6	yes	complemented
838	#535	—	53	3	no	—
839	#535	—	53	6	no	—
840	#535	—	53	6	no	—
841	#535	—	53	6	no	—
842	#535	—	53	6	no	—
843	#535	—	53	6	no	—
844	#535	C₂×D₅₃	1	3	yes	complemented
845	#534	—	53	3	no	—
846	#534	—	53	6	no	—
847	#534	—	53	6	no	—
848	#534	—	53	6	no	—
849	#534	—	53	6	no	—
850	#534	—	53	6	no	—
851	#534	—	53	6	no	—
852	#534	—	53	6	no	—
853	#534	—	53	6	no	—
854	#534	C₂×D₅₃	1	3	yes	complemented
855	#525	—	53	3	no	—
856	#525	—	53	6	no	—
857	#525	—	53	6	no	—
858	#525	—	53	6	no	—
859	#525	—	53	6	no	—
860	#525	—	53	6	no	—
861	#525	—	53	3	no	—
862	C₂×#120	—	53	3	no	—
863	C₂×#120	—	53	6	no	—
864	C₂×#120	—	53	3	no	—
865	C₂×#120	—	53	3	no	—
866	C₂×#120	—	53	6	no	—
867	C₂×#120	—	53	6	no	—
868	C₂×#120	—	53	6	no	—
869	C₂×#120	—	53	6	no	—
870	C₂×#120	—	53	6	no	—
871	C₂×#120	—	53	6	no	—
872	C₂×#120	—	53	6	no	—
873	C₂×#120	—	53	6	no	—
874	C₂×#120	—	53	6	no	—
875	C₂×#120	—	53	6	no	—
876	C₂×#120	—	53	3	no	—
877	C₂×#120	—	53	3	no	—
878	C₂×#120	C₂×D₅₃	1	3	yes	complemented
879	#518	—	53	6	no	—
880	#518	—	53	6	no	—
881	#518	—	53	3	no	—
882	#518	—	53	3	no	—
883	C₂²×C₂²⋊C₄	—	53	3	no	—
884	C₂²×C₂²⋊C₄	—	53	6	no	—
885	C₅₃	#62817	1	1	yes	characteristic, complemented, Sylow
886	C₂⁵	—	53	3	no	—
887	C₂⁵	—	53	6	no	—
888	C₂⁵	—	53	2	no	—
889	C₂⁵	—	53	3	no	—
890	C₂⁵	—	53	3	no	—
891	C₂⁵	—	212	12	no	—
892	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
893	H(5,𝔽₂)	—	212	12	no	—
894	H(5,𝔽₂)	—	212	12	no	—
895	C₂×#41	—	53	6	no	—
896	C₂×#41	—	53	6	no	—
897	C₂×#41	—	53	6	no	—
898	C₂×#41	—	53	3	no	—
899	C₂×#41	—	53	6	no	—
900	C₂×#41	—	53	6	no	—
901	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
902	C₂²×D₄	—	53	3	no	—
903	C₂²×D₄	—	53	3	no	—
904	C₂²×D₄	—	53	6	no	—
905	C₂²×D₄	—	53	6	no	—
906	C₂²×D₄	—	53	3	no	—
907	C₂²×D₄	—	53	6	no	—
908	C₂²×D₄	—	53	6	no	—
909	C₂²×D₄	—	53	6	no	—
910	C₂²×D₄	—	53	6	no	—
911	C₂²×D₄	—	53	6	no	—
912	C₂²×D₄	—	53	6	no	—
913	C₂²×D₄	—	53	6	no	—
914	C₂²×D₄	—	53	6	no	—
915	C₂²×D₄	—	53	6	no	—
916	C₂²×D₄	—	53	6	no	—
917	C₂²×D₄	—	53	6	no	—
918	C₂²×D₄	—	53	6	no	—
919	C₂²×D₄	—	53	6	no	—
920	C₂²×D₄	—	53	6	no	—
921	C₂²×D₄	—	53	6	no	—
922	C₂²×D₄	—	53	6	no	—
923	C₂²×D₄	—	53	3	no	—
924	C₂²×D₄	—	53	6	no	—
925	C₂²×D₄	—	53	6	no	—
926	C₂²×D₄	—	212	12	no	—
927	C₂²×D₄	—	212	24	no	—
928	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
929	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
930	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
931	C₂³×C₄	—	53	3	no	—
932	C₂³×C₄	—	53	6	no	—
933	#127	—	53	3	no	—
934	#127	—	53	6	no	—
935	#127	—	53	3	no	—
936	#127	—	53	6	no	—
937	#127	—	53	2	no	—
938	#127	C₂²×D₅₃	1	3	yes	complemented
939	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
940	#126	—	53	6	no	—
941	#126	—	53	6	no	—
942	#126	—	53	6	no	—
943	#126	—	53	6	no	—
944	#126	—	53	6	no	—
945	#126	—	53	6	no	—
946	#126	—	53	2	no	—
947	#126	—	53	2	no	—
948	#126	C₂²×D₅₃	1	6	yes	complemented
949	#126	C₂²×D₅₃	1	2	yes	complemented
950	#124	—	53	6	no	—
951	#124	—	53	3	no	—
952	#124	—	53	6	no	—
953	#124	—	53	3	no	—
954	#124	—	53	6	no	—
955	#124	—	53	6	no	—
956	#124	—	53	6	no	—
957	#124	—	53	6	no	—
958	#124	—	53	6	no	—
959	#124	—	53	6	no	—
960	#124	—	53	6	no	—
961	#124	C₂²×D₅₃	1	6	yes	complemented
962	#124	C₂²×D₅₃	1	3	yes	complemented
963	#124	C₂²×D₅₃	1	3	yes	complemented
964	#123	—	53	6	no	—
965	#123	—	53	3	no	—
966	#123	—	53	3	no	—
967	#123	—	53	6	no	—
968	#123	—	53	6	no	—
969	#123	—	53	6	no	—
970	#123	—	53	6	no	—
971	#123	—	53	6	no	—
972	#123	—	53	6	no	—
973	#123	—	53	6	no	—
974	#123	—	53	6	no	—
975	#123	—	53	6	no	—
976	#123	—	53	6	no	—
977	#123	—	53	6	no	—
978	#123	—	53	6	no	—
979	#123	—	53	6	no	—
980	#123	—	53	6	no	—
981	#123	—	53	6	no	—
982	#123	—	53	6	no	—
983	#123	—	53	6	no	—
984	#123	—	53	6	no	—
985	#123	—	53	6	no	—
986	#123	C₂²×D₅₃	1	6	yes	complemented
987	#123	C₂²×D₅₃	1	3	yes	complemented
988	#123	C₂²×D₅₃	1	3	yes	complemented
989	#123	C₂²×D₅₃	1	6	yes	complemented
990	C₂²⋊Q₈	—	53	6	no	—
991	C₂²⋊Q₈	—	53	6	no	—
992	C₂²⋊Q₈	—	53	6	no	—
993	C₂²⋊Q₈	—	53	6	no	—
994	C₂²⋊Q₈	—	53	6	no	—
995	C₂²⋊Q₈	—	53	6	no	—
996	C₂²⋊Q₈	—	53	6	no	—
997	C₂²⋊Q₈	—	53	6	no	—
998	C₂²⋊Q₈	—	53	6	no	—
