Subgroups — #72338255

Order 2048.

At least 10127 conjugacy classes of subgroups; only the 1756 normal subgroups are shown.

The subgroup lattice has 843 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338254	C₂	1	8	yes	maximal, complemented
2	#72338253	C₂	1	8	yes	maximal, complemented
3	#72338239	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338224	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338216	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338215	C₂	1	1	yes	maximal, characteristic, complemented
7	#72316811	C₂	1	1	yes	maximal, characteristic, complemented
8	#72316683	C₂	1	1	yes	maximal, characteristic, complemented
9	#72310294	C₂	1	1	yes	maximal, characteristic, complemented
10	#72282687	C₂	1	1	yes	maximal, characteristic, complemented
11	#72280381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10576116	C₂	1	1	yes	maximal, characteristic, complemented
13	#72280259	C₂	1	1	yes	maximal, characteristic, complemented
14	#72279493	C₂	1	1	yes	maximal, characteristic, complemented
15	#72257774	C₂	1	1	yes	maximal, characteristic, complemented
16	#72226741	C₂	1	1	yes	maximal, characteristic, complemented
17	#72214607	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#62812	C₂²	1	1	yes	characteristic
19	C₂²×#3498	C₂²	1	1	yes	characteristic
20	#10576116	C₂²	1	8	yes	—
21	C₂²×#3151	C₂²	1	1	yes	characteristic
22	C₂×#60561	C₂²	1	1	yes	characteristic
23	C₂×#60561	C₂²	1	1	yes	characteristic, complemented
24	C₂×#60415	C₂²	1	1	yes	characteristic
25	C₂²×#3038	C₂²	1	1	yes	characteristic
26	C₂²×#3038	C₂²	1	1	yes	characteristic, complemented
27	C₂×#60144	C₂²	1	1	yes	characteristic
28	C₂×C₄×#575	C₂²	1	1	yes	characteristic
29	#7628157	C₂²	1	1	yes	characteristic, complemented
30	#7628157	C₂²	1	1	yes	characteristic, complemented
31	#6512748	C₂²	1	4	yes	complemented
32	#6512747	C₂²	1	4	yes	complemented
33	#6374554	C₂²	1	1	yes	characteristic
34	#6374537	C₂²	1	1	yes	characteristic, complemented
35	#6374304	C₂²	1	1	yes	characteristic, complemented
36	#6374304	C₂²	1	1	yes	characteristic, complemented
37	#6372358	C₂²	1	1	yes	characteristic, complemented
38	#6370997	C₂²	1	1	yes	characteristic, complemented
39	#6370997	C₂²	1	1	yes	characteristic, complemented
40	#6346498	C₂²	1	4	yes	complemented
41	#6346497	C₂²	1	4	yes	complemented
42	#6344036	C₂²	1	1	yes	characteristic
43	C₂×#17745	C₂²	1	1	yes	characteristic, complemented
44	C₂×#17741	C₂²	1	1	yes	characteristic, complemented
45	#6343377	C₂²	1	1	yes	characteristic
46	#6343377	C₂²	1	1	yes	characteristic, complemented
47	#6343377	C₂²	1	1	yes	characteristic, complemented
48	#6342924	C₂²	1	1	yes	characteristic, complemented
49	C₂×#17451	C₂²	1	1	yes	characteristic, complemented
50	C₂×#17451	C₂²	1	1	yes	characteristic, complemented
51	#6342561	C₂²	1	1	yes	characteristic, complemented
52	#414624	C₂²	1	4	yes	complemented
53	#411628	C₂²	1	4	yes	complemented
54	#353776	C₂²	1	1	yes	characteristic, complemented
55	#235218	C₂²	1	4	yes	complemented
56	#235216	C₂²	1	4	yes	complemented
57	#233944	C₂²	1	4	yes	complemented
58	#233936	C₂²	1	4	yes	complemented
59	#233082	C₂²	1	4	yes	complemented
60	#233080	C₂²	1	4	yes	complemented
61	#195379	C₂²	1	4	yes	complemented
62	#195378	C₂²	1	4	yes	complemented
63	#186273	C₂²	1	8	yes	complemented
64	#186271	C₂²	1	8	yes	complemented
65	#181791	C₂²	1	1	yes	characteristic, complemented
66	#181771	C₂²	1	1	yes	characteristic, complemented
67	#181433	C₂²	1	1	yes	characteristic, complemented
68	#181175	C₂²	1	1	yes	characteristic, complemented
69	#181055	C₂²	1	1	yes	characteristic, complemented
70	#114129	C₂²	1	8	yes	complemented
71	#111814	C₂²	1	8	yes	complemented
72	#111803	C₂²	1	8	yes	complemented
73	#111577	C₂²	1	8	yes	complemented
74	#107922	C₂²	1	8	yes	complemented
75	C₂²×#575	D₄	1	1	yes	characteristic
76	#62812	D₄	1	4	yes	complemented
77	#62812	C₂³	1	4	yes	—
78	C₂×#3498	D₄	1	4	yes	complemented
79	C₂×#3498	C₂³	1	4	yes	—
80	C₂×#3497	D₄	1	2	yes	complemented
81	C₂×#3496	D₄	1	2	yes	complemented
82	C₂²×#550	D₄	1	2	yes	complemented
83	C₂²×D₄²	D₄	1	2	yes	complemented
84	C₂²×#532	C₂³	1	1	yes	characteristic
85	C₂²×#532	C₂³	1	1	yes	characteristic
86	C₂³×#127	C₂³	1	1	yes	characteristic
87	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
88	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
