Finite Group Databasebeta

← C₇₉×#87705 #44538593

Subgroups — C₇₉×#87705 #44538593

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	C₁₉⋊C₃×C₇₉	—	7	1	no	maximal, Hall
3	ΓL(1,𝔽₈)×C₇₉	—	19	1	no	maximal, Hall
4	C₁₉×C₇₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
5	C₇×C₇₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
6	#87705	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇₉	—	133	1	no	Hall
8	C₇×C₁₉	C₃×C₇₉	1	1	yes	characteristic, complemented, Hall
9	C₇₉	#87705	1	1	yes	characteristic, direct product factor, Sylow
10	C₁₉⋊C₃	—	7	1	no	Hall
11	ΓL(1,𝔽₈)	—	19	1	no	Hall
12	C₁₉	ΓL(1,𝔽₈)×C₇₉	1	1	yes	characteristic, complemented, Sylow
13	C₇	C₁₉⋊C₃×C₇₉	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₉	#87705
commutator, cosocle, hypocenter	C₇×C₁₉	C₃×C₇₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₇₉	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₇₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₇₉	C₃	semidirect
4. C₁₉×C₇₉	ΓL(1,𝔽₈)	semidirect
5. C₇×C₇₉	C₁₉⋊C₃	semidirect
6. #87705	C₇₉	direct (N × H)
8. C₇×C₁₉	C₃×C₇₉	semidirect
9. C₇₉	#87705	direct (N × H)
12. C₁₉	ΓL(1,𝔽₈)×C₇₉	semidirect
13. C₇	C₁₉⋊C₃×C₇₉	semidirect

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
C₁₉⋊C₃×C₇₉	7
ΓL(1,𝔽₈)×C₇₉	19
#87705	79