Subgroups — #46850428

Order 34688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774616	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774614	C₂	1	1	yes	maximal, characteristic, complemented
3	#31774601	C₂	1	1	yes	maximal, characteristic, complemented
4	#31774594	C₂	1	1	yes	maximal, characteristic, complemented
5	#31774590	C₂	1	1	yes	maximal, characteristic, complemented
6	#31774590	C₂	1	1	yes	maximal, characteristic, complemented
7	#31774589	C₂	1	1	yes	maximal, characteristic, complemented
8	#31774584	C₂	1	1	yes	maximal, characteristic, complemented
9	#31774583	C₂	1	1	yes	maximal, characteristic, complemented
10	#31774578	C₂	1	1	yes	maximal, characteristic, complemented
11	#31774578	C₂	1	1	yes	maximal, characteristic, complemented
12	#31774577	C₂	1	1	yes	maximal, characteristic, complemented
13	#31774575	C₂	1	1	yes	maximal, characteristic, complemented
14	#31774547	C₂	1	1	yes	maximal, characteristic, complemented
15	#31774534	C₂	1	1	yes	maximal, characteristic, complemented
16	#31774534	C₂	1	1	yes	maximal, characteristic, complemented
17	#31774511	C₂	1	1	yes	maximal, characteristic, complemented
18	#31774504	C₂	1	1	yes	maximal, characteristic, complemented
19	#31774490	C₂	1	1	yes	maximal, characteristic, complemented
20	#31774489	C₂	1	1	yes	maximal, characteristic, complemented
21	#31774479	C₂	1	1	yes	maximal, characteristic, complemented
22	#31774428	C₂	1	1	yes	maximal, characteristic, complemented
23	#31774427	C₂	1	1	yes	maximal, characteristic, complemented
24	#31774426	C₂	1	1	yes	maximal, characteristic, complemented
25	#31774424	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#22576153	C₂	1	1	yes	maximal, characteristic, complemented
27	#126×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
28	#31774376	C₂	1	1	yes	maximal, characteristic, complemented
29	#31774370	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#16864653	C₂	1	1	yes	maximal, characteristic, complemented
31	#538×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864653	C₂²	1	1	yes	characteristic
33	C₂×#16864653	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
35	#22576159	C₂²	1	1	yes	characteristic, complemented
36	#22576158	C₂²	1	1	yes	characteristic, complemented
37	#22576155	C₂²	1	1	yes	characteristic, complemented
38	#22576155	C₂²	1	1	yes	characteristic, complemented
39	#22576155	C₂²	1	1	yes	characteristic, complemented
40	#22576155	C₂²	1	1	yes	characteristic, complemented
41	#22576154	C₂²	1	1	yes	characteristic, complemented
42	#22576153	C₂²	1	1	yes	characteristic
43	#22576153	C₂²	1	1	yes	characteristic
44	#22576153	C₂²	1	1	yes	characteristic
45	#22576153	C₂²	1	1	yes	characteristic
46	#22576153	C₂²	1	1	yes	characteristic
47	#22576153	C₂²	1	1	yes	characteristic
48	#22576153	C₂²	1	1	yes	characteristic
49	#22576153	C₂²	1	1	yes	characteristic
50	#22576153	C₂²	1	1	yes	characteristic, complemented
51	#22576153	C₂²	1	1	yes	characteristic, complemented
52	#22576153	C₂²	1	1	yes	characteristic, complemented
53	#22576153	C₂²	1	1	yes	characteristic, complemented
54	#22576153	C₂²	1	1	yes	characteristic, complemented
55	#22576153	C₂²	1	1	yes	characteristic, complemented
56	#22576153	C₂²	1	1	yes	characteristic, complemented
57	#22576152	C₂²	1	1	yes	characteristic, complemented
58	#22576151	C₂²	1	1	yes	characteristic, complemented
59	#22576151	C₂²	1	1	yes	characteristic, complemented
60	#22576151	C₂²	1	1	yes	characteristic, complemented
61	#22576150	C₂²	1	1	yes	characteristic, complemented
62	#22576150	C₂²	1	1	yes	characteristic, complemented
63	#22576150	C₂²	1	1	yes	characteristic, complemented
64	#22576150	C₂²	1	1	yes	characteristic, complemented
65	#22576150	C₂²	1	1	yes	characteristic, complemented
66	#22576147	C₂²	1	1	yes	characteristic
67	#22576147	C₂²	1	1	yes	characteristic
68	#22576146	C₂²	1	1	yes	characteristic
