Subgroups — #72313805

Order 2048.

At least 10994 conjugacy classes of subgroups; only the 2092 normal subgroups are shown.

The subgroup lattice has 1070 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313793	C₂	1	4	yes	maximal, complemented
2	C₂×#480392	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#493957	C₂	1	1	yes	maximal, characteristic, complemented
4	#72313544	C₂	1	4	yes	maximal, complemented
5	#72313526	C₂	1	2	yes	maximal, complemented
6	#72313498	C₂	1	2	yes	maximal, complemented
7	#72313469	C₂	1	2	yes	maximal, complemented
8	#72313412	C₂	1	2	yes	maximal, complemented
9	#72311806	C₂	1	1	yes	maximal, characteristic
10	#72306056	C₂	1	2	yes	maximal, complemented
11	#72285068	C₂	1	2	yes	maximal, complemented
12	#72282369	C₂	1	4	yes	maximal, complemented
13	#72281788	C₂	1	4	yes	maximal, complemented
14	C₂×#62812	C₄	1	1	yes	characteristic, complemented
15	C₂×#62812	C₂²	1	1	yes	characteristic
16	#7672761	C₄	1	1	yes	characteristic, complemented
17	#7672761	C₂²	1	1	yes	characteristic
18	#7672751	C₄	1	1	yes	characteristic, complemented
19	#7672751	C₂²	1	1	yes	characteristic
20	#7672684	C₄	1	1	yes	characteristic, complemented
21	#7672684	C₄	1	1	yes	characteristic, complemented
22	#7672684	C₂²	1	1	yes	characteristic
23	#7672684	C₂²	1	1	yes	characteristic
24	#7672442	C₄	1	2	yes	complemented
25	#7672442	C₂²	1	2	yes	—
26	#7672197	C₄	1	2	yes	complemented
27	#7671575	C₂²	1	2	yes	—
28	#7636738	C₄	1	2	yes	complemented
29	#7636738	C₂²	1	2	yes	—
30	C₂×#36644	C₄	1	1	yes	characteristic, complemented
31	D₄×#532	C₄	1	2	yes	complemented
32	D₄×#532	C₂²	1	2	yes	—
33	#7628665	C₄	1	1	yes	characteristic, complemented
34	#7628665	C₂²	1	1	yes	characteristic
35	C₂×C₄×#532	C₄	1	1	yes	characteristic, complemented
36	C₂×C₄×#532	C₂²	1	1	yes	characteristic
37	C₂×#20723	C₂²	1	2	yes	complemented
38	C₂×#17363	C₂²	1	2	yes	complemented
39	#493957	C₂²	1	2	yes	complemented
40	#493957	C₂²	1	2	yes	complemented
41	#493957	C₂²	1	2	yes	complemented
42	#493957	C₂²	1	2	yes	complemented
43	C₂×#12798	C₂²	1	2	yes	complemented
44	C₂×#12797	C₂²	1	2	yes	complemented
45	#482368	C₂²	1	8	yes	complemented
46	#482364	C₂²	1	4	yes	complemented
47	#482363	C₂²	1	4	yes	complemented
48	#482050	C₂²	1	8	yes	complemented
49	#480392	C₂²	1	2	yes	complemented
50	#480392	C₂²	1	2	yes	complemented
51	#480392	C₂²	1	2	yes	complemented
52	#480392	C₂²	1	2	yes	complemented
53	C₂×#11477	C₂²	1	2	yes	complemented
54	C₂×#11475	C₂²	1	2	yes	complemented
55	#185661	C₂²	1	4	yes	complemented
56	#185660	C₂²	1	4	yes	complemented
57	#185645	C₂²	1	8	yes	complemented
58	#185627	C₂²	1	8	yes	complemented
59	#130775	C₂²	1	8	yes	complemented
60	#130774	C₂²	1	8	yes	complemented
61	#130773	C₂²	1	8	yes	complemented
62	#130772	C₂²	1	8	yes	complemented
63	#130771	C₂²	1	8	yes	complemented
64	#130770	C₂²	1	8	yes	complemented
65	#130769	C₂²	1	8	yes	complemented
66	#130768	C₂²	1	8	yes	complemented
67	C₂×#3499	C₂×C₄	1	1	yes	characteristic
68	C₂×#3499	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×#3499	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×#3499	D₄	1	2	yes	—
71	C₂×#3499	C₂³	1	1	yes	characteristic
72	C₂×#3498	C₂×C₄	1	1	yes	characteristic
73	C₂×#3498	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×#3498	C₂×C₄	1	1	yes	characteristic, complemented
75	C₂×#3498	D₄	1	2	yes	—
76	C₂×#3498	C₂³	1	1	yes	characteristic
77	C₂×#3497	C₂×C₄	1	2	yes	—
78	C₂×#3497	C₂×C₄	1	2	yes	—
79	C₂×#3496	C₂×C₄	1	2	yes	—
80	C₂×#3496	D₄	1	4	yes	—
81	C₂×#3496	C₂³	1	2	yes	—
82	C₂×D₄×#41	C₂×C₄	1	2	yes	—
83	C₂×D₄×#41	C₂×C₄	1	2	yes	complemented
84	C₂×D₄×#41	C₂×C₄	1	2	yes	complemented
85	C₂×D₄×#41	D₄	1	4	yes	—
86	C₂×D₄×#41	C₂³	1	2	yes	—
87	C₂²×#532	C₂×C₄	1	1	yes	characteristic
88	C₂²×#532	C₂×C₄	1	1	yes	characteristic
89	C₂²×#532	C₂×C₄	1	1	yes	characteristic
90	C₂²×#532	D₄	1	2	yes	—
91	C₂²×#532	D₄	1	2	yes	—
92	C₂²×#532	D₄	1	1	yes	characteristic
93	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
95	#39363	C₂×C₄	1	2	yes	complemented
96	#39363	C₂×C₄	1	2	yes	complemented
97	#39363	C₂×C₄	1	2	yes	complemented
98	#39363	C₂×C₄	1	2	yes	complemented
99	#39362	C₂×C₄	1	2	yes	—
100	#39362	C₂×C₄	1	2	yes	—
101	#39362	C₂³	1	2	yes	—
102	#39362	C₂³	1	2	yes	—
103	#39361	C₂×C₄	1	2	yes	—
104	#39361	C₂×C₄	1	2	yes	complemented
105	#39361	C₂×C₄	1	2	yes	complemented
106	#39361	C₂³	1	2	yes	—
107	#39360	C₂×C₄	1	2	yes	—
108	#39360	C₂×C₄	1	2	yes	complemented
109	#39360	C₂×C₄	1	2	yes	complemented
110	#39360	C₂³	1	2	yes	—
111	#36644	C₂×C₄	1	2	yes	—
112	#36644	C₂×C₄	1	2	yes	—
113	#36644	C₂×C₄	1	2	yes	complemented
114	#36644	C₂×C₄	1	2	yes	complemented
115	C₂×#2868	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂×#2867	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×#2858	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×#2858	C₂×C₄	1	1	yes	characteristic, complemented
119	#36128	C₂×C₄	1	2	yes	complemented
120	#36128	C₂×C₄	1	2	yes	complemented
121	#36127	C₂×C₄	1	2	yes	—
122	#36127	C₂³	1	2	yes	—
123	#36125	C₂×C₄	1	2	yes	—
124	#36125	C₂×C₄	1	2	yes	complemented
125	#36125	C₂×C₄	1	2	yes	complemented
126	#36125	C₂³	1	2	yes	—
127	D₄×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
128	D₄×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
129	D₄×#127	C₂×C₄	1	2	yes	—
130	D₄×#127	C₂³	1	2	yes	—
131	D₄×#124	C₂×C₄	1	2	yes	—
132	D₄×#124	C₂×C₄	1	2	yes	complemented
133	D₄×#124	C₂×C₄	1	2	yes	complemented
134	D₄×#124	C₂³	1	2	yes	—
135	#35328	D₄	1	4	yes	—
136	#35316	C₂×C₄	1	1	yes	characteristic
137	#35316	C₂×C₄	1	1	yes	characteristic, complemented
138	#35316	C₂×C₄	1	1	yes	characteristic, complemented
139	#35316	C₂³	1	1	yes	characteristic
140	#35272	C₂×C₄	1	1	yes	characteristic
141	#35272	C₂×C₄	1	1	yes	characteristic, complemented
142	#35272	C₂×C₄	1	1	yes	characteristic, complemented
143	#35272	C₂³	1	1	yes	characteristic
144	#35178	C₂×C₄	1	2	yes	—
145	#35178	C₂×C₄	1	2	yes	—
