Subgroups — C₂×C₄×C₅×C₂²⋊C₈ #11943091

Order 1280.

2414 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₂²⋊C₈	C₂	1	2	yes	maximal
3	C₂²×C₄×C₅×C₈	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×C₂²⋊C₈	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#336	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₅	C₄	1	2	yes	—
7	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₅×C₈	C₂²	1	4	yes	—
9	C₂²×C₄²×C₅	—	2	8	no	—
10	C₂²×C₄²×C₅	C₄	1	2	yes	—
11	C₂²×C₄²×C₅	C₄	1	4	yes	—
12	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₅	C₂²	1	4	yes	—
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₂²⋊C₈	C₄	1	16	yes	direct product factor
16	C₂×C₅×C₂²⋊C₈	C₂²	1	8	yes	—
17	C₂×C₄×C₅×C₈	—	2	8	no	—
18	C₂×C₄×C₅×C₈	C₂²	1	8	yes	complemented
19	C₅×#336	C₂²	1	8	yes	complemented
20	C₂×C₄×C₂²⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₅	—	2	8	no	—
23	C₂³×C₄×C₅	—	2	8	no	—
24	C₂³×C₄×C₅	—	2	4	no	—
25	C₂³×C₄×C₅	—	2	4	no	—
26	C₂³×C₄×C₅	C₈	1	16	yes	complemented
27	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₅	C₂×C₄	1	8	yes	—
30	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₅	C₂×C₄	1	8	yes	—
32	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₅	C₂³	1	2	yes	—
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×C₈	—	2	8	no	—
36	C₂²×C₅×C₈	—	2	8	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	16	yes	complemented
38	C₂²×C₅×C₈	C₂³	1	8	yes	—
39	C₂×C₄²×C₅	—	2	8	no	—
40	C₂×C₄²×C₅	—	2	4	no	—
41	C₂×C₄²×C₅	—	2	16	no	—
42	C₂×C₄²×C₅	—	2	16	no	—
43	C₂×C₄²×C₅	C₂×C₄	1	8	yes	—
44	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₅	D₄	1	8	yes	—
47	C₂×C₄²×C₅	C₂³	1	2	yes	—
48	C₂×C₄²×C₅	C₂³	1	2	yes	—
49	C₅×C₂²⋊C₈	C₂×C₄	1	32	yes	direct product factor
50	C₄×C₅×C₈	—	2	16	no	—
51	C₂³×C₄²	C₂×C₅	1	1	yes	characteristic
52	C₂²×C₂²⋊C₈	C₂×C₅	1	2	yes	—
53	C₂²×C₄×C₈	C₂×C₅	1	2	yes	complemented
54	C₄×C₂²⋊C₈	C₂×C₅	1	8	yes	direct product factor
55	C₂×#336	C₂×C₅	1	2	yes	complemented
56	C₂⁴×C₅	—	2	2	no	—
57	C₂⁴×C₅	—	2	2	no	—
58	C₂⁴×C₅	—	2	4	no	—
59	C₂⁴×C₅	C₄²	1	4	yes	—
60	C₂⁴×C₅	C₂×C₈	1	8	yes	—
61	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
62	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	—	2	2	no	—
64	C₂²×C₄×C₅	—	2	4	no	—
65	C₂²×C₄×C₅	—	2	2	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	—	2	64	no	—
68	C₂²×C₄×C₅	—	2	4	no	—
69	C₂²×C₄×C₅	—	2	16	no	—
70	C₂²×C₄×C₅	—	2	4	no	—
71	C₂²×C₄×C₅	—	2	32	no	—
72	C₂²×C₄×C₅	—	2	16	no	—
73	C₂²×C₄×C₅	—	2	4	no	—
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	C₄²	1	4	yes	—
76	C₂²×C₄×C₅	C₄²	1	8	yes	—
77	C₂²×C₄×C₅	C₂²⋊C₄	1	8	yes	—
78	C₂²×C₄×C₅	C₂×C₈	1	8	yes	—
79	C₂²×C₄×C₅	C₂×C₈	1	8	yes	—
80	C₂²×C₄×C₅	C₂×C₈	1	32	yes	complemented
81	C₂²×C₄×C₅	M₁₆	1	8	yes	—
82	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
84	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₅	#41	1	4	yes	—
90	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₅×C₈	—	2	32	no	—
92	C₂×C₅×C₈	—	2	8	no	—
93	C₂×C₅×C₈	—	2	8	no	—
