Subgroups — C₂²×#394064 #72250897

Order 2048.

At least 6808 conjugacy classes of subgroups; only the 11912 normal subgroups are shown.

The subgroup lattice has 706 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×#10991	C₂	1	2	yes	maximal, complemented
2	C₂²×#23444	C₂	1	2	yes	maximal, complemented
3	C₂³×#3026	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×#1913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#10754	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#20609	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×#1781	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10972	C₂	1	2	yes	maximal, complemented
9	C₂²×#34980	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#394064	C₂	1	48	yes	maximal, direct product factor
11	C₂³×#2021	C₂	1	2	yes	maximal, complemented
12	C₂³×#3484	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂⁶×D₄	C₂²	1	1	yes	characteristic
15	C₂²×#3484	C₂²	1	24	yes	complemented
16	C₂³×#534	C₂²	1	2	yes	—
17	C₂³×#534	C₂²	1	1	yes	characteristic
18	C₂³×#534	C₂²	1	1	yes	characteristic, complemented
19	C₂³×#534	C₂²	1	2	yes	complemented
20	C₂⁴×#120	C₂²	1	2	yes	—
21	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
22	C₂³×#518	C₂²	1	1	yes	characteristic
23	C₂²×#3026	C₂²	1	24	yes	complemented
24	C₂⁴×#99	C₂²	1	1	yes	characteristic
25	C₂⁴×#99	C₂²	1	1	yes	characteristic
26	C₂⁴×#99	C₂²	1	2	yes	complemented
27	C₂⁴×#99	C₂²	1	2	yes	complemented
28	C₂⁴×#99	C₂²	1	2	yes	complemented
29	C₂⁴×#99	C₂²	1	2	yes	complemented
30	C₂×#34980	C₂²	1	24	yes	complemented
31	C₂²×#2308	C₂²	1	1	yes	characteristic
32	C₂²×#2308	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#2308	C₂²	1	2	yes	complemented
34	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
35	C₂³×#379	C₂²	1	2	yes	complemented
36	C₂×#23444	C₂²	1	48	yes	complemented
37	C₂²×#2021	C₂²	1	48	yes	complemented
38	C₂²×#1913	C₂²	1	24	yes	complemented
39	C₂×#20609	C₂²	1	24	yes	complemented
40	C₂²×#1781	C₂²	1	24	yes	complemented
41	C₂³×#342	C₂²	1	2	yes	complemented
42	C₂³×#342	C₂²	1	2	yes	complemented
43	C₂³×#342	C₂²	1	2	yes	complemented
44	#394064	C₂²	1	256	yes	direct product factor
45	C₂×#10991	C₂²	1	48	yes	complemented
46	C₂×#10972	C₂²	1	48	yes	complemented
47	C₂×#10754	C₂²	1	24	yes	complemented
48	C₂⁸	D₄	1	1	yes	characteristic, complemented
49	C₂⁸	C₂³	1	1	yes	characteristic
50	C₂³×H(5,𝔽₂)	D₄	1	16	yes	complemented
51	C₂³×H(5,𝔽₂)	C₂³	1	12	yes	—
52	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
53	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
54	C₂⁵×D₄	D₄	1	12	yes	complemented
55	C₂⁵×D₄	C₂³	1	2	yes	—
56	C₂⁵×D₄	C₂³	1	1	yes	characteristic
57	C₂⁵×D₄	C₂³	1	1	yes	characteristic
58	C₂⁵×D₄	C₂³	1	1	yes	characteristic
59	C₂⁵×D₄	C₂³	1	12	yes	—
60	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
61	C₂×#3484	C₂³	1	64	yes	complemented
62	C₂²×#534	D₄	1	24	yes	complemented
63	C₂²×#534	D₄	1	12	yes	complemented
64	C₂²×#534	C₂³	1	12	yes	—
65	C₂²×#534	C₂³	1	24	yes	—
66	C₂²×#534	C₂³	1	12	yes	complemented
67	C₂²×#534	C₂³	1	24	yes	complemented
68	C₂³×#123	D₄	1	4	yes	complemented
69	C₂³×#123	D₄	1	2	yes	complemented
70	C₂³×#120	D₄	1	32	yes	complemented
71	C₂³×#120	D₄	1	4	yes	complemented
72	C₂³×#120	D₄	1	2	yes	complemented
73	C₂³×#120	C₂³	1	24	yes	—
74	C₂³×#120	C₂³	1	12	yes	complemented
75	C₂²×#518	D₄	1	16	yes	complemented
76	C₂²×#518	C₂³	1	12	yes	—
77	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
78	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
79	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
80	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
