Subgroups — C₂×#72216320 #72255198

Order 2048.

At least 11557 conjugacy classes of subgroups; only the 4792 normal subgroups are shown.

The subgroup lattice has 929 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6442738	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#419463	C₂	1	2	yes	maximal, complemented
3	C₂×#385872	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#449600	C₂	1	2	yes	maximal, complemented
5	C₂×#417617	C₂	1	2	yes	maximal, complemented
6	C₂×#427241	C₂	1	2	yes	maximal, complemented
7	C₂×#419783	C₂	1	2	yes	maximal, complemented
8	C₂×#430055	C₂	1	2	yes	maximal, complemented
9	C₂×#383149	C₂	1	2	yes	maximal, complemented
10	C₂×#10575416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#6437575	C₂	1	2	yes	maximal, complemented
12	C₂×#454389	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#453994	C₂	1	2	yes	maximal, complemented
14	C₂×#395191	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#394195	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#364416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#6437616	C₂	1	2	yes	maximal, complemented
18	C₂×#394108	C₂	1	2	yes	maximal, complemented
19	C₂×#393988	C₂	1	2	yes	maximal, complemented
20	#72216320	C₂	1	32	yes	maximal, direct product factor
21	C₂×#63090	C₂²	1	1	yes	characteristic, complemented
22	C₂×#62811	C₂²	1	2	yes	complemented
23	C₂³×#525	C₂²	1	2	yes	complemented
24	#10575416	C₂²	1	16	yes	complemented
25	C₂×#60511	C₂²	1	2	yes	complemented
26	C₂×#60511	C₂²	1	2	yes	complemented
27	C₂×#60444	C₂²	1	1	yes	characteristic
28	C₂×#60444	C₂²	1	1	yes	characteristic, complemented
29	C₂×#60444	C₂²	1	2	yes	complemented
30	C₂×#60444	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#3025	C₂²	1	2	yes	—
32	C₂²×#3025	C₂²	1	2	yes	complemented
33	C₂×#60387	C₂²	1	2	yes	complemented
34	C₂×#60359	C₂²	1	2	yes	—
35	C₂×#60359	C₂²	1	2	yes	complemented
36	C₂×#60359	C₂²	1	2	yes	complemented
37	C₂×#60141	C₂²	1	1	yes	characteristic, complemented
38	C₂³×#407	C₂²	1	1	yes	characteristic, complemented
39	C₂×#36614	C₂²	1	1	yes	characteristic
40	C₂×#36614	C₂²	1	2	yes	complemented
41	#6442738	C₂²	1	16	yes	complemented
42	#6437616	C₂²	1	32	yes	complemented
43	#6437575	C₂²	1	32	yes	complemented
44	C₂×#23535	C₂²	1	2	yes	complemented
45	C₂×#23535	C₂²	1	1	yes	characteristic, complemented
46	C₂×#23443	C₂²	1	2	yes	—
47	C₂×#23443	C₂²	1	2	yes	complemented
48	C₂×#23443	C₂²	1	2	yes	complemented
49	C₂×#23443	C₂²	1	2	yes	complemented
50	C₂×#23414	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#2010	C₂²	1	2	yes	—
52	C₂²×#2010	C₂²	1	2	yes	complemented
53	C₂²×#2010	C₂²	1	2	yes	complemented
54	C₂²×#2010	C₂²	1	2	yes	complemented
55	C₂²×#2010	C₂²	1	2	yes	complemented
56	C₂×#23412	C₂²	1	2	yes	complemented
57	C₂×#23412	C₂²	1	2	yes	complemented
58	C₂×#23412	C₂²	1	2	yes	complemented
59	C₂×#21244	C₂²	1	1	yes	characteristic, complemented
60	C₂×#21244	C₂²	1	1	yes	characteristic, complemented
61	C₂×#21009	C₂²	1	2	yes	complemented
62	C₂×#21000	C₂²	1	2	yes	complemented
63	C₂×#20998	C₂²	1	2	yes	complemented
64	C₂×#20998	C₂²	1	2	yes	complemented
65	C₂×#20989	C₂²	1	1	yes	characteristic, complemented
66	C₂×#20983	C₂²	1	2	yes	complemented
67	C₂×#20983	C₂²	1	2	yes	complemented
68	C₂×#20979	C₂²	1	2	yes	complemented
69	C₂²×#1891	C₂²	1	2	yes	complemented
70	C₂×#20959	C₂²	1	2	yes	complemented
71	C₂×#20959	C₂²	1	2	yes	complemented
72	C₂×#20902	C₂²	1	2	yes	complemented
73	C₂×#20671	C₂²	1	1	yes	characteristic, complemented
74	C₂×#20623	C₂²	1	2	yes	complemented
75	C₂×#20620	C₂²	1	2	yes	complemented
76	C₂×#20605	C₂²	1	2	yes	complemented
77	C₂×#20584	C₂²	1	2	yes	complemented
78	C₂×#20579	C₂²	1	1	yes	characteristic, complemented
79	#454389	C₂²	1	16	yes	complemented
80	#453994	C₂²	1	32	yes	complemented
81	#449600	C₂²	1	32	yes	complemented
82	#430055	C₂²	1	32	yes	complemented
83	#427241	C₂²	1	32	yes	complemented
84	#419783	C₂²	1	32	yes	complemented
85	#419463	C₂²	1	32	yes	complemented
86	#417617	C₂²	1	32	yes	complemented
87	#395191	C₂²	1	16	yes	complemented
88	#394195	C₂²	1	16	yes	complemented
89	#394108	C₂²	1	32	yes	complemented
90	#393988	C₂²	1	32	yes	complemented
91	#385872	C₂²	1	16	yes	complemented
92	#383149	C₂²	1	32	yes	complemented
93	#364416	C₂²	1	16	yes	complemented
94	C₂×#11361	C₂²	1	2	yes	complemented
95	C₂×#11277	C₂²	1	2	yes	complemented
96	C₂×#11234	C₂²	1	1	yes	characteristic, complemented
97	C₂×#11186	C₂²	1	2	yes	complemented
98	C₂×#11180	C₂²	1	2	yes	complemented
99	C₂×#11178	C₂²	1	2	yes	complemented
100	C₂×#11178	C₂²	1	2	yes	complemented
101	C₂×#11138	C₂²	1	2	yes	complemented
102	C₂×#11132	C₂²	1	2	yes	complemented
103	C₂×#11132	C₂²	1	2	yes	complemented
104	C₂×#11119	C₂²	1	2	yes	complemented
105	C₂×#11115	C₂²	1	2	yes	complemented
106	C₂×#11102	C₂²	1	1	yes	characteristic, complemented
107	C₂×#11100	C₂²	1	2	yes	complemented
108	C₂×#11071	C₂²	1	2	yes	complemented
109	C₂×#11033	C₂²	1	2	yes	complemented
110	C₂×#11033	C₂²	1	2	yes	complemented
111	C₂×#11003	C₂²	1	2	yes	complemented
112	C₂×#11000	C₂²	1	2	yes	complemented
113	C₂×#10994	C₂²	1	2	yes	complemented
114	C₂×#10994	C₂²	1	2	yes	complemented
115	C₂×#10994	C₂²	1	2	yes	complemented