89	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
90	C₂×#3151	D₄	1	4	yes	complemented
91	C₂×#3151	C₂³	1	4	yes	—
92	C₂²×#493	D₄	1	2	yes	complemented
93	C₂²×#492	D₄	1	2	yes	complemented
94	C₂×#3112	D₄	1	2	yes	—
95	C₂×#3109	D₄	1	2	yes	—
96	C₂×#3103	C₂³	1	2	yes	—
97	C₂×#3103	C₂³	1	2	yes	complemented
98	C₂×#3100	C₂³	1	2	yes	—
99	C₂×#3100	C₂³	1	2	yes	complemented
100	C₂×#3094	D₄	1	2	yes	—
101	#60415	D₄	1	4	yes	complemented
102	#60415	C₂³	1	4	yes	—
103	C₂×#3038	D₄	1	4	yes	complemented
104	C₂×#3038	C₂³	1	4	yes	—
105	C₂×#3037	D₄	1	2	yes	complemented
106	C₂×#3036	D₄	1	2	yes	complemented
107	C₂²×#460	D₄	1	2	yes	complemented
108	C₂²×#460	C₂³	1	2	yes	complemented
109	C₂²×#459	D₄	1	2	yes	complemented
110	C₂²×#459	C₂³	1	2	yes	complemented
111	C₂×#3006	D₄	1	2	yes	—
112	C₄×#575	D₄	1	4	yes	—
113	C₄×#575	C₂³	1	4	yes	—
114	#60144	D₄	1	4	yes	complemented
115	#60144	C₂³	1	4	yes	—
116	C₂×#2932	D₄	1	4	yes	complemented
117	C₂×#2920	C₂³	1	1	yes	characteristic
118	C₂×#2920	C₂³	1	1	yes	characteristic
119	C₂×#2920	C₂³	1	1	yes	characteristic
120	C₂×#2920	C₂³	1	1	yes	characteristic
121	C₂×#2911	D₄	1	1	yes	characteristic
122	C₂²×#423	C₂³	1	1	yes	characteristic
123	C₂²×#423	C₂³	1	1	yes	characteristic
124	C₂×#2896	D₄	1	1	yes	characteristic
125	C₂×#2896	D₄	1	1	yes	characteristic
126	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
127	#34952	C₂³	1	2	yes	complemented
128	#34952	C₂³	1	2	yes	complemented
129	#34935	C₂³	1	2	yes	complemented
130	#34935	C₂³	1	2	yes	complemented
131	#34012	C₂³	1	1	yes	characteristic
132	#34012	C₂³	1	1	yes	characteristic
133	#21891	D₄	1	4	yes	complemented
134	#21884	C₂³	1	4	yes	—
135	#21847	C₂³	1	4	yes	complemented
136	#21803	C₂³	1	4	yes	complemented
137	#21803	C₂³	1	4	yes	complemented
138	#21313	D₄	1	2	yes	complemented
139	#21303	C₂³	1	2	yes	complemented
140	#21260	D₄	1	2	yes	complemented
141	#21190	C₂³	1	2	yes	complemented
142	#20654	C₂³	1	4	yes	complemented
143	#20654	C₂³	1	4	yes	complemented
144	#17704	C₂³	1	4	yes	—
145	C₂×#1547	C₂³	1	4	yes	complemented
146	C₂×#1545	C₂³	1	4	yes	complemented
147	#17574	C₂³	1	4	yes	—
148	#17574	C₂³	1	4	yes	complemented
149	#17574	C₂³	1	4	yes	complemented
150	#17561	D₄	1	4	yes	complemented
151	#17544	D₄	1	4	yes	complemented
152	C₂×#1487	C₂³	1	2	yes	complemented
153	C₂×#1486	C₂³	1	2	yes	complemented
154	#17437	C₂³	1	4	yes	complemented
155	C₂×#1477	C₂³	1	4	yes	complemented
156	#17349	C₂³	1	4	yes	complemented
157	#10837	C₂³	1	4	yes	complemented
158	#8079	C₂³	1	4	yes	complemented
159	#8045	C₂³	1	4	yes	complemented
160	#7957	C₂³	1	4	yes	complemented
161	#7918	C₂³	1	4	yes	complemented
162	#7873	C₂³	1	4	yes	complemented
163	C₂³×#41	C₂×D₄	1	1	yes	characteristic
164	C₂³×#41	C₂×D₄	1	1	yes	characteristic
165	C₂³×#41	C₂×D₄	1	1	yes	characteristic
166	C₂×#575	C₂×D₄	1	4	yes	—
167	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
168	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
169	#3497	C₂×D₄	1	8	yes	—
170	#3496	C₂×D₄	1	8	yes	—
171	C₂×#550	C₂×D₄	1	8	yes	—
172	C₂×D₄²	C₂×D₄	1	8	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	C₂×#532	C₂×D₄	1	2	yes	—
177	C₂×#532	C₂×D₄	1	2	yes	—
178	C₂×#532	C₂×D₄	1	2	yes	—
179	C₂×#532	C₂×D₄	1	2	yes	—
180	C₂×#532	C₂×D₄	1	2	yes	—
181	C₂×#532	C₂×D₄	1	2	yes	—
182	C₂×#532	C₂×D₄	1	2	yes	—
183	C₂×#532	C₂×D₄	1	2	yes	—
184	C₂×#532	C₂×D₄	1	2	yes	—
185	C₂×#532	C₂×D₄	1	2	yes	—
186	C₂×#532	C₂×D₄	1	2	yes	—
187	C₂×#532	#41	1	2	yes	—
188	C₂×#532	#41	1	2	yes	—
189	C₂×#532	C₂⁴	1	2	yes	—
190	C₂×#532	C₂⁴	1	2	yes	—
191	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
193	C₂²×#127	C₂×D₄	1	2	yes	—
194	C₂²×#127	C₂×D₄	1	1	yes	characteristic
195	C₂²×#127	C₂×D₄	1	2	yes	—
196	C₂²×#127	C₂×D₄	1	2	yes	—
197	C₂²×#127	C₂×D₄	1	2	yes	—
198	C₂²×#127	C₂×D₄	1	2	yes	—
199	C₂²×#127	C₂×D₄	1	2	yes	—
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#127	C₂⁴	1	2	yes	—
202	C₂²×#121	C₂×D₄	1	2	yes	—
203	C₂×C₄×#41	C₂×D₄	1	2	yes	—
204	C₂×C₄×#41	C₂×D₄	1	2	yes	—
205	C₂×C₄×#41	C₂×D₄	1	2	yes	—
206	C₂×C₄×#41	C₂×D₄	1	2	yes	—
207	C₂×C₄×#41	C₂×D₄	1	2	yes	—
208	C₂×C₄×#41	C₂×D₄	1	2	yes	—
209	C₂×C₄×#41	C₂⁴	1	2	yes	—
210	C₂×C₄×#41	C₂⁴	1	2	yes	—
211	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×Q₈	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
222	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
224	C₂²×#117	C₂×D₄	1	1	yes	characteristic
