Subgroups — C₂×#72238034 #72314980

Order 2048.

At least 6155 conjugacy classes of subgroups; only the 11912 normal subgroups are shown.

The subgroup lattice has 792 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×#357529	C₂	1	2	yes	maximal, complemented
2	C₂×#394061	C₂	1	8	yes	maximal, complemented
3	C₂²×#23445	C₂	1	2	yes	maximal, complemented
4	C₂×#357531	C₂	1	2	yes	maximal, complemented
5	C₂²×#20985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#20586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#353409	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#7630502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#23443	C₂	1	2	yes	maximal, complemented
10	C₂×#517415	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#35222	C₂	1	1	yes	maximal, characteristic, complemented
12	#72238034	C₂	1	32	yes	maximal, direct product factor
13	C₂³×#3484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#394058	C₂	1	8	yes	maximal, complemented
15	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
16	C₂⁶×D₄	C₂²	1	1	yes	characteristic
17	C₂²×#3484	C₂²	1	16	yes	complemented
18	C₂²×#3449	C₂²	1	2	yes	complemented
19	C₂³×#535	C₂²	1	2	yes	—
20	C₂³×#535	C₂²	1	1	yes	characteristic
21	C₂³×#535	C₂²	1	1	yes	characteristic, complemented
22	C₂³×#534	C₂²	1	4	yes	—
23	C₂³×#525	C₂²	1	2	yes	—
24	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×#120	C₂²	1	4	yes	—
26	C₂³×#518	C₂²	1	1	yes	characteristic
27	C₂³×#410	C₂²	1	2	yes	complemented
28	C₂³×#410	C₂²	1	2	yes	complemented
29	C₂³×#410	C₂²	1	2	yes	complemented
30	C₂²×#2846	C₂²	1	4	yes	complemented
31	#7630502	C₂²	1	16	yes	complemented
32	C₂×#35222	C₂²	1	16	yes	complemented
33	C₂×#34980	C₂²	1	8	yes	complemented
34	C₂²×#2613	C₂²	1	4	yes	complemented
35	C₂×#34044	C₂²	1	2	yes	complemented
36	C₂²×#2309	C₂²	1	1	yes	characteristic
37	C₂²×#2309	C₂²	1	1	yes	characteristic
38	C₂²×#2309	C₂²	1	1	yes	characteristic
39	C₂²×#2309	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#2309	C₂²	1	2	yes	complemented
41	C₂²×#2280	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#2280	C₂²	1	2	yes	complemented
43	C₂×#23445	C₂²	1	32	yes	complemented
44	C₂×#23443	C₂²	1	32	yes	complemented
45	C₂²×#2022	C₂²	1	8	yes	complemented
46	C₂²×#2021	C₂²	1	8	yes	complemented
47	C₂²×#2021	C₂²	1	16	yes	complemented
48	C₂×#20985	C₂²	1	16	yes	complemented
49	C₂²×#1898	C₂²	1	8	yes	complemented
50	C₂×#20586	C₂²	1	16	yes	complemented
51	C₂²×#1781	C₂²	1	8	yes	complemented
52	C₂²×#1740	C₂²	1	2	yes	complemented
53	C₂²×#1740	C₂²	1	2	yes	complemented
54	C₂²×#1740	C₂²	1	2	yes	complemented
55	C₂×#14679	C₂²	1	4	yes	complemented
56	#517415	C₂²	1	16	yes	complemented
57	C₂×#14335	C₂²	1	4	yes	complemented
58	#394061	C₂²	1	128	yes	complemented
59	#394058	C₂²	1	128	yes	complemented
60	#357531	C₂²	1	32	yes	complemented
61	#357529	C₂²	1	32	yes	complemented
62	C₂×#10992	C₂²	1	8	yes	complemented
63	C₂×#10991	C₂²	1	16	yes	complemented
64	C₂×#10991	C₂²	1	8	yes	complemented
65	#353409	C₂²	1	16	yes	complemented
66	C₂×#10735	C₂²	1	8	yes	complemented
67	C₂⁸	C₂³	1	2	yes	—
68	C₂³×H(5,𝔽₂)	D₄	1	8	yes	complemented
69	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
70	C₂⁴×#41	D₄	1	4	yes	complemented
71	C₂⁴×#41	C₂³	1	2	yes	—
72	C₂⁴×#41	C₂³	1	1	yes	characteristic
73	C₂⁵×D₄	D₄	1	4	yes	complemented
74	C₂⁵×D₄	D₄	1	16	yes	complemented
75	C₂⁵×D₄	C₂³	1	4	yes	—
76	C₂⁵×D₄	C₂³	1	1	yes	characteristic
77	C₂⁵×D₄	C₂³	1	2	yes	—
78	C₂⁵×D₄	C₂³	1	8	yes	—
79	C₂⁵×D₄	C₂³	1	1	yes	characteristic
80	C₂⁶×C₄	C₂³	1	1	yes	characteristic
81	C₂×#3449	C₂³	1	16	yes	complemented
82	C₂²×#535	D₄	1	32	yes	complemented
83	C₂²×#535	D₄	1	8	yes	complemented
84	C₂²×#535	C₂³	1	16	yes	—
85	C₂²×#535	C₂³	1	8	yes	—
86	C₂²×#535	C₂³	1	8	yes	complemented
87	C₂²×#534	C₂³	1	8	yes	—
88	C₂²×#534	C₂³	1	32	yes	—
89	C₂³×#127	D₄	1	2	yes	complemented
90	C₂³×#124	D₄	1	2	yes	complemented
91	C₂²×#525	D₄	1	32	yes	complemented
92	C₂²×#525	C₂³	1	16	yes	—
93	C₂²×#525	C₂³	1	8	yes	complemented
94	C₂³×#123	C₂³	1	4	yes	—
95	C₂³×#123	C₂³	1	2	yes	—
96	C₂³×#121	D₄	1	4	yes	complemented
