Subgroups — #72316974

Order 2048.

At least 9429 conjugacy classes of subgroups; only the 1984 normal subgroups are shown.

The subgroup lattice has 920 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316900	C₂	1	1	yes	maximal, characteristic, complemented
2	#72316839	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316740	C₂	1	8	yes	maximal, complemented
4	#72316705	C₂	1	8	yes	maximal, complemented
5	#72312553	C₂	1	1	yes	maximal, characteristic, complemented
6	#72281567	C₂	1	1	yes	maximal, characteristic, complemented
7	#72281322	C₂	1	1	yes	maximal, characteristic, complemented
8	#72279835	C₂	1	1	yes	maximal, characteristic, complemented
9	#72240305	C₂	1	4	yes	maximal, complemented
10	#72231038	C₂	1	4	yes	maximal, complemented
11	C₂×#7737411	C₂	1	1	yes	maximal, characteristic
12	C₂²×#3498	C₂²	1	1	yes	characteristic
13	C₂³×D₄²	C₄	1	1	yes	characteristic, complemented
14	#7737411	C₄	1	4	yes	complemented
15	#7737411	C₄	1	4	yes	complemented
16	#7737411	C₂²	1	4	yes	—
17	#7737411	C₂²	1	4	yes	—
18	C₂×#38904	C₄	1	2	yes	complemented
19	C₂×#38904	C₂²	1	2	yes	—
20	C₂×D₄×#120	C₄	1	2	yes	complemented
21	C₂×D₄×#120	C₂²	1	2	yes	—
22	C₂×#35237	C₄	1	1	yes	characteristic, complemented
23	C₂×#35237	C₄	1	1	yes	characteristic, complemented
24	C₂×#34963	C₂²	1	1	yes	characteristic
25	C₂×#34963	C₂²	1	1	yes	characteristic
26	C₂×#34364	C₄	1	1	yes	characteristic, complemented
27	#6370950	C₂²	1	1	yes	characteristic, complemented
28	#6370937	C₂²	1	1	yes	characteristic, complemented
29	#6342561	C₂²	1	1	yes	characteristic, complemented
30	#6342561	C₂²	1	1	yes	characteristic, complemented
31	#496520	C₂²	1	4	yes	complemented
32	#496508	C₂²	1	4	yes	complemented
33	#493995	C₂²	1	4	yes	complemented
34	#482657	C₂²	1	4	yes	complemented
35	#482633	C₂²	1	4	yes	complemented
36	#482443	C₂²	1	2	yes	complemented
37	#482424	C₂²	1	2	yes	complemented
38	#482377	C₂²	1	2	yes	complemented
39	#482357	C₂²	1	2	yes	complemented
40	#482258	C₂²	1	4	yes	complemented
41	#482234	C₂²	1	4	yes	complemented
42	#480583	C₂²	1	4	yes	complemented
43	#480580	C₂²	1	4	yes	complemented
44	#480376	C₂²	1	4	yes	complemented
45	#185785	C₂²	1	4	yes	complemented
46	#185755	C₂²	1	4	yes	complemented
47	#185733	C₂²	1	4	yes	complemented
48	#185660	C₂²	1	4	yes	complemented
49	#185643	C₂²	1	4	yes	complemented
50	#185628	C₂²	1	4	yes	complemented
51	#130982	C₂²	1	32	yes	complemented
52	#130740	C₂²	1	32	yes	complemented
53	C₂⁵×D₄	C₂×C₄	1	2	yes	—
54	C₂×#3498	C₂×C₄	1	2	yes	—
55	C₂×#3498	C₂×C₄	1	2	yes	—
56	C₂×#3498	D₄	1	2	yes	—
57	C₂×#3498	D₄	1	2	yes	—
58	C₂×#3498	D₄	1	2	yes	—
59	C₂×#3498	D₄	1	2	yes	—
60	C₂×#3498	C₂³	1	2	yes	—
61	C₂×#3498	C₂³	1	2	yes	—
62	C₂²×#550	D₄	1	2	yes	—
63	C₂²×D₄²	C₂×C₄	1	2	yes	—
64	C₂²×D₄²	C₂×C₄	1	4	yes	—
65	C₂²×D₄²	C₂×C₄	1	4	yes	—
66	C₂²×D₄²	D₄	1	2	yes	—
67	C₂²×D₄²	C₂³	1	2	yes	—
68	C₂²×#532	C₂×C₄	1	1	yes	characteristic
69	C₂²×#532	D₄	1	1	yes	characteristic
70	C₂²×#532	D₄	1	1	yes	characteristic
71	C₂³×#127	C₂×C₄	1	1	yes	characteristic
72	C₂³×#127	D₄	1	1	yes	characteristic
73	C₂³×#127	D₄	1	1	yes	characteristic
74	C₂³×#121	C₂×C₄	1	2	yes	—
75	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
76	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
78	#38904	C₂×C₄	1	8	yes	—
79	#38904	C₂×C₄	1	8	yes	—
80	#38904	C₂×C₄	1	8	yes	—
81	#38904	C₂³	1	8	yes	—
82	C₂×#2847	C₂×C₄	1	2	yes	—
83	C₂×#2847	C₂×C₄	1	2	yes	—
84	D₄×#120	C₂×C₄	1	8	yes	—
85	D₄×#120	C₂×C₄	1	8	yes	—
86	D₄×#120	C₂×C₄	1	8	yes	—
87	D₄×#120	C₂³	1	8	yes	—
88	#35237	C₂×C₄	1	4	yes	—
89	#35237	C₂×C₄	1	4	yes	—
90	#35237	C₂×C₄	1	4	yes	—
91	#35237	C₂×C₄	1	4	yes	—
92	#34963	C₂×C₄	1	2	yes	—
93	#34963	C₂×C₄	1	2	yes	—
94	#34963	C₂×C₄	1	2	yes	—
95	#34963	C₂×C₄	1	2	yes	—
96	#34963	D₄	1	2	yes	—
97	#34963	D₄	1	2	yes	—
98	#34963	D₄	1	2	yes	—
99	#34963	D₄	1	2	yes	—
100	#34963	D₄	1	2	yes	—
101	#34963	D₄	1	2	yes	—
102	#34963	D₄	1	2	yes	—
103	#34963	D₄	1	2	yes	—
104	#34963	C₂³	1	2	yes	—
105	#34963	C₂³	1	2	yes	—
106	#34963	C₂³	1	2	yes	—
107	#34963	C₂³	1	2	yes	—
108	C₂×#2598	D₄	1	2	yes	—
109	C₂×#2598	D₄	1	2	yes	—
110	C₂×#2482	D₄	1	2	yes	—
111	C₂×#2504	C₂×C₄	1	2	yes	—
112	C₂×#2487	C₂×C₄	1	1	yes	characteristic
113	C₂×#2487	D₄	1	1	yes	characteristic
114	C₂×#2487	D₄	1	1	yes	characteristic
115	C₂×#2487	C₂³	1	1	yes	characteristic
116	C₂×#2404	D₄	1	2	yes	—
117	C₂×#2433	C₂×C₄	1	2	yes	—
118	C₂×#2408	C₂×C₄	1	1	yes	characteristic
119	C₂×#2408	D₄	1	1	yes	characteristic
