Subgroups — C₃⋊(C₃₁⋊#64480) #42124784

Order 27900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊#1044)	—	3	1	no	maximal
3	C₃₁⋊#64480	—	3	3	no	maximal
4	C₃×C₃₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃₁×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	—
7	C₃₁⋊#1044	—	9	1	no	Hall
8	C₃₁×C₅²⋊C₃	Dic₃	1	3	yes	complemented
9	C₃×C₅²×C₃₁	Dic₃	1	1	yes	characteristic, complemented
10	C₃⋊(C₃₁⋊AGL(1,𝔽₅))	—	15	2	no	—
11	C₃₁×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
12	C₃⋊Dic₉₃	—	25	1	no	maximal, Hall
13	C₃×D₅×C₃₁	—	15	2	no	—
14	C₃⋊#64480	—	31	1	no	maximal, Hall
15	C₅²×C₃₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃₁⋊AGL(1,𝔽₅)	—	45	2	no	—
17	C₂×C₃²×C₃₁	—	25	1	no	—
18	C₃×C₅×C₃₁	—	3	2	no	—
19	C₃×(C₅⋊D₅)⋊C₃	D₃₁	1	1	yes	characteristic
20	Dic₉₃	—	75	1	no	—
21	Dic₉₃	—	75	3	no	—
22	D₅×C₃₁	—	15	2	no	—
23	C₃⋊#1044	—	93	1	no	—
24	#64480	—	93	3	no	—
25	C₃²×C₃₁	—	25	1	no	Hall
26	C₃×C₅²⋊C₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₃₁	—	25	3	no	—
28	C₂×C₃×C₃₁	—	25	1	no	—
29	C₅×C₃₁	—	3	2	no	—
30	C₃×C₅⋊D₅	D₉₃	1	1	yes	characteristic
31	(C₅⋊D₅)⋊C₃	D₉₃	1	3	yes	—
32	Dic₃₁	—	225	1	no	Hall
33	#1044	—	279	1	no	Hall
34	C₃×C₃₁	—	25	3	no	—
35	C₃×C₃₁	#64480	1	1	yes	characteristic, complemented
36	C₃×C₅²	Dic₉₃	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	Dic₉₃	1	3	yes	complemented
38	C₂×C₃₁	—	25	1	no	—
39	ΓL(1,𝔽₁₆)	—	465	2	no	—
40	C₅⋊D₅	C₃⋊D₉₃	1	1	yes	characteristic
41	C₃⋊Dic₃	—	775	1	no	Hall
42	C₃₁	C₃⋊#64480	1	1	yes	characteristic, complemented, Sylow
43	C₃×D₅	—	15	2	no	—
44	C₅²	C₃⋊Dic₉₃	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	1395	2	no	—
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	Dic₃	—	2325	1	no	—
49	Dic₃	—	2325	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	6975	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	C₃₁⋊#64480	1	1	yes	characteristic, complemented
58	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₃₁×C₅²⋊C₃	C₄
Fitting, socle	C₃×C₅²×C₃₁	Dic₃
prime radical, cosocle	C₃×C₃₁×(C₅⋊D₅)⋊C₃	C₂
LCS	G ▷ C₃×C₃₁×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
4. C₃×C₃₁×C₅²⋊C₃	C₄	semidirect
8. C₃₁×C₅²⋊C₃	Dic₃	semidirect
9. C₃×C₅²×C₃₁	Dic₃	semidirect
15. C₅²×C₃₁	C₃⋊Dic₃	semidirect
26. C₃×C₅²⋊C₃	Dic₃₁	semidirect
35. C₃×C₃₁	#64480	semidirect
36. C₃×C₅²	Dic₉₃	semidirect
37. C₅²⋊C₃	Dic₉₃	semidirect
42. C₃₁	C₃⋊#64480	semidirect
44. C₅²	C₃⋊Dic₉₃	semidirect
57. C₃	C₃₁⋊#64480	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₁×(C₅⋊D₅)⋊C₃	2
C₃⋊(C₃₁⋊#1044)	3
C₃₁⋊#64480	3
C₃⋊Dic₉₃	25
C₃⋊#64480	31

Subgroups — C3⋊(C31⋊#64480) #42124784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃₁⋊#64480) #42124784