Finite Group Databasebeta

← C₇×#17985163 #44538585

Subgroups — C₇×#17985163 #44538585

Order 31521.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#17985163	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₇₉⋊C₃	—	19	1	no	maximal, Hall
4	C₁₉×C₇₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₇₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
6	C₇×C₁₉⋊C₃	—	79	1	no	maximal, Hall
7	C₇₉⋊C₃	—	19	1	no	Hall
8	C₇×C₁₉	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Hall
9	C₇₉	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
10	C₁₉⋊C₃	—	79	1	no	Hall
11	C₃×C₇	—	1501	1	no	Hall
12	C₁₉	C₇×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₇	#17985163	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	1501	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#17985163
commutator, cosocle, hypocenter	C₁₉×C₇₉	C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₇₉	C₃
LCS	G ▷ C₁₉×C₇₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₇₉	C₃	semidirect
2. #17985163	C₇	direct (N × H)
4. C₁₉×C₇₉	C₃×C₇	semidirect
5. C₇×C₇₉	C₁₉⋊C₃	semidirect
8. C₇×C₁₉	C₇₉⋊C₃	semidirect
9. C₇₉	C₇×C₁₉⋊C₃	semidirect
12. C₁₉	C₇×C₇₉⋊C₃	semidirect
13. C₇	#17985163	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×C₇₉	3
#17985163	7
C₇×C₇₉⋊C₃	19
C₇×C₁₉⋊C₃	79