Subgroups — #1042×C₃₁⋊C₉ #42124498

Order 27900.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁×#1042	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₃₁⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×C₃₁⋊C₉	—	5	1	no	maximal
5	Dic₅×C₃₁⋊C₉	—	5	1	no	maximal
6	C₃×C₅×D₅×C₃₁	C₂×C₃	1	1	yes	characteristic
7	C₃₁×#1042	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×C₃₁⋊C₉	—	5	1	no	—
9	D₅×C₃₁⋊C₉	D₅	1	1	yes	characteristic
10	C₃×C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic
11	C₃×AGL(1,𝔽₅)×C₃₁	—	5	1	no	—
12	C₃×Dic₅×C₃₁	—	5	1	no	—
13	C₅×D₅×C₃₁	C₂×C₉	1	1	yes	characteristic
14	C₅×C₃₁⋊C₉	—	4	1	no	—
15	C₅×C₃₁⋊C₉	Dic₅	1	1	yes	characteristic, complemented
16	C₅×C₃₁⋊C₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₄×C₃₁⋊C₉	—	25	1	no	Hall
18	C₂×C₃×C₅×C₃₁	—	5	1	no	—
19	C₃×D₅×C₃₁	C₃×D₅	1	1	yes	characteristic
20	C₉×#1042	—	31	1	no	maximal, Hall
21	C₅²×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
22	AGL(1,𝔽₅)×C₃₁	—	5	1	no	—
23	Dic₅×C₃₁	—	5	1	no	—
24	C₂×C₃₁⋊C₉	—	5	1	no	—
25	C₃×C₅×C₃₁	—	4	1	no	—
26	C₃×C₅×C₃₁	C₃×Dic₅	1	1	yes	characteristic
27	C₃×C₅×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅×C₉×D₅	—	31	1	no	—
29	C₃×C₄×C₃₁	—	25	1	no	—
30	C₂×C₅×C₃₁	—	5	1	no	—
31	D₅×C₃₁	C₉×D₅	1	1	yes	characteristic
32	C₃×#1042	C₃₁⋊C₃	1	1	yes	characteristic
33	C₃₁⋊C₉	#1042	1	1	yes	characteristic, direct product factor, Hall
34	C₅²×C₉	—	31	1	no	Hall
35	C₂×C₃×C₃₁	—	5	1	no	—
36	C₉×AGL(1,𝔽₅)	—	155	1	no	—
37	C₉×Dic₅	—	155	1	no	—
38	C₅×C₃₁	—	4	1	no	—
39	C₅×C₃₁	C₉×Dic₅	1	1	yes	characteristic, complemented
40	C₅×C₃₁	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
41	C₃×C₅×D₅	C₂×C₃₁⋊C₃	1	1	yes	characteristic
42	C₄×C₃₁	—	25	1	no	Hall
43	#1042	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₃₁	C₃×#1042	1	1	yes	characteristic
45	C₂×C₅×C₉	—	155	1	no	—
46	C₉×D₅	—	31	1	no	—
47	C₃×C₅²	C₄×C₃₁⋊C₃	1	1	yes	characteristic
48	C₂×C₃₁	—	5	1	no	—
49	C₃×AGL(1,𝔽₅)	—	5	1	no	—
50	C₃×Dic₅	—	5	1	no	—
51	C₅×D₅	C₂×C₃₁⋊C₉	1	1	yes	characteristic
52	C₅×C₉	—	31	1	no	—
53	C₅×C₉	—	31	1	no	—
54	C₅×C₉	—	124	1	no	—
55	C₄×C₉	—	775	1	no	Hall
56	C₃₁	C₉×#1042	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃×C₅	—	5	1	no	—
58	C₃×D₅	D₅×C₃₁⋊C₃	1	1	yes	characteristic
59	C₅²	C₄×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
60	AGL(1,𝔽₅)	—	5	1	no	—
61	Dic₅	—	5	1	no	—
62	C₂×C₉	—	155	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	Dic₅×C₃₁⋊C₃	1	1	yes	characteristic
65	C₃×C₅	AGL(1,𝔽₅)×C₃₁⋊C₃	1	1	yes	characteristic
66	C₃×C₄	—	25	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	D₅×C₃₁⋊C₉	1	1	yes	characteristic
69	C₉	—	31	1	no	Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	Dic₅×C₃₁⋊C₉	1	1	yes	characteristic, complemented
73	C₅	AGL(1,𝔽₅)×C₃₁⋊C₉	1	1	yes	characteristic, complemented
74	C₄	—	25	1	no	Sylow
75	C₃	C₃₁⋊C₃×#1042	1	1	yes	characteristic
76	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₃₁⋊C₃×#1042
commutator, hypocenter	C₅²×C₃₁	C₄×C₉
Fitting, socle	C₃×C₅²×C₃₁	C₃×C₄
prime radical, cosocle	C₃×C₅×D₅×C₃₁	C₂×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅²×C₃₁⋊C₉	C₄	semidirect
7. C₃₁×#1042	C₉	semidirect
15. C₅×C₃₁⋊C₉	Dic₅	semidirect
16. C₅×C₃₁⋊C₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₃₁	C₄×C₉	semidirect
33. C₃₁⋊C₉	#1042	direct (N × H)
39. C₅×C₃₁	C₉×Dic₅	semidirect
40. C₅×C₃₁	C₉×AGL(1,𝔽₅)	semidirect
43. #1042	C₃₁⋊C₉	direct (N × H)
56. C₃₁	C₉×#1042	semidirect
59. C₅²	C₄×C₃₁⋊C₉	semidirect
72. C₅	Dic₅×C₃₁⋊C₉	semidirect
73. C₅	AGL(1,𝔽₅)×C₃₁⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₃₁⋊C₉	2
C₃×C₃₁×#1042	3
AGL(1,𝔽₅)×C₃₁⋊C₉	5
Dic₅×C₃₁⋊C₉	5
C₉×#1042	31

Subgroups — #1042×C31⋊C9 #42124498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1042×C₃₁⋊C₉ #42124498