Subgroups — #72271035

Order 1536.

At least 7666 conjugacy classes of subgroups; only the 711 normal subgroups are shown.

The subgroup lattice has 699 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11705060	C₂	1	1	yes	maximal, characteristic, complemented
2	#10991609	C₂	1	1	yes	maximal, characteristic, complemented
3	#10990485	C₂	1	1	yes	maximal, characteristic, complemented
4	#67×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	#10901331	C₂	1	1	yes	maximal, characteristic, complemented
6	#10900893	C₂	1	1	yes	maximal, characteristic, complemented
7	#10900889	C₂	1	1	yes	maximal, characteristic, complemented
8	#10850465	C₂	1	1	yes	maximal, characteristic, complemented
9	#10848559	C₂	1	1	yes	maximal, characteristic, complemented
10	#10848556	C₂	1	1	yes	maximal, characteristic, complemented
11	#10848327	C₂	1	1	yes	maximal, characteristic, complemented
12	#10848326	C₂	1	1	yes	maximal, characteristic, complemented
13	#10832528	C₂	1	1	yes	maximal, characteristic, complemented
14	#10832527	C₂	1	1	yes	maximal, characteristic, complemented
15	#10832524	C₂	1	1	yes	maximal, characteristic, complemented
16	#10832521	C₂	1	1	yes	maximal, characteristic, complemented
17	#10830821	C₂	1	1	yes	maximal, characteristic, complemented
18	#10829373	C₂	1	1	yes	maximal, characteristic, complemented
19	#10829369	C₂	1	1	yes	maximal, characteristic, complemented
20	#10827632	C₂	1	1	yes	maximal, characteristic, complemented
21	#10827631	C₂	1	1	yes	maximal, characteristic, complemented
22	#10826766	C₂	1	1	yes	maximal, characteristic, complemented
23	#10826765	C₂	1	1	yes	maximal, characteristic, complemented
24	#10826763	C₂	1	1	yes	maximal, characteristic, complemented
25	#10823687	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#71671	C₂	1	1	yes	maximal, characteristic, complemented
27	D₃×#2021	C₂	1	1	yes	maximal, characteristic, complemented
28	#10811315	C₂	1	1	yes	maximal, characteristic, complemented
29	#10810507	C₂	1	1	yes	maximal, characteristic, complemented
30	#10810505	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃×#23900	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×#67	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3484	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×#120	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#953	C₂²	1	1	yes	characteristic, complemented
36	#87284	C₂²	1	1	yes	characteristic, complemented
37	#87281	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×#67	C₂²	1	1	yes	characteristic
39	C₂×#5804	C₂²	1	1	yes	characteristic, complemented
40	#86308	C₂²	1	1	yes	characteristic, complemented
41	D₃×#534	C₂²	1	1	yes	characteristic, complemented
42	#86299	C₂²	1	1	yes	characteristic, complemented
43	#86295	C₂²	1	1	yes	characteristic, complemented
44	#85919	C₂²	1	1	yes	characteristic, complemented
45	C₂×#5591	C₂²	1	1	yes	characteristic
46	C₂×#5590	C₂²	1	1	yes	characteristic
47	C₂×D₃×#120	C₂²	1	1	yes	characteristic, complemented
48	C₂×D₃×#120	C₂²	1	1	yes	characteristic, complemented
49	#85913	C₂²	1	1	yes	characteristic, complemented
50	#85868	C₂²	1	1	yes	characteristic, complemented
51	#85861	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
54	C₃×#2846	C₂²	1	1	yes	characteristic, complemented
55	C₃×#2846	C₂²	1	1	yes	characteristic, complemented
56	#84128	C₂²	1	1	yes	characteristic, complemented
57	C₂×#5247	C₂²	1	1	yes	characteristic, complemented
58	C₂×#5244	C₂²	1	1	yes	characteristic, complemented
59	#84052	C₂²	1	1	yes	characteristic, complemented
60	C₂²×#834	C₂²	1	1	yes	characteristic, complemented
61	#82612	C₂²	1	1	yes	characteristic, complemented
62	#82612	C₂²	1	1	yes	characteristic, complemented
63	#82606	C₂²	1	1	yes	characteristic, complemented
64	#82606	C₂²	1	1	yes	characteristic, complemented
65	#82605	C₂²	1	1	yes	characteristic, complemented
66	#82605	C₂²	1	1	yes	characteristic, complemented
67	#82604	C₂²	1	1	yes	characteristic, complemented
68	#82604	C₂²	1	1	yes	characteristic, complemented
69	C₂×#5032	C₂²	1	1	yes	characteristic, complemented
70	C₂×#5032	C₂²	1	1	yes	characteristic, complemented
71	#82601	C₂²	1	1	yes	characteristic, complemented
72	#82601	C₂²	1	1	yes	characteristic, complemented
73	#82588	C₂²	1	1	yes	characteristic, complemented
74	#82588	C₂²	1	1	yes	characteristic, complemented
75	#82582	C₂²	1	1	yes	characteristic, complemented
76	#82582	C₂²	1	1	yes	characteristic, complemented
77	Dic₃×#120	C₂²	1	1	yes	characteristic, complemented
78	Dic₃×#120	C₂²	1	1	yes	characteristic, complemented
79	#82127	C₂²	1	1	yes	characteristic, complemented
80	C₂²⋊C₄×#67	C₂²	1	1	yes	characteristic, complemented
81	C₂²×#806	C₂²	1	1	yes	characteristic, complemented
82	C₂×D₃×#99	C₂²	1	1	yes	characteristic, complemented
83	C₂×D₃×#99	C₂²	1	1	yes	characteristic, complemented
84	C₂×#4741	C₂²	1	1	yes	characteristic, complemented
85	#73861	C₂²	1	1	yes	characteristic, complemented
86	#73854	C₂²	1	1	yes	characteristic, complemented
87	#73853	C₂²	1	1	yes	characteristic, complemented
88	#73852	C₂²	1	1	yes	characteristic, complemented
89	#73850	C₂²	1	1	yes	characteristic, complemented
90	#73850	C₂²	1	1	yes	characteristic, complemented
91	D₃×#379	C₂²	1	1	yes	characteristic, complemented
92	#73846	C₂²	1	1	yes	characteristic, complemented
93	#73827	C₂²	1	1	yes	characteristic, complemented
94	#73824	C₂²	1	1	yes	characteristic, complemented
95	#73823	C₂²	1	1	yes	characteristic, complemented
96	#73818	C₂²	1	1	yes	characteristic, complemented
