Subgroups — #72266701

Order 4096.

At least 36470 conjugacy classes of subgroups; only the 759 normal subgroups are shown.

The subgroup lattice has 746 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266700	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266697	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266582	C₂	1	1	yes	maximal, characteristic
4	#72266567	C₄	1	1	yes	characteristic, complemented
5	#72266566	C₄	1	1	yes	characteristic, complemented
6	#72266565	C₄	1	1	yes	characteristic, complemented
7	#72266560	C₄	1	1	yes	characteristic, complemented
8	#72266557	C₄	1	1	yes	characteristic, complemented
9	#72266539	C₄	1	1	yes	characteristic, complemented
10	#72266446	C₂	1	1	yes	maximal, characteristic, complemented
11	#72266446	C₂	1	1	yes	maximal, characteristic, complemented
12	#72266352	C₂	1	1	yes	maximal, characteristic, complemented
13	#72266308	C₂	1	1	yes	maximal, characteristic, complemented
14	#72266307	C₂²	1	1	yes	characteristic, complemented
15	#72266279	C₂	1	1	yes	maximal, characteristic, complemented
16	#72266265	C₂²	1	1	yes	characteristic
17	#72266165	C₂	1	1	yes	maximal, characteristic, complemented
18	#72266163	C₂	1	1	yes	maximal, characteristic, complemented
19	#72266043	C₂	1	1	yes	maximal, characteristic, complemented
20	#72266041	C₂²	1	1	yes	characteristic, complemented
21	#72265766	C₂²	1	1	yes	characteristic, complemented
22	#72265766	C₂²	1	1	yes	characteristic, complemented
23	#72263168	C₄	1	1	yes	characteristic, complemented
24	#72262637	C₂²	1	1	yes	characteristic, complemented
25	#72259010	C₂	1	1	yes	maximal, characteristic, complemented
26	#72259008	C₂²	1	1	yes	characteristic, complemented
27	#72258997	C₂	1	1	yes	maximal, characteristic, complemented
28	#72258912	C₂²	1	1	yes	characteristic
29	#72241123	C₂²	1	1	yes	characteristic
30	#72240132	C₂²	1	1	yes	characteristic, complemented
31	#72240132	C₂²	1	1	yes	characteristic, complemented
32	#72240132	C₂²	1	1	yes	characteristic, complemented
33	#72238446	C₂²	1	1	yes	characteristic, complemented
34	#72235991	C₄	1	1	yes	characteristic, complemented
35	#72235847	C₂²	1	1	yes	characteristic, complemented
36	#72235740	C₂	1	1	yes	maximal, characteristic, complemented
37	#72235740	C₂	1	1	yes	maximal, characteristic, complemented
38	#72235718	C₂²	1	1	yes	characteristic, complemented
39	#72235718	C₂²	1	1	yes	characteristic, complemented
40	#72235186	C₂²	1	1	yes	characteristic, complemented
41	#72235186	C₂²	1	1	yes	characteristic, complemented
42	#72235186	C₂²	1	1	yes	characteristic, complemented
43	#72234668	C₂²	1	1	yes	characteristic, complemented
44	#72234668	C₂²	1	1	yes	characteristic, complemented
45	#72234636	C₂²	1	1	yes	characteristic
46	#72234636	C₂²	1	1	yes	characteristic
47	#72232723	C₂²	1	1	yes	characteristic, complemented
48	#72232723	C₂²	1	1	yes	characteristic, complemented
49	#72232723	C₂²	1	1	yes	characteristic, complemented
50	#72232723	C₂²	1	1	yes	characteristic, complemented
51	#72232723	C₂²	1	1	yes	characteristic, complemented
52	#72232723	C₂²	1	1	yes	characteristic, complemented
53	C₂×#139716	C₂²	1	1	yes	characteristic, complemented
54	C₂×#139716	C₂²	1	1	yes	characteristic, complemented
55	C₂×#139716	C₂²	1	1	yes	characteristic, complemented
56	#72219264	C₂²	1	1	yes	characteristic
57	#72219264	C₂²	1	1	yes	characteristic
58	#72219241	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#3532	D₄	1	1	yes	characteristic
60	C₂²×#3532	D₄	1	1	yes	characteristic
61	C₂×#46996	D₄	1	1	yes	characteristic
62	C₂×#46996	D₄	1	1	yes	characteristic
63	C₂×#34980	C₂³	1	1	yes	characteristic
64	C₂×#34980	C₂³	1	1	yes	characteristic
65	C₂²×#2403	D₄	1	1	yes	characteristic
66	#7626202	C₂³	1	1	yes	characteristic
67	C₂²×#2308	D₄	1	1	yes	characteristic
68	C₂×#21746	C₂³	1	1	yes	characteristic
69	C₂×#21746	C₂³	1	1	yes	characteristic
70	C₂×#21746	C₂³	1	1	yes	characteristic
71	#5123779	C₂×C₄	1	1	yes	characteristic
72	#5123779	D₄	1	1	yes	characteristic
73	#5119613	C₂×C₄	1	1	yes	characteristic
74	#5119613	D₄	1	1	yes	characteristic
75	#5063443	C₂×C₄	1	1	yes	characteristic
76	#5063443	D₄	1	1	yes	characteristic
77	#5063442	C₂×C₄	1	1	yes	characteristic
78	#5063442	D₄	1	1	yes	characteristic
79	#5025789	C₂×C₄	1	1	yes	characteristic
80	#5025789	D₄	1	1	yes	characteristic
81	#5025782	C₂×C₄	1	1	yes	characteristic
82	#5025782	D₄	1	1	yes	characteristic
83	#5024691	C₂×C₄	1	1	yes	characteristic
84	#5024691	D₄	1	1	yes	characteristic
85	#5021140	C₂×C₄	1	1	yes	characteristic
86	#5021140	D₄	1	1	yes	characteristic
87	#5021138	C₂×C₄	1	1	yes	characteristic
88	#5021138	D₄	1	1	yes	characteristic
89	#5020751	C₂×C₄	1	1	yes	characteristic
90	#5020751	D₄	1	1	yes	characteristic
91	#4893962	D₄	1	1	yes	characteristic
92	#4866548	D₄	1	1	yes	characteristic
93	#4466055	C₂×C₄	1	1	yes	characteristic
