Subgroups — C₃×C₅×#1534 #14274568

Order 1920.

392 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	2	yes	maximal
3	C₃×C₅×#330	C₂	1	4	yes	maximal, complemented
4	C₅×#1534	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×#125	—	2	2	no	—
6	C₃×C₅×#125	C₄	1	2	yes	—
7	C₃×C₅×#125	C₂²	1	2	yes	—
8	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
9	C₂×C₃×C₅×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₄⋊C₈	—	2	2	no	—
12	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
13	C₃×C₅×#97	C₂²	1	4	yes	—
14	C₃×#1534	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
16	C₅×#432	C₂×C₃	1	2	yes	—
17	C₅×#330	C₂×C₃	1	4	yes	complemented
18	C₂²×C₃×C₄×C₅	—	2	2	no	—
19	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
21	C₂×C₃×C₅×C₈	—	2	4	no	—
22	C₃×C₅×C₄⋊C₄	—	2	4	no	—
23	C₃×C₅×C₄⋊C₄	—	2	2	no	—
24	C₃×C₅×C₄⋊C₄	—	2	4	no	—
25	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
26	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
27	C₃×C₄²×C₅	D₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
30	C₃×#432	C₂×C₅	1	2	yes	—
31	C₃×#330	C₂×C₅	1	4	yes	complemented
32	C₅×#125	—	2	2	no	—
33	C₅×#125	C₃×C₄	1	2	yes	—
34	C₅×#125	C₂²×C₃	1	2	yes	—
35	C₂×C₅×C₄⋊C₄	—	2	2	no	—
36	C₂×C₅×C₄⋊C₄	C₃×C₄	1	2	yes	—
37	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
38	C₅×C₄⋊C₈	—	2	2	no	—
39	C₅×C₂²⋊C₈	—	2	2	no	—
40	C₅×#97	C₂²×C₃	1	4	yes	—
41	#1534	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₅	—	2	2	no	—
44	C₂×C₃×C₄×C₅	—	2	4	no	—
45	C₂×C₃×C₄×C₅	—	4	2	no	—
46	C₂×C₃×C₄×C₅	—	4	4	no	—
47	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
51	C₃×C₅×C₈	—	4	4	no	—
52	C₃×#125	—	2	2	no	—
53	C₃×#125	C₄×C₅	1	2	yes	—
54	C₃×#125	C₂²×C₅	1	2	yes	—
55	C₂×C₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
57	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
58	C₃×C₄⋊C₈	—	2	2	no	—
59	C₃×C₂²⋊C₈	—	2	2	no	—
60	C₃×#97	C₂²×C₅	1	4	yes	—
61	C₂²×C₄×C₅	—	2	2	no	—
62	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
64	C₂×C₅×C₈	—	2	4	no	—
65	C₅×C₄⋊C₄	—	2	4	no	—
66	C₅×C₄⋊C₄	—	2	2	no	—
67	C₅×C₄⋊C₄	—	2	4	no	—
68	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
69	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
70	C₄²×C₅	C₃×D₄	1	2	yes	—
71	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
72	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
73	#432	C₂×C₃×C₅	1	2	yes	—
74	#330	C₂×C₃×C₅	1	4	yes	complemented
75	C₂²×C₃×C₅	—	2	2	no	—
76	C₂²×C₃×C₅	#101	1	2	yes	—
77	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₃×C₄×C₅	—	2	1	no	—
79	C₃×C₄×C₅	—	2	1	no	—
80	C₃×C₄×C₅	—	2	2	no	—
81	C₃×C₄×C₅	—	2	2	no	—
82	C₃×C₄×C₅	—	4	4	no	—
83	C₂²×C₃×C₄	—	2	2	no	—
84	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
85	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
86	C₂×C₃×C₈	—	2	4	no	—
87	C₃×C₄⋊C₄	—	2	4	no	—
88	C₃×C₄⋊C₄	—	2	2	no	—
89	C₃×C₄⋊C₄	—	2	4	no	—
90	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
91	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
92	C₃×C₄²	C₅×D₄	1	2	yes	—
93	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
94	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₅	—	2	2	no	—
