Subgroups — C₁₁×C₁₇×A₅ #26014445

Order 11220.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×A₄×C₁₇	—	5	1	no	maximal, Hall
2	D₅×C₁₁×C₁₇	—	6	1	no	maximal
3	D₃×C₁₁×C₁₇	—	10	1	no	maximal
4	C₁₇×A₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₁₇	—	6	1	no	Hall
6	C₂²×C₁₁×C₁₇	—	5	1	no	Hall
7	C₁₁×A₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₁×C₁₇	—	10	1	no	Hall
9	C₂×C₁₁×C₁₇	—	15	1	no	—
10	A₄×C₁₇	—	5	1	no	Hall
11	C₁₁×C₁₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
12	D₅×C₁₇	—	6	1	no	—
13	C₁₁×A₄	—	5	1	no	Hall
14	D₅×C₁₁	—	6	1	no	—
15	D₃×C₁₇	—	10	1	no	—
16	C₅×C₁₇	—	6	1	no	Hall
17	C₂²×C₁₇	—	5	1	no	Hall
18	D₃×C₁₁	—	10	1	no	—
19	A₅	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	—	6	1	no	Hall
21	C₃×C₁₇	—	10	1	no	Hall
22	C₂²×C₁₁	—	5	1	no	Hall
23	C₂×C₁₇	—	15	1	no	—
24	C₃×C₁₁	—	10	1	no	Hall
25	C₂×C₁₁	—	15	1	no	—
26	C₁₇	C₁₁×A₅	1	1	yes	characteristic, direct product factor, Sylow
27	A₄	—	5	1	no	Hall
28	C₁₁	C₁₇×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.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.