Subgroups — C₂×C₅×C₁₉×ΓL(1,𝔽₃₂) #44441303

Order 29450.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₉×ΓL(1,𝔽₃₂)	C₅	1	5	yes	maximal, direct product factor
3	C₂×C₅×C₁₉×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
5	C₁₉×ΓL(1,𝔽₃₂)	C₂×C₅	1	5	yes	direct product factor
6	C₂×C₅×ΓL(1,𝔽₃₂)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉×C₃₁	C₅²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅²×C₁₉	—	31	1	no	maximal, Hall
9	C₅×ΓL(1,𝔽₃₂)	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₁₉×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
11	C₅²×C₁₉	—	31	1	no	Hall
12	C₂×C₅×C₃₁	C₅×C₁₉	1	1	yes	characteristic, complemented
13	C₂×ΓL(1,𝔽₃₂)	C₅×C₁₉	1	5	yes	direct product factor
14	C₂×C₅×C₁₉	—	31	5	no	—
15	C₂×C₅×C₁₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
16	C₅×C₃₁	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
17	ΓL(1,𝔽₃₂)	C₂×C₅×C₁₉	1	5	yes	direct product factor
18	C₅×C₁₉	—	31	5	no	—
19	C₅×C₁₉	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	C₅²×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²	—	31	1	no	Hall
22	C₂×C₁₉	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
23	C₃₁	C₂×C₅²×C₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₅²	—	31	1	no	Sylow
25	C₁₉	C₂×C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	31	5	no	—
27	C₂×C₅	C₁₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
28	C₅	—	31	5	no	—
29	C₅	C₂×C₁₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
30	C₂	C₅×C₁₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₂×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×ΓL(1,𝔽₃₂)	C₂	direct (N × H)
2. C₂×C₁₉×ΓL(1,𝔽₃₂)	C₅	direct (N × H)
3. C₂×C₅×C₁₉×C₃₁	C₅	semidirect
4. C₅×C₁₉×C₃₁	C₂×C₅	semidirect
5. C₁₉×ΓL(1,𝔽₃₂)	C₂×C₅	direct (N × H)
6. C₂×C₅×ΓL(1,𝔽₃₂)	C₁₉	direct (N × H)
7. C₂×C₁₉×C₃₁	C₅²	semidirect
9. C₅×ΓL(1,𝔽₃₂)	C₂×C₁₉	direct (N × H)
10. C₁₉×C₃₁	C₂×C₅²	semidirect
12. C₂×C₅×C₃₁	C₅×C₁₉	semidirect
13. C₂×ΓL(1,𝔽₃₂)	C₅×C₁₉	direct (N × H)
15. C₂×C₅×C₁₉	ΓL(1,𝔽₃₂)	direct (N × H)
16. C₅×C₃₁	C₂×C₅×C₁₉	semidirect
17. ΓL(1,𝔽₃₂)	C₂×C₅×C₁₉	direct (N × H)
19. C₅×C₁₉	C₂×ΓL(1,𝔽₃₂)	direct (N × H)
20. C₂×C₃₁	C₅²×C₁₉	semidirect
22. C₂×C₁₉	C₅×ΓL(1,𝔽₃₂)	direct (N × H)
23. C₃₁	C₂×C₅²×C₁₉	semidirect
25. C₁₉	C₂×C₅×ΓL(1,𝔽₃₂)	direct (N × H)
27. C₂×C₅	C₁₉×ΓL(1,𝔽₃₂)	direct (N × H)
29. C₅	C₂×C₁₉×ΓL(1,𝔽₃₂)	direct (N × H)
30. C₂	C₅×C₁₉×ΓL(1,𝔽₃₂)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×ΓL(1,𝔽₃₂)	2
C₂×C₁₉×ΓL(1,𝔽₃₂)	5
C₂×C₅×C₁₉×C₃₁	5
C₂×C₅×ΓL(1,𝔽₃₂)	19
C₂×C₅²×C₁₉	31

Subgroups — C2×C5×C19×ΓL(1,𝔽32) #44441303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₉×ΓL(1,𝔽₃₂) #44441303