225	C₂²×#117	C₂×D₄	1	1	yes	characteristic
226	C₂²×#117	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
228	C₂×#493	C₂×D₄	1	8	yes	—
229	C₂×#492	C₂×D₄	1	8	yes	—
230	C₂×#481	C₂×D₄	1	4	yes	—
231	C₂×#480	C₂×D₄	1	4	yes	—
232	#3037	C₂×D₄	1	8	yes	—
233	#3036	C₂×D₄	1	8	yes	—
234	C₂×#460	C₂×D₄	1	8	yes	—
235	C₂×#459	C₂×D₄	1	8	yes	—
236	C₂×#448	C₂×D₄	1	4	yes	—
237	C₂×#447	C₂×D₄	1	4	yes	—
238	#2932	C₂×D₄	1	16	yes	—
239	#2920	C₂×D₄	1	2	yes	—
240	#2920	C₂×D₄	1	2	yes	—
241	C₂×#432	C₂×D₄	1	2	yes	—
242	C₂×#431	C₂⁴	1	2	yes	—
243	C₂×#431	C₂⁴	1	2	yes	—
244	C₂×#431	C₂⁴	1	2	yes	—
245	#2911	C₂×D₄	1	4	yes	—
246	C₂×#423	C₂×D₄	1	2	yes	—
247	C₂×#423	C₂×D₄	1	2	yes	—
248	C₂×#423	C₂×D₄	1	2	yes	—
249	C₂×#423	C₂×D₄	1	2	yes	—
250	C₂×#423	C₂×D₄	1	2	yes	—
251	C₂×#423	C₂×D₄	1	2	yes	—
252	C₂×#423	C₂×D₄	1	2	yes	—
253	C₂×#423	C₂⁴	1	2	yes	—
254	C₂×#423	C₂⁴	1	2	yes	—
255	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
256	C₂²×C₄⋊C₈	C₂⁴	1	2	yes	—
257	#2896	C₂×D₄	1	4	yes	—
258	#2896	C₂×D₄	1	4	yes	—
259	C₂×#407	C₂×D₄	1	2	yes	—
260	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
261	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
262	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
263	C₂×C₄×M₁₆	C₂⁴	1	2	yes	—
264	C₂²×#97	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₈	C₂×D₄	1	2	yes	—
266	#2285	C₂⁴	1	2	yes	—
267	#2285	C₂⁴	1	2	yes	—
268	#2283	C₂×D₄	1	2	yes	—
269	#2283	C₂×D₄	1	2	yes	—
270	C₄×#117	C₂×D₄	1	2	yes	—
271	C₄×#117	C₂×D₄	1	2	yes	—
272	#1988	C₂×D₄	1	8	yes	—
273	#1982	C₂×D₄	1	8	yes	—
274	#1502	C₂×D₄	1	16	yes	—
275	C₂²×#41	#120	1	2	yes	—
276	C₂²×#41	#120	1	2	yes	—
277	C₂²×#41	C₂²×D₄	1	2	yes	—
278	C₂²×#41	C₂²×D₄	1	2	yes	—
279	C₂³×Q₈	#120	1	1	yes	characteristic
280	C₂³×Q₈	#120	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
282	C₂³×D₄	#120	1	1	yes	characteristic
283	C₂³×D₄	#120	1	1	yes	characteristic
284	C₂³×D₄	#120	1	2	yes	—
285	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
286	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
288	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
289	#575	AGL(1,ℤ/8)	1	16	yes	complemented
290	C₂²×M₁₆	#120	1	2	yes	—
291	C₂²×M₁₆	#120	1	2	yes	—
292	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
293	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
294	C₂³×C₈	#120	1	2	yes	—
295	C₂³×C₈	#120	1	2	yes	—
296	#532	#120	1	4	yes	—
297	#532	#120	1	4	yes	—
298	#532	#120	1	4	yes	—
299	#532	#120	1	4	yes	—
300	#532	#120	1	4	yes	—
301	#532	#120	1	4	yes	—
302	#532	#121	1	4	yes	—
303	#532	#121	1	4	yes	—
304	#532	#121	1	4	yes	—
305	#532	#121	1	4	yes	—
306	#532	#121	1	4	yes	—
307	#532	#121	1	4	yes	—
308	#532	#127	1	4	yes	—
309	#532	#127	1	4	yes	—
310	#532	C₂²×D₄	1	4	yes	—
311	#532	C₂²×D₄	1	4	yes	—
312	#532	C₂²×D₄	1	4	yes	—
313	#532	C₂²×D₄	1	4	yes	—
314	#532	C₂²×D₄	1	4	yes	—
315	#532	C₂×#41	1	4	yes	—
316	C₂×C₄⋊Q₈	#120	1	2	yes	—
317	C₂×C₄⋊Q₈	#120	1	2	yes	—
318	C₂×C₄⋊Q₈	#120	1	2	yes	—
319	C₂×C₄⋊Q₈	#121	1	2	yes	—
320	C₂×C₄⋊Q₈	#121	1	2	yes	—
321	C₂×C₄⋊Q₈	#127	1	2	yes	—
322	C₂×C₄⋊Q₈	#127	1	2	yes	—
323	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
324	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
325	C₂×#127	#120	1	4	yes	—
326	C₂×#127	#120	1	4	yes	—
327	C₂×#127	#120	1	2	yes	—
328	C₂×#127	#120	1	2	yes	—
329	C₂×#127	#120	1	4	yes	—
330	C₂×#127	#120	1	4	yes	—
331	C₂×#127	#120	1	2	yes	—
332	C₂×#127	#121	1	2	yes	—
333	C₂×#127	#121	1	2	yes	—
334	C₂×#127	#127	1	2	yes	—
335	C₂×#127	#127	1	2	yes	—
336	C₂×#127	C₂²×D₄	1	4	yes	—
337	C₂×#127	C₂²×D₄	1	2	yes	—
338	C₂×#127	C₂²×D₄	1	4	yes	—
339	C₂×#127	C₂²×D₄	1	4	yes	—
340	C₂×#127	C₂²×D₄	1	2	yes	—
341	C₂×#121	#120	1	4	yes	—
342	C₂×#121	#120	1	4	yes	—
343	C₂×#121	#120	1	4	yes	—
344	C₂×#121	#121	1	4	yes	—
345	C₂×#121	#121	1	4	yes	—
346	C₂×#121	C₂²×D₄	1	4	yes	—
347	C₂×C₄×Q₈	#120	1	2	yes	—
348	C₂×C₄×Q₈	#120	1	2	yes	—
349	C₂×C₄×Q₈	#120	1	2	yes	—
350	C₂×C₄×Q₈	#120	1	2	yes	—
351	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
352	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
353	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
354	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
355	C₂×C₄×D₄	#120	1	2	yes	—
356	C₂×C₄×D₄	#120	1	2	yes	—
357	C₂×C₄×D₄	#120	1	2	yes	—
358	C₂×C₄×D₄	#120	1	2	yes	—
359	C₂×C₄×D₄	#120	1	4	yes	—
360	C₂×C₄×D₄	#120	1	4	yes	—
361	C₂×C₄×D₄	#120	1	4	yes	—
