Subgroups — #72338742

Order 2048.

At least 7264 conjugacy classes of subgroups; only the 1896 normal subgroups are shown.

The subgroup lattice has 846 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338732	C₂	1	8	yes	maximal, complemented
2	#72338729	C₂	1	8	yes	maximal, complemented
3	#72338724	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338689	C₂	1	4	yes	maximal, complemented
5	#72338672	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338659	C₂	1	1	yes	maximal, characteristic, complemented
7	#72312553	C₂	1	1	yes	maximal, characteristic, complemented
8	#72302151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#8195808	C₂	1	1	yes	maximal, characteristic
10	#72281322	C₂	1	1	yes	maximal, characteristic, complemented
11	#72231282	C₂	1	4	yes	maximal, complemented
12	#10574447	C₂²	1	1	yes	characteristic, complemented
13	#8195808	C₄	1	4	yes	complemented
14	#8195808	C₄	1	4	yes	complemented
15	#8195808	C₂²	1	4	yes	—
16	#8195808	C₂²	1	4	yes	—
17	C₂×#56384	C₄	1	4	yes	complemented
18	C₂×#52988	C₄	1	2	yes	complemented
19	C₂×#45599	C₂²	1	2	yes	—
20	C₂×#45355	C₄	1	2	yes	complemented
21	C₂×#58997	C₂²	1	2	yes	—
22	C₂×#35272	C₂²	1	1	yes	characteristic
23	C₂×#34963	C₂²	1	1	yes	characteristic
24	C₂×#34963	C₂²	1	1	yes	characteristic
25	#6370950	C₂²	1	1	yes	characteristic, complemented
26	#6370937	C₂²	1	1	yes	characteristic, complemented
27	#6342561	C₂²	1	1	yes	characteristic, complemented
28	#496520	C₂²	1	4	yes	complemented
29	#496508	C₂²	1	4	yes	complemented
30	#493995	C₂²	1	4	yes	complemented
31	#482657	C₂²	1	4	yes	complemented
32	#482443	C₂²	1	2	yes	complemented
33	#482377	C₂²	1	2	yes	complemented
34	#482369	C₂²	1	4	yes	complemented
35	#482363	C₂²	1	4	yes	complemented
36	#482258	C₂²	1	4	yes	complemented
37	#482051	C₂²	1	4	yes	complemented
38	#201391	C₂²	1	4	yes	complemented
39	#201388	C₂²	1	2	yes	complemented
40	#201386	C₂²	1	2	yes	complemented
41	#201373	C₂²	1	4	yes	complemented
42	#200593	C₂²	1	4	yes	complemented
43	#200564	C₂²	1	4	yes	complemented
44	#200521	C₂²	1	4	yes	complemented
45	#193892	C₂²	1	4	yes	complemented
46	#193890	C₂²	1	4	yes	complemented
47	#193878	C₂²	1	4	yes	complemented
48	#130355	C₂²	1	32	yes	complemented
49	#130260	C₂²	1	32	yes	complemented
50	C₂³×#127	D₄	1	1	yes	characteristic
51	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
52	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
53	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
54	#60282	C₂³	1	2	yes	complemented
55	#60276	C₂³	1	2	yes	complemented
56	#60230	C₂³	1	2	yes	—
57	#58997	C₂×C₄	1	8	yes	—
58	#58997	C₂³	1	8	yes	—
59	#56384	C₂×C₄	1	16	yes	—
60	#56384	C₂×C₄	1	16	yes	—
61	#52988	C₂×C₄	1	8	yes	—
62	#52988	C₂×C₄	1	8	yes	—
63	C₂×#2675	C₂×C₄	1	4	yes	—
64	C₂×#2668	C₂×C₄	1	4	yes	—
65	#45599	C₂×C₄	1	8	yes	—
66	#45599	C₂³	1	8	yes	—
67	#45355	C₂×C₄	1	8	yes	—
68	#45355	C₂×C₄	1	8	yes	—
69	C₂×#2826	C₂×C₄	1	4	yes	—
70	#35272	C₂×C₄	1	2	yes	—
71	#35272	C₂×C₄	1	2	yes	—
72	#35272	D₄	1	2	yes	—
73	#35272	D₄	1	2	yes	—
74	#35272	D₄	1	2	yes	—
75	#35272	D₄	1	2	yes	—
76	#35272	C₂³	1	2	yes	—
77	#35272	C₂³	1	2	yes	—
78	#34963	C₂×C₄	1	2	yes	—
79	#34963	C₂×C₄	1	2	yes	—
80	#34963	C₂×C₄	1	2	yes	—
81	#34963	C₂×C₄	1	2	yes	—
82	#34963	D₄	1	2	yes	—
83	#34963	D₄	1	2	yes	—
84	#34963	D₄	1	2	yes	—
85	#34963	D₄	1	2	yes	—
86	#34963	D₄	1	2	yes	—
87	#34963	D₄	1	2	yes	—
88	#34963	D₄	1	2	yes	—
89	#34963	D₄	1	2	yes	—
90	#34963	C₂³	1	2	yes	—
91	#34963	C₂³	1	2	yes	—
92	#34963	C₂³	1	2	yes	—
93	#34963	C₂³	1	2	yes	—
94	C₂×#2548	D₄	1	2	yes	—
95	C₂×#2541	C₂³	1	2	yes	—
96	C₂×#2598	C₂×C₄	1	2	yes	—
97	C₂×#2598	D₄	1	2	yes	—
98	C₂×#2482	C₂×C₄	1	2	yes	—
99	C₂×#2487	C₂×C₄	1	1	yes	characteristic
100	C₂×#2487	D₄	1	1	yes	characteristic
101	C₂×#2487	D₄	1	1	yes	characteristic
