Subgroups — C₂×#72239358 #72317118

Order 2048.

Only the 11928 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 944 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×#394068	C₂	1	4	yes	maximal, complemented
2	C₂×#394069	C₂	1	4	yes	maximal, complemented
3	C₂×#394067	C₂	1	4	yes	maximal, complemented
4	C₂×#357420	C₂	1	2	yes	maximal, complemented
5	C₂×#353426	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#20608	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#357480	C₂	1	2	yes	maximal, complemented
8	C₂²×#20959	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#23443	C₂	1	2	yes	maximal, complemented
10	C₂²×#20584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#62811	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#608658	C₂	1	2	yes	maximal, complemented
13	C₂²×#34736	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#3025	C₂	1	1	yes	maximal, characteristic, complemented
15	#72239358	C₂	1	32	yes	maximal, direct product factor
16	C₂×#394066	C₂	1	4	yes	maximal, complemented
17	C₂³×#585	C₂²	1	1	yes	characteristic
18	C₂⁵×#41	C₂²	1	1	yes	characteristic
19	C₂×#62811	C₂²	1	16	yes	complemented
20	C₂²×#3485	C₂²	1	4	yes	—
21	C₂²×#3484	C₂²	1	4	yes	—
22	C₂²×#3449	C₂²	1	2	yes	—
23	C₂³×#525	C₂²	1	1	yes	characteristic
24	C₂³×#525	C₂²	1	2	yes	—
25	C₂³×#525	C₂²	1	2	yes	complemented
26	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#3428	C₂²	1	1	yes	characteristic
28	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#3025	C₂²	1	16	yes	complemented
30	C₂³×#458	C₂²	1	4	yes	complemented
31	C₂³×B(4,𝔽₂)	C₂²	1	4	yes	complemented
32	C₂³×#410	C₂²	1	1	yes	characteristic
33	C₂³×#410	C₂²	1	1	yes	characteristic
34	C₂³×#410	C₂²	1	2	yes	complemented
35	C₂³×#410	C₂²	1	2	yes	complemented
36	C₂³×#410	C₂²	1	2	yes	complemented
37	C₂×#34736	C₂²	1	16	yes	complemented
38	C₂²×#2406	C₂²	1	2	yes	complemented
39	C₂²×#2404	C₂²	1	2	yes	complemented
40	C₂²×#2405	C₂²	1	2	yes	complemented
41	C₂²×#2403	C₂²	1	2	yes	complemented
42	C₂²×#2297	C₂²	1	1	yes	characteristic
43	C₂²×#2297	C₂²	1	2	yes	complemented
44	C₂²×#2297	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#2280	C₂²	1	2	yes	complemented
46	C₂²×#2280	C₂²	1	2	yes	complemented
47	C₂²×#2280	C₂²	1	1	yes	characteristic, complemented
48	C₂×#23443	C₂²	1	32	yes	complemented
49	C₂²×#2022	C₂²	1	8	yes	complemented
50	C₂²×#2021	C₂²	1	8	yes	complemented
51	C₂×#20959	C₂²	1	16	yes	complemented
52	C₂²×#1890	C₂²	1	4	yes	complemented
53	C₂²×#1889	C₂²	1	4	yes	complemented
54	C₂×#20608	C₂²	1	16	yes	complemented
55	C₂²×#1790	C₂²	1	4	yes	complemented
56	C₂²×#1790	C₂²	1	4	yes	complemented
57	C₂×#20584	C₂²	1	16	yes	complemented
58	C₂²×#1782	C₂²	1	4	yes	complemented
59	C₂²×#1781	C₂²	1	4	yes	complemented
60	C₂²×#1740	C₂²	1	2	yes	complemented
61	C₂²×#1740	C₂²	1	2	yes	complemented
62	#608658	C₂²	1	32	yes	complemented
63	C₂×#15069	C₂²	1	4	yes	complemented
64	C₂×#14911	C₂²	1	4	yes	complemented
65	C₂×#14911	C₂²	1	4	yes	complemented
66	C₂×#14715	C₂²	1	4	yes	complemented
67	C₂×#13756	C₂²	1	2	yes	complemented
68	#394069	C₂²	1	64	yes	complemented
69	#394068	C₂²	1	64	yes	complemented
70	#394067	C₂²	1	64	yes	complemented
71	#394066	C₂²	1	64	yes	complemented
72	#357480	C₂²	1	32	yes	complemented
73	C₂×#10995	C₂²	1	8	yes	complemented
74	C₂×#10995	C₂²	1	8	yes	complemented
75	#357420	C₂²	1	32	yes	complemented
76	C₂×#10966	C₂²	1	8	yes	complemented
77	C₂×#10965	C₂²	1	8	yes	complemented
78	#353426	C₂²	1	16	yes	complemented
79	C₂×#10745	C₂²	1	4	yes	complemented
80	C₂×#10745	C₂²	1	4	yes	complemented
81	C₂²×#585	D₄	1	16	yes	complemented
82	C₂²×#585	C₂³	1	8	yes	—
83	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
84	C₂⁴×#41	D₄	1	2	yes	complemented
85	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
86	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
87	C₂⁴×#41	D₄	1	8	yes	complemented
88	C₂⁴×#41	C₂³	1	1	yes	characteristic
89	C₂⁴×#41	C₂³	1	2	yes	—
90	C₂⁴×#41	C₂³	1	1	yes	characteristic
91	C₂⁴×#41	C₂³	1	2	yes	—
92	C₂⁴×#41	C₂³	1	8	yes	—
93	C₂⁵×Q₈	D₄	1	1	yes	characteristic, complemented
94	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
95	C₂⁵×D₄	C₂³	1	2	yes	—
96	C₂⁵×D₄	C₂³	1	1	yes	characteristic
97	C₂⁶×C₄	D₄	1	2	yes	complemented
98	C₂⁶×C₄	C₂³	1	1	yes	characteristic
99	C₂⁶×C₄	C₂³	1	1	yes	characteristic
100	C₂×#3485	C₂³	1	32	yes	—
101	C₂×#3484	C₂³	1	32	yes	—
102	C₂×#3449	D₄	1	32	yes	complemented
103	C₂×#3449	C₂³	1	16	yes	—
104	C₂²×#534	C₂³	1	8	yes	—
105	C₂²×#525	D₄	1	16	yes	complemented
106	C₂²×#525	D₄	1	16	yes	complemented
107	C₂²×#525	C₂³	1	16	yes	—
108	C₂²×#525	C₂³	1	8	yes	—
109	C₂²×#525	C₂³	1	16	yes	complemented
110	C₂²×#525	C₂³	1	8	yes	complemented
111	C₂³×#123	C₂³	1	4	yes	—
112	C₂³×#123	C₂³	1	2	yes	—
113	C₂³×#123	C₂³	1	4	yes	—
114	C₂³×#123	C₂³	1	2	yes	—
115	C₂³×C₂²⋊Q₈	D₄	1	4	yes	complemented
