Subgroups — #72265091

Order 4096.

At least 31133 conjugacy classes of subgroups; only the 1967 normal subgroups are shown.

The subgroup lattice has 1193 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265022	C₂	1	2	yes	maximal, complemented
2	#72265005	C₂	1	2	yes	maximal, complemented
3	#72264993	C₂	1	1	yes	maximal, characteristic, complemented
4	#72264938	C₂	1	1	yes	maximal, characteristic, complemented
5	#72264912	C₂	1	1	yes	maximal, characteristic, complemented
6	#72264872	C₂	1	1	yes	maximal, characteristic, complemented
7	#72264856	C₂	1	2	yes	maximal, complemented
8	#72264838	C₂	1	2	yes	maximal, complemented
9	#72264811	C₂	1	1	yes	maximal, characteristic, complemented
10	#72264789	C₂	1	1	yes	maximal, characteristic, complemented
11	#72264683	C₂	1	2	yes	maximal, complemented
12	#72264676	C₂²	1	2	yes	complemented
13	#72264665	C₂	1	2	yes	maximal, complemented
14	#72264658	C₂²	1	2	yes	complemented
15	#72264656	C₂²	1	2	yes	complemented
16	#72264656	C₂²	1	2	yes	complemented
17	#72264652	C₂²	1	2	yes	—
18	#72264652	C₂²	1	2	yes	—
19	#72264643	C₂	1	1	yes	maximal, characteristic, complemented
20	#72264637	C₂²	1	1	yes	characteristic, complemented
21	#72264628	C₂²	1	2	yes	complemented
22	#72264622	C₂²	1	2	yes	complemented
23	#72264610	C₂	1	1	yes	maximal, characteristic, complemented
24	#72264593	C₂	1	1	yes	maximal, characteristic, complemented
25	#72264585	C₂²	1	1	yes	characteristic, complemented
26	#72264573	C₂²	1	2	yes	complemented
27	#72264573	C₂²	1	2	yes	complemented
28	#72264565	C₂²	1	1	yes	characteristic, complemented
29	#72264565	C₂²	1	1	yes	characteristic, complemented
30	#72264551	C₂	1	1	yes	maximal, characteristic, complemented
31	#72264532	C₂²	1	2	yes	complemented
32	#72264520	C₂²	1	1	yes	characteristic, complemented
33	#72264514	C₂²	1	1	yes	characteristic, complemented
34	#72264498	C₂²	1	2	yes	complemented
35	#72264483	C₂²	1	1	yes	characteristic, complemented
36	#72264461	C₂	1	1	yes	maximal, characteristic, complemented
37	#72264452	C₂²	1	2	yes	complemented
38	#72264452	C₂²	1	2	yes	complemented
39	#72264444	C₂²	1	1	yes	characteristic, complemented
40	#72264433	C₂²	1	1	yes	characteristic, complemented
41	#72264424	C₂²	1	1	yes	characteristic, complemented
42	#72264417	C₂	1	2	yes	maximal, complemented
43	#72264414	C₂²	1	2	yes	complemented
44	#72264410	C₂²	1	2	yes	complemented
45	#72264405	C₂²	1	2	yes	complemented
46	#72264405	C₂²	1	2	yes	complemented
47	#72264402	C₂²	1	2	yes	complemented
48	#72264395	C₂	1	2	yes	maximal, complemented
49	#72264388	C₂²	1	2	yes	complemented
50	#72264384	C₂²	1	1	yes	characteristic, complemented
51	#72264382	C₂²	1	2	yes	complemented
52	#72264382	C₂²	1	2	yes	complemented
53	#72264375	C₂²	1	2	yes	complemented
54	#72264371	C₂²	1	2	yes	complemented
55	#72264371	C₂²	1	2	yes	complemented
56	#72264364	C₂²	1	2	yes	complemented
57	#72264364	C₂²	1	2	yes	complemented
58	#72264358	C₂²	1	2	yes	complemented
59	#72264358	C₂²	1	2	yes	complemented
60	#72264350	C₂²	1	2	yes	complemented
61	#72264346	C₂	1	1	yes	maximal, characteristic, complemented
62	#72264345	C₂²	1	2	yes	complemented
63	#72264345	C₂²	1	2	yes	complemented
64	#72264341	C₂²	1	2	yes	complemented
65	#72264341	C₂²	1	2	yes	complemented
66	#72264341	C₂²	1	2	yes	complemented
67	#72264341	C₂²	1	2	yes	complemented
68	#72264337	C₂²	1	1	yes	characteristic, complemented
69	#72264336	C₂²	1	2	yes	complemented
70	#72264333	C₂²	1	2	yes	—
71	#72264331	C₂²	1	2	yes	complemented
72	#72264331	C₂²	1	2	yes	complemented
73	#72264330	C₂²	1	1	yes	characteristic, complemented
74	#72264327	C₂²	1	1	yes	characteristic, complemented
75	#72264322	C₂	1	1	yes	maximal, characteristic, complemented
76	#72264321	C₂²	1	2	yes	complemented
77	#72264305	C₂²	1	2	yes	—
78	#72264297	C₂²	1	1	yes	characteristic, complemented
79	#72264297	C₂²	1	1	yes	characteristic, complemented
80	#72264292	C₂²	1	2	yes	complemented
81	#72264285	C₂²	1	1	yes	characteristic, complemented
82	#72264273	C₂	1	1	yes	maximal, characteristic, complemented
83	#72264272	C₂²	1	2	yes	—
84	#72264260	C₂²	1	1	yes	characteristic
85	#72264254	C₂²	1	1	yes	characteristic
86	C₂×#6468700	C₂²	1	1	yes	characteristic, complemented
87	#72264239	C₂²	1	1	yes	characteristic, complemented
88	#72264235	C₂²	1	1	yes	characteristic, complemented
89	#72264232	C₂²	1	1	yes	characteristic, complemented
90	#72264227	C₂²	1	2	yes	—
91	#72264227	C₂²	1	1	yes	characteristic
92	#72264221	C₂²	1	1	yes	characteristic, complemented
93	#72264218	C₂²	1	1	yes	characteristic, complemented
94	#72264213	C₂²	1	1	yes	characteristic, complemented
95	#72264209	C₂²	1	1	yes	characteristic, complemented
96	#72264205	C₂²	1	1	yes	characteristic, complemented
97	C₂×#6453737	C₂²	1	1	yes	characteristic, complemented
98	#72264190	C₂²	1	1	yes	characteristic, complemented
99	D₄×#34736	C₂	1	1	yes	maximal, characteristic, complemented
100	C₂³×D₄×#41	C₂²	1	1	yes	characteristic
101	#72264120	C₂²	1	1	yes	characteristic
102	C₄×#34736	C₂²	1	1	yes	characteristic
103	#72264118	C₂²	1	2	yes	—
104	D₄×#2405	C₂²	1	2	yes	—
105	#72264116	C₂²	1	1	yes	characteristic
106	#72264114	C₂²	1	1	yes	characteristic
107	D₄×#2280	C₂²	1	1	yes	characteristic
108	#72264106	C₂²	1	2	yes	complemented
109	#72264101	C₂²	1	2	yes	complemented
110	#72264084	C₂²	1	2	yes	complemented
111	#72264082	C₂²	1	2	yes	—
112	C₂²×C₄×D₄²	C₂²	1	1	yes	characteristic
113	#72237676	C₂²	1	2	yes	—
114	#72237676	C₂²	1	2	yes	—
115	#72237676	C₂²	1	2	yes	—
116	#72237157	C₂²	1	1	yes	characteristic
117	#72237157	C₂²	1	1	yes	characteristic
118	#72237157	C₂²	1	1	yes	characteristic
119	C₂²×#21452	C₂²	1	1	yes	characteristic
120	#72235738	C₂²	1	2	yes	—
121	#72235738	C₂²	1	1	yes	characteristic
122	D₄×#2403	C₂²	1	2	yes	—
123	C₂³×#550	D₄	1	1	yes	characteristic, complemented
124	C₂³×#547	D₄	1	1	yes	characteristic, complemented
125	C₂³×#547	C₂³	1	2	yes	—
126	C₂³×D₄×Q₈	D₄	1	1	yes	characteristic, complemented
127	C₂³×D₄²	D₄	1	1	yes	characteristic, complemented
128	C₂³×D₄²	C₂³	1	1	yes	characteristic
129	C₂³×D₄²	C₂³	1	2	yes	—
130	C₂³×#532	D₄	1	2	yes	complemented
131	C₂³×#532	C₂³	1	1	yes	characteristic
132	C₂³×C₄×#41	C₂³	1	1	yes	characteristic
133	C₂⁴×C₄×D₄	D₄	1	1	yes	characteristic, complemented
134	C₂⁴×C₄×D₄	D₄	1	2	yes	complemented
135	C₂⁴×C₄×D₄	C₂³	1	1	yes	characteristic
136	C₂³×#447	C₂³	1	1	yes	characteristic
137	C₂³×#442	D₄	1	2	yes	complemented
138	C₂×#34736	D₄	1	1	yes	characteristic
139	C₂²×#2366	D₄	1	1	yes	characteristic, complemented
140	C₂²×#2361	D₄	1	1	yes	characteristic, complemented
141	C₂²×#2361	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₄⋊C₄	D₄	1	1	yes	characteristic, complemented