146	#35165	C₂×C₄	1	2	yes	—
147	#35165	C₂³	1	2	yes	—
148	#35000	D₄	1	4	yes	—
149	#34937	C₂×C₄	1	2	yes	—
150	#34937	C₂×C₄	1	2	yes	complemented
151	#34937	C₂×C₄	1	2	yes	complemented
152	#34937	C₂³	1	2	yes	—
153	#34935	D₄	1	4	yes	—
154	#34633	D₄	1	4	yes	—
155	C₄×#532	C₂×C₄	1	2	yes	—
156	C₄×#532	C₂×C₄	1	2	yes	—
157	C₄×#532	C₂×C₄	1	1	yes	characteristic
158	C₄×#532	C₂×C₄	1	1	yes	characteristic
159	C₄×#532	C₂×C₄	1	1	yes	characteristic
160	C₄×#532	C₂×C₄	1	1	yes	characteristic
161	C₄×#532	C₂×C₄	1	1	yes	characteristic, complemented
162	C₄×#532	C₂×C₄	1	1	yes	characteristic, complemented
163	C₄×#532	C₂×C₄	1	1	yes	characteristic, complemented
164	C₄×#532	C₂×C₄	1	1	yes	characteristic, complemented
165	C₄×#532	D₄	1	1	yes	characteristic
166	C₄×#532	D₄	1	1	yes	characteristic
167	C₄×#532	D₄	1	1	yes	characteristic
168	C₄×#532	D₄	1	1	yes	characteristic
169	C₄×#532	D₄	1	1	yes	characteristic
170	C₄×#532	D₄	1	1	yes	characteristic
171	C₄×#532	D₄	1	1	yes	characteristic
172	C₄×#532	D₄	1	1	yes	characteristic
173	C₄×#532	C₂³	1	1	yes	characteristic
174	C₄×#532	C₂³	1	1	yes	characteristic
175	C₄×#532	C₂³	1	1	yes	characteristic
176	C₄×#532	C₂³	1	1	yes	characteristic
177	C₂×C₄×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄⋊Q₈	D₄	1	1	yes	characteristic
179	C₂×C₄×#127	D₄	1	1	yes	characteristic
180	C₂×C₄×#127	C₂³	1	1	yes	characteristic
181	C₂×C₄×#124	C₂×C₄	1	1	yes	characteristic
182	C₂×C₄×#124	D₄	1	1	yes	characteristic
183	C₂×C₄×#124	D₄	1	1	yes	characteristic
184	C₂×C₄×#124	C₂³	1	1	yes	characteristic
185	C₂×#2297	D₄	1	1	yes	characteristic
186	C₂×#2297	D₄	1	1	yes	characteristic
187	C₂×#2293	C₂×C₄	1	2	yes	complemented
188	C₂×#2285	C₂×C₄	1	1	yes	characteristic
189	C₂×#2285	D₄	1	1	yes	characteristic
190	C₂×C₄²×D₄	C₂×C₄	1	2	yes	complemented
191	C₂²×C₄³	C₂×C₄	1	1	yes	characteristic
192	#20723	C₂³	1	4	yes	—
193	#20723	C₂³	1	4	yes	—
194	C₂×#1799	C₂³	1	4	yes	—
195	#17363	C₂³	1	4	yes	—
196	#17363	C₂³	1	4	yes	—
197	C₂×#1459	C₂³	1	4	yes	—
198	#12798	C₂³	1	4	yes	—
199	#12798	C₂³	1	4	yes	—
200	#12797	C₂³	1	4	yes	—
201	#12797	C₂³	1	4	yes	—
202	#11878	C₂³	1	16	yes	—
203	#11877	C₂³	1	16	yes	—
204	#11477	C₂³	1	4	yes	—
205	#11477	C₂³	1	4	yes	—
206	#11475	C₂³	1	4	yes	—
207	#11475	C₂³	1	4	yes	—
208	#8376	C₂³	1	16	yes	—
209	#8375	C₂³	1	16	yes	—
210	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×#41	C₂×D₄	1	1	yes	characteristic
212	C₂×#550	C₂²⋊C₄	1	4	yes	—
213	C₂×#550	C₂²×C₄	1	2	yes	—
214	C₂×#550	C₂²×C₄	1	2	yes	—
215	C₂×#550	C₂²×C₄	1	2	yes	—
216	C₂×#550	C₂²×C₄	1	2	yes	—
217	C₂×D₄×Q₈	C₂²⋊C₄	1	4	yes	—
218	C₂×D₄×Q₈	C₂²×C₄	1	2	yes	—
219	C₂×D₄×Q₈	C₂²×C₄	1	2	yes	—
220	C₂×D₄×Q₈	C₂²×C₄	1	2	yes	—
221	C₂×D₄×Q₈	C₂²×C₄	1	2	yes	—
222	C₂×#547	C₂²⋊C₄	1	4	yes	—
223	C₂×#547	C₂²⋊C₄	1	4	yes	—
224	C₂×#547	C₂²×C₄	1	2	yes	—
225	C₂×#547	C₂²×C₄	1	2	yes	—
226	C₂×#547	C₂²×C₄	1	2	yes	—
227	C₂×#547	C₂×D₄	1	4	yes	—
228	C₂×#547	C₂×D₄	1	4	yes	—
229	C₂×#547	C₂×D₄	1	4	yes	—
230	C₂×#547	C₂⁴	1	2	yes	—
231	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
232	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
233	C₂×D₄²	C₂²×C₄	1	2	yes	—
234	C₂×D₄²	C₂²×C₄	1	2	yes	—
235	C₂×D₄²	C₂²×C₄	1	2	yes	—
236	C₂×D₄²	C₂×D₄	1	4	yes	—
237	C₂×D₄²	C₂×D₄	1	4	yes	—
238	C₂×D₄²	C₂×D₄	1	4	yes	—
239	C₂×D₄²	C₂⁴	1	2	yes	—
240	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
241	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
242	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
243	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
244	C₂×#532	C₂²⋊C₄	1	2	yes	—
245	C₂×#532	C₂²⋊C₄	1	2	yes	—
246	C₂×#532	C₂²⋊C₄	1	2	yes	—
247	C₂×#532	C₂²⋊C₄	1	2	yes	—
248	C₂×#532	C₂²⋊C₄	1	4	yes	—
249	C₂×#532	C₂²⋊C₄	1	4	yes	—
250	C₂×#532	C₂²⋊C₄	1	4	yes	—
251	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
252	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
253	C₂×#532	C₂²⋊C₄	1	2	yes	—
254	C₂×#532	C₂²⋊C₄	1	2	yes	—
255	C₂×#532	C₂²⋊C₄	1	2	yes	—
256	C₂×#532	C₂²×C₄	1	2	yes	—
257	C₂×#532	C₂²×C₄	1	2	yes	—
258	C₂×#532	C₂²×C₄	1	2	yes	—
259	C₂×#532	C₂²×C₄	1	2	yes	—
260	C₂×#532	C₂²×C₄	1	2	yes	—
261	C₂×#532	C₂²×C₄	1	1	yes	characteristic
262	C₂×#532	C₂²×C₄	1	1	yes	characteristic
263	C₂×#532	C₂×D₄	1	1	yes	characteristic
264	C₂×#532	C₂×D₄	1	1	yes	characteristic
265	C₂×#532	C₂×D₄	1	1	yes	characteristic
266	C₂×#532	C₂×D₄	1	1	yes	characteristic
267	C₂×#532	C₂×D₄	1	2	yes	—
268	C₂×#532	C₂×D₄	1	2	yes	—
269	C₂×#532	C₂×D₄	1	4	yes	—
270	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	2	yes	—
273	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
274	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
275	C₂²×C₄⋊Q₈	C₂×D₄	1	2	yes	—
276	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×#127	C₂²⋊C₄	1	2	yes	—
278	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
279	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
280	C₂²×#127	C₂×D₄	1	2	yes	—
281	C₂²×#127	C₂×D₄	1	1	yes	characteristic
282	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×#124	C₂×D₄	1	1	yes	characteristic
284	C₂²×#121	C₂²⋊C₄	1	2	yes	—
285	C₂²×#121	C₂²⋊C₄	1	2	yes	—
286	C₂²×#121	C₂²⋊C₄	1	2	yes	—
287	C₂²×#121	C₂×D₄	1	4	yes	—
288	C₂²×#121	C₂×D₄	1	4	yes	—
289	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
294	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
295	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
296	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
298	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
299	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
300	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
301	C₂×C₄×#41	C₂×D₄	1	2	yes	—
302	C₂×C₄×#41	C₂×D₄	1	2	yes	—
303	C₂×C₄×#41	C₂×D₄	1	2	yes	—
304	C₂×C₄×#41	C₂×D₄	1	2	yes	—
305	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
306	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
307	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
