Subgroups — C₅²×D₆₃₃ #44539574

Order 31650.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₂₁₁	—	3	1	no	maximal, Hall
3	C₅×D₆₃₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₂₁₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₂₁₁	C₂×C₅	1	6	yes	complemented
6	C₅×D₂₁₁	—	3	6	no	—
7	D₆₃₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₁₁	C₅×D₃	1	6	yes	complemented
9	C₃×C₂₁₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	D₂₁₁	—	3	1	no	Hall
11	C₂₁₁	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
12	C₅²×D₃	—	211	1	no	maximal, Hall
13	C₃×C₅²	D₂₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅²	—	633	1	no	Hall
15	C₅×D₃	—	211	6	no	—
16	C₅²	D₆₃₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₅×D₂₁₁	1	6	yes	complemented
18	C₂×C₅	—	633	6	no	—
19	D₃	—	211	1	no	Hall
20	C₅	C₅×D₆₃₃	1	6	yes	direct product factor
21	C₃	C₅²×D₂₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	633	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₆₃₃
commutator, cosocle, hypocenter	C₃×C₂₁₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₁₁	C₂
LCS	G ▷ C₃×C₂₁₁
UCS	C₁ ◁ C₅²

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.