Subgroups — C₄×C₁₁×C₁₅₁⋊C₅ #45684698

Order 33220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₅₁⋊C₅	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁×C₁₅₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₁₅₁⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₅₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₅₁⋊C₅	C₂×C₁₁	1	1	yes	characteristic
8	C₁₅₁⋊C₅	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₅₁	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₅₁	C₂×C₅×C₁₁	1	1	yes	characteristic
11	C₄×C₅×C₁₁	—	151	1	no	maximal, Hall
12	C₁₅₁	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅×C₁₁	—	151	1	no	—
14	C₅×C₁₁	—	151	1	no	Hall
15	C₄×C₁₁	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁	C₂×C₁₅₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	151	1	no	Hall
18	C₁₁	C₄×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	151	1	no	—
20	C₅	—	151	1	no	Sylow
21	C₄	C₁₁×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₁×C₁₅₁⋊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.