308	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×Q₈	C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
311	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
312	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×D₄	C₂²⋊C₄	1	4	yes	—
314	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
316	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
317	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
320	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
322	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
323	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
324	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×#117	C₂×D₄	1	1	yes	characteristic
326	C₂²×#117	C₂×D₄	1	2	yes	—
327	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
328	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
329	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
330	C₂³×C₄²	C₂×D₄	1	2	yes	—
331	#2868	C₂²×C₄	1	2	yes	—
332	#2868	C₂²×C₄	1	2	yes	—
333	#2867	C₂²×C₄	1	2	yes	—
334	#2867	C₂²×C₄	1	2	yes	—
335	#2858	C₂²×C₄	1	2	yes	—
336	#2858	C₂²×C₄	1	2	yes	—
337	#2858	C₂²×C₄	1	2	yes	—
338	#2858	C₂²×C₄	1	2	yes	—
339	#2621	C₂²⋊C₄	1	4	yes	—
340	#2621	C₂×D₄	1	4	yes	—
341	#2619	C₂²⋊C₄	1	4	yes	—
342	#2619	C₂×D₄	1	4	yes	—
343	#2618	C₂²⋊C₄	1	8	yes	—
344	#2617	C₂×D₄	1	8	yes	—
345	#2548	C₂²×C₄	1	2	yes	—
346	#2548	C₂²×C₄	1	2	yes	—
347	#2548	C₂²×C₄	1	2	yes	—
348	#2548	C₂²×C₄	1	2	yes	—
349	#2547	C₂²×C₄	1	2	yes	—
350	#2547	C₂²×C₄	1	2	yes	—
351	#2547	C₂²×C₄	1	2	yes	—
352	#2547	C₂⁴	1	2	yes	—
353	#2546	C₂²×C₄	1	2	yes	—
354	#2546	C₂²×C₄	1	2	yes	—
355	#2546	C₂²×C₄	1	2	yes	—
356	#2546	C₂²×C₄	1	2	yes	—
357	#2543	C₂²⋊C₄	1	8	yes	—
358	#2543	C₂×D₄	1	8	yes	—
359	#2541	C₂²×C₄	1	2	yes	—
360	#2541	C₂²×C₄	1	2	yes	—
361	#2541	C₂²×C₄	1	2	yes	—
362	#2541	C₂⁴	1	2	yes	—
363	#2536	C₂²⋊C₄	1	8	yes	—
364	#2535	C₂×D₄	1	8	yes	—
365	#2486	C₂²⋊C₄	1	4	yes	—
366	#2486	C₂×D₄	1	4	yes	—
367	#2408	C₂²⋊C₄	1	4	yes	—
368	#2408	C₂×D₄	1	4	yes	—
369	#2392	C₂²⋊C₄	1	8	yes	—
370	#2392	C₂×D₄	1	8	yes	—
371	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
372	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
373	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
374	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
375	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
376	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
377	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
378	C₄×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
379	C₄×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
380	C₄×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
381	C₄×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
382	C₄×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
383	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
384	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
385	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
386	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
387	C₄×#127	C₂²⋊C₄	1	1	yes	characteristic
388	C₄×#127	C₂²⋊C₄	1	1	yes	characteristic
389	C₄×#127	C₂²⋊C₄	1	1	yes	characteristic
390	C₄×#127	C₂²⋊C₄	1	1	yes	characteristic
391	C₄×#127	C₂²×C₄	1	1	yes	characteristic
392	C₄×#127	C₂²×C₄	1	1	yes	characteristic
393	C₄×#127	C₂×D₄	1	1	yes	characteristic
394	C₄×#127	C₂×D₄	1	1	yes	characteristic
395	C₄×#127	C₂×D₄	1	1	yes	characteristic
396	C₄×#127	C₂×D₄	1	1	yes	characteristic
397	C₄×#127	C₂×D₄	1	1	yes	characteristic
398	C₄×#127	C₂×D₄	1	1	yes	characteristic
399	C₄×#127	C₂×D₄	1	1	yes	characteristic
400	C₄×#127	C₂×D₄	1	1	yes	characteristic
401	C₄×#127	C₂⁴	1	1	yes	characteristic
402	C₄×#127	C₂⁴	1	1	yes	characteristic
403	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
404	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
405	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
406	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
407	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
408	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
409	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
410	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
411	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
412	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
413	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
414	C₄×#124	C₂²⋊C₄	1	1	yes	characteristic
415	C₄×#124	C₂²×C₄	1	1	yes	characteristic
416	C₄×#124	C₂²×C₄	1	1	yes	characteristic
417	C₄×#124	C₂²×C₄	1	1	yes	characteristic
418	C₄×#124	C₂²×C₄	1	1	yes	characteristic
419	C₄×#124	C₂²×C₄	1	1	yes	characteristic
420	C₄×#124	C₂²×C₄	1	1	yes	characteristic
421	C₄×#124	C₂×D₄	1	1	yes	characteristic
422	C₄×#124	C₂×D₄	1	1	yes	characteristic
423	C₄×#124	C₂×D₄	1	1	yes	characteristic
424	C₄×#124	C₂×D₄	1	1	yes	characteristic
425	C₄×#124	C₂×D₄	1	1	yes	characteristic
426	C₄×#124	C₂×D₄	1	1	yes	characteristic
427	C₄×#124	C₂×D₄	1	1	yes	characteristic
428	C₄×#124	C₂×D₄	1	1	yes	characteristic
429	C₄×#124	C₂×D₄	1	1	yes	characteristic
430	C₄×#124	C₂×D₄	1	1	yes	characteristic
431	C₄×#124	C₂×D₄	1	1	yes	characteristic
432	C₄×#124	C₂×D₄	1	1	yes	characteristic
433	C₄×#124	C₂⁴	1	1	yes	characteristic
434	C₄×#124	C₂⁴	1	1	yes	characteristic
435	#2297	C₂²⋊C₄	1	1	yes	characteristic
436	#2297	C₂²⋊C₄	1	1	yes	characteristic
437	#2297	C₂²⋊C₄	1	1	yes	characteristic
438	#2297	C₂²⋊C₄	1	1	yes	characteristic
439	#2297	C₂²⋊C₄	1	1	yes	characteristic
440	#2297	C₂²⋊C₄	1	1	yes	characteristic
441	#2297	C₂²⋊C₄	1	1	yes	characteristic
442	#2297	C₂²⋊C₄	1	1	yes	characteristic
443	#2297	C₂×D₄	1	1	yes	characteristic
444	#2297	C₂×D₄	1	1	yes	characteristic
445	#2297	C₂×D₄	1	1	yes	characteristic
446	#2297	C₂×D₄	1	1	yes	characteristic
447	#2297	C₂×D₄	1	1	yes	characteristic
448	#2297	C₂×D₄	1	1	yes	characteristic
449	#2297	C₂×D₄	1	1	yes	characteristic
450	#2297	C₂×D₄	1	1	yes	characteristic
451	C₂×#391	C₂²⋊C₄	1	1	yes	characteristic
452	C₂×#391	C₂²⋊C₄	1	1	yes	characteristic
