Subgroups — #72271867

Order 1536.

At least 7306 conjugacy classes of subgroups; only the 719 normal subgroups are shown.

The subgroup lattice has 702 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11707305	C₂	1	1	yes	maximal, characteristic, complemented
2	#10991609	C₂	1	1	yes	maximal, characteristic, complemented
3	#10991603	C₂	1	1	yes	maximal, characteristic, complemented
4	#10990485	C₂	1	1	yes	maximal, characteristic, complemented
5	#10945064	C₂	1	1	yes	maximal, characteristic, complemented
6	#10945062	C₂	1	1	yes	maximal, characteristic, complemented
7	#10944214	C₂	1	1	yes	maximal, characteristic, complemented
8	#10852214	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	#10848332	C₂	1	1	yes	maximal, characteristic, complemented
12	#10848327	C₂	1	1	yes	maximal, characteristic, complemented
13	#10848326	C₂	1	1	yes	maximal, characteristic, complemented
14	#10848323	C₂	1	1	yes	maximal, characteristic, complemented
15	#10832527	C₂	1	1	yes	maximal, characteristic, complemented
16	#10832521	C₂	1	1	yes	maximal, characteristic, complemented
17	#10831847	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	#10827635	C₂	1	1	yes	maximal, characteristic, complemented
21	#10827632	C₂	1	1	yes	maximal, characteristic, complemented
22	#10827631	C₂	1	1	yes	maximal, characteristic, complemented
23	#10826766	C₂	1	1	yes	maximal, characteristic, complemented
24	#10826763	C₂	1	1	yes	maximal, characteristic, complemented
25	#10811315	C₂	1	1	yes	maximal, characteristic, complemented
26	#10811313	C₂	1	1	yes	maximal, characteristic, complemented
27	#10810507	C₂	1	1	yes	maximal, characteristic, complemented
28	#10801172	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#69499	C₂	1	1	yes	maximal, characteristic, complemented
30	D₃×#1889	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃×#23984	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×#67	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3490	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#953	C₂²	1	1	yes	characteristic
35	#86579	C₂²	1	1	yes	characteristic, complemented
36	#86574	C₂²	1	1	yes	characteristic, complemented
37	#86308	C₂²	1	1	yes	characteristic, complemented
38	#86299	C₂²	1	1	yes	characteristic, complemented
39	#85919	C₂²	1	1	yes	characteristic, complemented
40	C₂×#5591	C₂²	1	1	yes	characteristic
41	C₂×#5590	C₂²	1	1	yes	characteristic
42	C₂×D₃×#120	C₂²	1	1	yes	characteristic
43	#85913	C₂²	1	1	yes	characteristic, complemented
44	#85868	C₂²	1	1	yes	characteristic, complemented
45	D₃×#518	C₂²	1	1	yes	characteristic, complemented
46	#85861	C₂²	1	1	yes	characteristic, complemented
47	#85857	C₂²	1	1	yes	characteristic, complemented
48	C₂×#5490	C₂²	1	1	yes	characteristic
49	C₂×#5486	C₂²	1	1	yes	characteristic, complemented
50	C₃×#2846	C₂²	1	1	yes	characteristic, complemented
51	C₃×#2846	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×#379	C₂²	1	1	yes	characteristic, complemented
53	#84128	C₂²	1	1	yes	characteristic, complemented
54	C₂×#5247	C₂²	1	1	yes	characteristic, complemented
55	#82612	C₂²	1	1	yes	characteristic, complemented
56	#82606	C₂²	1	1	yes	characteristic, complemented
57	#82606	C₂²	1	1	yes	characteristic, complemented
58	#82605	C₂²	1	1	yes	characteristic, complemented
59	#82604	C₂²	1	1	yes	characteristic
60	C₂×#5032	C₂²	1	1	yes	characteristic
61	C₂×#5032	C₂²	1	1	yes	characteristic, complemented
62	#82601	C₂²	1	1	yes	characteristic, complemented
63	#82588	C₂²	1	1	yes	characteristic, complemented
64	#82582	C₂²	1	1	yes	characteristic, complemented
65	Dic₃×#120	C₂²	1	1	yes	characteristic, complemented
66	#82127	C₂²	1	1	yes	characteristic, complemented
67	#82126	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊C₄×#67	C₂²	1	1	yes	characteristic, complemented
69	C₂²×#806	C₂²	1	1	yes	characteristic, complemented
70	C₂×D₃×#99	C₂²	1	1	yes	characteristic, complemented
71	C₂×#4741	C₂²	1	1	yes	characteristic, complemented
72	#73861	C₂²	1	1	yes	characteristic, complemented
73	#73861	C₂²	1	1	yes	characteristic, complemented
74	#73854	C₂²	1	1	yes	characteristic, complemented
75	#73854	C₂²	1	1	yes	characteristic, complemented
76	#73853	C₂²	1	1	yes	characteristic, complemented
77	#73853	C₂²	1	1	yes	characteristic, complemented
