Subgroups — C₂×#72310284 #72310402

Order 2048.

At least 6042 conjugacy classes of subgroups; only the 6056 normal subgroups are shown.

The subgroup lattice has 849 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×#233055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#233367	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#233936	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#233080	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#18786	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#197729	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#6453897	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#193647	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#197777	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#193537	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#18746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#186614	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#244792	C₂	1	4	yes	maximal, complemented
14	C₂×#244791	C₂	1	4	yes	maximal, complemented
15	C₂×#249527	C₂	1	4	yes	maximal, complemented
16	C₂×#249463	C₂	1	4	yes	maximal, complemented
17	#72310284	C₂	1	32	yes	maximal, direct product factor
18	C₂³×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6442656	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×D₄×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄²	C₂²	1	1	yes	characteristic
23	C₂³×D₄²	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
25	C₂²×#3272	C₂²	1	2	yes	complemented
26	C₂²×#3274	C₂²	1	2	yes	complemented
27	C₂²×D₄×SD₁₆	C₂²	1	2	yes	complemented
28	C₂²×D₄×D₈	C₂²	1	4	yes	—
29	C₂²×D₄×D₈	C₂²	1	16	yes	complemented
30	C₂²×D₄×D₈	C₂²	1	4	yes	complemented
31	C₂²×D₄×D₈	C₂²	1	2	yes	complemented
32	C₂²×#3205	C₂²	1	1	yes	characteristic, complemented
33	C₂³×#493	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#3151	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#3100	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#3038	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#3038	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#3036	C₂²	1	1	yes	characteristic
39	C₂³×#459	C₂²	1	1	yes	characteristic
40	C₂³×#459	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂³×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
44	C₂³×C₄×D₈	C₂²	1	1	yes	characteristic
45	C₂×#34935	C₂²	1	1	yes	characteristic, complemented
46	#6453897	C₂²	1	16	yes	complemented
47	C₂×#24184	C₂²	1	2	yes	complemented
48	C₂×#24116	C₂²	1	2	yes	complemented
49	C₂×#24326	C₂²	1	2	yes	complemented
50	#6442656	C₂²	1	16	yes	complemented
51	C₂×#24240	C₂²	1	4	yes	complemented
52	C₂×#24236	C₂²	1	4	yes	complemented
53	C₂×#24236	C₂²	1	2	yes	complemented
54	C₂×#21803	C₂²	1	1	yes	characteristic, complemented
55	C₂×#21401	C₂²	1	1	yes	characteristic, complemented
56	C₂×#21373	C₂²	1	1	yes	characteristic, complemented
57	C₂×#21203	C₂²	1	1	yes	characteristic, complemented
58	C₂×#21190	C₂²	1	1	yes	characteristic, complemented
59	C₂×#20732	C₂²	1	1	yes	characteristic, complemented
60	C₂×#20646	C₂²	1	1	yes	characteristic, complemented
61	C₂×#18786	C₂²	1	16	yes	complemented
62	C₂×#18746	C₂²	1	16	yes	complemented
63	C₂²×#1621	C₂²	1	2	yes	complemented
64	C₂²×#1627	C₂²	1	2	yes	complemented
65	C₂²×#1625	C₂²	1	2	yes	complemented
66	C₂²×#1639	C₂²	1	4	yes	complemented
67	C₂²×#1619	C₂²	1	4	yes	complemented
68	C₂²×#1619	C₂²	1	2	yes	complemented
69	C₂²×#1547	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#1545	C₂²	1	1	yes	characteristic, complemented
71	C₂²×#1545	C₂²	1	1	yes	characteristic, complemented
72	C₂²×#1486	C₂²	1	1	yes	characteristic, complemented
73	C₂²×#1486	C₂²	1	1	yes	characteristic, complemented
74	C₂²×#1477	C₂²	1	1	yes	characteristic, complemented
75	C₂²×#1478	C₂²	1	1	yes	characteristic, complemented
76	#249527	C₂²	1	64	yes	complemented
77	#249463	C₂²	1	64	yes	complemented
78	#244792	C₂²	1	64	yes	complemented
79	#244791	C₂²	1	64	yes	complemented
80	#233936	C₂²	1	16	yes	complemented
81	C₂×#10229	C₂²	1	4	yes	complemented
82	C₂×#10228	C₂²	1	4	yes	complemented
83	#233367	C₂²	1	16	yes	complemented
84	C₂×#10305	C₂²	1	4	yes	complemented
85	C₂×#10304	C₂²	1	4	yes	complemented
86	#233080	C₂²	1	16	yes	complemented
87	#233055	C₂²	1	16	yes	complemented
88	C₂×#10266	C₂²	1	4	yes	complemented
89	C₂×#10262	C₂²	1	4	yes	complemented
90	C₂×#10260	C₂²	1	4	yes	complemented
91	C₂×#10260	C₂²	1	4	yes	complemented
92	#197777	C₂²	1	16	yes	complemented
93	#197729	C₂²	1	16	yes	complemented
94	C₂×#9229	C₂²	1	4	yes	complemented
95	C₂×#9221	C₂²	1	4	yes	complemented
96	C₂×#9221	C₂²	1	4	yes	complemented
97	C₂×#9217	C₂²	1	4	yes	complemented
98	#193647	C₂²	1	16	yes	complemented
99	C₂×#8951	C₂²	1	4	yes	complemented
100	#193537	C₂²	1	16	yes	complemented
101	C₂×#8947	C₂²	1	4	yes	complemented
102	C₂×#8947	C₂²	1	4	yes	complemented
103	C₂×#8945	C₂²	1	4	yes	complemented
104	#186614	C₂²	1	16	yes	complemented
105	C₂×#8443	C₂²	1	4	yes	complemented
106	C₂×#8443	C₂²	1	4	yes	complemented
107	C₂×#8045	C₂²	1	1	yes	characteristic, complemented
