Subgroups — #72263417

Order 2048.

At least 10478 conjugacy classes of subgroups; only the 1032 normal subgroups are shown.

The subgroup lattice has 808 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263415	C₂	1	1	yes	maximal, characteristic
2	#72238031	C₂	1	1	yes	maximal, characteristic, complemented
3	#72236717	C₂	1	1	yes	maximal, characteristic
4	#72236704	C₂	1	1	yes	maximal, characteristic
5	#72236670	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236598	C₂	1	2	yes	maximal, complemented
7	#72236598	C₂	1	2	yes	maximal, complemented
8	C₂×#106766	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#128073	C₂	1	1	yes	maximal, characteristic, complemented
10	#72210473	C₂	1	2	yes	maximal, complemented
11	#72210462	C₂	1	2	yes	maximal, complemented
12	C₂×#35222	C₂²	1	1	yes	characteristic
13	C₂×#34171	C₂²	1	1	yes	characteristic
14	C₂²×#1783	C₂²	1	1	yes	characteristic
15	C₂²×#1781	C₂²	1	1	yes	characteristic
16	C₂²×#1781	C₂²	1	1	yes	characteristic
17	#606706	C₄	1	1	yes	characteristic, complemented
18	#606700	C₄	1	1	yes	characteristic, complemented
19	#606342	C₄	1	1	yes	characteristic, complemented
20	#606302	C₄	1	1	yes	characteristic, complemented
21	#582589	C₄	1	1	yes	characteristic, complemented
22	#582567	C₄	1	1	yes	characteristic, complemented
23	#582133	C₂²	1	1	yes	characteristic
24	#582133	C₂²	1	1	yes	characteristic
25	#581605	C₂²	1	1	yes	characteristic
26	#581603	C₂²	1	1	yes	characteristic
27	#538267	C₄	1	1	yes	characteristic, complemented
28	#537841	C₄	1	1	yes	characteristic, complemented
29	#517411	C₂²	1	1	yes	characteristic
30	C₂×#13867	C₂²	1	1	yes	characteristic
31	#494713	C₄	1	4	yes	complemented
32	#494713	C₄	1	4	yes	complemented
33	#493883	C₂²	1	2	yes	—
34	#493370	C₂²	1	2	yes	—
35	#379759	C₄	1	4	yes	complemented
36	#374045	C₄	1	4	yes	complemented
37	#359869	C₂²	1	2	yes	—
38	#359509	C₂²	1	2	yes	—
39	#128073	C₂²	1	2	yes	—
40	#128073	C₂²	1	2	yes	—
41	#128073	C₂²	1	2	yes	—
42	#128073	C₂²	1	2	yes	—
43	#106766	C₂²	1	2	yes	—
44	#106766	C₂²	1	2	yes	—
45	#106766	C₂²	1	2	yes	—
46	#106766	C₂²	1	2	yes	—
47	C₂⁵×D₄	C₂³	1	1	yes	characteristic
48	C₂²×#535	D₄	1	1	yes	characteristic
49	C₂²×#535	C₂³	1	1	yes	characteristic
50	C₂²×#525	D₄	1	1	yes	characteristic
51	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
52	C₂³×#100	C₂×C₄	1	2	yes	complemented
53	C₂³×#99	C₂×C₄	1	2	yes	complemented
54	C₂³×#99	C₂×C₄	1	2	yes	complemented
55	#35222	C₂×C₄	1	2	yes	—
56	#35222	C₂×C₄	1	2	yes	—
57	#35222	C₂×C₄	1	2	yes	—
58	#35222	C₂×C₄	1	2	yes	—
59	#35222	D₄	1	2	yes	—
60	#35222	D₄	1	2	yes	—
61	#35222	Q₈	1	2	yes	—
62	#35222	Q₈	1	2	yes	—
63	C₂×#2435	C₂×C₄	1	1	yes	characteristic
64	C₂×#2435	C₂×C₄	1	1	yes	characteristic
65	C₂×#2435	D₄	1	1	yes	characteristic
66	C₂×#2435	D₄	1	1	yes	characteristic
67	C₂×#2433	C₂×C₄	1	1	yes	characteristic
68	C₂×#2433	C₂×C₄	1	1	yes	characteristic
69	C₂×#2433	D₄	1	1	yes	characteristic
70	C₂×#2433	D₄	1	1	yes	characteristic
71	#34171	C₂×C₄	1	2	yes	complemented
72	#34171	C₂³	1	2	yes	—
73	C₂×#2309	C₂×C₄	1	2	yes	complemented
74	C₂×#2309	D₄	1	1	yes	characteristic
75	C₂×#2309	C₂³	1	1	yes	characteristic
76	C₂×#2280	D₄	1	1	yes	characteristic
77	C₂²×#379	D₄	1	1	yes	characteristic
78	C₂²×#379	D₄	1	1	yes	characteristic
79	C₂²×#379	D₄	1	1	yes	characteristic
80	C₂×#2127	C₂×C₄	1	8	yes	complemented
81	C₂×#1783	C₂×C₄	1	2	yes	complemented
82	C₂×#1783	C₂³	1	2	yes	—
83	C₂×#1781	C₂×C₄	1	2	yes	complemented
84	C₂×#1781	C₂×C₄	1	2	yes	complemented
85	C₂×#1781	C₂³	1	2	yes	—
86	C₂×#1781	C₂³	1	2	yes	—
87	#14667	C₂×C₄	1	1	yes	characteristic, complemented
88	#14667	C₂×C₄	1	1	yes	characteristic, complemented
89	#14662	C₂×C₄	1	1	yes	characteristic, complemented
90	#14661	C₂×C₄	1	1	yes	characteristic, complemented
91	#14503	C₂×C₄	1	1	yes	characteristic, complemented
92	#14503	C₂×C₄	1	1	yes	characteristic, complemented
93	#14492	C₂×C₄	1	1	yes	characteristic, complemented
94	#14492	C₂×C₄	1	1	yes	characteristic, complemented
95	#14445	C₂×C₄	1	1	yes	characteristic, complemented
96	#14445	C₂×C₄	1	1	yes	characteristic, complemented
97	#14419	C₂×C₄	1	1	yes	characteristic, complemented
