Finite Group Databasebeta

← C₅×C₇³×C₁₃ #72199739

Subgroups — C₅×C₇³×C₁₃ #72199739

Order 22295.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇³×C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₇²×C₁₃	C₇	1	57	yes	maximal, direct product factor
3	C₅×C₇³	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇²×C₁₃	C₅×C₇	1	57	yes	direct product factor
5	C₅×C₇×C₁₃	C₇²	1	57	yes	direct product factor
6	C₇³	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₅×C₇²	C₇×C₁₃	1	57	yes	direct product factor
8	C₇×C₁₃	C₅×C₇²	1	57	yes	direct product factor
9	C₅×C₁₃	C₇³	1	1	yes	characteristic, direct product factor, Hall
10	C₇²	C₅×C₇×C₁₃	1	57	yes	direct product factor
11	C₅×C₇	C₇²×C₁₃	1	57	yes	direct product factor
12	C₁₃	C₅×C₇³	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₅×C₇²×C₁₃	1	57	yes	direct product factor
14	C₅	C₇³×C₁₃	1	1	yes	characteristic, direct product factor, Sylow

	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. C₇³×C₁₃	C₅	direct (N × H)
2. C₅×C₇²×C₁₃	C₇	direct (N × H)
3. C₅×C₇³	C₁₃	direct (N × H)
4. C₇²×C₁₃	C₅×C₇	direct (N × H)
5. C₅×C₇×C₁₃	C₇²	direct (N × H)
6. C₇³	C₅×C₁₃	direct (N × H)
7. C₅×C₇²	C₇×C₁₃	direct (N × H)
8. C₇×C₁₃	C₅×C₇²	direct (N × H)
9. C₅×C₁₃	C₇³	direct (N × H)
10. C₇²	C₅×C₇×C₁₃	direct (N × H)
11. C₅×C₇	C₇²×C₁₃	direct (N × H)
12. C₁₃	C₅×C₇³	direct (N × H)
13. C₇	C₅×C₇²×C₁₃	direct (N × H)
14. C₅	C₇³×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇³×C₁₃	5
C₅×C₇²×C₁₃	7
C₅×C₇³	13