Subgroups — C₃⋊(#1043⋊(C₃₁⋊C₃)) #42124787

Order 27900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₅⋊D₅)⋊(C₃₁⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₃⋊#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	#1043⋊(C₃₁⋊C₃)	—	3	1	no	maximal
4	C₃×C₅²⋊(C₃₁⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	(C₅⋊D₅)⋊(C₃₁⋊C₃)	—	2	1	no	—
7	(C₅⋊D₅)⋊(C₃₁⋊C₃)	D₃	1	1	yes	characteristic
8	C₃₁×#1043	—	3	1	no	Hall
9	C₅²⋊(C₃₁⋊C₃)	—	2	1	no	—
10	C₅²⋊(C₃₁⋊C₃)	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃₁×ΓL(1,𝔽₁₆)	—	15	2	no	—
13	C₃₁×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	Dic₃×C₃₁⋊C₃	—	25	1	no	maximal, Hall
15	C₃×D₅×C₃₁	—	15	2	no	—
16	C₃⋊(#1043⋊C₃)	—	31	1	no	maximal, Hall
17	C₅²×C₃₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	AGL(1,𝔽₅)×C₃₁	—	45	2	no	—
19	C₂×C₃×C₃₁⋊C₃	—	25	1	no	—
20	C₃×C₅×C₃₁	—	3	2	no	—
21	C₃×(C₅⋊D₅)⋊C₃	—	31	1	no	—
22	Dic₃×C₃₁	—	25	1	no	—
23	C₄×C₃₁⋊C₃	—	75	1	no	—
24	D₅×C₃₁	—	15	2	no	—
25	C₃⋊#1043	C₃₁⋊C₃	1	1	yes	characteristic, complemented
26	#1043⋊C₃	—	93	1	no	—
27	C₃×C₃₁⋊C₃	—	25	1	no	Hall
28	C₃×C₅²⋊C₃	—	31	1	no	Hall
29	C₂×C₃×C₃₁	—	25	1	no	—
30	C₂×C₃₁⋊C₃	—	25	1	no	—
31	C₂×C₃₁⋊C₃	—	50	1	no	—
32	C₅×C₃₁	—	3	2	no	—
33	C₃×C₅⋊D₅	C₂×C₃₁⋊C₃	1	1	yes	characteristic
34	(C₅⋊D₅)⋊C₃	—	31	1	no	—
35	(C₅⋊D₅)⋊C₃	—	62	1	no	—
36	C₄×C₃₁	—	75	1	no	Hall
37	#1043	—	3	1	no	Hall
38	C₃×C₃₁	#1043⋊C₃	1	1	yes	characteristic, complemented
39	C₃₁⋊C₃	—	25	1	no	—
40	C₃₁⋊C₃	—	50	1	no	—
41	C₃×C₅²	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	31	1	no	—
43	C₅²⋊C₃	—	62	1	no	—
44	C₂×C₃₁	—	25	1	no	—
45	ΓL(1,𝔽₁₆)	—	15	2	no	—
46	C₅⋊D₅	D₃×C₃₁⋊C₃	1	1	yes	characteristic
47	C₃×Dic₃	—	775	1	no	Hall
48	C₃₁	C₃⋊(#1043⋊C₃)	1	1	yes	characteristic, complemented, Sylow
49	C₃×D₅	—	15	2	no	—
50	C₅²	Dic₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	45	2	no	—
52	C₂×C₃²	—	775	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2325	1	no	—
55	Dic₃	—	25	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	775	1	no	Sylow
58	C₂×C₃	—	775	1	no	—
59	C₂×C₃	—	1550	1	no	—
60	C₂×C₃	—	25	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	75	1	no	Sylow
63	C₃	—	775	1	no	—
64	C₃	—	1550	1	no	—
65	C₃	#1043⋊(C₃₁⋊C₃)	1	1	yes	characteristic, complemented
66	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃₁×C₃⋊#1043	C₃	semidirect
4. C₃×C₅²⋊(C₃₁⋊C₃)	C₄	semidirect
10. C₅²⋊(C₃₁⋊C₃)	Dic₃	semidirect
11. C₃×C₅²×C₃₁	C₃×C₄	semidirect
17. C₅²×C₃₁	C₃×Dic₃	semidirect
25. C₃⋊#1043	C₃₁⋊C₃	semidirect
38. C₃×C₃₁	#1043⋊C₃	semidirect
41. C₃×C₅²	C₄×C₃₁⋊C₃	semidirect
48. C₃₁	C₃⋊(#1043⋊C₃)	semidirect
50. C₅²	Dic₃×C₃₁⋊C₃	semidirect
65. C₃	#1043⋊(C₃₁⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₅⋊D₅)⋊(C₃₁⋊C₃)	2
C₃₁×C₃⋊#1043	3
#1043⋊(C₃₁⋊C₃)	3
Dic₃×C₃₁⋊C₃	25
C₃⋊(#1043⋊C₃)	31

Subgroups — C3⋊(#1043⋊(C31⋊C3)) #42124787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#1043⋊(C₃₁⋊C₃)) #42124787