97	C₂³×#120	C₂³	1	32	yes	—
98	C₂³×#120	C₂³	1	4	yes	—
99	C₂³×#120	C₂³	1	8	yes	—
100	C₂³×#120	C₂³	1	2	yes	—
101	C₂³×#120	C₂³	1	4	yes	—
102	C₂³×#120	C₂³	1	4	yes	—
103	C₂²×#518	D₄	1	16	yes	complemented
104	C₂²×#518	C₂³	1	8	yes	—
105	C₂³×#117	C₂³	1	2	yes	—
106	C₂³×#117	C₂³	1	1	yes	characteristic
107	C₂³×#117	C₂³	1	1	yes	characteristic
108	C₂³×#117	C₂³	1	2	yes	—
109	C₂³×#117	C₂³	1	1	yes	characteristic
110	C₂³×#117	C₂³	1	2	yes	—
111	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂²×#410	C₂³	1	16	yes	complemented
113	C₂²×#410	C₂³	1	16	yes	complemented
114	C₂²×#410	C₂³	1	16	yes	complemented
115	C₂³×#99	C₂³	1	8	yes	—
116	C₂³×#99	C₂³	1	8	yes	—
117	C₂³×#99	C₂³	1	8	yes	—
118	C₂×#2846	C₂³	1	32	yes	complemented
119	#34980	C₂³	1	64	yes	complemented
120	C₂×#2613	C₂³	1	32	yes	complemented
121	#34044	C₂³	1	16	yes	complemented
122	C₂×#2309	D₄	1	8	yes	complemented
123	C₂×#2309	D₄	1	16	yes	complemented
124	C₂×#2309	C₂³	1	8	yes	—
125	C₂×#2309	C₂³	1	8	yes	—
126	C₂×#2309	C₂³	1	8	yes	—
127	C₂×#2309	C₂³	1	8	yes	complemented
128	C₂×#2309	C₂³	1	16	yes	complemented
129	C₂×#2308	C₂³	1	8	yes	—
130	C₂²×#390	D₄	1	8	yes	complemented
131	C₂×#2280	C₂³	1	8	yes	complemented
132	C₂×#2280	C₂³	1	16	yes	complemented
133	C₂²×#381	C₂³	1	2	yes	—
134	C₂²×#381	C₂³	1	4	yes	—
135	C₂²×#379	C₂³	1	2	yes	—
136	C₂²×#379	C₂³	1	4	yes	—
137	C₂²×#379	C₂³	1	4	yes	—
138	C₂²×#379	C₂³	1	4	yes	—
139	C₂²×#379	C₂³	1	8	yes	—
140	C₂²×#379	C₂³	1	4	yes	—
141	C₂²×#379	C₂³	1	4	yes	—
142	C₂×#2022	C₂³	1	64	yes	complemented
143	C₂×#2021	C₂³	1	64	yes	complemented
144	C₂×#2021	C₂³	1	128	yes	complemented
145	C₂×#1898	C₂³	1	64	yes	complemented
146	C₂×#1781	C₂³	1	64	yes	complemented
147	C₂×#1740	C₂³	1	16	yes	complemented
148	C₂×#1740	C₂³	1	16	yes	complemented
149	C₂×#1740	C₂³	1	16	yes	complemented
150	C₂²×#342	C₂³	1	8	yes	—
151	C₂²×#342	C₂³	1	8	yes	—
152	C₂²×#342	C₂³	1	8	yes	—
153	#14679	C₂³	1	32	yes	complemented
154	#14335	C₂³	1	32	yes	complemented
155	#10992	C₂³	1	64	yes	complemented
156	#10991	C₂³	1	64	yes	complemented
157	#10991	C₂³	1	128	yes	complemented
158	#10735	C₂³	1	64	yes	complemented
159	C₂⁷	C₂×D₄	1	4	yes	—
160	C₂⁷	C₂×D₄	1	16	yes	—
161	C₂⁷	C₂⁴	1	1	yes	characteristic
162	C₂⁷	C₂⁴	1	2	yes	—
163	C₂⁷	C₂⁴	1	8	yes	—
164	C₂⁷	C₂⁴	1	2	yes	—
165	C₂³×#41	C₂×D₄	1	16	yes	—
166	C₂³×#41	C₂×D₄	1	16	yes	—
167	C₂³×#41	C₂×D₄	1	8	yes	—
168	C₂³×#41	C₂×D₄	1	32	yes	complemented
169	C₂³×#41	C₂×D₄	1	4	yes	complemented
170	C₂³×#41	C₂⁴	1	8	yes	—
171	C₂³×#41	C₂⁴	1	4	yes	—
172	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
173	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
174	C₂⁴×D₄	C₂×D₄	1	16	yes	—
175	C₂⁴×D₄	C₂×D₄	1	8	yes	—
176	C₂⁴×D₄	C₂×D₄	1	2	yes	—
177	C₂⁴×D₄	C₂×D₄	1	16	yes	—
178	C₂⁴×D₄	C₂×D₄	1	8	yes	—
179	C₂⁴×D₄	C₂×D₄	1	16	yes	—
180	C₂⁴×D₄	C₂×D₄	1	4	yes	—
181	C₂⁴×D₄	C₂×D₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	2	yes	—
183	C₂⁴×D₄	C₂×D₄	1	4	yes	—
184	C₂⁴×D₄	C₂×D₄	1	4	yes	—
185	C₂⁴×D₄	C₂×D₄	1	8	yes	—
186	C₂⁴×D₄	C₂×D₄	1	8	yes	—
187	C₂⁴×D₄	C₂×D₄	1	4	yes	—
188	C₂⁴×D₄	C₂×D₄	1	8	yes	—
189	C₂⁴×D₄	C₂×D₄	1	4	yes	—
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
191	C₂⁴×D₄	C₂×D₄	1	64	yes	complemented
192	C₂⁴×D₄	C₂×D₄	1	32	yes	complemented
193	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
194	C₂⁴×D₄	#41	1	8	yes	—
195	C₂⁴×D₄	C₂⁴	1	2	yes	—
196	C₂⁴×D₄	C₂⁴	1	4	yes	—
197	C₂⁴×D₄	C₂⁴	1	16	yes	—
198	C₂⁴×D₄	C₂⁴	1	4	yes	—
199	C₂⁴×D₄	C₂⁴	1	8	yes	—
200	C₂⁴×D₄	C₂⁴	1	4	yes	—
201	C₂⁵×C₄	C₂×D₄	1	16	yes	—
202	C₂⁵×C₄	C₂×D₄	1	8	yes	—
203	C₂⁵×C₄	C₂×D₄	1	4	yes	—
204	C₂⁵×C₄	C₂×D₄	1	4	yes	—
205	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
206	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
207	C₂⁵×C₄	C₂⁴	1	4	yes	—
208	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
209	C₂×#535	C₂×D₄	1	128	yes	complemented
210	C₂×#534	C₂⁴	1	32	yes	—
211	C₂²×#127	C₂×D₄	1	16	yes	complemented
212	C₂²×#124	C₂×D₄	1	16	yes	complemented
213	C₂×#525	C₂×D₄	1	128	yes	complemented
214	C₂²×#123	C₂×D₄	1	32	yes	—
215	C₂²×#123	C₂⁴	1	16	yes	—
216	C₂²×#123	C₂⁴	1	8	yes	—