108	C₂×#7874	C₂²	1	1	yes	characteristic, complemented
109	C₂×#7873	C₂²	1	1	yes	characteristic, complemented
110	C₂×#7848	C₂²	1	1	yes	characteristic, complemented
111	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
112	C₂⁴×D₈	D₄	1	1	yes	characteristic
113	C₂×D₄×#41	C₂³	1	8	yes	complemented
114	C₂²×#550	C₂³	1	1	yes	characteristic, complemented
115	C₂²×#547	C₂³	1	1	yes	characteristic, complemented
116	C₂²×D₄×Q₈	C₂³	1	1	yes	characteristic, complemented
117	C₂²×D₄²	D₄	1	16	yes	complemented
118	C₂²×D₄²	C₂³	1	4	yes	—
119	C₂²×D₄²	C₂³	1	2	yes	—
120	C₂²×D₄²	C₂³	1	2	yes	—
121	C₂²×D₄²	C₂³	1	8	yes	—
122	C₂²×D₄²	C₂³	1	8	yes	complemented
123	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
124	C₂²×#532	C₂³	1	1	yes	characteristic
125	C₂³×#127	C₂³	1	1	yes	characteristic
126	C₂³×#127	C₂³	1	1	yes	characteristic
127	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
128	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
129	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
130	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
131	C₂×D₄×SD₁₆	C₂³	1	16	yes	complemented
132	C₂×D₄×D₈	C₂³	1	32	yes	—
133	C₂×D₄×D₈	C₂³	1	32	yes	complemented
134	C₂×D₄×D₈	C₂³	1	16	yes	complemented
135	C₂×#3274	C₂³	1	16	yes	complemented
136	C₂×#3272	C₂³	1	16	yes	complemented
137	C₂×#3205	C₂³	1	8	yes	complemented
138	C₂×#3151	C₂³	1	8	yes	complemented
139	C₂²×#493	C₂³	1	4	yes	—
140	C₂²×#493	C₂³	1	8	yes	complemented
141	C₂²×#493	C₂³	1	2	yes	complemented
142	C₂²×#493	C₂³	1	2	yes	complemented
143	C₂²×#492	C₂³	1	2	yes	complemented
144	C₂²×#486	C₂³	1	2	yes	complemented
145	C₂×#3100	C₂³	1	8	yes	complemented
146	C₂²×#474	C₂³	1	2	yes	complemented
147	C₂×#3038	C₂³	1	8	yes	complemented
148	C₂×#3038	C₂³	1	8	yes	complemented
149	C₂×#3036	D₄	1	16	yes	complemented
150	C₂×#3036	C₂³	1	8	yes	—
151	C₂²×#460	C₂³	1	2	yes	complemented
152	C₂²×#460	C₂³	1	2	yes	complemented
153	C₂²×#461	C₂³	1	2	yes	—
154	C₂²×#459	D₄	1	16	yes	complemented
155	C₂²×#459	C₂³	1	4	yes	—
156	C₂²×#459	C₂³	1	2	yes	—
157	C₂²×#459	C₂³	1	2	yes	—
158	C₂²×#459	C₂³	1	2	yes	—
159	C₂²×#459	C₂³	1	8	yes	—
160	C₂²×#459	C₂³	1	8	yes	complemented
161	C₂²×#459	C₂³	1	2	yes	complemented
162	C₂²×#459	C₂³	1	2	yes	complemented
163	C₂²×#459	C₂³	1	2	yes	complemented
164	C₂×C₄×AGL(1,ℤ/8)	D₄	1	8	yes	—
165	C₂×C₄×AGL(1,ℤ/8)	C₂³	1	8	yes	—
166	C₂²×#442	D₄	1	2	yes	—
167	C₂²×#440	D₄	1	2	yes	—
168	C₂²×C₄×SD₁₆	C₂³	1	2	yes	—
169	C₂²×C₄×D₈	D₄	1	2	yes	—
170	C₂²×C₄×D₈	D₄	1	2	yes	—
171	C₂²×C₄×D₈	D₄	1	8	yes	—
172	C₂²×C₄×D₈	C₂³	1	2	yes	—
173	C₂²×C₄×D₈	C₂³	1	8	yes	—
174	C₂²×C₄×D₈	C₂³	1	2	yes	—
175	C₂²×C₄×D₈	C₂³	1	2	yes	—
176	C₂×D₄×M₁₆	C₂³	1	8	yes	complemented
177	C₂²×#436	C₂³	1	2	yes	complemented
178	C₂²×C₈×D₄	C₂³	1	4	yes	—
179	C₂²×C₈×D₄	C₂³	1	8	yes	complemented
180	C₂²×C₈×D₄	C₂³	1	2	yes	complemented
181	C₂²×#431	C₂³	1	1	yes	characteristic
182	C₂²×#431	C₂³	1	1	yes	characteristic
183	C₂²×#428	D₄	1	1	yes	characteristic
184	C₂³×#107	D₄	1	1	yes	characteristic
185	C₂²×#423	C₂³	1	1	yes	characteristic
186	C₂²×#423	C₂³	1	1	yes	characteristic
187	C₂³×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₂²×#417	D₄	1	1	yes	characteristic
189	C₂²×#418	D₄	1	1	yes	characteristic
190	C₂³×#102	D₄	1	1	yes	characteristic
191	C₂³×#102	D₄	1	1	yes	characteristic
192	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₈	C₂³	1	1	yes	characteristic
194	#34935	C₂³	1	8	yes	complemented
195	C₂×#2538	C₂³	1	2	yes	complemented
196	C₂×#2537	C₂³	1	2	yes	complemented
197	C₂×#2285	C₂³	1	1	yes	characteristic
198	#24326	C₂³	1	16	yes	complemented
199	#24240	C₂³	1	32	yes	complemented
200	#24236	C₂³	1	32	yes	complemented
201	#24236	C₂³	1	16	yes	complemented
202	#24184	C₂³	1	16	yes	complemented
203	#24116	C₂³	1	16	yes	complemented
204	#21803	C₂³	1	8	yes	complemented
205	#21401	C₂³	1	8	yes	complemented
206	#21373	C₂³	1	8	yes	complemented
207	C₂×#1990	C₂³	1	2	yes	complemented
208	C₂×#1984	C₂³	1	2	yes	complemented
209	#21203	C₂³	1	8	yes	complemented
210	C₂×#1957	C₂³	1	2	yes	complemented
211	C₂×#1957	C₂³	1	4	yes	complemented
212	C₂×#1957	C₂³	1	4	yes	complemented
213	#21190	C₂³	1	8	yes	complemented
214	C₂×#1954	C₂³	1	4	yes	complemented
215	C₂×#1954	C₂³	1	2	yes	complemented
216	#20732	C₂³	1	8	yes	complemented
217	#20646	C₂³	1	8	yes	complemented
218	C₂×#1802	C₂³	1	4	yes	—
219	C₂×#1802	C₂³	1	2	yes	complemented
220	C₂×#1802	C₂³	1	2	yes	complemented
221	C₂×#1621	C₂³	1	16	yes	complemented
222	C₂×#1627	C₂³	1	16	yes	complemented
223	C₂×#1625	C₂³	1	16	yes	complemented
224	C₂×#1639	C₂³	1	32	yes	complemented
225	C₂×#1619	C₂³	1	32	yes	complemented
226	C₂×#1619	C₂³	1	16	yes	complemented
227	C₂×#1547	C₂³	1	8	yes	complemented
228	C₂×#1545	C₂³	1	8	yes	complemented
229	C₂×#1545	C₂³	1	8	yes	complemented
230	C₂²×#332	C₂³	1	2	yes	complemented
231	C₂²×#331	C₂³	1	2	yes	complemented
232	C₂²×#331	C₂³	1	4	yes	complemented
233	C₂²×#331	C₂³	1	4	yes	complemented
234	C₂×#1486	C₂³	1	8	yes	complemented
235	C₂×#1486	C₂³	1	8	yes	complemented
236	C₂×#1477	C₂³	1	8	yes	complemented
237	C₂×#1478	C₂³	1	8	yes	complemented