116	C₂×#10994	C₂²	1	2	yes	complemented
117	C₂×#10994	C₂²	1	2	yes	complemented
118	C₂×#10994	C₂²	1	2	yes	complemented
119	C₂×#10993	C₂²	1	2	yes	complemented
120	C₂×#10951	C₂²	1	2	yes	complemented
121	C₂×#10937	C₂²	1	2	yes	complemented
122	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
123	C₂×#10792	C₂²	1	2	yes	complemented
124	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
125	C₂×#10717	C₂²	1	1	yes	characteristic, complemented
126	C₂×#10716	C₂²	1	2	yes	complemented
127	C₂²×#585	C₂³	1	2	yes	—
128	C₂⁴×#41	C₂³	1	2	yes	—
129	C₂⁶×C₄	C₂³	1	1	yes	characteristic
130	#63090	C₂³	1	8	yes	complemented
131	C₂²×#575	C₂³	1	1	yes	characteristic
132	C₂²×#575	C₂³	1	2	yes	—
133	C₂²×#575	C₂³	1	1	yes	characteristic
134	C₂²×#575	C₂³	1	2	yes	—
135	C₂²×#575	C₂³	1	2	yes	—
136	C₂²×#575	C₂³	1	1	yes	characteristic
137	C₂²×#568	C₂³	1	1	yes	characteristic
138	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
139	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
140	#62811	C₂³	1	16	yes	complemented
141	C₂×#3449	C₂³	1	2	yes	—
142	C₂×#3449	C₂³	1	2	yes	—
143	C₂²×#525	C₂³	1	2	yes	—
144	C₂²×#525	C₂³	1	2	yes	—
145	C₂²×#525	C₂³	1	1	yes	characteristic
146	C₂²×#525	C₂³	1	2	yes	—
147	C₂²×#525	C₂³	1	2	yes	—
148	C₂²×#525	C₂³	1	2	yes	—
149	C₂²×#525	C₂³	1	2	yes	—
150	C₂²×#525	C₂³	1	2	yes	—
151	C₂²×#525	C₂³	1	2	yes	—
152	C₂²×#525	C₂³	1	16	yes	complemented
153	C₂×#3428	C₂³	1	2	yes	—
154	C₂³×#117	C₂³	1	2	yes	—
155	#60511	C₂³	1	16	yes	complemented
156	#60511	C₂³	1	16	yes	complemented
157	#60444	D₄	1	8	yes	complemented
158	#60444	C₂³	1	8	yes	—
159	#60444	C₂³	1	16	yes	complemented
160	#60444	C₂³	1	8	yes	complemented
161	#60444	C₂³	1	8	yes	complemented
162	C₂×#3054	D₄	1	4	yes	complemented
163	C₂×#3050	D₄	1	4	yes	complemented
164	C₂×#3025	C₂³	1	16	yes	—
165	C₂×#3025	C₂³	1	16	yes	complemented
166	#60387	C₂³	1	16	yes	complemented
167	#60359	D₄	1	16	yes	complemented
168	#60359	C₂³	1	16	yes	—
169	#60359	C₂³	1	16	yes	complemented
170	#60359	C₂³	1	16	yes	complemented
171	C₂×#3005	D₄	1	4	yes	complemented
172	C₂×#3005	D₄	1	4	yes	complemented
173	C₂×#3004	D₄	1	4	yes	complemented
174	C₂×#3003	D₄	1	4	yes	complemented
175	#60141	C₂³	1	8	yes	complemented
176	C₂×#2911	C₂³	1	1	yes	characteristic
177	C₂×#2911	C₂³	1	2	yes	—
178	C₂×#2911	C₂³	1	1	yes	characteristic
179	C₂×#2911	C₂³	1	1	yes	characteristic
180	C₂×#2905	C₂³	1	1	yes	characteristic
181	C₂²×#421	C₂³	1	2	yes	—
182	C₂²×#421	C₂³	1	2	yes	—
183	C₂²×#421	C₂³	1	2	yes	—
184	C₂²×#421	C₂³	1	2	yes	—
185	C₂²×#421	C₂³	1	2	yes	—
186	C₂²×#421	C₂³	1	2	yes	—
187	C₂²×#421	C₂³	1	2	yes	—
188	C₂²×#421	C₂³	1	2	yes	—
189	C₂×#2896	C₂³	1	2	yes	—
190	C₂×#2896	C₂³	1	2	yes	—
191	C₂×#2896	C₂³	1	2	yes	—
192	C₂×#2896	C₂³	1	2	yes	—
193	C₂×#2896	C₂³	1	2	yes	—
194	C₂×#2896	C₂³	1	2	yes	—
195	C₂×#2896	C₂³	1	2	yes	—
196	C₂²×#413	C₂³	1	2	yes	—
197	C₂²×#410	C₂³	1	2	yes	—
198	C₂²×#410	C₂³	1	2	yes	—
199	C₂²×#410	C₂³	1	2	yes	—
200	C₂²×#410	C₂³	1	2	yes	—
201	C₂²×#410	C₂³	1	2	yes	—
202	C₂²×#410	C₂³	1	2	yes	—
203	C₂²×#410	C₂³	1	2	yes	—
204	C₂²×#410	C₂³	1	2	yes	—
205	C₂×#2879	C₂³	1	1	yes	characteristic
206	C₂²×#407	C₂³	1	2	yes	—
207	C₂²×#407	C₂³	1	2	yes	—
208	C₂²×#407	C₂³	1	1	yes	characteristic
209	C₂²×#407	C₂³	1	2	yes	—
210	C₂²×#407	C₂³	1	1	yes	characteristic
211	C₂²×#407	C₂³	1	2	yes	—
212	C₂²×#407	C₂³	1	8	yes	complemented
213	C₂×#2873	C₂³	1	1	yes	characteristic
214	#36614	D₄	1	8	yes	—
215	#36614	C₂³	1	8	yes	—
216	#36614	C₂³	1	16	yes	complemented
217	C₂×#2849	D₄	1	4	yes	—
218	C₂×#2849	D₄	1	2	yes	—
219	C₂×#2846	D₄	1	2	yes	—
220	C₂×#2280	C₂³	1	2	yes	—
221	C₂×#2280	C₂³	1	2	yes	—
222	C₂×#2280	C₂³	1	2	yes	—
223	C₂×#2280	C₂³	1	2	yes	—
224	C₂×#2280	C₂³	1	1	yes	characteristic
225	#23535	C₂³	1	16	yes	complemented
226	#23535	C₂³	1	8	yes	complemented
227	#23443	C₂³	1	16	yes	—
228	#23443	C₂³	1	16	yes	complemented
229	#23443	C₂³	1	16	yes	complemented
230	#23443	C₂³	1	16	yes	complemented
231	#23414	C₂³	1	8	yes	complemented
232	C₂×#2010	C₂³	1	16	yes	—
233	C₂×#2010	C₂³	1	16	yes	complemented
234	C₂×#2010	C₂³	1	16	yes	complemented
235	C₂×#2010	C₂³	1	16	yes	complemented
236	C₂×#2010	C₂³	1	16	yes	complemented
237	#23412	C₂³	1	16	yes	complemented
238	#23412	C₂³	1	16	yes	complemented
239	#23412	C₂³	1	16	yes	complemented
240	#21244	C₂³	1	8	yes	complemented
241	#21244	C₂³	1	8	yes	complemented
242	#21009	C₂³	1	16	yes	complemented
243	#21000	C₂³	1	16	yes	complemented
244	#20998	C₂³	1	16	yes	complemented
245	#20998	C₂³	1	16	yes	complemented
246	#20989	C₂³	1	8	yes	complemented
247	#20983	C₂³	1	16	yes	complemented
248	#20983	C₂³	1	16	yes	complemented
249	#20979	C₂³	1	16	yes	complemented
250	C₂×#1891	C₂³	1	16	yes	complemented
251	#20959	C₂³	1	16	yes	complemented
252	#20959	C₂³	1	16	yes	complemented
253	#20902	C₂³	1	16	yes	complemented
254	#20671	C₂³	1	8	yes	complemented
255	#20623	C₂³	1	16	yes	complemented
256	#20620	C₂³	1	16	yes	complemented
257	#20605	C₂³	1	16	yes	complemented
258	#20584	C₂³	1	16	yes	complemented
259	#20579	C₂³	1	8	yes	complemented
260	C₂²×#344	C₂³	1	2	yes	—
261	C₂²×#344	C₂³	1	2	yes	—
262	C₂²×#344	C₂³	1	2	yes	—
263	C₂²×#344	C₂³	1	2	yes	—
264	C₂×#1742	C₂³	1	2	yes	—
265	C₂×#1740	C₂³	1	2	yes	—
266	C₂×#1740	C₂³	1	2	yes	—
267	C₂×#1740	C₂³	1	2	yes	—
