Subgroups — #46850405

Order 34688.

1124 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774614	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774603	C₂	1	1	yes	maximal, characteristic, complemented
3	#31774601	C₂	1	1	yes	maximal, characteristic, complemented
4	#31774584	C₂	1	1	yes	maximal, characteristic, complemented
5	#31774579	C₂	1	1	yes	maximal, characteristic, complemented
6	#31774575	C₂	1	1	yes	maximal, characteristic, complemented
7	#31774574	C₂	1	1	yes	maximal, characteristic, complemented
8	#31774572	C₂	1	1	yes	maximal, characteristic, complemented
9	#31774570	C₂	1	1	yes	maximal, characteristic, complemented
10	#31774560	C₂	1	1	yes	maximal, characteristic, complemented
11	#31774557	C₂	1	1	yes	maximal, characteristic, complemented
12	#31774553	C₂	1	1	yes	maximal, characteristic, complemented
13	#31774545	C₂	1	1	yes	maximal, characteristic, complemented
14	#31774545	C₂	1	1	yes	maximal, characteristic, complemented
15	#31774539	C₂	1	1	yes	maximal, characteristic, complemented
16	#31774536	C₂	1	1	yes	maximal, characteristic, complemented
17	#31774517	C₂	1	1	yes	maximal, characteristic, complemented
18	#31774515	C₂	1	1	yes	maximal, characteristic, complemented
19	#31774495	C₂	1	1	yes	maximal, characteristic, complemented
20	#31774489	C₂	1	1	yes	maximal, characteristic, complemented
21	#31774488	C₂	1	1	yes	maximal, characteristic, complemented
22	#31774453	C₂	1	1	yes	maximal, characteristic, complemented
23	#31774430	C₂	1	1	yes	maximal, characteristic, complemented
24	#31774406	C₂	1	1	yes	maximal, characteristic, complemented
25	#31774405	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#22576138	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂²⋊Q₈×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
28	#31774378	C₂	1	1	yes	maximal, characteristic, complemented
29	#31774376	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₄×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
31	#539×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864654	C₂²	1	1	yes	characteristic
33	C₂×#16864654	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864653	C₂²	1	1	yes	characteristic
35	C₂×#16864653	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
41	#22576159	C₂²	1	1	yes	characteristic, complemented
42	#22576159	C₂²	1	1	yes	characteristic, complemented
43	#22576159	C₂²	1	1	yes	characteristic, complemented
44	#22576158	C₂²	1	1	yes	characteristic, complemented
45	#22576155	C₂²	1	1	yes	characteristic, complemented
46	#22576155	C₂²	1	1	yes	characteristic, complemented
47	#22576155	C₂²	1	1	yes	characteristic, complemented
48	#22576155	C₂²	1	1	yes	characteristic, complemented
49	#22576154	C₂²	1	1	yes	characteristic, complemented
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	#22576152	C₂²	1	1	yes	characteristic, complemented
54	#22576151	C₂²	1	1	yes	characteristic, complemented
55	#22576150	C₂²	1	1	yes	characteristic, complemented
56	#22576150	C₂²	1	1	yes	characteristic, complemented
57	#22576150	C₂²	1	1	yes	characteristic, complemented
58	#22576149	C₂²	1	1	yes	characteristic, complemented
59	#22576147	C₂²	1	1	yes	characteristic, complemented
60	#22576146	C₂²	1	1	yes	characteristic
61	#22576146	C₂²	1	1	yes	characteristic
62	#22576146	C₂²	1	1	yes	characteristic, complemented
63	#22576146	C₂²	1	1	yes	characteristic, complemented
64	#22576146	C₂²	1	1	yes	characteristic, complemented
65	#22576145	C₂²	1	1	yes	characteristic
66	#22576145	C₂²	1	1	yes	characteristic
67	#22576145	C₂²	1	1	yes	characteristic
68	#22576145	C₂²	1	1	yes	characteristic, complemented
69	#22576145	C₂²	1	1	yes	characteristic, complemented
70	#22576145	C₂²	1	1	yes	characteristic, complemented
71	#22576144	C₂²	1	1	yes	characteristic, complemented
72	#22576144	C₂²	1	1	yes	characteristic, complemented
73	#22576143	C₂²	1	1	yes	characteristic, complemented
