Subgroups — C₄×C₅×C₂₃×C₆₁ #43242593

Order 28060.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₆₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₂₃×C₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₆₁	C₂×C₅	1	1	yes	characteristic
5	C₂₃×C₆₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₅×C₆₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₆₁	C₂×C₂₃	1	1	yes	characteristic
8	C₄×C₅×C₂₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₆₁	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₆₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₂₃	C₂×C₆₁	1	1	yes	characteristic
12	C₂×C₆₁	C₂×C₅×C₂₃	1	1	yes	characteristic
13	C₅×C₂₃	C₄×C₆₁	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₂₃	C₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
15	C₆₁	C₄×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₃	C₂×C₅×C₆₁	1	1	yes	characteristic
17	C₂₃	C₄×C₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₅	C₂₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₂₃×C₆₁	1	1	yes	characteristic
20	C₅	C₄×C₂₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₂₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₂₃×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₂₃×C₆₁
socle, prime radical	C₂×C₅×C₂₃×C₆₁	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×C₂₃×C₆₁	C₄	direct (N × H)
3. C₄×C₂₃×C₆₁	C₅	direct (N × H)
5. C₂₃×C₆₁	C₄×C₅	direct (N × H)
6. C₄×C₅×C₆₁	C₂₃	direct (N × H)
8. C₄×C₅×C₂₃	C₆₁	direct (N × H)
9. C₅×C₆₁	C₄×C₂₃	direct (N × H)
10. C₄×C₆₁	C₅×C₂₃	direct (N × H)
13. C₅×C₂₃	C₄×C₆₁	direct (N × H)
14. C₄×C₂₃	C₅×C₆₁	direct (N × H)
15. C₆₁	C₄×C₅×C₂₃	direct (N × H)
17. C₂₃	C₄×C₅×C₆₁	direct (N × H)
18. C₄×C₅	C₂₃×C₆₁	direct (N × H)
20. C₅	C₄×C₂₃×C₆₁	direct (N × H)
21. C₄	C₅×C₂₃×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
C₂×C₅×C₂₃×C₆₁	2
C₄×C₂₃×C₆₁	5
C₄×C₅×C₆₁	23
C₄×C₅×C₂₃	61

Subgroups — C4×C5×C23×C61 #43242593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₂₃×C₆₁ #43242593