Subgroups — #28293142

Order 13568.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288786	C₂	1	8	yes	maximal, complemented
2	#20288748	C₂	1	8	yes	maximal, complemented
3	#20288677	C₂	1	8	yes	maximal, complemented
4	#20288658	C₂	1	8	yes	maximal, complemented
5	#20288569	C₂	1	2	yes	maximal, complemented
6	#20288556	C₂	1	4	yes	maximal, complemented
7	#20288479	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288436	C₂	1	2	yes	maximal, complemented
9	#20288405	C₂	1	4	yes	maximal, complemented
10	#20288351	C₂	1	2	yes	maximal, complemented
11	#20288138	C₂	1	2	yes	maximal, complemented
12	#20288127	C₂	1	4	yes	maximal, complemented
13	#20288107	C₂	1	2	yes	maximal, complemented
14	C₂×#16811213	C₂	1	4	yes	maximal, complemented
15	#20287919	C₂	1	2	yes	maximal, complemented
16	C₂×#16811095	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133262	C₂²	1	2	yes	—
19	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
20	#16811358	C₂²	1	8	yes	complemented
21	#16811347	C₂²	1	8	yes	complemented
22	#16811346	C₂²	1	4	yes	complemented
23	#16811339	C₂²	1	8	yes	complemented
24	#16811339	C₂²	1	4	yes	complemented
25	#16811326	C₂²	1	8	yes	complemented
26	#16811326	C₂²	1	8	yes	complemented
27	#16811321	C₂²	1	16	yes	complemented
28	#16811321	C₂²	1	8	yes	complemented
29	#16811315	C₂²	1	8	yes	complemented
30	#16811311	C₂²	1	8	yes	complemented
31	#16811300	C₂²	1	16	yes	complemented
32	#16811300	C₂²	1	16	yes	complemented
33	#16811300	C₂²	1	16	yes	complemented
34	#16811295	C₂²	1	4	yes	complemented
35	#16811284	C₂²	1	8	yes	complemented
36	#16811277	C₂²	1	4	yes	complemented
37	#16811276	C₂²	1	4	yes	complemented
38	#16811268	C₂²	1	8	yes	complemented
39	#16811268	C₂²	1	8	yes	complemented
40	#16811268	C₂²	1	8	yes	complemented
41	#16811264	C₂²	1	16	yes	complemented
42	#16811264	C₂²	1	16	yes	complemented
43	#16811264	C₂²	1	8	yes	complemented
44	D₄×D₂₁₂	C₂²	1	8	yes	complemented
45	D₄×D₂₁₂	C₂²	1	8	yes	complemented
46	D₄×D₂₁₂	C₂²	1	4	yes	complemented
47	#16811247	C₂²	1	4	yes	complemented
48	#16811247	C₂²	1	4	yes	complemented
49	#16811247	C₂²	1	8	yes	complemented
50	#16811236	C₂²	1	4	yes	complemented
51	#16811229	C₂²	1	4	yes	complemented
52	#16811229	C₂²	1	8	yes	complemented
53	#16811222	C₂²	1	4	yes	complemented
54	#16811222	C₂²	1	4	yes	complemented
55	#16811222	C₂²	1	16	yes	complemented
56	#16811213	C₂²	1	4	yes	complemented
57	#16811213	C₂²	1	8	yes	complemented
58	#16811213	C₂²	1	4	yes	complemented
59	#16811213	C₂²	1	8	yes	complemented
60	#16811213	C₂²	1	8	yes	complemented
61	#16811213	C₂²	1	16	yes	complemented
62	#16811213	C₂²	1	16	yes	complemented
63	#16811213	C₂²	1	16	yes	complemented
64	#16811204	C₂²	1	2	yes	complemented
65	#16811192	C₂²	1	4	yes	complemented
66	#16811185	C₂²	1	8	yes	complemented
67	#16811185	C₂²	1	4	yes	complemented
68	#16811174	C₂²	1	8	yes	complemented
69	#16811173	C₂²	1	2	yes	complemented
70	#16811160	C₂²	1	8	yes	complemented
71	#16811160	C₂²	1	8	yes	complemented
72	#16811159	C₂²	1	8	yes	complemented
73	#16811159	C₂²	1	16	yes	complemented
74	#16811158	C₂²	1	8	yes	complemented
75	C₂×#13133212	C₂²	1	8	yes	complemented
76	C₂×#13133206	C₂²	1	8	yes	complemented
77	#16811136	C₂²	1	8	yes	complemented
78	#16811136	C₂²	1	8	yes	complemented
79	#16811136	C₂²	1	16	yes	complemented
80	#16811135	C₂²	1	4	yes	complemented
81	C₂×#13133202	C₂²	1	8	yes	complemented
82	C₂×#13133192	C₂²	1	8	yes	complemented
83	C₂×#13133191	C₂²	1	4	yes	complemented
84	C₂×#13133187	C₂²	1	8	yes	complemented
85	#16811103	C₂²	1	4	yes	complemented
86	#16811102	C₂²	1	8	yes	complemented
87	#16811096	C₂²	1	8	yes	complemented
88	#16811095	C₂²	1	8	yes	complemented
89	#16811095	C₂²	1	8	yes	complemented
90	#16811095	C₂²	1	8	yes	complemented
91	#16811091	C₂²	1	4	yes	complemented
92	C₄×#11719947	C₂²	1	8	yes	complemented
93	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
94	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
95	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
97	C₂×#13133177	C₂²	1	2	yes	complemented
98	C₂×#13133177	C₂²	1	8	yes	complemented
99	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
100	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
101	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
102	C₂²×#11719921	C₂²	1	2	yes	complemented
103	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
104	C₅₃×#554	C₂²	1	8	yes	complemented
105	C₅₃×#554	C₂²	1	4	yes	complemented
106	D₄×Q₈×C₅₃	C₂²	1	4	yes	complemented
107	C₅₃×#544	C₂²	1	2	yes	complemented
108	C₅₃×#543	C₂²	1	4	yes	complemented
109	C₅₃×#533	C₂²	1	2	yes	complemented
110	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
111	C₅₃×#518	C₂²	1	2	yes	—
112	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₂⁴×D₅₃	C₂³	1	2	yes	—
114	#13133262	—	2	16	no	—
115	C₂×#11719949	C₂³	1	8	yes	complemented
116	C₂×#11719949	C₂³	1	8	yes	complemented
117	C₂×#11719945	C₂³	1	4	yes	—
118	C₂×#11719947	C₂³	1	8	yes	—
