Subgroups — #72317002

Order 2048.

At least 7516 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.

The subgroup lattice has 801 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316800	C₂	1	1	yes	maximal, characteristic, complemented
2	#72316775	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316772	C₂	1	4	yes	maximal, complemented
4	#72316742	C₂	1	4	yes	maximal, complemented
5	#72316707	C₂	1	8	yes	maximal, complemented
6	#72316243	C₂	1	1	yes	maximal, characteristic, complemented
7	#72312553	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#6487648	C₂	1	1	yes	maximal, characteristic
9	#72308410	C₂	1	1	yes	maximal, characteristic, complemented
10	#72308403	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282520	C₂	1	4	yes	maximal, complemented
12	#72282292	C₂	1	4	yes	maximal, complemented
13	C₂×#62812	C₂²	1	1	yes	characteristic
14	C₂×#34963	C₂²	1	1	yes	characteristic
15	#6487648	C₄	1	4	yes	complemented
16	#6487648	C₄	1	2	yes	complemented
17	#6487648	C₄	1	2	yes	complemented
18	#6487648	C₂²	1	4	yes	—
19	#6487648	C₂²	1	2	yes	—
20	#6487648	C₂²	1	2	yes	—
21	C₂×#25900	C₄	1	2	yes	complemented
22	C₂×#25771	C₄	1	2	yes	complemented
23	C₂×#24260	C₂²	1	4	yes	—
24	C₂×#29636	C₄	1	4	yes	complemented
25	#6412344	C₂²	1	4	yes	complemented
26	#6412326	C₂²	1	2	yes	complemented
27	#6412324	C₂²	1	2	yes	complemented
28	#6407465	C₂²	1	2	yes	complemented
29	#6381486	C₂²	1	2	yes	complemented
30	#6374537	C₂²	1	1	yes	characteristic
31	#6372358	C₂²	1	1	yes	characteristic
32	#6370950	C₂²	1	1	yes	characteristic
33	#6370937	C₂²	1	1	yes	characteristic
34	C₂×#20723	C₂²	1	1	yes	characteristic
35	#496520	C₂²	1	4	yes	complemented
36	#496508	C₂²	1	2	yes	complemented
37	#496508	C₂²	1	2	yes	complemented
38	#493995	C₂²	1	4	yes	complemented
39	#185412	C₂²	1	4	yes	complemented
40	#185410	C₂²	1	2	yes	—
41	#185410	C₂²	1	2	yes	—
42	#185373	C₂²	1	4	yes	complemented
43	#185348	C₂²	1	4	yes	complemented
44	#185339	C₂²	1	4	yes	—
45	#185332	C₂²	1	4	yes	complemented
46	#139612	C₂²	1	16	yes	complemented
47	#139610	C₂²	1	16	yes	complemented
48	#139546	C₂²	1	16	yes	complemented
49	#139544	C₂²	1	16	yes	complemented
50	#127399	C₂²	1	4	yes	complemented
51	#127396	C₂²	1	4	yes	complemented
52	#127395	C₂²	1	2	yes	complemented
53	#127395	C₂²	1	2	yes	complemented
54	#127389	C₂²	1	4	yes	complemented
55	#127388	C₂²	1	4	yes	complemented
56	#127377	C₂²	1	4	yes	complemented
57	#62812	C₂×C₄	1	2	yes	—
58	#62812	C₂×C₄	1	2	yes	—
59	#62812	C₂³	1	2	yes	—
60	#62812	C₂³	1	2	yes	—
61	C₂×#3496	C₂×C₄	1	2	yes	—
62	C₂×#3496	C₂³	1	2	yes	—
63	C₂×#3449	C₂×C₄	1	2	yes	—
64	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
65	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
66	C₂×#2920	D₄	1	1	yes	characteristic, complemented
67	C₂×#2920	D₄	1	1	yes	characteristic, complemented
68	C₂²×#423	D₄	1	1	yes	characteristic, complemented
69	C₂²×C₄×M₁₆	D₄	1	1	yes	characteristic, complemented
70	#34963	C₂×C₄	1	1	yes	characteristic
71	#34963	C₂×C₄	1	1	yes	characteristic
72	#34963	C₂×C₄	1	2	yes	—
73	#34963	D₄	1	2	yes	—
74	#34963	D₄	1	1	yes	characteristic
75	#34963	D₄	1	1	yes	characteristic
76	#34963	D₄	1	1	yes	characteristic
77	#34963	D₄	1	1	yes	characteristic
78	#34963	D₄	1	2	yes	—
79	#34963	C₂³	1	1	yes	characteristic
80	#34963	C₂³	1	1	yes	characteristic
81	#34963	C₂³	1	2	yes	—
82	C₂×#2482	C₂×C₄	1	2	yes	—
83	C₂×#2487	C₂×C₄	1	1	yes	characteristic
84	C₂×#2487	D₄	1	1	yes	characteristic
85	C₂×#2404	D₄	1	2	yes	—
86	C₂×#2408	C₂×C₄	1	1	yes	characteristic
87	C₂×#2408	D₄	1	1	yes	characteristic
88	C₂×C₄×#120	D₄	1	2	yes	—
89	C₂×C₄×#120	C₂³	1	2	yes	—
90	C₂×#2283	D₄	1	1	yes	characteristic
91	#29636	C₂×C₄	1	8	yes	—
92	#29636	C₂×C₄	1	8	yes	—
93	#29636	C₂×C₄	1	8	yes	—
