Subgroups — C₂²×#6437575 #72310951

Order 2048.

At least 7858 conjugacy classes of subgroups; only the 47296 normal subgroups are shown.

The subgroup lattice has 1096 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#23884	C₂	1	4	yes	maximal, complemented
2	C₂²×#20623	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#21009	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#20998	C₂	1	2	yes	maximal, complemented
5	C₂²×#23885	C₂	1	4	yes	maximal, complemented
6	C₂²×#23412	C₂	1	2	yes	maximal, complemented
7	C₂²×#60387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#63090	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#60359	C₂	1	2	yes	maximal, complemented
10	C₂²×#62811	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#23883	C₂	1	4	yes	maximal, complemented
12	C₂³×#3025	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×#1891	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#2010	C₂	1	2	yes	maximal, complemented
15	C₂×#6437575	C₂	1	96	yes	maximal, direct product factor
16	C₂²×#23882	C₂	1	4	yes	maximal, complemented
17	C₂³×#585	C₂²	1	1	yes	characteristic
18	C₂³×#585	C₂²	1	1	yes	characteristic, complemented
19	C₂⁵×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂×#63090	C₂²	1	48	yes	complemented
21	C₂²×#3586	C₂²	1	4	yes	complemented
22	C₂²×#3585	C₂²	1	4	yes	complemented
23	C₂³×#575	C₂²	1	2	yes	—
24	C₂³×#575	C₂²	1	2	yes	complemented
25	C₂³×#575	C₂²	1	2	yes	complemented
26	C₂³×#568	C₂²	1	1	yes	characteristic, complemented
27	C₂×#62811	C₂²	1	48	yes	complemented
28	C₂²×#3487	C₂²	1	2	yes	complemented
29	C₂²×#3486	C₂²	1	2	yes	complemented
30	C₂²×#3485	C₂²	1	2	yes	complemented
31	C₂²×#3484	C₂²	1	2	yes	complemented
32	C₂²×#3449	C₂²	1	1	yes	characteristic
33	C₂²×#3449	C₂²	1	1	yes	characteristic, complemented
34	C₂³×#525	C₂²	1	1	yes	characteristic
35	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
36	C₂³×#525	C₂²	1	2	yes	complemented
37	C₂²×#3428	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#3025	C₂²	1	4	yes	complemented
39	C₂²×#3025	C₂²	1	4	yes	complemented
40	C₂²×#3025	C₂²	1	48	yes	complemented
41	C₂²×#3004	C₂²	1	4	yes	complemented
42	C₂²×#3022	C₂²	1	4	yes	complemented
43	C₂×#60387	C₂²	1	48	yes	complemented
44	C₂×#60359	C₂²	1	96	yes	complemented
45	C₂²×#3021	C₂²	1	4	yes	complemented
46	C₂²×#3005	C₂²	1	4	yes	complemented
47	C₂²×#3005	C₂²	1	4	yes	complemented
48	C₂²×#3003	C₂²	1	4	yes	complemented
49	C₂³×#407	C₂²	1	2	yes	complemented
50	C₂³×#410	C₂²	1	2	yes	complemented
51	C₂³×#410	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#2896	C₂²	1	2	yes	complemented
53	C₂²×#2896	C₂²	1	2	yes	complemented
54	C₂³×#413	C₂²	1	1	yes	characteristic, complemented
55	C₂³×#421	C₂²	1	2	yes	complemented
56	C₂³×#421	C₂²	1	2	yes	complemented
57	#6437575	C₂²	1	1024	yes	direct product factor
58	C₂×#23885	C₂²	1	192	yes	complemented
59	C₂×#23884	C₂²	1	192	yes	complemented
60	C₂×#23883	C₂²	1	192	yes	complemented
61	C₂×#23882	C₂²	1	192	yes	complemented
62	C₂²×#2010	C₂²	1	8	yes	complemented
63	C₂²×#2010	C₂²	1	8	yes	complemented
64	C₂²×#2010	C₂²	1	96	yes	complemented
65	C₂×#23412	C₂²	1	96	yes	complemented
66	C₂²×#2009	C₂²	1	8	yes	complemented
67	C₂²×#2008	C₂²	1	8	yes	complemented
68	C₂×#21009	C₂²	1	48	yes	complemented
69	C₂²×#1910	C₂²	1	4	yes	complemented
70	C₂²×#1909	C₂²	1	4	yes	complemented
71	C₂×#20998	C₂²	1	96	yes	complemented
72	C₂²×#1905	C₂²	1	8	yes	complemented
73	C₂²×#1904	C₂²	1	8	yes	complemented
74	C₂²×#1891	C₂²	1	4	yes	complemented
75	C₂²×#1891	C₂²	1	4	yes	complemented
76	C₂²×#1891	C₂²	1	48	yes	complemented
77	C₂×#20623	C₂²	1	48	yes	complemented
78	C₂²×#1796	C₂²	1	4	yes	complemented
79	C₂²×#1795	C₂²	1	4	yes	complemented
80	C₂³×#344	C₂²	1	2	yes	complemented
81	C₂³×H(3,ℤ/4)	C₂²	1	2	yes	complemented
82	C₂²×#585	D₄	1	24	yes	complemented
83	C₂²×#585	C₂³	1	24	yes	—
84	C₂²×#585	C₂³	1	4	yes	—
85	C₂²×#585	C₂³	1	24	yes	complemented
86	C₂³×2₋¹⁺⁴	D₄	1	2	yes	complemented
87	C₂³×2₋¹⁺⁴	C₂³	1	2	yes	—
88	C₂³×H(5,𝔽₂)	D₄	1	2	yes	complemented
89	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
90	C₂⁴×#41	D₄	1	4	yes	complemented
91	C₂⁴×#41	C₂³	1	1	yes	characteristic
92	C₂⁴×#41	C₂³	1	2	yes	—
93	C₂⁴×#41	C₂³	1	1	yes	characteristic
94	C₂⁴×#41	C₂³	1	1	yes	characteristic
95	C₂⁴×#41	C₂³	1	1	yes	characteristic
96	C₂⁴×#41	C₂³	1	1	yes	characteristic, complemented
97	C₂⁴×#41	C₂³	1	1	yes	characteristic, complemented
98	C₂⁴×#41	C₂³	1	24	yes	complemented
99	C₂⁵×Q₈	C₂³	1	1	yes	characteristic, complemented
100	C₂⁵×D₄	C₂³	1	1	yes	characteristic, complemented
101	C₂⁶×C₄	C₂³	1	1	yes	characteristic
102	#63090	C₂³	1	256	yes	complemented
103	C₂×#3586	C₂³	1	96	yes	complemented
104	C₂×#3585	C₂³	1	96	yes	complemented
105	C₂²×#575	D₄	1	48	yes	complemented
106	C₂²×#575	C₂³	1	8	yes	—
107	C₂²×#575	C₂³	1	48	yes	—
108	C₂²×#575	C₂³	1	48	yes	complemented
109	C₂²×#575	C₂³	1	48	yes	complemented
110	C₂³×#137	D₄	1	4	yes	complemented
111	C₂³×#137	C₂³	1	4	yes	—
112	C₂³×#137	C₂³	1	4	yes	—
113	C₂³×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
114	C₂³×AGL(1,ℤ/8)	C₂³	1	4	yes	—
115	C₂³×AGL(1,ℤ/8)	C₂³	1	4	yes	—
116	C₂³×#135	D₄	1	8	yes	complemented
117	C₂²×#568	C₂³	1	4	yes	—
118	C₂²×#568	C₂³	1	24	yes	complemented
119	C₂⁴×M₁₆	C₂³	1	2	yes	—
120	C₂⁴×M₁₆	C₂³	1	2	yes	—
121	#62811	C₂³	1	256	yes	complemented
122	C₂×#3487	C₂³	1	48	yes	complemented
123	C₂×#3486	C₂³	1	48	yes	complemented
124	C₂×#3485	C₂³	1	48	yes	complemented
125	C₂×#3484	C₂³	1	48	yes	complemented
126	C₂×#3449	D₄	1	24	yes	complemented
127	C₂×#3449	C₂³	1	24	yes	—
128	C₂×#3449	C₂³	1	24	yes	complemented
129	C₂²×#536	D₄	1	2	yes	complemented
130	C₂²×#536	C₂³	1	2	yes	—
131	C₂²×#536	C₂³	1	2	yes	complemented
132	C₂²×#535	D₄	1	2	yes	complemented
133	C₂²×#535	C₂³	1	2	yes	—
134	C₂²×#535	C₂³	1	2	yes	complemented
135	C₂²×#532	D₄	1	4	yes	complemented
136	C₂²×#525	D₄	1	2	yes	—
137	C₂²×#525	D₄	1	2	yes	—
138	C₂²×#525	D₄	1	24	yes	—
139	C₂²×#525	C₂³	1	2	yes	—
140	C₂²×#525	C₂³	1	2	yes	—
141	C₂²×#525	C₂³	1	24	yes	—
142	C₂²×#525	C₂³	1	4	yes	—
143	C₂²×#525	C₂³	1	4	yes	—
144	C₂²×#525	C₂³	1	2	yes	complemented