78	#73852	C₂²	1	1	yes	characteristic
79	#73850	C₂²	1	1	yes	characteristic, complemented
80	#73850	C₂²	1	1	yes	characteristic, complemented
81	D₃×#379	C₂²	1	1	yes	characteristic, complemented
82	D₃×#379	C₂²	1	1	yes	characteristic, complemented
83	#73846	C₂²	1	1	yes	characteristic, complemented
84	#73846	C₂²	1	1	yes	characteristic, complemented
85	#73827	C₂²	1	1	yes	characteristic, complemented
86	#73827	C₂²	1	1	yes	characteristic, complemented
87	#73824	C₂²	1	1	yes	characteristic
88	#73824	C₂²	1	1	yes	characteristic, complemented
89	#73823	C₂²	1	1	yes	characteristic, complemented
90	#73818	C₂²	1	1	yes	characteristic
91	#73818	C₂²	1	1	yes	characteristic, complemented
92	C₃×#2029	C₂²	1	1	yes	characteristic, complemented
93	C₃×#2029	C₂²	1	1	yes	characteristic, complemented
94	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
95	C₃×#2021	C₂²	1	1	yes	characteristic, complemented
96	C₃×#1898	C₂²	1	1	yes	characteristic, complemented
97	C₃×#1898	C₂²	1	1	yes	characteristic, complemented
98	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
99	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
100	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
101	C₃×#1889	C₂²	1	1	yes	characteristic, complemented
102	C₃×#1819	C₂²	1	1	yes	characteristic, complemented
103	#71897	C₂²	1	1	yes	characteristic, complemented
104	#71895	C₂²	1	1	yes	characteristic, complemented
105	#71851	C₂²	1	1	yes	characteristic, complemented
106	#71850	C₂²	1	1	yes	characteristic, complemented
107	#71671	C₂²	1	1	yes	characteristic, complemented
108	#71671	C₂²	1	1	yes	characteristic, complemented
109	#71671	C₂²	1	1	yes	characteristic, complemented
110	#71671	C₂²	1	1	yes	characteristic, complemented
111	#71670	C₂²	1	1	yes	characteristic, complemented
112	#71670	C₂²	1	1	yes	characteristic, complemented
113	#71669	C₂²	1	1	yes	characteristic, complemented
114	#71669	C₂²	1	1	yes	characteristic, complemented
115	#71657	C₂²	1	1	yes	characteristic, complemented
116	#71657	C₂²	1	1	yes	characteristic, complemented
117	#71654	C₂²	1	1	yes	characteristic, complemented
118	#71654	C₂²	1	1	yes	characteristic, complemented
119	C₂×#4527	C₂²	1	1	yes	characteristic, complemented
120	C₂×#4526	C₂²	1	1	yes	characteristic, complemented
121	#70037	C₂²	1	1	yes	characteristic, complemented
122	#70037	C₂²	1	1	yes	characteristic, complemented
123	#70036	C₂²	1	1	yes	characteristic, complemented
124	#70036	C₂²	1	1	yes	characteristic, complemented
125	#70035	C₂²	1	1	yes	characteristic, complemented
126	#70033	C₂²	1	1	yes	characteristic, complemented
127	#70032	C₂²	1	1	yes	characteristic, complemented
128	#70032	C₂²	1	1	yes	characteristic, complemented
129	#70030	C₂²	1	1	yes	characteristic, complemented
130	#70030	C₂²	1	1	yes	characteristic, complemented
131	#70028	C₂²	1	1	yes	characteristic, complemented
132	Dic₃×#99	C₂²	1	1	yes	characteristic, complemented
133	#70022	C₂²	1	1	yes	characteristic, complemented
134	#70021	C₂²	1	1	yes	characteristic, complemented
135	#69500	C₂²	1	1	yes	characteristic, complemented
136	#69500	C₂²	1	1	yes	characteristic, complemented
137	#69499	C₂²	1	1	yes	characteristic
138	#69499	C₂²	1	1	yes	characteristic
139	#69499	C₂²	1	1	yes	characteristic
140	#69499	C₂²	1	1	yes	characteristic, complemented
141	#69499	C₂²	1	1	yes	characteristic, complemented
142	#69499	C₂²	1	1	yes	characteristic, complemented
143	#69499	C₂²	1	1	yes	characteristic, complemented
144	#69499	C₂²	1	1	yes	characteristic, complemented
145	#69499	C₂²	1	1	yes	characteristic, complemented
146	#69499	C₂²	1	1	yes	characteristic, complemented
147	#69499	C₂²	1	1	yes	characteristic, complemented
148	#69499	C₂²	1	1	yes	characteristic, complemented
149	#69498	C₂²	1	1	yes	characteristic, complemented
150	#69497	C₂²	1	1	yes	characteristic, complemented
151	#69497	C₂²	1	1	yes	characteristic, complemented
152	#69496	C₂²	1	1	yes	characteristic, complemented
153	#69496	C₂²	1	1	yes	characteristic, complemented
154	#69495	C₂²	1	1	yes	characteristic, complemented
155	#68971	C₂²	1	1	yes	characteristic, complemented
156	#68970	C₂²	1	1	yes	characteristic, complemented
157	#68970	C₂²	1	1	yes	characteristic, complemented
158	#68970	C₂²	1	1	yes	characteristic, complemented