94	#29636	C₂×C₄	1	8	yes	—
95	#25900	C₂×C₄	1	8	yes	—
96	#25900	C₂×C₄	1	4	yes	—
97	#25900	C₂×C₄	1	4	yes	—
98	#25771	C₂×C₄	1	8	yes	—
99	#25771	C₂×C₄	1	4	yes	—
100	#25771	C₂×C₄	1	4	yes	—
101	#24260	C₂×C₄	1	8	yes	—
102	#24260	C₂×C₄	1	8	yes	—
103	#24260	C₂³	1	8	yes	—
104	#24260	C₂³	1	8	yes	—
105	C₂×#2044	C₂×C₄	1	8	yes	—
106	C₂×#2021	C₂×C₄	1	8	yes	—
107	#23307	C₂³	1	4	yes	complemented
108	#23306	C₂³	1	4	yes	complemented
109	#22850	C₂³	1	4	yes	complemented
110	#22842	C₂³	1	4	yes	complemented
111	#21851	D₄	1	2	yes	complemented
112	#21851	C₂³	1	2	yes	—
113	#21847	D₄	1	2	yes	complemented
114	#21847	C₂³	1	2	yes	—
115	#21380	D₄	1	2	yes	complemented
116	#21380	C₂³	1	2	yes	—
117	#21373	D₄	1	2	yes	complemented
118	#21373	C₂³	1	2	yes	—
119	#21303	D₄	1	1	yes	characteristic, complemented
120	#21303	D₄	1	1	yes	characteristic, complemented
121	#21190	C₂³	1	1	yes	characteristic
122	#21190	C₂³	1	1	yes	characteristic
123	#20898	D₄	1	2	yes	complemented
124	#20898	C₂³	1	2	yes	—
125	#20728	C₂³	1	2	yes	—
126	#20726	C₂³	1	2	yes	—
127	#20723	C₂×C₄	1	2	yes	—
128	#20723	C₂×C₄	1	2	yes	—
129	#20723	C₂³	1	2	yes	—
130	#20723	C₂³	1	2	yes	—
131	#20723	C₂³	1	2	yes	—
132	#20722	C₂³	1	2	yes	—
133	C₂×#1820	C₂×C₄	1	2	yes	—
134	#20637	C₂³	1	2	yes	—
135	#20632	C₂³	1	2	yes	—
136	C₂×#1799	C₂³	1	2	yes	—
137	C₂×C₄×#99	C₂×C₄	1	2	yes	—
138	#12793	C₂³	1	8	yes	complemented
139	#12793	C₂³	1	8	yes	complemented
140	#8353	C₂³	1	8	yes	—
141	#8353	C₂³	1	8	yes	—
142	#8350	C₂³	1	16	yes	—
143	#7237	C₂³	1	8	yes	complemented
144	#7237	C₂³	1	8	yes	complemented
145	#7236	C₂³	1	16	yes	complemented
146	C₂³×#41	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
148	C₂⁵×C₄	C₂×D₄	1	2	yes	—
149	C₂³×M₁₆	C₂×D₄	1	2	yes	—
150	#3496	C₂²×C₄	1	4	yes	—
151	#3496	C₂²×C₄	1	4	yes	—
152	#3496	C₂²×C₄	1	4	yes	—
153	#3496	C₂⁴	1	4	yes	—
154	#3449	C₂²×C₄	1	4	yes	—
155	#3449	C₂²×C₄	1	4	yes	—
156	C₂×#534	C₂²×C₄	1	4	yes	—
157	C₂²×#120	C₂²⋊C₄	1	2	yes	—
158	C₂²×#120	C₂×D₄	1	2	yes	—
159	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×#41	#41	1	1	yes	characteristic
170	C₂×C₄×#41	#41	1	1	yes	characteristic
171	C₂×C₄×#41	#41	1	1	yes	characteristic
172	C₂×C₄×#41	#41	1	1	yes	characteristic
173	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
177	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
179	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
183	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×D₄	#41	1	1	yes	characteristic
188	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
189	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
190	C₂²×#117	#41	1	1	yes	characteristic
191	C₂²×#117	#41	1	1	yes	characteristic
192	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
194	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
196	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
197	C₂×#432	C₂×D₄	1	2	yes	complemented
198	C₂×#432	C₂×D₄	1	2	yes	complemented
199	C₂×#431	C₂×D₄	1	2	yes	complemented
200	C₂×#431	C₂×D₄	1	2	yes	complemented
201	C₂×#423	C₂×D₄	1	1	yes	characteristic
202	C₂×#423	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	complemented
204	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	complemented
205	C₂×#407	C₂×D₄	1	2	yes	—
206	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	complemented
209	C₂²×C₄×C₈	C₂×D₄	1	2	yes	complemented
210	#2487	C₂²⋊C₄	1	1	yes	characteristic
211	#2487	C₂²⋊C₄	1	1	yes	characteristic
212	#2487	C₂²⋊C₄	1	2	yes	—
213	#2487	C₂²⋊C₄	1	2	yes	—
214	#2487	C₂²⋊C₄	1	1	yes	characteristic
215	#2487	C₂²⋊C₄	1	1	yes	characteristic
216	#2487	C₂²×C₄	1	1	yes	characteristic
217	#2487	C₂²×C₄	1	1	yes	characteristic
218	#2487	C₂²×C₄	1	2	yes	—
219	#2487	C₂×D₄	1	2	yes	—
220	#2487	C₂×D₄	1	1	yes	characteristic