145	C₂²×#525	C₂³	1	2	yes	complemented
146	C₂²×#525	C₂³	1	24	yes	complemented
147	C₂²×#525	C₂³	1	48	yes	complemented
148	C₂³×#123	D₄	1	2	yes	—
149	C₂³×#120	D₄	1	2	yes	—
150	C₂×#3428	C₂³	1	24	yes	complemented
151	C₂²×#519	C₂³	1	2	yes	complemented
152	C₂²×#518	C₂³	1	2	yes	complemented
153	C₂³×#117	C₂³	1	2	yes	—
154	C₂³×#117	C₂³	1	1	yes	characteristic
155	C₂³×#117	C₂³	1	1	yes	characteristic
156	C₂×#3025	C₂³	1	96	yes	complemented
157	C₂×#3025	C₂³	1	96	yes	complemented
158	C₂×#3025	C₂³	1	256	yes	complemented
159	#60387	C₂³	1	256	yes	complemented
160	C₂×#3022	C₂³	1	96	yes	complemented
161	C₂×#3021	C₂³	1	96	yes	complemented
162	#60359	C₂³	1	512	yes	complemented
163	C₂×#3005	C₂³	1	96	yes	complemented
164	C₂×#3005	C₂³	1	96	yes	complemented
165	C₂×#3004	C₂³	1	96	yes	complemented
166	C₂×#3003	C₂³	1	96	yes	complemented
167	C₂²×#421	C₂³	1	8	yes	—
168	C₂²×#421	C₂³	1	48	yes	complemented
169	C₂²×#421	C₂³	1	8	yes	complemented
170	C₂²×#421	C₂³	1	48	yes	complemented
171	C₂×#2896	C₂³	1	48	yes	complemented
172	C₂×#2896	C₂³	1	48	yes	complemented
173	C₂²×#419	C₂³	1	4	yes	complemented
174	C₂²×#419	C₂³	1	4	yes	complemented
175	C₂²×#418	C₂³	1	4	yes	complemented
176	C₂²×#418	C₂³	1	4	yes	complemented
177	C₂²×#413	C₂³	1	4	yes	—
178	C₂²×#413	C₂³	1	24	yes	complemented
179	C₂²×#410	C₂³	1	4	yes	—
180	C₂²×#410	C₂³	1	8	yes	—
181	C₂²×#410	C₂³	1	24	yes	complemented
182	C₂²×#410	C₂³	1	48	yes	complemented
183	C₂²×#407	C₂³	1	4	yes	complemented
184	C₂²×#407	C₂³	1	4	yes	complemented
185	C₂²×#407	C₂³	1	48	yes	complemented
186	#23885	C₂³	1	1024	yes	complemented
187	#23884	C₂³	1	1024	yes	complemented
188	#23883	C₂³	1	1024	yes	complemented
189	#23882	C₂³	1	1024	yes	complemented
190	C₂×#2010	C₂³	1	192	yes	complemented
191	C₂×#2010	C₂³	1	192	yes	complemented
192	C₂×#2010	C₂³	1	512	yes	complemented
193	#23412	C₂³	1	512	yes	complemented
194	C₂×#2009	C₂³	1	192	yes	complemented
195	C₂×#2008	C₂³	1	192	yes	complemented
196	#21009	C₂³	1	256	yes	complemented
197	C₂×#1910	C₂³	1	96	yes	complemented
198	C₂×#1909	C₂³	1	96	yes	complemented
199	#20998	C₂³	1	512	yes	complemented
200	C₂×#1905	C₂³	1	192	yes	complemented
201	C₂×#1904	C₂³	1	192	yes	complemented
202	C₂×#1891	C₂³	1	96	yes	complemented
203	C₂×#1891	C₂³	1	96	yes	complemented
204	C₂×#1891	C₂³	1	256	yes	complemented
205	#20623	C₂³	1	256	yes	complemented
206	C₂×#1796	C₂³	1	96	yes	complemented
207	C₂×#1795	C₂³	1	96	yes	complemented
208	C₂²×#344	C₂³	1	8	yes	complemented
209	C₂²×#344	C₂³	1	48	yes	complemented
210	C₂²×H(3,ℤ/4)	C₂³	1	8	yes	complemented
211	C₂²×H(3,ℤ/4)	C₂³	1	48	yes	complemented
212	C₂⁷	C₂×D₄	1	1	yes	characteristic
213	C₂×#585	C₂×D₄	1	192	yes	complemented
214	C₂×#585	C₂⁴	1	64	yes	—
215	C₂×#585	C₂⁴	1	48	yes	—
216	C₂×#585	C₂⁴	1	64	yes	complemented
217	C₂²×2₋¹⁺⁴	C₂×D₄	1	24	yes	complemented
218	C₂²×2₋¹⁺⁴	C₂×D₄	1	48	yes	complemented
219	C₂²×2₋¹⁺⁴	C₂⁴	1	24	yes	—
220	C₂²×H(5,𝔽₂)	C₂×D₄	1	24	yes	complemented
221	C₂²×H(5,𝔽₂)	C₂×D₄	1	48	yes	complemented
222	C₂²×H(5,𝔽₂)	C₂⁴	1	24	yes	—
223	C₂³×#41	C₂×D₄	1	2	yes	—
224	C₂³×#41	C₂×D₄	1	2	yes	—
225	C₂³×#41	C₂×D₄	1	12	yes	—
226	C₂³×#41	C₂×D₄	1	2	yes	—
227	C₂³×#41	C₂×D₄	1	12	yes	—
228	C₂³×#41	C₂×D₄	1	4	yes	—
229	C₂³×#41	C₂×D₄	1	4	yes	—
230	C₂³×#41	C₂×D₄	1	2	yes	—
231	C₂³×#41	C₂×D₄	1	2	yes	—
232	C₂³×#41	C₂×D₄	1	12	yes	—
233	C₂³×#41	C₂×D₄	1	24	yes	—
234	C₂³×#41	C₂×D₄	1	2	yes	—
235	C₂³×#41	C₂×D₄	1	12	yes	—
236	C₂³×#41	C₂×D₄	1	2	yes	—
237	C₂³×#41	C₂×D₄	1	12	yes	—
238	C₂³×#41	C₂×D₄	1	2	yes	—
239	C₂³×#41	C₂×D₄	1	12	yes	—
240	C₂³×#41	C₂×D₄	1	4	yes	complemented
241	C₂³×#41	C₂×D₄	1	4	yes	complemented
242	C₂³×#41	C₂×D₄	1	4	yes	complemented
243	C₂³×#41	C₂×D₄	1	24	yes	complemented
244	C₂³×#41	C₂×D₄	1	96	yes	complemented
245	C₂³×#41	C₂⁴	1	4	yes	—
246	C₂³×#41	C₂⁴	1	2	yes	—
247	C₂³×#41	C₂⁴	1	12	yes	—
248	C₂³×#41	C₂⁴	1	24	yes	—
249	C₂³×#41	C₂⁴	1	12	yes	—
250	C₂³×#41	C₂⁴	1	12	yes	—
251	C₂³×#41	C₂⁴	1	2	yes	—
252	C₂³×#41	C₂⁴	1	12	yes	—
253	C₂³×#41	C₂⁴	1	12	yes	complemented
254	C₂³×#41	C₂⁴	1	12	yes	complemented
255	C₂³×#41	C₂⁴	1	64	yes	complemented
256	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
257	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
258	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
259	C₂⁴×Q₈	C₂×D₄	1	4	yes	complemented
260	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
261	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
262	C₂⁴×Q₈	C₂⁴	1	12	yes	complemented
263	C₂⁴×D₄	C₂×D₄	1	2	yes	—
264	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
265	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
266	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
267	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
268	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
269	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
270	C₂⁴×D₄	C₂⁴	1	12	yes	complemented
271	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
272	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
273	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
274	C₂⁵×C₄	C₂×D₄	1	12	yes	—
275	C₂⁵×C₄	C₂×D₄	1	2	yes	—
276	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
277	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
278	C₂⁵×C₄	C₂⁴	1	12	yes	—
279	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
280	#3586	C₂⁴	1	256	yes	complemented
281	#3585	C₂⁴	1	256	yes	complemented
282	C₂×#575	C₂×D₄	1	384	yes	complemented
283	C₂×#575	C₂⁴	1	96	yes	—
284	C₂×#575	C₂⁴	1	128	yes	—
285	C₂×#575	C₂⁴	1	128	yes	complemented
286	C₂×#575	C₂⁴	1	128	yes	complemented
287	C₂²×#137	C₂×D₄	1	48	yes	complemented
288	C₂²×#137	C₂×D₄	1	96	yes	complemented
289	C₂²×#137	C₂⁴	1	48	yes	—
290	C₂²×#137	C₂⁴	1	48	yes	—
291	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	48	yes	complemented
292	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	96	yes	complemented
293	C₂²×AGL(1,ℤ/8)	C₂⁴	1	48	yes	—
294	C₂²×AGL(1,ℤ/8)	C₂⁴	1	48	yes	—
295	C₂²×#135	C₂×D₄	1	192	yes	complemented
296	C₂³×Q₁₆	C₂×D₄	1	8	yes	complemented
297	C₂³×SD₁₆	C₂×D₄	1	8	yes	complemented
298	C₂³×SD₁₆	C₂×D₄	1	8	yes	complemented
299	C₂³×D₈	C₂×D₄	1	8	yes	complemented