453	C₂×#391	C₂²⋊C₄	1	1	yes	characteristic
454	C₂×#391	C₂×D₄	1	1	yes	characteristic
455	#2293	C₂²×C₄	1	2	yes	—
456	#2293	C₂²×C₄	1	2	yes	—
457	#2293	C₂²×C₄	1	2	yes	—
458	#2293	C₂²×C₄	1	2	yes	—
459	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
460	C₂×#390	C₂×D₄	1	1	yes	characteristic
461	C₂×#390	C₂×D₄	1	1	yes	characteristic
462	C₂×#390	C₂×D₄	1	1	yes	characteristic
463	#2285	C₂²⋊C₄	1	2	yes	—
464	#2285	C₂²⋊C₄	1	2	yes	—
465	#2285	C₂²⋊C₄	1	1	yes	characteristic
466	#2285	C₂²⋊C₄	1	1	yes	characteristic
467	#2285	C₂²⋊C₄	1	1	yes	characteristic
468	#2285	C₂²⋊C₄	1	1	yes	characteristic
469	#2285	C₂²×C₄	1	2	yes	—
470	#2285	C₂²×C₄	1	1	yes	characteristic
471	#2285	C₂²×C₄	1	1	yes	characteristic
472	#2285	C₂×D₄	1	1	yes	characteristic
473	#2285	C₂×D₄	1	1	yes	characteristic
474	#2285	C₂×D₄	1	1	yes	characteristic
475	#2285	C₂×D₄	1	1	yes	characteristic
476	C₂×#384	C₂²⋊C₄	1	1	yes	characteristic
477	C₂×#384	C₂×D₄	1	1	yes	characteristic
478	C₂×#382	C₂²⋊C₄	1	2	yes	—
479	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic
480	C₂×#382	C₂×D₄	1	1	yes	characteristic
481	C₂×#380	C₂²⋊C₄	1	2	yes	—
482	C₄²×D₄	C₂²×C₄	1	2	yes	—
483	C₄²×D₄	C₂²×C₄	1	2	yes	—
484	C₄²×D₄	C₂²×C₄	1	2	yes	—
485	C₄²×D₄	C₂²×C₄	1	2	yes	—
486	C₂×C₄×C₄⋊C₄	C₂²×C₄	1	2	yes	—
487	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
488	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
489	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
490	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
491	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
492	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
493	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
495	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
496	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
497	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
498	C₂×C₄³	C₂²×C₄	1	1	yes	characteristic
499	#1799	C₂⁴	1	8	yes	—
500	#1459	C₂⁴	1	8	yes	—
501	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
502	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
503	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
504	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
505	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
506	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²×#41	#120	1	2	yes	—
508	C₂²×#41	#120	1	2	yes	—
509	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
510	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
511	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
514	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
516	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
517	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
518	C₂³×D₄	#120	1	2	yes	—
519	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
520	C₂³×D₄	C₂²×D₄	1	4	yes	—
521	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
522	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
524	C₂⁴×C₄	#120	1	2	yes	—
525	C₂⁴×C₄	#120	1	2	yes	—
526	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
527	#532	#99	1	2	yes	—
528	#532	#99	1	2	yes	—
529	#532	#99	1	2	yes	—
530	#532	#99	1	2	yes	—
531	#532	#99	1	2	yes	—
532	#532	#99	1	2	yes	—
533	#532	#99	1	2	yes	—
534	#532	#99	1	2	yes	—
535	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
536	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
537	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
538	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
539	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
540	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
541	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
542	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
543	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
544	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
545	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
546	C₂×C₄⋊Q₈	C₂³×C₄	1	2	yes	—
547	C₂×C₄⋊Q₈	C₂³×C₄	1	2	yes	—
548	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
549	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
550	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
551	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
552	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
553	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
554	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
555	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
556	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
557	C₂×#127	AGL(1,ℤ/8)	1	8	yes	—
558	C₂×#127	C₂³×C₄	1	2	yes	—
559	C₂×#127	C₂³×C₄	1	2	yes	—
560	C₂×#127	C₂²×D₄	1	1	yes	characteristic
561	C₂×#127	C₂²×D₄	1	1	yes	characteristic
562	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
568	C₂×#124	AGL(1,ℤ/8)	1	8	yes	—
569	C₂×#124	C₂²×D₄	1	1	yes	characteristic
570	C₂×#124	C₂²×D₄	1	1	yes	characteristic
571	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
572	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
573	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
574	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
575	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
576	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
577	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
578	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
579	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
580	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
581	C₂×#121	C₂²×D₄	1	4	yes	—
582	C₂×#121	C₂²×D₄	1	4	yes	—
583	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
584	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
585	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
589	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
590	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
591	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
