Subgroups — C₂×C₃⋊(C₁₃⋊(D₂₉⋊C₇)) #44539804

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₁₃⋊(D₂₉⋊C₇))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃⋊(D₂₉⋊C₇)	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊(D₂₉⋊C₇)	—	3	2	no	—
6	C₂×C₁₃×C₂₉⋊C₇	D₃	1	1	yes	characteristic, complemented
7	C₂×D₁₁₃₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
8	C₁₃×C₂₉⋊C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃⋊(D₂₉⋊C₇)	—	13	1	no	maximal, Hall
10	D₁₁₃₁	C₂×C₇	1	2	yes	complemented
11	C₂×C₃×C₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
12	C₂×D₃₇₇	—	3	1	no	Hall
13	C₂×C₃×C₂₉⋊C₇	D₁₃	1	1	yes	characteristic, complemented
14	C₃⋊(D₂₉⋊C₇)	—	13	2	no	—
15	C₃×C₁₃×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×D₃₉	—	29	1	no	maximal, Hall
17	C₂×D₂₉⋊C₇	—	39	1	no	Hall
18	C₂×C₁₃×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
19	D₃₇₇	—	3	2	no	—
20	C₃×C₂₉⋊C₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×C₁₃	—	29	1	no	—
22	C₇×D₃₉	—	29	2	no	—
23	C₂×C₂₉⋊C₇	D₃₉	1	1	yes	characteristic, complemented
24	D₂₉⋊C₇	—	39	2	no	—
25	C₁₃×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×D₁₃	—	87	1	no	Hall
27	C₂×D₈₇	—	13	1	no	Hall
28	C₃×C₇×C₁₃	—	29	1	no	Hall
29	C₂₉⋊C₇	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	—	29	1	no	—
31	C₇×D₁₃	—	87	2	no	—
32	C₂×C₃×C₂₉	C₇×D₁₃	1	1	yes	characteristic, complemented
33	D₈₇	—	13	2	no	—
34	C₂×D₃₉	—	29	1	no	Hall
35	C₂×D₂₉	—	39	1	no	Hall
36	C₇×C₁₃	—	29	1	no	Hall
37	C₃×C₂₉	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃×C₇	—	377	1	no	Hall
39	C₂×C₃×C₁₃	D₂₉⋊C₇	1	1	yes	characteristic, complemented
40	D₃₉	—	29	2	no	—
41	C₂×C₂₉	C₇×D₃₉	1	1	yes	characteristic, complemented
42	D₂₉	—	39	2	no	—
43	C₂×D₁₃	—	87	1	no	Hall
44	C₂×C₃×C₇	—	29	1	no	—
45	D₃×C₇	—	377	2	no	—
46	C₃×C₁₃	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
47	C₂₉	C₂×C₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₇	—	1131	1	no	Hall
49	C₂×C₁₃	C₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, complemented
50	D₁₃	—	87	2	no	—
51	C₃×C₇	—	29	1	no	Hall
52	C₂×C₇	—	29	1	no	—
53	C₂×C₇	—	1131	2	no	—
54	C₁₃	C₂×C₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₃	—	377	1	no	Hall
56	C₇	—	29	1	no	Sylow
57	C₂×C₃	C₁₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, complemented
58	D₃	—	377	2	no	—
59	C₂²	—	1131	1	no	Sylow
60	C₃	C₂×C₁₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	1131	2	no	—
62	C₂	C₃⋊(C₁₃⋊(D₂₉⋊C₇))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₁₃⋊(D₂₉⋊C₇))
commutator, cosocle, hypocenter	C₃×C₁₃×C₂₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₂₉	C₂×C₇
LCS	G ▷ C₃×C₁₃×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₁₃⋊(D₂₉⋊C₇))	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₂₉⋊C₇	C₂	semidirect
4. C₃×C₁₃×C₂₉⋊C₇	C₂²	semidirect
6. C₂×C₁₃×C₂₉⋊C₇	D₃	semidirect
7. C₂×D₁₁₃₁	C₇	semidirect
8. C₁₃×C₂₉⋊C₇	C₂×D₃	semidirect
10. D₁₁₃₁	C₂×C₇	semidirect
11. C₂×C₃×C₁₃×C₂₉	C₂×C₇	semidirect
13. C₂×C₃×C₂₉⋊C₇	D₁₃	semidirect
15. C₃×C₁₃×C₂₉	C₂²×C₇	semidirect
18. C₂×C₁₃×C₂₉	D₃×C₇	semidirect
20. C₃×C₂₉⋊C₇	C₂×D₁₃	semidirect
23. C₂×C₂₉⋊C₇	D₃₉	semidirect
25. C₁₃×C₂₉	C₂×D₃×C₇	semidirect
29. C₂₉⋊C₇	C₂×D₃₉	semidirect
32. C₂×C₃×C₂₉	C₇×D₁₃	semidirect
37. C₃×C₂₉	C₂×C₇×D₁₃	semidirect
39. C₂×C₃×C₁₃	D₂₉⋊C₇	semidirect
41. C₂×C₂₉	C₇×D₃₉	semidirect
46. C₃×C₁₃	C₂×D₂₉⋊C₇	semidirect
47. C₂₉	C₂×C₇×D₃₉	semidirect
49. C₂×C₁₃	C₃⋊(D₂₉⋊C₇)	semidirect
54. C₁₃	C₂×C₃⋊(D₂₉⋊C₇)	semidirect
57. C₂×C₃	C₁₃⋊(D₂₉⋊C₇)	semidirect
60. C₃	C₂×C₁₃⋊(D₂₉⋊C₇)	semidirect
62. C₂	C₃⋊(C₁₃⋊(D₂₉⋊C₇))	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⋊(D₂₉⋊C₇))	2
C₂×C₃×C₁₃×C₂₉⋊C₇	2
C₂×C₁₃⋊(D₂₉⋊C₇)	3
C₂×D₁₁₃₁	7
C₂×C₃⋊(D₂₉⋊C₇)	13
C₂×C₇×D₃₉	29

Subgroups — C2×C3⋊(C13⋊(D29⋊C7)) #44539804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₁₃⋊(D₂₉⋊C₇)) #44539804