Subgroups — (C₃₁⋊C₃)⋊#1044 #22604848

Order 9300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃₁⋊#1044	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	—	5	2	no	maximal
5	C₃₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	D₅×C₃₁⋊C₃	—	5	2	no	—
7	D₅×C₃₁⋊C₃	—	10	2	no	—
8	C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃₁⋊AGL(1,𝔽₅)	—	5	2	no	—
10	C₅×C₃₁⋊C₃	—	2	2	no	—
11	C₅×C₃₁⋊C₃	AGL(1,𝔽₅)	1	2	yes	complemented
12	(C₃₁⋊C₃)⋊C₄	—	25	1	no	Hall
13	D₅×C₃₁	—	5	2	no	—
14	D₅×C₃₁	—	10	2	no	—
15	C₃×#1044	—	31	1	no	maximal, Hall
16	C₂×C₃₁⋊C₃	—	25	1	no	—
17	C₅×C₃₁	—	2	2	no	—
18	C₅×C₃₁	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
19	C₃×C₅⋊D₅	—	31	1	no	—
20	Dic₃₁	—	25	1	no	Hall
21	#1044	—	31	1	no	Hall
22	C₃₁⋊C₃	#1044	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅²	—	31	1	no	Hall
24	C₂×C₃₁	—	25	1	no	—
25	C₃×AGL(1,𝔽₅)	—	155	2	no	—
26	C₅⋊D₅	D₃₁⋊C₃	1	1	yes	characteristic
27	C₃₁	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
28	C₃×D₅	—	310	2	no	—
29	C₃×D₅	—	155	2	no	—
30	C₅²	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
31	AGL(1,𝔽₅)	—	155	2	no	—
32	C₃×C₅	—	31	2	no	—
33	C₃×C₅	—	62	2	no	—
34	C₃×C₄	—	775	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	775	1	no	—
38	C₅	—	2	2	no	—
39	C₅	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	1	2	yes	complemented
40	C₄	—	775	1	no	Sylow
41	C₃	—	31	1	no	Sylow
42	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃₁⋊#1044	C₃	semidirect
3. C₅²×C₃₁⋊C₃	C₄	semidirect
8. C₅²×C₃₁	C₃×C₄	semidirect
11. C₅×C₃₁⋊C₃	AGL(1,𝔽₅)	semidirect
18. C₅×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
22. C₃₁⋊C₃	#1044	semidirect
27. C₃₁	C₃×#1044	semidirect
30. C₅²	(C₃₁⋊C₃)⋊C₄	semidirect
39. C₅	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	semidirect

Subgroups — (C31⋊C3)⋊#1044 #22604848

Conjugacy classes of subgroups

Complements

Subgroups — (C₃₁⋊C₃)⋊#1044 #22604848