Subgroups — C₂²×#394261 #72303223

Order 2048.

At least 7131 conjugacy classes of subgroups; only the 10912 normal subgroups are shown.

The subgroup lattice has 974 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×#11083	C₂	1	2	yes	maximal, complemented
2	C₂²×#11041	C₂	1	2	yes	maximal, complemented
3	C₂²×#20902	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#20898	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#60359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10716	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10994	C₂	1	2	yes	maximal, complemented
9	C₂²×#34737	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#34736	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×#2010	C₂	1	2	yes	maximal, complemented
12	C₂×#394261	C₂	1	48	yes	maximal, direct product factor
13	C₂⁵×#41	C₂²	1	1	yes	characteristic
14	C₂³×#575	C₂²	1	2	yes	—
15	C₂⁵×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×#525	C₂²	1	2	yes	—
17	C₂³×#525	C₂²	1	1	yes	characteristic
18	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic
20	C₂⁴×#117	C₂²	1	1	yes	characteristic
21	C₂×#60359	C₂²	1	24	yes	complemented
22	C₂³×#407	C₂²	1	1	yes	characteristic
23	C₂³×#407	C₂²	1	2	yes	complemented
24	C₂²×#2896	C₂²	1	2	yes	—
25	C₂³×#421	C₂²	1	2	yes	—
26	C₂³×#421	C₂²	1	2	yes	—
27	C₂³×#421	C₂²	1	24	yes	complemented
28	C₂³×#421	C₂²	1	2	yes	complemented
29	C₂×#34737	C₂²	1	24	yes	complemented
30	C₂×#34736	C₂²	1	24	yes	complemented
31	C₂²×#2297	C₂²	1	2	yes	—
32	C₂²×#2297	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#2296	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#2280	C₂²	1	1	yes	characteristic
35	C₂²×#2280	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#2010	C₂²	1	48	yes	complemented
37	C₂×#20902	C₂²	1	24	yes	complemented
38	C₂×#20898	C₂²	1	24	yes	complemented
39	C₂²×#1733	C₂²	1	2	yes	complemented
40	C₂³×H(3,ℤ/4)	C₂²	1	2	yes	complemented
41	C₂³×H(3,ℤ/4)	C₂²	1	2	yes	complemented
42	C₂²×#1728	C₂²	1	2	yes	complemented
43	#394261	C₂²	1	256	yes	direct product factor
44	C₂×#11083	C₂²	1	48	yes	complemented
45	C₂×#10994	C₂²	1	48	yes	complemented
46	C₂×#11041	C₂²	1	48	yes	complemented
47	C₂×#10716	C₂²	1	24	yes	complemented
48	C₂⁴×#41	D₄	1	2	yes	complemented
49	C₂⁴×#41	D₄	1	12	yes	complemented
50	C₂⁴×#41	C₂³	1	1	yes	characteristic
51	C₂⁴×#41	C₂³	1	2	yes	—
52	C₂⁴×#41	C₂³	1	12	yes	—
53	C₂⁵×Q₈	D₄	1	1	yes	characteristic, complemented
54	C₂⁵×D₄	D₄	1	1	yes	characteristic
55	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
56	C₂⁶×C₄	C₂³	1	1	yes	characteristic
57	C₂⁶×C₄	C₂³	1	1	yes	characteristic
58	C₂²×#575	C₂³	1	24	yes	—
59	C₂⁴×M₁₆	C₂³	1	2	yes	—
60	C₂⁴×M₁₆	C₂³	1	12	yes	—
61	C₂⁴×M₁₆	C₂³	1	2	yes	—
62	C₂²×#525	D₄	1	12	yes	complemented
63	C₂²×#525	C₂³	1	24	yes	—
64	C₂²×#525	C₂³	1	12	yes	—
65	C₂²×#525	C₂³	1	12	yes	complemented
66	C₂³×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
67	C₂³×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
68	C₂³×#121	D₄	1	1	yes	characteristic, complemented
69	C₂³×#121	D₄	1	1	yes	characteristic, complemented
70	C₂³×C₄×D₄	D₄	1	12	yes	—
71	C₂³×C₄×D₄	C₂³	1	12	yes	—
72	C₂³×#117	D₄	1	2	yes	complemented
73	C₂³×#117	D₄	1	12	yes	complemented
74	C₂³×#117	C₂³	1	1	yes	characteristic
75	C₂³×#117	C₂³	1	2	yes	—
76	C₂³×#117	C₂³	1	1	yes	characteristic
77	C₂³×#117	C₂³	1	1	yes	characteristic
78	C₂³×#117	C₂³	1	12	yes	—
79	C₂⁴×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
81	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
82	C₂⁴×C₄²	D₄	1	2	yes	complemented
83	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
84	#60359	C₂³	1	64	yes	complemented
85	C₂²×#421	D₄	1	32	yes	complemented
86	C₂²×#421	C₂³	1	24	yes	—
87	C₂²×#421	C₂³	1	24	yes	—
88	C₂²×#421	C₂³	1	64	yes	complemented
89	C₂²×#421	C₂³	1	24	yes	complemented
90	C₂×#2896	C₂³	1	24	yes	—
91	C₂²×#407	D₄	1	12	yes	complemented
92	C₂²×#407	C₂³	1	12	yes	—
93	C₂²×#407	C₂³	1	24	yes	complemented
94	C₂³×C₂²⋊C₈	D₄	1	2	yes	complemented
95	C₂³×C₂²⋊C₈	D₄	1	2	yes	complemented
96	#34737	C₂³	1	64	yes	complemented
97	#34736	C₂³	1	64	yes	complemented
98	C₂×#2297	C₂³	1	24	yes	—
99	C₂×#2297	C₂³	1	12	yes	complemented
100	C₂×#2296	C₂³	1	12	yes	complemented
101	C₂×#2280	D₄	1	12	yes	complemented
102	C₂×#2280	C₂³	1	12	yes	—
103	C₂×#2280	C₂³	1	12	yes	complemented
104	C₂²×C₄×C₂²⋊C₄	D₄	1	2	yes	complemented
105	C₂²×C₄×C₂²⋊C₄	D₄	1	2	yes	complemented
106	C₂×#2010	C₂³	1	128	yes	complemented
107	#20902	C₂³	1	64	yes	complemented
108	#20898	C₂³	1	64	yes	complemented
109	C₂×#1733	C₂³	1	24	yes	complemented
110	C₂²×H(3,ℤ/4)	C₂³	1	24	yes	complemented
111	C₂²×H(3,ℤ/4)	C₂³	1	24	yes	complemented
112	C₂×#1728	C₂³	1	24	yes	complemented
