Subgroups — C₂×C₅⋊D₁₂₀₅ #37562913

Order 24100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₁₂₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₂₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₂₀₅	—	5	6	no	maximal
5	C₂×C₅×C₂₄₁	D₅	1	6	yes	complemented
6	D₁₂₀₅	—	5	12	no	—
7	C₅×C₂₄₁	C₂×D₅	1	6	yes	complemented
8	C₂×D₂₄₁	—	25	1	no	Hall
9	C₂×C₂₄₁	C₅⋊D₅	1	1	yes	characteristic, complemented
10	D₂₄₁	—	25	2	no	—
11	C₂₄₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅⋊D₅	—	241	1	no	maximal, Hall
13	C₂×C₅²	D₂₄₁	1	1	yes	characteristic, complemented
14	C₅⋊D₅	—	241	2	no	—
15	C₅²	C₂×D₂₄₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅	—	1205	6	no	—
17	C₂×C₅	D₁₂₀₅	1	6	yes	complemented
18	D₅	—	1205	12	no	—
19	C₅	C₂×D₁₂₀₅	1	6	yes	complemented
20	C₂²	—	6025	1	no	Sylow
21	C₂	—	6025	2	no	—
22	C₂	C₅⋊D₁₂₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₁₂₀₅
commutator, cosocle, hypocenter	C₅²×C₂₄₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₄₁	C₂
LCS	G ▷ C₅²×C₂₄₁
UCS	C₁ ◁ C₂

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.