97	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
98	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
99	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
100	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
101	C₃×#1898	C₂²	1	1	yes	characteristic, complemented
102	C₃×#1898	C₂²	1	1	yes	characteristic, complemented
103	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
104	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
105	C₃×#1781	C₂²	1	1	yes	characteristic, complemented
106	#72142	C₂²	1	1	yes	characteristic, complemented
107	#71851	C₂²	1	1	yes	characteristic, complemented
108	#71851	C₂²	1	1	yes	characteristic, complemented
109	#71850	C₂²	1	1	yes	characteristic, complemented
110	#71850	C₂²	1	1	yes	characteristic, complemented
111	#71671	C₂²	1	1	yes	characteristic, complemented
112	#71671	C₂²	1	1	yes	characteristic, complemented
113	#71671	C₂²	1	1	yes	characteristic, complemented
114	#71671	C₂²	1	1	yes	characteristic, complemented
115	#71671	C₂²	1	1	yes	characteristic, complemented
116	#71671	C₂²	1	1	yes	characteristic, complemented
117	#71671	C₂²	1	1	yes	characteristic, complemented
118	#71671	C₂²	1	1	yes	characteristic, complemented
119	#71671	C₂²	1	1	yes	characteristic, complemented
120	#71671	C₂²	1	1	yes	characteristic, complemented
121	#71671	C₂²	1	1	yes	characteristic, complemented
122	#71671	C₂²	1	1	yes	characteristic, complemented
123	#71670	C₂²	1	1	yes	characteristic, complemented
124	#71670	C₂²	1	1	yes	characteristic, complemented
125	#71669	C₂²	1	1	yes	characteristic, complemented
126	#71669	C₂²	1	1	yes	characteristic, complemented
127	#71657	C₂²	1	1	yes	characteristic, complemented
128	#71654	C₂²	1	1	yes	characteristic, complemented
129	C₂×#4527	C₂²	1	1	yes	characteristic, complemented
130	#70037	C₂²	1	1	yes	characteristic, complemented
131	#70037	C₂²	1	1	yes	characteristic, complemented
132	#70037	C₂²	1	1	yes	characteristic, complemented
133	#70037	C₂²	1	1	yes	characteristic, complemented
134	#70037	C₂²	1	1	yes	characteristic, complemented
135	#70037	C₂²	1	1	yes	characteristic, complemented
136	#70036	C₂²	1	1	yes	characteristic, complemented
137	#70036	C₂²	1	1	yes	characteristic, complemented
138	#70036	C₂²	1	1	yes	characteristic, complemented
139	#70036	C₂²	1	1	yes	characteristic, complemented
140	#70035	C₂²	1	1	yes	characteristic, complemented
141	#70035	C₂²	1	1	yes	characteristic, complemented
142	#70033	C₂²	1	1	yes	characteristic, complemented
143	#70032	C₂²	1	1	yes	characteristic, complemented
144	#70032	C₂²	1	1	yes	characteristic, complemented
145	#70032	C₂²	1	1	yes	characteristic, complemented
146	#70032	C₂²	1	1	yes	characteristic, complemented
147	#70032	C₂²	1	1	yes	characteristic, complemented
148	#70032	C₂²	1	1	yes	characteristic, complemented
149	#70030	C₂²	1	1	yes	characteristic, complemented
150	#70030	C₂²	1	1	yes	characteristic, complemented
151	#70030	C₂²	1	1	yes	characteristic, complemented
152	#70030	C₂²	1	1	yes	characteristic, complemented
153	#70028	C₂²	1	1	yes	characteristic, complemented
154	#70028	C₂²	1	1	yes	characteristic, complemented
155	Dic₃×#99	C₂²	1	1	yes	characteristic, complemented
156	Dic₃×#99	C₂²	1	1	yes	characteristic, complemented
157	#70022	C₂²	1	1	yes	characteristic, complemented
158	#70021	C₂²	1	1	yes	characteristic, complemented
159	#69500	C₂²	1	1	yes	characteristic, complemented
160	#69500	C₂²	1	1	yes	characteristic, complemented
161	#69499	C₂²	1	1	yes	characteristic, complemented
162	#69499	C₂²	1	1	yes	characteristic, complemented
163	#69499	C₂²	1	1	yes	characteristic, complemented
164	#69499	C₂²	1	1	yes	characteristic, complemented
165	#69498	C₂²	1	1	yes	characteristic, complemented
166	#69497	C₂²	1	1	yes	characteristic, complemented
167	#69497	C₂²	1	1	yes	characteristic, complemented
168	#69496	C₂²	1	1	yes	characteristic, complemented
169	#69496	C₂²	1	1	yes	characteristic, complemented
170	#69495	C₂²	1	1	yes	characteristic, complemented
171	#68971	C₂²	1	1	yes	characteristic, complemented
172	#68970	C₂²	1	1	yes	characteristic, complemented
173	#68970	C₂²	1	1	yes	characteristic, complemented
174	#68969	C₂²	1	1	yes	characteristic, complemented
175	D₃×#342	C₂²	1	1	yes	characteristic, complemented
176	#68965	C₂²	1	1	yes	characteristic, complemented
177	#68962	C₂²	1	1	yes	characteristic, complemented
178	#68962	C₂²	1	1	yes	characteristic, complemented
179	#68961	C₂²	1	1	yes	characteristic, complemented
180	#68961	C₂²	1	1	yes	characteristic, complemented
181	#68959	C₂²	1	1	yes	characteristic, complemented
182	#68958	C₂²	1	1	yes	characteristic, complemented
183	#68957	C₂²	1	1	yes	characteristic, complemented
184	#68955	C₂²	1	1	yes	characteristic, complemented
185	#68955	C₂²	1	1	yes	characteristic, complemented
186	#68952	C₂²	1	1	yes	characteristic, complemented
187	#23900	D₃	1	1	yes	characteristic, complemented
188	C₂⁶×C₃	C₂³	1	1	yes	characteristic
189	C₂⁵×D₃	C₂³	1	1	yes	characteristic
190	C₂×C₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
191	C₂³×C₃×D₄	C₂³	1	1	yes	characteristic
192	C₂³×#67	D₄	1	1	yes	characteristic, complemented
193	C₂³×#67	C₂³	1	1	yes	characteristic
194	C₂³×#67	C₂³	1	1	yes	characteristic
195	C₂³×#67	C₂³	1	1	yes	characteristic
196	C₂³×#67	C₂³	1	1	yes	characteristic
197	C₂³×#67	C₂³	1	1	yes	characteristic
198	C₂⁴×Dic₃	C₂³	1	1	yes	characteristic
199	C₂×#1004	C₂³	1	1	yes	characteristic
200	C₂²×#237	D₄	1	1	yes	characteristic, complemented