98	#14419	C₂×C₄	1	1	yes	characteristic, complemented
99	#14335	C₂×C₄	1	1	yes	characteristic
100	#14335	C₂×C₄	1	1	yes	characteristic
101	#14335	D₄	1	1	yes	characteristic
102	#14335	D₄	1	1	yes	characteristic
103	#14169	C₂×C₄	1	1	yes	characteristic, complemented
104	#14157	C₂×C₄	1	1	yes	characteristic, complemented
105	#14157	C₂×C₄	1	1	yes	characteristic, complemented
106	#14154	C₂×C₄	1	1	yes	characteristic, complemented
107	#13867	C₂×C₄	1	1	yes	characteristic
108	#13867	C₂×C₄	1	1	yes	characteristic
109	#13867	C₂×C₄	1	1	yes	characteristic
110	#13867	C₂×C₄	1	1	yes	characteristic
111	#13867	D₄	1	1	yes	characteristic
112	#13867	D₄	1	1	yes	characteristic
113	#13867	D₄	1	1	yes	characteristic
114	#13867	D₄	1	1	yes	characteristic
115	#13867	D₄	1	1	yes	characteristic
116	#13867	D₄	1	1	yes	characteristic
117	#13867	D₄	1	1	yes	characteristic
118	#13867	D₄	1	1	yes	characteristic
119	#13867	C₂³	1	1	yes	characteristic
120	#13867	C₂³	1	1	yes	characteristic
121	#13867	C₂³	1	1	yes	characteristic
122	#13867	C₂³	1	1	yes	characteristic
123	C₂×#1438	C₂×C₄	1	1	yes	characteristic
124	C₂×#1438	C₂×C₄	1	1	yes	characteristic
125	C₂×#1438	D₄	1	1	yes	characteristic
126	C₂×#1438	D₄	1	1	yes	characteristic
127	#12582	C₂×C₄	1	8	yes	complemented
128	#11155	C₂×C₄	1	8	yes	complemented
129	#10989	C₂×C₄	1	8	yes	complemented
130	C₂⁷	C₂×D₄	1	1	yes	characteristic
131	C₂⁷	C₂×D₄	1	1	yes	characteristic
132	C₂³×#41	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
135	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
136	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
137	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
138	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂×Q₈	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×Q₈	1	1	yes	characteristic
152	C₂⁴×D₄	#41	1	1	yes	characteristic
153	C₂⁴×D₄	#41	1	1	yes	characteristic
154	C₂⁴×D₄	#41	1	1	yes	characteristic
155	C₂⁴×D₄	#41	1	1	yes	characteristic
156	C₂⁴×D₄	#41	1	1	yes	characteristic
157	C₂⁴×D₄	#41	1	1	yes	characteristic
158	C₂⁴×D₄	#41	1	1	yes	characteristic
159	C₂⁴×D₄	#41	1	1	yes	characteristic
160	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
161	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×#535	C₂²⋊C₄	1	2	yes	—
163	C₂×#535	C₂²⋊C₄	1	2	yes	—
164	C₂×#535	C₄⋊C₄	1	2	yes	—
165	C₂×#535	C₄⋊C₄	1	2	yes	—
166	C₂×#535	C₂²×C₄	1	2	yes	—
167	C₂×#535	C₂²×C₄	1	2	yes	—
168	C₂×#535	C₂×D₄	1	2	yes	—
169	C₂×#535	C₂×Q₈	1	2	yes	—
170	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
173	C₂²×#127	C₂×D₄	1	1	yes	characteristic
174	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
177	C₂²×#124	C₂×D₄	1	1	yes	characteristic
178	C₂×#525	C₂²⋊C₄	1	2	yes	—
179	C₂×#525	C₂²⋊C₄	1	2	yes	—
180	C₂×#525	C₄⋊C₄	1	2	yes	—
181	C₂×#525	C₄⋊C₄	1	2	yes	—
182	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×#117	C₂×D₄	1	1	yes	characteristic
187	C₂²×#117	C₂×D₄	1	1	yes	characteristic
188	C₂²×#117	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₂²×#100	C₂²×C₄	1	4	yes	—
202	C₂²×#99	C₂²×C₄	1	4	yes	—
203	C₂²×#99	C₂²×C₄	1	4	yes	—
204	#2435	C₄²	1	2	yes	—
205	#2435	C₄²	1	2	yes	—
206	#2435	C₄²	1	2	yes	—
207	#2435	C₄²	1	2	yes	—
208	#2435	C₂²⋊C₄	1	2	yes	—
209	#2435	C₂²⋊C₄	1	2	yes	—
210	#2435	C₂²⋊C₄	1	2	yes	—
211	#2435	C₂²⋊C₄	1	2	yes	—
212	#2435	C₄⋊C₄	1	2	yes	—
213	#2435	C₄⋊C₄	1	2	yes	—
214	#2435	C₄⋊C₄	1	2	yes	—
215	#2435	C₄⋊C₄	1	2	yes	—
216	#2435	C₄⋊C₄	1	2	yes	—
217	#2435	C₄⋊C₄	1	2	yes	—
218	#2435	C₄⋊C₄	1	2	yes	—
219	#2435	C₄⋊C₄	1	2	yes	—
220	#2433	C₄²	1	2	yes	—
221	#2433	C₄²	1	2	yes	—
222	#2433	C₄²	1	2	yes	—
223	#2433	C₄²	1	2	yes	—
224	#2433	C₂²⋊C₄	1	2	yes	—
225	#2433	C₂²⋊C₄	1	2	yes	—
226	#2433	C₂²⋊C₄	1	2	yes	—
227	#2433	C₂²⋊C₄	1	2	yes	—
228	#2433	C₄⋊C₄	1	2	yes	—
229	#2433	C₄⋊C₄	1	2	yes	—
230	#2433	C₄⋊C₄	1	2	yes	—
231	#2433	C₄⋊C₄	1	2	yes	—
232	#2433	C₄⋊C₄	1	2	yes	—
233	#2433	C₄⋊C₄	1	2	yes	—
234	#2433	C₄⋊C₄	1	2	yes	—
235	#2433	C₄⋊C₄	1	2	yes	—
236	#2309	C₂²⋊C₄	1	2	yes	—
237	#2309	C₂²⋊C₄	1	2	yes	—
238	#2309	C₄⋊C₄	1	2	yes	—
239	#2309	C₄⋊C₄	1	2	yes	—
240	#2309	C₂²×C₄	1	4	yes	—
241	#2309	C₂²×C₄	1	2	yes	—
242	#2309	C₂²×C₄	1	2	yes	—
