Finite Group Databasebeta

← C₃×C₁₉×D₂₇₇ #44539055

Subgroups — C₃×C₁₉×D₂₇₇ #44539055

Order 31578.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₇₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₂₇₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₇₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₇₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	D₂₇₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂₇₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₁₉	—	277	1	no	maximal, Hall
9	C₃×C₁₉	D₂₇₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₉	—	277	1	no	Hall
11	C₁₉	C₃×D₂₇₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	277	1	no	Hall
13	C₃	C₁₉×D₂₇₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	277	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₂₇₇
commutator, cosocle, hypocenter	C₂₇₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₇₇	C₂
LCS	G ▷ C₂₇₇
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₂₇₇	C₂	semidirect
2. C₁₉×D₂₇₇	C₃	direct (N × H)
3. C₁₉×C₂₇₇	C₂×C₃	semidirect
4. C₃×D₂₇₇	C₁₉	direct (N × H)
5. C₃×C₂₇₇	C₂×C₁₉	semidirect
6. D₂₇₇	C₃×C₁₉	direct (N × H)
7. C₂₇₇	C₂×C₃×C₁₉	semidirect
9. C₃×C₁₉	D₂₇₇	direct (N × H)
11. C₁₉	C₃×D₂₇₇	direct (N × H)
13. C₃	C₁₉×D₂₇₇	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×C₁₉×C₂₇₇	2
C₁₉×D₂₇₇	3
C₃×D₂₇₇	19
C₂×C₃×C₁₉	277