592	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
593	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
594	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
595	C₂×C₄×Q₈	#120	1	2	yes	—
596	C₂×C₄×Q₈	#120	1	2	yes	—
597	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
598	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
599	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
600	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
601	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
604	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
605	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
606	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
607	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
608	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
609	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
610	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
611	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
612	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
613	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
620	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
622	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
623	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
624	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
625	C₂×C₄×D₄	#120	1	2	yes	—
626	C₂×C₄×D₄	#120	1	2	yes	—
627	C₂×C₄×D₄	#120	1	2	yes	—
628	C₂×C₄×D₄	#120	1	2	yes	—
629	C₂×C₄×D₄	#120	1	2	yes	—
630	C₂×C₄×D₄	#120	1	2	yes	—
631	C₂×C₄×D₄	#120	1	2	yes	—
632	C₂×C₄×D₄	#120	1	2	yes	—
633	C₂×C₄×D₄	#120	1	2	yes	—
634	C₂×C₄×D₄	#120	1	2	yes	—
635	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
636	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
637	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
639	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
640	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
641	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
645	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
646	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
647	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
649	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
650	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
651	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
652	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
653	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
654	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
655	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
656	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
657	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
658	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
659	C₂×#117	#120	1	2	yes	—
660	C₂×#117	#120	1	2	yes	—
661	C₂×#117	#120	1	2	yes	—
662	C₂×#117	#120	1	2	yes	—
663	C₂×#117	#120	1	2	yes	—
664	C₂×#117	#120	1	2	yes	—
665	C₂×#117	C₂²×D₄	1	2	yes	—
666	C₂×#117	C₂²×D₄	1	2	yes	—
667	C₂×#117	C₂²×D₄	1	1	yes	characteristic
668	C₂×#117	C₂²×D₄	1	1	yes	characteristic
669	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
670	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
671	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
672	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
673	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
674	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
675	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
676	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
677	C₂²×C₄⋊C₄	#120	1	2	yes	—
678	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
679	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
680	C₂²×C₂²⋊C₄	#120	1	2	yes	—
681	C₂²×C₂²⋊C₄	#120	1	2	yes	—
682	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
683	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
684	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
685	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
686	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
687	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
688	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
689	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
690	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
691	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
692	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
693	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
694	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
695	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
696	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
697	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
698	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
699	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
700	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
701	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
702	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
703	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
704	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
705	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
706	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
707	C₂²×C₄²	#120	1	2	yes	—
708	C₂²×C₄²	#120	1	2	yes	—
709	C₂²×C₄²	#120	1	2	yes	—
710	C₂²×C₄²	#120	1	2	yes	—
711	C₂²×C₄²	#120	1	2	yes	—
712	C₂²×C₄²	#120	1	2	yes	—
713	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
714	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
715	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
716	C₂²×C₄²	C₂²×D₄	1	2	yes	—
717	C₂²×C₄²	C₂²×D₄	1	2	yes	—
718	#398	C₂×C₂²⋊C₄	1	8	yes	—
719	#398	C₂×C₂²⋊C₄	1	8	yes	—
720	#397	C₂×C₂²⋊C₄	1	8	yes	—
721	#397	C₂²×D₄	1	8	yes	—
722	#394	C₂×C₂²⋊C₄	1	8	yes	—
723	#394	C₂×C₂²⋊C₄	1	8	yes	—
724	#392	C₂×C₂²⋊C₄	1	8	yes	—
725	#392	C₂²×D₄	1	8	yes	—