362	C₂×C₄×D₄	#121	1	4	yes	—
363	C₂×C₄×D₄	#121	1	4	yes	—
364	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
365	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
366	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
367	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
368	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
369	C₂×#117	#120	1	2	yes	—
370	C₂×#117	#120	1	2	yes	—
371	C₂×#117	C₂²×D₄	1	2	yes	—
372	C₂×#117	C₂²×D₄	1	2	yes	—
373	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
377	C₂²×C₄⋊C₄	#120	1	2	yes	—
378	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
382	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
385	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
391	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
392	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
393	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
394	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
399	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
400	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
406	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
408	#431	C₂²×D₄	1	4	yes	—
409	#423	#120	1	4	yes	—
410	#423	#120	1	4	yes	—
411	#423	C₂²×D₄	1	4	yes	—
412	#423	C₂²×D₄	1	4	yes	—
413	C₂×C₄⋊C₈	#120	1	4	yes	—
414	C₂×C₄⋊C₈	#120	1	4	yes	—
415	C₂×C₄⋊C₈	C₂²×D₄	1	4	yes	—
416	C₂×C₄⋊C₈	C₂²×D₄	1	4	yes	—
417	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
418	C₂×#97	#120	1	4	yes	—
419	C₂×#97	C₂²×D₄	1	4	yes	—
420	C₂×C₄×C₈	#120	1	4	yes	—
421	C₂×C₄×C₈	C₂²×D₄	1	4	yes	—
422	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
423	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
424	C₂⁵	D₄²	1	1	yes	characteristic
425	C₂×#41	C₂×AGL(1,ℤ/8)	1	8	yes	—
426	C₂×#41	C₂×AGL(1,ℤ/8)	1	8	yes	—
427	C₂²×Q₈	C₂×#120	1	2	yes	—
428	C₂²×Q₈	C₂×#120	1	2	yes	—
429	C₂²×D₄	#392	1	4	yes	—
430	C₂²×D₄	#392	1	4	yes	—
431	C₂²×D₄	C₂×#120	1	2	yes	—
432	C₂²×D₄	C₂×#120	1	2	yes	—
433	C₂²×D₄	C₂×#120	1	4	yes	—
434	C₂³×C₄	C₂×#120	1	1	yes	characteristic
435	C₂³×C₄	C₂×#120	1	1	yes	characteristic
436	C₂³×C₄	C₂×#120	1	1	yes	characteristic
437	C₂³×C₄	C₂×#120	1	1	yes	characteristic
438	C₂³×C₄	C₂×#120	1	1	yes	characteristic
439	C₂³×C₄	C₂×#120	1	1	yes	characteristic
440	C₂³×C₄	C₂×#120	1	1	yes	characteristic
441	C₂³×C₄	C₂×#120	1	1	yes	characteristic
442	C₂³×C₄	C₂×#120	1	1	yes	characteristic
443	C₂³×C₄	C₂×#120	1	1	yes	characteristic
444	C₂³×C₄	C₂×#121	1	1	yes	characteristic
445	C₂³×C₄	C₂×#121	1	1	yes	characteristic
446	C₂³×C₄	#534	1	1	yes	characteristic
447	C₂³×C₄	#534	1	1	yes	characteristic
448	C₂³×C₄	#534	1	1	yes	characteristic
449	C₂³×C₄	#534	1	1	yes	characteristic
450	C₂³×C₄	#535	1	1	yes	characteristic
451	C₂³×C₄	#535	1	1	yes	characteristic
452	C₂³×C₄	D₄²	1	1	yes	characteristic
453	C₂³×C₄	D₄²	1	1	yes	characteristic
454	C₂³×C₄	D₄²	1	1	yes	characteristic
455	C₂³×C₄	D₄²	1	1	yes	characteristic
456	C₂³×C₄	D₄²	1	1	yes	characteristic
457	C₂³×C₄	D₄²	1	1	yes	characteristic
458	C₂³×C₄	D₄²	1	1	yes	characteristic
459	C₂³×C₄	D₄²	1	1	yes	characteristic
460	C₂³×C₄	D₄²	1	1	yes	characteristic
461	C₂³×C₄	D₄²	1	1	yes	characteristic
462	C₂³×C₄	D₄²	1	1	yes	characteristic
463	C₂³×C₄	D₄²	1	1	yes	characteristic
464	C₂³×C₄	D₄²	1	1	yes	characteristic
465	C₂³×C₄	D₄²	1	1	yes	characteristic
466	C₂³×C₄	D₄²	1	1	yes	characteristic
467	C₂³×C₄	D₄²	1	1	yes	characteristic
468	C₂³×C₄	D₄²	1	1	yes	characteristic
469	C₂³×C₄	#546	1	1	yes	characteristic
470	C₂³×C₄	#546	1	1	yes	characteristic
471	C₂³×C₄	#546	1	1	yes	characteristic
472	C₂³×C₄	#546	1	1	yes	characteristic
473	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
474	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
475	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×M₁₆	C₂×AGL(1,ℤ/8)	1	8	yes	—
477	C₂²×C₈	C₂×#120	1	4	yes	—
478	C₂²×C₈	C₂×#120	1	4	yes	—
479	C₄⋊Q₈	#392	1	4	yes	—
480	C₄⋊Q₈	#392	1	4	yes	—
481	C₄⋊Q₈	C₂×#120	1	4	yes	—
482	C₄⋊Q₈	C₂×#121	1	4	yes	—
483	C₄⋊Q₈	C₂×#127	1	4	yes	—
484	#127	#392	1	4	yes	—
485	#127	#392	1	4	yes	—
486	#127	C₂×#120	1	8	yes	—
487	#127	C₂×#120	1	4	yes	—
488	#127	C₂×#121	1	4	yes	—
489	#127	C₂×#127	1	4	yes	—
490	#121	#392	1	8	yes	—
491	#121	#392	1	8	yes	—
492	#121	C₂×#120	1	8	yes	—
493	#121	C₂×#121	1	8	yes	—
494	C₄×D₄	#392	1	8	yes	—
495	C₄×D₄	#392	1	8	yes	—
496	C₄×D₄	C₂×#120	1	8	yes	—
497	C₄×D₄	C₂×#121	1	8	yes	—
