Finite Group Databasebeta

← C₃×D₁₃×C₃₉₇ #44526337

Subgroups — C₃×D₁₃×C₃₉₇ #44526337

Order 30966.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₃₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₃₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₃₉₇	—	13	1	no	maximal, Hall
5	C₃×C₃₉₇	D₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₉₇	—	13	1	no	Hall
7	C₃₉₇	C₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₁₃	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₃	C₂×C₃₉₇	1	1	yes	characteristic, complemented, Hall
10	D₁₃	C₃×C₃₉₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃	C₂×C₃×C₃₉₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	13	1	no	Hall
13	C₃	D₁₃×C₃₉₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₉₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₃₉₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₉₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₃₉₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₃₉₇	C₂	semidirect
2. D₁₃×C₃₉₇	C₃	direct (N × H)
3. C₁₃×C₃₉₇	C₂×C₃	semidirect
5. C₃×C₃₉₇	D₁₃	direct (N × H)
7. C₃₉₇	C₃×D₁₃	direct (N × H)
8. C₃×D₁₃	C₃₉₇	direct (N × H)
9. C₃×C₁₃	C₂×C₃₉₇	semidirect
10. D₁₃	C₃×C₃₉₇	direct (N × H)
11. C₁₃	C₂×C₃×C₃₉₇	semidirect
13. C₃	D₁₃×C₃₉₇	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×C₁₃×C₃₉₇	2
D₁₃×C₃₉₇	3
C₂×C₃×C₃₉₇	13
C₃×D₁₃	397