159	#68970	C₂²	1	1	yes	characteristic, complemented
160	#68969	C₂²	1	1	yes	characteristic, complemented
161	#68969	C₂²	1	1	yes	characteristic, complemented
162	D₃×#342	C₂²	1	1	yes	characteristic, complemented
163	D₃×#342	C₂²	1	1	yes	characteristic, complemented
164	#68965	C₂²	1	1	yes	characteristic, complemented
165	#68962	C₂²	1	1	yes	characteristic, complemented
166	#68962	C₂²	1	1	yes	characteristic, complemented
167	#68962	C₂²	1	1	yes	characteristic, complemented
168	#68962	C₂²	1	1	yes	characteristic, complemented
169	#68962	C₂²	1	1	yes	characteristic, complemented
170	#68962	C₂²	1	1	yes	characteristic, complemented
171	#68961	C₂²	1	1	yes	characteristic, complemented
172	#68961	C₂²	1	1	yes	characteristic, complemented
173	#68961	C₂²	1	1	yes	characteristic, complemented
174	#68961	C₂²	1	1	yes	characteristic, complemented
175	#68961	C₂²	1	1	yes	characteristic, complemented
176	#68961	C₂²	1	1	yes	characteristic, complemented
177	#68959	C₂²	1	1	yes	characteristic, complemented
178	#68959	C₂²	1	1	yes	characteristic, complemented
179	#68958	C₂²	1	1	yes	characteristic, complemented
180	#68957	C₂²	1	1	yes	characteristic, complemented
181	#68955	C₂²	1	1	yes	characteristic, complemented
182	#68955	C₂²	1	1	yes	characteristic, complemented
183	#68955	C₂²	1	1	yes	characteristic, complemented
184	#68955	C₂²	1	1	yes	characteristic, complemented
185	#68952	C₂²	1	1	yes	characteristic, complemented
186	#68952	C₂²	1	1	yes	characteristic, complemented
187	#23984	D₃	1	1	yes	characteristic, complemented
188	C₂⁶×C₃	C₂³	1	1	yes	characteristic
189	C₂⁵×D₃	C₂³	1	1	yes	characteristic
190	C₂³×#67	C₂³	1	1	yes	characteristic
191	C₂³×#67	C₂³	1	1	yes	characteristic
192	C₂³×#67	C₂³	1	1	yes	characteristic
193	C₂³×#67	C₂³	1	1	yes	characteristic
194	C₂³×#67	C₂³	1	1	yes	characteristic
195	C₂⁴×Dic₃	C₂³	1	1	yes	characteristic
196	C₂×#1004	C₂³	1	1	yes	characteristic
197	C₂²×#237	D₄	1	1	yes	characteristic, complemented
198	C₂²×D₃×D₄	D₄	1	1	yes	characteristic, complemented
199	C₂²×D₃×D₄	C₂³	1	1	yes	characteristic
200	C₂²×#235	D₄	1	1	yes	characteristic, complemented
201	C₃×#543	C₂³	1	1	yes	characteristic
202	C₃×#534	C₂³	1	1	yes	characteristic
203	C₂×C₃×#120	C₂³	1	1	yes	characteristic
204	C₂×C₃×#120	C₂³	1	1	yes	characteristic
205	C₂×C₃×#120	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	C₃×#518	C₂³	1	1	yes	characteristic
210	C₃×#518	C₂³	1	1	yes	characteristic
211	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂²×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×#953	C₂³	1	1	yes	characteristic
214	C₂×#953	C₂³	1	1	yes	characteristic
215	C₂×#953	C₂³	1	1	yes	characteristic
216	C₂×#953	C₂³	1	1	yes	characteristic
217	C₂×#953	C₂³	1	1	yes	characteristic
218	C₂×#953	C₂³	1	1	yes	characteristic
219	C₂×#953	C₂³	1	1	yes	characteristic
220	C₂²×#217	C₂³	1	1	yes	characteristic
221	C₂²×#217	C₂³	1	1	yes	characteristic
222	C₂²×#217	C₂³	1	1	yes	characteristic
223	#5804	C₂³	1	1	yes	characteristic
224	#5804	C₂³	1	1	yes	characteristic
225	C₂×#940	D₄	1	1	yes	characteristic, complemented
226	C₂×#939	D₄	1	1	yes	characteristic, complemented
227	C₂×#939	D₄	1	1	yes	characteristic, complemented
228	C₂×#939	D₄	1	1	yes	characteristic, complemented
229	C₂×#939	C₂³	1	1	yes	characteristic
230	C₂×#938	D₄	1	1	yes	characteristic, complemented
231	C₂×#937	D₄	1	1	yes	characteristic, complemented
232	C₂×#937	C₂³	1	1	yes	characteristic
233	C₂×#937	C₂³	1	1	yes	characteristic
234	C₂×#937	C₂³	1	1	yes	characteristic
235	#5798	C₂³	1	1	yes	characteristic
236	C₂×D₄×Dic₃	C₂³	1	1	yes	characteristic
237	C₂×#930	D₄	1	1	yes	characteristic, complemented
238	C₂×#929	D₄	1	1	yes	characteristic, complemented
239	C₂×C₄×#67	D₄	1	1	yes	characteristic, complemented
240	#5493	C₂³	1	1	yes	characteristic
241	C₂×#886	D₄	1	1	yes	characteristic, complemented
242	C₂×#885	D₄	1	1	yes	characteristic, complemented
243	C₂×#885	D₄	1	1	yes	characteristic, complemented
244	C₂×#884	D₄	1	1	yes	characteristic, complemented
245	C₂×#884	D₄	1	1	yes	characteristic, complemented
246	C₂×#884	D₄	1	1	yes	characteristic, complemented
247	C₂×#884	D₄	1	1	yes	characteristic, complemented
248	C₂×#883	D₄	1	1	yes	characteristic, complemented
249	C₂×#883	D₄	1	1	yes	characteristic, complemented
