Subgroups — C₁₉×C₇⋊D₁₁₉ #44539617

Order 31654.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₁₁₉	—	7	8	no	maximal
3	C₇×C₁₇×C₁₉	D₇	1	8	yes	complemented
4	C₁₉×C₇⋊D₇	—	17	1	no	maximal, Hall
5	C₇⋊D₁₁₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇²×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
7	C₇²×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₁₉×D₁₇	—	49	1	no	Hall
9	C₁₇×C₁₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
10	D₇×C₁₉	—	119	8	no	—
11	D₁₁₉	—	7	8	no	—
12	C₇×C₁₉	D₁₁₉	1	8	yes	complemented
13	C₇×C₁₇	D₇×C₁₉	1	8	yes	complemented
14	C₇⋊D₇	—	17	1	no	Hall
15	C₇²	C₁₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	833	1	no	Hall
17	D₁₇	—	49	1	no	Hall
18	C₁₉	C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₁₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
20	D₇	—	119	8	no	—
21	C₇	C₁₉×D₁₁₉	1	8	yes	complemented
22	C₂	—	833	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₇⋊D₁₁₉
commutator, cosocle, hypocenter	C₇²×C₁₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₇×C₁₉	C₂
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₁₉

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

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