74	#22576142	C₂²	1	1	yes	characteristic
75	#22576142	C₂²	1	1	yes	characteristic, complemented
76	#22576142	C₂²	1	1	yes	characteristic, complemented
77	#22576142	C₂²	1	1	yes	characteristic, complemented
78	#22576141	C₂²	1	1	yes	characteristic
79	#22576140	C₂²	1	1	yes	characteristic
80	#22576140	C₂²	1	1	yes	characteristic, complemented
81	#22576140	C₂²	1	1	yes	characteristic, complemented
82	#22576139	C₂²	1	1	yes	characteristic, complemented
83	#22576138	C₂²	1	1	yes	characteristic
84	#22576138	C₂²	1	1	yes	characteristic
85	#22576138	C₂²	1	1	yes	characteristic
86	#22576138	C₂²	1	1	yes	characteristic
87	#22576138	C₂²	1	1	yes	characteristic
88	#22576138	C₂²	1	1	yes	characteristic
89	#22576138	C₂²	1	1	yes	characteristic
90	#22576138	C₂²	1	1	yes	characteristic, complemented
91	#22576138	C₂²	1	1	yes	characteristic, complemented
92	#22576138	C₂²	1	1	yes	characteristic, complemented
93	#22576138	C₂²	1	1	yes	characteristic, complemented
94	#22576138	C₂²	1	1	yes	characteristic, complemented
95	#22576138	C₂²	1	1	yes	characteristic, complemented
96	#22576138	C₂²	1	1	yes	characteristic, complemented
97	#22576138	C₂²	1	1	yes	characteristic, complemented
98	#22576137	C₂²	1	1	yes	characteristic, complemented
99	#22576137	C₂²	1	1	yes	characteristic, complemented
100	#22576137	C₂²	1	1	yes	characteristic, complemented
101	#22576137	C₂²	1	1	yes	characteristic, complemented
102	#22576137	C₂²	1	1	yes	characteristic, complemented
103	#22576137	C₂²	1	1	yes	characteristic, complemented
104	#22576136	C₂²	1	1	yes	characteristic
105	#22576135	C₂²	1	1	yes	characteristic
106	#22576133	C₂²	1	1	yes	characteristic
107	#22576133	C₂²	1	1	yes	characteristic
108	#22576133	C₂²	1	1	yes	characteristic
109	#22576133	C₂²	1	1	yes	characteristic, complemented
110	#22576132	C₂²	1	1	yes	characteristic
111	#22576132	C₂²	1	1	yes	characteristic
112	#22576132	C₂²	1	1	yes	characteristic, complemented
113	#22576130	C₂²	1	1	yes	characteristic
114	#22576130	C₂²	1	1	yes	characteristic
115	#22576128	C₂²	1	1	yes	characteristic
116	#22576128	C₂²	1	1	yes	characteristic
117	C₄×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
118	#22576125	C₂²	1	1	yes	characteristic, complemented
119	#22576125	C₂²	1	1	yes	characteristic, complemented
120	#22576125	C₂²	1	1	yes	characteristic, complemented
121	#22576125	C₂²	1	1	yes	characteristic, complemented
122	#22576125	C₂²	1	1	yes	characteristic, complemented
123	#22576125	C₂²	1	1	yes	characteristic, complemented
124	C₄×D₁₀₈₄	C₂²	1	1	yes	characteristic
125	C₄×D₁₀₈₄	C₂²	1	1	yes	characteristic
126	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic
127	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
128	#22576122	C₂²	1	1	yes	characteristic
129	#22576122	C₂²	1	1	yes	characteristic
130	#22576122	C₂²	1	1	yes	characteristic
131	#22576122	C₂²	1	1	yes	characteristic, complemented
132	#22576122	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
135	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
136	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
137	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
139	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
140	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
141	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
142	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
143	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
144	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
145	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	#22576119	C₂²	1	1	yes	characteristic, complemented
148	#22576118	C₂²	1	1	yes	characteristic
149	#22576118	C₂²	1	1	yes	characteristic
150	#22576118	C₂²	1	1	yes	characteristic, complemented
151	#22576118	C₂²	1	1	yes	characteristic, complemented
152	#22576117	C₂²	1	1	yes	characteristic, complemented
153	#22576117	C₂²	1	1	yes	characteristic, complemented
