Subgroups — #28292972

Order 13568.

8650 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289046	C₂	1	4	yes	maximal, complemented
2	#20289041	C₂	1	8	yes	maximal, complemented
3	#20289040	C₂	1	8	yes	maximal, complemented
4	#20289039	C₂	1	4	yes	maximal, complemented
5	#20288591	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288590	C₂	1	2	yes	maximal, complemented
7	#20288589	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288585	C₂	1	4	yes	maximal, complemented
9	#20288584	C₂	1	4	yes	maximal, complemented
10	#20288491	C₂	1	4	yes	maximal, complemented
11	#20288489	C₂	1	2	yes	maximal, complemented
12	#20288488	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288487	C₂	1	4	yes	maximal, complemented
14	#20288349	C₂	1	2	yes	maximal, complemented
15	#20288346	C₂	1	2	yes	maximal, complemented
16	#20288343	C₂	1	8	yes	maximal, complemented
17	#20288010	C₂	1	1	yes	maximal, characteristic, complemented
18	#20288008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#13133263	C₂²	1	2	yes	complemented
22	C₂×#13133262	C₂²	1	8	yes	complemented
23	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
25	#16811362	C₂²	1	16	yes	complemented
26	#16811361	C₂²	1	16	yes	complemented
27	#16811359	C₂²	1	4	yes	complemented
28	#16811358	C₂²	1	4	yes	complemented
29	#16811356	C₂²	1	8	yes	complemented
30	#16811355	C₂²	1	8	yes	complemented
31	#16811294	C₂²	1	4	yes	complemented
32	#16811294	C₂²	1	4	yes	complemented
33	#16811293	C₂²	1	4	yes	complemented
34	#16811293	C₂²	1	8	yes	complemented
35	#16811293	C₂²	1	8	yes	complemented
36	#16811292	C₂²	1	8	yes	complemented
37	#16811291	C₂²	1	8	yes	complemented
38	#16811270	C₂²	1	8	yes	complemented
39	#16811270	C₂²	1	8	yes	complemented
40	#16811269	C₂²	1	8	yes	complemented
41	#16811268	C₂²	1	8	yes	complemented
42	#16811267	C₂²	1	8	yes	complemented
43	#16811266	C₂²	1	8	yes	complemented
44	#16811262	C₂²	1	16	yes	complemented
45	#16811261	C₂²	1	8	yes	complemented
46	#16811261	C₂²	1	8	yes	complemented
47	#16811260	C₂²	1	16	yes	complemented
48	D₄×D₂₁₂	C₂²	1	4	yes	complemented
49	#16811258	C₂²	1	8	yes	complemented
50	#16811258	C₂²	1	8	yes	complemented
51	#16811257	C₂²	1	8	yes	complemented
52	#16811257	C₂²	1	8	yes	complemented
53	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
54	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
55	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
56	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
57	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
58	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
59	#16811255	C₂²	1	16	yes	complemented
60	#16811228	C₂²	1	4	yes	complemented
61	#16811227	C₂²	1	4	yes	complemented
62	#16811226	C₂²	1	8	yes	complemented
63	#16811226	C₂²	1	8	yes	complemented
64	#16811224	C₂²	1	8	yes	complemented
65	#16811223	C₂²	1	16	yes	complemented
66	#16811191	C₂²	1	4	yes	complemented
67	#16811190	C₂²	1	2	yes	complemented
68	#16811190	C₂²	1	8	yes	complemented
69	#16811190	C₂²	1	4	yes	complemented
70	#16811189	C₂²	1	8	yes	complemented
71	#16811188	C₂²	1	16	yes	complemented
72	#16811187	C₂²	1	2	yes	complemented
73	#16811187	C₂²	1	2	yes	complemented
74	#16811187	C₂²	1	4	yes	complemented
75	#16811186	C₂²	1	8	yes	complemented
76	#16811186	C₂²	1	8	yes	complemented
77	#16811183	C₂²	1	8	yes	complemented
78	#16811183	C₂²	1	16	yes	complemented
79	#16811182	C₂²	1	8	yes	complemented
80	#16811181	C₂²	1	16	yes	complemented
81	#16811180	C₂²	1	1	yes	characteristic, complemented
82	#16811178	C₂²	1	2	yes	complemented
83	#16811177	C₂²	1	2	yes	complemented
84	#16811176	C₂²	1	1	yes	characteristic, complemented
85	#16811174	C₂²	1	2	yes	complemented
86	#16811173	C₂²	1	4	yes	complemented
87	#16811171	C₂²	1	4	yes	complemented
88	#16811171	C₂²	1	2	yes	complemented
89	#16811170	C₂²	1	2	yes	complemented
90	#16811169	C₂²	1	1	yes	characteristic, complemented
91	#16811169	C₂²	1	4	yes	complemented
92	#16811168	C₂²	1	8	yes	complemented
93	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
94	C₂×#13133213	C₂²	1	4	yes	complemented
95	C₂×#13133213	C₂²	1	2	yes	complemented
96	C₂×#13133213	C₂²	1	4	yes	complemented
97	#127×D₅₃	C₂²	1	4	yes	complemented
98	#127×D₅₃	C₂²	1	4	yes	complemented
99	#127×D₅₃	C₂²	1	4	yes	complemented
100	#127×D₅₃	C₂²	1	4	yes	complemented
101	#127×D₅₃	C₂²	1	2	yes	complemented
102	#16811160	C₂²	1	2	yes	complemented
103	#16811155	C₂²	1	2	yes	complemented
104	#16811155	C₂²	1	4	yes	complemented
105	#16811154	C₂²	1	4	yes	complemented
106	#16811153	C₂²	1	4	yes	complemented
107	#16811152	C₂²	1	4	yes	complemented
108	#16811151	C₂²	1	4	yes	complemented
109	#16811135	C₂²	1	1	yes	characteristic, complemented
110	#16811133	C₂²	1	4	yes	complemented
111	#16811132	C₂²	1	4	yes	complemented
112	#16811130	C₂²	1	1	yes	characteristic, complemented
113	#16811130	C₂²	1	2	yes	complemented
114	C₂×#13133185	C₂²	1	8	yes	complemented
115	#120×D₅₃	C₂²	1	8	yes	complemented
116	#16811098	C₂²	1	2	yes	complemented
117	#16811097	C₂²	1	2	yes	complemented
118	#16811095	C₂²	1	8	yes	complemented
119	#41×Dic₅₃	C₂²	1	2	yes	complemented
120	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
121	C₄×#11719945	C₂²	1	4	yes	complemented
122	C₄×#11719947	C₂²	1	4	yes	complemented
123	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
125	C₅₃×#550	C₂²	1	4	yes	complemented
126	D₄²×C₅₃	C₂²	1	8	yes	complemented
127	D₄²×C₅₃	C₂²	1	4	yes	complemented
128	C₅₃×#535	C₂²	1	2	yes	complemented
129	C₅₃×#535	C₂²	1	4	yes	complemented
130	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#532	C₂²	1	2	yes	complemented
132	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
134	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂⁴×D₅₃	C₂³	1	4	yes	—
136	#13133263	—	4	8	no	—
137	#13133262	—	4	32	no	—
138	C₂×#11719949	C₂³	1	4	yes	complemented
139	C₂×#11719945	C₂³	1	4	yes	—
140	C₂×#11719945	C₂³	1	1	yes	characteristic
141	C₂×#11719945	C₂³	1	8	yes	complemented
142	C₂×#11719945	C₂³	1	4	yes	complemented
143	C₂×#11719947	C₂³	1	4	yes	—
144	C₂×#11719947	C₂³	1	8	yes	complemented
145	C₂×#11719947	C₂³	1	16	yes	complemented
146	C₂²×D₂₁₂	C₂³	1	2	yes	—