243	#2309	C₂×D₄	1	2	yes	—
244	#2309	C₂×Q₈	1	2	yes	—
245	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
246	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
247	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
248	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
249	C₂×#390	C₂²×C₄	1	1	yes	characteristic
250	C₂×#390	C₂²×C₄	1	1	yes	characteristic
251	C₂×#390	C₂×D₄	1	1	yes	characteristic
252	C₂×#390	C₂×D₄	1	1	yes	characteristic
253	#2280	C₂²⋊C₄	1	2	yes	—
254	#2280	C₂²⋊C₄	1	2	yes	—
255	#2280	C₄⋊C₄	1	2	yes	—
256	#2280	C₄⋊C₄	1	2	yes	—
257	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
259	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#379	C₂×D₄	1	1	yes	characteristic
266	C₂×#379	C₂×D₄	1	1	yes	characteristic
267	C₂×#379	C₂×D₄	1	1	yes	characteristic
268	C₂×#379	C₂×D₄	1	1	yes	characteristic
269	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
273	#1438	C₂²⋊C₄	1	1	yes	characteristic
274	#1438	C₂²⋊C₄	1	1	yes	characteristic
275	#1438	C₂²⋊C₄	1	1	yes	characteristic
276	#1438	C₂²⋊C₄	1	1	yes	characteristic
277	#1438	C₂²⋊C₄	1	1	yes	characteristic
278	#1438	C₂²⋊C₄	1	1	yes	characteristic
279	#1438	C₂²⋊C₄	1	1	yes	characteristic
280	#1438	C₂²⋊C₄	1	1	yes	characteristic
281	#1438	C₂²⋊C₄	1	1	yes	characteristic
282	#1438	C₂²⋊C₄	1	1	yes	characteristic
283	#1438	C₂²⋊C₄	1	1	yes	characteristic
284	#1438	C₂²⋊C₄	1	1	yes	characteristic
285	#1438	C₂²⋊C₄	1	1	yes	characteristic
286	#1438	C₂²⋊C₄	1	1	yes	characteristic
287	#1438	C₂²⋊C₄	1	1	yes	characteristic
288	#1438	C₂²⋊C₄	1	1	yes	characteristic
289	#1438	C₂²×C₄	1	1	yes	characteristic
290	#1438	C₂²×C₄	1	1	yes	characteristic
291	#1438	C₂²×C₄	1	1	yes	characteristic
292	#1438	C₂²×C₄	1	1	yes	characteristic
293	#1438	C₂²×C₄	1	1	yes	characteristic
294	#1438	C₂²×C₄	1	1	yes	characteristic
295	#1438	C₂²×C₄	1	1	yes	characteristic
296	#1438	C₂²×C₄	1	1	yes	characteristic
297	#1438	C₂×D₄	1	1	yes	characteristic
298	#1438	C₂×D₄	1	1	yes	characteristic
299	#1438	C₂×D₄	1	1	yes	characteristic
300	#1438	C₂×D₄	1	1	yes	characteristic
301	#1438	C₂×D₄	1	1	yes	characteristic
302	#1438	C₂×D₄	1	1	yes	characteristic
303	#1438	C₂×D₄	1	1	yes	characteristic
304	#1438	C₂×D₄	1	1	yes	characteristic
305	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂⁶	C₄×D₄	1	1	yes	characteristic
310	C₂⁶	C₄×D₄	1	1	yes	characteristic
311	C₂⁶	C₄×D₄	1	1	yes	characteristic
312	C₂⁶	C₄×D₄	1	1	yes	characteristic
313	C₂⁶	C₄×D₄	1	1	yes	characteristic
314	C₂⁶	C₄×D₄	1	1	yes	characteristic
315	C₂⁶	C₄×D₄	1	1	yes	characteristic
316	C₂⁶	C₄×D₄	1	1	yes	characteristic
317	C₂⁶	#120	1	1	yes	characteristic
318	C₂⁶	#120	1	1	yes	characteristic
319	C₂⁶	#120	1	1	yes	characteristic
320	C₂⁶	#120	1	1	yes	characteristic
321	C₂⁶	#120	1	1	yes	characteristic
322	C₂⁶	#120	1	1	yes	characteristic
323	C₂⁶	#120	1	1	yes	characteristic
324	C₂⁶	#121	1	1	yes	characteristic
325	C₂⁶	#121	1	1	yes	characteristic
326	C₂⁶	#121	1	1	yes	characteristic
327	C₂⁶	#121	1	1	yes	characteristic
328	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
329	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
330	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
331	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
332	C₂⁶	C₂²×D₄	1	1	yes	characteristic
333	C₂⁶	C₂²×D₄	1	1	yes	characteristic
334	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
335	C₂²×#41	C₂×C₄⋊C₄	1	2	yes	—
336	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
338	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
339	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
340	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
341	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
350	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
355	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
356	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
357	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
358	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
359	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
360	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
