Subgroups — C₂×C₁₃×D₆₅₁ #46799643

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₆₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₂₁₇	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₂₁₇	—	3	2	no	—
6	C₂×C₇×C₁₃×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₃×D₉₃	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×D₆₅₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₃×D₉₃	—	7	2	no	—
11	C₂×C₃×C₁₃×C₃₁	D₇	1	1	yes	characteristic, complemented
12	C₂×C₁₃×D₃₁	—	21	1	no	Hall
13	C₂×C₃×C₇×C₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented
14	D₆₅₁	C₂×C₁₃	1	2	yes	direct product factor
15	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃×D₂₁	—	31	1	no	maximal, Hall
17	C₂×D₂₁₇	—	3	1	no	Hall
18	C₂×C₁₃×C₃₁	D₂₁	1	1	yes	characteristic, complemented
19	C₁₃×D₃₁	—	21	2	no	—
20	C₃×C₇×C₃₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₃	D₃₁	1	1	yes	characteristic, complemented
22	C₁₃×D₂₁	—	31	2	no	—
23	C₂×C₇×C₃₁	D₃×C₁₃	1	1	yes	characteristic, complemented
24	D₂₁₇	—	3	2	no	—
25	C₁₃×C₃₁	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
26	C₂×D₉₃	—	7	1	no	Hall
27	C₂×C₁₃×D₇	—	93	1	no	Hall
28	C₃×C₇×C₁₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
29	C₇×C₃₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₃₁	C₁₃×D₇	1	1	yes	characteristic, complemented
31	D₉₃	—	7	2	no	—
32	C₂×C₇×C₁₃	D₉₃	1	1	yes	characteristic, complemented
33	C₁₃×D₇	—	93	2	no	—
34	C₂×D₃×C₁₃	—	217	1	no	Hall
35	C₂×D₃₁	—	21	1	no	Hall
36	C₃×C₃₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₃	C₂×D₉₃	1	1	yes	characteristic, complemented, Hall
38	C₂×D₂₁	—	31	1	no	Hall
39	C₂×C₃×C₁₃	D₂₁₇	1	1	yes	characteristic, complemented
40	D₃×C₁₃	—	217	2	no	—
41	C₂×C₃₁	C₁₃×D₂₁	1	1	yes	characteristic, complemented
42	D₃₁	—	21	2	no	—
43	C₂²×C₁₃	—	651	1	no	Hall
44	C₂×C₃×C₇	C₁₃×D₃₁	1	1	yes	characteristic, complemented
45	D₂₁	—	31	2	no	—
46	C₃×C₁₃	C₂×D₂₁₇	1	1	yes	characteristic, complemented, Hall
47	C₃₁	C₂×C₁₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₇	—	93	1	no	Hall
49	C₂×C₁₃	—	651	2	no	—
50	C₂×C₁₃	D₆₅₁	1	1	yes	characteristic, direct product factor
51	C₃×C₇	C₂×C₁₃×D₃₁	1	1	yes	characteristic, complemented, Hall
52	C₂×C₇	C₁₃×D₉₃	1	1	yes	characteristic, complemented
53	D₇	—	93	2	no	—
54	C₁₃	C₂×D₆₅₁	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×D₃	—	217	1	no	Hall
56	C₇	C₂×C₁₃×D₉₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	C₁₃×D₂₁₇	1	1	yes	characteristic, complemented
58	D₃	—	217	2	no	—
59	C₂²	—	651	1	no	Sylow
60	C₃	C₂×C₁₃×D₂₁₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	651	2	no	—
62	C₂	C₁₃×D₆₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₆₅₁
commutator, cosocle, hypocenter	C₃×C₇×C₃₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₃×C₇×C₃₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₆₅₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃×C₃₁	C₂	semidirect
4. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
6. C₂×C₇×C₁₃×C₃₁	D₃	semidirect
8. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
9. C₂×D₆₅₁	C₁₃	direct (N × H)
11. C₂×C₃×C₁₃×C₃₁	D₇	semidirect
13. C₂×C₃×C₇×C₃₁	C₂×C₁₃	semidirect
14. D₆₅₁	C₂×C₁₃	direct (N × H)
15. C₃×C₁₃×C₃₁	C₂×D₇	semidirect
18. C₂×C₁₃×C₃₁	D₂₁	semidirect
20. C₃×C₇×C₃₁	C₂²×C₁₃	semidirect
21. C₂×C₃×C₇×C₁₃	D₃₁	semidirect
23. C₂×C₇×C₃₁	D₃×C₁₃	semidirect
25. C₁₃×C₃₁	C₂×D₂₁	semidirect
28. C₃×C₇×C₁₃	C₂×D₃₁	semidirect
29. C₇×C₃₁	C₂×D₃×C₁₃	semidirect
30. C₂×C₃×C₃₁	C₁₃×D₇	semidirect
32. C₂×C₇×C₁₃	D₉₃	semidirect
36. C₃×C₃₁	C₂×C₁₃×D₇	semidirect
37. C₇×C₁₃	C₂×D₉₃	semidirect
39. C₂×C₃×C₁₃	D₂₁₇	semidirect
41. C₂×C₃₁	C₁₃×D₂₁	semidirect
44. C₂×C₃×C₇	C₁₃×D₃₁	semidirect
46. C₃×C₁₃	C₂×D₂₁₇	semidirect
47. C₃₁	C₂×C₁₃×D₂₁	semidirect
50. C₂×C₁₃	D₆₅₁	direct (N × H)
51. C₃×C₇	C₂×C₁₃×D₃₁	semidirect
52. C₂×C₇	C₁₃×D₉₃	semidirect
54. C₁₃	C₂×D₆₅₁	direct (N × H)
56. C₇	C₂×C₁₃×D₉₃	semidirect
57. C₂×C₃	C₁₃×D₂₁₇	semidirect
60. C₃	C₂×C₁₃×D₂₁₇	semidirect
62. C₂	C₁₃×D₆₅₁	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×D₆₅₁	2
C₂×C₃×C₇×C₁₃×C₃₁	2
C₂×C₁₃×D₂₁₇	3
C₂×C₁₃×D₉₃	7
C₂×D₆₅₁	13
C₂×C₁₃×D₂₁	31

Subgroups — C2×C13×D651 #46799643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₆₅₁ #46799643