268	C₂×#1740	C₂³	1	2	yes	—
269	C₂×#1733	C₂³	1	2	yes	—
270	C₂×#1733	C₂³	1	2	yes	—
271	C₂×#1733	C₂³	1	2	yes	—
272	C₂×#1733	C₂³	1	2	yes	—
273	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
274	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
275	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
276	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
277	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
278	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
279	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
280	#11361	C₂³	1	16	yes	complemented
281	#11277	C₂³	1	16	yes	complemented
282	#11234	C₂³	1	8	yes	complemented
283	#11186	C₂³	1	16	yes	complemented
284	#11180	C₂³	1	16	yes	complemented
285	#11178	C₂³	1	16	yes	complemented
286	#11178	C₂³	1	16	yes	complemented
287	#11138	C₂³	1	16	yes	complemented
288	#11132	C₂³	1	16	yes	complemented
289	#11132	C₂³	1	16	yes	complemented
290	#11119	C₂³	1	16	yes	complemented
291	#11115	C₂³	1	16	yes	complemented
292	#11102	C₂³	1	8	yes	complemented
293	#11100	C₂³	1	16	yes	complemented
294	#11071	C₂³	1	16	yes	complemented
295	#11033	C₂³	1	16	yes	complemented
296	#11033	C₂³	1	16	yes	complemented
297	#11003	C₂³	1	16	yes	complemented
298	#11000	C₂³	1	16	yes	complemented
299	#10994	C₂³	1	16	yes	complemented
300	#10994	C₂³	1	16	yes	complemented
301	#10994	C₂³	1	16	yes	complemented
302	#10994	C₂³	1	16	yes	complemented
303	#10994	C₂³	1	16	yes	complemented
304	#10994	C₂³	1	16	yes	complemented
305	#10993	C₂³	1	16	yes	complemented
306	#10951	C₂³	1	16	yes	complemented
307	#10937	C₂³	1	16	yes	complemented
308	#10792	C₂³	1	16	yes	complemented
309	#10737	C₂³	1	8	yes	complemented
310	#10729	C₂³	1	8	yes	complemented
311	#10717	C₂³	1	8	yes	complemented
312	#10716	C₂³	1	16	yes	complemented
313	C₂⁷	C₂×D₄	1	1	yes	characteristic
314	C₂×#585	C₂⁴	1	8	yes	—
315	C₂³×#41	C₂×D₄	1	2	yes	complemented
316	C₂³×#41	C₂×D₄	1	2	yes	complemented
317	C₂³×#41	C₂×D₄	1	8	yes	complemented
318	C₂³×#41	C₂⁴	1	8	yes	—
319	C₂³×#41	C₂⁴	1	2	yes	—
320	C₂³×#41	C₂⁴	1	2	yes	—
321	C₂³×#41	C₂⁴	1	2	yes	—
322	C₂³×#41	C₂⁴	1	1	yes	characteristic
323	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
324	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
325	C₂⁵×C₄	C₂×D₄	1	2	yes	—
326	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
327	C₂⁵×C₄	C₂×D₄	1	4	yes	—
328	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
329	C₂⁵×C₄	C₂⁴	1	2	yes	—
330	C₂⁵×C₄	C₂⁴	1	4	yes	—
331	C₂×#575	C₂×D₄	1	8	yes	—
332	C₂×#575	C₂×D₄	1	8	yes	—
333	C₂×#575	C₂×D₄	1	4	yes	—
334	C₂×#575	C₂⁴	1	8	yes	—
335	C₂×#575	C₂⁴	1	4	yes	—
336	C₂×#575	C₂⁴	1	4	yes	—
337	C₂×#575	C₂⁴	1	8	yes	—
338	C₂×#575	C₂⁴	1	8	yes	—
339	C₂×#575	C₂⁴	1	4	yes	—
340	C₂²×#137	C₂×D₄	1	4	yes	—
341	C₂²×#137	C₂×D₄	1	4	yes	—
342	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
343	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
344	C₂²×#135	C₂×D₄	1	4	yes	—
345	C₂×#568	C₂⁴	1	4	yes	—
346	C₂³×M₁₆	C₂×D₄	1	2	yes	complemented
347	C₂³×M₁₆	C₂×D₄	1	4	yes	complemented
348	C₂³×M₁₆	C₂⁴	1	2	yes	—
349	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
350	C₂³×M₁₆	C₂⁴	1	2	yes	—
351	C₂³×M₁₆	C₂⁴	1	4	yes	—
352	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
353	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
354	C₂³×M₁₆	C₂⁴	1	4	yes	—
355	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
356	C₂⁴×C₈	C₂×D₄	1	2	yes	complemented
357	#3449	C₂⁴	1	8	yes	—
358	#3449	C₂⁴	1	8	yes	—
359	C₂×#525	C₂×D₄	1	8	yes	—
360	C₂×#525	C₂×D₄	1	4	yes	—
361	C₂×#525	C₂×D₄	1	4	yes	—
362	C₂×#525	C₂×D₄	1	4	yes	—
363	C₂×#525	C₂×D₄	1	8	yes	—
364	C₂×#525	C₂×D₄	1	4	yes	complemented
365	C₂×#525	C₂×D₄	1	4	yes	complemented
366	C₂×#525	C₂×D₄	1	8	yes	complemented
367	C₂×#525	C₂⁴	1	8	yes	—
368	C₂×#525	C₂⁴	1	8	yes	—
369	C₂×#525	C₂⁴	1	4	yes	—
370	C₂×#525	C₂⁴	1	8	yes	—
371	C₂×#525	C₂⁴	1	8	yes	—
372	C₂×#525	C₂⁴	1	8	yes	—
373	C₂×#525	C₂⁴	1	8	yes	—
374	C₂×#525	C₂⁴	1	8	yes	—
375	C₂×#525	C₂⁴	1	8	yes	—
376	C₂²×#123	C₂×D₄	1	4	yes	—
377	C₂²×#123	C₂×D₄	1	2	yes	—
378	C₂²×#120	C₂×D₄	1	4	yes	—
379	C₂²×#120	C₂×D₄	1	2	yes	—
380	#3428	C₂⁴	1	8	yes	—
381	C₂²×#117	C₂⁴	1	2	yes	—
382	C₂²×#117	C₂⁴	1	2	yes	—
383	C₂²×#117	C₂⁴	1	2	yes	—
384	C₂²×#117	C₂⁴	1	2	yes	—
385	C₂²×#117	C₂⁴	1	2	yes	—
386	C₂²×#117	C₂⁴	1	8	yes	—
387	C₂²×#117	C₂⁴	1	2	yes	—
388	C₂²×#117	C₂⁴	1	1	yes	characteristic
389	#3054	C₂×D₄	1	32	yes	complemented
390	#3050	C₂×D₄	1	32	yes	complemented
391	#3005	C₂×D₄	1	32	yes	complemented
392	#3005	C₂×D₄	1	32	yes	complemented
393	#3004	C₂×D₄	1	32	yes	complemented
394	#3003	C₂×D₄	1	32	yes	complemented
395	#2911	C₂×D₄	1	4	yes	complemented
396	#2911	C₂⁴	1	8	yes	—
397	#2911	C₂⁴	1	4	yes	—
398	#2911	C₂⁴	1	4	yes	—
399	#2911	C₂⁴	1	4	yes	—
400	C₂×#427	C₂×D₄	1	4	yes	complemented
401	#2905	C₂⁴	1	4	yes	—
402	C₂×#421	C₂⁴	1	8	yes	—
403	C₂×#421	C₂⁴	1	8	yes	—
404	C₂×#421	C₂⁴	1	8	yes	—
405	C₂×#421	C₂⁴	1	8	yes	—
406	C₂×#421	C₂⁴	1	8	yes	—
407	C₂×#421	C₂⁴	1	8	yes	—
408	C₂×#421	C₂⁴	1	8	yes	—
409	C₂×#421	C₂⁴	1	8	yes	—
410	#2896	C₂×D₄	1	8	yes	complemented
411	#2896	C₂×D₄	1	8	yes	complemented
412	#2896	C₂×D₄	1	8	yes	complemented
413	#2896	C₂⁴	1	8	yes	—
414	#2896	C₂⁴	1	8	yes	—
415	#2896	C₂⁴	1	8	yes	—
416	#2896	C₂⁴	1	8	yes	—