102	C₂×#2487	C₂³	1	1	yes	characteristic
103	C₂×#2404	D₄	1	2	yes	—
104	C₂×#2408	C₂×C₄	1	1	yes	characteristic
105	C₂×#2408	C₂×C₄	1	2	yes	—
106	C₂×#2408	D₄	1	1	yes	characteristic
107	C₂×#2408	D₄	1	2	yes	—
108	C₂×#2408	D₄	1	1	yes	characteristic
109	C₂×#2408	C₂³	1	1	yes	characteristic
110	C₂×#2403	C₂×C₄	1	4	yes	—
111	C₂×#2619	C₂×C₄	1	2	yes	—
112	C₂×#2619	D₄	1	2	yes	—
113	C₂×#2398	D₄	1	2	yes	—
114	C₂×#2397	C₂×C₄	1	2	yes	—
115	C₂×C₄×#120	D₄	1	2	yes	—
116	C₂×C₄×#120	C₂³	1	2	yes	—
117	C₂×#2285	D₄	1	1	yes	characteristic
118	C₂×#2283	D₄	1	1	yes	characteristic
119	C₂×#2283	D₄	1	1	yes	characteristic
120	#20728	C₂³	1	2	yes	complemented
121	#20726	C₂³	1	2	yes	—
122	#20723	C₂³	1	2	yes	complemented
123	#20722	C₂³	1	2	yes	—
124	#20637	C₂³	1	2	yes	complemented
125	#20632	C₂³	1	2	yes	complemented
126	#17363	C₂³	1	2	yes	complemented
127	#17362	C₂³	1	2	yes	—
128	#17349	C₂³	1	2	yes	complemented
129	#12793	C₂³	1	16	yes	complemented
130	#11903	C₂³	1	8	yes	complemented
131	#11880	C₂³	1	8	yes	complemented
132	#11877	C₂³	1	16	yes	complemented
133	#9469	C₂³	1	8	yes	complemented
134	#9468	C₂³	1	8	yes	complemented
135	#9397	C₂³	1	16	yes	complemented
136	#8965	C₂³	1	16	yes	complemented
137	C₂³×#41	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁵×C₄	C₂×D₄	1	2	yes	—
142	C₂²×#127	C₂²⋊C₄	1	2	yes	—
143	C₂²×#127	C₂²⋊C₄	1	2	yes	—
144	C₂²×#127	C₂²⋊C₄	1	2	yes	—
145	C₂²×#127	C₂×D₄	1	2	yes	—
146	C₂²×#127	C₂×D₄	1	2	yes	—
147	C₂²×#127	C₂×D₄	1	2	yes	—
148	C₂²×#120	C₂²⋊C₄	1	2	yes	—
149	C₂²×#120	C₂×D₄	1	2	yes	—
150	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×#41	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
169	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
172	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
173	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
174	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
176	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
177	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
178	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
179	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
184	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
185	C₂²×#117	C₂×D₄	1	1	yes	characteristic
186	C₂²×#117	C₂×D₄	1	1	yes	characteristic
187	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
190	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
192	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
193	#2972	C₂⁴	1	4	yes	—
194	#2826	C₂²×C₄	1	16	yes	—
195	#2675	C₂²×C₄	1	16	yes	—
196	#2668	C₂²×C₄	1	16	yes	—
197	#2619	C₂²⋊C₄	1	4	yes	—
198	#2619	C₂²⋊C₄	1	4	yes	—
199	#2619	C₂²⋊C₄	1	4	yes	—
200	#2619	C₂²⋊C₄	1	4	yes	—
201	#2619	C₂²×C₄	1	4	yes	—
202	#2619	C₂²×C₄	1	4	yes	—
203	#2619	C₂×D₄	1	4	yes	—
204	#2619	C₂×D₄	1	4	yes	—
205	#2598	C₂²⋊C₄	1	4	yes	—
206	#2598	C₂²⋊C₄	1	4	yes	—
207	#2598	C₂²⋊C₄	1	4	yes	—
208	#2598	C₂²⋊C₄	1	4	yes	—
209	#2598	C₂²×C₄	1	4	yes	—
210	#2598	C₂²×C₄	1	4	yes	—
211	#2598	C₂×D₄	1	4	yes	—
212	#2598	C₂×D₄	1	4	yes	—
213	#2548	C₂²⋊C₄	1	4	yes	—
214	#2548	C₂²⋊C₄	1	4	yes	—
215	#2548	C₂×D₄	1	4	yes	—
216	#2548	C₂×D₄	1	4	yes	—
217	#2541	C₂²×C₄	1	4	yes	—
218	#2541	C₂×D₄	1	4	yes	—
219	#2541	C₂×D₄	1	4	yes	—
220	#2541	C₂⁴	1	4	yes	—
221	#2487	C₂²⋊C₄	1	2	yes	—
222	#2487	C₂²⋊C₄	1	2	yes	—
223	#2487	C₂²⋊C₄	1	2	yes	—
224	#2487	C₂²⋊C₄	1	2	yes	—
225	#2487	C₂²⋊C₄	1	2	yes	—
226	#2487	C₂²⋊C₄	1	2	yes	—
227	#2487	C₂²×C₄	1	2	yes	—
228	#2487	C₂²×C₄	1	2	yes	—
229	#2487	C₂²×C₄	1	2	yes	—
230	#2487	C₂×D₄	1	2	yes	—
231	#2487	C₂×D₄	1	2	yes	—
232	#2487	C₂×D₄	1	2	yes	—
233	#2487	C₂×D₄	1	2	yes	—
234	#2487	C₂×D₄	1	2	yes	—
235	#2487	C₂×D₄	1	2	yes	—
236	#2487	C₂⁴	1	2	yes	—
237	#2482	C₂²⋊C₄	1	4	yes	—
238	#2482	C₂²⋊C₄	1	4	yes	—
239	#2482	C₂²×C₄	1	4	yes	—
240	#2482	C₂²×C₄	1	4	yes	—
241	#2408	C₂²⋊C₄	1	2	yes	—