69	#22576146	C₂²	1	1	yes	characteristic
70	#22576146	C₂²	1	1	yes	characteristic, complemented
71	#22576144	C₂²	1	1	yes	characteristic
72	#22576144	C₂²	1	1	yes	characteristic
73	#22576143	C₂²	1	1	yes	characteristic, complemented
74	#22576142	C₂²	1	1	yes	characteristic
75	#22576142	C₂²	1	1	yes	characteristic
76	#22576142	C₂²	1	1	yes	characteristic, complemented
77	#22576142	C₂²	1	1	yes	characteristic, complemented
78	#22576142	C₂²	1	1	yes	characteristic, complemented
79	#22576142	C₂²	1	1	yes	characteristic, complemented
80	#22576141	C₂²	1	1	yes	characteristic
81	#22576141	C₂²	1	1	yes	characteristic
82	#22576141	C₂²	1	1	yes	characteristic, complemented
83	#22576141	C₂²	1	1	yes	characteristic, complemented
84	#22576141	C₂²	1	1	yes	characteristic, complemented
85	#22576141	C₂²	1	1	yes	characteristic, complemented
86	#22576141	C₂²	1	1	yes	characteristic, complemented
87	#22576139	C₂²	1	1	yes	characteristic, complemented
88	#22576138	C₂²	1	1	yes	characteristic, complemented
89	#22576138	C₂²	1	1	yes	characteristic, complemented
90	#22576138	C₂²	1	1	yes	characteristic, complemented
91	#22576137	C₂²	1	1	yes	characteristic
92	#22576137	C₂²	1	1	yes	characteristic
93	#22576137	C₂²	1	1	yes	characteristic, complemented
94	#22576137	C₂²	1	1	yes	characteristic, complemented
95	#22576137	C₂²	1	1	yes	characteristic, complemented
96	#22576137	C₂²	1	1	yes	characteristic, complemented
97	#22576137	C₂²	1	1	yes	characteristic, complemented
98	#22576137	C₂²	1	1	yes	characteristic, complemented
99	#22576136	C₂²	1	1	yes	characteristic, complemented
100	#22576136	C₂²	1	1	yes	characteristic, complemented
101	#22576132	C₂²	1	1	yes	characteristic
102	#22576132	C₂²	1	1	yes	characteristic
103	#22576132	C₂²	1	1	yes	characteristic
104	#22576132	C₂²	1	1	yes	characteristic
105	#22576132	C₂²	1	1	yes	characteristic, complemented
106	#22576131	C₂²	1	1	yes	characteristic
107	#22576131	C₂²	1	1	yes	characteristic
108	#22576131	C₂²	1	1	yes	characteristic, complemented
109	#22576128	C₂²	1	1	yes	characteristic
110	#22576128	C₂²	1	1	yes	characteristic
111	Q₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
113	C₄×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
115	#22576125	C₂²	1	1	yes	characteristic, complemented
116	#22576125	C₂²	1	1	yes	characteristic, complemented
117	#22576125	C₂²	1	1	yes	characteristic, complemented
118	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic
119	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic
120	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
121	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
122	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
123	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
124	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
126	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
127	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
128	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
129	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
130	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
131	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
132	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
133	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
134	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
135	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
136	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
137	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
138	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
139	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
140	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
141	#22576119	C₂²	1	1	yes	characteristic, complemented
142	#22576118	C₂²	1	1	yes	characteristic, complemented
143	#22576118	C₂²	1	1	yes	characteristic, complemented