498	C₂×C₄⋊C₄	#392	1	4	yes	—
499	C₂×C₄⋊C₄	#392	1	4	yes	—
500	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
501	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
502	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
503	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
504	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
505	C₂×C₄²	C₂×#120	1	1	yes	characteristic
506	C₂×C₄²	C₂×#120	1	1	yes	characteristic
507	C₂×C₄²	C₂×#120	1	1	yes	characteristic
508	C₂×C₄²	C₂×#120	1	1	yes	characteristic
509	C₂×C₄²	C₂×#120	1	1	yes	characteristic
510	C₂×C₄²	C₂×#120	1	1	yes	characteristic
511	C₂×C₄²	C₂×#120	1	1	yes	characteristic
512	C₂×C₄²	C₂×#120	1	1	yes	characteristic
513	C₂×C₄²	C₂×#120	1	1	yes	characteristic
514	C₂×C₄²	C₂×#120	1	1	yes	characteristic
515	C₂×C₄²	C₂×#120	1	1	yes	characteristic
516	C₂×C₄²	C₂×#120	1	1	yes	characteristic
517	C₂×C₄²	C₂×#120	1	1	yes	characteristic
518	C₂×C₄²	C₂×#120	1	1	yes	characteristic
519	C₂×C₄²	C₂×#120	1	1	yes	characteristic
520	C₂×C₄²	C₂×#120	1	1	yes	characteristic
521	C₂×C₄²	C₂×#120	1	1	yes	characteristic
522	C₂×C₄²	C₂×#120	1	1	yes	characteristic
523	C₂×C₄²	C₂×#120	1	1	yes	characteristic
524	C₂×C₄²	C₂×#120	1	1	yes	characteristic
525	C₂×C₄²	C₂×#120	1	1	yes	characteristic
526	C₂×C₄²	C₂×#120	1	1	yes	characteristic
527	C₂×C₄²	C₂×#120	1	1	yes	characteristic
528	C₂×C₄²	C₂×#120	1	1	yes	characteristic
529	C₂×C₄²	C₂×#120	1	1	yes	characteristic
530	C₂×C₄²	C₂×#120	1	1	yes	characteristic
531	C₂×C₄²	C₂×#121	1	1	yes	characteristic
532	C₂×C₄²	C₂×#121	1	1	yes	characteristic
533	C₂×C₄²	C₂×#121	1	1	yes	characteristic
534	C₂×C₄²	C₂×#121	1	1	yes	characteristic
535	C₂×C₄²	C₂×#121	1	1	yes	characteristic
536	C₂×C₄²	C₂×#121	1	1	yes	characteristic
537	C₂×C₄²	C₂×#121	1	1	yes	characteristic
538	C₂×C₄²	C₂×#121	1	1	yes	characteristic
539	C₂×C₄²	C₂×#121	1	1	yes	characteristic
540	C₂×C₄²	C₂×#121	1	1	yes	characteristic
541	C₂×C₄²	C₂×#127	1	1	yes	characteristic
542	C₂×C₄²	C₂×#127	1	1	yes	characteristic
543	C₂×C₄²	C₂×#127	1	1	yes	characteristic
544	C₂×C₄²	C₂×#127	1	1	yes	characteristic
545	C₂×C₄²	#534	1	1	yes	characteristic
546	C₂×C₄²	#534	1	1	yes	characteristic
547	C₂×C₄²	#534	1	1	yes	characteristic
548	C₂×C₄²	#534	1	1	yes	characteristic
549	C₂×C₄²	#534	1	1	yes	characteristic
550	C₂×C₄²	#534	1	1	yes	characteristic
551	C₂×C₄²	#534	1	1	yes	characteristic
552	C₂×C₄²	#534	1	1	yes	characteristic
553	C₂×C₄²	#534	1	1	yes	characteristic
554	C₂×C₄²	#534	1	1	yes	characteristic
555	C₂×C₄²	#534	1	1	yes	characteristic
556	C₂×C₄²	#534	1	1	yes	characteristic
557	C₂×C₄²	#535	1	1	yes	characteristic
558	C₂×C₄²	#535	1	1	yes	characteristic
559	C₂×C₄²	#535	1	1	yes	characteristic
560	C₂×C₄²	#535	1	1	yes	characteristic
561	C₂×C₄²	#535	1	1	yes	characteristic
562	C₂×C₄²	#535	1	1	yes	characteristic
563	C₂×C₄²	D₄²	1	1	yes	characteristic
564	C₂×C₄²	D₄²	1	1	yes	characteristic
565	C₂×C₄²	D₄²	1	1	yes	characteristic
566	C₂×C₄²	D₄²	1	1	yes	characteristic
567	C₂×C₄²	D₄²	1	1	yes	characteristic
568	C₂×C₄²	D₄²	1	1	yes	characteristic
569	C₂×C₄²	D₄²	1	1	yes	characteristic
570	C₂×C₄²	D₄²	1	1	yes	characteristic
571	C₂×C₄²	D₄²	1	1	yes	characteristic
572	C₂×C₄²	D₄²	1	1	yes	characteristic
573	C₂×C₄²	D₄²	1	1	yes	characteristic
574	C₂×C₄²	D₄²	1	1	yes	characteristic
575	C₂×C₄²	D₄²	1	1	yes	characteristic
576	C₂×C₄²	D₄²	1	1	yes	characteristic
577	C₂×C₄²	D₄²	1	1	yes	characteristic
578	C₂×C₄²	D₄²	1	1	yes	characteristic
579	C₂×C₄²	D₄²	1	1	yes	characteristic
580	C₂×C₄²	D₄²	1	1	yes	characteristic
581	C₂×C₄²	D₄²	1	1	yes	characteristic
582	C₂×C₄²	D₄²	1	1	yes	characteristic
583	C₂×C₄²	D₄²	1	1	yes	characteristic
584	C₂×C₄²	D₄²	1	1	yes	characteristic
585	C₂×C₄²	D₄²	1	1	yes	characteristic
586	C₂×C₄²	D₄²	1	1	yes	characteristic
587	C₂×C₄²	D₄²	1	1	yes	characteristic
588	C₂×C₄²	D₄²	1	1	yes	characteristic
589	C₂×C₄²	D₄²	1	1	yes	characteristic
590	C₂×C₄²	D₄²	1	1	yes	characteristic
591	C₂×C₄²	D₄²	1	1	yes	characteristic
592	C₂×C₄²	D₄²	1	1	yes	characteristic
593	C₂×C₄²	#546	1	1	yes	characteristic
594	C₂×C₄²	#546	1	1	yes	characteristic
595	C₂×C₄²	#546	1	1	yes	characteristic
596	C₂×C₄²	#546	1	1	yes	characteristic
597	C₂×C₄²	#546	1	1	yes	characteristic
598	C₂×C₄²	#546	1	1	yes	characteristic
599	C₂×C₄²	#546	1	1	yes	characteristic
600	C₂×C₄²	#546	1	1	yes	characteristic
601	C₂×C₄²	#546	1	1	yes	characteristic
602	C₂×C₄²	#546	1	1	yes	characteristic