119	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
120	C₂²×D₂₁₂	C₂³	1	8	yes	—
121	C₂²×D₂₁₂	C₂³	1	8	yes	—
122	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
123	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
124	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
125	C₂×D₄×D₅₃	—	2	8	no	—
126	C₂×D₄×D₅₃	C₂³	1	8	yes	—
127	C₂×D₄×D₅₃	C₂³	1	8	yes	—
128	C₂³×Dic₅₃	C₂³	1	2	yes	—
129	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
131	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
132	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
133	#13133217	C₂³	1	2	yes	complemented
134	#13133214	C₂³	1	8	yes	—
135	#13133214	C₂³	1	2	yes	complemented
136	#13133212	C₂³	1	8	yes	—
137	#13133212	C₂³	1	16	yes	—
138	#13133212	C₂³	1	8	yes	—
139	#13133212	C₂³	1	8	yes	complemented
140	#13133212	C₂³	1	16	yes	complemented
141	#13133212	C₂³	1	16	yes	complemented
142	#13133212	C₂³	1	16	yes	complemented
143	#13133212	C₂³	1	8	yes	complemented
144	#13133208	C₂³	1	8	yes	complemented
145	#13133208	C₂³	1	8	yes	complemented
146	#13133208	C₂³	1	8	yes	complemented
147	#13133206	C₂³	1	8	yes	—
148	#13133206	C₂³	1	16	yes	—
149	#13133206	C₂³	1	8	yes	—
150	#13133206	C₂³	1	8	yes	complemented
151	#13133206	C₂³	1	16	yes	complemented
152	#13133206	C₂³	1	16	yes	complemented
153	#13133205	C₂³	1	8	yes	—
154	#13133205	C₂³	1	4	yes	complemented
155	#13133202	C₂³	1	8	yes	—
156	#13133202	C₂³	1	16	yes	—
157	#13133202	C₂³	1	8	yes	—
158	#13133202	C₂³	1	8	yes	complemented
159	#13133202	C₂³	1	16	yes	complemented
160	#13133202	C₂³	1	16	yes	complemented
161	#13133202	C₂³	1	16	yes	complemented
162	#13133202	C₂³	1	16	yes	complemented
163	#13133202	C₂³	1	8	yes	complemented
164	#13133201	C₂³	1	16	yes	—
165	#13133201	C₂³	1	8	yes	—
166	#13133201	C₂³	1	16	yes	complemented
167	#13133197	C₂³	1	4	yes	—
168	#13133197	C₂³	1	4	yes	—
169	#13133197	C₂³	1	8	yes	complemented
170	#13133193	C₂³	1	8	yes	complemented
171	#13133193	C₂³	1	8	yes	complemented
172	#13133193	C₂³	1	8	yes	complemented
173	#13133193	C₂³	1	8	yes	complemented
174	#13133192	C₂³	1	8	yes	—
175	#13133192	C₂³	1	16	yes	—
176	#13133192	C₂³	1	8	yes	—
177	#13133192	C₂³	1	8	yes	—
178	#13133192	C₂³	1	4	yes	—
179	#13133192	C₂³	1	4	yes	—
180	#13133192	C₂³	1	8	yes	—
181	#13133192	C₂³	1	8	yes	complemented
182	#13133192	C₂³	1	8	yes	complemented
183	#13133192	C₂³	1	16	yes	complemented
184	#13133192	C₂³	1	8	yes	complemented
185	#13133192	C₂³	1	16	yes	complemented
186	#13133191	C₂³	1	16	yes	—
187	#13133191	C₂³	1	16	yes	—
188	#13133191	C₂³	1	4	yes	—
189	#13133191	C₂³	1	8	yes	—
190	#13133191	C₂³	1	4	yes	—
191	#13133191	C₂³	1	8	yes	complemented
192	#13133191	C₂³	1	8	yes	complemented
193	#13133187	C₂³	1	16	yes	—
194	#13133187	C₂³	1	16	yes	—
195	#13133187	C₂³	1	16	yes	—
196	#13133187	C₂³	1	8	yes	—
197	#13133187	C₂³	1	16	yes	—
198	#13133187	C₂³	1	16	yes	complemented
199	Q₈×Dic₅₃	C₂³	1	8	yes	complemented
200	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
201	#13133182	C₂³	1	4	yes	complemented
202	#13133182	C₂³	1	4	yes	complemented
203	C₄×D₂₁₂	C₂³	1	8	yes	—
204	C₄×D₂₁₂	C₂³	1	8	yes	—
205	C₄×D₂₁₂	C₂³	1	4	yes	—
206	C₄×D₂₁₂	C₂³	1	4	yes	—
207	C₄×D₂₁₂	C₂³	1	4	yes	complemented
208	C₄×D₂₁₂	C₂³	1	4	yes	complemented
209	C₄×D₂₁₂	C₂³	1	8	yes	complemented
210	D₄×Dic₅₃	C₂³	1	8	yes	—
211	#13133179	C₂³	1	8	yes	—
212	#13133179	C₂³	1	16	yes	complemented
213	#13133179	C₂³	1	16	yes	complemented
214	#13133179	C₂³	1	8	yes	complemented
215	#13133179	C₂³	1	4	yes	complemented
216	#13133179	C₂³	1	4	yes	complemented
217	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
218	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
219	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
220	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
221	#13133177	C₂³	1	8	yes	—
222	#13133177	C₂³	1	16	yes	—
223	#13133177	C₂³	1	16	yes	—
224	#13133177	C₂³	1	8	yes	—
225	#13133177	C₂³	1	16	yes	complemented
226	#13133177	C₂³	1	16	yes	complemented
227	#13133175	C₂³	1	8	yes	—
228	#13133175	C₂³	1	8	yes	complemented
229	#13133175	C₂³	1	8	yes	complemented
230	#13133175	C₂³	1	16	yes	complemented
231	#13133175	C₂³	1	8	yes	complemented
232	#13133174	C₂³	1	4	yes	—
233	#13133174	C₂³	1	4	yes	—
234	#13133174	C₂³	1	8	yes	complemented
235	#13133173	C₂³	1	16	yes	complemented
236	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	8	yes	complemented
241	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
242	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
243	C₂×#11719921	C₂³	1	8	yes	—
244	C₂×#11719921	C₂³	1	8	yes	—
245	C₂×#11719921	C₂³	1	1	yes	characteristic
246	C₂×#11719921	C₂³	1	2	yes	—
247	C₂×#11719921	C₂³	1	1	yes	characteristic
248	C₂×#11719921	C₂³	1	2	yes	—
249	C₂×#11719921	C₂³	1	2	yes	—
250	C₂×#11719921	C₂³	1	8	yes	—
251	C₂×#11719921	C₂³	1	8	yes	—
252	C₂×#11719921	C₂³	1	8	yes	complemented
253	C₂×#11719921	C₂³	1	8	yes	complemented
254	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