113	#11083	C₂³	1	128	yes	complemented
114	#11041	C₂³	1	128	yes	complemented
115	#10994	C₂³	1	128	yes	complemented
116	#10716	C₂³	1	64	yes	complemented
117	C₂⁷	C₂×D₄	1	1	yes	characteristic
118	C₂⁷	C₂×D₄	1	1	yes	characteristic
119	C₂³×#41	C₂×D₄	1	16	yes	—
120	C₂³×#41	C₂×D₄	1	6	yes	—
121	C₂³×#41	C₂×D₄	1	12	yes	—
122	C₂³×#41	C₂×D₄	1	24	yes	complemented
123	C₂³×#41	C₂×D₄	1	48	yes	complemented
124	C₂³×#41	#41	1	16	yes	—
125	C₂³×#41	C₂⁴	1	6	yes	—
126	C₂³×#41	C₂⁴	1	12	yes	—
127	C₂³×#41	C₂⁴	1	16	yes	—
128	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
130	C₂⁴×Q₈	C₂×D₄	1	12	yes	complemented
131	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
132	C₂⁴×D₄	C₂×D₄	1	2	yes	—
133	C₂⁴×D₄	C₂×D₄	1	12	yes	—
134	C₂⁴×D₄	C₂×D₄	1	12	yes	complemented
135	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁵×C₄	C₂×D₄	1	6	yes	—
137	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
138	C₂⁵×C₄	C₂×D₄	1	6	yes	—
139	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁵×C₄	C₂×D₄	1	6	yes	—
143	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁵×C₄	C₂×D₄	1	6	yes	—
145	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁵×C₄	C₂×D₄	1	6	yes	—
148	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁵×C₄	C₂×D₄	1	6	yes	—
152	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁵×C₄	C₂×D₄	1	6	yes	—
154	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
155	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁵×C₄	#41	1	1	yes	characteristic
157	C₂⁵×C₄	#41	1	1	yes	characteristic
158	C₂⁵×C₄	#41	1	6	yes	—
159	C₂⁵×C₄	C₂⁴	1	6	yes	—
160	C₂⁵×C₄	C₂⁴	1	6	yes	—
161	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
162	C₂×#575	C₂⁴	1	32	yes	—
163	C₂³×M₁₆	C₂×D₄	1	16	yes	—
164	C₂³×M₁₆	C₂×D₄	1	12	yes	—
165	C₂³×M₁₆	C₂⁴	1	12	yes	—
166	C₂³×M₁₆	C₂⁴	1	16	yes	—
167	C₂³×M₁₆	C₂⁴	1	12	yes	—
168	C₂⁴×C₈	C₂×D₄	1	4	yes	—
169	C₂×#525	C₂×D₄	1	48	yes	complemented
170	C₂×#525	C₂⁴	1	32	yes	—
171	C₂×#525	C₂⁴	1	16	yes	—
172	C₂×#525	C₂⁴	1	16	yes	complemented
173	C₂²×C₂²⋊Q₈	C₂×D₄	1	12	yes	complemented
174	C₂²×C₂²⋊Q₈	C₂×D₄	1	12	yes	complemented
175	C₂²×#121	C₂×D₄	1	12	yes	complemented
176	C₂²×#121	C₂×D₄	1	12	yes	complemented
177	C₂²×C₄×D₄	C₂×D₄	1	48	yes	—
178	C₂²×C₄×D₄	C₂⁴	1	16	yes	—
179	C₂²×#117	C₂×D₄	1	12	yes	—
180	C₂²×#117	C₂×D₄	1	6	yes	—
181	C₂²×#117	C₂×D₄	1	6	yes	—
182	C₂²×#117	C₂×D₄	1	16	yes	—
183	C₂²×#117	C₂×D₄	1	6	yes	—
184	C₂²×#117	C₂×D₄	1	48	yes	complemented
185	C₂²×#117	C₂×D₄	1	24	yes	complemented
186	C₂²×#117	C₂⁴	1	12	yes	—
187	C₂²×#117	C₂⁴	1	6	yes	—
188	C₂²×#117	C₂⁴	1	16	yes	—
189	C₂²×#117	C₂⁴	1	6	yes	—
190	C₂²×#117	C₂⁴	1	6	yes	—
191	C₂³×C₄⋊C₄	C₂×D₄	1	12	yes	—
192	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₂³×C₂²⋊C₄	C₂×D₄	1	12	yes	—
195	C₂³×C₂²⋊C₄	C₂×D₄	1	12	yes	—
196	C₂³×C₄²	C₂×D₄	1	4	yes	—
197	C₂³×C₄²	C₂×D₄	1	2	yes	—
198	C₂³×C₄²	C₂×D₄	1	2	yes	—
199	C₂³×C₄²	C₂×D₄	1	6	yes	—
200	C₂³×C₄²	C₂×D₄	1	24	yes	complemented
201	C₂³×C₄²	C₂⁴	1	6	yes	—
202	C₂×#421	C₂×D₄	1	192	yes	complemented
203	C₂×#421	C₂⁴	1	32	yes	—
204	C₂×#421	C₂⁴	1	32	yes	—
205	C₂×#421	C₂⁴	1	32	yes	complemented
206	#2896	C₂⁴	1	32	yes	—
207	C₂×#407	C₂×D₄	1	48	yes	complemented
208	C₂×#407	C₂⁴	1	16	yes	—
209	C₂×#407	C₂⁴	1	32	yes	complemented
210	C₂²×C₂²⋊C₈	C₂×D₄	1	24	yes	complemented
211	C₂²×C₂²⋊C₈	C₂×D₄	1	24	yes	complemented
212	#2297	C₂⁴	1	32	yes	—
213	#2297	C₂⁴	1	16	yes	complemented
214	#2296	C₂⁴	1	16	yes	complemented
215	#2280	C₂×D₄	1	48	yes	complemented
216	#2280	C₂⁴	1	16	yes	—
217	#2280	C₂⁴	1	16	yes	complemented
218	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	24	yes	complemented
219	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	24	yes	complemented
220	#1733	C₂⁴	1	32	yes	complemented
221	C₂×H(3,ℤ/4)	C₂⁴	1	32	yes	complemented
222	C₂×H(3,ℤ/4)	C₂⁴	1	32	yes	complemented
223	#1728	C₂⁴	1	32	yes	complemented
224	C₂⁶	#120	1	1	yes	characteristic
225	C₂⁶	#120	1	1	yes	characteristic
226	C₂⁶	#120	1	1	yes	characteristic
227	C₂⁶	#120	1	1	yes	characteristic
228	C₂⁶	#120	1	6	yes	—
229	C₂⁶	#120	1	6	yes	—
230	C₂⁶	#121	1	1	yes	characteristic
231	C₂⁶	#121	1	1	yes	characteristic
232	C₂⁶	#121	1	6	yes	—
233	C₂⁶	C₂²×D₄	1	6	yes	—
234	C₂⁶	C₂²×D₄	1	6	yes	—
235	C₂⁶	C₂²×D₄	1	1	yes	characteristic
236	C₂²×#41	#121	1	96	yes	complemented
237	C₂²×#41	C₂²×D₄	1	48	yes	—
238	C₂²×#41	C₂²×D₄	1	12	yes	—
239	C₂²×#41	C₂²×D₄	1	24	yes	—
240	C₂²×#41	C₂²×D₄	1	32	yes	complemented
241	C₂²×#41	C₂×#41	1	48	yes	—
242	C₂²×#41	C₂⁵	1	4	yes	—
243	C₂²×#41	C₂⁵	1	8	yes	—
244	C₂³×Q₈	#121	1	16	yes	complemented
245	C₂³×Q₈	C₂²×D₄	1	6	yes	—
246	C₂³×Q₈	C₂²×D₄	1	12	yes	—
247	C₂³×Q₈	C₂²×D₄	1	16	yes	complemented
248	C₂³×D₄	#121	1	16	yes	complemented
