Subgroups — C₂×C₃×D₇₁₅ #22575190

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₁₄₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₇₁₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
9	C₃×D₁₄₃	—	5	2	no	—
10	C₂×C₃×D₆₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×D₅₅	—	13	1	no	maximal, Hall
13	C₂×D₁₄₃	—	5	1	no	Hall
14	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	D₁₁	1	1	yes	characteristic, complemented
16	C₃×D₆₅	—	11	2	no	—
17	C₂×C₃×C₅×C₁₁	D₁₃	1	1	yes	characteristic, complemented
18	C₃×D₅₅	—	13	2	no	—
19	C₂×C₁₁×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
20	D₁₄₃	—	5	2	no	—
21	C₂×D₆₅	—	11	1	no	Hall
22	C₂×D₅₅	—	13	1	no	Hall
23	C₃×C₅×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₃	—	55	1	no	Hall
26	C₁₁×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₁₁	—	65	1	no	Hall
28	C₂×C₅×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
29	D₆₅	—	11	2	no	—
30	C₂×C₅×C₁₁	C₃×D₁₃	1	1	yes	characteristic, complemented
31	D₅₅	—	13	2	no	—
32	C₂×C₃×C₁₃	D₅₅	1	1	yes	characteristic, complemented
33	C₃×D₁₃	—	55	2	no	—
34	C₂×C₃×C₁₁	D₆₅	1	1	yes	characteristic, complemented
35	C₃×D₁₁	—	65	2	no	—
36	C₅×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×D₅	—	143	1	no	Hall
38	C₅×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂×D₁₃	—	55	1	no	Hall
40	C₂×D₁₁	—	65	1	no	Hall
41	C₃×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	D₁₄₃	1	1	yes	characteristic, complemented
44	C₃×D₅	—	143	2	no	—
45	C₂×C₁₃	C₃×D₅₅	1	1	yes	characteristic, complemented
46	D₁₃	—	55	2	no	—
47	C₂×C₁₁	C₃×D₆₅	1	1	yes	characteristic, complemented
48	D₁₁	—	65	2	no	—
49	C₂×D₅	—	143	1	no	Hall
50	C₃×C₅	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
51	C₁₃	C₂×C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	715	1	no	Hall
53	C₁₁	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	C₃×D₁₄₃	1	1	yes	characteristic, complemented
55	D₅	—	143	2	no	—
56	C₂×C₃	—	715	2	no	—
57	C₂×C₃	D₇₁₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	715	1	no	Sylow
60	C₃	C₂×D₇₁₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	715	2	no	—
62	C₂	C₃×D₇₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇₁₅
commutator, hypocenter	C₅×C₁₁×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₃	C₂	semidirect
3. C₂×D₇₁₅	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
7. D₇₁₅	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁×C₁₃	D₅	semidirect
11. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
14. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
15. C₂×C₃×C₅×C₁₃	D₁₁	semidirect
17. C₂×C₃×C₅×C₁₁	D₁₃	semidirect
19. C₂×C₁₁×C₁₃	C₃×D₅	semidirect
23. C₃×C₅×C₁₃	C₂×D₁₁	semidirect
24. C₃×C₅×C₁₁	C₂×D₁₃	semidirect
26. C₁₁×C₁₃	C₂×C₃×D₅	semidirect
28. C₂×C₅×C₁₃	C₃×D₁₁	semidirect
30. C₂×C₅×C₁₁	C₃×D₁₃	semidirect
32. C₂×C₃×C₁₃	D₅₅	semidirect
34. C₂×C₃×C₁₁	D₆₅	semidirect
36. C₅×C₁₃	C₂×C₃×D₁₁	semidirect
38. C₅×C₁₁	C₂×C₃×D₁₃	semidirect
41. C₃×C₁₃	C₂×D₅₅	semidirect
42. C₃×C₁₁	C₂×D₆₅	semidirect
43. C₂×C₃×C₅	D₁₄₃	semidirect
45. C₂×C₁₃	C₃×D₅₅	semidirect
47. C₂×C₁₁	C₃×D₆₅	semidirect
50. C₃×C₅	C₂×D₁₄₃	semidirect
51. C₁₃	C₂×C₃×D₅₅	semidirect
53. C₁₁	C₂×C₃×D₆₅	semidirect
54. C₂×C₅	C₃×D₁₄₃	semidirect
57. C₂×C₃	D₇₁₅	direct (N × H)
58. C₅	C₂×C₃×D₁₄₃	semidirect
60. C₃	C₂×D₇₁₅	direct (N × H)
62. C₂	C₃×D₇₁₅	direct (N × H)

Subgroups — C2×C3×D715 #22575190

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₇₁₅ #22575190