221	#2487	C₂×D₄	1	1	yes	characteristic
222	#2482	C₂²⋊C₄	1	2	yes	—
223	#2482	C₂²⋊C₄	1	2	yes	—
224	#2482	C₂²⋊C₄	1	2	yes	—
225	#2482	C₂²⋊C₄	1	2	yes	—
226	#2482	C₂²×C₄	1	2	yes	—
227	#2482	C₂²×C₄	1	2	yes	—
228	#2482	C₂²×C₄	1	2	yes	—
229	#2482	C₂²×C₄	1	2	yes	—
230	#2408	C₂²⋊C₄	1	1	yes	characteristic
231	#2408	C₂²⋊C₄	1	2	yes	—
232	#2408	C₂²⋊C₄	1	1	yes	characteristic
233	#2408	C₂²⋊C₄	1	1	yes	characteristic
234	#2408	C₂²⋊C₄	1	1	yes	characteristic
235	#2408	C₂²⋊C₄	1	2	yes	—
236	#2408	C₂²×C₄	1	1	yes	characteristic
237	#2408	C₂²×C₄	1	1	yes	characteristic
238	#2408	C₂²×C₄	1	2	yes	—
239	#2408	C₂×D₄	1	2	yes	—
240	#2408	C₂×D₄	1	1	yes	characteristic
241	#2408	C₂×D₄	1	1	yes	characteristic
242	#2404	C₂²⋊C₄	1	2	yes	—
243	#2404	C₂²⋊C₄	1	2	yes	—
244	#2404	C₂²⋊C₄	1	2	yes	—
245	#2404	C₂²⋊C₄	1	2	yes	—
246	#2404	C₂×D₄	1	2	yes	—
247	#2404	C₂×D₄	1	2	yes	—
248	#2404	C₂×D₄	1	2	yes	—
249	#2404	C₂×D₄	1	2	yes	—
250	C₄×#120	C₂²⋊C₄	1	2	yes	—
251	C₄×#120	C₂²⋊C₄	1	2	yes	—
252	C₄×#120	C₂²⋊C₄	1	2	yes	—
253	C₄×#120	C₂²⋊C₄	1	2	yes	—
254	C₄×#120	C₂²×C₄	1	2	yes	—
255	C₄×#120	C₂²×C₄	1	2	yes	—
256	C₄×#120	C₂×D₄	1	2	yes	—
257	C₄×#120	C₂×D₄	1	2	yes	—
258	C₄×#120	C₂×D₄	1	2	yes	—
259	C₄×#120	C₂×D₄	1	2	yes	—
260	C₄×#120	C₂×D₄	1	2	yes	—
261	C₄×#120	C₂×D₄	1	2	yes	—
262	C₄×#120	C₂×D₄	1	2	yes	—
263	C₄×#120	C₂×D₄	1	2	yes	—
264	C₄×#120	C₂⁴	1	2	yes	—
265	C₄×#120	C₂⁴	1	2	yes	—
266	C₂×#386	C₂²⋊C₄	1	2	yes	—
267	C₂×#386	C₂×D₄	1	2	yes	—
268	C₂×#385	C₂²⋊C₄	1	2	yes	—
269	C₂×#385	C₂²×C₄	1	2	yes	—
270	#2283	C₂²⋊C₄	1	2	yes	—
271	#2283	C₂²⋊C₄	1	1	yes	characteristic
272	#2283	C₂²⋊C₄	1	1	yes	characteristic
273	#2283	C₂×D₄	1	1	yes	characteristic
274	#2283	C₂×D₄	1	1	yes	characteristic
275	#2283	C₂×D₄	1	2	yes	—
276	C₂×#381	C₂²⋊C₄	1	2	yes	—
277	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
278	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#379	C₂²⋊C₄	1	2	yes	—
280	C₂×#379	C₂²×C₄	1	2	yes	—
281	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
282	#2044	C₂²×C₄	1	16	yes	—
283	#2044	C₂²×C₄	1	16	yes	—
284	#2021	C₂²×C₄	1	16	yes	—
285	#2021	C₂²×C₄	1	16	yes	—
286	#1984	C₂×D₄	1	2	yes	complemented
287	#1984	C₂×D₄	1	2	yes	complemented
288	#1984	C₂×D₄	1	2	yes	complemented
289	#1984	C₂×D₄	1	2	yes	complemented
290	#1954	C₂×D₄	1	2	yes	—
291	#1954	C₂×D₄	1	2	yes	—
292	#1954	C₂⁴	1	2	yes	—
293	#1954	C₂⁴	1	2	yes	—
294	#1869	C₂×D₄	1	4	yes	—
295	#1869	C₂×D₄	1	4	yes	complemented
296	#1869	C₂×D₄	1	4	yes	complemented
297	#1869	C₂⁴	1	4	yes	—
298	#1820	C₂²×C₄	1	4	yes	—
299	#1820	C₂²×C₄	1	4	yes	—
300	#1800	C₂⁴	1	4	yes	—
301	#1799	C₂²×C₄	1	4	yes	—
302	#1799	C₂⁴	1	4	yes	—
303	#1799	C₂⁴	1	4	yes	—
304	C₄×#99	C₂²×C₄	1	4	yes	—
305	C₄×#99	C₂²×C₄	1	4	yes	—
306	C₂×#342	C₂²×C₄	1	4	yes	—
307	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×#41	#121	1	1	yes	characteristic
311	C₂²×#41	#121	1	1	yes	characteristic
312	C₂²×#41	#121	1	1	yes	characteristic
313	C₂²×#41	#121	1	1	yes	characteristic
314	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
315	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
316	C₂³×Q₈	#121	1	1	yes	characteristic
317	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
320	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂³×D₄	#121	1	1	yes	characteristic
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
326	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	#120	1	1	yes	characteristic
330	C₂⁴×C₄	#121	1	1	yes	characteristic
331	C₂⁴×C₄	#121	1	1	yes	characteristic
332	C₂⁴×C₄	#121	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
336	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
337	C₂³×C₈	C₂²×D₄	1	4	yes	—
338	#534	C₂³×C₄	1	8	yes	—
339	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂×#120	C₂²×D₄	1	2	yes	—
