Subgroups — C₂×C₄₃×D₃₁⋊C₅ #40998621

Order 26660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×D₃₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₃×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃₁×C₄₃	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₃×D₃₁	C₂×C₅	1	2	yes	complemented
7	C₃₁×C₄₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₄₃	—	31	1	no	maximal, Hall
9	C₂×D₃₁⋊C₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₄₃	—	31	2	no	—
11	C₂×C₅×C₄₃	—	31	1	no	—
12	C₂×ΓL(1,𝔽₃₂)	C₂×C₄₃	1	1	yes	characteristic, complemented
13	D₃₁⋊C₅	C₂×C₄₃	1	2	yes	direct product factor
14	C₅×C₄₃	—	31	1	no	Hall
15	C₂²×C₄₃	—	31	1	no	Hall
16	ΓL(1,𝔽₃₂)	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃₁	C₅×C₄₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₃	—	31	2	no	—
19	C₂×C₄₃	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	C₂×C₅×C₄₃	1	1	yes	characteristic, complemented
21	D₃₁	C₂×C₅×C₄₃	1	2	yes	complemented
22	C₄₃	C₂×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂²×C₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅	—	31	1	no	Hall
25	C₂×C₅	—	31	2	no	—
26	C₂×C₅	—	31	1	no	—
27	C₅	—	31	1	no	Sylow
28	C₂²	—	31	1	no	Sylow
29	C₂	—	31	2	no	—
30	C₂	C₄₃×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₃	D₃₁⋊C₅
commutator, cosocle, hypocenter	C₃₁	C₂²×C₅×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₄₃	C₂×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×D₃₁⋊C₅	C₂	direct (N × H)
2. C₂×C₄₃×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₄₃×ΓL(1,𝔽₃₂)	C₂²	semidirect
4. C₂×C₄₃×D₃₁	C₅	semidirect
5. C₂×C₃₁×C₄₃	C₂×C₅	semidirect
6. C₄₃×D₃₁	C₂×C₅	semidirect
7. C₃₁×C₄₃	C₂²×C₅	semidirect
9. C₂×D₃₁⋊C₅	C₄₃	direct (N × H)
12. C₂×ΓL(1,𝔽₃₂)	C₂×C₄₃	semidirect
13. D₃₁⋊C₅	C₂×C₄₃	direct (N × H)
16. ΓL(1,𝔽₃₂)	C₂²×C₄₃	semidirect
17. C₂×D₃₁	C₅×C₄₃	semidirect
19. C₂×C₄₃	D₃₁⋊C₅	direct (N × H)
20. C₂×C₃₁	C₂×C₅×C₄₃	semidirect
21. D₃₁	C₂×C₅×C₄₃	semidirect
22. C₄₃	C₂×D₃₁⋊C₅	direct (N × H)
23. C₃₁	C₂²×C₅×C₄₃	semidirect
30. C₂	C₄₃×D₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×D₃₁⋊C₅	2
C₂×C₄₃×ΓL(1,𝔽₃₂)	2
C₂×C₄₃×D₃₁	5
C₂²×C₅×C₄₃	31
C₂×D₃₁⋊C₅	43

Subgroups — C2×C43×D31⋊C5 #40998621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×D₃₁⋊C₅ #40998621