Subgroups — C₃×D₅×#401 #14332585

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	C₃×D₅×#95	C₂	1	7	yes	maximal
3	C₃×C₅⋊#401	C₂	1	7	yes	maximal, complemented
4	D₅×#401	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₄×D₅	C₂²	1	7	yes	—
6	C₃×C₅×#95	C₂²	1	7	yes	—
7	C₃×#3963	C₂²	1	21	yes	—
8	C₂×C₃×#401	—	5	1	no	maximal, Hall
9	C₅×#401	C₂×C₃	1	1	yes	characteristic, complemented
10	D₅×#95	C₂×C₃	1	7	yes	—
11	C₅⋊#401	C₂×C₃	1	7	yes	complemented
12	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₅	C₂³	1	7	yes	—
14	C₂²×C₃×Dic₅	C₂³	1	7	yes	—
15	C₂×C₃×C₄×D₅	—	2	42	no	—
16	C₃×#401	—	5	7	no	—
17	C₃×#401	D₅	1	1	yes	characteristic, direct product factor
18	C₂×C₃×#95	—	5	7	no	—
19	C₂²×C₄×D₅	C₂²×C₃	1	7	yes	—
20	C₅×#95	C₂²×C₃	1	7	yes	—
21	#3963	C₂²×C₃	1	21	yes	—
22	C₂×#401	—	5	1	no	Sylow
23	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
24	C₂²×C₃×D₅	#41	1	14	yes	—
25	C₂×C₃×C₄×C₅	—	2	21	no	—
26	C₂×C₃×Dic₅	—	2	21	no	—
27	C₃×C₄×D₅	—	4	28	no	—
28	C₂³×C₃×C₄	—	5	7	no	—
29	C₃×#95	—	5	21	no	—
30	C₃×#95	C₂×D₅	1	7	yes	—
31	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
32	C₂²×C₄×C₅	C₂³×C₃	1	7	yes	—
33	C₂²×Dic₅	C₂³×C₃	1	7	yes	—
34	C₂×C₄×D₅	—	2	42	no	—
35	#401	—	5	7	no	—
36	#401	C₃×D₅	1	1	yes	characteristic, direct product factor
37	C₂×#95	—	5	7	no	—
38	C₂²×C₃×C₅	C₂×#41	1	7	yes	—
39	C₂×C₃×D₅	#126	1	28	yes	—
40	C₃×C₄×C₅	—	4	7	no	—
41	C₃×Dic₅	—	4	7	no	—
42	C₂⁴×C₃	—	5	1	no	—
43	C₂²×C₃×C₄	—	5	7	no	—
44	C₂²×C₃×C₄	—	10	42	no	—
45	C₂²×C₃×C₄	C₂²×D₅	1	7	yes	—
46	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
47	C₂²×D₅	C₃×#41	1	14	yes	—
48	C₂×C₄×C₅	—	2	21	no	—
49	C₂×Dic₅	—	2	21	no	—
50	C₄×D₅	—	4	28	no	—
51	C₂³×C₄	—	5	7	no	—
52	#95	—	5	21	no	—
53	#95	C₂×C₃×D₅	1	7	yes	—
54	C₂×C₃×C₅	C₂×#126	1	7	yes	—
55	C₃×D₅	#401	1	8	yes	direct product factor
56	C₂³×C₃	—	5	14	no	—
57	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
58	C₂×C₃×C₄	—	2	21	no	—
59	C₂×C₃×C₄	—	10	21	no	—
60	C₂×C₃×C₄	—	20	28	no	—
61	C₂²×C₅	C₂×C₃×#41	1	7	yes	—
62	C₂×D₅	C₃×#126	1	28	yes	—
63	C₄×C₅	—	4	7	no	—
64	Dic₅	—	4	7	no	—
65	C₂⁴	—	5	1	no	—
66	C₂²×C₄	—	5	7	no	—
67	C₂²×C₄	—	10	42	no	—
68	C₂²×C₄	C₂²×C₃×D₅	1	7	yes	—
69	C₃×C₅	C₂×#401	1	1	yes	characteristic, complemented, Hall
70	C₂²×C₃	—	5	28	no	—
71	C₂²×C₃	D₅×#41	1	7	yes	—
72	C₃×C₄	—	4	7	no	—
73	C₃×C₄	—	20	7	no	—
74	C₂×C₅	C₂×C₃×#126	1	7	yes	—
75	D₅	C₃×#401	1	8	yes	direct product factor
76	C₂³	—	5	14	no	—
77	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
78	C₂×C₄	—	2	21	no	—
79	C₂×C₄	—	10	21	no	—
80	C₂×C₄	—	20	28	no	—
81	C₂×C₃	—	5	8	no	—
82	C₂×C₃	D₅×#126	1	7	yes	—
83	C₅	C₂×C₃×#401	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	5	28	no	—
85	C₂²	C₃×D₅×#41	1	7	yes	—
86	C₄	—	4	7	no	—
87	C₄	—	20	7	no	—
88	C₃	D₅×#401	1	1	yes	characteristic, direct product factor, Sylow
89	C₂	—	5	8	no	—
90	C₂	C₃×D₅×#126	1	7	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂³×C₅	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#401	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₃×#401	D₅
hypocenter	C₅	C₂×C₃×#401
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#401

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#401	C₂	semidirect
3. C₃×C₅⋊#401	C₂	semidirect
4. D₅×#401	C₃	direct (N × H)
9. C₅×#401	C₂×C₃	semidirect
11. C₅⋊#401	C₂×C₃	semidirect
17. C₃×#401	D₅	direct (N × H)
36. #401	C₃×D₅	direct (N × H)
55. C₃×D₅	#401	direct (N × H)
69. C₃×C₅	C₂×#401	semidirect
75. D₅	C₃×#401	direct (N × H)
83. C₅	C₂×C₃×#401	semidirect
88. C₃	D₅×#401	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×#401	2
C₃×D₅×#95	2
C₃×C₅⋊#401	2
D₅×#401	3
C₂×C₃×#401	5

Subgroups — C3×D5×#401 #14332585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#401 #14332585