250	C₂×#882	D₄	1	1	yes	characteristic, complemented
251	C₂×#882	C₂³	1	1	yes	characteristic
252	C₂×#882	C₂³	1	1	yes	characteristic
253	C₂×#882	C₂³	1	1	yes	characteristic
254	C₂×#882	C₂³	1	1	yes	characteristic
255	C₂×#882	C₂³	1	1	yes	characteristic
256	#5486	C₂³	1	1	yes	characteristic
257	#5486	C₂³	1	1	yes	characteristic
258	#5486	C₂³	1	1	yes	characteristic
259	#5486	C₂³	1	1	yes	characteristic
260	#5486	C₂³	1	1	yes	characteristic
261	#5486	C₂³	1	1	yes	characteristic
262	C₂×#67⋊C₄	D₄	1	1	yes	characteristic, complemented
263	C₂×#67⋊C₄	D₄	1	1	yes	characteristic, complemented
264	C₂×#67⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×#67⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	#5483	C₂³	1	1	yes	characteristic
272	C₂×#878	C₂³	1	1	yes	characteristic
273	C₂×#878	C₂³	1	1	yes	characteristic
274	C₂×C₃×#99	C₂³	1	1	yes	characteristic
275	C₂×C₃×#99	C₂³	1	1	yes	characteristic
276	C₂×C₃×#99	C₂³	1	1	yes	characteristic
277	C₂×C₃×#99	C₂³	1	1	yes	characteristic
278	C₃×#379	C₂³	1	1	yes	characteristic
279	C₃×#379	C₂³	1	1	yes	characteristic
280	C₃×#379	C₂³	1	1	yes	characteristic
281	C₃×#379	C₂³	1	1	yes	characteristic
282	C₃×#379	C₂³	1	1	yes	characteristic
283	C₃×#379	C₂³	1	1	yes	characteristic
284	C₃×#379	C₂³	1	1	yes	characteristic
285	C₃×#379	C₂³	1	1	yes	characteristic
286	C₃×#379	C₂³	1	1	yes	characteristic
287	C₃×#379	C₂³	1	1	yes	characteristic
288	#5247	C₂³	1	1	yes	characteristic
289	#5247	C₂³	1	1	yes	characteristic
290	#5247	C₂³	1	1	yes	characteristic
291	#5247	C₂³	1	1	yes	characteristic
292	#5247	C₂³	1	1	yes	characteristic
293	#5247	C₂³	1	1	yes	characteristic
294	#5247	C₂³	1	1	yes	characteristic
295	#5220	C₂³	1	1	yes	characteristic
296	#5220	C₂³	1	1	yes	characteristic
297	C₂×#834	C₂³	1	1	yes	characteristic
298	C₂×#834	C₂³	1	1	yes	characteristic
299	C₂×#834	C₂³	1	1	yes	characteristic
300	C₂×#834	C₂³	1	1	yes	characteristic
301	#4958	C₂³	1	1	yes	characteristic
302	#4958	C₂³	1	1	yes	characteristic
303	#4958	C₂³	1	1	yes	characteristic
304	#4955	C₂³	1	1	yes	characteristic
305	#4955	C₂³	1	1	yes	characteristic
306	#4955	C₂³	1	1	yes	characteristic
307	#4955	C₂³	1	1	yes	characteristic
308	#4955	C₂³	1	1	yes	characteristic
309	#4955	C₂³	1	1	yes	characteristic
310	#4955	C₂³	1	1	yes	characteristic
311	#4955	C₂³	1	1	yes	characteristic
312	#4955	C₂³	1	1	yes	characteristic
313	#4955	C₂³	1	1	yes	characteristic
314	C₂×#806	C₂³	1	1	yes	characteristic
315	C₂×#806	C₂³	1	1	yes	characteristic
316	C₂×#806	C₂³	1	1	yes	characteristic
317	C₂×#806	C₂³	1	1	yes	characteristic
318	C₂×#806	C₂³	1	1	yes	characteristic
319	C₂×#806	C₂³	1	1	yes	characteristic
320	C₂×#806	C₂³	1	1	yes	characteristic
321	C₂×#806	C₂³	1	1	yes	characteristic
322	C₂×#806	C₂³	1	1	yes	characteristic
323	C₂×#806	C₂³	1	1	yes	characteristic
324	C₂×#806	C₂³	1	1	yes	characteristic
325	C₂×#806	C₂³	1	1	yes	characteristic
326	#4950	C₂³	1	1	yes	characteristic
327	#4950	C₂³	1	1	yes	characteristic
328	#4950	C₂³	1	1	yes	characteristic
329	#4946	C₂³	1	1	yes	characteristic
330	#4946	C₂³	1	1	yes	characteristic
331	#4946	C₂³	1	1	yes	characteristic
332	#4946	C₂³	1	1	yes	characteristic
333	#4942	C₂³	1	1	yes	characteristic
334	#4942	C₂³	1	1	yes	characteristic
335	#4942	C₂³	1	1	yes	characteristic
336	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
339	C₃×#342	C₂³	1	1	yes	characteristic
340	C₃×#342	C₂³	1	1	yes	characteristic
341	C₃×#342	C₂³	1	1	yes	characteristic
342	C₃×#342	C₂³	1	1	yes	characteristic
343	C₃×#342	C₂³	1	1	yes	characteristic
344	C₃×#342	C₂³	1	1	yes	characteristic
345	C₃×#342	C₂³	1	1	yes	characteristic
346	C₃×#342	C₂³	1	1	yes	characteristic
347	#4527	C₂³	1	1	yes	characteristic
348	#4527	C₂³	1	1	yes	characteristic
349	#4527	C₂³	1	1	yes	characteristic
350	#4527	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	#4526	C₂³	1	1	yes	characteristic
360	#4526	C₂³	1	1	yes	characteristic
361	#4526	C₂³	1	1	yes	characteristic
362	#4526	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	#3490	C₂×D₃	1	1	yes	characteristic, complemented
368	#2846	C₂×D₃	1	1	yes	characteristic, complemented
369	#2846	C₂×D₃	1	1	yes	characteristic, complemented
370	C₂×#379	C₂×D₃	1	1	yes	characteristic, complemented
371	#2029	C₂×D₃	1	1	yes	characteristic, complemented