361	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
362	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
363	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
364	C₂³×D₄	#117	1	1	yes	characteristic
365	C₂³×D₄	#117	1	1	yes	characteristic
366	C₂³×D₄	#117	1	1	yes	characteristic
367	C₂³×D₄	#117	1	1	yes	characteristic
368	C₂³×D₄	#117	1	1	yes	characteristic
369	C₂³×D₄	#117	1	1	yes	characteristic
370	C₂³×D₄	#117	1	1	yes	characteristic
371	C₂³×D₄	#117	1	1	yes	characteristic
372	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
373	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
374	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
375	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
376	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
377	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
378	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
379	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
380	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
381	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
382	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
383	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
384	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
385	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
386	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
387	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
388	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
389	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
390	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
391	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
392	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
393	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
394	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
395	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
396	C₂³×D₄	#120	1	1	yes	characteristic
397	C₂³×D₄	#120	1	1	yes	characteristic
398	C₂³×D₄	#120	1	1	yes	characteristic
399	C₂³×D₄	#120	1	1	yes	characteristic
400	C₂³×D₄	#120	1	1	yes	characteristic
401	C₂³×D₄	#120	1	1	yes	characteristic
402	C₂³×D₄	#121	1	1	yes	characteristic
403	C₂³×D₄	#121	1	1	yes	characteristic
404	C₂³×D₄	#121	1	1	yes	characteristic
405	C₂³×D₄	#121	1	1	yes	characteristic
406	C₂³×D₄	#121	1	1	yes	characteristic
407	C₂³×D₄	#121	1	1	yes	characteristic
408	C₂³×D₄	#121	1	1	yes	characteristic
409	C₂³×D₄	#121	1	1	yes	characteristic
410	C₂³×D₄	#121	1	1	yes	characteristic
411	C₂³×D₄	#121	1	1	yes	characteristic
412	C₂³×D₄	#121	1	1	yes	characteristic
413	C₂³×D₄	#121	1	1	yes	characteristic
414	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
415	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
416	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
417	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
418	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
419	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
420	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
421	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
422	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
423	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
424	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
425	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
426	C₂³×D₄	#123	1	1	yes	characteristic
427	C₂³×D₄	#123	1	1	yes	characteristic
428	C₂³×D₄	#123	1	1	yes	characteristic
429	C₂³×D₄	#123	1	1	yes	characteristic
430	C₂³×D₄	#123	1	1	yes	characteristic
431	C₂³×D₄	#123	1	1	yes	characteristic
432	C₂³×D₄	#123	1	1	yes	characteristic
433	C₂³×D₄	#123	1	1	yes	characteristic
434	C₂³×D₄	#123	1	1	yes	characteristic
435	C₂³×D₄	#123	1	1	yes	characteristic
436	C₂³×D₄	#123	1	1	yes	characteristic
437	C₂³×D₄	#123	1	1	yes	characteristic
438	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
439	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
440	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
441	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
442	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