94	#4466055	C₂×C₄	1	1	yes	characteristic
95	#4466055	D₄	1	1	yes	characteristic
96	#4466055	D₄	1	1	yes	characteristic
97	#4464171	D₄	1	1	yes	characteristic
98	#4430405	C₂×C₄	1	1	yes	characteristic
99	#4430405	D₄	1	1	yes	characteristic
100	#4422949	C₂×C₄	1	1	yes	characteristic
101	#4422949	D₄	1	1	yes	characteristic
102	#4420586	C₂×C₄	1	1	yes	characteristic
103	#4420586	D₄	1	1	yes	characteristic
104	#4335643	D₄	1	1	yes	characteristic
105	#4335643	D₄	1	1	yes	characteristic
106	#4335643	D₄	1	1	yes	characteristic
107	#4335643	D₄	1	1	yes	characteristic
108	#2435299	C₂×C₄	1	1	yes	characteristic
109	#2435299	D₄	1	1	yes	characteristic
110	#2356274	C₂×C₄	1	1	yes	characteristic
111	#2356274	D₄	1	1	yes	characteristic
112	#2108865	C₂×C₄	1	1	yes	characteristic
113	#2108865	D₄	1	1	yes	characteristic
114	#2108839	C₂×C₄	1	1	yes	characteristic
115	#2108839	D₄	1	1	yes	characteristic
116	#2039146	C₂×C₄	1	1	yes	characteristic
117	#2039146	C₂×C₄	1	1	yes	characteristic
118	#2039146	D₄	1	1	yes	characteristic
119	#2039146	D₄	1	1	yes	characteristic
120	#763333	D₄	1	1	yes	characteristic
121	#763333	D₄	1	1	yes	characteristic
122	#686187	C₂×C₄	1	1	yes	characteristic
123	#686187	D₄	1	1	yes	characteristic
124	#648360	C₂×C₄	1	1	yes	characteristic
125	#648360	D₄	1	1	yes	characteristic
126	#647656	C₂×C₄	1	1	yes	characteristic
127	#647656	D₄	1	1	yes	characteristic
128	#621871	C₂×C₄	1	1	yes	characteristic
129	#621871	C₂×C₄	1	1	yes	characteristic
130	#621871	D₄	1	1	yes	characteristic
131	#621871	D₄	1	1	yes	characteristic
132	#616969	C₂×C₄	1	1	yes	characteristic
133	#616969	C₂×C₄	1	1	yes	characteristic
134	#616969	D₄	1	1	yes	characteristic
135	#616969	D₄	1	1	yes	characteristic
136	#616961	D₄	1	1	yes	characteristic
137	#616961	C₂³	1	1	yes	characteristic
138	#616961	C₂³	1	1	yes	characteristic
139	#616961	C₂³	1	1	yes	characteristic
140	#616960	D₄	1	1	yes	characteristic
141	#616960	D₄	1	1	yes	characteristic
142	C₂×#15947	C₂³	1	1	yes	characteristic
143	#587363	D₄	1	1	yes	characteristic
144	#587363	D₄	1	1	yes	characteristic
145	#576160	D₄	1	1	yes	characteristic
146	#576160	D₄	1	1	yes	characteristic
147	#556820	D₄	1	1	yes	characteristic
148	#556752	D₄	1	1	yes	characteristic
149	#556752	C₂³	1	1	yes	characteristic
150	#552671	D₄	1	1	yes	characteristic
151	#552670	D₄	1	1	yes	characteristic
152	#552670	D₄	1	1	yes	characteristic
153	#517411	D₄	1	1	yes	characteristic
154	C₂×#8547	C₂³	1	1	yes	characteristic
155	C₂×#8547	C₂³	1	1	yes	characteristic
156	C₂×#8547	C₂³	1	1	yes	characteristic
157	C₂×#8541	C₂³	1	1	yes	characteristic
158	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂²×#551	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×#551	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	C₂²×H(3,𝔽₄)	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×H(3,𝔽₄)	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	C₂²×#560	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×#560	C₂²⋊C₄	1	1	yes	characteristic, complemented
168	C₂²×#535	C₂×D₄	1	1	yes	characteristic
169	C₂²×#535	C₂×D₄	1	1	yes	characteristic
170	C₂²×#535	C₂×D₄	1	1	yes	characteristic
171	C₂²×#534	C₂×D₄	1	1	yes	characteristic
172	C₂²×#534	C₂×D₄	1	1	yes	characteristic
173	C₂²×#534	C₂×D₄	1	1	yes	characteristic
174	C₂²×#534	C₂×D₄	1	1	yes	characteristic
175	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	C₂³×#120	C₂×D₄	1	1	yes	characteristic
178	C₂³×#120	C₂×D₄	1	1	yes	characteristic
179	C₂³×#120	C₂×D₄	1	1	yes	characteristic
180	C₂³×#120	C₂⁴	1	1	yes	characteristic
181	C₂×#2760	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	C₂×#2760	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	C₂×#2760	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	C₂×#2760	C₂²⋊C₄	1	1	yes	characteristic, complemented
185	C₂×#2840	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	C₂×#2840	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	C₂×#2849	C₂²×C₄	1	1	yes	characteristic
188	C₂×#2849	C₂×D₄	1	1	yes	characteristic
189	C₂×#2849	C₂×D₄	1	1	yes	characteristic
190	C₂×#2849	C₂×D₄	1	1	yes	characteristic
191	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
192	C₂×#2846	C₂×D₄	1	1	yes	characteristic
193	C₂×#2846	C₂×D₄	1	1	yes	characteristic
194	C₂×#2846	C₂×D₄	1	1	yes	characteristic
195	C₂×#2404	C₂×D₄	1	1	yes	characteristic
196	C₂×#2404	C₂×D₄	1	1	yes	characteristic
197	C₂×#2404	C₂×D₄	1	1	yes	characteristic
198	C₂×#2404	C₂×D₄	1	1	yes	characteristic
199	C₂×#2404	C₂×D₄	1	1	yes	characteristic
200	C₂×#2404	C₂×D₄	1	1	yes	characteristic
201	C₂×#2403	C₂²⋊C₄	1	1	yes	characteristic, complemented
202	C₂×#2403	C₂²⋊C₄	1	1	yes	characteristic, complemented
203	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
204	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
205	C₂×#2613	C₂×D₄	1	1	yes	characteristic
206	C₂×#2613	C₂×D₄	1	1	yes	characteristic
