Subgroups — #46850385

Order 34688.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774609	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774601	C₂	1	1	yes	maximal, characteristic, complemented
3	#31774596	C₂	1	1	yes	maximal, characteristic, complemented
4	#31774596	C₂	1	1	yes	maximal, characteristic, complemented
5	#31774592	C₂	1	1	yes	maximal, characteristic, complemented
6	#31774590	C₂	1	1	yes	maximal, characteristic, complemented
7	#31774565	C₂	1	1	yes	maximal, characteristic, complemented
8	#31774539	C₂	1	1	yes	maximal, characteristic, complemented
9	#31774537	C₂	1	1	yes	maximal, characteristic, complemented
10	#31774537	C₂	1	1	yes	maximal, characteristic, complemented
11	#31774536	C₂	1	1	yes	maximal, characteristic, complemented
12	#31774535	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₂²⋊D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#31774529	C₂	1	1	yes	maximal, characteristic, complemented
15	#31774529	C₂	1	1	yes	maximal, characteristic, complemented
16	#31774499	C₂	1	1	yes	maximal, characteristic, complemented
17	#31774497	C₂	1	1	yes	maximal, characteristic, complemented
18	#31774487	C₂	1	1	yes	maximal, characteristic, complemented
19	#31774482	C₂	1	1	yes	maximal, characteristic, complemented
20	#31774481	C₂	1	1	yes	maximal, characteristic, complemented
21	#31774479	C₂	1	1	yes	maximal, characteristic, complemented
22	#31774443	C₂	1	1	yes	maximal, characteristic, complemented
23	#31774424	C₂	1	1	yes	maximal, characteristic, complemented
24	#31774406	C₂	1	1	yes	maximal, characteristic, complemented
25	#31774403	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#22576132	C₂	1	1	yes	maximal, characteristic, complemented
27	#121×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
28	#31774370	C₂	1	1	yes	maximal, characteristic, complemented
29	#31774369	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×(C₂²⋊D₂₇₁)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
31	#546×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864654	C₂²	1	1	yes	characteristic, complemented
33	C₂×#16864654	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864653	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic
40	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
43	C₂³×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
45	#22576158	C₂²	1	1	yes	characteristic, complemented
46	#22576156	C₂²	1	1	yes	characteristic, complemented
47	#22576156	C₂²	1	1	yes	characteristic, complemented
48	#22576156	C₂²	1	1	yes	characteristic, complemented
49	#22576155	C₂²	1	1	yes	characteristic, complemented
50	#22576155	C₂²	1	1	yes	characteristic, complemented
51	#22576154	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	#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	#22576149	C₂²	1	1	yes	characteristic, complemented
60	#22576147	C₂²	1	1	yes	characteristic, complemented
61	#22576146	C₂²	1	1	yes	characteristic, complemented
62	#22576146	C₂²	1	1	yes	characteristic, complemented
63	#22576146	C₂²	1	1	yes	characteristic, complemented
64	#22576145	C₂²	1	1	yes	characteristic, complemented
65	#22576145	C₂²	1	1	yes	characteristic, complemented
66	#22576145	C₂²	1	1	yes	characteristic, complemented
67	#22576144	C₂²	1	1	yes	characteristic, complemented
68	#22576143	C₂²	1	1	yes	characteristic, complemented
69	#22576143	C₂²	1	1	yes	characteristic, complemented
70	#22576143	C₂²	1	1	yes	characteristic, complemented
71	#22576142	C₂²	1	1	yes	characteristic, complemented
72	#22576142	C₂²	1	1	yes	characteristic, complemented
73	#22576142	C₂²	1	1	yes	characteristic, complemented
74	#22576141	C₂²	1	1	yes	characteristic, complemented
75	#22576141	C₂²	1	1	yes	characteristic, complemented
76	#22576138	C₂²	1	1	yes	characteristic, complemented
77	#22576138	C₂²	1	1	yes	characteristic, complemented
78	#22576137	C₂²	1	1	yes	characteristic, complemented
79	#22576137	C₂²	1	1	yes	characteristic, complemented
80	#22576137	C₂²	1	1	yes	characteristic, complemented
81	#22576136	C₂²	1	1	yes	characteristic, complemented
82	#22576135	C₂²	1	1	yes	characteristic, complemented
83	#22576135	C₂²	1	1	yes	characteristic, complemented
84	#22576134	C₂²	1	1	yes	characteristic, complemented
85	#22576134	C₂²	1	1	yes	characteristic, complemented
86	#22576134	C₂²	1	1	yes	characteristic, complemented
87	#22576133	C₂²	1	1	yes	characteristic, complemented
88	#22576133	C₂²	1	1	yes	characteristic, complemented
89	#22576133	C₂²	1	1	yes	characteristic, complemented
90	#22576133	C₂²	1	1	yes	characteristic, complemented
91	#22576133	C₂²	1	1	yes	characteristic, complemented
92	#22576133	C₂²	1	1	yes	characteristic, complemented
93	#22576133	C₂²	1	1	yes	characteristic, complemented
94	#22576133	C₂²	1	1	yes	characteristic, complemented
95	#22576133	C₂²	1	1	yes	characteristic, complemented