443	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
444	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
445	C₂³×D₄	C₂²×Q₈	1	1	yes	characteristic
446	C₂³×D₄	C₂×#41	1	1	yes	characteristic
447	C₂³×D₄	C₂×#41	1	1	yes	characteristic
448	C₂³×D₄	C₂×#41	1	1	yes	characteristic
449	C₂³×D₄	C₂×#41	1	1	yes	characteristic
450	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂⁴×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
455	C₂⁴×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
456	C₂⁴×C₄	#120	1	1	yes	characteristic
457	C₂⁴×C₄	#120	1	1	yes	characteristic
458	C₂⁴×C₄	#120	1	1	yes	characteristic
459	C₂⁴×C₄	#123	1	1	yes	characteristic
460	C₂⁴×C₄	#123	1	1	yes	characteristic
461	C₂⁴×C₄	#123	1	1	yes	characteristic
462	C₂⁴×C₄	#123	1	1	yes	characteristic
463	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
464	C₂×#127	#95	1	2	yes	—
465	C₂×#127	#95	1	2	yes	—
466	C₂×#127	#95	1	2	yes	—
467	C₂×#127	#95	1	2	yes	—
468	C₂×#127	C₂×C₄²	1	2	yes	—
469	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
470	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
471	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
472	C₂×#124	#95	1	2	yes	—
473	C₂×#124	#95	1	2	yes	—
474	C₂×#124	#95	1	2	yes	—
475	C₂×#124	#95	1	2	yes	—
476	C₂×#124	C₂×C₄²	1	2	yes	—
477	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
478	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
479	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
480	C₂×C₂²⋊Q₈	#95	1	2	yes	—
481	C₂×C₂²⋊Q₈	#95	1	2	yes	—
482	C₂×C₂²⋊Q₈	#95	1	2	yes	—
483	C₂×C₂²⋊Q₈	#95	1	2	yes	—
484	C₂×#121	#95	1	2	yes	—
485	C₂×#121	#95	1	2	yes	—
486	C₂×#121	#95	1	2	yes	—
487	C₂×#121	#95	1	2	yes	—
488	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
489	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
490	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
491	C₂×#117	C₂×C₄⋊C₄	1	2	yes	—
492	C₂×#117	C₂×C₄⋊C₄	1	2	yes	—
493	C₂×#117	C₂×C₄⋊C₄	1	2	yes	—
494	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
496	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
497	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
498	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
499	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
503	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
504	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
505	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
506	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
508	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
510	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	#390	#95	1	2	yes	—
517	#390	#95	1	2	yes	—
518	#390	#95	1	2	yes	—
519	#390	#95	1	2	yes	—
520	#390	#95	1	2	yes	—
521	#390	#95	1	2	yes	—
522	#390	#95	1	2	yes	—
523	#390	#95	1	2	yes	—
524	#390	C₂×C₄²	1	2	yes	—
525	#390	C₂×C₄²	1	2	yes	—
526	#390	C₂×C₂²⋊C₄	1	2	yes	—
527	#390	C₂×C₂²⋊C₄	1	2	yes	—
528	#390	C₂×C₄⋊C₄	1	2	yes	—
529	#390	C₂×C₄⋊C₄	1	2	yes	—
530	#390	C₂×C₄⋊C₄	1	2	yes	—
531	#390	C₂×C₄⋊C₄	1	2	yes	—
532	C₄×C₂²⋊C₄	#95	1	2	yes	—
533	C₄×C₂²⋊C₄	#95	1	2	yes	—
534	C₄×C₂²⋊C₄	#95	1	2	yes	—
535	C₄×C₂²⋊C₄	#95	1	2	yes	—
536	C₄×C₂²⋊C₄	#95	1	2	yes	—
537	C₄×C₂²⋊C₄	#95	1	2	yes	—
538	C₄×C₂²⋊C₄	#95	1	2	yes	—
539	C₄×C₂²⋊C₄	#95	1	2	yes	—
540	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
541	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
542	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
543	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
544	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
545	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
546	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
547	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
548	C₂⁵	#379	1	1	yes	characteristic
549	C₂⁵	#379	1	1	yes	characteristic
550	C₂⁵	#379	1	1	yes	characteristic
551	C₂⁵	#379	1	1	yes	characteristic
552	C₂⁵	#379	1	1	yes	characteristic
553	C₂⁵	#379	1	1	yes	characteristic
554	C₂⁵	#380	1	1	yes	characteristic
555	C₂⁵	#380	1	1	yes	characteristic
556	C₂⁵	#380	1	1	yes	characteristic
557	C₂⁵	#380	1	1	yes	characteristic