217	C₂²×#121	C₂×D₄	1	32	yes	complemented
218	C₂²×#120	C₂×D₄	1	32	yes	—
219	C₂²×#120	C₂×D₄	1	64	yes	—
220	C₂²×#120	C₂×D₄	1	16	yes	complemented
221	C₂²×#120	C₂⁴	1	16	yes	—
222	C₂²×#120	C₂⁴	1	32	yes	—
223	C₂²×#120	C₂⁴	1	8	yes	—
224	C₂²×#120	C₂⁴	1	16	yes	—
225	C₂²×#120	C₂⁴	1	16	yes	—
226	C₂×#518	C₂×D₄	1	64	yes	complemented
227	C₂²×#117	C₂×D₄	1	16	yes	—
228	C₂²×#117	C₂×D₄	1	16	yes	—
229	C₂²×#117	C₂×D₄	1	16	yes	—
230	C₂²×#117	C₂×D₄	1	8	yes	complemented
231	C₂²×#117	C₂×D₄	1	8	yes	complemented
232	C₂²×#117	C₂×D₄	1	4	yes	complemented
233	C₂²×#117	C₂×D₄	1	8	yes	complemented
234	C₂²×#117	C₂⁴	1	8	yes	—
235	C₂²×#117	C₂⁴	1	4	yes	—
236	C₂²×#117	C₂⁴	1	4	yes	—
237	C₂²×#117	C₂⁴	1	8	yes	—
238	C₂²×#117	C₂⁴	1	4	yes	—
239	C₂²×#117	C₂⁴	1	8	yes	—
240	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
241	C₂³×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
242	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	—
243	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
244	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
245	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
246	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
247	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
248	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
249	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
250	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
251	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
252	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
253	C₂³×C₄²	C₂×D₄	1	4	yes	complemented
254	C₂²×#99	C₂⁴	1	32	yes	—
255	C₂²×#99	C₂⁴	1	32	yes	—
256	C₂²×#99	C₂⁴	1	32	yes	—
257	#2309	C₂×D₄	1	64	yes	complemented
258	#2308	C₂⁴	1	32	yes	—
259	C₂×#390	C₂×D₄	1	64	yes	complemented
260	C₂×#381	C₂⁴	1	8	yes	—
261	C₂×#381	C₂⁴	1	16	yes	—
262	C₂×#379	C₂×D₄	1	32	yes	complemented
263	C₂×#379	C₂×D₄	1	16	yes	complemented
264	C₂×#379	C₂⁴	1	8	yes	—
265	C₂×#379	C₂⁴	1	16	yes	—
266	C₂×#379	C₂⁴	1	16	yes	—
267	C₂×#379	C₂⁴	1	16	yes	—
268	C₂×#379	C₂⁴	1	32	yes	—
269	C₂×#379	C₂⁴	1	16	yes	—
270	C₂×#379	C₂⁴	1	16	yes	—
271	C₂×#342	C₂⁴	1	32	yes	—
272	C₂×#342	C₂⁴	1	32	yes	—
273	C₂×#342	C₂⁴	1	32	yes	—
274	C₂⁶	C₂²×D₄	1	2	yes	—
275	C₂⁶	C₂²×D₄	1	8	yes	—
276	C₂⁶	C₂²×D₄	1	4	yes	—
277	C₂⁶	C₂²×D₄	1	4	yes	—
278	C₂⁶	C₂²×D₄	1	16	yes	—
279	C₂⁶	C₂²×D₄	1	8	yes	—
280	C₂⁶	C₂²×D₄	1	16	yes	—
281	C₂⁶	C₂²×D₄	1	32	yes	—
282	C₂⁶	C₂²×D₄	1	4	yes	—
283	C₂⁶	C₂²×D₄	1	4	yes	—
284	C₂⁶	C₂²×D₄	1	4	yes	—
285	C₂⁶	C₂²×D₄	1	4	yes	—
286	C₂⁶	C₂²×D₄	1	8	yes	—
287	C₂⁶	C₂²×D₄	1	4	yes	—
288	C₂⁶	C₂²×D₄	1	8	yes	—
289	C₂⁶	C₂²×D₄	1	8	yes	—
290	C₂⁶	C₂²×D₄	1	4	yes	—
291	C₂⁶	C₂×#41	1	8	yes	—
292	C₂⁶	C₂⁵	1	2	yes	—
293	C₂⁶	C₂⁵	1	4	yes	—
294	C₂⁶	C₂⁵	1	4	yes	—
295	C₂⁶	C₂⁵	1	1	yes	characteristic
296	C₂²×#41	#120	1	64	yes	complemented
297	C₂²×#41	C₂²×D₄	1	32	yes	—
298	C₂²×#41	C₂²×D₄	1	32	yes	—
299	C₂³×Q₈	#120	1	16	yes	complemented
300	C₂³×Q₈	C₂²×D₄	1	8	yes	—
301	C₂³×Q₈	C₂²×D₄	1	4	yes	complemented
302	C₂³×D₄	#120	1	32	yes	—
303	C₂³×D₄	#120	1	32	yes	—
304	C₂³×D₄	#120	1	32	yes	—
305	C₂³×D₄	#120	1	16	yes	—
306	C₂³×D₄	#120	1	16	yes	—
307	C₂³×D₄	#120	1	16	yes	—
308	C₂³×D₄	#120	1	8	yes	—
309	C₂³×D₄	#120	1	8	yes	—
310	C₂³×D₄	#120	1	8	yes	—
311	C₂³×D₄	#120	1	8	yes	—
312	C₂³×D₄	#120	1	16	yes	—
313	C₂³×D₄	#120	1	64	yes	complemented
314	C₂³×D₄	#120	1	16	yes	complemented
315	C₂³×D₄	#121	1	32	yes	—
316	C₂³×D₄	#121	1	32	yes	—
317	C₂³×D₄	#121	1	32	yes	—
318	C₂³×D₄	#121	1	32	yes	—
319	C₂³×D₄	#121	1	16	yes	—
320	C₂³×D₄	#121	1	16	yes	—
321	C₂³×D₄	#121	1	32	yes	—
322	C₂³×D₄	#127	1	32	yes	—
323	C₂³×D₄	#127	1	32	yes	—
324	C₂³×D₄	C₂²×D₄	1	16	yes	—
325	C₂³×D₄	C₂²×D₄	1	16	yes	—
326	C₂³×D₄	C₂²×D₄	1	4	yes	—
327	C₂³×D₄	C₂²×D₄	1	8	yes	—
328	C₂³×D₄	C₂²×D₄	1	32	yes	—
329	C₂³×D₄	C₂²×D₄	1	16	yes	—
330	C₂³×D₄	C₂²×D₄	1	8	yes	—
331	C₂³×D₄	C₂²×D₄	1	32	yes	—
332	C₂³×D₄	C₂²×D₄	1	32	yes	—
333	C₂³×D₄	C₂²×D₄	1	16	yes	—
334	C₂³×D₄	C₂²×D₄	1	8	yes	—
335	C₂³×D₄	C₂²×D₄	1	8	yes	—
336	C₂³×D₄	C₂²×D₄	1	16	yes	—
337	C₂³×D₄	C₂²×D₄	1	16	yes	—
338	C₂³×D₄	C₂²×D₄	1	16	yes	—
339	C₂³×D₄	C₂²×D₄	1	16	yes	—
340	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