201	C₂²×D₃×D₄	D₄	1	1	yes	characteristic, complemented
202	C₂²×D₃×D₄	C₂³	1	1	yes	characteristic
203	C₂²×D₃×D₄	C₂³	1	1	yes	characteristic
204	C₃×#534	C₂³	1	1	yes	characteristic
205	C₃×#534	C₂³	1	1	yes	characteristic
206	C₂×C₃×#120	C₂³	1	1	yes	characteristic
207	C₂×C₃×#120	C₂³	1	1	yes	characteristic
208	C₂×C₃×#120	C₂³	1	1	yes	characteristic
209	C₂×C₃×#120	C₂³	1	1	yes	characteristic
210	C₂×C₃×#120	C₂³	1	1	yes	characteristic
211	C₂×C₃×#120	C₂³	1	1	yes	characteristic
212	C₂×C₃×#120	C₂³	1	1	yes	characteristic
213	C₂×C₃×#120	C₂³	1	1	yes	characteristic
214	C₂×C₃×#120	C₂³	1	1	yes	characteristic
215	C₂×C₃×#120	C₂³	1	1	yes	characteristic
216	C₃×#518	C₂³	1	1	yes	characteristic
217	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×#953	D₄	1	1	yes	characteristic, complemented
219	C₂×#953	C₂³	1	1	yes	characteristic
220	C₂×#953	C₂³	1	1	yes	characteristic
221	C₂×#953	C₂³	1	1	yes	characteristic
222	C₂×#953	C₂³	1	1	yes	characteristic
223	C₂×#953	C₂³	1	1	yes	characteristic
224	C₂×#953	C₂³	1	1	yes	characteristic
225	C₂×#953	C₂³	1	1	yes	characteristic
226	C₂²×#217	C₂³	1	1	yes	characteristic
227	C₂²×#217	C₂³	1	1	yes	characteristic
228	C₂²×#217	C₂³	1	1	yes	characteristic
229	#5804	C₂³	1	1	yes	characteristic
230	#5804	C₂³	1	1	yes	characteristic
231	#5804	C₂³	1	1	yes	characteristic
232	#5804	C₂³	1	1	yes	characteristic
233	#5804	C₂³	1	1	yes	characteristic
234	#5804	C₂³	1	1	yes	characteristic
235	C₂×#940	D₄	1	1	yes	characteristic, complemented
236	C₂×#940	D₄	1	1	yes	characteristic, complemented
237	C₂×#939	D₄	1	1	yes	characteristic, complemented
238	C₂×#939	D₄	1	1	yes	characteristic, complemented
239	C₂×#939	D₄	1	1	yes	characteristic, complemented
240	C₂×#939	D₄	1	1	yes	characteristic, complemented
241	C₂×#939	C₂³	1	1	yes	characteristic
242	C₂×#939	C₂³	1	1	yes	characteristic
243	C₂×#938	D₄	1	1	yes	characteristic, complemented
244	C₂×#938	D₄	1	1	yes	characteristic, complemented
245	C₂×#937	D₄	1	1	yes	characteristic, complemented
246	C₂×#937	D₄	1	1	yes	characteristic, complemented
247	C₂×#937	C₂³	1	1	yes	characteristic
248	C₂×#937	C₂³	1	1	yes	characteristic
249	C₂×#937	C₂³	1	1	yes	characteristic
250	C₂×#937	C₂³	1	1	yes	characteristic
251	C₂×#937	C₂³	1	1	yes	characteristic
252	C₂×#937	C₂³	1	1	yes	characteristic
253	#5798	C₂³	1	1	yes	characteristic
254	C₂×D₄×Dic₃	C₂³	1	1	yes	characteristic
255	C₂×D₄×Dic₃	C₂³	1	1	yes	characteristic
256	C₂×#930	D₄	1	1	yes	characteristic, complemented
257	C₂×C₄×#67	D₄	1	1	yes	characteristic, complemented
258	#5493	C₂³	1	1	yes	characteristic
259	C₂×#886	D₄	1	1	yes	characteristic, complemented
260	C₂×#885	D₄	1	1	yes	characteristic, complemented
261	C₂×#884	D₄	1	1	yes	characteristic, complemented
262	C₂×#884	D₄	1	1	yes	characteristic, complemented
263	C₂×#883	D₄	1	1	yes	characteristic, complemented
264	C₂×#882	D₄	1	1	yes	characteristic, complemented
265	C₂×#882	C₂³	1	1	yes	characteristic
266	C₂×#882	C₂³	1	1	yes	characteristic
267	C₂×#882	C₂³	1	1	yes	characteristic
268	C₂×#882	C₂³	1	1	yes	characteristic
269	#5486	C₂³	1	1	yes	characteristic
270	#5486	C₂³	1	1	yes	characteristic
271	C₂×#67⋊C₄	D₄	1	1	yes	characteristic, complemented
272	C₂×#67⋊C₄	D₄	1	1	yes	characteristic, complemented
273	C₂×#67⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	#5483	C₂³	1	1	yes	characteristic
279	C₂×#878	C₂³	1	1	yes	characteristic
280	C₂×C₃×#99	C₂³	1	1	yes	characteristic
281	C₂×C₃×#99	C₂³	1	1	yes	characteristic
282	C₂×C₃×#99	C₂³	1	1	yes	characteristic
283	C₂×C₃×#99	C₂³	1	1	yes	characteristic
284	C₂×C₃×#99	C₂³	1	1	yes	characteristic
285	C₂×C₃×#99	C₂³	1	1	yes	characteristic
286	C₂×C₃×#99	C₂³	1	1	yes	characteristic
287	C₂×C₃×#99	C₂³	1	1	yes	characteristic
288	C₃×#379	C₂³	1	1	yes	characteristic
289	C₃×#379	C₂³	1	1	yes	characteristic
290	C₃×#379	C₂³	1	1	yes	characteristic
291	C₃×#379	C₂³	1	1	yes	characteristic
292	C₃×#379	C₂³	1	1	yes	characteristic
293	C₃×#379	C₂³	1	1	yes	characteristic
294	#5247	C₂³	1	1	yes	characteristic
295	#5247	C₂³	1	1	yes	characteristic
296	#5247	C₂³	1	1	yes	characteristic
297	#5247	C₂³	1	1	yes	characteristic
298	#5247	C₂³	1	1	yes	characteristic
299	#5247	C₂³	1	1	yes	characteristic
300	#5247	C₂³	1	1	yes	characteristic
301	#5220	C₂³	1	1	yes	characteristic
302	#5220	C₂³	1	1	yes	characteristic
303	#5220	C₂³	1	1	yes	characteristic
304	#5220	C₂³	1	1	yes	characteristic
305	C₂×#834	C₂³	1	1	yes	characteristic
306	C₂×#834	C₂³	1	1	yes	characteristic
307	C₂×#834	C₂³	1	1	yes	characteristic
308	C₂×#834	C₂³	1	1	yes	characteristic
309	C₂×#834	C₂³	1	1	yes	characteristic
310	C₂×#834	C₂³	1	1	yes	characteristic
311	C₂×#834	C₂³	1	1	yes	characteristic
312	C₂×#834	C₂³	1	1	yes	characteristic
313	#4958	C₂³	1	1	yes	characteristic
314	#4958	C₂³	1	1	yes	characteristic
315	#4958	C₂³	1	1	yes	characteristic
316	#4955	C₂³	1	1	yes	characteristic
317	#4955	C₂³	1	1	yes	characteristic
318	#4955	C₂³	1	1	yes	characteristic
319	#4955	C₂³	1	1	yes	characteristic
320	#4955	C₂³	1	1	yes	characteristic
321	#4955	C₂³	1	1	yes	characteristic
322	#4955	C₂³	1	1	yes	characteristic
323	#4955	C₂³	1	1	yes	characteristic
324	C₂×#806	C₂³	1	1	yes	characteristic
325	C₂×#806	C₂³	1	1	yes	characteristic
326	C₂×#806	C₂³	1	1	yes	characteristic
327	C₂×#806	C₂³	1	1	yes	characteristic
328	C₂×#806	C₂³	1	1	yes	characteristic
329	C₂×#806	C₂³	1	1	yes	characteristic
330	C₂×#806	C₂³	1	1	yes	characteristic
331	C₂×#806	C₂³	1	1	yes	characteristic
332	C₂×#806	C₂³	1	1	yes	characteristic
333	C₂×#806	C₂³	1	1	yes	characteristic
