Subgroups — C₂³×D₅×D₁₁ #13183472

Order 1760.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅×D₁₁	C₂	1	28	yes	maximal, direct product factor
5	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
6	C₂²×D₅₅	C₂²	1	14	yes	complemented
7	C₂²×D₅×C₁₁	C₂²	1	14	yes	complemented
8	C₂²×C₅×D₁₁	C₂²	1	14	yes	complemented
9	C₂×D₅×D₁₁	C₂²	1	112	yes	direct product factor
10	C₂⁴×D₁₁	—	5	1	no	maximal, Hall
11	C₂²×C₅×C₁₁	C₂³	1	7	yes	complemented
12	C₂×D₅₅	C₂³	1	28	yes	complemented
13	C₂×D₅×C₁₁	C₂³	1	28	yes	complemented
14	C₂×C₅×D₁₁	C₂³	1	28	yes	complemented
15	D₅×D₁₁	C₂³	1	64	yes	direct product factor
16	C₂⁴×C₁₁	—	5	1	no	—
17	C₂³×D₁₁	—	5	1	no	—
18	C₂³×D₁₁	—	5	28	no	—
19	C₂³×D₁₁	D₅	1	1	yes	characteristic, direct product factor
20	C₂⁴×D₅	—	11	1	no	maximal, Hall
21	C₂×C₅×C₁₁	C₂⁴	1	7	yes	complemented
22	D₅₅	C₂⁴	1	8	yes	complemented
23	C₅×D₁₁	C₂⁴	1	8	yes	complemented
24	D₅×C₁₁	C₂⁴	1	8	yes	complemented
25	C₂³×C₁₁	—	5	14	no	—
26	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
27	C₂²×D₁₁	—	5	14	no	—
28	C₂²×D₁₁	—	5	112	no	—
29	C₂²×D₁₁	C₂×D₅	1	14	yes	direct product factor
30	C₂⁴×C₅	—	11	1	no	—
31	C₂³×D₅	—	11	1	no	—
32	C₂³×D₅	—	11	28	no	—
33	C₂³×D₅	D₁₁	1	1	yes	characteristic, direct product factor
34	C₅×C₁₁	C₂⁵	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₁₁	—	5	28	no	—
36	C₂²×C₁₁	C₂²×D₅	1	7	yes	complemented
37	C₂×D₁₁	—	5	28	no	—
38	C₂×D₁₁	—	5	64	no	—
39	C₂×D₁₁	C₂²×D₅	1	28	yes	direct product factor
40	C₂³×C₅	—	11	14	no	—
41	C₂³×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented
42	C₂²×D₅	—	11	14	no	—
43	C₂²×D₅	—	11	112	no	—
44	C₂²×D₅	C₂×D₁₁	1	14	yes	direct product factor
45	C₂⁵	—	55	1	no	Sylow
46	C₂×C₁₁	—	5	8	no	—
47	C₂×C₁₁	C₂³×D₅	1	7	yes	complemented
48	D₁₁	—	5	8	no	—
49	D₁₁	C₂³×D₅	1	8	yes	direct product factor
50	C₂²×C₅	—	11	28	no	—
51	C₂²×C₅	C₂²×D₁₁	1	7	yes	complemented
52	C₂×D₅	—	11	28	no	—
53	C₂×D₅	—	11	64	no	—
54	C₂×D₅	C₂²×D₁₁	1	28	yes	direct product factor
55	C₂⁴	—	5	1	no	—
56	C₂⁴	—	11	1	no	—
57	C₂⁴	—	55	28	no	—
58	C₂⁴	—	55	1	no	—
59	C₁₁	C₂⁴×D₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₅	—	11	8	no	—
61	C₂×C₅	C₂³×D₁₁	1	7	yes	complemented
62	D₅	—	11	8	no	—
63	D₅	C₂³×D₁₁	1	8	yes	direct product factor
64	C₂³	—	5	14	no	—
65	C₂³	—	11	14	no	—
66	C₂³	—	55	112	no	—
67	C₂³	—	55	14	no	—
68	C₂³	D₅×D₁₁	1	1	yes	characteristic, direct product factor
69	C₅	C₂⁴×D₁₁	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	5	28	no	—
71	C₂²	—	11	28	no	—
72	C₂²	—	55	64	no	—
73	C₂²	—	55	28	no	—
74	C₂²	C₂×D₅×D₁₁	1	7	yes	direct product factor
75	C₂	—	5	8	no	—
76	C₂	—	11	8	no	—
77	C₂	—	55	8	no	—
78	C₂	C₂²×D₅×D₁₁	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂³×C₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×D₅₅	C₂	semidirect
2. C₂³×D₅×C₁₁	C₂	semidirect
3. C₂³×C₅×D₁₁	C₂	semidirect
4. C₂²×D₅×D₁₁	C₂	direct (N × H)
5. C₂³×C₅×C₁₁	C₂²	semidirect
6. C₂²×D₅₅	C₂²	semidirect
7. C₂²×D₅×C₁₁	C₂²	semidirect
8. C₂²×C₅×D₁₁	C₂²	semidirect
9. C₂×D₅×D₁₁	C₂²	direct (N × H)
11. C₂²×C₅×C₁₁	C₂³	semidirect
12. C₂×D₅₅	C₂³	semidirect
13. C₂×D₅×C₁₁	C₂³	semidirect
14. C₂×C₅×D₁₁	C₂³	semidirect
15. D₅×D₁₁	C₂³	direct (N × H)
19. C₂³×D₁₁	D₅	direct (N × H)
21. C₂×C₅×C₁₁	C₂⁴	semidirect
22. D₅₅	C₂⁴	semidirect
23. C₅×D₁₁	C₂⁴	semidirect
24. D₅×C₁₁	C₂⁴	semidirect
26. C₂³×C₁₁	C₂×D₅	semidirect
29. C₂²×D₁₁	C₂×D₅	direct (N × H)
33. C₂³×D₅	D₁₁	direct (N × H)
34. C₅×C₁₁	C₂⁵	semidirect
36. C₂²×C₁₁	C₂²×D₅	semidirect
39. C₂×D₁₁	C₂²×D₅	direct (N × H)
41. C₂³×C₅	C₂×D₁₁	semidirect
44. C₂²×D₅	C₂×D₁₁	direct (N × H)
47. C₂×C₁₁	C₂³×D₅	semidirect
49. D₁₁	C₂³×D₅	direct (N × H)
51. C₂²×C₅	C₂²×D₁₁	semidirect
54. C₂×D₅	C₂²×D₁₁	direct (N × H)
59. C₁₁	C₂⁴×D₅	semidirect
61. C₂×C₅	C₂³×D₁₁	semidirect
63. D₅	C₂³×D₁₁	direct (N × H)
68. C₂³	D₅×D₁₁	direct (N × H)
69. C₅	C₂⁴×D₁₁	semidirect
74. C₂²	C₂×D₅×D₁₁	direct (N × H)
78. C₂	C₂²×D₅×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
C₂³×D₅₅	2
C₂³×D₅×C₁₁	2
C₂³×C₅×D₁₁	2
C₂²×D₅×D₁₁	2
C₂⁴×D₁₁	5
C₂⁴×D₅	11

Subgroups — C23×D5×D11 #13183472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₅×D₁₁ #13183472