143	C₂²×D₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
145	C₂²×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
146	C₂²×C₄×#127	D₄	1	1	yes	characteristic, complemented
147	C₂²×C₄×#121	D₄	1	1	yes	characteristic, complemented
148	C₂²×C₄×#121	C₂³	1	1	yes	characteristic
149	C₂²×C₄×#121	C₂³	1	1	yes	characteristic
150	C₂²×C₄²×D₄	D₄	1	1	yes	characteristic, complemented
151	C₂²×C₄²×D₄	C₂³	1	1	yes	characteristic
152	C₂×#27601	C₂³	1	1	yes	characteristic
153	C₂×#24005	C₂³	1	2	yes	—
154	C₂×#24005	C₂³	1	1	yes	characteristic
155	C₂×#24002	C₂³	1	1	yes	characteristic
156	C₂×#23918	C₂³	1	2	yes	—
157	C₂×#23918	C₂³	1	1	yes	characteristic
158	C₂²×#1879	D₄	1	2	yes	complemented
159	C₂²×#1874	C₂³	1	1	yes	characteristic
160	C₂²×#1864	D₄	1	2	yes	complemented
161	C₂²×#1853	C₂³	1	1	yes	characteristic
162	C₂×#20739	D₄	1	4	yes	complemented
163	C₂×#20715	C₂³	1	1	yes	characteristic
164	C₂×#20715	C₂³	1	1	yes	characteristic
165	C₂×#20715	C₂³	1	1	yes	characteristic
166	C₂²×#1786	C₂³	1	1	yes	characteristic
167	C₂²×#1762	D₄	1	2	yes	complemented
168	C₂²×#1749	C₂³	1	1	yes	characteristic
169	#759738	D₄	1	4	yes	complemented
170	#759465	C₂³	1	2	yes	—
171	#759292	C₂³	1	2	yes	—
172	#615581	C₂³	1	1	yes	characteristic
173	#615501	C₂³	1	1	yes	characteristic
174	#615501	C₂³	1	2	yes	—
175	#614416	D₄	1	2	yes	complemented
176	#613956	D₄	1	2	yes	complemented
177	#613651	D₄	1	2	yes	complemented
178	#613649	D₄	1	2	yes	complemented
179	#612625	C₂³	1	1	yes	characteristic
180	#612625	C₂³	1	2	yes	—
181	#612624	C₂³	1	2	yes	—
182	#612431	C₂³	1	1	yes	characteristic
183	#612431	C₂³	1	2	yes	—
184	#612431	C₂³	1	2	yes	—
185	#612431	C₂³	1	2	yes	—
186	#611060	D₄	1	4	yes	complemented
187	#608662	D₄	1	2	yes	complemented
188	#608659	D₄	1	2	yes	complemented
189	#607927	D₄	1	4	yes	complemented
190	#607565	C₂³	1	1	yes	characteristic
191	#607563	C₂³	1	1	yes	characteristic
192	#607563	C₂³	1	1	yes	characteristic
193	#607563	C₂³	1	1	yes	characteristic
194	#520498	C₂³	1	2	yes	—
195	#520487	D₄	1	2	yes	complemented
196	D₄×#380	D₄	1	2	yes	complemented
197	D₄×#379	C₂³	1	2	yes	—
198	C₄×#2405	D₄	1	2	yes	—
199	C₄×#2405	C₂³	1	2	yes	—
200	C₄×#2403	D₄	1	2	yes	—
201	C₄×#2403	C₂³	1	2	yes	—
202	#514566	D₄	1	1	yes	characteristic
203	#514204	D₄	1	1	yes	characteristic
204	#514119	D₄	1	2	yes	complemented
205	#514052	D₄	1	1	yes	characteristic
206	C₄×D₄×C₂²⋊C₄	D₄	1	2	yes	complemented
207	C₄×#2280	C₂³	1	1	yes	characteristic
208	#392385	C₂³	1	2	yes	—
209	#392266	D₄	1	4	yes	complemented
210	#392216	C₂³	1	2	yes	—
211	#392216	C₂³	1	2	yes	—
212	#392216	C₂³	1	1	yes	characteristic
213	#392216	C₂³	1	1	yes	characteristic
214	#392160	D₄	1	4	yes	complemented
215	#392147	C₂³	1	2	yes	—
216	#392147	C₂³	1	2	yes	—
217	#392147	C₂³	1	2	yes	—
218	#392118	C₂³	1	2	yes	—
219	#392118	C₂³	1	1	yes	characteristic
220	#392118	C₂³	1	2	yes	—
221	#392118	C₂³	1	1	yes	characteristic
222	#362849	C₂³	1	2	yes	—
223	#361599	C₂³	1	2	yes	—
224	#359878	C₂³	1	1	yes	characteristic
225	#359878	C₂³	1	1	yes	characteristic
226	#359793	C₂³	1	1	yes	characteristic
227	#359793	C₂³	1	1	yes	characteristic
228	#359519	C₂³	1	1	yes	characteristic
229	#359519	C₂³	1	2	yes	—
230	#359519	C₂³	1	1	yes	characteristic
231	#359519	C₂³	1	2	yes	—
232	#359422	C₂³	1	2	yes	—
233	#359422	C₂³	1	2	yes	—
234	#359422	C₂³	1	1	yes	characteristic
235	#359422	C₂³	1	1	yes	characteristic
236	#354808	D₄	1	4	yes	complemented
237	#189842	C₂³	1	2	yes	—
238	#189840	C₂³	1	2	yes	—
239	#189840	C₂³	1	2	yes	—
240	#189688	C₂³	1	2	yes	—
241	#185046	C₂³	1	2	yes	—
242	#185046	C₂³	1	2	yes	—
243	#185046	C₂³	1	2	yes	—
244	#185046	C₂³	1	2	yes	—
245	#185046	C₂³	1	2	yes	—
246	#185046	C₂³	1	2	yes	—
247	#185046	C₂³	1	2	yes	—
248	#184743	C₂³	1	2	yes	—
249	#184743	C₂³	1	2	yes	—
250	#184743	C₂³	1	2	yes	—
251	C₄⋊#1304	C₂³	1	2	yes	—
252	C₄⋊#1304	C₂³	1	2	yes	—
253	#105542	C₂³	1	2	yes	—
254	#105542	C₂³	1	2	yes	—
255	#105520	C₂³	1	2	yes	—
256	#105520	C₂³	1	2	yes	—
257	#95216	C₂³	1	2	yes	—
258	#95216	C₂³	1	2	yes	—
259	#95216	C₂³	1	2	yes	—
260	#95216	C₂³	1	2	yes	—
261	#95109	C₂³	1	2	yes	—
262	#95109	C₂³	1	2	yes	—
263	C₂⁴×#41	C₂×D₄	1	1	yes	characteristic
264	C₂⁵×D₄	C₂×D₄	1	2	yes	—
265	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
266	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
267	C₂⁴×D₈	C₂×D₄	1	2	yes	—
268	C₂²×#532	C₂×D₄	1	2	yes	—
269	C₂²×#532	C₂×D₄	1	2	yes	—
270	C₂²×#532	C₂×D₄	1	2	yes	—
271	C₂²×#532	C₂×D₄	1	2	yes	—
272	C₂³×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
273	C₂³×C₄⋊Q₈	C₂×D₄	1	2	yes	—
274	C₂³×#127	C₂×D₄	1	1	yes	characteristic
275	C₂³×#127	C₂×D₄	1	1	yes	characteristic
276	C₂³×#127	C₂×D₄	1	2	yes	—
277	C₂³×#121	C₂×D₄	1	2	yes	—
278	C₂³×#121	C₂×D₄	1	1	yes	characteristic
279	C₂³×#121	C₂×D₄	1	2	yes	—
280	C₂³×#121	C₂⁴	1	1	yes	characteristic
281	C₂³×#121	C₂⁴	1	1	yes	characteristic
282	C₂³×#121	C₂⁴	1	2	yes	—
283	C₂³×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
284	C₂³×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
285	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
286	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
287	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
288	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
289	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
291	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
292	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
294	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
295	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
299	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
300	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
301	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
302	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
303	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
304	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
307	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
308	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
309	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
310	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
311	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
312	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
313	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
314	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
315	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
316	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
317	C₂³×C₄×D₄	#41	1	2	yes	—
318	C₂³×C₄×D₄	#41	1	2	yes	—
319	C₂³×C₄×D₄	C₂⁴	1	2	yes	—
320	C₂³×C₄×D₄	C₂⁴	1	1	yes	characteristic
321	C₂³×#117	C₂×D₄	1	2	yes	—
322	C₂³×#117	C₂×D₄	1	1	yes	characteristic
