Finite Group Databasebeta

← C₅²×C₇×C₁₁₃ #34089889

Subgroups — C₅²×C₇×C₁₁₃ #34089889

Order 19775.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁₃	C₅	1	6	yes	maximal, direct product factor
2	C₅²×C₁₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
4	C₅×C₁₁₃	C₅×C₇	1	6	yes	direct product factor
5	C₅²×C₇	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁₃	C₅²×C₇	1	1	yes	characteristic, direct product factor, Sylow
7	C₅×C₇	C₅×C₁₁₃	1	6	yes	direct product factor
8	C₅²	C₇×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₇	C₅²×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₅	C₅×C₇×C₁₁₃	1	6	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. C₅×C₇×C₁₁₃	C₅	direct (N × H)
2. C₅²×C₁₁₃	C₇	direct (N × H)
3. C₇×C₁₁₃	C₅²	direct (N × H)
4. C₅×C₁₁₃	C₅×C₇	direct (N × H)
5. C₅²×C₇	C₁₁₃	direct (N × H)
6. C₁₁₃	C₅²×C₇	direct (N × H)
7. C₅×C₇	C₅×C₁₁₃	direct (N × H)
8. C₅²	C₇×C₁₁₃	direct (N × H)
9. C₇	C₅²×C₁₁₃	direct (N × H)
10. C₅	C₅×C₇×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₁₃	5
C₅²×C₁₁₃	7
C₅²×C₇	113