116	C₂³×#121	D₄	1	4	yes	complemented
117	C₂³×#120	C₂³	1	4	yes	—
118	C₂³×#120	C₂³	1	2	yes	—
119	C₂³×#120	C₂³	1	4	yes	—
120	C₂³×#120	C₂³	1	2	yes	—
121	C₂×#3428	D₄	1	16	yes	complemented
122	C₂×#3428	C₂³	1	8	yes	—
123	C₂²×#518	C₂³	1	4	yes	—
124	C₂³×C₄×D₄	D₄	1	8	yes	complemented
125	C₂³×C₄×D₄	C₂³	1	8	yes	complemented
126	C₂³×#117	C₂³	1	2	yes	—
127	C₂³×#117	C₂³	1	1	yes	characteristic
128	C₂³×#117	C₂³	1	1	yes	characteristic
129	C₂³×#117	C₂³	1	2	yes	—
130	C₂³×#117	C₂³	1	2	yes	—
131	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
133	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
134	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
135	C₂²×#458	C₂³	1	32	yes	complemented
136	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	complemented
137	C₂²×#410	D₄	1	16	yes	complemented
138	C₂²×#410	C₂³	1	8	yes	—
139	C₂²×#410	C₂³	1	8	yes	—
140	C₂²×#410	C₂³	1	16	yes	complemented
141	C₂²×#410	C₂³	1	16	yes	complemented
142	C₂²×#410	C₂³	1	16	yes	complemented
143	C₂³×#99	C₂³	1	4	yes	—
144	C₂³×#99	C₂³	1	8	yes	—
145	C₂³×#99	C₂³	1	8	yes	—
146	C₂³×#99	C₂³	1	8	yes	—
147	C₂³×#99	C₂³	1	4	yes	—
148	C₂×#2406	C₂³	1	16	yes	complemented
149	C₂×#2404	C₂³	1	16	yes	complemented
150	C₂×#2405	C₂³	1	16	yes	complemented
151	C₂×#2403	C₂³	1	16	yes	complemented
152	C₂×#2297	D₄	1	16	yes	complemented
153	C₂×#2297	C₂³	1	8	yes	—
154	C₂×#2297	C₂³	1	8	yes	complemented
155	C₂×#2297	C₂³	1	16	yes	complemented
156	C₂²×#386	C₂³	1	2	yes	—
157	C₂²×#386	C₂³	1	2	yes	—
158	C₂²×#386	C₂³	1	2	yes	—
159	C₂²×#386	C₂³	1	2	yes	—
160	C₂²×#386	C₂³	1	4	yes	—
161	C₂²×#386	C₂³	1	4	yes	—
162	C₂×#2280	C₂³	1	8	yes	complemented
163	C₂×#2280	C₂³	1	16	yes	complemented
164	C₂×#2280	C₂³	1	16	yes	complemented
165	C₂²×#381	C₂³	1	2	yes	—
166	C₂²×#381	C₂³	1	4	yes	—
167	C₂²×#381	C₂³	1	4	yes	—
168	C₂²×#379	C₂³	1	2	yes	—
169	C₂²×#379	C₂³	1	4	yes	—
170	C₂²×#379	C₂³	1	4	yes	—
171	C₂×#2022	C₂³	1	64	yes	complemented
172	C₂×#2021	C₂³	1	64	yes	complemented
173	C₂×#1890	C₂³	1	32	yes	complemented
174	C₂×#1889	C₂³	1	32	yes	complemented
175	C₂×#1790	C₂³	1	32	yes	complemented
176	C₂×#1790	C₂³	1	32	yes	complemented
177	C₂×#1782	C₂³	1	32	yes	complemented
178	C₂×#1781	C₂³	1	32	yes	complemented
179	C₂×#1740	C₂³	1	16	yes	complemented
180	C₂×#1740	C₂³	1	16	yes	complemented
181	C₂²×#342	C₂³	1	8	yes	—
182	C₂²×#342	C₂³	1	8	yes	—
183	#15069	C₂³	1	32	yes	complemented
184	#14911	C₂³	1	32	yes	complemented
185	#14911	C₂³	1	32	yes	complemented
186	#14715	C₂³	1	32	yes	complemented
187	#13756	C₂³	1	16	yes	complemented
188	C₂×C₂²⋊#95	C₂³	1	4	yes	—
189	C₂×C₂²⋊#95	C₂³	1	4	yes	—
190	#10995	C₂³	1	64	yes	complemented
191	#10995	C₂³	1	64	yes	complemented
192	#10966	C₂³	1	64	yes	complemented
193	#10965	C₂³	1	64	yes	complemented
194	#10745	C₂³	1	32	yes	complemented
195	#10745	C₂³	1	32	yes	complemented
196	C₂⁷	C₂×D₄	1	2	yes	—
197	C₂⁷	C₂⁴	1	1	yes	characteristic
198	C₂⁷	C₂⁴	1	1	yes	characteristic
199	C₂×#585	C₂×D₄	1	64	yes	complemented
200	C₂²×H(5,𝔽₂)	C₂×D₄	1	32	yes	—
201	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
202	C₂³×#41	C₂×D₄	1	8	yes	—
203	C₂³×#41	C₂×D₄	1	8	yes	—
204	C₂³×#41	C₂×D₄	1	8	yes	—
205	C₂³×#41	C₂×D₄	1	8	yes	—
206	C₂³×#41	C₂×D₄	1	16	yes	—
207	C₂³×#41	C₂×D₄	1	16	yes	—
208	C₂³×#41	C₂×D₄	1	16	yes	—
209	C₂³×#41	C₂×D₄	1	8	yes	—
210	C₂³×#41	C₂×D₄	1	8	yes	—
211	C₂³×#41	C₂×D₄	1	4	yes	—
212	C₂³×#41	C₂×D₄	1	4	yes	—
213	C₂³×#41	C₂×D₄	1	8	yes	—
214	C₂³×#41	C₂×D₄	1	16	yes	complemented
215	C₂³×#41	C₂×D₄	1	8	yes	complemented
216	C₂³×#41	C₂×D₄	1	8	yes	complemented
217	C₂³×#41	#41	1	8	yes	—
218	C₂³×#41	C₂⁴	1	8	yes	—
219	C₂³×#41	C₂⁴	1	4	yes	—
220	C₂³×#41	C₂⁴	1	8	yes	—
221	C₂³×#41	C₂⁴	1	4	yes	—
222	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
225	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
226	C₂⁴×Q₈	C₂×D₄	1	8	yes	complemented
227	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
228	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂⁴×D₄	C₂×D₄	1	2	yes	—
230	C₂⁴×D₄	C₂×D₄	1	2	yes	—
231	C₂⁴×D₄	C₂×D₄	1	2	yes	—
232	C₂⁴×D₄	C₂×D₄	1	2	yes	—
233	C₂⁴×D₄	C₂×D₄	1	8	yes	—
234	C₂⁴×D₄	C₂×D₄	1	8	yes	—
235	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
236	C₂⁴×D₄	C₂⁴	1	2	yes	—
237	C₂⁴×D₄	C₂⁴	1	2	yes	—
238	C₂⁴×D₄	C₂⁴	1	4	yes	—
239	C₂⁴×D₄	C₂⁴	1	8	yes	—
240	C₂⁴×D₄	C₂⁴	1	4	yes	—
241	C₂⁵×C₄	C₂×D₄	1	2	yes	—
242	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
243	C₂⁵×C₄	C₂×D₄	1	2	yes	—
244	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
245	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
246	C₂⁵×C₄	C₂×D₄	1	4	yes	—
247	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
248	C₂⁵×C₄	C₂×D₄	1	4	yes	—
249	C₂⁵×C₄	C₂×D₄	1	4	yes	—
250	C₂⁵×C₄	C₂×D₄	1	8	yes	—
251	C₂⁵×C₄	C₂×D₄	1	4	yes	—
252	C₂⁵×C₄	C₂×D₄	1	2	yes	—
253	C₂⁵×C₄	C₂×D₄	1	2	yes	—
254	C₂⁵×C₄	C₂×D₄	1	2	yes	—
255	C₂⁵×C₄	C₂×D₄	1	16	yes	complemented
256	C₂⁵×C₄	C₂×D₄	1	8	yes	complemented
