Subgroups — C₂₅⋊(D₇₃⋊C₃) #24926536

Order 10950.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₈₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊(D₇₃⋊C₃)	—	5	1	no	maximal
4	C₂₅×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇₃⋊C₃	D₅	1	1	yes	characteristic
6	D₃₆₅	—	5	1	no	—
7	D₇₃⋊C₃	—	25	1	no	Hall
8	C₅×C₇₃	C₃×D₅	1	1	yes	characteristic
9	C₇₃⋊C₃	D₂₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₅	—	73	1	no	maximal, Hall
11	D₇₃	—	25	1	no	Hall
12	C₃×C₂₅	—	73	1	no	Hall
13	C₇₃	C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
14	D₂₅	—	73	1	no	Hall
15	C₃×D₅	—	365	1	no	—
16	C₂₅	D₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	—	73	1	no	—
18	D₅	—	365	1	no	—
19	C₂×C₃	—	1825	1	no	Hall
20	C₅	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic
21	C₃	—	73	1	no	Sylow
22	C₂	—	1825	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₇₃	C₂×C₃
Frattini	C₅	C₅⋊(D₇₃⋊C₃)
socle	C₅×C₇₃	C₃×D₅
LCS	G ▷ C₂₅×C₇₃
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.