207	C₂×#2613	C₂×D₄	1	1	yes	characteristic
208	C₂×#2613	C₂×D₄	1	1	yes	characteristic
209	C₂×#2613	C₂×D₄	1	1	yes	characteristic
210	C₂×#2613	C₂×D₄	1	1	yes	characteristic
211	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
212	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
213	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
214	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
215	C₂×#2308	C₂×D₄	1	1	yes	characteristic
216	C₂×#2308	C₂×D₄	1	1	yes	characteristic
217	C₂×#2308	C₂×D₄	1	1	yes	characteristic
218	C₂×#2308	C₂×D₄	1	1	yes	characteristic
219	C₂²×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
220	C₂²×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
221	C₂²×#379	C₂×D₄	1	1	yes	characteristic
222	C₂²×#379	C₂×D₄	1	1	yes	characteristic
223	C₂²×#379	C₂×D₄	1	1	yes	characteristic
224	C₂²×#379	C₂×D₄	1	1	yes	characteristic
225	#17271	C₂²⋊C₄	1	1	yes	characteristic, complemented
226	#17271	C₂²⋊C₄	1	1	yes	characteristic, complemented
227	#17198	C₂²⋊C₄	1	1	yes	characteristic, complemented
228	#17137	C₂²⋊C₄	1	1	yes	characteristic, complemented
229	#17137	C₂²⋊C₄	1	1	yes	characteristic, complemented
230	#17105	C₂²⋊C₄	1	1	yes	characteristic, complemented
231	#17105	C₂²⋊C₄	1	1	yes	characteristic, complemented
232	#17102	C₂²⋊C₄	1	1	yes	characteristic, complemented
233	#16247	C₂²⋊C₄	1	1	yes	characteristic, complemented
234	#16211	C₂²⋊C₄	1	1	yes	characteristic, complemented
235	#15948	C₂²⋊C₄	1	1	yes	characteristic
236	#15948	C₂²⋊C₄	1	1	yes	characteristic
237	#15948	C₂²⋊C₄	1	1	yes	characteristic, complemented
238	#15948	C₂²⋊C₄	1	1	yes	characteristic, complemented
239	#15947	C₂²⋊C₄	1	1	yes	characteristic
240	#15947	C₂²⋊C₄	1	1	yes	characteristic
241	#15947	C₂²⋊C₄	1	1	yes	characteristic, complemented
242	#15947	C₂²⋊C₄	1	1	yes	characteristic, complemented
243	#15947	C₂²×C₄	1	1	yes	characteristic
244	#15947	C₂²×C₄	1	1	yes	characteristic
245	#15947	C₂×D₄	1	1	yes	characteristic
246	#15947	C₂×D₄	1	1	yes	characteristic
247	#15947	C₂×D₄	1	1	yes	characteristic
248	#15947	C₂×D₄	1	1	yes	characteristic
249	#15947	C₂×D₄	1	1	yes	characteristic
250	#15947	C₂×D₄	1	1	yes	characteristic
251	#15930	C₂²⋊C₄	1	1	yes	characteristic, complemented
252	#15930	C₂²⋊C₄	1	1	yes	characteristic, complemented
253	#15930	C₂²⋊C₄	1	1	yes	characteristic, complemented
254	#15930	C₂²⋊C₄	1	1	yes	characteristic, complemented
255	#15636	C₂²⋊C₄	1	1	yes	characteristic, complemented
256	#15636	C₂²⋊C₄	1	1	yes	characteristic, complemented
257	#15561	C₂²⋊C₄	1	1	yes	characteristic, complemented
258	#15561	C₂²⋊C₄	1	1	yes	characteristic, complemented
259	#15561	C₂²⋊C₄	1	1	yes	characteristic, complemented
260	#15561	C₂²⋊C₄	1	1	yes	characteristic, complemented
261	#15467	C₂²⋊C₄	1	1	yes	characteristic, complemented
262	#15467	C₂²⋊C₄	1	1	yes	characteristic, complemented
263	#15467	C₂²⋊C₄	1	1	yes	characteristic, complemented
264	#15467	C₂²⋊C₄	1	1	yes	characteristic, complemented
265	#15267	C₂²⋊C₄	1	1	yes	characteristic, complemented
266	#15267	C₂²⋊C₄	1	1	yes	characteristic, complemented
267	#15267	C₂²⋊C₄	1	1	yes	characteristic, complemented
268	#15267	C₂²⋊C₄	1	1	yes	characteristic, complemented
269	#15262	C₂²⋊C₄	1	1	yes	characteristic
270	#15262	C₂²⋊C₄	1	1	yes	characteristic, complemented
271	#15261	C₂²⋊C₄	1	1	yes	characteristic
272	#15261	C₂²⋊C₄	1	1	yes	characteristic, complemented
273	#15259	C₂²⋊C₄	1	1	yes	characteristic
274	#15259	C₂²⋊C₄	1	1	yes	characteristic, complemented
275	#15259	C₂²⋊C₄	1	1	yes	characteristic, complemented
276	#15259	C₂²⋊C₄	1	1	yes	characteristic, complemented
277	#15259	C₂²×C₄	1	1	yes	characteristic
278	#15259	C₂²×C₄	1	1	yes	characteristic
279	#15259	C₂²×C₄	1	1	yes	characteristic
280	#15259	C₂×D₄	1	1	yes	characteristic
281	#15259	C₂×D₄	1	1	yes	characteristic
282	#15259	C₂×D₄	1	1	yes	characteristic
283	#15259	C₂×D₄	1	1	yes	characteristic
284	#15259	C₂×D₄	1	1	yes	characteristic
285	#15259	C₂×D₄	1	1	yes	characteristic
286	#15259	C₂×D₄	1	1	yes	characteristic
287	#15259	C₂×D₄	1	1	yes	characteristic
288	#15259	C₂×D₄	1	1	yes	characteristic
289	#15258	C₂²⋊C₄	1	1	yes	characteristic
290	#15258	C₂²⋊C₄	1	1	yes	characteristic, complemented
291	#15258	C₂²⋊C₄	1	1	yes	characteristic, complemented
292	#15258	C₂²⋊C₄	1	1	yes	characteristic, complemented
293	#15258	C₂²×C₄	1	1	yes	characteristic
294	#15258	C₂²×C₄	1	1	yes	characteristic
295	#15258	C₂²×C₄	1	1	yes	characteristic
296	#15258	C₂×D₄	1	1	yes	characteristic
297	#15258	C₂×D₄	1	1	yes	characteristic
298	#15258	C₂×D₄	1	1	yes	characteristic
299	#15258	C₂×D₄	1	1	yes	characteristic
300	#15258	C₂×D₄	1	1	yes	characteristic
301	#15258	C₂×D₄	1	1	yes	characteristic
302	#15258	C₂×D₄	1	1	yes	characteristic
303	#15258	C₂×D₄	1	1	yes	characteristic
304	#15258	C₂×D₄	1	1	yes	characteristic
