Subgroups — #72316803

Order 2048.

At least 6858 conjugacy classes of subgroups; only the 1544 normal subgroups are shown.

The subgroup lattice has 761 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316800	C₂	1	1	yes	maximal, characteristic, complemented
2	#72316799	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316777	C₂	1	1	yes	maximal, characteristic, complemented
4	#72316735	C₂	1	4	yes	maximal, complemented
5	#72316725	C₂	1	4	yes	maximal, complemented
6	#72316690	C₂	1	8	yes	maximal, complemented
7	#72312543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#6385980	C₂	1	1	yes	maximal, characteristic, complemented
9	#72282149	C₂	1	8	yes	maximal, complemented
10	#72279835	C₂	1	1	yes	maximal, characteristic, complemented
11	#72279460	C₂	1	1	yes	maximal, characteristic
12	C₂²×#3498	C₂²	1	1	yes	characteristic
13	C₂×#60803	C₄	1	1	yes	characteristic, complemented
14	C₂²×#3151	C₄	1	1	yes	characteristic, complemented
15	#7628578	C₂²	1	1	yes	characteristic
16	#6516798	C₄	1	4	yes	complemented
17	#6516798	C₂²	1	4	yes	—
18	#6516758	C₄	1	2	yes	complemented
19	#6516758	C₂²	1	2	yes	—
20	#6516757	C₄	1	2	yes	complemented
21	#6516757	C₂²	1	2	yes	—
22	#6449228	C₄	1	4	yes	complemented
23	#6443168	C₂²	1	4	yes	—
24	#6385980	C₂²	1	4	yes	—
25	#6385980	C₂²	1	4	yes	complemented
26	C₂×D₄×#99	C₂²	1	4	yes	complemented
27	#6374304	C₄	1	1	yes	characteristic, complemented
28	#6372442	C₄	1	1	yes	characteristic, complemented
29	#6372358	C₂²	1	1	yes	characteristic
30	#6370937	C₂²	1	1	yes	characteristic
31	C₂×#20723	C₂²	1	1	yes	characteristic
32	C₂×#20723	C₂²	1	1	yes	characteristic
33	#6342561	C₂²	1	1	yes	characteristic
34	#496537	C₂²	1	4	yes	complemented
35	#496398	C₂²	1	2	yes	complemented
36	#496311	C₂²	1	2	yes	complemented
37	#495599	C₂²	1	4	yes	complemented
38	#482642	C₂²	1	4	yes	complemented
39	#482430	C₂²	1	2	yes	complemented
40	#482363	C₂²	1	2	yes	complemented
41	#482253	C₂²	1	4	yes	complemented
42	#185660	C₂²	1	4	yes	—
43	#185643	C₂²	1	4	yes	complemented
44	#185628	C₂²	1	4	yes	complemented
45	#138952	C₂²	1	32	yes	complemented
46	#138892	C₂²	1	32	yes	complemented
47	#127396	C₂²	1	4	yes	complemented
48	#127395	C₂²	1	4	yes	complemented
49	#127377	C₂²	1	4	yes	complemented
50	#127143	C₂²	1	4	yes	complemented
51	#127126	C₂²	1	4	yes	complemented
52	#127110	C₂²	1	4	yes	complemented
53	C₂×#3498	C₂×C₄	1	2	yes	—
54	C₂×#3498	C₂×C₄	1	2	yes	—
55	C₂×#3498	D₄	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	C₂³	1	2	yes	—
60	C₂×#3498	C₂³	1	2	yes	—
61	C₂²×#550	C₂×C₄	1	2	yes	—
62	C₂²×D₄²	D₄	1	2	yes	—
63	C₂²×D₄²	D₄	1	2	yes	—
64	C₂²×D₄²	C₂³	1	2	yes	—
65	C₂²×#532	C₂×C₄	1	1	yes	characteristic
66	C₂²×#532	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂²×#532	D₄	1	1	yes	characteristic
68	C₂²×#532	D₄	1	1	yes	characteristic
69	C₂³×#127	C₂×C₄	1	1	yes	characteristic
70	C₂³×#127	D₄	1	1	yes	characteristic
71	C₂³×#127	D₄	1	1	yes	characteristic
72	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
73	C₂×#3214	C₂×C₄	1	4	yes	complemented
74	C₂×#3206	C₂×C₄	1	2	yes	complemented
75	C₂×#3205	C₂×C₄	1	2	yes	complemented
76	C₂×#3151	C₂×C₄	1	4	yes	complemented
77	C₂×#3151	C₂×C₄	1	4	yes	complemented
78	C₂²×#493	C₂×C₄	1	2	yes	complemented
79	C₂²×#492	C₂×C₄	1	2	yes	complemented
80	C₂×#3036	C₂×C₄	1	4	yes	complemented
81	C₂×#2920	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂²×C₄×M₁₆	C₂×C₄	1	1	yes	characteristic, complemented
83	#35279	C₂×C₄	1	1	yes	characteristic, complemented
84	#35279	C₂³	1	1	yes	characteristic
85	#35272	C₂×C₄	1	1	yes	characteristic, complemented
86	#35272	C₂³	1	1	yes	characteristic
87	#35190	C₂×C₄	1	2	yes	complemented
88	#35190	C₂³	1	2	yes	—
89	#34955	C₂×C₄	1	2	yes	complemented
90	#34936	C₂³	1	2	yes	—
91	#34012	C₂×C₄	1	1	yes	characteristic, complemented