94	C₂×C₅×C₈	C₂²×C₄	1	16	yes	complemented
95	C₄²×C₅	—	2	4	no	—
96	C₄²×C₅	—	2	16	no	—
97	C₄²×C₅	—	2	4	no	—
98	C₄²×C₅	C₂²⋊C₄	1	8	yes	—
99	C₄²×C₅	C₂×D₄	1	8	yes	—
100	C₂⁴×C₄	C₄×C₅	1	2	yes	—
101	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂³×C₈	C₂²×C₅	1	4	yes	—
103	C₂²×C₄²	—	2	8	no	—
104	C₂²×C₄²	C₄×C₅	1	2	yes	—
105	C₂²×C₄²	C₄×C₅	1	4	yes	—
106	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₄²	C₂²×C₅	1	4	yes	—
108	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₂²⋊C₈	C₄×C₅	1	16	yes	direct product factor
110	C₂×C₂²⋊C₈	C₂²×C₅	1	8	yes	—
111	C₂×C₄×C₈	—	2	8	no	—
112	C₂×C₄×C₈	C₂²×C₅	1	8	yes	complemented
113	#336	C₂²×C₅	1	8	yes	complemented
114	C₂³×C₅	—	2	2	no	—
115	C₂³×C₅	—	2	2	no	—
116	C₂³×C₅	—	2	4	no	—
117	C₂³×C₅	—	2	8	no	—
118	C₂³×C₅	—	2	8	no	—
119	C₂³×C₅	—	2	16	no	—
120	C₂³×C₅	—	2	16	no	—
121	C₂³×C₅	C₄×C₈	1	16	yes	complemented
122	C₂³×C₅	C₂×C₄²	1	4	yes	—
123	C₂³×C₅	C₂×C₄²	1	2	yes	—
124	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
125	C₂³×C₅	#117	1	2	yes	—
126	C₂³×C₅	C₂²×C₈	1	8	yes	—
127	C₂³×C₅	C₂²×C₈	1	4	yes	—
128	C₂³×C₅	C₂×M₁₆	1	4	yes	—
129	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	2	2	no	—
132	C₂×C₄×C₅	—	2	2	no	—
133	C₂×C₄×C₅	—	2	4	no	—
134	C₂×C₄×C₅	—	2	8	no	—
135	C₂×C₄×C₅	—	2	16	no	—
136	C₂×C₄×C₅	—	2	16	no	—
137	C₂×C₄×C₅	—	2	16	no	—
138	C₂×C₄×C₅	—	2	64	no	—
139	C₂×C₄×C₅	C₂²⋊C₈	1	32	yes	direct product factor
140	C₂×C₄×C₅	C₂×C₄²	1	4	yes	—
141	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	—
144	C₂×C₄×C₅	#117	1	2	yes	—
145	C₂×C₄×C₅	C₄×D₄	1	16	yes	—
146	C₂×C₄×C₅	C₂²×C₈	1	8	yes	—
147	C₂×C₄×C₅	C₂²×C₈	1	8	yes	—
148	C₂×C₄×C₅	C₂×M₁₆	1	8	yes	—
149	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₅	C₂×#41	1	2	yes	—
152	C₅×C₈	—	2	16	no	—
153	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
154	C₂³×C₄	—	2	8	no	—
155	C₂³×C₄	—	2	8	no	—
156	C₂³×C₄	—	2	4	no	—
157	C₂³×C₄	—	2	4	no	—
158	C₂³×C₄	C₅×C₈	1	16	yes	complemented
159	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
160	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
161	C₂³×C₄	C₂×C₄×C₅	1	8	yes	—
162	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
163	C₂³×C₄	C₂×C₄×C₅	1	8	yes	—
164	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
165	C₂³×C₄	C₂³×C₅	1	2	yes	—
166	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₂²×C₈	—	2	8	no	—
168	C₂²×C₈	—	2	8	no	—
169	C₂²×C₈	C₂×C₄×C₅	1	16	yes	complemented
170	C₂²×C₈	C₂³×C₅	1	8	yes	—
171	C₂×C₄²	—	2	8	no	—
172	C₂×C₄²	—	2	4	no	—
173	C₂×C₄²	—	2	16	no	—
174	C₂×C₄²	—	2	16	no	—
175	C₂×C₄²	C₂×C₄×C₅	1	8	yes	—
176	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
177	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
178	C₂×C₄²	C₅×D₄	1	8	yes	—
179	C₂×C₄²	C₂³×C₅	1	2	yes	—
180	C₂×C₄²	C₂³×C₅	1	2	yes	—
181	C₂²⋊C₈	C₂×C₄×C₅	1	32	yes	direct product factor
182	C₄×C₈	—	2	16	no	—
183	C₂²×C₅	—	2	4	no	—
184	C₂²×C₅	—	2	8	no	—
185	C₂²×C₅	—	2	8	no	—
186	C₂²×C₅	—	2	32	no	—
187	C₂²×C₅	—	2	4	no	—
188	C₂²×C₅	C₄×C₂²⋊C₄	1	4	yes	—