417	#2896	C₂⁴	1	8	yes	—
418	#2896	C₂⁴	1	8	yes	—
419	#2896	C₂⁴	1	8	yes	—
420	C₂×#419	C₂×D₄	1	4	yes	complemented
421	C₂×#419	C₂×D₄	1	4	yes	complemented
422	C₂×#418	C₂×D₄	1	4	yes	complemented
423	C₂×#418	C₂×D₄	1	4	yes	complemented
424	C₂×#416	C₂×D₄	1	8	yes	complemented
425	C₂×#413	C₂⁴	1	8	yes	—
426	C₂×#410	C₂⁴	1	8	yes	—
427	C₂×#410	C₂⁴	1	8	yes	—
428	C₂×#410	C₂⁴	1	8	yes	—
429	C₂×#410	C₂⁴	1	8	yes	—
430	C₂×#410	C₂⁴	1	8	yes	—
431	C₂×#410	C₂⁴	1	8	yes	—
432	C₂×#410	C₂⁴	1	8	yes	—
433	C₂×#410	C₂⁴	1	8	yes	—
434	#2879	C₂⁴	1	4	yes	—
435	C₂×#407	C₂×D₄	1	4	yes	complemented
436	C₂×#407	C₂×D₄	1	4	yes	complemented
437	C₂×#407	C₂×D₄	1	8	yes	complemented
438	C₂×#407	C₂⁴	1	8	yes	—
439	C₂×#407	C₂⁴	1	8	yes	—
440	C₂×#407	C₂⁴	1	4	yes	—
441	C₂×#407	C₂⁴	1	8	yes	—
442	C₂×#407	C₂⁴	1	4	yes	—
443	C₂×#407	C₂⁴	1	8	yes	—
444	#2873	C₂⁴	1	4	yes	—
445	#2849	C₂×D₄	1	32	yes	—
446	#2849	C₂×D₄	1	16	yes	—
447	#2846	C₂×D₄	1	16	yes	—
448	#2280	C₂×D₄	1	8	yes	—
449	#2280	C₂×D₄	1	4	yes	—
450	#2280	C₂⁴	1	8	yes	—
451	#2280	C₂⁴	1	8	yes	—
452	#2280	C₂⁴	1	8	yes	—
453	#2280	C₂⁴	1	8	yes	—
454	#2280	C₂⁴	1	4	yes	—
455	C₂×#381	C₂×D₄	1	4	yes	—
456	C₂×#381	C₂×D₄	1	2	yes	—
457	C₂×#379	C₂×D₄	1	4	yes	—
458	C₂×#379	C₂×D₄	1	2	yes	—
459	C₂×#344	C₂⁴	1	8	yes	—
460	C₂×#344	C₂⁴	1	8	yes	—
461	C₂×#344	C₂⁴	1	8	yes	—
462	C₂×#344	C₂⁴	1	8	yes	—
463	#1742	C₂⁴	1	8	yes	—
464	#1740	C₂⁴	1	8	yes	—
465	#1740	C₂⁴	1	8	yes	—
466	#1740	C₂⁴	1	8	yes	—
467	#1740	C₂⁴	1	8	yes	—
468	#1733	C₂⁴	1	8	yes	—
469	#1733	C₂⁴	1	8	yes	—
470	#1733	C₂⁴	1	8	yes	—
471	#1733	C₂⁴	1	8	yes	—
472	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
473	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
474	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
475	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
476	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
477	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
478	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
479	C₂⁶	C₂²×D₄	1	2	yes	—
480	C₂⁶	C₂²×D₄	1	1	yes	characteristic
481	C₂⁶	C₂²×D₄	1	4	yes	—
482	C₂²×#41	C₂²×D₄	1	4	yes	—
483	C₂²×#41	C₂²×D₄	1	4	yes	—
484	C₂²×#41	C₂²×D₄	1	4	yes	—
485	C₂²×#41	C₂²×D₄	1	4	yes	—
486	C₂²×#41	C₂²×D₄	1	4	yes	—
487	C₂²×#41	C₂²×D₄	1	4	yes	—
488	C₂²×#41	C₂²×D₄	1	2	yes	—
489	C₂²×#41	C₂²×D₄	1	8	yes	complemented
490	C₂²×#41	C₂²×D₄	1	8	yes	complemented
491	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
492	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
493	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
494	C₂²×#41	C₂⁵	1	4	yes	—
495	C₂²×#41	C₂⁵	1	4	yes	—
496	C₂²×#41	C₂⁵	1	4	yes	—
497	C₂²×#41	C₂⁵	1	2	yes	—
498	C₂³×Q₈	C₂²×D₄	1	2	yes	—
499	C₂³×Q₈	C₂²×D₄	1	2	yes	—
500	C₂³×Q₈	C₂²×D₄	1	8	yes	complemented
501	C₂³×Q₈	H(5,𝔽₂)	1	2	yes	—
502	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
503	C₂³×D₄	C₂²×D₄	1	2	yes	—
504	C₂³×D₄	C₂²×D₄	1	2	yes	—
505	C₂³×D₄	C₂²×D₄	1	2	yes	—
506	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
507	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
508	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
509	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
510	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
511	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
513	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
514	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
515	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
516	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
519	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
521	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
522	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
523	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
524	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
525	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
526	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
527	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
528	C₂⁴×C₄	C₂⁵	1	4	yes	—
529	C₂⁴×C₄	C₂⁵	1	2	yes	—
530	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
531	C₂×#137	#120	1	16	yes	complemented
532	C₂×#137	C₂²×D₄	1	16	yes	—
533	C₂×#137	C₂²×D₄	1	16	yes	—
534	C₂×AGL(1,ℤ/8)	#120	1	16	yes	complemented
535	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	16	yes	—
536	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	16	yes	—
537	C₂×#135	#120	1	16	yes	complemented
538	C₂×#135	C₂²×D₄	1	16	yes	—
539	C₂²×Q₁₆	#120	1	4	yes	complemented
540	C₂²×SD₁₆	#120	1	8	yes	complemented
541	C₂²×D₈	#120	1	4	yes	complemented
542	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
543	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
544	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
545	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
546	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
547	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
548	C₂²×M₁₆	C₂²×D₄	1	8	yes	complemented
549	C₂²×M₁₆	H(5,𝔽₂)	1	2	yes	—
550	C₂²×M₁₆	C₂⁵	1	2	yes	—
551	C₂²×M₁₆	C₂⁵	1	4	yes	—
552	C₂²×M₁₆	C₂⁵	1	4	yes	—
553	C₂²×M₁₆	C₂⁵	1	2	yes	—
554	C₂²×M₁₆	C₂⁵	1	2	yes	—
555	C₂²×M₁₆	C₂⁵	1	2	yes	—
556	C₂³×C₈	C₂²×D₄	1	2	yes	—
557	C₂³×C₈	C₂²×D₄	1	2	yes	—