92	#25757	C₂×C₄	1	8	yes	complemented
93	#25757	C₂³	1	8	yes	—
94	#25753	C₂×C₄	1	8	yes	complemented
95	#25753	C₂³	1	8	yes	—
96	#25631	C₂×C₄	1	8	yes	complemented
97	#25631	C₂×C₄	1	8	yes	complemented
98	#25627	C₂×C₄	1	8	yes	complemented
99	#25627	C₂×C₄	1	8	yes	complemented
100	D₄×#99	C₂³	1	16	yes	—
101	#21810	C₂×C₄	1	4	yes	complemented
102	#21803	C₂×C₄	1	2	yes	complemented
103	#21803	C₂×C₄	1	2	yes	complemented
104	#21405	C₂×C₄	1	4	yes	complemented
105	#21401	C₂×C₄	1	2	yes	complemented
106	#21401	C₂×C₄	1	2	yes	complemented
107	#21380	C₂×C₄	1	2	yes	complemented
108	#21380	C₂³	1	2	yes	—
109	#21373	C₂×C₄	1	2	yes	complemented
110	#21373	C₂³	1	2	yes	—
111	#21303	C₂×C₄	1	2	yes	complemented
112	#21260	C₂×C₄	1	4	yes	complemented
113	#21190	C₂³	1	2	yes	—
114	#20723	D₄	1	2	yes	—
115	#20723	D₄	1	2	yes	—
116	#20723	D₄	1	2	yes	—
117	#20723	D₄	1	2	yes	—
118	#20723	C₂³	1	2	yes	—
119	#20723	C₂³	1	2	yes	—
120	#20723	C₂³	1	2	yes	—
121	#20723	C₂³	1	2	yes	—
122	#20723	C₂³	1	2	yes	—
123	#20722	C₂³	1	2	yes	—
124	C₂×#1820	D₄	1	2	yes	—
125	#20632	C₂³	1	2	yes	—
126	C₂×#1799	D₄	1	2	yes	—
127	C₂×#1799	C₂³	1	2	yes	—
128	C₂×#1782	D₄	1	2	yes	—
129	C₄×#418	C₂×C₄	1	4	yes	complemented
130	C₂×C₄×#99	D₄	1	2	yes	—
131	C₂×C₄×#99	C₂³	1	2	yes	—
132	#17363	C₂³	1	2	yes	—
133	#17362	C₂³	1	2	yes	—
134	#17349	C₂³	1	2	yes	—
135	#13298	C₂³	1	8	yes	complemented
136	#13223	C₂³	1	8	yes	complemented
137	#11901	C₂³	1	8	yes	complemented
138	#11877	C₂³	1	8	yes	complemented
139	#8375	C₂³	1	16	yes	—
140	#7237	C₂³	1	16	yes	complemented
141	#7205	C₂³	1	16	yes	complemented
142	C₂³×#41	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
144	C₂⁴×D₄	C₂×D₄	1	2	yes	—
145	C₂⁴×D₄	C₂×D₄	1	2	yes	—
146	C₂×#550	C₂²⋊C₄	1	4	yes	—
147	C₂×#550	C₂²⋊C₄	1	4	yes	—
148	C₂×#550	C₂²×C₄	1	4	yes	—
149	C₂×#550	C₂²×C₄	1	4	yes	—
150	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
151	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
152	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
153	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
154	C₂×D₄²	C₂²×C₄	1	4	yes	—
155	C₂×D₄²	C₂×D₄	1	4	yes	—
156	C₂×D₄²	C₂×D₄	1	4	yes	—
157	C₂×D₄²	C₂×D₄	1	4	yes	—
158	C₂×D₄²	C₂×D₄	1	4	yes	—
159	C₂×D₄²	C₂×D₄	1	4	yes	—
160	C₂×D₄²	C₂×D₄	1	4	yes	—
161	C₂×D₄²	C₂⁴	1	4	yes	—
162	C₂×#532	C₂²⋊C₄	1	2	yes	—
163	C₂×#532	C₂²⋊C₄	1	2	yes	—
164	C₂×#532	C₂²⋊C₄	1	2	yes	—
165	C₂×#532	C₂²⋊C₄	1	2	yes	—
166	C₂×#532	C₂²⋊C₄	1	2	yes	—
167	C₂×#532	C₂²⋊C₄	1	2	yes	—
168	C₂×#532	C₂²×C₄	1	2	yes	—
169	C₂×#532	C₂²×C₄	1	2	yes	—
170	C₂×#532	C₂²×C₄	1	2	yes	—
171	C₂×#532	C₂²×C₄	1	2	yes	complemented
172	C₂×#532	C₂×D₄	1	2	yes	—
173	C₂×#532	C₂×D₄	1	2	yes	—
174	C₂×#532	C₂×D₄	1	2	yes	—
175	C₂×#532	C₂×D₄	1	2	yes	—
176	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
178	C₂²×#127	C₂²⋊C₄	1	2	yes	—
179	C₂²×#127	C₂²⋊C₄	1	2	yes	—
180	C₂²×#127	C₂²⋊C₄	1	2	yes	—
181	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×#127	C₂²⋊C₄	1	2	yes	—
183	C₂²×#127	C₂²⋊C₄	1	2	yes	—
184	C₂²×#127	C₂²⋊C₄	1	2	yes	—
185	C₂²×#127	C₂²⋊C₄	1	2	yes	—
186	C₂²×#127	C₂²⋊C₄	1	2	yes	—
187	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×#127	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, complemented
193	C₂²×#127	C₂×D₄	1	2	yes	—
194	C₂²×#127	C₂×D₄	1	2	yes	—
195	C₂²×#127	C₂×D₄	1	2	yes	—
196	C₂²×#127	C₂×D₄	1	2	yes	—
197	C₂²×#121	C₂²⋊C₄	1	2	yes	—
198	C₂²×#121	C₂×D₄	1	2	yes	—
199	C₂²×#121	C₂×D₄	1	2	yes	—
200	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
209	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
210	C₂×C₄×#41	#41	1	1	yes	characteristic
211	C₂×C₄×#41	#41	1	1	yes	characteristic
212	C₂×C₄×#41	#41	1	1	yes	characteristic
213	C₂×C₄×#41	#41	1	1	yes	characteristic
214	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