154	#22576116	C₂²	1	1	yes	characteristic, complemented
155	#22576116	C₂²	1	1	yes	characteristic, complemented
156	#22576116	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	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
161	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
165	C₂×(C₂×D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
166	C₂×(C₂×D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
171	C₄²×D₂₇₁	C₂²	1	1	yes	characteristic
172	#126×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
173	#126×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
174	#125×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
175	#125×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	#123×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
179	#123×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
183	#121×C₂₇₁	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
188	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
189	#16864654	—	2	4	no	—
190	#16864654	—	4	2	no	—
191	#16864653	—	2	4	no	—
192	#16864653	—	4	2	no	—
193	C₂×Dic₅₄₂	—	4	2	no	—
194	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
195	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
196	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
197	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
198	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
199	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
200	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
201	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
202	Q₈×D₂₇₁	—	4	2	no	—
203	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
204	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
205	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
206	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
215	D₄×D₂₇₁	—	2	4	no	—
216	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
217	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
218	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
219	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
220	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
221	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₂₇₁	—	4	2	no	—
223	C₂×C₄×D₂₇₁	—	4	2	no	—
224	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₂₇₁	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	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
269	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
270	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₂₇₁⋊C₄	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	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₂₇₁)⋊C₄	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	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₂₇₁)⋊C₄	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	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
311	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
312	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
313	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
314	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
315	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
316	C₂×Q₈×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	C₂×D₄×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	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
324	C₂²×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	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
338	C₄⋊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	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
349	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
350	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
351	C₂²×D₂₇₁	—	2	2	no	—
352	C₂²×D₂₇₁	—	2	2	no	—
353	C₂²×D₂₇₁	—	2	2	no	—
354	C₂²×D₂₇₁	—	2	2	no	—
355	C₂²×D₂₇₁	—	4	1	no	—
356	C₂²×D₂₇₁	—	4	1	no	—
357	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
