Subgroups — C₅×D₂₀₂₃ #35202201

Order 20230.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₀₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₂₈₉	—	7	1	no	maximal, Hall
4	C₇×C₂₈₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₈₉	D₇	1	1	yes	characteristic, complemented, Hall
6	C₅×D₁₁₉	—	17	1	no	maximal
7	C₅×C₇×C₁₇	D₁₇	1	1	yes	characteristic
8	D₂₈₉	—	7	1	no	Hall
9	C₂₈₉	C₅×D₇	1	1	yes	characteristic, complemented, Sylow
10	D₁₁₉	—	17	1	no	—
11	C₅×D₁₇	—	119	1	no	—
12	C₇×C₁₇	C₅×D₁₇	1	1	yes	characteristic
13	C₅×C₁₇	D₁₁₉	1	1	yes	characteristic
14	C₅×D₇	—	289	1	no	Hall
15	C₅×C₇	D₂₈₉	1	1	yes	characteristic, complemented, Hall
16	D₁₇	—	119	1	no	—
17	C₁₇	C₅×D₁₁₉	1	1	yes	characteristic
18	D₇	—	289	1	no	Hall
19	C₂×C₅	—	2023	1	no	Hall
20	C₇	C₅×D₂₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₂₀₂₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	2023	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₀₂₃
commutator, cosocle, hypocenter	C₇×C₂₈₉	C₂×C₅
Frattini	C₁₇	C₅×D₁₁₉
Fitting	C₅×C₇×C₂₈₉	C₂
socle	C₅×C₇×C₁₇	D₁₇
LCS	G ▷ C₇×C₂₈₉
UCS	C₁ ◁ C₅

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.