999	C₂²⋊Q₈	—	53	6	no	—
1000	C₂²⋊Q₈	—	53	6	no	—
1001	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1002	#121	—	53	6	no	—
1003	#121	—	53	6	no	—
1004	#121	—	53	6	no	—
1005	#121	—	53	6	no	—
1006	#121	—	53	6	no	—
1007	#121	—	53	6	no	—
1008	#121	—	53	6	no	—
1009	#121	—	53	6	no	—
1010	#121	—	53	6	no	—
1011	#121	—	53	6	no	—
1012	#121	—	53	6	no	—
1013	#121	—	53	6	no	—
1014	#121	—	53	6	no	—
1015	#121	—	53	6	no	—
1016	#121	—	53	6	no	—
1017	#121	—	53	6	no	—
1018	#121	—	53	6	no	—
1019	#121	—	53	6	no	—
1020	#121	—	53	6	no	—
1021	#121	—	53	6	no	—
1022	#121	—	53	6	no	—
1023	#121	—	53	6	no	—
1024	#121	—	53	6	no	—
1025	#121	—	53	6	no	—
1026	#121	—	53	6	no	—
1027	#121	—	53	6	no	—
1028	#121	—	53	6	no	—
1029	#121	—	53	6	no	—
1030	#121	—	53	6	no	—
1031	#121	—	53	6	no	—
1032	#121	—	53	6	no	—
1033	#121	C₂²×D₅₃	1	6	yes	complemented
1034	#121	C₂²×D₅₃	1	6	yes	complemented
1035	#121	C₂²×D₅₃	1	6	yes	complemented
1036	#121	C₂²×D₅₃	1	6	yes	complemented
1037	#121	C₂²×D₅₃	1	6	yes	complemented
1038	#120	—	53	6	no	—
1039	#120	—	53	6	no	—
1040	#120	—	53	6	no	—
1041	#120	—	53	6	no	—
1042	#120	—	53	6	no	—
1043	#120	—	53	2	no	—
1044	#120	—	53	6	no	—
1045	#120	—	53	6	no	—
1046	#120	—	53	6	no	—
1047	#120	—	53	6	no	—
1048	#120	—	53	6	no	—
1049	#120	—	53	6	no	—
1050	#120	—	53	6	no	—
1051	#120	—	53	6	no	—
1052	#120	—	53	3	no	—
1053	#120	—	53	6	no	—
1054	#120	—	53	6	no	—
1055	#120	—	53	3	no	—
1056	#120	—	53	3	no	—
1057	#120	—	53	3	no	—
1058	#120	—	53	6	no	—
1059	#120	—	53	3	no	—
1060	#120	—	53	3	no	—
1061	#120	—	53	6	no	—
1062	#120	—	53	6	no	—
1063	#120	—	53	6	no	—
1064	#120	—	53	6	no	—
1065	#120	—	53	6	no	—
1066	#120	—	53	6	no	—
1067	#120	—	53	6	no	—
1068	#120	—	53	6	no	—
1069	#120	—	53	6	no	—
1070	#120	—	53	6	no	—
1071	#120	—	53	6	no	—
1072	#120	—	53	6	no	—
1073	#120	—	53	6	no	—
1074	#120	—	53	6	no	—
1075	#120	—	53	6	no	—
1076	#120	—	53	6	no	—
1077	#120	—	53	6	no	—
1078	#120	—	53	6	no	—
1079	#120	—	53	6	no	—
1080	#120	—	53	6	no	—
1081	#120	—	53	6	no	—
1082	#120	—	53	6	no	—
1083	#120	—	53	6	no	—
1084	#120	C₂²×D₅₃	1	3	yes	—
1085	#120	C₂²×D₅₃	1	3	yes	—
1086	#120	C₂²×D₅₃	1	6	yes	complemented
1087	#120	C₂²×D₅₃	1	6	yes	complemented
1088	#120	C₂²×D₅₃	1	3	yes	complemented
1089	#120	C₂²×D₅₃	1	3	yes	complemented
1090	#120	C₂²×D₅₃	1	6	yes	complemented
1091	#120	C₂²×D₅₃	1	3	yes	complemented
1092	#120	C₂²×D₅₃	1	1	yes	characteristic, complemented
1093	C₄×D₄	—	53	6	no	—
1094	C₄×D₄	—	53	6	no	—
1095	C₄×D₄	—	53	6	no	—
1096	C₄×D₄	—	53	6	no	—
1097	C₄×D₄	—	53	6	no	—
1098	C₄×D₄	—	53	6	no	—
1099	C₄×D₄	—	53	6	no	—
1100	C₄×D₄	—	53	6	no	—
1101	C₄×D₄	—	53	6	no	—
1102	C₄×D₄	—	53	6	no	—
1103	C₄×D₄	—	53	6	no	—
1104	C₄×D₄	—	53	6	no	—
1105	C₄×D₄	—	53	6	no	—
1106	C₄×D₄	—	53	6	no	—
1107	C₄×D₄	—	53	6	no	—
1108	C₄×D₄	—	53	6	no	—
1109	C₄×D₄	—	53	6	no	—
1110	C₄×D₄	—	53	6	no	—
1111	C₄×D₄	—	53	6	no	—
1112	C₄×D₄	—	53	6	no	—
1113	C₄×D₄	—	53	6	no	—
1114	C₄×D₄	—	53	6	no	—
1115	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1116	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1117	#117	—	53	3	no	—
1118	#117	—	53	6	no	—
1119	#117	—	53	6	no	—
1120	#117	—	53	6	no	—
1121	#117	—	53	6	no	—
1122	#117	—	53	6	no	—
1123	#117	C₂²×D₅₃	1	3	yes	complemented
1124	C₂×C₂²⋊C₄	—	53	3	no	—
1125	C₂×C₂²⋊C₄	—	53	6	no	—
1126	C₂×C₂²⋊C₄	—	53	3	no	—
1127	C₂×C₂²⋊C₄	—	53	6	no	—
1128	C₂×C₂²⋊C₄	—	53	6	no	—
1129	C₂×C₂²⋊C₄	—	53	6	no	—
1130	C₂×C₂²⋊C₄	—	53	6	no	—
1131	C₂×C₂²⋊C₄	—	53	6	no	—
1132	C₂×C₂²⋊C₄	—	53	6	no	—
1133	C₂×C₂²⋊C₄	—	53	6	no	—
1134	C₂×C₂²⋊C₄	—	53	6	no	—
1135	C₂×C₂²⋊C₄	—	53	6	no	—
1136	C₂×C₂²⋊C₄	—	53	6	no	—
1137	C₂×C₂²⋊C₄	—	53	6	no	—
1138	C₂×C₂²⋊C₄	—	53	6	no	—
1139	C₂×C₂²⋊C₄	—	53	6	no	—
1140	C₂×C₂²⋊C₄	—	53	6	no	—
1141	C₂×C₂²⋊C₄	—	53	6	no	—
1142	C₂×C₂²⋊C₄	—	53	6	no	—
1143	C₂×C₂²⋊C₄	—	53	6	no	—
1144	C₂×C₂²⋊C₄	—	53	6	no	—
1145	C₂×C₂²⋊C₄	—	53	6	no	—
1146	C₂×C₂²⋊C₄	—	53	6	no	—
1147	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1148	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	complemented
1149	C₂×C₂²⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1150	C₂⁴	—	4	6	no	—
1151	C₂⁴	—	53	3	no	—
1152	C₂⁴	—	53	3	no	—
1153	C₂⁴	—	53	6	no	—