358	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
359	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
360	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
361	Dic₅₄₂	—	2	2	no	—
362	Dic₅₄₂	—	2	2	no	—
363	Dic₅₄₂	—	2	2	no	—
364	Dic₅₄₂	—	2	2	no	—
365	Dic₅₄₂	—	2	2	no	—
366	Dic₅₄₂	—	4	1	no	—
367	Dic₅₄₂	—	4	1	no	—
368	Dic₅₄₂	—	4	1	no	—
369	D₁₀₈₄	—	2	2	no	—
370	D₁₀₈₄	—	2	2	no	—
371	D₁₀₈₄	—	2	2	no	—
372	D₁₀₈₄	—	4	1	no	—
373	C₂²⋊D₂₇₁	—	2	2	no	—
374	C₂²⋊D₂₇₁	—	2	2	no	—
375	C₂²⋊D₂₇₁	—	2	2	no	—
376	C₂²⋊D₂₇₁	—	2	2	no	—
377	C₂²⋊D₂₇₁	—	2	2	no	—
378	C₂²⋊D₂₇₁	—	4	1	no	—
379	C₂²⋊D₂₇₁	—	4	1	no	—
380	C₂²⋊D₂₇₁	#41	1	4	yes	complemented
381	C₂×Dic₂₇₁	—	2	2	no	—
382	C₂×Dic₂₇₁	—	2	2	no	—
383	C₂×Dic₂₇₁	—	2	2	no	—
384	C₂×Dic₂₇₁	—	2	2	no	—
385	C₂×Dic₂₇₁	—	4	1	no	—
386	C₂×Dic₂₇₁	—	4	1	no	—
387	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
399	C₄×D₂₇₁	—	2	2	no	—
400	C₄×D₂₇₁	—	2	2	no	—
401	C₄×D₂₇₁	—	2	2	no	—
402	C₄×D₂₇₁	—	2	2	no	—
403	C₄×D₂₇₁	—	2	2	no	—
404	C₄×D₂₇₁	—	2	2	no	—
405	C₄×D₂₇₁	—	2	2	no	—
406	C₄×D₂₇₁	—	2	2	no	—
407	C₄×D₂₇₁	—	4	1	no	—
408	C₄×D₂₇₁	—	4	1	no	—
409	C₄×D₂₇₁	—	4	1	no	—
410	C₄×D₂₇₁	—	4	1	no	—
411	C₄×D₂₇₁	—	4	1	no	—
412	C₄×D₂₇₁	—	4	1	no	—
413	C₄×D₂₇₁	—	4	1	no	—
414	C₄×D₂₇₁	—	4	1	no	—
415	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
416	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
417	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
418	Q₈×C₂₇₁	—	4	1	no	—
419	D₄×C₂₇₁	—	2	2	no	—
420	D₄×C₂₇₁	—	2	2	no	—
421	D₄×C₂₇₁	—	4	1	no	—
422	C₂×C₄×C₂₇₁	—	2	2	no	—
423	C₂×C₄×C₂₇₁	—	4	1	no	—
424	C₂×C₄×C₂₇₁	—	4	1	no	—
425	C₂×C₄×C₂₇₁	—	4	1	no	—
426	C₂×C₄×C₂₇₁	—	4	1	no	—
427	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
431	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
432	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
437	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
439	C₂²×C₂₇₁	—	2	1	no	—
440	C₂²×C₂₇₁	—	2	1	no	—
441	C₂²×C₂₇₁	—	2	1	no	—
442	C₂²×C₂₇₁	—	2	1	no	—
443	C₂²×C₂₇₁	—	2	1	no	—
444	C₂²×C₂₇₁	—	2	1	no	—
445	C₂²×C₂₇₁	—	2	1	no	—
446	C₂²×C₂₇₁	—	2	1	no	—
447	C₂²×C₂₇₁	C₂×#41	1	2	yes	—
448	C₂²×C₂₇₁	C₂⁵	1	1	yes	characteristic
449	C₂×D₂₇₁	—	2	1	no	—
450	C₂×D₂₇₁	—	2	1	no	—
451	C₂×D₂₇₁	—	2	1	no	—
452	C₂×D₂₇₁	—	2	1	no	—
453	C₂×D₂₇₁	—	2	1	no	—
454	C₂×D₂₇₁	—	2	1	no	—
455	C₂×D₂₇₁	—	2	1	no	—
456	C₂×D₂₇₁	—	2	1	no	—
457	C₂×D₂₇₁	—	2	1	no	—
458	C₂×D₂₇₁	—	2	1	no	—
459	C₂×D₂₇₁	—	4	4	no	—
460	C₂×D₂₇₁	—	4	4	no	—
461	C₂×D₂₇₁	C₂×#41	1	2	yes	—
462	C₂×D₂₇₁	2₋¹⁺⁴	1	2	yes	—
463	C₄×C₂₇₁	—	2	1	no	—
464	C₄×C₂₇₁	—	2	1	no	—
465	C₄×C₂₇₁	—	2	1	no	—
466	C₄×C₂₇₁	—	2	1	no	—
467	C₄×C₂₇₁	—	2	1	no	—
468	C₄×C₂₇₁	—	2	1	no	—
469	C₄×C₂₇₁	—	2	1	no	—
470	C₄×C₂₇₁	—	2	1	no	—
471	C₄×C₂₇₁	—	2	1	no	—
472	C₄×C₂₇₁	—	2	1	no	—
473	C₄×C₂₇₁	—	2	1	no	—
474	C₄×C₂₇₁	—	2	1	no	—
475	Dic₂₇₁	—	2	1	no	—
476	Dic₂₇₁	—	2	1	no	—
477	Dic₂₇₁	—	2	1	no	—
478	Dic₂₇₁	—	2	1	no	—
479	Dic₂₇₁	—	2	1	no	—
480	Dic₂₇₁	—	2	1	no	—
481	Dic₂₇₁	—	2	1	no	—
482	Dic₂₇₁	—	2	1	no	—
483	Dic₂₇₁	—	2	1	no	—
484	Dic₂₇₁	—	2	1	no	—
485	Dic₂₇₁	C₂×#41	1	2	yes	—
486	Dic₂₇₁	H(5,𝔽₂)	1	2	yes	—
487	C₂×C₂₇₁	—	2	2	no	—
488	C₂×C₂₇₁	—	4	1	no	—
489	C₂×C₂₇₁	—	4	1	no	—
490	C₂×C₂₇₁	C₂²×#41	1	1	yes	characteristic
491	C₂×C₂₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂×C₂₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	D₂₇₁	—	2	2	no	—
494	D₂₇₁	—	2	2	no	—
495	D₂₇₁	—	4	1	no	—
496	D₂₇₁	—	4	1	no	—
497	C₂₇₁	#3520	1	1	yes	characteristic, complemented, Sylow
498	#3520	—	271	1	no	maximal, Sylow
499	#556	—	271	1	no	—
500	#554	—	271	1	no	—
501	#554	—	271	1	no	—
502	#552	—	271	1	no	—
503	#552	—	271	1	no	—
504	#551	—	271	1	no	—
505	#551	—	271	1	no	—
506	#551	—	271	1	no	—
507	#551	—	271	1	no	—
508	D₄×Q₈	—	271	1	no	—
509	#548	—	271	1	no	—
510	#548	—	271	1	no	—
511	#547	—	271	1	no	—
512	#547	—	271	1	no	—
513	#546	—	271	1	no	—
514	#546	—	271	1	no	—
515	#542	—	271	1	no	—
516	#542	—	271	1	no	—
517	#539	—	271	1	no	—