96	#22576132	C₂²	1	1	yes	characteristic
97	#22576132	C₂²	1	1	yes	characteristic, complemented
98	#22576132	C₂²	1	1	yes	characteristic, complemented
99	#22576132	C₂²	1	1	yes	characteristic, complemented
100	#22576132	C₂²	1	1	yes	characteristic, complemented
101	#22576132	C₂²	1	1	yes	characteristic, complemented
102	#22576132	C₂²	1	1	yes	characteristic, complemented
103	#22576132	C₂²	1	1	yes	characteristic, complemented
104	#22576132	C₂²	1	1	yes	characteristic, complemented
105	#22576132	C₂²	1	1	yes	characteristic, complemented
106	#22576132	C₂²	1	1	yes	characteristic, complemented
107	#22576132	C₂²	1	1	yes	characteristic, complemented
108	#22576132	C₂²	1	1	yes	characteristic, complemented
109	#22576132	C₂²	1	1	yes	characteristic, complemented
110	#22576132	C₂²	1	1	yes	characteristic, complemented
111	#22576132	C₂²	1	1	yes	characteristic, complemented
112	#22576131	C₂²	1	1	yes	characteristic, complemented
113	#22576131	C₂²	1	1	yes	characteristic, complemented
114	#22576130	C₂²	1	1	yes	characteristic, complemented
115	#22576130	C₂²	1	1	yes	characteristic, complemented
116	#22576130	C₂²	1	1	yes	characteristic, complemented
117	#22576130	C₂²	1	1	yes	characteristic, complemented
118	#22576129	C₂²	1	1	yes	characteristic, complemented
119	#22576129	C₂²	1	1	yes	characteristic, complemented
120	#22576128	C₂²	1	1	yes	characteristic, complemented
121	#22576128	C₂²	1	1	yes	characteristic, complemented
122	#22576128	C₂²	1	1	yes	characteristic, complemented
123	#22576128	C₂²	1	1	yes	characteristic, complemented
124	#22576125	C₂²	1	1	yes	characteristic, complemented
125	C₄×D₁₀₈₄	C₂²	1	1	yes	characteristic, complemented
126	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
127	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
128	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
129	#22576122	C₂²	1	1	yes	characteristic, complemented
130	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
131	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
135	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
137	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic, complemented
139	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
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, complemented
143	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
144	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
145	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
148	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	#22576118	C₂²	1	1	yes	characteristic, complemented
155	#22576117	C₂²	1	1	yes	characteristic, complemented
156	#22576117	C₂²	1	1	yes	characteristic, complemented
157	#22576116	C₂²	1	1	yes	characteristic, complemented
158	#22576116	C₂²	1	1	yes	characteristic, complemented
159	#22576116	C₂²	1	1	yes	characteristic, complemented
160	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	C₂×Dic₂₇₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
164	C₂×(C₂×D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂×(C₂×D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
171	C₂×C₄×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
173	C₂²×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
174	#124×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
175	#123×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
176	#123×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
177	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
178	#121×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
179	#121×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
180	#121×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
181	#120×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
182	#120×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊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	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
190	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
191	#16864654	—	4	2	no	—
192	#16864654	—	4	2	no	—
193	#16864653	—	4	2	no	—
194	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
195	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
196	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
197	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
198	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
199	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
200	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
201	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₇₁	—	2	4	no	—
203	C₂×C₂²⋊D₂₇₁	—	2	4	no	—
204	C₂×C₂²⋊D₂₇₁	—	4	2	no	—
205	C₂×C₂²⋊D₂₇₁	—	4	2	no	—
206	C₂×C₂²⋊D₂₇₁	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	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
228	D₄×D₂₇₁	—	2	4	no	—
229	D₄×D₂₇₁	—	4	2	no	—
230	D₄×D₂₇₁	—	4	2	no	—
231	D₄×D₂₇₁	—	4	2	no	—