257	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
258	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
259	C₂⁵×C₄	C₂⁴	1	4	yes	—
260	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
261	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
262	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
263	C₂⁵×C₄	C₂⁴	1	4	yes	—
264	#3449	C₂×D₄	1	128	yes	complemented
265	C₂×#534	C₂×D₄	1	64	yes	—
266	C₂×#534	C₂⁴	1	32	yes	—
267	C₂×#525	C₂×D₄	1	64	yes	complemented
268	C₂²×#123	C₂×D₄	1	16	yes	—
269	C₂²×#123	C₂×D₄	1	16	yes	complemented
270	C₂²×#123	C₂⁴	1	16	yes	—
271	C₂²×#123	C₂⁴	1	8	yes	—
272	C₂²×#123	C₂⁴	1	16	yes	—
273	C₂²×#123	C₂⁴	1	8	yes	—
274	C₂²×C₂²⋊Q₈	C₂×D₄	1	32	yes	complemented
275	C₂²×#121	C₂×D₄	1	32	yes	complemented
276	C₂²×#120	C₂×D₄	1	16	yes	—
277	C₂²×#120	C₂×D₄	1	16	yes	complemented
278	C₂²×#120	C₂⁴	1	16	yes	—
279	C₂²×#120	C₂⁴	1	8	yes	—
280	C₂²×#120	C₂⁴	1	16	yes	—
281	C₂²×#120	C₂⁴	1	8	yes	—
282	#3428	C₂×D₄	1	64	yes	complemented
283	C₂×#518	C₂×D₄	1	32	yes	—
284	C₂×#518	C₂⁴	1	16	yes	—
285	C₂²×C₄×D₄	C₂×D₄	1	64	yes	complemented
286	C₂²×#117	C₂×D₄	1	16	yes	—
287	C₂²×#117	C₂×D₄	1	16	yes	—
288	C₂²×#117	C₂×D₄	1	8	yes	—
289	C₂²×#117	C₂×D₄	1	16	yes	complemented
290	C₂²×#117	C₂×D₄	1	8	yes	complemented
291	C₂²×#117	C₂×D₄	1	8	yes	complemented
292	C₂²×#117	C₂⁴	1	8	yes	—
293	C₂²×#117	C₂⁴	1	4	yes	—
294	C₂²×#117	C₂⁴	1	4	yes	—
295	C₂²×#117	C₂⁴	1	8	yes	—
296	C₂²×#117	C₂⁴	1	8	yes	—
297	C₂³×C₄⋊C₄	C₂×D₄	1	4	yes	—
298	C₂³×C₄⋊C₄	C₂×D₄	1	8	yes	—
299	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
300	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
301	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
302	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
303	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
304	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
305	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
306	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
307	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
308	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
309	C₂³×C₄²	C₂×D₄	1	4	yes	—
310	C₂³×C₄²	C₂×D₄	1	8	yes	complemented
311	C₂³×C₄²	C₂⁴	1	4	yes	—
312	C₂×#410	C₂×D₄	1	64	yes	complemented
313	C₂²×#99	C₂×D₄	1	32	yes	complemented
314	C₂²×#99	C₂⁴	1	16	yes	—
315	C₂²×#99	C₂⁴	1	32	yes	—
316	C₂²×#99	C₂⁴	1	32	yes	—
317	C₂²×#99	C₂⁴	1	32	yes	—
318	C₂²×#99	C₂⁴	1	16	yes	—
319	#2297	C₂×D₄	1	64	yes	complemented
320	C₂×#386	C₂×D₄	1	16	yes	complemented
321	C₂×#386	C₂×D₄	1	16	yes	complemented
322	C₂×#386	C₂⁴	1	16	yes	—
323	C₂×#386	C₂⁴	1	8	yes	—
324	C₂×#386	C₂⁴	1	8	yes	—
325	C₂×#386	C₂⁴	1	16	yes	—
326	C₂×#386	C₂⁴	1	8	yes	—
327	C₂×#386	C₂⁴	1	8	yes	—
328	C₂×#381	C₂⁴	1	16	yes	—
329	C₂×#381	C₂⁴	1	16	yes	—
330	C₂×#381	C₂⁴	1	8	yes	—
331	C₂×#379	C₂⁴	1	16	yes	—
332	C₂×#379	C₂⁴	1	16	yes	—
333	C₂×#379	C₂⁴	1	8	yes	—
334	C₂×#342	C₂⁴	1	32	yes	—
335	C₂×#342	C₂⁴	1	32	yes	—
336	C₂²⋊#95	C₂⁴	1	16	yes	—
337	C₂²⋊#95	C₂⁴	1	16	yes	—
338	C₂⁶	C₂²×D₄	1	2	yes	—
339	C₂⁶	C₂²×D₄	1	1	yes	characteristic
340	C₂⁶	C₂²×D₄	1	2	yes	—
341	C₂⁶	C₂²×D₄	1	1	yes	characteristic
342	C₂⁶	C₂²×D₄	1	2	yes	—
343	C₂⁶	C₂²×D₄	1	4	yes	—
344	C₂⁶	C₂²×D₄	1	4	yes	—
345	C₂⁶	C₂²×D₄	1	4	yes	—
346	C₂⁶	C₂²×D₄	1	8	yes	—
347	C₂⁶	C₂²×D₄	1	4	yes	—
348	C₂⁶	C₂⁵	1	1	yes	characteristic
349	C₂⁶	C₂⁵	1	2	yes	—
350	C₂⁶	C₂⁵	1	2	yes	—
351	C₂×H(5,𝔽₂)	C₂²×D₄	1	64	yes	—
352	C₂²×#41	#120	1	32	yes	—
353	C₂²×#41	#120	1	32	yes	—
354	C₂²×#41	#120	1	32	yes	—
355	C₂²×#41	#120	1	64	yes	—
356	C₂²×#41	#120	1	64	yes	complemented
357	C₂²×#41	#121	1	32	yes	—
358	C₂²×#41	#121	1	64	yes	—
359	C₂²×#41	#121	1	64	yes	—
360	C₂²×#41	#127	1	64	yes	—
361	C₂²×#41	C₂²×D₄	1	32	yes	—
362	C₂²×#41	C₂²×D₄	1	16	yes	—
363	C₂²×#41	C₂²×D₄	1	16	yes	—
364	C₂²×#41	C₂²×D₄	1	16	yes	—
365	C₂²×#41	C₂²×D₄	1	16	yes	—
366	C₂²×#41	C₂²×D₄	1	32	yes	—
367	C₂²×#41	C₂²×D₄	1	32	yes	—
368	C₂²×#41	C₂²×D₄	1	16	yes	—
369	C₂²×#41	C₂×#41	1	16	yes	—
370	C₂³×Q₈	#120	1	8	yes	—
371	C₂³×Q₈	#120	1	8	yes	—
372	C₂³×Q₈	#120	1	8	yes	—
373	C₂³×Q₈	#120	1	16	yes	complemented
374	C₂³×Q₈	#121	1	8	yes	—
375	C₂³×Q₈	C₂²×D₄	1	8	yes	—
376	C₂³×Q₈	C₂²×D₄	1	4	yes	—
377	C₂³×Q₈	C₂²×D₄	1	4	yes	—
378	C₂³×Q₈	C₂²×D₄	1	8	yes	—
379	C₂³×D₄	#120	1	8	yes	—
380	C₂³×D₄	#120	1	8	yes	—
381	C₂³×D₄	#120	1	8	yes	—
382	C₂³×D₄	#120	1	16	yes	complemented
383	C₂³×D₄	#121	1	8	yes	—
384	C₂³×D₄	C₂²×D₄	1	8	yes	—
385	C₂³×D₄	C₂²×D₄	1	8	yes	—
386	C₂³×D₄	C₂²×D₄	1	8	yes	—
387	C₂³×D₄	C₂²×D₄	1	8	yes	—
388	C₂³×D₄	C₂²×D₄	1	16	yes	—
389	C₂³×D₄	C₂²×D₄	1	16	yes	—
390	C₂³×D₄	C₂²×D₄	1	16	yes	—
391	C₂³×D₄	C₂²×D₄	1	8	yes	—
392	C₂³×D₄	C₂²×D₄	1	4	yes	—
393	C₂³×D₄	C₂²×D₄	1	4	yes	—
394	C₂³×D₄	C₂²×D₄	1	4	yes	—
395	C₂³×D₄	C₂²×D₄	1	4	yes	—
396	C₂³×D₄	C₂²×D₄	1	8	yes	—
397	C₂³×D₄	C₂²×D₄	1	8	yes	—
398	C₂³×D₄	C₂²×D₄	1	8	yes	—
399	C₂³×D₄	C₂²×D₄	1	8	yes	—
400	C₂³×D₄	C₂²×D₄	1	8	yes	—