242	#2408	C₂²⋊C₄	1	2	yes	—
243	#2408	C₂²⋊C₄	1	4	yes	—
244	#2408	C₂²⋊C₄	1	4	yes	—
245	#2408	C₂²⋊C₄	1	4	yes	—
246	#2408	C₂²⋊C₄	1	4	yes	—
247	#2408	C₂²⋊C₄	1	2	yes	—
248	#2408	C₂²⋊C₄	1	2	yes	—
249	#2408	C₂²⋊C₄	1	2	yes	—
250	#2408	C₂²⋊C₄	1	2	yes	—
251	#2408	C₂²×C₄	1	4	yes	—
252	#2408	C₂²×C₄	1	4	yes	—
253	#2408	C₂²×C₄	1	2	yes	—
254	#2408	C₂²×C₄	1	2	yes	—
255	#2408	C₂²×C₄	1	2	yes	—
256	#2408	C₂×D₄	1	2	yes	—
257	#2408	C₂×D₄	1	4	yes	—
258	#2408	C₂×D₄	1	4	yes	—
259	#2408	C₂×D₄	1	2	yes	—
260	#2408	C₂×D₄	1	2	yes	—
261	#2408	C₂×D₄	1	2	yes	—
262	#2408	C₂×D₄	1	2	yes	—
263	#2408	C₂×D₄	1	2	yes	—
264	#2408	C₂⁴	1	2	yes	—
265	#2404	C₂²⋊C₄	1	4	yes	—
266	#2404	C₂²⋊C₄	1	4	yes	—
267	#2404	C₂×D₄	1	4	yes	—
268	#2404	C₂×D₄	1	4	yes	—
269	#2403	C₂²×C₄	1	16	yes	—
270	#2398	C₂²⋊C₄	1	4	yes	—
271	#2398	C₂²⋊C₄	1	4	yes	—
272	#2398	C₂×D₄	1	4	yes	—
273	#2398	C₂×D₄	1	4	yes	—
274	#2397	C₂²⋊C₄	1	4	yes	—
275	#2397	C₂²⋊C₄	1	4	yes	—
276	#2397	C₂²×C₄	1	4	yes	—
277	#2397	C₂²×C₄	1	4	yes	—
278	C₂×#400	C₂²⋊C₄	1	2	yes	—
279	C₂×#400	C₂×D₄	1	2	yes	—
280	C₂×#399	C₂²⋊C₄	1	2	yes	—
281	C₂×#399	C₂²×C₄	1	2	yes	—
282	C₂×#394	C₂²⋊C₄	1	2	yes	—
283	C₂×#394	C₂²⋊C₄	1	4	yes	—
284	C₂×#394	C₂²⋊C₄	1	4	yes	—
285	C₂×#394	C₂×D₄	1	2	yes	—
286	C₂×#392	C₂²⋊C₄	1	2	yes	—
287	C₂×#392	C₂²×C₄	1	2	yes	—
288	C₂×#392	C₂²×C₄	1	4	yes	—
289	C₂×#392	C₂×D₄	1	4	yes	—
290	C₄×#120	C₂²⋊C₄	1	4	yes	—
291	C₄×#120	C₂²⋊C₄	1	4	yes	—
292	C₄×#120	C₂²×C₄	1	4	yes	—
293	C₄×#120	C₂×D₄	1	4	yes	—
294	C₄×#120	C₂×D₄	1	4	yes	—
295	C₄×#120	C₂×D₄	1	4	yes	—
296	C₄×#120	C₂×D₄	1	4	yes	—
297	C₄×#120	C₂⁴	1	4	yes	—
298	C₂×#386	C₂²⋊C₄	1	2	yes	—
299	C₂×#386	C₂×D₄	1	2	yes	—
300	C₂×#385	C₂²⋊C₄	1	2	yes	—
301	C₂×#385	C₂²×C₄	1	2	yes	—
302	#2285	C₂²⋊C₄	1	2	yes	—
303	#2285	C₂²⋊C₄	1	2	yes	—
304	#2285	C₂×D₄	1	2	yes	—
305	#2285	C₂×D₄	1	2	yes	—
306	#2283	C₂²⋊C₄	1	2	yes	—
307	#2283	C₂²⋊C₄	1	2	yes	—
308	#2283	C₂²⋊C₄	1	2	yes	—
309	#2283	C₂²⋊C₄	1	2	yes	—
310	#2283	C₂×D₄	1	2	yes	—
311	#2283	C₂×D₄	1	2	yes	—
312	#2283	C₂×D₄	1	2	yes	—
313	#2283	C₂×D₄	1	2	yes	—
314	C₂×#383	C₂²⋊C₄	1	2	yes	—
315	C₂×#382	C₂²⋊C₄	1	2	yes	—
316	C₂×#381	C₂²⋊C₄	1	2	yes	—
317	C₂×#380	C₂²⋊C₄	1	2	yes	—
318	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
319	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
320	C₂×#380	C₂×D₄	1	1	yes	characteristic
321	C₂×#380	C₂×D₄	1	1	yes	characteristic
322	C₂×#379	C₂²⋊C₄	1	2	yes	—
323	C₂×#379	C₂²×C₄	1	2	yes	—
324	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
325	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₂×#376	C₂²⋊C₄	1	2	yes	—
327	#1800	C₂⁴	1	4	yes	—
328	#1799	C₂⁴	1	4	yes	—
329	#1459	C₂⁴	1	4	yes	—
330	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×#41	#120	1	1	yes	characteristic
334	C₂²×#41	#120	1	1	yes	characteristic
335	C₂²×#41	#120	1	1	yes	characteristic
336	C₂²×#41	#120	1	1	yes	characteristic
337	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
338	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
339	C₂³×Q₈	#120	1	1	yes	characteristic
340	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
345	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
346	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
347	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂³×D₄	#120	1	1	yes	characteristic
349	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
350	C₂³×D₄	C₂²×D₄	1	2	yes	—
351	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
355	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂⁴×C₄	#120	1	1	yes	characteristic
357	C₂⁴×C₄	#120	1	1	yes	characteristic
358	C₂⁴×C₄	#120	1	1	yes	characteristic
359	C₂⁴×C₄	#120	1	1	yes	characteristic
360	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
363	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
364	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
