Subgroups — C₂×C₃×C₁₃×D₇×C₃₁ #46799634

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₇×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₇×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₇×C₃₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₃×C₁₃×C₃₁	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×D₇×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₃×C₃₁	—	7	2	no	—
11	C₂×C₃×C₁₃×C₃₁	D₇	1	1	yes	characteristic, direct product factor
12	C₂²×C₁₃×C₃₁	—	7	1	no	Hall
13	C₂×C₃×C₇×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₃×D₇×C₃₁	C₂×C₁₃	1	2	yes	direct product factor
15	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₁₃×D₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×D₇×C₃₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₁₃×C₃₁	—	7	2	no	—
19	C₂×C₁₃×C₃₁	C₃×D₇	1	1	yes	characteristic, direct product factor
20	C₃×C₇×C₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₃	C₂×C₃₁	1	1	yes	characteristic, complemented
22	C₃×C₁₃×D₇	C₂×C₃₁	1	2	yes	direct product factor
23	C₂×C₇×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
24	D₇×C₃₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
25	C₁₃×C₃₁	C₂×C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₃₁	—	7	1	no	Hall
27	C₂×C₁₃×D₇	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₇×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₇×C₃₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₃₁	—	7	2	no	—
31	C₂×C₃×C₃₁	C₁₃×D₇	1	1	yes	characteristic, direct product factor
32	C₂×C₇×C₁₃	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
33	C₁₃×D₇	C₂×C₃×C₃₁	1	2	yes	direct product factor
34	C₂²×C₃×C₁₃	—	7	1	no	Hall
35	C₂²×C₃₁	—	7	1	no	Hall
36	C₃×C₃₁	C₂×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Hall
37	C₇×C₁₃	C₂²×C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃×D₇	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃×C₁₃	—	7	2	no	—
40	C₂×C₃×C₁₃	D₇×C₃₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃₁	—	7	2	no	—
42	C₂×C₃₁	C₃×C₁₃×D₇	1	1	yes	characteristic, direct product factor
43	C₂²×C₁₃	—	7	1	no	Hall
44	C₂×C₃×C₇	C₂×C₁₃×C₃₁	1	1	yes	characteristic, complemented
45	C₃×D₇	C₂×C₁₃×C₃₁	1	2	yes	direct product factor
46	C₃×C₁₃	C₂×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
47	C₃₁	C₂×C₃×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₇	C₃×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₁₃	—	7	2	no	—
50	C₂×C₁₃	C₃×D₇×C₃₁	1	1	yes	characteristic, direct product factor
51	C₃×C₇	C₂²×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Hall
52	C₂×C₇	C₂×C₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented
53	D₇	C₂×C₃×C₁₃×C₃₁	1	2	yes	direct product factor
54	C₁₃	C₂×C₃×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₃	—	7	1	no	Hall
56	C₇	C₂²×C₃×C₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	7	2	no	—
58	C₂×C₃	C₁₃×D₇×C₃₁	1	1	yes	characteristic, direct product factor
59	C₂²	—	7	1	no	Sylow
60	C₃	C₂×C₁₃×D₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	7	2	no	—
62	C₂	C₃×C₁₃×D₇×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃×C₃₁	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₇×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₃₁	C₂	semidirect
3. C₂×C₁₃×D₇×C₃₁	C₃	direct (N × H)
4. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
5. C₁₃×D₇×C₃₁	C₂×C₃	direct (N × H)
6. C₂×C₇×C₁₃×C₃₁	C₂×C₃	semidirect
8. C₇×C₁₃×C₃₁	C₂²×C₃	semidirect
9. C₂×C₃×D₇×C₃₁	C₁₃	direct (N × H)
11. C₂×C₃×C₁₃×C₃₁	D₇	direct (N × H)
13. C₂×C₃×C₇×C₃₁	C₂×C₁₃	semidirect
14. C₃×D₇×C₃₁	C₂×C₁₃	direct (N × H)
15. C₃×C₁₃×C₃₁	C₂×D₇	direct (N × H)
16. C₂×C₃×C₁₃×D₇	C₃₁	direct (N × H)
17. C₂×D₇×C₃₁	C₃×C₁₃	direct (N × H)
19. C₂×C₁₃×C₃₁	C₃×D₇	direct (N × H)
20. C₃×C₇×C₃₁	C₂²×C₁₃	semidirect
21. C₂×C₃×C₇×C₁₃	C₂×C₃₁	semidirect
22. C₃×C₁₃×D₇	C₂×C₃₁	direct (N × H)
23. C₂×C₇×C₃₁	C₂×C₃×C₁₃	semidirect
24. D₇×C₃₁	C₂×C₃×C₁₃	direct (N × H)
25. C₁₃×C₃₁	C₂×C₃×D₇	direct (N × H)
27. C₂×C₁₃×D₇	C₃×C₃₁	direct (N × H)
28. C₃×C₇×C₁₃	C₂²×C₃₁	semidirect
29. C₇×C₃₁	C₂²×C₃×C₁₃	semidirect
31. C₂×C₃×C₃₁	C₁₃×D₇	direct (N × H)
32. C₂×C₇×C₁₃	C₂×C₃×C₃₁	semidirect
33. C₁₃×D₇	C₂×C₃×C₃₁	direct (N × H)
36. C₃×C₃₁	C₂×C₁₃×D₇	direct (N × H)
37. C₇×C₁₃	C₂²×C₃×C₃₁	semidirect
38. C₂×C₃×D₇	C₁₃×C₃₁	direct (N × H)
40. C₂×C₃×C₁₃	D₇×C₃₁	direct (N × H)
42. C₂×C₃₁	C₃×C₁₃×D₇	direct (N × H)
44. C₂×C₃×C₇	C₂×C₁₃×C₃₁	semidirect
45. C₃×D₇	C₂×C₁₃×C₃₁	direct (N × H)
46. C₃×C₁₃	C₂×D₇×C₃₁	direct (N × H)
47. C₃₁	C₂×C₃×C₁₃×D₇	direct (N × H)
48. C₂×D₇	C₃×C₁₃×C₃₁	direct (N × H)
50. C₂×C₁₃	C₃×D₇×C₃₁	direct (N × H)
51. C₃×C₇	C₂²×C₁₃×C₃₁	semidirect
52. C₂×C₇	C₂×C₃×C₁₃×C₃₁	semidirect
53. D₇	C₂×C₃×C₁₃×C₃₁	direct (N × H)
54. C₁₃	C₂×C₃×D₇×C₃₁	direct (N × H)
56. C₇	C₂²×C₃×C₁₃×C₃₁	semidirect
58. C₂×C₃	C₁₃×D₇×C₃₁	direct (N × H)
60. C₃	C₂×C₁₃×D₇×C₃₁	direct (N × H)
62. C₂	C₃×C₁₃×D₇×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
C₃×C₁₃×D₇×C₃₁	2
C₂×C₃×C₇×C₁₃×C₃₁	2
C₂×C₁₃×D₇×C₃₁	3
C₂²×C₃×C₁₃×C₃₁	7
C₂×C₃×D₇×C₃₁	13
C₂×C₃×C₁₃×D₇	31

Subgroups — C2×C3×C13×D7×C31 #46799634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×D₇×C₃₁ #46799634