300	C₂×#568	C₂⁴	1	48	yes	—
301	C₂×#568	C₂⁴	1	64	yes	complemented
302	C₂³×M₁₆	C₂×D₄	1	4	yes	complemented
303	C₂³×M₁₆	C₂×D₄	1	24	yes	complemented
304	C₂³×M₁₆	C₂⁴	1	4	yes	—
305	C₂³×M₁₆	C₂⁴	1	24	yes	—
306	C₂³×M₁₆	C₂⁴	1	4	yes	—
307	C₂³×M₁₆	C₂⁴	1	24	yes	—
308	C₂⁴×C₈	C₂×D₄	1	4	yes	complemented
309	#3487	C₂⁴	1	128	yes	complemented
310	#3486	C₂⁴	1	128	yes	complemented
311	#3485	C₂⁴	1	128	yes	complemented
312	#3484	C₂⁴	1	128	yes	complemented
313	#3449	C₂×D₄	1	192	yes	complemented
314	#3449	C₂⁴	1	64	yes	—
315	#3449	C₂⁴	1	64	yes	complemented
316	C₂×#536	C₂×D₄	1	24	yes	complemented
317	C₂×#536	C₂×D₄	1	48	yes	complemented
318	C₂×#536	C₂⁴	1	24	yes	—
319	C₂×#536	C₂⁴	1	24	yes	complemented
320	C₂×#535	C₂×D₄	1	24	yes	complemented
321	C₂×#535	C₂×D₄	1	48	yes	complemented
322	C₂×#535	C₂⁴	1	24	yes	—
323	C₂×#535	C₂⁴	1	24	yes	complemented
324	C₂×#532	C₂×D₄	1	96	yes	complemented
325	C₂²×C₄⋊Q₈	C₂×D₄	1	4	yes	complemented
326	C₂²×#127	C₂×D₄	1	4	yes	complemented
327	C₂²×#124	C₂×D₄	1	4	yes	complemented
328	C₂²×#124	C₂×D₄	1	4	yes	complemented
329	C₂×#525	C₂×D₄	1	24	yes	—
330	C₂×#525	C₂×D₄	1	24	yes	—
331	C₂×#525	C₂×D₄	1	192	yes	—
332	C₂×#525	C₂×D₄	1	48	yes	—
333	C₂×#525	C₂×D₄	1	48	yes	—
334	C₂×#525	C₂⁴	1	24	yes	—
335	C₂×#525	C₂⁴	1	24	yes	—
336	C₂×#525	C₂⁴	1	64	yes	—
337	C₂×#525	C₂⁴	1	48	yes	—
338	C₂×#525	C₂⁴	1	48	yes	—
339	C₂×#525	C₂⁴	1	24	yes	complemented
340	C₂×#525	C₂⁴	1	24	yes	complemented
341	C₂×#525	C₂⁴	1	64	yes	complemented
342	C₂×#525	C₂⁴	1	128	yes	complemented
343	C₂²×#123	C₂×D₄	1	48	yes	—
344	C₂²×#123	C₂×D₄	1	4	yes	—
345	C₂²×#123	C₂×D₄	1	4	yes	—
346	C₂²×#120	C₂×D₄	1	48	yes	—
347	C₂²×#120	C₂×D₄	1	4	yes	—
348	C₂²×#120	C₂×D₄	1	4	yes	—
349	#3428	C₂⁴	1	64	yes	complemented
350	C₂×#519	C₂⁴	1	24	yes	complemented
351	C₂×#518	C₂⁴	1	24	yes	complemented
352	C₂²×#117	C₂×D₄	1	2	yes	—
353	C₂²×#117	C₂×D₄	1	12	yes	—
354	C₂²×#117	C₂×D₄	1	2	yes	—
355	C₂²×#117	C₂×D₄	1	12	yes	—
356	C₂²×#117	C₂⁴	1	4	yes	—
357	C₂²×#117	C₂⁴	1	24	yes	—
358	C₂²×#117	C₂⁴	1	2	yes	—
359	C₂²×#117	C₂⁴	1	12	yes	—
360	C₂²×#117	C₂⁴	1	2	yes	—
361	C₂²×#117	C₂⁴	1	12	yes	—
362	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
363	C₂³×C₄²	C₂×D₄	1	2	yes	—
364	#3025	C₂⁴	1	256	yes	complemented
365	#3025	C₂⁴	1	256	yes	complemented
366	#3022	C₂⁴	1	256	yes	complemented
367	#3021	C₂⁴	1	256	yes	complemented
368	#3005	C₂⁴	1	256	yes	complemented
369	#3005	C₂⁴	1	256	yes	complemented
370	#3004	C₂⁴	1	256	yes	complemented
371	#3003	C₂⁴	1	256	yes	complemented
372	C₂×#421	C₂⁴	1	96	yes	—
373	C₂×#421	C₂⁴	1	128	yes	complemented
374	C₂×#421	C₂⁴	1	96	yes	complemented
375	C₂×#421	C₂⁴	1	128	yes	complemented
376	#2896	C₂⁴	1	128	yes	complemented
377	#2896	C₂⁴	1	128	yes	complemented
378	C₂×#419	C₂⁴	1	48	yes	complemented
379	C₂×#419	C₂⁴	1	48	yes	complemented
380	C₂×#418	C₂⁴	1	48	yes	complemented
381	C₂×#418	C₂⁴	1	48	yes	complemented
382	C₂×#413	C₂⁴	1	48	yes	—
383	C₂×#413	C₂⁴	1	64	yes	complemented
384	C₂×#410	C₂⁴	1	96	yes	—
385	C₂×#410	C₂⁴	1	48	yes	—
386	C₂×#410	C₂⁴	1	128	yes	complemented
387	C₂×#410	C₂⁴	1	64	yes	complemented
388	C₂×#407	C₂⁴	1	48	yes	complemented
389	C₂×#407	C₂⁴	1	48	yes	complemented
390	C₂×#407	C₂⁴	1	128	yes	complemented
391	#2010	C₂⁴	1	512	yes	complemented
392	#2010	C₂⁴	1	512	yes	complemented
393	#2009	C₂⁴	1	512	yes	complemented
394	#2008	C₂⁴	1	512	yes	complemented
395	#1910	C₂⁴	1	256	yes	complemented
396	#1909	C₂⁴	1	256	yes	complemented
397	#1905	C₂⁴	1	512	yes	complemented
398	#1904	C₂⁴	1	512	yes	complemented
399	#1891	C₂⁴	1	256	yes	complemented
400	#1891	C₂⁴	1	256	yes	complemented
401	#1796	C₂⁴	1	256	yes	complemented
402	#1795	C₂⁴	1	256	yes	complemented
403	C₂×#344	C₂⁴	1	96	yes	complemented
404	C₂×#344	C₂⁴	1	128	yes	complemented
405	C₂×H(3,ℤ/4)	C₂⁴	1	96	yes	complemented
406	C₂×H(3,ℤ/4)	C₂⁴	1	128	yes	complemented
407	C₂⁶	#120	1	2	yes	—
408	C₂⁶	C₂²×D₄	1	1	yes	characteristic
409	C₂⁶	C₂²×D₄	1	1	yes	characteristic
410	C₂⁶	C₂²×D₄	1	12	yes	—
411	C₂⁶	C₂²×D₄	1	1	yes	characteristic
412	#585	C₂⁵	1	64	yes	—
413	C₂×2₋¹⁺⁴	C₂²×D₄	1	128	yes	complemented
414	C₂×2₋¹⁺⁴	C₂²×D₄	1	96	yes	complemented
415	C₂×2₋¹⁺⁴	C₂⁵	1	32	yes	—
416	C₂×H(5,𝔽₂)	C₂²×D₄	1	128	yes	complemented
417	C₂×H(5,𝔽₂)	C₂²×D₄	1	96	yes	complemented
418	C₂×H(5,𝔽₂)	C₂⁵	1	32	yes	—
419	C₂²×#41	#120	1	4	yes	—
420	C₂²×#41	#120	1	4	yes	—
421	C₂²×#41	#120	1	24	yes	—
422	C₂²×#41	#120	1	8	yes	—
423	C₂²×#41	#120	1	24	yes	—
424	C₂²×#41	#120	1	48	yes	—
425	C₂²×#41	#120	1	48	yes	—
426	C₂²×#41	#120	1	96	yes	—
427	C₂²×#41	#120	1	24	yes	—
428	C₂²×#41	#120	1	24	yes	—
429	C₂²×#41	#120	1	24	yes	—
430	C₂²×#41	#120	1	96	yes	—
431	C₂²×#41	C₂²×D₄	1	24	yes	—
432	C₂²×#41	C₂²×D₄	1	24	yes	—
433	C₂²×#41	C₂²×D₄	1	48	yes	—
434	C₂²×#41	C₂²×D₄	1	24	yes	—
435	C₂²×#41	C₂²×D₄	1	12	yes	—
436	C₂²×#41	C₂²×D₄	1	48	yes	—
437	C₂²×#41	C₂²×D₄	1	24	yes	—
438	C₂²×#41	C₂²×D₄	1	24	yes	—
439	C₂²×#41	C₂²×D₄	1	24	yes	—
440	C₂²×#41	C₂²×D₄	1	48	yes	—
441	C₂²×#41	C₂²×D₄	1	48	yes	—
442	C₂²×#41	C₂²×D₄	1	96	yes	—
443	C₂²×#41	C₂²×D₄	1	48	yes	—
444	C₂²×#41	C₂²×D₄	1	24	yes	—
445	C₂²×#41	C₂²×D₄	1	12	yes	—
446	C₂²×#41	C₂²×D₄	1	48	yes	—
447	C₂²×#41	C₂²×D₄	1	24	yes	—
448	C₂²×#41	C₂²×D₄	1	12	yes	—
449	C₂²×#41	C₂²×D₄	1	48	yes	—
450	C₂²×#41	C₂²×D₄	1	12	yes	—
451	C₂²×#41	C₂²×D₄	1	24	yes	—
452	C₂²×#41	C₂²×D₄	1	48	yes	—
453	C₂²×#41	C₂²×D₄	1	48	yes	complemented
454	C₂²×#41	C₂²×D₄	1	48	yes	complemented
455	C₂²×#41	C₂²×D₄	1	48	yes	complemented
456	C₂²×#41	C₂²×D₄	1	96	yes	complemented
457	C₂²×#41	C₂²×D₄	1	256	yes	complemented
458	C₂²×#41	C₂⁵	1	12	yes	—
459	C₂²×#41	C₂⁵	1	24	yes	—
460	C₂²×#41	C₂⁵	1	16	yes	—
461	C₂²×#41	C₂⁵	1	32	yes	—
462	C₂²×#41	C₂⁵	1	16	yes	—
463	C₂²×#41	C₂⁵	1	16	yes	—
464	C₂²×#41	C₂⁵	1	12	yes	—
465	C₂²×#41	C₂⁵	1	16	yes	—
466	C₂²×#41	C₂⁵	1	16	yes	complemented
467	C₂²×#41	C₂⁵	1	16	yes	complemented
468	C₂³×Q₈	#120	1	2	yes	—
469	C₂³×Q₈	#120	1	12	yes	—
470	C₂³×Q₈	C₂²×D₄	1	2	yes	—
471	C₂³×Q₈	C₂²×D₄	1	6	yes	—
472	C₂³×Q₈	C₂²×D₄	1	2	yes	—
473	C₂³×Q₈	C₂²×D₄	1	12	yes	—
474	C₂³×Q₈	C₂²×D₄	1	4	yes	—
475	C₂³×Q₈	C₂²×D₄	1	2	yes	—
476	C₂³×Q₈	C₂²×D₄	1	4	yes	—
477	C₂³×Q₈	C₂²×D₄	1	12	yes	—
478	C₂³×Q₈	C₂²×D₄	1	6	yes	—
479	C₂³×Q₈	C₂²×D₄	1	2	yes	—