346	C₂×#120	C₂²×D₄	1	2	yes	—
347	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
348	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
349	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
351	C₂×C₄×Q₈	#120	1	1	yes	characteristic
352	C₂×C₄×Q₈	#120	1	1	yes	characteristic
353	C₂×C₄×Q₈	#121	1	1	yes	characteristic
354	C₂×C₄×Q₈	#121	1	1	yes	characteristic
355	C₂×C₄×Q₈	#121	1	1	yes	characteristic
356	C₂×C₄×Q₈	#121	1	1	yes	characteristic
357	C₂×C₄×Q₈	#123	1	1	yes	characteristic
358	C₂×C₄×Q₈	#123	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
370	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
371	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
372	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
373	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
374	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
375	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
376	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
377	C₂×C₄×D₄	#120	1	1	yes	characteristic
378	C₂×C₄×D₄	#120	1	1	yes	characteristic
379	C₂×C₄×D₄	#120	1	1	yes	characteristic
380	C₂×C₄×D₄	#120	1	1	yes	characteristic
381	C₂×C₄×D₄	#121	1	1	yes	characteristic
382	C₂×C₄×D₄	#121	1	1	yes	characteristic
383	C₂×C₄×D₄	#121	1	1	yes	characteristic
384	C₂×C₄×D₄	#121	1	1	yes	characteristic
385	C₂×C₄×D₄	#121	1	1	yes	characteristic
386	C₂×C₄×D₄	#121	1	1	yes	characteristic
387	C₂×C₄×D₄	#121	1	1	yes	characteristic
388	C₂×C₄×D₄	#121	1	1	yes	characteristic
389	C₂×C₄×D₄	#123	1	1	yes	characteristic
390	C₂×C₄×D₄	#123	1	1	yes	characteristic
391	C₂×C₄×D₄	#123	1	1	yes	characteristic
392	C₂×C₄×D₄	#123	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
411	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
413	C₂×#117	C₄×D₄	1	1	yes	characteristic
414	C₂×#117	C₄×D₄	1	1	yes	characteristic
415	C₂×#117	C₄×D₄	1	1	yes	characteristic
416	C₂×#117	C₄×D₄	1	1	yes	characteristic
417	C₂×#117	C₄×D₄	1	1	yes	characteristic
418	C₂×#117	C₄×D₄	1	1	yes	characteristic
419	C₂×#117	C₄×D₄	1	1	yes	characteristic
420	C₂×#117	C₄×D₄	1	1	yes	characteristic
421	C₂×#117	#121	1	1	yes	characteristic
422	C₂×#117	#121	1	1	yes	characteristic
423	C₂×#117	#121	1	1	yes	characteristic
424	C₂×#117	#121	1	1	yes	characteristic
425	C₂×#117	#123	1	1	yes	characteristic
426	C₂×#117	#123	1	1	yes	characteristic
427	C₂×#117	#123	1	1	yes	characteristic
428	C₂×#117	#123	1	1	yes	characteristic
429	C₂×#117	C₂³×C₄	1	1	yes	characteristic
430	C₂×#117	C₂³×C₄	1	1	yes	characteristic
431	C₂×#117	C₂×#41	1	1	yes	characteristic
432	C₂×#117	C₂×#41	1	1	yes	characteristic
433	C₂×#117	C₂×#41	1	1	yes	characteristic
434	C₂×#117	C₂×#41	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	#123	1	1	yes	characteristic
443	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
445	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
448	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
449	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
450	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	#123	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
456	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
459	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
460	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
461	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
462	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
463	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
464	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
465	C₂²×C₄²	#120	1	1	yes	characteristic
466	C₂²×C₄²	#120	1	1	yes	characteristic
467	C₂²×C₄²	#120	1	1	yes	characteristic
468	C₂²×C₄²	#120	1	1	yes	characteristic
469	C₂²×C₄²	#120	1	1	yes	characteristic
470	C₂²×C₄²	#120	1	1	yes	characteristic
