Subgroups — C₃×D₅×#157 #11762165

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×#4379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#157	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×#157	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₃⋊D₁₅	C₄	1	1	yes	characteristic, complemented
6	C₃×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃³×D₅	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃×#157	—	5	1	no	maximal, Hall
9	D₅×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
10	C₃×D₃×D₅	—	6	2	no	—
11	#4379	C₂×C₃	1	1	yes	characteristic, complemented
12	C₅×#157	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃³×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×C₄×D₅	—	9	1	no	maximal
15	C₂×C₃×C₃⋊D₃	—	5	1	no	—
16	C₃×#157	—	5	1	no	—
17	C₃×#157	D₅	1	1	yes	characteristic, direct product factor
18	C₃⋊D₁₅	C₃×C₄	1	1	yes	characteristic, complemented
19	C₅×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
20	C₃×D₁₅	—	6	2	no	—
21	C₃×C₅×D₃	—	6	2	no	—
22	C₃²×D₅	—	2	2	no	—
23	C₃²×D₅	—	4	2	no	—
24	C₃²×D₅	C₃×C₄	1	1	yes	characteristic, complemented
25	C₂×#157	—	5	1	no	—
26	C₂×C₃×D₅	—	9	1	no	—
27	D₃×D₅	—	6	2	no	—
28	C₃×C₄×C₅	—	9	1	no	—
29	C₃×Dic₅	—	9	1	no	—
30	C₂×C₃³	—	5	1	no	—
31	C₃×C₃⋊D₃	—	5	1	no	—
32	C₃×C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
33	C₃²×C₅	—	2	2	no	—
34	C₃²×C₅	—	4	2	no	—
35	C₃²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
36	C₄×D₅	—	9	1	no	Hall
37	C₂×C₃⋊D₃	—	5	1	no	—
38	C₂×C₃×D₃	—	30	2	no	—
39	#157	—	5	1	no	—
40	#157	C₃×D₅	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₅	—	9	1	no	—
42	D₁₅	—	6	2	no	—
43	C₃×D₅	—	2	2	no	—
44	C₃×D₅	—	4	2	no	—
45	C₃×D₅	—	9	1	no	—
46	C₃×D₅	#157	1	1	yes	characteristic, direct product factor
47	C₅×D₃	—	6	2	no	—
48	C₃³	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₄	—	45	1	no	—
50	C₂×D₅	—	9	1	no	—
51	C₄×C₅	—	9	1	no	—
52	Dic₅	—	9	1	no	—
53	C₂×C₃²	—	5	1	no	—
54	C₂×C₃²	—	10	2	no	—
55	C₂×C₃²	—	20	2	no	—
56	C₃⋊D₃	—	5	1	no	—
57	C₃⋊D₃	C₂×C₃×D₅	1	1	yes	characteristic
58	C₃×D₃	—	6	2	no	—
59	C₃×D₃	—	30	2	no	—
60	C₃×C₅	—	2	2	no	—
61	C₃×C₅	—	4	2	no	—
62	C₃×C₅	C₂×#157	1	1	yes	characteristic, complemented
63	C₂²×C₃	—	45	1	no	—
64	C₂×D₃	—	30	2	no	—
65	C₃×C₄	—	9	1	no	—
66	C₃×C₄	—	45	1	no	—
67	C₂×C₅	—	9	1	no	—
68	D₅	—	9	1	no	—
69	D₅	C₃×#157	1	1	yes	characteristic, direct product factor
70	C₃²	—	2	2	no	—
71	C₃²	—	4	2	no	—
72	C₃²	C₃×C₄×D₅	1	1	yes	characteristic, complemented
73	C₂×C₄	—	45	1	no	Sylow
74	C₂×C₃	—	5	1	no	—
75	C₂×C₃	—	9	1	no	—
76	C₂×C₃	—	10	2	no	—
77	C₂×C₃	—	20	2	no	—
78	C₂×C₃	—	45	1	no	—
79	D₃	—	6	2	no	—
80	D₃	—	30	2	no	—
81	C₅	C₂×C₃×#157	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	45	1	no	—
83	C₄	—	9	1	no	—
84	C₄	—	45	1	no	—
85	C₃	—	2	2	no	—
86	C₃	—	4	2	no	—
87	C₃	D₅×#157	1	1	yes	characteristic, direct product factor
88	C₂	—	5	1	no	—
89	C₂	—	9	1	no	—
90	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	C₅×C₃⋊D₃	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×#4379	C₂	semidirect
3. C₃×C₅×#157	C₂	semidirect
4. D₅×#157	C₃	direct (N × H)
5. C₃×C₃⋊D₁₅	C₄	semidirect
7. C₃³×D₅	C₄	semidirect
11. #4379	C₂×C₃	semidirect
12. C₅×#157	C₂×C₃	semidirect
13. C₃³×C₅	C₂×C₄	semidirect
17. C₃×#157	D₅	direct (N × H)
18. C₃⋊D₁₅	C₃×C₄	semidirect
24. C₃²×D₅	C₃×C₄	semidirect
35. C₃²×C₅	C₂×C₃×C₄	semidirect
40. #157	C₃×D₅	direct (N × H)
46. C₃×D₅	#157	direct (N × H)
48. C₃³	C₄×D₅	semidirect
62. C₃×C₅	C₂×#157	semidirect
69. D₅	C₃×#157	direct (N × H)
72. C₃²	C₃×C₄×D₅	semidirect
81. C₅	C₂×C₃×#157	semidirect
87. 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×#4379	2
C₃×C₅×#157	2
D₅×#157	3
C₂×C₃×#157	5
C₃×C₄×D₅	9

Subgroups — C3×D5×#157 #11762165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#157 #11762165