305	#14681	C₂²⋊C₄	1	1	yes	characteristic, complemented
306	#14681	C₂²⋊C₄	1	1	yes	characteristic, complemented
307	#14679	C₂²⋊C₄	1	1	yes	characteristic, complemented
308	#14679	C₂²⋊C₄	1	1	yes	characteristic, complemented
309	#14658	C₂²⋊C₄	1	1	yes	characteristic
310	#14658	C₂²⋊C₄	1	1	yes	characteristic, complemented
311	#14657	C₂²⋊C₄	1	1	yes	characteristic
312	#14657	C₂²⋊C₄	1	1	yes	characteristic, complemented
313	#14657	C₂²⋊C₄	1	1	yes	characteristic, complemented
314	#14657	C₂²⋊C₄	1	1	yes	characteristic, complemented
315	#14649	C₂²⋊C₄	1	1	yes	characteristic, complemented
316	#14649	C₂²⋊C₄	1	1	yes	characteristic, complemented
317	#14609	C₂²⋊C₄	1	1	yes	characteristic, complemented
318	#14609	C₂²⋊C₄	1	1	yes	characteristic, complemented
319	#14533	C₂²⋊C₄	1	1	yes	characteristic, complemented
320	#14533	C₂²⋊C₄	1	1	yes	characteristic, complemented
321	#14507	C₂²⋊C₄	1	1	yes	characteristic, complemented
322	#14507	C₂²⋊C₄	1	1	yes	characteristic, complemented
323	#14507	C₂²⋊C₄	1	1	yes	characteristic, complemented
324	#14507	C₂²⋊C₄	1	1	yes	characteristic, complemented
325	#14492	C₂²⋊C₄	1	1	yes	characteristic, complemented
326	#14492	C₂²⋊C₄	1	1	yes	characteristic, complemented
327	#14419	C₂²⋊C₄	1	1	yes	characteristic, complemented
328	#14419	C₂²⋊C₄	1	1	yes	characteristic, complemented
329	#14341	C₂×D₄	1	1	yes	characteristic
330	#14341	C₂×D₄	1	1	yes	characteristic
331	#14335	C₂×D₄	1	1	yes	characteristic
332	#14335	C₂×D₄	1	1	yes	characteristic
333	#14335	C₂×D₄	1	1	yes	characteristic
334	#14335	C₂×D₄	1	1	yes	characteristic
335	#14335	C₂×D₄	1	1	yes	characteristic
336	#14262	C₂²⋊C₄	1	1	yes	characteristic, complemented
337	#14262	C₂²⋊C₄	1	1	yes	characteristic, complemented
338	#14262	C₂²⋊C₄	1	1	yes	characteristic, complemented
339	#14262	C₂²⋊C₄	1	1	yes	characteristic, complemented
340	#14255	C₂²×C₄	1	1	yes	characteristic
341	#14255	C₂²×C₄	1	1	yes	characteristic
342	#14255	C₂×D₄	1	1	yes	characteristic
343	#14255	C₂×D₄	1	1	yes	characteristic
344	#14255	C₂×D₄	1	1	yes	characteristic
345	#14255	C₂×D₄	1	1	yes	characteristic
346	#14255	C₂×D₄	1	1	yes	characteristic
347	#14255	C₂×D₄	1	1	yes	characteristic
348	#14207	C₂²⋊C₄	1	1	yes	characteristic, complemented
349	#14207	C₂²⋊C₄	1	1	yes	characteristic, complemented
350	#14167	C₂²⋊C₄	1	1	yes	characteristic
351	#14167	C₂²⋊C₄	1	1	yes	characteristic, complemented
352	#14134	C₂²⋊C₄	1	1	yes	characteristic
353	#14134	C₂²⋊C₄	1	1	yes	characteristic, complemented
354	#14134	C₂²⋊C₄	1	1	yes	characteristic, complemented
355	#14134	C₂²⋊C₄	1	1	yes	characteristic, complemented
356	#13868	C₂×D₄	1	1	yes	characteristic
357	#13868	C₂×D₄	1	1	yes	characteristic
358	#13868	C₂×D₄	1	1	yes	characteristic
359	#13868	C₂×D₄	1	1	yes	characteristic
360	#13868	C₂×D₄	1	1	yes	characteristic
361	#13868	C₂×D₄	1	1	yes	characteristic
362	C₂×#1438	C₂×D₄	1	1	yes	characteristic
363	C₂×#1438	C₂×D₄	1	1	yes	characteristic
364	C₂×#1438	C₂×D₄	1	1	yes	characteristic
365	#13827	C₂²⋊C₄	1	1	yes	characteristic, complemented
366	#13827	C₂²⋊C₄	1	1	yes	characteristic, complemented
367	C₂²⋊C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
368	C₂²⋊C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
369	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂⁷	#120	1	1	yes	characteristic
371	C₂⁷	#120	1	1	yes	characteristic
372	C₂⁷	C₂²×D₄	1	1	yes	characteristic
373	C₂³×#41	#120	1	1	yes	characteristic
374	C₂³×#41	#120	1	1	yes	characteristic
375	C₂³×#41	#120	1	1	yes	characteristic
376	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂⁴×D₄	#120	1	1	yes	characteristic
379	C₂⁴×D₄	#120	1	1	yes	characteristic
380	C₂⁴×D₄	#120	1	1	yes	characteristic
381	C₂⁴×D₄	#120	1	1	yes	characteristic
382	C₂⁴×D₄	#120	1	1	yes	characteristic
383	C₂⁴×D₄	#120	1	1	yes	characteristic
384	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
385	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
386	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
387	C₂⁵×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂⁵×C₄	#120	1	1	yes	characteristic
389	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×#127	#120	1	1	yes	characteristic
393	C₂²×#127	#120	1	1	yes	characteristic
394	C₂²×#127	#120	1	1	yes	characteristic
395	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂²×#124	#120	1	1	yes	characteristic
399	C₂²×#124	#120	1	1	yes	characteristic
400	C₂²×#124	#120	1	1	yes	characteristic
401	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂²×#123	#120	1	1	yes	characteristic
406	C₂²×#123	#120	1	1	yes	characteristic
407	C₂²×#123	#120	1	1	yes	characteristic
408	C₂²×#123	#120	1	1	yes	characteristic
409	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
410	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
411	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
412	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