558	C₂³×C₈	C₂²×D₄	1	8	yes	complemented
559	C₂³×C₈	H(5,𝔽₂)	1	2	yes	—
560	#525	C₂²×D₄	1	16	yes	—
561	#525	C₂²×D₄	1	16	yes	—
562	#525	C₂²×D₄	1	16	yes	complemented
563	#525	C₂²×D₄	1	16	yes	complemented
564	C₂×#123	C₂²×D₄	1	16	yes	—
565	C₂×#123	C₂²×D₄	1	8	yes	—
566	C₂×#120	C₂²×D₄	1	16	yes	—
567	C₂×#120	C₂²×D₄	1	8	yes	—
568	C₂×#117	C₂²×D₄	1	4	yes	—
569	C₂×#117	C₂²×D₄	1	4	yes	—
570	C₂×#117	C₂²×D₄	1	4	yes	—
571	C₂×#117	C₂²×D₄	1	4	yes	—
572	C₂×#117	C₂²×D₄	1	2	yes	—
573	C₂×#117	C₂²×D₄	1	4	yes	—
574	C₂×#117	H(5,𝔽₂)	1	4	yes	—
575	C₂×#117	C₂⁵	1	4	yes	—
576	C₂×#117	C₂⁵	1	4	yes	—
577	C₂×#117	C₂⁵	1	4	yes	—
578	C₂×#117	C₂⁵	1	4	yes	—
579	C₂×#117	C₂⁵	1	2	yes	—
580	C₂×#117	C₂⁵	1	4	yes	—
581	C₂×#117	C₂⁵	1	4	yes	—
582	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
583	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
584	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
585	#427	C₂²×D₄	1	16	yes	complemented
586	#419	C₂²×D₄	1	16	yes	complemented
587	#419	C₂²×D₄	1	16	yes	complemented
588	#418	C₂²×D₄	1	16	yes	complemented
589	#418	C₂²×D₄	1	16	yes	complemented
590	#416	C₂²×D₄	1	32	yes	complemented
591	#407	C₂²×D₄	1	16	yes	complemented
592	#407	C₂²×D₄	1	16	yes	complemented
593	#381	C₂²×D₄	1	8	yes	—
594	#381	C₂²×D₄	1	16	yes	—
595	#379	C₂²×D₄	1	8	yes	—
596	#379	C₂²×D₄	1	16	yes	—
597	C₂⁵	#534	1	2	yes	—
598	C₂⁵	D₄²	1	1	yes	characteristic
599	C₂⁵	D₄²	1	2	yes	—
600	C₂⁵	D₄²	1	2	yes	—
601	C₂⁵	D₄²	1	4	yes	—
602	C₂⁵	D₄²	1	1	yes	characteristic
603	C₂⁵	D₄²	1	2	yes	—
604	C₂⁵	C₂³×D₄	1	4	yes	—
605	C₂⁵	C₂³×D₄	1	2	yes	—
606	C₂⁵	C₂³×D₄	1	1	yes	characteristic
607	C₂×#41	C₂×#120	1	8	yes	—
608	C₂×#41	C₂×#120	1	8	yes	—
609	C₂×#41	C₂³×D₄	1	8	yes	—
610	C₂×#41	C₂³×D₄	1	8	yes	—
611	C₂²×Q₈	C₂×#120	1	4	yes	—
612	C₂²×Q₈	C₂×#120	1	4	yes	—
613	C₂²×Q₈	#534	1	2	yes	—
614	C₂²×Q₈	C₂³×D₄	1	4	yes	—
615	C₂²×Q₈	C₂³×D₄	1	4	yes	—
616	C₂²×Q₈	C₂×H(5,𝔽₂)	1	4	yes	—
617	C₂²×Q₈	C₂×H(5,𝔽₂)	1	2	yes	—
618	C₂²×D₄	C₂×#120	1	4	yes	—
619	C₂²×D₄	C₂×#120	1	4	yes	—
620	C₂²×D₄	#534	1	4	yes	—
621	C₂²×D₄	#534	1	2	yes	—
622	C₂²×D₄	C₂³×D₄	1	4	yes	—
623	C₂²×D₄	C₂³×D₄	1	4	yes	—
624	C₂²×D₄	C₂³×D₄	1	4	yes	—
625	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
626	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
627	C₂³×C₄	#534	1	2	yes	—
628	C₂³×C₄	#534	1	4	yes	—
629	C₂³×C₄	D₄²	1	2	yes	—
630	C₂³×C₄	D₄²	1	4	yes	—
631	C₂³×C₄	D₄²	1	4	yes	—
632	C₂³×C₄	D₄²	1	4	yes	—
633	C₂³×C₄	D₄²	1	4	yes	—
634	C₂³×C₄	D₄²	1	1	yes	characteristic
635	C₂³×C₄	D₄²	1	1	yes	characteristic
636	C₂³×C₄	D₄²	1	2	yes	—
637	C₂³×C₄	D₄²	1	2	yes	—
638	C₂³×C₄	D₄²	1	2	yes	—
639	C₂³×C₄	D₄²	1	2	yes	—
640	C₂³×C₄	D₄²	1	2	yes	—
641	C₂³×C₄	D₄²	1	2	yes	—
642	C₂³×C₄	D₄²	1	4	yes	—
643	C₂³×C₄	C₂³×D₄	1	4	yes	—
644	C₂³×C₄	C₂³×D₄	1	4	yes	—
645	C₂³×C₄	C₂³×D₄	1	2	yes	—
646	C₂³×C₄	C₂³×D₄	1	2	yes	—
647	C₂³×C₄	C₂³×D₄	1	4	yes	—
648	C₂³×C₄	C₂³×D₄	1	2	yes	—
649	C₂³×C₄	C₂³×D₄	1	2	yes	—
650	C₂³×C₄	C₂³×D₄	1	2	yes	—
651	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
652	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
653	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
654	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
655	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
656	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
657	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
658	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
659	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
664	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
665	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
668	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
669	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
670	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
672	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
673	C₂³×C₄	#585	1	1	yes	characteristic
674	C₂³×C₄	#585	1	1	yes	characteristic
675	C₂³×C₄	C₂⁶	1	1	yes	characteristic
676	C₂×Q₁₆	C₂×#120	1	16	yes	complemented
677	C₂×SD₁₆	C₂×#120	1	32	yes	complemented
678	C₂×D₈	C₂×#120	1	16	yes	complemented
679	C₂×M₁₆	C₂×#120	1	8	yes	—
680	C₂×M₁₆	C₂³×D₄	1	8	yes	—
681	C₂×M₁₆	C₂³×D₄	1	8	yes	—
682	C₂²×C₈	C₂×#120	1	4	yes	—
683	C₂²×C₈	C₂×#120	1	4	yes	—
684	C₂²×C₈	C₂³×D₄	1	4	yes	—
685	C₂²×C₈	C₂³×D₄	1	4	yes	—
686	C₂²×C₈	C₂×H(5,𝔽₂)	1	4	yes	—
687	#117	C₂³×D₄	1	8	yes	—
688	#117	C₂³×D₄	1	8	yes	—
689	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
690	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
691	C₂×C₄²	C₂×H(5,𝔽₂)	1	8	yes	—
692	C₂⁴	C₂×#534	1	4	yes	—
693	C₂⁴	C₂×#534	1	1	yes	characteristic
694	C₂⁴	C₂×#534	1	1	yes	characteristic
695	C₂⁴	C₂×D₄²	1	2	yes	—
696	C₂⁴	C₂×D₄²	1	4	yes	—
697	C₂⁴	C₂×D₄²	1	4	yes	—
698	C₂⁴	C₂×D₄²	1	2	yes	—
699	C₂⁴	C₂×D₄²	1	2	yes	—
700	C₂⁴	C₂×D₄²	1	1	yes	characteristic
701	C₂⁴	C₂×D₄²	1	2	yes	—
702	C₂⁴	C₂×D₄²	1	1	yes	characteristic
703	C₂⁴	#3484	1	2	yes	—
704	C₂⁴	#3484	1	2	yes	—
705	C₂⁴	#3496	1	1	yes	characteristic
706	C₂⁴	#3496	1	1	yes	characteristic
707	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
708	C₂×Q₈	C₂²×#120	1	8	yes	—
709	C₂×D₄	C₂²×#120	1	8	yes	—
710	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
711	C₂²×C₄	C₂²×#120	1	2	yes	—
712	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