238	C₂²×Q₈⋊C₈	C₂³	1	2	yes	complemented
239	C₂²×D₄⋊C₈	C₂³	1	4	yes	—
240	C₂²×D₄⋊C₈	C₂³	1	2	yes	complemented
241	C₂²×D₄⋊C₈	C₂³	1	4	yes	complemented
242	C₂²×D₄⋊C₈	C₂³	1	2	yes	complemented
243	C₂²×D₄⋊C₈	C₂³	1	2	yes	complemented
244	#10305	C₂³	1	32	yes	complemented
245	#10304	C₂³	1	32	yes	complemented
246	#10266	C₂³	1	32	yes	complemented
247	#10262	C₂³	1	32	yes	complemented
248	#10260	C₂³	1	32	yes	complemented
249	#10260	C₂³	1	32	yes	complemented
250	#10229	C₂³	1	32	yes	complemented
251	#10228	C₂³	1	32	yes	complemented
252	#9229	C₂³	1	32	yes	complemented
253	#9221	C₂³	1	32	yes	complemented
254	#9221	C₂³	1	32	yes	complemented
255	#9217	C₂³	1	32	yes	complemented
256	#8951	C₂³	1	32	yes	complemented
257	#8947	C₂³	1	32	yes	complemented
258	#8947	C₂³	1	32	yes	complemented
259	#8945	C₂³	1	32	yes	complemented
260	#8443	C₂³	1	32	yes	complemented
261	#8443	C₂³	1	32	yes	complemented
262	#8045	C₂³	1	8	yes	complemented
263	C₂×#1296	C₂³	1	4	yes	complemented
264	#7874	C₂³	1	8	yes	complemented
265	#7873	C₂³	1	8	yes	complemented
266	C₂×#1277	C₂³	1	4	yes	complemented
267	C₂×#1277	C₂³	1	4	yes	complemented
268	#7848	C₂³	1	8	yes	complemented
269	C₂×#1273	C₂³	1	4	yes	complemented
270	C₂³×#41	C₂×D₄	1	1	yes	characteristic
271	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
272	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
273	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
274	C₂²×AGL(1,ℤ/8)	D₈	1	16	yes	complemented
275	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	—
276	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
277	C₂³×D₈	C₂×D₄	1	8	yes	—
278	C₂³×D₈	C₂×D₄	1	2	yes	—
279	C₂³×D₈	C₂×D₄	1	2	yes	—
280	C₂³×D₈	C₂×D₄	1	2	yes	—
281	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
282	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
283	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
284	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
285	C₂×#550	C₂⁴	1	4	yes	complemented
286	C₂×D₄×Q₈	C₂⁴	1	4	yes	complemented
287	C₂×#547	C₂⁴	1	4	yes	complemented
288	C₂×D₄²	C₂×D₄	1	16	yes	—
289	C₂×D₄²	C₂×D₄	1	16	yes	—
290	C₂×D₄²	C₂×D₄	1	64	yes	complemented
291	C₂×D₄²	C₂⁴	1	16	yes	—
292	C₂×D₄²	C₂⁴	1	8	yes	—
293	C₂×D₄²	C₂⁴	1	8	yes	—
294	C₂×D₄²	C₂⁴	1	4	yes	complemented
295	C₂×#532	C₂×D₄	1	8	yes	—
296	C₂×#532	C₂⁴	1	4	yes	—
297	C₂²×C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
298	C₂²×#127	C₂×D₄	1	8	yes	—
299	C₂²×#127	C₂×D₄	1	8	yes	—
300	C₂²×#127	C₂⁴	1	2	yes	—
301	C₂²×#127	C₂⁴	1	2	yes	—
302	C₂²×#127	C₂⁴	1	1	yes	characteristic
303	C₂²×#127	C₂⁴	1	4	yes	—
304	C₂²×#127	C₂⁴	1	4	yes	—
305	C₂×C₄×#41	C₂×D₄	1	4	yes	—
306	C₂×C₄×#41	C₂⁴	1	4	yes	—
307	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×Q₈	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
310	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
311	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
312	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
313	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
315	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
316	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
317	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
318	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
321	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
322	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
324	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
325	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
328	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
329	C₂²×#117	C₂×D₄	1	1	yes	characteristic
330	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
333	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
334	C₂×#493	C₂⁴	1	16	yes	—
335	C₂×#493	C₂⁴	1	8	yes	complemented
336	C₂×#493	C₂⁴	1	8	yes	complemented
337	C₂×#492	C₂⁴	1	8	yes	complemented
338	C₂×#486	C₂⁴	1	8	yes	complemented
339	C₂×#474	C₂⁴	1	8	yes	complemented
340	#3036	C₂×D₄	1	64	yes	complemented
341	C₂×#460	C₂⁴	1	8	yes	complemented
342	C₂×#460	C₂⁴	1	8	yes	complemented
343	C₂×#461	C₂×D₄	1	16	yes	—
344	C₂×#461	C₂⁴	1	8	yes	—
345	C₂×#459	C₂×D₄	1	16	yes	—
346	C₂×#459	C₂×D₄	1	16	yes	—
347	C₂×#459	C₂×D₄	1	16	yes	—
348	C₂×#459	C₂×D₄	1	64	yes	complemented
349	C₂×#459	C₂⁴	1	16	yes	—
350	C₂×#459	C₂⁴	1	8	yes	—
351	C₂×#459	C₂⁴	1	8	yes	—
352	C₂×#459	C₂⁴	1	8	yes	—
353	C₂×#459	C₂⁴	1	8	yes	complemented
354	C₂×#459	C₂⁴	1	8	yes	complemented
355	C₂×#459	C₂⁴	1	8	yes	complemented
356	C₂×#442	C₂×D₄	1	16	yes	—
357	C₂×#440	C₂×D₄	1	16	yes	—
358	C₂×C₄×SD₁₆	C₂×D₄	1	8	yes	—
359	C₂×C₄×SD₁₆	C₂⁴	1	8	yes	—
360	C₂×C₄×D₈	C₂×D₄	1	8	yes	—
361	C₂×C₄×D₈	C₂×D₄	1	16	yes	—
362	C₂×C₄×D₈	C₂×D₄	1	8	yes	—
363	C₂×C₄×D₈	C₂×D₄	1	8	yes	—
364	C₂×C₄×D₈	C₂×D₄	1	16	yes	—
365	C₂×C₄×D₈	C₂⁴	1	8	yes	—
366	C₂×C₄×D₈	C₂⁴	1	8	yes	—
367	C₂×C₄×D₈	C₂⁴	1	8	yes	—
368	C₂×#436	C₂⁴	1	8	yes	complemented
369	C₂×C₈×D₄	C₂⁴	1	16	yes	—
370	C₂×C₈×D₄	C₂⁴	1	8	yes	complemented
371	C₂×#431	C₂⁴	1	4	yes	—
372	C₂×#431	C₂⁴	1	4	yes	—
373	C₂×#428	C₂×D₄	1	8	yes	—
374	C₂²×#107	C₂×D₄	1	8	yes	—
375	C₂²×#107	C₂×D₄	1	2	yes	—
