Finite Group Databasebeta

← C₂×C₇₉×D₇₃ #37528035

Subgroups — C₂×C₇₉×D₇₃ #37528035

Order 23068.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₃×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×D₇₃	C₂	1	2	yes	maximal, direct product factor
3	C₇₃×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₇₉	—	73	1	no	maximal, Hall
5	C₂×D₇₃	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇₉	—	73	2	no	—
7	C₂×C₇₉	D₇₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇₃	C₂×C₇₉	1	1	yes	characteristic, complemented
9	D₇₃	C₂×C₇₉	1	2	yes	direct product factor
10	C₇₉	C₂×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₇₃	C₂²×C₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	73	1	no	Sylow
13	C₂	—	73	2	no	—
14	C₂	C₇₉×D₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₉	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂²×C₇₉
Frattini	C₁	G
Fitting, socle	C₂×C₇₃×C₇₉	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₇₃×C₇₉	C₂	semidirect
2. C₇₉×D₇₃	C₂	direct (N × H)
3. C₇₃×C₇₉	C₂²	semidirect
5. C₂×D₇₃	C₇₉	direct (N × H)
7. C₂×C₇₉	D₇₃	direct (N × H)
8. C₂×C₇₃	C₂×C₇₉	semidirect
9. D₇₃	C₂×C₇₉	direct (N × H)
10. C₇₉	C₂×D₇₃	direct (N × H)
11. C₇₃	C₂²×C₇₉	semidirect
14. C₂	C₇₉×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇₃×C₇₉	2
C₇₉×D₇₃	2
C₂²×C₇₉	73
C₂×D₇₃	79