Subgroups — C₃×C₅×#1840 #14274874

Order 1920.

392 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#336	C₂	1	6	yes	maximal
3	C₅×#1840	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	—
5	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
6	C₃×C₅×#95	C₄	1	4	yes	—
7	C₃×#1840	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#376	C₂×C₃	1	1	yes	characteristic
9	C₅×#336	C₂×C₃	1	6	yes	—
10	C₂²×C₃×C₄×C₅	C₂×C₄	1	6	yes	—
11	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
12	C₂×C₃×C₅×C₈	—	2	12	no	—
13	C₃×C₄²×C₅	—	2	6	no	—
14	C₃×#376	C₂×C₅	1	1	yes	characteristic
15	C₃×#336	C₂×C₅	1	6	yes	—
16	C₂²×C₅×C₈	C₂²×C₃	1	4	yes	—
17	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
18	C₅×#95	C₃×C₄	1	4	yes	—
19	#1840	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₃×C₄×C₅	—	2	6	no	—
22	C₂×C₃×C₄×C₅	—	2	12	no	—
23	C₂×C₃×C₄×C₅	#41	1	6	yes	—
24	C₃×C₅×C₈	—	4	4	no	—
25	C₂²×C₃×C₈	C₂²×C₅	1	4	yes	—
26	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
27	C₃×#95	C₄×C₅	1	4	yes	—
28	C₂²×C₄×C₅	C₂×C₃×C₄	1	6	yes	—
29	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
30	C₂×C₅×C₈	—	2	12	no	—
31	C₄²×C₅	—	2	6	no	—
32	#376	C₂×C₃×C₅	1	1	yes	characteristic
33	#336	C₂×C₃×C₅	1	6	yes	—
34	C₂²×C₃×C₅	#117	1	3	yes	—
35	C₂²×C₃×C₅	#131	1	4	yes	—
36	C₃×C₄×C₅	—	4	6	no	—
37	C₃×C₄×C₅	#126	1	4	yes	—
38	C₂²×C₃×C₄	C₂×C₄×C₅	1	6	yes	—
39	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
40	C₂×C₃×C₈	—	2	12	no	—
41	C₃×C₄²	—	2	6	no	—
42	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅	—	2	6	no	—
44	C₂×C₄×C₅	—	2	12	no	—
45	C₂×C₄×C₅	C₃×#41	1	6	yes	—
46	C₅×C₈	—	4	4	no	—
47	C₂²×C₈	C₂²×C₃×C₅	1	4	yes	—
48	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	—
49	#95	C₃×C₄×C₅	1	4	yes	—
50	C₂×C₃×C₅	#383	1	1	yes	characteristic
51	C₂×C₃×C₅	#433	1	6	yes	—
52	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
53	C₂×C₃×C₄	—	2	6	no	—
54	C₂×C₃×C₄	—	2	12	no	—
55	C₂×C₃×C₄	C₅×#41	1	6	yes	—
56	C₃×C₈	—	4	4	no	—
57	C₂²×C₅	C₃×#117	1	3	yes	—
58	C₂²×C₅	C₃×#131	1	4	yes	—
59	C₄×C₅	—	4	6	no	—
60	C₄×C₅	C₃×#126	1	4	yes	—
61	C₂²×C₄	C₂×C₃×C₄×C₅	1	6	yes	—
62	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
63	C₂×C₈	—	2	12	no	—
64	C₄²	—	2	6	no	—
65	C₃×C₅	#1840	1	1	yes	characteristic, direct product factor, Hall
66	C₂²×C₃	C₅×#117	1	3	yes	—
67	C₂²×C₃	C₅×#131	1	4	yes	—
68	C₃×C₄	—	4	6	no	—
69	C₃×C₄	C₅×#126	1	4	yes	—
70	C₂×C₅	C₃×#383	1	1	yes	characteristic
71	C₂×C₅	C₃×#433	1	6	yes	—
72	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	12	no	—
75	C₂×C₄	C₃×C₅×#41	1	6	yes	—
76	C₈	—	4	4	no	—
77	C₂×C₃	C₅×#383	1	1	yes	characteristic
78	C₂×C₃	C₅×#433	1	6	yes	—
79	C₅	C₃×#1840	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	C₃×C₅×#117	1	3	yes	—
81	C₂²	C₃×C₅×#131	1	4	yes	—
82	C₄	—	4	6	no	—
83	C₄	C₃×C₅×#126	1	4	yes	—
84	C₃	C₅×#1840	1	1	yes	characteristic, direct product factor, Sylow
85	C₂	C₃×C₅×#383	1	1	yes	characteristic
86	C₂	C₃×C₅×#433	1	6	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂³	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1840	C₃	direct (N × H)
7. C₃×#1840	C₅	direct (N × H)
19. #1840	C₃×C₅	direct (N × H)
65. C₃×C₅	#1840	direct (N × H)
79. C₅	C₃×#1840	direct (N × H)
84. C₃	C₅×#1840	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×#376	2
C₃×C₅×#336	2
C₅×#1840	3
C₃×#1840	5

Subgroups — C3×C5×#1840 #14274874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1840 #14274874