334	C₂×#806	C₂³	1	1	yes	characteristic
335	C₂×#806	C₂³	1	1	yes	characteristic
336	#4950	C₂³	1	1	yes	characteristic
337	#4950	C₂³	1	1	yes	characteristic
338	#4950	C₂³	1	1	yes	characteristic
339	#4946	C₂³	1	1	yes	characteristic
340	#4946	C₂³	1	1	yes	characteristic
341	#4942	C₂³	1	1	yes	characteristic
342	#4942	C₂³	1	1	yes	characteristic
343	#4942	C₂³	1	1	yes	characteristic
344	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
345	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
346	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
347	C₃×#342	C₂³	1	1	yes	characteristic
348	C₃×#342	C₂³	1	1	yes	characteristic
349	C₃×#342	C₂³	1	1	yes	characteristic
350	C₃×#342	C₂³	1	1	yes	characteristic
351	#4527	C₂³	1	1	yes	characteristic
352	#4527	C₂³	1	1	yes	characteristic
353	#4527	C₂³	1	1	yes	characteristic
354	#4527	C₂³	1	1	yes	characteristic
355	#4527	C₂³	1	1	yes	characteristic
356	#4527	C₂³	1	1	yes	characteristic
357	#4527	C₂³	1	1	yes	characteristic
358	#4527	C₂³	1	1	yes	characteristic
359	#4527	C₂³	1	1	yes	characteristic
360	#4527	C₂³	1	1	yes	characteristic
361	#4527	C₂³	1	1	yes	characteristic
362	#4527	C₂³	1	1	yes	characteristic
363	#4526	C₂³	1	1	yes	characteristic
364	#4526	C₂³	1	1	yes	characteristic
365	#4526	C₂³	1	1	yes	characteristic
366	#4526	C₂³	1	1	yes	characteristic
367	#3484	C₂×D₃	1	1	yes	characteristic, complemented
368	C₂²×#120	C₂×D₃	1	1	yes	characteristic, complemented
369	C₂×B(4,𝔽₂)	C₂×D₃	1	1	yes	characteristic, complemented
370	C₂×B(4,𝔽₂)	C₂×D₃	1	1	yes	characteristic, complemented
371	#2846	C₂×D₃	1	1	yes	characteristic, complemented
372	#2846	C₂×D₃	1	1	yes	characteristic, complemented
373	#2021	C₂×D₃	1	1	yes	characteristic, complemented
374	#2021	C₂×D₃	1	1	yes	characteristic, complemented
375	#2021	C₂×D₃	1	1	yes	characteristic, complemented
376	#2021	C₂×D₃	1	1	yes	characteristic, complemented
377	#1898	C₂×D₃	1	1	yes	characteristic, complemented
378	#1898	C₂×D₃	1	1	yes	characteristic, complemented
379	#1889	C₂×D₃	1	1	yes	characteristic, complemented
380	#1889	C₂×D₃	1	1	yes	characteristic, complemented
381	#1781	C₂×D₃	1	1	yes	characteristic, complemented
382	C₂⁵×C₃	C₂×D₄	1	1	yes	characteristic, complemented
383	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
384	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
385	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic, complemented
387	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic, complemented
388	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic, complemented
389	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
390	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
392	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
393	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
394	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
395	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
396	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
397	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
401	C₂³×C₃×C₄	C₂×D₄	1	1	yes	characteristic, complemented
402	C₂²×#67	C₂×D₄	1	1	yes	characteristic
403	C₂²×#67	C₂×D₄	1	1	yes	characteristic
404	C₂²×#67	C₂×D₄	1	1	yes	characteristic
405	C₂²×#67	C₂×D₄	1	1	yes	characteristic
406	C₂²×#67	C₂×D₄	1	1	yes	characteristic
407	C₂²×#67	C₂×D₄	1	1	yes	characteristic
408	C₂²×#67	C₂×D₄	1	1	yes	characteristic
409	C₂²×#67	C₂×D₄	1	1	yes	characteristic
410	C₂²×#67	C₂×D₄	1	1	yes	characteristic
411	C₂²×#67	C₂×D₄	1	1	yes	characteristic
412	C₂²×#67	C₂×D₄	1	1	yes	characteristic
413	C₂²×#67	C₂×D₄	1	1	yes	characteristic
414	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
415	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
416	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
417	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
418	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
419	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
420	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
421	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
422	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
423	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
424	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
425	C₂²×#67	C₂×D₄	1	1	yes	characteristic, complemented
426	C₂²×#67	C₂⁴	1	1	yes	characteristic
427	C₂²×#67	C₂⁴	1	1	yes	characteristic
428	C₂²×#67	C₂⁴	1	1	yes	characteristic
429	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
430	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
431	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
432	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
433	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
434	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
435	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
436	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
437	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
438	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
439	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
440	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
441	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
442	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
443	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
444	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
445	C₂²×Dic₆	C₂×D₄	1	1	yes	characteristic, complemented
446	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