255	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
256	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
258	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
259	C₄²×D₅₃	C₂³	1	8	yes	complemented
260	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
261	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
263	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
264	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
265	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
266	#125×C₅₃	C₂³	1	8	yes	complemented
267	#125×C₅₃	C₂³	1	4	yes	complemented
268	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
269	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
270	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
271	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
272	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
273	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
274	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
275	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
276	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
277	C₄×D₄×C₅₃	C₂³	1	4	yes	—
278	C₄×D₄×C₅₃	C₂³	1	8	yes	—
279	C₄×D₄×C₅₃	C₂³	1	8	yes	—
280	C₄×D₄×C₅₃	C₂³	1	4	yes	—
281	#117×C₅₃	C₂³	1	4	yes	—
282	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
284	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
287	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
288	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
289	C₂³×D₅₃	—	2	8	no	—
290	C₂³×D₅₃	—	8	2	no	—
291	C₂³×D₅₃	—	8	2	no	—
292	C₂³×D₅₃	C₂⁴	1	8	yes	—
293	C₂³×D₅₃	C₂⁴	1	8	yes	—
294	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
295	C₂³×D₅₃	C₂⁴	1	2	yes	—
296	C₂×Q₈×C₅₃	—	8	4	no	—
297	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
300	C₂×D₄×C₅₃	#41	1	8	yes	complemented
301	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₅₃	—	8	2	no	—
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂×C₂²⋊D₅₃	—	2	8	no	—
312	C₂×C₂²⋊D₅₃	—	2	32	no	—
313	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
314	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
315	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
316	C₂²×Dic₅₃	—	8	2	no	—
317	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
318	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
319	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
320	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
321	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
322	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
323	#11719949	—	8	8	no	—
324	#11719949	—	8	8	no	—
325	#11719947	—	2	32	no	—
326	D₄×D₅₃	—	2	32	no	—
327	D₄×D₅₃	—	2	32	no	—
328	#11719945	—	2	16	no	—
329	C₂×D₂₁₂	—	2	4	no	—
330	C₂×D₂₁₂	—	8	8	no	—
331	C₂×D₂₁₂	—	8	8	no	—
332	C₂×D₂₁₂	—	8	4	no	—
333	C₂×D₂₁₂	C₂⁴	1	4	yes	—
334	C₂×D₂₁₂	C₂⁴	1	4	yes	—
335	C₂×D₂₁₂	C₂⁴	1	16	yes	—
336	C₂×D₂₁₂	C₂⁴	1	16	yes	—
337	C₂×D₂₁₂	C₂⁴	1	8	yes	—
338	C₂×D₂₁₂	C₂⁴	1	8	yes	—
339	C₂×D₂₁₂	C₂⁴	1	8	yes	—
340	C₂×D₂₁₂	C₂⁴	1	4	yes	—
341	C₂×D₂₁₂	C₂⁴	1	4	yes	—
342	C₂×C₄×D₅₃	—	2	4	no	—
343	C₂×C₄×D₅₃	—	8	2	no	—
344	C₂×C₄×D₅₃	—	8	2	no	—
345	C₂×C₄×D₅₃	—	8	8	no	—
346	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
347	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
348	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
349	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
350	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
351	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
352	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
353	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
356	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
357	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
358	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
359	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
360	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
361	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
363	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
364	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
365	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
366	C₄²×C₅₃	C₂⁴	1	2	yes	—
367	C₄²×C₅₃	C₂⁴	1	2	yes	—
368	C₄²×C₅₃	C₂⁴	1	8	yes	—
369	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
370	#11719921	C₂⁴	1	4	yes	—
371	#11719921	C₂⁴	1	8	yes	—
372	#11719921	C₂⁴	1	8	yes	—
373	#11719921	C₂⁴	1	16	yes	—
374	#11719921	C₂⁴	1	2	yes	—
375	#11719921	C₂⁴	1	2	yes	—
376	#11719921	C₂⁴	1	8	yes	—
377	#11719921	C₂⁴	1	4	yes	—
378	#11719921	C₂⁴	1	4	yes	—
379	#11719921	C₂⁴	1	8	yes	—
380	#11719921	C₂⁴	1	8	yes	—
381	#11719921	C₂⁴	1	16	yes	—
382	#11719921	C₂⁴	1	16	yes	—
383	#11719921	C₂⁴	1	8	yes	—
384	#11719921	C₂⁴	1	8	yes	—
385	#11719921	C₂⁴	1	16	yes	—
386	#11719921	C₂⁴	1	8	yes	—
387	#11719921	C₂⁴	1	8	yes	—
388	#11719921	C₂⁴	1	8	yes	—
389	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
390	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
