Subgroups — C₅×D₃×#376 #14319346

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×C₄²×C₅×D₃	C₂	1	3	yes	maximal
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4932	C₂	1	3	yes	maximal, complemented
4	C₅×D₃×#95	C₂	1	4	yes	maximal
5	C₅×#4648	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#376	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₂²	1	6	yes	—
8	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
10	C₂×C₄×C₅×Dic₃	C₂²	1	6	yes	—
11	C₂×C₄×C₅×Dic₃	C₂²	1	3	yes	—
12	C₄²×C₅×D₃	C₄	1	24	yes	complemented
13	C₃×C₅×#95	C₂²	1	4	yes	—
14	C₅×C₃⋊#95	C₂²	1	12	yes	—
15	D₃×#376	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₄²×C₅	—	3	3	no	—
17	C₅×#376	—	3	4	no	—
18	C₅×#376	—	3	3	no	—
19	C₅×#376	D₃	1	1	yes	characteristic, direct product factor
20	C₂×C₅×#95	—	3	4	no	—
21	C₂³×C₅×D₃	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×C₅×Dic₃	C₂³	1	6	yes	—
25	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₅×D₃	—	2	24	no	—
27	C₂×C₄×C₅×D₃	C₂×C₄	1	24	yes	—
28	C₂×C₄×C₅×D₃	C₂×C₄	1	12	yes	—
29	C₃×C₄²×C₅	C₂×C₄	1	12	yes	complemented
30	C₄×C₅×Dic₃	C₂×C₄	1	12	yes	complemented
31	C₄×C₅×Dic₃	C₂×C₄	1	24	yes	complemented
32	C₂×C₄²×D₃	C₂×C₅	1	3	yes	—
33	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
34	#4932	C₂×C₅	1	3	yes	complemented
35	D₃×#95	C₂×C₅	1	4	yes	—
36	#4648	C₂×C₅	1	4	yes	complemented
37	C₂³×C₄×C₅	—	3	1	no	—
38	C₂³×C₄×C₅	—	3	6	no	—
39	C₂×C₄²×C₅	—	3	6	no	—
40	C₂×C₄²×C₅	—	3	3	no	—
41	C₂×C₄²×C₅	—	3	24	no	—
42	C₂×C₄²×C₅	C₂×D₃	1	3	yes	—
43	C₅×#95	—	3	12	no	—
44	C₅×#95	C₂×D₃	1	4	yes	—
45	C₂×#376	—	3	1	no	Sylow
46	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
47	C₂²×C₅×D₃	C₂²×C₄	1	6	yes	—
48	C₂²×C₅×D₃	#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×C₅×Dic₃	—	2	12	no	—
53	C₂×C₅×Dic₃	C₂²×C₄	1	12	yes	—
54	C₂×C₅×Dic₃	C₂²×C₄	1	6	yes	—
55	C₄×C₅×D₃	—	2	48	no	—
56	C₄×C₅×D₃	C₄²	1	16	yes	—
57	C₂²×C₄×D₃	C₂²×C₅	1	6	yes	—
58	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
60	C₂×C₄×Dic₃	C₂²×C₅	1	6	yes	—
61	C₂×C₄×Dic₃	C₂²×C₅	1	3	yes	—
62	C₄²×D₃	C₄×C₅	1	24	yes	complemented
63	C₃×#95	C₂²×C₅	1	4	yes	—
64	C₃⋊#95	C₂²×C₅	1	12	yes	—
65	C₂⁴×C₅	—	3	1	no	—
66	C₂²×C₄×C₅	—	3	1	no	—
67	C₂²×C₄×C₅	—	3	12	no	—
68	C₂²×C₄×C₅	—	3	6	no	—
69	C₂²×C₄×C₅	—	3	24	no	—
70	C₂²×C₄×C₅	—	6	24	no	—
71	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
72	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
73	C₄²×C₅	—	3	24	no	—
74	C₄²×C₅	—	3	12	no	—
75	C₄²×C₅	C₄×D₃	1	12	yes	complemented
76	C₂²×C₄²	—	3	3	no	—
77	#376	—	3	3	no	—
78	#376	—	3	4	no	—
79	#376	C₅×D₃	1	1	yes	characteristic, direct product factor
80	C₂×#95	—	3	4	no	—
81	C₂²×C₃×C₅	C₂³×C₄	1	3	yes	—
82	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
83	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
84	C₂×C₅×D₃	#117	1	24	yes	—
85	C₃×C₄×C₅	—	2	12	no	—
86	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
87	C₅×Dic₃	—	2	12	no	—
88	C₅×Dic₃	C₂×C₄²	1	4	yes	—
89	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
91	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
92	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
93	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
94	C₂×C₄×D₃	—	2	24	no	—
95	C₂×C₄×D₃	C₂×C₄×C₅	1	24	yes	—
96	C₂×C₄×D₃	C₂×C₄×C₅	1	12	yes	—
97	C₃×C₄²	C₂×C₄×C₅	1	12	yes	complemented