447	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
448	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
449	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
450	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
456	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
457	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
458	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
459	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
460	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
461	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
462	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
463	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
464	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
465	C₂×#217	C₂×D₄	1	1	yes	characteristic, complemented
466	C₂×#217	C₂⁴	1	1	yes	characteristic
467	C₂×#217	C₂⁴	1	1	yes	characteristic
468	C₂×#217	C₂⁴	1	1	yes	characteristic
469	C₂×#217	C₂⁴	1	1	yes	characteristic
470	C₂×#217	C₂⁴	1	1	yes	characteristic
471	C₂×#217	C₂⁴	1	1	yes	characteristic
472	C₂×#217	C₂⁴	1	1	yes	characteristic
473	C₂×#217	C₂⁴	1	1	yes	characteristic
474	C₂×#217	C₂⁴	1	1	yes	characteristic
475	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
476	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
477	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
478	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
479	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
480	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
481	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
482	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
483	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
484	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
485	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
486	C₂×C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
487	C₂×C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
488	C₂×C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
489	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
490	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
491	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
492	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
493	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
494	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
495	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
496	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂⁶	C₂²×D₃	1	1	yes	characteristic
498	C₂×H(5,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
499	C₂³×D₄	C₂²×D₃	1	1	yes	characteristic
500	#534	C₂²×D₃	1	1	yes	characteristic
501	#534	C₂²×D₃	1	1	yes	characteristic
502	C₂×#120	C₂²×D₃	1	1	yes	characteristic
503	C₂×#120	C₂²×D₃	1	1	yes	characteristic
504	C₂×#120	C₂²×D₃	1	1	yes	characteristic
505	C₂×#120	C₂²×D₃	1	1	yes	characteristic
506	C₂×#120	C₂²×D₃	1	1	yes	characteristic
507	C₂×#120	C₂²×D₃	1	1	yes	characteristic
508	C₂×#120	C₂²×D₃	1	1	yes	characteristic
509	C₂×#120	C₂²×D₃	1	1	yes	characteristic
510	C₂×#120	C₂²×D₃	1	1	yes	characteristic
511	C₂×#120	C₂²×D₃	1	1	yes	characteristic
512	#518	C₂²×D₃	1	1	yes	characteristic
513	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
514	C₂×#99	C₂²×D₃	1	1	yes	characteristic
515	C₂×#99	C₂²×D₃	1	1	yes	characteristic
516	C₂×#99	C₂²×D₃	1	1	yes	characteristic
517	C₂×#99	C₂²×D₃	1	1	yes	characteristic
518	C₂×#99	C₂²×D₃	1	1	yes	characteristic
519	C₂×#99	C₂²×D₃	1	1	yes	characteristic
520	C₂×#99	C₂²×D₃	1	1	yes	characteristic
521	C₂×#99	C₂²×D₃	1	1	yes	characteristic
522	#379	C₂²×D₃	1	1	yes	characteristic
523	#379	C₂²×D₃	1	1	yes	characteristic
524	#379	C₂²×D₃	1	1	yes	characteristic
525	#379	C₂²×D₃	1	1	yes	characteristic
526	#379	C₂²×D₃	1	1	yes	characteristic
527	#379	C₂²×D₃	1	1	yes	characteristic
528	#342	C₂²×D₃	1	1	yes	characteristic
529	#342	C₂²×D₃	1	1	yes	characteristic
530	#342	C₂²×D₃	1	1	yes	characteristic
531	#342	C₂²×D₃	1	1	yes	characteristic
532	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
533	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
534	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
535	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
536	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
537	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
538	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
539	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
540	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
541	C₂⁴×C₃	C₂²×D₄	1	1	yes	characteristic
542	C₂⁴×C₃	H(5,𝔽₂)	1	2	yes	complemented
543	C₂⁴×C₃	C₂⁵	1	1	yes	characteristic
544	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
545	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
546	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
547	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
548	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
549	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
550	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
551	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
552	C₂³×D₃	C₂²×D₄	1	1	yes	characteristic
553	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
556	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
557	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
560	C₂²×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
561	C₂×#67	#120	1	1	yes	characteristic
