Subgroups — C₃×C₅×#1712 #14274746

Order 1920.

560 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#493	C₂	1	6	yes	maximal, complemented
2	C₃×C₅×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1712	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×D₈	—	2	12	no	—
5	C₃×C₅×#127	C₂²	1	4	yes	—
6	C₃×C₄×C₅×C₈	C₂²	1	3	yes	—
7	C₃×#1712	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#493	C₂×C₃	1	6	yes	complemented
9	C₅×C₈²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₅×D₄	—	2	12	no	—
11	C₃×C₅×D₈	—	4	24	no	—
12	C₂×C₃×C₅×C₈	D₄	1	6	yes	—
13	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
14	C₃×#493	C₂×C₅	1	6	yes	complemented
15	C₃×C₈²	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂×C₅×D₈	—	2	12	no	—
17	C₅×#127	C₂²×C₃	1	4	yes	—
18	C₄×C₅×C₈	C₂²×C₃	1	3	yes	—
19	#1712	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₂³×C₃×C₅	—	4	4	no	—
21	C₃×C₅×D₄	—	4	24	no	—
22	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
23	C₃×C₅×C₈	D₈	1	12	yes	complemented
24	C₂×C₃×D₈	—	2	12	no	—
25	C₃×#127	C₂²×C₅	1	4	yes	—
26	C₃×C₄×C₈	C₂²×C₅	1	3	yes	—
27	C₂×C₅×D₄	—	2	12	no	—
28	C₅×D₈	—	4	24	no	—
29	C₂×C₅×C₈	C₃×D₄	1	6	yes	—
30	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
31	#493	C₂×C₃×C₅	1	6	yes	complemented
32	C₈²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂²×C₃×C₅	—	8	12	no	—
34	C₂²×C₃×C₅	#127	1	1	yes	characteristic
35	C₃×C₄×C₅	C₂×D₈	1	6	yes	—
36	C₂×C₃×D₄	—	2	12	no	—
37	C₃×D₈	—	4	24	no	—
38	C₂×C₃×C₈	C₅×D₄	1	6	yes	—
39	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
40	C₂³×C₅	—	4	4	no	—
41	C₅×D₄	—	4	24	no	—
42	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
43	C₅×C₈	C₃×D₈	1	12	yes	complemented
44	C₂×D₈	—	2	12	no	—
45	#127	C₂²×C₃×C₅	1	4	yes	—
46	C₄×C₈	C₂²×C₃×C₅	1	3	yes	—
47	C₂×C₃×C₅	—	16	4	no	—
48	C₂×C₃×C₅	#493	1	3	yes	—
49	C₂³×C₃	—	4	4	no	—
50	C₃×D₄	—	4	24	no	—
51	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
52	C₃×C₈	C₅×D₈	1	12	yes	complemented
53	C₂²×C₅	—	8	12	no	—
54	C₂²×C₅	C₃×#127	1	1	yes	characteristic
55	C₄×C₅	C₂×C₃×D₈	1	6	yes	—
56	C₂×D₄	—	2	12	no	—
57	D₈	—	4	24	no	—
58	C₂×C₈	C₃×C₅×D₄	1	6	yes	—
59	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
60	C₃×C₅	#1712	1	1	yes	characteristic, direct product factor, Hall
61	C₂²×C₃	—	8	12	no	—
62	C₂²×C₃	C₅×#127	1	1	yes	characteristic
63	C₃×C₄	C₂×C₅×D₈	1	6	yes	—
64	C₂×C₅	—	16	4	no	—
65	C₂×C₅	C₃×#493	1	3	yes	—
66	C₂³	—	4	4	no	—
67	D₄	—	4	24	no	—
68	C₂×C₄	C₂×C₃×C₅×D₄	1	3	yes	—
69	C₈	C₃×C₅×D₈	1	12	yes	complemented
70	C₂×C₃	—	16	4	no	—
71	C₂×C₃	C₅×#493	1	3	yes	—
72	C₅	C₃×#1712	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	—	8	12	no	—
74	C₂²	C₃×C₅×#127	1	1	yes	characteristic
75	C₄	C₂×C₃×C₅×D₈	1	6	yes	—
76	C₃	C₅×#1712	1	1	yes	characteristic, direct product factor, Sylow
77	C₂	—	16	4	no	—
78	C₂	C₃×C₅×#493	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#493	C₂	semidirect
2. C₃×C₅×C₈²	C₂	semidirect
3. C₅×#1712	C₃	direct (N × H)
7. C₃×#1712	C₅	direct (N × H)
8. C₅×#493	C₂×C₃	semidirect
9. C₅×C₈²	C₂×C₃	semidirect
14. C₃×#493	C₂×C₅	semidirect
15. C₃×C₈²	C₂×C₅	semidirect
19. #1712	C₃×C₅	direct (N × H)
23. C₃×C₅×C₈	D₈	semidirect
31. #493	C₂×C₃×C₅	semidirect
32. C₈²	C₂×C₃×C₅	semidirect
43. C₅×C₈	C₃×D₈	semidirect
52. C₃×C₈	C₅×D₈	semidirect
60. C₃×C₅	#1712	direct (N × H)
69. C₈	C₃×C₅×D₈	semidirect
72. C₅	C₃×#1712	direct (N × H)
76. C₃	C₅×#1712	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×C₅×#493	2
C₃×C₅×C₈²	2
C₅×#1712	3
C₃×#1712	5

Subgroups — C3×C5×#1712 #14274746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1712 #14274746