341	C₂³×D₄	C₂²×D₄	1	32	yes	complemented
342	C₂³×D₄	C₂×#41	1	16	yes	—
343	C₂³×D₄	C₂⁵	1	4	yes	—
344	C₂³×D₄	C₂⁵	1	8	yes	—
345	C₂⁴×C₄	#120	1	64	yes	complemented
346	C₂⁴×C₄	#120	1	32	yes	complemented
347	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
348	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
349	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
350	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
351	C₂⁴×C₄	C₂²×D₄	1	32	yes	—
352	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
353	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
354	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
355	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
356	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
357	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
358	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
359	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
360	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
361	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
362	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
363	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
365	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
366	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
367	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
368	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
369	C₂⁴×C₄	C₂²×D₄	1	8	yes	complemented
370	C₂⁴×C₄	C₂×#41	1	4	yes	—
371	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
372	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
373	C₂⁴×C₄	C₂⁵	1	2	yes	—
374	C₂⁴×C₄	C₂⁵	1	2	yes	—
375	C₂×#123	C₂²×D₄	1	64	yes	—
376	C₂×#120	C₂²×D₄	1	64	yes	—
377	C₂×#120	C₂²×D₄	1	128	yes	—
378	C₂×#117	#120	1	128	yes	complemented
379	C₂×#117	C₂²×D₄	1	32	yes	—
380	C₂×#117	C₂²×D₄	1	32	yes	—
381	C₂×#117	C₂²×D₄	1	32	yes	—
382	C₂×#117	C₂²×D₄	1	16	yes	complemented
383	C₂×#117	C₂²×D₄	1	16	yes	complemented
384	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	complemented
385	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	complemented
386	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
387	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
388	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
389	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
390	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	—
391	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
392	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
393	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
394	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
395	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
396	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
397	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
398	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
399	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
400	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
401	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
402	C₂²×C₄²	C₂²×D₄	1	8	yes	complemented
403	C₂²×C₄²	C₂²×D₄	1	16	yes	complemented
404	#379	C₂²×D₄	1	64	yes	complemented
405	C₂⁵	C₂×#120	1	8	yes	—
406	C₂⁵	C₂×#120	1	16	yes	—
407	C₂⁵	C₂×#120	1	16	yes	—
408	C₂⁵	C₂×#120	1	32	yes	—
409	C₂⁵	C₂×#120	1	16	yes	—
410	C₂⁵	C₂×#120	1	8	yes	—
411	C₂⁵	C₂×#120	1	16	yes	—
412	C₂⁵	C₂×#120	1	8	yes	—
413	C₂⁵	C₂×#120	1	8	yes	—
414	C₂⁵	C₂×#120	1	16	yes	—
415	C₂⁵	C₂×#120	1	16	yes	—
416	C₂⁵	C₂×#121	1	16	yes	—
417	C₂⁵	C₂×#121	1	16	yes	—
418	C₂⁵	C₂×#121	1	16	yes	—
419	C₂⁵	C₂×#121	1	16	yes	—
420	C₂⁵	C₂×#121	1	16	yes	—
421	C₂⁵	C₂×#121	1	16	yes	—
422	C₂⁵	C₂×#127	1	16	yes	—
423	C₂⁵	C₂×#127	1	16	yes	—
424	C₂⁵	C₂³×D₄	1	1	yes	characteristic
425	C₂⁵	C₂³×D₄	1	1	yes	characteristic
426	C₂⁵	C₂³×D₄	1	1	yes	characteristic
427	C₂⁵	C₂³×D₄	1	4	yes	—
428	C₂⁵	C₂³×D₄	1	8	yes	—
429	C₂⁵	C₂³×D₄	1	4	yes	—
430	C₂⁵	C₂³×D₄	1	8	yes	—
431	C₂⁵	C₂³×D₄	1	8	yes	—
432	C₂⁵	C₂³×D₄	1	16	yes	—
433	C₂⁵	C₂³×D₄	1	8	yes	—
434	C₂⁵	C₂³×D₄	1	8	yes	—
435	C₂⁵	C₂³×D₄	1	8	yes	—