249	C₂³×D₄	C₂²×D₄	1	6	yes	—
250	C₂³×D₄	C₂²×D₄	1	12	yes	—
251	C₂³×D₄	C₂²×D₄	1	16	yes	—
252	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
253	C₂⁴×C₄	#120	1	1	yes	characteristic
254	C₂⁴×C₄	#120	1	1	yes	characteristic
255	C₂⁴×C₄	#120	1	6	yes	—
256	C₂⁴×C₄	#120	1	1	yes	characteristic
257	C₂⁴×C₄	#120	1	1	yes	characteristic
258	C₂⁴×C₄	#120	1	6	yes	—
259	C₂⁴×C₄	#120	1	6	yes	—
260	C₂⁴×C₄	#120	1	6	yes	—
261	C₂⁴×C₄	#120	1	6	yes	—
262	C₂⁴×C₄	#120	1	6	yes	—
263	C₂⁴×C₄	#120	1	24	yes	—
264	C₂⁴×C₄	#120	1	1	yes	characteristic
265	C₂⁴×C₄	#120	1	6	yes	—
266	C₂⁴×C₄	#120	1	1	yes	characteristic
267	C₂⁴×C₄	#120	1	6	yes	—
268	C₂⁴×C₄	#120	1	6	yes	—
269	C₂⁴×C₄	#120	1	6	yes	—
270	C₂⁴×C₄	#120	1	6	yes	—
271	C₂⁴×C₄	#120	1	24	yes	—
272	C₂⁴×C₄	#120	1	1	yes	characteristic
273	C₂⁴×C₄	#120	1	6	yes	—
274	C₂⁴×C₄	#120	1	1	yes	characteristic
275	C₂⁴×C₄	#120	1	6	yes	—
276	C₂⁴×C₄	#120	1	6	yes	—
277	C₂⁴×C₄	#120	1	6	yes	—
278	C₂⁴×C₄	#120	1	6	yes	—
279	C₂⁴×C₄	#120	1	24	yes	—
280	C₂⁴×C₄	#121	1	1	yes	characteristic
281	C₂⁴×C₄	#121	1	1	yes	characteristic
282	C₂⁴×C₄	#121	1	6	yes	—
283	C₂⁴×C₄	#121	1	1	yes	characteristic
284	C₂⁴×C₄	#121	1	1	yes	characteristic
285	C₂⁴×C₄	#121	1	6	yes	—
286	C₂⁴×C₄	#121	1	6	yes	—
287	C₂⁴×C₄	#121	1	6	yes	—
288	C₂⁴×C₄	#121	1	1	yes	characteristic
289	C₂⁴×C₄	#121	1	1	yes	characteristic
290	C₂⁴×C₄	#121	1	6	yes	—
291	C₂⁴×C₄	#121	1	6	yes	—
292	C₂⁴×C₄	#121	1	24	yes	—
293	C₂⁴×C₄	#121	1	6	yes	—
294	C₂⁴×C₄	#121	1	6	yes	—
295	C₂⁴×C₄	#121	1	6	yes	—
296	C₂⁴×C₄	#121	1	1	yes	characteristic
297	C₂⁴×C₄	#121	1	1	yes	characteristic
298	C₂⁴×C₄	#121	1	6	yes	—
299	C₂⁴×C₄	#121	1	6	yes	—
300	C₂⁴×C₄	#121	1	24	yes	—
301	C₂⁴×C₄	#121	1	6	yes	—
302	C₂⁴×C₄	#121	1	1	yes	characteristic
303	C₂⁴×C₄	#121	1	1	yes	characteristic
304	C₂⁴×C₄	#121	1	6	yes	—
305	C₂⁴×C₄	#121	1	6	yes	—
306	C₂⁴×C₄	#121	1	6	yes	—
307	C₂⁴×C₄	#121	1	6	yes	—
308	C₂⁴×C₄	#121	1	6	yes	—
309	C₂⁴×C₄	#121	1	24	yes	—
310	C₂⁴×C₄	#127	1	6	yes	—
311	C₂⁴×C₄	#127	1	6	yes	—
312	C₂⁴×C₄	#127	1	6	yes	—
313	C₂⁴×C₄	#127	1	6	yes	—
314	C₂⁴×C₄	#127	1	6	yes	—
315	C₂⁴×C₄	#127	1	6	yes	—
316	C₂⁴×C₄	#127	1	24	yes	—
317	C₂⁴×C₄	#127	1	1	yes	characteristic
318	C₂⁴×C₄	#127	1	1	yes	characteristic
319	C₂⁴×C₄	#127	1	1	yes	characteristic
320	C₂⁴×C₄	#127	1	1	yes	characteristic
321	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
322	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
323	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
324	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
325	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
326	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
327	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
328	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
329	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
330	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
331	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
332	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
333	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
334	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
335	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
336	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
337	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
338	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
339	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
340	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
341	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
342	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
343	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
345	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
346	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
349	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
350	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
351	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×D₄	1	3	yes	—
353	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂⁴×C₄	C₂×#41	1	6	yes	—
355	C₂⁴×C₄	C₂×#41	1	6	yes	—
356	C₂⁴×C₄	C₂×#41	1	12	yes	—
357	C₂⁴×C₄	C₂×#41	1	3	yes	—
358	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
359	C₂⁴×C₄	C₂×#41	1	8	yes	—
360	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
361	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
362	C₂⁴×C₄	C₂⁵	1	4	yes	—
363	C₂⁴×C₄	C₂⁵	1	4	yes	—
364	C₂⁴×C₄	C₂⁵	1	3	yes	—
365	C₂²×M₁₆	C₂²×D₄	1	48	yes	—
366	C₂²×M₁₆	C₂²×D₄	1	24	yes	—
367	C₂²×M₁₆	C₂⁵	1	8	yes	—
368	C₂²×M₁₆	C₂⁵	1	8	yes	—
369	C₂³×C₈	C₂²×D₄	1	24	yes	—
370	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	complemented
371	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	complemented