218	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
219	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
220	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×D₄	#41	1	1	yes	characteristic
226	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
227	C₂²×#117	C₂×D₄	1	1	yes	characteristic
228	C₂²×#117	#41	1	1	yes	characteristic
229	C₂²×#117	#41	1	1	yes	characteristic
230	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
231	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
233	C₂×#493	C₂²×C₄	1	8	yes	complemented
234	C₂×#492	C₂²×C₄	1	8	yes	complemented
235	C₂×#461	C₂²×C₄	1	8	yes	complemented
236	C₂×#459	C₂²×C₄	1	8	yes	complemented
237	C₂×#432	C₂²×C₄	1	2	yes	complemented
238	C₂×#431	C₂²×C₄	1	2	yes	complemented
239	C₂×#423	C₂²×C₄	1	2	yes	—
240	C₂²×#99	C₂×D₄	1	4	yes	—
241	C₂×C₄×M₁₆	C₂²×C₄	1	2	yes	—
242	C₂×C₄×M₁₆	C₂²×C₄	1	2	yes	complemented
243	C₂²×C₄×C₈	C₂²×C₄	1	2	yes	complemented
244	#2568	C₂²×C₄	1	2	yes	complemented
245	#2568	C₂²×C₄	1	2	yes	complemented
246	#2548	C₂²×C₄	1	2	yes	complemented
247	#2548	C₂²×C₄	1	2	yes	complemented
248	#2542	C₂²×C₄	1	2	yes	—
249	#2542	C₂⁴	1	2	yes	—
250	#2541	C₂²×C₄	1	2	yes	—
251	#2541	C₂⁴	1	2	yes	—
252	#2285	C₂²×C₄	1	1	yes	characteristic, complemented
253	#2285	C₂²×C₄	1	1	yes	characteristic, complemented
254	#2283	C₂²×C₄	1	2	yes	complemented
255	C₄×#117	C₂²×C₄	1	2	yes	—
256	#1984	C₂²×C₄	1	4	yes	complemented
257	#1984	C₂²×C₄	1	4	yes	complemented
258	#1982	C₂²×C₄	1	8	yes	complemented
259	#1982	C₂²×C₄	1	8	yes	complemented
260	#1954	C₂²×C₄	1	4	yes	—
261	#1954	C₂⁴	1	4	yes	—
262	#1820	C₂×D₄	1	4	yes	—
263	#1820	C₂×D₄	1	4	yes	—
264	#1799	C₂×D₄	1	4	yes	—
265	#1799	C₂×D₄	1	4	yes	—
266	#1799	C₂×D₄	1	4	yes	—
267	#1799	C₂⁴	1	4	yes	—
268	#1799	C₂⁴	1	4	yes	—
269	#1782	C₂×D₄	1	4	yes	—
270	#1782	C₂×D₄	1	4	yes	—
271	C₄×#102	C₂²×C₄	1	8	yes	complemented
272	C₄×#102	C₂²×C₄	1	8	yes	complemented
273	C₄×#99	C₂×D₄	1	4	yes	—
274	C₄×#99	C₂×D₄	1	4	yes	—
275	C₄×#99	C₂×D₄	1	4	yes	—
276	C₄×#99	C₂⁴	1	4	yes	—
277	C₂×#342	C₂×D₄	1	4	yes	—
278	#1459	C₂⁴	1	4	yes	—
279	C₂²×#41	C₄×D₄	1	1	yes	characteristic
280	C₂²×#41	C₄×D₄	1	1	yes	characteristic
281	C₂²×#41	#120	1	1	yes	characteristic
282	C₂²×#41	#120	1	1	yes	characteristic
283	C₂²×#41	#121	1	1	yes	characteristic
284	C₂²×#41	#121	1	1	yes	characteristic
285	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
286	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
287	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic
288	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
290	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
293	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
294	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
295	C₂³×D₄	#120	1	1	yes	characteristic
296	C₂³×D₄	#121	1	1	yes	characteristic
297	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂³×D₄	C₂²×D₄	1	4	yes	—
299	C₂³×D₄	C₂²×D₄	1	4	yes	—
300	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
302	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
303	C₂⁴×C₄	#120	1	1	yes	characteristic
304	C₂⁴×C₄	#120	1	1	yes	characteristic
305	C₂⁴×C₄	#121	1	1	yes	characteristic
306	C₂⁴×C₄	#121	1	1	yes	characteristic
307	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
308	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂×C₄⋊Q₈	C₂³×C₄	1	2	yes	—
312	C₂×#127	#99	1	2	yes	—
313	C₂×#127	#99	1	2	yes	—
314	C₂×#127	#99	1	2	yes	—
315	C₂×#127	#99	1	2	yes	—
316	C₂×#127	#99	1	2	yes	—
317	C₂×#127	#99	1	2	yes	—
318	C₂×#127	#99	1	2	yes	—
319	C₂×#127	#99	1	2	yes	—
320	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
323	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
324	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
325	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