147	C₂²×D₂₁₂	C₂³	1	4	yes	—
148	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
149	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	—
150	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
151	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
152	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
153	C₂×D₄×D₅₃	—	4	8	no	—
154	C₂×D₄×D₅₃	—	4	16	no	—
155	C₂×D₄×D₅₃	C₂³	1	8	yes	—
156	C₂×D₄×D₅₃	C₂³	1	8	yes	—
157	C₂×D₄×D₅₃	C₂³	1	8	yes	—
158	C₂×D₄×D₅₃	C₂³	1	8	yes	—
159	C₂×D₄×D₅₃	C₂³	1	16	yes	—
160	C₂×D₄×D₅₃	C₂³	1	8	yes	—
161	C₂×D₄×D₅₃	C₂³	1	8	yes	—
162	C₂×D₄×D₅₃	C₂³	1	8	yes	—
163	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
164	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
165	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
167	#13133217	C₂³	1	2	yes	complemented
168	#13133216	C₂³	1	2	yes	complemented
169	#13133215	C₂³	1	1	yes	characteristic, complemented
170	#13133214	C₂³	1	4	yes	—
171	#13133214	C₂³	1	2	yes	—
172	#13133214	C₂³	1	2	yes	—
173	#13133213	C₂³	1	8	yes	—
174	#13133213	C₂³	1	8	yes	—
175	#13133213	C₂³	1	8	yes	—
176	#13133213	C₂³	1	4	yes	—
177	#13133213	C₂³	1	8	yes	—
178	#13133213	C₂³	1	4	yes	—
179	#13133213	C₂³	1	8	yes	—
180	#13133213	C₂³	1	16	yes	complemented
181	#13133213	C₂³	1	4	yes	complemented
182	#13133213	C₂³	1	4	yes	complemented
183	#13133213	C₂³	1	8	yes	complemented
184	#13133213	C₂³	1	4	yes	complemented
185	#13133213	C₂³	1	1	yes	characteristic, complemented
186	#13133212	C₂³	1	4	yes	complemented
187	#13133210	C₂³	1	8	yes	complemented
188	#13133210	C₂³	1	4	yes	complemented
189	#13133209	C₂³	1	2	yes	complemented
190	#13133208	C₂³	1	4	yes	complemented
191	#13133208	C₂³	1	2	yes	complemented
192	#13133207	C₂³	1	4	yes	complemented
193	#13133206	C₂³	1	4	yes	complemented
194	#13133206	C₂³	1	4	yes	complemented
195	#13133206	C₂³	1	1	yes	characteristic, complemented
196	#13133205	C₂³	1	8	yes	complemented
197	#13133204	C₂³	1	8	yes	complemented
198	#13133204	C₂³	1	4	yes	complemented
199	#13133204	C₂³	1	4	yes	complemented
200	#13133204	C₂³	1	1	yes	characteristic, complemented
201	#13133203	C₂³	1	16	yes	complemented
202	#13133203	C₂³	1	4	yes	complemented
203	#13133202	C₂³	1	4	yes	—
204	#13133202	C₂³	1	16	yes	complemented
205	#13133201	C₂³	1	2	yes	—
206	#13133201	C₂³	1	16	yes	complemented
207	#13133200	C₂³	1	16	yes	complemented
208	#13133199	C₂³	1	4	yes	—
209	#13133199	C₂³	1	8	yes	—
210	#13133199	C₂³	1	16	yes	complemented
211	#13133199	C₂³	1	16	yes	complemented
212	#13133198	C₂³	1	2	yes	—
213	#13133198	C₂³	1	4	yes	—
214	#13133198	C₂³	1	16	yes	complemented
215	#13133197	C₂³	1	4	yes	—
216	#13133197	C₂³	1	2	yes	—
217	#13133196	C₂³	1	4	yes	—
218	#13133195	C₂³	1	4	yes	—
219	#13133194	C₂³	1	4	yes	—
220	#13133193	C₂³	1	4	yes	—
221	#13133193	C₂³	1	2	yes	—
222	#13133192	C₂³	1	2	yes	—
223	#13133192	C₂³	1	8	yes	complemented
224	#13133191	C₂³	1	16	yes	complemented
225	#13133191	C₂³	1	8	yes	complemented
226	#13133191	C₂³	1	8	yes	complemented
227	#13133191	C₂³	1	8	yes	complemented
228	#13133190	C₂³	1	4	yes	—
229	#13133190	C₂³	1	16	yes	complemented
230	#13133190	C₂³	1	16	yes	complemented
231	#13133190	C₂³	1	16	yes	complemented
232	#13133189	C₂³	1	4	yes	—
233	#13133189	C₂³	1	16	yes	complemented
234	#13133189	C₂³	1	16	yes	complemented
235	#13133189	C₂³	1	16	yes	complemented
236	#13133189	C₂³	1	16	yes	complemented
237	#13133189	C₂³	1	16	yes	complemented
238	#13133189	C₂³	1	16	yes	complemented
239	#13133188	C₂³	1	4	yes	—
240	#13133188	C₂³	1	2	yes	—
241	#13133188	C₂³	1	4	yes	—
242	#13133188	C₂³	1	8	yes	complemented
243	#13133188	C₂³	1	8	yes	complemented
244	#13133188	C₂³	1	16	yes	complemented
245	#13133188	C₂³	1	16	yes	complemented
246	#13133188	C₂³	1	16	yes	complemented
247	#13133187	C₂³	1	16	yes	—
248	#13133187	C₂³	1	2	yes	—
249	#13133187	C₂³	1	16	yes	complemented
250	#13133186	C₂³	1	8	yes	—
251	#13133186	C₂³	1	16	yes	complemented
252	#13133186	C₂³	1	16	yes	complemented
253	#13133185	C₂³	1	8	yes	—
254	#13133185	C₂³	1	16	yes	—
255	#13133185	C₂³	1	16	yes	—
256	#13133185	C₂³	1	4	yes	—
257	#13133185	C₂³	1	2	yes	—
258	#13133185	C₂³	1	16	yes	—
259	#13133185	C₂³	1	8	yes	—
260	#13133185	C₂³	1	16	yes	complemented
261	#13133185	C₂³	1	16	yes	complemented
262	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
263	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
264	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
265	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
266	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
267	#13133182	C₂³	1	4	yes	complemented
268	C₄×D₂₁₂	C₂³	1	4	yes	—
269	C₄×D₂₁₂	C₂³	1	4	yes	—
270	C₄×D₂₁₂	C₂³	1	8	yes	complemented
271	C₄×D₂₁₂	C₂³	1	8	yes	complemented
272	C₄×D₂₁₂	C₂³	1	2	yes	complemented
273	D₄×Dic₅₃	C₂³	1	8	yes	—
274	D₄×Dic₅₃	C₂³	1	8	yes	complemented
275	D₄×Dic₅₃	C₂³	1	4	yes	complemented
276	D₄×Dic₅₃	C₂³	1	4	yes	complemented
277	D₄×Dic₅₃	C₂³	1	8	yes	complemented
278	D₄×Dic₅₃	C₂³	1	8	yes	complemented
279	#13133179	C₂³	1	8	yes	complemented
280	#13133179	C₂³	1	8	yes	complemented
281	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
282	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
283	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
284	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
285	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
286	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
287	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
288	#13133177	C₂³	1	8	yes	—
289	#13133177	C₂³	1	16	yes	complemented
290	#13133176	C₂³	1	1	yes	characteristic
291	#13133176	C₂³	1	2	yes	—
292	#13133176	C₂³	1	4	yes	complemented
293	#13133176	C₂³	1	4	yes	complemented
294	#13133175	C₂³	1	4	yes	—
295	#13133174	C₂³	1	4	yes	—
296	#13133174	C₂³	1	2	yes	complemented
297	#13133174	C₂³	1	4	yes	complemented
298	#13133173	C₂³	1	8	yes	complemented
299	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
300	C₂×#11719921	C₂³	1	16	yes	—
301	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
302	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
305	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
306	C₄²×D₅₃	C₂³	1	2	yes	—