376	C₂²×#107	C₂×D₄	1	2	yes	—
377	C₂²×#107	C₂×D₄	1	2	yes	—
378	C₂²×#106	C₂×D₄	1	2	yes	—
379	C₂×#423	C₂×D₄	1	8	yes	—
380	C₂×#423	C₂⁴	1	4	yes	—
381	C₂×#423	C₂⁴	1	4	yes	—
382	C₂²×C₄⋊C₈	C₂×D₄	1	8	yes	—
383	C₂²×C₄⋊C₈	C₂⁴	1	2	yes	—
384	C₂²×C₄⋊C₈	C₂⁴	1	2	yes	—
385	C₂²×C₄⋊C₈	C₂⁴	1	2	yes	—
386	C₂²×C₄⋊C₈	C₂⁴	1	2	yes	—
387	C₂²×C₄⋊C₈	C₂⁴	1	4	yes	—
388	C₂×#417	C₂×D₄	1	8	yes	—
389	C₂×#418	C₂×D₄	1	8	yes	—
390	C₂²×#103	C₂×D₄	1	2	yes	—
391	C₂²×#102	C₂×D₄	1	2	yes	—
392	C₂²×#102	C₂×D₄	1	2	yes	—
393	C₂²×#102	C₂×D₄	1	2	yes	—
394	C₂²×#102	C₂×D₄	1	2	yes	—
395	C₂²×#102	C₂×D₄	1	2	yes	—
396	C₂²×#102	C₂×D₄	1	8	yes	—
397	C₂²×#102	C₂×D₄	1	2	yes	—
398	C₂²×#102	C₂×D₄	1	2	yes	—
399	C₂²×#102	C₂×D₄	1	8	yes	—
400	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
401	C₂×C₄×M₁₆	C₂⁴	1	4	yes	—
402	C₂²×#97	C₂×D₄	1	2	yes	—
403	C₂²×C₄×C₈	C₂×D₄	1	4	yes	—
404	C₂²×C₄×C₈	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₈	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₈	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₈	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₈	C₂⁴	1	2	yes	—
409	#2538	C₂⁴	1	8	yes	complemented
410	#2537	C₂⁴	1	8	yes	complemented
411	#2285	C₂⁴	1	4	yes	—
412	C₂×#384	C₂⁴	1	2	yes	—
413	#1990	C₂⁴	1	8	yes	complemented
414	#1984	C₂⁴	1	8	yes	complemented
415	#1957	C₂⁴	1	8	yes	complemented
416	#1957	C₂⁴	1	16	yes	complemented
417	#1957	C₂⁴	1	16	yes	complemented
418	#1954	C₂⁴	1	8	yes	complemented
419	#1954	C₂⁴	1	16	yes	complemented
420	#1802	C₂⁴	1	16	yes	—
421	#1802	C₂⁴	1	8	yes	complemented
422	#1802	C₂⁴	1	8	yes	complemented
423	C₂×#332	C₂⁴	1	8	yes	complemented
424	C₂×#331	C₂⁴	1	8	yes	complemented
425	C₂×#331	C₂⁴	1	16	yes	complemented
426	C₂×#331	C₂⁴	1	16	yes	complemented
427	C₂×Q₈⋊C₈	C₂⁴	1	8	yes	complemented
428	C₂×D₄⋊C₈	C₂⁴	1	16	yes	—
429	C₂×D₄⋊C₈	C₂⁴	1	8	yes	complemented
430	C₂×D₄⋊C₈	C₂⁴	1	16	yes	complemented
431	C₂×D₄⋊C₈	C₂⁴	1	8	yes	complemented
432	C₂×D₄⋊C₈	C₂⁴	1	8	yes	complemented
433	#1296	C₂⁴	1	16	yes	complemented
434	#1277	C₂⁴	1	16	yes	complemented
435	#1277	C₂⁴	1	16	yes	complemented
436	#1273	C₂⁴	1	16	yes	complemented
437	C₂²×#41	C₂×D₈	1	8	yes	complemented
438	C₂²×#41	C₂²×D₄	1	4	yes	—
439	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
440	C₂³×D₄	#120	1	8	yes	—
441	C₂³×D₄	#120	1	8	yes	—
442	C₂³×D₄	C₂×D₈	1	8	yes	—
443	C₂³×D₄	AGL(1,ℤ/8)	1	8	yes	—
444	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
445	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
446	C₂³×D₄	C₂²×D₄	1	2	yes	—
447	C₂³×D₄	C₂²×D₄	1	4	yes	—
448	C₂³×D₄	C₂²×D₄	1	4	yes	—
449	C₂³×D₄	C₂²×D₄	1	2	yes	—
450	C₂³×D₄	C₂²×D₄	1	4	yes	—
451	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
452	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
453	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
454	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×AGL(1,ℤ/8)	C₂×D₈	1	64	yes	complemented
456	C₂²×SD₁₆	C₂×D₈	1	16	yes	complemented
457	C₂²×SD₁₆	C₂²×D₄	1	8	yes	—
458	C₂²×D₈	C₂×D₈	1	16	yes	complemented
459	C₂²×D₈	AGL(1,ℤ/8)	1	16	yes	complemented
460	C₂²×D₈	C₂²×D₄	1	8	yes	—
461	C₂²×D₈	C₂²×D₄	1	8	yes	—
462	C₂²×D₈	C₂²×D₄	1	8	yes	—
463	C₂²×M₁₆	C₂×D₈	1	8	yes	complemented
464	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
465	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
466	C₂³×C₈	C₂²×D₄	1	2	yes	—
467	C₂³×C₈	C₂²×D₄	1	4	yes	—
468	C₂³×C₈	C₂²×D₄	1	2	yes	—
469	C₂³×C₈	C₂²×D₄	1	2	yes	—
470	C₂³×C₈	C₂²×D₄	1	2	yes	—
471	C₂³×C₈	C₂²×D₄	1	4	yes	—
472	D₄²	C₂²×D₄	1	32	yes	—
473	D₄²	C₂²×D₄	1	32	yes	—
474	#532	C₂²×D₄	1	16	yes	—
475	C₂×C₄⋊Q₈	C₂²×D₄	1	4	yes	—
476	C₂×C₄⋊Q₈	C₂⁵	1	2	yes	—
477	C₂×#127	C₂²×D₄	1	8	yes	—
478	C₂×#127	C₂²×D₄	1	8	yes	—
479	C₂×#127	C₂²×D₄	1	4	yes	—
480	C₂×#127	C₂²×D₄	1	16	yes	—
481	C₂×#127	C₂²×D₄	1	16	yes	—
482	C₂×#127	C₂⁵	1	4	yes	—
483	C₂×#127	C₂⁵	1	4	yes	—
484	C₂×#127	C₂⁵	1	2	yes	—
485	C₂×C₄×Q₈	C₂²×D₄	1	4	yes	—
486	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
487	C₂×C₄×Q₈	C₂⁵	1	2	yes	—
488	C₂×C₄×D₄	#120	1	8	yes	—
489	C₂×C₄×D₄	#120	1	8	yes	—
490	C₂×C₄×D₄	#120	1	32	yes	—
491	C₂×C₄×D₄	#120	1	16	yes	—
492	C₂×C₄×D₄	#120	1	32	yes	—
493	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
494	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
495	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
496	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
497	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
498	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
499	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
500	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
501	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
502	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
503	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
504	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
505	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
506	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
507	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
508	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
