Subgroups — C₃×C₅×#1842 #14274876

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#1842	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	—
5	C₂×C₃×C₄²×C₅	C₄	1	3	yes	—
6	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
8	C₃×C₅×C₄⋊C₈	—	2	12	no	—
9	C₃×#1842	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₄⋊C₈	C₂×C₃	1	6	yes	—
11	C₄³×C₅	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
13	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
14	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×C₃×C₅×C₈	—	2	12	no	—
16	C₃×C₄²×C₅	—	2	6	no	—
17	C₃×C₄²×C₅	C₈	1	4	yes	complemented
18	C₃×C₄²×C₅	D₄	1	6	yes	—
19	C₃×C₄²×C₅	Q₈	1	6	yes	—
20	C₂×C₃×C₄⋊C₈	C₂×C₅	1	6	yes	—
21	C₃×C₄³	C₂×C₅	1	1	yes	characteristic
22	C₂²×C₅×C₈	C₂²×C₃	1	4	yes	—
23	C₂×C₄²×C₅	C₃×C₄	1	3	yes	—
24	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
26	C₅×C₄⋊C₈	—	2	12	no	—
27	#1842	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄×C₅	—	2	6	no	—
30	C₂×C₃×C₄×C₅	C₄⋊C₄	1	6	yes	—
31	C₂×C₃×C₄×C₅	C₄⋊C₄	1	6	yes	—
32	C₂×C₃×C₄×C₅	C₂×C₈	1	6	yes	—
33	C₂×C₃×C₄×C₅	M₁₆	1	6	yes	—
34	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
35	C₂×C₃×C₄×C₅	C₂×Q₈	1	3	yes	—
36	C₃×C₅×C₈	—	4	4	no	—
37	C₂²×C₃×C₈	C₂²×C₅	1	4	yes	—
38	C₂×C₃×C₄²	C₄×C₅	1	3	yes	—
39	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic
40	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
41	C₃×C₄⋊C₈	—	2	12	no	—
42	C₂²×C₄×C₅	C₂×C₃×C₄	1	3	yes	—
43	C₂²×C₄×C₅	C₂×C₃×C₄	1	3	yes	—
44	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
45	C₂×C₅×C₈	—	2	12	no	—
46	C₄²×C₅	—	2	6	no	—
47	C₄²×C₅	C₃×C₈	1	4	yes	complemented
48	C₄²×C₅	C₃×D₄	1	6	yes	—
49	C₄²×C₅	C₃×Q₈	1	6	yes	—
50	C₂×C₄⋊C₈	C₂×C₃×C₅	1	6	yes	—
51	C₄³	C₂×C₃×C₅	1	1	yes	characteristic
52	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	3	yes	—
53	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
54	C₂²×C₃×C₅	C₂×M₁₆	1	3	yes	—
55	C₃×C₄×C₅	—	2	6	no	—
56	C₃×C₄×C₅	C₄⋊C₈	1	12	yes	complemented
57	C₃×C₄×C₅	#127	1	1	yes	characteristic
58	C₃×C₄×C₅	C₄⋊Q₈	1	3	yes	—
59	C₂²×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
60	C₂²×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
61	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
62	C₂×C₃×C₈	—	2	12	no	—
63	C₃×C₄²	—	2	6	no	—
64	C₃×C₄²	C₅×C₈	1	4	yes	complemented
65	C₃×C₄²	C₅×D₄	1	6	yes	—
66	C₃×C₄²	C₅×Q₈	1	6	yes	—
67	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅	—	2	6	no	—
69	C₂×C₄×C₅	C₃×C₄⋊C₄	1	6	yes	—
70	C₂×C₄×C₅	C₃×C₄⋊C₄	1	6	yes	—
71	C₂×C₄×C₅	C₂×C₃×C₈	1	6	yes	—
72	C₂×C₄×C₅	C₃×M₁₆	1	6	yes	—
73	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
74	C₂×C₄×C₅	C₂×C₃×Q₈	1	3	yes	—
75	C₅×C₈	—	4	4	no	—
76	C₂²×C₈	C₂²×C₃×C₅	1	4	yes	—
77	C₂×C₄²	C₃×C₄×C₅	1	3	yes	—
78	C₂×C₄²	C₃×C₄×C₅	1	1	yes	characteristic
79	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	—
80	C₄⋊C₈	—	2	12	no	—
81	C₂×C₃×C₅	#384	1	1	yes	characteristic
82	C₂×C₃×C₅	C₂×C₄⋊C₈	1	3	yes	—
83	C₂×C₃×C₅	#423	1	3	yes	—