307	C₄²×D₅₃	C₂³	1	2	yes	—
308	C₄²×D₅₃	C₂³	1	2	yes	—
309	C₄²×D₅₃	C₂³	1	2	yes	—
310	C₄²×D₅₃	C₂³	1	2	yes	complemented
311	H(5,𝔽₂)×C₅₃	—	4	8	no	—
312	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×#41×C₅₃	C₂³	1	2	yes	—
314	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
315	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
316	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
317	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
318	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
319	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
320	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
321	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
322	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
323	#127×C₅₃	C₂³	1	4	yes	—
324	#127×C₅₃	C₂³	1	2	yes	—
325	#127×C₅₃	C₂³	1	2	yes	—
326	#127×C₅₃	C₂³	1	4	yes	complemented
327	#127×C₅₃	C₂³	1	8	yes	complemented
328	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
329	#124×C₅₃	C₂³	1	4	yes	complemented
330	#124×C₅₃	C₂³	1	2	yes	complemented
331	#121×C₅₃	C₂³	1	4	yes	—
332	#121×C₅₃	C₂³	1	8	yes	complemented
333	#121×C₅₃	C₂³	1	8	yes	complemented
334	#121×C₅₃	C₂³	1	16	yes	complemented
335	#120×C₅₃	C₂³	1	8	yes	—
336	#120×C₅₃	C₂³	1	16	yes	complemented
337	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
338	C₄×D₄×C₅₃	C₂³	1	4	yes	—
339	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
340	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
341	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
342	#117×C₅₃	C₂³	1	1	yes	characteristic
343	#117×C₅₃	C₂³	1	2	yes	complemented
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
346	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
347	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
348	C₂³×D₅₃	—	4	16	no	—
349	C₂³×D₅₃	—	4	8	no	—
350	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
351	C₂³×D₅₃	C₂⁴	1	4	yes	—
352	C₂³×D₅₃	C₂⁴	1	16	yes	—
353	C₂³×D₅₃	C₂⁴	1	8	yes	—
354	#41×C₅₃	—	2	4	no	—
355	#41×C₅₃	—	2	8	no	—
356	#41×C₅₃	—	4	8	no	—
357	#41×C₅₃	—	4	8	no	—
358	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
360	C₂×D₄×C₅₃	—	2	8	no	—
361	C₂×D₄×C₅₃	—	4	8	no	—
362	C₂×D₄×C₅₃	—	4	8	no	—
363	C₂×D₄×C₅₃	—	4	8	no	—
364	C₂×D₄×C₅₃	—	4	16	no	—
365	C₂×D₄×C₅₃	—	4	16	no	—
366	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
369	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
373	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
375	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
376	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
377	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
378	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₂²⋊D₅₃	—	4	16	no	—
385	C₂×C₂²⋊D₅₃	—	4	32	no	—
386	C₂×C₂²⋊D₅₃	—	4	8	no	—
387	C₂×C₂²⋊D₅₃	—	4	32	no	—
388	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
389	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
390	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
392	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
393	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
394	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
395	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
396	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
397	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
398	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
399	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
402	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
403	#11719949	—	4	8	no	—
404	#11719947	—	2	16	no	—
405	#11719947	—	4	16	no	—
406	#11719947	—	4	32	no	—
407	D₄×D₅₃	—	2	32	no	—
408	D₄×D₅₃	—	4	16	no	—
409	D₄×D₅₃	—	4	16	no	—
410	D₄×D₅₃	—	4	16	no	—
411	D₄×D₅₃	—	4	16	no	—
412	D₄×D₅₃	—	4	8	no	—
413	D₄×D₅₃	—	4	16	no	—
414	D₄×D₅₃	—	4	16	no	—
415	D₄×D₅₃	—	4	32	no	—
416	D₄×D₅₃	—	4	16	no	—
417	#11719945	—	2	4	no	—
418	#11719945	—	2	16	no	—
419	#11719945	—	4	16	no	—
420	#11719945	—	4	8	no	—
421	C₂×D₂₁₂	—	2	8	no	—
422	C₂×D₂₁₂	—	4	8	no	—
423	C₂×D₂₁₂	—	4	8	no	—
424	C₂×D₂₁₂	C₂⁴	1	4	yes	—
425	C₂×D₂₁₂	C₂⁴	1	8	yes	—
426	C₂×D₂₁₂	C₂⁴	1	4	yes	—
427	C₂×D₂₁₂	C₂⁴	1	4	yes	—
428	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
429	C₂×D₂₁₂	C₂⁴	1	8	yes	—
430	C₂×D₂₁₂	C₂⁴	1	8	yes	—
431	C₂×C₄×D₅₃	—	2	4	no	—
432	C₂×C₄×D₅₃	—	2	8	no	—
433	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
434	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
435	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
436	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
437	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
438	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
439	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
440	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
441	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
442	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
443	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
444	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
445	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
448	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
453	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅₃	C₂⁴	1	2	yes	—
456	C₄²×C₅₃	C₂⁴	1	2	yes	—
457	C₄²×C₅₃	C₂⁴	1	4	yes	—
458	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
459	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
460	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
461	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
462	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
463	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
464	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
465	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
466	#11719921	C₂⁴	1	4	yes	—
467	#11719921	C₂⁴	1	8	yes	—
468	#11719921	C₂⁴	1	16	yes	—
469	#11719921	C₂⁴	1	4	yes	—
470	#11719921	C₂⁴	1	16	yes	—
471	#11719921	C₂⁴	1	16	yes	—
472	#11719921	C₂⁴	1	4	yes	—
473	#11719921	C₂⁴	1	4	yes	—
474	#11719921	C₂⁴	1	4	yes	—
475	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
476	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