365	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
366	C₂×#127	C₂²×D₄	1	4	yes	—
367	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
368	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
369	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
370	C₂×#120	C₂²×D₄	1	4	yes	—
371	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄×Q₈	#120	1	1	yes	characteristic
376	C₂×C₄×Q₈	#120	1	1	yes	characteristic
377	C₂×C₄×Q₈	#120	1	1	yes	characteristic
378	C₂×C₄×Q₈	#120	1	1	yes	characteristic
379	C₂×C₄×Q₈	#120	1	1	yes	characteristic
380	C₂×C₄×Q₈	#120	1	1	yes	characteristic
381	C₂×C₄×Q₈	#120	1	1	yes	characteristic
382	C₂×C₄×Q₈	#120	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
388	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
389	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
390	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
391	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂×C₄×D₄	#120	1	1	yes	characteristic
406	C₂×C₄×D₄	#120	1	1	yes	characteristic
407	C₂×C₄×D₄	#120	1	1	yes	characteristic
408	C₂×C₄×D₄	#120	1	1	yes	characteristic
409	C₂×C₄×D₄	#120	1	1	yes	characteristic
410	C₂×C₄×D₄	#120	1	1	yes	characteristic
411	C₂×C₄×D₄	#120	1	1	yes	characteristic
412	C₂×C₄×D₄	#120	1	1	yes	characteristic
413	C₂×C₄×D₄	#120	1	1	yes	characteristic
414	C₂×C₄×D₄	#120	1	1	yes	characteristic
415	C₂×C₄×D₄	#120	1	1	yes	characteristic
416	C₂×C₄×D₄	#120	1	1	yes	characteristic
417	C₂×C₄×D₄	#120	1	1	yes	characteristic
418	C₂×C₄×D₄	#120	1	1	yes	characteristic
419	C₂×C₄×D₄	#120	1	1	yes	characteristic
420	C₂×C₄×D₄	#120	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
439	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
440	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
444	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×#117	#120	1	1	yes	characteristic
450	C₂×#117	#120	1	1	yes	characteristic
451	C₂×#117	#120	1	1	yes	characteristic
452	C₂×#117	#120	1	1	yes	characteristic
453	C₂×#117	#120	1	1	yes	characteristic
454	C₂×#117	#120	1	1	yes	characteristic
455	C₂×#117	#120	1	1	yes	characteristic
456	C₂×#117	#120	1	1	yes	characteristic
457	C₂×#117	C₂³×C₄	1	1	yes	characteristic
458	C₂×#117	C₂³×C₄	1	1	yes	characteristic
459	C₂×#117	C₂²×D₄	1	1	yes	characteristic
460	C₂×#117	C₂²×D₄	1	1	yes	characteristic
461	C₂×#117	C₂²×D₄	1	1	yes	characteristic
462	C₂×#117	C₂²×D₄	1	1	yes	characteristic
463	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
464	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
465	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
466	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
467	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
471	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
472	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
473	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
475	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
476	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
478	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
483	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
485	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
486	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
487	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
488	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
489	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
490	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
491	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
492	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
493	C₂²×C₄²	#120	1	1	yes	characteristic
494	C₂²×C₄²	#120	1	1	yes	characteristic
495	C₂²×C₄²	#120	1	1	yes	characteristic
496	C₂²×C₄²	#120	1	1	yes	characteristic