391	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
392	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
393	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
394	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
395	#11719919	C₂⁴	1	16	yes	—
396	#11719919	C₂⁴	1	4	yes	—
397	#11719919	C₂⁴	1	2	yes	—
398	#11719919	C₂⁴	1	2	yes	—
399	#11719919	C₂⁴	1	8	yes	—
400	#11719919	C₂⁴	1	8	yes	—
401	C₄×Dic₅₃	C₂⁴	1	4	yes	—
402	C₄×Dic₅₃	C₂⁴	1	8	yes	—
403	C₄×Dic₅₃	C₂⁴	1	8	yes	—
404	C₄×Dic₅₃	C₂⁴	1	8	yes	—
405	C₄×Dic₅₃	C₂⁴	1	16	yes	—
406	C₂³×C₅₃	—	4	2	no	—
407	C₂³×C₅₃	—	4	2	no	—
408	C₂³×C₅₃	C₂×#41	1	8	yes	—
409	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
410	C₂³×C₅₃	C₂⁵	1	4	yes	—
411	C₂²×D₅₃	—	2	2	no	—
412	C₂²×D₅₃	—	2	4	no	—
413	C₂²×D₅₃	—	2	16	no	—
414	C₂²×D₅₃	—	2	16	no	—
415	C₂²×D₅₃	—	4	2	no	—
416	C₂²×D₅₃	—	4	2	no	—
417	C₂²×D₅₃	—	4	1	no	—
418	C₂²×D₅₃	—	4	1	no	—
419	C₂²×D₅₃	—	4	8	no	—
420	C₂²×D₅₃	—	4	8	no	—
421	C₂²×D₅₃	—	4	8	no	—
422	C₂²×D₅₃	—	4	8	no	—
423	C₂²×D₅₃	—	8	16	no	—
424	C₂²×D₅₃	C₂⁵	1	8	yes	—
425	C₂²×D₅₃	C₂⁵	1	4	yes	—
426	C₂²×D₅₃	C₂⁵	1	2	yes	—
427	Q₈×C₅₃	—	4	4	no	—
428	Q₈×C₅₃	—	4	8	no	—
429	Q₈×C₅₃	—	4	4	no	—
430	D₄×C₅₃	C₂×#41	1	16	yes	—
431	C₂×C₄×C₅₃	—	4	1	no	—
432	C₂×C₄×C₅₃	—	4	8	no	—
433	C₂×C₄×C₅₃	—	4	2	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	8	no	—
436	C₂×C₄×C₅₃	—	4	1	no	—
437	C₂×C₄×C₅₃	—	4	4	no	—
438	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
439	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
440	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
441	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
442	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
443	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
444	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
445	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
446	C₂²⋊D₅₃	—	2	16	no	—
447	C₂²⋊D₅₃	—	2	16	no	—
448	C₂²⋊D₅₃	—	2	32	no	—
449	C₂×Dic₅₃	—	2	2	no	—
450	C₂×Dic₅₃	—	2	16	no	—
451	C₂×Dic₅₃	—	4	1	no	—
452	C₂×Dic₅₃	—	4	2	no	—
453	C₂×Dic₅₃	—	4	8	no	—
454	C₂×Dic₅₃	—	4	1	no	—
455	C₂×Dic₅₃	C₂⁵	1	8	yes	—
456	C₂×Dic₅₃	C₂⁵	1	2	yes	—
457	C₂×Dic₅₃	C₂⁵	1	4	yes	—
458	C₂×Dic₅₃	C₂⁵	1	2	yes	—
459	C₂×Dic₅₃	C₂⁵	1	2	yes	—
460	D₂₁₂	—	2	8	no	—
461	D₂₁₂	—	2	8	no	—
462	D₂₁₂	—	4	8	no	—
463	D₂₁₂	—	4	8	no	—
464	D₂₁₂	—	4	4	no	—
465	D₂₁₂	—	4	16	no	—
466	D₂₁₂	—	4	8	no	—
467	D₂₁₂	—	4	16	no	—
468	D₂₁₂	—	4	4	no	—
469	C₄×D₅₃	—	2	8	no	—
470	C₄×D₅₃	—	2	16	no	—
471	C₄×D₅₃	—	4	8	no	—
472	C₄×D₅₃	—	4	8	no	—
473	C₄×D₅₃	—	4	8	no	—
474	C₄×D₅₃	—	4	16	no	—
475	C₄×D₅₃	—	4	8	no	—
476	Dic₁₀₆	—	2	8	no	—
477	#62846	—	53	1	no	maximal, Sylow
478	C₂²×C₅₃	—	2	1	no	—
479	C₂²×C₅₃	—	2	4	no	—
480	C₂²×C₅₃	—	2	1	no	—
481	C₂²×C₅₃	—	2	4	no	—
482	C₂²×C₅₃	—	4	8	no	—
483	C₂²×C₅₃	C₂²×#41	1	8	yes	—
484	C₂²×C₅₃	C₂²×#41	1	2	yes	—
485	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
486	C₂×D₅₃	—	2	2	no	—
487	C₂×D₅₃	—	2	8	no	—
488	C₂×D₅₃	—	2	4	no	—
489	C₂×D₅₃	—	2	8	no	—
490	C₂×D₅₃	—	2	4	no	—
491	C₂×D₅₃	—	2	4	no	—
492	C₂×D₅₃	—	2	8	no	—
493	C₂×D₅₃	—	2	2	no	—
494	C₂×D₅₃	—	2	2	no	—
495	C₂×D₅₃	—	4	8	no	—
496	C₂×D₅₃	—	4	4	no	—
497	C₂×D₅₃	—	8	16	no	—
498	C₂×D₅₃	—	8	16	no	—
499	C₄×C₅₃	—	2	2	no	—
500	C₄×C₅₃	—	2	8	no	—
501	C₄×C₅₃	—	2	4	no	—
502	C₄×C₅₃	—	2	8	no	—
503	C₄×C₅₃	—	2	1	no	—
504	C₄×C₅₃	—	2	1	no	—
505	C₄×C₅₃	C₂²×#41	1	4	yes	—
506	Dic₅₃	—	2	8	no	—
507	Dic₅₃	—	2	2	no	—
508	Dic₅₃	—	2	2	no	—
509	Dic₅₃	—	2	4	no	—
510	Dic₅₃	—	2	2	no	—
511	#3521	—	53	8	no	—
512	#3519	—	53	8	no	—
513	#3514	—	53	8	no	—
514	#3513	—	53	8	no	—
515	#3506	—	53	2	no	—
516	#3505	—	53	4	no	—
517	#3501	D₅₃	1	1	yes	characteristic, complemented
518	#3496	—	53	1	no	—
519	#3493	—	53	2	no	—
520	#3490	—	53	4	no	—
521	#3484	—	53	2	no	—
522	#3460	—	53	2	no	—
523	#3459	—	53	4	no	—
524	#3455	—	53	2	no	—
525	C₂×#538	—	53	4	no	—
526	C₄×H(5,𝔽₂)	—	53	2	no	—
527	C₂×#518	—	53	1	no	—
528	C₂×C₅₃	—	2	2	no	—
529	C₂×C₅₃	—	2	8	no	—
530	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
531	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
532	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
533	D₅₃	—	4	4	no	—
534	D₅₃	—	4	2	no	—
535	D₅₃	—	4	8	no	—
536	C₂×H(5,𝔽₂)	—	53	2	no	—
537	C₂³×D₄	—	53	1	no	—
538	#559	—	53	8	no	—
539	#556	—	53	8	no	—
540	#556	—	53	4	no	—
541	#555	—	53	8	no	—
542	#555	—	53	4	no	—
543	#554	C₂×D₅₃	1	4	yes	complemented
544	#554	C₂×D₅₃	1	8	yes	complemented
545	#553	—	53	8	no	—
546	#553	—	53	8	no	—
547	#553	—	53	8	no	—
548	#553	—	53	16	no	—
549	#552	—	53	8	no	—
550	#552	—	53	8	no	—
551	#551	—	53	16	no	—
552	#551	—	53	16	no	—
553	#551	—	53	16	no	—
554	#550	—	53	4	no	—
555	D₄×Q₈	C₂×D₅₃	1	4	yes	complemented
556	#548	—	53	8	no	—
557	#547	—	53	4	no	—
558	#547	—	53	4	no	—
559	#546	—	53	16	no	—
560	#546	—	53	16	no	—
561	#546	—	53	8	no	—
562	#546	—	53	8	no	—
563	#546	—	53	8	no	—
564	#546	—	53	8	no	—
565	D₄²	—	53	8	no	—
566	D₄²	—	53	8	no	—
567	D₄²	—	53	4	no	—
568	#544	C₂×D₅₃	1	2	yes	complemented