477	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
478	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
479	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
480	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
481	#11719919	C₂⁴	1	8	yes	—
482	#11719919	C₂⁴	1	8	yes	—
483	#11719919	C₂⁴	1	4	yes	—
484	#11719919	C₂⁴	1	4	yes	—
485	#11719919	C₂⁴	1	4	yes	—
486	#11719919	C₂⁴	1	4	yes	—
487	#11719919	C₂⁴	1	4	yes	—
488	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
489	C₄×Dic₅₃	C₂⁴	1	2	yes	—
490	C₄×Dic₅₃	C₂⁴	1	2	yes	—
491	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
492	C₄×Dic₅₃	C₂⁴	1	2	yes	—
493	C₄×Dic₅₃	C₂⁴	1	2	yes	—
494	C₄×Dic₅₃	C₂⁴	1	2	yes	—
495	C₄×Dic₅₃	C₂⁴	1	4	yes	—
496	C₄×Dic₅₃	C₂⁴	1	2	yes	—
497	C₄×Dic₅₃	C₂⁴	1	8	yes	—
498	C₄×Dic₅₃	C₂⁴	1	4	yes	—
499	C₂³×C₅₃	—	2	8	no	—
500	C₂³×C₅₃	—	4	8	no	—
501	C₂³×C₅₃	—	4	16	no	—
502	C₂³×C₅₃	—	4	8	no	—
503	C₂³×C₅₃	C₂⁵	1	4	yes	—
504	C₂³×C₅₃	C₂⁵	1	8	yes	—
505	C₂³×C₅₃	C₂⁵	1	2	yes	—
506	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
507	C₂²×D₅₃	—	2	2	no	—
508	C₂²×D₅₃	—	2	4	no	—
509	C₂²×D₅₃	—	2	8	no	—
510	C₂²×D₅₃	—	2	32	no	—
511	C₂²×D₅₃	—	4	8	no	—
512	C₂²×D₅₃	—	4	16	no	—
513	C₂²×D₅₃	—	4	16	no	—
514	C₂²×D₅₃	—	4	8	no	—
515	C₂²×D₅₃	—	4	16	no	—
516	C₂²×D₅₃	—	8	32	no	—
517	C₂²×D₅₃	C₂⁵	1	2	yes	—
518	C₂²×D₅₃	C₂⁵	1	8	yes	—
519	C₂²×D₅₃	C₂⁵	1	2	yes	—
520	Q₈×C₅₃	—	2	4	no	—
521	Q₈×C₅₃	—	2	2	no	—
522	D₄×C₅₃	—	2	8	no	—
523	D₄×C₅₃	—	2	4	no	—
524	D₄×C₅₃	—	2	16	no	—
525	D₄×C₅₃	—	2	8	no	—
526	D₄×C₅₃	—	2	8	no	—
527	D₄×C₅₃	—	2	8	no	—
528	D₄×C₅₃	—	2	4	no	—
529	D₄×C₅₃	—	2	2	no	—
530	D₄×C₅₃	—	4	8	no	—
531	D₄×C₅₃	—	4	16	no	—
532	D₄×C₅₃	—	4	8	no	—
533	D₄×C₅₃	—	4	8	no	—
534	C₂×C₄×C₅₃	—	2	4	no	—
535	C₂×C₄×C₅₃	—	2	8	no	—
536	C₂×C₄×C₅₃	—	2	8	no	—
537	C₂×C₄×C₅₃	—	2	4	no	—
538	C₂×C₄×C₅₃	—	4	8	no	—
539	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
540	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
541	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
542	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
543	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
544	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
545	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
547	C₂²⋊D₅₃	—	2	4	no	—
548	C₂²⋊D₅₃	—	2	8	no	—
549	C₂²⋊D₅₃	—	2	16	no	—
550	C₂²⋊D₅₃	—	2	8	no	—
551	C₂²⋊D₅₃	—	2	32	no	—
552	C₂²⋊D₅₃	—	4	8	no	—
553	C₂²⋊D₅₃	—	4	16	no	—
554	C₂²⋊D₅₃	—	4	16	no	—
555	C₂²⋊D₅₃	—	4	16	no	—
556	C₂²⋊D₅₃	—	4	16	no	—
557	C₂²⋊D₅₃	—	4	16	no	—
558	C₂×Dic₅₃	—	2	2	no	—
559	C₂×Dic₅₃	—	2	4	no	—
560	C₂×Dic₅₃	—	2	16	no	—
561	C₂×Dic₅₃	—	4	16	no	—
562	C₂×Dic₅₃	C₂⁵	1	2	yes	—
563	C₂×Dic₅₃	C₂⁵	1	8	yes	—
564	C₂×Dic₅₃	C₂⁵	1	4	yes	—
565	C₂×Dic₅₃	C₂⁵	1	2	yes	—
566	C₂×Dic₅₃	C₂⁵	1	2	yes	—
567	C₂×Dic₅₃	C₂⁵	1	2	yes	—
568	D₂₁₂	—	2	8	no	—
569	D₂₁₂	—	2	8	no	—
570	D₂₁₂	—	2	8	no	—
571	D₂₁₂	—	2	2	no	—
572	D₂₁₂	—	2	16	no	—
573	D₂₁₂	—	4	8	no	—
574	D₂₁₂	—	4	8	no	—
575	C₄×D₅₃	—	2	4	no	—
576	C₄×D₅₃	—	2	4	no	—
577	C₄×D₅₃	—	2	4	no	—
578	C₄×D₅₃	—	2	4	no	—
579	C₄×D₅₃	—	2	8	no	—
580	C₄×D₅₃	—	2	4	no	—
581	C₄×D₅₃	—	2	4	no	—
582	C₄×D₅₃	—	4	16	no	—
583	C₄×D₅₃	—	4	8	no	—
584	C₄×D₅₃	H(5,𝔽₂)	1	8	yes	complemented
585	Dic₁₀₆	—	2	2	no	—
586	Dic₁₀₆	—	2	8	no	—
587	Dic₁₀₆	—	2	8	no	—
588	#62832	—	53	1	no	maximal, Sylow
589	C₂²×C₅₃	—	2	2	no	—
590	C₂²×C₅₃	—	2	8	no	—
591	C₂²×C₅₃	—	2	16	no	—
592	C₂²×C₅₃	—	2	4	no	—
593	C₂²×C₅₃	—	2	4	no	—
594	C₂²×C₅₃	—	2	8	no	—
595	C₂²×C₅₃	—	2	2	no	—
596	C₂²×C₅₃	—	8	8	no	—
597	C₂²×C₅₃	—	16	8	no	—
598	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
599	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
600	C₂×D₅₃	—	2	8	no	—
601	C₂×D₅₃	—	2	2	no	—
602	C₂×D₅₃	—	2	2	no	—
603	C₂×D₅₃	—	2	2	no	—
604	C₂×D₅₃	—	2	4	no	—
605	C₂×D₅₃	—	2	8	no	—
606	C₂×D₅₃	—	2	16	no	—
607	C₂×D₅₃	—	8	32	no	—
608	C₂×D₅₃	—	8	8	no	—
609	C₂×D₅₃	—	16	8	no	—
610	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
611	C₄×C₅₃	—	2	4	no	—
612	C₄×C₅₃	—	2	2	no	—
613	C₄×C₅₃	—	2	4	no	—
614	C₄×C₅₃	—	2	2	no	—
615	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
616	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
617	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
618	Dic₅₃	—	2	2	no	—
619	Dic₅₃	—	2	4	no	—
620	Dic₅₃	—	2	8	no	—
621	Dic₅₃	—	2	2	no	—
622	Dic₅₃	—	2	2	no	—
623	Dic₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
624	#3543	—	53	4	no	—
625	#3543	—	53	8	no	—
626	#3543	—	53	4	no	—
627	#3543	—	53	8	no	—
628	#3508	—	53	4	no	—
629	#3508	—	53	2	no	—
630	#3508	—	53	4	no	—
631	#3508	—	53	1	no	—
632	#3508	—	53	1	no	—
633	#3498	—	53	2	no	—
634	#3498	—	53	4	no	—
635	#3498	—	53	1	no	—
636	#3498	—	53	4	no	—
637	#3498	D₅₃	1	1	yes	characteristic, complemented
638	#3484	—	53	2	no	—
639	#3484	—	53	8	no	—
640	#3484	—	53	2	no	—
641	#3444	—	53	1	no	—
642	#3444	—	53	1	no	—
643	C₂²×#127	—	53	1	no	—
644	C₂×C₅₃	—	2	2	no	—
645	C₂×C₅₃	—	4	8	no	—
646	C₂×C₅₃	—	4	4	no	—
647	C₂×C₅₃	—	4	2	no	—
648	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
649	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
650	D₅₃	—	2	4	no	—
651	D₅₃	—	4	8	no	—
652	D₅₃	—	4	2	no	—
653	C₂×H(5,𝔽₂)	—	53	2	no	—
654	C₂×H(5,𝔽₂)	—	53	8	no	—
655	C₂×H(5,𝔽₂)	C₂×D₅₃	1	2	yes	complemented
656	C₂³×D₄	—	53	2	no	—
657	C₂³×D₄	—	53	4	no	—
658	#560	—	53	16	no	—
659	#560	—	53	16	no	—
660	#559	—	53	4	no	—
661	#559	—	53	8	no	—
662	#559	—	53	4	no	—
663	#559	—	53	8	no	—
664	#550	—	53	8	no	—
665	#550	—	53	4	no	—
666	#550	—	53	8	no	—
667	#550	—	53	8	no	—
668	#550	—	53	8	no	—
669	#550	—	53	4	no	—
670	#550	—	53	4	no	—
671	#550	C₂×D₅₃	1	4	yes	complemented
672	#546	—	53	8	no	—
673	#546	—	53	8	no	—
674	#546	—	53	8	no	—
675	#546	—	53	8	no	—
676	#546	—	53	8	no	—
677	#546	—	53	8	no	—
678	#546	—	53	16	no	—
679	#546	—	53	16	no	—
680	#546	—	53	8	no	—
681	#546	—	53	8	no	—
682	D₄²	—	53	16	no	—
683	D₄²	—	53	8	no	—
684	D₄²	—	53	8	no	—
685	D₄²	—	53	8	no	—
686	D₄²	—	53	8	no	—
687	D₄²	—	53	8	no	—
688	D₄²	—	53	8	no	—
689	D₄²	—	53	8	no	—
690	D₄²	—	53	8	no	—
691	D₄²	—	53	8	no	—
692	D₄²	—	53	16	no	—
693	D₄²	—	53	4	no	—
694	D₄²	C₂×D₅₃	1	8	yes	complemented
695	D₄²	C₂×D₅₃	1	4	yes	complemented
696	#540	—	53	4	no	—
697	#540	—	53	16	no	—
698	#540	—	53	8	no	—
699	#540	—	53	8	no	—