497	C₂²×C₄²	#120	1	1	yes	characteristic
498	C₂²×C₄²	#120	1	1	yes	characteristic
499	C₂²×C₄²	#120	1	1	yes	characteristic
500	C₂²×C₄²	#120	1	1	yes	characteristic
501	C₂²×C₄²	#120	1	1	yes	characteristic
502	C₂²×C₄²	#120	1	1	yes	characteristic
503	C₂²×C₄²	#120	1	1	yes	characteristic
504	C₂²×C₄²	#120	1	1	yes	characteristic
505	C₂²×C₄²	#120	1	1	yes	characteristic
506	C₂²×C₄²	#120	1	1	yes	characteristic
507	C₂²×C₄²	#120	1	1	yes	characteristic
508	C₂²×C₄²	#120	1	1	yes	characteristic
509	C₂²×C₄²	#120	1	1	yes	characteristic
510	C₂²×C₄²	#120	1	1	yes	characteristic
511	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
512	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
513	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
514	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
515	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
516	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
517	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
518	#400	C₂×C₂²⋊C₄	1	4	yes	—
519	#400	C₂×C₂²⋊C₄	1	4	yes	—
520	#400	C₂×C₂²⋊C₄	1	4	yes	—
521	#400	C₂²×D₄	1	4	yes	—
522	#399	C₂×C₂²⋊C₄	1	4	yes	—
523	#399	C₂×C₂²⋊C₄	1	4	yes	—
524	#399	C₂×C₂²⋊C₄	1	4	yes	—
525	#399	C₂³×C₄	1	4	yes	—
526	#394	C₂×C₂²⋊C₄	1	8	yes	—
527	#394	C₂×C₂²⋊C₄	1	8	yes	—
528	#394	C₂×C₂²⋊C₄	1	4	yes	—
529	#394	C₂×C₂²⋊C₄	1	4	yes	—
530	#394	C₂×C₂²⋊C₄	1	4	yes	—
531	#394	C₂×C₂²⋊C₄	1	8	yes	—
532	#394	C₂×C₂²⋊C₄	1	8	yes	—
533	#394	C₂²×D₄	1	4	yes	—
534	#392	C₂×C₂²⋊C₄	1	8	yes	—
535	#392	C₂×C₂²⋊C₄	1	4	yes	—
536	#392	C₂×C₂²⋊C₄	1	4	yes	—
537	#392	C₂×C₂²⋊C₄	1	4	yes	—
538	#392	C₂×C₂²⋊C₄	1	8	yes	—
539	#392	C₂³×C₄	1	8	yes	—
540	#392	C₂³×C₄	1	4	yes	—
541	#392	C₂²×D₄	1	8	yes	—
542	#386	C₂×C₂²⋊C₄	1	4	yes	—
543	#386	C₂×C₂²⋊C₄	1	4	yes	—
544	#386	C₂×C₂²⋊C₄	1	4	yes	—
545	#386	C₂²×D₄	1	4	yes	—
546	#385	C₂×C₂²⋊C₄	1	4	yes	—
547	#385	C₂×C₂²⋊C₄	1	4	yes	—
548	#385	C₂×C₂²⋊C₄	1	4	yes	—
549	#385	C₂³×C₄	1	4	yes	—
550	#383	C₂×C₂²⋊C₄	1	4	yes	—
551	#383	C₂×C₂²⋊C₄	1	4	yes	—
552	#382	C₂×C₂²⋊C₄	1	4	yes	—
553	#382	C₂×C₂²⋊C₄	1	4	yes	—
554	#381	C₂×C₂²⋊C₄	1	4	yes	—
555	#381	C₂×C₂²⋊C₄	1	4	yes	—
556	#380	C₂×C₂²⋊C₄	1	2	yes	—
557	#380	C₂×C₂²⋊C₄	1	2	yes	—
558	#380	C₂×C₂²⋊C₄	1	2	yes	—
559	#380	C₂×C₂²⋊C₄	1	2	yes	—
560	#380	C₂×C₂²⋊C₄	1	4	yes	—
561	#380	C₂×C₂²⋊C₄	1	4	yes	—
562	#380	C₂×C₂²⋊C₄	1	2	yes	—
563	#380	C₂×C₂²⋊C₄	1	2	yes	—
564	#380	C₂²×D₄	1	2	yes	—
565	#380	C₂²×D₄	1	2	yes	—
566	#379	C₂×C₂²⋊C₄	1	4	yes	—
567	#379	C₂×C₂²⋊C₄	1	4	yes	—
568	#379	C₂×C₂²⋊C₄	1	4	yes	—
569	#379	C₂³×C₄	1	4	yes	—
570	C₄×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
571	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
572	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
573	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
574	#376	C₂×C₂²⋊C₄	1	4	yes	—
575	#376	C₂×C₂²⋊C₄	1	4	yes	—
576	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
577	C₂×#95	C₂×C₂²⋊C₄	1	4	yes	—
578	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
579	C₂⁵	#379	1	1	yes	characteristic
580	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
581	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
582	C₂⁵	C₂×#120	1	1	yes	characteristic
583	C₂²×Q₈	#379	1	1	yes	characteristic
584	C₂²×Q₈	#379	1	1	yes	characteristic
585	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
586	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
587	C₂²×D₄	#379	1	1	yes	characteristic
588	C₂²×D₄	#379	1	1	yes	characteristic
589	C₂²×D₄	#379	1	1	yes	characteristic
590	C₂²×D₄	#379	1	1	yes	characteristic
591	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
592	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
593	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
596	C₂²×D₄	C₂×#120	1	1	yes	characteristic
597	C₂²×D₄	C₂×#120	1	1	yes	characteristic