81	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
82	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×#3026	C₂³	1	64	yes	complemented
84	C₂³×#99	D₄	1	16	yes	complemented
85	C₂³×#99	C₂³	1	12	yes	—
86	C₂³×#99	C₂³	1	12	yes	—
87	C₂³×#99	C₂³	1	24	yes	complemented
88	C₂³×#99	C₂³	1	24	yes	complemented
89	C₂³×#99	C₂³	1	24	yes	complemented
90	C₂³×#99	C₂³	1	24	yes	complemented
91	#34980	C₂³	1	64	yes	complemented
92	C₂×#2308	D₄	1	12	yes	complemented
93	C₂×#2308	C₂³	1	12	yes	—
94	C₂×#2308	C₂³	1	12	yes	complemented
95	C₂×#2308	C₂³	1	24	yes	complemented
96	C₂²×#386	D₄	1	4	yes	complemented
97	C₂²×#379	C₂³	1	12	yes	complemented
98	C₂²×#379	C₂³	1	24	yes	complemented
99	#23444	C₂³	1	128	yes	complemented
100	C₂×#2021	C₂³	1	128	yes	complemented
101	C₂×#1913	C₂³	1	64	yes	complemented
102	#20609	C₂³	1	64	yes	complemented
103	C₂×#1781	C₂³	1	64	yes	complemented
104	C₂²×#342	C₂³	1	24	yes	complemented
105	C₂²×#342	C₂³	1	24	yes	complemented
106	C₂²×#342	C₂³	1	24	yes	complemented
107	#10991	C₂³	1	128	yes	complemented
108	#10972	C₂³	1	128	yes	complemented
109	#10754	C₂³	1	64	yes	complemented
110	C₂⁷	C₂×D₄	1	1	yes	characteristic
111	C₂⁷	C₂×D₄	1	16	yes	—
112	C₂⁷	C₂×D₄	1	1	yes	characteristic
113	C₂⁷	C₂×D₄	1	6	yes	—
114	C₂⁷	C₂×D₄	1	1	yes	characteristic
115	C₂⁷	C₂×D₄	1	2	yes	—
116	C₂⁷	C₂×D₄	1	1	yes	characteristic
117	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
118	C₂⁷	C₂×D₄	1	12	yes	complemented
119	C₂⁷	C₂⁴	1	6	yes	—
120	C₂⁷	C₂⁴	1	1	yes	characteristic
121	C₂²×H(5,𝔽₂)	C₂×D₄	1	96	yes	complemented
122	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
123	C₂⁴×D₄	C₂×D₄	1	4	yes	—
124	C₂⁴×D₄	C₂×D₄	1	12	yes	—
125	C₂⁴×D₄	C₂×D₄	1	2	yes	—
126	C₂⁴×D₄	C₂×D₄	1	6	yes	—
127	C₂⁴×D₄	C₂×D₄	1	8	yes	—
128	C₂⁴×D₄	C₂×D₄	1	8	yes	—
129	C₂⁴×D₄	C₂×D₄	1	2	yes	—
130	C₂⁴×D₄	C₂×D₄	1	6	yes	—
131	C₂⁴×D₄	C₂×D₄	1	16	yes	—
132	C₂⁴×D₄	C₂×D₄	1	16	yes	—
133	C₂⁴×D₄	C₂×D₄	1	8	yes	—
134	C₂⁴×D₄	C₂×D₄	1	6	yes	—
135	C₂⁴×D₄	C₂×D₄	1	12	yes	—
136	C₂⁴×D₄	C₂×D₄	1	6	yes	—
137	C₂⁴×D₄	C₂×D₄	1	12	yes	complemented
138	C₂⁴×D₄	C₂×D₄	1	12	yes	complemented
139	C₂⁴×D₄	C₂×D₄	1	6	yes	complemented
140	C₂⁴×D₄	C₂×D₄	1	48	yes	complemented
141	C₂⁴×D₄	#41	1	8	yes	—
142	C₂⁴×D₄	C₂⁴	1	6	yes	—
143	C₂⁴×D₄	C₂⁴	1	12	yes	—
144	C₂⁴×D₄	C₂⁴	1	6	yes	—
145	C₂⁴×D₄	C₂⁴	1	6	yes	—
146	C₂⁴×D₄	C₂⁴	1	16	yes	—
147	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂⁵×C₄	C₂×D₄	1	2	yes	—
149	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
151	C₂⁵×C₄	C₂×D₄	1	12	yes	complemented
152	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
153	C₂×#534	C₂×D₄	1	96	yes	complemented
154	C₂×#534	C₂×D₄	1	48	yes	complemented
155	C₂×#534	C₂⁴	1	16	yes	—
156	C₂×#534	C₂⁴	1	32	yes	—
157	C₂×#534	C₂⁴	1	16	yes	complemented
158	C₂×#534	C₂⁴	1	32	yes	complemented
159	C₂²×#123	C₂×D₄	1	48	yes	complemented
160	C₂²×#123	C₂×D₄	1	24	yes	complemented
161	C₂²×#120	C₂×D₄	1	192	yes	complemented
162	C₂²×#120	C₂×D₄	1	48	yes	complemented
163	C₂²×#120	C₂×D₄	1	24	yes	complemented
164	C₂²×#120	C₂⁴	1	32	yes	—
165	C₂²×#120	C₂⁴	1	16	yes	complemented
166	C₂×#518	C₂×D₄	1	96	yes	complemented
167	C₂×#518	C₂⁴	1	16	yes	—
168	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
169	C₂³×C₂²⋊C₄	C₂×D₄	1	12	yes	—
170	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
171	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
172	C₂³×C₂²⋊C₄	C₂×D₄	1	6	yes	complemented
173	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
174	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
175	C₂³×C₂²⋊C₄	C₂×D₄	1	6	yes	complemented
176	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
177	C₂³×C₂²⋊C₄	C₂×D₄	1	6	yes	complemented
178	C₂³×C₂²⋊C₄	C₂⁴	1	12	yes	—