471	C₂²×C₄²	#120	1	1	yes	characteristic
472	C₂²×C₄²	#120	1	1	yes	characteristic
473	C₂²×C₄²	#120	1	1	yes	characteristic
474	C₂²×C₄²	#121	1	1	yes	characteristic
475	C₂²×C₄²	#121	1	1	yes	characteristic
476	C₂²×C₄²	#121	1	1	yes	characteristic
477	C₂²×C₄²	#121	1	1	yes	characteristic
478	C₂²×C₄²	#121	1	1	yes	characteristic
479	C₂²×C₄²	#123	1	1	yes	characteristic
480	C₂²×C₄²	#123	1	1	yes	characteristic
481	C₂²×C₄²	#123	1	1	yes	characteristic
482	C₂²×C₄²	#123	1	1	yes	characteristic
483	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
484	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
485	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
486	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
487	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
488	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
489	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
491	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
492	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
493	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
495	#386	C₂×C₂²⋊C₄	1	2	yes	—
496	#386	C₂×C₂²⋊C₄	1	2	yes	—
497	#386	C₂×C₂²⋊C₄	1	2	yes	—
498	#386	C₂×C₂²⋊C₄	1	2	yes	—
499	#386	C₂×C₂²⋊C₄	1	2	yes	—
500	#386	C₂×C₂²⋊C₄	1	2	yes	—
501	#386	C₂²×D₄	1	2	yes	—
502	#386	C₂²×D₄	1	2	yes	—
503	#385	C₂×C₂²⋊C₄	1	2	yes	—
504	#385	C₂×C₂²⋊C₄	1	2	yes	—
505	#385	C₂×C₂²⋊C₄	1	2	yes	—
506	#385	C₂×C₂²⋊C₄	1	2	yes	—
507	#385	C₂×C₂²⋊C₄	1	2	yes	—
508	#385	C₂×C₂²⋊C₄	1	2	yes	—
509	#385	C₂³×C₄	1	2	yes	—
510	#385	C₂³×C₄	1	2	yes	—
511	#381	C₂×C₂²⋊C₄	1	2	yes	—
512	#381	C₂×C₂²⋊C₄	1	2	yes	—
513	#381	C₂×C₂²⋊C₄	1	2	yes	—
514	#381	C₂×C₂²⋊C₄	1	2	yes	—
515	#380	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	#380	C₂×C₂²⋊C₄	1	1	yes	characteristic
517	#380	C₂×C₂²⋊C₄	1	2	yes	—
518	#380	C₂×C₂²⋊C₄	1	1	yes	characteristic
519	#380	C₂×C₂²⋊C₄	1	1	yes	characteristic
520	#380	C₂×C₂²⋊C₄	1	2	yes	—
521	#379	C₂×C₂²⋊C₄	1	2	yes	—
522	#379	C₂×C₂²⋊C₄	1	2	yes	—
523	#379	C₂×C₂²⋊C₄	1	2	yes	—
524	#379	C₂×C₂²⋊C₄	1	2	yes	—
525	#379	C₂×C₂²⋊C₄	1	2	yes	—
526	#379	C₂×C₂²⋊C₄	1	2	yes	—
527	#379	C₂³×C₄	1	2	yes	—
528	#379	C₂³×C₄	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
533	#342	C₂³×C₄	1	8	yes	—
534	C₂⁵	#386	1	1	yes	characteristic
535	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
536	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
537	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
538	C₂⁵	C₂×#121	1	1	yes	characteristic
539	C₂²×Q₈	#386	1	1	yes	characteristic
540	C₂²×Q₈	#386	1	1	yes	characteristic
541	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
542	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
543	C₂²×D₄	#386	1	1	yes	characteristic
544	C₂²×D₄	#386	1	1	yes	characteristic
545	C₂²×D₄	#386	1	1	yes	characteristic
546	C₂²×D₄	#386	1	1	yes	characteristic
547	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
548	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
549	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
550	C₂²×D₄	C₂×#121	1	1	yes	characteristic
551	C₂²×D₄	C₂×#121	1	1	yes	characteristic
552	C₂²×D₄	C₂×#121	1	1	yes	characteristic
553	C₂²×D₄	C₂×#121	1	1	yes	characteristic
554	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
555	C₂³×C₄	#386	1	1	yes	characteristic
556	C₂³×C₄	#386	1	1	yes	characteristic
557	C₂³×C₄	#386	1	1	yes	characteristic
558	C₂³×C₄	#386	1	1	yes	characteristic
559	C₂³×C₄	#386	1	1	yes	characteristic
560	C₂³×C₄	#386	1	1	yes	characteristic
561	C₂³×C₄	#386	1	1	yes	characteristic
562	C₂³×C₄	#386	1	1	yes	characteristic
563	C₂³×C₄	#386	1	1	yes	characteristic
564	C₂³×C₄	#386	1	1	yes	characteristic
565	C₂³×C₄	#386	1	1	yes	characteristic
566	C₂³×C₄	#386	1	1	yes	characteristic