1154	C₂⁴	—	53	3	no	—
1155	C₂⁴	—	53	6	no	—
1156	C₂⁴	—	53	6	no	—
1157	C₂⁴	—	53	6	no	—
1158	C₂⁴	—	53	6	no	—
1159	C₂⁴	—	53	3	no	—
1160	C₂⁴	—	53	1	no	—
1161	C₂⁴	—	53	3	no	—
1162	C₂⁴	—	106	24	no	—
1163	C₂⁴	—	106	12	no	—
1164	C₂⁴	—	212	6	no	—
1165	C₂⁴	—	212	12	no	—
1166	C₂⁴	—	212	6	no	—
1167	C₂⁴	—	212	12	no	—
1168	C₂⁴	—	212	12	no	—
1169	C₂⁴	—	212	12	no	—
1170	C₂⁴	—	212	12	no	—
1171	C₂⁴	—	212	12	no	—
1172	C₂⁴	—	212	64	no	—
1173	C₂⁴	C₂³×D₅₃	1	3	yes	—
1174	C₂⁴	C₂³×D₅₃	1	3	yes	—
1175	C₂⁴	C₂³×D₅₃	1	3	yes	—
1176	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1177	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic, complemented
1178	#41	—	4	6	no	—
1179	#41	—	212	6	no	—
1180	#41	—	212	12	no	—
1181	#41	—	212	12	no	—
1182	#41	—	212	12	no	—
1183	#41	—	212	12	no	—
1184	#41	—	212	12	no	—
1185	C₂×Q₈	—	53	3	no	—
1186	C₂×Q₈	—	53	6	no	—
1187	C₂×Q₈	C₂³×D₅₃	1	3	yes	complemented
1188	C₂×D₄	—	4	6	no	—
1189	C₂×D₄	—	4	12	no	—
1190	C₂×D₄	—	4	6	no	—
1191	C₂×D₄	—	53	6	no	—
1192	C₂×D₄	—	53	6	no	—
1193	C₂×D₄	—	53	6	no	—
1194	C₂×D₄	—	53	6	no	—
1195	C₂×D₄	—	53	6	no	—
1196	C₂×D₄	—	53	6	no	—
1197	C₂×D₄	—	53	6	no	—
1198	C₂×D₄	—	53	6	no	—
1199	C₂×D₄	—	53	6	no	—
1200	C₂×D₄	—	53	6	no	—
1201	C₂×D₄	—	53	6	no	—
1202	C₂×D₄	—	53	6	no	—
1203	C₂×D₄	—	53	6	no	—
1204	C₂×D₄	—	53	6	no	—
1205	C₂×D₄	—	53	6	no	—
1206	C₂×D₄	—	53	6	no	—
1207	C₂×D₄	—	53	6	no	—
1208	C₂×D₄	—	53	6	no	—
1209	C₂×D₄	—	53	6	no	—
1210	C₂×D₄	—	53	6	no	—
1211	C₂×D₄	—	53	6	no	—
1212	C₂×D₄	—	53	3	no	—
1213	C₂×D₄	—	53	6	no	—
1214	C₂×D₄	—	106	12	no	—
1215	C₂×D₄	—	106	24	no	—
1216	C₂×D₄	—	106	24	no	—
1217	C₂×D₄	—	106	12	no	—
1218	C₂×D₄	—	212	12	no	—
1219	C₂×D₄	—	212	12	no	—
1220	C₂×D₄	—	212	12	no	—
1221	C₂×D₄	—	212	12	no	—
1222	C₂×D₄	—	212	6	no	—
1223	C₂×D₄	—	212	12	no	—
1224	C₂×D₄	—	212	12	no	—
1225	C₂×D₄	—	212	12	no	—
1226	C₂×D₄	—	212	12	no	—
1227	C₂×D₄	—	212	12	no	—
1228	C₂×D₄	—	212	12	no	—
1229	C₂×D₄	—	212	12	no	—
1230	C₂×D₄	—	212	12	no	—
1231	C₂×D₄	—	212	12	no	—
1232	C₂×D₄	—	212	12	no	—
1233	C₂×D₄	—	212	12	no	—
1234	C₂×D₄	—	212	12	no	—
1235	C₂×D₄	—	212	6	no	—
1236	C₂×D₄	—	212	12	no	—
1237	C₂×D₄	—	212	12	no	—
1238	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1239	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1240	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1241	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1242	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1243	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1244	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1245	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1246	C₂×D₄	C₂³×D₅₃	1	6	yes	complemented
1247	C₂×D₄	C₂³×D₅₃	1	3	yes	complemented
1248	C₂²×C₄	—	53	3	no	—
1249	C₂²×C₄	—	53	6	no	—
1250	C₂²×C₄	—	53	3	no	—
1251	C₂²×C₄	—	53	6	no	—
1252	C₂²×C₄	—	53	6	no	—
1253	C₂²×C₄	—	53	6	no	—
1254	C₂²×C₄	—	53	6	no	—
1255	C₂²×C₄	—	53	6	no	—
1256	C₂²×C₄	—	53	6	no	—
1257	C₂²×C₄	—	53	6	no	—
1258	C₂²×C₄	—	53	6	no	—
1259	C₂²×C₄	—	53	6	no	—
1260	C₂²×C₄	—	53	6	no	—
1261	C₂²×C₄	—	212	6	no	—
1262	C₂²×C₄	—	212	12	no	—
1263	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1264	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1265	C₂²×C₄	C₂³×D₅₃	1	3	yes	complemented
1266	C₂²×C₄	C₂³×D₅₃	1	6	yes	complemented
1267	C₄⋊C₄	—	53	6	no	—
1268	C₄⋊C₄	—	53	6	no	—
1269	C₄⋊C₄	—	53	6	no	—
1270	C₄⋊C₄	—	53	6	no	—
1271	C₄⋊C₄	—	53	6	no	—
1272	C₄⋊C₄	—	53	6	no	—
1273	C₄⋊C₄	—	53	6	no	—
1274	C₄⋊C₄	—	53	6	no	—
1275	C₄⋊C₄	—	53	6	no	—
1276	C₄⋊C₄	C₂³×D₅₃	1	6	yes	complemented
1277	C₄⋊C₄	C₂³×D₅₃	1	6	yes	complemented
1278	C₄⋊C₄	C₂³×D₅₃	1	6	yes	complemented
1279	C₂²⋊C₄	—	53	6	no	—
1280	C₂²⋊C₄	—	53	6	no	—
1281	C₂²⋊C₄	—	53	3	no	—
1282	C₂²⋊C₄	—	53	3	no	—
1283	C₂²⋊C₄	—	53	6	no	—
1284	C₂²⋊C₄	—	53	6	no	—
1285	C₂²⋊C₄	—	53	6	no	—
1286	C₂²⋊C₄	—	53	3	no	—
1287	C₂²⋊C₄	—	53	3	no	—
1288	C₂²⋊C₄	—	53	6	no	—
1289	C₂²⋊C₄	—	53	6	no	—
1290	C₂²⋊C₄	—	53	6	no	—
1291	C₂²⋊C₄	—	53	6	no	—
1292	C₂²⋊C₄	—	53	6	no	—
1293	C₂²⋊C₄	—	53	6	no	—
1294	C₂²⋊C₄	—	53	6	no	—
1295	C₂²⋊C₄	—	53	6	no	—
1296	C₂²⋊C₄	—	53	6	no	—
1297	C₂²⋊C₄	—	53	6	no	—
1298	C₂²⋊C₄	—	53	6	no	—
1299	C₂²⋊C₄	—	53	6	no	—
1300	C₂²⋊C₄	—	53	6	no	—
