Subgroups — C₄×C₅×C₂₃×C₄₃ #34089902

Order 19780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₄₃	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₂₃×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₄₃	C₂×C₅	1	1	yes	characteristic
5	C₂₃×C₄₃	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₅×C₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₅×C₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₄₃	C₂×C₂₃	1	1	yes	characteristic
9	C₂×C₅×C₂₃	C₂×C₄₃	1	1	yes	characteristic
10	C₅×C₄₃	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₄₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₂₃	C₄×C₄₃	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₂₃	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄₃	C₂×C₅×C₂₃	1	1	yes	characteristic
15	C₂×C₂₃	C₂×C₅×C₄₃	1	1	yes	characteristic
16	C₄₃	C₄×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₃	C₄×C₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₅	C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₂₃×C₄₃	1	1	yes	characteristic
20	C₅	C₄×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₂₃×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₂₃×C₄₃
socle, prime radical	C₂×C₅×C₂₃×C₄₃	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×C₄₃	C₄	direct (N × H)
3. C₄×C₂₃×C₄₃	C₅	direct (N × H)
5. C₂₃×C₄₃	C₄×C₅	direct (N × H)
6. C₄×C₅×C₄₃	C₂₃	direct (N × H)
7. C₄×C₅×C₂₃	C₄₃	direct (N × H)
10. C₅×C₄₃	C₄×C₂₃	direct (N × H)
11. C₄×C₄₃	C₅×C₂₃	direct (N × H)
12. C₅×C₂₃	C₄×C₄₃	direct (N × H)
13. C₄×C₂₃	C₅×C₄₃	direct (N × H)
16. C₄₃	C₄×C₅×C₂₃	direct (N × H)
17. C₂₃	C₄×C₅×C₄₃	direct (N × H)
18. C₄×C₅	C₂₃×C₄₃	direct (N × H)
20. C₅	C₄×C₂₃×C₄₃	direct (N × H)
21. C₄	C₅×C₂₃×C₄₃	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×C₄₃	2
C₄×C₂₃×C₄₃	5
C₄×C₅×C₄₃	23
C₄×C₅×C₂₃	43

Subgroups — C4×C5×C23×C43 #34089902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₂₃×C₄₃ #34089902