Subgroups — C₃×D₅×#376 #14319347

Order 1920.

1680 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	3	yes	maximal
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65221	C₂	1	3	yes	maximal, complemented
4	C₃×D₅×#95	C₂	1	4	yes	maximal
5	C₃×#64937	C₂	1	4	yes	maximal, complemented
6	D₅×#376	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	6	yes	—
8	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
10	C₂×C₃×C₄×Dic₅	C₂²	1	6	yes	—
11	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	—
12	C₃×C₄²×D₅	C₄	1	24	yes	complemented
13	C₃×C₅×#95	C₂²	1	4	yes	—
14	C₃×#3963	C₂²	1	12	yes	—
15	C₂×C₃×#376	—	5	1	no	maximal, Hall
16	C₂×C₄²×D₅	C₂×C₃	1	3	yes	—
17	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
18	#65221	C₂×C₃	1	3	yes	complemented
19	D₅×#95	C₂×C₃	1	4	yes	—
20	#64937	C₂×C₃	1	4	yes	complemented
21	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
23	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
25	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
26	C₂×C₃×C₄×D₅	—	2	24	no	—
27	C₂×C₃×C₄×D₅	C₂×C₄	1	24	yes	—
28	C₂×C₃×C₄×D₅	C₂×C₄	1	12	yes	—
29	C₃×C₄²×C₅	C₂×C₄	1	12	yes	complemented
30	C₃×C₄×Dic₅	C₂×C₄	1	12	yes	complemented
31	C₃×C₄×Dic₅	C₂×C₄	1	24	yes	complemented
32	C₂²×C₃×C₄²	—	5	3	no	—
33	C₃×#376	—	5	3	no	—
34	C₃×#376	—	5	4	no	—
35	C₃×#376	D₅	1	1	yes	characteristic, direct product factor
36	C₂×C₃×#95	—	5	4	no	—
37	C₂²×C₄×D₅	C₂²×C₃	1	6	yes	—
38	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
40	C₂×C₄×Dic₅	C₂²×C₃	1	6	yes	—
41	C₂×C₄×Dic₅	C₂²×C₃	1	3	yes	—
42	C₄²×D₅	C₃×C₄	1	24	yes	complemented
43	C₅×#95	C₂²×C₃	1	4	yes	—
44	#3963	C₂²×C₃	1	12	yes	—
45	C₂×#376	—	5	1	no	Sylow
46	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
47	C₂²×C₃×D₅	C₂²×C₄	1	6	yes	—
48	C₂²×C₃×D₅	#41	1	8	yes	—
49	C₂×C₃×C₄×C₅	—	2	12	no	—
50	C₂×C₃×C₄×C₅	C₂²×C₄	1	12	yes	—
51	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
52	C₂×C₃×Dic₅	—	2	12	no	—
53	C₂×C₃×Dic₅	C₂²×C₄	1	12	yes	—
54	C₂×C₃×Dic₅	C₂²×C₄	1	6	yes	—
55	C₃×C₄×D₅	—	2	48	no	—
56	C₃×C₄×D₅	C₄²	1	16	yes	—
57	C₂³×C₃×C₄	—	5	1	no	—
58	C₂³×C₃×C₄	—	5	6	no	—
59	C₂×C₃×C₄²	—	5	6	no	—
60	C₂×C₃×C₄²	—	5	3	no	—
61	C₂×C₃×C₄²	—	5	24	no	—
62	C₂×C₃×C₄²	C₂×D₅	1	3	yes	—
63	C₃×#95	—	5	12	no	—
64	C₃×#95	C₂×D₅	1	4	yes	—
65	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
66	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
67	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
68	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