372	#2029	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	#1898	C₂×D₃	1	1	yes	characteristic, complemented
376	#1898	C₂×D₃	1	1	yes	characteristic, complemented
377	#1889	C₂×D₃	1	1	yes	characteristic, complemented
378	#1889	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	#1819	C₂×D₃	1	1	yes	characteristic, complemented
382	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
383	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
384	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
385	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic
386	C₂⁴×D₃	C₂×D₄	1	1	yes	characteristic
387	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
388	C₂⁴×D₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×D₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₃×D₄	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×D₄	C₂⁴	1	1	yes	characteristic
395	C₂³×C₃×C₄	C₂×D₄	1	1	yes	characteristic, complemented
396	C₂³×C₃×C₄	C₂×D₄	1	1	yes	characteristic, complemented
397	C₂²×#67	C₂×D₄	1	1	yes	characteristic
398	C₂²×#67	C₂×D₄	1	1	yes	characteristic
399	C₂²×#67	C₂×D₄	1	1	yes	characteristic
400	C₂²×#67	C₂×D₄	1	1	yes	characteristic
401	C₂²×#67	C₂×D₄	1	1	yes	characteristic
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, complemented
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	C₂⁴	1	1	yes	characteristic
418	C₂²×#67	C₂⁴	1	1	yes	characteristic
419	C₂²×#67	C₂⁴	1	1	yes	characteristic
420	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic
421	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
422	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
423	C₂³×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
424	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
425	C₂³×Dic₃	C₂⁴	1	1	yes	characteristic
426	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic
427	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic
428	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic
429	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
430	C₂²×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
431	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
434	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
435	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
436	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
437	C₂²×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
438	C₂²×Dic₆	C₂×D₄	1	1	yes	characteristic, complemented
439	C₂²×Dic₆	C₂×D₄	1	1	yes	characteristic, complemented
440	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
443	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
444	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
445	C₂×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
446	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₂×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
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	#953	#41	1	4	yes	complemented
457	C₂×#217	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
464	C₂×#217	C₂⁴	1	1	yes	characteristic
465	C₂×#217	C₂⁴	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
473	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
474	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
475	C₂×(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₄⋊Dic₃	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×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
489	C₂×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
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×Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
495	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic
496	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
498	C₂⁶	C₂²×D₃	1	1	yes	characteristic
499	#543	C₂²×D₃	1	1	yes	characteristic
500	#534	C₂²×D₃	1	1	yes	characteristic
501	C₂×#120	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	#518	C₂²×D₃	1	1	yes	characteristic
508	#518	C₂²×D₃	1	1	yes	characteristic
509	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
510	C₂²×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
511	C₂×#99	C₂²×D₃	1	1	yes	characteristic
512	C₂×#99	C₂²×D₃	1	1	yes	characteristic
513	C₂×#99	C₂²×D₃	1	1	yes	characteristic
514	C₂×#99	C₂²×D₃	1	1	yes	characteristic