401	C₂³×D₄	C₂²×D₄	1	32	yes	—
402	C₂³×D₄	C₂×#41	1	8	yes	—
403	C₂³×D₄	C₂⁵	1	4	yes	—
404	C₂³×D₄	C₂⁵	1	4	yes	—
405	C₂³×D₄	C₂⁵	1	8	yes	—
406	C₂⁴×C₄	#120	1	16	yes	—
407	C₂⁴×C₄	#120	1	16	yes	—
408	C₂⁴×C₄	#120	1	4	yes	—
409	C₂⁴×C₄	#120	1	4	yes	—
410	C₂⁴×C₄	#120	1	4	yes	—
411	C₂⁴×C₄	#120	1	16	yes	—
412	C₂⁴×C₄	#120	1	2	yes	—
413	C₂⁴×C₄	#120	1	16	yes	—
414	C₂⁴×C₄	#120	1	4	yes	—
415	C₂⁴×C₄	#120	1	4	yes	—
416	C₂⁴×C₄	#120	1	2	yes	—
417	C₂⁴×C₄	#120	1	4	yes	—
418	C₂⁴×C₄	#120	1	16	yes	—
419	C₂⁴×C₄	#120	1	2	yes	—
420	C₂⁴×C₄	#120	1	2	yes	—
421	C₂⁴×C₄	#120	1	32	yes	complemented
422	C₂⁴×C₄	#121	1	16	yes	—
423	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
425	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
426	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
427	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
428	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
429	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
430	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
431	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
432	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
433	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
434	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
435	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
436	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
437	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
438	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
439	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
440	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
441	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
442	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
443	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
444	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
445	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
446	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
447	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
448	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
449	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
450	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
451	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
452	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
453	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
454	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
455	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
456	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
457	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
458	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
459	C₂⁴×C₄	C₂²×D₄	1	16	yes	complemented
460	C₂⁴×C₄	C₂×#41	1	4	yes	—
461	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
462	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
463	C₂⁴×C₄	C₂⁵	1	2	yes	—
464	C₂⁴×C₄	C₂⁵	1	2	yes	—
465	C₂⁴×C₄	C₂⁵	1	2	yes	—
466	C₂⁴×C₄	C₂⁵	1	2	yes	—
467	C₂⁴×C₄	C₂⁵	1	2	yes	—
468	#534	C₂²×D₄	1	128	yes	—
469	C₂×#123	C₂²×D₄	1	32	yes	complemented
470	C₂×#120	C₂²×D₄	1	32	yes	complemented
471	#518	C₂²×D₄	1	64	yes	—
472	C₂×#117	#120	1	64	yes	complemented
473	C₂×#117	C₂²×D₄	1	32	yes	—
474	C₂×#117	C₂²×D₄	1	32	yes	—
475	C₂×#117	C₂²×D₄	1	32	yes	complemented
476	C₂×#117	C₂²×D₄	1	16	yes	complemented
477	C₂×#117	C₂²×D₄	1	16	yes	complemented
478	C₂²×C₄⋊C₄	#120	1	32	yes	complemented
479	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	—
480	C₂²×C₄⋊C₄	C₂²×D₄	1	32	yes	—
481	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
482	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
483	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
484	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
485	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
486	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
487	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
488	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
489	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
490	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
491	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
492	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
493	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
494	C₂²×C₄²	#120	1	32	yes	complemented
495	C₂²×C₄²	C₂²×D₄	1	16	yes	—
496	C₂²×C₄²	C₂²×D₄	1	16	yes	complemented
497	C₂×#99	C₂²×D₄	1	64	yes	complemented
498	#386	C₂²×D₄	1	32	yes	complemented
499	#386	C₂²×D₄	1	32	yes	complemented
500	C₂⁵	C₂×#120	1	8	yes	—
501	C₂⁵	C₂×#120	1	8	yes	—
502	C₂⁵	C₂×#120	1	2	yes	—
503	C₂⁵	C₂×#120	1	8	yes	—
504	C₂⁵	C₂×#120	1	2	yes	—
505	C₂⁵	C₂×#120	1	2	yes	—
506	C₂⁵	C₂×#120	1	8	yes	—
507	C₂⁵	C₂×#120	1	16	yes	—
508	C₂⁵	C₂×#120	1	2	yes	—
509	C₂⁵	C₂×#121	1	8	yes	—
510	C₂⁵	C₂³×D₄	1	4	yes	—
511	C₂⁵	C₂³×D₄	1	8	yes	—
512	C₂⁵	C₂³×D₄	1	8	yes	—