323	C₂⁴×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₂⁴×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₂⁴×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
326	C₂⁴×C₄²	C₂×D₄	1	2	yes	—
327	C₂⁴×C₄²	C₂×D₄	1	1	yes	characteristic
328	C₂⁴×C₄²	C₂⁴	1	1	yes	characteristic
329	C₂²×#432	C₂×D₄	1	2	yes	complemented
330	C₂³×#106	C₂×D₄	1	2	yes	complemented
331	C₂³×#102	C₂×D₄	1	2	yes	—
332	C₂³×#102	C₂×D₄	1	2	yes	—
333	C₂³×#102	C₂×D₄	1	2	yes	—
334	C₂³×#102	C₂×D₄	1	2	yes	complemented
335	C₂³×C₂²⋊C₈	C₂⁴	1	1	yes	characteristic
336	C₂³×C₂²⋊C₈	C₂⁴	1	1	yes	characteristic
337	C₂³×#97	C₂×D₄	1	2	yes	complemented
338	C₂×#2405	C₂×D₄	1	2	yes	—
339	C₂×#2403	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
341	C₂×C₄×#121	C₂×D₄	1	2	yes	—
342	C₂×C₄×#121	C₂×D₄	1	2	yes	—
343	C₂×C₄×#121	C₂×D₄	1	2	yes	—
344	C₂×C₄×#121	C₂×D₄	1	2	yes	—
345	C₂²×#390	C₂×D₄	1	1	yes	characteristic
346	C₂²×#390	C₂×D₄	1	1	yes	characteristic
347	C₂²×#390	C₂×D₄	1	1	yes	characteristic
348	C₂²×#390	C₂×D₄	1	1	yes	characteristic
349	C₂²×#390	C₂×D₄	1	1	yes	characteristic, complemented
350	C₂²×#389	C₂×D₄	1	1	yes	characteristic
351	C₂²×#389	C₂×D₄	1	1	yes	characteristic
352	C₂²×#389	C₂×D₄	1	1	yes	characteristic, complemented
353	C₂²×#384	C₂×D₄	1	1	yes	characteristic
354	C₂×#2283	C₂×D₄	1	2	yes	complemented
355	C₂×#2280	C₂×D₄	1	1	yes	characteristic
356	C₂×#2280	C₂×D₄	1	1	yes	characteristic
357	C₂²×#380	C₂×D₄	1	1	yes	characteristic
358	C₂²×#380	C₂⁴	1	1	yes	characteristic
359	C₂²×#380	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
367	C₂²×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄³	C₂×D₄	1	1	yes	characteristic
374	C₂×#1823	C₂×D₄	1	4	yes	complemented
375	C₂×#1823	C₂×D₄	1	4	yes	complemented
376	C₂×#1817	C₂×D₄	1	2	yes	complemented
377	C₂×#1797	C₂×D₄	1	2	yes	complemented
378	C₂×#1786	C₂×D₄	1	8	yes	—
379	C₂×#1786	C₂×D₄	1	4	yes	—
380	C₂×#1786	C₂×D₄	1	4	yes	—
381	C₂×#1779	C₂⁴	1	2	yes	—
382	C₂×#1779	C₂⁴	1	2	yes	—
383	C₂×#1779	C₂⁴	1	1	yes	characteristic
384	C₂×#1779	C₂⁴	1	1	yes	characteristic
385	C₂×#1749	C₂×D₄	1	2	yes	complemented
386	C₂²×#340	C₂×D₄	1	2	yes	complemented
387	C₂²×#340	C₂×D₄	1	2	yes	complemented
388	C₂²×#336	C₂×D₄	1	2	yes	complemented
389	#16363	C₂×D₄	1	8	yes	—
390	#16252	C₂×D₄	1	8	yes	—
391	#14926	C₂×D₄	1	4	yes	—
392	#14913	C₂×D₄	1	4	yes	—
393	#14821	C₂×D₄	1	4	yes	—
394	#14820	C₂×D₄	1	4	yes	—
395	#14719	C₂×D₄	1	4	yes	—
396	#14719	C₂×D₄	1	4	yes	—
397	#14716	C₂×D₄	1	4	yes	—
398	#14716	C₂×D₄	1	4	yes	—
399	#14686	C₂×D₄	1	2	yes	—
400	#14685	C₂×D₄	1	2	yes	—
401	#14685	C₂×D₄	1	2	yes	complemented
402	#14682	C₂×D₄	1	2	yes	—
403	#14682	C₂×D₄	1	2	yes	complemented
404	#14680	C₂⁴	1	2	yes	—
405	#14680	C₂⁴	1	1	yes	characteristic
406	#14680	C₂⁴	1	2	yes	—
407	#14680	C₂⁴	1	1	yes	characteristic
408	#14680	C₂⁴	1	2	yes	—
409	#14127	C₂×D₄	1	2	yes	—
410	#14127	C₂×D₄	1	2	yes	—
411	#13907	C₂×D₄	1	4	yes	—
412	#13902	C₂×D₄	1	4	yes	—
413	#13869	C₂×D₄	1	2	yes	—
414	#13867	C₂×D₄	1	2	yes	—
415	#13867	C₂×D₄	1	2	yes	—
416	#13867	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₄⋊C₄	C₂×D₄	1	4	yes	—
418	C₄×#380	C₂×D₄	1	2	yes	—
419	C₄×#380	C₂×D₄	1	2	yes	—
420	C₄×#380	C₂×D₄	1	2	yes	—
421	C₄×#380	C₂×D₄	1	2	yes	—
422	C₄×#380	C₂×D₄	1	2	yes	complemented
423	C₄×#379	C₂×D₄	1	2	yes	—
424	C₄×#379	C₂⁴	1	2	yes	—
425	#13756	C₂×D₄	1	2	yes	—
426	#13753	C₂×D₄	1	2	yes	—
427	C₄²×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	#10730	C₂×D₄	1	8	yes	complemented
429	C₂⁴×Q₈	#120	1	1	yes	characteristic
430	C₂⁴×D₄	#120	1	1	yes	characteristic
431	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
432	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
433	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
434	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
435	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
436	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
437	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
438	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
439	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
440	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
441	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
442	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
443	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
444	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
445	C₂⁴×D₄	C₂×#41	1	2	yes	—
446	C₂⁵×C₄	#120	1	2	yes	—
447	C₂⁵×C₄	#120	1	1	yes	characteristic
448	C₂⁵×C₄	#120	1	1	yes	characteristic
449	C₂⁵×C₄	#120	1	2	yes	—
450	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
452	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
453	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
454	C₂⁵×C₄	C₂⁵	1	1	yes	characteristic
455	C₂⁴×C₈	C₂²×D₄	1	2	yes	—
456	C₂⁴×C₈	C₂²×D₄	1	2	yes	—
457	C₂²×C₄⋊Q₈	#120	1	2	yes	—
458	C₂²×C₄⋊Q₈	#120	1	2	yes	—
459	C₂²×#127	#120	1	2	yes	—
460	C₂²×#127	#120	1	2	yes	—
461	C₂²×#121	C₂²×D₄	1	4	yes	—
462	C₂²×#121	C₂²×D₄	1	2	yes	—
463	C₂²×#121	C₂²×D₄	1	2	yes	—
464	C₂²×#121	C₂²×D₄	1	4	yes	—
465	C₂²×C₄×D₄	#120	1	2	yes	—
466	C₂²×C₄×D₄	#120	1	1	yes	characteristic
467	C₂²×C₄×D₄	#120	1	1	yes	characteristic
468	C₂²×C₄×D₄	#120	1	1	yes	characteristic
469	C₂²×C₄×D₄	#120	1	1	yes	characteristic
470	C₂²×C₄×D₄	#120	1	2	yes	—
471	C₂²×C₄×D₄	#120	1	2	yes	—
472	C₂²×C₄×D₄	#120	1	2	yes	—
473	C₂²×C₄×D₄	#120	1	2	yes	—
474	C₂²×C₄×D₄	#120	1	2	yes	—
475	C₂²×C₄×D₄	#120	1	2	yes	—
476	C₂²×C₄×D₄	#120	1	2	yes	—
477	C₂²×C₄×D₄	#120	1	2	yes	—
478	C₂²×C₄×D₄	#120	1	2	yes	—
479	C₂²×C₄×D₄	#120	1	2	yes	—
480	C₂²×C₄×D₄	#120	1	4	yes	—
481	C₂²×C₄×D₄	#120	1	2	yes	—
482	C₂²×C₄×D₄	#120	1	4	yes	—
483	C₂²×C₄×D₄	#120	1	2	yes	—
484	C₂²×C₄×D₄	#120	1	2	yes	—
485	C₂²×C₄×D₄	#120	1	2	yes	—
486	C₂²×C₄×D₄	#120	1	2	yes	—
487	C₂²×C₄×D₄	#120	1	2	yes	—
488	C₂²×C₄×D₄	#120	1	2	yes	—
489	C₂²×C₄×D₄	#120	1	1	yes	characteristic
490	C₂²×C₄×D₄	#120	1	1	yes	characteristic
491	C₂²×C₄×D₄	#120	1	1	yes	characteristic
492	C₂²×C₄×D₄	#120	1	1	yes	characteristic
493	C₂²×C₄×D₄	#120	1	1	yes	characteristic
494	C₂²×C₄×D₄	#120	1	1	yes	characteristic
495	C₂²×C₄×D₄	#120	1	1	yes	characteristic
496	C₂²×C₄×D₄	#120	1	1	yes	characteristic
497	C₂²×C₄×D₄	#120	1	1	yes	characteristic
498	C₂²×C₄×D₄	#120	1	1	yes	characteristic
499	C₂²×C₄×D₄	#120	1	1	yes	characteristic
500	C₂²×C₄×D₄	#120	1	1	yes	characteristic
501	C₂²×C₄×D₄	#121	1	2	yes	—
502	C₂²×C₄×D₄	#121	1	2	yes	—
503	C₂²×C₄×D₄	#121	1	2	yes	—
504	C₂²×C₄×D₄	#121	1	2	yes	—
505	C₂²×C₄×D₄	#121	1	2	yes	—
506	C₂²×C₄×D₄	#121	1	2	yes	—
507	C₂²×C₄×D₄	#121	1	2	yes	—
508	C₂²×C₄×D₄	#121	1	2	yes	—
509	C₂²×C₄×D₄	#121	1	2	yes	—
510	C₂²×C₄×D₄	#121	1	2	yes	—
511	C₂²×C₄×D₄	#121	1	2	yes	—
512	C₂²×C₄×D₄	#121	1	2	yes	—
513	C₂²×C₄×D₄	#121	1	2	yes	—
514	C₂²×C₄×D₄	#121	1	2	yes	—