515	#379	C₂²×D₃	1	1	yes	characteristic
516	#379	C₂²×D₃	1	1	yes	characteristic
517	#379	C₂²×D₃	1	1	yes	characteristic
518	#379	C₂²×D₃	1	1	yes	characteristic
519	#379	C₂²×D₃	1	1	yes	characteristic
520	#379	C₂²×D₃	1	1	yes	characteristic
521	#379	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	#342	C₂²×D₃	1	1	yes	characteristic
526	#342	C₂²×D₃	1	1	yes	characteristic
527	#342	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	#342	C₂²×D₃	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	C₂×#41	1	2	yes	complemented
542	C₂⁴×C₃	C₂⁵	1	1	yes	characteristic
543	C₂³×D₃	C₂²×D₄	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	C₂²×C₃×C₄	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	C₂²×C₃×C₄	C₂²×D₄	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	C₂×#67	#120	1	1	yes	characteristic
578	C₂×#67	C₂×#41	1	2	yes	—
579	C₂×#67	H(5,𝔽₂)	1	2	yes	—
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	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
593	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
594	C₂²×Dic₃	C₂²×D₄	1	1	yes	characteristic
595	#217	C₂×#41	1	2	yes	complemented
596	C₂⁵	C₂³×D₃	1	1	yes	characteristic
597	C₂⁵	C₂³×D₃	1	1	yes	characteristic
598	C₂⁵	C₂³×D₃	1	1	yes	characteristic
599	C₂²×D₄	D₃×D₄	1	1	yes	characteristic
600	C₂²×D₄	D₃×D₄	1	1	yes	characteristic
601	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
602	C₂²×D₄	D₃×D₄	1	1	yes	characteristic, complemented
603	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
604	C₂²×D₄	C₂³×D₃	1	1	yes	characteristic
605	C₂³×C₄	D₃×D₄	1	1	yes	characteristic, complemented
606	C₂³×C₄	D₃×D₄	1	1	yes	characteristic, complemented
607	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×D₃	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	C₂×#120	1	1	yes	characteristic
626	C₂³×C₃	C₂×#120	1	1	yes	characteristic
627	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
628	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
629	C₂³×C₃	C₂³×D₄	1	1	yes	characteristic
630	C₂³×C₃	C₂²×#41	1	1	yes	characteristic
631	C₂³×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂³×C₃	#585	1	1	yes	characteristic
633	C₂³×C₃	#585	1	1	yes	characteristic
634	C₂²×D₃	C₂×#120	1	1	yes	characteristic
635	C₂²×D₃	C₂×#120	1	1	yes	characteristic
636	C₂²×D₃	C₂×#120	1	1	yes	characteristic
637	C₂²×D₃	C₂×#120	1	1	yes	characteristic
638	C₂²×D₃	#546	1	2	yes	complemented
639	#67	B(4,𝔽₂)	1	4	yes	complemented
640	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
641	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
642	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
643	C₂×Dic₃	C₂×#120	1	1	yes	characteristic
644	C₂×Dic₃	#546	1	2	yes	complemented
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	C₂×D₃×D₄	1	1	yes	characteristic
652	C₂⁴	C₂×D₃×D₄	1	1	yes	characteristic
653	C₂⁴	D₃×#41	1	2	yes	complemented
654	C₂⁴	C₂⁴×D₃	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	C₂×D₃×D₄	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₃×D₄	1	1	yes	characteristic
665	C₂²×C₃	C₂×B(4,𝔽₂)	1	2	yes	—
666	C₂²×C₃	C₂²×#120	1	1	yes	characteristic
667	C₂²×C₃	C₂×#546	1	1	yes	characteristic
668	C₂²×C₃	D₄×#41	1	1	yes	characteristic
669	C₂²×C₃	D₄×#41	1	1	yes	characteristic
670	C₂²×C₃	#3485	1	1	yes	characteristic
671	C₂²×C₃	#3488	1	1	yes	characteristic
672	C₂²×C₃	#3488	1	1	yes	characteristic
673	C₂×D₃	C₂×B(4,𝔽₂)	1	2	yes	—
674	Dic₃	C₂×B(4,𝔽₂)	1	2	yes	—
675	C₂³	D₃×#120	1	1	yes	characteristic
676	C₂³	D₃×#120	1	1	yes	characteristic
677	C₂³	D₃×#120	1	1	yes	characteristic
678	C₂³	D₃×#120	1	1	yes	characteristic
679	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
680	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
681	C₂³	C₂²×D₃×D₄	1	1	yes	characteristic
682	C₂³	C₂×D₃×#41	1	1	yes	characteristic
683	C₂³	#5964	1	1	yes	characteristic
684	C₂³	D₃×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂³	#5966	1	1	yes	characteristic
686	C₂×C₃	#36212	1	1	yes	characteristic
687	C₂×C₃	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
688	C₂×C₃	#60399	1	1	yes	characteristic
689	C₂²	D₃×B(4,𝔽₂)	1	2	yes	—
690	C₂²	C₂×D₃×#120	1	1	yes	characteristic
691	C₂²	#86037	1	1	yes	characteristic
692	C₂²	#86331	1	1	yes	characteristic
693	C₂²	#86626	1	1	yes	characteristic
694	C₂²	#86629	1	1	yes	characteristic