513	C₂⁵	C₂³×D₄	1	2	yes	—
514	C₂⁵	C₂³×D₄	1	2	yes	—
515	C₂⁵	C₂³×D₄	1	4	yes	—
516	C₂⁵	C₂³×D₄	1	1	yes	characteristic
517	C₂⁵	C₂³×D₄	1	1	yes	characteristic
518	C₂⁵	C₂³×D₄	1	2	yes	—
519	C₂⁵	C₂³×D₄	1	2	yes	—
520	C₂⁵	C₂³×D₄	1	2	yes	—
521	C₂⁵	C₂³×D₄	1	4	yes	—
522	C₂⁵	C₂³×D₄	1	2	yes	—
523	C₂⁵	C₂³×D₄	1	4	yes	—
524	C₂⁵	C₂³×D₄	1	2	yes	—
525	C₂⁵	C₂³×D₄	1	2	yes	—
526	C₂⁵	C₂³×D₄	1	2	yes	—
527	C₂⁵	C₂²×#41	1	2	yes	—
528	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
529	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
530	C₂⁵	C₂⁶	1	1	yes	characteristic
531	C₂×#41	#392	1	256	yes	complemented
532	C₂×#41	C₂×#120	1	64	yes	—
533	C₂×#41	C₂×#121	1	64	yes	—
534	C₂×#41	C₂×#121	1	64	yes	—
535	C₂×#41	C₂×#127	1	64	yes	—
536	C₂²×Q₈	#392	1	64	yes	complemented
537	C₂²×Q₈	C₂×#120	1	16	yes	—
538	C₂²×Q₈	C₂×#120	1	16	yes	—
539	C₂²×Q₈	C₂×#120	1	16	yes	—
540	C₂²×Q₈	C₂×#120	1	32	yes	complemented
541	C₂²×Q₈	C₂×#121	1	16	yes	—
542	C₂²×D₄	#392	1	64	yes	complemented
543	C₂²×D₄	C₂×#120	1	32	yes	—
544	C₂²×D₄	C₂×#120	1	16	yes	—
545	C₂²×D₄	C₂×#120	1	16	yes	—
546	C₂²×D₄	C₂×#120	1	16	yes	—
547	C₂²×D₄	C₂×#120	1	16	yes	—
548	C₂²×D₄	C₂×#120	1	16	yes	—
549	C₂²×D₄	C₂×#120	1	16	yes	—
550	C₂²×D₄	C₂×#120	1	32	yes	—
551	C₂²×D₄	C₂×#120	1	32	yes	complemented
552	C₂²×D₄	C₂×#121	1	32	yes	—
553	C₂²×D₄	C₂×#121	1	32	yes	—
554	C₂²×D₄	C₂×#121	1	16	yes	—
555	C₂²×D₄	C₂×#121	1	16	yes	—
556	C₂²×D₄	C₂×#127	1	32	yes	—
557	C₂²×D₄	C₂³×D₄	1	8	yes	—
558	C₂²×D₄	C₂³×D₄	1	8	yes	—
559	C₂²×D₄	C₂³×D₄	1	8	yes	—
560	C₂²×D₄	C₂³×D₄	1	8	yes	—
561	C₂²×D₄	C₂³×D₄	1	16	yes	—
562	C₂²×D₄	C₂³×D₄	1	16	yes	—
563	C₂²×D₄	C₂³×D₄	1	16	yes	—
564	C₂²×D₄	C₂³×D₄	1	8	yes	—
565	C₂²×D₄	C₂²×#41	1	8	yes	—
566	C₂³×C₄	#392	1	128	yes	complemented
567	C₂³×C₄	C₂×#120	1	4	yes	—
568	C₂³×C₄	C₂×#120	1	4	yes	—
569	C₂³×C₄	C₂×#120	1	8	yes	—
570	C₂³×C₄	C₂×#120	1	2	yes	—
571	C₂³×C₄	C₂×#120	1	4	yes	—
572	C₂³×C₄	C₂×#120	1	2	yes	—
573	C₂³×C₄	C₂×#120	1	1	yes	characteristic
574	C₂³×C₄	C₂×#120	1	4	yes	—
575	C₂³×C₄	C₂×#120	1	2	yes	—
576	C₂³×C₄	C₂×#120	1	4	yes	—
577	C₂³×C₄	C₂×#120	1	8	yes	—
578	C₂³×C₄	C₂×#120	1	4	yes	—
579	C₂³×C₄	C₂×#120	1	8	yes	—
580	C₂³×C₄	C₂×#120	1	8	yes	—
581	C₂³×C₄	C₂×#120	1	16	yes	—
582	C₂³×C₄	C₂×#120	1	8	yes	—
583	C₂³×C₄	C₂×#120	1	16	yes	—
584	C₂³×C₄	C₂×#120	1	8	yes	—
585	C₂³×C₄	C₂×#120	1	4	yes	—
586	C₂³×C₄	C₂×#120	1	4	yes	—
587	C₂³×C₄	C₂×#120	1	16	yes	—
588	C₂³×C₄	C₂×#120	1	8	yes	—
589	C₂³×C₄	C₂×#120	1	8	yes	—
590	C₂³×C₄	C₂×#120	1	8	yes	—
591	C₂³×C₄	C₂×#120	1	32	yes	—
592	C₂³×C₄	C₂×#120	1	32	yes	—
593	C₂³×C₄	C₂×#120	1	32	yes	—
594	C₂³×C₄	C₂×#120	1	16	yes	—
595	C₂³×C₄	C₂×#120	1	8	yes	—
596	C₂³×C₄	C₂×#120	1	8	yes	—
597	C₂³×C₄	C₂×#120	1	16	yes	—
598	C₂³×C₄	C₂×#120	1	8	yes	—
599	C₂³×C₄	C₂×#120	1	8	yes	—
600	C₂³×C₄	C₂×#120	1	2	yes	—
601	C₂³×C₄	C₂×#120	1	2	yes	—
602	C₂³×C₄	C₂×#120	1	8	yes	—
603	C₂³×C₄	C₂×#120	1	2	yes	—
604	C₂³×C₄	C₂×#120	1	2	yes	—
605	C₂³×C₄	C₂×#120	1	8	yes	—
606	C₂³×C₄	C₂×#120	1	32	yes	—
607	C₂³×C₄	C₂×#120	1	16	yes	—
608	C₂³×C₄	C₂×#120	1	1	yes	characteristic
609	C₂³×C₄	C₂×#120	1	64	yes	complemented
610	C₂³×C₄	C₂×#121	1	16	yes	—
611	C₂³×C₄	C₂×#121	1	4	yes	—
612	C₂³×C₄	C₂×#121	1	4	yes	—
613	C₂³×C₄	C₂×#121	1	16	yes	—
614	C₂³×C₄	C₂×#121	1	8	yes	—
615	C₂³×C₄	C₂×#121	1	8	yes	—
616	C₂³×C₄	C₂×#121	1	32	yes	—
617	C₂³×C₄	C₂×#127	1	16	yes	—
618	C₂³×C₄	#534	1	4	yes	—
619	C₂³×C₄	#534	1	4	yes	—
620	C₂³×C₄	#534	1	8	yes	—
621	C₂³×C₄	#534	1	8	yes	—
622	C₂³×C₄	#534	1	32	yes	—
623	C₂³×C₄	#534	1	4	yes	—
624	C₂³×C₄	#534	1	4	yes	—
625	C₂³×C₄	#535	1	32	yes	—
626	C₂³×C₄	D₄²	1	8	yes	—
627	C₂³×C₄	D₄²	1	16	yes	—
628	C₂³×C₄	D₄²	1	32	yes	—
629	C₂³×C₄	D₄²	1	8	yes	—
630	C₂³×C₄	D₄²	1	8	yes	—
631	C₂³×C₄	D₄²	1	8	yes	—
632	C₂³×C₄	D₄²	1	16	yes	—
633	C₂³×C₄	D₄²	1	16	yes	—
634	C₂³×C₄	D₄²	1	32	yes	—
635	C₂³×C₄	D₄²	1	32	yes	—
636	C₂³×C₄	D₄²	1	8	yes	—
637	C₂³×C₄	D₄²	1	8	yes	—
638	C₂³×C₄	#546	1	8	yes	—
639	C₂³×C₄	#546	1	16	yes	—
640	C₂³×C₄	#546	1	32	yes	—
641	C₂³×C₄	#546	1	8	yes	—
642	C₂³×C₄	C₂³×D₄	1	2	yes	—
643	C₂³×C₄	C₂³×D₄	1	2	yes	—
644	C₂³×C₄	C₂³×D₄	1	4	yes	—
645	C₂³×C₄	C₂³×D₄	1	4	yes	—
646	C₂³×C₄	C₂³×D₄	1	4	yes	—
647	C₂³×C₄	C₂³×D₄	1	8	yes	—
648	C₂³×C₄	C₂³×D₄	1	4	yes	—
649	C₂³×C₄	C₂³×D₄	1	4	yes	—
650	C₂³×C₄	C₂³×D₄	1	4	yes	—
651	C₂³×C₄	C₂³×D₄	1	4	yes	—
652	C₂³×C₄	C₂³×D₄	1	4	yes	—
653	C₂³×C₄	C₂³×D₄	1	16	yes	—
654	C₂³×C₄	C₂³×D₄	1	8	yes	—
655	C₂³×C₄	C₂³×D₄	1	8	yes	—
656	C₂³×C₄	C₂³×D₄	1	2	yes	—
657	C₂³×C₄	C₂³×D₄	1	4	yes	—
658	C₂³×C₄	C₂³×D₄	1	2	yes	—
659	C₂³×C₄	C₂³×D₄	1	4	yes	—
660	C₂³×C₄	C₂³×D₄	1	4	yes	—
661	C₂³×C₄	C₂³×D₄	1	4	yes	—
662	C₂³×C₄	C₂²×#41	1	4	yes	—
663	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
664	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
665	C₂×C₄⋊C₄	C₂×#120	1	64	yes	complemented
666	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	—
667	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