515	C₂²×C₄×D₄	#121	1	2	yes	—
516	C₂²×C₄×D₄	#121	1	2	yes	—
517	C₂²×C₄×D₄	#121	1	2	yes	—
518	C₂²×C₄×D₄	#121	1	2	yes	—
519	C₂²×C₄×D₄	#121	1	2	yes	—
520	C₂²×C₄×D₄	#121	1	2	yes	—
521	C₂²×C₄×D₄	#121	1	2	yes	—
522	C₂²×C₄×D₄	#121	1	2	yes	—
523	C₂²×C₄×D₄	#121	1	2	yes	—
524	C₂²×C₄×D₄	#121	1	2	yes	—
525	C₂²×C₄×D₄	#127	1	2	yes	—
526	C₂²×C₄×D₄	#127	1	2	yes	—
527	C₂²×C₄×D₄	#127	1	2	yes	—
528	C₂²×C₄×D₄	#127	1	2	yes	—
529	C₂²×C₄×D₄	#127	1	2	yes	—
530	C₂²×C₄×D₄	#127	1	2	yes	—
531	C₂²×C₄×D₄	#127	1	2	yes	—
532	C₂²×C₄×D₄	#127	1	2	yes	—
533	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
534	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
535	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
536	C₂³×C₄⋊C₄	#120	1	2	yes	—
537	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
538	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
539	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
540	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
541	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
542	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
545	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
549	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
551	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
552	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂³×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
556	C₂³×C₄⋊C₄	C₂×#41	1	2	yes	—
557	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
558	C₂³×C₂²⋊C₄	#120	1	2	yes	—
559	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
560	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
561	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
563	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
564	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
565	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂³×C₄²	#120	1	1	yes	characteristic
567	C₂³×C₄²	#120	1	1	yes	characteristic
568	C₂³×C₄²	#120	1	2	yes	—
569	C₂³×C₄²	#120	1	2	yes	—
570	C₂³×C₄²	#120	1	1	yes	characteristic
571	C₂³×C₄²	#120	1	1	yes	characteristic
572	C₂³×C₄²	#120	1	1	yes	characteristic
573	C₂³×C₄²	#120	1	1	yes	characteristic
574	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
575	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
576	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
577	C₂³×C₄²	C₂²×D₄	1	2	yes	—
578	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
579	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
580	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
581	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
582	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
583	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
584	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
585	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
586	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
587	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
588	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
589	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
590	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
591	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
592	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
593	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
594	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
595	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
596	C₂³×C₄²	C₂×#41	1	1	yes	characteristic
597	C₂³×C₄²	C₂×#41	1	1	yes	characteristic
598	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
599	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
600	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
601	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
602	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
603	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
604	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
605	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
606	C₂²×C₂²⋊C₈	C₂²×D₄	1	2	yes	—
607	C₂²×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
608	C₂²×C₂²⋊C₈	C₂²×D₄	1	2	yes	—
609	#2405	AGL(1,ℤ/8)	1	8	yes	—
610	#2403	AGL(1,ℤ/8)	1	8	yes	—
611	C₂×#390	#120	1	2	yes	—
612	C₂×#390	#120	1	2	yes	—
613	C₂×#389	#120	1	2	yes	—
614	C₂×#389	#120	1	2	yes	—
615	C₂×#380	#120	1	2	yes	—
616	C₂×#380	#120	1	2	yes	—
617	C₂×#380	C₂²×D₄	1	4	yes	—
618	C₂×#380	C₂²×D₄	1	2	yes	—
619	C₂×#380	C₂²×D₄	1	2	yes	—
620	C₂×#380	C₂²×D₄	1	4	yes	—
621	C₂×#380	C₂²×D₄	1	2	yes	—
622	C₂×#380	C₂²×D₄	1	2	yes	—
623	C₂×#379	C₂²×D₄	1	2	yes	—
624	C₂×#379	C₂²×D₄	1	2	yes	—
625	C₂×C₄×C₄⋊C₄	#120	1	2	yes	—
626	C₂×C₄×C₄⋊C₄	#120	1	2	yes	—
627	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
628	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
629	C₂×C₄×C₂²⋊C₄	#120	1	4	yes	—
630	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
631	C₂²×#95	#120	1	1	yes	characteristic
632	C₂²×#95	#120	1	1	yes	characteristic
633	C₂²×#95	#120	1	1	yes	characteristic
634	C₂²×#95	#120	1	1	yes	characteristic
635	C₂²×#95	C₂²×D₄	1	1	yes	characteristic
636	C₂²×#95	C₂²×D₄	1	1	yes	characteristic
637	C₄⋊#95	#120	1	4	yes	—
638	C₄⋊#95	#120	1	4	yes	—
639	#1434	#120	1	4	yes	—
640	C₂²⋊#95	#120	1	4	yes	—
641	C₂²⋊#95	C₂²×D₄	1	4	yes	—
642	C₂²⋊#95	C₂²×D₄	1	4	yes	—
643	C₂²⋊#95	C₂²×D₄	1	4	yes	—
644	C₄×#95	#120	1	4	yes	—
645	C₂⁶	C₂×#120	1	2	yes	—
646	C₂⁶	C₂×#120	1	1	yes	characteristic
647	C₂⁶	C₂³×D₄	1	1	yes	characteristic
648	C₂³×D₄	C₂×#120	1	1	yes	characteristic
649	C₂³×D₄	C₂×#120	1	1	yes	characteristic
650	C₂³×D₄	C₂×#120	1	1	yes	characteristic
651	C₂³×D₄	C₂×#120	1	2	yes	—
652	C₂³×D₄	C₂×#120	1	2	yes	—
653	C₂³×D₄	C₂×#120	1	2	yes	—
654	C₂³×D₄	C₂×#120	1	2	yes	—
655	C₂³×D₄	C₂×#120	1	1	yes	characteristic
656	C₂³×D₄	C₂×#120	1	2	yes	—
657	C₂³×D₄	C₂×#120	1	4	yes	—
658	C₂³×D₄	C₂×#121	1	2	yes	—
659	C₂³×D₄	C₂×#121	1	2	yes	—
660	C₂³×D₄	C₂×#121	1	2	yes	—
661	C₂³×D₄	C₂×#121	1	2	yes	—
662	C₂³×D₄	C₂×#121	1	2	yes	—
663	C₂³×D₄	C₂×#121	1	2	yes	—
664	C₂³×D₄	C₂×#127	1	2	yes	—
665	C₂³×D₄	C₂×#127	1	2	yes	—
666	C₂³×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
667	C₂³×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
668	C₂³×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
669	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
670	C₂⁴×C₄	C₂×#120	1	2	yes	—
671	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
672	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
673	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
674	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
675	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
676	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