96	C₂×C₄×C₅	—	2	4	no	—
97	C₂×C₄×C₅	—	4	2	no	—
98	C₂×C₄×C₅	—	4	4	no	—
99	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
100	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
102	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
103	C₅×C₈	—	4	4	no	—
104	#125	—	2	2	no	—
105	#125	C₃×C₄×C₅	1	2	yes	—
106	#125	C₂²×C₃×C₅	1	2	yes	—
107	C₂×C₄⋊C₄	—	2	2	no	—
108	C₂×C₄⋊C₄	C₃×C₄×C₅	1	2	yes	—
109	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
110	C₄⋊C₈	—	2	2	no	—
111	C₂²⋊C₈	—	2	2	no	—
112	#97	C₂²×C₃×C₅	1	4	yes	—
113	C₂×C₃×C₅	—	2	2	no	—
114	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
115	C₂×C₃×C₅	#421	1	2	yes	—
116	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₃×C₄	—	2	2	no	—
118	C₂×C₃×C₄	—	2	4	no	—
119	C₂×C₃×C₄	—	4	2	no	—
120	C₂×C₃×C₄	—	4	4	no	—
121	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
122	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
125	C₃×C₈	—	4	4	no	—
126	C₂²×C₅	—	2	2	no	—
127	C₂²×C₅	C₃×#101	1	2	yes	—
128	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
129	C₄×C₅	—	2	1	no	—
130	C₄×C₅	—	2	1	no	—
131	C₄×C₅	—	2	2	no	—
132	C₄×C₅	—	2	2	no	—
133	C₄×C₅	—	4	4	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
136	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
137	C₂×C₈	—	2	4	no	—
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	—	2	4	no	—
141	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
142	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
143	C₄²	C₃×C₅×D₄	1	2	yes	—
144	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
145	C₃×C₅	#1534	1	1	yes	characteristic, direct product factor, Hall
146	C₂²×C₃	—	2	2	no	—
147	C₂²×C₃	C₅×#101	1	2	yes	—
148	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
149	C₃×C₄	—	2	1	no	—
150	C₃×C₄	—	2	1	no	—
151	C₃×C₄	—	2	2	no	—
152	C₃×C₄	—	2	2	no	—
153	C₃×C₄	—	4	4	no	—
154	C₂×C₅	—	2	2	no	—
155	C₂×C₅	C₂×C₃×#101	1	1	yes	characteristic
156	C₂×C₅	C₃×#421	1	2	yes	—
157	C₂³	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
165	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
166	C₈	—	4	4	no	—
167	C₂×C₃	—	2	2	no	—
168	C₂×C₃	C₂×C₅×#101	1	1	yes	characteristic
169	C₂×C₃	C₅×#421	1	2	yes	—
170	C₅	C₃×#1534	1	1	yes	characteristic, direct product factor, Sylow
171	C₂²	—	2	2	no	—
172	C₂²	C₃×C₅×#101	1	2	yes	—
173	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	4	4	no	—
179	C₃	C₅×#1534	1	1	yes	characteristic, direct product factor, Sylow
180	C₂	—	2	2	no	—
181	C₂	C₂×C₃×C₅×#101	1	1	yes	characteristic
182	C₂	C₃×C₅×#421	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#330	C₂	semidirect
4. C₅×#1534	C₃	direct (N × H)
14. C₃×#1534	C₅	direct (N × H)
17. C₅×#330	C₂×C₃	semidirect
31. C₃×#330	C₂×C₅	semidirect
41. #1534	C₃×C₅	direct (N × H)
74. #330	C₂×C₃×C₅	semidirect
145. C₃×C₅	#1534	direct (N × H)
170. C₅	C₃×#1534	direct (N × H)
179. C₃	C₅×#1534	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×#125	2
C₃×C₅×#432	2
C₃×C₅×#330	2
C₅×#1534	3
C₃×#1534	5

Subgroups — C3×C5×#1534 #14274568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1534 #14274568