69	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
70	C₂×C₄×D₅	—	2	24	no	—
71	C₂×C₄×D₅	C₂×C₃×C₄	1	24	yes	—
72	C₂×C₄×D₅	C₂×C₃×C₄	1	12	yes	—
73	C₄²×C₅	C₂×C₃×C₄	1	12	yes	complemented
74	C₄×Dic₅	C₂×C₃×C₄	1	12	yes	complemented
75	C₄×Dic₅	C₂×C₃×C₄	1	24	yes	complemented
76	C₂²×C₄²	—	5	3	no	—
77	#376	—	5	3	no	—
78	#376	—	5	4	no	—
79	#376	C₃×D₅	1	1	yes	characteristic, direct product factor
80	C₂×#95	—	5	4	no	—
81	C₂²×C₃×C₅	C₂³×C₄	1	3	yes	—
82	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
83	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
84	C₂×C₃×D₅	#117	1	24	yes	—
85	C₃×C₄×C₅	—	2	12	no	—
86	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
87	C₃×Dic₅	—	2	12	no	—
88	C₃×Dic₅	C₂×C₄²	1	4	yes	—
89	C₂⁴×C₃	—	5	1	no	—
90	C₂²×C₃×C₄	—	5	1	no	—
91	C₂²×C₃×C₄	—	5	12	no	—
92	C₂²×C₃×C₄	—	5	6	no	—
93	C₂²×C₃×C₄	—	5	24	no	—
94	C₂²×C₃×C₄	—	10	24	no	—
95	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
96	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
97	C₃×C₄²	—	5	24	no	—
98	C₃×C₄²	—	5	12	no	—
99	C₃×C₄²	C₄×D₅	1	12	yes	complemented
100	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
101	C₂²×D₅	C₂²×C₃×C₄	1	6	yes	—
102	C₂²×D₅	C₃×#41	1	8	yes	—
103	C₂×C₄×C₅	—	2	12	no	—
104	C₂×C₄×C₅	C₂²×C₃×C₄	1	12	yes	—
105	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
106	C₂×Dic₅	—	2	12	no	—
107	C₂×Dic₅	C₂²×C₃×C₄	1	12	yes	—
108	C₂×Dic₅	C₂²×C₃×C₄	1	6	yes	—
109	C₄×D₅	—	2	48	no	—
110	C₄×D₅	C₃×C₄²	1	16	yes	—
111	C₂³×C₄	—	5	1	no	—
112	C₂³×C₄	—	5	6	no	—
113	C₂×C₄²	—	5	6	no	—
114	C₂×C₄²	—	5	3	no	—
115	C₂×C₄²	—	5	24	no	—
116	C₂×C₄²	C₂×C₃×D₅	1	3	yes	—
117	#95	—	5	12	no	—
118	#95	C₂×C₃×D₅	1	4	yes	—
119	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
120	C₂×C₃×C₅	C₂×#117	1	6	yes	—
121	C₃×D₅	#376	1	8	yes	direct product factor
122	C₂³×C₃	—	5	6	no	—
123	C₂³×C₃	—	5	8	no	—
124	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
125	C₂×C₃×C₄	—	2	12	no	—
126	C₂×C₃×C₄	—	5	6	no	—
127	C₂×C₃×C₄	—	5	16	no	—
128	C₂×C₃×C₄	—	5	12	no	—
129	C₂×C₃×C₄	—	10	48	no	—
130	C₂×C₃×C₄	—	10	12	no	—
131	C₂×C₃×C₄	C₂×C₄×D₅	1	12	yes	—
132	C₂×C₃×C₄	C₂×C₄×D₅	1	6	yes	—
133	C₂²×C₅	C₂³×C₃×C₄	1	3	yes	—
134	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
135	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
136	C₂×D₅	C₃×#117	1	24	yes	—
137	C₄×C₅	—	2	12	no	—
138	C₄×C₅	C₂×C₃×C₄²	1	4	yes	—
139	Dic₅	—	2	12	no	—
140	Dic₅	C₂×C₃×C₄²	1	4	yes	—
141	C₂⁴	—	5	1	no	—
142	C₂²×C₄	—	5	1	no	—
143	C₂²×C₄	—	5	12	no	—
144	C₂²×C₄	—	5	6	no	—
145	C₂²×C₄	—	5	24	no	—