562	C₂×#67	#120	1	1	yes	characteristic
563	C₂×#67	#120	1	1	yes	characteristic
564	C₂×#67	#120	1	1	yes	characteristic
565	C₂×#67	#120	1	1	yes	characteristic
566	C₂×#67	#120	1	1	yes	characteristic
567	C₂×#67	#120	1	1	yes	characteristic
568	C₂×#67	#120	1	1	yes	characteristic
569	C₂×#67	#120	1	1	yes	characteristic
570	C₂×#67	#120	1	1	yes	characteristic
571	C₂×#67	#120	1	1	yes	characteristic
572	C₂×#67	#120	1	1	yes	characteristic
573	C₂×#67	#120	1	1	yes	characteristic
574	C₂×#67	#120	1	1	yes	characteristic
575	C₂×#67	#120	1	1	yes	characteristic
576	C₂×#67	#120	1	1	yes	characteristic
577	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
578	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
579	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
580	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
581	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
582	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
583	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
584	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
585	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
586	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
587	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
588	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
589	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
590	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
591	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
592	C₃×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	complemented
593	#217	H(5,𝔽₂)	1	2	yes	complemented
594	C₂⁵	D₃×D₄	1	1	yes	characteristic, complemented
595	C₂⁵	C₂³×D₃	1	1	yes	characteristic
596	C₂⁵	C₂³×D₃	1	1	yes	characteristic
597	C₂⁵	C₂³×D₃	1	1	yes	characteristic
598	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
599	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
600	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
601	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
602	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
603	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
604	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
605	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
606	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
607	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
608	C₂³×C₄	D₃×D₄	1	1	yes	characteristic, complemented
609	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic, complemented
610	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic, complemented
611	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic, complemented
612	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic, complemented
613	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
621	C₂³×C₃	C₂×#120	1	1	yes	characteristic
622	C₂³×C₃	C₂×#120	1	1	yes	characteristic
623	C₂³×C₃	C₂×#120	1	1	yes	characteristic
624	C₂³×C₃	C₂×#120	1	1	yes	characteristic
625	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
626	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
627	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
628	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂³×C₃	#585	1	1	yes	characteristic
632	C₂²×D₃	C₂×#120	1	1	yes	characteristic
633	C₂²×D₃	C₂×#120	1	1	yes	characteristic
634	C₂²×D₃	C₂×#120	1	1	yes	characteristic
635	C₂²×D₃	C₂×#120	1	1	yes	characteristic
636	#67	B(4,𝔽₂)	1	4	yes	complemented
637	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
638	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
639	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
640	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
641	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
642	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
643	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
644	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
645	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
646	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
647	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
648	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
649	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
650	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
651	C₂⁴	#1004	1	2	yes	complemented
652	C₂⁴	C₂⁴×D₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
661	C₂²⋊C₄	#1004	1	2	yes	complemented
662	C₂²×C₃	C₂×B(4,𝔽₂)	1	2	yes	—
663	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
664	C₂²×C₃	#3484	1	1	yes	characteristic
665	C₂²×C₃	#3484	1	1	yes	characteristic
666	C₂²×C₃	#3488	1	1	yes	characteristic
667	C₂²×C₃	#3496	1	1	yes	characteristic
668	C₂²×C₃	#3496	1	1	yes	characteristic
669	C₂²×C₃	#3498	1	1	yes	characteristic
670	C₂×D₃	C₂×B(4,𝔽₂)	1	2	yes	—
671	Dic₃	C₂×B(4,𝔽₂)	1	2	yes	—
672	C₂³	D₃×#120	1	1	yes	characteristic
673	C₂³	D₃×#120	1	1	yes	characteristic
674	C₂³	D₃×#120	1	1	yes	characteristic
675	C₂³	D₃×#120	1	1	yes	characteristic
676	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
677	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
678	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
679	C₂³	C₂×#1004	1	1	yes	characteristic
680	C₂³	C₂×#1004	1	1	yes	characteristic
681	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂³	#5966	1	1	yes	characteristic
683	C₂×C₃	#35680	1	1	yes	characteristic
684	C₂×C₃	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
685	C₂×C₃	#60399	1	1	yes	characteristic