436	C₂⁵	C₂³×D₄	1	8	yes	—
437	C₂⁵	C₂³×D₄	1	8	yes	—
438	C₂⁵	C₂³×D₄	1	8	yes	—
439	C₂⁵	C₂³×D₄	1	1	yes	characteristic
440	C₂⁵	C₂³×D₄	1	2	yes	—
441	C₂⁵	C₂³×D₄	1	2	yes	—
442	C₂⁵	C₂³×D₄	1	4	yes	—
443	C₂⁵	C₂³×D₄	1	4	yes	—
444	C₂⁵	C₂³×D₄	1	1	yes	characteristic
445	C₂⁵	C₂³×D₄	1	1	yes	characteristic
446	C₂⁵	C₂³×D₄	1	2	yes	—
447	C₂⁵	C₂²×#41	1	8	yes	—
448	C₂⁵	C₂²×#41	1	2	yes	—
449	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
450	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
451	C₂⁵	C₂⁶	1	1	yes	characteristic
452	C₂²×Q₈	C₂×#120	1	32	yes	complemented
453	C₂²×D₄	#392	1	64	yes	—
454	C₂²×D₄	#392	1	64	yes	—
455	C₂²×D₄	#392	1	64	yes	—
456	C₂²×D₄	#392	1	64	yes	—
457	C₂²×D₄	#392	1	128	yes	—
458	C₂²×D₄	#392	1	128	yes	—
459	C₂²×D₄	C₂×#120	1	32	yes	—
460	C₂²×D₄	C₂×#120	1	64	yes	—
461	C₂²×D₄	C₂×#120	1	32	yes	—
462	C₂²×D₄	C₂×#120	1	32	yes	—
463	C₂²×D₄	C₂×#120	1	32	yes	—
464	C₂²×D₄	C₂×#120	1	32	yes	—
465	C₂²×D₄	C₂×#120	1	32	yes	complemented
466	C₂²×D₄	C₂×#120	1	64	yes	complemented
467	C₂²×D₄	C₂×#121	1	32	yes	—
468	C₂²×D₄	C₂×#121	1	32	yes	—
469	C₂²×D₄	C₂×#121	1	64	yes	—
470	C₂²×D₄	C₂×#121	1	64	yes	—
471	C₂²×D₄	C₂×#127	1	64	yes	—
472	C₂²×D₄	C₂³×D₄	1	16	yes	—
473	C₂²×D₄	C₂³×D₄	1	16	yes	—
474	C₂³×C₄	C₂×#120	1	16	yes	—
475	C₂³×C₄	C₂×#120	1	16	yes	—
476	C₂³×C₄	C₂×#120	1	8	yes	—
477	C₂³×C₄	C₂×#120	1	8	yes	—
478	C₂³×C₄	C₂×#120	1	8	yes	—
479	C₂³×C₄	C₂×#120	1	8	yes	—
480	C₂³×C₄	C₂×#120	1	16	yes	—
481	C₂³×C₄	C₂×#120	1	16	yes	—
482	C₂³×C₄	C₂×#120	1	16	yes	—
483	C₂³×C₄	C₂×#120	1	32	yes	—
484	C₂³×C₄	C₂×#120	1	4	yes	—
485	C₂³×C₄	C₂×#120	1	2	yes	—
486	C₂³×C₄	C₂×#120	1	4	yes	—
487	C₂³×C₄	C₂×#120	1	4	yes	—
488	C₂³×C₄	C₂×#120	1	4	yes	—
489	C₂³×C₄	C₂×#120	1	8	yes	—
490	C₂³×C₄	C₂×#120	1	2	yes	—
491	C₂³×C₄	C₂×#120	1	2	yes	—
492	C₂³×C₄	C₂×#120	1	2	yes	—
493	C₂³×C₄	C₂×#120	1	64	yes	complemented
494	C₂³×C₄	C₂×#120	1	64	yes	complemented
495	C₂³×C₄	C₂×#121	1	4	yes	—
496	C₂³×C₄	C₂×#121	1	8	yes	—
497	C₂³×C₄	C₂×#121	1	4	yes	—
498	C₂³×C₄	C₂×#121	1	8	yes	—
499	C₂³×C₄	C₂×#121	1	8	yes	—
500	C₂³×C₄	C₂×#121	1	8	yes	—
501	C₂³×C₄	C₂×#121	1	8	yes	—
502	C₂³×C₄	C₂×#127	1	8	yes	—
503	C₂³×C₄	C₂×#127	1	8	yes	—
504	C₂³×C₄	#534	1	8	yes	—
505	C₂³×C₄	#534	1	8	yes	—
506	C₂³×C₄	#534	1	16	yes	—
507	C₂³×C₄	#534	1	16	yes	—
508	C₂³×C₄	#534	1	16	yes	—
509	C₂³×C₄	#535	1	32	yes	—
510	C₂³×C₄	D₄²	1	8	yes	—
511	C₂³×C₄	D₄²	1	8	yes	—
512	C₂³×C₄	D₄²	1	16	yes	—
513	C₂³×C₄	D₄²	1	16	yes	—
514	C₂³×C₄	D₄²	1	8	yes	—
515	C₂³×C₄	D₄²	1	8	yes	—
516	C₂³×C₄	D₄²	1	8	yes	—
517	C₂³×C₄	D₄²	1	8	yes	—
518	C₂³×C₄	D₄²	1	8	yes	—
519	C₂³×C₄	D₄²	1	32	yes	—
520	C₂³×C₄	D₄²	1	16	yes	—
521	C₂³×C₄	D₄²	1	32	yes	—
522	C₂³×C₄	D₄²	1	16	yes	—
523	C₂³×C₄	D₄²	1	8	yes	—
524	C₂³×C₄	#546	1	32	yes	—
525	C₂³×C₄	#546	1	32	yes	—
526	C₂³×C₄	C₂³×D₄	1	4	yes	—
527	C₂³×C₄	C₂³×D₄	1	8	yes	—
528	C₂³×C₄	C₂³×D₄	1	4	yes	—
529	C₂³×C₄	C₂³×D₄	1	8	yes	—
530	C₂³×C₄	C₂³×D₄	1	16	yes	—
531	C₂³×C₄	C₂³×D₄	1	8	yes	—
532	C₂³×C₄	C₂³×D₄	1	4	yes	—
533	C₂³×C₄	C₂³×D₄	1	4	yes	—
534	C₂³×C₄	C₂³×D₄	1	4	yes	—
535	C₂³×C₄	C₂³×D₄	1	8	yes	—
536	C₂³×C₄	C₂³×D₄	1	8	yes	—
537	C₂³×C₄	C₂³×D₄	1	2	yes	—
538	C₂³×C₄	C₂³×D₄	1	2	yes	—
539	C₂³×C₄	C₂³×D₄	1	4	yes	—
540	C₂³×C₄	C₂³×D₄	1	4	yes	—
541	C₂³×C₄	C₂²×#41	1	4	yes	—
542	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
543	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
544	#117	C₂×#120	1	128	yes	complemented
545	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	—
546	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
547	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
548	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
549	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
550	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
551	C₂⁴	C₂×#392	1	32	yes	—
552	C₂⁴	C₂×#392	1	32	yes	—
553	C₂⁴	C₂×#392	1	32	yes	—
554	C₂⁴	C₂×#392	1	32	yes	—
555	C₂⁴	C₂²×#120	1	16	yes	—
556	C₂⁴	C₂²×#120	1	4	yes	—
557	C₂⁴	C₂²×#120	1	2	yes	—
558	C₂⁴	C₂²×#120	1	1	yes	characteristic
559	C₂⁴	C₂²×#120	1	1	yes	characteristic
560	C₂⁴	C₂²×#120	1	1	yes	characteristic
561	C₂⁴	C₂²×#120	1	2	yes	—