1301	C₂²⋊C₄	—	53	6	no	—
1302	C₂²⋊C₄	—	53	6	no	—
1303	C₂²⋊C₄	—	53	6	no	—
1304	C₂²⋊C₄	—	53	6	no	—
1305	C₂²⋊C₄	—	53	6	no	—
1306	C₂²⋊C₄	—	53	6	no	—
1307	C₂²⋊C₄	—	53	6	no	—
1308	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1309	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1310	C₂²⋊C₄	C₂³×D₅₃	1	3	yes	—
1311	C₂²⋊C₄	C₂³×D₅₃	1	3	yes	—
1312	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1313	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1314	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1315	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	complemented
1316	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	complemented
1317	C₂²⋊C₄	C₂³×D₅₃	1	3	yes	complemented
1318	C₂²⋊C₄	C₂³×D₅₃	1	3	yes	complemented
1319	C₄²	—	53	3	no	—
1320	C₄²	—	53	3	no	—
1321	C₄²	—	53	6	no	—
1322	C₄²	—	53	6	no	—
1323	C₄²	C₂³×D₅₃	1	2	yes	complemented
1324	C₄²	C₂³×D₅₃	1	3	yes	complemented
1325	C₄²	C₂³×D₅₃	1	1	yes	characteristic, complemented
1326	C₂³	—	2	12	no	—
1327	C₂³	—	2	6	no	—
1328	C₂³	—	2	6	no	—
1329	C₂³	—	4	3	no	—
1330	C₂³	—	4	6	no	—
1331	C₂³	—	4	3	no	—
1332	C₂³	—	4	6	no	—
1333	C₂³	—	4	3	no	—
1334	C₂³	—	4	16	no	—
1335	C₂³	—	53	6	no	—
1336	C₂³	—	53	12	no	—
1337	C₂³	—	53	2	no	—
1338	C₂³	—	53	6	no	—
1339	C₂³	—	106	12	no	—
1340	C₂³	—	106	12	no	—
1341	C₂³	—	106	12	no	—
1342	C₂³	—	106	12	no	—
1343	C₂³	—	106	12	no	—
1344	C₂³	—	106	12	no	—
1345	C₂³	—	106	12	no	—
1346	C₂³	—	106	12	no	—
1347	C₂³	—	106	6	no	—
1348	C₂³	—	106	6	no	—
1349	C₂³	—	106	12	no	—
1350	C₂³	—	424	24	no	—
1351	C₂³	—	212	6	no	—
1352	C₂³	—	212	3	no	—
1353	C₂³	—	212	6	no	—
1354	C₂³	—	212	6	no	—
1355	C₂³	—	212	6	no	—
1356	C₂³	—	212	6	no	—
1357	C₂³	—	212	6	no	—
1358	C₂³	—	212	6	no	—
1359	C₂³	—	212	6	no	—
1360	C₂³	—	212	3	no	—
1361	C₂³	—	212	6	no	—
1362	C₂³	—	212	6	no	—
1363	C₂³	—	212	6	no	—
1364	C₂³	—	212	3	no	—
1365	C₂³	—	212	96	no	—
1366	C₂³	—	212	48	no	—
1367	C₂³	—	212	48	no	—
1368	C₂³	—	212	32	no	—
1369	C₂³	C₂⁴×D₅₃	1	3	yes	—
1370	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1371	C₂³	C₂⁴×D₅₃	1	3	yes	—
1372	C₂³	C₂⁴×D₅₃	1	3	yes	—
1373	C₂³	C₂⁴×D₅₃	1	3	yes	—
1374	Q₈	—	4	3	no	—
1375	Q₈	—	212	3	no	—
1376	Q₈	—	212	6	no	—
1377	D₄	—	2	12	no	—
1378	D₄	—	2	12	no	—
1379	D₄	—	4	3	no	—
1380	D₄	—	4	3	no	—
1381	D₄	—	4	3	no	—
1382	D₄	—	4	3	no	—
1383	D₄	—	4	6	no	—
1384	D₄	—	4	6	no	—
1385	D₄	—	4	6	no	—
1386	D₄	—	4	3	no	—
1387	D₄	—	106	12	no	—
1388	D₄	—	106	12	no	—
1389	D₄	—	106	12	no	—
1390	D₄	—	106	12	no	—
1391	D₄	—	106	12	no	—
1392	D₄	—	106	12	no	—
1393	D₄	—	106	12	no	—
1394	D₄	—	106	12	no	—
1395	D₄	—	106	12	no	—
1396	D₄	—	106	12	no	—
1397	D₄	—	212	6	no	—
1398	D₄	—	212	6	no	—
1399	D₄	—	212	3	no	—
1400	D₄	—	212	6	no	—
1401	D₄	—	212	6	no	—
1402	D₄	—	212	6	no	—
1403	D₄	—	212	6	no	—
1404	D₄	—	212	6	no	—
1405	D₄	—	212	6	no	—
1406	D₄	—	212	6	no	—
1407	D₄	—	212	6	no	—
1408	D₄	—	212	6	no	—
1409	D₄	—	212	6	no	—
1410	C₂×C₄	—	2	6	no	—
1411	C₂×C₄	—	4	6	no	—
1412	C₂×C₄	—	4	3	no	—
1413	C₂×C₄	—	4	6	no	—
1414	C₂×C₄	—	53	6	no	—
1415	C₂×C₄	—	53	6	no	—
1416	C₂×C₄	—	53	6	no	—
1417	C₂×C₄	—	106	12	no	—
1418	C₂×C₄	—	106	12	no	—
1419	C₂×C₄	—	106	6	no	—
1420	C₂×C₄	—	212	6	no	—
1421	C₂×C₄	—	212	6	no	—
1422	C₂×C₄	—	212	6	no	—
1423	C₂×C₄	—	212	6	no	—
1424	C₂×C₄	—	212	6	no	—
1425	C₂×C₄	—	212	6	no	—
1426	C₂×C₄	—	212	6	no	—
1427	C₂×C₄	—	212	6	no	—
1428	C₂×C₄	—	212	6	no	—
1429	C₂×C₄	—	212	3	no	—
1430	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1431	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1432	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1433	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1434	C₂²	—	2	6	no	—
1435	C₂²	—	2	6	no	—
1436	C₂²	—	2	3	no	—
1437	C₂²	—	2	6	no	—
1438	C₂²	—	2	3	no	—
1439	C₂²	—	2	3	no	—
1440	C₂²	—	2	6	no	—
1441	C₂²	—	2	3	no	—
1442	C₂²	—	4	12	no	—
1443	C₂²	—	4	12	no	—
1444	C₂²	—	4	4	no	—
1445	C₂²	—	8	6	no	—
1446	C₂²	—	16	1	no	—
1447	C₂²	—	53	12	no	—
1448	C₂²	—	848	3	no	—
1449	C₂²	—	106	24	no	—
1450	C₂²	—	106	6	no	—
1451	C₂²	—	106	6	no	—
1452	C₂²	—	106	6	no	—
1453	C₂²	—	106	6	no	—
1454	C₂²	—	106	6	no	—
1455	C₂²	—	106	6	no	—
1456	C₂²	—	424	6	no	—
1457	C₂²	—	424	12	no	—