232	C₂²×Dic₂₇₁	—	4	2	no	—
233	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
234	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
235	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
236	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
237	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
238	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
239	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
240	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
241	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
242	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₂₇₁	—	4	2	no	—
244	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
255	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
256	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
257	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
258	C₄⋊Dic₂₇₁	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	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
273	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
274	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
275	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
276	Dic₂₇₁⋊C₄	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	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₂₇₁	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	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₂₇₁)⋊C₄	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	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
317	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
318	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
319	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
320	C₂⁴×C₂₇₁	C₂³	1	1	yes	characteristic
321	C₂⁴×C₂₇₁	C₂³	1	1	yes	characteristic
322	#41×C₂₇₁	—	4	2	no	—
323	C₂×Q₈×C₂₇₁	C₂³	1	1	yes	characteristic
324	C₂×D₄×C₂₇₁	—	4	2	no	—
325	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
326	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
327	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
328	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
329	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
330	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
331	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
332	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
333	C₂×D₄×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	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
341	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
342	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
343	C₄⋊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	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
351	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
352	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
353	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
354	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
355	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
356	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
357	C₂²×D₂₇₁	—	2	2	no	—
358	C₂²×D₂₇₁	—	2	2	no	—
359	C₂²×D₂₇₁	—	2	2	no	—
360	C₂²×D₂₇₁	—	2	2	no	—
361	C₂²×D₂₇₁	—	2	2	no	—
362	C₂²×D₂₇₁	—	4	1	no	—
363	C₂²×D₂₇₁	—	4	1	no	—
364	C₂²×D₂₇₁	—	4	1	no	—
365	C₂²×D₂₇₁	—	4	1	no	—
366	C₂²×D₂₇₁	—	4	1	no	—
367	C₂²×D₂₇₁	—	4	1	no	—
368	C₂²×D₂₇₁	—	4	1	no	—
369	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
370	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
371	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
372	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
373	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
374	Dic₅₄₂	—	2	2	no	—
375	Dic₅₄₂	—	4	1	no	—
376	D₁₀₈₄	—	2	2	no	—
377	D₁₀₈₄	—	4	1	no	—
378	D₁₀₈₄	—	4	1	no	—
379	D₁₀₈₄	—	4	1	no	—
380	D₁₀₈₄	—	4	1	no	—
381	D₁₀₈₄	—	4	1	no	—
382	C₂²⋊D₂₇₁	—	2	2	no	—
383	C₂²⋊D₂₇₁	—	2	2	no	—
384	C₂²⋊D₂₇₁	—	2	2	no	—
385	C₂²⋊D₂₇₁	—	2	2	no	—
386	C₂²⋊D₂₇₁	—	2	2	no	—
387	C₂²⋊D₂₇₁	—	2	2	no	—
388	C₂²⋊D₂₇₁	—	2	2	no	—
389	C₂²⋊D₂₇₁	—	2	2	no	—
390	C₂²⋊D₂₇₁	—	2	2	no	—
391	C₂²⋊D₂₇₁	—	2	2	no	—
392	C₂²⋊D₂₇₁	—	2	2	no	—
393	C₂²⋊D₂₇₁	—	2	2	no	—
394	C₂²⋊D₂₇₁	—	2	2	no	—
395	C₂²⋊D₂₇₁	—	4	1	no	—
396	C₂²⋊D₂₇₁	—	4	1	no	—
397	C₂²⋊D₂₇₁	—	4	1	no	—
398	C₂²⋊D₂₇₁	—	4	1	no	—
399	C₂²⋊D₂₇₁	—	4	1	no	—
400	C₂²⋊D₂₇₁	—	4	1	no	—
401	C₂²⋊D₂₇₁	—	4	1	no	—
402	C₂²⋊D₂₇₁	—	4	1	no	—
403	C₂²⋊D₂₇₁	#41	1	4	yes	complemented
404	C₂×Dic₂₇₁	—	2	2	no	—
405	C₂×Dic₂₇₁	—	2	2	no	—
406	C₂×Dic₂₇₁	—	2	2	no	—
407	C₂×Dic₂₇₁	—	2	2	no	—
408	C₂×Dic₂₇₁	—	2	2	no	—
409	C₂×Dic₂₇₁	—	4	1	no	—
410	C₂×Dic₂₇₁	—	4	1	no	—
411	C₂×Dic₂₇₁	—	4	1	no	—
412	C₂×Dic₂₇₁	—	4	1	no	—
413	C₂×Dic₂₇₁	—	4	1	no	—
414	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
425	C₄×D₂₇₁	—	2	2	no	—
426	C₄×D₂₇₁	—	2	2	no	—
427	C₄×D₂₇₁	—	2	2	no	—
428	C₄×D₂₇₁	—	4	1	no	—
429	C₄×D₂₇₁	—	4	1	no	—