518	#539	—	271	1	no	—
519	#539	—	271	1	no	—
520	#539	D₂₇₁	1	1	yes	characteristic, complemented
521	#533	—	271	1	no	—
522	#529	—	271	1	no	—
523	#525	—	271	1	no	—
524	#525	—	271	1	no	—
525	C₂×C₂²⋊Q₈	—	271	1	no	—
526	C₂×C₂²⋊Q₈	—	271	1	no	—
527	#520	—	271	1	no	—
528	#520	—	271	1	no	—
529	C₂×C₄×D₄	—	271	1	no	—
530	C₂×#41	—	271	1	no	—
531	C₂×#41	—	271	1	no	—
532	C₂×#41	—	271	1	no	—
533	C₂×#41	—	271	1	no	—
534	C₂²×Q₈	—	271	1	no	—
535	C₂²×Q₈	—	271	1	no	—
536	C₂²×D₄	—	271	1	no	—
537	C₂³×C₄	—	271	1	no	—
538	C₂³×C₄	—	271	1	no	—
539	C₄⋊Q₈	—	271	1	no	—
540	C₄⋊Q₈	—	271	1	no	—
541	C₄⋊Q₈	—	271	1	no	—
542	C₄⋊Q₈	—	271	1	no	—
543	#126	—	271	1	no	—
544	#126	—	271	1	no	—
545	#126	—	271	1	no	—
546	#126	—	271	1	no	—
547	#126	—	271	1	no	—
548	#126	—	271	1	no	—
549	#126	—	271	1	no	—
550	#126	—	271	1	no	—
551	#126	C₂×D₂₇₁	1	1	yes	characteristic, complemented
552	#126	C₂×D₂₇₁	1	1	yes	characteristic, complemented
553	#125	—	271	1	no	—
554	#125	—	271	1	no	—
555	#125	—	271	1	no	—
556	#125	—	271	1	no	—
557	#125	—	271	1	no	—
558	#125	C₂×D₂₇₁	1	1	yes	characteristic, complemented
559	#125	C₂×D₂₇₁	1	1	yes	characteristic, complemented
560	#124	—	271	1	no	—
561	#124	—	271	1	no	—
562	#124	—	271	1	no	—
563	#124	—	271	1	no	—
564	#124	—	271	1	no	—
565	#124	—	271	1	no	—
566	#124	—	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	—	271	1	no	—
576	#123	—	271	1	no	—
577	#123	—	271	1	no	—
578	#123	—	271	1	no	—
579	#123	—	271	1	no	—
580	#123	—	271	1	no	—
581	#123	C₂×D₂₇₁	1	1	yes	characteristic
582	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
583	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
584	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
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	—	271	1	no	—
592	C₂²⋊Q₈	—	271	1	no	—
593	C₂²⋊Q₈	—	271	1	no	—
594	C₂²⋊Q₈	—	271	1	no	—
595	C₂²⋊Q₈	—	271	1	no	—
596	C₂²⋊Q₈	—	271	1	no	—
597	C₂²⋊Q₈	—	271	1	no	—
598	C₂²⋊Q₈	—	271	1	no	—
599	C₂²⋊Q₈	—	271	1	no	—
600	C₂²⋊Q₈	—	271	1	no	—
601	C₂²⋊Q₈	—	271	1	no	—
602	C₂²⋊Q₈	—	271	1	no	—
603	C₂²⋊Q₈	—	271	1	no	—
604	C₂²⋊Q₈	—	271	1	no	—
605	C₂²⋊Q₈	—	271	1	no	—
606	C₂²⋊Q₈	—	271	1	no	—
607	C₂²⋊Q₈	—	271	1	no	—
608	C₂²⋊Q₈	—	271	1	no	—
609	C₂²⋊Q₈	—	271	1	no	—
610	C₂²⋊Q₈	—	271	1	no	—
611	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
612	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
613	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
614	#121	—	271	1	no	—
615	#121	—	271	1	no	—
616	#121	—	271	1	no	—
617	#121	—	271	1	no	—
618	#121	—	271	1	no	—
619	#121	—	271	1	no	—
620	#121	—	271	1	no	—
621	#121	—	271	1	no	—
622	#121	C₂×D₂₇₁	1	1	yes	characteristic
623	#120	—	271	1	no	—
624	#120	—	271	1	no	—
625	#120	—	271	1	no	—
626	#120	—	271	1	no	—
627	C₄×Q₈	—	271	1	no	—
628	C₄×Q₈	—	271	1	no	—
629	C₄×Q₈	—	271	1	no	—
630	C₄×Q₈	—	271	1	no	—
631	C₄×Q₈	—	271	1	no	—
632	C₄×Q₈	—	271	1	no	—
633	C₄×Q₈	—	271	1	no	—
634	C₄×D₄	—	271	1	no	—
635	C₄×D₄	—	271	1	no	—
636	C₄×D₄	—	271	1	no	—
637	C₄×D₄	—	271	1	no	—
638	C₄×D₄	—	271	1	no	—
639	C₄×D₄	—	271	1	no	—
640	C₄×D₄	—	271	1	no	—
641	C₄×D₄	—	271	1	no	—
642	C₄×D₄	—	271	1	no	—
643	C₄×D₄	—	271	1	no	—
644	C₄×D₄	—	271	1	no	—
645	C₄×D₄	—	271	1	no	—
646	C₄×D₄	—	271	1	no	—
647	C₄×D₄	—	271	1	no	—
648	C₄×D₄	—	271	1	no	—
649	C₄×D₄	—	271	1	no	—
650	C₄×D₄	—	271	1	no	—
651	C₄×D₄	—	271	1	no	—
652	C₄×D₄	—	271	1	no	—
653	C₄×D₄	—	271	1	no	—
654	C₄×D₄	—	271	1	no	—
655	C₄×D₄	—	271	1	no	—
656	C₄×D₄	—	271	1	no	—
657	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic
658	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
659	#117	—	271	1	no	—
660	#117	—	271	1	no	—
661	#117	—	271	1	no	—
662	#117	—	271	1	no	—
663	#117	—	271	1	no	—
664	#117	—	271	1	no	—
665	#117	—	271	1	no	—
666	#117	—	271	1	no	—
667	#117	—	271	1	no	—
668	#117	—	271	1	no	—
669	C₂×C₄⋊C₄	—	271	1	no	—
670	C₂×C₄⋊C₄	—	271	1	no	—
671	C₂×C₄⋊C₄	—	271	1	no	—
672	C₂×C₄⋊C₄	—	271	1	no	—
673	C₂×C₄⋊C₄	—	271	1	no	—
674	C₂×C₄⋊C₄	—	271	1	no	—