326	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
327	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×#127	C₂³×C₄	1	4	yes	—
332	C₂×#127	C₂³×C₄	1	2	yes	—
333	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
334	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
335	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
336	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
337	C₂×#121	C₂²×D₄	1	4	yes	—
338	C₂×#121	C₂²×D₄	1	4	yes	—
339	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
343	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
344	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
345	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
347	C₂×C₄×Q₈	#121	1	1	yes	characteristic
348	C₂×C₄×Q₈	#121	1	1	yes	characteristic
349	C₂×C₄×Q₈	#123	1	1	yes	characteristic
350	C₂×C₄×Q₈	#123	1	1	yes	characteristic
351	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
352	C₂×C₄×Q₈	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
356	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
357	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
358	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
359	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
360	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
365	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
366	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
367	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
368	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
369	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
370	C₂×C₄×D₄	#120	1	1	yes	characteristic
371	C₂×C₄×D₄	#120	1	1	yes	characteristic
372	C₂×C₄×D₄	#120	1	1	yes	characteristic
373	C₂×C₄×D₄	#120	1	1	yes	characteristic
374	C₂×C₄×D₄	#120	1	1	yes	characteristic
375	C₂×C₄×D₄	#120	1	1	yes	characteristic
376	C₂×C₄×D₄	#121	1	1	yes	characteristic
377	C₂×C₄×D₄	#121	1	1	yes	characteristic
378	C₂×C₄×D₄	#121	1	1	yes	characteristic
379	C₂×C₄×D₄	#121	1	1	yes	characteristic
380	C₂×C₄×D₄	#121	1	1	yes	characteristic
381	C₂×C₄×D₄	#121	1	1	yes	characteristic
382	C₂×C₄×D₄	#121	1	1	yes	characteristic
383	C₂×C₄×D₄	#121	1	1	yes	characteristic
384	C₂×C₄×D₄	#121	1	1	yes	characteristic
385	C₂×C₄×D₄	#121	1	1	yes	characteristic
386	C₂×C₄×D₄	#123	1	1	yes	characteristic
387	C₂×C₄×D₄	#123	1	1	yes	characteristic
388	C₂×C₄×D₄	#123	1	1	yes	characteristic
389	C₂×C₄×D₄	#123	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂³×C₄	1	4	yes	—
391	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
409	C₂×#117	C₄×D₄	1	1	yes	characteristic
410	C₂×#117	C₄×D₄	1	1	yes	characteristic
411	C₂×#117	C₄×D₄	1	1	yes	characteristic
412	C₂×#117	C₄×D₄	1	1	yes	characteristic
413	C₂×#117	C₄×D₄	1	1	yes	characteristic
414	C₂×#117	C₄×D₄	1	1	yes	characteristic
415	C₂×#117	#120	1	1	yes	characteristic
416	C₂×#117	#120	1	1	yes	characteristic
417	C₂×#117	#121	1	1	yes	characteristic
418	C₂×#117	#121	1	1	yes	characteristic
419	C₂×#117	#121	1	1	yes	characteristic
420	C₂×#117	#121	1	1	yes	characteristic
421	C₂×#117	#121	1	1	yes	characteristic
422	C₂×#117	#121	1	1	yes	characteristic
423	C₂×#117	#123	1	1	yes	characteristic
424	C₂×#117	#123	1	1	yes	characteristic
425	C₂×#117	#123	1	1	yes	characteristic
426	C₂×#117	#123	1	1	yes	characteristic
427	C₂×#117	C₂²×D₄	1	1	yes	characteristic
428	C₂×#117	C₂²×D₄	1	1	yes	characteristic
429	C₂×#117	C₂×#41	1	1	yes	characteristic
430	C₂×#117	C₂×#41	1	1	yes	characteristic
431	C₂×#117	C₂×#41	1	1	yes	characteristic
432	C₂×#117	C₂×#41	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
434	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	#123	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	#123	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