372	C₂×#121	C₂²×D₄	1	16	yes	complemented
373	C₂×#121	C₂²×D₄	1	16	yes	complemented
374	C₂×#117	#120	1	48	yes	complemented
375	C₂×#117	C₂²×D₄	1	12	yes	—
376	C₂×#117	C₂²×D₄	1	48	yes	—
377	C₂×#117	C₂²×D₄	1	12	yes	—
378	C₂×#117	C₂²×D₄	1	24	yes	—
379	C₂×#117	C₂²×D₄	1	12	yes	—
380	C₂×#117	C₂²×D₄	1	32	yes	complemented
381	C₂×#117	C₂⁵	1	4	yes	—
382	C₂×#117	C₂⁵	1	4	yes	—
383	C₂×#117	C₂⁵	1	8	yes	—
384	C₂×#117	C₂⁵	1	4	yes	—
385	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	—
386	C₂²×C₄⋊C₄	C₂²×D₄	1	6	yes	—
387	C₂²×C₄⋊C₄	C₂²×D₄	1	6	yes	—
388	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
389	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
390	C₂²×C₄²	#120	1	16	yes	complemented
391	C₂²×C₄²	C₂²×D₄	1	12	yes	—
392	C₂²×C₄²	C₂²×D₄	1	12	yes	—
393	C₂²×C₄²	C₂²×D₄	1	24	yes	—
394	C₂²×C₄²	C₂²×D₄	1	12	yes	—
395	C₂²×C₄²	C₂²×D₄	1	32	yes	complemented
396	C₂²×C₄²	C₂⁵	1	4	yes	—
397	#421	C₂²×D₄	1	128	yes	complemented
398	C₂×C₂²⋊C₈	C₂²×D₄	1	32	yes	complemented
399	C₂×C₂²⋊C₈	C₂²×D₄	1	32	yes	complemented
400	C₄×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
401	C₄×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
402	C₂⁵	#392	1	1	yes	characteristic
403	C₂⁵	#392	1	1	yes	characteristic
404	C₂⁵	#392	1	1	yes	characteristic
405	C₂⁵	#392	1	6	yes	—
406	C₂⁵	#392	1	6	yes	—
407	C₂⁵	#392	1	6	yes	—
408	C₂⁵	#392	1	1	yes	characteristic
409	C₂⁵	#392	1	6	yes	—
410	C₂⁵	#392	1	6	yes	—
411	C₂⁵	#392	1	6	yes	—
412	C₂⁵	#392	1	24	yes	—
413	C₂⁵	C₂×#120	1	6	yes	—
414	C₂⁵	C₂×#120	1	6	yes	—
415	C₂⁵	C₂×#120	1	1	yes	characteristic
416	C₂⁵	C₂×#120	1	1	yes	characteristic
417	C₂⁵	C₂×#120	1	6	yes	—
418	C₂⁵	C₂×#120	1	6	yes	—
419	C₂⁵	C₂×#120	1	12	yes	—
420	C₂⁵	C₂×#120	1	12	yes	—
421	C₂⁵	C₂×#120	1	3	yes	—
422	C₂⁵	C₂×#120	1	3	yes	—
423	C₂⁵	C₂×#121	1	6	yes	—
424	C₂⁵	C₂×#121	1	1	yes	characteristic
425	C₂⁵	C₂×#121	1	6	yes	—
426	C₂⁵	C₂×#121	1	12	yes	—
427	C₂⁵	C₂×#121	1	3	yes	—
428	C₂⁵	D₄²	1	8	yes	—
429	C₂⁵	#546	1	8	yes	—
430	C₂⁵	C₂³×D₄	1	4	yes	—
431	C₂⁵	C₂³×D₄	1	4	yes	—
432	C₂⁵	C₂³×D₄	1	3	yes	—
433	C₂×#41	C₂×#121	1	96	yes	complemented
434	C₂×#41	C₂³×D₄	1	16	yes	—
435	C₂×#41	C₂²×#41	1	16	yes	—
436	C₂²×Q₈	C₂×#121	1	48	yes	complemented
437	C₂²×Q₈	C₂³×D₄	1	4	yes	—
438	C₂²×Q₈	C₂³×D₄	1	8	yes	—
439	C₂²×D₄	C₂×#121	1	48	yes	complemented
440	C₂²×D₄	C₂³×D₄	1	4	yes	—
441	C₂²×D₄	C₂³×D₄	1	8	yes	—
442	C₂³×C₄	#392	1	1	yes	characteristic
443	C₂³×C₄	#392	1	1	yes	characteristic
444	C₂³×C₄	#392	1	1	yes	characteristic
445	C₂³×C₄	#392	1	1	yes	characteristic
446	C₂³×C₄	#392	1	6	yes	—
447	C₂³×C₄	#392	1	6	yes	—
448	C₂³×C₄	#392	1	6	yes	—
449	C₂³×C₄	#392	1	6	yes	—
450	C₂³×C₄	#392	1	6	yes	—
451	C₂³×C₄	#392	1	6	yes	—
452	C₂³×C₄	#392	1	24	yes	—
453	C₂³×C₄	#392	1	6	yes	—
454	C₂³×C₄	#392	1	6	yes	—
455	C₂³×C₄	#392	1	6	yes	—
456	C₂³×C₄	#392	1	6	yes	—
457	C₂³×C₄	#392	1	6	yes	—
458	C₂³×C₄	#392	1	6	yes	—
459	C₂³×C₄	#392	1	6	yes	—
460	C₂³×C₄	#392	1	6	yes	—
461	C₂³×C₄	#392	1	24	yes	—
462	C₂³×C₄	#392	1	24	yes	—
463	C₂³×C₄	#392	1	6	yes	—
464	C₂³×C₄	#392	1	6	yes	—
465	C₂³×C₄	#392	1	6	yes	—
466	C₂³×C₄	#392	1	6	yes	—
467	C₂³×C₄	#392	1	6	yes	—
468	C₂³×C₄	#392	1	6	yes	—
469	C₂³×C₄	#392	1	6	yes	—
470	C₂³×C₄	#392	1	6	yes	—
471	C₂³×C₄	#392	1	24	yes	—
472	C₂³×C₄	#392	1	24	yes	—
473	C₂³×C₄	#392	1	24	yes	—
474	C₂³×C₄	#392	1	24	yes	—
475	C₂³×C₄	#392	1	24	yes	—
476	C₂³×C₄	#392	1	24	yes	—
477	C₂³×C₄	#392	1	24	yes	—
478	C₂³×C₄	#392	1	24	yes	—
479	C₂³×C₄	#392	1	24	yes	—
480	C₂³×C₄	#392	1	24	yes	—
481	C₂³×C₄	C₂×#120	1	6	yes	—
482	C₂³×C₄	C₂×#120	1	6	yes	—
483	C₂³×C₄	C₂×#120	1	12	yes	—
484	C₂³×C₄	C₂×#120	1	6	yes	—
485	C₂³×C₄	C₂×#120	1	6	yes	—
486	C₂³×C₄	C₂×#120	1	12	yes	—
487	C₂³×C₄	C₂×#120	1	12	yes	—
488	C₂³×C₄	C₂×#120	1	12	yes	—
489	C₂³×C₄	C₂×#120	1	12	yes	—
490	C₂³×C₄	C₂×#120	1	12	yes	—
491	C₂³×C₄	C₂×#120	1	12	yes	—
492	C₂³×C₄	C₂×#120	1	12	yes	—
493	C₂³×C₄	C₂×#120	1	12	yes	—
494	C₂³×C₄	C₂×#120	1	12	yes	—
495	C₂³×C₄	C₂×#120	1	6	yes	—
496	C₂³×C₄	C₂×#120	1	6	yes	—
497	C₂³×C₄	C₂×#120	1	6	yes	—
498	C₂³×C₄	C₂×#120	1	6	yes	—
499	C₂³×C₄	C₂×#120	1	12	yes	—
500	C₂³×C₄	C₂×#120	1	12	yes	—
501	C₂³×C₄	C₂×#120	1	12	yes	—
502	C₂³×C₄	C₂×#120	1	12	yes	—
503	C₂³×C₄	C₂×#120	1	12	yes	—
504	C₂³×C₄	C₂×#120	1	12	yes	—
505	C₂³×C₄	C₂×#120	1	12	yes	—
506	C₂³×C₄	C₂×#120	1	4	yes	—
507	C₂³×C₄	C₂×#120	1	3	yes	—
508	C₂³×C₄	C₂×#120	1	6	yes	—
509	C₂³×C₄	C₂×#120	1	3	yes	—
510	C₂³×C₄	C₂×#120	1	3	yes	—
511	C₂³×C₄	C₂×#120	1	6	yes	—
512	C₂³×C₄	C₂×#120	1	3	yes	—
513	C₂³×C₄	C₂×#120	1	1	yes	characteristic
514	C₂³×C₄	C₂×#120	1	3	yes	—
515	C₂³×C₄	C₂×#120	1	3	yes	—
516	C₂³×C₄	C₂×#120	1	3	yes	—
517	C₂³×C₄	C₂×#120	1	6	yes	—
518	C₂³×C₄	C₂×#121	1	6	yes	—
519	C₂³×C₄	C₂×#121	1	6	yes	—