1458	C₂²	—	424	12	no	—
1459	C₂²	—	212	12	no	—
1460	C₂²	—	212	24	no	—
1461	C₂²	—	212	24	no	—
1462	C₂²	—	212	12	no	—
1463	C₂²	—	212	24	no	—
1464	C₂²	—	212	4	no	—
1465	C₂²	H(5,𝔽₂)×D₅₃	1	6	yes	—
1466	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1467	C₄	—	2	3	no	—
1468	C₄	—	2	3	no	—
1469	C₄	—	2	6	no	—
1470	C₄	—	2	6	no	—
1471	C₄	—	106	6	no	—
1472	C₄	—	106	6	no	—
1473	C₄	—	106	6	no	—
1474	C₂	—	2	6	no	—
1475	C₂	—	4	3	no	—
1476	C₂	—	4	1	no	—
1477	C₂	—	4	3	no	—
1478	C₂	—	4	3	no	—
1479	C₂	—	106	12	no	—
1480	C₂	—	212	6	no	—
1481	C₂	—	212	2	no	—
1482	C₂	C₂×H(5,𝔽₂)×D₅₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3532	C₂
hypercenter	#3532	D₅₃
hypocenter	C₅₃	#62817
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3532

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20288872	C₂	semidirect
2. #20288870	C₂	semidirect
3. #20288869	C₂	semidirect
4. #20288868	C₂	semidirect
5. #20288867	C₂	semidirect
6. #20288866	C₂	semidirect
7. #20288401	C₂	semidirect
8. #20288399	C₂	semidirect
9. #20288397	C₂	semidirect
10. #20288349	C₂	semidirect
11. #20288347	C₂	semidirect
12. #20288345	C₂	semidirect
13. #20288343	C₂	semidirect
14. C₂×#120×D₅₃	C₂	semidirect
15. C₅₃×#3532	C₂	semidirect
16. C₂⁵×D₅₃	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
18. C₂×#13133262	C₂²	semidirect
19. C₂²×D₄×D₅₃	C₂²	semidirect
20. C₂²×D₄×D₅₃	C₂²	semidirect
21. #16811366	C₂²	semidirect
22. #16811366	C₂²	semidirect
23. #16811365	C₂²	semidirect
24. #16811364	C₂²	semidirect
25. #16811363	C₂²	semidirect
26. #16811362	C₂²	semidirect
27. #16811362	C₂²	semidirect
28. #16811361	C₂²	semidirect
29. #16811360	C₂²	semidirect
30. #16811304	C₂²	semidirect
31. #16811303	C₂²	semidirect
32. #16811303	C₂²	semidirect
33. #16811302	C₂²	semidirect
34. #16811301	C₂²	semidirect
35. #16811301	C₂²	semidirect
36. #16811300	C₂²	semidirect
37. #16811299	C₂²	semidirect
38. #16811298	C₂²	semidirect
39. #16811298	C₂²	semidirect
40. #16811298	C₂²	semidirect
41. #16811297	C₂²	semidirect
42. #16811296	C₂²	semidirect
43. #16811270	C₂²	semidirect
44. #16811270	C₂²	semidirect
45. #16811270	C₂²	semidirect
46. #16811269	C₂²	semidirect
47. #16811268	C₂²	semidirect
48. #16811267	C₂²	semidirect
49. #16811266	C₂²	semidirect
50. #16811266	C₂²	semidirect
51. #16811266	C₂²	semidirect
52. #16811265	C₂²	semidirect
53. #16811265	C₂²	semidirect
54. #16811265	C₂²	semidirect
55. #16811265	C₂²	semidirect
56. #16811264	C₂²	semidirect
57. #16811263	C₂²	semidirect
58. #16811263	C₂²	semidirect
59. #16811262	C₂²	semidirect
60. #16811262	C₂²	semidirect
61. #16811262	C₂²	semidirect
62. #16811262	C₂²	semidirect
63. #16811261	C₂²	semidirect
64. #16811260	C₂²	semidirect
65. #16811260	C₂²	semidirect
66. D₄×D₂₁₂	C₂²	semidirect
67. #16811258	C₂²	semidirect
68. #16811258	C₂²	semidirect
69. #16811257	C₂²	semidirect
70. #16811257	C₂²	semidirect
71. #16811257	C₂²	semidirect
72. #16811257	C₂²	semidirect
73. D₄×C₂²⋊D₅₃	C₂²	semidirect
74. D₄×C₂²⋊D₅₃	C₂²	semidirect
75. #16811255	C₂²	semidirect
76. #16811255	C₂²	semidirect
77. #16811255	C₂²	semidirect
78. #16811255	C₂²	semidirect
79. #16811248	C₂²	semidirect
80. #16811212	C₂²	semidirect
81. #16811212	C₂²	semidirect
82. #16811211	C₂²	semidirect
83. #16811209	C₂²	semidirect
84. #16811209	C₂²	semidirect
85. #16811208	C₂²	semidirect
86. #16811208	C₂²	semidirect
87. #16811207	C₂²	semidirect
88. #16811207	C₂²	semidirect
89. #16811205	C₂²	semidirect
90. #16811205	C₂²	semidirect
91. #16811191	C₂²	semidirect
92. #16811190	C₂²	semidirect
93. #16811189	C₂²	semidirect
94. #16811189	C₂²	semidirect
95. #16811188	C₂²	semidirect
96. #16811186	C₂²	semidirect
97. #16811184	C₂²	semidirect
98. #16811184	C₂²	semidirect
99. #16811183	C₂²	semidirect
100. #16811183	C₂²	semidirect
101. #16811183	C₂²	semidirect
102. #16811182	C₂²	semidirect
103. #16811181	C₂²	semidirect
104. #16811181	C₂²	semidirect
105. #16811181	C₂²	semidirect
106. #16811136	C₂²	semidirect
107. #16811135	C₂²	semidirect
108. #16811133	C₂²	semidirect
109. #16811132	C₂²	semidirect
110. #16811132	C₂²	semidirect
111. #16811131	C₂²	semidirect
112. #16811130	C₂²	semidirect