430	C₄×D₂₇₁	—	4	1	no	—
431	C₄×D₂₇₁	—	4	1	no	—
432	C₄×D₂₇₁	—	4	1	no	—
433	C₄×D₂₇₁	—	4	1	no	—
434	C₄×D₂₇₁	—	4	1	no	—
435	C₄×D₂₇₁	—	4	1	no	—
436	C₂³×C₂₇₁	—	2	2	no	—
437	C₂³×C₂₇₁	—	2	2	no	—
438	C₂³×C₂₇₁	—	2	2	no	—
439	C₂³×C₂₇₁	—	4	1	no	—
440	C₂³×C₂₇₁	—	4	1	no	—
441	C₂³×C₂₇₁	—	4	1	no	—
442	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
443	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
444	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
445	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
446	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
447	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
448	Q₈×C₂₇₁	—	4	1	no	—
449	D₄×C₂₇₁	—	2	2	no	—
450	D₄×C₂₇₁	—	2	2	no	—
451	D₄×C₂₇₁	—	2	2	no	—
452	D₄×C₂₇₁	—	2	2	no	—
453	D₄×C₂₇₁	—	4	1	no	—
454	D₄×C₂₇₁	—	4	1	no	—
455	D₄×C₂₇₁	—	4	1	no	—
456	D₄×C₂₇₁	—	4	1	no	—
457	D₄×C₂₇₁	—	4	1	no	—
458	C₂×C₄×C₂₇₁	—	2	2	no	—
459	C₂×C₄×C₂₇₁	—	4	1	no	—
460	C₂×C₄×C₂₇₁	—	4	1	no	—
461	C₂×C₄×C₂₇₁	—	4	1	no	—
462	C₂×C₄×C₂₇₁	—	4	1	no	—
463	C₂×C₄×C₂₇₁	—	4	1	no	—
464	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
465	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
466	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
467	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
468	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
469	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
470	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
471	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
472	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
473	C₂²×C₂₇₁	—	2	1	no	—
474	C₂²×C₂₇₁	—	2	1	no	—
475	C₂²×C₂₇₁	—	2	1	no	—
476	C₂²×C₂₇₁	—	2	1	no	—
477	C₂²×C₂₇₁	—	2	1	no	—
478	C₂²×C₂₇₁	—	2	1	no	—
479	C₂²×C₂₇₁	—	2	1	no	—
480	C₂²×C₂₇₁	—	2	1	no	—
481	C₂²×C₂₇₁	—	2	1	no	—
482	C₂²×C₂₇₁	—	2	1	no	—
483	C₂²×C₂₇₁	—	2	1	no	—
484	C₂²×C₂₇₁	—	2	1	no	—
485	C₂²×C₂₇₁	—	2	1	no	—
486	C₂²×C₂₇₁	—	2	1	no	—
487	C₂²×C₂₇₁	—	2	1	no	—
488	C₂²×C₂₇₁	—	2	1	no	—
489	C₂²×C₂₇₁	—	4	4	no	—
490	C₂²×C₂₇₁	—	8	2	no	—
491	C₂²×C₂₇₁	C₂×#41	1	2	yes	—
492	C₂²×C₂₇₁	H(5,𝔽₂)	1	2	yes	—
493	C₂²×C₂₇₁	C₂⁵	1	1	yes	characteristic
494	C₂×D₂₇₁	—	2	1	no	—
495	C₂×D₂₇₁	—	2	1	no	—
496	C₂×D₂₇₁	—	2	1	no	—
497	C₂×D₂₇₁	—	2	1	no	—
498	C₂×D₂₇₁	—	2	1	no	—
499	C₂×D₂₇₁	—	2	1	no	—
500	C₂×D₂₇₁	—	2	1	no	—
501	C₂×D₂₇₁	—	2	1	no	—
502	C₂×D₂₇₁	—	2	1	no	—
503	C₂×D₂₇₁	—	2	1	no	—
504	C₂×D₂₇₁	—	2	1	no	—
505	C₂×D₂₇₁	—	2	1	no	—
506	C₂×D₂₇₁	—	2	1	no	—
507	C₂×D₂₇₁	—	2	1	no	—
508	C₂×D₂₇₁	—	4	4	no	—
509	C₂×D₂₇₁	—	8	2	no	—
510	C₂×D₂₇₁	—	8	2	no	—
511	C₂×D₂₇₁	—	8	2	no	—
512	C₂×D₂₇₁	C₂×#41	1	2	yes	—
513	C₄×C₂₇₁	—	2	1	no	—
514	C₄×C₂₇₁	—	2	1	no	—
515	C₄×C₂₇₁	—	2	1	no	—
516	C₄×C₂₇₁	—	2	1	no	—
517	C₄×C₂₇₁	—	2	1	no	—
518	C₄×C₂₇₁	—	2	1	no	—
519	C₄×C₂₇₁	—	2	1	no	—
520	C₄×C₂₇₁	—	2	1	no	—
521	C₄×C₂₇₁	—	2	1	no	—
522	Dic₂₇₁	—	2	1	no	—
523	Dic₂₇₁	—	2	1	no	—
524	Dic₂₇₁	—	2	1	no	—
525	Dic₂₇₁	—	2	1	no	—
526	Dic₂₇₁	—	2	1	no	—
527	Dic₂₇₁	—	2	1	no	—
528	Dic₂₇₁	—	2	1	no	—
529	Dic₂₇₁	—	2	1	no	—
530	Dic₂₇₁	—	2	1	no	—
531	Dic₂₇₁	C₂×#41	1	2	yes	—
532	Dic₂₇₁	H(5,𝔽₂)	1	2	yes	—
533	C₂×C₂₇₁	—	2	2	no	—
534	C₂×C₂₇₁	—	2	2	no	—
535	C₂×C₂₇₁	—	4	1	no	—
536	C₂×C₂₇₁	—	4	1	no	—
537	C₂×C₂₇₁	—	4	1	no	—
538	C₂×C₂₇₁	—	4	1	no	—
539	C₂×C₂₇₁	C₂²×#41	1	1	yes	characteristic
540	C₂×C₂₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂×C₂₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
542	D₂₇₁	—	2	2	no	—
543	D₂₇₁	—	4	1	no	—
544	D₂₇₁	—	4	1	no	—
545	D₂₇₁	—	4	1	no	—
546	D₂₇₁	—	4	1	no	—
547	C₂₇₁	#3519	1	1	yes	characteristic, complemented, Sylow
548	#3519	—	271	1	no	maximal, Sylow
549	#555	—	271	1	no	—
550	#554	—	271	1	no	—
551	#553	—	271	1	no	—
552	#553	—	271	1	no	—
553	#553	—	271	1	no	—
554	#553	—	271	1	no	—
555	#550	—	271	1	no	—
556	#546	—	271	1	no	—
557	#546	—	271	1	no	—
558	#546	—	271	1	no	—
559	#546	—	271	1	no	—
560	#546	—	271	1	no	—
561	#546	D₂₇₁	1	1	yes	characteristic, complemented
562	D₄²	—	271	1	no	—
563	D₄²	—	271	1	no	—
564	D₄²	—	271	1	no	—
565	#540	—	271	1	no	—
566	#540	—	271	1	no	—
567	#538	—	271	1	no	—
568	#538	—	271	1	no	—
569	#538	—	271	1	no	—
570	#538	—	271	1	no	—
571	#532	—	271	1	no	—
572	#529	—	271	1	no	—
573	#525	—	271	1	no	—
574	#525	—	271	1	no	—
575	C₂×#121	—	271	1	no	—
576	C₂×#121	—	271	1	no	—
577	#518	—	271	1	no	—
578	#518	—	271	1	no	—
579	C₂×C₄×D₄	—	271	1	no	—
580	C₂×#41	—	271	1	no	—
581	C₂×#41	—	271	1	no	—
582	C₂×#41	—	271	1	no	—
583	C₂×#41	C₂×D₂₇₁	1	1	yes	characteristic, complemented
584	C₂²×D₄	—	271	1	no	—
585	C₂²×D₄	—	271	1	no	—
586	C₂²×D₄	—	271	1	no	—
587	C₂²×D₄	—	271	1	no	—
588	C₂²×D₄	—	271	1	no	—
589	C₂²×D₄	—	271	1	no	—
590	C₂²×D₄	—	271	1	no	—
591	C₂²×D₄	—	271	1	no	—
592	C₂²×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
593	C₂³×C₄	—	271	1	no	—
594	C₂³×C₄	—	271	1	no	—
595	C₄⋊Q₈	—	271	1	no	—
596	#127	—	271	1	no	—
597	#127	—	271	1	no	—
598	#127	—	271	1	no	—
599	#126	—	271	1	no	—