120	C₂×#2408	D₄	1	1	yes	characteristic
121	C₂×#2408	C₂³	1	1	yes	characteristic
122	C₂×#2398	D₄	1	2	yes	—
123	C₂×#2397	D₄	1	2	yes	—
124	#34364	C₂×C₄	1	4	yes	—
125	#34364	C₂×C₄	1	4	yes	—
126	C₂×D₄×C₂²⋊C₄	C₂×C₄	1	2	yes	—
127	C₂×D₄×C₂²⋊C₄	C₂×C₄	1	2	yes	—
128	C₂×C₄×#120	C₂×C₄	1	2	yes	—
129	C₂×C₄×#120	C₂³	1	2	yes	—
130	C₂×#2283	C₂×C₄	1	1	yes	characteristic
131	C₂×#2283	C₂×C₄	1	1	yes	characteristic
132	#20728	C₂³	1	2	yes	complemented
133	#20726	C₂³	1	2	yes	—
134	#20723	C₂³	1	2	yes	complemented
135	#20722	C₂³	1	2	yes	—
136	#20637	C₂³	1	2	yes	complemented
137	#20632	C₂³	1	2	yes	complemented
138	#17366	C₂³	1	2	yes	complemented
139	#17364	C₂³	1	2	yes	—
140	#17363	C₂³	1	2	yes	complemented
141	#17362	C₂³	1	2	yes	—
142	#17349	C₂³	1	2	yes	complemented
143	#17349	C₂³	1	2	yes	complemented
144	#12793	C₂³	1	16	yes	complemented
145	#11903	C₂³	1	8	yes	complemented
146	#11899	C₂³	1	8	yes	complemented
147	#11880	C₂³	1	8	yes	complemented
148	#11873	C₂³	1	8	yes	complemented
149	#11471	C₂³	1	16	yes	complemented
150	#8383	C₂³	1	16	yes	complemented
151	#8375	C₂³	1	16	yes	complemented
152	C₂³×#41	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
154	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
155	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
156	C₂⁴×D₄	C₂²×C₄	1	8	yes	—
157	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
158	C₂⁴×D₄	C₂×D₄	1	2	yes	—
159	C₂⁵×C₄	C₂²×C₄	1	2	yes	—
160	C₂×#550	C₂²⋊C₄	1	4	yes	—
161	C₂×#550	C₂²⋊C₄	1	4	yes	—
162	C₂×#550	C₂×D₄	1	4	yes	—
163	C₂×#550	C₂×D₄	1	4	yes	—
164	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
165	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
166	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
167	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
168	C₂×D₄²	C₂²×C₄	1	4	yes	—
169	C₂×D₄²	C₂²×C₄	1	4	yes	—
170	C₂×D₄²	C₂²×C₄	1	4	yes	—
171	C₂×D₄²	C₂×D₄	1	4	yes	—
172	C₂×D₄²	C₂×D₄	1	4	yes	—
173	C₂×D₄²	C₂×D₄	1	4	yes	—
174	C₂×D₄²	C₂×D₄	1	4	yes	—
175	C₂×D₄²	C₂⁴	1	4	yes	—
176	C₂×#532	C₂²⋊C₄	1	2	yes	—
177	C₂×#532	C₂²⋊C₄	1	2	yes	—
178	C₂×#532	C₂²⋊C₄	1	2	yes	—
179	C₂×#532	C₂²⋊C₄	1	2	yes	—
180	C₂×#532	C₂²⋊C₄	1	2	yes	—
181	C₂×#532	C₂²⋊C₄	1	2	yes	—
182	C₂×#532	C₂²×C₄	1	2	yes	—
183	C₂×#532	C₂²×C₄	1	2	yes	—
184	C₂×#532	C₂×D₄	1	2	yes	—
185	C₂×#532	C₂×D₄	1	2	yes	—
186	C₂×#532	C₂×D₄	1	2	yes	—
187	C₂×#532	C₂×D₄	1	2	yes	—
188	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×#127	C₂²⋊C₄	1	2	yes	—
190	C₂²×#127	C₂²⋊C₄	1	2	yes	—
191	C₂²×#127	C₂²⋊C₄	1	2	yes	—
192	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×#127	C₂²⋊C₄	1	2	yes	—
194	C₂²×#127	C₂²⋊C₄	1	2	yes	—
195	C₂²×#127	C₂²⋊C₄	1	2	yes	—
196	C₂²×#127	C₂²⋊C₄	1	2	yes	—
197	C₂²×#127	C₂²⋊C₄	1	2	yes	—
198	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×#127	C₂²×C₄	1	2	yes	—
201	C₂²×#127	C₂²×C₄	1	2	yes	—
202	C₂²×#127	C₂×D₄	1	2	yes	—
203	C₂²×#127	C₂×D₄	1	2	yes	—
204	C₂²×#127	C₂×D₄	1	2	yes	—
205	C₂²×#127	C₂×D₄	1	2	yes	—
206	C₂²×#127	C₂×D₄	1	2	yes	—
207	C₂²×#121	C₂²⋊C₄	1	2	yes	—
208	C₂²×#121	C₂²×C₄	1	2	yes	—
209	C₂²×#121	C₂²×C₄	1	8	yes	—
210	C₂²×#121	C₂×D₄	1	2	yes	—
211	C₂²×#120	C₂²⋊C₄	1	2	yes	—
212	C₂²×#120	C₂×D₄	1	2	yes	—
213	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
216	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
217	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
219	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
220	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
221	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
222	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
223	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
224	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
226	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
227	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
232	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
233	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
234	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
235	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
236	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
237	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
238	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
239	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
240	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
241	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
242	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