567	C₂³×C₄	#386	1	1	yes	characteristic
568	C₂³×C₄	#386	1	1	yes	characteristic
569	C₂³×C₄	#386	1	1	yes	characteristic
570	C₂³×C₄	#386	1	1	yes	characteristic
571	C₂³×C₄	#386	1	1	yes	characteristic
572	C₂³×C₄	#386	1	1	yes	characteristic
573	C₂³×C₄	#386	1	1	yes	characteristic
574	C₂³×C₄	#386	1	1	yes	characteristic
575	C₂³×C₄	#386	1	1	yes	characteristic
576	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
577	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
578	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
579	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
580	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
581	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
582	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
583	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
584	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
585	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
586	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
587	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
588	C₂³×C₄	C₂×#120	1	1	yes	characteristic
589	C₂³×C₄	C₂×#120	1	1	yes	characteristic
590	C₂³×C₄	C₂×#120	1	1	yes	characteristic
591	C₂³×C₄	C₂×#120	1	1	yes	characteristic
592	C₂³×C₄	C₂×#120	1	1	yes	characteristic
593	C₂³×C₄	C₂×#121	1	1	yes	characteristic
594	C₂³×C₄	C₂×#121	1	1	yes	characteristic
595	C₂³×C₄	C₂×#121	1	1	yes	characteristic
596	C₂³×C₄	C₂×#121	1	1	yes	characteristic
597	C₂³×C₄	C₂×#121	1	1	yes	characteristic
598	C₂³×C₄	C₂×#121	1	1	yes	characteristic
599	C₂³×C₄	C₂×#121	1	1	yes	characteristic
600	C₂³×C₄	C₂×#121	1	1	yes	characteristic
601	C₂³×C₄	C₂×#123	1	1	yes	characteristic
602	C₂³×C₄	C₂×#123	1	1	yes	characteristic
603	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
604	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
606	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
607	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
608	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
609	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
610	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
611	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
612	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
613	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
614	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂²×#41	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂⁴×C₄	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂²×#41	1	1	yes	characteristic
657	C₂×C₄²	#386	1	1	yes	characteristic
658	C₂×C₄²	#386	1	1	yes	characteristic
659	C₂×C₄²	#386	1	1	yes	characteristic
660	C₂×C₄²	#386	1	1	yes	characteristic
661	C₂×C₄²	#386	1	1	yes	characteristic
662	C₂×C₄²	#386	1	1	yes	characteristic
663	C₂×C₄²	#386	1	1	yes	characteristic
664	C₂×C₄²	#386	1	1	yes	characteristic
665	C₂×C₄²	#386	1	1	yes	characteristic
666	C₂×C₄²	#386	1	1	yes	characteristic
667	C₂×C₄²	#386	1	1	yes	characteristic
668	C₂×C₄²	#386	1	1	yes	characteristic
669	C₂×C₄²	#386	1	1	yes	characteristic
670	C₂×C₄²	#386	1	1	yes	characteristic
671	C₂×C₄²	#386	1	1	yes	characteristic
672	C₂×C₄²	#386	1	1	yes	characteristic
673	C₂×C₄²	#386	1	1	yes	characteristic
674	C₂×C₄²	#386	1	1	yes	characteristic
675	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
678	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
680	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
681	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
682	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
683	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
685	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
686	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