677	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
678	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
679	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
680	C₂⁴×C₄	C₂×#120	1	2	yes	—
681	C₂⁴×C₄	C₂×#120	1	2	yes	—
682	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
683	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
684	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
685	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
686	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
687	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
688	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
689	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
690	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
691	C₂⁴×C₄	D₄²	1	1	yes	characteristic
692	C₂⁴×C₄	D₄²	1	1	yes	characteristic
693	C₂⁴×C₄	D₄²	1	1	yes	characteristic
694	C₂⁴×C₄	D₄²	1	1	yes	characteristic
695	C₂⁴×C₄	D₄²	1	1	yes	characteristic
696	C₂⁴×C₄	D₄²	1	1	yes	characteristic
697	C₂⁴×C₄	D₄²	1	1	yes	characteristic
698	C₂⁴×C₄	D₄²	1	1	yes	characteristic
699	C₂⁴×C₄	D₄²	1	1	yes	characteristic
700	C₂⁴×C₄	D₄²	1	1	yes	characteristic
701	C₂⁴×C₄	D₄²	1	1	yes	characteristic
702	C₂⁴×C₄	D₄²	1	1	yes	characteristic
703	C₂⁴×C₄	#546	1	1	yes	characteristic
704	C₂⁴×C₄	#546	1	1	yes	characteristic
705	C₂⁴×C₄	#546	1	1	yes	characteristic
706	C₂⁴×C₄	#546	1	1	yes	characteristic
707	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
708	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
709	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
710	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
711	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
712	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
713	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
714	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
715	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
716	C₂⁴×C₄	C₂²×#41	1	1	yes	characteristic
717	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×C₄×D₄	#392	1	2	yes	—
722	C₂×C₄×D₄	#392	1	2	yes	—
723	C₂×C₄×D₄	#392	1	2	yes	—
724	C₂×C₄×D₄	#392	1	2	yes	—
725	C₂×C₄×D₄	#392	1	2	yes	—
726	C₂×C₄×D₄	#392	1	2	yes	—
727	C₂×C₄×D₄	#392	1	2	yes	—
728	C₂×C₄×D₄	#392	1	2	yes	—
729	C₂×C₄×D₄	#392	1	2	yes	—
730	C₂×C₄×D₄	#392	1	2	yes	—
731	C₂×C₄×D₄	#392	1	2	yes	—
732	C₂×C₄×D₄	#392	1	2	yes	—
733	C₂×C₄×D₄	#392	1	2	yes	—
734	C₂×C₄×D₄	#392	1	2	yes	—
735	C₂×C₄×D₄	#392	1	2	yes	—
736	C₂×C₄×D₄	#392	1	2	yes	—
737	C₂×C₄×D₄	#392	1	2	yes	—
738	C₂×C₄×D₄	#392	1	2	yes	—
739	C₂×C₄×D₄	#392	1	2	yes	—
740	C₂×C₄×D₄	#392	1	2	yes	—
741	C₂×C₄×D₄	#392	1	2	yes	—
742	C₂×C₄×D₄	#392	1	2	yes	—
743	C₂×C₄×D₄	#392	1	2	yes	—
744	C₂×C₄×D₄	#392	1	2	yes	—
745	C₂×C₄×D₄	#392	1	2	yes	—
746	C₂×C₄×D₄	#392	1	2	yes	—
747	C₂×C₄×D₄	#392	1	2	yes	—
748	C₂×C₄×D₄	#392	1	2	yes	—
749	C₂×C₄×D₄	#392	1	2	yes	—
750	C₂×C₄×D₄	#392	1	2	yes	—
751	C₂×C₄×D₄	#392	1	2	yes	—
752	C₂×C₄×D₄	#392	1	2	yes	—
753	C₂×C₄×D₄	B(4,𝔽₂)	1	16	yes	—
754	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
755	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
756	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
757	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
758	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
759	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
760	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
761	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
762	C₂²×C₄⋊C₄	C₂×#120	1	4	yes	—
763	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
764	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
765	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
766	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
767	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
768	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
769	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
770	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
771	C₂²×C₄⋊C₄	C₂×#121	1	2	yes	—
772	C₂²×C₄⋊C₄	C₂×#127	1	2	yes	—
773	C₂²×C₄⋊C₄	C₂×#127	1	2	yes	—
774	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
775	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
776	C₂²×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
777	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
778	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
779	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
780	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
781	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
782	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
783	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
784	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
785	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
786	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
787	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
788	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
789	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
790	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
791	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
792	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
793	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
794	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
795	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
796	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
797	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
798	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
799	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
800	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
801	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
802	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
803	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
804	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
805	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
806	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
807	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
808	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
809	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
810	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
811	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
812	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
813	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
814	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
815	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
816	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
817	C₂²×C₄²	#534	1	1	yes	characteristic
818	C₂²×C₄²	#534	1	1	yes	characteristic