603	C₂×C₄²	#546	1	1	yes	characteristic
604	C₂×C₄²	#546	1	1	yes	characteristic
605	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
606	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
607	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
608	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
609	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
610	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
611	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
612	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
613	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
614	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₄⋊C₈	C₂×#120	1	8	yes	—
618	C₂⁴	#2403	1	1	yes	characteristic
619	C₂⁴	#2403	1	1	yes	characteristic
620	C₂⁴	#2403	1	1	yes	characteristic
621	C₂⁴	#2403	1	1	yes	characteristic
622	C₂⁴	#2408	1	1	yes	characteristic
623	C₂⁴	#2408	1	1	yes	characteristic
624	C₂⁴	C₂×D₄²	1	1	yes	characteristic
625	C₂×Q₈	#3003	1	4	yes	—
626	C₂×Q₈	#3003	1	4	yes	complemented
627	C₂×D₄	C₂×#392	1	8	yes	—
628	C₂×D₄	#3003	1	4	yes	—
629	C₂×D₄	#3003	1	4	yes	complemented
630	C₂²×C₄	C₂×#392	1	1	yes	characteristic
631	C₂²×C₄	C₂×#392	1	1	yes	characteristic
632	C₂²×C₄	C₂×#392	1	1	yes	characteristic
633	C₂²×C₄	C₂×#392	1	1	yes	characteristic
634	C₂²×C₄	#2403	1	1	yes	characteristic
635	C₂²×C₄	#2403	1	1	yes	characteristic
636	C₂²×C₄	#2403	1	1	yes	characteristic
637	C₂²×C₄	#2403	1	1	yes	characteristic
638	C₂²×C₄	#2403	1	1	yes	characteristic
639	C₂²×C₄	#2403	1	1	yes	characteristic
640	C₂²×C₄	#2403	1	1	yes	characteristic
641	C₂²×C₄	#2403	1	1	yes	characteristic
642	C₂²×C₄	#2403	1	1	yes	characteristic
643	C₂²×C₄	#2403	1	1	yes	characteristic
644	C₂²×C₄	#2403	1	1	yes	characteristic
645	C₂²×C₄	#2403	1	1	yes	characteristic
646	C₂²×C₄	#2403	1	1	yes	characteristic
647	C₂²×C₄	#2403	1	1	yes	characteristic
648	C₂²×C₄	#2403	1	1	yes	characteristic
649	C₂²×C₄	#2403	1	1	yes	characteristic
650	C₂²×C₄	#2403	1	1	yes	characteristic
651	C₂²×C₄	#2403	1	1	yes	characteristic
652	C₂²×C₄	#2403	1	1	yes	characteristic
653	C₂²×C₄	#2403	1	1	yes	characteristic
654	C₂²×C₄	#2408	1	1	yes	characteristic
655	C₂²×C₄	#2408	1	1	yes	characteristic
656	C₂²×C₄	#2408	1	1	yes	characteristic
657	C₂²×C₄	#2408	1	1	yes	characteristic
658	C₂²×C₄	#2408	1	1	yes	characteristic
659	C₂²×C₄	#2408	1	1	yes	characteristic
660	C₂²×C₄	#2408	1	1	yes	characteristic
661	C₂²×C₄	#2408	1	1	yes	characteristic
662	C₂²×C₄	#2408	1	1	yes	characteristic
663	C₂²×C₄	#2408	1	1	yes	characteristic
664	C₂²×C₄	#2410	1	1	yes	characteristic
665	C₂²×C₄	#2410	1	1	yes	characteristic
666	C₂²×C₄	#2410	1	1	yes	characteristic
667	C₂²×C₄	#2410	1	1	yes	characteristic
668	C₂²×C₄	#2410	1	1	yes	characteristic
669	C₂²×C₄	#2410	1	1	yes	characteristic
670	C₂²×C₄	#2410	1	1	yes	characteristic
671	C₂²×C₄	#2410	1	1	yes	characteristic
672	C₂²×C₄	#2410	1	1	yes	characteristic
673	C₂²×C₄	#2410	1	1	yes	characteristic
674	C₂²×C₄	#2410	1	1	yes	characteristic
675	C₂²×C₄	#2410	1	1	yes	characteristic
676	C₂²×C₄	#2410	1	1	yes	characteristic
677	C₂²×C₄	#2410	1	1	yes	characteristic
678	C₂²×C₄	#2410	1	1	yes	characteristic
679	C₂²×C₄	#2410	1	1	yes	characteristic
680	C₂²×C₄	#2433	1	1	yes	characteristic
681	C₂²×C₄	#2433	1	1	yes	characteristic
682	C₂²×C₄	#2433	1	1	yes	characteristic
683	C₂²×C₄	#2433	1	1	yes	characteristic
684	C₂²×C₄	#2433	1	1	yes	characteristic
685	C₂²×C₄	#2433	1	1	yes	characteristic
686	C₂²×C₄	#2433	1	1	yes	characteristic
687	C₂²×C₄	#2433	1	1	yes	characteristic
688	C₂²×C₄	#2613	1	1	yes	characteristic
689	C₂²×C₄	#2613	1	1	yes	characteristic
690	C₂²×C₄	#2613	1	1	yes	characteristic
691	C₂²×C₄	#2613	1	1	yes	characteristic
692	C₂²×C₄	#2846	1	1	yes	characteristic
693	C₂²×C₄	#2846	1	1	yes	characteristic
694	C₂²×C₄	#2846	1	1	yes	characteristic
695	C₂²×C₄	#2846	1	1	yes	characteristic
696	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
697	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
698	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
699	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
700	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
701	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
702	C₂²×C₄	C₂×#534	1	1	yes	characteristic
703	C₂²×C₄	C₂×#534	1	1	yes	characteristic
704	C₂²×C₄	C₂×#535	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