600	#126	—	271	1	no	—
601	#126	—	271	1	no	—
602	#126	—	271	1	no	—
603	#126	—	271	1	no	—
604	#126	—	271	1	no	—
605	#125	—	271	1	no	—
606	#125	—	271	1	no	—
607	#125	—	271	1	no	—
608	#124	—	271	1	no	—
609	#124	—	271	1	no	—
610	#124	—	271	1	no	—
611	#124	—	271	1	no	—
612	#124	—	271	1	no	—
613	#124	—	271	1	no	—
614	#124	C₂×D₂₇₁	1	1	yes	characteristic, complemented
615	#123	—	271	1	no	—
616	#123	—	271	1	no	—
617	#123	—	271	1	no	—
618	#123	—	271	1	no	—
619	#123	—	271	1	no	—
620	#123	—	271	1	no	—
621	#123	—	271	1	no	—
622	#123	—	271	1	no	—
623	#123	—	271	1	no	—
624	#123	—	271	1	no	—
625	#123	—	271	1	no	—
626	#123	—	271	1	no	—
627	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
628	#123	C₂×D₂₇₁	1	1	yes	characteristic, complemented
629	C₂²⋊Q₈	—	271	1	no	—
630	C₂²⋊Q₈	—	271	1	no	—
631	C₂²⋊Q₈	—	271	1	no	—
632	C₂²⋊Q₈	—	271	1	no	—
633	C₂²⋊Q₈	—	271	1	no	—
634	C₂²⋊Q₈	—	271	1	no	—
635	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
636	#121	—	271	1	no	—
637	#121	—	271	1	no	—
638	#121	—	271	1	no	—
639	#121	—	271	1	no	—
640	#121	—	271	1	no	—
641	#121	—	271	1	no	—
642	#121	—	271	1	no	—
643	#121	—	271	1	no	—
644	#121	—	271	1	no	—
645	#121	—	271	1	no	—
646	#121	—	271	1	no	—
647	#121	—	271	1	no	—
648	#121	—	271	1	no	—
649	#121	—	271	1	no	—
650	#121	—	271	1	no	—
651	#121	—	271	1	no	—
652	#121	—	271	1	no	—
653	#121	—	271	1	no	—
654	#121	—	271	1	no	—
655	#121	—	271	1	no	—
656	#121	—	271	1	no	—
657	#121	—	271	1	no	—
658	#121	—	271	1	no	—
659	#121	—	271	1	no	—
660	#121	—	271	1	no	—
661	#121	—	271	1	no	—
662	#121	—	271	1	no	—
663	#121	—	271	1	no	—
664	#121	—	271	1	no	—
665	#121	—	271	1	no	—
666	#121	—	271	1	no	—
667	#121	—	271	1	no	—
668	#121	C₂×D₂₇₁	1	1	yes	characteristic, complemented
669	#121	C₂×D₂₇₁	1	1	yes	characteristic, complemented
670	#121	C₂×D₂₇₁	1	1	yes	characteristic, complemented
671	#120	—	271	1	no	—
672	#120	—	271	1	no	—
673	#120	—	271	1	no	—
674	#120	—	271	1	no	—
675	#120	—	271	1	no	—
676	#120	—	271	1	no	—
677	#120	—	271	1	no	—
678	#120	—	271	1	no	—
679	#120	—	271	1	no	—
680	#120	—	271	1	no	—
681	#120	C₂×D₂₇₁	1	1	yes	characteristic, complemented
682	#120	C₂×D₂₇₁	1	1	yes	characteristic, complemented
683	C₄×Q₈	—	271	1	no	—
684	C₄×D₄	—	271	1	no	—
685	C₄×D₄	—	271	1	no	—
686	C₄×D₄	—	271	1	no	—
687	C₄×D₄	—	271	1	no	—
688	C₄×D₄	—	271	1	no	—
689	C₄×D₄	—	271	1	no	—
690	C₄×D₄	—	271	1	no	—
691	C₄×D₄	—	271	1	no	—
692	C₄×D₄	—	271	1	no	—
693	C₄×D₄	—	271	1	no	—
694	C₄×D₄	—	271	1	no	—
695	C₄×D₄	—	271	1	no	—
696	C₄×D₄	—	271	1	no	—
697	C₄×D₄	—	271	1	no	—
698	C₄×D₄	—	271	1	no	—
699	C₄×D₄	—	271	1	no	—
700	C₄×D₄	—	271	1	no	—
701	C₄×D₄	—	271	1	no	—
702	C₄×D₄	—	271	1	no	—
703	C₄×D₄	—	271	1	no	—
704	C₄×D₄	—	271	1	no	—
705	C₄×D₄	—	271	1	no	—
706	C₄×D₄	—	271	1	no	—
707	C₄×D₄	—	271	1	no	—
708	C₄×D₄	—	271	1	no	—
709	C₄×D₄	—	271	1	no	—
710	C₄×D₄	—	271	1	no	—
711	C₄×D₄	—	271	1	no	—
712	C₄×D₄	—	271	1	no	—
713	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
714	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
715	#117	—	271	1	no	—
716	#117	—	271	1	no	—
717	#117	—	271	1	no	—
718	#117	—	271	1	no	—
719	#117	—	271	1	no	—
720	#117	—	271	1	no	—
721	C₂×C₄⋊C₄	—	271	1	no	—
722	C₂×C₄⋊C₄	—	271	1	no	—
723	C₂×C₄⋊C₄	—	271	1	no	—
724	C₂×C₂²⋊C₄	—	271	1	no	—
725	C₂×C₂²⋊C₄	—	271	1	no	—
726	C₂×C₂²⋊C₄	—	271	1	no	—
727	C₂×C₂²⋊C₄	—	271	1	no	—
728	C₂×C₂²⋊C₄	—	271	1	no	—
729	C₂×C₂²⋊C₄	—	271	1	no	—
730	C₂×C₂²⋊C₄	—	271	1	no	—
731	C₂×C₂²⋊C₄	—	271	1	no	—
732	C₂×C₂²⋊C₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
733	C₂×C₂²⋊C₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
734	C₂×C₄²	—	271	1	no	—
735	C₂⁴	—	271	1	no	—
736	C₂⁴	—	271	1	no	—
737	C₂⁴	—	271	1	no	—
738	C₂⁴	—	271	1	no	—
739	C₂⁴	C₂²×D₂₇₁	1	1	yes	characteristic
740	C₂⁴	C₂²×D₂₇₁	1	1	yes	characteristic
741	#41	—	4	2	no	—
742	#41	—	1084	2	no	—
743	#41	—	1084	2	no	—
744	#41	—	1084	2	no	—
745	C₂×Q₈	—	271	1	no	—
746	C₂×Q₈	—	271	1	no	—
747	C₂×Q₈	C₂²×D₂₇₁	1	1	yes	characteristic
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	271	1	no	—
750	C₂×D₄	—	271	1	no	—
751	C₂×D₄	—	271	1	no	—
752	C₂×D₄	—	271	1	no	—
753	C₂×D₄	—	271	1	no	—
754	C₂×D₄	—	271	1	no	—
755	C₂×D₄	—	271	1	no	—
756	C₂×D₄	—	271	1	no	—
757	C₂×D₄	—	271	1	no	—
758	C₂×D₄	—	271	1	no	—
759	C₂×D₄	—	271	1	no	—
760	C₂×D₄	—	271	1	no	—
761	C₂×D₄	—	271	1	no	—
762	C₂×D₄	—	271	1	no	—
763	C₂×D₄	—	271	1	no	—
764	C₂×D₄	—	271	1	no	—
765	C₂×D₄	—	271	1	no	—
766	C₂×D₄	—	271	1	no	—
767	C₂×D₄	—	271	1	no	—
768	C₂×D₄	—	271	1	no	—
769	C₂×D₄	—	271	1	no	—
770	C₂×D₄	—	271	1	no	—
771	C₂×D₄	—	271	1	no	—
772	C₂×D₄	—	271	1	no	—
773	C₂×D₄	—	271	1	no	—
774	C₂×D₄	—	271	1	no	—
775	C₂×D₄	—	271	1	no	—
776	C₂×D₄	—	271	1	no	—
777	C₂×D₄	—	542	4	no	—
778	C₂×D₄	—	542	4	no	—
779	C₂×D₄	—	542	4	no	—
780	C₂×D₄	—	1084	2	no	—
781	C₂×D₄	—	1084	2	no	—
782	C₂×D₄	—	1084	2	no	—
783	C₂×D₄	—	1084	2	no	—
784	C₂×D₄	—	1084	2	no	—
