Finite Group Databasebeta

← C₇×C₁₉⋊C₃×C₆₁ #37566670

Subgroups — C₇×C₁₉⋊C₃×C₆₁ #37566670

Order 24339.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×C₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₆₁	—	19	1	no	maximal, Hall
4	C₁₉×C₆₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₆₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₇×C₁₉⋊C₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₆₁	—	19	1	no	Hall
8	C₇×C₁₉	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
9	C₆₁	C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₁₉⋊C₃	C₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇	—	19	1	no	Hall
12	C₁₉	C₃×C₇×C₆₁	1	1	yes	characteristic, complemented, Sylow
13	C₇	C₁₉⋊C₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₆₁	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₇×C₆₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₆₁	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₆₁	C₃	semidirect
2. C₁₉⋊C₃×C₆₁	C₇	direct (N × H)
4. C₁₉×C₆₁	C₃×C₇	semidirect
5. C₇×C₆₁	C₁₉⋊C₃	direct (N × H)
6. C₇×C₁₉⋊C₃	C₆₁	direct (N × H)
8. C₇×C₁₉	C₃×C₆₁	semidirect
9. C₆₁	C₇×C₁₉⋊C₃	direct (N × H)
10. C₁₉⋊C₃	C₇×C₆₁	direct (N × H)
12. C₁₉	C₃×C₇×C₆₁	semidirect
13. C₇	C₁₉⋊C₃×C₆₁	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×C₁₉×C₆₁	3
C₁₉⋊C₃×C₆₁	7
C₃×C₇×C₆₁	19
C₇×C₁₉⋊C₃	61