179	C₂³×C₂²⋊C₄	C₂⁴	1	6	yes	—
180	C₂³×C₂²⋊C₄	C₂⁴	1	12	yes	—
181	C₂³×C₂²⋊C₄	C₂⁴	1	6	yes	—
182	C₂³×C₂²⋊C₄	C₂⁴	1	6	yes	—
183	C₂³×C₂²⋊C₄	C₂⁴	1	12	yes	—
184	C₂²×#99	C₂×D₄	1	96	yes	complemented
185	C₂²×#99	C₂⁴	1	16	yes	—
186	C₂²×#99	C₂⁴	1	16	yes	—
187	C₂²×#99	C₂⁴	1	32	yes	complemented
188	C₂²×#99	C₂⁴	1	32	yes	complemented
189	C₂²×#99	C₂⁴	1	32	yes	complemented
190	C₂²×#99	C₂⁴	1	32	yes	complemented
191	#2308	C₂×D₄	1	48	yes	complemented
192	#2308	C₂⁴	1	16	yes	—
193	#2308	C₂⁴	1	16	yes	complemented
194	#2308	C₂⁴	1	32	yes	complemented
195	C₂×#386	C₂×D₄	1	48	yes	complemented
196	C₂×#379	C₂⁴	1	16	yes	complemented
197	C₂×#379	C₂⁴	1	32	yes	complemented
198	C₂×#342	C₂⁴	1	32	yes	complemented
199	C₂×#342	C₂⁴	1	32	yes	complemented
200	C₂×#342	C₂⁴	1	32	yes	complemented
201	C₂⁶	#120	1	8	yes	—
202	C₂⁶	#120	1	2	yes	—
203	C₂⁶	#120	1	8	yes	—
204	C₂⁶	#120	1	48	yes	—
205	C₂⁶	#120	1	6	yes	—
206	C₂⁶	#120	1	2	yes	—
207	C₂⁶	#120	1	8	yes	—
208	C₂⁶	#120	1	6	yes	—
209	C₂⁶	#120	1	16	yes	complemented
210	C₂⁶	#121	1	8	yes	—
211	C₂⁶	C₂²×D₄	1	6	yes	—
212	C₂⁶	C₂²×D₄	1	48	yes	—
213	C₂⁶	C₂²×D₄	1	6	yes	—
214	C₂⁶	C₂²×D₄	1	6	yes	—
215	C₂⁶	C₂²×D₄	1	12	yes	—
216	C₂⁶	C₂²×D₄	1	12	yes	—
217	C₂⁶	C₂²×D₄	1	6	yes	—
218	C₂⁶	C₂²×D₄	1	1	yes	characteristic
219	C₂⁶	C₂²×D₄	1	2	yes	—
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	3	yes	—
223	C₂⁶	C₂²×D₄	1	4	yes	—
224	C₂⁶	C₂²×D₄	1	4	yes	—
225	C₂⁶	C₂²×D₄	1	8	yes	—
226	C₂⁶	C₂²×D₄	1	6	yes	—
227	C₂⁶	C₂²×D₄	1	3	yes	—
228	C₂⁶	C₂²×D₄	1	3	yes	—
229	C₂⁶	C₂²×D₄	1	4	yes	—
230	C₂⁶	C₂²×D₄	1	6	yes	complemented
231	C₂⁶	C₂²×D₄	1	16	yes	complemented
232	C₂⁶	C₂×#41	1	4	yes	—
233	C₂⁶	H(5,𝔽₂)	1	2	yes	—
234	C₂⁶	H(5,𝔽₂)	1	6	yes	—
235	C₂⁶	H(5,𝔽₂)	1	8	yes	—
236	C₂⁶	C₂⁵	1	4	yes	—
237	C₂⁶	C₂⁵	1	3	yes	—
238	C₂×H(5,𝔽₂)	C₂²×D₄	1	64	yes	complemented
239	C₂³×D₄	#120	1	24	yes	—
240	C₂³×D₄	#120	1	24	yes	—
241	C₂³×D₄	#120	1	24	yes	—
242	C₂³×D₄	#120	1	48	yes	—
243	C₂³×D₄	#120	1	12	yes	—
244	C₂³×D₄	#120	1	12	yes	—
245	C₂³×D₄	#120	1	16	yes	—
246	C₂³×D₄	#120	1	48	yes	—
247	C₂³×D₄	#120	1	96	yes	complemented
248	C₂³×D₄	#121	1	48	yes	—
249	C₂³×D₄	#121	1	16	yes	—
250	C₂³×D₄	#121	1	48	yes	—
251	C₂³×D₄	#121	1	16	yes	—
252	C₂³×D₄	#121	1	48	yes	—
253	C₂³×D₄	#127	1	16	yes	—
254	C₂³×D₄	#127	1	48	yes	—
255	C₂³×D₄	C₂²×D₄	1	24	yes	—
256	C₂³×D₄	C₂²×D₄	1	24	yes	—
257	C₂³×D₄	C₂²×D₄	1	12	yes	—
258	C₂³×D₄	C₂²×D₄	1	12	yes	—
259	C₂³×D₄	C₂²×D₄	1	24	yes	—
260	C₂³×D₄	C₂²×D₄	1	12	yes	—
261	C₂³×D₄	C₂²×D₄	1	24	yes	—
262	C₂³×D₄	C₂²×D₄	1	12	yes	—
263	C₂³×D₄	C₂²×D₄	1	48	yes	—
264	C₂³×D₄	C₂²×D₄	1	48	yes	—
265	C₂³×D₄	C₂²×D₄	1	24	yes	—
266	C₂³×D₄	C₂²×D₄	1	12	yes	—
267	C₂³×D₄	C₂²×D₄	1	24	yes	—
268	C₂³×D₄	C₂²×D₄	1	12	yes	—
269	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
270	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
271	C₂³×D₄	C₂²×D₄	1	12	yes	complemented
272	C₂³×D₄	C₂×#41	1	24	yes	—
273	C₂³×D₄	C₂⁵	1	4	yes	—
274	C₂³×D₄	C₂⁵	1	8	yes	—
275	C₂³×D₄	C₂⁵	1	4	yes	—
276	C₂³×D₄	C₂⁵	1	4	yes	—
277	C₂⁴×C₄	#120	1	2	yes	—
278	C₂⁴×C₄	#120	1	6	yes	—
279	C₂⁴×C₄	#120	1	8	yes	—
280	C₂⁴×C₄	#120	1	2	yes	—
281	C₂⁴×C₄	#120	1	6	yes	—
282	C₂⁴×C₄	#120	1	16	yes	complemented
283	C₂⁴×C₄	#121	1	8	yes	—
284	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
285	C₂⁴×C₄	C₂²×D₄	1	12	yes	—
286	C₂⁴×C₄	C₂²×D₄	1	6	yes	—
287	C₂⁴×C₄	C₂²×D₄	1	6	yes	complemented
288	C₂⁴×C₄	C₂²×D₄	1	16	yes	complemented
289	C₂⁴×C₄	C₂²×D₄	1	12	yes	complemented
290	C₂×#123	C₂²×D₄	1	64	yes	complemented
291	C₂×#123	C₂²×D₄	1	32	yes	complemented
292	C₂×#120	C₂²×D₄	1	128	yes	complemented
293	C₂×#120	C₂²×D₄	1	64	yes	complemented
294	C₂×#120	C₂²×D₄	1	32	yes	complemented
