Subgroups — C₃⋊(C₃⋊(C₃₁⋊#1035)) #42124433

Order 27900.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊#1035)	—	3	4	no	maximal
3	C₃²×C₂₅×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊(C₃₁⋊AGL(1,𝔽₅)))	—	5	1	no	maximal
5	C₃×C₃₁×D₂₅	D₃	1	4	yes	—
6	C₃₁⋊#1035	—	9	1	no	Hall
7	C₃²×D₅×C₃₁	—	5	1	no	—
8	C₃×C₂₅×C₃₁	Dic₃	1	4	yes	complemented
9	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	—	15	4	no	—
10	C₃₁×D₂₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₃⋊Dic₉₃	—	25	1	no	Hall
13	C₃×D₅×C₃₁	—	5	4	no	—
14	C₃⋊(C₃⋊#1035)	—	31	1	no	maximal, Hall
15	C₂₅×C₃₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃₁⋊AGL(1,𝔽₅)	—	45	1	no	—
17	C₂×C₃²×C₃₁	—	25	1	no	—
18	C₃×C₅×C₃₁	ΓL(1,𝔽₁₆)	1	4	yes	—
19	C₃²×D₂₅	D₃₁	1	1	yes	characteristic
20	Dic₉₃	—	75	4	no	—
21	D₅×C₃₁	—	5	1	no	—
22	C₃⋊#1035	—	93	4	no	—
23	C₃²×C₃₁	#1035	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₂₅	Dic₃₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₁	—	25	4	no	—
26	C₃⋊ΓL(1,𝔽₁₆)	—	155	1	no	—
27	C₅×C₃₁	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
28	C₃×D₂₅	D₉₃	1	4	yes	—
29	Dic₃₁	—	225	1	no	Hall
30	#1035	—	279	1	no	Hall
31	C₃×C₃₁	C₃⋊#1035	1	4	yes	complemented
32	C₃²×D₅	—	5	1	no	—
33	C₃×C₂₅	Dic₉₃	1	4	yes	complemented
34	C₂×C₃₁	—	25	1	no	—
35	ΓL(1,𝔽₁₆)	—	465	4	no	—
36	D₂₅	C₃⋊D₉₃	1	1	yes	characteristic
37	C₃²×C₅	C₃₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₃⋊Dic₃	—	775	1	no	Hall
39	C₃₁	C₃⋊(C₃⋊#1035)	1	1	yes	characteristic, complemented, Sylow
40	C₃×D₅	—	5	4	no	—
41	C₂₅	C₃⋊Dic₉₃	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	1395	1	no	—
43	C₂×C₃²	—	25	1	no	—
44	C₃×C₅	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	1	4	yes	—
45	Dic₃	—	2325	4	no	—
46	D₅	—	5	1	no	—
47	C₃²	C₃₁⋊#1035	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	4	no	—
49	C₅	C₃⋊(C₃⋊(C₃₁⋊AGL(1,𝔽₅)))	1	1	yes	characteristic
50	C₄	—	6975	1	no	Sylow
51	C₃	C₃⋊(C₃₁⋊#1035)	1	4	yes	complemented
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₅×C₃₁	C₄
Frattini	C₅	C₃⋊(C₃⋊(C₃₁⋊AGL(1,𝔽₅)))
socle	C₃²×C₅×C₃₁	AGL(1,𝔽₅)
prime radical, cosocle	C₃²×C₃₁×D₂₅	C₂
LCS	G ▷ C₃²×C₂₅×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₂₅×C₃₁	C₄	semidirect
8. C₃×C₂₅×C₃₁	Dic₃	semidirect
15. C₂₅×C₃₁	C₃⋊Dic₃	semidirect
23. C₃²×C₃₁	#1035	semidirect
24. C₃²×C₂₅	Dic₃₁	semidirect
31. C₃×C₃₁	C₃⋊#1035	semidirect
33. C₃×C₂₅	Dic₉₃	semidirect
39. C₃₁	C₃⋊(C₃⋊#1035)	semidirect
41. C₂₅	C₃⋊Dic₉₃	semidirect
47. C₃²	C₃₁⋊#1035	semidirect
51. C₃	C₃⋊(C₃₁⋊#1035)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₃₁×D₂₅	2
C₃⋊(C₃₁⋊#1035)	3
C₃⋊(C₃⋊(C₃₁⋊AGL(1,𝔽₅)))	5
C₃⋊(C₃⋊#1035)	31

Subgroups — C3⋊(C3⋊(C31⋊#1035)) #42124433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₃₁⋊#1035)) #42124433