Finite Group Databasebeta

← C₃×C₅₃×C₂₉⋊C₇ #44567693

Subgroups — C₃×C₅₃×C₂₉⋊C₇ #44567693

Order 32277.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₉×C₅₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₅₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₅₃	—	29	1	no	maximal, Hall
5	C₃×C₂₉⋊C₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₅₃	—	29	1	no	Hall
7	C₂₉⋊C₇	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₉	C₇×C₅₃	1	1	yes	characteristic, complemented, Hall
10	C₅₃	C₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	C₃×C₇×C₅₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₇	—	29	1	no	Hall
13	C₇	—	29	1	no	Sylow
14	C₃	C₅₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅₃	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₃×C₇×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₅₃	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×C₂₉⋊C₇	C₃	direct (N × H)
2. C₃×C₂₉×C₅₃	C₇	semidirect
3. C₂₉×C₅₃	C₃×C₇	semidirect
5. C₃×C₂₉⋊C₇	C₅₃	direct (N × H)
7. C₂₉⋊C₇	C₃×C₅₃	direct (N × H)
8. C₃×C₅₃	C₂₉⋊C₇	direct (N × H)
9. C₃×C₂₉	C₇×C₅₃	semidirect
10. C₅₃	C₃×C₂₉⋊C₇	direct (N × H)
11. C₂₉	C₃×C₇×C₅₃	semidirect
14. C₃	C₅₃×C₂₉⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×C₂₉⋊C₇	3
C₃×C₂₉×C₅₃	7
C₃×C₇×C₅₃	29
C₃×C₂₉⋊C₇	53