480	C₂³×Q₈	C₂²×D₄	1	12	yes	—
481	C₂³×Q₈	C₂²×D₄	1	24	yes	complemented
482	C₂³×Q₈	C₂²×D₄	1	48	yes	complemented
483	C₂³×Q₈	C₂⁵	1	6	yes	—
484	C₂³×Q₈	C₂⁵	1	6	yes	—
485	C₂³×Q₈	C₂⁵	1	16	yes	complemented
486	C₂³×D₄	#120	1	4	yes	—
487	C₂³×D₄	#120	1	2	yes	—
488	C₂³×D₄	#120	1	24	yes	—
489	C₂³×D₄	#120	1	12	yes	—
490	C₂³×D₄	C₂²×D₄	1	4	yes	—
491	C₂³×D₄	C₂²×D₄	1	24	yes	—
492	C₂³×D₄	C₂²×D₄	1	2	yes	—
493	C₂³×D₄	C₂²×D₄	1	6	yes	—
494	C₂³×D₄	C₂²×D₄	1	2	yes	—
495	C₂³×D₄	C₂²×D₄	1	12	yes	—
496	C₂³×D₄	C₂²×D₄	1	4	yes	—
497	C₂³×D₄	C₂²×D₄	1	2	yes	—
498	C₂³×D₄	C₂²×D₄	1	12	yes	—
499	C₂³×D₄	C₂²×D₄	1	2	yes	—
500	C₂³×D₄	C₂²×D₄	1	4	yes	—
501	C₂³×D₄	C₂²×D₄	1	12	yes	—
502	C₂³×D₄	C₂²×D₄	1	6	yes	—
503	C₂³×D₄	C₂²×D₄	1	24	yes	complemented
504	C₂³×D₄	C₂²×D₄	1	48	yes	complemented
505	C₂³×D₄	C₂⁵	1	6	yes	—
506	C₂³×D₄	C₂⁵	1	6	yes	—
507	C₂³×D₄	C₂⁵	1	16	yes	complemented
508	C₂⁴×C₄	#120	1	4	yes	—
509	C₂⁴×C₄	#120	1	2	yes	—
510	C₂⁴×C₄	#120	1	24	yes	—
511	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
513	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
515	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
516	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
517	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
518	C₂⁴×C₄	C₂²×D₄	1	48	yes	—
519	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	24	yes	—
521	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
524	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
526	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
527	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
528	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
529	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
531	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
532	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
533	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
534	C₂⁴×C₄	H(5,𝔽₂)	1	12	yes	—
535	C₂⁴×C₄	C₂⁵	1	6	yes	—
536	C₂⁴×C₄	C₂⁵	1	6	yes	—
537	C₂⁴×C₄	C₂⁵	1	16	yes	—
538	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
539	C₂⁴×C₄	C₂⁵	1	6	yes	—
540	#575	C₂⁵	1	128	yes	—
541	C₂×#137	C₂²×D₄	1	192	yes	complemented
542	C₂×#137	C₂²×D₄	1	256	yes	complemented
543	C₂×#137	C₂⁵	1	64	yes	—
544	C₂×#137	C₂⁵	1	64	yes	—
545	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	192	yes	complemented
546	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	256	yes	complemented
547	C₂×AGL(1,ℤ/8)	C₂⁵	1	64	yes	—
548	C₂×AGL(1,ℤ/8)	C₂⁵	1	64	yes	—
549	C₂×#135	C₂²×D₄	1	512	yes	complemented
550	C₂²×Q₁₆	C₂²×D₄	1	96	yes	complemented
551	C₂²×SD₁₆	C₂²×D₄	1	96	yes	complemented
552	C₂²×SD₁₆	C₂²×D₄	1	96	yes	complemented
553	C₂²×D₈	C₂²×D₄	1	96	yes	complemented
554	#568	C₂⁵	1	64	yes	—
555	C₂²×M₁₆	C₂²×D₄	1	24	yes	—
556	C₂²×M₁₆	C₂²×D₄	1	48	yes	complemented
557	C₂²×M₁₆	C₂²×D₄	1	96	yes	complemented
558	C₂²×M₁₆	C₂⁵	1	24	yes	—
559	C₂²×M₁₆	C₂⁵	1	32	yes	—
560	C₂²×M₁₆	C₂⁵	1	24	yes	—
561	C₂²×M₁₆	C₂⁵	1	32	yes	—
562	C₂³×C₈	C₂²×D₄	1	8	yes	—
563	C₂³×C₈	C₂²×D₄	1	48	yes	complemented
564	#536	C₂²×D₄	1	128	yes	complemented
565	#536	C₂²×D₄	1	96	yes	complemented
566	#536	C₂⁵	1	32	yes	—
567	#536	C₂⁵	1	32	yes	complemented
568	#535	C₂²×D₄	1	128	yes	complemented
569	#535	C₂²×D₄	1	96	yes	complemented
570	#535	C₂⁵	1	32	yes	—
571	#535	C₂⁵	1	32	yes	complemented
572	#532	C₂²×D₄	1	256	yes	complemented
573	C₂×C₄⋊Q₈	C₂²×D₄	1	48	yes	complemented
574	C₂×#127	C₂²×D₄	1	48	yes	complemented
575	C₂×#124	C₂²×D₄	1	48	yes	complemented
576	C₂×#124	C₂²×D₄	1	48	yes	complemented
577	#525	C₂²×D₄	1	128	yes	—
578	#525	C₂²×D₄	1	128	yes	—
579	#525	C₂²×D₄	1	96	yes	—
580	#525	C₂²×D₄	1	96	yes	—
581	#525	C₂⁵	1	32	yes	—
582	#525	C₂⁵	1	32	yes	—
583	#525	C₂⁵	1	64	yes	—
584	#525	C₂⁵	1	64	yes	—
585	#525	C₂⁵	1	32	yes	complemented
586	#525	C₂⁵	1	32	yes	complemented
587	C₂×#123	C₂²×D₄	1	48	yes	—
588	C₂×#123	C₂²×D₄	1	48	yes	—
589	C₂×#123	C₂²×D₄	1	128	yes	—
590	C₂×#120	C₂²×D₄	1	48	yes	—
591	C₂×#120	C₂²×D₄	1	48	yes	—
592	C₂×#120	C₂²×D₄	1	128	yes	—
593	#519	C₂⁵	1	32	yes	complemented
594	#518	C₂⁵	1	32	yes	complemented
595	C₂×#117	C₂²×D₄	1	24	yes	—
596	C₂×#117	C₂²×D₄	1	12	yes	—
597	C₂×#117	C₂²×D₄	1	48	yes	—
598	C₂×#117	C₂²×D₄	1	12	yes	—
599	C₂×#117	C₂²×D₄	1	24	yes	—
600	C₂×#117	C₂²×D₄	1	48	yes	—
601	C₂×#117	C₂⁵	1	24	yes	—
602	C₂×#117	C₂⁵	1	32	yes	—
603	C₂×#117	C₂⁵	1	12	yes	—
604	C₂×#117	C₂⁵	1	16	yes	—
605	C₂×#117	C₂⁵	1	12	yes	—
606	C₂×#117	C₂⁵	1	16	yes	—
607	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
608	C₂²×C₂²⋊C₄	C₂²×D₄	1	24	yes	—
609	C₂²×C₄²	C₂²×D₄	1	4	yes	—
610	C₂²×C₄²	C₂²×D₄	1	24	yes	—
611	#421	C₂⁵	1	128	yes	—
612	#421	C₂⁵	1	128	yes	complemented
613	#419	C₂⁵	1	64	yes	complemented
614	#419	C₂⁵	1	64	yes	complemented
615	#418	C₂⁵	1	64	yes	complemented
616	#418	C₂⁵	1	64	yes	complemented
617	#413	C₂⁵	1	64	yes	—
618	#410	C₂⁵	1	64	yes	—
619	#410	C₂⁵	1	128	yes	—
620	#407	C₂⁵	1	64	yes	complemented
621	#407	C₂⁵	1	64	yes	complemented
622	#344	C₂⁵	1	128	yes	complemented
623	H(3,ℤ/4)	C₂⁵	1	128	yes	complemented
624	C₂⁵	C₂×#120	1	4	yes	—
625	C₂⁵	C₂×#120	1	24	yes	—
626	C₂⁵	C₂×#120	1	1	yes	characteristic
627	C₂⁵	C₂×#120	1	1	yes	characteristic
628	C₂⁵	C₂×#120	1	6	yes	—
629	C₂⁵	D₄²	1	2	yes	—
630	C₂⁵	D₄²	1	2	yes	—
631	C₂⁵	D₄²	1	12	yes	—
632	C₂⁵	C₂³×D₄	1	6	yes	—
633	C₂⁵	C₂³×D₄	1	6	yes	—
634	C₂⁵	C₂³×D₄	1	16	yes	—
635	C₂⁵	C₂³×D₄	1	1	yes	characteristic
636	C₂⁵	C₂³×D₄	1	6	yes	—
637	C₂×#41	C₂×#120	1	48	yes	—
638	C₂×#41	C₂×#120	1	96	yes	—
639	C₂×#41	C₂×#120	1	192	yes	—
640	C₂×#41	C₂×#120	1	48	yes	—
641	C₂×#41	C₂×#120	1	192	yes	—
642	C₂×#41	C₂×#120	1	96	yes	—
643	C₂×#41	C₂×#120	1	96	yes	—
644	C₂×#41	C₂×#120	1	96	yes	—
645	C₂×#41	C₂×#120	1	96	yes	—
646	C₂×#41	C₂×#120	1	48	yes	—
647	C₂×#41	C₂×#120	1	96	yes	—
648	C₂×#41	C₂³×D₄	1	32	yes	—
649	C₂×#41	C₂³×D₄	1	32	yes	—
650	C₂×#41	C₂³×D₄	1	24	yes	—
651	C₂×#41	C₂³×D₄	1	48	yes	—
652	C₂×#41	C₂³×D₄	1	32	yes	—
653	C₂×#41	C₂³×D₄	1	32	yes	—
654	C₂×#41	C₂³×D₄	1	32	yes	—
655	C₂×#41	C₂³×D₄	1	64	yes	—
656	C₂×#41	C₂³×D₄	1	64	yes	—
657	C₂×#41	C₂³×D₄	1	24	yes	—
658	C₂×#41	C₂³×D₄	1	32	yes	—
659	C₂×#41	C₂³×D₄	1	32	yes	—
660	C₂×#41	C₂³×D₄	1	24	yes	—
661	C₂×#41	C₂³×D₄	1	32	yes	—