562	C₂⁴	C₂²×#120	1	16	yes	—
563	C₂⁴	C₂²×#120	1	8	yes	—
564	C₂⁴	C₂²×#120	1	16	yes	—
565	C₂⁴	C₂²×#120	1	16	yes	—
566	C₂⁴	C₂²×#120	1	16	yes	—
567	C₂⁴	C₂²×#120	1	4	yes	—
568	C₂⁴	C₂²×#120	1	4	yes	—
569	C₂⁴	C₂²×#120	1	4	yes	—
570	C₂⁴	C₂²×#120	1	8	yes	—
571	C₂⁴	C₂²×#120	1	2	yes	—
572	C₂⁴	C₂²×#120	1	2	yes	—
573	C₂⁴	C₂²×#120	1	1	yes	characteristic
574	C₂⁴	C₂²×#121	1	2	yes	—
575	C₂⁴	C₂²×#121	1	2	yes	—
576	C₂⁴	C₂²×#121	1	2	yes	—
577	C₂⁴	C₂²×#121	1	16	yes	—
578	C₂⁴	C₂²×#121	1	16	yes	—
579	C₂⁴	C₂²×#121	1	16	yes	—
580	C₂⁴	C₂²×#121	1	2	yes	—
581	C₂⁴	C₂²×#121	1	2	yes	—
582	C₂⁴	C₂²×#121	1	2	yes	—
583	C₂⁴	C₂²×#127	1	2	yes	—
584	C₂⁴	C₂²×#127	1	16	yes	—
585	C₂⁴	C₂²×#127	1	2	yes	—
586	C₂⁴	C₂×#534	1	4	yes	—
587	C₂⁴	C₂×#534	1	4	yes	—
588	C₂⁴	C₂×#534	1	4	yes	—
589	C₂⁴	C₂×#534	1	4	yes	—
590	C₂⁴	C₂×#535	1	8	yes	—
591	C₂⁴	C₂×D₄²	1	4	yes	—
592	C₂⁴	C₂×D₄²	1	4	yes	—
593	C₂⁴	C₂×D₄²	1	4	yes	—
594	C₂⁴	C₂×D₄²	1	4	yes	—
595	C₂⁴	C₂×D₄²	1	4	yes	—
596	C₂⁴	C₂×D₄²	1	4	yes	—
597	C₂⁴	C₂×D₄²	1	4	yes	—
598	C₂⁴	C₂×D₄²	1	8	yes	—
599	C₂⁴	C₂×D₄²	1	4	yes	—
600	C₂⁴	C₂×D₄²	1	8	yes	—
601	C₂⁴	C₂×#546	1	8	yes	—
602	C₂⁴	C₂×#546	1	8	yes	—
603	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
604	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
605	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
606	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
607	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
608	C₂⁴	C₂⁴×D₄	1	2	yes	—
609	C₂⁴	C₂⁴×D₄	1	2	yes	—
610	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
611	C₂⁴	C₂³×#41	1	1	yes	characteristic
612	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
613	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
614	C₂×D₄	C₂×#392	1	128	yes	—
615	C₂×D₄	C₂×#392	1	128	yes	—
616	C₂²×C₄	C₂×#392	1	8	yes	—
617	C₂²×C₄	C₂×#392	1	8	yes	—
618	C₂²×C₄	C₂×#392	1	8	yes	—
619	C₂²×C₄	C₂×#392	1	8	yes	—
620	C₂²×C₄	C₂×#392	1	16	yes	—
621	C₂²×C₄	C₂×#392	1	16	yes	—
622	C₂²×C₄	#2403	1	8	yes	—
623	C₂²×C₄	#2403	1	16	yes	—
624	C₂²×C₄	#2403	1	8	yes	—
625	C₂²×C₄	#2403	1	16	yes	—
626	C₂²×C₄	#2403	1	16	yes	—
627	C₂²×C₄	#2403	1	8	yes	—
628	C₂²×C₄	#2403	1	16	yes	—
629	C₂²×C₄	#2403	1	8	yes	—
630	C₂²×C₄	#2403	1	16	yes	—
631	C₂²×C₄	#2403	1	16	yes	—
632	C₂²×C₄	#2403	1	16	yes	—
633	C₂²×C₄	#2403	1	32	yes	—
634	C₂²×C₄	#2403	1	16	yes	—
635	C₂²×C₄	#2403	1	16	yes	—
636	C₂²×C₄	#2403	1	32	yes	—
637	C₂²×C₄	#2403	1	16	yes	—
638	C₂²×C₄	#2408	1	32	yes	—
639	C₂²×C₄	#2408	1	32	yes	—
640	C₂²×C₄	#2408	1	64	yes	—
641	C₂²×C₄	#2410	1	32	yes	—
642	C₂²×C₄	#2410	1	32	yes	—
643	C₂²×C₄	#2410	1	32	yes	—
644	C₂²×C₄	#2410	1	32	yes	—
645	C₂²×C₄	#2410	1	32	yes	—
646	C₂²×C₄	#2410	1	32	yes	—
647	C₂²×C₄	#2410	1	64	yes	—
648	C₂²×C₄	#2433	1	32	yes	—
649	C₂²×C₄	#2433	1	32	yes	—
650	C₂²×C₄	#2433	1	64	yes	—
651	C₂²×C₄	#2613	1	32	yes	—
652	C₂²×C₄	#2613	1	32	yes	—
653	C₂²×C₄	#2846	1	32	yes	—
654	C₂²×C₄	#2846	1	32	yes	—
655	C₂²×C₄	C₂²×#120	1	16	yes	—
656	C₂²×C₄	C₂²×#120	1	8	yes	—
657	C₂²×C₄	C₂²×#120	1	8	yes	—
658	C₂²×C₄	C₂²×#120	1	8	yes	—
659	C₂²×C₄	C₂²×#120	1	8	yes	—
660	C₂²×C₄	C₂²×#120	1	8	yes	—
661	C₂²×C₄	C₂²×#120	1	16	yes	—
662	C₂²×C₄	C₂²×#120	1	8	yes	—
663	C₂²×C₄	C₂²×#120	1	4	yes	—
664	C₂²×C₄	C₂²×#120	1	4	yes	—
665	C₂²×C₄	C₂²×#120	1	4	yes	—
666	C₂²×C₄	C₂²×#120	1	4	yes	—
667	C₂²×C₄	C₂²×#121	1	8	yes	—
668	C₂²×C₄	C₂²×#121	1	8	yes	—
669	C₂²×C₄	C₂²×#121	1	4	yes	—
670	C₂²×C₄	C₂²×#121	1	4	yes	—
671	C₂²×C₄	C₂²×#127	1	8	yes	—
672	C₂²×C₄	C₂×#534	1	8	yes	—
673	C₂²×C₄	C₂×#534	1	8	yes	—
674	C₂²×C₄	C₂×#534	1	8	yes	—
675	C₂²×C₄	C₂×#534	1	8	yes	—
676	C₂²×C₄	C₂×#535	1	16	yes	—
677	C₂²×C₄	C₂×D₄²	1	8	yes	—
678	C₂²×C₄	C₂×D₄²	1	8	yes	—
679	C₂²×C₄	C₂×D₄²	1	8	yes	—
680	C₂²×C₄	C₂×D₄²	1	8	yes	—
681	C₂²×C₄	C₂×D₄²	1	8	yes	—
682	C₂²×C₄	C₂×D₄²	1	8	yes	—
683	C₂²×C₄	C₂×D₄²	1	8	yes	—
684	C₂²×C₄	C₂×D₄²	1	8	yes	—
685	C₂²×C₄	C₂×D₄²	1	16	yes	—
686	C₂²×C₄	C₂×D₄²	1	16	yes	—
687	C₂²×C₄	C₂×#546	1	16	yes	—
688	C₂²×C₄	C₂×#546	1	16	yes	—
689	C₂²⋊C₄	C₂²×#120	1	32	yes	—
690	C₂³	C₂²×#392	1	32	yes	—
691	C₂³	C₂²×#392	1	2	yes	—
692	C₂³	C₂²×#392	1	2	yes	—
693	C₂³	C₂²×#392	1	2	yes	—
694	C₂³	C₂²×#392	1	2	yes	—