569	#543	C₂×D₅₃	1	4	yes	complemented
570	#542	—	53	4	no	—
571	#542	—	53	4	no	—
572	#542	—	53	8	no	—
573	#541	—	53	4	no	—
574	#540	—	53	4	no	—
575	#540	—	53	8	no	—
576	#539	—	53	4	no	—
577	#539	—	53	4	no	—
578	#539	—	53	16	no	—
579	#538	—	53	4	no	—
580	#538	—	53	8	no	—
581	#538	—	53	8	no	—
582	#538	—	53	8	no	—
583	#538	—	53	4	no	—
584	#538	—	53	16	no	—
585	#538	—	53	16	no	—
586	#538	—	53	16	no	—
587	#537	—	53	2	no	—
588	#535	—	53	4	no	—
589	#534	—	53	8	no	—
590	#534	—	53	4	no	—
591	#533	C₂×D₅₃	1	2	yes	complemented
592	#532	—	53	8	no	—
593	#532	—	53	2	no	—
594	#529	—	53	8	no	—
595	#529	—	53	8	no	—
596	#529	—	53	16	no	—
597	#529	—	53	8	no	—
598	#529	—	53	8	no	—
599	C₂×#126	—	53	8	no	—
600	C₂×#124	—	53	8	no	—
601	#525	—	53	8	no	—
602	#525	—	53	8	no	—
603	#525	—	53	16	no	—
604	#525	—	53	4	no	—
605	C₂×#123	—	53	8	no	—
606	C₂×C₂²⋊Q₈	C₂×D₅₃	1	4	yes	complemented
607	C₂×#121	—	53	4	no	—
608	C₂×#121	—	53	8	no	—
609	C₂×#120	—	53	8	no	—
610	#520	—	53	8	no	—
611	#520	—	53	4	no	—
612	#518	—	53	8	no	—
613	#518	—	53	8	no	—
614	#518	—	53	8	no	—
615	#518	—	53	8	no	—
616	#518	C₂×D₅₃	1	2	yes	—
617	C₄×#41	—	53	8	no	—
618	C₄×#41	—	53	4	no	—
619	C₂×C₄×D₄	—	53	1	no	—
620	C₂×C₄×D₄	—	53	2	no	—
621	C₂×C₄×D₄	—	53	8	no	—
622	C₂×C₄×D₄	—	53	1	no	—
623	C₂×C₄×D₄	—	53	2	no	—
624	C₂×C₄×D₄	—	53	8	no	—
625	C₂×C₄×D₄	—	53	1	no	—
626	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
627	C₂×#117	—	53	1	no	—
628	C₂×#117	—	53	1	no	—
629	C₂²×C₂²⋊C₄	—	53	2	no	—
630	C₂²×C₂²⋊C₄	—	53	2	no	—
631	C₅₃	#62846	1	1	yes	characteristic, complemented, Sylow
632	C₂⁵	—	53	2	no	—
633	H(5,𝔽₂)	—	106	16	no	—
634	C₂×#41	—	53	8	no	—
635	C₂×#41	—	53	8	no	—
636	C₂×#41	—	53	8	no	—
637	C₂×#41	—	53	4	no	—
638	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
639	C₂²×D₄	—	53	2	no	—
640	C₂²×D₄	—	53	8	no	—
641	C₂²×D₄	—	53	8	no	—
642	C₂²×D₄	—	53	8	no	—
643	C₂²×D₄	—	53	1	no	—
644	C₂²×D₄	—	53	8	no	—
645	C₂²×D₄	—	53	8	no	—
646	C₂²×D₄	—	53	4	no	—
647	C₂²×D₄	—	106	8	no	—
648	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
649	C₂³×C₄	—	53	2	no	—
650	C₂³×C₄	—	53	1	no	—
651	C₂³×C₄	—	53	2	no	—
652	C₂³×C₄	—	53	2	no	—
653	C₂³×C₄	—	53	8	no	—
654	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
655	C₄⋊Q₈	—	53	2	no	—
656	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
657	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
658	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
659	#127	—	53	8	no	—
660	#127	—	53	2	no	—
661	#126	—	53	8	no	—
662	#126	—	53	16	no	—
663	#126	—	53	16	no	—
664	#126	—	53	16	no	—
665	#126	—	53	8	no	—
666	#126	—	53	16	no	—
667	#126	—	53	8	no	—
668	#126	—	53	8	no	—
669	#125	—	53	8	no	—
670	#125	—	53	8	no	—
671	#125	—	53	8	no	—
672	#125	C₂²×D₅₃	1	8	yes	complemented
673	#125	C₂²×D₅₃	1	4	yes	complemented
674	#124	—	53	8	no	—
675	#124	—	53	16	no	—
676	#124	—	53	16	no	—
677	#124	—	53	16	no	—
678	#124	—	53	8	no	—
679	#124	—	53	8	no	—
680	#124	—	53	8	no	—
681	#124	—	53	4	no	—
682	#123	—	53	8	no	—
683	#123	—	53	16	no	—
684	#123	—	53	16	no	—
685	#123	—	53	16	no	—
686	#123	—	53	8	no	—
687	#123	—	53	16	no	—
688	#123	—	53	16	no	—
689	#123	—	53	8	no	—
690	#123	—	53	8	no	—
691	#123	—	53	8	no	—
692	#123	—	53	16	no	—
693	#123	—	53	16	no	—
694	C₂²⋊Q₈	—	53	8	no	—
695	C₂²⋊Q₈	—	53	8	no	—
696	C₂²⋊Q₈	—	53	8	no	—
697	C₂²⋊Q₈	—	53	8	no	—
698	C₂²⋊Q₈	—	53	4	no	—
699	C₂²⋊Q₈	—	53	4	no	—
700	C₂²⋊Q₈	—	53	8	no	—
701	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
702	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	—
703	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
704	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
705	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
706	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
707	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
708	#121	—	53	4	no	—
709	#121	—	53	8	no	—
710	#121	—	53	8	no	—
711	#121	—	53	8	no	—
712	#121	—	53	4	no	—
713	#121	—	53	16	no	—
714	#121	—	53	16	no	—
715	#121	—	53	8	no	—
716	#121	—	53	16	no	—
717	#121	—	53	16	no	—
718	#121	—	53	16	no	—
719	#121	—	53	8	no	—
720	#121	—	53	8	no	—
721	#121	—	53	4	no	—
722	#121	—	53	4	no	—
723	#121	—	53	8	no	—
724	#121	—	53	8	no	—
725	#121	—	53	8	no	—
726	#121	—	53	8	no	—
727	#120	—	53	8	no	—
728	#120	—	53	16	no	—
729	#120	—	53	16	no	—
730	#120	—	53	16	no	—
731	#120	—	53	16	no	—
732	#120	—	53	16	no	—
733	C₄×Q₈	—	53	8	no	—
734	C₄×Q₈	—	53	4	no	—
735	C₄×Q₈	—	53	4	no	—
736	C₄×Q₈	—	53	8	no	—
737	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
738	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
739	C₄×D₄	—	53	8	no	—
740	C₄×D₄	—	53	8	no	—
741	C₄×D₄	—	53	8	no	—
742	C₄×D₄	—	53	16	no	—
743	C₄×D₄	—	53	16	no	—
744	C₄×D₄	—	53	4	no	—
745	C₄×D₄	—	53	8	no	—
746	C₄×D₄	—	53	4	no	—
747	C₄×D₄	—	53	16	no	—
748	C₄×D₄	—	53	8	no	—
749	C₄×D₄	—	53	16	no	—
750	C₄×D₄	—	53	8	no	—
751	C₄×D₄	—	53	16	no	—
752	C₄×D₄	—	53	16	no	—
753	C₄×D₄	—	53	16	no	—
754	C₄×D₄	—	53	16	no	—
755	C₄×D₄	—	53	8	no	—
756	C₄×D₄	—	53	4	no	—