687	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
688	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
689	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₂×#120	1	1	yes	characteristic
691	C₂×C₄²	C₂×#120	1	1	yes	characteristic
692	C₂×C₄²	C₂×#120	1	1	yes	characteristic
693	C₂×C₄²	C₂×#120	1	1	yes	characteristic
694	C₂×C₄²	C₂×#120	1	1	yes	characteristic
695	C₂×C₄²	C₂×#120	1	1	yes	characteristic
696	C₂×C₄²	C₂×#120	1	1	yes	characteristic
697	C₂×C₄²	C₂×#121	1	1	yes	characteristic
698	C₂×C₄²	C₂×#121	1	1	yes	characteristic
699	C₂×C₄²	C₂×#121	1	1	yes	characteristic
700	C₂×C₄²	C₂×#123	1	1	yes	characteristic
701	C₂×C₄²	C₂×#123	1	1	yes	characteristic
702	C₂×C₄²	C₂×#123	1	1	yes	characteristic
703	C₂×C₄²	C₂×#123	1	1	yes	characteristic
704	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
705	C₂⁴	C₂×#386	1	1	yes	characteristic
706	C₂⁴	C₂×#386	1	1	yes	characteristic
707	C₂⁴	C₂×#386	1	1	yes	characteristic
708	C₂⁴	C₂×#386	1	1	yes	characteristic
709	C₂⁴	C₂×#386	1	1	yes	characteristic
710	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
711	C₂⁴	C₂²×#121	1	1	yes	characteristic
712	C₂×D₄	#1910	1	4	yes	—
713	C₂×D₄	#3585	1	4	yes	—
714	C₂²×C₄	#1889	1	1	yes	characteristic
715	C₂²×C₄	#1889	1	1	yes	characteristic
716	C₂²×C₄	#1889	1	1	yes	characteristic
717	C₂²×C₄	#1889	1	1	yes	characteristic
718	C₂²×C₄	#1889	1	1	yes	characteristic
719	C₂²×C₄	#1889	1	1	yes	characteristic
720	C₂²×C₄	#1889	1	1	yes	characteristic
721	C₂²×C₄	#1889	1	1	yes	characteristic
722	C₂²×C₄	C₂×#386	1	1	yes	characteristic
723	C₂²×C₄	C₂×#386	1	1	yes	characteristic
724	C₂²×C₄	C₂×#386	1	1	yes	characteristic
725	C₂²×C₄	C₂×#386	1	1	yes	characteristic
726	C₂²×C₄	C₂×#386	1	1	yes	characteristic
727	C₂²×C₄	C₂×#386	1	1	yes	characteristic
728	C₂²×C₄	C₂×#386	1	1	yes	characteristic
729	C₂²×C₄	C₂×#386	1	1	yes	characteristic
730	C₂²×C₄	C₂×#386	1	1	yes	characteristic
731	C₂²×C₄	C₂×#386	1	1	yes	characteristic
732	C₂²×C₄	C₂×#386	1	1	yes	characteristic
733	C₂²×C₄	C₂×#386	1	1	yes	characteristic
734	C₂²×C₄	C₂×#386	1	1	yes	characteristic
735	C₂²×C₄	C₂×#386	1	1	yes	characteristic
736	C₂²×C₄	C₂×#386	1	1	yes	characteristic
737	C₂²×C₄	C₂×#386	1	1	yes	characteristic
738	C₂²×C₄	C₂×#386	1	1	yes	characteristic
739	C₂²×C₄	C₂×#386	1	1	yes	characteristic
740	C₂²×C₄	C₂×#386	1	1	yes	characteristic
741	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
742	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
743	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
744	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
745	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
746	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
747	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
748	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
749	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
750	C₄²	#1889	1	1	yes	characteristic
751	C₄²	#1889	1	1	yes	characteristic
752	C₄²	#1889	1	1	yes	characteristic
753	C₄²	#1889	1	1	yes	characteristic
754	C₄²	#1889	1	1	yes	characteristic
755	C₄²	#1889	1	1	yes	characteristic
756	C₄²	#1889	1	1	yes	characteristic
757	C₄²	#1889	1	1	yes	characteristic
758	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
759	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
760	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
761	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
762	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
763	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
764	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
765	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
766	C₂³	C₂×#1889	1	1	yes	characteristic
767	C₂³	C₂×#1889	1	1	yes	characteristic
768	C₂³	C₂×#1910	1	2	yes	—