700	#540	—	53	8	no	—
701	#540	—	53	4	no	—
702	#535	—	53	2	no	—
703	#535	—	53	2	no	—
704	#535	—	53	4	no	—
705	#535	—	53	2	no	—
706	#535	—	53	4	no	—
707	#535	—	53	8	no	—
708	#535	—	53	8	no	—
709	#535	—	53	8	no	—
710	#535	—	53	4	no	—
711	#535	—	53	8	no	—
712	#535	—	53	16	no	—
713	#535	C₂×D₅₃	1	2	yes	complemented
714	#535	C₂×D₅₃	1	4	yes	complemented
715	#534	—	53	8	no	—
716	#534	—	53	16	no	—
717	#534	—	53	8	no	—
718	#534	—	53	16	no	—
719	#533	—	53	2	no	—
720	#533	—	53	2	no	—
721	#533	—	53	1	no	—
722	#533	—	53	1	no	—
723	#532	—	53	1	no	—
724	#532	—	53	4	no	—
725	#532	—	53	2	no	—
726	#532	—	53	4	no	—
727	#532	—	53	2	no	—
728	#532	—	53	8	no	—
729	#532	—	53	2	no	—
730	#532	—	53	4	no	—
731	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
732	#532	C₂×D₅₃	1	2	yes	complemented
733	C₂×#127	—	53	2	no	—
734	C₂×#127	—	53	4	no	—
735	C₂×#127	—	53	4	no	—
736	C₂×#127	—	53	4	no	—
737	C₂×#127	—	53	4	no	—
738	C₂×#127	—	53	4	no	—
739	C₂×#127	—	53	4	no	—
740	C₂×#127	—	53	2	no	—
741	C₂×#127	—	53	1	no	—
742	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
743	C₂×#127	C₂×D₅₃	1	2	yes	complemented
744	#529	—	53	4	no	—
745	#529	—	53	4	no	—
746	#529	—	53	2	no	—
747	#529	—	53	4	no	—
748	#529	—	53	4	no	—
749	#529	—	53	2	no	—
750	#529	—	53	4	no	—
751	#525	—	53	2	no	—
752	#525	—	53	1	no	—
753	#525	—	53	4	no	—
754	#525	—	53	4	no	—
755	#525	—	53	1	no	—
756	C₂×#120	—	53	8	no	—
757	C₂×#120	—	53	8	no	—
758	#518	—	53	2	no	—
759	#518	—	53	8	no	—
760	#518	—	53	2	no	—
761	C₄×#41	—	53	2	no	—
762	C₄×#41	—	53	4	no	—
763	C₄×#41	—	53	1	no	—
764	C₄×#41	—	53	4	no	—
765	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
766	C₂²×C₄²	—	53	1	no	—
767	C₅₃	#62832	1	1	yes	characteristic, complemented, Sylow
768	C₂⁵	—	53	4	no	—
769	H(5,𝔽₂)	—	4	8	no	—
770	H(5,𝔽₂)	—	212	32	no	—
771	H(5,𝔽₂)	—	212	8	no	—
772	C₂×#41	—	53	4	no	—
773	C₂×#41	—	53	4	no	—
774	C₂×#41	—	53	16	no	—
775	C₂×#41	—	53	8	no	—
776	C₂×#41	—	53	4	no	—
777	C₂×#41	—	53	1	no	—
778	C₂×#41	—	53	4	no	—
779	C₂×#41	—	53	8	no	—
780	C₂×#41	C₂²×D₅₃	1	2	yes	—
781	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
782	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
783	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
784	C₂²×D₄	—	53	16	no	—
785	C₂²×D₄	—	53	4	no	—
786	C₂²×D₄	—	53	8	no	—
787	C₂²×D₄	—	53	16	no	—
788	C₂²×D₄	—	53	8	no	—
789	C₂²×D₄	—	53	16	no	—
790	C₂²×D₄	—	53	8	no	—
791	C₂²×D₄	—	53	8	no	—
792	C₂²×D₄	—	53	8	no	—
793	C₂²×D₄	—	53	8	no	—
794	C₂²×D₄	—	53	8	no	—
795	C₂²×D₄	—	53	8	no	—
796	C₂²×D₄	—	53	4	no	—
797	C₂²×D₄	—	53	8	no	—
798	C₂²×D₄	—	53	2	no	—
799	C₂²×D₄	—	53	4	no	—
800	C₂²×D₄	—	53	4	no	—
801	C₂²×D₄	—	212	8	no	—
802	C₂²×D₄	—	212	16	no	—
803	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
804	C₂²×D₄	C₂²×D₅₃	1	8	yes	—
805	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
806	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
807	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
808	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
809	C₂³×C₄	—	53	2	no	—
810	C₂³×C₄	—	53	1	no	—
811	C₄⋊Q₈	—	53	1	no	—
812	C₄⋊Q₈	—	53	2	no	—
813	C₄⋊Q₈	—	53	2	no	—
814	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
815	#127	—	53	4	no	—
816	#127	—	53	1	no	—
817	#127	—	53	8	no	—
818	#127	—	53	4	no	—
819	#127	—	53	8	no	—
820	#127	—	53	8	no	—
821	#127	—	53	8	no	—
822	#127	—	53	8	no	—
823	#127	—	53	16	no	—
824	#127	—	53	4	no	—
825	#127	—	53	4	no	—
826	#127	—	53	8	no	—
827	#127	—	53	4	no	—
828	#127	—	53	2	no	—
829	#127	—	53	2	no	—
830	#127	—	53	4	no	—
831	#127	C₂²×D₅₃	1	2	yes	—
832	#127	C₂²×D₅₃	1	2	yes	—
833	#127	C₂²×D₅₃	1	4	yes	—
834	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
835	#127	C₂²×D₅₃	1	8	yes	complemented
836	#127	C₂²×D₅₃	1	4	yes	complemented
837	#126	—	53	4	no	—
838	#126	—	53	8	no	—
839	#126	—	53	4	no	—
840	#125	—	53	4	no	—
841	#125	—	53	4	no	—
842	#125	—	53	2	no	—
843	#125	—	53	2	no	—
844	#124	—	53	1	no	—
845	#124	—	53	4	no	—
846	#124	—	53	4	no	—
847	#124	—	53	4	no	—
848	#124	—	53	1	no	—
849	#124	—	53	4	no	—
850	#124	—	53	8	no	—
851	#124	—	53	4	no	—
852	#124	—	53	16	no	—
853	#124	—	53	8	no	—
854	#124	C₂²×D₅₃	1	2	yes	complemented
855	#124	C₂²×D₅₃	1	4	yes	complemented
856	#123	—	53	4	no	—
857	#123	—	53	2	no	—
858	#123	—	53	16	no	—
859	#123	—	53	16	no	—
860	#123	—	53	4	no	—
861	#123	—	53	16	no	—
862	#123	—	53	8	no	—
863	#123	—	53	4	no	—
864	#123	—	53	2	no	—
865	#123	—	53	16	no	—
866	#123	—	53	16	no	—
867	#123	—	53	16	no	—
868	C₂²⋊Q₈	—	53	4	no	—
869	C₂²⋊Q₈	—	53	2	no	—
870	C₂²⋊Q₈	—	53	4	no	—
871	C₂²⋊Q₈	—	53	4	no	—
872	C₂²⋊Q₈	—	53	4	no	—
873	C₂²⋊Q₈	—	53	2	no	—
874	C₂²⋊Q₈	—	53	4	no	—
875	#121	—	53	4	no	—
876	#121	—	53	4	no	—
877	#121	—	53	2	no	—
878	#121	—	53	4	no	—
879	#121	—	53	8	no	—
880	#121	—	53	8	no	—
881	#121	—	53	16	no	—
882	#121	—	53	16	no	—
883	#121	—	53	16	no	—
884	#121	—	53	16	no	—
885	#121	—	53	16	no	—
886	#121	—	53	16	no	—
887	#121	—	53	16	no	—
888	#121	—	53	16	no	—
889	#121	—	53	16	no	—
890	#121	—	53	8	no	—
891	#121	—	53	8	no	—
892	#121	—	53	8	no	—
893	#121	—	53	16	no	—
894	#121	—	53	2	no	—
895	#121	—	53	8	no	—
896	#121	—	53	4	no	—
897	#121	—	53	16	no	—
898	#121	—	53	16	no	—
899	#121	—	53	16	no	—
900	#121	C₂²×D₅₃	1	4	yes	—
901	#121	C₂²×D₅₃	1	8	yes	complemented
902	#121	C₂²×D₅₃	1	8	yes	complemented
903	#121	C₂²×D₅₃	1	16	yes	complemented
904	#120	—	53	8	no	—
905	#120	—	53	16	no	—
906	#120	—	53	16	no	—
907	#120	—	53	4	no	—
908	#120	—	53	2	no	—
909	#120	—	53	8	no	—
910	#120	—	53	8	no	—
911	#120	—	53	16	no	—
912	#120	—	53	16	no	—
913	#120	—	53	16	no	—
914	#120	—	53	16	no	—
915	#120	—	53	16	no	—
916	#120	—	53	2	no	—
917	#120	—	53	16	no	—
918	#120	—	53	16	no	—
919	#120	C₂²×D₅₃	1	8	yes	—
920	#120	C₂²×D₅₃	1	16	yes	complemented
921	C₄×Q₈	—	53	4	no	—
922	C₄×Q₈	—	53	4	no	—
923	C₄×Q₈	—	53	4	no	—
924	C₄×Q₈	—	53	4	no	—
925	C₄×Q₈	—	53	4	no	—
926	C₄×Q₈	—	53	2	no	—
927	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
928	C₄×D₄	—	53	8	no	—
929	C₄×D₄	—	53	4	no	—
930	C₄×D₄	—	53	4	no	—
931	C₄×D₄	—	53	8	no	—
932	C₄×D₄	—	53	8	no	—
933	C₄×D₄	—	53	8	no	—
934	C₄×D₄	—	53	4	no	—
935	C₄×D₄	—	53	8	no	—
936	C₄×D₄	—	53	4	no	—
937	C₄×D₄	—	53	4	no	—