695	C₂³	C₂×#2613	1	4	yes	—
696	C₂³	C₂×#2613	1	4	yes	—
697	C₂³	C₂×#2403	1	4	yes	—
698	C₂³	C₂×#2403	1	4	yes	—
699	C₂³	C₂×#2403	1	4	yes	—
700	C₂³	C₂×#2403	1	4	yes	—
701	C₂³	C₂×#2403	1	4	yes	—
702	C₂³	C₂×#2403	1	4	yes	—
703	C₂³	C₂×#2403	1	4	yes	—
704	C₂³	C₂×#2403	1	4	yes	—
705	C₂³	C₂×#2410	1	8	yes	—
706	C₂³	C₂×#2410	1	4	yes	—
707	C₂³	C₂×#2410	1	4	yes	—
708	C₂³	C₂×#2410	1	4	yes	—
709	C₂³	C₂×#2410	1	8	yes	—
710	C₂³	C₂×#2410	1	4	yes	—
711	C₂³	C₂×#2408	1	8	yes	—
712	C₂³	C₂×#2408	1	8	yes	—
713	C₂³	C₂×#2433	1	8	yes	—
714	C₂³	C₂×#2433	1	8	yes	—
715	C₂³	C₂×#2846	1	4	yes	—
716	C₂³	C₂×#2846	1	4	yes	—
717	C₂³	#60399	1	8	yes	—
718	C₂³	C₂³×#120	1	1	yes	characteristic
719	C₂³	C₂³×#120	1	2	yes	—
720	C₂³	C₂³×#120	1	1	yes	characteristic
721	C₂³	C₂³×#120	1	1	yes	characteristic
722	C₂³	C₂³×#120	1	1	yes	characteristic
723	C₂³	C₂³×#120	1	2	yes	—
724	C₂³	C₂³×#120	1	1	yes	characteristic
725	C₂³	C₂³×#121	1	1	yes	characteristic
726	C₂³	C₂³×#121	1	1	yes	characteristic
727	C₂³	C₂³×#121	1	1	yes	characteristic
728	C₂³	C₂³×#127	1	1	yes	characteristic
729	C₂³	C₂²×#534	1	2	yes	—
730	C₂³	C₂²×#534	1	1	yes	characteristic
731	C₂³	C₂²×#534	1	1	yes	characteristic
732	C₂³	C₂²×#535	1	2	yes	—
733	C₂³	C₂²×D₄²	1	2	yes	—
734	C₂³	C₂²×D₄²	1	2	yes	—
735	C₂³	C₂²×D₄²	1	2	yes	—
736	C₂³	C₂²×D₄²	1	2	yes	—
737	C₂³	C₂²×D₄²	1	2	yes	—
738	C₂³	C₂²×D₄²	1	2	yes	—
739	C₂³	C₂²×#546	1	2	yes	—
740	C₂³	C₂²×#546	1	2	yes	—
741	C₂×C₄	#14715	1	32	yes	—
742	C₂×C₄	#14715	1	32	yes	—
743	C₂×C₄	#14715	1	64	yes	—
744	C₂×C₄	#14715	1	32	yes	—
745	C₂×C₄	#14715	1	32	yes	—
746	C₂×C₄	#14715	1	64	yes	—
747	C₂×C₄	C₂²×#392	1	8	yes	—
748	C₂×C₄	C₂²×#392	1	8	yes	—
749	C₂×C₄	C₂×#2613	1	16	yes	—
750	C₂×C₄	C₂×#2403	1	8	yes	—
751	C₂×C₄	C₂×#2403	1	8	yes	—
752	C₂×C₄	C₂×#2403	1	8	yes	—
753	C₂×C₄	C₂×#2403	1	8	yes	—
754	C₂×C₄	C₂×#2403	1	8	yes	—
755	C₂×C₄	C₂×#2403	1	8	yes	—
756	C₂×C₄	C₂×#2403	1	8	yes	—
757	C₂×C₄	C₂×#2403	1	8	yes	—
758	C₂×C₄	C₂×#2410	1	16	yes	—
759	C₂×C₄	C₂×#2410	1	16	yes	—
760	C₂×C₄	C₂×#2410	1	16	yes	—
761	C₂×C₄	C₂×#2410	1	16	yes	—
762	C₂×C₄	C₂×#2408	1	16	yes	—
763	C₂×C₄	C₂×#2408	1	16	yes	—
764	C₂×C₄	C₂×#2433	1	16	yes	—
765	C₂×C₄	C₂×#2433	1	16	yes	—
766	C₂×C₄	C₂×#2846	1	16	yes	—
767	C₂²	C₂×#14715	1	4	yes	—
768	C₂²	C₂×#14715	1	4	yes	—
769	C₂²	C₂×#14715	1	4	yes	—
770	C₂²	C₂×#14715	1	4	yes	—
771	C₂²	#6431795	1	8	yes	—
772	C₂²	#6437633	1	16	yes	—
773	C₂²	C₂³×#392	1	1	yes	characteristic
774	C₂²	C₂²×#2613	1	1	yes	characteristic
775	C₂²	C₂²×#2403	1	1	yes	characteristic
776	C₂²	C₂²×#2403	1	1	yes	characteristic
777	C₂²	C₂²×#2403	1	2	yes	—
778	C₂²	C₂²×#2410	1	2	yes	—
779	C₂²	C₂²×#2410	1	1	yes	characteristic
780	C₂²	C₂²×#2410	1	1	yes	characteristic
781	C₂²	C₂²×#2408	1	2	yes	—
782	C₂²	C₂²×#2433	1	2	yes	—
783	C₂²	C₂²×#2846	1	1	yes	characteristic
784	C₂²	C₂×#60399	1	4	yes	—
785	C₄	C₂×#14715	1	16	yes	—
786	C₄	C₂×#14715	1	16	yes	—
787	C₂	C₂×#6431795	1	2	yes	—
788	C₂	#72238034	1	8	yes	direct product factor
789	C₂	C₂²×#14715	1	1	yes	characteristic
790	C₂	C₂×#6437633	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂²×#120
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#357529	C₂	semidirect
2. C₂×#394061	C₂	semidirect
3. C₂²×#23445	C₂	semidirect
4. C₂×#357531	C₂	semidirect
5. C₂²×#20985	C₂	semidirect
6. C₂²×#20586	C₂	semidirect
7. C₂×#353409	C₂	semidirect
8. C₂×#7630502	C₂	semidirect
9. C₂²×#23443	C₂	semidirect
10. C₂×#517415	C₂	semidirect
11. C₂²×#35222	C₂	semidirect
12. #72238034	C₂	direct (N × H)
13. C₂³×#3484	C₂	semidirect
14. C₂×#394058	C₂	semidirect
17. C₂²×#3484	C₂²	semidirect
18. C₂²×#3449	C₂²	semidirect
21. C₂³×#535	C₂²	semidirect
24. C₂³×#525	C₂²	semidirect
27. C₂³×#410	C₂²	semidirect
28. C₂³×#410	C₂²	semidirect
29. C₂³×#410	C₂²	semidirect
30. C₂²×#2846	C₂²	semidirect
31. #7630502	C₂²	semidirect
32. C₂×#35222	C₂²	semidirect
33. C₂×#34980	C₂²	semidirect
34. C₂²×#2613	C₂²	semidirect
35. C₂×#34044	C₂²	semidirect
39. C₂²×#2309	C₂²	semidirect
40. C₂²×#2309	C₂²	semidirect
41. C₂²×#2280	C₂²	semidirect
42. C₂²×#2280	C₂²	semidirect
43. C₂×#23445	C₂²	semidirect
44. C₂×#23443	C₂²	semidirect
