Subgroups — C₁₃×D₇×C₂₉⋊C₇ #49149232

Order 36946.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₂₉⋊C₇	—	7	1	no	maximal
4	D₇×C₂₉⋊C₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
6	C₁₃×C₂₉⋊C₇	—	2	3	no	—
7	C₁₃×C₂₉⋊C₇	D₇	1	1	yes	characteristic, direct product factor
8	C₇×C₂₉⋊C₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₃×D₇	—	29	1	no	maximal, Hall
10	C₂×C₁₃×C₂₉	—	7	1	no	Hall
11	C₇²×C₁₃	—	29	1	no	Hall
12	D₇×C₂₉	C₇×C₁₃	1	1	yes	characteristic, complemented
13	C₂×C₂₉⋊C₇	—	7	1	no	—
14	C₁₃×C₂₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
15	C₇×C₂₉	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
16	C₂₉⋊C₇	—	2	3	no	—
17	C₂₉⋊C₇	C₁₃×D₇	1	1	yes	characteristic, direct product factor
18	C₂×C₇×C₁₃	—	203	1	no	—
19	C₁₃×D₇	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
20	C₇×D₇	—	29	1	no	Hall
21	C₇×C₁₃	—	29	1	no	—
22	C₇×C₁₃	—	58	3	no	—
23	C₇×C₁₃	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented
24	C₂×C₂₉	—	7	1	no	Hall
25	C₇²	—	29	1	no	Sylow
26	C₂₉	C₇×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	7	1	no	Hall
28	C₂×C₇	—	203	1	no	—
29	D₇	C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
30	C₁₃	D₇×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₇	—	29	1	no	—
32	C₇	—	58	3	no	—
33	C₇	C₂×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₇×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₇×C₂₉	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₂×C₇
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₂₉⋊C₇	C₂	semidirect
2. C₁₃×D₇×C₂₉	C₇	semidirect
4. D₇×C₂₉⋊C₇	C₁₃	direct (N × H)
5. C₇×C₁₃×C₂₉	C₂×C₇	semidirect
7. C₁₃×C₂₉⋊C₇	D₇	direct (N × H)
8. C₇×C₂₉⋊C₇	C₂×C₁₃	semidirect
12. D₇×C₂₉	C₇×C₁₃	semidirect
14. C₁₃×C₂₉	C₇×D₇	semidirect
15. C₇×C₂₉	C₂×C₇×C₁₃	semidirect
17. C₂₉⋊C₇	C₁₃×D₇	direct (N × H)
19. C₁₃×D₇	C₂₉⋊C₇	direct (N × H)
23. C₇×C₁₃	C₂×C₂₉⋊C₇	semidirect
26. C₂₉	C₇×C₁₃×D₇	semidirect
29. D₇	C₁₃×C₂₉⋊C₇	direct (N × H)
30. C₁₃	D₇×C₂₉⋊C₇	direct (N × H)
33. C₇	C₂×C₁₃×C₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₂₉⋊C₇	2
C₁₃×D₇×C₂₉	7
C₂×C₁₃×C₂₉⋊C₇	7
D₇×C₂₉⋊C₇	13
C₇×C₁₃×D₇	29

Subgroups — C13×D7×C29⋊C7 #49149232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₇×C₂₉⋊C₇ #49149232