243	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
245	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
250	C₂²×#117	C₂×D₄	1	1	yes	characteristic
251	C₂²×#117	C₂×D₄	1	1	yes	characteristic
252	C₂²×#117	C₂×D₄	1	1	yes	characteristic
253	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
254	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
256	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
257	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
258	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
259	#2847	C₂²×C₄	1	8	yes	—
260	#2847	C₂²×C₄	1	8	yes	—
261	#2598	C₂²⋊C₄	1	4	yes	—
262	#2598	C₂²⋊C₄	1	4	yes	—
263	#2598	C₂²⋊C₄	1	4	yes	—
264	#2598	C₂²⋊C₄	1	4	yes	—
265	#2598	C₂×D₄	1	4	yes	—
266	#2598	C₂×D₄	1	4	yes	—
267	#2598	C₂×D₄	1	4	yes	—
268	#2598	C₂×D₄	1	4	yes	—
269	#2504	C₂²×C₄	1	8	yes	—
270	#2487	C₂²⋊C₄	1	2	yes	—
271	#2487	C₂²⋊C₄	1	2	yes	—
272	#2487	C₂²⋊C₄	1	2	yes	—
273	#2487	C₂²⋊C₄	1	2	yes	—
274	#2487	C₂²⋊C₄	1	2	yes	—
275	#2487	C₂²⋊C₄	1	2	yes	—
276	#2487	C₂²×C₄	1	2	yes	—
277	#2487	C₂²×C₄	1	2	yes	—
278	#2487	C₂²×C₄	1	2	yes	—
279	#2487	C₂×D₄	1	2	yes	—
280	#2487	C₂×D₄	1	2	yes	—
281	#2487	C₂×D₄	1	2	yes	—
282	#2487	C₂×D₄	1	2	yes	—
283	#2487	C₂×D₄	1	2	yes	—
284	#2487	C₂×D₄	1	2	yes	—
285	#2487	C₂⁴	1	2	yes	—
286	#2482	C₂²⋊C₄	1	4	yes	—
287	#2482	C₂²⋊C₄	1	4	yes	—
288	#2482	C₂×D₄	1	4	yes	—
289	#2482	C₂×D₄	1	4	yes	—
290	#2433	C₂²×C₄	1	8	yes	—
291	#2408	C₂²⋊C₄	1	2	yes	—
292	#2408	C₂²⋊C₄	1	2	yes	—
293	#2408	C₂²⋊C₄	1	2	yes	—
294	#2408	C₂²⋊C₄	1	2	yes	—
295	#2408	C₂²⋊C₄	1	2	yes	—
296	#2408	C₂²⋊C₄	1	2	yes	—
297	#2408	C₂²×C₄	1	2	yes	—
298	#2408	C₂²×C₄	1	2	yes	—
299	#2408	C₂²×C₄	1	2	yes	—
300	#2408	C₂×D₄	1	2	yes	—
301	#2408	C₂×D₄	1	2	yes	—
302	#2408	C₂×D₄	1	2	yes	—
303	#2408	C₂×D₄	1	2	yes	—
304	#2408	C₂×D₄	1	2	yes	—
305	#2408	C₂×D₄	1	2	yes	—
306	#2408	C₂⁴	1	2	yes	—
307	#2404	C₂²⋊C₄	1	4	yes	—
308	#2404	C₂²⋊C₄	1	4	yes	—
309	#2404	C₂×D₄	1	4	yes	—
310	#2404	C₂×D₄	1	4	yes	—
311	#2398	C₂²⋊C₄	1	4	yes	—
312	#2398	C₂²⋊C₄	1	4	yes	—
313	#2398	C₂×D₄	1	4	yes	—
314	#2398	C₂×D₄	1	4	yes	—
315	#2397	C₂²⋊C₄	1	4	yes	—
316	#2397	C₂²⋊C₄	1	4	yes	—
317	#2397	C₂×D₄	1	4	yes	—
318	#2397	C₂×D₄	1	4	yes	—
319	C₂×#400	C₂²⋊C₄	1	2	yes	—
320	C₂×#400	C₂×D₄	1	2	yes	—
321	C₂×#399	C₂²⋊C₄	1	2	yes	—
322	C₂×#399	C₂×D₄	1	2	yes	—
323	C₂×#394	C₂²⋊C₄	1	2	yes	—
324	C₂×#394	C₂×D₄	1	2	yes	—
325	C₂×#392	C₂²⋊C₄	1	2	yes	—
326	C₂×#392	C₂×D₄	1	2	yes	—
327	D₄×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
328	D₄×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
329	C₄×#120	C₂²⋊C₄	1	4	yes	—
330	C₄×#120	C₂²⋊C₄	1	4	yes	—
331	C₄×#120	C₂²×C₄	1	4	yes	—
332	C₄×#120	C₂²×C₄	1	4	yes	—
333	C₄×#120	C₂²×C₄	1	4	yes	—
334	C₄×#120	C₂×D₄	1	4	yes	—
335	C₄×#120	C₂×D₄	1	4	yes	—
336	C₄×#120	C₂⁴	1	4	yes	—
337	C₂×#386	C₂²⋊C₄	1	2	yes	—
338	C₂×#386	C₂×D₄	1	2	yes	—
339	C₂×#385	C₂²⋊C₄	1	2	yes	—
340	C₂×#385	C₂×D₄	1	2	yes	—
341	#2283	C₂²⋊C₄	1	2	yes	—
342	#2283	C₂²⋊C₄	1	2	yes	—
343	#2283	C₂²⋊C₄	1	2	yes	—
344	#2283	C₂²⋊C₄	1	2	yes	—
345	#2283	C₂²×C₄	1	2	yes	—
346	#2283	C₂²×C₄	1	2	yes	—
347	#2283	C₂²×C₄	1	2	yes	—
348	#2283	C₂²×C₄	1	2	yes	—
349	C₂×#383	C₂²⋊C₄	1	2	yes	—
350	C₂×#381	C₂²⋊C₄	1	2	yes	—
351	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
352	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
353	C₂×#380	C₂²×C₄	1	1	yes	characteristic
354	C₂×#380	C₂²×C₄	1	1	yes	characteristic
355	C₂×#379	C₂²⋊C₄	1	2	yes	—
356	C₂×#379	C₂×D₄	1	2	yes	—
357	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
358	C₂×#376	C₂²⋊C₄	1	2	yes	—
359	#1800	C₂⁴	1	4	yes	—
360	#1799	C₂⁴	1	4	yes	—
361	#1460	C₂⁴	1	4	yes	—
362	#1459	C₂⁴	1	4	yes	—
363	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
364	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×#41	#120	1	1	yes	characteristic
367	C₂²×#41	#120	1	1	yes	characteristic
368	C₂²×#41	#120	1	1	yes	characteristic
369	C₂²×#41	#120	1	1	yes	characteristic
370	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
371	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
372	C₂³×Q₈	#120	1	1	yes	characteristic
373	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
375	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
376	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
378	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
379	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
380	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
381	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