144	#22576117	C₂²	1	1	yes	characteristic, complemented
145	#22576117	C₂²	1	1	yes	characteristic, complemented
146	#22576116	C₂²	1	1	yes	characteristic
147	#22576116	C₂²	1	1	yes	characteristic
148	#22576116	C₂²	1	1	yes	characteristic, complemented
149	#22576116	C₂²	1	1	yes	characteristic, complemented
150	#22576116	C₂²	1	1	yes	characteristic, complemented
151	#22576116	C₂²	1	1	yes	characteristic, complemented
152	#22576116	C₂²	1	1	yes	characteristic, complemented
153	#22576116	C₂²	1	1	yes	characteristic, complemented
154	#22576116	C₂²	1	1	yes	characteristic, complemented
155	C₂×C₄⋊Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
156	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
161	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
162	C₂×C₂²⋊Dic₂₇₁	C₂²	1	1	yes	characteristic
163	C₂×C₂²⋊Dic₂₇₁	C₂²	1	1	yes	characteristic
164	C₂×C₂²⋊Dic₂₇₁	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
169	C₂×C₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
170	C₂×C₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
172	#126×C₂₇₁	C₂²	1	1	yes	characteristic
173	#126×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
174	#124×C₂₇₁	C₂²	1	1	yes	characteristic
175	#124×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
176	#123×C₂₇₁	C₂²	1	1	yes	characteristic
177	#123×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
179	#121×C₂₇₁	C₂²	1	1	yes	characteristic
180	#121×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
181	#121×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
182	#120×C₂₇₁	C₂²	1	1	yes	characteristic
183	#120×C₂₇₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₂₇₁	C₂²	1	1	yes	characteristic
187	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
188	#16864653	—	2	4	no	—
189	#16864653	—	2	4	no	—
190	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
191	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
192	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
193	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊D₂₇₁	—	2	4	no	—
195	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
203	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
204	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
205	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
206	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
207	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
208	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
211	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
212	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
213	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
234	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
282	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
294	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
295	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
296	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
297	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
298	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
299	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
300	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
301	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
302	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
303	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
304	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
305	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
306	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
307	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
308	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
309	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
310	C₂⁴×C₂₇₁	C₂³	1	1	yes	characteristic
311	C₂×Q₈×C₂₇₁	C₂³	1	1	yes	characteristic
312	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