938	C₄×D₄	—	53	4	no	—
939	C₄×D₄	—	53	4	no	—
940	C₄×D₄	—	53	16	no	—
941	C₄×D₄	—	53	8	no	—
942	C₄×D₄	—	53	8	no	—
943	C₄×D₄	—	53	8	no	—
944	C₄×D₄	—	53	16	no	—
945	C₄×D₄	—	53	4	no	—
946	C₄×D₄	—	53	4	no	—
947	C₄×D₄	—	53	2	no	—
948	C₄×D₄	—	53	8	no	—
949	C₄×D₄	—	53	8	no	—
950	C₄×D₄	C₂²×D₅₃	1	4	yes	—
951	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
952	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
953	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
954	#117	—	53	2	no	—
955	#117	—	53	1	no	—
956	#117	—	53	4	no	—
957	#117	—	53	4	no	—
958	#117	—	53	4	no	—
959	#117	—	53	8	no	—
960	#117	—	53	4	no	—
961	#117	—	53	4	no	—
962	#117	—	53	2	no	—
963	#117	C₂²×D₅₃	1	1	yes	characteristic
964	#117	C₂²×D₅₃	1	2	yes	complemented
965	C₂×C₂²⋊C₄	—	53	8	no	—
966	C₂×C₂²⋊C₄	—	53	16	no	—
967	C₂×C₂²⋊C₄	—	53	8	no	—
968	C₂×C₂²⋊C₄	—	53	16	no	—
969	C₂×C₄²	—	53	4	no	—
970	C₂×C₄²	—	53	1	no	—
971	C₂×C₄²	—	53	2	no	—
972	C₂×C₄²	—	53	2	no	—
973	C₂×C₄²	—	53	2	no	—
974	C₂×C₄²	—	53	2	no	—
975	C₂×C₄²	—	53	2	no	—
976	C₂×C₄²	—	53	2	no	—
977	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
978	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
979	C₂⁴	—	53	1	no	—
980	C₂⁴	—	53	16	no	—
981	C₂⁴	—	53	4	no	—
982	C₂⁴	—	53	8	no	—
983	C₂⁴	—	212	8	no	—
984	C₂⁴	—	212	16	no	—
985	C₂⁴	C₂³×D₅₃	1	4	yes	—
986	C₂⁴	C₂³×D₅₃	1	8	yes	—
987	#41	—	2	4	no	—
988	#41	—	2	8	no	—
989	#41	—	4	8	no	—
990	#41	—	4	8	no	—
991	#41	—	106	16	no	—
992	#41	—	106	16	no	—
993	#41	—	106	4	no	—
994	#41	—	212	16	no	—
995	#41	—	212	8	no	—
996	#41	—	212	16	no	—
997	#41	—	212	32	no	—
998	#41	—	212	8	no	—
999	C₂×Q₈	—	53	4	no	—
1000	C₂×Q₈	—	53	4	no	—
1001	C₂×Q₈	—	53	1	no	—
1002	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1003	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1004	C₂×D₄	—	2	8	no	—
1005	C₂×D₄	—	4	8	no	—
1006	C₂×D₄	—	4	8	no	—
1007	C₂×D₄	—	4	8	no	—
1008	C₂×D₄	—	4	16	no	—
1009	C₂×D₄	—	4	16	no	—
1010	C₂×D₄	—	53	8	no	—
1011	C₂×D₄	—	53	4	no	—
1012	C₂×D₄	—	53	2	no	—
1013	C₂×D₄	—	53	16	no	—
1014	C₂×D₄	—	53	4	no	—
1015	C₂×D₄	—	53	8	no	—
1016	C₂×D₄	—	53	16	no	—
1017	C₂×D₄	—	53	16	no	—
1018	C₂×D₄	—	53	16	no	—
1019	C₂×D₄	—	53	16	no	—
1020	C₂×D₄	—	53	16	no	—
1021	C₂×D₄	—	53	4	no	—
1022	C₂×D₄	—	53	8	no	—
1023	C₂×D₄	—	53	4	no	—
1024	C₂×D₄	—	53	1	no	—
1025	C₂×D₄	—	53	4	no	—
1026	C₂×D₄	—	53	8	no	—
1027	C₂×D₄	—	53	8	no	—
1028	C₂×D₄	—	106	32	no	—
1029	C₂×D₄	—	106	8	no	—
1030	C₂×D₄	—	212	8	no	—
1031	C₂×D₄	—	212	8	no	—
1032	C₂×D₄	—	212	16	no	—
1033	C₂×D₄	—	212	16	no	—
1034	C₂×D₄	—	212	16	no	—
1035	C₂×D₄	—	212	16	no	—
1036	C₂×D₄	—	212	8	no	—
1037	C₂×D₄	—	212	16	no	—
1038	C₂×D₄	—	212	16	no	—
1039	C₂×D₄	—	212	16	no	—
1040	C₂×D₄	—	212	32	no	—
1041	C₂×D₄	—	212	8	no	—
1042	C₂×D₄	—	212	16	no	—
1043	C₂×D₄	—	212	32	no	—
1044	C₂×D₄	—	212	32	no	—
1045	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1046	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1047	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1048	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1049	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1050	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1051	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1052	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1053	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1054	C₂×D₄	C₂³×D₅₃	1	16	yes	—
1055	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1056	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1057	C₂²×C₄	—	53	2	no	—
1058	C₂²×C₄	—	53	2	no	—
1059	C₂²×C₄	—	53	1	no	—
1060	C₂²×C₄	—	53	8	no	—
1061	C₂²×C₄	—	53	16	no	—
1062	C₂²×C₄	—	53	2	no	—
1063	C₂²×C₄	—	53	2	no	—
1064	C₂²×C₄	—	53	2	no	—
1065	C₂²×C₄	—	53	2	no	—
1066	C₂²×C₄	—	53	2	no	—
1067	C₂²×C₄	—	53	4	no	—
1068	C₂²×C₄	—	53	2	no	—
1069	C₂²×C₄	—	53	8	no	—
1070	C₂²×C₄	—	53	16	no	—
1071	C₂²×C₄	—	106	8	no	—
1072	C₂²×C₄	—	106	4	no	—
1073	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1074	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1075	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1076	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1077	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1078	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1079	C₄⋊C₄	—	53	4	no	—
1080	C₄⋊C₄	—	53	4	no	—
1081	C₄⋊C₄	—	53	4	no	—
1082	C₄⋊C₄	—	53	2	no	—
1083	C₄⋊C₄	—	53	4	no	—
1084	C₄⋊C₄	—	53	8	no	—
1085	C₄⋊C₄	—	53	4	no	—
1086	C₄⋊C₄	—	53	4	no	—
1087	C₄⋊C₄	—	53	8	no	—
1088	C₄⋊C₄	—	53	4	no	—
1089	C₄⋊C₄	—	53	8	no	—
1090	C₄⋊C₄	—	53	4	no	—
1091	C₄⋊C₄	—	53	4	no	—
1092	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1093	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1094	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1095	C₂²⋊C₄	—	53	2	no	—
1096	C₂²⋊C₄	—	53	4	no	—
1097	C₂²⋊C₄	—	53	16	no	—
1098	C₂²⋊C₄	—	53	16	no	—
1099	C₂²⋊C₄	—	53	8	no	—
1100	C₂²⋊C₄	—	53	8	no	—
1101	C₂²⋊C₄	—	53	4	no	—
1102	C₂²⋊C₄	—	53	4	no	—
1103	C₂²⋊C₄	—	53	8	no	—
1104	C₂²⋊C₄	—	53	4	no	—
1105	C₂²⋊C₄	—	53	4	no	—
1106	C₂²⋊C₄	—	53	16	no	—
1107	C₂²⋊C₄	—	53	16	no	—
1108	C₂²⋊C₄	—	53	16	no	—
1109	C₂²⋊C₄	—	53	4	no	—
1110	C₂²⋊C₄	—	53	4	no	—
1111	C₂²⋊C₄	—	53	4	no	—
1112	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1113	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1114	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1115	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1116	C₄²	—	53	1	no	—
1117	C₄²	—	53	2	no	—
1118	C₄²	—	53	2	no	—
1119	C₄²	—	53	1	no	—
1120	C₄²	—	53	2	no	—
1121	C₄²	—	53	2	no	—
1122	C₄²	—	53	2	no	—
1123	C₄²	—	53	8	no	—
1124	C₄²	—	53	4	no	—
1125	C₄²	—	53	4	no	—
1126	C₄²	—	53	2	no	—
1127	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1128	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1129	C₄²	C₂³×D₅₃	1	2	yes	—
1130	C₄²	C₂³×D₅₃	1	4	yes	—
1131	C₄²	C₂³×D₅₃	1	2	yes	—
1132	C₂³	—	2	8	no	—
1133	C₂³	—	4	8	no	—
1134	C₂³	—	4	8	no	—
1135	C₂³	—	4	16	no	—
1136	C₂³	—	53	2	no	—
1137	C₂³	—	53	2	no	—
1138	C₂³	—	53	8	no	—
1139	C₂³	—	106	4	no	—
1140	C₂³	—	106	32	no	—
1141	C₂³	—	106	2	no	—
1142	C₂³	—	106	8	no	—
1143	C₂³	—	424	32	no	—
1144	C₂³	—	212	16	no	—
1145	C₂³	—	212	8	no	—
1146	C₂³	—	212	8	no	—