520	C₂³×C₄	C₂×#121	1	12	yes	—
521	C₂³×C₄	C₂×#121	1	12	yes	—
522	C₂³×C₄	C₂×#121	1	12	yes	—
523	C₂³×C₄	C₂×#121	1	12	yes	—
524	C₂³×C₄	C₂×#121	1	12	yes	—
525	C₂³×C₄	C₂×#121	1	6	yes	—
526	C₂³×C₄	C₂×#121	1	6	yes	—
527	C₂³×C₄	C₂×#121	1	6	yes	—
528	C₂³×C₄	C₂×#121	1	6	yes	—
529	C₂³×C₄	C₂×#121	1	12	yes	—
530	C₂³×C₄	C₂×#121	1	12	yes	—
531	C₂³×C₄	C₂×#121	1	6	yes	—
532	C₂³×C₄	C₂×#121	1	6	yes	—
533	C₂³×C₄	C₂×#121	1	6	yes	—
534	C₂³×C₄	C₂×#121	1	6	yes	—
535	C₂³×C₄	C₂×#121	1	12	yes	—
536	C₂³×C₄	C₂×#121	1	12	yes	—
537	C₂³×C₄	C₂×#121	1	12	yes	—
538	C₂³×C₄	C₂×#121	1	12	yes	—
539	C₂³×C₄	C₂×#121	1	12	yes	—
540	C₂³×C₄	C₂×#121	1	12	yes	—
541	C₂³×C₄	C₂×#121	1	12	yes	—
542	C₂³×C₄	C₂×#121	1	12	yes	—
543	C₂³×C₄	C₂×#121	1	12	yes	—
544	C₂³×C₄	C₂×#121	1	12	yes	—
545	C₂³×C₄	C₂×#121	1	3	yes	—
546	C₂³×C₄	C₂×#121	1	3	yes	—
547	C₂³×C₄	C₂×#121	1	6	yes	—
548	C₂³×C₄	C₂×#121	1	1	yes	characteristic
549	C₂³×C₄	C₂×#121	1	3	yes	—
550	C₂³×C₄	C₂×#121	1	8	yes	—
551	C₂³×C₄	C₂×#121	1	24	yes	—
552	C₂³×C₄	C₂×#121	1	3	yes	—
553	C₂³×C₄	C₂×#121	1	3	yes	—
554	C₂³×C₄	C₂×#121	1	6	yes	—
555	C₂³×C₄	C₂×#121	1	1	yes	characteristic
556	C₂³×C₄	C₂×#121	1	3	yes	—
557	C₂³×C₄	C₂×#121	1	3	yes	—
558	C₂³×C₄	C₂×#121	1	3	yes	—
559	C₂³×C₄	C₂×#121	1	6	yes	—
560	C₂³×C₄	#525	1	4	yes	—
561	C₂³×C₄	#525	1	12	yes	—
562	C₂³×C₄	#525	1	8	yes	—
563	C₂³×C₄	#525	1	24	yes	—
564	C₂³×C₄	C₂×#127	1	6	yes	—
565	C₂³×C₄	C₂×#127	1	6	yes	—
566	C₂³×C₄	C₂×#127	1	6	yes	—
567	C₂³×C₄	C₂×#127	1	6	yes	—
568	C₂³×C₄	C₂×#127	1	12	yes	—
569	C₂³×C₄	C₂×#127	1	12	yes	—
570	C₂³×C₄	C₂×#127	1	12	yes	—
571	C₂³×C₄	C₂×#127	1	12	yes	—
572	C₂³×C₄	C₂×#127	1	12	yes	—
573	C₂³×C₄	C₂×#127	1	12	yes	—
574	C₂³×C₄	C₂×#127	1	3	yes	—
575	C₂³×C₄	C₂×#127	1	3	yes	—
576	C₂³×C₄	C₂×#127	1	6	yes	—
577	C₂³×C₄	C₂×#127	1	3	yes	—
578	C₂³×C₄	C₂×#127	1	1	yes	characteristic
579	C₂³×C₄	#534	1	12	yes	—
580	C₂³×C₄	#534	1	4	yes	—
581	C₂³×C₄	#534	1	8	yes	—
582	C₂³×C₄	#534	1	24	yes	—
583	C₂³×C₄	#535	1	4	yes	—
584	C₂³×C₄	#535	1	12	yes	—
585	C₂³×C₄	#538	1	8	yes	—
586	C₂³×C₄	#538	1	24	yes	—
587	C₂³×C₄	D₄²	1	24	yes	—
588	C₂³×C₄	D₄²	1	8	yes	—
589	C₂³×C₄	D₄²	1	24	yes	—
590	C₂³×C₄	D₄²	1	8	yes	—
591	C₂³×C₄	D₄²	1	24	yes	—
592	C₂³×C₄	D₄²	1	24	yes	—
593	C₂³×C₄	D₄²	1	8	yes	—
594	C₂³×C₄	#546	1	24	yes	—
595	C₂³×C₄	#546	1	8	yes	—
596	C₂³×C₄	#546	1	24	yes	—
597	C₂³×C₄	#546	1	8	yes	—
598	C₂³×C₄	#546	1	24	yes	—
599	C₂³×C₄	#546	1	24	yes	—
600	C₂³×C₄	#546	1	8	yes	—
601	C₂³×C₄	C₂³×D₄	1	4	yes	—
602	C₂³×C₄	C₂³×D₄	1	4	yes	—
603	C₂³×C₄	C₂³×D₄	1	4	yes	—
604	C₂³×C₄	C₂³×D₄	1	4	yes	—
605	C₂³×C₄	C₂³×D₄	1	4	yes	—
606	C₂³×C₄	C₂³×D₄	1	4	yes	—
607	C₂³×C₄	C₂³×D₄	1	4	yes	—
608	C₂³×C₄	C₂³×D₄	1	4	yes	—
609	C₂³×C₄	C₂³×D₄	1	4	yes	—
610	C₂³×C₄	C₂³×D₄	1	4	yes	—
611	C₂³×C₄	C₂³×D₄	1	4	yes	—
612	C₂³×C₄	C₂³×D₄	1	4	yes	—
613	C₂³×C₄	C₂³×D₄	1	4	yes	—
614	C₂³×C₄	C₂³×D₄	1	4	yes	—
615	C₂³×C₄	C₂³×D₄	1	3	yes	—
616	C₂³×C₄	C₂³×D₄	1	3	yes	—
617	C₂³×C₄	C₂³×D₄	1	3	yes	—
618	C₂³×C₄	C₂³×D₄	1	3	yes	—
619	C₂³×C₄	C₂³×D₄	1	3	yes	—
620	C₂³×C₄	C₂³×D₄	1	3	yes	—
621	C₂³×C₄	C₂³×D₄	1	12	yes	—
622	C₂³×C₄	C₂³×D₄	1	3	yes	—
623	C₂³×C₄	C₂³×D₄	1	3	yes	—
624	C₂³×C₄	C₂³×D₄	1	3	yes	—
625	C₂³×C₄	C₂³×D₄	1	3	yes	—
626	C₂³×C₄	C₂³×D₄	1	3	yes	—
627	C₂³×C₄	C₂²×#41	1	4	yes	—
628	C₂³×C₄	C₂²×#41	1	4	yes	—
629	C₂³×C₄	C₂²×#41	1	3	yes	—
630	C₂³×C₄	C₂²×#41	1	3	yes	—
631	C₂³×C₄	C₂²×#41	1	12	yes	—
632	C₂³×C₄	C₂×H(5,𝔽₂)	1	12	yes	—
633	C₂³×C₄	C₂×H(5,𝔽₂)	1	12	yes	—
634	C₂³×C₄	C₂⁶	1	1	yes	characteristic
635	C₂×M₁₆	C₂³×D₄	1	16	yes	—
636	C₂²×C₈	C₂³×D₄	1	16	yes	—
637	#117	C₂×#120	1	48	yes	complemented
638	#117	C₂³×D₄	1	16	yes	—
639	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
641	C₂×C₄²	C₂×#120	1	48	yes	complemented
642	C₂×C₄²	C₂³×D₄	1	8	yes	—
643	C₂×C₄²	C₂³×D₄	1	16	yes	—
644	C₂×C₄²	C₂³×D₄	1	8	yes	—
645	C₂⁴	#2010	1	8	yes	complemented
646	C₂⁴	C₂×#392	1	6	yes	—
647	C₂⁴	C₂×#392	1	6	yes	—
648	C₂⁴	C₂×#392	1	6	yes	—
649	C₂⁴	C₂×#392	1	12	yes	—
650	C₂⁴	C₂×#392	1	12	yes	—
651	C₂⁴	C₂×#392	1	12	yes	—
652	C₂⁴	C₂×#392	1	6	yes	—
653	C₂⁴	C₂×#392	1	3	yes	—
654	C₂⁴	C₂×#392	1	3	yes	—
655	C₂⁴	C₂×#392	1	3	yes	—
656	C₂⁴	C₂×#392	1	12	yes	—
657	C₂⁴	C₂×#392	1	12	yes	—
658	C₂⁴	C₂×#392	1	12	yes	—
659	C₂⁴	C₂×#392	1	6	yes	—
660	C₂⁴	C₂×#392	1	1	yes	characteristic
661	C₂⁴	#2403	1	4	yes	—
662	C₂⁴	#2403	1	12	yes	—
663	C₂⁴	#2404	1	4	yes	—
664	C₂⁴	#2404	1	12	yes	—
665	C₂⁴	#2410	1	8	yes	—
666	C₂⁴	#2410	1	24	yes	—
667	C₂⁴	#2424	1	8	yes	—
668	C₂⁴	#2424	1	24	yes	—
669	C₂⁴	C₂²×#120	1	4	yes	—
670	C₂⁴	C₂²×#120	1	4	yes	—
671	C₂⁴	C₂²×#120	1	3	yes	—
672	C₂⁴	C₂²×#120	1	3	yes	—
673	C₂⁴	C₂²×#120	1	4	yes	—
674	C₂⁴	C₂²×#120	1	4	yes	—
675	C₂⁴	C₂²×#120	1	3	yes	—
676	C₂⁴	C₂²×#120	1	3	yes	—
677	C₂⁴	C₂²×#121	1	4	yes	—
678	C₂⁴	C₂²×#121	1	3	yes	—