695	C₂²	D₃×#546	1	1	yes	characteristic
696	C₂²	#86663	1	1	yes	characteristic
697	C₃	#6595772	1	1	yes	characteristic, complemented, Sylow
698	C₂	#10992724	1	1	yes	characteristic
699	C₂	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
700	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×#23984	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	#23984	D₃
hypocenter	C₃	#6595772
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #23984

Complements

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

N	H ≅ G/N	type
1. #11707305	C₂	semidirect
2. #10991609	C₂	semidirect
3. #10991603	C₂	semidirect
4. #10990485	C₂	semidirect
5. #10945064	C₂	semidirect
6. #10945062	C₂	semidirect
7. #10944214	C₂	semidirect
8. #10852214	C₂	semidirect
9. #10848559	C₂	semidirect
10. #10848556	C₂	semidirect
11. #10848332	C₂	semidirect
12. #10848327	C₂	semidirect
13. #10848326	C₂	semidirect
14. #10848323	C₂	semidirect
15. #10832527	C₂	semidirect
16. #10832521	C₂	semidirect
17. #10831847	C₂	semidirect
18. #10829373	C₂	semidirect
19. #10829369	C₂	semidirect
20. #10827635	C₂	semidirect
21. #10827632	C₂	semidirect
22. #10827631	C₂	semidirect
23. #10826766	C₂	semidirect
24. #10826763	C₂	semidirect
25. #10811315	C₂	semidirect
26. #10811313	C₂	semidirect
27. #10810507	C₂	semidirect
28. #10801172	C₂	semidirect
29. C₂×#69499	C₂	semidirect
30. D₃×#1889	C₂	semidirect
31. C₃×#23984	C₂	semidirect
32. C₂⁴×#67	C₂²	semidirect
33. C₃×#3490	C₂²	semidirect
35. #86579	C₂²	semidirect
36. #86574	C₂²	semidirect
37. #86308	C₂²	semidirect
38. #86299	C₂²	semidirect
39. #85919	C₂²	semidirect
43. #85913	C₂²	semidirect
44. #85868	C₂²	semidirect
45. D₃×#518	C₂²	semidirect
46. #85861	C₂²	semidirect
47. #85857	C₂²	semidirect
49. C₂×#5486	C₂²	semidirect
50. C₃×#2846	C₂²	semidirect
51. C₃×#2846	C₂²	semidirect
52. C₂×C₃×#379	C₂²	semidirect
53. #84128	C₂²	semidirect
54. C₂×#5247	C₂²	semidirect
55. #82612	C₂²	semidirect
56. #82606	C₂²	semidirect
57. #82606	C₂²	semidirect
58. #82605	C₂²	semidirect
61. C₂×#5032	C₂²	semidirect
62. #82601	C₂²	semidirect
63. #82588	C₂²	semidirect
64. #82582	C₂²	semidirect
65. Dic₃×#120	C₂²	semidirect
66. #82127	C₂²	semidirect
67. #82126	C₂²	semidirect
68. C₂²⋊C₄×#67	C₂²	semidirect
69. C₂²×#806	C₂²	semidirect
70. C₂×D₃×#99	C₂²	semidirect
71. C₂×#4741	C₂²	semidirect
72. #73861	C₂²	semidirect
73. #73861	C₂²	semidirect
74. #73854	C₂²	semidirect
75. #73854	C₂²	semidirect
76. #73853	C₂²	semidirect
77. #73853	C₂²	semidirect
79. #73850	C₂²	semidirect
80. #73850	C₂²	semidirect
81. D₃×#379	C₂²	semidirect
82. D₃×#379	C₂²	semidirect
83. #73846	C₂²	semidirect
84. #73846	C₂²	semidirect
85. #73827	C₂²	semidirect
86. #73827	C₂²	semidirect
88. #73824	C₂²	semidirect
89. #73823	C₂²	semidirect
91. #73818	C₂²	semidirect
92. C₃×#2029	C₂²	semidirect
93. C₃×#2029	C₂²	semidirect
94. C₃×#2021	C₂²	semidirect
95. C₃×#2021	C₂²	semidirect
96. C₃×#1898	C₂²	semidirect
97. C₃×#1898	C₂²	semidirect
98. C₃×#1889	C₂²	semidirect
99. C₃×#1889	C₂²	semidirect
100. C₃×#1889	C₂²	semidirect
101. C₃×#1889	C₂²	semidirect
102. C₃×#1819	C₂²	semidirect
103. #71897	C₂²	semidirect
104. #71895	C₂²	semidirect
105. #71851	C₂²	semidirect
106. #71850	C₂²	semidirect
107. #71671	C₂²	semidirect
108. #71671	C₂²	semidirect
109. #71671	C₂²	semidirect
110. #71671	C₂²	semidirect
111. #71670	C₂²	semidirect
112. #71670	C₂²	semidirect
113. #71669	C₂²	semidirect
114. #71669	C₂²	semidirect
115. #71657	C₂²	semidirect
116. #71657	C₂²	semidirect
117. #71654	C₂²	semidirect
118. #71654	C₂²	semidirect
119. C₂×#4527	C₂²	semidirect
120. C₂×#4526	C₂²	semidirect
121. #70037	C₂²	semidirect
122. #70037	C₂²	semidirect
123. #70036	C₂²	semidirect
124. #70036	C₂²	semidirect
125. #70035	C₂²	semidirect
126. #70033	C₂²	semidirect
127. #70032	C₂²	semidirect
128. #70032	C₂²	semidirect
129. #70030	C₂²	semidirect
130. #70030	C₂²	semidirect
131. #70028	C₂²	semidirect
132. Dic₃×#99	C₂²	semidirect
133. #70022	C₂²	semidirect
134. #70021	C₂²	semidirect
135. #69500	C₂²	semidirect
136. #69500	C₂²	semidirect
140. #69499	C₂²	semidirect
141. #69499	C₂²	semidirect
142. #69499	C₂²	semidirect
143. #69499	C₂²	semidirect
144. #69499	C₂²	semidirect
145. #69499	C₂²	semidirect
146. #69499	C₂²	semidirect