45. C₂²×#2022	C₂²	semidirect
46. C₂²×#2021	C₂²	semidirect
47. C₂²×#2021	C₂²	semidirect
48. C₂×#20985	C₂²	semidirect
49. C₂²×#1898	C₂²	semidirect
50. C₂×#20586	C₂²	semidirect
51. C₂²×#1781	C₂²	semidirect
52. C₂²×#1740	C₂²	semidirect
53. C₂²×#1740	C₂²	semidirect
54. C₂²×#1740	C₂²	semidirect
55. C₂×#14679	C₂²	semidirect
56. #517415	C₂²	semidirect
57. C₂×#14335	C₂²	semidirect
58. #394061	C₂²	semidirect
59. #394058	C₂²	semidirect
60. #357531	C₂²	semidirect
61. #357529	C₂²	semidirect
62. C₂×#10992	C₂²	semidirect
63. C₂×#10991	C₂²	semidirect
64. C₂×#10991	C₂²	semidirect
65. #353409	C₂²	semidirect
66. C₂×#10735	C₂²	semidirect
68. C₂³×H(5,𝔽₂)	D₄	semidirect
70. C₂⁴×#41	D₄	semidirect
73. C₂⁵×D₄	D₄	semidirect
74. C₂⁵×D₄	D₄	semidirect
81. C₂×#3449	C₂³	semidirect
82. C₂²×#535	D₄	semidirect
83. C₂²×#535	D₄	semidirect
86. C₂²×#535	C₂³	semidirect
89. C₂³×#127	D₄	semidirect
90. C₂³×#124	D₄	semidirect
91. C₂²×#525	D₄	semidirect
93. C₂²×#525	C₂³	semidirect
96. C₂³×#121	D₄	semidirect
103. C₂²×#518	D₄	semidirect
112. C₂²×#410	C₂³	semidirect
113. C₂²×#410	C₂³	semidirect
114. C₂²×#410	C₂³	semidirect
118. C₂×#2846	C₂³	semidirect
119. #34980	C₂³	semidirect
120. C₂×#2613	C₂³	semidirect
121. #34044	C₂³	semidirect
122. C₂×#2309	D₄	semidirect
123. C₂×#2309	D₄	semidirect
127. C₂×#2309	C₂³	semidirect
128. C₂×#2309	C₂³	semidirect
130. C₂²×#390	D₄	semidirect
131. C₂×#2280	C₂³	semidirect
132. C₂×#2280	C₂³	semidirect
142. C₂×#2022	C₂³	semidirect
143. C₂×#2021	C₂³	semidirect
144. C₂×#2021	C₂³	semidirect
145. C₂×#1898	C₂³	semidirect
146. C₂×#1781	C₂³	semidirect
147. C₂×#1740	C₂³	semidirect
148. C₂×#1740	C₂³	semidirect
149. C₂×#1740	C₂³	semidirect
153. #14679	C₂³	semidirect
154. #14335	C₂³	semidirect
155. #10992	C₂³	semidirect
156. #10991	C₂³	semidirect
157. #10991	C₂³	semidirect
158. #10735	C₂³	semidirect
168. C₂³×#41	C₂×D₄	semidirect
169. C₂³×#41	C₂×D₄	semidirect
173. C₂⁴×Q₈	C₂×D₄	semidirect
190. C₂⁴×D₄	C₂×D₄	semidirect
191. C₂⁴×D₄	C₂×D₄	semidirect
192. C₂⁴×D₄	C₂×D₄	semidirect
193. C₂⁴×D₄	C₂×D₄	semidirect
205. C₂⁵×C₄	C₂×D₄	semidirect
209. C₂×#535	C₂×D₄	semidirect
211. C₂²×#127	C₂×D₄	semidirect
212. C₂²×#124	C₂×D₄	semidirect
213. C₂×#525	C₂×D₄	semidirect
217. C₂²×#121	C₂×D₄	semidirect
220. C₂²×#120	C₂×D₄	semidirect
226. C₂×#518	C₂×D₄	semidirect
230. C₂²×#117	C₂×D₄	semidirect
231. C₂²×#117	C₂×D₄	semidirect
232. C₂²×#117	C₂×D₄	semidirect
233. C₂²×#117	C₂×D₄	semidirect
240. C₂³×C₄⋊C₄	C₂×D₄	semidirect
241. C₂³×C₄⋊C₄	C₂×D₄	semidirect
243. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
244. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
252. C₂³×C₄²	C₂×D₄	semidirect
253. C₂³×C₄²	C₂×D₄	semidirect
257. #2309	C₂×D₄	semidirect
259. C₂×#390	C₂×D₄	semidirect
262. C₂×#379	C₂×D₄	semidirect
263. C₂×#379	C₂×D₄	semidirect
296. C₂²×#41	#120	semidirect
299. C₂³×Q₈	#120	semidirect
301. C₂³×Q₈	C₂²×D₄	semidirect
313. C₂³×D₄	#120	semidirect
314. C₂³×D₄	#120	semidirect
340. C₂³×D₄	C₂²×D₄	semidirect
341. C₂³×D₄	C₂²×D₄	semidirect
345. C₂⁴×C₄	#120	semidirect
346. C₂⁴×C₄	#120	semidirect
369. C₂⁴×C₄	C₂²×D₄	semidirect
378. C₂×#117	#120	semidirect
382. C₂×#117	C₂²×D₄	semidirect
383. C₂×#117	C₂²×D₄	semidirect
384. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
385. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
394. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
395. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
402. C₂²×C₄²	C₂²×D₄	semidirect
403. C₂²×C₄²	C₂²×D₄	semidirect
404. #379	C₂²×D₄	semidirect
452. C₂²×Q₈	C₂×#120	semidirect
465. C₂²×D₄	C₂×#120	semidirect
466. C₂²×D₄	C₂×#120	semidirect
493. C₂³×C₄	C₂×#120	semidirect
494. C₂³×C₄	C₂×#120	semidirect
544. #117	C₂×#120	semidirect
788. C₂	#72238034	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×#357529	2
C₂×#394061	2
C₂²×#23445	2
C₂×#357531	2
C₂²×#20985	2
C₂²×#20586	2
C₂×#353409	2
C₂×#7630502	2
C₂²×#23443	2
C₂×#517415	2
C₂²×#35222	2
#72238034	2
C₂³×#3484	2
C₂×#394058	2

Subgroups — C2×#72238034 #72314980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72238034 #72314980