819	C₂²×C₄²	#534	1	1	yes	characteristic
820	C₂²×C₄²	#534	1	1	yes	characteristic
821	C₂²×C₄²	#534	1	1	yes	characteristic
822	C₂²×C₄²	#534	1	1	yes	characteristic
823	C₂²×C₄²	#534	1	1	yes	characteristic
824	C₂²×C₄²	#534	1	1	yes	characteristic
825	C₂²×C₄²	#534	1	1	yes	characteristic
826	C₂²×C₄²	#534	1	1	yes	characteristic
827	C₂²×C₄²	#534	1	1	yes	characteristic
828	C₂²×C₄²	#534	1	1	yes	characteristic
829	C₂²×C₄²	#534	1	1	yes	characteristic
830	C₂²×C₄²	#534	1	1	yes	characteristic
831	C₂²×C₄²	#534	1	1	yes	characteristic
832	C₂²×C₄²	#534	1	1	yes	characteristic
833	C₂²×C₄²	#535	1	1	yes	characteristic
834	C₂²×C₄²	#535	1	1	yes	characteristic
835	C₂²×C₄²	#535	1	1	yes	characteristic
836	C₂²×C₄²	#535	1	1	yes	characteristic
837	C₂²×C₄²	#535	1	1	yes	characteristic
838	C₂²×C₄²	#535	1	1	yes	characteristic
839	C₂²×C₄²	#535	1	1	yes	characteristic
840	C₂²×C₄²	#535	1	1	yes	characteristic
841	C₂²×C₄²	D₄²	1	1	yes	characteristic
842	C₂²×C₄²	D₄²	1	1	yes	characteristic
843	C₂²×C₄²	D₄²	1	1	yes	characteristic
844	C₂²×C₄²	D₄²	1	1	yes	characteristic
845	C₂²×C₄²	D₄²	1	1	yes	characteristic
846	C₂²×C₄²	D₄²	1	1	yes	characteristic
847	C₂²×C₄²	D₄²	1	1	yes	characteristic
848	C₂²×C₄²	D₄²	1	1	yes	characteristic
849	C₂²×C₄²	D₄²	1	1	yes	characteristic
850	C₂²×C₄²	D₄²	1	1	yes	characteristic
851	C₂²×C₄²	D₄²	1	1	yes	characteristic
852	C₂²×C₄²	D₄²	1	1	yes	characteristic
853	C₂²×C₄²	D₄²	1	1	yes	characteristic
854	C₂²×C₄²	D₄²	1	1	yes	characteristic
855	C₂²×C₄²	D₄²	1	1	yes	characteristic
856	C₂²×C₄²	D₄²	1	1	yes	characteristic
857	C₂²×C₄²	D₄²	1	1	yes	characteristic
858	C₂²×C₄²	D₄²	1	1	yes	characteristic
859	C₂²×C₄²	D₄²	1	1	yes	characteristic
860	C₂²×C₄²	D₄²	1	1	yes	characteristic
861	C₂²×C₄²	D₄²	1	1	yes	characteristic
862	C₂²×C₄²	D₄²	1	1	yes	characteristic
863	C₂²×C₄²	D₄²	1	1	yes	characteristic
864	C₂²×C₄²	D₄²	1	1	yes	characteristic
865	C₂²×C₄²	D₄²	1	1	yes	characteristic
866	C₂²×C₄²	D₄²	1	1	yes	characteristic
867	C₂²×C₄²	D₄²	1	1	yes	characteristic
868	C₂²×C₄²	D₄²	1	1	yes	characteristic
869	C₂²×C₄²	D₄²	1	1	yes	characteristic
870	C₂²×C₄²	D₄²	1	1	yes	characteristic
871	C₂²×C₄²	D₄²	1	1	yes	characteristic
872	C₂²×C₄²	D₄²	1	1	yes	characteristic
873	C₂²×C₄²	D₄²	1	1	yes	characteristic
874	C₂²×C₄²	D₄²	1	1	yes	characteristic
875	C₂²×C₄²	D₄²	1	1	yes	characteristic
876	C₂²×C₄²	D₄²	1	1	yes	characteristic
877	C₂²×C₄²	#546	1	1	yes	characteristic
878	C₂²×C₄²	#546	1	1	yes	characteristic
879	C₂²×C₄²	#546	1	1	yes	characteristic
880	C₂²×C₄²	#546	1	1	yes	characteristic
881	C₂²×C₄²	#546	1	1	yes	characteristic
882	C₂²×C₄²	#546	1	1	yes	characteristic
883	C₂²×C₄²	#546	1	1	yes	characteristic
884	C₂²×C₄²	#546	1	1	yes	characteristic
885	C₂²×C₄²	#546	1	1	yes	characteristic
886	C₂²×C₄²	#546	1	1	yes	characteristic
887	C₂²×C₄²	#546	1	1	yes	characteristic
888	C₂²×C₄²	#546	1	1	yes	characteristic
889	#379	C₂×AGL(1,ℤ/8)	1	4	yes	—
890	#379	C₂×AGL(1,ℤ/8)	1	4	yes	—
891	C₂×#95	C₂×#120	1	8	yes	—
892	C₂⁵	#3003	1	2	yes	—
893	C₂⁵	#3003	1	4	yes	—
894	C₂⁵	C₂²×#120	1	1	yes	characteristic
895	C₂⁵	C₂²×#120	1	1	yes	characteristic
896	C₂⁵	C₂²×#120	1	1	yes	characteristic
897	C₂⁵	C₂×D₄²	1	1	yes	characteristic
898	C₂⁵	C₂×D₄²	1	1	yes	characteristic
899	C₂⁵	C₂×D₄²	1	1	yes	characteristic
900	C₂⁵	C₂×#546	1	1	yes	characteristic
901	C₂⁵	C₂²×AGL(1,ℤ/8)	1	2	yes	—
902	C₂⁵	C₂²×AGL(1,ℤ/8)	1	2	yes	—
903	C₂⁵	#3585	1	2	yes	—
904	C₂⁵	#3585	1	2	yes	—
905	C₂²×D₄	C₂×#392	1	2	yes	—
906	C₂²×D₄	C₂×#392	1	2	yes	—
907	C₂²×D₄	C₂×#392	1	2	yes	—
908	C₂²×D₄	C₂×#392	1	2	yes	—
909	C₂²×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
910	C₂²×D₄	#3025	1	4	yes	—
911	C₂²×D₄	#3025	1	8	yes	—
912	C₂³×C₄	#2403	1	1	yes	characteristic
913	C₂³×C₄	#2403	1	1	yes	characteristic
914	C₂³×C₄	#2403	1	1	yes	characteristic
915	C₂³×C₄	#2403	1	1	yes	characteristic
916	C₂³×C₄	#2403	1	1	yes	characteristic
917	C₂³×C₄	#2403	1	1	yes	characteristic
918	C₂³×C₄	#2403	1	1	yes	characteristic
919	C₂³×C₄	#2403	1	1	yes	characteristic
920	C₂³×C₄	#2403	1	1	yes	characteristic
921	C₂³×C₄	#2403	1	1	yes	characteristic
922	C₂³×C₄	#2403	1	1	yes	characteristic
923	C₂³×C₄	#2403	1	1	yes	characteristic
924	C₂³×C₄	#2403	1	1	yes	characteristic
925	C₂³×C₄	#2403	1	1	yes	characteristic
926	C₂³×C₄	#2403	1	1	yes	characteristic
927	C₂³×C₄	#2403	1	1	yes	characteristic
928	C₂³×C₄	#2408	1	1	yes	characteristic
929	C₂³×C₄	#2408	1	1	yes	characteristic
930	C₂³×C₄	#2408	1	1	yes	characteristic
931	C₂³×C₄	#2408	1	1	yes	characteristic
932	C₂³×C₄	#2408	1	1	yes	characteristic
933	C₂³×C₄	#2408	1	1	yes	characteristic
934	C₂³×C₄	#2408	1	1	yes	characteristic
935	C₂³×C₄	#2408	1	1	yes	characteristic
936	C₂³×C₄	#2410	1	1	yes	characteristic
937	C₂³×C₄	#2410	1	1	yes	characteristic
938	C₂³×C₄	#2410	1	1	yes	characteristic
939	C₂³×C₄	#2410	1	1	yes	characteristic
940	C₂³×C₄	#2410	1	1	yes	characteristic
941	C₂³×C₄	#2410	1	1	yes	characteristic
942	C₂³×C₄	#2410	1	1	yes	characteristic
943	C₂³×C₄	#2410	1	1	yes	characteristic
944	C₂³×C₄	#2410	1	1	yes	characteristic
945	C₂³×C₄	#2410	1	1	yes	characteristic
946	C₂³×C₄	#2410	1	1	yes	characteristic
947	C₂³×C₄	#2410	1	1	yes	characteristic
948	C₂³×C₄	#2410	1	1	yes	characteristic
949	C₂³×C₄	#2410	1	1	yes	characteristic
950	C₂³×C₄	#2410	1	1	yes	characteristic
951	C₂³×C₄	#2410	1	1	yes	characteristic
952	C₂³×C₄	#2433	1	1	yes	characteristic
953	C₂³×C₄	#2433	1	1	yes	characteristic
954	C₂³×C₄	#2433	1	1	yes	characteristic
955	C₂³×C₄	#2433	1	1	yes	characteristic
956	C₂³×C₄	#2433	1	1	yes	characteristic
957	C₂³×C₄	#2433	1	1	yes	characteristic
958	C₂³×C₄	#2433	1	1	yes	characteristic
959	C₂³×C₄	#2433	1	1	yes	characteristic
960	C₂³×C₄	#2846	1	1	yes	characteristic
961	C₂³×C₄	#2846	1	1	yes	characteristic
962	C₂³×C₄	#2846	1	1	yes	characteristic
963	C₂³×C₄	#2846	1	1	yes	characteristic
964	C₂³×C₄	#2846	1	1	yes	characteristic
965	C₂³×C₄	#2846	1	1	yes	characteristic
966	C₂³×C₄	#2846	1	1	yes	characteristic
967	C₂³×C₄	#2846	1	1	yes	characteristic
968	C₂³×C₄	#3003	1	2	yes	—
969	C₂³×C₄	#3003	1	2	yes	—
970	C₂³×C₄	#3003	1	2	yes	—
971	C₂³×C₄	#3003	1	4	yes	—
972	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
973	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
974	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
975	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
976	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
977	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
978	C₂³×C₄	C₂²×#121	1	1	yes	characteristic
979	C₂³×C₄	C₂²×#121	1	1	yes	characteristic
980	C₂³×C₄	C₂²×#121	1	1	yes	characteristic
981	C₂³×C₄	C₂²×#127	1	1	yes	characteristic
982	C₂³×C₄	C₂×#534	1	1	yes	characteristic
983	C₂³×C₄	C₂×#534	1	1	yes	characteristic
984	C₂³×C₄	C₂×#534	1	1	yes	characteristic
