Subgroups — (C₅⋊D₅)⋊D₁₀₇ #24924161

Order 10700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅₃₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₁₀₇	—	5	2	no	maximal
5	D₅₃₅	D₅	1	2	yes	complemented
6	C₅×D₁₀₇	—	5	2	no	—
7	D₅×C₁₀₇	—	5	2	no	—
8	D₅×C₁₀₇	—	10	2	no	—
9	C₅×C₁₀₇	—	2	2	no	—
10	C₅×C₁₀₇	C₂×D₅	1	2	yes	complemented
11	C₂×D₁₀₇	—	25	1	no	Hall
12	C₂×C₁₀₇	—	25	1	no	—
13	D₁₀₇	—	5	2	no	—
14	C₁₀₇	D₅²	1	1	yes	characteristic, complemented, Sylow
15	D₅²	—	107	1	no	maximal, Hall
16	C₅⋊D₅	D₁₀₇	1	1	yes	characteristic, complemented
17	C₅×D₅	—	107	2	no	—
18	C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₅	—	535	2	no	—
20	C₂×C₅	—	535	2	no	—
21	D₅	—	5	2	no	—
22	D₅	—	10	2	no	—
23	D₅	—	107	2	no	—
24	C₅	—	2	2	no	—
25	C₅	D₅×D₁₀₇	1	2	yes	complemented
26	C₂²	—	2675	1	no	Sylow
27	C₂	—	535	2	no	—
28	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₀₇	C₂²
LCS	G ▷ C₅²×C₁₀₇
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.