679	C₂⁴	C₂²×#121	1	4	yes	—
680	C₂⁴	C₂²×#121	1	3	yes	—
681	C₂⁴	C₂×D₄²	1	12	yes	—
682	C₂⁴	C₂×#546	1	12	yes	—
683	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
684	C₂×Q₈	C₂²×#121	1	16	yes	complemented
685	C₂×D₄	C₂²×#121	1	16	yes	complemented
686	C₂²×C₄	C₂×#392	1	6	yes	—
687	C₂²×C₄	C₂×#392	1	6	yes	—
688	C₂²×C₄	C₂×#392	1	6	yes	—
689	C₂²×C₄	C₂×#392	1	6	yes	—
690	C₂²×C₄	C₂×#392	1	12	yes	—
691	C₂²×C₄	C₂×#392	1	12	yes	—
692	C₂²×C₄	C₂×#392	1	12	yes	—
693	C₂²×C₄	C₂×#392	1	12	yes	—
694	C₂²×C₄	C₂×#392	1	12	yes	—
695	C₂²×C₄	C₂×#392	1	12	yes	—
696	C₂²×C₄	C₂×#392	1	12	yes	—
697	C₂²×C₄	C₂×#392	1	12	yes	—
698	C₂²×C₄	C₂×#392	1	12	yes	—
699	C₂²×C₄	C₂×#392	1	12	yes	—
700	C₂²×C₄	C₂×#392	1	12	yes	—
701	C₂²×C₄	C₂×#392	1	12	yes	—
702	C₂²×C₄	C₂×#392	1	12	yes	—
703	C₂²×C₄	C₂×#392	1	12	yes	—
704	C₂²×C₄	C₂×#392	1	12	yes	—
705	C₂²×C₄	C₂×#392	1	12	yes	—
706	C₂²×C₄	C₂×#392	1	12	yes	—
707	C₂²×C₄	C₂×#392	1	12	yes	—
708	C₂²×C₄	C₂×#392	1	12	yes	—
709	C₂²×C₄	C₂×#392	1	12	yes	—
710	C₂²×C₄	C₂×#392	1	12	yes	—
711	C₂²×C₄	C₂×#392	1	12	yes	—
712	C₂²×C₄	C₂×#392	1	3	yes	—
713	C₂²×C₄	C₂×#392	1	3	yes	—
714	C₂²×C₄	C₂×#392	1	6	yes	—
715	C₂²×C₄	C₂×#392	1	3	yes	—
716	C₂²×C₄	C₂×#392	1	3	yes	—
717	C₂²×C₄	C₂×#392	1	6	yes	—
718	C₂²×C₄	C₂×#392	1	6	yes	—
719	C₂²×C₄	C₂×#392	1	6	yes	—
720	C₂²×C₄	C₂×#392	1	6	yes	—
721	C₂²×C₄	C₂×#392	1	6	yes	—
722	C₂²×C₄	#2403	1	12	yes	—
723	C₂²×C₄	#2403	1	12	yes	—
724	C₂²×C₄	#2403	1	24	yes	—
725	C₂²×C₄	#2404	1	12	yes	—
726	C₂²×C₄	#2404	1	12	yes	—
727	C₂²×C₄	#2404	1	24	yes	—
728	C₂²×C₄	#2410	1	8	yes	—
729	C₂²×C₄	#2410	1	24	yes	—
730	C₂²×C₄	#2410	1	24	yes	—
731	C₂²×C₄	#2410	1	24	yes	—
732	C₂²×C₄	#2410	1	48	yes	—
733	C₂²×C₄	#2410	1	24	yes	—
734	C₂²×C₄	#2410	1	24	yes	—
735	C₂²×C₄	#2410	1	48	yes	—
736	C₂²×C₄	#2424	1	8	yes	—
737	C₂²×C₄	#2424	1	24	yes	—
738	C₂²×C₄	#2424	1	24	yes	—
739	C₂²×C₄	#2424	1	24	yes	—
740	C₂²×C₄	#2424	1	48	yes	—
741	C₂²×C₄	#2424	1	24	yes	—
742	C₂²×C₄	#2424	1	24	yes	—
743	C₂²×C₄	#2424	1	48	yes	—
744	C₂²×C₄	#2433	1	4	yes	—
745	C₂²×C₄	#2433	1	12	yes	—
746	C₂²×C₄	#2433	1	12	yes	—
747	C₂²×C₄	#2433	1	12	yes	—
748	C₂²×C₄	#2433	1	24	yes	—
749	C₂²×C₄	#2539	1	4	yes	—
750	C₂²×C₄	#2539	1	12	yes	—
751	C₂²×C₄	#2539	1	12	yes	—
752	C₂²×C₄	#2539	1	12	yes	—
753	C₂²×C₄	#2539	1	24	yes	—
754	C₂²×C₄	#2617	1	4	yes	—
755	C₂²×C₄	#2617	1	12	yes	—
756	C₂²×C₄	#2617	1	12	yes	—
757	C₂²×C₄	#2617	1	12	yes	—
758	C₂²×C₄	#2617	1	24	yes	—
759	C₂²×C₄	#2847	1	4	yes	—
760	C₂²×C₄	#2847	1	12	yes	—
761	C₂²×C₄	#2847	1	12	yes	—
762	C₂²×C₄	#2847	1	12	yes	—
763	C₂²×C₄	#2847	1	24	yes	—
764	C₂²×C₄	C₂²×#120	1	4	yes	—
765	C₂²×C₄	C₂²×#120	1	4	yes	—
766	C₂²×C₄	C₂²×#120	1	4	yes	—
767	C₂²×C₄	C₂²×#120	1	4	yes	—
768	C₂²×C₄	C₂²×#120	1	4	yes	—
769	C₂²×C₄	C₂²×#120	1	4	yes	—
770	C₂²×C₄	C₂²×#120	1	4	yes	—
771	C₂²×C₄	C₂²×#120	1	4	yes	—
772	C₂²×C₄	C₂²×#120	1	6	yes	—
773	C₂²×C₄	C₂²×#120	1	6	yes	—
774	C₂²×C₄	C₂²×#120	1	3	yes	—
775	C₂²×C₄	C₂²×#120	1	3	yes	—
776	C₂²×C₄	C₂²×#120	1	3	yes	—
777	C₂²×C₄	C₂²×#120	1	3	yes	—
778	C₂²×C₄	C₂²×#120	1	3	yes	—
779	C₂²×C₄	C₂²×#120	1	3	yes	—
780	C₂²×C₄	C₂²×#120	1	3	yes	—
781	C₂²×C₄	C₂²×#120	1	3	yes	—
782	C₂²×C₄	C₂²×#121	1	4	yes	—
783	C₂²×C₄	C₂²×#121	1	4	yes	—
784	C₂²×C₄	C₂²×#121	1	4	yes	—
785	C₂²×C₄	C₂²×#121	1	4	yes	—
786	C₂²×C₄	C₂²×#121	1	4	yes	—
787	C₂²×C₄	C₂²×#121	1	4	yes	—
788	C₂²×C₄	C₂²×#121	1	4	yes	—
789	C₂²×C₄	C₂²×#121	1	4	yes	—
790	C₂²×C₄	C₂²×#121	1	4	yes	—
791	C₂²×C₄	C₂²×#121	1	4	yes	—
792	C₂²×C₄	C₂²×#121	1	12	yes	—
793	C₂²×C₄	C₂²×#121	1	12	yes	—
794	C₂²×C₄	C₂²×#121	1	3	yes	—
795	C₂²×C₄	C₂²×#121	1	3	yes	—
796	C₂²×C₄	C₂²×#121	1	3	yes	—
797	C₂²×C₄	C₂²×#121	1	3	yes	—
798	C₂²×C₄	C₂²×#121	1	3	yes	—
799	C₂²×C₄	C₂²×#121	1	3	yes	—
800	C₂²×C₄	C₂²×#121	1	3	yes	—
801	C₂²×C₄	C₂²×#121	1	3	yes	—
802	C₂²×C₄	C₂²×#121	1	3	yes	—
803	C₂²×C₄	C₂²×#121	1	3	yes	—
804	C₂²×C₄	C₂×#525	1	6	yes	—
805	C₂²×C₄	C₂×#525	1	6	yes	—
806	C₂²×C₄	C₂×#525	1	12	yes	—
807	C₂²×C₄	C₂×#525	1	12	yes	—
808	C₂²×C₄	C₂²×#127	1	4	yes	—
809	C₂²×C₄	C₂²×#127	1	4	yes	—
810	C₂²×C₄	C₂²×#127	1	4	yes	—
811	C₂²×C₄	C₂²×#127	1	4	yes	—
812	C₂²×C₄	C₂²×#127	1	3	yes	—
813	C₂²×C₄	C₂²×#127	1	3	yes	—
814	C₂²×C₄	C₂²×#127	1	3	yes	—
815	C₂²×C₄	C₂²×#127	1	3	yes	—
816	C₂²×C₄	C₂×#534	1	6	yes	—
817	C₂²×C₄	C₂×#534	1	6	yes	—
818	C₂²×C₄	C₂×#534	1	12	yes	—
819	C₂²×C₄	C₂×#534	1	12	yes	—
820	C₂²×C₄	C₂×#535	1	6	yes	—
821	C₂²×C₄	C₂×#535	1	6	yes	—
822	C₂²×C₄	C₂×#538	1	12	yes	—
823	C₂²×C₄	C₂×#538	1	12	yes	—
824	C₂²×C₄	C₂×D₄²	1	12	yes	—
825	C₂²×C₄	C₂×D₄²	1	12	yes	—
826	C₂²×C₄	C₂×D₄²	1	12	yes	—
827	C₂²×C₄	C₂×D₄²	1	12	yes	—
828	C₂²×C₄	C₂×D₄²	1	12	yes	—
829	C₂²×C₄	C₂×D₄²	1	12	yes	—
830	C₂²×C₄	C₂×D₄²	1	12	yes	—
831	C₂²×C₄	C₂×#546	1	12	yes	—
832	C₂²×C₄	C₂×#546	1	12	yes	—