713	C₂²×C₄	C₂×#534	1	4	yes	—
714	C₂²×C₄	C₂×#534	1	1	yes	characteristic
715	C₂²×C₄	C₂×#534	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄²	1	4	yes	—
717	C₂²×C₄	C₂×D₄²	1	4	yes	—
718	C₂²×C₄	C₂×D₄²	1	2	yes	—
719	C₂²×C₄	C₂×D₄²	1	2	yes	—
720	C₂²×C₄	C₂×D₄²	1	2	yes	—
721	C₂²×C₄	C₂×D₄²	1	2	yes	—
722	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
724	C₂²×C₄	#3484	1	2	yes	—
725	C₂²×C₄	#3484	1	2	yes	—
726	C₂²×C₄	#3484	1	2	yes	—
727	C₂²×C₄	#3484	1	2	yes	—
728	C₂²×C₄	#3484	1	2	yes	—
729	C₂²×C₄	#3484	1	2	yes	—
730	C₂²×C₄	#3484	1	2	yes	—
731	C₂²×C₄	#3484	1	2	yes	—
732	C₂²×C₄	#3484	1	2	yes	—
733	C₂²×C₄	#3484	1	2	yes	—
734	C₂²×C₄	#3484	1	2	yes	—
735	C₂²×C₄	#3484	1	2	yes	—
736	C₂²×C₄	#3484	1	2	yes	—
737	C₂²×C₄	#3484	1	2	yes	—
738	C₂²×C₄	#3484	1	1	yes	characteristic
739	C₂²×C₄	#3484	1	1	yes	characteristic
740	C₂²×C₄	#3484	1	1	yes	characteristic
741	C₂²×C₄	#3484	1	1	yes	characteristic
742	C₂²×C₄	#3484	1	2	yes	—
743	C₂²×C₄	#3484	1	2	yes	—
744	C₂²×C₄	#3484	1	2	yes	—
745	C₂²×C₄	#3484	1	2	yes	—
746	C₂²×C₄	#3484	1	1	yes	characteristic
747	C₂²×C₄	#3484	1	2	yes	—
748	C₂²×C₄	#3484	1	1	yes	characteristic
749	C₂²×C₄	#3484	1	2	yes	—
750	C₂²×C₄	#3484	1	1	yes	characteristic
751	C₂²×C₄	#3484	1	1	yes	characteristic
752	C₂²×C₄	#3488	1	1	yes	characteristic
753	C₂²×C₄	#3488	1	1	yes	characteristic
754	C₂²×C₄	#3488	1	1	yes	characteristic
755	C₂²×C₄	#3488	1	1	yes	characteristic
756	C₂²×C₄	#3496	1	2	yes	—
757	C₂²×C₄	#3496	1	2	yes	—
758	C₂²×C₄	#3496	1	2	yes	—
759	C₂²×C₄	#3496	1	2	yes	—
760	C₂²×C₄	#3496	1	1	yes	characteristic
761	C₂²×C₄	#3496	1	1	yes	characteristic
762	C₂²×C₄	#3498	1	2	yes	—
763	C₂²×C₄	#3498	1	1	yes	characteristic
764	C₂²×C₄	#3498	1	1	yes	characteristic
765	C₂²×C₄	#3532	1	2	yes	—
766	C₂²×C₄	#3532	1	2	yes	—
767	C₂²×C₄	#3532	1	2	yes	—
768	C₂²×C₄	#3532	1	2	yes	—
769	C₂²×C₄	#3532	1	2	yes	—
770	C₂²×C₄	#3532	1	2	yes	—
771	C₂²×C₄	#3532	1	2	yes	—
772	C₂²×C₄	#3532	1	2	yes	—
773	C₂²×C₄	#3534	1	1	yes	characteristic
774	C₂²×C₄	#3534	1	1	yes	characteristic
775	C₂²×C₄	#3534	1	1	yes	characteristic
776	C₂²×C₄	#3534	1	1	yes	characteristic
777	C₂²×C₄	#3534	1	2	yes	—
778	C₂²×C₄	#3534	1	2	yes	—
779	C₂²×C₄	#3534	1	2	yes	—
780	C₂²×C₄	#3534	1	2	yes	—
781	C₂²×C₄	#3537	1	2	yes	—
782	C₂²×C₄	#3537	1	2	yes	—
783	C₂²×C₄	#3537	1	2	yes	—
784	C₂²×C₄	#3537	1	2	yes	—
785	C₂²×C₄	#3537	1	1	yes	characteristic
786	C₂²×C₄	#3537	1	1	yes	characteristic
787	C₂²×C₄	#3537	1	1	yes	characteristic
788	C₂²×C₄	#3537	1	1	yes	characteristic
789	C₂²×C₄	#3543	1	2	yes	—
790	C₂²×C₄	#3543	1	2	yes	—
791	C₂²×C₄	#3543	1	2	yes	—
792	C₂²×C₄	#3543	1	2	yes	—
793	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
794	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
795	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
796	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
797	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
798	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
801	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂²×C₄	C₂×#585	1	1	yes	characteristic
803	C₂×C₈	C₂²×#120	1	8	yes	—
804	C₂³	D₄×#120	1	1	yes	characteristic
805	C₂³	D₄×#120	1	1	yes	characteristic
806	C₂³	D₄×#120	1	2	yes	—
807	C₂³	#37644	1	2	yes	—
808	C₂³	#37644	1	2	yes	—
809	C₂³	#37644	1	2	yes	—
810	C₂³	#37644	1	2	yes	—
811	C₂³	#37672	1	1	yes	characteristic
812	C₂³	#37672	1	1	yes	characteristic
813	C₂³	#37672	1	1	yes	characteristic
814	C₂³	#37672	1	1	yes	characteristic
815	C₂³	#42996	1	2	yes	—
816	C₂³	#42996	1	2	yes	—
817	C₂³	#42996	1	2	yes	—
818	C₂³	#42996	1	2	yes	—
819	C₂³	#43001	1	1	yes	characteristic
820	C₂³	#43001	1	1	yes	characteristic
821	C₂³	#43001	1	2	yes	—
822	C₂³	C₂²×#534	1	1	yes	characteristic
823	C₂³	C₂²×D₄²	1	2	yes	—
824	C₂³	C₂²×D₄²	1	1	yes	characteristic
825	C₂³	C₂×#3484	1	2	yes	—
826	C₂³	C₂×#3496	1	1	yes	characteristic
827	C₂×C₄	#35346	1	1	yes	characteristic
828	C₂×C₄	#35346	1	1	yes	characteristic
829	C₂×C₄	#35346	1	1	yes	characteristic
830	C₂×C₄	#35346	1	1	yes	characteristic
831	C₂×C₄	#35346	1	2	yes	—
832	C₂×C₄	#35346	1	2	yes	—
833	C₂×C₄	#35680	1	1	yes	characteristic
834	C₂×C₄	#35680	1	1	yes	characteristic
835	C₂×C₄	#35680	1	1	yes	characteristic
836	C₂×C₄	#35680	1	1	yes	characteristic
837	C₂×C₄	#35680	1	2	yes	—
838	C₂×C₄	#35680	1	2	yes	—
839	C₂×C₄	D₄×#120	1	1	yes	characteristic
840	C₂×C₄	D₄×#120	1	2	yes	—
841	C₂×C₄	D₄×#120	1	1	yes	characteristic
842	C₂×C₄	#37644	1	2	yes	—
843	C₂×C₄	#37644	1	2	yes	—
844	C₂×C₄	#37644	1	2	yes	—
845	C₂×C₄	#37644	1	2	yes	—
846	C₂×C₄	#37672	1	1	yes	characteristic
847	C₂×C₄	#37672	1	1	yes	characteristic
848	C₂×C₄	#37672	1	1	yes	characteristic
849	C₂×C₄	#37672	1	1	yes	characteristic
850	C₂×C₄	#42996	1	2	yes	—
851	C₂×C₄	#42996	1	2	yes	—
852	C₂×C₄	#42996	1	2	yes	—
853	C₂×C₄	#42996	1	2	yes	—
854	C₂×C₄	#43001	1	1	yes	characteristic
855	C₂×C₄	#43001	1	2	yes	—
856	C₂×C₄	#43001	1	1	yes	characteristic
857	C₂×C₄	#46350	1	2	yes	—
858	C₂×C₄	#46350	1	2	yes	—
859	C₂×C₄	#46350	1	2	yes	—
860	C₂×C₄	#46350	1	2	yes	—
861	C₂×C₄	#46350	1	2	yes	—
862	C₂×C₄	#46350	1	2	yes	—
863	C₂×C₄	#46350	1	2	yes	—
864	C₂×C₄	#46350	1	2	yes	—
865	C₂×C₄	#46355	1	2	yes	—
866	C₂×C₄	#46355	1	1	yes	characteristic
867	C₂×C₄	#46355	1	1	yes	characteristic