675	C₂×C₄⋊C₄	—	271	1	no	—
676	C₂×C₄⋊C₄	—	271	1	no	—
677	C₂×C₄⋊C₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
678	C₂×C₂²⋊C₄	—	271	1	no	—
679	C₂×C₂²⋊C₄	—	271	1	no	—
680	C₂×C₂²⋊C₄	—	271	1	no	—
681	C₂×C₂²⋊C₄	—	271	1	no	—
682	C₂×C₂²⋊C₄	—	271	1	no	—
683	C₂×C₂²⋊C₄	—	271	1	no	—
684	C₂×C₄²	—	271	1	no	—
685	C₂⁴	—	271	1	no	—
686	C₂⁴	—	271	1	no	—
687	#41	—	542	4	no	—
688	#41	—	542	4	no	—
689	#41	—	1084	2	no	—
690	#41	—	1084	2	no	—
691	C₂×Q₈	—	271	1	no	—
692	C₂×Q₈	—	271	1	no	—
693	C₂×Q₈	—	271	1	no	—
694	C₂×Q₈	—	271	1	no	—
695	C₂×Q₈	—	271	1	no	—
696	C₂×Q₈	—	271	1	no	—
697	C₂×Q₈	—	271	1	no	—
698	C₂×Q₈	—	271	1	no	—
699	C₂×Q₈	—	1084	2	no	—
700	C₂×Q₈	—	1084	2	no	—
701	C₂×Q₈	C₂²×D₂₇₁	1	1	yes	characteristic
702	C₂×D₄	—	271	1	no	—
703	C₂×D₄	—	271	1	no	—
704	C₂×D₄	—	271	1	no	—
705	C₂×D₄	—	271	1	no	—
706	C₂×D₄	—	271	1	no	—
707	C₂×D₄	—	271	1	no	—
708	C₂×D₄	—	271	1	no	—
709	C₂×D₄	—	271	1	no	—
710	C₂×D₄	—	271	1	no	—
711	C₂×D₄	—	271	1	no	—
712	C₂×D₄	—	271	1	no	—
713	C₂×D₄	—	271	1	no	—
714	C₂×D₄	—	542	4	no	—
715	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
716	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
717	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
718	C₂²×C₄	—	271	1	no	—
719	C₂²×C₄	—	271	1	no	—
720	C₂²×C₄	—	271	1	no	—
721	C₂²×C₄	—	271	1	no	—
722	C₂²×C₄	—	271	1	no	—
723	C₂²×C₄	—	271	1	no	—
724	C₂²×C₄	—	271	1	no	—
725	C₂²×C₄	—	271	1	no	—
726	C₂²×C₄	—	271	1	no	—
727	C₂²×C₄	—	271	1	no	—
728	C₂²×C₄	—	271	1	no	—
729	C₂²×C₄	—	271	1	no	—
730	C₂²×C₄	—	271	1	no	—
731	C₂²×C₄	—	271	1	no	—
732	C₂²×C₄	—	271	1	no	—
733	C₂²×C₄	—	271	1	no	—
734	C₂²×C₄	—	271	1	no	—
735	C₂²×C₄	—	271	1	no	—
736	C₂²×C₄	—	271	1	no	—
737	C₂²×C₄	—	271	1	no	—
738	C₂²×C₄	—	271	1	no	—
739	C₂²×C₄	—	271	1	no	—
740	C₂²×C₄	—	1084	2	no	—
741	C₂²×C₄	—	1084	2	no	—
742	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
746	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
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	—	271	1	no	—
760	C₄⋊C₄	—	271	1	no	—
761	C₄⋊C₄	—	271	1	no	—
762	C₄⋊C₄	—	271	1	no	—
763	C₄⋊C₄	—	271	1	no	—
764	C₄⋊C₄	—	271	1	no	—
765	C₄⋊C₄	—	271	1	no	—
766	C₄⋊C₄	—	271	1	no	—
767	C₄⋊C₄	—	271	1	no	—
768	C₄⋊C₄	—	271	1	no	—
769	C₄⋊C₄	—	271	1	no	—
770	C₄⋊C₄	—	271	1	no	—
771	C₄⋊C₄	—	271	1	no	—
772	C₄⋊C₄	—	271	1	no	—
773	C₄⋊C₄	—	271	1	no	—
774	C₄⋊C₄	—	271	1	no	—
775	C₄⋊C₄	—	271	1	no	—
776	C₄⋊C₄	—	271	1	no	—
777	C₄⋊C₄	—	271	1	no	—
778	C₄⋊C₄	—	271	1	no	—
779	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
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	—	271	1	no	—
798	C₂²⋊C₄	—	271	1	no	—
799	C₂²⋊C₄	—	271	1	no	—
800	C₂²⋊C₄	—	271	1	no	—
801	C₂²⋊C₄	—	271	1	no	—
802	C₂²⋊C₄	—	271	1	no	—
803	C₂²⋊C₄	—	271	1	no	—
804	C₂²⋊C₄	—	271	1	no	—
805	C₂²⋊C₄	—	271	1	no	—
806	C₂²⋊C₄	—	271	1	no	—
807	C₂²⋊C₄	—	271	1	no	—
808	C₂²⋊C₄	—	271	1	no	—
809	C₂²⋊C₄	—	271	1	no	—
810	C₂²⋊C₄	—	271	1	no	—
811	C₂²⋊C₄	—	271	1	no	—
812	C₂²⋊C₄	—	271	1	no	—
813	C₂²⋊C₄	—	271	1	no	—
814	C₂²⋊C₄	—	271	1	no	—
815	C₂²⋊C₄	—	271	1	no	—
816	C₂²⋊C₄	—	271	1	no	—
817	C₂²⋊C₄	—	271	1	no	—
818	C₂²⋊C₄	—	271	1	no	—
819	C₂²⋊C₄	—	271	1	no	—
820	C₂²⋊C₄	—	271	1	no	—
821	C₂²⋊C₄	—	271	1	no	—
822	C₂²⋊C₄	—	271	1	no	—
823	C₂²⋊C₄	—	271	1	no	—
824	C₂²⋊C₄	—	271	1	no	—
825	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
835	C₄²	—	271	1	no	—
836	C₄²	—	271	1	no	—
837	C₄²	—	271	1	no	—
838	C₄²	—	271	1	no	—
839	C₄²	—	271	1	no	—
840	C₄²	—	271	1	no	—
841	C₄²	—	271	1	no	—
842	C₄²	—	271	1	no	—
843	C₄²	—	271	1	no	—
844	C₄²	—	271	1	no	—
845	C₄²	—	271	1	no	—
846	C₄²	—	271	1	no	—
847	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
848	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
849	C₂³	—	271	1	no	—
850	C₂³	—	271	1	no	—
851	C₂³	—	271	1	no	—
852	C₂³	—	271	1	no	—
853	C₂³	—	542	2	no	—
854	C₂³	—	542	2	no	—
855	C₂³	—	542	2	no	—
856	C₂³	—	542	2	no	—
857	C₂³	—	1084	1	no	—
858	C₂³	—	1084	1	no	—