113. C₂×#13133187	C₂²	semidirect
114. C₂×#13133187	C₂²	semidirect
115. C₂×#13133187	C₂²	semidirect
116. C₂×#13133186	C₂²	semidirect
117. C₂×#13133185	C₂²	semidirect
118. C₂×#13133185	C₂²	semidirect
119. C₂×#13133185	C₂²	semidirect
120. #120×D₅₃	C₂²	semidirect
121. #120×D₅₃	C₂²	semidirect
122. #120×D₅₃	C₂²	semidirect
123. #120×D₅₃	C₂²	semidirect
124. #120×D₅₃	C₂²	semidirect
125. #120×D₅₃	C₂²	semidirect
126. #120×D₅₃	C₂²	semidirect
127. #120×D₅₃	C₂²	semidirect
128. #120×D₅₃	C₂²	semidirect
129. #16811097	C₂²	semidirect
130. #16811096	C₂²	semidirect
131. #16811095	C₂²	semidirect
132. #16811095	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
134. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
135. C₅₃×H(3,𝔽₄)	C₂²	semidirect
136. C₅₃×#560	C₂²	semidirect
137. C₅₃×#551	C₂²	semidirect
138. C₅₃×#546	C₂²	semidirect
139. D₄²×C₅₃	C₂²	semidirect
140. C₅₃×#538	C₂²	semidirect
141. C₅₃×#535	C₂²	semidirect
142. C₅₃×#534	C₂²	semidirect
143. C₂×#120×C₅₃	C₂²	semidirect
149. C₂⁴×D₅₃	C₂³	semidirect
152. C₂×#11719949	C₂³	semidirect
153. C₂×#11719945	C₂³	semidirect
154. C₂×#11719945	C₂³	semidirect
155. C₂×#11719945	C₂³	semidirect
156. C₂×#11719947	C₂³	semidirect
157. C₂×#11719947	C₂³	semidirect
159. C₂²×D₂₁₂	C₂³	semidirect
160. C₂²×D₂₁₂	C₂³	semidirect
162. C₂²×C₂²⋊D₅₃	C₂³	semidirect
163. C₂²×C₂²⋊D₅₃	C₂³	semidirect
164. C₂²×C₂²⋊D₅₃	C₂³	semidirect
165. C₂²×C₂²⋊D₅₃	C₂³	semidirect
166. C₂²×C₂²⋊D₅₃	C₂³	semidirect
171. C₂×D₄×D₅₃	C₂³	semidirect
172. C₂×D₄×D₅₃	C₂³	semidirect
173. C₂×D₄×D₅₃	C₂³	semidirect
174. C₂×D₄×D₅₃	C₂³	semidirect
175. C₂×D₄×D₅₃	C₂³	semidirect
176. C₂×D₄×D₅₃	C₂³	semidirect
177. C₂×D₄×D₅₃	C₂³	semidirect
178. C₂×D₄×D₅₃	C₂³	semidirect
179. C₂×D₄×D₅₃	C₂³	semidirect
180. C₂×D₄×D₅₃	C₂³	semidirect
181. C₂×D₄×D₅₃	C₂³	semidirect
182. C₂×D₄×D₅₃	C₂³	semidirect
183. C₂×D₄×D₅₃	C₂³	semidirect
184. C₂²×C₄×D₅₃	C₂³	semidirect
185. C₂²×C₄×D₅₃	C₂³	semidirect
186. #13133214	C₂³	semidirect
187. #13133213	C₂³	semidirect
188. #13133213	C₂³	semidirect
189. #13133213	C₂³	semidirect
190. #13133213	C₂³	semidirect
191. #13133212	C₂³	semidirect
192. #13133212	C₂³	semidirect
193. #13133211	C₂³	semidirect
194. #13133211	C₂³	semidirect
195. #13133210	C₂³	semidirect
196. #13133210	C₂³	semidirect
197. #13133210	C₂³	semidirect
198. #13133210	C₂³	semidirect
199. #13133206	C₂³	semidirect
200. #13133205	C₂³	semidirect
201. #13133204	C₂³	semidirect
202. #13133204	C₂³	semidirect
203. #13133204	C₂³	semidirect
204. #13133203	C₂³	semidirect
205. #13133203	C₂³	semidirect
206. #13133203	C₂³	semidirect
207. #13133203	C₂³	semidirect
208. #13133203	C₂³	semidirect
209. #13133203	C₂³	semidirect
210. #13133202	C₂³	semidirect
211. #13133202	C₂³	semidirect
212. #13133202	C₂³	semidirect
213. #13133202	C₂³	semidirect
214. #13133202	C₂³	semidirect
215. #13133202	C₂³	semidirect
216. #13133201	C₂³	semidirect
217. #13133201	C₂³	semidirect
218. #13133200	C₂³	semidirect
219. #13133200	C₂³	semidirect
220. #13133199	C₂³	semidirect
221. #13133199	C₂³	semidirect
222. #13133199	C₂³	semidirect
223. #13133199	C₂³	semidirect
224. #13133199	C₂³	semidirect
225. #13133199	C₂³	semidirect
226. #13133199	C₂³	semidirect
227. #13133199	C₂³	semidirect
228. #13133198	C₂³	semidirect
229. #13133198	C₂³	semidirect
230. #13133198	C₂³	semidirect
231. #13133198	C₂³	semidirect
232. #13133197	C₂³	semidirect
233. #13133197	C₂³	semidirect
234. #13133196	C₂³	semidirect
235. #13133195	C₂³	semidirect
236. #13133195	C₂³	semidirect
237. #13133195	C₂³	semidirect
238. #13133195	C₂³	semidirect
239. #13133194	C₂³	semidirect
240. #13133194	C₂³	semidirect
241. #13133193	C₂³	semidirect
242. #13133193	C₂³	semidirect
243. #13133192	C₂³	semidirect
244. #13133192	C₂³	semidirect
245. #13133192	C₂³	semidirect
246. #13133192	C₂³	semidirect
247. #13133191	C₂³	semidirect
248. #13133191	C₂³	semidirect
249. #13133191	C₂³	semidirect
250. #13133190	C₂³	semidirect
251. #13133190	C₂³	semidirect
252. #13133190	C₂³	semidirect
253. #13133190	C₂³	semidirect
254. #13133190	C₂³	semidirect
255. #13133190	C₂³	semidirect
256. #13133190	C₂³	semidirect
257. #13133190	C₂³	semidirect