785	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
786	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
787	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
788	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
789	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
790	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
791	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
792	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
793	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
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	—	1084	2	no	—
816	C₂²×C₄	—	1084	2	no	—
817	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
818	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
819	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
820	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
821	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
822	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
823	C₄⋊C₄	—	271	1	no	—
824	C₄⋊C₄	—	271	1	no	—
825	C₄⋊C₄	—	271	1	no	—
826	C₄⋊C₄	—	271	1	no	—
827	C₄⋊C₄	—	271	1	no	—
828	C₄⋊C₄	—	271	1	no	—
829	C₄⋊C₄	—	271	1	no	—
830	C₄⋊C₄	—	271	1	no	—
831	C₄⋊C₄	—	271	1	no	—
832	C₄⋊C₄	—	271	1	no	—
833	C₄⋊C₄	—	271	1	no	—
834	C₄⋊C₄	—	271	1	no	—
835	C₄⋊C₄	—	271	1	no	—
836	C₄⋊C₄	—	271	1	no	—
837	C₄⋊C₄	—	271	1	no	—
838	C₄⋊C₄	—	271	1	no	—
839	C₄⋊C₄	—	271	1	no	—
840	C₄⋊C₄	—	271	1	no	—
841	C₄⋊C₄	—	271	1	no	—
842	C₄⋊C₄	—	271	1	no	—
843	C₄⋊C₄	—	271	1	no	—
844	C₄⋊C₄	—	271	1	no	—
845	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
846	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
847	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
848	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
849	C₂²⋊C₄	—	271	1	no	—
850	C₂²⋊C₄	—	271	1	no	—
851	C₂²⋊C₄	—	271	1	no	—
852	C₂²⋊C₄	—	271	1	no	—
853	C₂²⋊C₄	—	271	1	no	—
854	C₂²⋊C₄	—	271	1	no	—
855	C₂²⋊C₄	—	271	1	no	—
856	C₂²⋊C₄	—	271	1	no	—
857	C₂²⋊C₄	—	271	1	no	—
858	C₂²⋊C₄	—	271	1	no	—
859	C₂²⋊C₄	—	271	1	no	—
860	C₂²⋊C₄	—	271	1	no	—
861	C₂²⋊C₄	—	271	1	no	—
862	C₂²⋊C₄	—	271	1	no	—
863	C₂²⋊C₄	—	271	1	no	—
864	C₂²⋊C₄	—	271	1	no	—
865	C₂²⋊C₄	—	271	1	no	—
866	C₂²⋊C₄	—	271	1	no	—
867	C₂²⋊C₄	—	271	1	no	—
868	C₂²⋊C₄	—	271	1	no	—
869	C₂²⋊C₄	—	271	1	no	—
870	C₂²⋊C₄	—	271	1	no	—
871	C₂²⋊C₄	—	271	1	no	—
872	C₂²⋊C₄	—	271	1	no	—
873	C₂²⋊C₄	—	271	1	no	—
874	C₂²⋊C₄	—	271	1	no	—
875	C₂²⋊C₄	—	271	1	no	—
876	C₂²⋊C₄	—	271	1	no	—
877	C₂²⋊C₄	—	271	1	no	—
878	C₂²⋊C₄	—	271	1	no	—
879	C₂²⋊C₄	—	271	1	no	—
880	C₂²⋊C₄	—	271	1	no	—
881	C₂²⋊C₄	—	271	1	no	—
882	C₂²⋊C₄	—	271	1	no	—
883	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
889	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
890	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
891	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
892	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
893	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
894	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
895	C₄²	—	271	1	no	—
896	C₄²	—	271	1	no	—
897	C₄²	—	271	1	no	—
898	C₄²	—	271	1	no	—
899	C₄²	—	271	1	no	—
900	C₄²	—	271	1	no	—
901	C₄²	—	271	1	no	—
902	C₄²	—	271	1	no	—
903	C₄²	—	271	1	no	—
904	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	1	no	—
910	C₂³	—	4	1	no	—
911	C₂³	—	271	1	no	—
912	C₂³	—	271	1	no	—
913	C₂³	—	271	1	no	—
914	C₂³	—	271	1	no	—
915	C₂³	—	271	1	no	—
916	C₂³	—	542	2	no	—
917	C₂³	—	542	2	no	—
918	C₂³	—	542	2	no	—
919	C₂³	—	542	2	no	—
920	C₂³	—	542	2	no	—
921	C₂³	—	1084	1	no	—
922	C₂³	—	1084	1	no	—
923	C₂³	—	1084	1	no	—
924	C₂³	—	1084	1	no	—
925	C₂³	—	1084	1	no	—
926	C₂³	—	1084	1	no	—
927	C₂³	—	1084	1	no	—
928	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
929	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
930	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
931	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
932	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
933	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
934	Q₈	—	4	1	no	—
935	Q₈	—	542	2	no	—
936	Q₈	—	1084	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	4	1	no	—
942	D₄	—	4	1	no	—
943	D₄	—	4	1	no	—
944	D₄	—	4	1	no	—
945	D₄	—	4	1	no	—
946	D₄	—	271	4	no	—
947	D₄	—	542	2	no	—
948	D₄	—	542	2	no	—
949	D₄	—	542	2	no	—
950	D₄	—	542	2	no	—
951	D₄	—	542	2	no	—
952	D₄	—	542	2	no	—
953	D₄	—	542	2	no	—
954	D₄	—	542	2	no	—
955	D₄	—	542	2	no	—
956	D₄	—	542	2	no	—
957	D₄	—	542	2	no	—
958	D₄	—	542	2	no	—
959	D₄	—	542	2	no	—
960	D₄	—	542	2	no	—
961	D₄	—	1084	1	no	—
962	D₄	—	1084	1	no	—
963	D₄	—	1084	1	no	—
964	D₄	—	1084	1	no	—
965	D₄	—	1084	1	no	—
966	D₄	—	1084	1	no	—
967	D₄	—	1084	1	no	—
968	D₄	—	1084	1	no	—
969	D₄	—	1084	1	no	—
970	D₄	—	1084	1	no	—
971	D₄	—	1084	1	no	—
972	D₄	—	1084	1	no	—
973	D₄	—	1084	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	1	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	271	1	no	—