662	C₂×#41	C₂³×D₄	1	24	yes	—
663	C₂×#41	C₂³×D₄	1	64	yes	complemented
664	C₂×#41	C₂³×D₄	1	64	yes	complemented
665	C₂×#41	C₂³×D₄	1	64	yes	complemented
666	C₂×#41	C₂⁶	1	16	yes	—
667	C₂×#41	C₂⁶	1	8	yes	—
668	C₂×#41	C₂⁶	1	8	yes	—
669	C₂²×Q₈	C₂×#120	1	4	yes	—
670	C₂²×Q₈	C₂×#120	1	24	yes	—
671	C₂²×Q₈	C₂×#120	1	12	yes	—
672	C₂²×Q₈	C₂×#120	1	24	yes	—
673	C₂²×Q₈	C₂×#120	1	24	yes	—
674	C₂²×Q₈	C₂×#120	1	12	yes	—
675	C₂²×Q₈	C₂×#120	1	48	yes	—
676	C₂²×Q₈	C₂³×D₄	1	12	yes	—
677	C₂²×Q₈	C₂³×D₄	1	12	yes	—
678	C₂²×Q₈	C₂³×D₄	1	16	yes	—
679	C₂²×Q₈	C₂³×D₄	1	24	yes	—
680	C₂²×Q₈	C₂³×D₄	1	12	yes	—
681	C₂²×Q₈	C₂³×D₄	1	12	yes	—
682	C₂²×Q₈	C₂³×D₄	1	12	yes	—
683	C₂²×Q₈	C₂³×D₄	1	24	yes	—
684	C₂²×Q₈	C₂³×D₄	1	24	yes	—
685	C₂²×Q₈	C₂³×D₄	1	12	yes	—
686	C₂²×Q₈	C₂³×D₄	1	16	yes	—
687	C₂²×Q₈	C₂³×D₄	1	32	yes	complemented
688	C₂²×Q₈	C₂³×D₄	1	64	yes	complemented
689	C₂²×Q₈	C₂⁶	1	4	yes	—
690	C₂²×Q₈	C₂⁶	1	4	yes	—
691	C₂²×D₄	C₂×#120	1	24	yes	—
692	C₂²×D₄	C₂×#120	1	48	yes	—
693	C₂²×D₄	C₂×#120	1	96	yes	—
694	C₂²×D₄	C₂×#120	1	24	yes	—
695	C₂²×D₄	C₂×#120	1	12	yes	—
696	C₂²×D₄	C₂×#120	1	48	yes	—
697	C₂²×D₄	C₂×#120	1	4	yes	—
698	C₂²×D₄	C₂×#120	1	24	yes	—
699	C₂²×D₄	C₂×#120	1	12	yes	—
700	C₂²×D₄	C₂×#120	1	24	yes	—
701	C₂²×D₄	C₂³×D₄	1	12	yes	—
702	C₂²×D₄	C₂³×D₄	1	12	yes	—
703	C₂²×D₄	C₂³×D₄	1	16	yes	—
704	C₂²×D₄	C₂³×D₄	1	24	yes	—
705	C₂²×D₄	C₂³×D₄	1	12	yes	—
706	C₂²×D₄	C₂³×D₄	1	12	yes	—
707	C₂²×D₄	C₂³×D₄	1	16	yes	—
708	C₂²×D₄	C₂³×D₄	1	12	yes	—
709	C₂²×D₄	C₂³×D₄	1	12	yes	—
710	C₂²×D₄	C₂³×D₄	1	24	yes	—
711	C₂²×D₄	C₂³×D₄	1	24	yes	—
712	C₂²×D₄	C₂³×D₄	1	24	yes	—
713	C₂²×D₄	C₂³×D₄	1	32	yes	—
714	C₂²×D₄	C₂³×D₄	1	32	yes	complemented
715	C₂²×D₄	C₂³×D₄	1	64	yes	complemented
716	C₂²×D₄	C₂⁶	1	4	yes	—
717	C₂²×D₄	C₂⁶	1	4	yes	—
718	C₂³×C₄	C₂×#120	1	4	yes	—
719	C₂³×C₄	C₂×#120	1	24	yes	—
720	C₂³×C₄	C₂×#120	1	48	yes	—
721	C₂³×C₄	C₂×#120	1	24	yes	—
722	C₂³×C₄	C₂×#120	1	96	yes	—
723	C₂³×C₄	C₂×#120	1	1	yes	characteristic
724	C₂³×C₄	C₂×#120	1	6	yes	—
725	C₂³×C₄	C₂×#120	1	6	yes	—
726	C₂³×C₄	C₂×#120	1	6	yes	—
727	C₂³×C₄	C₂×#120	1	24	yes	—
728	C₂³×C₄	C₂×#120	1	6	yes	—
729	C₂³×C₄	C₂×#120	1	6	yes	—
730	C₂³×C₄	C₂×#120	1	1	yes	characteristic
731	C₂³×C₄	C₂×#120	1	2	yes	—
732	C₂³×C₄	C₂×#120	1	12	yes	—
733	C₂³×C₄	C₂×#120	1	1	yes	characteristic
734	C₂³×C₄	C₂×#120	1	6	yes	—
735	C₂³×C₄	C₂×#120	1	6	yes	—
736	C₂³×C₄	C₂×#120	1	12	yes	—
737	C₂³×C₄	C₂×#120	1	24	yes	—
738	C₂³×C₄	C₂×#120	1	1	yes	characteristic
739	C₂³×C₄	#534	1	1	yes	characteristic
740	C₂³×C₄	#534	1	6	yes	—
741	C₂³×C₄	#534	1	2	yes	—
742	C₂³×C₄	#534	1	12	yes	—
743	C₂³×C₄	#534	1	6	yes	—
744	C₂³×C₄	#534	1	12	yes	—
745	C₂³×C₄	#534	1	24	yes	—
746	C₂³×C₄	#534	1	1	yes	characteristic
747	C₂³×C₄	D₄²	1	2	yes	—
748	C₂³×C₄	D₄²	1	12	yes	—
749	C₂³×C₄	D₄²	1	12	yes	—
750	C₂³×C₄	D₄²	1	12	yes	—
751	C₂³×C₄	D₄²	1	12	yes	—
752	C₂³×C₄	D₄²	1	48	yes	—
753	C₂³×C₄	D₄²	1	12	yes	—
754	C₂³×C₄	D₄²	1	2	yes	—
755	C₂³×C₄	D₄²	1	2	yes	—
756	C₂³×C₄	D₄²	1	12	yes	—
757	C₂³×C₄	D₄²	1	2	yes	—
758	C₂³×C₄	D₄²	1	2	yes	—
759	C₂³×C₄	D₄²	1	12	yes	—
760	C₂³×C₄	D₄²	1	12	yes	—
761	C₂³×C₄	D₄²	1	12	yes	—
762	C₂³×C₄	D₄²	1	12	yes	—
763	C₂³×C₄	D₄²	1	12	yes	—
764	C₂³×C₄	D₄²	1	48	yes	—
765	C₂³×C₄	D₄²	1	2	yes	—
766	C₂³×C₄	C₂³×D₄	1	6	yes	—
767	C₂³×C₄	C₂³×D₄	1	6	yes	—
768	C₂³×C₄	C₂³×D₄	1	16	yes	—
769	C₂³×C₄	C₂³×D₄	1	16	yes	—
770	C₂³×C₄	C₂³×D₄	1	12	yes	—
771	C₂³×C₄	C₂³×D₄	1	16	yes	—
772	C₂³×C₄	C₂³×D₄	1	12	yes	—
773	C₂³×C₄	C₂³×D₄	1	24	yes	—
774	C₂³×C₄	C₂³×D₄	1	32	yes	—
775	C₂³×C₄	C₂³×D₄	1	6	yes	—
776	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
777	C₂³×C₄	C₂³×D₄	1	3	yes	—
778	C₂³×C₄	C₂³×D₄	1	12	yes	—
779	C₂³×C₄	C₂³×D₄	1	6	yes	—
780	C₂³×C₄	C₂³×D₄	1	2	yes	—
781	C₂³×C₄	C₂³×D₄	1	12	yes	—
782	C₂³×C₄	C₂³×D₄	1	12	yes	—
783	C₂³×C₄	C₂³×D₄	1	6	yes	—
784	C₂³×C₄	C₂³×D₄	1	24	yes	—
785	C₂³×C₄	C₂³×D₄	1	6	yes	—
786	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
787	C₂³×C₄	C₂³×D₄	1	3	yes	—
788	C₂³×C₄	C₂³×D₄	1	12	yes	—
789	C₂³×C₄	C₂³×D₄	1	6	yes	—
790	C₂³×C₄	C₂³×D₄	1	6	yes	—
791	C₂³×C₄	C₂³×D₄	1	3	yes	—
792	C₂³×C₄	C₂³×D₄	1	12	yes	—
793	C₂³×C₄	C₂×H(5,𝔽₂)	1	6	yes	—
794	C₂³×C₄	C₂×H(5,𝔽₂)	1	12	yes	—
795	C₂³×C₄	C₂×H(5,𝔽₂)	1	24	yes	—
796	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
797	C₂³×C₄	C₂×H(5,𝔽₂)	1	12	yes	—
798	C₂³×C₄	C₂⁶	1	4	yes	—
799	C₂³×C₄	C₂⁶	1	4	yes	—
800	C₂³×C₄	C₂⁶	1	3	yes	—
801	C₂³×C₄	C₂⁶	1	4	yes	—
802	C₂×Q₁₆	C₂³×D₄	1	128	yes	complemented
803	C₂×SD₁₆	C₂³×D₄	1	128	yes	complemented
804	C₂×SD₁₆	C₂³×D₄	1	128	yes	complemented
805	C₂×D₈	C₂³×D₄	1	128	yes	complemented
806	C₂×M₁₆	C₂³×D₄	1	48	yes	—
807	C₂×M₁₆	C₂³×D₄	1	64	yes	complemented
808	C₂×M₁₆	C₂⁶	1	16	yes	—
809	C₂×M₁₆	C₂⁶	1	16	yes	—
810	C₂²×C₈	C₂³×D₄	1	48	yes	—
811	C₂²×C₈	C₂³×D₄	1	64	yes	complemented
812	C₄⋊Q₈	C₂³×D₄	1	64	yes	complemented
813	#127	C₂³×D₄	1	64	yes	complemented
814	#124	C₂³×D₄	1	64	yes	complemented
815	#124	C₂³×D₄	1	64	yes	complemented
816	#123	C₂³×D₄	1	64	yes	—
817	#123	C₂³×D₄	1	64	yes	—
818	#120	C₂³×D₄	1	64	yes	—
819	#120	C₂³×D₄	1	64	yes	—
820	#117	C₂³×D₄	1	32	yes	—
821	#117	C₂³×D₄	1	24	yes	—
822	#117	C₂³×D₄	1	24	yes	—
823	#117	C₂³×D₄	1	32	yes	—
824	#117	C₂⁶	1	16	yes	—
825	#117	C₂⁶	1	8	yes	—
826	#117	C₂⁶	1	8	yes	—
827	C₂×C₂²⋊C₄	C₂³×D₄	1	24	yes	—
828	C₂×C₂²⋊C₄	C₂³×D₄	1	32	yes	—
829	C₂×C₄²	C₂³×D₄	1	24	yes	—
830	C₂×C₄²	C₂³×D₄	1	32	yes	—
831	C₂⁴	#2403	1	1	yes	characteristic
832	C₂⁴	#2403	1	1	yes	characteristic
833	C₂⁴	#2403	1	2	yes	—
834	C₂⁴	#2403	1	6	yes	—
835	C₂⁴	#2403	1	6	yes	—
836	C₂⁴	#2403	1	12	yes	—
837	C₂⁴	#2403	1	12	yes	—
838	C₂⁴	#2403	1	24	yes	—
839	C₂⁴	C₂²×#120	1	1	yes	characteristic
840	C₂⁴	C₂²×#120	1	24	yes	—
841	C₂⁴	C₂²×#120	1	32	yes	—
842	C₂⁴	C₂²×#120	1	3	yes	—
843	C₂⁴	C₂²×#120	1	6	yes	—
844	C₂⁴	C₂²×#120	1	6	yes	—
845	C₂⁴	C₂²×#120	1	12	yes	—
846	C₂⁴	C₂×D₄²	1	2	yes	—
847	C₂⁴	C₂×D₄²	1	6	yes	—
848	C₂⁴	C₂×D₄²	1	12	yes	—
849	C₂⁴	C₂×D₄²	1	12	yes	—
850	C₂⁴	C₂×D₄²	1	24	yes	—
851	C₂⁴	C₂⁴×D₄	1	4	yes	—
852	C₂⁴	C₂⁴×D₄	1	4	yes	—
853	C₂⁴	C₂⁴×D₄	1	3	yes	—
854	C₂⁴	C₂⁴×D₄	1	4	yes	—
855	#41	C₂²×#120	1	64	yes	—
856	#41	C₂²×#120	1	128	yes	—
857	#41	C₂²×#120	1	64	yes	—
858	C₂×Q₈	C₂²×#120	1	24	yes	—
859	C₂×Q₈	C₂²×#120	1	48	yes	—
860	C₂×Q₈	C₂²×#120	1	24	yes	—