509	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
510	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
511	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
512	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
513	C₂×C₄×D₄	C₂⁵	1	4	yes	—
514	C₂×C₄×D₄	C₂⁵	1	2	yes	—
515	C₂×C₄×D₄	C₂⁵	1	4	yes	—
516	C₂×C₄×D₄	C₂⁵	1	2	yes	—
517	C₂×C₄×D₄	C₂⁵	1	2	yes	—
518	C₂×#117	C₂²×D₄	1	4	yes	—
519	C₂²×C₄⋊C₄	#120	1	8	yes	—
520	C₂²×C₄⋊C₄	#120	1	8	yes	—
521	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
522	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
525	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
526	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
529	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
530	C₂²×C₄²	C₂²×D₄	1	4	yes	—
531	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
532	C₂²×C₄²	C₂²×D₄	1	2	yes	—
533	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
534	C₂²×C₄²	C₂²×D₄	1	2	yes	—
535	C₂²×C₄²	C₂²×D₄	1	4	yes	—
536	C₂²×C₄²	C₂²×D₄	1	4	yes	—
537	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
539	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
540	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
541	C₂²×C₄²	C₂⁵	1	2	yes	—
542	#461	C₂²×D₄	1	32	yes	—
543	#459	C₂²×D₄	1	32	yes	—
544	#459	C₂²×D₄	1	32	yes	—
545	#459	C₂²×D₄	1	32	yes	—
546	C₂×#107	C₂²×D₄	1	8	yes	—
547	C₂×#107	C₂²×D₄	1	8	yes	—
548	C₂×#107	C₂²×D₄	1	8	yes	—
549	C₂×#106	C₂²×D₄	1	8	yes	—
550	#423	C₂²×D₄	1	16	yes	—
551	C₂×C₄⋊C₈	C₂²×D₄	1	8	yes	—
552	C₂×C₄⋊C₈	C₂²×D₄	1	8	yes	—
553	C₂×C₄⋊C₈	C₂²×D₄	1	16	yes	—
554	C₂×C₄⋊C₈	C₂⁵	1	4	yes	—
555	C₂×C₄⋊C₈	C₂⁵	1	4	yes	—
556	C₂×C₄⋊C₈	C₂⁵	1	4	yes	—
557	C₂×C₄⋊C₈	C₂⁵	1	4	yes	—
558	C₂×#103	C₂²×D₄	1	8	yes	—
559	C₂×#102	C₂²×D₄	1	8	yes	—
560	C₂×#102	C₂²×D₄	1	8	yes	—
561	C₂×#102	C₂²×D₄	1	8	yes	—
562	C₂×#102	C₂²×D₄	1	8	yes	—
563	C₂×#102	C₂²×D₄	1	8	yes	—
564	C₂×#102	C₂²×D₄	1	8	yes	—
565	C₂×#102	C₂²×D₄	1	8	yes	—
566	C₂×#97	C₂²×D₄	1	8	yes	—
567	C₂×C₄×C₈	C₂²×D₄	1	4	yes	—
568	C₂×C₄×C₈	C₂²×D₄	1	8	yes	—
569	C₂×C₄×C₈	C₂²×D₄	1	4	yes	—
570	C₂×C₄×C₈	C₂⁵	1	4	yes	—
571	C₂×C₄×C₈	C₂⁵	1	4	yes	—
572	C₂×C₄×C₈	C₂⁵	1	4	yes	—
573	#384	C₂⁵	1	4	yes	—
574	C₂⁵	D₄²	1	1	yes	characteristic
575	C₂×#41	C₂²×D₈	1	16	yes	complemented
576	C₂²×Q₈	C₂²×D₈	1	4	yes	complemented
577	C₂²×Q₈	C₂³×D₄	1	2	yes	—
578	C₂²×D₄	#447	1	64	yes	complemented
579	C₂²×D₄	C₂×#120	1	4	yes	—
580	C₂²×D₄	C₂×#120	1	16	yes	—
581	C₂²×D₄	C₂×#120	1	8	yes	—
582	C₂²×D₄	C₂×#120	1	16	yes	—
583	C₂²×D₄	C₂×#120	1	4	yes	—
584	C₂²×D₄	C₂²×D₈	1	8	yes	—
585	C₂²×D₄	C₂²×D₈	1	16	yes	—
586	C₂²×D₄	C₂²×D₈	1	4	yes	complemented
587	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
588	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	16	yes	—
589	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
590	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
591	C₂²×D₄	C₂³×D₄	1	2	yes	—
592	C₂²×D₄	C₂³×D₄	1	2	yes	—
593	C₂²×D₄	C₂³×D₄	1	4	yes	—
594	C₂²×D₄	C₂³×D₄	1	4	yes	—
595	C₂²×D₄	C₂³×D₄	1	2	yes	—
596	C₂³×C₄	C₂×#120	1	4	yes	—
597	C₂³×C₄	C₂×#120	1	4	yes	—
598	C₂³×C₄	#534	1	4	yes	—
599	C₂³×C₄	D₄²	1	2	yes	—
600	C₂³×C₄	D₄²	1	1	yes	characteristic
601	C₂³×C₄	D₄²	1	1	yes	characteristic
602	C₂³×C₄	D₄²	1	4	yes	—
603	C₂³×C₄	D₄²	1	2	yes	—
604	C₂³×C₄	D₄²	1	4	yes	—
605	C₂³×C₄	D₄²	1	2	yes	—
606	C₂³×C₄	D₄²	1	1	yes	characteristic
607	C₂³×C₄	D₄²	1	4	yes	—
608	C₂³×C₄	C₂²×D₈	1	4	yes	—
609	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
610	C₂³×C₄	#576	1	4	yes	—
611	C₂³×C₄	#576	1	4	yes	—
612	C₂³×C₄	C₂³×D₄	1	2	yes	—
613	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
614	C₂³×C₄	C₂³×D₄	1	2	yes	—
615	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
616	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
618	C₂×SD₁₆	C₂²×D₈	1	32	yes	complemented
619	C₂×D₈	C₂²×D₈	1	32	yes	complemented
620	C₂×D₈	C₂×AGL(1,ℤ/8)	1	32	yes	complemented
621	C₂×M₁₆	C₂²×D₈	1	16	yes	complemented
622	C₂²×C₈	C₂²×D₈	1	8	yes	complemented
623	C₂²×C₈	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
624	C₂²×C₈	C₂³×D₄	1	4	yes	—
625	C₂²×C₈	C₂³×D₄	1	4	yes	—
626	C₂²×C₈	C₂³×D₄	1	4	yes	—
627	C₂²×C₈	C₂³×D₄	1	4	yes	—
628	C₄⋊Q₈	C₂³×D₄	1	4	yes	—
629	#127	C₂³×D₄	1	8	yes	—
630	#127	C₂³×D₄	1	8	yes	—
631	#127	C₂³×D₄	1	4	yes	—
632	C₄×D₄	C₂×#120	1	16	yes	—
633	C₄×D₄	C₂×#120	1	16	yes	—
634	C₄×D₄	C₂×#120	1	16	yes	—
635	C₄×D₄	C₂×#120	1	32	yes	—
636	C₄×D₄	C₂×#120	1	8	yes	—
637	C₄×D₄	C₂×#120	1	8	yes	—
638	C₄×D₄	C₂³×D₄	1	8	yes	—
639	C₄×D₄	C₂³×D₄	1	4	yes	—
640	C₄×D₄	C₂³×D₄	1	8	yes	—
641	C₄×D₄	C₂³×D₄	1	4	yes	—
642	C₄×D₄	C₂³×D₄	1	4	yes	—
643	C₄×D₄	C₂³×D₄	1	4	yes	—
644	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
645	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
646	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
647	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
648	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
649	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
650	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
654	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
655	C₂×C₄²	C₂×#120	1	4	yes	—