859	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
860	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
861	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
862	Q₈	—	4	1	no	—
863	Q₈	—	542	2	no	—
864	Q₈	—	542	2	no	—
865	Q₈	—	542	2	no	—
866	Q₈	—	542	2	no	—
867	Q₈	—	542	2	no	—
868	Q₈	—	1084	1	no	—
869	Q₈	—	1084	1	no	—
870	Q₈	—	1084	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	4	1	no	—
874	D₄	—	271	4	no	—
875	D₄	—	542	2	no	—
876	D₄	—	542	2	no	—
877	D₄	—	542	2	no	—
878	D₄	—	542	2	no	—
879	D₄	—	542	2	no	—
880	D₄	—	542	2	no	—
881	D₄	—	542	2	no	—
882	D₄	—	542	2	no	—
883	D₄	—	1084	1	no	—
884	D₄	—	1084	1	no	—
885	D₄	—	1084	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	271	1	no	—
892	C₂×C₄	—	271	1	no	—
893	C₂×C₄	—	271	1	no	—
894	C₂×C₄	—	271	1	no	—
895	C₂×C₄	—	271	1	no	—
896	C₂×C₄	—	271	1	no	—
897	C₂×C₄	—	271	1	no	—
898	C₂×C₄	—	271	1	no	—
899	C₂×C₄	—	271	1	no	—
900	C₂×C₄	—	271	1	no	—
901	C₂×C₄	—	271	1	no	—
902	C₂×C₄	—	271	1	no	—
903	C₂×C₄	—	542	2	no	—
904	C₂×C₄	—	542	2	no	—
905	C₂×C₄	—	542	2	no	—
906	C₂×C₄	—	542	2	no	—
907	C₂×C₄	—	542	2	no	—
908	C₂×C₄	—	542	2	no	—
909	C₂×C₄	—	542	2	no	—
910	C₂×C₄	—	542	2	no	—
911	C₂×C₄	—	542	2	no	—
912	C₂×C₄	—	542	2	no	—
913	C₂×C₄	—	542	2	no	—
914	C₂×C₄	—	542	2	no	—
915	C₂×C₄	—	1084	1	no	—
916	C₂×C₄	—	1084	1	no	—
917	C₂×C₄	—	1084	1	no	—
918	C₂×C₄	—	1084	1	no	—
919	C₂×C₄	—	1084	1	no	—
920	C₂×C₄	—	1084	1	no	—
921	C₂×C₄	—	1084	1	no	—
922	C₂×C₄	—	1084	1	no	—
923	C₂×C₄	—	1084	1	no	—
924	C₂×C₄	—	1084	1	no	—
925	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
926	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
936	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	271	2	no	—
946	C₂²	—	271	2	no	—
947	C₂²	—	542	1	no	—
948	C₂²	—	542	1	no	—
949	C₂²	—	542	1	no	—
950	C₂²	—	542	1	no	—
951	C₂²	—	542	1	no	—
952	C₂²	—	542	1	no	—
953	C₂²	—	542	1	no	—
954	C₂²	—	542	1	no	—
955	C₂²	—	542	1	no	—
956	C₂²	—	542	1	no	—
957	C₂²	—	1084	4	no	—
958	C₂²	—	1084	4	no	—
959	C₂²	#41×D₂₇₁	1	2	yes	—
960	C₂²	C₂⁴×D₂₇₁	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	271	2	no	—
974	C₄	—	271	2	no	—
975	C₄	—	542	1	no	—
976	C₄	—	542	1	no	—
977	C₄	—	542	1	no	—
978	C₄	—	542	1	no	—
979	C₄	—	542	1	no	—
980	C₄	—	542	1	no	—
981	C₄	—	542	1	no	—
982	C₄	—	542	1	no	—
983	C₄	—	542	1	no	—
984	C₄	—	542	1	no	—
985	C₂	—	2	2	no	—
986	C₂	—	4	1	no	—
987	C₂	—	4	1	no	—
988	C₂	—	542	2	no	—
989	C₂	—	542	2	no	—
990	C₂	—	1084	1	no	—
991	C₂	—	1084	1	no	—
992	C₂	C₂×#41×D₂₇₁	1	1	yes	characteristic
993	C₂	H(5,𝔽₂)×D₂₇₁	1	1	yes	characteristic
994	C₂	2₋¹⁺⁴×D₂₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₇₁
commutator, socle, cosocle	C₂²×C₂₇₁	C₂⁵
Fitting	#539×C₂₇₁	C₂
hypercenter	#539	D₂₇₁
hypocenter	C₂₇₁	#3520
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #31774614	C₂	semidirect
2. #31774603	C₂	semidirect
3. #31774601	C₂	semidirect
4. #31774584	C₂	semidirect
5. #31774579	C₂	semidirect
6. #31774575	C₂	semidirect
7. #31774574	C₂	semidirect
8. #31774572	C₂	semidirect
9. #31774570	C₂	semidirect
10. #31774560	C₂	semidirect
11. #31774557	C₂	semidirect
12. #31774553	C₂	semidirect
13. #31774545	C₂	semidirect
14. #31774545	C₂	semidirect
15. #31774539	C₂	semidirect
16. #31774536	C₂	semidirect
17. #31774517	C₂	semidirect
18. #31774515	C₂	semidirect
19. #31774495	C₂	semidirect
20. #31774489	C₂	semidirect
21. #31774488	C₂	semidirect
22. #31774453	C₂	semidirect
23. #31774430	C₂	semidirect
24. #31774406	C₂	semidirect
25. #31774405	C₂	semidirect
26. C₂×#22576138	C₂	semidirect
27. C₂²⋊Q₈×D₂₇₁	C₂	semidirect
28. #31774378	C₂	semidirect
29. #31774376	C₂	semidirect
30. C₄×D₄×D₂₇₁	C₂	semidirect
31. #539×C₂₇₁	C₂	semidirect
33. C₂×#16864654	C₂²	semidirect
35. C₂×#16864653	C₂²	semidirect
36. C₂²×Dic₅₄₂	C₂²	semidirect
37. C₂×Q₈×D₂₇₁	C₂²	semidirect
41. #22576159	C₂²	semidirect
42. #22576159	C₂²	semidirect
43. #22576159	C₂²	semidirect
44. #22576158	C₂²	semidirect
45. #22576155	C₂²	semidirect