416	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×#120	#120	1	1	yes	characteristic
420	C₂²×#120	#120	1	1	yes	characteristic
421	C₂²×#120	#120	1	1	yes	characteristic
422	C₂²×#120	#120	1	1	yes	characteristic
423	C₂²×#120	#120	1	1	yes	characteristic
424	C₂²×#120	#120	1	1	yes	characteristic
425	C₂²×#120	#120	1	1	yes	characteristic
426	C₂²×#120	#120	1	1	yes	characteristic
427	C₂²×#120	#120	1	1	yes	characteristic
428	C₂²×#120	#120	1	1	yes	characteristic
429	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
430	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
431	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
432	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
433	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
434	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
435	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
436	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
437	C₂²×#117	#120	1	1	yes	characteristic
438	C₂²×#117	#120	1	1	yes	characteristic
439	C₂²×#117	#120	1	1	yes	characteristic
440	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
443	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
444	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
445	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
446	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
447	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
448	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
449	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
450	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
451	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
454	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×#393	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×#393	#120	1	1	yes	characteristic
461	C₂×#393	#120	1	1	yes	characteristic
462	C₂×#393	#120	1	1	yes	characteristic
463	C₂×#393	#120	1	1	yes	characteristic
464	C₂×#393	#120	1	1	yes	characteristic
465	C₂×#393	#120	1	1	yes	characteristic
466	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂×#392	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂×#392	#120	1	1	yes	characteristic
473	C₂×#392	#120	1	1	yes	characteristic
474	C₂×#392	#120	1	1	yes	characteristic
475	C₂×#392	#120	1	1	yes	characteristic
476	C₂×#392	#120	1	1	yes	characteristic
477	C₂×#392	#120	1	1	yes	characteristic
478	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×#381	#120	1	1	yes	characteristic
483	C₂×#381	#120	1	1	yes	characteristic
484	C₂×#381	#120	1	1	yes	characteristic
485	C₂×#381	#120	1	1	yes	characteristic
486	C₂×#381	#120	1	1	yes	characteristic
487	C₂×#381	#120	1	1	yes	characteristic
488	C₂×#381	#120	1	1	yes	characteristic
489	C₂×#381	#120	1	1	yes	characteristic
490	C₂×#381	#120	1	1	yes	characteristic
491	C₂×#381	#120	1	1	yes	characteristic
492	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
493	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
494	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
495	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
497	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
498	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
499	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
500	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
501	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
502	C₂×#379	#120	1	1	yes	characteristic
503	C₂×#379	#120	1	1	yes	characteristic
504	C₂×#379	#120	1	1	yes	characteristic
505	C₂×#379	#120	1	1	yes	characteristic
506	C₂×#379	#120	1	1	yes	characteristic
507	C₂×#379	#120	1	1	yes	characteristic
508	C₂×#379	#120	1	1	yes	characteristic
509	C₂×#379	#120	1	1	yes	characteristic
510	C₂×#379	#120	1	1	yes	characteristic
511	C₂×#379	#120	1	1	yes	characteristic
512	C₂×#379	#120	1	1	yes	characteristic
513	C₂×#379	#120	1	1	yes	characteristic
514	C₂×#379	#120	1	1	yes	characteristic
515	C₂×#379	#120	1	1	yes	characteristic
516	#1440	C₂×C₂²⋊C₄	1	1	yes	characteristic
517	#1440	C₂×C₂²⋊C₄	1	1	yes	characteristic
518	#1440	C₂×C₂²⋊C₄	1	1	yes	characteristic
519	#1440	C₂×C₂²⋊C₄	1	1	yes	characteristic
520	#1440	#120	1	1	yes	characteristic
521	#1440	#120	1	1	yes	characteristic
522	#1440	#120	1	1	yes	characteristic
523	#1440	#120	1	1	yes	characteristic
524	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
525	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
526	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
527	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
528	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
529	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
530	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
531	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
532	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
