Subgroups — C₃×C₅×#2104 #14275138

Order 1920.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#342	C₂	1	7	yes	maximal
2	C₅×#2104	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	7	yes	—
4	C₃×#2104	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#342	C₂×C₃	1	7	yes	—
6	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
7	C₂²×C₃×C₄×C₅	—	2	7	no	—
8	C₃×C₅×C₂²⋊C₄	—	2	14	no	—
9	C₃×#342	C₂×C₅	1	7	yes	—
10	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	7	yes	—
11	#2104	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³×C₃×C₅	—	8	1	no	—
13	C₂³×C₃×C₅	#41	1	7	yes	—
14	C₂×C₃×C₄×C₅	—	4	7	no	—
15	C₂×C₃×C₄×C₅	—	8	7	no	—
16	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	7	yes	—
17	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
18	C₂²×C₄×C₅	—	2	7	no	—
19	C₅×C₂²⋊C₄	—	2	14	no	—
20	#342	C₂×C₃×C₅	1	7	yes	—
21	C₂²×C₃×C₅	—	4	7	no	—
22	C₂²×C₃×C₅	#126	1	7	yes	—
23	C₃×C₄×C₅	—	8	7	no	—
24	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
25	C₂²×C₃×C₄	—	2	7	no	—
26	C₃×C₂²⋊C₄	—	2	14	no	—
27	C₂³×C₅	—	8	1	no	—
28	C₂³×C₅	C₃×#41	1	7	yes	—
29	C₂×C₄×C₅	—	4	7	no	—
30	C₂×C₄×C₅	—	8	7	no	—
31	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	7	yes	—
32	C₂×C₃×C₅	—	2	7	no	—
33	C₂×C₃×C₅	#401	1	1	yes	characteristic
34	C₂³×C₃	—	8	1	no	—
35	C₂³×C₃	C₅×#41	1	7	yes	—
36	C₂×C₃×C₄	—	4	7	no	—
37	C₂×C₃×C₄	—	8	7	no	—
38	C₂²×C₅	—	4	7	no	—
39	C₂²×C₅	C₃×#126	1	7	yes	—
40	C₄×C₅	—	8	7	no	—
41	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
42	C₂²×C₄	—	2	7	no	—
43	C₂²⋊C₄	—	2	14	no	—
44	C₃×C₅	#2104	1	1	yes	characteristic, direct product factor, Hall
45	C₂²×C₃	—	4	7	no	—
46	C₂²×C₃	C₅×#126	1	7	yes	—
47	C₃×C₄	—	8	7	no	—
48	C₂×C₅	—	2	7	no	—
49	C₂×C₅	C₃×#401	1	1	yes	characteristic
50	C₂³	—	8	1	no	—
51	C₂³	C₃×C₅×#41	1	7	yes	—
52	C₂×C₄	—	4	7	no	—
53	C₂×C₄	—	8	7	no	—
54	C₂×C₃	—	2	7	no	—
55	C₂×C₃	C₅×#401	1	1	yes	characteristic
56	C₅	C₃×#2104	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	—	4	7	no	—
58	C₂²	C₃×C₅×#126	1	7	yes	—
59	C₄	—	8	7	no	—
60	C₃	C₅×#2104	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2	7	no	—
62	C₂	C₃×C₅×#401	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#2104	C₃	direct (N × H)
4. C₃×#2104	C₅	direct (N × H)
11. #2104	C₃×C₅	direct (N × H)
44. C₃×C₅	#2104	direct (N × H)
56. C₅	C₃×#2104	direct (N × H)
60. C₃	C₅×#2104	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×#342	2
C₅×#2104	3
C₃×#2104	5

Subgroups — C3×C5×#2104 #14275138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2104 #14275138