382	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
383	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
384	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂³×D₄	#120	1	1	yes	characteristic
386	C₂³×D₄	C₂³×C₄	1	4	yes	—
387	C₂³×D₄	C₂³×C₄	1	2	yes	—
388	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
389	C₂³×D₄	C₂²×D₄	1	4	yes	—
390	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
394	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
395	C₂⁴×C₄	#120	1	1	yes	characteristic
396	C₂⁴×C₄	#120	1	1	yes	characteristic
397	C₂⁴×C₄	#120	1	1	yes	characteristic
398	C₂⁴×C₄	#120	1	1	yes	characteristic
399	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
400	C₂⁴×C₄	C₂³×C₄	1	4	yes	—
401	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
403	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
404	C₂×#127	#99	1	2	yes	—
405	C₂×#127	#99	1	2	yes	—
406	C₂×#127	#99	1	2	yes	—
407	C₂×#127	#99	1	2	yes	—
408	C₂×#127	#99	1	2	yes	—
409	C₂×#127	#99	1	2	yes	—
410	C₂×#127	#99	1	2	yes	—
411	C₂×#127	#99	1	2	yes	—
412	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
413	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
414	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
415	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
416	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
417	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
418	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
419	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
420	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
421	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
422	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
423	C₂×#127	C₂²×D₄	1	4	yes	—
424	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
425	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
426	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
427	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
428	C₂×#121	C₂³×C₄	1	4	yes	—
429	C₂×#121	C₂²×D₄	1	4	yes	—
430	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
431	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
432	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
433	C₂×#120	C₂²×D₄	1	4	yes	—
434	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
438	C₂×C₄×Q₈	#120	1	1	yes	characteristic
439	C₂×C₄×Q₈	#120	1	1	yes	characteristic
440	C₂×C₄×Q₈	#120	1	1	yes	characteristic
441	C₂×C₄×Q₈	#120	1	1	yes	characteristic
442	C₂×C₄×Q₈	#120	1	1	yes	characteristic
443	C₂×C₄×Q₈	#120	1	1	yes	characteristic
444	C₂×C₄×Q₈	#120	1	1	yes	characteristic
445	C₂×C₄×Q₈	#120	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
451	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
452	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
453	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
454	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
455	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
456	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
457	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
458	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
459	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂×C₄×D₄	#120	1	1	yes	characteristic
474	C₂×C₄×D₄	#120	1	1	yes	characteristic
475	C₂×C₄×D₄	#120	1	1	yes	characteristic
476	C₂×C₄×D₄	#120	1	1	yes	characteristic
477	C₂×C₄×D₄	#120	1	1	yes	characteristic
478	C₂×C₄×D₄	#120	1	1	yes	characteristic
479	C₂×C₄×D₄	#120	1	1	yes	characteristic
480	C₂×C₄×D₄	#120	1	1	yes	characteristic
481	C₂×C₄×D₄	#120	1	1	yes	characteristic
482	C₂×C₄×D₄	#120	1	1	yes	characteristic
483	C₂×C₄×D₄	#120	1	1	yes	characteristic
484	C₂×C₄×D₄	#120	1	1	yes	characteristic
485	C₂×C₄×D₄	#120	1	1	yes	characteristic
486	C₂×C₄×D₄	#120	1	1	yes	characteristic
487	C₂×C₄×D₄	#120	1	1	yes	characteristic
488	C₂×C₄×D₄	#120	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
506	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
508	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
510	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂×#117	#120	1	1	yes	characteristic
515	C₂×#117	#120	1	1	yes	characteristic
516	C₂×#117	#120	1	1	yes	characteristic
517	C₂×#117	#120	1	1	yes	characteristic
518	C₂×#117	#120	1	1	yes	characteristic
519	C₂×#117	#120	1	1	yes	characteristic
520	C₂×#117	#120	1	1	yes	characteristic
521	C₂×#117	#120	1	1	yes	characteristic