313	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
329	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
343	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
344	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
345	C₂²×D₂₇₁	—	2	2	no	—
346	C₂²×D₂₇₁	—	4	1	no	—
347	C₂²×D₂₇₁	—	4	1	no	—
348	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
349	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
350	Dic₅₄₂	—	2	2	no	—
351	Dic₅₄₂	—	2	2	no	—
352	Dic₅₄₂	—	4	1	no	—
353	Dic₅₄₂	—	4	1	no	—
354	C₂²⋊D₂₇₁	—	2	2	no	—
355	C₂²⋊D₂₇₁	—	2	2	no	—
356	C₂²⋊D₂₇₁	—	2	2	no	—
357	C₂²⋊D₂₇₁	—	2	2	no	—
358	C₂²⋊D₂₇₁	—	2	2	no	—
359	C₂²⋊D₂₇₁	—	4	1	no	—
360	C₂²⋊D₂₇₁	—	4	1	no	—
361	C₂²⋊D₂₇₁	#41	1	4	yes	—
362	C₂×Dic₂₇₁	—	2	2	no	—
363	C₂×Dic₂₇₁	—	2	2	no	—
364	C₂×Dic₂₇₁	—	2	2	no	—
365	C₂×Dic₂₇₁	—	2	2	no	—
366	C₂×Dic₂₇₁	—	2	2	no	—
367	C₂×Dic₂₇₁	—	4	1	no	—
368	C₂×Dic₂₇₁	—	4	1	no	—
369	C₂×Dic₂₇₁	—	4	1	no	—
370	C₂×Dic₂₇₁	—	4	1	no	—
371	C₂×Dic₂₇₁	—	4	1	no	—
372	C₂×Dic₂₇₁	—	4	1	no	—
373	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
387	C₄×D₂₇₁	—	2	2	no	—
388	C₄×D₂₇₁	—	2	2	no	—
389	C₄×D₂₇₁	—	4	1	no	—
390	C₄×D₂₇₁	—	4	1	no	—
391	C₄×D₂₇₁	—	4	1	no	—
392	C₄×D₂₇₁	—	4	1	no	—
393	C₄×D₂₇₁	—	4	1	no	—
394	C₄×D₂₇₁	—	4	1	no	—
395	C₂³×C₂₇₁	—	2	2	no	—
396	C₂³×C₂₇₁	—	4	1	no	—
397	C₂³×C₂₇₁	—	4	1	no	—
398	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
399	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
400	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
401	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
402	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
403	Q₈×C₂₇₁	—	4	1	no	—
404	D₄×C₂₇₁	—	2	2	no	—
405	D₄×C₂₇₁	—	2	2	no	—
406	D₄×C₂₇₁	—	4	1	no	—
407	D₄×C₂₇₁	—	4	1	no	—
408	D₄×C₂₇₁	—	4	1	no	—
409	D₄×C₂₇₁	—	4	1	no	—
410	D₄×C₂₇₁	—	4	1	no	—
411	C₂×C₄×C₂₇₁	—	4	1	no	—
412	C₂×C₄×C₂₇₁	—	4	1	no	—
413	C₂×C₄×C₂₇₁	—	4	1	no	—
414	C₂×C₄×C₂₇₁	—	4	1	no	—
415	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
425	C₂²×C₂₇₁	—	2	1	no	—
426	C₂²×C₂₇₁	—	2	1	no	—
427	C₂²×C₂₇₁	—	2	1	no	—
428	C₂²×C₂₇₁	—	2	1	no	—
429	C₂²×C₂₇₁	—	2	1	no	—
430	C₂²×C₂₇₁	—	2	1	no	—
431	C₂²×C₂₇₁	—	2	1	no	—
432	C₂²×C₂₇₁	—	2	1	no	—
433	C₂²×C₂₇₁	—	2	1	no	—
434	C₂²×C₂₇₁	—	2	1	no	—
435	C₂²×C₂₇₁	—	2	1	no	—
436	C₂²×C₂₇₁	—	2	1	no	—
437	C₂²×C₂₇₁	—	2	1	no	—
438	C₂²×C₂₇₁	—	2	1	no	—
439	C₂²×C₂₇₁	—	8	2	no	—
440	C₂²×C₂₇₁	C₂×#41	1	2	yes	—
441	C₂²×C₂₇₁	C₂⁵	1	1	yes	characteristic
442	C₂×D₂₇₁	—	2	1	no	—
443	C₂×D₂₇₁	—	2	1	no	—
444	C₂×D₂₇₁	—	2	1	no	—
445	C₂×D₂₇₁	—	2	1	no	—
446	C₂×D₂₇₁	—	2	1	no	—
447	C₂×D₂₇₁	—	8	2	no	—
448	C₂×D₂₇₁	C₂×#41	1	2	yes	—
449	C₄×C₂₇₁	—	2	1	no	—
450	C₄×C₂₇₁	—	2	1	no	—
451	C₄×C₂₇₁	—	2	1	no	—
452	C₄×C₂₇₁	—	2	1	no	—
453	C₄×C₂₇₁	—	2	1	no	—
454	C₄×C₂₇₁	—	2	1	no	—
455	C₄×C₂₇₁	—	2	1	no	—
456	C₄×C₂₇₁	—	2	1	no	—
457	C₄×C₂₇₁	—	2	1	no	—
458	C₄×C₂₇₁	—	2	1	no	—
459	Dic₂₇₁	—	2	1	no	—
460	Dic₂₇₁	—	2	1	no	—
461	Dic₂₇₁	—	2	1	no	—
462	Dic₂₇₁	—	2	1	no	—
463	Dic₂₇₁	—	2	1	no	—
464	Dic₂₇₁	—	2	1	no	—
465	Dic₂₇₁	—	2	1	no	—
466	Dic₂₇₁	—	2	1	no	—
467	Dic₂₇₁	—	2	1	no	—
468	Dic₂₇₁	—	2	1	no	—
469	Dic₂₇₁	—	2	1	no	—
470	Dic₂₇₁	—	2	1	no	—
471	Dic₂₇₁	—	2	1	no	—
472	Dic₂₇₁	C₂×#41	1	2	yes	—
473	C₂×C₂₇₁	—	2	2	no	—
474	C₂×C₂₇₁	—	4	1	no	—
475	C₂×C₂₇₁	—	4	1	no	—
476	C₂×C₂₇₁	—	4	1	no	—
477	C₂×C₂₇₁	—	4	1	no	—
478	C₂×C₂₇₁	C₂²×#41	1	1	yes	characteristic
479	C₂×C₂₇₁	#585	1	1	yes	characteristic
480	C₂×C₂₇₁	#585	1	1	yes	characteristic
481	D₂₇₁	—	2	2	no	—
482	D₂₇₁	—	4	1	no	—
483	C₂₇₁	#3521	1	1	yes	characteristic, complemented, Sylow
484	#3521	—	271	1	no	maximal, Sylow
485	#556	—	271	1	no	—
486	#556	—	271	1	no	—
487	#554	—	271	1	no	—
488	#553	—	271	1	no	—
489	#553	—	271	1	no	—
490	#553	—	271	1	no	—
491	#552	—	271	1	no	—
492	#552	—	271	1	no	—
493	#552	—	271	1	no	—
494	#551	—	271	1	no	—
495	#551	—	271	1	no	—
496	#551	—	271	1	no	—
497	#551	—	271	1	no	—
498	#547	—	271	1	no	—
499	#546	—	271	1	no	—
500	#546	—	271	1	no	—