445	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
446	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
449	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
456	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
457	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
458	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
459	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
460	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
461	C₂²×C₄²	#120	1	1	yes	characteristic
462	C₂²×C₄²	#120	1	1	yes	characteristic
463	C₂²×C₄²	#121	1	1	yes	characteristic
464	C₂²×C₄²	#121	1	1	yes	characteristic
465	C₂²×C₄²	#121	1	1	yes	characteristic
466	C₂²×C₄²	#121	1	1	yes	characteristic
467	C₂²×C₄²	#121	1	1	yes	characteristic
468	C₂²×C₄²	#121	1	1	yes	characteristic
469	C₂²×C₄²	#123	1	1	yes	characteristic
470	C₂²×C₄²	#123	1	1	yes	characteristic
471	C₂²×C₄²	#123	1	1	yes	characteristic
472	C₂²×C₄²	#123	1	1	yes	characteristic
473	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
474	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
475	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
477	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
478	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
479	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄⋊C₈	C₂³×C₄	1	4	yes	—
481	C₂×#99	C₂²×D₄	1	8	yes	—
482	C₂×C₄×C₈	C₂³×C₄	1	4	yes	—
483	C₄×C₄⋊C₄	C₂³×C₄	1	2	yes	—
484	C₄×C₄⋊C₄	C₂³×C₄	1	2	yes	—
485	#342	C₂²×D₄	1	8	yes	—
486	C₂⁵	#386	1	1	yes	characteristic
487	C₂⁵	C₂×#120	1	1	yes	characteristic
488	C₂⁵	C₂×#121	1	1	yes	characteristic
489	C₂²×Q₈	#386	1	1	yes	characteristic
490	C₂²×Q₈	#386	1	1	yes	characteristic
491	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
492	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
493	C₂²×D₄	#386	1	1	yes	characteristic
494	C₂²×D₄	#386	1	1	yes	characteristic
495	C₂²×D₄	#386	1	1	yes	characteristic
496	C₂²×D₄	#386	1	1	yes	characteristic
497	C₂²×D₄	C₂×#99	1	4	yes	—
498	C₂²×D₄	C₂×#99	1	4	yes	—
499	C₂²×D₄	C₂×#99	1	4	yes	—
500	C₂²×D₄	C₂×#99	1	4	yes	—
501	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
502	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
503	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
504	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
505	C₂²×D₄	C₂×#120	1	1	yes	characteristic
506	C₂²×D₄	C₂×#120	1	1	yes	characteristic
507	C₂²×D₄	C₂×#120	1	1	yes	characteristic
508	C₂²×D₄	C₂×#121	1	1	yes	characteristic
509	C₂²×D₄	C₂×#121	1	1	yes	characteristic
510	C₂²×D₄	C₂×#121	1	1	yes	characteristic
511	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
512	C₂³×C₄	#386	1	1	yes	characteristic
513	C₂³×C₄	#386	1	1	yes	characteristic
514	C₂³×C₄	#386	1	1	yes	characteristic
515	C₂³×C₄	#386	1	1	yes	characteristic
516	C₂³×C₄	#386	1	1	yes	characteristic
517	C₂³×C₄	#386	1	1	yes	characteristic
518	C₂³×C₄	#386	1	1	yes	characteristic
519	C₂³×C₄	#386	1	1	yes	characteristic
520	C₂³×C₄	#386	1	1	yes	characteristic
521	C₂³×C₄	#386	1	1	yes	characteristic
522	C₂³×C₄	#386	1	1	yes	characteristic
523	C₂³×C₄	#386	1	1	yes	characteristic
524	C₂³×C₄	#386	1	1	yes	characteristic
525	C₂³×C₄	#386	1	1	yes	characteristic
526	C₂³×C₄	#386	1	1	yes	characteristic
527	C₂³×C₄	#386	1	1	yes	characteristic
528	C₂³×C₄	#386	1	1	yes	characteristic
529	C₂³×C₄	#386	1	1	yes	characteristic
530	C₂³×C₄	#386	1	1	yes	characteristic
531	C₂³×C₄	#386	1	1	yes	characteristic
532	C₂³×C₄	#386	1	1	yes	characteristic
533	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
534	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
535	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
536	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
537	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