84	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
85	C₂×C₃×C₄	—	2	6	no	—
86	C₂×C₃×C₄	C₅×C₄⋊C₄	1	6	yes	—
87	C₂×C₃×C₄	C₅×C₄⋊C₄	1	6	yes	—
88	C₂×C₃×C₄	C₂×C₅×C₈	1	6	yes	—
89	C₂×C₃×C₄	C₅×M₁₆	1	6	yes	—
90	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
91	C₂×C₃×C₄	C₂×C₅×Q₈	1	3	yes	—
92	C₃×C₈	—	4	4	no	—
93	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	3	yes	—
94	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
95	C₂²×C₅	C₂×C₃×M₁₆	1	3	yes	—
96	C₄×C₅	—	2	6	no	—
97	C₄×C₅	C₃×C₄⋊C₈	1	12	yes	complemented
98	C₄×C₅	C₃×#127	1	1	yes	characteristic
99	C₄×C₅	C₃×C₄⋊Q₈	1	3	yes	—
100	C₂²×C₄	C₂×C₃×C₄×C₅	1	3	yes	—
101	C₂²×C₄	C₂×C₃×C₄×C₅	1	3	yes	—
102	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
103	C₂×C₈	—	2	12	no	—
104	C₄²	—	2	6	no	—
105	C₄²	C₃×C₅×C₈	1	4	yes	complemented
106	C₄²	C₃×C₅×D₄	1	6	yes	—
107	C₄²	C₃×C₅×Q₈	1	6	yes	—
108	C₃×C₅	#1842	1	1	yes	characteristic, direct product factor, Hall
109	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	3	yes	—
110	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
111	C₂²×C₃	C₂×C₅×M₁₆	1	3	yes	—
112	C₃×C₄	—	2	6	no	—
113	C₃×C₄	C₅×C₄⋊C₈	1	12	yes	complemented
114	C₃×C₄	C₅×#127	1	1	yes	characteristic
115	C₃×C₄	C₅×C₄⋊Q₈	1	3	yes	—
116	C₂×C₅	C₃×#384	1	1	yes	characteristic
117	C₂×C₅	C₂×C₃×C₄⋊C₈	1	3	yes	—
118	C₂×C₅	C₃×#423	1	3	yes	—
119	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
120	C₂×C₄	—	2	6	no	—
121	C₂×C₄	C₃×C₅×C₄⋊C₄	1	6	yes	—
122	C₂×C₄	C₃×C₅×C₄⋊C₄	1	6	yes	—
123	C₂×C₄	C₂×C₃×C₅×C₈	1	6	yes	—
124	C₂×C₄	C₃×C₅×M₁₆	1	6	yes	—
125	C₂×C₄	C₂×C₃×C₅×D₄	1	3	yes	—
126	C₂×C₄	C₂×C₃×C₅×Q₈	1	3	yes	—
127	C₈	—	4	4	no	—
128	C₂×C₃	C₅×#384	1	1	yes	characteristic
129	C₂×C₃	C₂×C₅×C₄⋊C₈	1	3	yes	—
130	C₂×C₃	C₅×#423	1	3	yes	—
131	C₅	C₃×#1842	1	1	yes	characteristic, direct product factor, Sylow
132	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	3	yes	—
133	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
134	C₂²	C₂×C₃×C₅×M₁₆	1	3	yes	—
135	C₄	—	2	6	no	—
136	C₄	C₃×C₅×C₄⋊C₈	1	12	yes	complemented
137	C₄	C₃×C₅×#127	1	1	yes	characteristic
138	C₄	C₃×C₅×C₄⋊Q₈	1	3	yes	—
139	C₃	C₅×#1842	1	1	yes	characteristic, direct product factor, Sylow
140	C₂	C₃×C₅×#384	1	1	yes	characteristic
141	C₂	C₂×C₃×C₅×C₄⋊C₈	1	3	yes	—
142	C₂	C₃×C₅×#423	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ 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×#1842	C₃	direct (N × H)
9. C₃×#1842	C₅	direct (N × H)
17. C₃×C₄²×C₅	C₈	semidirect
27. #1842	C₃×C₅	direct (N × H)
47. C₄²×C₅	C₃×C₈	semidirect
56. C₃×C₄×C₅	C₄⋊C₈	semidirect
64. C₃×C₄²	C₅×C₈	semidirect
97. C₄×C₅	C₃×C₄⋊C₈	semidirect
105. C₄²	C₃×C₅×C₈	semidirect
108. C₃×C₅	#1842	direct (N × H)
113. C₃×C₄	C₅×C₄⋊C₈	semidirect
131. C₅	C₃×#1842	direct (N × H)
136. C₄	C₃×C₅×C₄⋊C₈	semidirect
139. C₃	C₅×#1842	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₄³×C₅	2
C₅×#1842	3
C₃×#1842	5

Subgroups — C3×C5×#1842 #14274876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1842 #14274876