Subgroups — A₅×C₁₂₁ #20300132

Order 7260.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₂₁	—	5	1	no	maximal, Hall
2	D₅×C₁₂₁	—	6	1	no	maximal
3	D₃×C₁₂₁	—	10	1	no	maximal
4	C₁₁×A₅	C₁₁	1	1	yes	maximal, characteristic
5	C₅×C₁₂₁	—	6	1	no	Hall
6	C₂²×C₁₂₁	—	5	1	no	Hall
7	C₃×C₁₂₁	—	10	1	no	Hall
8	C₂×C₁₂₁	—	15	1	no	—
9	C₁₁×A₄	—	5	1	no	—
10	C₁₂₁	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
11	D₅×C₁₁	—	6	1	no	—
12	D₃×C₁₁	—	10	1	no	—
13	A₅	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₁	—	6	1	no	—
15	C₂²×C₁₁	—	5	1	no	—
16	C₃×C₁₁	—	10	1	no	—
17	C₂×C₁₁	—	15	1	no	—
18	A₄	—	5	1	no	Hall
19	C₁₁	C₁₁×A₅	1	1	yes	characteristic
20	D₅	—	6	1	no	—
21	D₃	—	10	1	no	—
22	C₅	—	6	1	no	Sylow
23	C₂²	—	5	1	no	Sylow
24	C₃	—	10	1	no	Sylow
25	C₂	—	15	1	no	—

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

N	H ≅ G/N	type
10. C₁₂₁	A₅	direct (N × H)
13. A₅	C₁₂₁	direct (N × H)