Subgroups — C₂×C₃×D₁₃×C₁₅₁ #37555596

Order 23556.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₁₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃×C₁₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₃×C₁₅₁	C₂×C₃	1	2	yes	direct product factor
7	C₁₃×C₁₅₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₁₅₁	—	13	1	no	maximal, Hall
9	C₂×C₃×C₁₅₁	—	13	2	no	—
10	C₂×C₃×C₁₅₁	D₁₃	1	1	yes	characteristic, direct product factor
11	C₂²×C₁₅₁	—	13	1	no	Hall
12	C₃×C₁₅₁	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₅₁	—	13	2	no	—
14	C₂×C₁₅₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃×D₁₃	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₅₁	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₁₃	C₂×C₁₅₁	1	1	yes	characteristic, complemented
18	C₃×D₁₃	C₂×C₁₅₁	1	2	yes	direct product factor
19	C₂×D₁₃	C₃×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₃	C₂²×C₁₅₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	C₂×C₃×C₁₅₁	1	1	yes	characteristic, complemented
22	D₁₃	C₂×C₃×C₁₅₁	1	2	yes	direct product factor
23	C₁₃	C₂²×C₃×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	13	1	no	Hall
25	C₂×C₃	—	13	2	no	—
26	C₂×C₃	D₁₃×C₁₅₁	1	1	yes	characteristic, direct product factor
27	C₂²	—	13	1	no	Sylow
28	C₃	C₂×D₁₃×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	13	2	no	—
30	C₂	C₃×D₁₃×C₁₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₅₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₁₅₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₅₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₅₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃×C₁₅₁	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₅₁	C₂	semidirect
3. C₂×D₁₃×C₁₅₁	C₃	direct (N × H)
4. C₃×C₁₃×C₁₅₁	C₂²	semidirect
5. C₂×C₁₃×C₁₅₁	C₂×C₃	semidirect
6. D₁₃×C₁₅₁	C₂×C₃	direct (N × H)
7. C₁₃×C₁₅₁	C₂²×C₃	semidirect
10. C₂×C₃×C₁₅₁	D₁₃	direct (N × H)
12. C₃×C₁₅₁	C₂×D₁₃	direct (N × H)
14. C₂×C₁₅₁	C₃×D₁₃	direct (N × H)
15. C₂×C₃×D₁₃	C₁₅₁	direct (N × H)
16. C₁₅₁	C₂×C₃×D₁₃	direct (N × H)
17. C₂×C₃×C₁₃	C₂×C₁₅₁	semidirect
18. C₃×D₁₃	C₂×C₁₅₁	direct (N × H)
19. C₂×D₁₃	C₃×C₁₅₁	direct (N × H)
20. C₃×C₁₃	C₂²×C₁₅₁	semidirect
21. C₂×C₁₃	C₂×C₃×C₁₅₁	semidirect
22. D₁₃	C₂×C₃×C₁₅₁	direct (N × H)
23. C₁₃	C₂²×C₃×C₁₅₁	semidirect
26. C₂×C₃	D₁₃×C₁₅₁	direct (N × H)
28. C₃	C₂×D₁₃×C₁₅₁	direct (N × H)
30. C₂	C₃×D₁₃×C₁₅₁	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×D₁₃×C₁₅₁	2
C₂×C₃×C₁₃×C₁₅₁	2
C₂×D₁₃×C₁₅₁	3
C₂²×C₃×C₁₅₁	13
C₂×C₃×D₁₃	151

Subgroups — C2×C3×D13×C151 #37555596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₃×C₁₅₁ #37555596