985	C₂³×C₄	C₂×#534	1	1	yes	characteristic
986	C₂³×C₄	C₂×#535	1	1	yes	characteristic
987	C₂³×C₄	C₂×#535	1	1	yes	characteristic
988	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
989	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
990	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
991	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
992	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
993	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
994	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
995	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
996	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
997	C₂³×C₄	C₂×#546	1	1	yes	characteristic
998	C₂³×C₄	C₂×#546	1	1	yes	characteristic
999	C₂³×C₄	C₂×#546	1	1	yes	characteristic
1000	C₄×D₄	#2021	1	8	yes	—
1001	C₄×D₄	#2021	1	8	yes	—
1002	C₄×D₄	#2021	1	8	yes	—
1003	C₄×D₄	#2021	1	8	yes	—
1004	C₂×C₄⋊C₄	C₂×#392	1	2	yes	—
1005	C₂×C₄⋊C₄	C₂×#392	1	2	yes	—
1006	C₂×C₄⋊C₄	C₂×#392	1	2	yes	—
1007	C₂×C₄⋊C₄	C₂×#392	1	2	yes	—
1008	C₂×C₄⋊C₄	C₂×B(4,𝔽₂)	1	8	yes	—
1009	C₂×C₂²⋊C₄	#3003	1	8	yes	—
1010	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1011	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1012	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1013	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1014	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1015	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1016	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1017	C₂×C₄²	C₂×#392	1	1	yes	characteristic
1018	C₂×C₄²	#2403	1	1	yes	characteristic
1019	C₂×C₄²	#2403	1	1	yes	characteristic
1020	C₂×C₄²	#2403	1	1	yes	characteristic
1021	C₂×C₄²	#2403	1	1	yes	characteristic
1022	C₂×C₄²	#2403	1	1	yes	characteristic
1023	C₂×C₄²	#2403	1	1	yes	characteristic
1024	C₂×C₄²	#2403	1	1	yes	characteristic
1025	C₂×C₄²	#2403	1	1	yes	characteristic
1026	C₂×C₄²	#2403	1	1	yes	characteristic
1027	C₂×C₄²	#2403	1	1	yes	characteristic
1028	C₂×C₄²	#2403	1	1	yes	characteristic
1029	C₂×C₄²	#2403	1	1	yes	characteristic
1030	C₂×C₄²	#2403	1	1	yes	characteristic
1031	C₂×C₄²	#2403	1	1	yes	characteristic
1032	C₂×C₄²	#2403	1	1	yes	characteristic
1033	C₂×C₄²	#2403	1	1	yes	characteristic
1034	C₂×C₄²	#2408	1	1	yes	characteristic
1035	C₂×C₄²	#2408	1	1	yes	characteristic
1036	C₂×C₄²	#2408	1	1	yes	characteristic
1037	C₂×C₄²	#2408	1	1	yes	characteristic
1038	C₂×C₄²	#2408	1	1	yes	characteristic
1039	C₂×C₄²	#2408	1	1	yes	characteristic
1040	C₂×C₄²	#2408	1	1	yes	characteristic
1041	C₂×C₄²	#2408	1	1	yes	characteristic
1042	C₂×C₄²	#2410	1	1	yes	characteristic
1043	C₂×C₄²	#2410	1	1	yes	characteristic
1044	C₂×C₄²	#2410	1	1	yes	characteristic
1045	C₂×C₄²	#2410	1	1	yes	characteristic
1046	C₂×C₄²	#2410	1	1	yes	characteristic
1047	C₂×C₄²	#2410	1	1	yes	characteristic
1048	C₂×C₄²	#2410	1	1	yes	characteristic
1049	C₂×C₄²	#2410	1	1	yes	characteristic
1050	C₂×C₄²	#2410	1	1	yes	characteristic
1051	C₂×C₄²	#2410	1	1	yes	characteristic
1052	C₂×C₄²	#2410	1	1	yes	characteristic
1053	C₂×C₄²	#2410	1	1	yes	characteristic
1054	C₂×C₄²	#2410	1	1	yes	characteristic
1055	C₂×C₄²	#2410	1	1	yes	characteristic
1056	C₂×C₄²	#2410	1	1	yes	characteristic
1057	C₂×C₄²	#2410	1	1	yes	characteristic
1058	C₂×C₄²	#2433	1	1	yes	characteristic
1059	C₂×C₄²	#2433	1	1	yes	characteristic
1060	C₂×C₄²	#2433	1	1	yes	characteristic
1061	C₂×C₄²	#2433	1	1	yes	characteristic
1062	C₂×C₄²	#2433	1	1	yes	characteristic
1063	C₂×C₄²	#2433	1	1	yes	characteristic
1064	C₂×C₄²	#2433	1	1	yes	characteristic
1065	C₂×C₄²	#2433	1	1	yes	characteristic
1066	C₂×C₄²	#2613	1	1	yes	characteristic
1067	C₂×C₄²	#2613	1	1	yes	characteristic
1068	C₂×C₄²	#2613	1	1	yes	characteristic
1069	C₂×C₄²	#2613	1	1	yes	characteristic
1070	C₂×C₄²	#2613	1	1	yes	characteristic
1071	C₂×C₄²	#2613	1	1	yes	characteristic
1072	C₂×C₄²	#2613	1	1	yes	characteristic
1073	C₂×C₄²	#2613	1	1	yes	characteristic
1074	C₂×C₄²	C₂×B(4,𝔽₂)	1	8	yes	—
1075	C₂⁴	C₂×#2403	1	1	yes	characteristic
1076	C₂⁴	C₂×#2403	1	1	yes	characteristic
1077	C₂⁴	C₂×#2410	1	1	yes	characteristic
1078	C₂⁴	C₂×#2410	1	1	yes	characteristic
1079	C₂⁴	C₂×#2408	1	1	yes	characteristic
1080	C₂⁴	C₂×#2433	1	1	yes	characteristic
1081	C₂⁴	C₂×#2846	1	1	yes	characteristic
1082	C₂⁴	C₂×#3003	1	2	yes	—
1083	C₂⁴	C₂×#3003	1	1	yes	characteristic
1084	C₂⁴	C₂×#3003	1	1	yes	characteristic
1085	C₂⁴	C₂×#3003	1	2	yes	—
1086	C₂⁴	#60367	1	2	yes	—
1087	C₂⁴	#60367	1	1	yes	characteristic
1088	C₂⁴	#60367	1	1	yes	characteristic
1089	C₂⁴	#60367	1	2	yes	—
1090	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1091	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1092	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1093	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1094	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1095	C₂⁴	D₄×AGL(1,ℤ/8)	1	2	yes	—
1096	C₂⁴	#61155	1	2	yes	—
1097	C₂⁴	#61155	1	2	yes	—
1098	C₂×D₄	C₂×#2021	1	4	yes	—
1099	C₂×D₄	C₂×#2021	1	4	yes	—
1100	C₂×D₄	#23443	1	4	yes	—
1101	C₂×D₄	#23443	1	4	yes	—
1102	C₂×D₄	#23443	1	4	yes	—
1103	C₂²×C₄	#14715	1	1	yes	characteristic
1104	C₂²×C₄	#14715	1	1	yes	characteristic
1105	C₂²×C₄	#14715	1	1	yes	characteristic
1106	C₂²×C₄	#14715	1	1	yes	characteristic
1107	C₂²×C₄	#14715	1	1	yes	characteristic
1108	C₂²×C₄	#14715	1	1	yes	characteristic
1109	C₂²×C₄	#14715	1	1	yes	characteristic
1110	C₂²×C₄	#14715	1	1	yes	characteristic
1111	C₂²×C₄	#14715	1	1	yes	characteristic
1112	C₂²×C₄	#14715	1	1	yes	characteristic
1113	C₂²×C₄	#14715	1	1	yes	characteristic
1114	C₂²×C₄	#14715	1	1	yes	characteristic
1115	C₂²×C₄	#14715	1	1	yes	characteristic
1116	C₂²×C₄	#14715	1	1	yes	characteristic
1117	C₂²×C₄	#14715	1	1	yes	characteristic
1118	C₂²×C₄	#14715	1	1	yes	characteristic
1119	C₂²×C₄	#23882	1	4	yes	—
1120	C₂²×C₄	#23900	1	4	yes	—
1121	C₂²×C₄	#23900	1	4	yes	—
1122	C₂²×C₄	C₂²×#392	1	1	yes	characteristic
1123	C₂²×C₄	C₂×#2613	1	1	yes	characteristic
1124	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
1125	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
1126	C₂²×C₄	C₂×#2410	1	1	yes	characteristic
1127	C₂²×C₄	C₂×#2410	1	1	yes	characteristic
1128	C₂²×C₄	C₂×#2408	1	1	yes	characteristic
1129	C₂²×C₄	C₂×#2433	1	1	yes	characteristic
1130	C₂²×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
1131	C₂²×C₄	C₂×#3025	1	2	yes	—
1132	C₂²×C₄	C₂×#3025	1	4	yes	—
1133	C₂²×C₄	#60398	1	2	yes	—
1134	C₄⋊C₄	C₂×#2021	1	4	yes	—
1135	C₄⋊C₄	C₂×#2021	1	4	yes	—
1136	C₄²	C₂×#2021	1	4	yes	—
1137	C₄²	C₂×#2021	1	4	yes	—
1138	C₄²	#23900	1	4	yes	—
1139	C₄²	#23900	1	4	yes	—
1140	C₂³	C₂×#14715	1	1	yes	characteristic
1141	C₂³	#6437510	1	1	yes	characteristic
1142	C₂³	#6437510	1	1	yes	characteristic