558	C₂⁵	#380	1	1	yes	characteristic
559	C₂⁵	#380	1	1	yes	characteristic
560	C₂⁵	#380	1	1	yes	characteristic
561	C₂⁵	#380	1	1	yes	characteristic
562	C₂⁵	#385	1	1	yes	characteristic
563	C₂⁵	#385	1	1	yes	characteristic
564	C₂⁵	#385	1	1	yes	characteristic
565	C₂⁵	#385	1	1	yes	characteristic
566	C₂⁵	#385	1	1	yes	characteristic
567	C₂⁵	#385	1	1	yes	characteristic
568	C₂⁵	#385	1	1	yes	characteristic
569	C₂⁵	#385	1	1	yes	characteristic
570	C₂⁵	#385	1	1	yes	characteristic
571	C₂⁵	#385	1	1	yes	characteristic
572	C₂⁵	#385	1	1	yes	characteristic
573	C₂⁵	#385	1	1	yes	characteristic
574	C₂⁵	#385	1	1	yes	characteristic
575	C₂⁵	#385	1	1	yes	characteristic
576	C₂⁵	#386	1	1	yes	characteristic
577	C₂⁵	#386	1	1	yes	characteristic
578	C₂⁵	#386	1	1	yes	characteristic
579	C₂⁵	#386	1	1	yes	characteristic
580	C₂⁵	#386	1	1	yes	characteristic
581	C₂⁵	#386	1	1	yes	characteristic
582	C₂⁵	#386	1	1	yes	characteristic
583	C₂⁵	#386	1	1	yes	characteristic
584	C₂⁵	#386	1	1	yes	characteristic
585	C₂⁵	#386	1	1	yes	characteristic
586	C₂⁵	#386	1	1	yes	characteristic
587	C₂⁵	#386	1	1	yes	characteristic
588	C₂⁵	#386	1	1	yes	characteristic
589	C₂⁵	#386	1	1	yes	characteristic
590	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
591	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
592	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
593	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
594	C₂⁵	#458	1	1	yes	characteristic
595	C₂⁵	#458	1	1	yes	characteristic
596	C₂⁵	#458	1	1	yes	characteristic
597	C₂⁵	#458	1	1	yes	characteristic
598	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
599	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
600	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
601	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
602	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
603	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
604	C₂⁵	C₂×#120	1	1	yes	characteristic
605	C₂⁵	C₂×#120	1	1	yes	characteristic
606	C₂⁵	C₂×#120	1	1	yes	characteristic
607	C₂⁵	C₂×#121	1	1	yes	characteristic
608	C₂⁵	C₂×#121	1	1	yes	characteristic
609	C₂⁵	C₂×C₂²⋊Q₈	1	1	yes	characteristic
610	C₂⁵	C₂×C₂²⋊Q₈	1	1	yes	characteristic
611	C₂²×Q₈	C₂×#95	1	2	yes	—
612	C₂²×D₄	C₂×#95	1	1	yes	characteristic
613	C₂²×D₄	C₂×#95	1	1	yes	characteristic
614	C₂²×D₄	C₂×#95	1	2	yes	—
615	C₂²×D₄	C₂×#95	1	1	yes	characteristic
616	C₂²×D₄	C₂×#95	1	1	yes	characteristic
617	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
618	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
619	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
620	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
621	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
622	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
623	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
624	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
625	C₂²×D₄	#380	1	1	yes	characteristic
626	C₂²×D₄	#380	1	1	yes	characteristic
627	C₂²×D₄	#380	1	1	yes	characteristic
628	C₂²×D₄	#380	1	1	yes	characteristic
629	C₂²×D₄	#380	1	1	yes	characteristic
630	C₂²×D₄	#380	1	1	yes	characteristic
631	C₂²×D₄	#380	1	1	yes	characteristic
632	C₂²×D₄	#380	1	1	yes	characteristic
633	C₂²×D₄	#381	1	1	yes	characteristic
634	C₂²×D₄	#381	1	1	yes	characteristic
635	C₂²×D₄	#381	1	1	yes	characteristic
636	C₂²×D₄	#381	1	1	yes	characteristic
637	C₂²×D₄	#385	1	1	yes	characteristic
638	C₂²×D₄	#385	1	1	yes	characteristic
639	C₂²×D₄	#385	1	1	yes	characteristic
640	C₂²×D₄	#385	1	1	yes	characteristic
641	C₂²×D₄	#385	1	1	yes	characteristic
642	C₂²×D₄	#385	1	1	yes	characteristic
643	C₂²×D₄	#385	1	1	yes	characteristic
644	C₂²×D₄	#385	1	1	yes	characteristic
645	C₂²×D₄	#385	1	1	yes	characteristic
646	C₂²×D₄	#385	1	1	yes	characteristic
647	C₂²×D₄	#385	1	1	yes	characteristic
648	C₂²×D₄	#385	1	1	yes	characteristic
649	C₂²×D₄	#386	1	1	yes	characteristic
650	C₂²×D₄	#386	1	1	yes	characteristic
651	C₂²×D₄	#386	1	1	yes	characteristic
652	C₂²×D₄	#386	1	1	yes	characteristic
653	C₂²×D₄	#386	1	1	yes	characteristic
654	C₂²×D₄	#386	1	1	yes	characteristic
