Finite Group Databasebeta

← C₅×C₇×C₁₇×C₅₃ #44538677

Subgroups — C₅×C₇×C₁₇×C₅₃ #44538677

Order 31535.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₁₇×C₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₇×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₅₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₇×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₅₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₅₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₇	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₇	C₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
10	C₅₃	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₅×C₇	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇	C₅×C₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₅×C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₅	C₇×C₁₇×C₅₃	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. C₇×C₁₇×C₅₃	C₅	direct (N × H)
2. C₅×C₁₇×C₅₃	C₇	direct (N × H)
3. C₅×C₇×C₅₃	C₁₇	direct (N × H)
4. C₁₇×C₅₃	C₅×C₇	direct (N × H)
5. C₅×C₇×C₁₇	C₅₃	direct (N × H)
6. C₇×C₅₃	C₅×C₁₇	direct (N × H)
7. C₅×C₅₃	C₇×C₁₇	direct (N × H)
8. C₇×C₁₇	C₅×C₅₃	direct (N × H)
9. C₅×C₁₇	C₇×C₅₃	direct (N × H)
10. C₅₃	C₅×C₇×C₁₇	direct (N × H)
11. C₅×C₇	C₁₇×C₅₃	direct (N × H)
12. C₁₇	C₅×C₇×C₅₃	direct (N × H)
13. C₇	C₅×C₁₇×C₅₃	direct (N × H)
14. C₅	C₇×C₁₇×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₅₃	5
C₅×C₁₇×C₅₃	7
C₅×C₇×C₅₃	17
C₅×C₇×C₁₇	53