Subgroups — C₂×C₃×C₅×#564 #14276564

Order 1920.

1792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#564	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×C₅×#125	C₂	1	15	yes	maximal
3	C₂×C₅×#564	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×#125	C₂²	1	120	yes	—
5	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	30	yes	—
6	C₂×C₃×C₄²×C₅	C₂²	1	5	yes	—
7	C₂×C₃×#564	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#564	C₂×C₃	1	16	yes	direct product factor
9	C₂×C₅×#125	C₂×C₃	1	15	yes	—
10	C₂²×C₃×C₄×C₅	C₂³	1	15	yes	—
11	C₃×C₅×C₄⋊C₄	C₂³	1	120	yes	—
12	C₃×C₄²×C₅	C₂³	1	20	yes	—
13	C₃×#564	C₂×C₅	1	16	yes	direct product factor
14	C₂×C₃×#125	C₂×C₅	1	15	yes	—
15	C₅×#125	C₂²×C₃	1	120	yes	—
16	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	30	yes	—
17	C₂×C₄²×C₅	C₂²×C₃	1	5	yes	—
18	C₂×#564	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
20	C₂×C₃×C₄×C₅	—	2	30	no	—
21	C₂×C₃×C₄×C₅	C₂⁴	1	30	yes	—
22	C₃×#125	C₂²×C₅	1	120	yes	—
23	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	30	yes	—
24	C₂×C₃×C₄²	C₂²×C₅	1	5	yes	—
25	C₂²×C₄×C₅	C₂³×C₃	1	15	yes	—
26	C₅×C₄⋊C₄	C₂³×C₃	1	120	yes	—
27	C₄²×C₅	C₂³×C₃	1	20	yes	—
28	#564	C₂×C₃×C₅	1	16	yes	direct product factor
29	C₂×#125	C₂×C₃×C₅	1	15	yes	—
30	C₂²×C₃×C₅	2₋¹⁺⁴	1	6	yes	—
31	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
32	C₃×C₄×C₅	—	2	30	no	—
33	C₂²×C₃×C₄	C₂³×C₅	1	15	yes	—
34	C₃×C₄⋊C₄	C₂³×C₅	1	120	yes	—
35	C₃×C₄²	C₂³×C₅	1	20	yes	—
36	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
37	C₂×C₄×C₅	—	2	30	no	—
38	C₂×C₄×C₅	C₂⁴×C₃	1	30	yes	—
39	#125	C₂²×C₃×C₅	1	120	yes	—
40	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	30	yes	—
41	C₂×C₄²	C₂²×C₃×C₅	1	5	yes	—
42	C₂×C₃×C₅	#564	1	4	yes	direct product factor
43	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	3	yes	—
44	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
45	C₂×C₃×C₄	—	2	30	no	—
46	C₂×C₃×C₄	C₂⁴×C₅	1	30	yes	—
47	C₂²×C₅	C₃×2₋¹⁺⁴	1	6	yes	—
48	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
49	C₄×C₅	—	2	30	no	—
50	C₂²×C₄	C₂³×C₃×C₅	1	15	yes	—
51	C₄⋊C₄	C₂³×C₃×C₅	1	120	yes	—
52	C₄²	C₂³×C₃×C₅	1	20	yes	—
53	C₃×C₅	C₂×#564	1	1	yes	characteristic, direct product factor, Hall
54	C₂²×C₃	C₅×2₋¹⁺⁴	1	6	yes	—
55	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
56	C₃×C₄	—	2	30	no	—
57	C₂×C₅	C₃×#564	1	4	yes	direct product factor
58	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	3	yes	—
59	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
60	C₂×C₄	—	2	30	no	—
61	C₂×C₄	C₂⁴×C₃×C₅	1	30	yes	—
62	C₂×C₃	C₅×#564	1	4	yes	direct product factor
63	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	3	yes	—
64	C₅	C₂×C₃×#564	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²	C₃×C₅×2₋¹⁺⁴	1	6	yes	—
66	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
67	C₄	—	2	30	no	—
68	C₃	C₂×C₅×#564	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×C₅×#564	1	4	yes	direct product factor
70	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#564	C₂	direct (N × H)
3. C₂×C₅×#564	C₃	direct (N × H)
7. C₂×C₃×#564	C₅	direct (N × H)
8. C₅×#564	C₂×C₃	direct (N × H)
13. C₃×#564	C₂×C₅	direct (N × H)
18. C₂×#564	C₃×C₅	direct (N × H)
28. #564	C₂×C₃×C₅	direct (N × H)
42. C₂×C₃×C₅	#564	direct (N × H)
53. C₃×C₅	C₂×#564	direct (N × H)
57. C₂×C₅	C₃×#564	direct (N × H)
62. C₂×C₃	C₅×#564	direct (N × H)
64. C₅	C₂×C₃×#564	direct (N × H)
68. C₃	C₂×C₅×#564	direct (N × H)
69. C₂	C₃×C₅×#564	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×#564	2
C₂×C₃×C₅×#125	2
C₂×C₅×#564	3
C₂×C₃×#564	5

Subgroups — C2×C3×C5×#564 #14276564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#564 #14276564