Subgroups — C₂×C₁₁⋊C₅×D₃₉ #22575111

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×D₃₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₁₁⋊C₅	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×D₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₁₃×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented
7	D₁₃×C₁₁⋊C₅	—	3	2	no	—
8	C₂×C₃×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₁₁×D₃₉	C₂×C₅	1	2	yes	complemented
10	C₂×C₅×D₃₉	—	11	1	no	maximal, Hall
11	C₁₃×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₃×C₁₁⋊C₅	—	13	1	no	maximal, Hall
13	C₂×C₁₁×D₁₃	—	3	1	no	Hall
14	C₃×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	—	11	1	no	—
16	C₅×D₃₉	—	11	2	no	—
17	C₂×C₃×C₁₁⋊C₅	D₁₃	1	1	yes	characteristic, complemented
18	D₃×C₁₁⋊C₅	—	13	2	no	—
19	C₂×C₁₁×C₁₃	C₅×D₃	1	1	yes	characteristic, complemented
20	C₁₁×D₁₃	—	3	2	no	—
21	C₂×C₅×D₁₃	—	33	1	no	Hall
22	C₂²×C₁₁⋊C₅	—	39	1	no	Hall
23	C₃×C₅×C₁₃	—	11	1	no	Hall
24	C₃×C₁₁⋊C₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁×C₁₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×D₃×C₁₁	—	13	1	no	Hall
28	C₂×C₅×C₁₃	—	11	1	no	—
29	C₅×D₁₃	—	33	2	no	—
30	C₂×C₁₁⋊C₅	—	39	2	no	—
31	C₂×C₁₁⋊C₅	D₃₉	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₁₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
33	D₃₉	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
34	C₂×C₃×C₁₁	C₅×D₁₃	1	1	yes	characteristic, complemented
35	D₃×C₁₁	—	13	2	no	—
36	C₅×C₁₃	—	11	1	no	Hall
37	C₂×C₅×D₃	—	143	1	no	Hall
38	C₁₁⋊C₅	C₂×D₃₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×D₁₃	—	3	1	no	Hall
40	C₂²×C₁₁	—	39	1	no	Hall
41	C₃×C₁₃	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	—	11	1	no	—
44	C₅×D₃	—	143	2	no	—
45	C₂×C₁₃	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
46	D₁₃	—	3	2	no	—
47	C₂×C₁₁	—	39	2	no	—
48	C₂×C₁₁	C₅×D₃₉	1	1	yes	characteristic, complemented
49	C₂²×C₅	—	429	1	no	Hall
50	C₃×C₅	—	11	1	no	Hall
51	C₁₃	C₂×D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₃	—	13	1	no	Hall
53	C₁₁	C₂×C₅×D₃₉	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	—	11	1	no	—
55	C₂×C₅	—	429	2	no	—
56	C₂×C₃	D₁₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
57	D₃	—	13	2	no	—
58	C₅	—	11	1	no	Sylow
59	C₂²	—	39	1	no	Sylow
60	C₃	C₂×D₁₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	39	2	no	—
62	C₂	C₁₁⋊C₅×D₃₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊C₅×D₃₉
commutator, hypocenter	C₃×C₁₁×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₁₃	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×D₃₉	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₁⋊C₅	C₂	semidirect
4. C₃×C₁₃×C₁₁⋊C₅	C₂²	semidirect
5. C₂×C₁₁×D₃₉	C₅	semidirect
6. C₂×C₁₃×C₁₁⋊C₅	D₃	semidirect
8. C₂×C₃×C₁₁×C₁₃	C₂×C₅	semidirect
9. C₁₁×D₃₉	C₂×C₅	semidirect
11. C₁₃×C₁₁⋊C₅	C₂×D₃	semidirect
14. C₃×C₁₁×C₁₃	C₂²×C₅	semidirect
17. C₂×C₃×C₁₁⋊C₅	D₁₃	semidirect
19. C₂×C₁₁×C₁₃	C₅×D₃	semidirect
24. C₃×C₁₁⋊C₅	C₂×D₁₃	semidirect
25. C₂×D₃₉	C₁₁⋊C₅	direct (N × H)
26. C₁₁×C₁₃	C₂×C₅×D₃	semidirect
31. C₂×C₁₁⋊C₅	D₃₉	direct (N × H)
32. C₂×C₃×C₁₃	C₂×C₁₁⋊C₅	semidirect
33. D₃₉	C₂×C₁₁⋊C₅	direct (N × H)
34. C₂×C₃×C₁₁	C₅×D₁₃	semidirect
38. C₁₁⋊C₅	C₂×D₃₉	direct (N × H)
41. C₃×C₁₃	C₂²×C₁₁⋊C₅	semidirect
42. C₃×C₁₁	C₂×C₅×D₁₃	semidirect
45. C₂×C₁₃	D₃×C₁₁⋊C₅	semidirect
48. C₂×C₁₁	C₅×D₃₉	semidirect
51. C₁₃	C₂×D₃×C₁₁⋊C₅	semidirect
53. C₁₁	C₂×C₅×D₃₉	semidirect
56. C₂×C₃	D₁₃×C₁₁⋊C₅	semidirect
60. C₃	C₂×D₁₃×C₁₁⋊C₅	semidirect
62. C₂	C₁₁⋊C₅×D₃₉	direct (N × H)

Subgroups — C2×C11⋊C5×D39 #22575111

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁⋊C₅×D₃₉ #22575111