522	C₂×#117	#120	1	1	yes	characteristic
523	C₂×#117	#120	1	1	yes	characteristic
524	C₂×#117	#120	1	1	yes	characteristic
525	C₂×#117	#120	1	1	yes	characteristic
526	C₂×#117	C₂²×D₄	1	1	yes	characteristic
527	C₂×#117	C₂²×D₄	1	1	yes	characteristic
528	C₂×#117	C₂²×D₄	1	1	yes	characteristic
529	C₂×#117	C₂²×D₄	1	1	yes	characteristic
530	C₂×#117	C₂²×D₄	1	1	yes	characteristic
531	C₂×#117	C₂²×D₄	1	1	yes	characteristic
532	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
533	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
534	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
535	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
536	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
537	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
538	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
539	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
540	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
541	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
542	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
543	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
545	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
546	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
547	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
548	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
549	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
550	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
551	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
552	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
555	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
556	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
557	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
558	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
559	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
560	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
561	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
562	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
563	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
564	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
565	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
566	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
567	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
568	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
569	C₂²×C₄²	#120	1	1	yes	characteristic
570	C₂²×C₄²	#120	1	1	yes	characteristic
571	C₂²×C₄²	#120	1	1	yes	characteristic
572	C₂²×C₄²	#120	1	1	yes	characteristic
573	C₂²×C₄²	#120	1	1	yes	characteristic
574	C₂²×C₄²	#120	1	1	yes	characteristic
575	C₂²×C₄²	#120	1	1	yes	characteristic
576	C₂²×C₄²	#120	1	1	yes	characteristic
577	C₂²×C₄²	#120	1	1	yes	characteristic
578	C₂²×C₄²	#120	1	1	yes	characteristic
579	C₂²×C₄²	#120	1	1	yes	characteristic
580	C₂²×C₄²	#120	1	1	yes	characteristic
581	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
582	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
583	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
584	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
585	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
586	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
587	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
588	#400	C₂×C₂²⋊C₄	1	4	yes	—
589	#400	C₂×C₂²⋊C₄	1	4	yes	—
590	#400	C₂×C₂²⋊C₄	1	4	yes	—
591	#400	C₂²×D₄	1	4	yes	—
592	#399	C₂×C₂²⋊C₄	1	4	yes	—
593	#399	C₂×C₂²⋊C₄	1	4	yes	—
594	#399	C₂×C₂²⋊C₄	1	4	yes	—
595	#399	C₂²×D₄	1	4	yes	—
596	#394	C₂×C₂²⋊C₄	1	4	yes	—
597	#394	C₂×C₂²⋊C₄	1	4	yes	—
598	#394	C₂×C₂²⋊C₄	1	4	yes	—
599	#394	C₂²×D₄	1	4	yes	—
600	#392	C₂×C₂²⋊C₄	1	4	yes	—
601	#392	C₂×C₂²⋊C₄	1	4	yes	—
602	#392	C₂×C₂²⋊C₄	1	4	yes	—
603	#392	C₂²×D₄	1	4	yes	—
604	#386	C₂×C₂²⋊C₄	1	4	yes	—
605	#386	C₂×C₂²⋊C₄	1	4	yes	—
606	#386	C₂×C₂²⋊C₄	1	4	yes	—
607	#386	C₂²×D₄	1	4	yes	—
608	#385	C₂×C₂²⋊C₄	1	4	yes	—
609	#385	C₂×C₂²⋊C₄	1	4	yes	—
610	#385	C₂×C₂²⋊C₄	1	4	yes	—
611	#385	C₂²×D₄	1	4	yes	—
612	#383	C₂×C₂²⋊C₄	1	4	yes	—
613	#383	C₂×C₂²⋊C₄	1	4	yes	—
614	#381	C₂×C₂²⋊C₄	1	4	yes	—
615	#381	C₂×C₂²⋊C₄	1	4	yes	—
616	#380	C₂×C₂²⋊C₄	1	2	yes	—
617	#380	C₂×C₂²⋊C₄	1	2	yes	—
618	#380	C₂×C₂²⋊C₄	1	2	yes	—
619	#380	C₂×C₂²⋊C₄	1	2	yes	—
620	#380	C₂×C₂²⋊C₄	1	2	yes	—
621	#380	C₂×C₂²⋊C₄	1	2	yes	—
622	#380	C₂³×C₄	1	2	yes	—
623	#380	C₂³×C₄	1	2	yes	—
624	#379	C₂×C₂²⋊C₄	1	4	yes	—
625	#379	C₂×C₂²⋊C₄	1	4	yes	—