769	C₂³	C₂×#1910	1	2	yes	—
770	C₂³	C₂²×#386	1	1	yes	characteristic
771	C₂³	#60087	1	2	yes	—
772	C₂³	#60454	1	2	yes	—
773	C₂×C₄	C₂×#1889	1	1	yes	characteristic
774	C₂×C₄	C₂×#1889	1	1	yes	characteristic
775	C₂×C₄	C₂×#1889	1	1	yes	characteristic
776	C₂×C₄	C₂×#1889	1	1	yes	characteristic
777	C₂×C₄	C₂×#1889	1	1	yes	characteristic
778	C₂×C₄	C₂×#1889	1	1	yes	characteristic
779	C₂×C₄	C₂×#1889	1	1	yes	characteristic
780	C₂×C₄	C₂×#1889	1	1	yes	characteristic
781	C₂×C₄	C₂×#1889	1	1	yes	characteristic
782	C₂×C₄	C₂×#1889	1	1	yes	characteristic
783	C₂×C₄	C₂×#1910	1	2	yes	—
784	C₂×C₄	#33559	1	2	yes	—
785	C₂×C₄	#33560	1	2	yes	—
786	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
787	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
788	C₂×C₄	#60454	1	2	yes	—
789	C₂²	#494583	1	2	yes	—
790	C₂²	C₂²×#1889	1	1	yes	characteristic
791	C₂²	#6371484	1	1	yes	characteristic
792	C₂²	C₂²×#1910	1	1	yes	characteristic
793	C₄	#494583	1	2	yes	—
794	C₄	#494587	1	2	yes	—
795	C₄	C₂×#33559	1	1	yes	characteristic
796	C₄	C₂×#33560	1	1	yes	characteristic
797	C₂	C₂×#494587	1	1	yes	characteristic
798	C₂	C₂×#494583	1	1	yes	characteristic
799	C₂	#72316677	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1889
commutator	C₂×C₂²⋊C₄	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	C₂×#6487648	C₂
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂²×C₄×#41 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72316800	C₂	semidirect
2. #72316775	C₂	semidirect
3. #72316772	C₂	semidirect
4. #72316742	C₂	semidirect
5. #72316707	C₂	semidirect
6. #72316243	C₂	semidirect
7. #72312553	C₂	semidirect
9. #72308410	C₂	semidirect
10. #72308403	C₂	semidirect
11. #72282520	C₂	semidirect
12. #72282292	C₂	semidirect
15. #6487648	C₄	semidirect
16. #6487648	C₄	semidirect
17. #6487648	C₄	semidirect
21. C₂×#25900	C₄	semidirect
22. C₂×#25771	C₄	semidirect
24. C₂×#29636	C₄	semidirect
25. #6412344	C₂²	semidirect
26. #6412326	C₂²	semidirect
27. #6412324	C₂²	semidirect
28. #6407465	C₂²	semidirect
29. #6381486	C₂²	semidirect
35. #496520	C₂²	semidirect
36. #496508	C₂²	semidirect
37. #496508	C₂²	semidirect
38. #493995	C₂²	semidirect
39. #185412	C₂²	semidirect
42. #185373	C₂²	semidirect
43. #185348	C₂²	semidirect
45. #185332	C₂²	semidirect
46. #139612	C₂²	semidirect
47. #139610	C₂²	semidirect
48. #139546	C₂²	semidirect
49. #139544	C₂²	semidirect
50. #127399	C₂²	semidirect
51. #127396	C₂²	semidirect
52. #127395	C₂²	semidirect
53. #127395	C₂²	semidirect
54. #127389	C₂²	semidirect
55. #127388	C₂²	semidirect
56. #127377	C₂²	semidirect
66. C₂×#2920	D₄	semidirect
67. C₂×#2920	D₄	semidirect
68. C₂²×#423	D₄	semidirect
69. C₂²×C₄×M₁₆	D₄	semidirect
107. #23307	C₂³	semidirect
108. #23306	C₂³	semidirect
109. #22850	C₂³	semidirect
110. #22842	C₂³	semidirect
111. #21851	D₄	semidirect
113. #21847	D₄	semidirect
115. #21380	D₄	semidirect
117. #21373	D₄	semidirect
119. #21303	D₄	semidirect
120. #21303	D₄	semidirect
123. #20898	D₄	semidirect
138. #12793	C₂³	semidirect
139. #12793	C₂³	semidirect
143. #7237	C₂³	semidirect
144. #7237	C₂³	semidirect
145. #7236	C₂³	semidirect
197. C₂×#432	C₂×D₄	semidirect
198. C₂×#432	C₂×D₄	semidirect
199. C₂×#431	C₂×D₄	semidirect
200. C₂×#431	C₂×D₄	semidirect
203. C₂²×C₄⋊C₈	C₂×D₄	semidirect
204. C₂²×C₄⋊C₈	C₂×D₄	semidirect
208. C₂×C₄×M₁₆	C₂×D₄	semidirect
209. C₂²×C₄×C₈	C₂×D₄	semidirect
286. #1984	C₂×D₄	semidirect
287. #1984	C₂×D₄	semidirect
288. #1984	C₂×D₄	semidirect
289. #1984	C₂×D₄	semidirect
295. #1869	C₂×D₄	semidirect
296. #1869	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72316800	2
#72316775	2
#72316772	2
#72316742	2
#72316707	2
#72316243	2
#72312553	2
C₂×#6487648	2
#72308410	2
#72308403	2
#72282520	2
#72282292	2