Subgroups — ΓL(1,𝔽₃₂)×C₃⋊D₃₉ #49136607

Order 36270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉×ΓL(1,𝔽₃₂)	—	3	4	no	maximal
3	C₃₁×C₃⋊D₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₃×ΓL(1,𝔽₃₂)	D₃	1	4	yes	complemented
5	D₁₃×ΓL(1,𝔽₃₂)	—	9	1	no	Hall
6	C₃²×C₁₃×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊D₃×ΓL(1,𝔽₃₂)	—	13	1	no	maximal, Hall
8	C₃₁×D₃₉	—	3	4	no	—
9	C₁₃×ΓL(1,𝔽₃₂)	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×ΓL(1,𝔽₃₂)	D₁₃	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×C₃₁	C₅×D₃	1	4	yes	complemented
12	C₅×C₃⋊D₃₉	—	31	1	no	maximal, Hall
13	D₃×ΓL(1,𝔽₃₂)	—	39	4	no	—
14	D₁₃×C₃₁	—	9	1	no	Hall
15	C₃²×C₅×C₁₃	—	31	1	no	Hall
16	C₃⋊D₃×C₃₁	—	13	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	D₃₉	1	4	yes	complemented
18	C₁₃×C₃₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃₉	—	93	4	no	—
20	C₂×ΓL(1,𝔽₃₂)	—	117	1	no	Hall
21	C₃²×C₃₁	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
22	C₃⋊D₃₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₃	—	31	4	no	—
24	D₃×C₃₁	—	39	4	no	—
25	ΓL(1,𝔽₃₂)	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor, Hall
26	C₅×D₁₃	—	279	1	no	Hall
27	C₃²×C₁₃	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₅×D₃₉	1	4	yes	complemented
29	C₅×C₃⋊D₃	—	403	1	no	Hall
30	D₃₉	—	3	4	no	—
31	C₅×C₁₃	—	31	1	no	Hall
32	C₂×C₃₁	—	117	1	no	Hall
33	C₃²×C₅	—	31	1	no	Hall
34	C₃×C₁₃	D₃×ΓL(1,𝔽₃₂)	1	4	yes	complemented
35	C₃₁	C₅×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	1209	4	no	—
37	D₁₃	—	9	1	no	Hall
38	C₃⋊D₃	—	13	1	no	Hall
39	C₃×C₅	—	31	4	no	—
40	C₁₃	C₃⋊D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	3627	1	no	Hall
42	C₃²	D₁₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	39	4	no	—
44	C₅	—	31	1	no	Sylow
45	C₃	D₃₉×ΓL(1,𝔽₃₂)	1	4	yes	complemented
46	C₂	—	117	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃×C₃₁	C₂×C₅
LCS	G ▷ C₃²×C₁₃×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₃₁×C₃⋊D₃₉	C₅	semidirect
4. C₃×C₁₃×ΓL(1,𝔽₃₂)	D₃	semidirect
6. C₃²×C₁₃×C₃₁	C₂×C₅	semidirect
9. C₁₃×ΓL(1,𝔽₃₂)	C₃⋊D₃	semidirect
10. C₃²×ΓL(1,𝔽₃₂)	D₁₃	semidirect
11. C₃×C₁₃×C₃₁	C₅×D₃	semidirect
17. C₃×ΓL(1,𝔽₃₂)	D₃₉	semidirect
18. C₁₃×C₃₁	C₅×C₃⋊D₃	semidirect
21. C₃²×C₃₁	C₅×D₁₃	semidirect
22. C₃⋊D₃₉	ΓL(1,𝔽₃₂)	direct (N × H)
25. ΓL(1,𝔽₃₂)	C₃⋊D₃₉	direct (N × H)
27. C₃²×C₁₃	C₂×ΓL(1,𝔽₃₂)	semidirect
28. C₃×C₃₁	C₅×D₃₉	semidirect
34. C₃×C₁₃	D₃×ΓL(1,𝔽₃₂)	semidirect
35. C₃₁	C₅×C₃⋊D₃₉	semidirect
40. C₁₃	C₃⋊D₃×ΓL(1,𝔽₃₂)	semidirect
42. C₃²	D₁₃×ΓL(1,𝔽₃₂)	semidirect
45. C₃	D₃₉×ΓL(1,𝔽₃₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×ΓL(1,𝔽₃₂)	2
D₃₉×ΓL(1,𝔽₃₂)	3
C₃₁×C₃⋊D₃₉	5
C₃⋊D₃×ΓL(1,𝔽₃₂)	13
C₅×C₃⋊D₃₉	31

Subgroups — ΓL(1,𝔽32)×C3⋊D39 #49136607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₃₂)×C₃⋊D₃₉ #49136607