626	#379	C₂×C₂²⋊C₄	1	4	yes	—
627	#379	C₂²×D₄	1	4	yes	—
628	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
629	C₄×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
630	#376	C₂×C₂²⋊C₄	1	4	yes	—
631	#376	C₂×C₂²⋊C₄	1	4	yes	—
632	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
633	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
634	C₂⁵	#379	1	1	yes	characteristic
635	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
636	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
637	C₂⁵	C₂×#120	1	1	yes	characteristic
638	C₂²×Q₈	#379	1	1	yes	characteristic
639	C₂²×Q₈	#379	1	1	yes	characteristic
640	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
641	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
642	C₂²×D₄	#379	1	1	yes	characteristic
643	C₂²×D₄	#379	1	1	yes	characteristic
644	C₂²×D₄	#379	1	1	yes	characteristic
645	C₂²×D₄	#379	1	1	yes	characteristic
646	C₂²×D₄	C₂×#99	1	4	yes	—
647	C₂²×D₄	C₂×#99	1	4	yes	—
648	C₂²×D₄	C₂×#99	1	4	yes	—
649	C₂²×D₄	C₂×#99	1	4	yes	—
650	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
651	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
652	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
653	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
654	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
655	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
656	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
657	C₂²×D₄	C₂×#120	1	1	yes	characteristic
658	C₂²×D₄	C₂×#120	1	1	yes	characteristic
659	C₂²×D₄	C₂×#120	1	1	yes	characteristic
660	C₂²×D₄	C₂×#120	1	1	yes	characteristic
661	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
662	C₂³×C₄	#379	1	1	yes	characteristic
663	C₂³×C₄	#379	1	1	yes	characteristic
664	C₂³×C₄	#379	1	1	yes	characteristic
665	C₂³×C₄	#379	1	1	yes	characteristic
666	C₂³×C₄	#379	1	1	yes	characteristic
667	C₂³×C₄	#379	1	1	yes	characteristic
668	C₂³×C₄	#379	1	1	yes	characteristic
669	C₂³×C₄	#379	1	1	yes	characteristic
670	C₂³×C₄	#379	1	1	yes	characteristic
671	C₂³×C₄	#379	1	1	yes	characteristic
672	C₂³×C₄	#379	1	1	yes	characteristic
673	C₂³×C₄	#379	1	1	yes	characteristic
674	C₂³×C₄	#379	1	1	yes	characteristic
675	C₂³×C₄	#379	1	1	yes	characteristic
676	C₂³×C₄	#379	1	1	yes	characteristic
677	C₂³×C₄	#379	1	1	yes	characteristic
678	C₂³×C₄	#379	1	1	yes	characteristic
679	C₂³×C₄	#379	1	1	yes	characteristic
680	C₂³×C₄	#379	1	1	yes	characteristic
681	C₂³×C₄	#379	1	1	yes	characteristic
682	C₂³×C₄	#379	1	1	yes	characteristic
683	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
684	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
685	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
686	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
687	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
688	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
689	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
690	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
691	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
692	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
693	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
694	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
695	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
696	C₂³×C₄	C₂×#120	1	1	yes	characteristic
697	C₂³×C₄	C₂×#120	1	1	yes	characteristic
698	C₂³×C₄	C₂×#120	1	1	yes	characteristic
699	C₂³×C₄	C₂×#120	1	1	yes	characteristic
700	C₂³×C₄	C₂×#120	1	1	yes	characteristic
701	C₂³×C₄	C₂×#120	1	1	yes	characteristic
702	C₂³×C₄	C₂×#120	1	1	yes	characteristic
703	C₂³×C₄	C₂×#120	1	1	yes	characteristic
704	C₂³×C₄	C₂×#120	1	1	yes	characteristic
705	C₂³×C₄	C₂×#120	1	1	yes	characteristic
706	C₂³×C₄	C₂×#120	1	1	yes	characteristic
707	C₂³×C₄	C₂×#120	1	1	yes	characteristic
708	C₂³×C₄	C₂×#120	1	1	yes	characteristic
709	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
710	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
711	#127	C₂×#99	1	4	yes	—
712	#127	C₂×#99	1	4	yes	—
713	#127	C₂×#99	1	4	yes	—
714	#127	C₂×#99	1	4	yes	—
715	#127	C₂×#99	1	4	yes	—
716	#127	C₂×#99	1	4	yes	—
717	#127	C₂×#99	1	4	yes	—
718	#127	C₂×#99	1	4	yes	—
719	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
720	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
721	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
722	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
723	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
