Subgroups — D₃×C₁₃×D₁₅₇ #37587641

Order 24492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₄₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₁₅₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₅₇	—	3	1	no	—
7	C₁₃×D₁₅₇	—	3	1	no	—
8	C₁₃×D₁₅₇	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₁₅₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₄₇₁	C₂×C₁₃	1	1	yes	characteristic, complemented
12	C₃×D₁₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
13	D₃×C₁₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₂×D₁₅₇	—	3	1	no	Hall
15	C₃×C₁₅₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₅₇	—	3	1	no	—
17	D₁₅₇	—	3	1	no	—
18	D₁₅₇	D₃×C₁₃	1	1	yes	characteristic, direct product factor
19	C₁₅₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃×C₁₃	—	157	1	no	maximal, Hall
21	C₂×C₃×C₁₃	—	157	1	no	—
22	D₃×C₁₃	—	157	1	no	—
23	D₃×C₁₃	D₁₅₇	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₃	—	471	1	no	Hall
25	C₃×C₁₃	C₂×D₁₅₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	C₂×C₁₃	—	157	1	no	—
28	C₂×C₁₃	—	471	1	no	—
29	C₁₃	D₃×D₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₃	—	157	1	no	Hall
31	C₂×C₃	—	157	1	no	—
32	D₃	—	157	1	no	—
33	D₃	C₁₃×D₁₅₇	1	1	yes	characteristic, direct product factor
34	C₂²	—	471	1	no	Sylow
35	C₃	C₂×C₁₃×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	157	1	no	—
38	C₂	—	471	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₁₅₇
commutator, cosocle, hypocenter	C₃×C₁₅₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₅₇	C₂²
LCS	G ▷ C₃×C₁₅₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₄₇₁	C₂	semidirect
2. D₃×C₁₃×C₁₅₇	C₂	semidirect
3. C₃×C₁₃×D₁₅₇	C₂	semidirect
5. C₃×C₁₃×C₁₅₇	C₂²	semidirect
8. C₁₃×D₁₅₇	D₃	direct (N × H)
9. C₁₃×C₁₅₇	C₂×D₃	semidirect
10. D₃×D₁₅₇	C₁₃	direct (N × H)
11. D₄₇₁	C₂×C₁₃	semidirect
12. C₃×D₁₅₇	C₂×C₁₃	semidirect
13. D₃×C₁₅₇	C₂×C₁₃	semidirect
15. C₃×C₁₅₇	C₂²×C₁₃	semidirect
18. D₁₅₇	D₃×C₁₃	direct (N × H)
19. C₁₅₇	C₂×D₃×C₁₃	semidirect
23. D₃×C₁₃	D₁₅₇	direct (N × H)
25. C₃×C₁₃	C₂×D₁₅₇	semidirect
29. C₁₃	D₃×D₁₅₇	direct (N × H)
33. D₃	C₁₃×D₁₅₇	direct (N × H)
35. C₃	C₂×C₁₃×D₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₄₇₁	2
D₃×C₁₃×C₁₅₇	2
C₃×C₁₃×D₁₅₇	2
C₂×C₁₃×D₁₅₇	3
D₃×D₁₅₇	13
C₂×D₃×C₁₃	157

Subgroups — D3×C13×D157 #37587641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₃×D₁₅₇ #37587641