598	C₂²×D₄	C₂×#120	1	1	yes	characteristic
599	C₂²×D₄	C₂×#120	1	1	yes	characteristic
600	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
601	C₂³×C₄	#379	1	1	yes	characteristic
602	C₂³×C₄	#379	1	1	yes	characteristic
603	C₂³×C₄	#379	1	1	yes	characteristic
604	C₂³×C₄	#379	1	1	yes	characteristic
605	C₂³×C₄	#379	1	1	yes	characteristic
606	C₂³×C₄	#379	1	1	yes	characteristic
607	C₂³×C₄	#379	1	1	yes	characteristic
608	C₂³×C₄	#379	1	1	yes	characteristic
609	C₂³×C₄	#379	1	1	yes	characteristic
610	C₂³×C₄	#379	1	1	yes	characteristic
611	C₂³×C₄	#379	1	1	yes	characteristic
612	C₂³×C₄	#379	1	1	yes	characteristic
613	C₂³×C₄	#379	1	1	yes	characteristic
614	C₂³×C₄	#379	1	1	yes	characteristic
615	C₂³×C₄	#379	1	1	yes	characteristic
616	C₂³×C₄	#379	1	1	yes	characteristic
617	C₂³×C₄	#379	1	1	yes	characteristic
618	C₂³×C₄	#379	1	1	yes	characteristic
619	C₂³×C₄	#379	1	1	yes	characteristic
620	C₂³×C₄	#379	1	1	yes	characteristic
621	C₂³×C₄	#379	1	1	yes	characteristic
622	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
623	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
624	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
625	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
626	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
627	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
628	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
629	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
630	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
631	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
632	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
633	C₂³×C₄	C₂×#120	1	1	yes	characteristic
634	C₂³×C₄	C₂×#120	1	1	yes	characteristic
635	C₂³×C₄	C₂×#120	1	1	yes	characteristic
636	C₂³×C₄	C₂×#120	1	1	yes	characteristic
637	C₂³×C₄	C₂×#120	1	1	yes	characteristic
638	C₂³×C₄	C₂×#120	1	1	yes	characteristic
639	C₂³×C₄	C₂×#120	1	1	yes	characteristic
640	C₂³×C₄	C₂×#120	1	1	yes	characteristic
641	C₂³×C₄	C₂×#120	1	1	yes	characteristic
642	C₂³×C₄	C₂×#120	1	1	yes	characteristic
643	C₂³×C₄	C₂×#120	1	1	yes	characteristic
644	C₂³×C₄	C₂×#120	1	1	yes	characteristic
645	C₂³×C₄	C₂×#120	1	1	yes	characteristic
646	C₂³×C₄	C₂×#120	1	1	yes	characteristic
647	C₂³×C₄	C₂×#120	1	1	yes	characteristic
648	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
649	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
650	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
651	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
652	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
653	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
654	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
655	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
656	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
657	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
658	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
659	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
661	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
684	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
685	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂⁴×C₄	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
701	C₂×C₄²	#379	1	1	yes	characteristic
702	C₂×C₄²	#379	1	1	yes	characteristic
703	C₂×C₄²	#379	1	1	yes	characteristic
704	C₂×C₄²	#379	1	1	yes	characteristic
705	C₂×C₄²	#379	1	1	yes	characteristic
706	C₂×C₄²	#379	1	1	yes	characteristic
707	C₂×C₄²	#379	1	1	yes	characteristic
708	C₂×C₄²	#379	1	1	yes	characteristic
709	C₂×C₄²	#379	1	1	yes	characteristic
710	C₂×C₄²	#379	1	1	yes	characteristic
711	C₂×C₄²	#379	1	1	yes	characteristic
712	C₂×C₄²	#379	1	1	yes	characteristic
713	C₂×C₄²	#379	1	1	yes	characteristic
714	C₂×C₄²	#379	1	1	yes	characteristic
