Subgroups — D₅₄₂₅ #24925746

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₈₅	—	5	1	no	maximal
3	D₇₇₅	—	7	1	no	maximal, Hall
4	C₅×C₇×C₃₁	D₅	1	1	yes	characteristic
5	C₂₅×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	D₂₁₇	—	25	1	no	Hall
7	D₁₇₅	—	31	1	no	maximal, Hall
8	D₁₅₅	—	35	1	no	—
9	C₇×C₃₁	D₂₅	1	1	yes	characteristic, complemented, Hall
10	C₇×C₂₅	D₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	D₃₅	1	1	yes	characteristic
12	D₃₅	—	155	1	no	—
13	D₃₁	—	175	1	no	Hall
14	D₂₅	—	217	1	no	Hall
15	C₅×C₇	D₁₅₅	1	1	yes	characteristic
16	C₃₁	D₁₇₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	D₂₁₇	1	1	yes	characteristic, complemented, Sylow
18	D₇	—	775	1	no	Hall
19	D₅	—	1085	1	no	—
20	C₇	D₇₇₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₁₀₈₅	1	1	yes	characteristic
22	C₂	—	5425	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₂₅×C₃₁	C₂
Frattini	C₅	D₁₀₈₅
socle	C₅×C₇×C₃₁	D₅
LCS	G ▷ C₇×C₂₅×C₃₁
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.