295	#518	C₂²×D₄	1	64	yes	complemented
296	C₂²×C₂²⋊C₄	#120	1	32	yes	complemented
297	C₂²×C₂²⋊C₄	#120	1	96	yes	complemented
298	C₂²×C₂²⋊C₄	C₂²×D₄	1	24	yes	—
299	C₂²×C₂²⋊C₄	C₂²×D₄	1	24	yes	—
300	C₂²×C₂²⋊C₄	C₂²×D₄	1	48	yes	—
301	C₂²×C₂²⋊C₄	C₂²×D₄	1	48	yes	—
302	C₂²×C₂²⋊C₄	C₂²×D₄	1	12	yes	complemented
303	C₂²×C₂²⋊C₄	C₂²×D₄	1	12	yes	complemented
304	C₂²×C₂²⋊C₄	C₂²×D₄	1	12	yes	complemented
305	C₂²×C₂²⋊C₄	C₂²×D₄	1	48	yes	complemented
306	C₂²×C₂²⋊C₄	C₂²×D₄	1	12	yes	complemented
307	C₂²×C₂²⋊C₄	C₂²×D₄	1	12	yes	complemented
308	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
309	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
310	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
311	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
312	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
313	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
314	C₂×#99	C₂²×D₄	1	64	yes	complemented
315	#386	C₂²×D₄	1	64	yes	complemented
316	C₂⁵	#392	1	16	yes	—
317	C₂⁵	#392	1	48	yes	—
318	C₂⁵	C₂×#120	1	1	yes	characteristic
319	C₂⁵	C₂×#120	1	1	yes	characteristic
320	C₂⁵	C₂×#120	1	12	yes	—
321	C₂⁵	C₂×#120	1	24	yes	—
322	C₂⁵	C₂×#120	1	24	yes	—
323	C₂⁵	C₂×#120	1	48	yes	—
324	C₂⁵	C₂×#120	1	12	yes	—
325	C₂⁵	C₂×#120	1	12	yes	—
326	C₂⁵	C₂×#120	1	24	yes	—
327	C₂⁵	C₂×#120	1	12	yes	—
328	C₂⁵	C₂×#120	1	4	yes	—
329	C₂⁵	C₂×#120	1	4	yes	—
330	C₂⁵	C₂×#120	1	3	yes	—
331	C₂⁵	C₂×#120	1	6	yes	—
332	C₂⁵	C₂×#120	1	8	yes	—
333	C₂⁵	C₂×#120	1	8	yes	—
334	C₂⁵	C₂×#120	1	3	yes	—
335	C₂⁵	C₂×#120	1	4	yes	—
336	C₂⁵	C₂×#120	1	3	yes	—
337	C₂⁵	C₂×#120	1	3	yes	—
338	C₂⁵	C₂×#120	1	12	yes	—
339	C₂⁵	C₂×#120	1	12	yes	—
340	C₂⁵	C₂×#120	1	6	yes	—
341	C₂⁵	C₂×#120	1	24	yes	—
342	C₂⁵	C₂×#120	1	24	yes	—
343	C₂⁵	C₂×#120	1	12	yes	—
344	C₂⁵	C₂×#120	1	6	yes	—
345	C₂⁵	C₂×#120	1	48	yes	complemented
346	C₂⁵	C₂×#121	1	24	yes	—
347	C₂⁵	C₂×#121	1	4	yes	—
348	C₂⁵	C₂×#121	1	4	yes	—
349	C₂⁵	C₂×#121	1	4	yes	—
350	C₂⁵	C₂×#121	1	12	yes	—
351	C₂⁵	C₂×#121	1	12	yes	—
352	C₂⁵	C₂×#121	1	12	yes	—
353	C₂⁵	C₂×#127	1	4	yes	—
354	C₂⁵	C₂×#127	1	12	yes	—
355	C₂⁵	#534	1	1	yes	characteristic
356	C₂⁵	#534	1	4	yes	—
357	C₂⁵	#534	1	3	yes	—
358	C₂⁵	#534	1	6	yes	—
359	C₂⁵	#534	1	8	yes	—
360	C₂⁵	#534	1	24	yes	—
361	C₂⁵	#534	1	12	yes	—
362	C₂⁵	#534	1	6	yes	—
363	C₂⁵	#535	1	8	yes	—
364	C₂⁵	#535	1	24	yes	—
365	C₂⁵	D₄²	1	2	yes	—
366	C₂⁵	D₄²	1	2	yes	—
367	C₂⁵	D₄²	1	6	yes	—
368	C₂⁵	D₄²	1	6	yes	—
369	C₂⁵	D₄²	1	8	yes	—
370	C₂⁵	D₄²	1	6	yes	—
371	C₂⁵	D₄²	1	6	yes	—
372	C₂⁵	D₄²	1	8	yes	—
373	C₂⁵	D₄²	1	8	yes	—
374	C₂⁵	D₄²	1	6	yes	—
375	C₂⁵	D₄²	1	6	yes	—
376	C₂⁵	D₄²	1	8	yes	—
377	C₂⁵	D₄²	1	12	yes	—
378	C₂⁵	D₄²	1	24	yes	—
379	C₂⁵	D₄²	1	12	yes	—
380	C₂⁵	D₄²	1	24	yes	—
381	C₂⁵	D₄²	1	24	yes	—
382	C₂⁵	D₄²	1	24	yes	—
383	C₂⁵	#546	1	8	yes	—
384	C₂⁵	#546	1	8	yes	—
385	C₂⁵	#546	1	24	yes	—
386	C₂⁵	#546	1	24	yes	—
387	C₂⁵	C₂³×D₄	1	4	yes	—
388	C₂⁵	C₂³×D₄	1	4	yes	—
389	C₂⁵	C₂³×D₄	1	4	yes	—
390	C₂⁵	C₂³×D₄	1	16	yes	—
391	C₂⁵	C₂³×D₄	1	8	yes	—
392	C₂⁵	C₂³×D₄	1	4	yes	—
393	C₂⁵	C₂³×D₄	1	3	yes	—
394	C₂⁵	C₂³×D₄	1	6	yes	—
395	C₂⁵	C₂³×D₄	1	3	yes	—
396	C₂⁵	C₂³×D₄	1	3	yes	—
397	C₂⁵	C₂³×D₄	1	3	yes	—
398	C₂⁵	C₂³×D₄	1	6	yes	—
399	C₂⁵	C₂³×D₄	1	6	yes	—
400	C₂⁵	C₂³×D₄	1	12	yes	—
401	C₂⁵	C₂³×D₄	1	6	yes	—
402	C₂⁵	C₂³×D₄	1	3	yes	—
403	C₂⁵	C₂³×D₄	1	3	yes	—
404	C₂⁵	C₂³×D₄	1	6	yes	—
405	C₂⁵	C₂³×D₄	1	4	yes	complemented
406	C₂⁵	C₂²×#41	1	6	yes	—
407	C₂⁵	C₂×H(5,𝔽₂)	1	6	yes	—
408	C₂⁵	C₂×H(5,𝔽₂)	1	6	yes	—
409	C₂⁵	C₂×H(5,𝔽₂)	1	12	yes	—
410	C₂⁵	C₂⁶	1	1	yes	characteristic
411	C₂²×D₄	#392	1	96	yes	—
412	C₂²×D₄	#392	1	96	yes	—
413	C₂²×D₄	#392	1	192	yes	—
414	C₂²×D₄	C₂×#120	1	48	yes	—
415	C₂²×D₄	C₂×#120	1	48	yes	—
416	C₂²×D₄	C₂×#120	1	48	yes	—
