Subgroups — C₂×C₅×Q₈×D₁₁ #13183417

Order 1760.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×Q₈×D₁₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×C₅×D₁₁	C₂	1	3	yes	maximal
4	C₂×C₅×Dic₂₂	C₂	1	3	yes	maximal, complemented
5	C₂²×C₅×D₁₁	C₂²	1	1	yes	characteristic
6	C₅×Q₈×C₁₁	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
8	C₂×C₅×Dic₁₁	C₂²	1	3	yes	—
9	C₄×C₅×D₁₁	C₂²	1	12	yes	—
10	C₅×Dic₂₂	C₂²	1	12	yes	complemented
11	C₂×Q₈×D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×C₅×D₁₁	Q₈	1	4	yes	direct product factor
14	C₂×C₅×D₁₁	C₂³	1	2	yes	—
15	C₄×C₅×C₁₁	C₂³	1	6	yes	—
16	C₅×Dic₁₁	C₂³	1	6	yes	—
17	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
18	Q₈×D₁₁	C₂×C₅	1	8	yes	direct product factor
19	C₂×C₄×D₁₁	C₂×C₅	1	3	yes	—
20	C₂×Dic₂₂	C₂×C₅	1	3	yes	complemented
21	C₂²×C₅×Q₈	—	11	1	no	maximal, Hall
22	C₂×C₅×C₁₁	C₂×Q₈	1	2	yes	complemented
23	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
24	C₅×D₁₁	C₂×Q₈	1	4	yes	direct product factor
25	C₂²×D₁₁	C₂²×C₅	1	1	yes	characteristic
26	Q₈×C₁₁	C₂²×C₅	1	4	yes	complemented
27	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
28	C₂×Dic₁₁	C₂²×C₅	1	3	yes	—
29	C₄×D₁₁	C₂²×C₅	1	12	yes	—
30	Dic₂₂	C₂²×C₅	1	12	yes	complemented
31	C₂×C₅×Q₈	—	11	8	no	—
32	C₂×C₅×Q₈	—	11	3	no	—
33	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic, direct product factor
34	C₂²×C₄×C₅	—	11	3	no	—
35	C₅×C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
37	C₂×D₁₁	C₅×Q₈	1	4	yes	direct product factor
38	C₂×D₁₁	C₂³×C₅	1	2	yes	—
39	C₄×C₁₁	C₂³×C₅	1	6	yes	—
40	Dic₁₁	C₂³×C₅	1	6	yes	—
41	C₂³×C₅	—	11	1	no	—
42	C₅×Q₈	—	11	12	no	—
43	C₅×Q₈	C₂×D₁₁	1	4	yes	direct product factor
44	C₂×C₄×C₅	—	11	3	no	—
45	C₂×C₄×C₅	—	11	12	no	—
46	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
47	C₂²×Q₈	—	11	1	no	Sylow
48	C₂×C₁₁	C₂×C₅×Q₈	1	2	yes	complemented
49	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
50	D₁₁	C₂×C₅×Q₈	1	4	yes	direct product factor
51	C₂²×C₅	—	11	4	no	—
52	C₂²×C₅	—	11	2	no	—
53	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
54	C₄×C₅	—	11	6	no	—
55	C₄×C₅	C₂²×D₁₁	1	6	yes	—
56	C₂×Q₈	—	11	8	no	—
57	C₂×Q₈	—	11	3	no	—
58	C₂×Q₈	C₅×D₁₁	1	1	yes	characteristic, direct product factor
59	C₂²×C₄	—	11	3	no	—
60	C₁₁	C₂²×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₅	—	11	4	no	—
62	C₂×C₅	Q₈×D₁₁	1	2	yes	direct product factor
63	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
64	C₂³	—	11	1	no	—
65	Q₈	—	11	12	no	—
66	Q₈	C₂×C₅×D₁₁	1	4	yes	direct product factor
67	C₂×C₄	—	11	3	no	—
68	C₂×C₄	—	11	12	no	—
69	C₂×C₄	C₂×C₅×D₁₁	1	3	yes	—
70	C₅	C₂×Q₈×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
71	C₂²	—	11	4	no	—
72	C₂²	—	11	2	no	—
73	C₂²	C₂²×C₅×D₁₁	1	1	yes	characteristic
74	C₄	—	11	6	no	—
75	C₄	C₂²×C₅×D₁₁	1	6	yes	—
76	C₂	—	11	4	no	—
77	C₂	C₅×Q₈×D₁₁	1	2	yes	direct product factor
78	C₂	C₂³×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×C₅×D₁₁	C₂²
hypercenter	C₂×C₅×Q₈	D₁₁
hypocenter	C₁₁	C₂²×C₅×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
2. C₅×Q₈×D₁₁	C₂	direct (N × H)
4. C₂×C₅×Dic₂₂	C₂	semidirect
6. C₅×Q₈×C₁₁	C₂²	semidirect
10. C₅×Dic₂₂	C₂²	semidirect
11. C₂×Q₈×D₁₁	C₅	direct (N × H)
13. C₂×C₅×D₁₁	Q₈	direct (N × H)
17. C₂×Q₈×C₁₁	C₂×C₅	semidirect
18. Q₈×D₁₁	C₂×C₅	direct (N × H)
20. C₂×Dic₂₂	C₂×C₅	semidirect
22. C₂×C₅×C₁₁	C₂×Q₈	semidirect
24. C₅×D₁₁	C₂×Q₈	direct (N × H)
26. Q₈×C₁₁	C₂²×C₅	semidirect
30. Dic₂₂	C₂²×C₅	semidirect
33. C₂×C₅×Q₈	D₁₁	direct (N × H)
35. C₅×C₁₁	C₂²×Q₈	semidirect
37. C₂×D₁₁	C₅×Q₈	direct (N × H)
43. C₅×Q₈	C₂×D₁₁	direct (N × H)
48. C₂×C₁₁	C₂×C₅×Q₈	semidirect
50. D₁₁	C₂×C₅×Q₈	direct (N × H)
58. C₂×Q₈	C₅×D₁₁	direct (N × H)
60. C₁₁	C₂²×C₅×Q₈	semidirect
62. C₂×C₅	Q₈×D₁₁	direct (N × H)
66. Q₈	C₂×C₅×D₁₁	direct (N × H)
70. C₅	C₂×Q₈×D₁₁	direct (N × H)
77. C₂	C₅×Q₈×D₁₁	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×C₅×Q₈×C₁₁	2
C₅×Q₈×D₁₁	2
C₂×C₄×C₅×D₁₁	2
C₂×C₅×Dic₂₂	2
C₂×Q₈×D₁₁	5
C₂²×C₅×Q₈	11

Subgroups — C2×C5×Q8×D11 #13183417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Q₈×D₁₁ #13183417