Subgroups — D₁₁₉₂₅ #37558679

Order 23850.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₇₅	—	3	1	no	maximal
3	D₂₃₈₅	—	5	1	no	maximal
4	C₃×C₂₅×C₅₃	D₃	1	1	yes	characteristic
5	D₁₃₂₅	—	9	1	no	Hall
6	C₅×C₉×C₅₃	D₅	1	1	yes	characteristic
7	D₇₉₅	—	15	1	no	—
8	C₂₅×C₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	D₄₇₇	—	25	1	no	Hall
10	C₃×C₅×C₅₃	D₁₅	1	1	yes	characteristic
11	D₂₆₅	—	45	1	no	—
12	C₉×C₅₃	D₂₅	1	1	yes	characteristic, complemented, Hall
13	D₂₂₅	—	53	1	no	maximal, Hall
14	D₁₅₉	—	75	1	no	—
15	C₅×C₅₃	D₄₅	1	1	yes	characteristic
16	C₉×C₂₅	D₅₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅₃	D₇₅	1	1	yes	characteristic
18	D₇₅	—	159	1	no	—
19	D₅₃	—	225	1	no	Hall
20	D₄₅	—	265	1	no	—
21	C₃×C₂₅	D₁₅₉	1	1	yes	characteristic
22	C₅₃	D₂₂₅	1	1	yes	characteristic, complemented, Sylow
23	D₂₅	—	477	1	no	Hall
24	C₅×C₉	D₂₆₅	1	1	yes	characteristic
25	D₁₅	—	795	1	no	—
26	C₂₅	D₄₇₇	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	1325	1	no	Hall
28	C₃×C₅	D₇₉₅	1	1	yes	characteristic
29	D₅	—	2385	1	no	—
30	C₉	D₁₃₂₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3975	1	no	—
32	C₅	D₂₃₈₅	1	1	yes	characteristic
33	C₃	D₃₉₇₅	1	1	yes	characteristic
34	C₂	—	11925	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅×C₅₃	C₂
Frattini	C₃×C₅	D₇₉₅
socle	C₃×C₅×C₅₃	D₁₅
LCS	G ▷ C₉×C₂₅×C₅₃
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.