715	C₂×C₄²	#379	1	1	yes	characteristic
716	C₂×C₄²	#379	1	1	yes	characteristic
717	C₂×C₄²	#379	1	1	yes	characteristic
718	C₂×C₄²	#379	1	1	yes	characteristic
719	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
720	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
721	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
722	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
723	C₂×C₄²	#458	1	1	yes	characteristic
724	C₂×C₄²	#458	1	1	yes	characteristic
725	C₂×C₄²	#458	1	1	yes	characteristic
726	C₂×C₄²	#458	1	1	yes	characteristic
727	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
728	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
729	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
730	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
731	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
732	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
733	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
734	C₂×C₄²	C₂×#120	1	1	yes	characteristic
735	C₂×C₄²	C₂×#120	1	1	yes	characteristic
736	C₂×C₄²	C₂×#120	1	1	yes	characteristic
737	C₂×C₄²	C₂×#120	1	1	yes	characteristic
738	C₂×C₄²	C₂×#120	1	1	yes	characteristic
739	C₂×C₄²	C₂×#120	1	1	yes	characteristic
740	C₂×C₄²	C₂×#120	1	1	yes	characteristic
741	C₂×C₄²	C₂×#120	1	1	yes	characteristic
742	C₂×C₄²	C₂×#120	1	1	yes	characteristic
743	C₂×C₄²	C₂×#120	1	1	yes	characteristic
744	C₂×C₄²	C₂×#120	1	1	yes	characteristic
745	C₂×C₄²	C₂×#120	1	1	yes	characteristic
746	C₂×C₄²	C₂×#120	1	1	yes	characteristic
747	C₂×C₄²	C₂×#120	1	1	yes	characteristic
748	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
749	#95	C₂²×C₂²⋊C₄	1	4	yes	—
750	#95	C₂²×C₂²⋊C₄	1	4	yes	—
751	#95	C₂²×C₂²⋊C₄	1	8	yes	—
752	C₂⁴	C₂×#379	1	1	yes	characteristic
753	C₂⁴	C₂×#379	1	1	yes	characteristic
754	C₂⁴	C₂×#379	1	1	yes	characteristic
755	C₂⁴	C₂×#379	1	1	yes	characteristic
756	C₂⁴	C₂×#379	1	1	yes	characteristic
757	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
758	C₂⁴	C₂²×#120	1	1	yes	characteristic
759	C₂×D₄	#3585	1	4	yes	—
760	C₂²×C₄	#1790	1	1	yes	characteristic
761	C₂²×C₄	#1790	1	1	yes	characteristic
762	C₂²×C₄	#1790	1	1	yes	characteristic
763	C₂²×C₄	#1790	1	1	yes	characteristic
764	C₂²×C₄	#1790	1	1	yes	characteristic
765	C₂²×C₄	#1790	1	1	yes	characteristic
766	C₂²×C₄	#1790	1	1	yes	characteristic
767	C₂²×C₄	#1790	1	1	yes	characteristic
768	C₂²×C₄	C₂×#379	1	1	yes	characteristic
769	C₂²×C₄	C₂×#379	1	1	yes	characteristic
770	C₂²×C₄	C₂×#379	1	1	yes	characteristic
771	C₂²×C₄	C₂×#379	1	1	yes	characteristic
772	C₂²×C₄	C₂×#379	1	1	yes	characteristic
773	C₂²×C₄	C₂×#379	1	1	yes	characteristic
774	C₂²×C₄	C₂×#379	1	1	yes	characteristic
775	C₂²×C₄	C₂×#379	1	1	yes	characteristic
776	C₂²×C₄	C₂×#379	1	1	yes	characteristic
777	C₂²×C₄	C₂×#379	1	1	yes	characteristic
778	C₂²×C₄	C₂×#379	1	1	yes	characteristic
779	C₂²×C₄	C₂×#379	1	1	yes	characteristic
780	C₂²×C₄	C₂×#379	1	1	yes	characteristic
781	C₂²×C₄	C₂×#379	1	1	yes	characteristic
782	C₂²×C₄	C₂×#379	1	1	yes	characteristic
783	C₂²×C₄	C₂×#379	1	1	yes	characteristic
784	C₂²×C₄	C₂×#379	1	1	yes	characteristic
785	C₂²×C₄	C₂×#379	1	1	yes	characteristic
786	C₂²×C₄	C₂×#379	1	1	yes	characteristic
787	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
788	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
789	C₂²×C₄	C₂×#458	1	1	yes	characteristic
790	C₂²×C₄	C₂×#458	1	1	yes	characteristic
791	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
792	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
793	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
794	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
795	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
796	C₄²	#1790	1	1	yes	characteristic
797	C₄²	#1790	1	1	yes	characteristic
