Subgroups — C₂×C₃×C₁₃×D₂₁₇ #46799635

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₂₁₇
commutator, cosocle, hypocenter	C₇×C₃₁	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

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

Subgroups — C2×C3×C13×D217 #46799635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×D₂₁₇ #46799635