1147	C₂³	—	212	16	no	—
1148	C₂³	—	212	16	no	—
1149	C₂³	C₂⁴×D₅₃	1	4	yes	—
1150	C₂³	C₂⁴×D₅₃	1	8	yes	—
1151	C₂³	C₂⁴×D₅₃	1	2	yes	—
1152	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	4	no	—
1155	Q₈	—	106	8	no	—
1156	Q₈	—	106	8	no	—
1157	Q₈	—	106	2	no	—
1158	D₄	—	2	4	no	—
1159	D₄	—	2	8	no	—
1160	D₄	—	2	16	no	—
1161	D₄	—	2	8	no	—
1162	D₄	—	2	8	no	—
1163	D₄	—	2	8	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	4	8	no	—
1167	D₄	—	4	8	no	—
1168	D₄	—	4	8	no	—
1169	D₄	—	4	16	no	—
1170	D₄	—	106	8	no	—
1171	D₄	—	106	32	no	—
1172	D₄	—	106	8	no	—
1173	D₄	—	106	8	no	—
1174	D₄	—	106	16	no	—
1175	D₄	—	106	4	no	—
1176	D₄	—	106	16	no	—
1177	D₄	—	106	8	no	—
1178	D₄	—	106	8	no	—
1179	D₄	—	106	2	no	—
1180	D₄	—	212	8	no	—
1181	D₄	—	212	8	no	—
1182	D₄	—	212	16	no	—
1183	D₄	—	212	16	no	—
1184	D₄	—	212	16	no	—
1185	D₄	—	212	16	no	—
1186	D₄	—	212	16	no	—
1187	D₄	—	212	8	no	—
1188	C₂×C₄	—	2	4	no	—
1189	C₂×C₄	—	2	8	no	—
1190	C₂×C₄	—	2	4	no	—
1191	C₂×C₄	—	2	8	no	—
1192	C₂×C₄	—	4	8	no	—
1193	C₂×C₄	—	53	2	no	—
1194	C₂×C₄	—	53	8	no	—
1195	C₂×C₄	—	53	2	no	—
1196	C₂×C₄	—	53	2	no	—
1197	C₂×C₄	—	53	8	no	—
1198	C₂×C₄	—	53	4	no	—
1199	C₂×C₄	—	53	2	no	—
1200	C₂×C₄	—	106	4	no	—
1201	C₂×C₄	—	106	4	no	—
1202	C₂×C₄	—	106	4	no	—
1203	C₂×C₄	—	106	16	no	—
1204	C₂×C₄	—	106	2	no	—
1205	C₂×C₄	—	106	4	no	—
1206	C₂×C₄	—	106	8	no	—
1207	C₂×C₄	—	106	4	no	—
1208	C₂×C₄	—	106	4	no	—
1209	C₂×C₄	—	106	4	no	—
1210	C₂×C₄	—	212	16	no	—
1211	C₂×C₄	—	212	8	no	—
1212	C₂×C₄	—	212	16	no	—
1213	C₂×C₄	#13133262	1	4	yes	complemented
1214	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1215	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1216	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1217	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1218	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1219	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1220	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	4	no	—
1223	C₂²	—	2	8	no	—
1224	C₂²	—	2	16	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	4	no	—
1227	C₂²	—	2	8	no	—
1228	C₂²	—	8	8	no	—
1229	C₂²	—	16	8	no	—
1230	C₂²	—	53	4	no	—
1231	C₂²	—	848	8	no	—
1232	C₂²	—	106	8	no	—
1233	C₂²	—	106	2	no	—
1234	C₂²	—	106	2	no	—
1235	C₂²	—	106	4	no	—
1236	C₂²	—	106	16	no	—
1237	C₂²	—	106	2	no	—
1238	C₂²	—	106	8	no	—
1239	C₂²	—	424	8	no	—
1240	C₂²	—	424	32	no	—
1241	C₂²	C₂×#13133262	1	2	yes	—
1242	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1243	C₄	—	2	2	no	—
1244	C₄	—	2	4	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	4	no	—
1247	C₄	—	53	4	no	—
1248	C₄	—	106	2	no	—
1249	C₄	—	106	8	no	—
1250	C₄	—	106	4	no	—
1251	C₄	—	106	2	no	—
1252	C₄	—	106	2	no	—
1253	C₄	H(5,𝔽₂)×D₅₃	1	4	yes	—
1254	C₄	C₂×#13133262	1	2	yes	—
1255	C₄	C₂×#13133262	1	2	yes	—
1256	C₂	—	2	2	no	—
1257	C₂	—	4	8	no	—
1258	C₂	—	4	2	no	—
1259	C₂	—	4	4	no	—
1260	C₂	—	106	4	no	—
1261	C₂	—	212	2	no	—
1262	C₂	—	212	8	no	—
1263	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—
1264	C₂	C₂²×#13133262	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3498	C₂
hypercenter	#3498	D₅₃
hypocenter	C₅₃	#62832
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3498

Complements

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

N	H ≅ G/N	type
1. #20289046	C₂	semidirect
2. #20289041	C₂	semidirect
3. #20289040	C₂	semidirect
4. #20289039	C₂	semidirect
5. #20288591	C₂	semidirect
6. #20288590	C₂	semidirect
7. #20288589	C₂	semidirect
8. #20288585	C₂	semidirect
9. #20288584	C₂	semidirect
10. #20288491	C₂	semidirect
11. #20288489	C₂	semidirect
12. #20288488	C₂	semidirect
13. #20288487	C₂	semidirect
14. #20288349	C₂	semidirect
15. #20288346	C₂	semidirect
16. #20288343	C₂	semidirect
17. #20288010	C₂	semidirect
18. #20288008	C₂	semidirect
19. C₂×#127×D₅₃	C₂	semidirect
20. C₅₃×#3498	C₂	semidirect
21. C₂×#13133263	C₂²	semidirect
22. C₂×#13133262	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. #16811362	C₂²	semidirect
26. #16811361	C₂²	semidirect
27. #16811359	C₂²	semidirect
28. #16811358	C₂²	semidirect
29. #16811356	C₂²	semidirect
30. #16811355	C₂²	semidirect
31. #16811294	C₂²	semidirect
32. #16811294	C₂²	semidirect
33. #16811293	C₂²	semidirect
34. #16811293	C₂²	semidirect
35. #16811293	C₂²	semidirect
36. #16811292	C₂²	semidirect
37. #16811291	C₂²	semidirect
38. #16811270	C₂²	semidirect
39. #16811270	C₂²	semidirect
40. #16811269	C₂²	semidirect
41. #16811268	C₂²	semidirect
42. #16811267	C₂²	semidirect
43. #16811266	C₂²	semidirect
44. #16811262	C₂²	semidirect
45. #16811261	C₂²	semidirect
46. #16811261	C₂²	semidirect
47. #16811260	C₂²	semidirect
48. D₄×D₂₁₂	C₂²	semidirect
49. #16811258	C₂²	semidirect
50. #16811258	C₂²	semidirect
51. #16811257	C₂²	semidirect
52. #16811257	C₂²	semidirect
53. D₄×C₂²⋊D₅₃	C₂²	semidirect
54. D₄×C₂²⋊D₅₃	C₂²	semidirect
55. D₄×C₂²⋊D₅₃	C₂²	semidirect
56. D₄×C₂²⋊D₅₃	C₂²	semidirect
57. D₄×C₂²⋊D₅₃	C₂²	semidirect
58. D₄×C₂²⋊D₅₃	C₂²	semidirect
59. #16811255	C₂²	semidirect
60. #16811228	C₂²	semidirect
61. #16811227	C₂²	semidirect
62. #16811226	C₂²	semidirect
63. #16811226	C₂²	semidirect
64. #16811224	C₂²	semidirect
65. #16811223	C₂²	semidirect
66. #16811191	C₂²	semidirect
67. #16811190	C₂²	semidirect
68. #16811190	C₂²	semidirect
69. #16811190	C₂²	semidirect
70. #16811189	C₂²	semidirect
71. #16811188	C₂²	semidirect
72. #16811187	C₂²	semidirect
73. #16811187	C₂²	semidirect
74. #16811187	C₂²	semidirect
75. #16811186	C₂²	semidirect
76. #16811186	C₂²	semidirect
77. #16811183	C₂²	semidirect
78. #16811183	C₂²	semidirect
79. #16811182	C₂²	semidirect
80. #16811181	C₂²	semidirect
81. #16811180	C₂²	semidirect
82. #16811178	C₂²	semidirect
83. #16811177	C₂²	semidirect
84. #16811176	C₂²	semidirect
85. #16811174	C₂²	semidirect
86. #16811173	C₂²	semidirect
87. #16811171	C₂²	semidirect
88. #16811171	C₂²	semidirect
89. #16811170	C₂²	semidirect
90. #16811169	C₂²	semidirect
91. #16811169	C₂²	semidirect
92. #16811168	C₂²	semidirect
93. C₂×#13133214	C₂²	semidirect
94. C₂×#13133213	C₂²	semidirect
95. C₂×#13133213	C₂²	semidirect
96. C₂×#13133213	C₂²	semidirect
97. #127×D₅₃	C₂²	semidirect
98. #127×D₅₃	C₂²	semidirect
