Subgroups — C₃₁×C₃⋊#1044 #22604912

Order 9300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1044	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₁×ΓL(1,𝔽₁₆)	—	5	2	no	maximal
5	C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₃₁	—	5	2	no	—
7	C₃×D₅×C₃₁	—	10	2	no	—
8	C₅²×C₃₁	Dic₃	1	1	yes	characteristic, complemented, Hall
9	AGL(1,𝔽₅)×C₃₁	—	15	2	no	—
10	C₃×C₅×C₃₁	—	2	2	no	—
11	C₃×C₅×C₃₁	AGL(1,𝔽₅)	1	2	yes	complemented
12	Dic₃×C₃₁	—	25	1	no	Hall
13	D₅×C₃₁	—	5	2	no	—
14	D₅×C₃₁	—	10	2	no	—
15	C₃⋊#1044	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₃₁	—	25	1	no	—
17	C₅×C₃₁	—	2	2	no	—
18	C₅×C₃₁	ΓL(1,𝔽₁₆)	1	2	yes	complemented
19	C₃×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic
20	C₄×C₃₁	—	75	1	no	Hall
21	#1044	—	3	1	no	Hall
22	C₃×C₃₁	#1044	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅²	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃₁	—	25	1	no	—
25	ΓL(1,𝔽₁₆)	—	5	2	no	—
26	C₅⋊D₅	D₃×C₃₁	1	1	yes	characteristic
27	C₃₁	C₃⋊#1044	1	1	yes	characteristic, direct product factor, Sylow
28	C₃×D₅	—	5	2	no	—
29	C₃×D₅	—	10	2	no	—
30	C₅²	Dic₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
31	AGL(1,𝔽₅)	—	15	2	no	—
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	AGL(1,𝔽₅)×C₃₁	1	2	yes	complemented
34	Dic₃	—	25	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃₁×ΓL(1,𝔽₁₆)	1	2	yes	complemented
40	C₄	—	75	1	no	Sylow
41	C₃	C₃₁×#1044	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	C₃⋊#1044
commutator, hypocenter	C₃×C₅²	C₄×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₄
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₃₁	C₄	semidirect
8. C₅²×C₃₁	Dic₃	semidirect
11. C₃×C₅×C₃₁	AGL(1,𝔽₅)	semidirect
15. C₃⋊#1044	C₃₁	direct (N × H)
18. C₅×C₃₁	ΓL(1,𝔽₁₆)	semidirect
22. C₃×C₃₁	#1044	semidirect
23. C₃×C₅²	C₄×C₃₁	semidirect
27. C₃₁	C₃⋊#1044	direct (N × H)
30. C₅²	Dic₃×C₃₁	semidirect
33. C₃×C₅	AGL(1,𝔽₅)×C₃₁	semidirect
39. C₅	C₃₁×ΓL(1,𝔽₁₆)	semidirect
41. C₃	C₃₁×#1044	semidirect

Subgroups — C31×C3⋊#1044 #22604912

Conjugacy classes of subgroups

Complements

Subgroups — C₃₁×C₃⋊#1044 #22604912