655	C₂²×D₄	#386	1	1	yes	characteristic
656	C₂²×D₄	#386	1	1	yes	characteristic
657	C₂²×D₄	#386	1	1	yes	characteristic
658	C₂²×D₄	#386	1	1	yes	characteristic
659	C₂²×D₄	#386	1	1	yes	characteristic
660	C₂²×D₄	#386	1	1	yes	characteristic
661	C₂²×D₄	C₂²×C₄²	1	1	yes	characteristic
662	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
663	C₂²×D₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
664	C₂²×D₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
665	C₂²×D₄	C₂×#117	1	1	yes	characteristic
666	C₂²×D₄	C₂×#117	1	1	yes	characteristic
667	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
668	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
669	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
670	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
671	C₂²×D₄	C₂×#121	1	1	yes	characteristic
672	C₂²×D₄	C₂×#121	1	1	yes	characteristic
673	C₂²×D₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
674	C₂²×D₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
675	C₂²×D₄	C₂×#123	1	1	yes	characteristic
676	C₂²×D₄	C₂×#123	1	1	yes	characteristic
677	C₂³×C₄	C₂×#95	1	1	yes	characteristic
678	C₂³×C₄	C₂×#95	1	1	yes	characteristic
679	C₂³×C₄	C₂×#95	1	1	yes	characteristic
680	C₂³×C₄	C₂×#95	1	1	yes	characteristic
681	C₂³×C₄	#379	1	1	yes	characteristic
682	C₂³×C₄	#379	1	1	yes	characteristic
683	C₂³×C₄	#381	1	1	yes	characteristic
684	C₂³×C₄	#381	1	1	yes	characteristic
685	C₂³×C₄	#381	1	1	yes	characteristic
686	C₂³×C₄	#381	1	1	yes	characteristic
687	C₂³×C₄	#385	1	1	yes	characteristic
688	C₂³×C₄	#385	1	1	yes	characteristic
689	C₂³×C₄	#385	1	1	yes	characteristic
690	C₂³×C₄	#385	1	1	yes	characteristic
691	C₂³×C₄	#385	1	1	yes	characteristic
692	C₂³×C₄	#385	1	1	yes	characteristic
693	C₂³×C₄	#386	1	1	yes	characteristic
694	C₂³×C₄	#386	1	1	yes	characteristic
695	C₂³×C₄	#386	1	1	yes	characteristic
696	C₂³×C₄	#386	1	1	yes	characteristic
697	C₂³×C₄	#386	1	1	yes	characteristic
698	C₂³×C₄	#386	1	1	yes	characteristic
699	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
700	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
701	C₂³×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
702	C₂³×C₄	C₂×#120	1	1	yes	characteristic
703	C₂³×C₄	C₂×#123	1	1	yes	characteristic
704	C₂³×C₄	C₂×#123	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂×#95	1	2	yes	—
706	C₂×C₄⋊C₄	C₂×#95	1	2	yes	—
707	C₂×C₄²	C₂×#95	1	2	yes	—
708	C₂×C₄²	C₂×#95	1	2	yes	—
709	C₂×C₄²	C₂×#95	1	2	yes	—
710	C₂×C₄²	C₂×#95	1	2	yes	—
711	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
712	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
713	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
714	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
715	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
716	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
717	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
718	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
719	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
720	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
721	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
722	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
723	C₂⁴	#1790	1	1	yes	characteristic
724	C₂⁴	#1790	1	1	yes	characteristic
725	C₂⁴	#1790	1	1	yes	characteristic
726	C₂⁴	#1790	1	1	yes	characteristic
727	C₂⁴	#1790	1	1	yes	characteristic
728	C₂⁴	#1790	1	1	yes	characteristic
729	C₂⁴	#1790	1	1	yes	characteristic
730	C₂⁴	#1790	1	1	yes	characteristic
731	C₂⁴	#1867	1	1	yes	characteristic
732	C₂⁴	#1867	1	1	yes	characteristic
733	C₂⁴	#1867	1	1	yes	characteristic
734	C₂⁴	#1867	1	1	yes	characteristic
735	C₂⁴	#1867	1	1	yes	characteristic
736	C₂⁴	#1867	1	1	yes	characteristic
737	C₂⁴	#1867	1	1	yes	characteristic
738	C₂⁴	#1867	1	1	yes	characteristic
739	C₂⁴	#1889	1	1	yes	characteristic
740	C₂⁴	#1889	1	1	yes	characteristic
741	C₂⁴	#1889	1	1	yes	characteristic
742	C₂⁴	#1889	1	1	yes	characteristic
743	C₂⁴	#1890	1	1	yes	characteristic
744	C₂⁴	#1890	1	1	yes	characteristic
745	C₂⁴	#1890	1	1	yes	characteristic
746	C₂⁴	#1890	1	1	yes	characteristic