533	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
534	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
535	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
536	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
537	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
538	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
539	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
540	#1438	#120	1	1	yes	characteristic
541	#1438	#120	1	1	yes	characteristic
542	#1438	#120	1	1	yes	characteristic
543	#1438	#120	1	1	yes	characteristic
544	#1438	#120	1	1	yes	characteristic
545	#1438	#120	1	1	yes	characteristic
546	#1438	#120	1	1	yes	characteristic
547	#1438	#120	1	1	yes	characteristic
548	#1438	#120	1	1	yes	characteristic
549	#1438	#120	1	1	yes	characteristic
550	#1438	#120	1	1	yes	characteristic
551	#1438	#120	1	1	yes	characteristic
552	#1438	#120	1	1	yes	characteristic
553	#1438	#120	1	1	yes	characteristic
554	#1438	#120	1	1	yes	characteristic
555	#1438	#120	1	1	yes	characteristic
556	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
557	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
558	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
559	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
560	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
561	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
562	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
563	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
564	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
565	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
566	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
567	#1437	C₂×C₂²⋊C₄	1	1	yes	characteristic
568	#1437	#120	1	1	yes	characteristic
569	#1437	#120	1	1	yes	characteristic
570	#1437	#120	1	1	yes	characteristic
571	#1437	#120	1	1	yes	characteristic
572	#1437	#120	1	1	yes	characteristic
573	#1437	#120	1	1	yes	characteristic
574	#1437	#120	1	1	yes	characteristic
575	#1437	#120	1	1	yes	characteristic
576	#1437	#120	1	1	yes	characteristic
577	#1437	#120	1	1	yes	characteristic
578	#1437	#120	1	1	yes	characteristic
579	#1437	#120	1	1	yes	characteristic
580	C₂⁶	#379	1	1	yes	characteristic
581	C₂⁶	#379	1	1	yes	characteristic
582	C₂⁶	#379	1	1	yes	characteristic
583	C₂⁶	#379	1	1	yes	characteristic
584	C₂⁶	#379	1	1	yes	characteristic
585	C₂⁶	#379	1	1	yes	characteristic
586	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
587	C₂⁶	C₂×#120	1	1	yes	characteristic
588	C₂⁶	C₂×#120	1	1	yes	characteristic
589	C₂⁶	C₂×#120	1	1	yes	characteristic
590	C₂⁶	C₂×#120	1	1	yes	characteristic
591	C₂⁶	C₂×#120	1	1	yes	characteristic
592	C₂⁶	C₂×#120	1	1	yes	characteristic
593	C₂⁶	C₂×#120	1	1	yes	characteristic
594	C₂³×Q₈	#379	1	1	yes	characteristic
595	C₂³×Q₈	#379	1	1	yes	characteristic
596	C₂³×Q₈	#379	1	1	yes	characteristic
597	C₂³×D₄	#379	1	1	yes	characteristic
598	C₂³×D₄	#379	1	1	yes	characteristic
599	C₂³×D₄	#379	1	1	yes	characteristic
600	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
601	C₂³×D₄	#458	1	2	yes	—
602	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
603	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
604	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
605	C₂³×D₄	C₂×#120	1	1	yes	characteristic
606	C₂³×D₄	C₂×#120	1	1	yes	characteristic
607	C₂³×D₄	C₂×#120	1	1	yes	characteristic
608	C₂³×D₄	C₂×#120	1	1	yes	characteristic
609	C₂³×D₄	C₂×#120	1	1	yes	characteristic
610	C₂³×D₄	C₂×#120	1	1	yes	characteristic
611	C₂³×D₄	C₂×#120	1	1	yes	characteristic
612	C₂³×D₄	C₂×#120	1	1	yes	characteristic
613	C₂³×D₄	C₂×#120	1	1	yes	characteristic
614	C₂⁴×C₄	#379	1	1	yes	characteristic
615	C₂⁴×C₄	#379	1	1	yes	characteristic
616	C₂⁴×C₄	#379	1	1	yes	characteristic
617	C₂⁴×C₄	#379	1	1	yes	characteristic
618	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
619	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
620	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
621	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
622	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
623	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
624	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
625	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
626	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
627	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
628	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
629	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
630	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
631	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
632	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
633	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
634	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
