Subgroups — C₅×D₆₀₅ #20258396

Order 6050.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₀₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₁₂₁	—	5	1	no	maximal
4	C₅×C₁₂₁	—	2	2	no	—
5	C₅×C₁₂₁	D₅	1	1	yes	characteristic, complemented
6	C₅×C₁₂₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×D₅₅	—	11	1	no	maximal
8	C₅²×C₁₁	D₁₁	1	1	yes	characteristic
9	D₁₂₁	—	5	1	no	Hall
10	C₁₂₁	C₅×D₅	1	1	yes	characteristic, complemented, Sylow
11	D₅₅	—	11	1	no	—
12	C₅×D₁₁	—	55	1	no	—
13	C₅×C₁₁	—	2	2	no	—
14	C₅×C₁₁	C₅×D₁₁	1	1	yes	characteristic
15	C₅×C₁₁	D₅₅	1	1	yes	characteristic
16	C₅×D₅	—	121	1	no	Hall
17	C₅²	D₁₂₁	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	55	1	no	—
19	C₁₁	C₅×D₅₅	1	1	yes	characteristic
20	C₂×C₅	—	605	1	no	—
21	D₅	—	121	1	no	—
22	C₅	—	2	2	no	—
23	C₅	C₅×D₁₂₁	1	1	yes	characteristic, complemented
24	C₅	D₆₀₅	1	1	yes	characteristic, direct product factor
25	C₂	—	605	1	no	Sylow

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