724	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
725	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
726	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
727	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
728	C₂×C₄⋊C₄	#379	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
730	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
731	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
754	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
755	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
771	C₂×C₄²	#379	1	1	yes	characteristic
772	C₂×C₄²	#379	1	1	yes	characteristic
773	C₂×C₄²	#379	1	1	yes	characteristic
774	C₂×C₄²	#379	1	1	yes	characteristic
775	C₂×C₄²	#379	1	1	yes	characteristic
776	C₂×C₄²	#379	1	1	yes	characteristic
777	C₂×C₄²	#379	1	1	yes	characteristic
778	C₂×C₄²	#379	1	1	yes	characteristic
779	C₂×C₄²	#379	1	1	yes	characteristic
780	C₂×C₄²	#379	1	1	yes	characteristic
781	C₂×C₄²	#379	1	1	yes	characteristic
782	C₂×C₄²	#379	1	1	yes	characteristic
783	C₂×C₄²	#379	1	1	yes	characteristic
784	C₂×C₄²	#379	1	1	yes	characteristic
785	C₂×C₄²	#379	1	1	yes	characteristic
786	C₂×C₄²	#379	1	1	yes	characteristic
787	C₂×C₄²	#379	1	1	yes	characteristic
788	C₂×C₄²	#379	1	1	yes	characteristic
789	C₂×C₄²	C₂×#99	1	1	yes	characteristic
790	C₂×C₄²	C₂×#99	1	1	yes	characteristic
791	C₂×C₄²	C₂×#99	1	1	yes	characteristic
792	C₂×C₄²	C₂×#99	1	1	yes	characteristic
793	C₂×C₄²	C₂×#99	1	1	yes	characteristic
794	C₂×C₄²	C₂×#99	1	1	yes	characteristic
795	C₂×C₄²	C₂×#99	1	1	yes	characteristic
796	C₂×C₄²	C₂×#99	1	1	yes	characteristic
797	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
798	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
799	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
800	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
801	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
802	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
803	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
804	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
805	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
806	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
807	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
808	C₂×C₄²	C₂×#120	1	1	yes	characteristic
809	C₂×C₄²	C₂×#120	1	1	yes	characteristic
810	C₂×C₄²	C₂×#120	1	1	yes	characteristic
811	C₂×C₄²	C₂×#120	1	1	yes	characteristic
812	C₂×C₄²	C₂×#120	1	1	yes	characteristic
813	C₂×C₄²	C₂×#120	1	1	yes	characteristic
814	C₂×C₄²	C₂×#120	1	1	yes	characteristic
815	C₂×C₄²	C₂×#120	1	1	yes	characteristic
816	C₂×C₄²	C₂×#120	1	1	yes	characteristic
817	C₂×C₄²	C₂×#120	1	1	yes	characteristic
818	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
819	#95	C₂²×C₂²⋊C₄	1	4	yes	—
820	#95	C₂²×C₂²⋊C₄	1	4	yes	—
821	C₂⁴	C₂×#379	1	1	yes	characteristic
822	C₂⁴	C₂×#379	1	1	yes	characteristic
823	C₂⁴	C₂×#379	1	1	yes	characteristic
824	C₂⁴	C₂×#379	1	1	yes	characteristic
825	C₂⁴	C₂×#379	1	1	yes	characteristic
826	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
827	C₂⁴	C₂²×#120	1	1	yes	characteristic
828	C₂×D₄	#1795	1	4	yes	—
829	C₂×D₄	C₂²×#99	1	8	yes	—
830	C₂×D₄	C₂²×#99	1	8	yes	—
831	C₂×D₄	#3585	1	4	yes	—
832	C₂²×C₄	#1781	1	1	yes	characteristic
833	C₂²×C₄	#1781	1	1	yes	characteristic
834	C₂²×C₄	#1781	1	1	yes	characteristic
835	C₂²×C₄	#1781	1	1	yes	characteristic
836	C₂²×C₄	#1781	1	1	yes	characteristic
837	C₂²×C₄	#1781	1	1	yes	characteristic
838	C₂²×C₄	#1781	1	1	yes	characteristic
839	C₂²×C₄	#1781	1	1	yes	characteristic
840	C₂²×C₄	C₂×#379	1	1	yes	characteristic
841	C₂²×C₄	C₂×#379	1	1	yes	characteristic
842	C₂²×C₄	C₂×#379	1	1	yes	characteristic
843	C₂²×C₄	C₂×#379	1	1	yes	characteristic
844	C₂²×C₄	C₂×#379	1	1	yes	characteristic
845	C₂²×C₄	C₂×#379	1	1	yes	characteristic
846	C₂²×C₄	C₂×#379	1	1	yes	characteristic
847	C₂²×C₄	C₂×#379	1	1	yes	characteristic
848	C₂²×C₄	C₂×#379	1	1	yes	characteristic
849	C₂²×C₄	C₂×#379	1	1	yes	characteristic
850	C₂²×C₄	C₂×#379	1	1	yes	characteristic
851	C₂²×C₄	C₂×#379	1	1	yes	characteristic
852	C₂²×C₄	C₂×#379	1	1	yes	characteristic
853	C₂²×C₄	C₂×#379	1	1	yes	characteristic
854	C₂²×C₄	C₂×#379	1	1	yes	characteristic
855	C₂²×C₄	C₂×#379	1	1	yes	characteristic
856	C₂²×C₄	C₂×#379	1	1	yes	characteristic
857	C₂²×C₄	C₂×#379	1	1	yes	characteristic
858	C₂²×C₄	C₂×#379	1	1	yes	characteristic
859	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