189	C₂²×C₅	C₂×C₄×C₈	1	4	yes	—
190	C₂²×C₅	C₂×C₄×C₈	1	8	yes	complemented
191	C₂²×C₅	C₄×M₁₆	1	4	yes	—
192	C₂²×C₅	C₂×C₂²⋊C₈	1	8	yes	—
193	C₂²×C₅	#431	1	8	yes	—
194	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
195	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₅	C₂×#117	1	1	yes	characteristic
197	C₂²×C₅	C₂³×C₈	1	2	yes	—
198	C₂²×C₅	C₂²×M₁₆	1	2	yes	—
199	C₄×C₅	—	2	8	no	—
200	C₄×C₅	—	2	4	no	—
201	C₄×C₅	C₄×C₂²⋊C₄	1	4	yes	—
202	C₄×C₅	C₂×C₂²⋊C₈	1	16	yes	direct product factor
203	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
204	C₂⁴	—	2	2	no	—
205	C₂⁴	—	2	2	no	—
206	C₂⁴	—	2	4	no	—
207	C₂⁴	C₄²×C₅	1	4	yes	—
208	C₂⁴	C₂×C₅×C₈	1	8	yes	—
209	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
210	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	2	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	16	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	2	32	no	—
219	C₂²×C₄	—	2	16	no	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	64	no	—
223	C₂²×C₄	C₄²×C₅	1	4	yes	—
224	C₂²×C₄	C₄²×C₅	1	8	yes	—
225	C₂²×C₄	C₅×C₂²⋊C₄	1	8	yes	—
226	C₂²×C₄	C₂×C₅×C₈	1	8	yes	—
227	C₂²×C₄	C₂×C₅×C₈	1	8	yes	—
228	C₂²×C₄	C₂×C₅×C₈	1	32	yes	complemented
229	C₂²×C₄	C₅×M₁₆	1	8	yes	—
230	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
231	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
232	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
233	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
236	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
237	C₂²×C₄	C₅×#41	1	4	yes	—
238	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
239	C₂×C₈	—	2	32	no	—
240	C₂×C₈	—	2	8	no	—
241	C₂×C₈	—	2	8	no	—
242	C₂×C₈	C₂²×C₄×C₅	1	16	yes	complemented
243	C₄²	—	2	4	no	—
244	C₄²	—	2	16	no	—
245	C₄²	—	2	4	no	—
246	C₄²	C₅×C₂²⋊C₄	1	8	yes	—
247	C₄²	C₂×C₅×D₄	1	8	yes	—
248	C₂×C₅	—	2	8	no	—
249	C₂×C₅	C₄×C₂²⋊C₈	1	8	yes	direct product factor
250	C₂×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₅	C₂²×C₄×C₈	1	1	yes	characteristic
252	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
253	C₂×C₅	C₂²×C₂²⋊C₈	1	2	yes	—
254	C₂×C₅	C₂×#431	1	2	yes	—
255	C₂³	—	2	8	no	—
256	C₂³	—	2	8	no	—
257	C₂³	—	2	16	no	—
258	C₂³	—	2	16	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	4	no	—
262	C₂³	C₄×C₅×C₈	1	16	yes	complemented
263	C₂³	C₂×C₄²×C₅	1	4	yes	—
264	C₂³	C₂×C₄²×C₅	1	2	yes	—
265	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
266	C₂³	C₅×#117	1	2	yes	—
267	C₂³	C₂²×C₅×C₈	1	8	yes	—
268	C₂³	C₂²×C₅×C₈	1	4	yes	—
269	C₂³	C₂×C₅×M₁₆	1	4	yes	—
270	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	2	16	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	16	no	—
278	C₂×C₄	—	2	64	no	—
279	C₂×C₄	—	2	16	no	—
280	C₂×C₄	C₅×C₂²⋊C₈	1	32	yes	direct product factor
281	C₂×C₄	C₂×C₄²×C₅	1	4	yes	—
282	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
283	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
284	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	8	yes	—
