Subgroups — C₂×C₅×C₁₁⋊(D₁₃⋊C₃) #22575113

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊(D₁₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₁×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁⋊(D₁₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₁₄₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₁×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₁₁⋊(D₁₃⋊C₃)	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₅×D₁₃⋊C₃	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×D₁₁	—	13	1	no	maximal, Hall
13	C₂×D₁₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented
16	C₅×D₁₃⋊C₃	—	11	2	no	—
17	C₂×C₃×C₅×C₁₁	—	13	1	no	—
18	C₃×C₅×D₁₁	—	13	2	no	—
19	C₂×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	D₁₄₃	C₂×C₃×C₅	1	2	yes	complemented
21	C₂×C₅×D₁₃	—	11	1	no	Hall
22	C₂×C₅×D₁₁	—	13	1	no	Hall
23	C₅×C₁₃⋊C₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	—	13	1	no	Hall
25	C₂×D₁₃⋊C₃	—	11	1	no	Hall
26	C₁₁×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₁₁	—	13	1	no	Hall
28	C₂×C₅×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
29	C₅×D₁₃	—	11	2	no	—
30	C₂×C₅×C₁₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₅×D₁₁	—	13	2	no	—
32	C₂×C₁₃⋊C₃	C₅×D₁₁	1	1	yes	characteristic, complemented
33	D₁₃⋊C₃	—	11	2	no	—
34	C₂×C₃×C₁₁	—	13	1	no	—
35	C₃×D₁₁	—	13	2	no	—
36	C₅×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃×C₅	—	143	1	no	Hall
38	C₅×C₁₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₃	—	11	1	no	Hall
40	C₂×D₁₁	—	13	1	no	Hall
41	C₁₃⋊C₃	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	—	13	1	no	Hall
43	C₂×C₃×C₅	—	13	1	no	—
44	C₂×C₃×C₅	—	143	2	no	—
45	C₂×C₁₃	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented
46	D₁₃	—	11	2	no	—
47	C₂×C₁₁	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
48	D₁₁	—	13	2	no	—
49	C₂²×C₅	—	143	1	no	Hall
50	C₃×C₅	—	13	1	no	Hall
51	C₁₃	C₂×C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	143	1	no	Hall
53	C₁₁	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	—	143	2	no	—
55	C₂×C₅	C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
56	C₂×C₃	—	13	1	no	—
57	C₂×C₃	—	143	2	no	—
58	C₅	C₂×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	143	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	143	2	no	—
62	C₂	C₅×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₁⋊(D₁₃⋊C₃)
commutator, hypocenter	C₁₁×C₁₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₃	C₂×C₃
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊(D₁₃⋊C₃)	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₅×D₁₄₃	C₃	semidirect
4. C₅×C₁₁×C₁₃⋊C₃	C₂²	semidirect
5. C₂×C₁₁⋊(D₁₃⋊C₃)	C₅	direct (N × H)
6. C₂×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₅×D₁₄₃	C₂×C₃	semidirect
8. C₂×C₁₁×C₁₃⋊C₃	C₂×C₅	semidirect
9. C₁₁⋊(D₁₃⋊C₃)	C₂×C₅	direct (N × H)
11. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
13. C₂×D₁₄₃	C₃×C₅	semidirect
14. C₁₁×C₁₃⋊C₃	C₂²×C₅	semidirect
15. C₂×C₅×C₁₃⋊C₃	D₁₁	semidirect
19. C₂×C₁₁×C₁₃	C₂×C₃×C₅	semidirect
20. D₁₄₃	C₂×C₃×C₅	semidirect
23. C₅×C₁₃⋊C₃	C₂×D₁₁	semidirect
26. C₁₁×C₁₃	C₂²×C₃×C₅	semidirect
28. C₂×C₅×C₁₃	C₃×D₁₁	semidirect
30. C₂×C₅×C₁₁	D₁₃⋊C₃	semidirect
32. C₂×C₁₃⋊C₃	C₅×D₁₁	semidirect
36. C₅×C₁₃	C₂×C₃×D₁₁	semidirect
38. C₅×C₁₁	C₂×D₁₃⋊C₃	semidirect
41. C₁₃⋊C₃	C₂×C₅×D₁₁	semidirect
45. C₂×C₁₃	C₃×C₅×D₁₁	semidirect
47. C₂×C₁₁	C₅×D₁₃⋊C₃	semidirect
51. C₁₃	C₂×C₃×C₅×D₁₁	semidirect
53. C₁₁	C₂×C₅×D₁₃⋊C₃	semidirect
55. C₂×C₅	C₁₁⋊(D₁₃⋊C₃)	direct (N × H)
58. C₅	C₂×C₁₁⋊(D₁₃⋊C₃)	direct (N × H)
62. C₂	C₅×C₁₁⋊(D₁₃⋊C₃)	direct (N × H)

Subgroups — C2×C5×C11⋊(D13⋊C3) #22575113

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₁₁⋊(D₁₃⋊C₃) #22575113