Subgroups — C₅⋊(C₇⋊D₂₅₉) #31827409

Order 18130.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₂₅₉	—	5	1	no	maximal, Hall
3	D₁₂₉₅	—	7	8	no	maximal
4	C₇²×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₃₇	D₇	1	8	yes	complemented
6	D₂₅₉	—	35	8	no	—
7	C₅⋊(C₇⋊D₇)	—	37	1	no	maximal, Hall
8	D₁₈₅	—	49	1	no	Hall
9	C₇×C₃₇	D₃₅	1	8	yes	complemented
10	C₅×C₇²	D₃₇	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₇	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
12	C₇⋊D₇	—	185	1	no	Hall
13	D₃₇	—	245	1	no	Hall
14	D₃₅	—	259	8	no	—
15	C₇²	D₁₈₅	1	1	yes	characteristic, complemented, Sylow
16	C₃₇	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₇	D₂₅₉	1	8	yes	complemented
18	D₇	—	1295	8	no	—
19	D₅	—	1813	1	no	Hall
20	C₇	D₁₂₉₅	1	8	yes	complemented
21	C₅	C₇⋊D₂₅₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	9065	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₃₇	C₂
LCS	G ▷ C₅×C₇²×C₃₇
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.