686	C₂²	D₃×B(4,𝔽₂)	1	2	yes	—
687	C₂²	C₂×D₃×#120	1	1	yes	characteristic
688	C₂²	#85919	1	1	yes	characteristic
689	C₂²	#86298	1	1	yes	characteristic
690	C₂²	#86607	1	1	yes	characteristic
691	C₂²	#86608	1	1	yes	characteristic
692	C₂²	#86620	1	1	yes	characteristic
693	C₂²	#86621	1	1	yes	characteristic
694	C₃	#6533135	1	1	yes	characteristic, complemented, Sylow
695	C₂	#10981243	1	1	yes	characteristic
696	C₂	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
697	C₂	#11661935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂⁴×C₃	C₂⁵
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₃×#23900	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	#23900	D₃
hypocenter	C₃	#6533135
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #23900

Complements

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

N	H ≅ G/N	type
1. #11705060	C₂	semidirect
2. #10991609	C₂	semidirect
3. #10990485	C₂	semidirect
4. #67×#120	C₂	semidirect
5. #10901331	C₂	semidirect
6. #10900893	C₂	semidirect
7. #10900889	C₂	semidirect
8. #10850465	C₂	semidirect
9. #10848559	C₂	semidirect
10. #10848556	C₂	semidirect
11. #10848327	C₂	semidirect
12. #10848326	C₂	semidirect
13. #10832528	C₂	semidirect
14. #10832527	C₂	semidirect
15. #10832524	C₂	semidirect
16. #10832521	C₂	semidirect
17. #10830821	C₂	semidirect
18. #10829373	C₂	semidirect
19. #10829369	C₂	semidirect
20. #10827632	C₂	semidirect
21. #10827631	C₂	semidirect
22. #10826766	C₂	semidirect
23. #10826765	C₂	semidirect
24. #10826763	C₂	semidirect
25. #10823687	C₂	semidirect
26. C₂×#71671	C₂	semidirect
27. D₃×#2021	C₂	semidirect
28. #10811315	C₂	semidirect
29. #10810507	C₂	semidirect
30. #10810505	C₂	semidirect
31. C₃×#23900	C₂	semidirect
32. C₂⁴×#67	C₂²	semidirect
33. C₃×#3484	C₂²	semidirect
34. C₂²×C₃×#120	C₂²	semidirect
35. C₂²×#953	C₂²	semidirect
36. #87284	C₂²	semidirect
37. #87281	C₂²	semidirect
39. C₂×#5804	C₂²	semidirect
40. #86308	C₂²	semidirect
41. D₃×#534	C₂²	semidirect
42. #86299	C₂²	semidirect
43. #86295	C₂²	semidirect
44. #85919	C₂²	semidirect
47. C₂×D₃×#120	C₂²	semidirect
48. C₂×D₃×#120	C₂²	semidirect
49. #85913	C₂²	semidirect
50. #85868	C₂²	semidirect
51. #85861	C₂²	semidirect
52. C₂×C₃×B(4,𝔽₂)	C₂²	semidirect
53. C₂×C₃×B(4,𝔽₂)	C₂²	semidirect
54. C₃×#2846	C₂²	semidirect
55. C₃×#2846	C₂²	semidirect
56. #84128	C₂²	semidirect
57. C₂×#5247	C₂²	semidirect
58. C₂×#5244	C₂²	semidirect
59. #84052	C₂²	semidirect
60. C₂²×#834	C₂²	semidirect
61. #82612	C₂²	semidirect
62. #82612	C₂²	semidirect
63. #82606	C₂²	semidirect
64. #82606	C₂²	semidirect
65. #82605	C₂²	semidirect
66. #82605	C₂²	semidirect
67. #82604	C₂²	semidirect
68. #82604	C₂²	semidirect
69. C₂×#5032	C₂²	semidirect
70. C₂×#5032	C₂²	semidirect
71. #82601	C₂²	semidirect
72. #82601	C₂²	semidirect
73. #82588	C₂²	semidirect
74. #82588	C₂²	semidirect
75. #82582	C₂²	semidirect
76. #82582	C₂²	semidirect
77. Dic₃×#120	C₂²	semidirect
78. Dic₃×#120	C₂²	semidirect
79. #82127	C₂²	semidirect
80. C₂²⋊C₄×#67	C₂²	semidirect
81. C₂²×#806	C₂²	semidirect
82. C₂×D₃×#99	C₂²	semidirect
83. C₂×D₃×#99	C₂²	semidirect
84. C₂×#4741	C₂²	semidirect
85. #73861	C₂²	semidirect
86. #73854	C₂²	semidirect
87. #73853	C₂²	semidirect
88. #73852	C₂²	semidirect
89. #73850	C₂²	semidirect
90. #73850	C₂²	semidirect
91. D₃×#379	C₂²	semidirect
92. #73846	C₂²	semidirect
93. #73827	C₂²	semidirect
94. #73824	C₂²	semidirect
95. #73823	C₂²	semidirect
96. #73818	C₂²	semidirect
97. C₃×#2021	C₂²	semidirect
98. C₃×#2021	C₂²	semidirect
99. C₃×#2021	C₂²	semidirect
100. C₃×#2021	C₂²	semidirect
101. C₃×#1898	C₂²	semidirect
102. C₃×#1898	C₂²	semidirect
103. C₃×#1889	C₂²	semidirect
104. C₃×#1889	C₂²	semidirect
105. C₃×#1781	C₂²	semidirect
106. #72142	C₂²	semidirect
107. #71851	C₂²	semidirect
108. #71851	C₂²	semidirect
109. #71850	C₂²	semidirect
110. #71850	C₂²	semidirect
111. #71671	C₂²	semidirect
112. #71671	C₂²	semidirect
113. #71671	C₂²	semidirect
114. #71671	C₂²	semidirect
115. #71671	C₂²	semidirect
116. #71671	C₂²	semidirect
117. #71671	C₂²	semidirect
118. #71671	C₂²	semidirect
119. #71671	C₂²	semidirect
120. #71671	C₂²	semidirect
121. #71671	C₂²	semidirect
122. #71671	C₂²	semidirect
123. #71670	C₂²	semidirect
124. #71670	C₂²	semidirect
125. #71669	C₂²	semidirect
126. #71669	C₂²	semidirect
127. #71657	C₂²	semidirect
128. #71654	C₂²	semidirect
129. C₂×#4527	C₂²	semidirect
130. #70037	C₂²	semidirect
131. #70037	C₂²	semidirect
132. #70037	C₂²	semidirect
133. #70037	C₂²	semidirect
134. #70037	C₂²	semidirect
135. #70037	C₂²	semidirect
136. #70036	C₂²	semidirect
137. #70036	C₂²	semidirect
138. #70036	C₂²	semidirect
139. #70036	C₂²	semidirect
140. #70035	C₂²	semidirect
141. #70035	C₂²	semidirect
142. #70033	C₂²	semidirect
143. #70032	C₂²	semidirect
144. #70032	C₂²	semidirect
145. #70032	C₂²	semidirect
146. #70032	C₂²	semidirect
147. #70032	C₂²	semidirect
148. #70032	C₂²	semidirect
149. #70030	C₂²	semidirect
150. #70030	C₂²	semidirect
151. #70030	C₂²	semidirect
152. #70030	C₂²	semidirect
153. #70028	C₂²	semidirect
154. #70028	C₂²	semidirect
155. Dic₃×#99	C₂²	semidirect
156. Dic₃×#99	C₂²	semidirect
157. #70022	C₂²	semidirect
158. #70021	C₂²	semidirect
159. #69500	C₂²	semidirect
160. #69500	C₂²	semidirect
161. #69499	C₂²	semidirect
162. #69499	C₂²	semidirect
163. #69499	C₂²	semidirect
164. #69499	C₂²	semidirect
165. #69498	C₂²	semidirect
166. #69497	C₂²	semidirect
167. #69497	C₂²	semidirect
168. #69496	C₂²	semidirect
169. #69496	C₂²	semidirect
