Finite Group Databasebeta

← C₂³×C₁₉×C₁₅₇ #72201159

Subgroups — C₂³×C₁₉×C₁₅₇ #72201159

Order 23864.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₁₅₇	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₁₉×C₁₅₇	C₂²	1	7	yes	direct product factor
3	C₁₉×C₁₅₇	C₂³	1	1	yes	characteristic, direct product factor, Hall
4	C₂³×C₁₅₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₁₅₇	C₂×C₁₉	1	7	yes	direct product factor
6	C₂×C₁₅₇	C₂²×C₁₉	1	7	yes	direct product factor
7	C₁₅₇	C₂³×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂³×C₁₉	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₁₉	C₂×C₁₅₇	1	7	yes	direct product factor
10	C₂×C₁₉	C₂²×C₁₅₇	1	7	yes	direct product factor
11	C₁₉	C₂³×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³	C₁₉×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²	C₂×C₁₉×C₁₅₇	1	7	yes	direct product factor
14	C₂	C₂²×C₁₉×C₁₅₇	1	7	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. C₂²×C₁₉×C₁₅₇	C₂	direct (N × H)
2. C₂×C₁₉×C₁₅₇	C₂²	direct (N × H)
3. C₁₉×C₁₅₇	C₂³	direct (N × H)
4. C₂³×C₁₅₇	C₁₉	direct (N × H)
5. C₂²×C₁₅₇	C₂×C₁₉	direct (N × H)
6. C₂×C₁₅₇	C₂²×C₁₉	direct (N × H)
7. C₁₅₇	C₂³×C₁₉	direct (N × H)
8. C₂³×C₁₉	C₁₅₇	direct (N × H)
9. C₂²×C₁₉	C₂×C₁₅₇	direct (N × H)
10. C₂×C₁₉	C₂²×C₁₅₇	direct (N × H)
11. C₁₉	C₂³×C₁₅₇	direct (N × H)
12. C₂³	C₁₉×C₁₅₇	direct (N × H)
13. C₂²	C₂×C₁₉×C₁₅₇	direct (N × H)
14. C₂	C₂²×C₁₉×C₁₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₁₅₇	2
C₂³×C₁₅₇	19
C₂³×C₁₉	157