258. #13133190	C₂³	semidirect
259. #13133190	C₂³	semidirect
260. #13133189	C₂³	semidirect
261. #13133189	C₂³	semidirect
262. #13133189	C₂³	semidirect
263. #13133189	C₂³	semidirect
264. #13133189	C₂³	semidirect
265. #13133189	C₂³	semidirect
266. #13133189	C₂³	semidirect
267. #13133189	C₂³	semidirect
268. #13133188	C₂³	semidirect
269. #13133188	C₂³	semidirect
270. #13133188	C₂³	semidirect
271. #13133188	C₂³	semidirect
272. #13133188	C₂³	semidirect
273. #13133188	C₂³	semidirect
279. #13133187	C₂³	semidirect
280. #13133187	C₂³	semidirect
281. #13133187	C₂³	semidirect
282. #13133187	C₂³	semidirect
283. #13133187	C₂³	semidirect
284. #13133187	C₂³	semidirect
285. #13133187	C₂³	semidirect
286. #13133187	C₂³	semidirect
287. #13133187	C₂³	semidirect
288. #13133187	C₂³	semidirect
289. #13133187	C₂³	semidirect
290. #13133187	C₂³	semidirect
291. #13133187	C₂³	semidirect
293. #13133186	C₂³	semidirect
294. #13133186	C₂³	semidirect
295. #13133186	C₂³	semidirect
296. #13133186	C₂³	semidirect
297. #13133186	C₂³	semidirect
304. #13133185	C₂³	semidirect
305. #13133185	C₂³	semidirect
306. #13133185	C₂³	semidirect
307. #13133185	C₂³	semidirect
308. #13133185	C₂³	semidirect
309. #13133185	C₂³	semidirect
310. #13133185	C₂³	semidirect
311. #13133185	C₂³	semidirect
312. #13133185	C₂³	semidirect
313. #13133185	C₂³	semidirect
314. #13133185	C₂³	semidirect
315. #13133185	C₂³	semidirect
316. #13133185	C₂³	semidirect
317. #13133185	C₂³	semidirect
318. #13133185	C₂³	semidirect
319. #13133185	C₂³	semidirect
320. C₄×D₂₁₂	C₂³	semidirect
321. C₄×D₂₁₂	C₂³	semidirect
322. C₄×D₂₁₂	C₂³	semidirect
323. C₄×D₂₁₂	C₂³	semidirect
324. D₄×Dic₅₃	C₂³	semidirect
325. D₄×Dic₅₃	C₂³	semidirect
326. #13133179	C₂³	semidirect
327. #13133179	C₂³	semidirect
328. #13133179	C₂³	semidirect
329. #13133179	C₂³	semidirect
330. C₄×C₂²⋊D₅₃	C₂³	semidirect
331. C₄×C₂²⋊D₅₃	C₂³	semidirect
332. C₄×C₂²⋊D₅₃	C₂³	semidirect
333. C₄×C₂²⋊D₅₃	C₂³	semidirect
334. C₄×C₂²⋊D₅₃	C₂³	semidirect
335. C₄×C₂²⋊D₅₃	C₂³	semidirect
336. #13133177	C₂³	semidirect
337. #13133177	C₂³	semidirect
338. #13133177	C₂³	semidirect
339. #13133177	C₂³	semidirect
340. #13133177	C₂³	semidirect
341. #13133177	C₂³	semidirect
342. #13133176	C₂³	semidirect
343. #13133175	C₂³	semidirect
344. #13133175	C₂³	semidirect
345. #13133174	C₂³	semidirect
346. #13133174	C₂³	semidirect
347. #13133173	C₂³	semidirect
348. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
349. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
350. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
352. C₂×#11719921	C₂³	semidirect
353. C₂×#11719921	C₂³	semidirect
354. C₂×#11719921	C₂³	semidirect
355. C₂×#11719921	C₂³	semidirect
358. C₂²⋊C₄×D₅₃	C₂³	semidirect
359. C₂²⋊C₄×D₅₃	C₂³	semidirect
360. C₂²⋊C₄×D₅₃	C₂³	semidirect
361. C₂²⋊C₄×D₅₃	C₂³	semidirect
362. C₂²⋊C₄×D₅₃	C₂³	semidirect
363. C₂²⋊C₄×D₅₃	C₂³	semidirect
364. C₂²⋊C₄×D₅₃	C₂³	semidirect
365. C₂²⋊C₄×D₅₃	C₂³	semidirect
366. C₂²⋊C₄×D₅₃	C₂³	semidirect
367. C₂²⋊C₄×D₅₃	C₂³	semidirect
368. C₂²⋊C₄×D₅₃	C₂³	semidirect
369. C₂²⋊C₄×D₅₃	C₂³	semidirect
370. C₂²⋊C₄×D₅₃	C₂³	semidirect
372. C₂×#41×C₅₃	C₂³	semidirect
373. C₂²×D₄×C₅₃	C₂³	semidirect
374. C₂²×D₄×C₅₃	C₂³	semidirect
375. C₂²×D₄×C₅₃	C₂³	semidirect
376. #127×C₅₃	C₂³	semidirect
377. #127×C₅₃	C₂³	semidirect
378. #126×C₅₃	C₂³	semidirect
379. #126×C₅₃	C₂³	semidirect
380. #124×C₅₃	C₂³	semidirect
381. #124×C₅₃	C₂³	semidirect
382. #124×C₅₃	C₂³	semidirect
383. #123×C₅₃	C₂³	semidirect
384. #123×C₅₃	C₂³	semidirect
385. #123×C₅₃	C₂³	semidirect
386. #123×C₅₃	C₂³	semidirect
387. C₂²⋊Q₈×C₅₃	C₂³	semidirect
388. #121×C₅₃	C₂³	semidirect
389. #121×C₅₃	C₂³	semidirect
390. #121×C₅₃	C₂³	semidirect
391. #121×C₅₃	C₂³	semidirect
392. #121×C₅₃	C₂³	semidirect
395. #120×C₅₃	C₂³	semidirect
396. #120×C₅₃	C₂³	semidirect
397. #120×C₅₃	C₂³	semidirect
398. #120×C₅₃	C₂³	semidirect
399. #120×C₅₃	C₂³	semidirect
400. #120×C₅₃	C₂³	semidirect
401. #120×C₅₃	C₂³	semidirect
402. C₄×D₄×C₅₃	C₂³	semidirect
403. C₄×D₄×C₅₃	C₂³	semidirect
404. #117×C₅₃	C₂³	semidirect
405. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
406. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
407. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
413. C₂⁴×C₅₃	C₂⁴	semidirect
435. C₂³×D₅₃	C₂⁴	semidirect
437. C₂×Q₈×C₅₃	C₂⁴	semidirect
449. C₂×D₄×C₅₃	C₂⁴	semidirect
450. C₂×D₄×C₅₃	C₂⁴	semidirect
453. C₂²×C₄×C₅₃	C₂⁴	semidirect
454. C₂²×C₄×C₅₃	C₂⁴	semidirect
473. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
474. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
475. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
478. C₂²×Dic₅₃	C₂⁴	semidirect
479. C₂²×Dic₅₃	C₂⁴	semidirect
510. C₂×D₂₁₂	C₂⁴	semidirect
511. C₂×D₂₁₂	C₂⁴	semidirect
520. C₂×C₄×D₅₃	C₂⁴	semidirect
521. C₂×C₄×D₅₃	C₂⁴	semidirect
522. C₂×C₄×D₅₃	C₂⁴	semidirect
523. C₂×Dic₁₀₆	C₂⁴	semidirect
524. C₂×Dic₁₀₆	C₂⁴	semidirect
525. C₄⋊C₄×C₅₃	C₂⁴	semidirect
526. C₄⋊C₄×C₅₃	C₂⁴	semidirect
527. C₄⋊C₄×C₅₃	C₂⁴	semidirect
535. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
536. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
537. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
538. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
539. C₄²×C₅₃	C₂⁴	semidirect
540. C₄²×C₅₃	C₂⁴	semidirect
541. C₄²×C₅₃	C₂⁴	semidirect
549. C₂²⋊Dic₅₃	C₂⁴	semidirect
550. C₂²⋊Dic₅₃	C₂⁴	semidirect
551. C₂²⋊Dic₅₃	C₂⁴	semidirect
552. C₂²⋊Dic₅₃	C₂⁴	semidirect
565. #11719921	C₂⁴	semidirect
566. #11719921	C₂⁴	semidirect
567. #11719921	C₂⁴	semidirect
568. #11719921	C₂⁴	semidirect
569. #11719921	C₂⁴	semidirect
570. #11719921	C₂⁴	semidirect
571. C₄⋊Dic₅₃	C₂⁴	semidirect
572. C₄⋊Dic₅₃	C₂⁴	semidirect
573. C₄⋊Dic₅₃	C₂⁴	semidirect
574. #11719919	C₂⁴	semidirect
575. #11719919	C₂⁴	semidirect
576. #11719919	C₂⁴	semidirect
577. #11719919	C₂⁴	semidirect
578. #11719919	C₂⁴	semidirect
579. #11719919	C₂⁴	semidirect
580. C₄×Dic₅₃	C₂⁴	semidirect
581. C₄×Dic₅₃	C₂⁴	semidirect
582. C₄×Dic₅₃	C₂⁴	semidirect
583. C₄×Dic₅₃	C₂⁴	semidirect
628. C₂²×D₅₃	H(5,𝔽₂)	semidirect
739. #3532	D₅₃	semidirect
765. H(3,𝔽₄)	C₂×D₅₃	semidirect
772. #560	C₂×D₅₃	semidirect
786. #551	C₂×D₅₃	semidirect
810. #546	C₂×D₅₃	semidirect
824. D₄²	C₂×D₅₃	semidirect
837. #538	C₂×D₅₃	semidirect
844. #535	C₂×D₅₃	semidirect
854. #534	C₂×D₅₃	semidirect
878. C₂×#120	C₂×D₅₃	semidirect
885. C₅₃	#62817	semidirect
901. C₂×#41	C₂²×D₅₃	semidirect
928. C₂²×D₄	C₂²×D₅₃	semidirect
929. C₂²×D₄	C₂²×D₅₃	semidirect
930. C₂²×D₄	C₂²×D₅₃	semidirect
938. #127	C₂²×D₅₃	semidirect
939. #127	C₂²×D₅₃	semidirect
948. #126	C₂²×D₅₃	semidirect
949. #126	C₂²×D₅₃	semidirect
961. #124	C₂²×D₅₃	semidirect
962. #124	C₂²×D₅₃	semidirect
963. #124	C₂²×D₅₃	semidirect
986. #123	C₂²×D₅₃	semidirect
987. #123	C₂²×D₅₃	semidirect
988. #123	C₂²×D₅₃	semidirect
989. #123	C₂²×D₅₃	semidirect
1001. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1033. #121	C₂²×D₅₃	semidirect
1034. #121	C₂²×D₅₃	semidirect
1035. #121	C₂²×D₅₃	semidirect
1036. #121	C₂²×D₅₃	semidirect
1037. #121	C₂²×D₅₃	semidirect
1086. #120	C₂²×D₅₃	semidirect
1087. #120	C₂²×D₅₃	semidirect
1088. #120	C₂²×D₅₃	semidirect
1089. #120	C₂²×D₅₃	semidirect
1090. #120	C₂²×D₅₃	semidirect
1091. #120	C₂²×D₅₃	semidirect
1092. #120	C₂²×D₅₃	semidirect
1115. C₄×D₄	C₂²×D₅₃	semidirect
1116. C₄×D₄	C₂²×D₅₃	semidirect
1123. #117	C₂²×D₅₃	semidirect
1147. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1148. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1149. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1177. C₂⁴	C₂³×D₅₃	semidirect
1187. C₂×Q₈	C₂³×D₅₃	semidirect
1246. C₂×D₄	C₂³×D₅₃	semidirect
1247. C₂×D₄	C₂³×D₅₃	semidirect
1265. C₂²×C₄	C₂³×D₅₃	semidirect
1266. C₂²×C₄	C₂³×D₅₃	semidirect
1276. C₄⋊C₄	C₂³×D₅₃	semidirect
1277. C₄⋊C₄	C₂³×D₅₃	semidirect
1278. C₄⋊C₄	C₂³×D₅₃	semidirect
1315. C₂²⋊C₄	C₂³×D₅₃	semidirect
1316. C₂²⋊C₄	C₂³×D₅₃	semidirect
1317. C₂²⋊C₄	C₂³×D₅₃	semidirect
1318. C₂²⋊C₄	C₂³×D₅₃	semidirect
1323. C₄²	C₂³×D₅₃	semidirect
1324. C₄²	C₂³×D₅₃	semidirect
1325. C₄²	C₂³×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20288872	2
#20288870	2
#20288869	2
#20288868	2
#20288867	2
#20288866	2
#20288401	2
#20288399	2
#20288397	2
#20288349	2
#20288347	2
#20288345	2
#20288343	2
C₂×#120×D₅₃	2
C₅₃×#3532	2
#62817	53