538	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
539	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
540	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
541	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
542	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
543	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
544	C₂³×C₄	C₂×#120	1	1	yes	characteristic
545	C₂³×C₄	C₂×#120	1	1	yes	characteristic
546	C₂³×C₄	C₂×#120	1	1	yes	characteristic
547	C₂³×C₄	C₂×#120	1	1	yes	characteristic
548	C₂³×C₄	C₂×#120	1	1	yes	characteristic
549	C₂³×C₄	C₂×#121	1	1	yes	characteristic
550	C₂³×C₄	C₂×#121	1	1	yes	characteristic
551	C₂³×C₄	C₂×#121	1	1	yes	characteristic
552	C₂³×C₄	C₂×#121	1	1	yes	characteristic
553	C₂³×C₄	C₂×#121	1	1	yes	characteristic
554	C₂³×C₄	C₂×#121	1	1	yes	characteristic
555	C₂³×C₄	C₂×#121	1	1	yes	characteristic
556	C₂³×C₄	C₂×#123	1	1	yes	characteristic
557	C₂³×C₄	C₂×#123	1	1	yes	characteristic
558	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
559	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
560	#127	C₂×#99	1	4	yes	—
561	#127	C₂×#99	1	4	yes	—
562	#127	C₂×#99	1	4	yes	—
563	#127	C₂×#99	1	4	yes	—
564	#127	C₂×#99	1	4	yes	—
565	#127	C₂×#99	1	4	yes	—
566	#127	C₂×#99	1	4	yes	—
567	#127	C₂×#99	1	4	yes	—
568	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
569	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
570	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
571	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
572	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
573	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
574	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
575	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
576	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
577	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
579	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂²×#41	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂²×#41	1	1	yes	characteristic
617	C₂×C₄²	#386	1	1	yes	characteristic
618	C₂×C₄²	#386	1	1	yes	characteristic
619	C₂×C₄²	#386	1	1	yes	characteristic
620	C₂×C₄²	#386	1	1	yes	characteristic
621	C₂×C₄²	#386	1	1	yes	characteristic
622	C₂×C₄²	#386	1	1	yes	characteristic
623	C₂×C₄²	#386	1	1	yes	characteristic
624	C₂×C₄²	#386	1	1	yes	characteristic
625	C₂×C₄²	#386	1	1	yes	characteristic
626	C₂×C₄²	#386	1	1	yes	characteristic
627	C₂×C₄²	#386	1	1	yes	characteristic
628	C₂×C₄²	#386	1	1	yes	characteristic
629	C₂×C₄²	#386	1	1	yes	characteristic
630	C₂×C₄²	#386	1	1	yes	characteristic
631	C₂×C₄²	#386	1	1	yes	characteristic
632	C₂×C₄²	#386	1	1	yes	characteristic
633	C₂×C₄²	#386	1	1	yes	characteristic
634	C₂×C₄²	#386	1	1	yes	characteristic
635	C₂×C₄²	C₂×#99	1	1	yes	characteristic
636	C₂×C₄²	C₂×#99	1	1	yes	characteristic
637	C₂×C₄²	C₂×#99	1	1	yes	characteristic
638	C₂×C₄²	C₂×#99	1	1	yes	characteristic
639	C₂×C₄²	C₂×#99	1	1	yes	characteristic
640	C₂×C₄²	C₂×#99	1	1	yes	characteristic
641	C₂×C₄²	C₂×#99	1	1	yes	characteristic
642	C₂×C₄²	C₂×#99	1	1	yes	characteristic
643	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
644	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
645	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
646	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
647	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
648	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
649	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
650	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
651	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
652	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
653	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