146	C₂²×C₄	—	10	24	no	—
147	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
148	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
149	C₄²	—	5	24	no	—
150	C₄²	—	5	12	no	—
151	C₄²	C₃×C₄×D₅	1	12	yes	complemented
152	C₃×C₅	C₂×#376	1	1	yes	characteristic, complemented, Hall
153	C₂²×C₃	—	5	4	no	—
154	C₂²×C₃	—	5	24	no	—
155	C₂²×C₃	C₂²×C₄×D₅	1	3	yes	—
156	C₂²×C₃	D₅×#41	1	4	yes	—
157	C₃×C₄	—	2	12	no	—
158	C₃×C₄	—	5	4	no	—
159	C₃×C₄	—	10	12	no	—
160	C₃×C₄	C₄²×D₅	1	4	yes	—
161	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
162	C₂×C₅	C₂×C₃×#117	1	6	yes	—
163	D₅	C₃×#376	1	8	yes	direct product factor
164	C₂³	—	5	6	no	—
165	C₂³	—	5	8	no	—
166	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
167	C₂×C₄	—	2	12	no	—
168	C₂×C₄	—	5	6	no	—
169	C₂×C₄	—	5	16	no	—
170	C₂×C₄	—	5	12	no	—
171	C₂×C₄	—	10	48	no	—
172	C₂×C₄	—	10	12	no	—
173	C₂×C₄	C₂×C₃×C₄×D₅	1	12	yes	—
174	C₂×C₄	C₂×C₃×C₄×D₅	1	6	yes	—
175	C₂×C₃	—	5	8	no	—
176	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
177	C₂×C₃	D₅×#117	1	6	yes	—
178	C₅	C₂×C₃×#376	1	1	yes	characteristic, complemented, Sylow
179	C₂²	—	5	24	no	—
180	C₂²	—	5	4	no	—
181	C₂²	C₂²×C₃×C₄×D₅	1	3	yes	—
182	C₂²	C₃×D₅×#41	1	4	yes	—
183	C₄	—	2	12	no	—
184	C₄	—	5	4	no	—
185	C₄	—	10	12	no	—
186	C₄	C₃×C₄²×D₅	1	4	yes	—
187	C₃	D₅×#376	1	1	yes	characteristic, direct product factor, Sylow
188	C₂	—	5	8	no	—
189	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
190	C₂	C₃×D₅×#117	1	6	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₂×C₃×#376
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
3. C₃×#65221	C₂	semidirect
5. C₃×#64937	C₂	semidirect
6. D₅×#376	C₃	direct (N × H)
12. C₃×C₄²×D₅	C₄	semidirect
17. C₅×#376	C₂×C₃	semidirect
18. #65221	C₂×C₃	semidirect
20. #64937	C₂×C₃	semidirect
29. C₃×C₄²×C₅	C₂×C₄	semidirect
30. C₃×C₄×Dic₅	C₂×C₄	semidirect
31. C₃×C₄×Dic₅	C₂×C₄	semidirect
35. C₃×#376	D₅	direct (N × H)
42. C₄²×D₅	C₃×C₄	semidirect
73. C₄²×C₅	C₂×C₃×C₄	semidirect
74. C₄×Dic₅	C₂×C₃×C₄	semidirect
75. C₄×Dic₅	C₂×C₃×C₄	semidirect
79. #376	C₃×D₅	direct (N × H)
99. C₃×C₄²	C₄×D₅	semidirect
121. C₃×D₅	#376	direct (N × H)
151. C₄²	C₃×C₄×D₅	semidirect
152. C₃×C₅	C₂×#376	semidirect
163. D₅	C₃×#376	direct (N × H)
178. C₅	C₂×C₃×#376	semidirect
187. C₃	D₅×#376	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×C₄²×D₅	2
C₃×C₅×#376	2
C₃×#65221	2
C₃×D₅×#95	2
C₃×#64937	2
D₅×#376	3
C₂×C₃×#376	5

Subgroups — C3×D5×#376 #14319347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#376 #14319347