668	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
669	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
670	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
671	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
672	C₂×C₄²	C₂×#120	1	64	yes	complemented
673	C₂⁴	C₂×#392	1	32	yes	—
674	C₂⁴	#3025	1	8	yes	complemented
675	C₂⁴	C₂²×#120	1	2	yes	—
676	C₂⁴	C₂²×#120	1	4	yes	—
677	C₂⁴	C₂²×#120	1	1	yes	characteristic
678	C₂⁴	C₂²×#120	1	2	yes	—
679	C₂⁴	C₂²×#120	1	2	yes	—
680	C₂⁴	C₂²×#120	1	4	yes	—
681	C₂⁴	C₂²×#120	1	1	yes	characteristic
682	C₂⁴	C₂²×#120	1	4	yes	—
683	C₂⁴	C₂²×#120	1	4	yes	—
684	C₂⁴	C₂²×#120	1	2	yes	—
685	C₂⁴	C₂²×#120	1	2	yes	—
686	C₂⁴	C₂²×#120	1	2	yes	—
687	C₂⁴	C₂²×#120	1	2	yes	—
688	C₂⁴	C₂²×#120	1	4	yes	—
689	C₂⁴	C₂²×#120	1	4	yes	—
690	C₂⁴	C₂²×#120	1	8	yes	—
691	C₂⁴	C₂²×#120	1	16	yes	—
692	C₂⁴	C₂²×#120	1	8	yes	—
693	C₂⁴	C₂²×#120	1	8	yes	—
694	C₂⁴	C₂²×#120	1	4	yes	—
695	C₂⁴	C₂²×#121	1	2	yes	—
696	C₂⁴	C₂²×#121	1	2	yes	—
697	C₂⁴	C₂²×#121	1	4	yes	—
698	C₂⁴	C₂²×#121	1	4	yes	—
699	C₂⁴	C₂²×#121	1	8	yes	—
700	C₂⁴	C₂²×#127	1	4	yes	—
701	C₂⁴	C₂×#534	1	2	yes	—
702	C₂⁴	C₂×#534	1	2	yes	—
703	C₂⁴	C₂×#534	1	2	yes	—
704	C₂⁴	C₂×#534	1	8	yes	—
705	C₂⁴	C₂×#534	1	2	yes	—
706	C₂⁴	C₂×#535	1	8	yes	—
707	C₂⁴	C₂×D₄²	1	4	yes	—
708	C₂⁴	C₂×D₄²	1	8	yes	—
709	C₂⁴	C₂×D₄²	1	4	yes	—
710	C₂⁴	C₂×D₄²	1	4	yes	—
711	C₂⁴	C₂×D₄²	1	4	yes	—
712	C₂⁴	C₂×D₄²	1	4	yes	—
713	C₂⁴	C₂×D₄²	1	8	yes	—
714	C₂⁴	C₂×D₄²	1	8	yes	—
715	C₂⁴	C₂×D₄²	1	4	yes	—
716	C₂⁴	C₂×#546	1	4	yes	—
717	C₂⁴	C₂×#546	1	4	yes	—
718	C₂⁴	C₂×#546	1	8	yes	—
719	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
720	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
721	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
722	C₂⁴	C₂⁴×D₄	1	2	yes	—
723	C₂⁴	C₂⁴×D₄	1	2	yes	—
724	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
725	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
726	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
727	C₂⁴	C₂³×#41	1	1	yes	characteristic
728	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
729	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
730	C₂×Q₈	C₂×#392	1	64	yes	complemented
731	C₂×D₄	C₂×#392	1	64	yes	—
732	C₂×D₄	C₂×#392	1	64	yes	complemented
733	C₂×D₄	C₂²×#120	1	16	yes	—
734	C₂×D₄	C₂²×#121	1	16	yes	—
735	C₂×D₄	C₂²×#121	1	16	yes	—
736	C₂×D₄	C₂²×#127	1	16	yes	—
737	C₂²×C₄	C₂×#392	1	16	yes	—
738	C₂²×C₄	C₂×#392	1	16	yes	—
739	C₂²×C₄	C₂×#392	1	32	yes	—
740	C₂²×C₄	C₂×#392	1	32	yes	—
741	C₂²×C₄	C₂×#392	1	128	yes	complemented
742	C₂²×C₄	#2403	1	16	yes	—
743	C₂²×C₄	#2403	1	8	yes	—
744	C₂²×C₄	#2403	1	8	yes	—
745	C₂²×C₄	#2403	1	16	yes	—
746	C₂²×C₄	#2403	1	16	yes	—
747	C₂²×C₄	#2403	1	32	yes	—
748	C₂²×C₄	#2403	1	16	yes	—
749	C₂²×C₄	#2403	1	32	yes	—
750	C₂²×C₄	#2403	1	32	yes	—
751	C₂²×C₄	#2403	1	64	yes	—
752	C₂²×C₄	#2403	1	4	yes	—
753	C₂²×C₄	#2403	1	8	yes	—
754	C₂²×C₄	#2403	1	4	yes	—
755	C₂²×C₄	#2408	1	32	yes	—
756	C₂²×C₄	#2408	1	64	yes	—
757	C₂²×C₄	#2408	1	32	yes	—
758	C₂²×C₄	#2410	1	4	yes	—
759	C₂²×C₄	#2410	1	8	yes	—
760	C₂²×C₄	#2410	1	16	yes	—
761	C₂²×C₄	#2410	1	8	yes	—
762	C₂²×C₄	#2410	1	8	yes	—
763	C₂²×C₄	#2410	1	16	yes	—
764	C₂²×C₄	#2410	1	16	yes	—
765	C₂²×C₄	#2410	1	32	yes	—
766	C₂²×C₄	#2410	1	16	yes	—
767	C₂²×C₄	#2410	1	32	yes	—
768	C₂²×C₄	#2410	1	32	yes	—
769	C₂²×C₄	#2410	1	64	yes	—
770	C₂²×C₄	#2410	1	4	yes	—
771	C₂²×C₄	#2433	1	32	yes	—
772	C₂²×C₄	#2433	1	64	yes	—
773	C₂²×C₄	#2433	1	32	yes	—
774	C₂²×C₄	#2613	1	16	yes	—
775	C₂²×C₄	#2613	1	16	yes	—
776	C₂²×C₄	#2613	1	32	yes	—
777	C₂²×C₄	#2846	1	4	yes	—
778	C₂²×C₄	#2846	1	8	yes	—
779	C₂²×C₄	#2846	1	8	yes	—
780	C₂²×C₄	#2846	1	8	yes	—
781	C₂²×C₄	#2846	1	16	yes	—
782	C₂²×C₄	#2846	1	16	yes	—
783	C₂²×C₄	#2846	1	4	yes	—
784	C₂²×C₄	C₂²×#120	1	2	yes	—
785	C₂²×C₄	C₂²×#120	1	4	yes	—
786	C₂²×C₄	C₂²×#120	1	4	yes	—
787	C₂²×C₄	C₂²×#120	1	2	yes	—
788	C₂²×C₄	C₂²×#120	1	8	yes	—
789	C₂²×C₄	C₂²×#120	1	4	yes	—
790	C₂²×C₄	C₂²×#120	1	8	yes	—
791	C₂²×C₄	C₂²×#120	1	8	yes	—
792	C₂²×C₄	C₂²×#120	1	8	yes	—
793	C₂²×C₄	C₂²×#120	1	4	yes	—
794	C₂²×C₄	C₂²×#120	1	4	yes	—
795	C₂²×C₄	C₂²×#120	1	4	yes	—
796	C₂²×C₄	C₂²×#120	1	4	yes	—
797	C₂²×C₄	C₂²×#120	1	8	yes	—
798	C₂²×C₄	C₂²×#120	1	8	yes	—
799	C₂²×C₄	C₂²×#120	1	8	yes	—
800	C₂²×C₄	C₂²×#120	1	32	yes	—
801	C₂²×C₄	C₂²×#120	1	4	yes	—
802	C₂²×C₄	C₂²×#120	1	4	yes	—
803	C₂²×C₄	C₂²×#120	1	8	yes	—
804	C₂²×C₄	C₂²×#120	1	16	yes	—
805	C₂²×C₄	C₂²×#121	1	4	yes	—
806	C₂²×C₄	C₂²×#121	1	4	yes	—
807	C₂²×C₄	C₂²×#121	1	8	yes	—
808	C₂²×C₄	C₂²×#121	1	8	yes	—
809	C₂²×C₄	C₂²×#121	1	8	yes	—
810	C₂²×C₄	C₂²×#127	1	8	yes	—
811	C₂²×C₄	C₂×#534	1	4	yes	—
812	C₂²×C₄	C₂×#534	1	4	yes	—
813	C₂²×C₄	C₂×#534	1	4	yes	—
814	C₂²×C₄	C₂×#534	1	4	yes	—
815	C₂²×C₄	C₂×#534	1	16	yes	—
816	C₂²×C₄	C₂×#535	1	16	yes	—
817	C₂²×C₄	C₂×D₄²	1	8	yes	—
818	C₂²×C₄	C₂×D₄²	1	16	yes	—
819	C₂²×C₄	C₂×D₄²	1	8	yes	—
820	C₂²×C₄	C₂×D₄²	1	8	yes	—