635	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
636	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
637	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
638	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
639	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
640	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
641	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
642	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
643	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
644	C₂²×C₂²⋊C₄	#458	1	2	yes	—
645	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
646	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
647	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
648	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
649	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
650	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
651	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
652	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
653	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
654	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
655	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
656	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
657	C₂²×C₄²	#379	1	1	yes	characteristic
658	C₂²×C₄²	#379	1	1	yes	characteristic
659	C₂²×C₄²	#379	1	1	yes	characteristic
660	C₂²×C₄²	#379	1	1	yes	characteristic
661	C₂²×C₄²	#379	1	1	yes	characteristic
662	C₂²×C₄²	#379	1	1	yes	characteristic
663	C₂×#95	#379	1	1	yes	characteristic
664	C₂×#95	#379	1	1	yes	characteristic
665	C₂×#95	#379	1	1	yes	characteristic
666	C₂×#95	#379	1	1	yes	characteristic
667	C₂×#95	#379	1	1	yes	characteristic
668	C₂×#95	#379	1	1	yes	characteristic
669	C₂×#95	#379	1	1	yes	characteristic
670	C₂×#95	#379	1	1	yes	characteristic
671	C₂×#95	#379	1	1	yes	characteristic
672	C₂×#95	#379	1	1	yes	characteristic
673	C₂×#95	#379	1	1	yes	characteristic
674	C₂×#95	#379	1	1	yes	characteristic
675	C₂⁵	#1790	1	2	yes	—
676	C₂⁵	C₂×#379	1	1	yes	characteristic
677	C₂⁵	C₂×#379	1	1	yes	characteristic
678	C₂⁵	C₂×#379	1	1	yes	characteristic
679	C₂⁵	C₂×#379	1	1	yes	characteristic
680	C₂⁵	#2846	1	1	yes	characteristic
681	C₂⁵	#2846	1	1	yes	characteristic
682	C₂⁵	#2846	1	1	yes	characteristic
683	C₂⁵	#2846	1	1	yes	characteristic
684	C₂⁵	#2846	1	1	yes	characteristic
685	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
686	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
687	C₂⁵	C₂×#458	1	1	yes	characteristic
688	C₂⁵	C₂×#458	1	1	yes	characteristic
689	C₂⁵	#3025	1	1	yes	characteristic
690	C₂⁵	#3025	1	1	yes	characteristic
691	C₂⁵	#3026	1	1	yes	characteristic
692	C₂⁵	#3026	1	1	yes	characteristic
693	C₂⁵	#3026	1	1	yes	characteristic
694	C₂⁵	#3026	1	1	yes	characteristic
695	C₂⁵	#3027	1	1	yes	characteristic
696	C₂⁵	#3028	1	1	yes	characteristic
697	C₂³×C₄	#1790	1	2	yes	—
698	C₂³×C₄	C₂×#379	1	1	yes	characteristic
699	C₂³×C₄	C₂×#379	1	1	yes	characteristic
700	C₂³×C₄	C₂×#379	1	1	yes	characteristic
701	C₂³×C₄	#2846	1	1	yes	characteristic
702	C₂³×C₄	#2846	1	1	yes	characteristic
703	C₂³×C₄	#2846	1	1	yes	characteristic
704	C₂×C₂²⋊C₄	#1790	1	2	yes	—
705	C₂×C₂²⋊C₄	#1790	1	2	yes	—
706	C₂⁴	#12753	1	4	yes	complemented
707	C₂⁴	#14679	1	1	yes	characteristic
708	C₂⁴	C₂×#1790	1	1	yes	characteristic
709	C₂⁴	C₂×#1790	1	1	yes	characteristic
710	C₂⁴	#20608	1	1	yes	characteristic
711	C₂⁴	#20609	1	1	yes	characteristic
712	C₂⁴	#20609	1	1	yes	characteristic
713	C₂⁴	#20610	1	1	yes	characteristic
714	C₂⁴	#32898	1	1	yes	characteristic
715	C₂⁴	#32898	1	1	yes	characteristic
716	C₂⁴	#32898	1	1	yes	characteristic
717	C₂⁴	#32898	1	1	yes	characteristic
718	C₂⁴	#32899	1	1	yes	characteristic
719	C₂⁴	#32899	1	1	yes	characteristic
720	C₂⁴	#32900	1	1	yes	characteristic
721	C₂⁴	#32900	1	1	yes	characteristic
722	C₂⁴	#32900	1	1	yes	characteristic
723	C₂⁴	#32900	1	1	yes	characteristic
724	C₂⁴	#32901	1	1	yes	characteristic
725	C₂⁴	#32901	1	1	yes	characteristic
726	C₂³	#347043	1	1	yes	characteristic
727	C₂³	#347049	1	1	yes	characteristic
728	C₂³	#347052	1	1	yes	characteristic
729	C₂³	#347055	1	1	yes	characteristic
730	C₂³	#392125	1	1	yes	characteristic
731	C₂³	#392125	1	1	yes	characteristic
732	C₂³	#392126	1	1	yes	characteristic
733	C₂³	C₂×#12753	1	2	yes	—
734	C₂³	#511790	1	2	yes	—
735	C₂²	#72218475	1	1	yes	characteristic
736	C₂²	#72218980	1	1	yes	characteristic
737	C₂²	#72237472	1	1	yes	characteristic
738	C₂²	#72238343	1	1	yes	characteristic
739	C₂²	#72258078	1	1	yes	characteristic
740	C₂²	#72258078	1	1	yes	characteristic
741	C₂²	#72265012	1	1	yes	characteristic
742	C₂	#72265774	1	1	yes	characteristic
743	C₂	#72265784	1	1	yes	characteristic
744	C₂	#72265978	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72265012
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	C₂³×#120	C₂⁴