417	C₂²×D₄	C₂×#120	1	48	yes	—
418	C₂²×D₄	C₂×#120	1	24	yes	—
419	C₂²×D₄	C₂×#120	1	24	yes	—
420	C₂²×D₄	C₂×#120	1	96	yes	complemented
421	C₂²×D₄	C₂×#121	1	48	yes	—
422	C₂²×D₄	C₂×#121	1	48	yes	—
423	C₂²×D₄	C₂×#121	1	48	yes	—
424	C₂²×D₄	C₂×#121	1	48	yes	—
425	C₂²×D₄	C₂×#121	1	48	yes	—
426	C₂²×D₄	C₂×#127	1	48	yes	—
427	C₂²×D₄	C₂×#127	1	48	yes	—
428	C₂²×D₄	C₂³×D₄	1	16	yes	—
429	C₂²×D₄	C₂³×D₄	1	8	yes	—
430	C₂²×D₄	C₂³×D₄	1	8	yes	—
431	C₂²×D₄	C₂³×D₄	1	8	yes	—
432	C₂²×D₄	C₂³×D₄	1	8	yes	—
433	C₂²×D₄	C₂³×D₄	1	16	yes	—
434	C₂²×D₄	C₂³×D₄	1	16	yes	—
435	C₂²×D₄	C₂³×D₄	1	8	yes	—
436	C₂²×D₄	C₂²×#41	1	8	yes	—
437	C₂³×C₄	#392	1	16	yes	—
438	C₂³×C₄	#392	1	48	yes	—
439	C₂³×C₄	C₂×#120	1	12	yes	—
440	C₂³×C₄	C₂×#120	1	12	yes	—
441	C₂³×C₄	C₂×#120	1	12	yes	—
442	C₂³×C₄	C₂×#120	1	24	yes	—
443	C₂³×C₄	C₂×#120	1	12	yes	—
444	C₂³×C₄	C₂×#120	1	48	yes	complemented
445	C₂³×C₄	C₂×#121	1	24	yes	—
446	C₂³×C₄	C₂³×D₄	1	4	yes	—
447	C₂³×C₄	C₂³×D₄	1	8	yes	—
448	C₂³×C₄	C₂³×D₄	1	4	yes	—
449	C₂³×C₄	C₂³×D₄	1	4	yes	complemented
450	C₂³×C₄	C₂³×D₄	1	8	yes	complemented
451	C₂×C₂²⋊C₄	C₂×#120	1	96	yes	complemented
452	C₂×C₂²⋊C₄	C₂×#120	1	96	yes	complemented
453	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
454	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
455	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
456	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	complemented
457	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	complemented
458	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	complemented
459	C₂⁴	C₂×#392	1	4	yes	—
460	C₂⁴	C₂×#392	1	48	yes	—
461	C₂⁴	C₂×#392	1	48	yes	—
462	C₂⁴	C₂×#392	1	12	yes	—
463	C₂⁴	C₂×#392	1	12	yes	—
464	C₂⁴	C₂×#392	1	12	yes	—
465	C₂⁴	C₂×#392	1	24	yes	—
466	C₂⁴	#2403	1	3	yes	—
467	C₂⁴	#2403	1	3	yes	—
468	C₂⁴	#2403	1	6	yes	—
469	C₂⁴	#2403	1	3	yes	—
470	C₂⁴	#2403	1	4	yes	—
471	C₂⁴	#2403	1	8	yes	—
472	C₂⁴	#2403	1	6	yes	—
473	C₂⁴	#2403	1	6	yes	—
474	C₂⁴	#2403	1	12	yes	—
475	C₂⁴	#2403	1	24	yes	—
476	C₂⁴	#2403	1	12	yes	—
477	C₂⁴	#2403	1	6	yes	—
478	C₂⁴	#2403	1	24	yes	—
479	C₂⁴	#2403	1	12	yes	—
480	C₂⁴	#2403	1	12	yes	—
481	C₂⁴	#2403	1	12	yes	—
482	C₂⁴	#2403	1	6	yes	—
483	C₂⁴	#2403	1	24	yes	—
484	C₂⁴	#2403	1	48	yes	—
485	C₂⁴	#2403	1	24	yes	—
486	C₂⁴	#2403	1	1	yes	characteristic
487	C₂⁴	#2408	1	8	yes	—
488	C₂⁴	#2408	1	24	yes	—
489	C₂⁴	#2408	1	24	yes	—
490	C₂⁴	#2408	1	24	yes	—
491	C₂⁴	#2408	1	48	yes	—
492	C₂⁴	#2410	1	4	yes	—
493	C₂⁴	#2410	1	4	yes	—
494	C₂⁴	#2410	1	8	yes	—
495	C₂⁴	#2410	1	12	yes	—
496	C₂⁴	#2410	1	12	yes	—
497	C₂⁴	#2410	1	24	yes	—
498	C₂⁴	#2410	1	24	yes	—
499	C₂⁴	#2410	1	24	yes	—
500	C₂⁴	#2410	1	24	yes	—
501	C₂⁴	#2410	1	24	yes	—
502	C₂⁴	#2410	1	24	yes	—
503	C₂⁴	#2410	1	48	yes	—
504	C₂⁴	#2410	1	24	yes	—
505	C₂⁴	#2433	1	8	yes	—
506	C₂⁴	#2433	1	24	yes	—
507	C₂⁴	#2433	1	24	yes	—
508	C₂⁴	#2433	1	24	yes	—
509	C₂⁴	#2433	1	48	yes	—
510	C₂⁴	#2613	1	4	yes	—
511	C₂⁴	#2613	1	12	yes	—
512	C₂⁴	#2613	1	24	yes	—
513	C₂⁴	#2613	1	24	yes	—
514	C₂⁴	#2846	1	4	yes	—
515	C₂⁴	#2846	1	12	yes	—
516	C₂⁴	#2846	1	24	yes	—
517	C₂⁴	#2846	1	24	yes	—
518	C₂⁴	C₂²×#120	1	3	yes	—
519	C₂⁴	C₂²×#120	1	3	yes	—
520	C₂⁴	C₂²×#120	1	8	yes	—
521	C₂⁴	C₂²×#120	1	8	yes	—
522	C₂⁴	C₂²×#120	1	8	yes	—
523	C₂⁴	C₂²×#120	1	8	yes	—
524	C₂⁴	C₂²×#120	1	8	yes	—
525	C₂⁴	C₂²×#120	1	6	yes	—
526	C₂⁴	C₂²×#120	1	3	yes	—
527	C₂⁴	C₂²×#120	1	6	yes	—
528	C₂⁴	C₂²×#120	1	12	yes	—
529	C₂⁴	C₂²×#120	1	12	yes	—
530	C₂⁴	C₂²×#120	1	6	yes	—
531	C₂⁴	C₂²×#120	1	3	yes	—
532	C₂⁴	C₂²×#120	1	6	yes	—
533	C₂⁴	C₂²×#120	1	3	yes	—
534	C₂⁴	C₂²×#120	1	3	yes	—
535	C₂⁴	C₂²×#120	1	6	yes	—
536	C₂⁴	C₂²×#120	1	12	yes	—
537	C₂⁴	C₂²×#120	1	12	yes	—