99. #127×D₅₃	C₂²	semidirect
100. #127×D₅₃	C₂²	semidirect
101. #127×D₅₃	C₂²	semidirect
102. #16811160	C₂²	semidirect
103. #16811155	C₂²	semidirect
104. #16811155	C₂²	semidirect
105. #16811154	C₂²	semidirect
106. #16811153	C₂²	semidirect
107. #16811152	C₂²	semidirect
108. #16811151	C₂²	semidirect
109. #16811135	C₂²	semidirect
110. #16811133	C₂²	semidirect
111. #16811132	C₂²	semidirect
112. #16811130	C₂²	semidirect
113. #16811130	C₂²	semidirect
114. C₂×#13133185	C₂²	semidirect
115. #120×D₅₃	C₂²	semidirect
116. #16811098	C₂²	semidirect
117. #16811097	C₂²	semidirect
118. #16811095	C₂²	semidirect
119. #41×Dic₅₃	C₂²	semidirect
120. C₄×#11719945	C₂²	semidirect
121. C₄×#11719945	C₂²	semidirect
122. C₄×#11719947	C₂²	semidirect
123. C₂×C₄²×D₅₃	C₂²	semidirect
124. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
125. C₅₃×#550	C₂²	semidirect
126. D₄²×C₅₃	C₂²	semidirect
127. D₄²×C₅₃	C₂²	semidirect
128. C₅₃×#535	C₂²	semidirect
129. C₅₃×#535	C₂²	semidirect
130. C₅₃×#532	C₂²	semidirect
131. C₅₃×#532	C₂²	semidirect
132. C₂×#127×C₅₃	C₂²	semidirect
133. C₂×#127×C₅₃	C₂²	semidirect
134. C₄×#41×C₅₃	C₂²	semidirect
138. C₂×#11719949	C₂³	semidirect
141. C₂×#11719945	C₂³	semidirect
142. C₂×#11719945	C₂³	semidirect
144. C₂×#11719947	C₂³	semidirect
145. C₂×#11719947	C₂³	semidirect
148. C₂²×D₂₁₂	C₂³	semidirect
152. C₂²×C₂²⋊D₅₃	C₂³	semidirect
163. C₂×D₄×D₅₃	C₂³	semidirect
164. C₂×D₄×D₅₃	C₂³	semidirect
167. #13133217	C₂³	semidirect
168. #13133216	C₂³	semidirect
169. #13133215	C₂³	semidirect
180. #13133213	C₂³	semidirect
181. #13133213	C₂³	semidirect
182. #13133213	C₂³	semidirect
183. #13133213	C₂³	semidirect
184. #13133213	C₂³	semidirect
185. #13133213	C₂³	semidirect
186. #13133212	C₂³	semidirect
187. #13133210	C₂³	semidirect
188. #13133210	C₂³	semidirect
189. #13133209	C₂³	semidirect
190. #13133208	C₂³	semidirect
191. #13133208	C₂³	semidirect
192. #13133207	C₂³	semidirect
193. #13133206	C₂³	semidirect
194. #13133206	C₂³	semidirect
195. #13133206	C₂³	semidirect
196. #13133205	C₂³	semidirect
197. #13133204	C₂³	semidirect
198. #13133204	C₂³	semidirect
199. #13133204	C₂³	semidirect
200. #13133204	C₂³	semidirect
201. #13133203	C₂³	semidirect
202. #13133203	C₂³	semidirect
204. #13133202	C₂³	semidirect
206. #13133201	C₂³	semidirect
207. #13133200	C₂³	semidirect
210. #13133199	C₂³	semidirect
211. #13133199	C₂³	semidirect
214. #13133198	C₂³	semidirect
223. #13133192	C₂³	semidirect
224. #13133191	C₂³	semidirect
225. #13133191	C₂³	semidirect
226. #13133191	C₂³	semidirect
227. #13133191	C₂³	semidirect
229. #13133190	C₂³	semidirect
230. #13133190	C₂³	semidirect
231. #13133190	C₂³	semidirect
233. #13133189	C₂³	semidirect
234. #13133189	C₂³	semidirect
235. #13133189	C₂³	semidirect
236. #13133189	C₂³	semidirect
237. #13133189	C₂³	semidirect
238. #13133189	C₂³	semidirect
242. #13133188	C₂³	semidirect
243. #13133188	C₂³	semidirect
244. #13133188	C₂³	semidirect
245. #13133188	C₂³	semidirect
246. #13133188	C₂³	semidirect
249. #13133187	C₂³	semidirect
251. #13133186	C₂³	semidirect
252. #13133186	C₂³	semidirect
260. #13133185	C₂³	semidirect
261. #13133185	C₂³	semidirect
262. Q₈×Dic₅₃	C₂³	semidirect
263. C₄×Dic₁₀₆	C₂³	semidirect
264. C₄×Dic₁₀₆	C₂³	semidirect
265. C₄×Dic₁₀₆	C₂³	semidirect
266. C₄×Dic₁₀₆	C₂³	semidirect
267. #13133182	C₂³	semidirect
270. C₄×D₂₁₂	C₂³	semidirect
271. C₄×D₂₁₂	C₂³	semidirect
272. C₄×D₂₁₂	C₂³	semidirect
274. D₄×Dic₅₃	C₂³	semidirect
275. D₄×Dic₅₃	C₂³	semidirect
276. D₄×Dic₅₃	C₂³	semidirect
277. D₄×Dic₅₃	C₂³	semidirect
278. D₄×Dic₅₃	C₂³	semidirect
279. #13133179	C₂³	semidirect
280. #13133179	C₂³	semidirect
285. C₄×C₂²⋊D₅₃	C₂³	semidirect
286. C₄×C₂²⋊D₅₃	C₂³	semidirect
287. C₄×C₂²⋊D₅₃	C₂³	semidirect
289. #13133177	C₂³	semidirect
292. #13133176	C₂³	semidirect
293. #13133176	C₂³	semidirect
296. #13133174	C₂³	semidirect
297. #13133174	C₂³	semidirect
298. #13133173	C₂³	semidirect
305. C₂×C₄×Dic₅₃	C₂³	semidirect
310. C₄²×D₅₃	C₂³	semidirect
314. C₂×#41×C₅₃	C₂³	semidirect
315. C₂×#41×C₅₃	C₂³	semidirect
319. C₂²×D₄×C₅₃	C₂³	semidirect
320. C₂²×D₄×C₅₃	C₂³	semidirect
321. C₂²×D₄×C₅₃	C₂³	semidirect
322. C₄⋊Q₈×C₅₃	C₂³	semidirect
326. #127×C₅₃	C₂³	semidirect
327. #127×C₅₃	C₂³	semidirect
328. #127×C₅₃	C₂³	semidirect
329. #124×C₅₃	C₂³	semidirect
330. #124×C₅₃	C₂³	semidirect
332. #121×C₅₃	C₂³	semidirect
333. #121×C₅₃	C₂³	semidirect
334. #121×C₅₃	C₂³	semidirect
336. #120×C₅₃	C₂³	semidirect
337. C₄×Q₈×C₅₃	C₂³	semidirect
339. C₄×D₄×C₅₃	C₂³	semidirect
340. C₄×D₄×C₅₃	C₂³	semidirect
341. C₄×D₄×C₅₃	C₂³	semidirect
343. #117×C₅₃	C₂³	semidirect
345. C₂×C₄²×C₅₃	C₂³	semidirect
539. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
584. C₄×D₅₃	H(5,𝔽₂)	semidirect
637. #3498	D₅₃	semidirect
655. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
671. #550	C₂×D₅₃	semidirect
694. D₄²	C₂×D₅₃	semidirect
695. D₄²	C₂×D₅₃	semidirect
713. #535	C₂×D₅₃	semidirect
714. #535	C₂×D₅₃	semidirect
731. #532	C₂×D₅₃	semidirect
732. #532	C₂×D₅₃	semidirect
742. C₂×#127	C₂×D₅₃	semidirect
743. C₂×#127	C₂×D₅₃	semidirect
765. C₄×#41	C₂×D₅₃	semidirect
767. C₅₃	#62832	semidirect
782. C₂×#41	C₂²×D₅₃	semidirect
783. C₂×#41	C₂²×D₅₃	semidirect
806. C₂²×D₄	C₂²×D₅₃	semidirect
807. C₂²×D₄	C₂²×D₅₃	semidirect
808. C₂²×D₄	C₂²×D₅₃	semidirect
814. C₄⋊Q₈	C₂²×D₅₃	semidirect
834. #127	C₂²×D₅₃	semidirect
835. #127	C₂²×D₅₃	semidirect
836. #127	C₂²×D₅₃	semidirect
854. #124	C₂²×D₅₃	semidirect
855. #124	C₂²×D₅₃	semidirect
901. #121	C₂²×D₅₃	semidirect
902. #121	C₂²×D₅₃	semidirect
903. #121	C₂²×D₅₃	semidirect
920. #120	C₂²×D₅₃	semidirect
927. C₄×Q₈	C₂²×D₅₃	semidirect
951. C₄×D₄	C₂²×D₅₃	semidirect
952. C₄×D₄	C₂²×D₅₃	semidirect
953. C₄×D₄	C₂²×D₅₃	semidirect
964. #117	C₂²×D₅₃	semidirect
978. C₂×C₄²	C₂²×D₅₃	semidirect
1213. C₂×C₄	#13133262	semidirect

Maximal subgroups

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

subgroup	index
#20289046	2
#20289041	2
#20289040	2
#20289039	2
#20288591	2
#20288590	2
#20288589	2
#20288585	2
#20288584	2
#20288491	2
#20288489	2
#20288488	2
#20288487	2
#20288349	2
#20288346	2
#20288343	2
#20288010	2
#20288008	2
C₂×#127×D₅₃	2
C₅₃×#3498	2
#62832	53