757	C₄×D₄	—	53	4	no	—
758	C₄×D₄	—	53	8	no	—
759	C₄×D₄	—	53	8	no	—
760	C₄×D₄	—	53	8	no	—
761	C₄×D₄	—	53	4	no	—
762	C₄×D₄	—	53	4	no	—
763	C₄×D₄	C₂²×D₅₃	1	8	yes	—
764	C₄×D₄	C₂²×D₅₃	1	4	yes	—
765	C₄×D₄	C₂²×D₅₃	1	4	yes	—
766	C₄×D₄	C₂²×D₅₃	1	8	yes	—
767	#117	—	53	8	no	—
768	#117	—	53	8	no	—
769	#117	—	53	8	no	—
770	#117	—	53	8	no	—
771	#117	—	53	16	no	—
772	#117	—	53	16	no	—
773	#117	—	53	4	no	—
774	#117	—	53	4	no	—
775	#117	—	53	8	no	—
776	#117	C₂²×D₅₃	1	4	yes	—
777	C₂×C₄⋊C₄	—	53	1	no	—
778	C₂×C₄⋊C₄	—	53	1	no	—
779	C₂×C₄⋊C₄	—	53	1	no	—
780	C₂×C₄⋊C₄	—	53	8	no	—
781	C₂×C₄⋊C₄	—	53	4	no	—
782	C₂×C₄⋊C₄	—	53	8	no	—
783	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
785	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
786	C₂×C₂²⋊C₄	—	53	2	no	—
787	C₂×C₂²⋊C₄	—	53	1	no	—
788	C₂×C₂²⋊C₄	—	53	2	no	—
789	C₂×C₂²⋊C₄	—	53	1	no	—
790	C₂×C₂²⋊C₄	—	53	2	no	—
791	C₂×C₂²⋊C₄	—	53	2	no	—
792	C₂×C₂²⋊C₄	—	53	8	no	—
793	C₂×C₂²⋊C₄	—	53	8	no	—
794	C₂×C₂²⋊C₄	—	53	8	no	—
795	C₂×C₂²⋊C₄	—	53	8	no	—
796	C₂×C₂²⋊C₄	—	53	8	no	—
797	C₂×C₂²⋊C₄	—	53	8	no	—
798	C₂×C₂²⋊C₄	—	53	16	no	—
799	C₂×C₂²⋊C₄	—	53	16	no	—
800	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
802	C₂×C₄²	—	53	1	no	—
803	C₂×C₄²	—	53	2	no	—
804	C₂×C₄²	—	53	8	no	—
805	C₂×C₄²	—	53	8	no	—
806	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
807	C₂⁴	—	53	8	no	—
808	C₂⁴	—	53	1	no	—
809	C₂⁴	—	53	8	no	—
810	C₂⁴	—	53	2	no	—
811	C₂⁴	—	106	8	no	—
812	C₂⁴	—	424	2	no	—
813	C₂⁴	—	424	2	no	—
814	C₂⁴	C₂³×D₅₃	1	2	yes	—
815	#41	—	106	32	no	—
816	#41	—	106	16	no	—
817	#41	—	424	8	no	—
818	#41	—	424	8	no	—
819	C₂×Q₈	—	8	4	no	—
820	C₂×Q₈	—	53	4	no	—
821	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
822	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
823	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
824	C₂×D₄	—	53	16	no	—
825	C₂×D₄	—	53	8	no	—
826	C₂×D₄	—	53	8	no	—
827	C₂×D₄	—	53	4	no	—
828	C₂×D₄	—	53	4	no	—
829	C₂×D₄	—	53	4	no	—
830	C₂×D₄	—	53	8	no	—
831	C₂×D₄	—	53	16	no	—
832	C₂×D₄	—	53	8	no	—
833	C₂×D₄	—	53	16	no	—
834	C₂×D₄	—	53	8	no	—
835	C₂×D₄	—	53	4	no	—
836	C₂×D₄	—	106	8	no	—
837	C₂×D₄	—	106	32	no	—
838	C₂×D₄	—	106	32	no	—
839	C₂×D₄	—	106	32	no	—
840	C₂×D₄	—	106	4	no	—
841	C₂×D₄	—	424	4	no	—
842	C₂×D₄	—	424	8	no	—
843	C₂×D₄	—	424	8	no	—
844	C₂×D₄	#11719949	1	8	yes	complemented
845	C₂×D₄	C₂³×D₅₃	1	4	yes	—
846	C₂²×C₄	—	8	2	no	—
847	C₂²×C₄	—	53	1	no	—
848	C₂²×C₄	—	53	8	no	—
849	C₂²×C₄	—	53	8	no	—
850	C₂²×C₄	—	53	1	no	—
851	C₂²×C₄	—	53	2	no	—
852	C₂²×C₄	—	53	1	no	—
853	C₂²×C₄	—	53	8	no	—
854	C₂²×C₄	—	53	4	no	—
855	C₂²×C₄	—	53	8	no	—
856	C₂²×C₄	—	53	8	no	—
857	C₂²×C₄	—	53	8	no	—
858	C₂²×C₄	—	53	8	no	—
859	C₂²×C₄	—	53	16	no	—
860	C₂²×C₄	—	106	4	no	—
861	C₂²×C₄	—	424	2	no	—
862	C₂²×C₄	—	424	2	no	—
863	C₂²×C₄	—	424	8	no	—
864	C₂²×C₄	—	424	2	no	—
865	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
866	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
867	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
868	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
869	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
870	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
871	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
872	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
873	C₄⋊C₄	—	53	4	no	—
874	C₄⋊C₄	—	53	8	no	—
875	C₄⋊C₄	—	53	16	no	—
876	C₄⋊C₄	—	53	4	no	—
877	C₄⋊C₄	—	53	2	no	—
878	C₄⋊C₄	—	53	4	no	—
879	C₄⋊C₄	—	53	2	no	—
880	C₄⋊C₄	—	53	8	no	—
881	C₄⋊C₄	—	53	8	no	—
882	C₄⋊C₄	—	53	8	no	—
883	C₄⋊C₄	—	53	4	no	—
884	C₄⋊C₄	—	53	8	no	—
885	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
886	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
887	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
888	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
889	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
890	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
891	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
892	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
893	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
894	C₂²⋊C₄	—	53	8	no	—
895	C₂²⋊C₄	—	53	2	no	—
896	C₂²⋊C₄	—	53	8	no	—
897	C₂²⋊C₄	—	53	4	no	—
898	C₂²⋊C₄	—	53	2	no	—
899	C₂²⋊C₄	—	53	4	no	—
900	C₂²⋊C₄	—	53	8	no	—
901	C₂²⋊C₄	—	53	4	no	—
902	C₂²⋊C₄	—	53	8	no	—
903	C₂²⋊C₄	—	53	8	no	—
904	C₂²⋊C₄	—	53	16	no	—
905	C₂²⋊C₄	—	53	8	no	—
906	C₂²⋊C₄	—	53	8	no	—
907	C₂²⋊C₄	—	53	8	no	—
908	C₂²⋊C₄	—	53	16	no	—
909	C₂²⋊C₄	—	53	16	no	—
910	C₂²⋊C₄	—	53	16	no	—
911	C₂²⋊C₄	—	53	8	no	—
912	C₂²⋊C₄	—	53	8	no	—
913	C₂²⋊C₄	—	53	8	no	—
914	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
915	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
916	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
917	C₄²	—	53	4	no	—
918	C₄²	—	53	8	no	—
919	C₄²	—	53	8	no	—
920	C₄²	—	53	8	no	—
921	C₄²	—	53	16	no	—
922	C₄²	C₂³×D₅₃	1	8	yes	—
923	C₄²	C₂³×D₅₃	1	2	yes	—
924	C₄²	C₂³×D₅₃	1	2	yes	—