726	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
727	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
728	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
729	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
730	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
731	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
732	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
733	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
734	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
735	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
736	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
737	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
738	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
739	#391	C₂×C₂²⋊C₄	1	1	yes	characteristic
740	#391	C₂²×D₄	1	1	yes	characteristic
741	#391	C₂²×D₄	1	1	yes	characteristic
742	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
743	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
744	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
745	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
746	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
747	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
748	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
749	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
750	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
751	#390	C₂×C₂²⋊C₄	1	1	yes	characteristic
752	#390	C₂²×D₄	1	1	yes	characteristic
753	#390	C₂²×D₄	1	1	yes	characteristic
754	#390	C₂²×D₄	1	1	yes	characteristic
755	#390	C₂²×D₄	1	1	yes	characteristic
756	#390	C₂²×D₄	1	1	yes	characteristic
757	#390	C₂²×D₄	1	1	yes	characteristic
758	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
759	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
760	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
761	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
762	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
763	#384	C₂×C₂²⋊C₄	1	1	yes	characteristic
764	#384	C₂²×D₄	1	1	yes	characteristic
765	#384	C₂²×D₄	1	1	yes	characteristic
766	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
767	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
768	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
769	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
770	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
771	#382	C₂×C₂²⋊C₄	1	1	yes	characteristic
772	#382	C₂×C₂²⋊C₄	1	2	yes	—
773	#382	C₂×C₂²⋊C₄	1	2	yes	—
774	#382	C₂×C₂²⋊C₄	1	4	yes	—
775	#382	C₂²×D₄	1	1	yes	characteristic
776	#382	C₂²×D₄	1	1	yes	characteristic
777	#380	C₂×C₂²⋊C₄	1	4	yes	—
778	#380	C₂×C₂²⋊C₄	1	2	yes	—
779	#380	C₂×C₂²⋊C₄	1	2	yes	—
780	C₄×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
781	C₄×C₄⋊C₄	C₂³×C₄	1	2	yes	—
782	C₄×C₄⋊C₄	C₂³×C₄	1	2	yes	—
783	C₂×#95	C₂×C₂²⋊C₄	1	4	yes	—
784	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
785	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
786	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
787	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
788	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
789	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
790	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
791	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
792	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
793	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
794	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
795	C₄³	C₂×C₂²⋊C₄	1	1	yes	characteristic
796	C₄³	C₂³×C₄	1	1	yes	characteristic
797	C₄³	C₂³×C₄	1	1	yes	characteristic
798	C₄³	C₂³×C₄	1	1	yes	characteristic
799	C₄³	C₂³×C₄	1	1	yes	characteristic
800	C₂⁵	#379	1	1	yes	characteristic
801	C₂⁵	C₂×#120	1	2	yes	—
802	C₂²×Q₈	#379	1	2	yes	—
803	C₂²×Q₈	#418	1	4	yes	—
804	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
805	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
806	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
807	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
808	C₂²×D₄	#379	1	2	yes	—
809	C₂²×D₄	#379	1	2	yes	—
810	C₂²×D₄	#418	1	4	yes	—
811	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
812	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
813	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
814	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
815	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
816	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
817	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
818	C₂²×D₄	C₂×#120	1	2	yes	—
819	C₂²×D₄	C₂×#120	1	2	yes	—
820	C₂²×D₄	C₂×#120	1	2	yes	—
821	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
822	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
823	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
824	C₂³×C₄	#379	1	2	yes	—
825	C₂³×C₄	#379	1	1	yes	characteristic
826	C₂³×C₄	#379	1	1	yes	characteristic
827	C₂³×C₄	#379	1	2	yes	—
828	C₂³×C₄	#379	1	2	yes	—
829	C₂³×C₄	#379	1	1	yes	characteristic
830	C₂³×C₄	#379	1	1	yes	characteristic
831	C₂³×C₄	#379	1	2	yes	—
832	C₂³×C₄	#379	1	1	yes	characteristic
833	C₂³×C₄	#379	1	1	yes	characteristic
834	C₂³×C₄	#379	1	2	yes	—
835	C₂³×C₄	#379	1	1	yes	characteristic
836	C₂³×C₄	#379	1	2	yes	—
837	C₂³×C₄	#379	1	1	yes	characteristic
838	C₂³×C₄	#379	1	1	yes	characteristic
839	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
840	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
841	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
842	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
843	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
844	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
845	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
846	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
847	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