860	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
861	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
862	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
863	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
864	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
865	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
866	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
867	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
868	C₄²	#1781	1	1	yes	characteristic
869	C₄²	#1781	1	1	yes	characteristic
870	C₄²	#1781	1	1	yes	characteristic
871	C₄²	#1781	1	1	yes	characteristic
872	C₄²	#1781	1	1	yes	characteristic
873	C₄²	#1781	1	1	yes	characteristic
874	C₄²	#1781	1	1	yes	characteristic
875	C₄²	#1781	1	1	yes	characteristic
876	C₄²	C₂²×#99	1	1	yes	characteristic
877	C₄²	C₂²×#99	1	1	yes	characteristic
878	C₄²	C₂²×#99	1	1	yes	characteristic
879	C₄²	C₂²×#99	1	1	yes	characteristic
880	C₄²	C₂²×#99	1	1	yes	characteristic
881	C₄²	C₂²×#99	1	1	yes	characteristic
882	C₄²	C₂²×#99	1	1	yes	characteristic
883	C₄²	C₂²×#99	1	1	yes	characteristic
884	C₂³	C₂×#1781	1	1	yes	characteristic
885	C₂³	C₂×#1781	1	1	yes	characteristic
886	C₂³	C₂×#1795	1	2	yes	—
887	C₂³	C₂×#1795	1	2	yes	—
888	C₂³	C₂²×#379	1	1	yes	characteristic
889	C₂³	#60087	1	2	yes	—
890	C₂³	#60367	1	2	yes	—
891	C₂×C₄	#12711	1	4	yes	—
892	C₂×C₄	C₂×#1781	1	1	yes	characteristic
893	C₂×C₄	C₂×#1781	1	1	yes	characteristic
894	C₂×C₄	C₂×#1781	1	1	yes	characteristic
895	C₂×C₄	C₂×#1781	1	1	yes	characteristic
896	C₂×C₄	C₂×#1781	1	1	yes	characteristic
897	C₂×C₄	C₂×#1781	1	1	yes	characteristic
898	C₂×C₄	C₂×#1781	1	1	yes	characteristic
899	C₂×C₄	C₂×#1781	1	1	yes	characteristic
900	C₂×C₄	C₂×#1781	1	1	yes	characteristic
901	C₂×C₄	C₂×#1781	1	1	yes	characteristic
902	C₂×C₄	C₂×#1795	1	2	yes	—
903	C₂×C₄	#33348	1	4	yes	—
904	C₂×C₄	C₂³×#99	1	1	yes	characteristic
905	C₂×C₄	C₂³×#99	1	1	yes	characteristic
906	C₂×C₄	#60367	1	2	yes	—
907	C₂²	C₂×#12711	1	2	yes	—
908	C₂²	#493425	1	2	yes	—
909	C₂²	C₂²×#1781	1	1	yes	characteristic
910	C₂²	#6370719	1	1	yes	characteristic
911	C₂²	C₂²×#1795	1	1	yes	characteristic
912	C₄	C₂×#12711	1	2	yes	—
913	C₄	C₂×#12711	1	2	yes	—
914	C₄	#493425	1	2	yes	—
915	C₄	C₂×#33348	1	2	yes	—
916	C₂	C₂²×#12711	1	1	yes	characteristic
917	C₂	C₂×#493425	1	1	yes	characteristic
918	C₂	#72235084	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1781
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	C₂×#7737411	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂²×#3498 ◁ 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. #72316900	C₂	semidirect
2. #72316839	C₂	semidirect
3. #72316740	C₂	semidirect
4. #72316705	C₂	semidirect
5. #72312553	C₂	semidirect
6. #72281567	C₂	semidirect
7. #72281322	C₂	semidirect
8. #72279835	C₂	semidirect
9. #72240305	C₂	semidirect
10. #72231038	C₂	semidirect
13. C₂³×D₄²	C₄	semidirect
14. #7737411	C₄	semidirect
15. #7737411	C₄	semidirect
18. C₂×#38904	C₄	semidirect
20. C₂×D₄×#120	C₄	semidirect
22. C₂×#35237	C₄	semidirect
23. C₂×#35237	C₄	semidirect
26. C₂×#34364	C₄	semidirect
27. #6370950	C₂²	semidirect
28. #6370937	C₂²	semidirect
29. #6342561	C₂²	semidirect
30. #6342561	C₂²	semidirect
31. #496520	C₂²	semidirect
32. #496508	C₂²	semidirect
33. #493995	C₂²	semidirect
34. #482657	C₂²	semidirect
35. #482633	C₂²	semidirect
36. #482443	C₂²	semidirect
37. #482424	C₂²	semidirect
38. #482377	C₂²	semidirect
39. #482357	C₂²	semidirect
40. #482258	C₂²	semidirect
41. #482234	C₂²	semidirect
42. #480583	C₂²	semidirect
43. #480580	C₂²	semidirect
44. #480376	C₂²	semidirect
45. #185785	C₂²	semidirect
46. #185755	C₂²	semidirect
47. #185733	C₂²	semidirect
48. #185660	C₂²	semidirect
49. #185643	C₂²	semidirect
50. #185628	C₂²	semidirect
51. #130982	C₂²	semidirect
52. #130740	C₂²	semidirect
132. #20728	C₂³	semidirect
134. #20723	C₂³	semidirect
136. #20637	C₂³	semidirect
137. #20632	C₂³	semidirect
138. #17366	C₂³	semidirect
140. #17363	C₂³	semidirect
142. #17349	C₂³	semidirect
143. #17349	C₂³	semidirect
144. #12793	C₂³	semidirect
145. #11903	C₂³	semidirect
146. #11899	C₂³	semidirect
147. #11880	C₂³	semidirect
148. #11873	C₂³	semidirect
149. #11471	C₂³	semidirect
150. #8383	C₂³	semidirect
151. #8375	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72316900	2
#72316839	2
#72316740	2
#72316705	2
#72312553	2
#72281567	2
#72281322	2
#72279835	2
#72240305	2
#72231038	2
C₂×#7737411	2