Subgroups — C₅²×D₂₁₇ #24925767

Order 10850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₂₁₇	C₅	1	6	yes	maximal, direct product factor
3	C₅²×D₃₁	—	7	1	no	maximal, Hall
4	C₅×C₇×C₃₁	C₂×C₅	1	6	yes	complemented
5	C₅²×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	D₂₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×D₇	—	31	1	no	maximal, Hall
8	C₅×D₃₁	—	7	6	no	—
9	C₇×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₅²×C₇	D₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	C₅×D₇	1	6	yes	complemented
12	C₅×D₇	—	31	6	no	—
13	D₃₁	—	7	1	no	Hall
14	C₂×C₅²	—	217	1	no	Hall
15	C₅×C₇	C₅×D₃₁	1	6	yes	complemented
16	C₃₁	C₅²×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₅²	D₂₁₇	1	1	yes	characteristic, direct product factor, Sylow
18	D₇	—	31	1	no	Hall
19	C₂×C₅	—	217	6	no	—
20	C₇	C₅²×D₃₁	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₅×D₂₁₇	1	6	yes	direct product factor
22	C₂	—	217	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₂₁₇
commutator, cosocle, hypocenter	C₇×C₃₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₁	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₅²

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.