848	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
849	C₂³×C₄	C₂×#120	1	2	yes	—
850	C₂³×C₄	C₂×#120	1	2	yes	—
851	C₂³×C₄	C₂×#120	1	2	yes	—
852	C₂³×C₄	C₂×#120	1	2	yes	—
853	C₂³×C₄	C₂×#120	1	2	yes	—
854	C₂³×C₄	C₂×#120	1	2	yes	—
855	C₂³×C₄	C₂×#120	1	2	yes	—
856	C₂³×C₄	C₂³×D₄	1	2	yes	—
857	C₄⋊Q₈	C₂×#99	1	2	yes	—
858	C₄⋊Q₈	C₂×#99	1	2	yes	—
859	C₄⋊Q₈	C₂×#99	1	2	yes	—
860	C₄⋊Q₈	C₂×#99	1	2	yes	—
861	#127	C₂×#99	1	2	yes	—
862	#127	C₂×#99	1	2	yes	—
863	#127	C₂×#99	1	2	yes	—
864	#127	C₂×#99	1	2	yes	—
865	#127	#418	1	4	yes	—
866	#127	#418	1	4	yes	—
867	#127	C₂×AGL(1,ℤ/8)	1	4	yes	—
868	#127	C₂×AGL(1,ℤ/8)	1	4	yes	—
869	#124	#418	1	4	yes	—
870	#124	#418	1	4	yes	—
871	#124	C₂×AGL(1,ℤ/8)	1	4	yes	—
872	#124	C₂×AGL(1,ℤ/8)	1	4	yes	—
873	#121	C₂×#99	1	4	yes	—
874	#121	C₂×#99	1	4	yes	—
875	#121	C₂×#99	1	4	yes	—
876	#121	C₂×#99	1	4	yes	—
877	C₄×D₄	C₂×#99	1	4	yes	—
878	C₄×D₄	C₂×#99	1	4	yes	—
879	C₄×D₄	C₂×#99	1	4	yes	—
880	C₄×D₄	C₂×#99	1	4	yes	—
881	C₂×C₄⋊C₄	#379	1	2	yes	—
882	C₂×C₄⋊C₄	#379	1	2	yes	—
883	C₂×C₄⋊C₄	#379	1	2	yes	—
884	C₂×C₄⋊C₄	#379	1	2	yes	—
885	C₂×C₄⋊C₄	#379	1	2	yes	—
886	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
887	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
888	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
889	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
894	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
897	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
898	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
900	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
901	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
902	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
903	C₂×C₂²⋊C₄	#379	1	2	yes	—
904	C₂×C₂²⋊C₄	#379	1	2	yes	—
905	C₂×C₂²⋊C₄	#379	1	2	yes	—
906	C₂×C₂²⋊C₄	#379	1	2	yes	—
907	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
908	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
909	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
910	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
911	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
912	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
913	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
914	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
915	C₂×C₄²	#379	1	1	yes	characteristic
916	C₂×C₄²	#379	1	1	yes	characteristic
917	C₂×C₄²	#379	1	2	yes	—
918	C₂×C₄²	#379	1	2	yes	—
919	C₂×C₄²	#379	1	1	yes	characteristic
920	C₂×C₄²	#379	1	1	yes	characteristic
921	C₂×C₄²	#379	1	2	yes	—
922	C₂×C₄²	#379	1	2	yes	—
923	C₂×C₄²	#379	1	2	yes	—
924	C₂×C₄²	#379	1	2	yes	—
925	C₂×C₄²	#379	1	1	yes	characteristic
926	C₂×C₄²	#379	1	1	yes	characteristic
927	C₂×C₄²	C₂×#99	1	1	yes	characteristic
928	C₂×C₄²	C₂×#99	1	1	yes	characteristic
929	C₂×C₄²	C₂×#99	1	1	yes	characteristic
930	C₂×C₄²	C₂×#99	1	1	yes	characteristic
931	C₂×C₄²	C₂×#99	1	1	yes	characteristic
932	C₂×C₄²	C₂×#99	1	1	yes	characteristic
933	C₂×C₄²	C₂×#99	1	1	yes	characteristic
934	C₂×C₄²	C₂×#99	1	1	yes	characteristic
935	C₂×C₄²	#418	1	4	yes	—
936	C₂×C₄²	#418	1	4	yes	—
937	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
938	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
939	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
940	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
941	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
942	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
943	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
944	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
945	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
946	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
947	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
948	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
949	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
950	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
951	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
952	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
953	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
954	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
955	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
956	C₂×C₄²	C₂×#120	1	2	yes	—
957	C₂×C₄²	C₂×#120	1	2	yes	—
958	C₂×C₄²	C₂×#120	1	2	yes	—
959	C₂×C₄²	C₂×#120	1	2	yes	—
960	C₂×C₄²	C₂⁴×C₄	1	1	yes	characteristic
961	#95	C₂²×C₂²⋊C₄	1	4	yes	—
962	#95	C₂²×C₂²⋊C₄	1	4	yes	—
963	C₂⁴	#1795	1	4	yes	—
964	C₂⁴	C₂×#379	1	2	yes	—
965	C₂⁴	C₂×#379	1	1	yes	characteristic
966	C₂⁴	C₂×#379	1	1	yes	characteristic
967	C₂⁴	C₂×#379	1	1	yes	characteristic
968	C₂⁴	#3003	1	8	yes	—
969	C₂⁴	C₂²×#120	1	2	yes	—
970	C₂×Q₈	C₂×#418	1	2	yes	—
971	C₂×Q₈	C₂×#418	1	2	yes	—
972	C₂×D₄	C₂²×#99	1	4	yes	—
973	C₂×D₄	C₂²×#99	1	4	yes	—
974	C₂×D₄	C₂×#418	1	2	yes	—
975	C₂×D₄	C₂×#418	1	2	yes	—
976	C₂×D₄	C₂×#418	1	2	yes	—
977	C₂×D₄	C₂×#418	1	2	yes	—
978	C₂×D₄	#3003	1	8	yes	—
979	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	2	yes	—
980	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	2	yes	—
981	C₂²×C₄	#1781	1	1	yes	characteristic
982	C₂²×C₄	#1781	1	1	yes	characteristic
983	C₂²×C₄	#1781	1	1	yes	characteristic
984	C₂²×C₄	#1781	1	1	yes	characteristic
985	C₂²×C₄	#1781	1	1	yes	characteristic
986	C₂²×C₄	#1781	1	1	yes	characteristic
987	C₂²×C₄	#1781	1	1	yes	characteristic
988	C₂²×C₄	#1781	1	1	yes	characteristic
989	C₂²×C₄	C₂×#379	1	2	yes	—
990	C₂²×C₄	C₂×#379	1	2	yes	—
991	C₂²×C₄	C₂×#379	1	1	yes	characteristic
992	C₂²×C₄	C₂×#379	1	1	yes	characteristic
993	C₂²×C₄	C₂×#379	1	1	yes	characteristic
994	C₂²×C₄	C₂×#379	1	1	yes	characteristic
995	C₂²×C₄	C₂×#379	1	2	yes	—
996	C₂²×C₄	C₂×#379	1	2	yes	—
997	C₂²×C₄	C₂×#379	1	2	yes	—
998	C₂²×C₄	C₂×#379	1	1	yes	characteristic
999	C₂²×C₄	C₂×#379	1	1	yes	characteristic
1000	C₂²×C₄	C₂×#379	1	1	yes	characteristic
1001	C₂²×C₄	C₂×#379	1	1	yes	characteristic
1002	C₂²×C₄	C₂×#379	1	1	yes	characteristic
