Subgroups — C₂×C₁₁×C₂₅×C₆₁ #46776641

Order 33550.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₅×C₆₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁×C₆₁	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₁×C₆₁	C₂×C₅	1	1	yes	characteristic
4	C₂×C₂₅×C₆₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₅×C₆₁	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₁×C₆₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₁₁×C₆₁	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₅×C₆₁	C₅×C₁₁	1	1	yes	characteristic
9	C₂×C₁₁×C₂₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₆₁	C₂×C₅×C₁₁	1	1	yes	characteristic
11	C₁₁×C₂₅	C₂×C₆₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₆₁	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁	C₅×C₆₁	1	1	yes	characteristic
14	C₆₁	C₂×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₅×C₁₁	C₂×C₅×C₆₁	1	1	yes	characteristic
16	C₂×C₂₅	C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂₅	C₂×C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₁₁	C₂×C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₅	C₅×C₁₁×C₆₁	1	1	yes	characteristic
21	C₅	C₂×C₅×C₁₁×C₆₁	1	1	yes	characteristic
22	C₂	C₁₁×C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₁₁×C₆₁
socle, prime radical	C₂×C₅×C₁₁×C₆₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₅×C₆₁	C₂	direct (N × H)
4. C₂×C₂₅×C₆₁	C₁₁	direct (N × H)
5. C₂₅×C₆₁	C₂×C₁₁	direct (N × H)
6. C₂×C₁₁×C₆₁	C₂₅	direct (N × H)
7. C₁₁×C₆₁	C₂×C₂₅	direct (N × H)
9. C₂×C₁₁×C₂₅	C₆₁	direct (N × H)
11. C₁₁×C₂₅	C₂×C₆₁	direct (N × H)
12. C₂×C₆₁	C₁₁×C₂₅	direct (N × H)
14. C₆₁	C₂×C₁₁×C₂₅	direct (N × H)
16. C₂×C₂₅	C₁₁×C₆₁	direct (N × H)
17. C₂₅	C₂×C₁₁×C₆₁	direct (N × H)
18. C₂×C₁₁	C₂₅×C₆₁	direct (N × H)
19. C₁₁	C₂×C₂₅×C₆₁	direct (N × H)
22. C₂	C₁₁×C₂₅×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂₅×C₆₁	2
C₂×C₅×C₁₁×C₆₁	5
C₂×C₂₅×C₆₁	11
C₂×C₁₁×C₂₅	61

Subgroups — C2×C11×C25×C61 #46776641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₂₅×C₆₁ #46776641