170. #69495	C₂²	semidirect
171. #68971	C₂²	semidirect
172. #68970	C₂²	semidirect
173. #68970	C₂²	semidirect
174. #68969	C₂²	semidirect
175. D₃×#342	C₂²	semidirect
176. #68965	C₂²	semidirect
177. #68962	C₂²	semidirect
178. #68962	C₂²	semidirect
179. #68961	C₂²	semidirect
180. #68961	C₂²	semidirect
181. #68959	C₂²	semidirect
182. #68958	C₂²	semidirect
183. #68957	C₂²	semidirect
184. #68955	C₂²	semidirect
185. #68955	C₂²	semidirect
186. #68952	C₂²	semidirect
187. #23900	D₃	semidirect
192. C₂³×#67	D₄	semidirect
200. C₂²×#237	D₄	semidirect
201. C₂²×D₃×D₄	D₄	semidirect
218. C₂×#953	D₄	semidirect
235. C₂×#940	D₄	semidirect
236. C₂×#940	D₄	semidirect
237. C₂×#939	D₄	semidirect
238. C₂×#939	D₄	semidirect
239. C₂×#939	D₄	semidirect
240. C₂×#939	D₄	semidirect
243. C₂×#938	D₄	semidirect
244. C₂×#938	D₄	semidirect
245. C₂×#937	D₄	semidirect
246. C₂×#937	D₄	semidirect
256. C₂×#930	D₄	semidirect
257. C₂×C₄×#67	D₄	semidirect
259. C₂×#886	D₄	semidirect
260. C₂×#885	D₄	semidirect
261. C₂×#884	D₄	semidirect
262. C₂×#884	D₄	semidirect
263. C₂×#883	D₄	semidirect
264. C₂×#882	D₄	semidirect
271. C₂×#67⋊C₄	D₄	semidirect
272. C₂×#67⋊C₄	D₄	semidirect
367. #3484	C₂×D₃	semidirect
368. C₂²×#120	C₂×D₃	semidirect
369. C₂×B(4,𝔽₂)	C₂×D₃	semidirect
370. C₂×B(4,𝔽₂)	C₂×D₃	semidirect
371. #2846	C₂×D₃	semidirect
372. #2846	C₂×D₃	semidirect
373. #2021	C₂×D₃	semidirect
374. #2021	C₂×D₃	semidirect
375. #2021	C₂×D₃	semidirect
376. #2021	C₂×D₃	semidirect
377. #1898	C₂×D₃	semidirect
378. #1898	C₂×D₃	semidirect
379. #1889	C₂×D₃	semidirect
380. #1889	C₂×D₃	semidirect
381. #1781	C₂×D₃	semidirect
382. C₂⁵×C₃	C₂×D₄	semidirect
386. C₂⁴×D₃	C₂×D₄	semidirect
387. C₂⁴×D₃	C₂×D₄	semidirect
388. C₂⁴×D₃	C₂×D₄	semidirect
391. C₂²×C₃×D₄	C₂×D₄	semidirect
392. C₂²×C₃×D₄	C₂×D₄	semidirect
393. C₂²×C₃×D₄	C₂×D₄	semidirect
394. C₂²×C₃×D₄	C₂×D₄	semidirect
395. C₂²×C₃×D₄	C₂×D₄	semidirect
396. C₂²×C₃×D₄	C₂×D₄	semidirect
401. C₂³×C₃×C₄	C₂×D₄	semidirect
414. C₂²×#67	C₂×D₄	semidirect
415. C₂²×#67	C₂×D₄	semidirect
416. C₂²×#67	C₂×D₄	semidirect
417. C₂²×#67	C₂×D₄	semidirect
418. C₂²×#67	C₂×D₄	semidirect
419. C₂²×#67	C₂×D₄	semidirect
420. C₂²×#67	C₂×D₄	semidirect
421. C₂²×#67	C₂×D₄	semidirect
422. C₂²×#67	C₂×D₄	semidirect
423. C₂²×#67	C₂×D₄	semidirect
424. C₂²×#67	C₂×D₄	semidirect
425. C₂²×#67	C₂×D₄	semidirect
429. C₂³×Dic₃	C₂×D₄	semidirect
430. C₂³×Dic₃	C₂×D₄	semidirect
431. C₂³×Dic₃	C₂×D₄	semidirect
432. C₂³×Dic₃	C₂×D₄	semidirect
433. C₂³×Dic₃	C₂×D₄	semidirect
436. C₂²×D₁₂	C₂×D₄	semidirect
437. C₂²×D₁₂	C₂×D₄	semidirect
438. C₂²×D₁₂	C₂×D₄	semidirect
439. C₂²×D₁₂	C₂×D₄	semidirect
440. C₂²×C₄×D₃	C₂×D₄	semidirect
441. C₂²×C₄×D₃	C₂×D₄	semidirect
442. C₂²×C₄×D₃	C₂×D₄	semidirect
443. C₂²×C₄×D₃	C₂×D₄	semidirect
444. C₂²×C₄×D₃	C₂×D₄	semidirect
445. C₂²×Dic₆	C₂×D₄	semidirect
446. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
447. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
448. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
449. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
458. C₂×#217	C₂×D₄	semidirect
459. C₂×#217	C₂×D₄	semidirect
460. C₂×#217	C₂×D₄	semidirect
461. C₂×#217	C₂×D₄	semidirect
462. C₂×#217	C₂×D₄	semidirect
463. C₂×#217	C₂×D₄	semidirect
464. C₂×#217	C₂×D₄	semidirect
465. C₂×#217	C₂×D₄	semidirect
475. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
476. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
477. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
478. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
479. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
480. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
481. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
482. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
483. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
484. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
485. C₂×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
486. C₂×C₄⋊Dic₃	C₂×D₄	semidirect
487. C₂×C₄⋊Dic₃	C₂×D₄	semidirect
488. C₂×C₄⋊Dic₃	C₂×D₄	semidirect
489. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
490. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
491. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
492. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
493. C₂×Dic₃⋊C₄	C₂×D₄	semidirect
494. C₂×C₄×Dic₃	C₂×D₄	semidirect
495. C₂×C₄×Dic₃	C₂×D₄	semidirect
496. C₂×C₄×Dic₃	C₂×D₄	semidirect
542. C₂⁴×C₃	H(5,𝔽₂)	semidirect
592. C₃×C₂²⋊C₄	H(5,𝔽₂)	semidirect
593. #217	H(5,𝔽₂)	semidirect
594. C₂⁵	D₃×D₄	semidirect
598. C₂²×D₄	D₃×D₄	semidirect
599. C₂²×D₄	D₃×D₄	semidirect
600. C₂²×D₄	D₃×D₄	semidirect
601. C₂²×D₄	D₃×D₄	semidirect
602. C₂²×D₄	D₃×D₄	semidirect
603. C₂²×D₄	D₃×D₄	semidirect
608. C₂³×C₄	D₃×D₄	semidirect
609. C₂×C₂²⋊C₄	D₃×D₄	semidirect
610. C₂×C₂²⋊C₄	D₃×D₄	semidirect
611. C₂×C₂²⋊C₄	D₃×D₄	semidirect
612. C₂×C₂²⋊C₄	D₃×D₄	semidirect
636. #67	B(4,𝔽₂)	semidirect
651. C₂⁴	#1004	semidirect
661. C₂²⋊C₄	#1004	semidirect
694. C₃	#6533135	semidirect

Maximal subgroups

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

subgroup	index
#11705060	2
#10991609	2
#10990485	2
#67×#120	2
#10901331	2
#10900893	2
#10900889	2
#10850465	2
#10848559	2
#10848556	2
#10848327	2
#10848326	2
#10832528	2
#10832527	2
#10832524	2
#10832521	2
#10830821	2
#10829373	2
#10829369	2
#10827632	2
#10827631	2
#10826766	2
#10826765	2
#10826763	2
#10823687	2
C₂×#71671	2
D₃×#2021	2
#10811315	2
#10810507	2
#10810505	2
C₃×#23900	2
#6533135	3