Subgroups — C₂×Q₈×D₅×C₁₁ #13183432

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	Q₈×D₅×C₁₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₅×C₁₁	C₂	1	3	yes	maximal
4	C₂×C₁₁×Dic₁₀	C₂	1	3	yes	maximal, complemented
5	C₂²×D₅×C₁₁	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×C₁₁×Dic₅	C₂²	1	3	yes	—
9	C₄×D₅×C₁₁	C₂²	1	12	yes	—
10	C₁₁×Dic₁₀	C₂²	1	12	yes	complemented
11	C₂²×Q₈×C₁₁	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₅×C₁₁	Q₈	1	4	yes	direct product factor
14	C₂×D₅×C₁₁	C₂³	1	2	yes	—
15	C₄×C₅×C₁₁	C₂³	1	6	yes	—
16	C₁₁×Dic₅	C₂³	1	6	yes	—
17	C₂×Q₈×C₁₁	—	5	8	no	—
18	C₂×Q₈×C₁₁	—	5	3	no	—
19	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, direct product factor
20	C₂²×C₄×C₁₁	—	5	3	no	—
21	C₂×Q₈×D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₁₁	C₂×Q₈	1	2	yes	complemented
23	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
24	D₅×C₁₁	C₂×Q₈	1	4	yes	direct product factor
25	C₂³×C₁₁	—	5	1	no	—
26	Q₈×C₁₁	—	5	12	no	—
27	Q₈×C₁₁	C₂×D₅	1	4	yes	direct product factor
28	C₂×C₄×C₁₁	—	5	3	no	—
29	C₂×C₄×C₁₁	—	5	12	no	—
30	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
31	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
32	Q₈×D₅	C₂×C₁₁	1	8	yes	direct product factor
33	C₂×C₄×D₅	C₂×C₁₁	1	3	yes	—
34	C₂×Dic₁₀	C₂×C₁₁	1	3	yes	complemented
35	C₅×C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₁	—	5	4	no	—
37	C₂²×C₁₁	—	5	2	no	—
38	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
39	C₄×C₁₁	—	5	6	no	—
40	C₄×C₁₁	C₂²×D₅	1	6	yes	—
41	C₂²×D₅	C₂²×C₁₁	1	1	yes	characteristic
42	C₅×Q₈	C₂²×C₁₁	1	4	yes	complemented
43	C₂×C₄×C₅	C₂²×C₁₁	1	3	yes	—
44	C₂×Dic₅	C₂²×C₁₁	1	3	yes	—
45	C₄×D₅	C₂²×C₁₁	1	12	yes	—
46	Dic₁₀	C₂²×C₁₁	1	12	yes	complemented
47	C₂²×Q₈	—	5	1	no	Sylow
48	C₂×C₁₁	—	5	4	no	—
49	C₂×C₁₁	Q₈×D₅	1	2	yes	direct product factor
50	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
51	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
52	C₂×D₅	Q₈×C₁₁	1	4	yes	direct product factor
53	C₂×D₅	C₂³×C₁₁	1	2	yes	—
54	C₄×C₅	C₂³×C₁₁	1	6	yes	—
55	Dic₅	C₂³×C₁₁	1	6	yes	—
56	C₂×Q₈	—	5	8	no	—
57	C₂×Q₈	—	5	3	no	—
58	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic, direct product factor
59	C₂²×C₄	—	5	3	no	—
60	C₁₁	C₂×Q₈×D₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₅	C₂×Q₈×C₁₁	1	2	yes	complemented
62	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
63	D₅	C₂×Q₈×C₁₁	1	4	yes	direct product factor
64	C₂³	—	5	1	no	—
65	Q₈	—	5	12	no	—
66	Q₈	C₂×D₅×C₁₁	1	4	yes	direct product factor
67	C₂×C₄	—	5	3	no	—
68	C₂×C₄	—	5	12	no	—
69	C₂×C₄	C₂×D₅×C₁₁	1	3	yes	—
70	C₅	C₂²×Q₈×C₁₁	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	5	4	no	—
72	C₂²	—	5	2	no	—
73	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
74	C₄	—	5	6	no	—
75	C₄	C₂²×D₅×C₁₁	1	6	yes	—
76	C₂	—	5	4	no	—
77	C₂	Q₈×D₅×C₁₁	1	2	yes	direct product factor
78	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×D₅×C₁₁	C₂²
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₂²×Q₈×C₁₁
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
2. Q₈×D₅×C₁₁	C₂	direct (N × H)
4. C₂×C₁₁×Dic₁₀	C₂	semidirect
6. C₅×Q₈×C₁₁	C₂²	semidirect
10. C₁₁×Dic₁₀	C₂²	semidirect
13. C₂×D₅×C₁₁	Q₈	direct (N × H)
19. C₂×Q₈×C₁₁	D₅	direct (N × H)
21. C₂×Q₈×D₅	C₁₁	direct (N × H)
22. C₂×C₅×C₁₁	C₂×Q₈	semidirect
24. D₅×C₁₁	C₂×Q₈	direct (N × H)
27. Q₈×C₁₁	C₂×D₅	direct (N × H)
31. C₂×C₅×Q₈	C₂×C₁₁	semidirect
32. Q₈×D₅	C₂×C₁₁	direct (N × H)
34. C₂×Dic₁₀	C₂×C₁₁	semidirect
35. C₅×C₁₁	C₂²×Q₈	semidirect
42. C₅×Q₈	C₂²×C₁₁	semidirect
46. Dic₁₀	C₂²×C₁₁	semidirect
49. C₂×C₁₁	Q₈×D₅	direct (N × H)
52. C₂×D₅	Q₈×C₁₁	direct (N × H)
58. C₂×Q₈	D₅×C₁₁	direct (N × H)
60. C₁₁	C₂×Q₈×D₅	direct (N × H)
61. C₂×C₅	C₂×Q₈×C₁₁	semidirect
63. D₅	C₂×Q₈×C₁₁	direct (N × H)
66. Q₈	C₂×D₅×C₁₁	direct (N × H)
70. C₅	C₂²×Q₈×C₁₁	semidirect
77. C₂	Q₈×D₅×C₁₁	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
Q₈×D₅×C₁₁	2
C₂×C₄×D₅×C₁₁	2
C₂×C₁₁×Dic₁₀	2
C₂²×Q₈×C₁₁	5
C₂×Q₈×D₅	11

Subgroups — C2×Q8×D5×C11 #13183432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×D₅×C₁₁ #13183432