833	C₂²×C₄	C₂×#546	1	12	yes	—
834	C₂²×C₄	C₂×#546	1	12	yes	—
835	C₂²×C₄	C₂×#546	1	12	yes	—
836	C₂²×C₄	C₂×#546	1	12	yes	—
837	C₂²×C₄	C₂×#546	1	12	yes	—
838	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
841	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
844	C₂²×C₄	C₂³×#41	1	1	yes	characteristic
845	C₂²×C₄	C₂³×#41	1	2	yes	—
846	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
847	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
848	C₄²	C₂²×#120	1	16	yes	complemented
849	C₂³	#14716	1	12	yes	—
850	C₂³	#14716	1	12	yes	—
851	C₂³	#14716	1	12	yes	—
852	C₂³	#14716	1	24	yes	—
853	C₂³	#14716	1	4	yes	—
854	C₂³	C₂×#2010	1	4	yes	—
855	C₂³	C₂×#2010	1	24	yes	complemented
856	C₂³	#23414	1	4	yes	—
857	C₂³	C₂²×#392	1	4	yes	—
858	C₂³	C₂²×#392	1	4	yes	—
859	C₂³	C₂²×#392	1	4	yes	—
860	C₂³	C₂²×#392	1	3	yes	—
861	C₂³	C₂²×#392	1	3	yes	—
862	C₂³	C₂²×#392	1	3	yes	—
863	C₂³	C₂²×#392	1	4	yes	—
864	C₂³	C₂²×#392	1	3	yes	—
865	C₂³	C₂×#2403	1	6	yes	—
866	C₂³	C₂×#2403	1	6	yes	—
867	C₂³	C₂×#2410	1	12	yes	—
868	C₂³	C₂×#2410	1	12	yes	—
869	C₂³	C₂×#2424	1	12	yes	—
870	C₂³	C₂×#2424	1	12	yes	—
871	C₂³	C₂×#2404	1	6	yes	—
872	C₂³	C₂×#2404	1	6	yes	—
873	C₂³	C₂³×#120	1	1	yes	characteristic
874	C₂³	C₂³×#120	1	1	yes	characteristic
875	C₂³	C₂³×#121	1	1	yes	characteristic
876	C₂³	C₂²×D₄²	1	2	yes	—
877	C₂³	C₂²×#546	1	2	yes	—
878	C₂×C₄	#14716	1	12	yes	—
879	C₂×C₄	#14716	1	12	yes	—
880	C₂×C₄	#14716	1	24	yes	—
881	C₂×C₄	#14716	1	12	yes	—
882	C₂×C₄	#14716	1	24	yes	—
883	C₂×C₄	#14716	1	12	yes	—
884	C₂×C₄	#14716	1	24	yes	—
885	C₂×C₄	#14716	1	24	yes	—
886	C₂×C₄	#14716	1	24	yes	—
887	C₂×C₄	#14716	1	24	yes	—
888	C₂×C₄	C₂²×#392	1	4	yes	—
889	C₂×C₄	C₂²×#392	1	4	yes	—
890	C₂×C₄	C₂²×#392	1	4	yes	—
891	C₂×C₄	C₂²×#392	1	4	yes	—
892	C₂×C₄	C₂²×#392	1	3	yes	—
893	C₂×C₄	C₂²×#392	1	3	yes	—
894	C₂×C₄	C₂²×#392	1	3	yes	—
895	C₂×C₄	C₂²×#392	1	3	yes	—
896	C₂×C₄	C₂×#2617	1	6	yes	—
897	C₂×C₄	C₂×#2617	1	6	yes	—
898	C₂×C₄	C₂×#2617	1	6	yes	—
899	C₂×C₄	C₂×#2617	1	6	yes	—
900	C₂×C₄	C₂×#2403	1	6	yes	—
901	C₂×C₄	C₂×#2403	1	6	yes	—
902	C₂×C₄	C₂×#2410	1	12	yes	—
903	C₂×C₄	C₂×#2410	1	12	yes	—
904	C₂×C₄	C₂×#2410	1	12	yes	—
905	C₂×C₄	C₂×#2410	1	12	yes	—
906	C₂×C₄	C₂×#2410	1	12	yes	—
907	C₂×C₄	C₂×#2410	1	12	yes	—
908	C₂×C₄	C₂×#2424	1	12	yes	—
909	C₂×C₄	C₂×#2424	1	12	yes	—
910	C₂×C₄	C₂×#2424	1	12	yes	—
911	C₂×C₄	C₂×#2424	1	12	yes	—
912	C₂×C₄	C₂×#2424	1	12	yes	—
913	C₂×C₄	C₂×#2424	1	12	yes	—
914	C₂×C₄	C₂×#2433	1	6	yes	—
915	C₂×C₄	C₂×#2433	1	6	yes	—
916	C₂×C₄	C₂×#2433	1	6	yes	—
917	C₂×C₄	C₂×#2433	1	6	yes	—
918	C₂×C₄	C₂×#2404	1	6	yes	—
919	C₂×C₄	C₂×#2404	1	6	yes	—
920	C₂×C₄	C₂×#2539	1	6	yes	—
921	C₂×C₄	C₂×#2539	1	6	yes	—
922	C₂×C₄	C₂×#2539	1	6	yes	—
923	C₂×C₄	C₂×#2539	1	6	yes	—
924	C₂×C₄	C₂×#2847	1	6	yes	—
925	C₂×C₄	C₂×#2847	1	6	yes	—
926	C₂×C₄	C₂×#2847	1	6	yes	—
927	C₂×C₄	C₂×#2847	1	6	yes	—
928	C₂×C₄	C₂³×#120	1	1	yes	characteristic
929	C₂×C₄	C₂³×#120	1	1	yes	characteristic
930	C₂×C₄	C₂³×#121	1	2	yes	—
931	C₂×C₄	C₂³×#121	1	1	yes	characteristic
932	C₂×C₄	C₂³×#121	1	1	yes	characteristic
933	C₂×C₄	C₂²×#525	1	2	yes	—
934	C₂×C₄	C₂²×#525	1	1	yes	characteristic
935	C₂×C₄	C₂³×#127	1	1	yes	characteristic
936	C₂×C₄	C₂²×#534	1	2	yes	—
937	C₂×C₄	C₂²×#534	1	1	yes	characteristic
938	C₂×C₄	C₂²×#538	1	2	yes	—
939	C₂×C₄	C₂²×#535	1	1	yes	characteristic
940	C₂×C₄	C₂²×D₄²	1	2	yes	—
941	C₂×C₄	C₂²×D₄²	1	2	yes	—
942	C₂×C₄	C₂²×D₄²	1	2	yes	—
943	C₂×C₄	C₂²×#546	1	2	yes	—
944	C₂×C₄	C₂²×#546	1	2	yes	—
945	C₂×C₄	C₂²×#546	1	2	yes	—
946	C₂²	#394261	1	16	yes	direct product factor
947	C₂²	C₂×#14716	1	6	yes	—
948	C₂²	C₂×#14716	1	6	yes	—
949	C₂²	C₂×#14716	1	6	yes	—
950	C₂²	C₂×#14716	1	6	yes	—
951	C₂²	C₂²×#2010	1	6	yes	—
952	C₂²	C₂²×#2010	1	8	yes	complemented
953	C₂²	C₂×#23414	1	6	yes	—
954	C₂²	C₂³×#392	1	1	yes	characteristic
955	C₂²	C₂²×#2403	1	1	yes	characteristic
956	C₂²	C₂²×#2410	1	2	yes	—
957	C₂²	C₂²×#2424	1	2	yes	—
958	C₂²	C₂²×#2404	1	1	yes	characteristic
959	C₄	C₂×#14716	1	6	yes	—
960	C₄	C₂×#14716	1	6	yes	—
961	C₄	C₂×#14716	1	6	yes	—
962	C₄	C₂×#14716	1	6	yes	—
963	C₄	C₂²×#2617	1	1	yes	characteristic
964	C₄	C₂²×#2410	1	2	yes	—
965	C₄	C₂²×#2424	1	2	yes	—
966	C₄	C₂²×#2433	1	1	yes	characteristic
967	C₄	C₂²×#2539	1	1	yes	characteristic
968	C₄	C₂²×#2847	1	1	yes	characteristic
969	C₂	C₂×#394261	1	12	yes	direct product factor
970	C₂	C₂³×#2010	1	1	yes	characteristic
971	C₂	C₂²×#14716	1	1	yes	characteristic
972	C₂	C₂²×#23414	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×#127
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
socle	C₂⁴	C₂×#392
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁶×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. C₂²×#11083	C₂	semidirect