861	C₂×Q₈	C₂²×#120	1	32	yes	—
862	C₂×Q₈	C₂²×#120	1	24	yes	—
863	C₂×Q₈	C₂⁴×D₄	1	8	yes	—
864	C₂×Q₈	C₂⁴×D₄	1	8	yes	—
865	C₂×Q₈	C₂⁴×D₄	1	16	yes	—
866	C₂×Q₈	C₂⁴×D₄	1	16	yes	—
867	C₂×Q₈	C₂⁴×D₄	1	8	yes	—
868	C₂×Q₈	C₂⁴×D₄	1	8	yes	—
869	C₂×D₄	C₂²×#120	1	48	yes	—
870	C₂×D₄	C₂²×#120	1	64	yes	—
871	C₂×D₄	C₂²×#120	1	32	yes	—
872	C₂×D₄	C₂²×#120	1	24	yes	—
873	C₂×D₄	C₂²×#120	1	24	yes	—
874	C₂×D₄	C₂²×#120	1	48	yes	—
875	C₂×D₄	C₂²×#120	1	24	yes	—
876	C₂×D₄	C₂⁴×D₄	1	8	yes	—
877	C₂×D₄	C₂⁴×D₄	1	8	yes	—
878	C₂×D₄	C₂⁴×D₄	1	16	yes	—
879	C₂×D₄	C₂⁴×D₄	1	8	yes	—
880	C₂×D₄	C₂⁴×D₄	1	16	yes	—
881	C₂×D₄	C₂⁴×D₄	1	8	yes	—
882	C₂×D₄	C₂⁴×D₄	1	16	yes	—
883	C₂²×C₄	#2403	1	1	yes	characteristic
884	C₂²×C₄	#2403	1	6	yes	—
885	C₂²×C₄	#2403	1	2	yes	—
886	C₂²×C₄	#2403	1	12	yes	—
887	C₂²×C₄	#2403	1	6	yes	—
888	C₂²×C₄	#2403	1	6	yes	—
889	C₂²×C₄	#2403	1	12	yes	—
890	C₂²×C₄	#2403	1	24	yes	—
891	C₂²×C₄	#2403	1	6	yes	—
892	C₂²×C₄	#2403	1	6	yes	—
893	C₂²×C₄	#2403	1	6	yes	—
894	C₂²×C₄	#2403	1	24	yes	—
895	C₂²×C₄	#2403	1	12	yes	—
896	C₂²×C₄	#2403	1	12	yes	—
897	C₂²×C₄	#2403	1	12	yes	—
898	C₂²×C₄	#2403	1	12	yes	—
899	C₂²×C₄	#2403	1	24	yes	—
900	C₂²×C₄	#2403	1	48	yes	—
901	C₂²×C₄	#2403	1	12	yes	—
902	C₂²×C₄	#2403	1	24	yes	—
903	C₂²×C₄	#2403	1	12	yes	—
904	C₂²×C₄	#2403	1	24	yes	—
905	C₂²×C₄	#2403	1	48	yes	—
906	C₂²×C₄	#2403	1	48	yes	—
907	C₂²×C₄	#2403	1	48	yes	—
908	C₂²×C₄	#2403	1	1	yes	characteristic
909	C₂²×C₄	C₂²×#120	1	24	yes	—
910	C₂²×C₄	C₂²×#120	1	32	yes	—
911	C₂²×C₄	C₂²×#120	1	64	yes	—
912	C₂²×C₄	C₂²×#120	1	48	yes	—
913	C₂²×C₄	C₂²×#120	1	6	yes	—
914	C₂²×C₄	C₂²×#120	1	3	yes	—
915	C₂²×C₄	C₂²×#120	1	3	yes	—
916	C₂²×C₄	C₂²×#120	1	12	yes	—
917	C₂²×C₄	C₂²×#120	1	12	yes	—
918	C₂²×C₄	C₂²×#120	1	6	yes	—
919	C₂²×C₄	C₂²×#120	1	12	yes	—
920	C₂²×C₄	C₂²×#120	1	12	yes	—
921	C₂²×C₄	C₂²×#120	1	12	yes	—
922	C₂²×C₄	C₂²×#120	1	6	yes	—
923	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
924	C₂²×C₄	C₂²×#120	1	6	yes	—
925	C₂²×C₄	C₂²×#120	1	12	yes	—
926	C₂²×C₄	C₂²×#120	1	6	yes	—
927	C₂²×C₄	C₂²×#120	1	24	yes	—
928	C₂²×C₄	C₂²×#120	1	6	yes	—
929	C₂²×C₄	C₂²×#120	1	3	yes	—
930	C₂²×C₄	C₂²×#120	1	12	yes	—
931	C₂²×C₄	C₂²×#120	1	12	yes	—
932	C₂²×C₄	C₂²×#120	1	24	yes	—
933	C₂²×C₄	C₂²×#120	1	6	yes	—
934	C₂²×C₄	C₂×#534	1	1	yes	characteristic
935	C₂²×C₄	C₂×#534	1	6	yes	—
936	C₂²×C₄	C₂×#534	1	3	yes	—
937	C₂²×C₄	C₂×#534	1	6	yes	—
938	C₂²×C₄	C₂×#534	1	12	yes	—
939	C₂²×C₄	C₂×#534	1	6	yes	—
940	C₂²×C₄	C₂×#534	1	12	yes	—
941	C₂²×C₄	C₂×#534	1	24	yes	—
942	C₂²×C₄	C₂×#534	1	6	yes	—
943	C₂²×C₄	C₂×#534	1	12	yes	—
944	C₂²×C₄	C₂×#534	1	24	yes	—
945	C₂²×C₄	C₂×D₄²	1	12	yes	—
946	C₂²×C₄	C₂×D₄²	1	6	yes	—
947	C₂²×C₄	C₂×D₄²	1	24	yes	—
948	C₂²×C₄	C₂×D₄²	1	12	yes	—
949	C₂²×C₄	C₂×D₄²	1	6	yes	—
950	C₂²×C₄	C₂×D₄²	1	24	yes	—
951	C₂²×C₄	C₂×D₄²	1	24	yes	—
952	C₂²×C₄	C₂×D₄²	1	12	yes	—
953	C₂²×C₄	C₂×D₄²	1	24	yes	—
954	C₂²×C₄	C₂×D₄²	1	24	yes	—
955	C₂²×C₄	C₂×D₄²	1	2	yes	—
956	C₂²×C₄	C₂×D₄²	1	12	yes	—
957	C₂²×C₄	C₂×D₄²	1	6	yes	—
958	C₂²×C₄	C₂×D₄²	1	12	yes	—
959	C₂²×C₄	C₂×D₄²	1	24	yes	—
960	C₂²×C₄	C₂×D₄²	1	6	yes	—
961	C₂²×C₄	C₂×D₄²	1	6	yes	—
962	C₂²×C₄	C₂×D₄²	1	12	yes	—
963	C₂²×C₄	C₂×D₄²	1	12	yes	—
964	C₂²×C₄	C₂×D₄²	1	24	yes	—
965	C₂²×C₄	C₂×D₄²	1	24	yes	—
966	C₂²×C₄	C₂×D₄²	1	12	yes	—
967	C₂²×C₄	C₂×D₄²	1	24	yes	—
968	C₂²×C₄	C₂×D₄²	1	24	yes	—
969	C₂²×C₄	C₂×D₄²	1	24	yes	—
970	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
971	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
972	C₂²×C₄	C₂⁴×D₄	1	16	yes	—
973	C₂²×C₄	C₂⁴×D₄	1	3	yes	—
974	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
975	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
976	C₂²×C₄	C₂⁴×D₄	1	3	yes	—
977	C₂²×C₄	C₂⁴×D₄	1	6	yes	—
978	C₂²×C₄	C₂⁴×D₄	1	8	yes	—
979	C₂²×C₄	C₂⁴×D₄	1	8	yes	—
980	C₂²×C₄	C₂⁴×D₄	1	6	yes	—
981	C₂²×C₄	C₂⁴×D₄	1	3	yes	—
982	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
983	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
984	C₂²×C₄	C₂⁴×D₄	1	3	yes	—
985	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
986	C₂²×C₄	C₂⁴×D₄	1	3	yes	—
987	C₂²×C₄	C₂²×H(5,𝔽₂)	1	6	yes	—
988	C₂²×C₄	C₂²×H(5,𝔽₂)	1	8	yes	—
989	C₂²×C₄	C₂²×H(5,𝔽₂)	1	6	yes	—
990	C₂²×C₄	C₂²×H(5,𝔽₂)	1	8	yes	—
991	C₂²×C₄	C₂⁷	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×D₄	1	32	yes	—
993	C₂²⋊C₄	C₂⁴×D₄	1	16	yes	—
994	C₄²	C₂⁴×D₄	1	16	yes	—
995	C₂³	C₂×#2403	1	3	yes	—
996	C₂³	C₂×#2403	1	6	yes	—
997	C₂³	C₂×#2403	1	6	yes	—
998	C₂³	C₂×#2403	1	6	yes	—
999	C₂³	C₂×#2403	1	12	yes	—
1000	C₂³	C₂×#2403	1	6	yes	—
1001	C₂³	C₂×#2403	1	12	yes	—
1002	C₂³	C₂×#2403	1	12	yes	—
1003	C₂³	C₂×#2403	1	24	yes	—
1004	C₂³	C₂×#2403	1	24	yes	—
1005	C₂³	C₂×#2403	1	1	yes	characteristic
1006	C₂³	C₂³×#120	1	3	yes	—
1007	C₂³	C₂³×#120	1	16	yes	—
1008	C₂³	C₂³×#120	1	3	yes	—
1009	C₂³	C₂³×#120	1	4	yes	—
1010	C₂³	C₂³×#120	1	4	yes	—
1011	C₂³	C₂²×D₄²	1	6	yes	—
1012	C₂³	C₂²×D₄²	1	6	yes	—
1013	C₂³	C₂²×D₄²	1	8	yes	—
1014	C₂³	C₂²×D₄²	1	8	yes	—
1015	C₂³	C₂⁵×D₄	1	1	yes	characteristic
1016	Q₈	C₂³×#120	1	16	yes	—
1017	D₄	C₂³×#120	1	16	yes	—
1018	C₂×C₄	C₂×#2403	1	6	yes	—
1019	C₂×C₄	C₂×#2403	1	6	yes	—
1020	C₂×C₄	C₂×#2403	1	12	yes	—
1021	C₂×C₄	C₂×#2403	1	12	yes	—
1022	C₂×C₄	C₂×#2403	1	3	yes	—
1023	C₂×C₄	C₂×#2403	1	24	yes	—
1024	C₂×C₄	C₂×#2403	1	12	yes	—
1025	C₂×C₄	C₂×#2403	1	12	yes	—
1026	C₂×C₄	C₂×#2403	1	24	yes	—
1027	C₂×C₄	C₂×#2403	1	3	yes	—
1028	C₂×C₄	C₂×#2403	1	6	yes	—
1029	C₂×C₄	C₂×#2403	1	12	yes	—
1030	C₂×C₄	C₂×#2403	1	12	yes	—
1031	C₂×C₄	C₂×#2403	1	12	yes	—
1032	C₂×C₄	C₂×#2403	1	6	yes	—
1033	C₂×C₄	C₂×#2403	1	24	yes	—
1034	C₂×C₄	C₂×#2403	1	6	yes	—
1035	C₂×C₄	C₂×#2403	1	12	yes	—
1036	C₂×C₄	C₂×#2403	1	24	yes	—
1037	C₂×C₄	C₂×#2403	1	24	yes	—
1038	C₂×C₄	C₂×#2403	1	24	yes	—
1039	C₂×C₄	C₂×#2403	1	12	yes	—
1040	C₂×C₄	C₂×#2403	1	24	yes	—
1041	C₂×C₄	C₂×#2403	1	24	yes	—
1042	C₂×C₄	C₂³×#120	1	16	yes	—
1043	C₂×C₄	C₂³×#120	1	3	yes	—
1044	C₂×C₄	C₂³×#120	1	4	yes	—
1045	C₂×C₄	C₂³×#120	1	8	yes	—
1046	C₂×C₄	C₂³×#120	1	6	yes	—
1047	C₂×C₄	C₂³×#120	1	4	yes	—
1048	C₂×C₄	C₂³×#120	1	3	yes	—
1049	C₂×C₄	C₂³×#120	1	4	yes	—
1050	C₂×C₄	C₂³×#120	1	3	yes	—
1051	C₂×C₄	C₂³×#120	1	3	yes	—
1052	C₂×C₄	C₂³×#120	1	4	yes	—
1053	C₂×C₄	C₂²×#534	1	3	yes	—
