Subgroups — C₃×(C₁₁⋊C₅)⋊C₈ #13050297

Order 1320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	(C₁₁⋊C₅)⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic
4	C₃×C₁₁⋊C₈	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₁⋊C₅	C₈	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₈	—	11	1	no	maximal, Hall
9	C₂×C₁₁⋊C₅	C₃×C₄	1	1	yes	characteristic
10	C₁₁⋊C₈	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₁	C₄×C₅	1	1	yes	characteristic
12	C₃×C₄×C₅	—	11	1	no	—
13	C₁₁⋊C₅	C₃×C₈	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₅×C₈	—	11	1	no	Hall
16	C₃×C₁₁	C₅×C₈	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅	—	11	1	no	—
18	C₃×C₈	—	11	1	no	Hall
19	C₂×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic
20	C₄×C₅	—	11	1	no	—
21	C₃×C₅	—	11	1	no	Hall
22	C₃×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
23	C₁₁	C₃×C₅×C₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₅	—	11	1	no	—
25	C₈	—	11	1	no	Sylow
26	C₂×C₃	Dic₁₁⋊C₅	1	1	yes	characteristic
27	C₅	—	11	1	no	Sylow
28	C₄	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₃	(C₁₁⋊C₅)⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×Dic₁₁⋊C₅	1	1	yes	characteristic

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.