712	C₂²×C₄	C₂×#546	1	1	yes	characteristic
713	C₂²×C₄	C₂×#546	1	1	yes	characteristic
714	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
715	C₂²×C₄	#3585	1	4	yes	—
716	C₂×C₈	#3003	1	8	yes	complemented
717	C₄⋊C₄	C₂×#392	1	8	yes	—
718	C₄²	C₂×#392	1	1	yes	characteristic
719	C₄²	C₂×#392	1	1	yes	characteristic
720	C₄²	C₂×#392	1	1	yes	characteristic
721	C₄²	C₂×#392	1	1	yes	characteristic
722	C₄²	#2403	1	1	yes	characteristic
723	C₄²	#2403	1	1	yes	characteristic
724	C₄²	#2403	1	1	yes	characteristic
725	C₄²	#2403	1	1	yes	characteristic
726	C₄²	#2403	1	1	yes	characteristic
727	C₄²	#2403	1	1	yes	characteristic
728	C₄²	#2403	1	1	yes	characteristic
729	C₄²	#2403	1	1	yes	characteristic
730	C₄²	#2408	1	1	yes	characteristic
731	C₄²	#2408	1	1	yes	characteristic
732	C₄²	#2408	1	1	yes	characteristic
733	C₄²	#2408	1	1	yes	characteristic
734	C₄²	#2410	1	1	yes	characteristic
735	C₄²	#2410	1	1	yes	characteristic
736	C₄²	#2410	1	1	yes	characteristic
737	C₄²	#2410	1	1	yes	characteristic
738	C₄²	#2410	1	1	yes	characteristic
739	C₄²	#2410	1	1	yes	characteristic
740	C₄²	#2410	1	1	yes	characteristic
741	C₄²	#2410	1	1	yes	characteristic
742	C₄²	#2410	1	1	yes	characteristic
743	C₄²	#2410	1	1	yes	characteristic
744	C₄²	#2410	1	1	yes	characteristic
745	C₄²	#2410	1	1	yes	characteristic
746	C₄²	#2410	1	1	yes	characteristic
747	C₄²	#2410	1	1	yes	characteristic
748	C₄²	#2410	1	1	yes	characteristic
749	C₄²	#2410	1	1	yes	characteristic
750	C₄²	#2433	1	1	yes	characteristic
751	C₄²	#2433	1	1	yes	characteristic
752	C₄²	#2433	1	1	yes	characteristic
753	C₄²	#2433	1	1	yes	characteristic
754	C₄²	#2433	1	1	yes	characteristic
755	C₄²	#2433	1	1	yes	characteristic
756	C₄²	#2433	1	1	yes	characteristic
757	C₄²	#2433	1	1	yes	characteristic
758	C₄²	#2613	1	1	yes	characteristic
759	C₄²	#2613	1	1	yes	characteristic
760	C₄²	#2613	1	1	yes	characteristic
761	C₄²	#2613	1	1	yes	characteristic
762	C₄²	#2846	1	1	yes	characteristic
763	C₄²	#2846	1	1	yes	characteristic
764	C₄²	#2846	1	1	yes	characteristic
765	C₄²	#2846	1	1	yes	characteristic
766	C₄²	C₂²×#120	1	1	yes	characteristic
767	C₄²	C₂²×#120	1	1	yes	characteristic
768	C₄²	C₂²×#120	1	1	yes	characteristic
769	C₄²	C₂²×#120	1	1	yes	characteristic
770	C₄²	C₂²×#121	1	1	yes	characteristic
771	C₄²	C₂²×#121	1	1	yes	characteristic
772	C₄²	C₂²×#127	1	1	yes	characteristic
773	C₄²	C₂×#534	1	1	yes	characteristic
774	C₄²	C₂×#534	1	1	yes	characteristic
775	C₄²	C₂×#535	1	1	yes	characteristic
776	C₄²	C₂×D₄²	1	1	yes	characteristic
777	C₄²	C₂×D₄²	1	1	yes	characteristic
778	C₄²	C₂×D₄²	1	1	yes	characteristic
779	C₄²	C₂×D₄²	1	1	yes	characteristic
780	C₄²	C₂×#546	1	1	yes	characteristic
781	C₄²	C₂×#546	1	1	yes	characteristic
782	C₂³	#14715	1	1	yes	characteristic
783	C₂³	#14715	1	1	yes	characteristic
784	C₂³	#14715	1	1	yes	characteristic
785	C₂³	#14715	1	1	yes	characteristic
786	C₂³	C₂×#2403	1	1	yes	characteristic
787	C₂³	C₂×#2403	1	1	yes	characteristic
788	C₂³	C₂×#2408	1	1	yes	characteristic
789	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
790	C₂×C₄	#14715	1	1	yes	characteristic
791	C₂×C₄	#14715	1	1	yes	characteristic
792	C₂×C₄	#14715	1	1	yes	characteristic
793	C₂×C₄	#14715	1	1	yes	characteristic
794	C₂×C₄	#14715	1	1	yes	characteristic
795	C₂×C₄	#14715	1	1	yes	characteristic
796	C₂×C₄	#14715	1	1	yes	characteristic
797	C₂×C₄	#14715	1	1	yes	characteristic
798	C₂×C₄	#14715	1	1	yes	characteristic
799	C₂×C₄	#14715	1	1	yes	characteristic
800	C₂×C₄	#14715	1	1	yes	characteristic
801	C₂×C₄	#14715	1	1	yes	characteristic
802	C₂×C₄	#23882	1	2	yes	—
803	C₂×C₄	#23883	1	2	yes	—
804	C₂×C₄	C₂²×#392	1	1	yes	characteristic
805	C₂×C₄	C₂×#2613	1	1	yes	characteristic
806	C₂×C₄	C₂×#2403	1	1	yes	characteristic
807	C₂×C₄	C₂×#2403	1	1	yes	characteristic
808	C₂×C₄	C₂×#2410	1	1	yes	characteristic
809	C₂×C₄	C₂×#2410	1	1	yes	characteristic
810	C₂×C₄	C₂×#2410	1	1	yes	characteristic
811	C₂×C₄	C₂×#2410	1	1	yes	characteristic
812	C₂×C₄	C₂×#2408	1	1	yes	characteristic
813	C₂×C₄	C₂×#2433	1	1	yes	characteristic
814	C₂×C₄	C₂×#2433	1	1	yes	characteristic
815	C₂×C₄	C₂×#2846	1	1	yes	characteristic
816	C₂×C₄	C₂×#3003	1	2	yes	—
817	C₂×C₄	C₂×#3003	1	2	yes	—
818	C₂×C₄	C₂×#3003	1	2	yes	—
819	C₂×C₄	#60367	1	2	yes	—
820	C₂×C₄	#60367	1	2	yes	—
821	C₂×C₄	#60367	1	2	yes	—
822	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
