Subgroups — C₁₁×C₁₃×A₅ #22575197

Order 8580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×A₄×C₁₃	—	5	1	no	maximal, Hall
2	D₅×C₁₁×C₁₃	—	6	1	no	maximal
3	D₃×C₁₁×C₁₃	—	10	1	no	maximal
4	C₁₃×A₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₁₃	—	6	1	no	Hall
6	C₁₁×A₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₁₁×C₁₃	—	5	1	no	Hall
8	C₃×C₁₁×C₁₃	—	10	1	no	Hall
9	C₂×C₁₁×C₁₃	—	15	1	no	—
10	A₄×C₁₃	—	5	1	no	Hall
11	C₁₁×C₁₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
12	C₁₁×A₄	—	5	1	no	Hall
13	D₅×C₁₃	—	6	1	no	—
14	D₅×C₁₁	—	6	1	no	—
15	D₃×C₁₃	—	10	1	no	—
16	D₃×C₁₁	—	10	1	no	—
17	C₅×C₁₃	—	6	1	no	Hall
18	A₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₁	—	6	1	no	Hall
20	C₂²×C₁₃	—	5	1	no	Hall
21	C₂²×C₁₁	—	5	1	no	Hall
22	C₃×C₁₃	—	10	1	no	Hall
23	C₃×C₁₁	—	10	1	no	Hall
24	C₂×C₁₃	—	15	1	no	—
25	C₂×C₁₁	—	15	1	no	—
26	C₁₃	C₁₁×A₅	1	1	yes	characteristic, direct product factor, Sylow
27	A₄	—	5	1	no	Hall
28	C₁₁	C₁₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
29	D₅	—	6	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	Sylow
32	C₂²	—	5	1	no	Sylow
33	C₃	—	10	1	no	Sylow
34	C₂	—	15	1	no	—

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