Subgroups — C₂×C₃×C₇×C₁₅₇⋊C₃ #34089990

Order 19782.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₅₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₅₇⋊C₃	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₁₅₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₁₅₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₅₇⋊C₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₇×C₁₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₅₇	C₃×C₇	1	1	yes	characteristic, complemented
11	C₂×C₁₅₇⋊C₃	C₃×C₇	1	3	yes	direct product factor
12	C₃×C₁₅₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
13	C₁₅₇⋊C₃	C₂×C₃×C₇	1	3	yes	direct product factor
14	C₂×C₁₅₇	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
15	C₁₅₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃²×C₇	—	157	1	no	maximal, Hall
17	C₃²×C₇	—	157	1	no	Hall
18	C₂×C₃×C₇	—	157	3	no	—
19	C₂×C₃×C₇	C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×C₇	—	157	3	no	—
21	C₃×C₇	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃²	—	157	1	no	Hall
23	C₂×C₇	C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²	—	157	1	no	Sylow
25	C₇	C₂×C₃×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃	—	157	3	no	—
27	C₂×C₃	C₇×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃	—	157	3	no	—
29	C₃	C₂×C₇×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₇×C₁₅₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	C₁₅₇⋊C₃
commutator, cosocle, hypocenter	C₁₅₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₅₇	C₃
LCS	G ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₅₇⋊C₃	C₂	direct (N × H)
2. C₂×C₇×C₁₅₇⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₅₇	C₃	semidirect
4. C₃×C₇×C₁₅₇	C₂×C₃	semidirect
5. C₇×C₁₅₇⋊C₃	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₅₇⋊C₃	C₇	direct (N × H)
7. C₂×C₇×C₁₅₇	C₃²	semidirect
8. C₃×C₁₅₇⋊C₃	C₂×C₇	direct (N × H)
9. C₇×C₁₅₇	C₂×C₃²	semidirect
10. C₂×C₃×C₁₅₇	C₃×C₇	semidirect
11. C₂×C₁₅₇⋊C₃	C₃×C₇	direct (N × H)
12. C₃×C₁₅₇	C₂×C₃×C₇	semidirect
13. C₁₅₇⋊C₃	C₂×C₃×C₇	direct (N × H)
14. C₂×C₁₅₇	C₃²×C₇	semidirect
15. C₁₅₇	C₂×C₃²×C₇	semidirect
19. C₂×C₃×C₇	C₁₅₇⋊C₃	direct (N × H)
21. C₃×C₇	C₂×C₁₅₇⋊C₃	direct (N × H)
23. C₂×C₇	C₃×C₁₅₇⋊C₃	direct (N × H)
25. C₇	C₂×C₃×C₁₅₇⋊C₃	direct (N × H)
27. C₂×C₃	C₇×C₁₅₇⋊C₃	direct (N × H)
29. C₃	C₂×C₇×C₁₅₇⋊C₃	direct (N × H)
30. C₂	C₃×C₇×C₁₅₇⋊C₃	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×C₁₅₇⋊C₃	2
C₂×C₇×C₁₅₇⋊C₃	3
C₂×C₃×C₇×C₁₅₇	3
C₂×C₃×C₁₅₇⋊C₃	7
C₂×C₃²×C₇	157

Subgroups — C2×C3×C7×C157⋊C3 #34089990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₅₇⋊C₃ #34089990