147. #69499	C₂²	semidirect
148. #69499	C₂²	semidirect
149. #69498	C₂²	semidirect
150. #69497	C₂²	semidirect
151. #69497	C₂²	semidirect
152. #69496	C₂²	semidirect
153. #69496	C₂²	semidirect
154. #69495	C₂²	semidirect
155. #68971	C₂²	semidirect
156. #68970	C₂²	semidirect
157. #68970	C₂²	semidirect
158. #68970	C₂²	semidirect
159. #68970	C₂²	semidirect
160. #68969	C₂²	semidirect
161. #68969	C₂²	semidirect
162. D₃×#342	C₂²	semidirect
163. D₃×#342	C₂²	semidirect
164. #68965	C₂²	semidirect
165. #68962	C₂²	semidirect
166. #68962	C₂²	semidirect
167. #68962	C₂²	semidirect
168. #68962	C₂²	semidirect
169. #68962	C₂²	semidirect
170. #68962	C₂²	semidirect
171. #68961	C₂²	semidirect
172. #68961	C₂²	semidirect
173. #68961	C₂²	semidirect
174. #68961	C₂²	semidirect
175. #68961	C₂²	semidirect
176. #68961	C₂²	semidirect
177. #68959	C₂²	semidirect
178. #68959	C₂²	semidirect
179. #68958	C₂²	semidirect
180. #68957	C₂²	semidirect
181. #68955	C₂²	semidirect
182. #68955	C₂²	semidirect
183. #68955	C₂²	semidirect
184. #68955	C₂²	semidirect
185. #68952	C₂²	semidirect
186. #68952	C₂²	semidirect
187. #23984	D₃	semidirect
197. C₂²×#237	D₄	semidirect
198. C₂²×D₃×D₄	D₄	semidirect
200. C₂²×#235	D₄	semidirect
225. C₂×#940	D₄	semidirect
226. C₂×#939	D₄	semidirect
227. C₂×#939	D₄	semidirect
228. C₂×#939	D₄	semidirect
230. C₂×#938	D₄	semidirect
231. C₂×#937	D₄	semidirect
237. C₂×#930	D₄	semidirect
238. C₂×#929	D₄	semidirect
239. C₂×C₄×#67	D₄	semidirect
241. C₂×#886	D₄	semidirect
242. C₂×#885	D₄	semidirect
243. C₂×#885	D₄	semidirect
244. C₂×#884	D₄	semidirect
245. C₂×#884	D₄	semidirect
246. C₂×#884	D₄	semidirect
247. C₂×#884	D₄	semidirect
248. C₂×#883	D₄	semidirect
249. C₂×#883	D₄	semidirect
250. C₂×#882	D₄	semidirect
262. C₂×#67⋊C₄	D₄	semidirect
263. C₂×#67⋊C₄	D₄	semidirect
367. #3490	C₂×D₃	semidirect
368. #2846	C₂×D₃	semidirect
369. #2846	C₂×D₃	semidirect
370. C₂×#379	C₂×D₃	semidirect
371. #2029	C₂×D₃	semidirect
372. #2029	C₂×D₃	semidirect
373. #2021	C₂×D₃	semidirect
374. #2021	C₂×D₃	semidirect
375. #1898	C₂×D₃	semidirect
376. #1898	C₂×D₃	semidirect
377. #1889	C₂×D₃	semidirect
378. #1889	C₂×D₃	semidirect
379. #1889	C₂×D₃	semidirect
380. #1889	C₂×D₃	semidirect
381. #1819	C₂×D₃	semidirect
391. C₂²×C₃×D₄	C₂×D₄	semidirect
392. C₂²×C₃×D₄	C₂×D₄	semidirect
395. C₂³×C₃×C₄	C₂×D₄	semidirect
396. C₂³×C₃×C₄	C₂×D₄	semidirect
413. C₂²×#67	C₂×D₄	semidirect
414. C₂²×#67	C₂×D₄	semidirect
415. C₂²×#67	C₂×D₄	semidirect
416. C₂²×#67	C₂×D₄	semidirect
421. C₂³×Dic₃	C₂×D₄	semidirect
422. C₂³×Dic₃	C₂×D₄	semidirect
423. C₂³×Dic₃	C₂×D₄	semidirect
429. C₂²×D₁₂	C₂×D₄	semidirect
430. C₂²×D₁₂	C₂×D₄	semidirect
433. C₂²×C₄×D₃	C₂×D₄	semidirect
434. C₂²×C₄×D₃	C₂×D₄	semidirect
435. C₂²×C₄×D₃	C₂×D₄	semidirect
436. C₂²×C₄×D₃	C₂×D₄	semidirect
437. C₂²×C₄×D₃	C₂×D₄	semidirect
438. C₂²×Dic₆	C₂×D₄	semidirect
439. C₂²×Dic₆	C₂×D₄	semidirect
442. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
443. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
444. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
445. C₂×C₃×C₂²⋊C₄	C₂×D₄	semidirect
456. #953	#41	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
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×C₄⋊Dic₃	C₂×D₄	semidirect
486. C₂×C₄⋊Dic₃	C₂×D₄	semidirect
487. C₂×C₄⋊Dic₃	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×Dic₃⋊C₄	C₂×D₄	semidirect
496. C₂×C₄×Dic₃	C₂×D₄	semidirect
497. C₂×C₄×Dic₃	C₂×D₄	semidirect
541. C₂⁴×C₃	C₂×#41	semidirect
595. #217	C₂×#41	semidirect
601. C₂²×D₄	D₃×D₄	semidirect
602. C₂²×D₄	D₃×D₄	semidirect
605. C₂³×C₄	D₃×D₄	semidirect
606. 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
638. C₂²×D₃	#546	semidirect
639. #67	B(4,𝔽₂)	semidirect
644. C₂×Dic₃	#546	semidirect
653. C₂⁴	D₃×#41	semidirect
697. C₃	#6595772	semidirect

Maximal subgroups

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

subgroup	index
#11707305	2
#10991609	2
#10991603	2
#10990485	2
#10945064	2
#10945062	2
#10944214	2
#10852214	2
#10848559	2
#10848556	2
#10848332	2
#10848327	2
#10848326	2
#10848323	2
#10832527	2
#10832521	2
#10831847	2
#10829373	2
#10829369	2
#10827635	2
#10827632	2
#10827631	2
#10826766	2
#10826763	2
#10811315	2
#10811313	2
#10810507	2
#10801172	2
C₂×#69499	2
D₃×#1889	2
C₃×#23984	2
#6595772	3