538	C₂⁴	C₂²×#120	1	6	yes	—
539	C₂⁴	C₂²×#120	1	6	yes	—
540	C₂⁴	C₂²×#120	1	16	yes	complemented
541	C₂⁴	C₂²×#121	1	8	yes	—
542	C₂⁴	C₂²×#121	1	6	yes	—
543	C₂⁴	C₂²×#121	1	6	yes	—
544	C₂⁴	C₂²×#121	1	6	yes	—
545	C₂⁴	C₂²×#121	1	6	yes	—
546	C₂⁴	C₂²×#121	1	6	yes	—
547	C₂⁴	C₂²×#121	1	6	yes	—
548	C₂⁴	C₂²×#127	1	6	yes	—
549	C₂⁴	C₂²×#127	1	6	yes	—
550	C₂⁴	C₂×#534	1	3	yes	—
551	C₂⁴	C₂×#534	1	3	yes	—
552	C₂⁴	C₂×#534	1	6	yes	—
553	C₂⁴	C₂×#534	1	6	yes	—
554	C₂⁴	C₂×#534	1	12	yes	—
555	C₂⁴	C₂×#534	1	12	yes	—
556	C₂⁴	C₂×#534	1	6	yes	—
557	C₂⁴	C₂×#535	1	12	yes	—
558	C₂⁴	C₂×#535	1	12	yes	—
559	C₂⁴	C₂×D₄²	1	6	yes	—
560	C₂⁴	C₂×D₄²	1	6	yes	—
561	C₂⁴	C₂×D₄²	1	6	yes	—
562	C₂⁴	C₂×D₄²	1	6	yes	—
563	C₂⁴	C₂×D₄²	1	12	yes	—
564	C₂⁴	C₂×D₄²	1	6	yes	—
565	C₂⁴	C₂×D₄²	1	6	yes	—
566	C₂⁴	C₂×D₄²	1	12	yes	—
567	C₂⁴	C₂×D₄²	1	12	yes	—
568	C₂⁴	C₂×D₄²	1	6	yes	—
569	C₂⁴	C₂×D₄²	1	6	yes	—
570	C₂⁴	C₂×D₄²	1	12	yes	—
571	C₂⁴	C₂×D₄²	1	12	yes	—
572	C₂⁴	C₂×D₄²	1	12	yes	—
573	C₂⁴	C₂×D₄²	1	12	yes	—
574	C₂⁴	C₂×D₄²	1	12	yes	—
575	C₂⁴	C₂×#546	1	12	yes	—
576	C₂⁴	C₂×#546	1	12	yes	—
577	C₂⁴	C₂×#546	1	12	yes	—
578	C₂⁴	C₂×#546	1	12	yes	—
579	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
580	C₂⁴	C₂⁴×D₄	1	2	yes	—
581	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
582	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
583	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
584	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
585	C₂⁴	C₂⁴×D₄	1	2	yes	—
586	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
587	C₂⁴	C₂³×#41	1	1	yes	characteristic
588	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
589	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
590	C₂×D₄	C₂×#392	1	96	yes	—
591	C₂×D₄	C₂×#392	1	96	yes	—
592	C₂×D₄	C₂²×#120	1	16	yes	—
593	C₂×D₄	C₂²×#121	1	16	yes	—
594	C₂×D₄	C₂²×#121	1	16	yes	—
595	C₂×D₄	C₂²×#127	1	16	yes	—
596	C₂²×C₄	C₂×#392	1	48	yes	—
597	C₂²×C₄	C₂×#392	1	48	yes	—
598	C₂²×C₄	C₂²×#120	1	8	yes	—
599	C₂²×C₄	C₂²×#120	1	8	yes	—
600	C₂²×C₄	C₂²×#120	1	8	yes	—
601	C₂²×C₄	C₂²×#120	1	16	yes	complemented
602	C₂²×C₄	C₂²×#121	1	8	yes	—
603	C₂²⋊C₄	C₂²×#120	1	32	yes	complemented
604	C₂³	#14715	1	12	yes	—
605	C₂³	#14715	1	12	yes	—
606	C₂³	#14715	1	12	yes	—
607	C₂³	#14715	1	24	yes	—
608	C₂³	#14715	1	24	yes	—
609	C₂³	#14715	1	24	yes	—
610	C₂³	#14715	1	48	yes	—
611	C₂³	#14715	1	24	yes	—
612	C₂³	#14715	1	24	yes	—
613	C₂³	#14715	1	48	yes	—
614	C₂³	#14715	1	4	yes	—
615	C₂³	#23895	1	8	yes	—
616	C₂³	C₂²×#392	1	6	yes	—
617	C₂³	C₂²×#392	1	16	yes	—
618	C₂³	C₂²×#392	1	6	yes	—
619	C₂³	C₂²×#392	1	6	yes	—
620	C₂³	C₂²×#392	1	6	yes	—
621	C₂³	C₂×#2613	1	6	yes	—
622	C₂³	C₂×#2613	1	6	yes	—
623	C₂³	C₂×#2613	1	12	yes	—
624	C₂³	C₂×#2403	1	3	yes	—
625	C₂³	C₂×#2403	1	3	yes	—
626	C₂³	C₂×#2403	1	6	yes	—
627	C₂³	C₂×#2403	1	3	yes	—
628	C₂³	C₂×#2403	1	6	yes	—
629	C₂³	C₂×#2403	1	12	yes	—
630	C₂³	C₂×#2403	1	6	yes	—
631	C₂³	C₂×#2403	1	6	yes	—
632	C₂³	C₂×#2403	1	12	yes	—
633	C₂³	C₂×#2403	1	12	yes	—
634	C₂³	C₂×#2403	1	6	yes	—
635	C₂³	C₂×#2403	1	6	yes	—
636	C₂³	C₂×#2403	1	12	yes	—
637	C₂³	C₂×#2403	1	3	yes	—
638	C₂³	C₂×#2410	1	6	yes	—
639	C₂³	C₂×#2410	1	6	yes	—
640	C₂³	C₂×#2410	1	12	yes	—
641	C₂³	C₂×#2410	1	6	yes	—
642	C₂³	C₂×#2410	1	6	yes	—
643	C₂³	C₂×#2410	1	12	yes	—
644	C₂³	C₂×#2410	1	12	yes	—
645	C₂³	C₂×#2410	1	12	yes	—
646	C₂³	C₂×#2410	1	12	yes	—
647	C₂³	C₂×#2410	1	12	yes	—
648	C₂³	C₂×#2408	1	12	yes	—
649	C₂³	C₂×#2408	1	12	yes	—
650	C₂³	C₂×#2408	1	12	yes	—
651	C₂³	C₂×#2408	1	12	yes	—
652	C₂³	C₂×#2433	1	12	yes	—
653	C₂³	C₂×#2433	1	12	yes	—
654	C₂³	C₂×#2433	1	12	yes	—
655	C₂³	C₂×#2433	1	12	yes	—
656	C₂³	C₂×#2846	1	6	yes	—
657	C₂³	C₂×#2846	1	6	yes	—