501	#542	—	271	1	no	—
502	#541	—	271	1	no	—
503	#539	—	271	1	no	—
504	#539	—	271	1	no	—
505	#538	—	271	1	no	—
506	#538	D₂₇₁	1	1	yes	characteristic, complemented
507	#529	—	271	1	no	—
508	#529	—	271	1	no	—
509	#529	—	271	1	no	—
510	#529	—	271	1	no	—
511	C₂×#126	—	271	1	no	—
512	C₂×#126	—	271	1	no	—
513	#520	—	271	1	no	—
514	#518	—	271	1	no	—
515	C₄×#41	—	271	1	no	—
516	C₂×#41	—	271	1	no	—
517	C₂×#41	—	271	1	no	—
518	C₂²×D₄	—	271	1	no	—
519	C₄⋊Q₈	—	271	1	no	—
520	C₄⋊Q₈	—	271	1	no	—
521	#126	—	271	1	no	—
522	#126	—	271	1	no	—
523	#126	—	271	1	no	—
524	#126	—	271	1	no	—
525	#126	—	271	1	no	—
526	#126	—	271	1	no	—
527	#126	—	271	1	no	—
528	#126	—	271	1	no	—
529	#126	—	271	1	no	—
530	#126	—	271	1	no	—
531	#126	—	271	1	no	—
532	#126	—	271	1	no	—
533	#126	—	271	1	no	—
534	#126	—	271	1	no	—
535	#126	—	271	1	no	—
536	#126	—	271	1	no	—
537	#126	—	271	1	no	—
538	#126	—	271	1	no	—
539	#126	—	271	1	no	—
540	#126	—	271	1	no	—
541	#126	C₂×D₂₇₁	1	1	yes	characteristic
542	#126	C₂×D₂₇₁	1	1	yes	characteristic, complemented
543	#125	—	271	1	no	—
544	#125	—	271	1	no	—
545	#125	—	271	1	no	—
546	#125	—	271	1	no	—
547	#125	—	271	1	no	—
548	#125	—	271	1	no	—
549	#125	—	271	1	no	—
550	#125	—	271	1	no	—
551	#125	—	271	1	no	—
552	#124	—	271	1	no	—
553	#124	—	271	1	no	—
554	#124	—	271	1	no	—
555	#124	—	271	1	no	—
556	#124	—	271	1	no	—
557	#124	C₂×D₂₇₁	1	1	yes	characteristic
558	#124	C₂×D₂₇₁	1	1	yes	characteristic, complemented
559	#123	—	271	1	no	—
560	#123	—	271	1	no	—
561	#123	—	271	1	no	—
562	#123	—	271	1	no	—
563	#123	—	271	1	no	—
564	#123	—	271	1	no	—
565	#123	—	271	1	no	—
566	#123	—	271	1	no	—
567	#123	—	271	1	no	—
568	#123	—	271	1	no	—
569	#123	—	271	1	no	—
570	#123	—	271	1	no	—
571	#123	—	271	1	no	—
572	#123	—	271	1	no	—
573	#123	—	271	1	no	—
574	#123	—	271	1	no	—
575	#123	C₂×D₂₇₁	1	1	yes	characteristic
576	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
577	C₂²⋊Q₈	—	271	1	no	—
578	C₂²⋊Q₈	—	271	1	no	—
579	C₂²⋊Q₈	—	271	1	no	—
580	C₂²⋊Q₈	—	271	1	no	—
581	C₂²⋊Q₈	—	271	1	no	—
582	C₂²⋊Q₈	—	271	1	no	—
583	C₂²⋊Q₈	—	271	1	no	—
584	C₂²⋊Q₈	—	271	1	no	—
585	C₂²⋊Q₈	—	271	1	no	—
586	C₂²⋊Q₈	—	271	1	no	—
587	C₂²⋊Q₈	—	271	1	no	—
588	C₂²⋊Q₈	—	271	1	no	—
589	C₂²⋊Q₈	—	271	1	no	—
590	C₂²⋊Q₈	—	271	1	no	—
591	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
592	#121	—	271	1	no	—
593	#121	—	271	1	no	—
594	#121	—	271	1	no	—
595	#121	—	271	1	no	—
596	#121	—	271	1	no	—
597	#121	—	271	1	no	—
598	#121	—	271	1	no	—
599	#121	—	271	1	no	—
600	#121	C₂×D₂₇₁	1	1	yes	characteristic
601	#121	C₂×D₂₇₁	1	1	yes	characteristic, complemented
602	#121	C₂×D₂₇₁	1	1	yes	characteristic, complemented
603	#120	—	271	1	no	—
604	#120	—	271	1	no	—
605	#120	C₂×D₂₇₁	1	1	yes	characteristic
606	#120	C₂×D₂₇₁	1	1	yes	characteristic
607	C₄×Q₈	—	271	1	no	—
608	C₄×Q₈	—	271	1	no	—
609	C₄×Q₈	—	271	1	no	—
610	C₄×Q₈	—	271	1	no	—
611	C₄×Q₈	—	271	1	no	—
612	C₄×Q₈	—	271	1	no	—
613	C₄×Q₈	—	271	1	no	—
614	C₄×D₄	—	271	1	no	—
615	C₄×D₄	—	271	1	no	—
616	C₄×D₄	—	271	1	no	—
617	C₄×D₄	—	271	1	no	—
618	C₄×D₄	—	271	1	no	—
619	C₄×D₄	—	271	1	no	—
620	C₄×D₄	—	271	1	no	—
621	C₄×D₄	—	271	1	no	—
622	C₄×D₄	—	271	1	no	—
623	C₄×D₄	—	271	1	no	—
624	C₄×D₄	—	271	1	no	—
625	C₄×D₄	—	271	1	no	—
626	C₄×D₄	—	271	1	no	—
627	C₄×D₄	—	271	1	no	—
628	C₄×D₄	—	271	1	no	—
629	C₄×D₄	—	271	1	no	—
630	C₄×D₄	—	271	1	no	—
631	C₄×D₄	—	271	1	no	—
632	C₄×D₄	—	271	1	no	—
633	C₄×D₄	—	271	1	no	—
634	C₄×D₄	—	271	1	no	—
635	C₄×D₄	—	271	1	no	—
636	C₄×D₄	—	271	1	no	—
637	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
638	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
639	#117	—	271	1	no	—
640	#117	—	271	1	no	—
641	#117	—	271	1	no	—
642	#117	—	271	1	no	—
643	#117	—	271	1	no	—
644	#117	—	271	1	no	—
645	#117	—	271	1	no	—
646	#117	—	271	1	no	—
647	#117	—	271	1	no	—
648	#117	—	271	1	no	—
649	#117	—	271	1	no	—
650	#117	—	271	1	no	—