1054	C₂×C₄	C₂²×#534	1	4	yes	—
1055	C₂×C₄	C₂²×#534	1	3	yes	—
1056	C₂×C₄	C₂²×#534	1	4	yes	—
1057	C₂×C₄	C₂²×#534	1	6	yes	—
1058	C₂×C₄	C₂²×#534	1	8	yes	—
1059	C₂×C₄	C₂²×D₄²	1	8	yes	—
1060	C₂×C₄	C₂²×D₄²	1	6	yes	—
1061	C₂×C₄	C₂²×D₄²	1	8	yes	—
1062	C₂×C₄	C₂²×D₄²	1	6	yes	—
1063	C₂×C₄	C₂²×D₄²	1	6	yes	—
1064	C₂×C₄	C₂²×D₄²	1	8	yes	—
1065	C₂×C₄	C₂²×D₄²	1	6	yes	—
1066	C₂×C₄	C₂²×D₄²	1	8	yes	—
1067	C₂×C₄	C₂²×D₄²	1	6	yes	—
1068	C₂×C₄	C₂²×D₄²	1	6	yes	—
1069	C₂×C₄	C₂²×D₄²	1	8	yes	—
1070	C₂×C₄	C₂²×D₄²	1	8	yes	—
1071	C₂×C₄	C₂⁵×D₄	1	1	yes	characteristic
1072	C₂×C₄	C₂⁵×D₄	1	2	yes	—
1073	C₂×C₄	C₂⁵×D₄	1	1	yes	characteristic
1074	C₂×C₄	C₂³×H(5,𝔽₂)	1	2	yes	—
1075	C₂²	#6437575	1	4	yes	direct product factor
1076	C₂²	C₂²×#2403	1	3	yes	—
1077	C₂²	C₂²×#2403	1	6	yes	—
1078	C₂²	C₂²×#2403	1	4	yes	—
1079	C₂²	C₂²×#2403	1	4	yes	—
1080	C₂²	C₂²×#2403	1	8	yes	—
1081	C₂²	C₂²×#2403	1	3	yes	—
1082	C₂²	C₂⁴×#120	1	1	yes	characteristic
1083	C₂²	C₂³×D₄²	1	2	yes	—
1084	C₄	C₂²×#2403	1	4	yes	—
1085	C₄	C₂²×#2403	1	4	yes	—
1086	C₄	C₂²×#2403	1	8	yes	—
1087	C₄	C₂²×#2403	1	3	yes	—
1088	C₄	C₂²×#2403	1	3	yes	—
1089	C₄	C₂²×#2403	1	6	yes	—
1090	C₄	C₂⁴×#120	1	1	yes	characteristic
1091	C₄	C₂³×#534	1	1	yes	characteristic
1092	C₄	C₂³×D₄²	1	2	yes	—
1093	C₂	C₂³×#2403	1	1	yes	characteristic
1094	C₂	C₂×#6437575	1	6	yes	direct product factor

	subgroup	G/H
center	C₂²×C₄	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁷
socle	C₂³	C₂×#2403
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#23884	C₂	semidirect
2. C₂²×#20623	C₂	semidirect
3. C₂²×#21009	C₂	semidirect
4. C₂²×#20998	C₂	semidirect
5. C₂²×#23885	C₂	semidirect
6. C₂²×#23412	C₂	semidirect
7. C₂²×#60387	C₂	semidirect
8. C₂²×#63090	C₂	semidirect
9. C₂²×#60359	C₂	semidirect
10. C₂²×#62811	C₂	semidirect
11. C₂²×#23883	C₂	semidirect
12. C₂³×#3025	C₂	semidirect
13. C₂³×#1891	C₂	semidirect
14. C₂³×#2010	C₂	semidirect
15. C₂×#6437575	C₂	direct (N × H)
16. C₂²×#23882	C₂	semidirect
18. C₂³×#585	C₂²	semidirect
19. C₂⁵×#41	C₂²	semidirect
20. C₂×#63090	C₂²	semidirect
21. C₂²×#3586	C₂²	semidirect
22. C₂²×#3585	C₂²	semidirect
24. C₂³×#575	C₂²	semidirect
25. C₂³×#575	C₂²	semidirect
26. C₂³×#568	C₂²	semidirect
27. C₂×#62811	C₂²	semidirect
28. C₂²×#3487	C₂²	semidirect
29. C₂²×#3486	C₂²	semidirect
30. C₂²×#3485	C₂²	semidirect
31. C₂²×#3484	C₂²	semidirect
33. C₂²×#3449	C₂²	semidirect
35. C₂³×#525	C₂²	semidirect
36. C₂³×#525	C₂²	semidirect
37. C₂²×#3428	C₂²	semidirect
38. C₂²×#3025	C₂²	semidirect
39. C₂²×#3025	C₂²	semidirect
40. C₂²×#3025	C₂²	semidirect
41. C₂²×#3004	C₂²	semidirect
42. C₂²×#3022	C₂²	semidirect
43. C₂×#60387	C₂²	semidirect
44. C₂×#60359	C₂²	semidirect
45. C₂²×#3021	C₂²	semidirect
46. C₂²×#3005	C₂²	semidirect
47. C₂²×#3005	C₂²	semidirect
48. C₂²×#3003	C₂²	semidirect
49. C₂³×#407	C₂²	semidirect
50. C₂³×#410	C₂²	semidirect
51. C₂³×#410	C₂²	semidirect
52. C₂²×#2896	C₂²	semidirect
53. C₂²×#2896	C₂²	semidirect
54. C₂³×#413	C₂²	semidirect
55. C₂³×#421	C₂²	semidirect
56. C₂³×#421	C₂²	semidirect
57. #6437575	C₂²	direct (N × H)
58. C₂×#23885	C₂²	semidirect
59. C₂×#23884	C₂²	semidirect
60. C₂×#23883	C₂²	semidirect
61. C₂×#23882	C₂²	semidirect
62. C₂²×#2010	C₂²	semidirect
63. C₂²×#2010	C₂²	semidirect
64. C₂²×#2010	C₂²	semidirect
65. C₂×#23412	C₂²	semidirect
66. C₂²×#2009	C₂²	semidirect
67. C₂²×#2008	C₂²	semidirect
68. C₂×#21009	C₂²	semidirect
69. C₂²×#1910	C₂²	semidirect
70. C₂²×#1909	C₂²	semidirect
71. C₂×#20998	C₂²	semidirect
72. C₂²×#1905	C₂²	semidirect
73. C₂²×#1904	C₂²	semidirect
74. C₂²×#1891	C₂²	semidirect
75. C₂²×#1891	C₂²	semidirect
76. C₂²×#1891	C₂²	semidirect
77. C₂×#20623	C₂²	semidirect
78. C₂²×#1796	C₂²	semidirect
79. C₂²×#1795	C₂²	semidirect
80. C₂³×#344	C₂²	semidirect
81. C₂³×H(3,ℤ/4)	C₂²	semidirect
82. C₂²×#585	D₄	semidirect
85. C₂²×#585	C₂³	semidirect
86. C₂³×2₋¹⁺⁴	D₄	semidirect
88. C₂³×H(5,𝔽₂)	D₄	semidirect
90. C₂⁴×#41	D₄	semidirect
96. C₂⁴×#41	C₂³	semidirect
97. C₂⁴×#41	C₂³	semidirect
98. C₂⁴×#41	C₂³	semidirect
99. C₂⁵×Q₈	C₂³	semidirect
100. C₂⁵×D₄	C₂³	semidirect
102. #63090	C₂³	semidirect
103. C₂×#3586	C₂³	semidirect
104. C₂×#3585	C₂³	semidirect
105. C₂²×#575	D₄	semidirect
108. C₂²×#575	C₂³	semidirect
109. C₂²×#575	C₂³	semidirect
110. C₂³×#137	D₄	semidirect
113. C₂³×AGL(1,ℤ/8)	D₄	semidirect
116. C₂³×#135	D₄	semidirect
118. C₂²×#568	C₂³	semidirect
121. #62811	C₂³	semidirect
122. C₂×#3487	C₂³	semidirect
123. C₂×#3486	C₂³	semidirect
124. C₂×#3485	C₂³	semidirect
125. C₂×#3484	C₂³	semidirect
126. C₂×#3449	D₄	semidirect
128. C₂×#3449	C₂³	semidirect
129. C₂²×#536	D₄	semidirect
131. C₂²×#536	C₂³	semidirect
132. C₂²×#535	D₄	semidirect
134. C₂²×#535	C₂³	semidirect
135. C₂²×#532	D₄	semidirect
144. C₂²×#525	C₂³	semidirect
145. C₂²×#525	C₂³	semidirect
146. C₂²×#525	C₂³	semidirect
147. C₂²×#525	C₂³	semidirect
150. C₂×#3428	C₂³	semidirect
151. C₂²×#519	C₂³	semidirect
152. C₂²×#518	C₂³	semidirect
156. C₂×#3025	C₂³	semidirect
157. C₂×#3025	C₂³	semidirect
158. C₂×#3025	C₂³	semidirect
159. #60387	C₂³	semidirect
160. C₂×#3022	C₂³	semidirect
161. C₂×#3021	C₂³	semidirect
162. #60359	C₂³	semidirect
163. C₂×#3005	C₂³	semidirect
164. C₂×#3005	C₂³	semidirect
165. C₂×#3004	C₂³	semidirect
166. C₂×#3003	C₂³	semidirect
168. C₂²×#421	C₂³	semidirect
169. C₂²×#421	C₂³	semidirect
170. C₂²×#421	C₂³	semidirect
171. C₂×#2896	C₂³	semidirect
172. C₂×#2896	C₂³	semidirect
173. C₂²×#419	C₂³	semidirect
174. C₂²×#419	C₂³	semidirect
175. C₂²×#418	C₂³	semidirect
176. C₂²×#418	C₂³	semidirect
178. C₂²×#413	C₂³	semidirect
181. C₂²×#410	C₂³	semidirect
182. C₂²×#410	C₂³	semidirect
183. C₂²×#407	C₂³	semidirect
184. C₂²×#407	C₂³	semidirect
185. C₂²×#407	C₂³	semidirect
186. #23885	C₂³	semidirect
187. #23884	C₂³	semidirect
188. #23883	C₂³	semidirect
189. #23882	C₂³	semidirect
190. C₂×#2010	C₂³	semidirect
191. C₂×#2010	C₂³	semidirect
192. C₂×#2010	C₂³	semidirect
193. #23412	C₂³	semidirect
194. C₂×#2009	C₂³	semidirect
195. C₂×#2008	C₂³	semidirect
196. #21009	C₂³	semidirect
197. C₂×#1910	C₂³	semidirect
198. C₂×#1909	C₂³	semidirect
199. #20998	C₂³	semidirect
200. C₂×#1905	C₂³	semidirect