1003	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
1004	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
1005	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
1006	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
1007	C₂²×C₄	C₂×#418	1	2	yes	—
1008	C₂²×C₄	C₂×#418	1	2	yes	—
1009	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
1010	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
1011	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
1012	C₂²×C₄	C₂²×#120	1	2	yes	—
1013	C₄⋊C₄	C₂²×#99	1	4	yes	—
1014	C₄⋊C₄	C₂²×#99	1	4	yes	—
1015	C₄²	#1781	1	1	yes	characteristic
1016	C₄²	#1781	1	1	yes	characteristic
1017	C₄²	#1781	1	1	yes	characteristic
1018	C₄²	#1781	1	1	yes	characteristic
1019	C₄²	#1781	1	1	yes	characteristic
1020	C₄²	#1781	1	1	yes	characteristic
1021	C₄²	#1781	1	1	yes	characteristic
1022	C₄²	#1781	1	1	yes	characteristic
1023	C₄²	C₂²×#99	1	1	yes	characteristic
1024	C₄²	C₂²×#99	1	1	yes	characteristic
1025	C₄²	C₂²×#99	1	1	yes	characteristic
1026	C₄²	C₂²×#99	1	1	yes	characteristic
1027	C₄²	C₂²×#99	1	1	yes	characteristic
1028	C₄²	C₂²×#99	1	1	yes	characteristic
1029	C₄²	C₂²×#99	1	1	yes	characteristic
1030	C₄²	C₂²×#99	1	1	yes	characteristic
1031	C₄²	C₂×#418	1	2	yes	—
1032	C₄²	C₂×#418	1	2	yes	—
1033	C₄²	C₂×#418	1	2	yes	—
1034	C₄²	C₂×#418	1	2	yes	—
1035	C₂³	C₂×#1781	1	1	yes	characteristic
1036	C₂³	C₂×#1781	1	1	yes	characteristic
1037	C₂³	#20598	1	4	yes	—
1038	C₂³	#20598	1	2	yes	—
1039	C₂³	C₂×#1795	1	2	yes	—
1040	C₂³	C₂×#1795	1	2	yes	—
1041	C₂³	C₂×#1795	1	2	yes	—
1042	C₂³	C₂²×#379	1	1	yes	characteristic
1043	C₂³	C₂×#3003	1	4	yes	—
1044	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1045	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1046	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1047	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1048	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1049	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1050	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1051	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1052	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1053	C₂×C₄	C₂×#1781	1	1	yes	characteristic
1054	C₂×C₄	#20598	1	2	yes	—
1055	C₂×C₄	C₂³×#99	1	1	yes	characteristic
1056	C₂×C₄	C₂³×#99	1	1	yes	characteristic
1057	C₂×C₄	C₂²×#418	1	1	yes	characteristic
1058	C₂×C₄	C₂²×#418	1	1	yes	characteristic
1059	C₂²	#185643	1	2	yes	—
1060	C₂²	#185643	1	2	yes	—
1061	C₂²	C₂²×#1781	1	1	yes	characteristic
1062	C₂²	C₂×#20598	1	1	yes	characteristic
1063	C₂²	C₂²×#1795	1	1	yes	characteristic
1064	C₄	#493419	1	2	yes	—
1065	C₄	#7622466	1	2	yes	—
1066	C₂	C₂×#185643	1	1	yes	characteristic
1067	C₂	#72302959	1	1	yes	characteristic
1068	C₂	C₂×#493419	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1781
commutator	C₂×C₄²	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	#72311806	C₂
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#62812 ◁ 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. #72313793	C₂	semidirect
2. C₂×#480392	C₂	semidirect
3. C₂×#493957	C₂	semidirect
4. #72313544	C₂	semidirect
5. #72313526	C₂	semidirect
6. #72313498	C₂	semidirect
7. #72313469	C₂	semidirect
8. #72313412	C₂	semidirect
10. #72306056	C₂	semidirect
11. #72285068	C₂	semidirect
12. #72282369	C₂	semidirect
13. #72281788	C₂	semidirect
14. C₂×#62812	C₄	semidirect
16. #7672761	C₄	semidirect
18. #7672751	C₄	semidirect
20. #7672684	C₄	semidirect
21. #7672684	C₄	semidirect
24. #7672442	C₄	semidirect
26. #7672197	C₄	semidirect
28. #7636738	C₄	semidirect
30. C₂×#36644	C₄	semidirect
31. D₄×#532	C₄	semidirect
33. #7628665	C₄	semidirect
35. C₂×C₄×#532	C₄	semidirect
37. C₂×#20723	C₂²	semidirect
38. C₂×#17363	C₂²	semidirect
39. #493957	C₂²	semidirect
40. #493957	C₂²	semidirect
41. #493957	C₂²	semidirect
42. #493957	C₂²	semidirect
43. C₂×#12798	C₂²	semidirect
44. C₂×#12797	C₂²	semidirect
45. #482368	C₂²	semidirect
46. #482364	C₂²	semidirect
47. #482363	C₂²	semidirect
48. #482050	C₂²	semidirect
49. #480392	C₂²	semidirect
50. #480392	C₂²	semidirect
51. #480392	C₂²	semidirect
52. #480392	C₂²	semidirect
53. C₂×#11477	C₂²	semidirect
54. C₂×#11475	C₂²	semidirect
55. #185661	C₂²	semidirect
56. #185660	C₂²	semidirect
57. #185645	C₂²	semidirect
58. #185627	C₂²	semidirect
59. #130775	C₂²	semidirect
60. #130774	C₂²	semidirect
61. #130773	C₂²	semidirect
62. #130772	C₂²	semidirect
63. #130771	C₂²	semidirect
64. #130770	C₂²	semidirect
65. #130769	C₂²	semidirect
66. #130768	C₂²	semidirect
68. C₂×#3499	C₂×C₄	semidirect
69. C₂×#3499	C₂×C₄	semidirect
73. C₂×#3498	C₂×C₄	semidirect
74. C₂×#3498	C₂×C₄	semidirect
83. C₂×D₄×#41	C₂×C₄	semidirect
84. C₂×D₄×#41	C₂×C₄	semidirect
95. #39363	C₂×C₄	semidirect
96. #39363	C₂×C₄	semidirect
97. #39363	C₂×C₄	semidirect
98. #39363	C₂×C₄	semidirect
104. #39361	C₂×C₄	semidirect
105. #39361	C₂×C₄	semidirect
108. #39360	C₂×C₄	semidirect
109. #39360	C₂×C₄	semidirect
113. #36644	C₂×C₄	semidirect
114. #36644	C₂×C₄	semidirect
115. C₂×#2868	C₂×C₄	semidirect
116. C₂×#2867	C₂×C₄	semidirect
117. C₂×#2858	C₂×C₄	semidirect
118. C₂×#2858	C₂×C₄	semidirect
119. #36128	C₂×C₄	semidirect
120. #36128	C₂×C₄	semidirect
124. #36125	C₂×C₄	semidirect
125. #36125	C₂×C₄	semidirect
127. D₄×C₄⋊Q₈	C₂×C₄	semidirect
128. D₄×C₄⋊Q₈	C₂×C₄	semidirect
132. D₄×#124	C₂×C₄	semidirect
133. D₄×#124	C₂×C₄	semidirect
137. #35316	C₂×C₄	semidirect
138. #35316	C₂×C₄	semidirect
141. #35272	C₂×C₄	semidirect
142. #35272	C₂×C₄	semidirect
150. #34937	C₂×C₄	semidirect
151. #34937	C₂×C₄	semidirect
161. C₄×#532	C₂×C₄	semidirect
162. C₄×#532	C₂×C₄	semidirect
163. C₄×#532	C₂×C₄	semidirect
164. C₄×#532	C₂×C₄	semidirect
187. C₂×#2293	C₂×C₄	semidirect
190. C₂×C₄²×D₄	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72313793	2
C₂×#480392	2
C₂×#493957	2
#72313544	2
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