925	C₂³	—	4	2	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	53	2	no	—
928	C₂³	—	53	4	no	—
929	C₂³	—	53	8	no	—
930	C₂³	—	106	16	no	—
931	C₂³	—	106	16	no	—
932	C₂³	—	106	2	no	—
933	C₂³	—	106	4	no	—
934	C₂³	—	424	16	no	—
935	C₂³	—	212	8	no	—
936	C₂³	—	212	8	no	—
937	C₂³	—	212	8	no	—
938	C₂³	—	212	8	no	—
939	C₂³	—	212	2	no	—
940	C₂³	—	212	2	no	—
941	C₂³	—	212	1	no	—
942	C₂³	—	212	1	no	—
943	C₂³	C₂×#11719949	1	8	yes	—
944	C₂³	C₂⁴×D₅₃	1	4	yes	—
945	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
946	Q₈	—	4	4	no	—
947	Q₈	—	4	8	no	—
948	Q₈	—	4	4	no	—
949	Q₈	—	106	8	no	—
950	D₄	—	106	16	no	—
951	D₄	—	106	32	no	—
952	D₄	—	106	16	no	—
953	D₄	—	106	8	no	—
954	D₄	—	106	8	no	—
955	D₄	—	212	4	no	—
956	D₄	—	212	8	no	—
957	D₄	—	212	8	no	—
958	D₄	—	212	8	no	—
959	D₄	—	212	16	no	—
960	D₄	—	212	16	no	—
961	D₄	—	212	4	no	—
962	D₄	C₂×#11719949	1	16	yes	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	8	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	53	2	no	—
971	C₂×C₄	—	53	4	no	—
972	C₂×C₄	—	53	2	no	—
973	C₂×C₄	—	53	8	no	—
974	C₂×C₄	—	53	2	no	—
975	C₂×C₄	—	106	2	no	—
976	C₂×C₄	—	106	16	no	—
977	C₂×C₄	—	106	8	no	—
978	C₂×C₄	—	106	16	no	—
979	C₂×C₄	—	212	8	no	—
980	C₂×C₄	—	212	8	no	—
981	C₂×C₄	—	212	16	no	—
982	C₂×C₄	—	212	8	no	—
983	C₂×C₄	—	212	8	no	—
984	C₂×C₄	—	212	1	no	—
985	C₂×C₄	—	212	8	no	—
986	C₂×C₄	—	212	2	no	—
987	C₂×C₄	—	212	1	no	—
988	C₂×C₄	C₂×#11719949	1	4	yes	—
989	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
990	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
991	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
992	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
993	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
994	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	4	8	no	—
1001	C₂²	—	106	2	no	—
1002	C₂²	—	106	8	no	—
1003	C₂²	—	106	4	no	—
1004	C₂²	—	106	4	no	—
1005	C₂²	—	106	8	no	—
1006	C₂²	—	106	2	no	—
1007	C₂²	—	106	8	no	—
1008	C₂²	—	106	4	no	—
1009	C₂²	—	106	2	no	—
1010	C₂²	—	424	16	no	—
1011	C₂²	—	424	16	no	—
1012	C₂²	—	212	4	no	—
1013	C₂²	—	212	8	no	—
1014	C₂²	C₂²×#11719949	1	8	yes	—
1015	C₂²	C₂²×#11719949	1	2	yes	—
1016	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	4	no	—
1020	C₄	—	2	8	no	—
1021	C₄	—	2	8	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	106	2	no	—
1024	C₄	—	106	8	no	—
1025	C₄	—	106	2	no	—
1026	C₄	—	106	2	no	—
1027	C₄	—	106	4	no	—
1028	C₄	C₂²×#11719949	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	212	2	no	—
1032	C₂	—	212	4	no	—
1033	C₂	—	212	8	no	—
1034	C₂	C₂³×#11719949	1	1	yes	characteristic
1035	C₂	#20289525	1	1	yes	characteristic
1036	C₂	#20289526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3501	C₂
hypercenter	#3501	D₅₃
hypocenter	C₅₃	#62846
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3501

Complements

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

N	H ≅ G/N	type
1. #20288786	C₂	semidirect
2. #20288748	C₂	semidirect
3. #20288677	C₂	semidirect
4. #20288658	C₂	semidirect
5. #20288569	C₂	semidirect
6. #20288556	C₂	semidirect
7. #20288479	C₂	semidirect
8. #20288436	C₂	semidirect
9. #20288405	C₂	semidirect
10. #20288351	C₂	semidirect
11. #20288138	C₂	semidirect
12. #20288127	C₂	semidirect
13. #20288107	C₂	semidirect
14. C₂×#16811213	C₂	semidirect
15. #20287919	C₂	semidirect
16. C₂×#16811095	C₂	semidirect
17. C₅₃×#3501	C₂	semidirect
20. #16811358	C₂²	semidirect
21. #16811347	C₂²	semidirect
22. #16811346	C₂²	semidirect
23. #16811339	C₂²	semidirect
24. #16811339	C₂²	semidirect
25. #16811326	C₂²	semidirect
26. #16811326	C₂²	semidirect
27. #16811321	C₂²	semidirect
28. #16811321	C₂²	semidirect
29. #16811315	C₂²	semidirect
30. #16811311	C₂²	semidirect
31. #16811300	C₂²	semidirect
32. #16811300	C₂²	semidirect
33. #16811300	C₂²	semidirect
34. #16811295	C₂²	semidirect
35. #16811284	C₂²	semidirect
36. #16811277	C₂²	semidirect
37. #16811276	C₂²	semidirect
38. #16811268	C₂²	semidirect
39. #16811268	C₂²	semidirect
40. #16811268	C₂²	semidirect
41. #16811264	C₂²	semidirect
42. #16811264	C₂²	semidirect
43. #16811264	C₂²	semidirect
44. D₄×D₂₁₂	C₂²	semidirect
45. D₄×D₂₁₂	C₂²	semidirect
46. D₄×D₂₁₂	C₂²	semidirect
47. #16811247	C₂²	semidirect
48. #16811247	C₂²	semidirect
49. #16811247	C₂²	semidirect
50. #16811236	C₂²	semidirect
51. #16811229	C₂²	semidirect
52. #16811229	C₂²	semidirect
53. #16811222	C₂²	semidirect
54. #16811222	C₂²	semidirect
55. #16811222	C₂²	semidirect
56. #16811213	C₂²	semidirect
57. #16811213	C₂²	semidirect
58. #16811213	C₂²	semidirect
59. #16811213	C₂²	semidirect
60. #16811213	C₂²	semidirect
61. #16811213	C₂²	semidirect
62. #16811213	C₂²	semidirect
63. #16811213	C₂²	semidirect
64. #16811204	C₂²	semidirect
65. #16811192	C₂²	semidirect
66. #16811185	C₂²	semidirect
67. #16811185	C₂²	semidirect
68. #16811174	C₂²	semidirect
69. #16811173	C₂²	semidirect
70. #16811160	C₂²	semidirect
71. #16811160	C₂²	semidirect
72. #16811159	C₂²	semidirect
73. #16811159	C₂²	semidirect