658	C₂³	C₂×#2846	1	12	yes	—
659	C₂³	C₂³×#120	1	1	yes	characteristic
660	C₂³	C₂³×#120	1	1	yes	characteristic
661	C₂³	C₂³×#120	1	1	yes	characteristic
662	C₂³	C₂³×#120	1	1	yes	characteristic
663	C₂³	C₂³×#120	1	2	yes	—
664	C₂³	C₂³×#120	1	2	yes	—
665	C₂³	C₂³×#120	1	1	yes	characteristic
666	C₂³	C₂³×#121	1	1	yes	characteristic
667	C₂³	C₂³×#121	1	1	yes	characteristic
668	C₂³	C₂³×#121	1	1	yes	characteristic
669	C₂³	C₂³×#127	1	1	yes	characteristic
670	C₂³	C₂²×#534	1	1	yes	characteristic
671	C₂³	C₂²×#534	1	1	yes	characteristic
672	C₂³	C₂²×#534	1	2	yes	—
673	C₂³	C₂²×#535	1	2	yes	—
674	C₂³	C₂²×D₄²	1	2	yes	—
675	C₂³	C₂²×D₄²	1	2	yes	—
676	C₂³	C₂²×D₄²	1	2	yes	—
677	C₂³	C₂²×D₄²	1	2	yes	—
678	C₂³	C₂²×D₄²	1	2	yes	—
679	C₂³	C₂²×D₄²	1	2	yes	—
680	C₂³	C₂²×#546	1	2	yes	—
681	C₂³	C₂²×#546	1	2	yes	—
682	C₂×C₄	C₂²×#392	1	16	yes	—
683	C₂²	#394064	1	16	yes	direct product factor
684	C₂²	C₂×#14715	1	6	yes	—
685	C₂²	C₂×#14715	1	6	yes	—
686	C₂²	C₂×#14715	1	6	yes	—
687	C₂²	C₂×#14715	1	12	yes	—
688	C₂²	C₂×#14715	1	12	yes	—
689	C₂²	C₂×#14715	1	6	yes	—
690	C₂²	C₂×#23895	1	12	yes	—
691	C₂²	C₂³×#392	1	1	yes	characteristic
692	C₂²	C₂²×#2613	1	1	yes	characteristic
693	C₂²	C₂²×#2403	1	1	yes	characteristic
694	C₂²	C₂²×#2403	1	2	yes	—
695	C₂²	C₂²×#2403	1	1	yes	characteristic
696	C₂²	C₂²×#2410	1	1	yes	characteristic
697	C₂²	C₂²×#2410	1	1	yes	characteristic
698	C₂²	C₂²×#2410	1	2	yes	—
699	C₂²	C₂²×#2408	1	2	yes	—
700	C₂²	C₂²×#2433	1	2	yes	—
701	C₂²	C₂²×#2846	1	1	yes	characteristic
702	C₂	C₂²×#23895	1	2	yes	—
703	C₂	C₂×#394064	1	12	yes	direct product factor
704	C₂	C₂²×#14715	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	#2403
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#10991	C₂	semidirect
2. C₂²×#23444	C₂	semidirect
3. C₂³×#3026	C₂	semidirect
4. C₂³×#1913	C₂	semidirect
5. C₂²×#10754	C₂	semidirect
6. C₂²×#20609	C₂	semidirect
7. C₂³×#1781	C₂	semidirect
8. C₂²×#10972	C₂	semidirect
9. C₂²×#34980	C₂	semidirect
10. C₂×#394064	C₂	direct (N × H)
11. C₂³×#2021	C₂	semidirect
12. C₂³×#3484	C₂	semidirect
15. C₂²×#3484	C₂²	semidirect
18. C₂³×#534	C₂²	semidirect
19. C₂³×#534	C₂²	semidirect
21. C₂⁴×#120	C₂²	semidirect
23. C₂²×#3026	C₂²	semidirect
26. C₂⁴×#99	C₂²	semidirect
27. C₂⁴×#99	C₂²	semidirect
28. C₂⁴×#99	C₂²	semidirect
29. C₂⁴×#99	C₂²	semidirect
30. C₂×#34980	C₂²	semidirect
32. C₂²×#2308	C₂²	semidirect
33. C₂²×#2308	C₂²	semidirect
34. C₂³×#379	C₂²	semidirect
35. C₂³×#379	C₂²	semidirect
36. C₂×#23444	C₂²	semidirect
37. C₂²×#2021	C₂²	semidirect
38. C₂²×#1913	C₂²	semidirect
39. C₂×#20609	C₂²	semidirect
40. C₂²×#1781	C₂²	semidirect
41. C₂³×#342	C₂²	semidirect
42. C₂³×#342	C₂²	semidirect
43. C₂³×#342	C₂²	semidirect
44. #394064	C₂²	direct (N × H)
45. C₂×#10991	C₂²	semidirect
46. C₂×#10972	C₂²	semidirect
47. C₂×#10754	C₂²	semidirect
48. C₂⁸	D₄	semidirect
50. C₂³×H(5,𝔽₂)	D₄	semidirect
52. C₂⁵×D₄	D₄	semidirect
53. C₂⁵×D₄	D₄	semidirect
54. C₂⁵×D₄	D₄	semidirect
60. C₂⁶×C₄	D₄	semidirect
61. C₂×#3484	C₂³	semidirect
62. C₂²×#534	D₄	semidirect
63. C₂²×#534	D₄	semidirect
66. C₂²×#534	C₂³	semidirect
67. C₂²×#534	C₂³	semidirect
68. C₂³×#123	D₄	semidirect
69. C₂³×#123	D₄	semidirect
70. C₂³×#120	D₄	semidirect
71. C₂³×#120	D₄	semidirect
72. C₂³×#120	D₄	semidirect
74. C₂³×#120	C₂³	semidirect
75. C₂²×#518	D₄	semidirect
83. C₂×#3026	C₂³	semidirect
84. C₂³×#99	D₄	semidirect
87. C₂³×#99	C₂³	semidirect
88. C₂³×#99	C₂³	semidirect
89. C₂³×#99	C₂³	semidirect
90. C₂³×#99	C₂³	semidirect
91. #34980	C₂³	semidirect
92. C₂×#2308	D₄	semidirect
94. C₂×#2308	C₂³	semidirect
95. C₂×#2308	C₂³	semidirect
96. C₂²×#386	D₄	semidirect
97. C₂²×#379	C₂³	semidirect