651	#117	—	271	1	no	—
652	#117	—	271	1	no	—
653	C₂×C₄⋊C₄	—	271	1	no	—
654	C₂×C₄⋊C₄	—	271	1	no	—
655	C₂×C₄⋊C₄	—	271	1	no	—
656	C₂×C₄⋊C₄	—	271	1	no	—
657	C₂×C₄⋊C₄	—	271	1	no	—
658	C₂×C₄⋊C₄	—	271	1	no	—
659	C₂×C₄⋊C₄	—	271	1	no	—
660	C₂×C₂²⋊C₄	—	271	1	no	—
661	C₂×C₂²⋊C₄	—	271	1	no	—
662	C₂×C₂²⋊C₄	—	271	1	no	—
663	C₂×C₂²⋊C₄	—	271	1	no	—
664	C₂×C₂²⋊C₄	—	271	1	no	—
665	C₂×C₂²⋊C₄	—	271	1	no	—
666	C₂×C₂²⋊C₄	—	271	1	no	—
667	C₂×C₂²⋊C₄	C₂×D₂₇₁	1	1	yes	characteristic
668	C₂×C₄²	—	271	1	no	—
669	C₂×C₄²	—	271	1	no	—
670	C₂×C₄²	—	271	1	no	—
671	C₂⁴	—	271	1	no	—
672	C₂⁴	C₂²×D₂₇₁	1	1	yes	characteristic
673	#41	—	542	4	no	—
674	#41	—	542	4	no	—
675	C₂×Q₈	—	271	1	no	—
676	C₂×Q₈	—	271	1	no	—
677	C₂×Q₈	—	271	1	no	—
678	C₂×Q₈	—	271	1	no	—
679	C₂×Q₈	C₂²×D₂₇₁	1	1	yes	characteristic
680	C₂×D₄	—	271	1	no	—
681	C₂×D₄	—	271	1	no	—
682	C₂×D₄	—	271	1	no	—
683	C₂×D₄	—	271	1	no	—
684	C₂×D₄	—	271	1	no	—
685	C₂×D₄	—	271	1	no	—
686	C₂×D₄	—	271	1	no	—
687	C₂×D₄	—	271	1	no	—
688	C₂×D₄	—	542	4	no	—
689	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
690	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
691	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
692	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
693	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
694	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
695	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
696	C₂²×C₄	—	271	1	no	—
697	C₂²×C₄	—	271	1	no	—
698	C₂²×C₄	—	271	1	no	—
699	C₂²×C₄	—	271	1	no	—
700	C₂²×C₄	—	271	1	no	—
701	C₂²×C₄	—	271	1	no	—
702	C₂²×C₄	—	271	1	no	—
703	C₂²×C₄	—	271	1	no	—
704	C₂²×C₄	—	271	1	no	—
705	C₂²×C₄	—	271	1	no	—
706	C₂²×C₄	—	271	1	no	—
707	C₂²×C₄	—	271	1	no	—
708	C₂²×C₄	—	271	1	no	—
709	C₂²×C₄	—	271	1	no	—
710	C₂²×C₄	—	271	1	no	—
711	C₂²×C₄	—	271	1	no	—
712	C₂²×C₄	—	271	1	no	—
713	C₂²×C₄	—	271	1	no	—
714	C₂²×C₄	—	271	1	no	—
715	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
719	C₄⋊C₄	—	271	1	no	—
720	C₄⋊C₄	—	271	1	no	—
721	C₄⋊C₄	—	271	1	no	—
722	C₄⋊C₄	—	271	1	no	—
723	C₄⋊C₄	—	271	1	no	—
724	C₄⋊C₄	—	271	1	no	—
725	C₄⋊C₄	—	271	1	no	—
726	C₄⋊C₄	—	271	1	no	—
727	C₄⋊C₄	—	271	1	no	—
728	C₄⋊C₄	—	271	1	no	—
729	C₄⋊C₄	—	271	1	no	—
730	C₄⋊C₄	—	271	1	no	—
731	C₄⋊C₄	—	271	1	no	—
732	C₄⋊C₄	—	271	1	no	—
733	C₄⋊C₄	—	271	1	no	—
734	C₄⋊C₄	—	271	1	no	—
735	C₄⋊C₄	—	271	1	no	—
736	C₄⋊C₄	—	271	1	no	—
737	C₄⋊C₄	—	271	1	no	—
738	C₄⋊C₄	—	271	1	no	—
739	C₄⋊C₄	—	271	1	no	—
740	C₄⋊C₄	—	271	1	no	—
741	C₄⋊C₄	—	271	1	no	—
742	C₄⋊C₄	—	271	1	no	—
743	C₄⋊C₄	—	271	1	no	—
744	C₄⋊C₄	—	271	1	no	—
745	C₄⋊C₄	—	271	1	no	—
746	C₄⋊C₄	—	271	1	no	—
747	C₄⋊C₄	—	271	1	no	—
748	C₄⋊C₄	—	271	1	no	—
749	C₄⋊C₄	—	271	1	no	—
750	C₄⋊C₄	—	271	1	no	—
751	C₄⋊C₄	—	271	1	no	—
752	C₄⋊C₄	—	271	1	no	—
753	C₄⋊C₄	—	271	1	no	—
754	C₄⋊C₄	—	271	1	no	—
755	C₄⋊C₄	—	271	1	no	—
756	C₄⋊C₄	—	271	1	no	—
757	C₄⋊C₄	—	271	1	no	—
758	C₄⋊C₄	—	271	1	no	—
759	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
765	C₂²⋊C₄	—	271	1	no	—
766	C₂²⋊C₄	—	271	1	no	—
767	C₂²⋊C₄	—	271	1	no	—
768	C₂²⋊C₄	—	271	1	no	—
769	C₂²⋊C₄	—	271	1	no	—
770	C₂²⋊C₄	—	271	1	no	—
771	C₂²⋊C₄	—	271	1	no	—
772	C₂²⋊C₄	—	271	1	no	—
773	C₂²⋊C₄	—	271	1	no	—
774	C₂²⋊C₄	—	271	1	no	—
775	C₂²⋊C₄	—	271	1	no	—
776	C₂²⋊C₄	—	271	1	no	—
777	C₂²⋊C₄	—	271	1	no	—
778	C₂²⋊C₄	—	271	1	no	—
779	C₂²⋊C₄	—	271	1	no	—
780	C₂²⋊C₄	—	271	1	no	—
781	C₂²⋊C₄	—	271	1	no	—
782	C₂²⋊C₄	—	271	1	no	—
783	C₂²⋊C₄	—	271	1	no	—
784	C₂²⋊C₄	—	271	1	no	—
785	C₂²⋊C₄	—	271	1	no	—
786	C₂²⋊C₄	—	271	1	no	—
787	C₂²⋊C₄	—	271	1	no	—
788	C₂²⋊C₄	—	271	1	no	—
789	C₂²⋊C₄	—	271	1	no	—
790	C₂²⋊C₄	—	271	1	no	—
791	C₂²⋊C₄	—	271	1	no	—
792	C₂²⋊C₄	—	271	1	no	—
793	C₂²⋊C₄	—	271	1	no	—
794	C₂²⋊C₄	—	271	1	no	—
795	C₂²⋊C₄	—	271	1	no	—
796	C₂²⋊C₄	—	271	1	no	—
797	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
811	C₄²	—	271	1	no	—
812	C₄²	—	271	1	no	—
813	C₄²	—	271	1	no	—
814	C₄²	—	271	1	no	—