823	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
824	C₂×C₄	#61155	1	4	yes	—
825	C₂²	#394080	1	2	yes	—
826	C₂²	C₂×#14715	1	1	yes	characteristic
827	C₂²	#6437510	1	2	yes	—
828	C₂²	#6437510	1	2	yes	—
829	C₂²	#6442656	1	2	yes	—
830	C₄	#394080	1	2	yes	—
831	C₄	#394133	1	2	yes	—
832	C₄	C₂×#23882	1	1	yes	characteristic
833	C₄	C₂×#23883	1	1	yes	characteristic
834	C₄	#6437838	1	2	yes	—
835	C₄	#6437838	1	2	yes	—
836	C₄	#6443168	1	2	yes	—
837	C₄	#6628842	1	1	yes	characteristic
838	C₄	#6628847	1	1	yes	characteristic
839	C₂	C₂×#394080	1	1	yes	characteristic
840	C₂	#72231796	1	1	yes	characteristic
841	C₂	C₂×#394133	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14715
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338254	C₂	semidirect
2. #72338253	C₂	semidirect
3. #72338239	C₂	semidirect
4. #72338224	C₂	semidirect
5. #72338216	C₂	semidirect
6. #72338215	C₂	semidirect
7. #72316811	C₂	semidirect
8. #72316683	C₂	semidirect
9. #72310294	C₂	semidirect
10. #72282687	C₂	semidirect
11. #72280381	C₂	semidirect
12. C₂×#10576116	C₂	semidirect
13. #72280259	C₂	semidirect
14. #72279493	C₂	semidirect
15. #72257774	C₂	semidirect
16. #72226741	C₂	semidirect
17. #72214607	C₂	semidirect
23. C₂×#60561	C₂²	semidirect
26. C₂²×#3038	C₂²	semidirect
29. #7628157	C₂²	semidirect
30. #7628157	C₂²	semidirect
31. #6512748	C₂²	semidirect
32. #6512747	C₂²	semidirect
34. #6374537	C₂²	semidirect
35. #6374304	C₂²	semidirect
36. #6374304	C₂²	semidirect
37. #6372358	C₂²	semidirect
38. #6370997	C₂²	semidirect
39. #6370997	C₂²	semidirect
40. #6346498	C₂²	semidirect
41. #6346497	C₂²	semidirect
43. C₂×#17745	C₂²	semidirect
44. C₂×#17741	C₂²	semidirect
46. #6343377	C₂²	semidirect
47. #6343377	C₂²	semidirect
48. #6342924	C₂²	semidirect
49. C₂×#17451	C₂²	semidirect
50. C₂×#17451	C₂²	semidirect
51. #6342561	C₂²	semidirect
52. #414624	C₂²	semidirect
53. #411628	C₂²	semidirect
54. #353776	C₂²	semidirect
55. #235218	C₂²	semidirect
56. #235216	C₂²	semidirect
57. #233944	C₂²	semidirect
58. #233936	C₂²	semidirect
59. #233082	C₂²	semidirect
60. #233080	C₂²	semidirect
61. #195379	C₂²	semidirect
62. #195378	C₂²	semidirect
63. #186273	C₂²	semidirect
64. #186271	C₂²	semidirect
65. #181791	C₂²	semidirect
66. #181771	C₂²	semidirect
67. #181433	C₂²	semidirect
68. #181175	C₂²	semidirect
69. #181055	C₂²	semidirect
70. #114129	C₂²	semidirect
71. #111814	C₂²	semidirect
72. #111803	C₂²	semidirect
73. #111577	C₂²	semidirect
74. #107922	C₂²	semidirect
76. #62812	D₄	semidirect
78. C₂×#3498	D₄	semidirect
80. C₂×#3497	D₄	semidirect
81. C₂×#3496	D₄	semidirect
82. C₂²×#550	D₄	semidirect
83. C₂²×D₄²	D₄	semidirect
90. C₂×#3151	D₄	semidirect
92. C₂²×#493	D₄	semidirect
93. C₂²×#492	D₄	semidirect
97. C₂×#3103	C₂³	semidirect
99. C₂×#3100	C₂³	semidirect
101. #60415	D₄	semidirect
103. C₂×#3038	D₄	semidirect
105. C₂×#3037	D₄	semidirect
106. C₂×#3036	D₄	semidirect
107. C₂²×#460	D₄	semidirect
108. C₂²×#460	C₂³	semidirect
109. C₂²×#459	D₄	semidirect
110. C₂²×#459	C₂³	semidirect
114. #60144	D₄	semidirect
116. C₂×#2932	D₄	semidirect
127. #34952	C₂³	semidirect
128. #34952	C₂³	semidirect
129. #34935	C₂³	semidirect
130. #34935	C₂³	semidirect
133. #21891	D₄	semidirect
135. #21847	C₂³	semidirect
136. #21803	C₂³	semidirect
137. #21803	C₂³	semidirect
138. #21313	D₄	semidirect
139. #21303	C₂³	semidirect
140. #21260	D₄	semidirect
141. #21190	C₂³	semidirect
142. #20654	C₂³	semidirect
143. #20654	C₂³	semidirect
145. C₂×#1547	C₂³	semidirect
146. C₂×#1545	C₂³	semidirect
148. #17574	C₂³	semidirect
149. #17574	C₂³	semidirect
150. #17561	D₄	semidirect
151. #17544	D₄	semidirect
152. C₂×#1487	C₂³	semidirect
153. C₂×#1486	C₂³	semidirect
154. #17437	C₂³	semidirect
155. C₂×#1477	C₂³	semidirect
156. #17349	C₂³	semidirect
157. #10837	C₂³	semidirect
158. #8079	C₂³	semidirect
159. #8045	C₂³	semidirect
160. #7957	C₂³	semidirect
161. #7918	C₂³	semidirect
162. #7873	C₂³	semidirect
289. #575	AGL(1,ℤ/8)	semidirect
626. C₂×Q₈	#3003	semidirect
629. C₂×D₄	#3003	semidirect
716. C₂×C₈	#3003	semidirect

Maximal subgroups

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

subgroup	index
#72338254	2
#72338253	2
#72338239	2
#72338224	2
#72338216	2
#72338215	2
#72316811	2
#72316683	2
#72310294	2
#72282687	2
#72280381	2
C₂×#10576116	2
#72280259	2
#72279493	2
#72257774	2
#72226741	2
#72214607	2