2. C₂²×#11041	C₂	semidirect
3. C₂²×#20902	C₂	semidirect
4. C₂⁴×#421	C₂	semidirect
5. C₂²×#20898	C₂	semidirect
6. C₂²×#60359	C₂	semidirect
7. C₂²×#10716	C₂	semidirect
8. C₂²×#10994	C₂	semidirect
9. C₂²×#34737	C₂	semidirect
10. C₂²×#34736	C₂	semidirect
11. C₂³×#2010	C₂	semidirect
12. C₂×#394261	C₂	direct (N × H)
18. C₂³×#525	C₂²	semidirect
21. C₂×#60359	C₂²	semidirect
23. C₂³×#407	C₂²	semidirect
27. C₂³×#421	C₂²	semidirect
28. C₂³×#421	C₂²	semidirect
29. C₂×#34737	C₂²	semidirect
30. C₂×#34736	C₂²	semidirect
32. C₂²×#2297	C₂²	semidirect
33. C₂²×#2296	C₂²	semidirect
35. C₂²×#2280	C₂²	semidirect
36. C₂²×#2010	C₂²	semidirect
37. C₂×#20902	C₂²	semidirect
38. C₂×#20898	C₂²	semidirect
39. C₂²×#1733	C₂²	semidirect
40. C₂³×H(3,ℤ/4)	C₂²	semidirect
41. C₂³×H(3,ℤ/4)	C₂²	semidirect
42. C₂²×#1728	C₂²	semidirect
43. #394261	C₂²	direct (N × H)
44. C₂×#11083	C₂²	semidirect
45. C₂×#10994	C₂²	semidirect
46. C₂×#11041	C₂²	semidirect
47. C₂×#10716	C₂²	semidirect
48. C₂⁴×#41	D₄	semidirect
49. C₂⁴×#41	D₄	semidirect
53. C₂⁵×Q₈	D₄	semidirect
55. C₂⁵×D₄	D₄	semidirect
62. C₂²×#525	D₄	semidirect
65. C₂²×#525	C₂³	semidirect
66. C₂³×C₂²⋊Q₈	D₄	semidirect
67. C₂³×C₂²⋊Q₈	D₄	semidirect
68. C₂³×#121	D₄	semidirect
69. C₂³×#121	D₄	semidirect
72. C₂³×#117	D₄	semidirect
73. C₂³×#117	D₄	semidirect
82. C₂⁴×C₄²	D₄	semidirect
84. #60359	C₂³	semidirect
85. C₂²×#421	D₄	semidirect
88. C₂²×#421	C₂³	semidirect
89. C₂²×#421	C₂³	semidirect
91. C₂²×#407	D₄	semidirect
93. C₂²×#407	C₂³	semidirect
94. C₂³×C₂²⋊C₈	D₄	semidirect
95. C₂³×C₂²⋊C₈	D₄	semidirect
96. #34737	C₂³	semidirect
97. #34736	C₂³	semidirect
99. C₂×#2297	C₂³	semidirect
100. C₂×#2296	C₂³	semidirect
101. C₂×#2280	D₄	semidirect
103. C₂×#2280	C₂³	semidirect
104. C₂²×C₄×C₂²⋊C₄	D₄	semidirect
105. C₂²×C₄×C₂²⋊C₄	D₄	semidirect
106. C₂×#2010	C₂³	semidirect
107. #20902	C₂³	semidirect
108. #20898	C₂³	semidirect
109. C₂×#1733	C₂³	semidirect
110. C₂²×H(3,ℤ/4)	C₂³	semidirect
111. C₂²×H(3,ℤ/4)	C₂³	semidirect
112. C₂×#1728	C₂³	semidirect
113. #11083	C₂³	semidirect
114. #11041	C₂³	semidirect
115. #10994	C₂³	semidirect
116. #10716	C₂³	semidirect
122. C₂³×#41	C₂×D₄	semidirect
123. C₂³×#41	C₂×D₄	semidirect
130. C₂⁴×Q₈	C₂×D₄	semidirect
134. C₂⁴×D₄	C₂×D₄	semidirect
169. C₂×#525	C₂×D₄	semidirect
172. C₂×#525	C₂⁴	semidirect
173. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
174. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
175. C₂²×#121	C₂×D₄	semidirect
176. C₂²×#121	C₂×D₄	semidirect
184. C₂²×#117	C₂×D₄	semidirect
185. C₂²×#117	C₂×D₄	semidirect
200. C₂³×C₄²	C₂×D₄	semidirect
202. C₂×#421	C₂×D₄	semidirect
205. C₂×#421	C₂⁴	semidirect
207. C₂×#407	C₂×D₄	semidirect
209. C₂×#407	C₂⁴	semidirect
210. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
211. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
213. #2297	C₂⁴	semidirect
214. #2296	C₂⁴	semidirect
215. #2280	C₂×D₄	semidirect
217. #2280	C₂⁴	semidirect
218. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
219. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
220. #1733	C₂⁴	semidirect
221. C₂×H(3,ℤ/4)	C₂⁴	semidirect
222. C₂×H(3,ℤ/4)	C₂⁴	semidirect
223. #1728	C₂⁴	semidirect
236. C₂²×#41	#121	semidirect
240. C₂²×#41	C₂²×D₄	semidirect
244. C₂³×Q₈	#121	semidirect
247. C₂³×Q₈	C₂²×D₄	semidirect
248. C₂³×D₄	#121	semidirect
252. C₂³×D₄	C₂²×D₄	semidirect
370. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
371. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
372. C₂×#121	C₂²×D₄	semidirect
373. C₂×#121	C₂²×D₄	semidirect
374. C₂×#117	#120	semidirect
380. C₂×#117	C₂²×D₄	semidirect
390. C₂²×C₄²	#120	semidirect
395. C₂²×C₄²	C₂²×D₄	semidirect
397. #421	C₂²×D₄	semidirect
398. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
399. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
400. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
401. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
433. C₂×#41	C₂×#121	semidirect
436. C₂²×Q₈	C₂×#121	semidirect
439. C₂²×D₄	C₂×#121	semidirect
637. #117	C₂×#120	semidirect
641. C₂×C₄²	C₂×#120	semidirect
645. C₂⁴	#2010	semidirect
684. C₂×Q₈	C₂²×#121	semidirect
685. C₂×D₄	C₂²×#121	semidirect
848. C₄²	C₂²×#120	semidirect
855. C₂³	C₂×#2010	semidirect
946. C₂²	#394261	direct (N × H)
952. C₂²	C₂²×#2010	semidirect
969. C₂	C₂×#394261	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×#11083	2
C₂²×#11041	2
C₂²×#20902	2
C₂⁴×#421	2
C₂²×#20898	2
C₂²×#60359	2
C₂²×#10716	2
C₂²×#10994	2
C₂²×#34737	2
C₂²×#34736	2
C₂³×#2010	2
C₂×#394261	2

Subgroups — C22×#394261 #72303223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#394261 #72303223