46. #22576155	C₂²	semidirect
47. #22576155	C₂²	semidirect
48. #22576155	C₂²	semidirect
49. #22576154	C₂²	semidirect
50. #22576153	C₂²	semidirect
51. #22576153	C₂²	semidirect
52. #22576153	C₂²	semidirect
53. #22576152	C₂²	semidirect
54. #22576151	C₂²	semidirect
55. #22576150	C₂²	semidirect
56. #22576150	C₂²	semidirect
57. #22576150	C₂²	semidirect
58. #22576149	C₂²	semidirect
59. #22576147	C₂²	semidirect
62. #22576146	C₂²	semidirect
63. #22576146	C₂²	semidirect
64. #22576146	C₂²	semidirect
68. #22576145	C₂²	semidirect
69. #22576145	C₂²	semidirect
70. #22576145	C₂²	semidirect
71. #22576144	C₂²	semidirect
72. #22576144	C₂²	semidirect
73. #22576143	C₂²	semidirect
75. #22576142	C₂²	semidirect
76. #22576142	C₂²	semidirect
77. #22576142	C₂²	semidirect
80. #22576140	C₂²	semidirect
81. #22576140	C₂²	semidirect
82. #22576139	C₂²	semidirect
90. #22576138	C₂²	semidirect
91. #22576138	C₂²	semidirect
92. #22576138	C₂²	semidirect
93. #22576138	C₂²	semidirect
94. #22576138	C₂²	semidirect
95. #22576138	C₂²	semidirect
96. #22576138	C₂²	semidirect
97. #22576138	C₂²	semidirect
98. #22576137	C₂²	semidirect
99. #22576137	C₂²	semidirect
100. #22576137	C₂²	semidirect
101. #22576137	C₂²	semidirect
102. #22576137	C₂²	semidirect
103. #22576137	C₂²	semidirect
109. #22576133	C₂²	semidirect
112. #22576132	C₂²	semidirect
117. C₄×Dic₅₄₂	C₂²	semidirect
118. #22576125	C₂²	semidirect
119. #22576125	C₂²	semidirect
120. #22576125	C₂²	semidirect
121. #22576125	C₂²	semidirect
122. #22576125	C₂²	semidirect
123. #22576125	C₂²	semidirect
127. D₄×Dic₂₇₁	C₂²	semidirect
131. #22576122	C₂²	semidirect
132. #22576122	C₂²	semidirect
137. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
138. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
139. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
145. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
146. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
147. #22576119	C₂²	semidirect
150. #22576118	C₂²	semidirect
151. #22576118	C₂²	semidirect
152. #22576117	C₂²	semidirect
153. #22576117	C₂²	semidirect
154. #22576116	C₂²	semidirect
155. #22576116	C₂²	semidirect
156. #22576116	C₂²	semidirect
157. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
158. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
159. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
161. C₄⋊C₄×D₂₇₁	C₂²	semidirect
162. C₄⋊C₄×D₂₇₁	C₂²	semidirect
163. C₄⋊C₄×D₂₇₁	C₂²	semidirect
164. C₄⋊C₄×D₂₇₁	C₂²	semidirect
172. #126×C₂₇₁	C₂²	semidirect
173. #126×C₂₇₁	C₂²	semidirect
174. #125×C₂₇₁	C₂²	semidirect
175. #125×C₂₇₁	C₂²	semidirect
177. #123×C₂₇₁	C₂²	semidirect
178. #123×C₂₇₁	C₂²	semidirect
179. #123×C₂₇₁	C₂²	semidirect
180. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
181. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
182. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
185. C₄×D₄×C₂₇₁	C₂²	semidirect
186. C₂×C₄⋊C₄×C₂₇₁	C₂²	semidirect
380. C₂²⋊D₂₇₁	#41	semidirect
497. C₂₇₁	#3520	semidirect
520. #539	D₂₇₁	semidirect
551. #126	C₂×D₂₇₁	semidirect
552. #126	C₂×D₂₇₁	semidirect
558. #125	C₂×D₂₇₁	semidirect
559. #125	C₂×D₂₇₁	semidirect
582. #123	C₂×D₂₇₁	semidirect
583. #123	C₂×D₂₇₁	semidirect
584. #123	C₂×D₂₇₁	semidirect
611. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
612. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
613. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
658. C₄×D₄	C₂×D₂₇₁	semidirect
677. C₂×C₄⋊C₄	C₂×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
#31774614	2
#31774603	2
#31774601	2
#31774584	2
#31774579	2
#31774575	2
#31774574	2
#31774572	2
#31774570	2
#31774560	2
#31774557	2
#31774553	2
#31774545	2
#31774539	2
#31774536	2
#31774517	2
#31774515	2
#31774495	2
#31774489	2
#31774488	2
#31774453	2
#31774430	2
#31774406	2
#31774405	2
C₂×#22576138	2
C₂²⋊Q₈×D₂₇₁	2
#31774378	2
#31774376	2
C₄×D₄×D₂₇₁	2
#539×C₂₇₁	2
#3520	271