747	C₂⁴	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
748	C₂⁴	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
749	C₂⁴	C₂×#379	1	1	yes	characteristic
750	C₂⁴	C₂×#380	1	1	yes	characteristic
751	C₂⁴	C₂×#380	1	1	yes	characteristic
752	C₂⁴	C₂×#385	1	1	yes	characteristic
753	C₂⁴	C₂×#385	1	1	yes	characteristic
754	C₂⁴	C₂×#385	1	1	yes	characteristic
755	C₂⁴	C₂×#386	1	1	yes	characteristic
756	C₂⁴	C₂×#386	1	1	yes	characteristic
757	C₂⁴	C₂×#386	1	1	yes	characteristic
758	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
759	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
760	C₂⁴	C₂×#458	1	1	yes	characteristic
761	C₂⁴	C₂×#458	1	1	yes	characteristic
762	C₂×D₄	#1913	1	4	yes	—
763	C₂×D₄	#2883	1	4	yes	—
764	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
765	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
766	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
767	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
768	C₂²×C₄	C₂²×#95	1	1	yes	characteristic
769	C₂²×C₄	C₂×#381	1	1	yes	characteristic
770	C₂²×C₄	C₂×#385	1	1	yes	characteristic
771	C₂²×C₄	C₂×#386	1	1	yes	characteristic
772	C₂³	#10745	1	1	yes	characteristic
773	C₂³	#10745	1	1	yes	characteristic
774	C₂³	#10745	1	1	yes	characteristic
775	C₂³	#10745	1	1	yes	characteristic
776	C₂³	#10745	1	1	yes	characteristic
777	C₂³	#10745	1	1	yes	characteristic
778	C₂³	#10745	1	1	yes	characteristic
779	C₂³	#10745	1	1	yes	characteristic
780	C₂³	#10754	1	2	yes	—
781	C₂³	#10754	1	2	yes	—
782	C₂³	#12753	1	2	yes	—
783	C₂³	#12754	1	2	yes	—
784	C₂³	C₂×C₂²⋊#95	1	1	yes	characteristic
785	C₂³	C₂×#1790	1	1	yes	characteristic
786	C₂³	C₂×#1790	1	1	yes	characteristic
787	C₂³	C₂×#1867	1	1	yes	characteristic
788	C₂³	C₂×#1867	1	1	yes	characteristic
789	C₂³	C₂×#1889	1	1	yes	characteristic
790	C₂³	C₂×#1890	1	1	yes	characteristic
791	C₂³	#20984	1	2	yes	—
792	C₂³	#20984	1	2	yes	—
793	C₂×C₄	#20354	1	2	yes	—
794	C₂×C₄	C₂×#1913	1	2	yes	—
795	C₂²	#146654	1	2	yes	—
796	C₂²	#146654	1	2	yes	—
797	C₂²	#353408	1	1	yes	characteristic
798	C₂²	C₂×#10745	1	1	yes	characteristic
799	C₂²	C₂×#10754	1	1	yes	characteristic
800	C₂²	C₂×#12753	1	1	yes	characteristic
801	C₂²	C₂×#12754	1	1	yes	characteristic
802	C₂²	#493562	1	1	yes	characteristic
803	C₂²	#493562	1	1	yes	characteristic
804	C₂	C₂×#146654	1	1	yes	characteristic
805	C₂	#72236441	1	1	yes	characteristic
806	C₂	#72256611	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#10745
commutator	C₂²×D₄	C₂²×C₄²
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	C₂×#35222	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72238031	C₂	semidirect
5. #72236670	C₂	semidirect
6. #72236598	C₂	semidirect
7. #72236598	C₂	semidirect
8. C₂×#106766	C₂	semidirect
9. C₂×#128073	C₂	semidirect
10. #72210473	C₂	semidirect
11. #72210462	C₂	semidirect
17. #606706	C₄	semidirect
18. #606700	C₄	semidirect
19. #606342	C₄	semidirect
20. #606302	C₄	semidirect
21. #582589	C₄	semidirect
22. #582567	C₄	semidirect
27. #538267	C₄	semidirect
28. #537841	C₄	semidirect
31. #494713	C₄	semidirect
32. #494713	C₄	semidirect
35. #379759	C₄	semidirect
36. #374045	C₄	semidirect
52. C₂³×#100	C₂×C₄	semidirect
53. C₂³×#99	C₂×C₄	semidirect
54. C₂³×#99	C₂×C₄	semidirect
71. #34171	C₂×C₄	semidirect
73. C₂×#2309	C₂×C₄	semidirect
80. C₂×#2127	C₂×C₄	semidirect
81. C₂×#1783	C₂×C₄	semidirect
83. C₂×#1781	C₂×C₄	semidirect
84. C₂×#1781	C₂×C₄	semidirect
87. #14667	C₂×C₄	semidirect
88. #14667	C₂×C₄	semidirect
89. #14662	C₂×C₄	semidirect
90. #14661	C₂×C₄	semidirect
91. #14503	C₂×C₄	semidirect
92. #14503	C₂×C₄	semidirect
93. #14492	C₂×C₄	semidirect
94. #14492	C₂×C₄	semidirect
95. #14445	C₂×C₄	semidirect
96. #14445	C₂×C₄	semidirect
97. #14419	C₂×C₄	semidirect
98. #14419	C₂×C₄	semidirect
103. #14169	C₂×C₄	semidirect
104. #14157	C₂×C₄	semidirect
105. #14157	C₂×C₄	semidirect
106. #14154	C₂×C₄	semidirect
127. #12582	C₂×C₄	semidirect
128. #11155	C₂×C₄	semidirect
129. #10989	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263415	2
#72238031	2
#72236717	2
#72236704	2
#72236670	2
#72236598	2
C₂×#106766	2
C₂×#128073	2
#72210473	2
#72210462	2