798	C₄²	#1790	1	1	yes	characteristic
799	C₄²	#1790	1	1	yes	characteristic
800	C₄²	#1790	1	1	yes	characteristic
801	C₄²	#1790	1	1	yes	characteristic
802	C₄²	#1790	1	1	yes	characteristic
803	C₄²	#1790	1	1	yes	characteristic
804	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
805	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
806	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
807	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
808	C₄²	C₂×#458	1	1	yes	characteristic
809	C₄²	C₂×#458	1	1	yes	characteristic
810	C₄²	C₂×#458	1	1	yes	characteristic
811	C₄²	C₂×#458	1	1	yes	characteristic
812	C₂³	C₂×#1790	1	1	yes	characteristic
813	C₂³	C₂×#1790	1	1	yes	characteristic
814	C₂³	#20620	1	2	yes	—
815	C₂³	C₂²×#379	1	1	yes	characteristic
816	C₂³	#60087	1	2	yes	—
817	C₂³	#60367	1	2	yes	—
818	C₂×C₄	#12755	1	4	yes	—
819	C₂×C₄	C₂×#1790	1	1	yes	characteristic
820	C₂×C₄	C₂×#1790	1	1	yes	characteristic
821	C₂×C₄	C₂×#1790	1	1	yes	characteristic
822	C₂×C₄	C₂×#1790	1	1	yes	characteristic
823	C₂×C₄	C₂×#1790	1	1	yes	characteristic
824	C₂×C₄	C₂×#1790	1	1	yes	characteristic
825	C₂×C₄	C₂×#1790	1	1	yes	characteristic
826	C₂×C₄	C₂×#1790	1	1	yes	characteristic
827	C₂×C₄	C₂×#1790	1	1	yes	characteristic
828	C₂×C₄	C₂×#1790	1	1	yes	characteristic
829	C₂×C₄	#33553	1	4	yes	—
830	C₂×C₄	#60367	1	2	yes	—
831	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
832	C₂×C₄	C₂²×#458	1	1	yes	characteristic
833	C₂²	C₂×#12755	1	2	yes	—
834	C₂²	#493584	1	2	yes	—
835	C₂²	#6370719	1	1	yes	characteristic
836	C₂²	C₂²×#1790	1	1	yes	characteristic
837	C₂²	C₂×#20620	1	1	yes	characteristic
838	C₄	C₂×#12755	1	2	yes	—
839	C₄	C₂×#12755	1	2	yes	—
840	C₄	#493584	1	2	yes	—
841	C₄	C₂×#33553	1	2	yes	—
842	C₂	#72238179	1	1	yes	characteristic
843	C₂	C₂²×#12755	1	1	yes	characteristic
844	C₂	C₂×#493584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1790
commutator	C₂×C₂²⋊C₄	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	C₂×#8195808	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. #72338732	C₂	semidirect
2. #72338729	C₂	semidirect
3. #72338724	C₂	semidirect
4. #72338689	C₂	semidirect
5. #72338672	C₂	semidirect
6. #72338659	C₂	semidirect
7. #72312553	C₂	semidirect
8. #72302151	C₂	semidirect
10. #72281322	C₂	semidirect
11. #72231282	C₂	semidirect
12. #10574447	C₂²	semidirect
13. #8195808	C₄	semidirect
14. #8195808	C₄	semidirect
17. C₂×#56384	C₄	semidirect
18. C₂×#52988	C₄	semidirect
20. C₂×#45355	C₄	semidirect
25. #6370950	C₂²	semidirect
26. #6370937	C₂²	semidirect
27. #6342561	C₂²	semidirect
28. #496520	C₂²	semidirect
29. #496508	C₂²	semidirect
30. #493995	C₂²	semidirect
31. #482657	C₂²	semidirect
32. #482443	C₂²	semidirect
33. #482377	C₂²	semidirect
34. #482369	C₂²	semidirect
35. #482363	C₂²	semidirect
36. #482258	C₂²	semidirect
37. #482051	C₂²	semidirect
38. #201391	C₂²	semidirect
39. #201388	C₂²	semidirect
40. #201386	C₂²	semidirect
41. #201373	C₂²	semidirect
42. #200593	C₂²	semidirect
43. #200564	C₂²	semidirect
44. #200521	C₂²	semidirect
45. #193892	C₂²	semidirect
46. #193890	C₂²	semidirect
47. #193878	C₂²	semidirect
48. #130355	C₂²	semidirect
49. #130260	C₂²	semidirect
54. #60282	C₂³	semidirect
55. #60276	C₂³	semidirect
120. #20728	C₂³	semidirect
122. #20723	C₂³	semidirect
124. #20637	C₂³	semidirect
125. #20632	C₂³	semidirect
126. #17363	C₂³	semidirect
128. #17349	C₂³	semidirect
129. #12793	C₂³	semidirect
130. #11903	C₂³	semidirect
131. #11880	C₂³	semidirect
132. #11877	C₂³	semidirect
133. #9469	C₂³	semidirect
134. #9468	C₂³	semidirect
135. #9397	C₂³	semidirect
136. #8965	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72338732	2
#72338729	2
#72338724	2
#72338689	2
#72338672	2
#72338659	2
#72312553	2
#72302151	2
C₂×#8195808	2
#72281322	2
#72231282	2