Finite Group Databasebeta

← C₃×C₅₃×D₇₉ #38737484

Subgroups — C₃×C₅₃×D₇₉ #38737484

Order 25122.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₃×D₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅₃	—	79	1	no	maximal, Hall
6	C₃×C₇₉	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅₃	D₇₉	1	1	yes	characteristic, direct product factor, Hall
8	D₇₉	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅₃	—	79	1	no	Hall
10	C₇₉	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
11	C₅₃	C₃×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	79	1	no	Hall
13	C₃	C₅₃×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	79	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅₃	D₇₉
commutator, cosocle, hypocenter	C₇₉	C₂×C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅₃×C₇₉	C₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₃×C₇₉	C₂	semidirect
2. C₅₃×D₇₉	C₃	direct (N × H)
3. C₅₃×C₇₉	C₂×C₃	semidirect
4. C₃×D₇₉	C₅₃	direct (N × H)
6. C₃×C₇₉	C₂×C₅₃	semidirect
7. C₃×C₅₃	D₇₉	direct (N × H)
8. D₇₉	C₃×C₅₃	direct (N × H)
10. C₇₉	C₂×C₃×C₅₃	semidirect
11. C₅₃	C₃×D₇₉	direct (N × H)
13. C₃	C₅₃×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅₃×C₇₉	2
C₅₃×D₇₉	3
C₃×D₇₉	53
C₂×C₃×C₅₃	79