821	C₂²×C₄	C₂×D₄²	1	8	yes	—
822	C₂²×C₄	C₂×D₄²	1	16	yes	—
823	C₂²×C₄	C₂×D₄²	1	16	yes	—
824	C₂²×C₄	C₂×D₄²	1	8	yes	—
825	C₂²×C₄	C₂×D₄²	1	8	yes	—
826	C₂²×C₄	C₂×#546	1	8	yes	—
827	C₂²×C₄	C₂×#546	1	16	yes	—
828	C₂²×C₄	C₂×#546	1	8	yes	—
829	C₂³	C₂²×#392	1	4	yes	—
830	C₂³	C₂²×#392	1	4	yes	—
831	C₂³	C₂²×#392	1	16	yes	—
832	C₂³	C₂×#2613	1	4	yes	—
833	C₂³	C₂×#2613	1	4	yes	—
834	C₂³	C₂×#2403	1	4	yes	—
835	C₂³	C₂×#2403	1	8	yes	—
836	C₂³	C₂×#2403	1	4	yes	—
837	C₂³	C₂×#2403	1	8	yes	—
838	C₂³	C₂×#2403	1	2	yes	—
839	C₂³	C₂×#2403	1	4	yes	—
840	C₂³	C₂×#2403	1	2	yes	—
841	C₂³	C₂×#2410	1	2	yes	—
842	C₂³	C₂×#2410	1	4	yes	—
843	C₂³	C₂×#2410	1	8	yes	—
844	C₂³	C₂×#2410	1	4	yes	—
845	C₂³	C₂×#2410	1	8	yes	—
846	C₂³	C₂×#2410	1	2	yes	—
847	C₂³	C₂×#2410	1	4	yes	—
848	C₂³	C₂×#2408	1	8	yes	—
849	C₂³	C₂×#2408	1	8	yes	—
850	C₂³	C₂×#2433	1	8	yes	—
851	C₂³	C₂×#2433	1	8	yes	—
852	C₂³	C₂×#2846	1	2	yes	—
853	C₂³	C₂×#2846	1	2	yes	—
854	C₂³	C₂×#2846	1	4	yes	—
855	C₂³	C₂×#3025	1	4	yes	—
856	C₂³	C₂×#3025	1	8	yes	complemented
857	C₂³	#60398	1	4	yes	—
858	C₂³	C₂³×#120	1	1	yes	characteristic
859	C₂³	C₂³×#120	1	1	yes	characteristic
860	C₂³	C₂³×#120	1	1	yes	characteristic
861	C₂³	C₂³×#120	1	1	yes	characteristic
862	C₂³	C₂³×#120	1	2	yes	—
863	C₂³	C₂³×#120	1	2	yes	—
864	C₂³	C₂³×#120	1	1	yes	characteristic
865	C₂³	C₂³×#121	1	1	yes	characteristic
866	C₂³	C₂³×#121	1	1	yes	characteristic
867	C₂³	C₂³×#121	1	1	yes	characteristic
868	C₂³	C₂³×#127	1	1	yes	characteristic
869	C₂³	C₂²×#534	1	2	yes	—
870	C₂³	C₂²×#534	1	1	yes	characteristic
871	C₂³	C₂²×#534	1	1	yes	characteristic
872	C₂³	C₂²×#535	1	2	yes	—
873	C₂³	C₂²×D₄²	1	2	yes	—
874	C₂³	C₂²×D₄²	1	2	yes	—
875	C₂³	C₂²×D₄²	1	2	yes	—
876	C₂³	C₂²×D₄²	1	2	yes	—
877	C₂³	C₂²×D₄²	1	2	yes	—
878	C₂³	C₂²×D₄²	1	2	yes	—
879	C₂³	C₂²×#546	1	2	yes	—
880	C₂³	C₂²×#546	1	2	yes	—
881	C₂×C₄	#14715	1	32	yes	—
882	C₂×C₄	#14715	1	32	yes	—
883	C₂×C₄	#14715	1	64	yes	—
884	C₂×C₄	#14715	1	64	yes	—
885	C₂×C₄	#14715	1	16	yes	—
886	C₂×C₄	#14715	1	32	yes	—
887	C₂×C₄	#14715	1	16	yes	—
888	C₂×C₄	C₂²×#392	1	8	yes	—
889	C₂×C₄	C₂²×#392	1	8	yes	—
890	C₂×C₄	C₂²×#392	1	16	yes	—
891	C₂×C₄	C₂×#2613	1	8	yes	—
892	C₂×C₄	C₂×#2613	1	8	yes	—
893	C₂×C₄	C₂×#2403	1	8	yes	—
894	C₂×C₄	C₂×#2403	1	16	yes	—
895	C₂×C₄	C₂×#2403	1	8	yes	—
896	C₂×C₄	C₂×#2403	1	16	yes	—
897	C₂×C₄	C₂×#2403	1	4	yes	—
898	C₂×C₄	C₂×#2403	1	8	yes	—
899	C₂×C₄	C₂×#2403	1	4	yes	—
900	C₂×C₄	C₂×#2410	1	8	yes	—
901	C₂×C₄	C₂×#2410	1	16	yes	—
902	C₂×C₄	C₂×#2410	1	8	yes	—
903	C₂×C₄	C₂×#2410	1	16	yes	—
904	C₂×C₄	C₂×#2410	1	4	yes	—
905	C₂×C₄	C₂×#2410	1	8	yes	—
906	C₂×C₄	C₂×#2410	1	4	yes	—
907	C₂×C₄	C₂×#2408	1	16	yes	—
908	C₂×C₄	C₂×#2408	1	16	yes	—
909	C₂×C₄	C₂×#2433	1	16	yes	—
910	C₂×C₄	C₂×#2433	1	16	yes	—
911	C₂×C₄	C₂×#2846	1	4	yes	—
912	C₂×C₄	C₂×#2846	1	8	yes	—
913	C₂×C₄	C₂×#2846	1	4	yes	—
914	C₂²	C₂×#14715	1	4	yes	—
915	C₂²	C₂×#14715	1	8	yes	—
916	C₂²	C₂×#14715	1	4	yes	—
917	C₂²	#6437616	1	4	yes	—
918	C₂²	#6437620	1	4	yes	—
919	C₂²	#6437994	1	8	yes	—
920	C₂²	#6628891	1	8	yes	—
921	C₂²	C₂³×#392	1	1	yes	characteristic
922	C₂²	C₂²×#2613	1	1	yes	characteristic
923	C₂²	C₂²×#2403	1	1	yes	characteristic
924	C₂²	C₂²×#2403	1	2	yes	—
925	C₂²	C₂²×#2403	1	1	yes	characteristic
926	C₂²	C₂²×#2410	1	1	yes	characteristic
927	C₂²	C₂²×#2410	1	2	yes	—
928	C₂²	C₂²×#2410	1	1	yes	characteristic
929	C₂²	C₂²×#2408	1	2	yes	—
930	C₂²	C₂²×#2433	1	2	yes	—
931	C₂²	C₂²×#2846	1	1	yes	characteristic
932	C₂²	C₂²×#3025	1	2	yes	—
933	C₂²	C₂×#60398	1	2	yes	—
934	C₄	C₂×#14715	1	8	yes	—
935	C₄	C₂×#14715	1	8	yes	—
936	C₄	C₂×#14715	1	16	yes	—
937	C₂	C₂×#6437616	1	1	yes	characteristic
938	C₂	#72239358	1	8	yes	direct product factor
939	C₂	C₂×#6628891	1	2	yes	—
940	C₂	C₂²×#14715	1	1	yes	characteristic
941	C₂	C₂×#6437994	1	2	yes	—
942	C₂	C₂×#6437620	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×#120
commutator, Frattini, cosocle	C₂⁵	C₂⁶
socle	C₂⁴	C₂²×#120
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#394068	C₂	semidirect
2. C₂×#394069	C₂	semidirect
3. C₂×#394067	C₂	semidirect
4. C₂×#357420	C₂	semidirect
5. C₂×#353426	C₂	semidirect
6. C₂²×#20608	C₂	semidirect
7. C₂×#357480	C₂	semidirect
8. C₂²×#20959	C₂	semidirect
9. C₂²×#23443	C₂	semidirect
10. C₂²×#20584	C₂	semidirect
11. C₂²×#62811	C₂	semidirect
12. C₂×#608658	C₂	semidirect
13. C₂²×#34736	C₂	semidirect
14. C₂³×#3025	C₂	semidirect
15. #72239358	C₂	direct (N × H)
16. C₂×#394066	C₂	semidirect
19. C₂×#62811	C₂²	semidirect
25. C₂³×#525	C₂²	semidirect
26. C₂³×#525	C₂²	semidirect
28. C₂⁴×C₄×D₄	C₂²	semidirect
29. C₂²×#3025	C₂²	semidirect
30. C₂³×#458	C₂²	semidirect
31. C₂³×B(4,𝔽₂)	C₂²	semidirect
34. C₂³×#410	C₂²	semidirect
35. C₂³×#410	C₂²	semidirect
36. C₂³×#410	C₂²	semidirect
37. C₂×#34736	C₂²	semidirect
38. C₂²×#2406	C₂²	semidirect
39. C₂²×#2404	C₂²	semidirect
40. C₂²×#2405	C₂²	semidirect
41. C₂²×#2403	C₂²	semidirect
