Subgroups — C₂×C₁₃×D₁₅×C₃₁ #37564010

Order 24180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₅×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₃×C₃₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₃×C₃₁	—	5	1	no	maximal, Hall
6	D₅×C₁₃×C₃₁	—	3	2	no	—
7	C₂×C₅×C₁₃×C₃₁	D₃	1	1	yes	characteristic, complemented
8	D₃×C₁₃×C₃₁	—	5	2	no	—
9	C₂×C₃×C₁₃×C₃₁	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₁₅×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₁₃×C₃₁	—	15	1	no	Hall
13	C₃×C₁₃×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
15	D₁₅×C₃₁	C₂×C₁₃	1	2	yes	direct product factor
16	C₂×C₁₃×C₃₁	—	15	2	no	—
17	C₂×C₁₃×C₃₁	D₁₅	1	1	yes	characteristic, direct product factor
18	C₂×C₁₃×D₁₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×D₅×C₃₁	—	3	1	no	Hall
20	C₃×C₅×C₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₃₁	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₃	C₂×C₃₁	1	1	yes	characteristic, complemented
23	C₁₃×D₁₅	C₂×C₃₁	1	2	yes	direct product factor
24	C₂×D₃×C₃₁	—	5	1	no	Hall
25	C₂×C₅×C₃₁	D₃×C₁₃	1	1	yes	characteristic, complemented
26	D₅×C₃₁	—	3	2	no	—
27	C₂×D₅×C₁₃	—	3	1	no	Hall
28	C₃×C₅×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₃₁	D₅×C₁₃	1	1	yes	characteristic, complemented
30	D₃×C₃₁	—	5	2	no	—
31	C₂×D₃×C₁₃	—	5	1	no	Hall
32	C₅×C₃₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₁₃	D₃×C₃₁	1	1	yes	characteristic, complemented
34	D₅×C₁₃	—	3	2	no	—
35	C₂²×C₃₁	—	15	1	no	Hall
36	C₃×C₃₁	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₁₃	D₅×C₃₁	1	1	yes	characteristic, complemented
38	D₃×C₁₃	—	5	2	no	—
39	C₅×C₁₃	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃₁	—	15	2	no	—
41	C₂×C₃₁	C₁₃×D₁₅	1	1	yes	characteristic, direct product factor
42	C₂×D₁₅	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
43	C₂²×C₁₃	—	15	1	no	Hall
44	C₃×C₁₃	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
45	C₃₁	C₂×C₁₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₃×C₅	C₂×C₁₃×C₃₁	1	1	yes	characteristic, complemented
47	D₁₅	C₂×C₁₃×C₃₁	1	2	yes	direct product factor
48	C₂×C₁₃	—	15	2	no	—
49	C₂×C₁₃	D₁₅×C₃₁	1	1	yes	characteristic, direct product factor
50	C₂×D₅	—	3	1	no	Hall
51	C₃×C₅	C₂²×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Hall
52	C₁₃	C₂×D₁₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×D₃	—	5	1	no	Hall
54	C₂×C₅	D₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented
55	D₅	—	3	2	no	—
56	C₂×C₃	D₅×C₁₃×C₃₁	1	1	yes	characteristic, complemented
57	D₃	—	5	2	no	—
58	C₅	C₂×D₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	15	1	no	Sylow
60	C₃	C₂×D₅×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	15	2	no	—
62	C₂	C₁₃×D₁₅×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₃₁	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₃₁	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₅×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃×C₃₁	C₂	semidirect
4. C₃×C₅×C₁₃×C₃₁	C₂²	semidirect
7. C₂×C₅×C₁₃×C₃₁	D₃	semidirect
9. C₂×C₃×C₁₃×C₃₁	D₅	semidirect
10. C₅×C₁₃×C₃₁	C₂×D₃	semidirect
11. C₂×D₁₅×C₃₁	C₁₃	direct (N × H)
13. C₃×C₁₃×C₃₁	C₂×D₅	semidirect
14. C₂×C₃×C₅×C₃₁	C₂×C₁₃	semidirect
15. D₁₅×C₃₁	C₂×C₁₃	direct (N × H)
17. C₂×C₁₃×C₃₁	D₁₅	direct (N × H)
18. C₂×C₁₃×D₁₅	C₃₁	direct (N × H)
20. C₃×C₅×C₃₁	C₂²×C₁₃	semidirect
21. C₁₃×C₃₁	C₂×D₁₅	direct (N × H)
22. C₂×C₃×C₅×C₁₃	C₂×C₃₁	semidirect
23. C₁₃×D₁₅	C₂×C₃₁	direct (N × H)
25. C₂×C₅×C₃₁	D₃×C₁₃	semidirect
28. C₃×C₅×C₁₃	C₂²×C₃₁	semidirect
29. C₂×C₃×C₃₁	D₅×C₁₃	semidirect
32. C₅×C₃₁	C₂×D₃×C₁₃	semidirect
33. C₂×C₅×C₁₃	D₃×C₃₁	semidirect
36. C₃×C₃₁	C₂×D₅×C₁₃	semidirect
37. C₂×C₃×C₁₃	D₅×C₃₁	semidirect
39. C₅×C₁₃	C₂×D₃×C₃₁	semidirect
41. C₂×C₃₁	C₁₃×D₁₅	direct (N × H)
42. C₂×D₁₅	C₁₃×C₃₁	direct (N × H)
44. C₃×C₁₃	C₂×D₅×C₃₁	semidirect
45. C₃₁	C₂×C₁₃×D₁₅	direct (N × H)
46. C₂×C₃×C₅	C₂×C₁₃×C₃₁	semidirect
47. D₁₅	C₂×C₁₃×C₃₁	direct (N × H)
49. C₂×C₁₃	D₁₅×C₃₁	direct (N × H)
51. C₃×C₅	C₂²×C₁₃×C₃₁	semidirect
52. C₁₃	C₂×D₁₅×C₃₁	direct (N × H)
54. C₂×C₅	D₃×C₁₃×C₃₁	semidirect
56. C₂×C₃	D₅×C₁₃×C₃₁	semidirect
58. C₅	C₂×D₃×C₁₃×C₃₁	semidirect
60. C₃	C₂×D₅×C₁₃×C₃₁	semidirect
62. C₂	C₁₃×D₁₅×C₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×D₁₅×C₃₁	2
C₂×C₃×C₅×C₁₃×C₃₁	2
C₂×D₅×C₁₃×C₃₁	3
C₂×D₃×C₁₃×C₃₁	5
C₂×D₁₅×C₃₁	13
C₂×C₁₃×D₁₅	31

Subgroups — C2×C13×D15×C31 #37564010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₁₅×C₃₁ #37564010