981	C₂×C₄	—	271	1	no	—
982	C₂×C₄	—	271	1	no	—
983	C₂×C₄	—	271	1	no	—
984	C₂×C₄	—	271	1	no	—
985	C₂×C₄	—	271	1	no	—
986	C₂×C₄	—	271	1	no	—
987	C₂×C₄	—	271	1	no	—
988	C₂×C₄	—	271	1	no	—
989	C₂×C₄	—	271	1	no	—
990	C₂×C₄	—	271	1	no	—
991	C₂×C₄	—	542	2	no	—
992	C₂×C₄	—	542	2	no	—
993	C₂×C₄	—	542	2	no	—
994	C₂×C₄	—	542	2	no	—
995	C₂×C₄	—	542	2	no	—
996	C₂×C₄	—	542	2	no	—
997	C₂×C₄	—	542	2	no	—
998	C₂×C₄	—	542	2	no	—
999	C₂×C₄	—	1084	1	no	—
1000	C₂×C₄	—	1084	1	no	—
1001	C₂×C₄	—	1084	1	no	—
1002	C₂×C₄	—	1084	1	no	—
1003	C₂×C₄	—	1084	1	no	—
1004	C₂×C₄	—	1084	1	no	—
1005	C₂×C₄	—	1084	1	no	—
1006	C₂×C₄	—	1084	1	no	—
1007	C₂×C₄	—	1084	1	no	—
1008	C₂×C₄	—	1084	1	no	—
1009	C₂×C₄	—	1084	1	no	—
1010	C₂×C₄	—	1084	1	no	—
1011	C₂×C₄	—	1084	1	no	—
1012	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1013	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1014	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1015	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1016	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1017	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1018	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1019	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1020	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	4	4	no	—
1038	C₂²	—	8	2	no	—
1039	C₂²	—	271	2	no	—
1040	C₂²	—	542	1	no	—
1041	C₂²	—	542	1	no	—
1042	C₂²	—	542	1	no	—
1043	C₂²	—	542	1	no	—
1044	C₂²	—	542	1	no	—
1045	C₂²	—	542	1	no	—
1046	C₂²	—	542	1	no	—
1047	C₂²	—	542	1	no	—
1048	C₂²	—	542	1	no	—
1049	C₂²	—	542	1	no	—
1050	C₂²	—	542	1	no	—
1051	C₂²	—	542	1	no	—
1052	C₂²	—	542	1	no	—
1053	C₂²	—	542	1	no	—
1054	C₂²	—	1084	4	no	—
1055	C₂²	—	2168	2	no	—
1056	C₂²	—	2168	2	no	—
1057	C₂²	—	2168	2	no	—
1058	C₂²	#41×D₂₇₁	1	2	yes	—
1059	C₂²	#22576205	1	2	yes	—
1060	C₂²	C₂⁴×D₂₇₁	1	1	yes	characteristic
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	271	2	no	—
1071	C₄	—	271	2	no	—
1072	C₄	—	542	1	no	—
1073	C₄	—	542	1	no	—
1074	C₄	—	542	1	no	—
1075	C₄	—	542	1	no	—
1076	C₄	—	542	1	no	—
1077	C₄	—	542	1	no	—
1078	C₄	—	542	1	no	—
1079	C₄	—	542	1	no	—
1080	C₄	—	542	1	no	—
1081	C₂	—	2	2	no	—
1082	C₂	—	2	2	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	1	no	—
1086	C₂	—	4	1	no	—
1087	C₂	—	542	2	no	—
1088	C₂	—	1084	1	no	—
1089	C₂	—	1084	1	no	—
1090	C₂	—	1084	1	no	—
1091	C₂	—	1084	1	no	—
1092	C₂	C₂×#41×D₂₇₁	1	1	yes	characteristic
1093	C₂	H(5,𝔽₂)×D₂₇₁	1	1	yes	characteristic
1094	C₂	C₂×#22576205	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₇₁
commutator, socle, cosocle	C₂²×C₂₇₁	C₂⁵
Fitting	#546×C₂₇₁	C₂
hypercenter	#546	D₂₇₁
hypocenter	C₂₇₁	#3519
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #31774609	C₂	semidirect
2. #31774601	C₂	semidirect
3. #31774596	C₂	semidirect
4. #31774596	C₂	semidirect
5. #31774592	C₂	semidirect
6. #31774590	C₂	semidirect
7. #31774565	C₂	semidirect
8. #31774539	C₂	semidirect
9. #31774537	C₂	semidirect
10. #31774537	C₂	semidirect
11. #31774536	C₂	semidirect
12. #31774535	C₂	semidirect
13. D₄×C₂²⋊D₂₇₁	C₂	semidirect
14. #31774529	C₂	semidirect
15. #31774529	C₂	semidirect
16. #31774499	C₂	semidirect
17. #31774497	C₂	semidirect
18. #31774487	C₂	semidirect
19. #31774482	C₂	semidirect
20. #31774481	C₂	semidirect
21. #31774479	C₂	semidirect
22. #31774443	C₂	semidirect
23. #31774424	C₂	semidirect
24. #31774406	C₂	semidirect
25. #31774403	C₂	semidirect
26. C₂×#22576132	C₂	semidirect
27. #121×D₂₇₁	C₂	semidirect
28. #31774370	C₂	semidirect
29. #31774369	C₂	semidirect
30. C₂×(C₂²⋊D₂₇₁)⋊C₄	C₂	semidirect
31. #546×C₂₇₁	C₂	semidirect
32. C₂×#16864654	C₂²	semidirect
33. C₂×#16864654	C₂²	semidirect
34. C₂×#16864653	C₂²	semidirect
37. C₂²×C₂²⋊D₂₇₁	C₂²	semidirect
38. C₂²×C₂²⋊D₂₇₁	C₂²	semidirect
40. C₂×D₄×D₂₇₁	C₂²	semidirect
41. C₂×D₄×D₂₇₁	C₂²	semidirect
42. C₂×D₄×D₂₇₁	C₂²	semidirect
43. C₂³×Dic₂₇₁	C₂²	semidirect
44. C₂²×C₄×D₂₇₁	C₂²	semidirect
45. #22576158	C₂²	semidirect
46. #22576156	C₂²	semidirect
47. #22576156	C₂²	semidirect
48. #22576156	C₂²	semidirect
49. #22576155	C₂²	semidirect
50. #22576155	C₂²	semidirect
51. #22576154	C₂²	semidirect
52. #22576153	C₂²	semidirect
53. #22576153	C₂²	semidirect
54. #22576153	C₂²	semidirect
55. #22576150	C₂²	semidirect
56. #22576150	C₂²	semidirect
57. #22576150	C₂²	semidirect
58. #22576149	C₂²	semidirect
59. #22576149	C₂²	semidirect
60. #22576147	C₂²	semidirect
61. #22576146	C₂²	semidirect
62. #22576146	C₂²	semidirect
63. #22576146	C₂²	semidirect
64. #22576145	C₂²	semidirect
65. #22576145	C₂²	semidirect
66. #22576145	C₂²	semidirect
67. #22576144	C₂²	semidirect
68. #22576143	C₂²	semidirect
69. #22576143	C₂²	semidirect
70. #22576143	C₂²	semidirect
71. #22576142	C₂²	semidirect
72. #22576142	C₂²	semidirect
73. #22576142	C₂²	semidirect
74. #22576141	C₂²	semidirect
75. #22576141	C₂²	semidirect
