Subgroups — C₅×D₃×#401 #14332584

Order 1920.

1032 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×#95	C₂	1	7	yes	maximal
3	C₅×C₃⋊#401	C₂	1	7	yes	maximal, complemented
4	C₂×C₅×#401	—	3	1	no	maximal, Hall
5	C₂²×C₄×C₅×D₃	C₂²	1	7	yes	—
6	C₃×C₅×#95	C₂²	1	7	yes	—
7	C₅×C₃⋊#95	C₂²	1	21	yes	—
8	D₃×#401	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×#401	—	3	7	no	—
10	C₅×#401	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₅×#95	—	3	7	no	—
12	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₅	C₂³	1	7	yes	—
14	C₂²×C₅×Dic₃	C₂³	1	7	yes	—
15	C₂×C₄×C₅×D₃	—	2	42	no	—
16	C₃×#401	C₂×C₅	1	1	yes	characteristic, complemented
17	D₃×#95	C₂×C₅	1	7	yes	—
18	C₃⋊#401	C₂×C₅	1	7	yes	complemented
19	C₂³×C₄×C₅	—	3	7	no	—
20	C₅×#95	—	3	21	no	—
21	C₅×#95	C₂×D₃	1	7	yes	—
22	C₂×#401	—	3	1	no	Sylow
23	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
24	C₂²×C₅×D₃	#41	1	14	yes	—
25	C₂×C₃×C₄×C₅	—	2	21	no	—
26	C₂×C₅×Dic₃	—	2	21	no	—
27	C₄×C₅×D₃	—	4	28	no	—
28	C₂²×C₄×D₃	C₂²×C₅	1	7	yes	—
29	C₃×#95	C₂²×C₅	1	7	yes	—
30	C₃⋊#95	C₂²×C₅	1	21	yes	—
31	C₂⁴×C₅	—	3	1	no	—
32	C₂²×C₄×C₅	—	3	7	no	—
33	C₂²×C₄×C₅	—	6	42	no	—
34	C₂²×C₄×C₅	C₂²×D₃	1	7	yes	—
35	#401	—	3	7	no	—
36	#401	C₅×D₃	1	1	yes	characteristic, direct product factor
37	C₂×#95	—	3	7	no	—
38	C₂²×C₃×C₅	C₂×#41	1	7	yes	—
39	C₂×C₅×D₃	#126	1	28	yes	—
40	C₃×C₄×C₅	—	4	7	no	—
41	C₅×Dic₃	—	4	7	no	—
42	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
43	C₂²×C₃×C₄	C₂³×C₅	1	7	yes	—
44	C₂²×Dic₃	C₂³×C₅	1	7	yes	—
45	C₂×C₄×D₃	—	2	42	no	—
46	C₂³×C₅	—	3	14	no	—
47	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
48	C₂×C₄×C₅	—	2	21	no	—
49	C₂×C₄×C₅	—	6	21	no	—
50	C₂×C₄×C₅	—	12	28	no	—
51	C₂³×C₄	—	3	7	no	—
52	#95	—	3	21	no	—
53	#95	C₂×C₅×D₃	1	7	yes	—
54	C₂×C₃×C₅	C₂×#126	1	7	yes	—
55	C₅×D₃	#401	1	8	yes	direct product factor
56	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
57	C₂²×D₃	C₅×#41	1	14	yes	—
58	C₂×C₃×C₄	—	2	21	no	—
59	C₂×Dic₃	—	2	21	no	—
60	C₄×D₃	—	4	28	no	—
61	C₂²×C₅	—	3	28	no	—
62	C₂²×C₅	D₃×#41	1	7	yes	—
63	C₄×C₅	—	4	7	no	—
64	C₄×C₅	—	12	7	no	—
65	C₂⁴	—	3	1	no	—
66	C₂²×C₄	—	3	7	no	—
67	C₂²×C₄	—	6	42	no	—
68	C₂²×C₄	C₂²×C₅×D₃	1	7	yes	—
69	C₃×C₅	C₂×#401	1	1	yes	characteristic, complemented, Hall
70	C₂²×C₃	C₂×C₅×#41	1	7	yes	—
71	C₂×D₃	C₅×#126	1	28	yes	—
72	C₃×C₄	—	4	7	no	—
73	Dic₃	—	4	7	no	—
74	C₂×C₅	—	3	8	no	—
75	C₂×C₅	D₃×#126	1	7	yes	—
76	C₂³	—	3	14	no	—
77	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
78	C₂×C₄	—	2	21	no	—
79	C₂×C₄	—	6	21	no	—
80	C₂×C₄	—	12	28	no	—
81	C₂×C₃	C₂×C₅×#126	1	7	yes	—
82	D₃	C₅×#401	1	8	yes	direct product factor
83	C₅	D₃×#401	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	—	3	28	no	—
85	C₂²	C₅×D₃×#41	1	7	yes	—
86	C₄	—	4	7	no	—
87	C₄	—	12	7	no	—
88	C₃	C₂×C₅×#401	1	1	yes	characteristic, complemented, Sylow
89	C₂	—	3	8	no	—
90	C₂	C₅×D₃×#126	1	7	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#401	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
hypercenter	C₅×#401	D₃
hypocenter	C₃	C₂×C₅×#401
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#401

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#401	C₂	semidirect
3. C₅×C₃⋊#401	C₂	semidirect
8. D₃×#401	C₅	direct (N × H)
10. C₅×#401	D₃	direct (N × H)
16. C₃×#401	C₂×C₅	semidirect
18. C₃⋊#401	C₂×C₅	semidirect
36. #401	C₅×D₃	direct (N × H)
55. C₅×D₃	#401	direct (N × H)
69. C₃×C₅	C₂×#401	semidirect
82. D₃	C₅×#401	direct (N × H)
83. C₅	D₃×#401	direct (N × H)
88. C₃	C₂×C₅×#401	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#401	2
C₅×D₃×#95	2
C₅×C₃⋊#401	2
C₂×C₅×#401	3
D₃×#401	5

Subgroups — C5×D3×#401 #14332584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#401 #14332584