Subgroups — C₂₃×C₂₉×C₅⋊D₅ #45688652

Order 33350.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₂₃×C₂₉	—	5	6	no	maximal
3	C₅×C₂₃×C₂₉	D₅	1	6	yes	complemented
4	C₂₉×C₅⋊D₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₂₉	—	25	1	no	Hall
6	C₂₃×C₅⋊D₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅²×C₂₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	C₂₃×C₂₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅²×C₂₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
10	D₅×C₂₉	—	5	6	no	—
11	D₅×C₂₃	—	5	6	no	—
12	C₅×C₂₉	D₅×C₂₃	1	6	yes	complemented
13	C₅×C₂₃	D₅×C₂₉	1	6	yes	complemented
14	C₂×C₂₉	—	25	1	no	Hall
15	C₅⋊D₅	C₂₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₂₃	—	25	1	no	Hall
17	C₂₉	C₂₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₅²	C₂×C₂₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
19	C₂₃	C₂₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
20	D₅	—	5	6	no	—
21	C₅	D₅×C₂₃×C₂₉	1	6	yes	complemented
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃×C₂₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₂₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₂₃×C₂₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂₃×C₂₉

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.