656	C₂×C₄²	C₂×#120	1	8	yes	—
657	C₂×C₄²	C₂×#120	1	4	yes	—
658	C₂×C₄²	C₂×#120	1	8	yes	—
659	C₂×C₄²	#534	1	4	yes	—
660	C₂×C₄²	#534	1	8	yes	—
661	C₂×C₄²	D₄²	1	2	yes	—
662	C₂×C₄²	D₄²	1	2	yes	—
663	C₂×C₄²	D₄²	1	2	yes	—
664	C₂×C₄²	D₄²	1	4	yes	—
665	C₂×C₄²	D₄²	1	4	yes	—
666	C₂×C₄²	D₄²	1	8	yes	—
667	C₂×C₄²	D₄²	1	4	yes	—
668	C₂×C₄²	D₄²	1	8	yes	—
669	C₂×C₄²	D₄²	1	8	yes	—
670	C₂×C₄²	C₂³×D₄	1	2	yes	—
671	C₂×C₄²	C₂³×D₄	1	4	yes	—
672	C₂×C₄²	C₂³×D₄	1	2	yes	—
673	C₂×C₄²	C₂³×D₄	1	2	yes	—
674	C₂×C₄²	C₂³×D₄	1	4	yes	—
675	C₂×C₄²	C₂³×D₄	1	4	yes	—
676	C₂×C₄²	C₂³×D₄	1	2	yes	—
677	C₂×C₄²	C₂³×D₄	1	2	yes	—
678	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
679	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
680	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
681	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
682	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
683	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂×C₄²	C₂⁶	1	1	yes	characteristic
685	C₄⋊C₈	C₂³×D₄	1	8	yes	—
686	C₄⋊C₈	C₂³×D₄	1	8	yes	—
687	C₂⁴	#2403	1	4	yes	—
688	C₂⁴	#3264	1	4	yes	—
689	C₂⁴	D₄×D₈	1	4	yes	—
690	C₂⁴	C₂×D₄²	1	2	yes	—
691	C₂⁴	C₂×D₄²	1	1	yes	characteristic
692	C₂×Q₈	C₂³×D₈	1	4	yes	complemented
693	C₂×D₄	C₂×#447	1	32	yes	—
694	C₂×D₄	C₂×#447	1	64	yes	complemented
695	C₂×D₄	#3003	1	16	yes	complemented
696	C₂×D₄	C₂²×#120	1	4	yes	—
697	C₂×D₄	C₂²×#120	1	8	yes	—
698	C₂×D₄	C₂²×#120	1	4	yes	—
699	C₂×D₄	C₂³×D₈	1	8	yes	—
700	C₂×D₄	C₂³×D₈	1	4	yes	complemented
701	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	8	yes	—
702	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	8	yes	—
703	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	8	yes	complemented
704	C₂²×C₄	#2403	1	4	yes	—
705	C₂²×C₄	#2403	1	4	yes	—
706	C₂²×C₄	#2403	1	8	yes	—
707	C₂²×C₄	#2403	1	8	yes	—
708	C₂²×C₄	#2403	1	4	yes	—
709	C₂²×C₄	#2403	1	8	yes	—
710	C₂²×C₄	C₂×#447	1	16	yes	—
711	C₂²×C₄	#3008	1	16	yes	—
712	C₂²×C₄	#3264	1	4	yes	—
713	C₂²×C₄	#3264	1	8	yes	—
714	C₂²×C₄	#3264	1	16	yes	—
715	C₂²×C₄	D₄×D₈	1	4	yes	—
716	C₂²×C₄	D₄×D₈	1	8	yes	—
717	C₂²×C₄	D₄×D₈	1	16	yes	—
718	C₂²×C₄	C₂²×#120	1	4	yes	—
719	C₂²×C₄	C₂²×#120	1	2	yes	—
720	C₂²×C₄	C₂²×#120	1	4	yes	—
721	C₂²×C₄	C₂²×#120	1	2	yes	—
722	C₂²×C₄	C₂×#534	1	2	yes	—
723	C₂²×C₄	C₂×#534	1	4	yes	—
724	C₂²×C₄	C₂×D₄²	1	2	yes	—
725	C₂²×C₄	C₂×D₄²	1	2	yes	—
726	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄²	1	4	yes	—
728	C₂²×C₄	C₂×D₄²	1	2	yes	—
729	C₂²×C₄	C₂×D₄²	1	4	yes	—
730	C₂²×C₄	C₂×D₄²	1	2	yes	—
731	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄²	1	2	yes	—
734	C₂²×C₄	C₂×D₄²	1	4	yes	—
735	C₂²×C₄	C₂×D₄²	1	2	yes	—
736	C₂²×C₄	C₂³×D₈	1	2	yes	—
737	C₂²×C₄	C₂³×D₈	1	4	yes	—
738	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	2	yes	—
739	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
740	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
741	C₂²×C₄	C₂×#576	1	2	yes	—
742	C₂²×C₄	C₂×#576	1	4	yes	—
743	C₂²×C₄	C₂×#576	1	2	yes	—
744	C₂²×C₄	C₂×#576	1	4	yes	—
745	C₂²×C₄	#3585	1	4	yes	—
746	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
748	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂×C₈	C₂³×D₈	1	8	yes	complemented
750	C₂×C₈	C₂²×AGL(1,ℤ/8)	1	8	yes	complemented
751	C₄⋊C₄	C₂²×#120	1	4	yes	—
752	C₄⋊C₄	C₂²×#120	1	4	yes	—
753	C₄⋊C₄	C₂²×#120	1	8	yes	—
754	C₄²	#2403	1	8	yes	—
755	C₄²	#2403	1	8	yes	—
756	C₄²	#2403	1	8	yes	—
757	C₄²	C₂²×#120	1	4	yes	—
758	C₄²	C₂²×#120	1	2	yes	—
759	C₄²	C₂²×#120	1	2	yes	—
760	C₄²	C₂²×#120	1	4	yes	—
761	C₄²	C₂×#534	1	4	yes	—
762	C₄²	C₂×#534	1	2	yes	—
763	C₄²	C₂×D₄²	1	4	yes	—
764	C₄²	C₂×D₄²	1	2	yes	—
765	C₄²	C₂×D₄²	1	4	yes	—
766	C₄²	C₂×D₄²	1	2	yes	—
767	C₄²	C₂×D₄²	1	4	yes	—
768	C₄²	C₂×D₄²	1	2	yes	—
769	C₄²	C₂⁴×D₄	1	1	yes	characteristic
770	C₄²	C₂⁴×D₄	1	1	yes	characteristic
771	C₄²	C₂⁴×D₄	1	1	yes	characteristic
772	C₄²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂³	#23848	1	16	yes	—
774	C₂³	C₂×#2403	1	4	yes	—
775	C₂³	C₂×#2403	1	2	yes	—
776	C₂³	C₂×#3264	1	4	yes	—
777	C₂³	C₂×#3264	1	2	yes	—
778	C₂³	C₂×D₄×D₈	1	4	yes	—
779	C₂³	C₂×D₄×D₈	1	2	yes	—
780	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
781	C₂³	#61106	1	4	yes	—
782	C₂³	C₂²×D₄²	1	1	yes	characteristic
783	D₄	C₂²×#447	1	16	yes	—
784	D₄	C₂×#3003	1	8	yes	complemented
785	C₂×C₄	#23848	1	16	yes	—
786	C₂×C₄	#23848	1	32	yes	—
787	C₂×C₄	C₂×#2403	1	4	yes	—
788	C₂×C₄	C₂×#2403	1	2	yes	—
789	C₂×C₄	C₂×#2403	1	4	yes	—
790	C₂×C₄	C₂×#2403	1	4	yes	—
791	C₂×C₄	C₂×#2403	1	2	yes	—
792	C₂×C₄	C₂×#2403	1	2	yes	—
793	C₂×C₄	C₂²×#447	1	4	yes	—
794	C₂×C₄	C₂²×#447	1	8	yes	—
795	C₂×C₄	C₂×#3003	1	4	yes	—
796	C₂×C₄	C₂×#3008	1	4	yes	—
797	C₂×C₄	C₂×#3008	1	8	yes	—
798	C₂×C₄	#60367	1	4	yes	—
799	C₂×C₄	C₂×#3264	1	4	yes	—
800	C₂×C₄	C₂×#3264	1	2	yes	—
801	C₂×C₄	C₂×#3264	1	4	yes	—
802	C₂×C₄	C₂×#3264	1	8	yes	—
803	C₂×C₄	C₂×D₄×D₈	1	4	yes	—
804	C₂×C₄	C₂×D₄×D₈	1	2	yes	—
805	C₂×C₄	C₂×D₄×D₈	1	4	yes	—
806	C₂×C₄	C₂×D₄×D₈	1	8	yes	—
807	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
808	C₂×C₄	D₄×AGL(1,ℤ/8)	1	8	yes	—
809	C₂×C₄	C₂³×#120	1	1	yes	characteristic
810	C₂×C₄	C₂³×#120	1	1	yes	characteristic
