Subgroups — C₅⋊(C₇⋊D₂₈₇) #34095607

Order 20090.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₂₈₇	—	5	1	no	maximal, Hall
3	D₁₄₃₅	—	7	8	no	maximal
4	C₇²×C₄₁	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₄₁	D₇	1	8	yes	complemented
6	D₂₈₇	—	35	8	no	—
7	C₅⋊(C₇⋊D₇)	—	41	1	no	maximal, Hall
8	D₂₀₅	—	49	1	no	Hall
9	C₇×C₄₁	D₃₅	1	8	yes	complemented
10	C₅×C₇²	D₄₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₄₁	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
12	C₇⋊D₇	—	205	1	no	Hall
13	D₄₁	—	245	1	no	Hall
14	D₃₅	—	287	8	no	—
15	C₇²	D₂₀₅	1	1	yes	characteristic, complemented, Sylow
16	C₄₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₇	D₂₈₇	1	8	yes	complemented
18	D₇	—	1435	8	no	—
19	D₅	—	2009	1	no	Hall
20	C₇	D₁₄₃₅	1	8	yes	complemented
21	C₅	C₇⋊D₂₈₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	10045	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₄₁	C₂
LCS	G ▷ C₅×C₇²×C₄₁
UCS	C₁

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.