868	C₂×C₄	#46355	1	2	yes	—
869	C₂×C₄	#46355	1	1	yes	characteristic
870	C₂×C₄	#46355	1	1	yes	characteristic
871	C₂×C₄	#47827	1	2	yes	—
872	C₂×C₄	#47827	1	2	yes	—
873	C₂×C₄	#47827	1	2	yes	—
874	C₂×C₄	#47827	1	2	yes	—
875	C₂×C₄	#47827	1	2	yes	—
876	C₂×C₄	#47827	1	2	yes	—
877	C₂×C₄	#47827	1	2	yes	—
878	C₂×C₄	#47827	1	2	yes	—
879	C₂×C₄	#47830	1	1	yes	characteristic
880	C₂×C₄	#47830	1	1	yes	characteristic
881	C₂×C₄	#47830	1	2	yes	—
882	C₂×C₄	#47830	1	2	yes	—
883	C₂×C₄	#47830	1	1	yes	characteristic
884	C₂×C₄	#47830	1	1	yes	characteristic
885	C₂×C₄	C₂³×#120	1	1	yes	characteristic
886	C₂×C₄	C₂×#3532	1	2	yes	—
887	C₂×C₄	C₂×#3532	1	2	yes	—
888	C₂×C₄	C₂×#3534	1	2	yes	—
889	C₂×C₄	C₂×#3534	1	1	yes	characteristic
890	C₂×C₄	C₂×#3537	1	1	yes	characteristic
891	C₂×C₄	C₂×#3537	1	2	yes	—
892	C₂×C₄	C₂×#3543	1	2	yes	—
893	C₂×C₄	C₂×#3484	1	1	yes	characteristic
894	C₂×C₄	C₂×#3484	1	1	yes	characteristic
895	C₂×C₄	C₂×#3484	1	1	yes	characteristic
896	C₂×C₄	C₂×#3484	1	2	yes	—
897	C₂×C₄	C₂×#3484	1	2	yes	—
898	C₂×C₄	C₂×#3484	1	2	yes	—
899	C₂×C₄	C₂×#3484	1	2	yes	—
900	C₂×C₄	C₂×#3496	1	2	yes	—
901	C₂×C₄	C₂×#3488	1	1	yes	characteristic
902	C₂×C₄	C₂×#3498	1	1	yes	characteristic
903	C₂²	#1082737	1	1	yes	characteristic
904	C₂²	#1082737	1	2	yes	—
905	C₂²	#1082737	1	2	yes	—
906	C₂²	#1082737	1	1	yes	characteristic
907	C₂²	#1082737	1	1	yes	characteristic
908	C₂²	#1082737	1	1	yes	characteristic
909	C₂²	C₂×D₄×#120	1	1	yes	characteristic
910	C₂²	C₂×#37644	1	2	yes	—
911	C₂²	C₂×#37672	1	1	yes	characteristic
912	C₂²	C₂×#42996	1	2	yes	—
913	C₂²	C₂×#43001	1	1	yes	characteristic
914	C₄	#1082737	1	1	yes	characteristic
915	C₄	#1082737	1	1	yes	characteristic
916	C₄	#1082737	1	2	yes	—
917	C₄	#1082737	1	2	yes	—
918	C₄	#1082737	1	1	yes	characteristic
919	C₄	#1082737	1	1	yes	characteristic
920	C₄	C₂×#35346	1	1	yes	characteristic
921	C₄	C₂×#35680	1	1	yes	characteristic
922	C₄	C₂×#46350	1	2	yes	—
923	C₄	C₂×#46355	1	1	yes	characteristic
924	C₄	C₂×#47827	1	2	yes	—
925	C₄	C₂×#47830	1	1	yes	characteristic
926	C₂	#72216320	1	2	yes	direct product factor
927	C₂	C₂×#1082737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#46355
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
socle	C₂²	#1082737
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#6442738	C₂	semidirect
2. C₂×#419463	C₂	semidirect
3. C₂×#385872	C₂	semidirect
4. C₂×#449600	C₂	semidirect
5. C₂×#417617	C₂	semidirect
6. C₂×#427241	C₂	semidirect
7. C₂×#419783	C₂	semidirect
8. C₂×#430055	C₂	semidirect
9. C₂×#383149	C₂	semidirect
10. C₂×#10575416	C₂	semidirect
11. C₂×#6437575	C₂	semidirect
12. C₂×#454389	C₂	semidirect
13. C₂×#453994	C₂	semidirect
14. C₂×#395191	C₂	semidirect
15. C₂×#394195	C₂	semidirect
16. C₂×#364416	C₂	semidirect
17. C₂×#6437616	C₂	semidirect
18. C₂×#394108	C₂	semidirect
19. C₂×#393988	C₂	semidirect
20. #72216320	C₂	direct (N × H)
21. C₂×#63090	C₂²	semidirect
22. C₂×#62811	C₂²	semidirect
23. C₂³×#525	C₂²	semidirect
24. #10575416	C₂²	semidirect
25. C₂×#60511	C₂²	semidirect
26. C₂×#60511	C₂²	semidirect
28. C₂×#60444	C₂²	semidirect
29. C₂×#60444	C₂²	semidirect
30. C₂×#60444	C₂²	semidirect
32. C₂²×#3025	C₂²	semidirect
33. C₂×#60387	C₂²	semidirect
35. C₂×#60359	C₂²	semidirect
36. C₂×#60359	C₂²	semidirect
37. C₂×#60141	C₂²	semidirect
38. C₂³×#407	C₂²	semidirect
40. C₂×#36614	C₂²	semidirect
41. #6442738	C₂²	semidirect
42. #6437616	C₂²	semidirect
43. #6437575	C₂²	semidirect
44. C₂×#23535	C₂²	semidirect
45. C₂×#23535	C₂²	semidirect
47. C₂×#23443	C₂²	semidirect
48. C₂×#23443	C₂²	semidirect
49. C₂×#23443	C₂²	semidirect
50. C₂×#23414	C₂²	semidirect
52. C₂²×#2010	C₂²	semidirect
53. C₂²×#2010	C₂²	semidirect
54. C₂²×#2010	C₂²	semidirect
55. C₂²×#2010	C₂²	semidirect
56. C₂×#23412	C₂²	semidirect
57. C₂×#23412	C₂²	semidirect
58. C₂×#23412	C₂²	semidirect
59. C₂×#21244	C₂²	semidirect
60. C₂×#21244	C₂²	semidirect
61. C₂×#21009	C₂²	semidirect
62. C₂×#21000	C₂²	semidirect
63. C₂×#20998	C₂²	semidirect
64. C₂×#20998	C₂²	semidirect
65. C₂×#20989	C₂²	semidirect
66. C₂×#20983	C₂²	semidirect
67. C₂×#20983	C₂²	semidirect
68. C₂×#20979	C₂²	semidirect
69. C₂²×#1891	C₂²	semidirect
70. C₂×#20959	C₂²	semidirect
71. C₂×#20959	C₂²	semidirect
72. C₂×#20902	C₂²	semidirect
73. C₂×#20671	C₂²	semidirect
74. C₂×#20623	C₂²	semidirect
75. C₂×#20620	C₂²	semidirect
76. C₂×#20605	C₂²	semidirect
77. C₂×#20584	C₂²	semidirect
78. C₂×#20579	C₂²	semidirect
79. #454389	C₂²	semidirect
80. #453994	C₂²	semidirect
81. #449600	C₂²	semidirect
82. #430055	C₂²	semidirect
83. #427241	C₂²	semidirect
84. #419783	C₂²	semidirect
85. #419463	C₂²	semidirect
86. #417617	C₂²	semidirect
87. #395191	C₂²	semidirect
88. #394195	C₂²	semidirect
89. #394108	C₂²	semidirect
90. #393988	C₂²	semidirect
91. #385872	C₂²	semidirect
92. #383149	C₂²	semidirect
93. #364416	C₂²	semidirect
94. C₂×#11361	C₂²	semidirect
95. C₂×#11277	C₂²	semidirect
96. C₂×#11234	C₂²	semidirect
97. C₂×#11186	C₂²	semidirect
98. C₂×#11180	C₂²	semidirect
99. C₂×#11178	C₂²	semidirect
100. C₂×#11178	C₂²	semidirect
101. C₂×#11138	C₂²	semidirect
102. C₂×#11132	C₂²	semidirect
103. C₂×#11132	C₂²	semidirect
104. C₂×#11119	C₂²	semidirect
105. C₂×#11115	C₂²	semidirect
106. C₂×#11102	C₂²	semidirect