815	C₄²	—	271	1	no	—
816	C₄²	—	271	1	no	—
817	C₄²	—	271	1	no	—
818	C₄²	—	271	1	no	—
819	C₄²	—	271	1	no	—
820	C₄²	—	271	1	no	—
821	C₄²	—	271	1	no	—
822	C₄²	—	271	1	no	—
823	C₄²	—	271	1	no	—
824	C₄²	—	271	1	no	—
825	C₄²	—	271	1	no	—
826	C₄²	—	271	1	no	—
827	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
828	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	271	1	no	—
833	C₂³	—	271	1	no	—
834	C₂³	—	542	2	no	—
835	C₂³	—	1084	1	no	—
836	C₂³	—	1084	1	no	—
837	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
838	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
839	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
840	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
841	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
842	Q₈	—	4	1	no	—
843	Q₈	—	542	2	no	—
844	Q₈	—	542	2	no	—
845	Q₈	—	1084	1	no	—
846	Q₈	—	1084	1	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	—	4	1	no	—
854	D₄	—	271	4	no	—
855	D₄	—	542	2	no	—
856	D₄	—	542	2	no	—
857	D₄	—	542	2	no	—
858	D₄	—	542	2	no	—
859	D₄	—	542	2	no	—
860	D₄	—	1084	1	no	—
861	D₄	—	1084	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	271	1	no	—
867	C₂×C₄	—	271	1	no	—
868	C₂×C₄	—	271	1	no	—
869	C₂×C₄	—	271	1	no	—
870	C₂×C₄	—	271	1	no	—
871	C₂×C₄	—	271	1	no	—
872	C₂×C₄	—	271	1	no	—
873	C₂×C₄	—	271	1	no	—
874	C₂×C₄	—	271	1	no	—
875	C₂×C₄	—	271	1	no	—
876	C₂×C₄	—	271	1	no	—
877	C₂×C₄	—	271	1	no	—
878	C₂×C₄	—	271	1	no	—
879	C₂×C₄	—	271	1	no	—
880	C₂×C₄	—	542	2	no	—
881	C₂×C₄	—	542	2	no	—
882	C₂×C₄	—	542	2	no	—
883	C₂×C₄	—	542	2	no	—
884	C₂×C₄	—	542	2	no	—
885	C₂×C₄	—	542	2	no	—
886	C₂×C₄	—	542	2	no	—
887	C₂×C₄	—	1084	1	no	—
888	C₂×C₄	—	1084	1	no	—
889	C₂×C₄	—	1084	1	no	—
890	C₂×C₄	—	1084	1	no	—
891	C₂×C₄	—	1084	1	no	—
892	C₂×C₄	—	1084	1	no	—
893	C₂×C₄	—	1084	1	no	—
894	C₂×C₄	—	1084	1	no	—
895	C₂×C₄	—	1084	1	no	—
896	C₂×C₄	—	1084	1	no	—
897	C₂×C₄	—	1084	1	no	—
898	C₂×C₄	—	1084	1	no	—
899	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	8	2	no	—
924	C₂²	—	271	2	no	—
925	C₂²	—	542	1	no	—
926	C₂²	—	542	1	no	—
927	C₂²	—	542	1	no	—
928	C₂²	—	542	1	no	—
929	C₂²	—	542	1	no	—
930	C₂²	—	2168	2	no	—
931	C₂²	#41×D₂₇₁	1	2	yes	—
932	C₂²	C₂⁴×D₂₇₁	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	271	2	no	—
944	C₄	—	542	1	no	—
945	C₄	—	542	1	no	—
946	C₄	—	542	1	no	—
947	C₄	—	542	1	no	—
948	C₄	—	542	1	no	—
949	C₄	—	542	1	no	—
950	C₄	—	542	1	no	—
951	C₄	—	542	1	no	—
952	C₄	—	542	1	no	—
953	C₄	—	542	1	no	—
954	C₄	—	542	1	no	—
955	C₄	—	542	1	no	—
956	C₄	—	542	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	4	1	no	—
962	C₂	—	542	2	no	—
963	C₂	—	1084	1	no	—
964	C₂	C₂×#41×D₂₇₁	1	1	yes	characteristic
965	C₂	#31774732	1	1	yes	characteristic
966	C₂	#31774732	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₇₁
commutator, socle, cosocle	C₂²×C₂₇₁	C₂⁵
Fitting	#538×C₂₇₁	C₂
hypercenter	#538	D₂₇₁
hypocenter	C₂₇₁	#3521
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #31774616	C₂	semidirect
2. #31774614	C₂	semidirect
3. #31774601	C₂	semidirect
4. #31774594	C₂	semidirect
5. #31774590	C₂	semidirect
6. #31774590	C₂	semidirect
7. #31774589	C₂	semidirect
8. #31774584	C₂	semidirect
9. #31774583	C₂	semidirect
10. #31774578	C₂	semidirect
11. #31774578	C₂	semidirect
12. #31774577	C₂	semidirect
13. #31774575	C₂	semidirect
14. #31774547	C₂	semidirect
15. #31774534	C₂	semidirect
16. #31774534	C₂	semidirect
17. #31774511	C₂	semidirect
18. #31774504	C₂	semidirect
19. #31774490	C₂	semidirect
20. #31774489	C₂	semidirect
21. #31774479	C₂	semidirect
22. #31774428	C₂	semidirect
23. #31774427	C₂	semidirect
24. #31774426	C₂	semidirect
25. #31774424	C₂	semidirect
26. C₂×#22576153	C₂	semidirect
27. #126×D₂₇₁	C₂	semidirect
28. #31774376	C₂	semidirect
29. #31774370	C₂	semidirect
30. C₄×#16864653	C₂	semidirect
31. #538×C₂₇₁	C₂	semidirect
35. #22576159	C₂²	semidirect
36. #22576158	C₂²	semidirect