201. C₂×#1904	C₂³	semidirect
202. C₂×#1891	C₂³	semidirect
203. C₂×#1891	C₂³	semidirect
204. C₂×#1891	C₂³	semidirect
205. #20623	C₂³	semidirect
206. C₂×#1796	C₂³	semidirect
207. C₂×#1795	C₂³	semidirect
208. C₂²×#344	C₂³	semidirect
209. C₂²×#344	C₂³	semidirect
210. C₂²×H(3,ℤ/4)	C₂³	semidirect
211. C₂²×H(3,ℤ/4)	C₂³	semidirect
213. C₂×#585	C₂×D₄	semidirect
216. C₂×#585	C₂⁴	semidirect
217. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
218. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
220. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
221. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
240. C₂³×#41	C₂×D₄	semidirect
241. C₂³×#41	C₂×D₄	semidirect
242. C₂³×#41	C₂×D₄	semidirect
243. C₂³×#41	C₂×D₄	semidirect
244. C₂³×#41	C₂×D₄	semidirect
253. C₂³×#41	C₂⁴	semidirect
254. C₂³×#41	C₂⁴	semidirect
255. C₂³×#41	C₂⁴	semidirect
258. C₂⁴×Q₈	C₂×D₄	semidirect
259. C₂⁴×Q₈	C₂×D₄	semidirect
262. C₂⁴×Q₈	C₂⁴	semidirect
266. C₂⁴×D₄	C₂×D₄	semidirect
267. C₂⁴×D₄	C₂×D₄	semidirect
270. C₂⁴×D₄	C₂⁴	semidirect
280. #3586	C₂⁴	semidirect
281. #3585	C₂⁴	semidirect
282. C₂×#575	C₂×D₄	semidirect
285. C₂×#575	C₂⁴	semidirect
286. C₂×#575	C₂⁴	semidirect
287. C₂²×#137	C₂×D₄	semidirect
288. C₂²×#137	C₂×D₄	semidirect
291. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
292. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
295. C₂²×#135	C₂×D₄	semidirect
296. C₂³×Q₁₆	C₂×D₄	semidirect
297. C₂³×SD₁₆	C₂×D₄	semidirect
298. C₂³×SD₁₆	C₂×D₄	semidirect
299. C₂³×D₈	C₂×D₄	semidirect
301. C₂×#568	C₂⁴	semidirect
302. C₂³×M₁₆	C₂×D₄	semidirect
303. C₂³×M₁₆	C₂×D₄	semidirect
308. C₂⁴×C₈	C₂×D₄	semidirect
309. #3487	C₂⁴	semidirect
310. #3486	C₂⁴	semidirect
311. #3485	C₂⁴	semidirect
312. #3484	C₂⁴	semidirect
313. #3449	C₂×D₄	semidirect
315. #3449	C₂⁴	semidirect
316. C₂×#536	C₂×D₄	semidirect
317. C₂×#536	C₂×D₄	semidirect
319. C₂×#536	C₂⁴	semidirect
320. C₂×#535	C₂×D₄	semidirect
321. C₂×#535	C₂×D₄	semidirect
323. C₂×#535	C₂⁴	semidirect
324. C₂×#532	C₂×D₄	semidirect
325. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
326. C₂²×#127	C₂×D₄	semidirect
327. C₂²×#124	C₂×D₄	semidirect
328. C₂²×#124	C₂×D₄	semidirect
339. C₂×#525	C₂⁴	semidirect
340. C₂×#525	C₂⁴	semidirect
341. C₂×#525	C₂⁴	semidirect
342. C₂×#525	C₂⁴	semidirect
349. #3428	C₂⁴	semidirect
350. C₂×#519	C₂⁴	semidirect
351. C₂×#518	C₂⁴	semidirect
364. #3025	C₂⁴	semidirect
365. #3025	C₂⁴	semidirect
366. #3022	C₂⁴	semidirect
367. #3021	C₂⁴	semidirect
368. #3005	C₂⁴	semidirect
369. #3005	C₂⁴	semidirect
370. #3004	C₂⁴	semidirect
371. #3003	C₂⁴	semidirect
373. C₂×#421	C₂⁴	semidirect
374. C₂×#421	C₂⁴	semidirect
375. C₂×#421	C₂⁴	semidirect
376. #2896	C₂⁴	semidirect
377. #2896	C₂⁴	semidirect
378. C₂×#419	C₂⁴	semidirect
379. C₂×#419	C₂⁴	semidirect
380. C₂×#418	C₂⁴	semidirect
381. C₂×#418	C₂⁴	semidirect
383. C₂×#413	C₂⁴	semidirect
386. C₂×#410	C₂⁴	semidirect
387. C₂×#410	C₂⁴	semidirect
388. C₂×#407	C₂⁴	semidirect
389. C₂×#407	C₂⁴	semidirect
390. C₂×#407	C₂⁴	semidirect
391. #2010	C₂⁴	semidirect
392. #2010	C₂⁴	semidirect
393. #2009	C₂⁴	semidirect
394. #2008	C₂⁴	semidirect
395. #1910	C₂⁴	semidirect
396. #1909	C₂⁴	semidirect
397. #1905	C₂⁴	semidirect
398. #1904	C₂⁴	semidirect
399. #1891	C₂⁴	semidirect
400. #1891	C₂⁴	semidirect
401. #1796	C₂⁴	semidirect
402. #1795	C₂⁴	semidirect
403. C₂×#344	C₂⁴	semidirect
404. C₂×#344	C₂⁴	semidirect
405. C₂×H(3,ℤ/4)	C₂⁴	semidirect
406. C₂×H(3,ℤ/4)	C₂⁴	semidirect
413. C₂×2₋¹⁺⁴	C₂²×D₄	semidirect
414. C₂×2₋¹⁺⁴	C₂²×D₄	semidirect
416. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
417. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
453. C₂²×#41	C₂²×D₄	semidirect
454. C₂²×#41	C₂²×D₄	semidirect
455. C₂²×#41	C₂²×D₄	semidirect
456. C₂²×#41	C₂²×D₄	semidirect
457. C₂²×#41	C₂²×D₄	semidirect
466. C₂²×#41	C₂⁵	semidirect
467. C₂²×#41	C₂⁵	semidirect
481. C₂³×Q₈	C₂²×D₄	semidirect
482. C₂³×Q₈	C₂²×D₄	semidirect
485. C₂³×Q₈	C₂⁵	semidirect
503. C₂³×D₄	C₂²×D₄	semidirect
504. C₂³×D₄	C₂²×D₄	semidirect
507. C₂³×D₄	C₂⁵	semidirect
541. C₂×#137	C₂²×D₄	semidirect
542. C₂×#137	C₂²×D₄	semidirect
545. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
546. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
549. C₂×#135	C₂²×D₄	semidirect
550. C₂²×Q₁₆	C₂²×D₄	semidirect
551. C₂²×SD₁₆	C₂²×D₄	semidirect
552. C₂²×SD₁₆	C₂²×D₄	semidirect
553. C₂²×D₈	C₂²×D₄	semidirect
556. C₂²×M₁₆	C₂²×D₄	semidirect
557. C₂²×M₁₆	C₂²×D₄	semidirect
563. C₂³×C₈	C₂²×D₄	semidirect
564. #536	C₂²×D₄	semidirect
565. #536	C₂²×D₄	semidirect
567. #536	C₂⁵	semidirect
568. #535	C₂²×D₄	semidirect
569. #535	C₂²×D₄	semidirect
571. #535	C₂⁵	semidirect
572. #532	C₂²×D₄	semidirect
573. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
574. C₂×#127	C₂²×D₄	semidirect
575. C₂×#124	C₂²×D₄	semidirect
576. C₂×#124	C₂²×D₄	semidirect
585. #525	C₂⁵	semidirect
586. #525	C₂⁵	semidirect
593. #519	C₂⁵	semidirect
594. #518	C₂⁵	semidirect
612. #421	C₂⁵	semidirect
613. #419	C₂⁵	semidirect
614. #419	C₂⁵	semidirect
615. #418	C₂⁵	semidirect
616. #418	C₂⁵	semidirect
620. #407	C₂⁵	semidirect
621. #407	C₂⁵	semidirect
622. #344	C₂⁵	semidirect
623. H(3,ℤ/4)	C₂⁵	semidirect
663. C₂×#41	C₂³×D₄	semidirect
664. C₂×#41	C₂³×D₄	semidirect
665. C₂×#41	C₂³×D₄	semidirect
687. C₂²×Q₈	C₂³×D₄	semidirect
688. C₂²×Q₈	C₂³×D₄	semidirect
714. C₂²×D₄	C₂³×D₄	semidirect
715. C₂²×D₄	C₂³×D₄	semidirect
802. C₂×Q₁₆	C₂³×D₄	semidirect
803. C₂×SD₁₆	C₂³×D₄	semidirect
804. C₂×SD₁₆	C₂³×D₄	semidirect
805. C₂×D₈	C₂³×D₄	semidirect
807. C₂×M₁₆	C₂³×D₄	semidirect
811. C₂²×C₈	C₂³×D₄	semidirect
812. C₄⋊Q₈	C₂³×D₄	semidirect
813. #127	C₂³×D₄	semidirect
814. #124	C₂³×D₄	semidirect
815. #124	C₂³×D₄	semidirect
1075. C₂²	#6437575	direct (N × H)
1094. C₂	C₂×#6437575	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#23884	2
C₂²×#20623	2
C₂²×#21009	2
C₂²×#20998	2
C₂²×#23885	2
C₂²×#23412	2
C₂²×#60387	2
C₂²×#63090	2
C₂²×#60359	2
C₂²×#62811	2
C₂²×#23883	2
C₂³×#3025	2
C₂³×#1891	2
C₂³×#2010	2
C₂×#6437575	2
C₂²×#23882	2

Subgroups — C22×#6437575 #72310951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6437575 #72310951