Subgroups — C₂×C₁₃×D₇×C₂₉ #24902243

Order 10556.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₇×C₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₃×C₂₉	—	7	1	no	maximal, Hall
5	C₂×D₇×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₃×C₂₉	—	7	2	no	—
7	C₂×C₁₃×C₂₉	D₇	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₂₉	C₂×C₁₃	1	1	yes	characteristic, complemented
9	D₇×C₂₉	C₂×C₁₃	1	2	yes	direct product factor
10	C₁₃×C₂₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₂₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₃	C₂×C₂₉	1	1	yes	characteristic, complemented
14	C₁₃×D₇	C₂×C₂₉	1	2	yes	direct product factor
15	C₂²×C₂₉	—	7	1	no	Hall
16	C₇×C₁₃	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₂₉	—	7	2	no	—
18	C₂×C₂₉	C₁₃×D₇	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₃	—	7	1	no	Hall
20	C₂₉	C₂×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×D₇	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₃	—	7	2	no	—
23	C₂×C₁₃	D₇×C₂₉	1	1	yes	characteristic, direct product factor
24	C₂×C₇	C₂×C₁₃×C₂₉	1	1	yes	characteristic, complemented
25	D₇	C₂×C₁₃×C₂₉	1	2	yes	direct product factor
26	C₁₃	C₂×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂²×C₁₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	7	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	C₁₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₂₉	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₁₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₂₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₇×C₂₉	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₂₉	C₂	semidirect
3. C₇×C₁₃×C₂₉	C₂²	semidirect
5. C₂×D₇×C₂₉	C₁₃	direct (N × H)
7. C₂×C₁₃×C₂₉	D₇	direct (N × H)
8. C₂×C₇×C₂₉	C₂×C₁₃	semidirect
9. D₇×C₂₉	C₂×C₁₃	direct (N × H)
10. C₁₃×C₂₉	C₂×D₇	direct (N × H)
11. C₂×C₁₃×D₇	C₂₉	direct (N × H)
12. C₇×C₂₉	C₂²×C₁₃	semidirect
13. C₂×C₇×C₁₃	C₂×C₂₉	semidirect
14. C₁₃×D₇	C₂×C₂₉	direct (N × H)
16. C₇×C₁₃	C₂²×C₂₉	semidirect
18. C₂×C₂₉	C₁₃×D₇	direct (N × H)
20. C₂₉	C₂×C₁₃×D₇	direct (N × H)
21. C₂×D₇	C₁₃×C₂₉	direct (N × H)
23. C₂×C₁₃	D₇×C₂₉	direct (N × H)
24. C₂×C₇	C₂×C₁₃×C₂₉	semidirect
25. D₇	C₂×C₁₃×C₂₉	direct (N × H)
26. C₁₃	C₂×D₇×C₂₉	direct (N × H)
27. C₇	C₂²×C₁₃×C₂₉	semidirect
30. C₂	C₁₃×D₇×C₂₉	direct (N × H)

Subgroups — C2×C13×D7×C29 #24902243

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×D₇×C₂₉ #24902243