1143	C₂³	#6437510	1	2	yes	—
1144	C₂³	C₂×#23882	1	2	yes	—
1145	C₂³	#6437575	1	2	yes	—
1146	C₂³	C₂×#23900	1	2	yes	—
1147	C₂³	#6437616	1	2	yes	—
1148	C₂³	#6437838	1	2	yes	—
1149	C₂³	#6437838	1	1	yes	characteristic
1150	C₂³	#6437838	1	1	yes	characteristic
1151	C₂³	#6442656	1	2	yes	—
1152	C₂³	#6443168	1	2	yes	—
1153	C₂³	#6628842	1	1	yes	characteristic
1154	C₂³	#6628847	1	1	yes	characteristic
1155	C₂³	#6628885	1	2	yes	—
1156	C₂³	#6628891	1	2	yes	—
1157	D₄	#233538	1	8	yes	—
1158	C₂×C₄	#394058	1	2	yes	—
1159	C₂×C₄	#394058	1	2	yes	—
1160	C₂×C₄	#394058	1	2	yes	—
1161	C₂×C₄	#394058	1	2	yes	—
1162	C₂×C₄	#394102	1	2	yes	—
1163	C₂×C₄	#394102	1	2	yes	—
1164	C₂×C₄	C₂²×#2021	1	2	yes	—
1165	C₂×C₄	C₂×#23443	1	2	yes	—
1166	C₂×C₄	C₂×#23443	1	1	yes	characteristic
1167	C₂×C₄	#6431794	1	1	yes	characteristic
1168	C₂×C₄	#6432948	1	2	yes	—
1169	C₂×C₄	C₂×#23900	1	2	yes	—
1170	C₂×C₄	#6437616	1	2	yes	—
1171	C₂²	#72214295	1	2	yes	—
1172	C₂²	#72214295	1	2	yes	—
1173	C₂²	C₂×#394058	1	1	yes	characteristic
1174	C₂²	#72231727	1	2	yes	—
1175	C₂²	#72231796	1	1	yes	characteristic
1176	C₂²	C₂×#394102	1	1	yes	characteristic
1177	C₂²	#72236780	1	1	yes	characteristic
1178	C₂²	#72249888	1	4	yes	—
1179	C₂²	#72249909	1	1	yes	characteristic
1180	C₂²	#72249917	1	2	yes	—
1181	C₂²	#72249921	1	1	yes	characteristic
1182	C₂²	#72251128	1	1	yes	characteristic
1183	C₄	#72236681	1	2	yes	—
1184	C₄	C₂×#233538	1	2	yes	—
1185	C₂	#72231803	1	1	yes	characteristic
1186	C₂	#72250016	1	1	yes	characteristic
1187	C₂	#72257387	1	1	yes	characteristic
1188	C₂	#72257589	1	1	yes	characteristic
1189	C₂	#72257720	1	1	yes	characteristic
1190	C₂	#72263972	1	1	yes	characteristic
1191	C₂	#72264040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#14715
commutator, Frattini, cosocle	C₂⁵×C₄	C₂⁵
LCS	G ▷ C₂⁵×C₄ ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄² ◁ G
LECS	G ▷ C₂⁵×C₄ ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265022	C₂	semidirect
2. #72265005	C₂	semidirect
3. #72264993	C₂	semidirect
4. #72264938	C₂	semidirect
5. #72264912	C₂	semidirect
6. #72264872	C₂	semidirect
7. #72264856	C₂	semidirect
8. #72264838	C₂	semidirect
9. #72264811	C₂	semidirect
10. #72264789	C₂	semidirect
11. #72264683	C₂	semidirect
12. #72264676	C₂²	semidirect
13. #72264665	C₂	semidirect
14. #72264658	C₂²	semidirect
15. #72264656	C₂²	semidirect
16. #72264656	C₂²	semidirect
19. #72264643	C₂	semidirect
20. #72264637	C₂²	semidirect
21. #72264628	C₂²	semidirect
22. #72264622	C₂²	semidirect
23. #72264610	C₂	semidirect
24. #72264593	C₂	semidirect
25. #72264585	C₂²	semidirect
26. #72264573	C₂²	semidirect
27. #72264573	C₂²	semidirect
28. #72264565	C₂²	semidirect
29. #72264565	C₂²	semidirect
30. #72264551	C₂	semidirect
31. #72264532	C₂²	semidirect
32. #72264520	C₂²	semidirect
33. #72264514	C₂²	semidirect
34. #72264498	C₂²	semidirect
35. #72264483	C₂²	semidirect
36. #72264461	C₂	semidirect
37. #72264452	C₂²	semidirect
38. #72264452	C₂²	semidirect
39. #72264444	C₂²	semidirect
40. #72264433	C₂²	semidirect
41. #72264424	C₂²	semidirect
42. #72264417	C₂	semidirect
43. #72264414	C₂²	semidirect
44. #72264410	C₂²	semidirect
45. #72264405	C₂²	semidirect
46. #72264405	C₂²	semidirect
47. #72264402	C₂²	semidirect
48. #72264395	C₂	semidirect
49. #72264388	C₂²	semidirect
50. #72264384	C₂²	semidirect
51. #72264382	C₂²	semidirect
52. #72264382	C₂²	semidirect
53. #72264375	C₂²	semidirect
54. #72264371	C₂²	semidirect
55. #72264371	C₂²	semidirect
56. #72264364	C₂²	semidirect
57. #72264364	C₂²	semidirect
58. #72264358	C₂²	semidirect
59. #72264358	C₂²	semidirect
60. #72264350	C₂²	semidirect
61. #72264346	C₂	semidirect
62. #72264345	C₂²	semidirect
63. #72264345	C₂²	semidirect
64. #72264341	C₂²	semidirect
65. #72264341	C₂²	semidirect
66. #72264341	C₂²	semidirect
67. #72264341	C₂²	semidirect
68. #72264337	C₂²	semidirect
69. #72264336	C₂²	semidirect
71. #72264331	C₂²	semidirect
72. #72264331	C₂²	semidirect
73. #72264330	C₂²	semidirect
74. #72264327	C₂²	semidirect
75. #72264322	C₂	semidirect
76. #72264321	C₂²	semidirect
78. #72264297	C₂²	semidirect
79. #72264297	C₂²	semidirect
80. #72264292	C₂²	semidirect
81. #72264285	C₂²	semidirect
82. #72264273	C₂	semidirect
86. C₂×#6468700	C₂²	semidirect
87. #72264239	C₂²	semidirect
88. #72264235	C₂²	semidirect
89. #72264232	C₂²	semidirect
92. #72264221	C₂²	semidirect
93. #72264218	C₂²	semidirect
94. #72264213	C₂²	semidirect
95. #72264209	C₂²	semidirect
96. #72264205	C₂²	semidirect
97. C₂×#6453737	C₂²	semidirect
98. #72264190	C₂²	semidirect
99. D₄×#34736	C₂	semidirect
108. #72264106	C₂²	semidirect
109. #72264101	C₂²	semidirect
110. #72264084	C₂²	semidirect
123. C₂³×#550	D₄	semidirect
124. C₂³×#547	D₄	semidirect
126. C₂³×D₄×Q₈	D₄	semidirect
127. C₂³×D₄²	D₄	semidirect
130. C₂³×#532	D₄	semidirect
133. C₂⁴×C₄×D₄	D₄	semidirect
134. C₂⁴×C₄×D₄	D₄	semidirect
137. C₂³×#442	D₄	semidirect
139. C₂²×#2366	D₄	semidirect
140. C₂²×#2361	D₄	semidirect
142. C₂²×D₄×C₄⋊C₄	D₄	semidirect
144. C₂²×D₄×C₂²⋊C₄	D₄	semidirect
146. C₂²×C₄×#127	D₄	semidirect
147. C₂²×C₄×#121	D₄	semidirect
150. C₂²×C₄²×D₄	D₄	semidirect
158. C₂²×#1879	D₄	semidirect
160. C₂²×#1864	D₄	semidirect
162. C₂×#20739	D₄	semidirect
167. C₂²×#1762	D₄	semidirect
169. #759738	D₄	semidirect
175. #614416	D₄	semidirect
176. #613956	D₄	semidirect
177. #613651	D₄	semidirect
178. #613649	D₄	semidirect
186. #611060	D₄	semidirect
187. #608662	D₄	semidirect
188. #608659	D₄	semidirect
189. #607927	D₄	semidirect
195. #520487	D₄	semidirect
196. D₄×#380	D₄	semidirect
204. #514119	D₄	semidirect
206. C₄×D₄×C₂²⋊C₄	D₄	semidirect
209. #392266	D₄	semidirect
214. #392160	D₄	semidirect
236. #354808	D₄	semidirect
316. C₂³×C₄×D₄	C₂×D₄	semidirect
329. C₂²×#432	C₂×D₄	semidirect
330. C₂³×#106	C₂×D₄	semidirect
334. C₂³×#102	C₂×D₄	semidirect
337. C₂³×#97	C₂×D₄	semidirect
349. C₂²×#390	C₂×D₄	semidirect
352. C₂²×#389	C₂×D₄	semidirect
354. C₂×#2283	C₂×D₄	semidirect
366. C₂²×C₄×C₄⋊C₄	C₂×D₄	semidirect
374. C₂×#1823	C₂×D₄	semidirect
375. C₂×#1823	C₂×D₄	semidirect
376. C₂×#1817	C₂×D₄	semidirect
377. C₂×#1797	C₂×D₄	semidirect
385. C₂×#1749	C₂×D₄	semidirect
386. C₂²×#340	C₂×D₄	semidirect
387. C₂²×#340	C₂×D₄	semidirect
388. C₂²×#336	C₂×D₄	semidirect
401. #14685	C₂×D₄	semidirect
403. #14682	C₂×D₄	semidirect
422. C₄×#380	C₂×D₄	semidirect
428. #10730	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72265022	2
#72265005	2
#72264993	2
#72264938	2
#72264912	2
#72264872	2
#72264856	2
#72264838	2
#72264811	2
#72264789	2
#72264683	2
#72264665	2
#72264643	2
#72264610	2
#72264593	2
#72264551	2
#72264461	2
#72264417	2
#72264395	2
#72264346	2
#72264322	2
#72264273	2
D₄×#34736	2