37. #22576155	C₂²	semidirect
38. #22576155	C₂²	semidirect
39. #22576155	C₂²	semidirect
40. #22576155	C₂²	semidirect
41. #22576154	C₂²	semidirect
50. #22576153	C₂²	semidirect
51. #22576153	C₂²	semidirect
52. #22576153	C₂²	semidirect
53. #22576153	C₂²	semidirect
54. #22576153	C₂²	semidirect
55. #22576153	C₂²	semidirect
56. #22576153	C₂²	semidirect
57. #22576152	C₂²	semidirect
58. #22576151	C₂²	semidirect
59. #22576151	C₂²	semidirect
60. #22576151	C₂²	semidirect
61. #22576150	C₂²	semidirect
62. #22576150	C₂²	semidirect
63. #22576150	C₂²	semidirect
64. #22576150	C₂²	semidirect
65. #22576150	C₂²	semidirect
70. #22576146	C₂²	semidirect
73. #22576143	C₂²	semidirect
76. #22576142	C₂²	semidirect
77. #22576142	C₂²	semidirect
78. #22576142	C₂²	semidirect
79. #22576142	C₂²	semidirect
82. #22576141	C₂²	semidirect
83. #22576141	C₂²	semidirect
84. #22576141	C₂²	semidirect
85. #22576141	C₂²	semidirect
86. #22576141	C₂²	semidirect
87. #22576139	C₂²	semidirect
88. #22576138	C₂²	semidirect
89. #22576138	C₂²	semidirect
90. #22576138	C₂²	semidirect
93. #22576137	C₂²	semidirect
94. #22576137	C₂²	semidirect
95. #22576137	C₂²	semidirect
96. #22576137	C₂²	semidirect
97. #22576137	C₂²	semidirect
98. #22576137	C₂²	semidirect
99. #22576136	C₂²	semidirect
100. #22576136	C₂²	semidirect
105. #22576132	C₂²	semidirect
108. #22576131	C₂²	semidirect
111. Q₈×Dic₂₇₁	C₂²	semidirect
112. C₄×Dic₅₄₂	C₂²	semidirect
113. C₄×Dic₅₄₂	C₂²	semidirect
114. C₄×Dic₅₄₂	C₂²	semidirect
115. #22576125	C₂²	semidirect
116. #22576125	C₂²	semidirect
117. #22576125	C₂²	semidirect
120. D₄×Dic₂₇₁	C₂²	semidirect
121. D₄×Dic₂₇₁	C₂²	semidirect
122. D₄×Dic₂₇₁	C₂²	semidirect
123. D₄×Dic₂₇₁	C₂²	semidirect
124. D₄×Dic₂₇₁	C₂²	semidirect
129. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
130. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
131. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
138. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
139. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
140. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
141. #22576119	C₂²	semidirect
142. #22576118	C₂²	semidirect
143. #22576118	C₂²	semidirect
144. #22576117	C₂²	semidirect
145. #22576117	C₂²	semidirect
148. #22576116	C₂²	semidirect
149. #22576116	C₂²	semidirect
150. #22576116	C₂²	semidirect
151. #22576116	C₂²	semidirect
152. #22576116	C₂²	semidirect
153. #22576116	C₂²	semidirect
154. #22576116	C₂²	semidirect
155. C₂×C₄⋊Dic₂₇₁	C₂²	semidirect
156. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
157. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
158. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
159. C₄⋊C₄×D₂₇₁	C₂²	semidirect
160. C₄⋊C₄×D₂₇₁	C₂²	semidirect
161. C₄⋊C₄×D₂₇₁	C₂²	semidirect
169. C₂×C₄×Dic₂₇₁	C₂²	semidirect
170. C₂×C₄×Dic₂₇₁	C₂²	semidirect
171. C₄²×D₂₇₁	C₂²	semidirect
173. #126×C₂₇₁	C₂²	semidirect
175. #124×C₂₇₁	C₂²	semidirect
177. #123×C₂₇₁	C₂²	semidirect
178. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
180. #121×C₂₇₁	C₂²	semidirect
181. #121×C₂₇₁	C₂²	semidirect
184. C₄×D₄×C₂₇₁	C₂²	semidirect
185. C₄×D₄×C₂₇₁	C₂²	semidirect
483. C₂₇₁	#3521	semidirect
506. #538	D₂₇₁	semidirect
542. #126	C₂×D₂₇₁	semidirect
558. #124	C₂×D₂₇₁	semidirect
576. #123	C₂×D₂₇₁	semidirect
591. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
601. #121	C₂×D₂₇₁	semidirect
602. #121	C₂×D₂₇₁	semidirect
637. C₄×D₄	C₂×D₂₇₁	semidirect
638. C₄×D₄	C₂×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
#31774616	2
#31774614	2
#31774601	2
#31774594	2
#31774590	2
#31774589	2
#31774584	2
#31774583	2
#31774578	2
#31774577	2
#31774575	2
#31774547	2
#31774534	2
#31774511	2
#31774504	2
#31774490	2
#31774489	2
#31774479	2
#31774428	2
#31774427	2
#31774426	2
#31774424	2
C₂×#22576153	2
#126×D₂₇₁	2
#31774376	2
#31774370	2
C₄×#16864653	2
#538×C₂₇₁	2
#3521	271