76. #22576138	C₂²	semidirect
77. #22576138	C₂²	semidirect
78. #22576137	C₂²	semidirect
79. #22576137	C₂²	semidirect
80. #22576137	C₂²	semidirect
81. #22576136	C₂²	semidirect
82. #22576135	C₂²	semidirect
83. #22576135	C₂²	semidirect
84. #22576134	C₂²	semidirect
85. #22576134	C₂²	semidirect
86. #22576134	C₂²	semidirect
87. #22576133	C₂²	semidirect
88. #22576133	C₂²	semidirect
89. #22576133	C₂²	semidirect
90. #22576133	C₂²	semidirect
91. #22576133	C₂²	semidirect
92. #22576133	C₂²	semidirect
93. #22576133	C₂²	semidirect
94. #22576133	C₂²	semidirect
95. #22576133	C₂²	semidirect
97. #22576132	C₂²	semidirect
98. #22576132	C₂²	semidirect
99. #22576132	C₂²	semidirect
100. #22576132	C₂²	semidirect
101. #22576132	C₂²	semidirect
102. #22576132	C₂²	semidirect
103. #22576132	C₂²	semidirect
104. #22576132	C₂²	semidirect
105. #22576132	C₂²	semidirect
106. #22576132	C₂²	semidirect
107. #22576132	C₂²	semidirect
108. #22576132	C₂²	semidirect
109. #22576132	C₂²	semidirect
110. #22576132	C₂²	semidirect
111. #22576132	C₂²	semidirect
112. #22576131	C₂²	semidirect
113. #22576131	C₂²	semidirect
114. #22576130	C₂²	semidirect
115. #22576130	C₂²	semidirect
116. #22576130	C₂²	semidirect
117. #22576130	C₂²	semidirect
118. #22576129	C₂²	semidirect
119. #22576129	C₂²	semidirect
120. #22576128	C₂²	semidirect
121. #22576128	C₂²	semidirect
122. #22576128	C₂²	semidirect
123. #22576128	C₂²	semidirect
124. #22576125	C₂²	semidirect
125. C₄×D₁₀₈₄	C₂²	semidirect
126. D₄×Dic₂₇₁	C₂²	semidirect
127. D₄×Dic₂₇₁	C₂²	semidirect
128. D₄×Dic₂₇₁	C₂²	semidirect
129. #22576122	C₂²	semidirect
131. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
132. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
133. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
134. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
135. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
136. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
137. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
138. C₄×C₂²⋊D₂₇₁	C₂²	semidirect
142. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
143. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
144. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
145. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
146. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
147. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
148. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
149. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
150. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₂₇₁)⋊C₄	C₂²	semidirect
154. #22576118	C₂²	semidirect
155. #22576117	C₂²	semidirect
156. #22576117	C₂²	semidirect
157. #22576116	C₂²	semidirect
158. #22576116	C₂²	semidirect
159. #22576116	C₂²	semidirect
160. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
161. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
162. C₄⋊C₄×D₂₇₁	C₂²	semidirect
163. C₂×C₂²⋊Dic₂₇₁	C₂²	semidirect
164. C₂×(C₂×D₂₇₁)⋊C₄	C₂²	semidirect
165. C₂×(C₂×D₂₇₁)⋊C₄	C₂²	semidirect
166. C₂×(C₂×D₂₇₁)⋊C₄	C₂²	semidirect
167. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
168. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
169. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
170. C₂²⋊C₄×D₂₇₁	C₂²	semidirect
171. C₂×C₄×Dic₂₇₁	C₂²	semidirect
172. C₂×#41×C₂₇₁	C₂²	semidirect
173. C₂²×D₄×C₂₇₁	C₂²	semidirect
174. #124×C₂₇₁	C₂²	semidirect
175. #123×C₂₇₁	C₂²	semidirect
176. #123×C₂₇₁	C₂²	semidirect
177. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
178. #121×C₂₇₁	C₂²	semidirect
179. #121×C₂₇₁	C₂²	semidirect
180. #121×C₂₇₁	C₂²	semidirect
181. #120×C₂₇₁	C₂²	semidirect
182. #120×C₂₇₁	C₂²	semidirect
183. C₄×D₄×C₂₇₁	C₂²	semidirect
184. C₄×D₄×C₂₇₁	C₂²	semidirect
185. C₂×C₂²⋊C₄×C₂₇₁	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₂₇₁	C₂²	semidirect
403. C₂²⋊D₂₇₁	#41	semidirect
547. C₂₇₁	#3519	semidirect
561. #546	D₂₇₁	semidirect
583. C₂×#41	C₂×D₂₇₁	semidirect
592. C₂²×D₄	C₂×D₂₇₁	semidirect
614. #124	C₂×D₂₇₁	semidirect
627. #123	C₂×D₂₇₁	semidirect
628. #123	C₂×D₂₇₁	semidirect
635. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
668. #121	C₂×D₂₇₁	semidirect
669. #121	C₂×D₂₇₁	semidirect
670. #121	C₂×D₂₇₁	semidirect
681. #120	C₂×D₂₇₁	semidirect
682. #120	C₂×D₂₇₁	semidirect
713. C₄×D₄	C₂×D₂₇₁	semidirect
714. C₄×D₄	C₂×D₂₇₁	semidirect
732. C₂×C₂²⋊C₄	C₂×D₂₇₁	semidirect
733. C₂×C₂²⋊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
#31774609	2
#31774601	2
#31774596	2
#31774592	2
#31774590	2
#31774565	2
#31774539	2
#31774537	2
#31774536	2
#31774535	2
D₄×C₂²⋊D₂₇₁	2
#31774529	2
#31774499	2
#31774497	2
#31774487	2
#31774482	2
#31774481	2
#31774479	2
#31774443	2
#31774424	2
#31774406	2
#31774403	2
C₂×#22576132	2
#121×D₂₇₁	2
#31774370	2
#31774369	2
C₂×(C₂²⋊D₂₇₁)⋊C₄	2
#546×C₂₇₁	2
#3519	271