811	C₂×C₄	C₂²×#534	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
815	C₂×C₄	C₂⁴×D₈	1	1	yes	characteristic
816	C₂×C₄	C₂³×AGL(1,ℤ/8)	1	1	yes	characteristic
817	C₂×C₄	C₂³×AGL(1,ℤ/8)	1	2	yes	—
818	C₂×C₄	C₂²×#576	1	1	yes	characteristic
819	C₂×C₄	C₂²×#576	1	1	yes	characteristic
820	C₂×C₄	C₂×#3585	1	2	yes	—
821	C₂²	D₈×AGL(1,ℤ/8)	1	8	yes	—
822	C₂²	#6360176	1	8	yes	—
823	C₂²	C₂×#23848	1	8	yes	—
824	C₂²	C₂×#23848	1	4	yes	—
825	C₂²	#6437510	1	4	yes	—
826	C₂²	#6437602	1	4	yes	—
827	C₂²	C₂²×#2403	1	1	yes	characteristic
828	C₂²	C₂²×D₄×D₈	1	1	yes	characteristic
829	C₂²	C₂²×#3264	1	1	yes	characteristic
830	C₂²	C₂×D₄×AGL(1,ℤ/8)	1	2	yes	—
831	C₂²	C₂×#61106	1	2	yes	—
832	C₄	C₂×#23848	1	8	yes	—
833	C₄	C₂×#23848	1	4	yes	—
834	C₄	#6437510	1	4	yes	—
835	C₄	C₂³×#447	1	1	yes	characteristic
836	C₄	C₂²×#3003	1	1	yes	characteristic
837	C₄	C₂²×#3008	1	1	yes	characteristic
838	C₄	C₂×#60367	1	1	yes	characteristic
839	C₄	C₂²×D₄×D₈	1	1	yes	characteristic
840	C₄	C₂²×#3264	1	1	yes	characteristic
841	C₄	C₂×D₄×AGL(1,ℤ/8)	1	2	yes	—
842	C₂	C₂×#6437510	1	1	yes	characteristic
843	C₂	C₂×D₈×AGL(1,ℤ/8)	1	2	yes	—
844	C₂	C₂²×#23848	1	1	yes	characteristic
845	C₂	#72310284	1	8	yes	direct product factor
846	C₂	C₂×#6360176	1	2	yes	—
847	C₂	C₂×#6437602	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄²	C₂⁶
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#233055	C₂	semidirect
2. C₂×#233367	C₂	semidirect
3. C₂×#233936	C₂	semidirect
4. C₂×#233080	C₂	semidirect
5. C₂²×#18786	C₂	semidirect
6. C₂×#197729	C₂	semidirect
7. C₂×#6453897	C₂	semidirect
8. C₂×#193647	C₂	semidirect
9. C₂×#197777	C₂	semidirect
10. C₂×#193537	C₂	semidirect
11. C₂²×#18746	C₂	semidirect
12. C₂×#186614	C₂	semidirect
13. C₂×#244792	C₂	semidirect
14. C₂×#244791	C₂	semidirect
15. C₂×#249527	C₂	semidirect
16. C₂×#249463	C₂	semidirect
17. #72310284	C₂	direct (N × H)
18. C₂³×D₄×D₈	C₂	semidirect
19. C₂×#6442656	C₂	semidirect
20. C₂²×D₄×AGL(1,ℤ/8)	C₂	semidirect
21. C₂²×D₄×#41	C₂²	semidirect
23. C₂³×D₄²	C₂²	semidirect
24. C₂×D₄×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×#3272	C₂²	semidirect
26. C₂²×#3274	C₂²	semidirect
27. C₂²×D₄×SD₁₆	C₂²	semidirect
29. C₂²×D₄×D₈	C₂²	semidirect
30. C₂²×D₄×D₈	C₂²	semidirect
31. C₂²×D₄×D₈	C₂²	semidirect
32. C₂²×#3205	C₂²	semidirect
33. C₂³×#493	C₂²	semidirect
34. C₂²×#3151	C₂²	semidirect
35. C₂²×#3100	C₂²	semidirect
36. C₂²×#3038	C₂²	semidirect
37. C₂²×#3038	C₂²	semidirect
40. C₂³×#459	C₂²	semidirect
41. C₂²×D₄×M₁₆	C₂²	semidirect
42. C₂³×C₈×D₄	C₂²	semidirect
45. C₂×#34935	C₂²	semidirect
46. #6453897	C₂²	semidirect
47. C₂×#24184	C₂²	semidirect
48. C₂×#24116	C₂²	semidirect
49. C₂×#24326	C₂²	semidirect
50. #6442656	C₂²	semidirect
51. C₂×#24240	C₂²	semidirect
52. C₂×#24236	C₂²	semidirect
53. C₂×#24236	C₂²	semidirect
54. C₂×#21803	C₂²	semidirect
55. C₂×#21401	C₂²	semidirect
56. C₂×#21373	C₂²	semidirect
57. C₂×#21203	C₂²	semidirect
58. C₂×#21190	C₂²	semidirect
59. C₂×#20732	C₂²	semidirect
60. C₂×#20646	C₂²	semidirect
61. C₂×#18786	C₂²	semidirect
62. C₂×#18746	C₂²	semidirect
63. C₂²×#1621	C₂²	semidirect
64. C₂²×#1627	C₂²	semidirect
65. C₂²×#1625	C₂²	semidirect
66. C₂²×#1639	C₂²	semidirect
67. C₂²×#1619	C₂²	semidirect
68. C₂²×#1619	C₂²	semidirect
69. C₂²×#1547	C₂²	semidirect
70. C₂²×#1545	C₂²	semidirect
71. C₂²×#1545	C₂²	semidirect
72. C₂²×#1486	C₂²	semidirect
73. C₂²×#1486	C₂²	semidirect
74. C₂²×#1477	C₂²	semidirect
75. C₂²×#1478	C₂²	semidirect
76. #249527	C₂²	semidirect
77. #249463	C₂²	semidirect
78. #244792	C₂²	semidirect
79. #244791	C₂²	semidirect
80. #233936	C₂²	semidirect
81. C₂×#10229	C₂²	semidirect
82. C₂×#10228	C₂²	semidirect
83. #233367	C₂²	semidirect
84. C₂×#10305	C₂²	semidirect
85. C₂×#10304	C₂²	semidirect
86. #233080	C₂²	semidirect
87. #233055	C₂²	semidirect
88. C₂×#10266	C₂²	semidirect
89. C₂×#10262	C₂²	semidirect
90. C₂×#10260	C₂²	semidirect
91. C₂×#10260	C₂²	semidirect
92. #197777	C₂²	semidirect
93. #197729	C₂²	semidirect
94. C₂×#9229	C₂²	semidirect
95. C₂×#9221	C₂²	semidirect
96. C₂×#9221	C₂²	semidirect
97. C₂×#9217	C₂²	semidirect
98. #193647	C₂²	semidirect
99. C₂×#8951	C₂²	semidirect
100. #193537	C₂²	semidirect
101. C₂×#8947	C₂²	semidirect
102. C₂×#8947	C₂²	semidirect
103. C₂×#8945	C₂²	semidirect
104. #186614	C₂²	semidirect
105. C₂×#8443	C₂²	semidirect
106. C₂×#8443	C₂²	semidirect
107. C₂×#8045	C₂²	semidirect
108. C₂×#7874	C₂²	semidirect
109. C₂×#7873	C₂²	semidirect
110. C₂×#7848	C₂²	semidirect
113. C₂×D₄×#41	C₂³	semidirect
114. C₂²×#550	C₂³	semidirect
115. C₂²×#547	C₂³	semidirect
116. C₂²×D₄×Q₈	C₂³	semidirect
117. C₂²×D₄²	D₄	semidirect
122. C₂²×D₄²	C₂³	semidirect
123. C₂²×D₄²	C₂³	semidirect
131. C₂×D₄×SD₁₆	C₂³	semidirect
133. C₂×D₄×D₈	C₂³	semidirect
134. C₂×D₄×D₈	C₂³	semidirect
135. C₂×#3274	C₂³	semidirect
136. C₂×#3272	C₂³	semidirect
137. C₂×#3205	C₂³	semidirect
138. C₂×#3151	C₂³	semidirect
140. C₂²×#493	C₂³	semidirect
141. C₂²×#493	C₂³	semidirect
142. C₂²×#493	C₂³	semidirect
143. C₂²×#492	C₂³	semidirect
144. C₂²×#486	C₂³	semidirect
