Subgroups — (C₃₁⋊C₃)⋊#66776 #44539308

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₃×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁⋊#66776	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₇×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₃₁⋊C₃)⋊#595	—	5	1	no	maximal, Hall
5	C₃₁×D₈₅	C₂×C₃	1	1	yes	characteristic
6	D₁₇×C₃₁⋊C₃	—	5	1	no	—
7	C₅×C₁₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃₁⋊#595	—	5	1	no	Hall
9	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	—	17	1	no	maximal, Hall
10	C₁₇×C₃₁⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃₁×D₁₇	—	5	1	no	—
12	C₃×#66776	—	31	1	no	maximal, Hall
13	D₅×C₃₁⋊C₃	—	17	1	no	—
14	C₃₁⋊AGL(1,𝔽₅)	—	17	1	no	Hall
15	C₁₇×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
16	C₃×D₈₅	—	31	1	no	—
17	C₅×C₃₁⋊C₃	#595	1	1	yes	characteristic, complemented, Hall
18	(C₃₁⋊C₃)⋊C₄	—	85	1	no	Hall
19	#66776	—	31	1	no	Hall
20	D₅×C₃₁	—	17	1	no	—
21	C₃×C₅×C₁₇	—	31	1	no	Hall
22	C₃×#595	—	155	1	no	Hall
23	C₂×C₃₁⋊C₃	—	85	1	no	—
24	D₈₅	D₃₁⋊C₃	1	1	yes	characteristic
25	C₅×C₃₁	C₃×#595	1	1	yes	characteristic, complemented, Hall
26	Dic₃₁	—	85	1	no	Hall
27	C₃×D₁₇	—	155	1	no	—
28	C₃₁⋊C₃	#66776	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
30	#595	—	155	1	no	Hall
31	C₂×C₃₁	—	85	1	no	—
32	C₃×AGL(1,𝔽₅)	—	527	1	no	Hall
33	C₃×C₁₇	—	31	1	no	Hall
34	D₁₇	—	5	1	no	—
35	C₃₁	C₃×#66776	1	1	yes	characteristic, complemented, Sylow
36	C₃×D₅	—	527	1	no	—
37	AGL(1,𝔽₅)	—	527	1	no	Hall
38	C₁₇	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	31	1	no	Hall
40	C₃×C₄	—	2635	1	no	Hall
41	D₅	—	17	1	no	—
42	C₂×C₃	—	2635	1	no	—
43	C₅	(C₃₁⋊C₃)⋊#595	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2635	1	no	Sylow
45	C₃	—	31	1	no	Sylow
46	C₂	—	85	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₃₁	C₃×C₄
prime radical	C₃₁⋊C₃×D₈₅	C₂
cosocle	C₃₁×D₈₅	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃₁⋊#66776	C₃	semidirect
3. C₅×C₁₇×C₃₁⋊C₃	C₄	semidirect
7. C₅×C₁₇×C₃₁	C₃×C₄	semidirect
10. C₁₇×C₃₁⋊C₃	AGL(1,𝔽₅)	semidirect
15. C₁₇×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
17. C₅×C₃₁⋊C₃	#595	semidirect
25. C₅×C₃₁	C₃×#595	semidirect
28. C₃₁⋊C₃	#66776	semidirect
29. C₅×C₁₇	(C₃₁⋊C₃)⋊C₄	semidirect
35. C₃₁	C₃×#66776	semidirect
38. C₁₇	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	semidirect
43. C₅	(C₃₁⋊C₃)⋊#595	semidirect

Maximal subgroups

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

subgroup	index
C₃₁⋊C₃×D₈₅	2
C₃₁⋊#66776	3
(C₃₁⋊C₃)⋊#595	5
(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	17
C₃×#66776	31

Subgroups — (C31⋊C3)⋊#66776 #44539308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃₁⋊C₃)⋊#66776 #44539308