Subgroups — C₃×D₅⋊#157 #11762164

Order 1080.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#4380	C₂	1	2	yes	maximal, complemented
3	D₅⋊#157	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₃⋊D₁₅	C₂²	1	1	yes	characteristic
5	C₃×C₅×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
6	C₃³×D₅	C₄	1	1	yes	characteristic, complemented
7	C₂×C₃×#157	—	5	1	no	maximal, Hall
8	D₅×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
9	C₃×D₃×D₅	—	6	2	no	—
10	#4380	C₂×C₃	1	2	yes	complemented
11	C₃³×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×AGL(1,𝔽₅)	—	9	1	no	maximal
13	C₂×C₃×C₃⋊D₃	—	5	1	no	—
14	C₃×#157	—	5	2	no	—
15	C₃⋊D₁₅	C₂²×C₃	1	1	yes	characteristic
16	C₅×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic, complemented
17	C₃×D₁₅	—	6	2	no	—
18	C₃×C₅×D₃	—	6	2	no	—
19	C₃²×D₅	—	2	2	no	—
20	C₃²×D₅	—	4	2	no	—
21	C₃²×D₅	C₃×C₄	1	1	yes	characteristic, complemented
22	C₂×#157	—	5	1	no	—
23	C₂×C₃×D₅	—	9	1	no	—
24	D₃×D₅	—	6	2	no	—
25	C₃×AGL(1,𝔽₅)	—	9	2	no	—
26	C₂×C₃³	—	5	1	no	—
27	C₃×C₃⋊D₃	—	5	1	no	—
28	C₃×C₃⋊D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
29	C₃²×C₅	—	2	2	no	—
30	C₃²×C₅	—	4	2	no	—
31	C₃²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
32	C₂×AGL(1,𝔽₅)	—	9	1	no	Hall
33	C₂×C₃⋊D₃	—	5	1	no	—
34	C₂×C₃×D₃	—	30	2	no	—
35	#157	—	5	2	no	—
36	C₂×C₃×C₅	—	9	1	no	—
37	D₁₅	—	6	2	no	—
38	C₃×D₅	—	2	2	no	—
39	C₃×D₅	—	4	2	no	—
40	C₃×D₅	—	9	1	no	—
41	C₃×D₅	#157	1	1	yes	characteristic, complemented
42	C₅×D₃	—	6	2	no	—
43	C₃³	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₄	—	45	1	no	—
45	C₂×D₅	—	9	1	no	—
46	AGL(1,𝔽₅)	—	9	2	no	—
47	C₂×C₃²	—	5	1	no	—
48	C₂×C₃²	—	10	2	no	—
49	C₂×C₃²	—	20	2	no	—
50	C₃⋊D₃	—	5	1	no	—
51	C₃⋊D₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
52	C₃×D₃	—	6	2	no	—
53	C₃×D₃	—	30	2	no	—
54	C₃×C₅	—	2	2	no	—
55	C₃×C₅	—	4	2	no	—
56	C₃×C₅	C₂×#157	1	1	yes	characteristic, complemented
57	C₂²×C₃	—	45	1	no	—
58	C₂×D₃	—	30	2	no	—
59	C₃×C₄	—	45	2	no	—
60	C₂×C₅	—	9	1	no	—
61	D₅	—	9	1	no	—
62	D₅	C₃×#157	1	1	yes	characteristic, complemented
63	C₃²	—	2	2	no	—
64	C₃²	—	4	2	no	—
65	C₃²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
66	C₂×C₄	—	45	1	no	Sylow
67	C₂×C₃	—	5	1	no	—
68	C₂×C₃	—	9	1	no	—
69	C₂×C₃	—	10	2	no	—
70	C₂×C₃	—	20	2	no	—
71	C₂×C₃	—	45	1	no	—
72	D₃	—	6	2	no	—
73	D₃	—	30	2	no	—
74	C₅	C₂×C₃×#157	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	45	1	no	—
76	C₄	—	45	2	no	—
77	C₃	—	2	2	no	—
78	C₃	—	4	2	no	—
79	C₃	D₅⋊#157	1	1	yes	characteristic, direct product factor
80	C₂	—	5	1	no	—
81	C₂	—	9	1	no	—
82	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅⋊#157
commutator, hypocenter	C₃²×C₅	C₂×C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃³×C₅	C₂×C₄
prime radical	C₃×D₅×C₃⋊D₃	C₂
cosocle	C₃⋊D₁₅	C₂²×C₃
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#4380	C₂	semidirect
3. D₅⋊#157	C₃	direct (N × H)
5. C₃×C₅×C₃⋊D₃	C₄	semidirect
6. C₃³×D₅	C₄	semidirect
10. #4380	C₂×C₃	semidirect
11. C₃³×C₅	C₂×C₄	semidirect
16. C₅×C₃⋊D₃	C₃×C₄	semidirect
21. C₃²×D₅	C₃×C₄	semidirect
28. C₃×C₃⋊D₃	AGL(1,𝔽₅)	semidirect
31. C₃²×C₅	C₂×C₃×C₄	semidirect
41. C₃×D₅	#157	semidirect
43. C₃³	C₂×AGL(1,𝔽₅)	semidirect
51. C₃⋊D₃	C₃×AGL(1,𝔽₅)	semidirect
56. C₃×C₅	C₂×#157	semidirect
62. D₅	C₃×#157	semidirect
65. C₃²	C₂×C₃×AGL(1,𝔽₅)	semidirect
74. C₅	C₂×C₃×#157	semidirect
79. C₃	D₅⋊#157	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×C₃⋊D₃	2
C₃×#4380	2
D₅⋊#157	3
C₂×C₃×#157	5
C₂×C₃×AGL(1,𝔽₅)	9

Subgroups — C3×D5⋊#157 #11762164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅⋊#157 #11762164