107. C₂×#11100	C₂²	semidirect
108. C₂×#11071	C₂²	semidirect
109. C₂×#11033	C₂²	semidirect
110. C₂×#11033	C₂²	semidirect
111. C₂×#11003	C₂²	semidirect
112. C₂×#11000	C₂²	semidirect
113. C₂×#10994	C₂²	semidirect
114. C₂×#10994	C₂²	semidirect
115. C₂×#10994	C₂²	semidirect
116. C₂×#10994	C₂²	semidirect
117. C₂×#10994	C₂²	semidirect
118. C₂×#10994	C₂²	semidirect
119. C₂×#10993	C₂²	semidirect
120. C₂×#10951	C₂²	semidirect
121. C₂×#10937	C₂²	semidirect
122. C₂×#10737	C₂²	semidirect
123. C₂×#10792	C₂²	semidirect
124. C₂×#10729	C₂²	semidirect
125. C₂×#10717	C₂²	semidirect
126. C₂×#10716	C₂²	semidirect
130. #63090	C₂³	semidirect
140. #62811	C₂³	semidirect
152. C₂²×#525	C₂³	semidirect
155. #60511	C₂³	semidirect
156. #60511	C₂³	semidirect
157. #60444	D₄	semidirect
159. #60444	C₂³	semidirect
160. #60444	C₂³	semidirect
161. #60444	C₂³	semidirect
162. C₂×#3054	D₄	semidirect
163. C₂×#3050	D₄	semidirect
165. C₂×#3025	C₂³	semidirect
166. #60387	C₂³	semidirect
167. #60359	D₄	semidirect
169. #60359	C₂³	semidirect
170. #60359	C₂³	semidirect
171. C₂×#3005	D₄	semidirect
172. C₂×#3005	D₄	semidirect
173. C₂×#3004	D₄	semidirect
174. C₂×#3003	D₄	semidirect
175. #60141	C₂³	semidirect
212. C₂²×#407	C₂³	semidirect
216. #36614	C₂³	semidirect
225. #23535	C₂³	semidirect
226. #23535	C₂³	semidirect
228. #23443	C₂³	semidirect
229. #23443	C₂³	semidirect
230. #23443	C₂³	semidirect
231. #23414	C₂³	semidirect
233. C₂×#2010	C₂³	semidirect
234. C₂×#2010	C₂³	semidirect
235. C₂×#2010	C₂³	semidirect
236. C₂×#2010	C₂³	semidirect
237. #23412	C₂³	semidirect
238. #23412	C₂³	semidirect
239. #23412	C₂³	semidirect
240. #21244	C₂³	semidirect
241. #21244	C₂³	semidirect
242. #21009	C₂³	semidirect
243. #21000	C₂³	semidirect
244. #20998	C₂³	semidirect
245. #20998	C₂³	semidirect
246. #20989	C₂³	semidirect
247. #20983	C₂³	semidirect
248. #20983	C₂³	semidirect
249. #20979	C₂³	semidirect
250. C₂×#1891	C₂³	semidirect
251. #20959	C₂³	semidirect
252. #20959	C₂³	semidirect
253. #20902	C₂³	semidirect
254. #20671	C₂³	semidirect
255. #20623	C₂³	semidirect
256. #20620	C₂³	semidirect
257. #20605	C₂³	semidirect
258. #20584	C₂³	semidirect
259. #20579	C₂³	semidirect
280. #11361	C₂³	semidirect
281. #11277	C₂³	semidirect
282. #11234	C₂³	semidirect
283. #11186	C₂³	semidirect
284. #11180	C₂³	semidirect
285. #11178	C₂³	semidirect
286. #11178	C₂³	semidirect
287. #11138	C₂³	semidirect
288. #11132	C₂³	semidirect
289. #11132	C₂³	semidirect
290. #11119	C₂³	semidirect
291. #11115	C₂³	semidirect
292. #11102	C₂³	semidirect
293. #11100	C₂³	semidirect
294. #11071	C₂³	semidirect
295. #11033	C₂³	semidirect
296. #11033	C₂³	semidirect
297. #11003	C₂³	semidirect
298. #11000	C₂³	semidirect
299. #10994	C₂³	semidirect
300. #10994	C₂³	semidirect
301. #10994	C₂³	semidirect
302. #10994	C₂³	semidirect
303. #10994	C₂³	semidirect
304. #10994	C₂³	semidirect
305. #10993	C₂³	semidirect
306. #10951	C₂³	semidirect
307. #10937	C₂³	semidirect
308. #10792	C₂³	semidirect
309. #10737	C₂³	semidirect
310. #10729	C₂³	semidirect
311. #10717	C₂³	semidirect
312. #10716	C₂³	semidirect
315. C₂³×#41	C₂×D₄	semidirect
316. C₂³×#41	C₂×D₄	semidirect
317. C₂³×#41	C₂×D₄	semidirect
323. C₂⁴×Q₈	C₂×D₄	semidirect
324. C₂⁴×D₄	C₂×D₄	semidirect
346. C₂³×M₁₆	C₂×D₄	semidirect
347. C₂³×M₁₆	C₂×D₄	semidirect
356. C₂⁴×C₈	C₂×D₄	semidirect
364. C₂×#525	C₂×D₄	semidirect
365. C₂×#525	C₂×D₄	semidirect
366. C₂×#525	C₂×D₄	semidirect
389. #3054	C₂×D₄	semidirect
390. #3050	C₂×D₄	semidirect
391. #3005	C₂×D₄	semidirect
392. #3005	C₂×D₄	semidirect
393. #3004	C₂×D₄	semidirect
394. #3003	C₂×D₄	semidirect
395. #2911	C₂×D₄	semidirect
400. C₂×#427	C₂×D₄	semidirect
410. #2896	C₂×D₄	semidirect
411. #2896	C₂×D₄	semidirect
412. #2896	C₂×D₄	semidirect
420. C₂×#419	C₂×D₄	semidirect
421. C₂×#419	C₂×D₄	semidirect
422. C₂×#418	C₂×D₄	semidirect
423. C₂×#418	C₂×D₄	semidirect
424. C₂×#416	C₂×D₄	semidirect
435. C₂×#407	C₂×D₄	semidirect
436. C₂×#407	C₂×D₄	semidirect
437. C₂×#407	C₂×D₄	semidirect
489. C₂²×#41	C₂²×D₄	semidirect
490. C₂²×#41	C₂²×D₄	semidirect
500. C₂³×Q₈	C₂²×D₄	semidirect
506. C₂³×D₄	C₂²×D₄	semidirect
531. C₂×#137	#120	semidirect
534. C₂×AGL(1,ℤ/8)	#120	semidirect
537. C₂×#135	#120	semidirect
539. C₂²×Q₁₆	#120	semidirect
540. C₂²×SD₁₆	#120	semidirect
541. C₂²×D₈	#120	semidirect
548. C₂²×M₁₆	C₂²×D₄	semidirect
558. C₂³×C₈	C₂²×D₄	semidirect
562. #525	C₂²×D₄	semidirect
563. #525	C₂²×D₄	semidirect
585. #427	C₂²×D₄	semidirect
586. #419	C₂²×D₄	semidirect
587. #419	C₂²×D₄	semidirect
588. #418	C₂²×D₄	semidirect
589. #418	C₂²×D₄	semidirect
590. #416	C₂²×D₄	semidirect
591. #407	C₂²×D₄	semidirect
592. #407	C₂²×D₄	semidirect
676. C₂×Q₁₆	C₂×#120	semidirect
677. C₂×SD₁₆	C₂×#120	semidirect
678. C₂×D₈	C₂×#120	semidirect
926. C₂	#72216320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#6442738	2
C₂×#419463	2
C₂×#385872	2
C₂×#449600	2
C₂×#417617	2
C₂×#427241	2
C₂×#419783	2
C₂×#430055	2
C₂×#383149	2
C₂×#10575416	2
C₂×#6437575	2
C₂×#454389	2
C₂×#453994	2
C₂×#395191	2
C₂×#394195	2
C₂×#364416	2
C₂×#6437616	2
C₂×#394108	2
C₂×#393988	2
#72216320	2

Subgroups — C2×#72216320 #72255198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72216320 #72255198