654	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×#121	1	1	yes	characteristic
657	C₂×C₄²	C₂×#121	1	1	yes	characteristic
658	C₂×C₄²	C₂×#121	1	1	yes	characteristic
659	C₂×C₄²	C₂×#121	1	1	yes	characteristic
660	C₂×C₄²	C₂×#123	1	1	yes	characteristic
661	C₂×C₄²	C₂×#123	1	1	yes	characteristic
662	C₂×C₄²	C₂×#123	1	1	yes	characteristic
663	C₂×C₄²	C₂×#123	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴×C₄	1	1	yes	characteristic
665	C₂⁴	C₂×#386	1	1	yes	characteristic
666	C₂⁴	C₂×#386	1	1	yes	characteristic
667	C₂⁴	C₂×#386	1	1	yes	characteristic
668	C₂⁴	C₂×#386	1	1	yes	characteristic
669	C₂⁴	C₂×#386	1	1	yes	characteristic
670	C₂⁴	C₂²×#120	1	1	yes	characteristic
671	C₂⁴	C₂²×#121	1	1	yes	characteristic
672	C₂×D₄	#1904	1	4	yes	—
673	C₂×D₄	C₂²×#99	1	8	yes	—
674	C₂×D₄	C₂²×#99	1	8	yes	—
675	C₂×D₄	#3585	1	4	yes	—
676	C₂²×C₄	#1898	1	1	yes	characteristic
677	C₂²×C₄	#1898	1	1	yes	characteristic
678	C₂²×C₄	#1898	1	1	yes	characteristic
679	C₂²×C₄	#1898	1	1	yes	characteristic
680	C₂²×C₄	#1898	1	1	yes	characteristic
681	C₂²×C₄	#1898	1	1	yes	characteristic
682	C₂²×C₄	#1898	1	1	yes	characteristic
683	C₂²×C₄	#1898	1	1	yes	characteristic
684	C₂²×C₄	C₂×#386	1	1	yes	characteristic
685	C₂²×C₄	C₂×#386	1	1	yes	characteristic
686	C₂²×C₄	C₂×#386	1	1	yes	characteristic
687	C₂²×C₄	C₂×#386	1	1	yes	characteristic
688	C₂²×C₄	C₂×#386	1	1	yes	characteristic
689	C₂²×C₄	C₂×#386	1	1	yes	characteristic
690	C₂²×C₄	C₂×#386	1	1	yes	characteristic
691	C₂²×C₄	C₂×#386	1	1	yes	characteristic
692	C₂²×C₄	C₂×#386	1	1	yes	characteristic
693	C₂²×C₄	C₂×#386	1	1	yes	characteristic
694	C₂²×C₄	C₂×#386	1	1	yes	characteristic
695	C₂²×C₄	C₂×#386	1	1	yes	characteristic
696	C₂²×C₄	C₂×#386	1	1	yes	characteristic
697	C₂²×C₄	C₂×#386	1	1	yes	characteristic
698	C₂²×C₄	C₂×#386	1	1	yes	characteristic
699	C₂²×C₄	C₂×#386	1	1	yes	characteristic
700	C₂²×C₄	C₂×#386	1	1	yes	characteristic
701	C₂²×C₄	C₂×#386	1	1	yes	characteristic
702	C₂²×C₄	C₂×#386	1	1	yes	characteristic
703	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
704	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
705	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
706	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
707	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
708	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
710	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
711	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
712	C₄²	#1898	1	1	yes	characteristic
713	C₄²	#1898	1	1	yes	characteristic
714	C₄²	#1898	1	1	yes	characteristic
715	C₄²	#1898	1	1	yes	characteristic
716	C₄²	#1898	1	1	yes	characteristic
717	C₄²	#1898	1	1	yes	characteristic
718	C₄²	#1898	1	1	yes	characteristic
719	C₄²	#1898	1	1	yes	characteristic
720	C₄²	C₂²×#99	1	1	yes	characteristic
721	C₄²	C₂²×#99	1	1	yes	characteristic
722	C₄²	C₂²×#99	1	1	yes	characteristic
723	C₄²	C₂²×#99	1	1	yes	characteristic
724	C₄²	C₂²×#99	1	1	yes	characteristic
725	C₄²	C₂²×#99	1	1	yes	characteristic
726	C₄²	C₂²×#99	1	1	yes	characteristic
727	C₄²	C₂²×#99	1	1	yes	characteristic
728	C₂³	C₂×#1898	1	1	yes	characteristic
729	C₂³	C₂×#1898	1	1	yes	characteristic
730	C₂³	C₂×#1904	1	2	yes	—
731	C₂³	C₂×#1904	1	2	yes	—
732	C₂³	C₂²×#386	1	1	yes	characteristic
733	C₂³	#60367	1	2	yes	—
734	C₂³	#60423	1	2	yes	—
735	C₂×C₄	C₂×#1898	1	1	yes	characteristic
736	C₂×C₄	C₂×#1898	1	1	yes	characteristic
737	C₂×C₄	C₂×#1898	1	1	yes	characteristic
738	C₂×C₄	C₂×#1898	1	1	yes	characteristic
739	C₂×C₄	C₂×#1898	1	1	yes	characteristic
740	C₂×C₄	C₂×#1898	1	1	yes	characteristic
741	C₂×C₄	C₂×#1898	1	1	yes	characteristic
742	C₂×C₄	C₂×#1898	1	1	yes	characteristic
743	C₂×C₄	C₂×#1898	1	1	yes	characteristic
744	C₂×C₄	C₂×#1898	1	1	yes	characteristic
745	C₂×C₄	C₂×#1904	1	2	yes	—
746	C₂×C₄	#33359	1	4	yes	—