prime radical	#72266582	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266700	C₂	semidirect
2. #72266697	C₂	semidirect
4. #72266567	C₄	semidirect
5. #72266566	C₄	semidirect
6. #72266565	C₄	semidirect
7. #72266560	C₄	semidirect
8. #72266557	C₄	semidirect
9. #72266539	C₄	semidirect
10. #72266446	C₂	semidirect
11. #72266446	C₂	semidirect
12. #72266352	C₂	semidirect
13. #72266308	C₂	semidirect
14. #72266307	C₂²	semidirect
15. #72266279	C₂	semidirect
17. #72266165	C₂	semidirect
18. #72266163	C₂	semidirect
19. #72266043	C₂	semidirect
20. #72266041	C₂²	semidirect
21. #72265766	C₂²	semidirect
22. #72265766	C₂²	semidirect
23. #72263168	C₄	semidirect
24. #72262637	C₂²	semidirect
25. #72259010	C₂	semidirect
26. #72259008	C₂²	semidirect
27. #72258997	C₂	semidirect
30. #72240132	C₂²	semidirect
31. #72240132	C₂²	semidirect
32. #72240132	C₂²	semidirect
33. #72238446	C₂²	semidirect
34. #72235991	C₄	semidirect
35. #72235847	C₂²	semidirect
36. #72235740	C₂	semidirect
37. #72235740	C₂	semidirect
38. #72235718	C₂²	semidirect
39. #72235718	C₂²	semidirect
40. #72235186	C₂²	semidirect
41. #72235186	C₂²	semidirect
42. #72235186	C₂²	semidirect
43. #72234668	C₂²	semidirect
44. #72234668	C₂²	semidirect
47. #72232723	C₂²	semidirect
48. #72232723	C₂²	semidirect
49. #72232723	C₂²	semidirect
50. #72232723	C₂²	semidirect
51. #72232723	C₂²	semidirect
52. #72232723	C₂²	semidirect
53. C₂×#139716	C₂²	semidirect
54. C₂×#139716	C₂²	semidirect
55. C₂×#139716	C₂²	semidirect
58. #72219241	C₂²	semidirect
161. C₂²×#551	C₂²⋊C₄	semidirect
163. C₂²×D₄²	C₂²⋊C₄	semidirect
165. C₂²×H(3,𝔽₄)	C₂²⋊C₄	semidirect
167. C₂²×#560	C₂²⋊C₄	semidirect
175. C₂³×#120	C₂²⋊C₄	semidirect
176. C₂³×#120	C₂²⋊C₄	semidirect
181. C₂×#2760	C₂²⋊C₄	semidirect
182. C₂×#2760	C₂²⋊C₄	semidirect
183. C₂×#2760	C₂²⋊C₄	semidirect
184. C₂×#2760	C₂²⋊C₄	semidirect
185. C₂×#2840	C₂²⋊C₄	semidirect
186. C₂×#2840	C₂²⋊C₄	semidirect
201. C₂×#2403	C₂²⋊C₄	semidirect
202. C₂×#2403	C₂²⋊C₄	semidirect
211. C₂×#2308	C₂²⋊C₄	semidirect
212. C₂×#2308	C₂²⋊C₄	semidirect
213. C₂×#2308	C₂²⋊C₄	semidirect
214. C₂×#2308	C₂²⋊C₄	semidirect
219. C₂²×#386	C₂²⋊C₄	semidirect
220. C₂²×#386	C₂²⋊C₄	semidirect
225. #17271	C₂²⋊C₄	semidirect
226. #17271	C₂²⋊C₄	semidirect
227. #17198	C₂²⋊C₄	semidirect
228. #17137	C₂²⋊C₄	semidirect
229. #17137	C₂²⋊C₄	semidirect
230. #17105	C₂²⋊C₄	semidirect
231. #17105	C₂²⋊C₄	semidirect
232. #17102	C₂²⋊C₄	semidirect
233. #16247	C₂²⋊C₄	semidirect
234. #16211	C₂²⋊C₄	semidirect
237. #15948	C₂²⋊C₄	semidirect
238. #15948	C₂²⋊C₄	semidirect
241. #15947	C₂²⋊C₄	semidirect
242. #15947	C₂²⋊C₄	semidirect
251. #15930	C₂²⋊C₄	semidirect
252. #15930	C₂²⋊C₄	semidirect
253. #15930	C₂²⋊C₄	semidirect
254. #15930	C₂²⋊C₄	semidirect
255. #15636	C₂²⋊C₄	semidirect
256. #15636	C₂²⋊C₄	semidirect
257. #15561	C₂²⋊C₄	semidirect
258. #15561	C₂²⋊C₄	semidirect
259. #15561	C₂²⋊C₄	semidirect
260. #15561	C₂²⋊C₄	semidirect
261. #15467	C₂²⋊C₄	semidirect
262. #15467	C₂²⋊C₄	semidirect
263. #15467	C₂²⋊C₄	semidirect
264. #15467	C₂²⋊C₄	semidirect
265. #15267	C₂²⋊C₄	semidirect
266. #15267	C₂²⋊C₄	semidirect
267. #15267	C₂²⋊C₄	semidirect
268. #15267	C₂²⋊C₄	semidirect
270. #15262	C₂²⋊C₄	semidirect
272. #15261	C₂²⋊C₄	semidirect
274. #15259	C₂²⋊C₄	semidirect
275. #15259	C₂²⋊C₄	semidirect
276. #15259	C₂²⋊C₄	semidirect
290. #15258	C₂²⋊C₄	semidirect
291. #15258	C₂²⋊C₄	semidirect
292. #15258	C₂²⋊C₄	semidirect
305. #14681	C₂²⋊C₄	semidirect
306. #14681	C₂²⋊C₄	semidirect
307. #14679	C₂²⋊C₄	semidirect
308. #14679	C₂²⋊C₄	semidirect
310. #14658	C₂²⋊C₄	semidirect
312. #14657	C₂²⋊C₄	semidirect
313. #14657	C₂²⋊C₄	semidirect
314. #14657	C₂²⋊C₄	semidirect
315. #14649	C₂²⋊C₄	semidirect
316. #14649	C₂²⋊C₄	semidirect
317. #14609	C₂²⋊C₄	semidirect
318. #14609	C₂²⋊C₄	semidirect
319. #14533	C₂²⋊C₄	semidirect
320. #14533	C₂²⋊C₄	semidirect
321. #14507	C₂²⋊C₄	semidirect
322. #14507	C₂²⋊C₄	semidirect
323. #14507	C₂²⋊C₄	semidirect
324. #14507	C₂²⋊C₄	semidirect
325. #14492	C₂²⋊C₄	semidirect
326. #14492	C₂²⋊C₄	semidirect
327. #14419	C₂²⋊C₄	semidirect
328. #14419	C₂²⋊C₄	semidirect
336. #14262	C₂²⋊C₄	semidirect
337. #14262	C₂²⋊C₄	semidirect
338. #14262	C₂²⋊C₄	semidirect
339. #14262	C₂²⋊C₄	semidirect
348. #14207	C₂²⋊C₄	semidirect
349. #14207	C₂²⋊C₄	semidirect
351. #14167	C₂²⋊C₄	semidirect
353. #14134	C₂²⋊C₄	semidirect
354. #14134	C₂²⋊C₄	semidirect
355. #14134	C₂²⋊C₄	semidirect
365. #13827	C₂²⋊C₄	semidirect
366. #13827	C₂²⋊C₄	semidirect
367. C₂²⋊C₄²	C₂²⋊C₄	semidirect
368. C₂²⋊C₄²	C₂²⋊C₄	semidirect
706. C₂⁴	#12753	semidirect

Maximal subgroups

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

subgroup	index
#72266700	2
#72266697	2
#72266582	2
#72266446	2
#72266352	2
#72266308	2
#72266279	2
#72266165	2
#72266163	2
#72266043	2
#72259010	2
#72258997	2
#72235740	2