74. #16811158	C₂²	semidirect
75. C₂×#13133212	C₂²	semidirect
76. C₂×#13133206	C₂²	semidirect
77. #16811136	C₂²	semidirect
78. #16811136	C₂²	semidirect
79. #16811136	C₂²	semidirect
80. #16811135	C₂²	semidirect
81. C₂×#13133202	C₂²	semidirect
82. C₂×#13133192	C₂²	semidirect
83. C₂×#13133191	C₂²	semidirect
84. C₂×#13133187	C₂²	semidirect
85. #16811103	C₂²	semidirect
86. #16811102	C₂²	semidirect
87. #16811096	C₂²	semidirect
88. #16811095	C₂²	semidirect
89. #16811095	C₂²	semidirect
90. #16811095	C₂²	semidirect
91. #16811091	C₂²	semidirect
92. C₄×#11719947	C₂²	semidirect
93. C₂×C₄×D₂₁₂	C₂²	semidirect
95. C₂×#13133179	C₂²	semidirect
96. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
97. C₂×#13133177	C₂²	semidirect
98. C₂×#13133177	C₂²	semidirect
99. C₄×D₄×D₅₃	C₂²	semidirect
100. C₂×#13133175	C₂²	semidirect
101. C₂×#13133174	C₂²	semidirect
102. C₂²×#11719921	C₂²	semidirect
103. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
104. C₅₃×#554	C₂²	semidirect
105. C₅₃×#554	C₂²	semidirect
106. D₄×Q₈×C₅₃	C₂²	semidirect
107. C₅₃×#544	C₂²	semidirect
108. C₅₃×#543	C₂²	semidirect
109. C₅₃×#533	C₂²	semidirect
110. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
115. C₂×#11719949	C₂³	semidirect
116. C₂×#11719949	C₂³	semidirect
122. C₂²×D₂₁₂	C₂³	semidirect
132. C₂²×C₄×D₅₃	C₂³	semidirect
133. #13133217	C₂³	semidirect
135. #13133214	C₂³	semidirect
139. #13133212	C₂³	semidirect
140. #13133212	C₂³	semidirect
141. #13133212	C₂³	semidirect
142. #13133212	C₂³	semidirect
143. #13133212	C₂³	semidirect
144. #13133208	C₂³	semidirect
145. #13133208	C₂³	semidirect
146. #13133208	C₂³	semidirect
150. #13133206	C₂³	semidirect
151. #13133206	C₂³	semidirect
152. #13133206	C₂³	semidirect
154. #13133205	C₂³	semidirect
158. #13133202	C₂³	semidirect
159. #13133202	C₂³	semidirect
160. #13133202	C₂³	semidirect
161. #13133202	C₂³	semidirect
162. #13133202	C₂³	semidirect
163. #13133202	C₂³	semidirect
166. #13133201	C₂³	semidirect
169. #13133197	C₂³	semidirect
170. #13133193	C₂³	semidirect
171. #13133193	C₂³	semidirect
172. #13133193	C₂³	semidirect
173. #13133193	C₂³	semidirect
181. #13133192	C₂³	semidirect
182. #13133192	C₂³	semidirect
183. #13133192	C₂³	semidirect
184. #13133192	C₂³	semidirect
185. #13133192	C₂³	semidirect
191. #13133191	C₂³	semidirect
192. #13133191	C₂³	semidirect
198. #13133187	C₂³	semidirect
199. Q₈×Dic₅₃	C₂³	semidirect
200. C₄×Dic₁₀₆	C₂³	semidirect
201. #13133182	C₂³	semidirect
202. #13133182	C₂³	semidirect
207. C₄×D₂₁₂	C₂³	semidirect
208. C₄×D₂₁₂	C₂³	semidirect
209. C₄×D₂₁₂	C₂³	semidirect
212. #13133179	C₂³	semidirect
213. #13133179	C₂³	semidirect
214. #13133179	C₂³	semidirect
215. #13133179	C₂³	semidirect
216. #13133179	C₂³	semidirect
219. C₄×C₂²⋊D₅₃	C₂³	semidirect
220. C₄×C₂²⋊D₅₃	C₂³	semidirect
225. #13133177	C₂³	semidirect
226. #13133177	C₂³	semidirect
228. #13133175	C₂³	semidirect
229. #13133175	C₂³	semidirect
230. #13133175	C₂³	semidirect
231. #13133175	C₂³	semidirect
234. #13133174	C₂³	semidirect
235. #13133173	C₂³	semidirect
237. C₂×C₄⋊Dic₅₃	C₂³	semidirect
240. C₂×#11719919	C₂³	semidirect
241. C₄⋊C₄×D₅₃	C₂³	semidirect
252. C₂×#11719921	C₂³	semidirect
253. C₂×#11719921	C₂³	semidirect
255. C₂²⋊C₄×D₅₃	C₂³	semidirect
258. C₂×C₄×Dic₅₃	C₂³	semidirect
259. C₄²×D₅₃	C₂³	semidirect
260. C₂²×Q₈×C₅₃	C₂³	semidirect
263. C₄⋊Q₈×C₅₃	C₂³	semidirect
264. C₄⋊Q₈×C₅₃	C₂³	semidirect
265. C₄⋊Q₈×C₅₃	C₂³	semidirect
266. #125×C₅₃	C₂³	semidirect
267. #125×C₅₃	C₂³	semidirect
271. C₂²⋊Q₈×C₅₃	C₂³	semidirect
272. C₂²⋊Q₈×C₅₃	C₂³	semidirect
273. C₂²⋊Q₈×C₅₃	C₂³	semidirect
274. C₂²⋊Q₈×C₅₃	C₂³	semidirect
275. C₄×Q₈×C₅₃	C₂³	semidirect
276. C₄×Q₈×C₅₃	C₂³	semidirect
283. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
284. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
300. C₂×D₄×C₅₃	#41	semidirect
517. #3501	D₅₃	semidirect
543. #554	C₂×D₅₃	semidirect
544. #554	C₂×D₅₃	semidirect
555. D₄×Q₈	C₂×D₅₃	semidirect
568. #544	C₂×D₅₃	semidirect
569. #543	C₂×D₅₃	semidirect
591. #533	C₂×D₅₃	semidirect
606. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
631. C₅₃	#62846	semidirect
638. C₂²×Q₈	C₂²×D₅₃	semidirect
656. C₄⋊Q₈	C₂²×D₅₃	semidirect
657. C₄⋊Q₈	C₂²×D₅₃	semidirect
658. C₄⋊Q₈	C₂²×D₅₃	semidirect
672. #125	C₂²×D₅₃	semidirect
673. #125	C₂²×D₅₃	semidirect
704. C₂²⋊Q₈	C₂²×D₅₃	semidirect
705. C₂²⋊Q₈	C₂²×D₅₃	semidirect
706. C₂²⋊Q₈	C₂²×D₅₃	semidirect
707. C₂²⋊Q₈	C₂²×D₅₃	semidirect
737. C₄×Q₈	C₂²×D₅₃	semidirect
738. C₄×Q₈	C₂²×D₅₃	semidirect
784. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
785. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
844. C₂×D₄	#11719949	semidirect

Maximal subgroups

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

subgroup	index
#20288786	2
#20288748	2
#20288677	2
#20288658	2
#20288569	2
#20288556	2
#20288479	2
#20288436	2
#20288405	2
#20288351	2
#20288138	2
#20288127	2
#20288107	2
C₂×#16811213	2
#20287919	2
C₂×#16811095	2
C₅₃×#3501	2
#62846	53