747	C₂×C₄	C₂³×#99	1	1	yes	characteristic
748	C₂×C₄	C₂³×#99	1	1	yes	characteristic
749	C₂×C₄	#60168	1	2	yes	—
750	C₂²	#494722	1	2	yes	—
751	C₂²	#6371420	1	1	yes	characteristic
752	C₂²	C₂²×#1898	1	1	yes	characteristic
753	C₂²	C₂²×#1904	1	1	yes	characteristic
754	C₄	#494722	1	2	yes	—
755	C₄	#494758	1	2	yes	—
756	C₄	C₂×#33359	1	2	yes	—
757	C₂	#72235984	1	1	yes	characteristic
758	C₂	C₂×#494758	1	1	yes	characteristic
759	C₂	C₂×#494722	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1898
commutator	C₂×C₄²	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	#72279460	C₂
LCS	G ▷ C₂×C₄² ▷ 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. #72316800	C₂	semidirect
2. #72316799	C₂	semidirect
3. #72316777	C₂	semidirect
4. #72316735	C₂	semidirect
5. #72316725	C₂	semidirect
6. #72316690	C₂	semidirect
7. #72312543	C₂	semidirect
8. C₂×#6385980	C₂	semidirect
9. #72282149	C₂	semidirect
10. #72279835	C₂	semidirect
13. C₂×#60803	C₄	semidirect
14. C₂²×#3151	C₄	semidirect
16. #6516798	C₄	semidirect
18. #6516758	C₄	semidirect
20. #6516757	C₄	semidirect
22. #6449228	C₄	semidirect
25. #6385980	C₂²	semidirect
26. C₂×D₄×#99	C₂²	semidirect
27. #6374304	C₄	semidirect
28. #6372442	C₄	semidirect
34. #496537	C₂²	semidirect
35. #496398	C₂²	semidirect
36. #496311	C₂²	semidirect
37. #495599	C₂²	semidirect
38. #482642	C₂²	semidirect
39. #482430	C₂²	semidirect
40. #482363	C₂²	semidirect
41. #482253	C₂²	semidirect
43. #185643	C₂²	semidirect
44. #185628	C₂²	semidirect
45. #138952	C₂²	semidirect
46. #138892	C₂²	semidirect
47. #127396	C₂²	semidirect
48. #127395	C₂²	semidirect
49. #127377	C₂²	semidirect
50. #127143	C₂²	semidirect
51. #127126	C₂²	semidirect
52. #127110	C₂²	semidirect
66. C₂²×#532	C₂×C₄	semidirect
73. C₂×#3214	C₂×C₄	semidirect
74. C₂×#3206	C₂×C₄	semidirect
75. C₂×#3205	C₂×C₄	semidirect
76. C₂×#3151	C₂×C₄	semidirect
77. C₂×#3151	C₂×C₄	semidirect
78. C₂²×#493	C₂×C₄	semidirect
79. C₂²×#492	C₂×C₄	semidirect
80. C₂×#3036	C₂×C₄	semidirect
81. C₂×#2920	C₂×C₄	semidirect
82. C₂²×C₄×M₁₆	C₂×C₄	semidirect
83. #35279	C₂×C₄	semidirect
85. #35272	C₂×C₄	semidirect
87. #35190	C₂×C₄	semidirect
89. #34955	C₂×C₄	semidirect
91. #34012	C₂×C₄	semidirect
92. #25757	C₂×C₄	semidirect
94. #25753	C₂×C₄	semidirect
96. #25631	C₂×C₄	semidirect
97. #25631	C₂×C₄	semidirect
98. #25627	C₂×C₄	semidirect
99. #25627	C₂×C₄	semidirect
101. #21810	C₂×C₄	semidirect
102. #21803	C₂×C₄	semidirect
103. #21803	C₂×C₄	semidirect
104. #21405	C₂×C₄	semidirect
105. #21401	C₂×C₄	semidirect
106. #21401	C₂×C₄	semidirect
107. #21380	C₂×C₄	semidirect
109. #21373	C₂×C₄	semidirect
111. #21303	C₂×C₄	semidirect
112. #21260	C₂×C₄	semidirect
129. C₄×#418	C₂×C₄	semidirect
135. #13298	C₂³	semidirect
136. #13223	C₂³	semidirect
137. #11901	C₂³	semidirect
138. #11877	C₂³	semidirect
140. #7237	C₂³	semidirect
141. #7205	C₂³	semidirect
171. C₂×#532	C₂²×C₄	semidirect
177. C₂²×C₄⋊Q₈	C₂²×C₄	semidirect
192. C₂²×#127	C₂²×C₄	semidirect
233. C₂×#493	C₂²×C₄	semidirect
234. C₂×#492	C₂²×C₄	semidirect
235. C₂×#461	C₂²×C₄	semidirect
236. C₂×#459	C₂²×C₄	semidirect
237. C₂×#432	C₂²×C₄	semidirect
238. C₂×#431	C₂²×C₄	semidirect
242. C₂×C₄×M₁₆	C₂²×C₄	semidirect
243. C₂²×C₄×C₈	C₂²×C₄	semidirect
244. #2568	C₂²×C₄	semidirect
245. #2568	C₂²×C₄	semidirect
246. #2548	C₂²×C₄	semidirect
247. #2548	C₂²×C₄	semidirect
252. #2285	C₂²×C₄	semidirect
253. #2285	C₂²×C₄	semidirect
254. #2283	C₂²×C₄	semidirect
256. #1984	C₂²×C₄	semidirect
257. #1984	C₂²×C₄	semidirect
258. #1982	C₂²×C₄	semidirect
259. #1982	C₂²×C₄	semidirect
271. C₄×#102	C₂²×C₄	semidirect
272. C₄×#102	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72316800	2
#72316799	2
#72316777	2
#72316735	2
#72316725	2
#72316690	2
#72312543	2
C₂×#6385980	2
#72282149	2
#72279835	2
#72279460	2