285	C₂×C₄	C₅×#117	1	2	yes	—
286	C₂×C₄	C₄×C₅×D₄	1	16	yes	—
287	C₂×C₄	C₂²×C₅×C₈	1	8	yes	—
288	C₂×C₄	C₂²×C₅×C₈	1	8	yes	—
289	C₂×C₄	C₂×C₅×M₁₆	1	8	yes	—
290	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
291	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
292	C₂×C₄	C₂×C₅×#41	1	2	yes	—
293	C₈	—	2	16	no	—
294	C₅	C₂×C₄×C₂²⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²	—	2	4	no	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	8	no	—
298	C₂²	—	2	8	no	—
299	C₂²	—	2	32	no	—
300	C₂²	C₄×C₅×C₂²⋊C₄	1	4	yes	—
301	C₂²	C₂×C₄×C₅×C₈	1	4	yes	—
302	C₂²	C₂×C₄×C₅×C₈	1	8	yes	complemented
303	C₂²	C₄×C₅×M₁₆	1	4	yes	—
304	C₂²	C₂×C₅×C₂²⋊C₈	1	8	yes	—
305	C₂²	C₅×#431	1	8	yes	—
306	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
307	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²	C₂×C₅×#117	1	1	yes	characteristic
309	C₂²	C₂³×C₅×C₈	1	2	yes	—
310	C₂²	C₂²×C₅×M₁₆	1	2	yes	—
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	C₄×C₅×C₂²⋊C₄	1	4	yes	—
314	C₄	C₂×C₅×C₂²⋊C₈	1	16	yes	direct product factor
315	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
316	C₂	—	2	8	no	—
317	C₂	C₄×C₅×C₂²⋊C₈	1	8	yes	direct product factor
318	C₂	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
319	C₂	C₂²×C₄×C₅×C₈	1	1	yes	characteristic
320	C₂	C₂×C₄×C₅×M₁₆	1	1	yes	characteristic
321	C₂	C₂²×C₅×C₂²⋊C₈	1	2	yes	—
322	C₂	C₂×C₅×#431	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²×C₅	C₂²
commutator	C₂	C₂²×C₄×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂⁴×C₅	C₂²×C₄
prime radical	C₂⁵×C₅	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₅×C₈	C₂	semidirect
4. C₄×C₅×C₂²⋊C₈	C₂	direct (N × H)
5. C₂×C₅×#336	C₂	semidirect
15. C₂×C₅×C₂²⋊C₈	C₄	direct (N × H)
18. C₂×C₄×C₅×C₈	C₂²	semidirect
19. C₅×#336	C₂²	semidirect
20. C₂×C₄×C₂²⋊C₈	C₅	direct (N × H)
26. C₂³×C₄×C₅	C₈	semidirect
37. C₂²×C₅×C₈	C₂×C₄	semidirect
49. C₅×C₂²⋊C₈	C₂×C₄	direct (N × H)
53. C₂²×C₄×C₈	C₂×C₅	semidirect
54. C₄×C₂²⋊C₈	C₂×C₅	direct (N × H)
55. C₂×#336	C₂×C₅	semidirect
80. C₂²×C₄×C₅	C₂×C₈	semidirect
94. C₂×C₅×C₈	C₂²×C₄	semidirect
109. C₂×C₂²⋊C₈	C₄×C₅	direct (N × H)
112. C₂×C₄×C₈	C₂²×C₅	semidirect
113. #336	C₂²×C₅	semidirect
121. C₂³×C₅	C₄×C₈	semidirect
139. C₂×C₄×C₅	C₂²⋊C₈	direct (N × H)
158. C₂³×C₄	C₅×C₈	semidirect
169. C₂²×C₈	C₂×C₄×C₅	semidirect
181. C₂²⋊C₈	C₂×C₄×C₅	direct (N × H)
190. C₂²×C₅	C₂×C₄×C₈	semidirect
202. C₄×C₅	C₂×C₂²⋊C₈	direct (N × H)
228. C₂²×C₄	C₂×C₅×C₈	semidirect
242. C₂×C₈	C₂²×C₄×C₅	semidirect
249. C₂×C₅	C₄×C₂²⋊C₈	direct (N × H)
262. C₂³	C₄×C₅×C₈	semidirect
280. C₂×C₄	C₅×C₂²⋊C₈	direct (N × H)
294. C₅	C₂×C₄×C₂²⋊C₈	direct (N × H)
302. C₂²	C₂×C₄×C₅×C₈	semidirect
314. C₄	C₂×C₅×C₂²⋊C₈	direct (N × H)
317. C₂	C₄×C₅×C₂²⋊C₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₄²×C₅	2
C₂²×C₅×C₂²⋊C₈	2
C₂²×C₄×C₅×C₈	2
C₄×C₅×C₂²⋊C₈	2
C₂×C₅×#336	2
C₂×C₄×C₂²⋊C₈	5

Subgroups — C2×C4×C5×C22⋊C8 #11943091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₂²⋊C₈ #11943091