Subgroups — C₄×C₅×C₁₁×C₁₅₁ #45684697

Order 33220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₁₅₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁×C₁₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₁×C₁₅₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₁₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₅₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₁₅₁	C₂×C₁₁	1	1	yes	characteristic
8	C₅×C₁₅₁	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₅₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₅₁	C₂×C₅×C₁₁	1	1	yes	characteristic
11	C₄×C₅×C₁₁	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₅₁	C₄×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₅×C₁₁	C₂×C₁₅₁	1	1	yes	characteristic
14	C₅×C₁₁	C₄×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁	C₂×C₅×C₁₅₁	1	1	yes	characteristic
17	C₄×C₅	C₁₁×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	C₄×C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₁×C₁₅₁	1	1	yes	characteristic
20	C₅	C₄×C₁₁×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₁₁×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₁₁×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₁₁×C₁₅₁
socle, prime radical	C₂×C₅×C₁₁×C₁₅₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×C₁₅₁	C₄	direct (N × H)
3. C₄×C₁₁×C₁₅₁	C₅	direct (N × H)
5. C₄×C₅×C₁₅₁	C₁₁	direct (N × H)
6. C₁₁×C₁₅₁	C₄×C₅	direct (N × H)
8. C₅×C₁₅₁	C₄×C₁₁	direct (N × H)
9. C₄×C₁₅₁	C₅×C₁₁	direct (N × H)
11. C₄×C₅×C₁₁	C₁₅₁	direct (N × H)
12. C₁₅₁	C₄×C₅×C₁₁	direct (N × H)
14. C₅×C₁₁	C₄×C₁₅₁	direct (N × H)
15. C₄×C₁₁	C₅×C₁₅₁	direct (N × H)
17. C₄×C₅	C₁₁×C₁₅₁	direct (N × H)
18. C₁₁	C₄×C₅×C₁₅₁	direct (N × H)
20. C₅	C₄×C₁₁×C₁₅₁	direct (N × H)
21. C₄	C₅×C₁₁×C₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₁×C₁₅₁	2
C₄×C₁₁×C₁₅₁	5
C₄×C₅×C₁₅₁	11
C₄×C₅×C₁₁	151

Subgroups — C4×C5×C11×C151 #45684697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₁₁×C₁₅₁ #45684697