98. C₂²×#379	C₂³	semidirect
99. #23444	C₂³	semidirect
100. C₂×#2021	C₂³	semidirect
101. C₂×#1913	C₂³	semidirect
102. #20609	C₂³	semidirect
103. C₂×#1781	C₂³	semidirect
104. C₂²×#342	C₂³	semidirect
105. C₂²×#342	C₂³	semidirect
106. C₂²×#342	C₂³	semidirect
107. #10991	C₂³	semidirect
108. #10972	C₂³	semidirect
109. #10754	C₂³	semidirect
117. C₂⁷	C₂×D₄	semidirect
118. C₂⁷	C₂×D₄	semidirect
121. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
137. C₂⁴×D₄	C₂×D₄	semidirect
138. C₂⁴×D₄	C₂×D₄	semidirect
139. C₂⁴×D₄	C₂×D₄	semidirect
140. C₂⁴×D₄	C₂×D₄	semidirect
150. C₂⁵×C₄	C₂×D₄	semidirect
151. C₂⁵×C₄	C₂×D₄	semidirect
152. C₂⁵×C₄	C₂×D₄	semidirect
153. C₂×#534	C₂×D₄	semidirect
154. C₂×#534	C₂×D₄	semidirect
157. C₂×#534	C₂⁴	semidirect
158. C₂×#534	C₂⁴	semidirect
159. C₂²×#123	C₂×D₄	semidirect
160. C₂²×#123	C₂×D₄	semidirect
161. C₂²×#120	C₂×D₄	semidirect
162. C₂²×#120	C₂×D₄	semidirect
163. C₂²×#120	C₂×D₄	semidirect
165. C₂²×#120	C₂⁴	semidirect
166. C₂×#518	C₂×D₄	semidirect
172. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
173. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
174. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
175. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
176. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
177. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
184. C₂²×#99	C₂×D₄	semidirect
187. C₂²×#99	C₂⁴	semidirect
188. C₂²×#99	C₂⁴	semidirect
189. C₂²×#99	C₂⁴	semidirect
190. C₂²×#99	C₂⁴	semidirect
191. #2308	C₂×D₄	semidirect
193. #2308	C₂⁴	semidirect
194. #2308	C₂⁴	semidirect
195. C₂×#386	C₂×D₄	semidirect
196. C₂×#379	C₂⁴	semidirect
197. C₂×#379	C₂⁴	semidirect
198. C₂×#342	C₂⁴	semidirect
199. C₂×#342	C₂⁴	semidirect
200. C₂×#342	C₂⁴	semidirect
209. C₂⁶	#120	semidirect
230. C₂⁶	C₂²×D₄	semidirect
231. C₂⁶	C₂²×D₄	semidirect
238. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
247. C₂³×D₄	#120	semidirect
269. C₂³×D₄	C₂²×D₄	semidirect
270. C₂³×D₄	C₂²×D₄	semidirect
271. C₂³×D₄	C₂²×D₄	semidirect
282. C₂⁴×C₄	#120	semidirect
287. C₂⁴×C₄	C₂²×D₄	semidirect
288. C₂⁴×C₄	C₂²×D₄	semidirect
289. C₂⁴×C₄	C₂²×D₄	semidirect
290. C₂×#123	C₂²×D₄	semidirect
291. C₂×#123	C₂²×D₄	semidirect
292. C₂×#120	C₂²×D₄	semidirect
293. C₂×#120	C₂²×D₄	semidirect
294. C₂×#120	C₂²×D₄	semidirect
295. #518	C₂²×D₄	semidirect
296. C₂²×C₂²⋊C₄	#120	semidirect
297. C₂²×C₂²⋊C₄	#120	semidirect
302. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
303. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
304. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
305. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
306. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
307. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
314. C₂×#99	C₂²×D₄	semidirect
315. #386	C₂²×D₄	semidirect
345. C₂⁵	C₂×#120	semidirect
405. C₂⁵	C₂³×D₄	semidirect
420. C₂²×D₄	C₂×#120	semidirect
444. C₂³×C₄	C₂×#120	semidirect
449. C₂³×C₄	C₂³×D₄	semidirect
450. C₂³×C₄	C₂³×D₄	semidirect
451. C₂×C₂²⋊C₄	C₂×#120	semidirect
452. C₂×C₂²⋊C₄	C₂×#120	semidirect
456. C₂×C₂²⋊C₄	C₂³×D₄	semidirect
457. C₂×C₂²⋊C₄	C₂³×D₄	semidirect
458. C₂×C₂²⋊C₄	C₂³×D₄	semidirect
540. C₂⁴	C₂²×#120	semidirect
601. C₂²×C₄	C₂²×#120	semidirect
603. C₂²⋊C₄	C₂²×#120	semidirect
683. C₂²	#394064	direct (N × H)
703. C₂	C₂×#394064	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×#10991	2
C₂²×#23444	2
C₂³×#3026	2
C₂³×#1913	2
C₂²×#10754	2
C₂²×#20609	2
C₂³×#1781	2
C₂²×#10972	2
C₂²×#34980	2
C₂×#394064	2
C₂³×#2021	2
C₂³×#3484	2

Subgroups — C22×#394064 #72250897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#394064 #72250897