145. C₂×#3100	C₂³	semidirect
146. C₂²×#474	C₂³	semidirect
147. C₂×#3038	C₂³	semidirect
148. C₂×#3038	C₂³	semidirect
149. C₂×#3036	D₄	semidirect
151. C₂²×#460	C₂³	semidirect
152. C₂²×#460	C₂³	semidirect
154. C₂²×#459	D₄	semidirect
160. C₂²×#459	C₂³	semidirect
161. C₂²×#459	C₂³	semidirect
162. C₂²×#459	C₂³	semidirect
163. C₂²×#459	C₂³	semidirect
176. C₂×D₄×M₁₆	C₂³	semidirect
177. C₂²×#436	C₂³	semidirect
179. C₂²×C₈×D₄	C₂³	semidirect
180. C₂²×C₈×D₄	C₂³	semidirect
194. #34935	C₂³	semidirect
195. C₂×#2538	C₂³	semidirect
196. C₂×#2537	C₂³	semidirect
198. #24326	C₂³	semidirect
199. #24240	C₂³	semidirect
200. #24236	C₂³	semidirect
201. #24236	C₂³	semidirect
202. #24184	C₂³	semidirect
203. #24116	C₂³	semidirect
204. #21803	C₂³	semidirect
205. #21401	C₂³	semidirect
206. #21373	C₂³	semidirect
207. C₂×#1990	C₂³	semidirect
208. C₂×#1984	C₂³	semidirect
209. #21203	C₂³	semidirect
210. C₂×#1957	C₂³	semidirect
211. C₂×#1957	C₂³	semidirect
212. C₂×#1957	C₂³	semidirect
213. #21190	C₂³	semidirect
214. C₂×#1954	C₂³	semidirect
215. C₂×#1954	C₂³	semidirect
216. #20732	C₂³	semidirect
217. #20646	C₂³	semidirect
219. C₂×#1802	C₂³	semidirect
220. C₂×#1802	C₂³	semidirect
221. C₂×#1621	C₂³	semidirect
222. C₂×#1627	C₂³	semidirect
223. C₂×#1625	C₂³	semidirect
224. C₂×#1639	C₂³	semidirect
225. C₂×#1619	C₂³	semidirect
226. C₂×#1619	C₂³	semidirect
227. C₂×#1547	C₂³	semidirect
228. C₂×#1545	C₂³	semidirect
229. C₂×#1545	C₂³	semidirect
230. C₂²×#332	C₂³	semidirect
231. C₂²×#331	C₂³	semidirect
232. C₂²×#331	C₂³	semidirect
233. C₂²×#331	C₂³	semidirect
234. C₂×#1486	C₂³	semidirect
235. C₂×#1486	C₂³	semidirect
236. C₂×#1477	C₂³	semidirect
237. C₂×#1478	C₂³	semidirect
238. C₂²×Q₈⋊C₈	C₂³	semidirect
240. C₂²×D₄⋊C₈	C₂³	semidirect
241. C₂²×D₄⋊C₈	C₂³	semidirect
242. C₂²×D₄⋊C₈	C₂³	semidirect
243. C₂²×D₄⋊C₈	C₂³	semidirect
244. #10305	C₂³	semidirect
245. #10304	C₂³	semidirect
246. #10266	C₂³	semidirect
247. #10262	C₂³	semidirect
248. #10260	C₂³	semidirect
249. #10260	C₂³	semidirect
250. #10229	C₂³	semidirect
251. #10228	C₂³	semidirect
252. #9229	C₂³	semidirect
253. #9221	C₂³	semidirect
254. #9221	C₂³	semidirect
255. #9217	C₂³	semidirect
256. #8951	C₂³	semidirect
257. #8947	C₂³	semidirect
258. #8947	C₂³	semidirect
259. #8945	C₂³	semidirect
260. #8443	C₂³	semidirect
261. #8443	C₂³	semidirect
262. #8045	C₂³	semidirect
263. C₂×#1296	C₂³	semidirect
264. #7874	C₂³	semidirect
265. #7873	C₂³	semidirect
266. C₂×#1277	C₂³	semidirect
267. C₂×#1277	C₂³	semidirect
268. #7848	C₂³	semidirect
269. C₂×#1273	C₂³	semidirect
274. C₂²×AGL(1,ℤ/8)	D₈	semidirect
285. C₂×#550	C₂⁴	semidirect
286. C₂×D₄×Q₈	C₂⁴	semidirect
287. C₂×#547	C₂⁴	semidirect
290. C₂×D₄²	C₂×D₄	semidirect
294. C₂×D₄²	C₂⁴	semidirect
335. C₂×#493	C₂⁴	semidirect
336. C₂×#493	C₂⁴	semidirect
337. C₂×#492	C₂⁴	semidirect
338. C₂×#486	C₂⁴	semidirect
339. C₂×#474	C₂⁴	semidirect
340. #3036	C₂×D₄	semidirect
341. C₂×#460	C₂⁴	semidirect
342. C₂×#460	C₂⁴	semidirect
348. C₂×#459	C₂×D₄	semidirect
353. C₂×#459	C₂⁴	semidirect
354. C₂×#459	C₂⁴	semidirect
355. C₂×#459	C₂⁴	semidirect
368. C₂×#436	C₂⁴	semidirect
370. C₂×C₈×D₄	C₂⁴	semidirect
409. #2538	C₂⁴	semidirect
410. #2537	C₂⁴	semidirect
413. #1990	C₂⁴	semidirect
414. #1984	C₂⁴	semidirect
415. #1957	C₂⁴	semidirect
416. #1957	C₂⁴	semidirect
417. #1957	C₂⁴	semidirect
418. #1954	C₂⁴	semidirect
419. #1954	C₂⁴	semidirect
421. #1802	C₂⁴	semidirect
422. #1802	C₂⁴	semidirect
423. C₂×#332	C₂⁴	semidirect
424. C₂×#331	C₂⁴	semidirect
425. C₂×#331	C₂⁴	semidirect
426. C₂×#331	C₂⁴	semidirect
427. C₂×Q₈⋊C₈	C₂⁴	semidirect
429. C₂×D₄⋊C₈	C₂⁴	semidirect
430. C₂×D₄⋊C₈	C₂⁴	semidirect
431. C₂×D₄⋊C₈	C₂⁴	semidirect
432. C₂×D₄⋊C₈	C₂⁴	semidirect
433. #1296	C₂⁴	semidirect
434. #1277	C₂⁴	semidirect
435. #1277	C₂⁴	semidirect
436. #1273	C₂⁴	semidirect
437. C₂²×#41	C₂×D₈	semidirect
455. C₂×AGL(1,ℤ/8)	C₂×D₈	semidirect
456. C₂²×SD₁₆	C₂×D₈	semidirect
458. C₂²×D₈	C₂×D₈	semidirect
459. C₂²×D₈	AGL(1,ℤ/8)	semidirect
463. C₂²×M₁₆	C₂×D₈	semidirect
575. C₂×#41	C₂²×D₈	semidirect
576. C₂²×Q₈	C₂²×D₈	semidirect
578. C₂²×D₄	#447	semidirect
586. C₂²×D₄	C₂²×D₈	semidirect
590. C₂²×D₄	C₂×AGL(1,ℤ/8)	semidirect
618. C₂×SD₁₆	C₂²×D₈	semidirect
619. C₂×D₈	C₂²×D₈	semidirect
620. C₂×D₈	C₂×AGL(1,ℤ/8)	semidirect
621. C₂×M₁₆	C₂²×D₈	semidirect
622. C₂²×C₈	C₂²×D₈	semidirect
623. C₂²×C₈	C₂×AGL(1,ℤ/8)	semidirect
692. C₂×Q₈	C₂³×D₈	semidirect
694. C₂×D₄	C₂×#447	semidirect
695. C₂×D₄	#3003	semidirect
700. C₂×D₄	C₂³×D₈	semidirect
703. C₂×D₄	C₂²×AGL(1,ℤ/8)	semidirect
749. C₂×C₈	C₂³×D₈	semidirect
750. C₂×C₈	C₂²×AGL(1,ℤ/8)	semidirect
784. D₄	C₂×#3003	semidirect
845. C₂	#72310284	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×#233055	2
C₂×#233367	2
C₂×#233936	2
C₂×#233080	2
C₂²×#18786	2
C₂×#197729	2
C₂×#6453897	2
C₂×#193647	2
C₂×#197777	2
C₂×#193537	2
C₂²×#18746	2
C₂×#186614	2
C₂×#244792	2
C₂×#244791	2
C₂×#249527	2
C₂×#249463	2
#72310284	2
C₂³×D₄×D₈	2
C₂×#6442656	2
C₂²×D₄×AGL(1,ℤ/8)	2

Subgroups — C2×#72310284 #72310402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72310284 #72310402