Subgroups — C₃²×C₇×C₁₃×C₂₉ #37557650

Order 23751.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₂₉	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₃×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₇×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃×C₂₉	C₃×C₇	1	4	yes	direct product factor
6	C₃²×C₇×C₁₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×C₂₉	C₃×C₁₃	1	4	yes	direct product factor
8	C₁₃×C₂₉	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₁₃	C₃×C₂₉	1	4	yes	direct product factor
10	C₃²×C₂₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₂₉	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₃	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₃	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₉	C₃×C₇×C₁₃	1	4	yes	direct product factor
15	C₃²×C₇	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃	C₃×C₇×C₂₉	1	4	yes	direct product factor
17	C₂₉	C₃²×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₇	C₃×C₁₃×C₂₉	1	4	yes	direct product factor
19	C₁₃	C₃²×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₃²	C₇×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₃²×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₇×C₁₃×C₂₉	1	4	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₂₉	C₃	direct (N × H)
2. C₃²×C₁₃×C₂₉	C₇	direct (N × H)
3. C₇×C₁₃×C₂₉	C₃²	direct (N × H)
4. C₃²×C₇×C₂₉	C₁₃	direct (N × H)
5. C₃×C₁₃×C₂₉	C₃×C₇	direct (N × H)
6. C₃²×C₇×C₁₃	C₂₉	direct (N × H)
7. C₃×C₇×C₂₉	C₃×C₁₃	direct (N × H)
8. C₁₃×C₂₉	C₃²×C₇	direct (N × H)
9. C₃×C₇×C₁₃	C₃×C₂₉	direct (N × H)
10. C₃²×C₂₉	C₇×C₁₃	direct (N × H)
11. C₇×C₂₉	C₃²×C₁₃	direct (N × H)
12. C₃²×C₁₃	C₇×C₂₉	direct (N × H)
13. C₇×C₁₃	C₃²×C₂₉	direct (N × H)
14. C₃×C₂₉	C₃×C₇×C₁₃	direct (N × H)
15. C₃²×C₇	C₁₃×C₂₉	direct (N × H)
16. C₃×C₁₃	C₃×C₇×C₂₉	direct (N × H)
17. C₂₉	C₃²×C₇×C₁₃	direct (N × H)
18. C₃×C₇	C₃×C₁₃×C₂₉	direct (N × H)
19. C₁₃	C₃²×C₇×C₂₉	direct (N × H)
20. C₃²	C₇×C₁₃×C₂₉	direct (N × H)
21. C₇	C₃²×C₁₃×C₂₉	direct (N × H)
22. C₃	C₃×C₇×C₁₃×C₂₉	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×C₇×C₁₃×C₂₉	3
C₃²×C₁₃×C₂₉	7
C₃²×C₇×C₂₉	13
C₃²×C₇×C₁₃	29

Subgroups — C32×C7×C13×C29 #37557650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₁₃×C₂₉ #37557650