43. C₂²×#2297	C₂²	semidirect
44. C₂²×#2297	C₂²	semidirect
45. C₂²×#2280	C₂²	semidirect
46. C₂²×#2280	C₂²	semidirect
47. C₂²×#2280	C₂²	semidirect
48. C₂×#23443	C₂²	semidirect
49. C₂²×#2022	C₂²	semidirect
50. C₂²×#2021	C₂²	semidirect
51. C₂×#20959	C₂²	semidirect
52. C₂²×#1890	C₂²	semidirect
53. C₂²×#1889	C₂²	semidirect
54. C₂×#20608	C₂²	semidirect
55. C₂²×#1790	C₂²	semidirect
56. C₂²×#1790	C₂²	semidirect
57. C₂×#20584	C₂²	semidirect
58. C₂²×#1782	C₂²	semidirect
59. C₂²×#1781	C₂²	semidirect
60. C₂²×#1740	C₂²	semidirect
61. C₂²×#1740	C₂²	semidirect
62. #608658	C₂²	semidirect
63. C₂×#15069	C₂²	semidirect
64. C₂×#14911	C₂²	semidirect
65. C₂×#14911	C₂²	semidirect
66. C₂×#14715	C₂²	semidirect
67. C₂×#13756	C₂²	semidirect
68. #394069	C₂²	semidirect
69. #394068	C₂²	semidirect
70. #394067	C₂²	semidirect
71. #394066	C₂²	semidirect
72. #357480	C₂²	semidirect
73. C₂×#10995	C₂²	semidirect
74. C₂×#10995	C₂²	semidirect
75. #357420	C₂²	semidirect
76. C₂×#10966	C₂²	semidirect
77. C₂×#10965	C₂²	semidirect
78. #353426	C₂²	semidirect
79. C₂×#10745	C₂²	semidirect
80. C₂×#10745	C₂²	semidirect
81. C₂²×#585	D₄	semidirect
84. C₂⁴×#41	D₄	semidirect
85. C₂⁴×#41	D₄	semidirect
86. C₂⁴×#41	D₄	semidirect
87. C₂⁴×#41	D₄	semidirect
93. C₂⁵×Q₈	D₄	semidirect
94. C₂⁵×D₄	D₄	semidirect
97. C₂⁶×C₄	D₄	semidirect
102. C₂×#3449	D₄	semidirect
105. C₂²×#525	D₄	semidirect
106. C₂²×#525	D₄	semidirect
109. C₂²×#525	C₂³	semidirect
110. C₂²×#525	C₂³	semidirect
115. C₂³×C₂²⋊Q₈	D₄	semidirect
116. C₂³×#121	D₄	semidirect
121. C₂×#3428	D₄	semidirect
124. C₂³×C₄×D₄	D₄	semidirect
125. C₂³×C₄×D₄	C₂³	semidirect
135. C₂²×#458	C₂³	semidirect
136. C₂²×B(4,𝔽₂)	C₂³	semidirect
137. C₂²×#410	D₄	semidirect
140. C₂²×#410	C₂³	semidirect
141. C₂²×#410	C₂³	semidirect
142. C₂²×#410	C₂³	semidirect
148. C₂×#2406	C₂³	semidirect
149. C₂×#2404	C₂³	semidirect
150. C₂×#2405	C₂³	semidirect
151. C₂×#2403	C₂³	semidirect
152. C₂×#2297	D₄	semidirect
154. C₂×#2297	C₂³	semidirect
155. C₂×#2297	C₂³	semidirect
162. C₂×#2280	C₂³	semidirect
163. C₂×#2280	C₂³	semidirect
164. C₂×#2280	C₂³	semidirect
171. C₂×#2022	C₂³	semidirect
172. C₂×#2021	C₂³	semidirect
173. C₂×#1890	C₂³	semidirect
174. C₂×#1889	C₂³	semidirect
175. C₂×#1790	C₂³	semidirect
176. C₂×#1790	C₂³	semidirect
177. C₂×#1782	C₂³	semidirect
178. C₂×#1781	C₂³	semidirect
179. C₂×#1740	C₂³	semidirect
180. C₂×#1740	C₂³	semidirect
183. #15069	C₂³	semidirect
184. #14911	C₂³	semidirect
185. #14911	C₂³	semidirect
186. #14715	C₂³	semidirect
187. #13756	C₂³	semidirect
190. #10995	C₂³	semidirect
191. #10995	C₂³	semidirect
192. #10966	C₂³	semidirect
193. #10965	C₂³	semidirect
194. #10745	C₂³	semidirect
195. #10745	C₂³	semidirect
199. C₂×#585	C₂×D₄	semidirect
214. C₂³×#41	C₂×D₄	semidirect
215. C₂³×#41	C₂×D₄	semidirect
216. C₂³×#41	C₂×D₄	semidirect
226. C₂⁴×Q₈	C₂×D₄	semidirect
235. C₂⁴×D₄	C₂×D₄	semidirect
255. C₂⁵×C₄	C₂×D₄	semidirect
256. C₂⁵×C₄	C₂×D₄	semidirect
264. #3449	C₂×D₄	semidirect
267. C₂×#525	C₂×D₄	semidirect
269. C₂²×#123	C₂×D₄	semidirect
274. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
275. C₂²×#121	C₂×D₄	semidirect
277. C₂²×#120	C₂×D₄	semidirect
282. #3428	C₂×D₄	semidirect
285. C₂²×C₄×D₄	C₂×D₄	semidirect
289. C₂²×#117	C₂×D₄	semidirect
290. C₂²×#117	C₂×D₄	semidirect
291. C₂²×#117	C₂×D₄	semidirect
310. C₂³×C₄²	C₂×D₄	semidirect
312. C₂×#410	C₂×D₄	semidirect
313. C₂²×#99	C₂×D₄	semidirect
319. #2297	C₂×D₄	semidirect
320. C₂×#386	C₂×D₄	semidirect
321. C₂×#386	C₂×D₄	semidirect
356. C₂²×#41	#120	semidirect
373. C₂³×Q₈	#120	semidirect
382. C₂³×D₄	#120	semidirect
421. C₂⁴×C₄	#120	semidirect
459. C₂⁴×C₄	C₂²×D₄	semidirect
469. C₂×#123	C₂²×D₄	semidirect
470. C₂×#120	C₂²×D₄	semidirect
472. C₂×#117	#120	semidirect
475. C₂×#117	C₂²×D₄	semidirect
476. C₂×#117	C₂²×D₄	semidirect
477. C₂×#117	C₂²×D₄	semidirect
478. C₂²×C₄⋊C₄	#120	semidirect
494. C₂²×C₄²	#120	semidirect
496. C₂²×C₄²	C₂²×D₄	semidirect
497. C₂×#99	C₂²×D₄	semidirect
498. #386	C₂²×D₄	semidirect
499. #386	C₂²×D₄	semidirect
531. C₂×#41	#392	semidirect
536. C₂²×Q₈	#392	semidirect
540. C₂²×Q₈	C₂×#120	semidirect
542. C₂²×D₄	#392	semidirect
551. C₂²×D₄	C₂×#120	semidirect
566. C₂³×C₄	#392	semidirect
609. C₂³×C₄	C₂×#120	semidirect
665. C₂×C₄⋊C₄	C₂×#120	semidirect
672. C₂×C₄²	C₂×#120	semidirect
674. C₂⁴	#3025	semidirect
730. C₂×Q₈	C₂×#392	semidirect
732. C₂×D₄	C₂×#392	semidirect
741. C₂²×C₄	C₂×#392	semidirect
856. C₂³	C₂×#3025	semidirect
938. C₂	#72239358	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×#394068	2
C₂×#394069	2
C₂×#394067	2
C₂×#357420	2
C₂×#353426	2
C₂²×#20608	2
C₂×#357480	2
C₂²×#20959	2
C₂²×#23443	2
C₂²×#20584	2
C₂²×#62811	2
C₂×#608658	2
C₂²×#34736	2
C₂³×#3025	2
#72239358	2
C₂×#394066	2

Subgroups — C2×#72239358 #72317118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72239358 #72317118