Subgroups — C₂×C₃×C₇×C₁₃×D₃₁ #46799631

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×D₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₃×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₃×D₃₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₃×D₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×D₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₃×D₃₁	C₂×C₇	1	2	yes	direct product factor
11	C₂×C₃×C₁₃×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented
12	C₂×C₁₃×D₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₃×C₇×D₃₁	C₂×C₁₃	1	2	yes	direct product factor
15	C₃×C₁₃×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃×C₇×C₁₃	—	31	1	no	maximal, Hall
17	C₂×C₇×D₃₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₁₃×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented
19	C₁₃×D₃₁	C₂×C₃×C₇	1	2	yes	direct product factor
20	C₃×C₇×C₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₃	—	31	2	no	—
22	C₂×C₃×C₇×C₁₃	D₃₁	1	1	yes	characteristic, direct product factor
23	C₂×C₇×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₇×D₃₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
25	C₁₃×C₃₁	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₃₁	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂²×C₇×C₁₃	—	31	1	no	Hall
28	C₃×C₇×C₁₃	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₇×C₃₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₃₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
31	C₃×D₃₁	C₂×C₇×C₁₃	1	2	yes	direct product factor
32	C₂×C₇×C₁₃	—	31	2	no	—
33	C₂×C₇×C₁₃	C₃×D₃₁	1	1	yes	characteristic, direct product factor
34	C₂²×C₃×C₁₃	—	31	1	no	Hall
35	C₂×D₃₁	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
36	C₃×C₃₁	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₃	C₂×C₃×D₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂²×C₃×C₇	—	31	1	no	Hall
39	C₂×C₃×C₁₃	—	31	2	no	—
40	C₂×C₃×C₁₃	C₇×D₃₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃₁	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented
42	D₃₁	C₂×C₃×C₇×C₁₃	1	2	yes	direct product factor
43	C₂²×C₁₃	—	31	1	no	Hall
44	C₂×C₃×C₇	—	31	2	no	—
45	C₂×C₃×C₇	C₁₃×D₃₁	1	1	yes	characteristic, direct product factor
46	C₃×C₁₃	C₂×C₇×D₃₁	1	1	yes	characteristic, direct product factor, Hall
47	C₃₁	C₂²×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₇	—	31	1	no	Hall
49	C₂×C₁₃	—	31	2	no	—
50	C₂×C₁₃	C₃×C₇×D₃₁	1	1	yes	characteristic, direct product factor
51	C₃×C₇	C₂×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor, Hall
52	C₂×C₇	—	31	2	no	—
53	C₂×C₇	C₃×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor
54	C₁₃	C₂×C₃×C₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₃	—	31	1	no	Hall
56	C₇	C₂×C₃×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	31	2	no	—
58	C₂×C₃	C₇×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor
59	C₂²	—	31	1	no	Sylow
60	C₃	C₂×C₇×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	31	2	no	—
62	C₂	C₃×C₇×C₁₃×D₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂²×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×D₃₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₃₁	C₂	semidirect
3. C₂×C₇×C₁₃×D₃₁	C₃	direct (N × H)
4. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
5. C₇×C₁₃×D₃₁	C₂×C₃	direct (N × H)
6. C₂×C₇×C₁₃×C₃₁	C₂×C₃	semidirect
7. C₂×C₃×C₁₃×D₃₁	C₇	direct (N × H)
8. C₇×C₁₃×C₃₁	C₂²×C₃	semidirect
9. C₂×C₃×C₇×D₃₁	C₁₃	direct (N × H)
10. C₃×C₁₃×D₃₁	C₂×C₇	direct (N × H)
11. C₂×C₃×C₁₃×C₃₁	C₂×C₇	semidirect
12. C₂×C₁₃×D₃₁	C₃×C₇	direct (N × H)
13. C₂×C₃×C₇×C₃₁	C₂×C₁₃	semidirect
14. C₃×C₇×D₃₁	C₂×C₁₃	direct (N × H)
15. C₃×C₁₃×C₃₁	C₂²×C₇	semidirect
17. C₂×C₇×D₃₁	C₃×C₁₃	direct (N × H)
18. C₂×C₁₃×C₃₁	C₂×C₃×C₇	semidirect
19. C₁₃×D₃₁	C₂×C₃×C₇	direct (N × H)
20. C₃×C₇×C₃₁	C₂²×C₁₃	semidirect
22. C₂×C₃×C₇×C₁₃	D₃₁	direct (N × H)
23. C₂×C₇×C₃₁	C₂×C₃×C₁₃	semidirect
24. C₇×D₃₁	C₂×C₃×C₁₃	direct (N × H)
25. C₁₃×C₃₁	C₂²×C₃×C₇	semidirect
26. C₂×C₃×D₃₁	C₇×C₁₃	direct (N × H)
28. C₃×C₇×C₁₃	C₂×D₃₁	direct (N × H)
29. C₇×C₃₁	C₂²×C₃×C₁₃	semidirect
30. C₂×C₃×C₃₁	C₂×C₇×C₁₃	semidirect
31. C₃×D₃₁	C₂×C₇×C₁₃	direct (N × H)
33. C₂×C₇×C₁₃	C₃×D₃₁	direct (N × H)
35. C₂×D₃₁	C₃×C₇×C₁₃	direct (N × H)
36. C₃×C₃₁	C₂²×C₇×C₁₃	semidirect
37. C₇×C₁₃	C₂×C₃×D₃₁	direct (N × H)
40. C₂×C₃×C₁₃	C₇×D₃₁	direct (N × H)
41. C₂×C₃₁	C₂×C₃×C₇×C₁₃	semidirect
42. D₃₁	C₂×C₃×C₇×C₁₃	direct (N × H)
45. C₂×C₃×C₇	C₁₃×D₃₁	direct (N × H)
46. C₃×C₁₃	C₂×C₇×D₃₁	direct (N × H)
47. C₃₁	C₂²×C₃×C₇×C₁₃	semidirect
50. C₂×C₁₃	C₃×C₇×D₃₁	direct (N × H)
51. C₃×C₇	C₂×C₁₃×D₃₁	direct (N × H)
53. C₂×C₇	C₃×C₁₃×D₃₁	direct (N × H)
54. C₁₃	C₂×C₃×C₇×D₃₁	direct (N × H)
56. C₇	C₂×C₃×C₁₃×D₃₁	direct (N × H)
58. C₂×C₃	C₇×C₁₃×D₃₁	direct (N × H)
60. C₃	C₂×C₇×C₁₃×D₃₁	direct (N × H)
62. C₂	C₃×C₇×C₁₃×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×D₃₁	2
C₂×C₃×C₇×C₁₃×C₃₁	2
C₂×C₇×C₁₃×D₃₁	3
C₂×C₃×C₁₃×D₃₁	7
C₂×C₃×C₇×D₃₁	13
C₂²×C₃×C₇×C₁₃	31

Subgroups — C2×C3×C7×C13×D31 #46799631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₃×D₃₁ #46799631