Subgroups — D₁₁₁₇₅ #36375310

Order 22350.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₂₅	—	3	1	no	maximal, Hall
3	D₂₂₃₅	—	5	1	no	maximal
4	C₂₅×C₁₄₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₄₉	D₅	1	1	yes	characteristic
6	D₇₄₅	—	15	1	no	—
7	D₄₄₇	—	25	1	no	Hall
8	C₅×C₁₄₉	D₁₅	1	1	yes	characteristic
9	C₃×C₁₄₉	D₂₅	1	1	yes	characteristic, complemented, Hall
10	D₁₄₉	—	75	1	no	Hall
11	D₇₅	—	149	1	no	maximal, Hall
12	C₁₄₉	D₇₅	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₂₅	D₁₄₉	1	1	yes	characteristic, complemented, Hall
14	D₂₅	—	447	1	no	Hall
15	D₁₅	—	745	1	no	—
16	C₂₅	D₄₄₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	D₇₄₅	1	1	yes	characteristic
18	D₅	—	2235	1	no	—
19	D₃	—	3725	1	no	Hall
20	C₅	D₂₂₃₅	1	1	yes	characteristic
21	C₃	D₃₇₂₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	11175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅×C₁₄₉	C₂
Frattini	C₅	D₂₂₃₅
socle	C₃×C₅×C₁₄₉	D₅
LCS	G ▷ C₃×C₂₅×C₁₄₉
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.