98	C₄×Dic₃	C₂×C₄×C₅	1	12	yes	complemented
99	C₄×Dic₃	C₂×C₄×C₅	1	24	yes	complemented
100	C₂³×C₅	—	3	6	no	—
101	C₂³×C₅	—	3	8	no	—
102	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
103	C₂×C₄×C₅	—	2	12	no	—
104	C₂×C₄×C₅	—	3	6	no	—
105	C₂×C₄×C₅	—	3	16	no	—
106	C₂×C₄×C₅	—	3	12	no	—
107	C₂×C₄×C₅	—	6	48	no	—
108	C₂×C₄×C₅	—	6	12	no	—
109	C₂×C₄×C₅	C₂×C₄×D₃	1	12	yes	—
110	C₂×C₄×C₅	C₂×C₄×D₃	1	6	yes	—
111	C₂³×C₄	—	3	1	no	—
112	C₂³×C₄	—	3	6	no	—
113	C₂×C₄²	—	3	6	no	—
114	C₂×C₄²	—	3	3	no	—
115	C₂×C₄²	—	3	24	no	—
116	C₂×C₄²	C₂×C₅×D₃	1	3	yes	—
117	#95	—	3	12	no	—
118	#95	C₂×C₅×D₃	1	4	yes	—
119	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
120	C₂×C₃×C₅	C₂×#117	1	6	yes	—
121	C₅×D₃	#376	1	8	yes	direct product factor
122	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
123	C₂²×D₃	C₂²×C₄×C₅	1	6	yes	—
124	C₂²×D₃	C₅×#41	1	8	yes	—
125	C₂×C₃×C₄	—	2	12	no	—
126	C₂×C₃×C₄	C₂²×C₄×C₅	1	12	yes	—
127	C₂×C₃×C₄	C₂²×C₄×C₅	1	6	yes	—
128	C₂×Dic₃	—	2	12	no	—
129	C₂×Dic₃	C₂²×C₄×C₅	1	12	yes	—
130	C₂×Dic₃	C₂²×C₄×C₅	1	6	yes	—
131	C₄×D₃	—	2	48	no	—
132	C₄×D₃	C₄²×C₅	1	16	yes	—
133	C₂²×C₅	—	3	4	no	—
134	C₂²×C₅	—	3	24	no	—
135	C₂²×C₅	C₂²×C₄×D₃	1	3	yes	—
136	C₂²×C₅	D₃×#41	1	4	yes	—
137	C₄×C₅	—	2	12	no	—
138	C₄×C₅	—	3	4	no	—
139	C₄×C₅	—	6	12	no	—
140	C₄×C₅	C₄²×D₃	1	4	yes	—
141	C₂⁴	—	3	1	no	—
142	C₂²×C₄	—	3	1	no	—
143	C₂²×C₄	—	3	12	no	—
144	C₂²×C₄	—	3	6	no	—
145	C₂²×C₄	—	3	24	no	—
146	C₂²×C₄	—	6	24	no	—
147	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
148	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
149	C₄²	—	3	24	no	—
150	C₄²	—	3	12	no	—
151	C₄²	C₄×C₅×D₃	1	12	yes	complemented
152	C₃×C₅	C₂×#376	1	1	yes	characteristic, complemented, Hall
153	C₂²×C₃	C₂³×C₄×C₅	1	3	yes	—
154	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
155	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
156	C₂×D₃	C₅×#117	1	24	yes	—
157	C₃×C₄	—	2	12	no	—
158	C₃×C₄	C₂×C₄²×C₅	1	4	yes	—
159	Dic₃	—	2	12	no	—
160	Dic₃	C₂×C₄²×C₅	1	4	yes	—
161	C₂×C₅	—	3	8	no	—
162	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
163	C₂×C₅	D₃×#117	1	6	yes	—
164	C₂³	—	3	6	no	—
165	C₂³	—	3	8	no	—
166	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
167	C₂×C₄	—	2	12	no	—
168	C₂×C₄	—	3	6	no	—
169	C₂×C₄	—	3	16	no	—
170	C₂×C₄	—	3	12	no	—
171	C₂×C₄	—	6	48	no	—
172	C₂×C₄	—	6	12	no	—
173	C₂×C₄	C₂×C₄×C₅×D₃	1	12	yes	—
174	C₂×C₄	C₂×C₄×C₅×D₃	1	6	yes	—
175	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
176	C₂×C₃	C₂×C₅×#117	1	6	yes	—
177	D₃	C₅×#376	1	8	yes	direct product factor
178	C₅	D₃×#376	1	1	yes	characteristic, direct product factor, Sylow
179	C₂²	—	3	4	no	—
180	C₂²	—	3	24	no	—
181	C₂²	C₂²×C₄×C₅×D₃	1	3	yes	—
182	C₂²	C₅×D₃×#41	1	4	yes	—
183	C₄	—	2	12	no	—
184	C₄	—	3	4	no	—
185	C₄	—	6	12	no	—
186	C₄	C₄²×C₅×D₃	1	4	yes	—
187	C₃	C₂×C₅×#376	1	1	yes	characteristic, complemented, Sylow
188	C₂	—	3	8	no	—
189	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
190	C₂	C₅×D₃×#117	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#376	D₃
hypocenter	C₃	C₂×C₅×#376
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
3. C₅×#4932	C₂	semidirect
5. C₅×#4648	C₂	semidirect
12. C₄²×C₅×D₃	C₄	semidirect
15. D₃×#376	C₅	direct (N × H)
19. C₅×#376	D₃	direct (N × H)
29. C₃×C₄²×C₅	C₂×C₄	semidirect
30. C₄×C₅×Dic₃	C₂×C₄	semidirect
31. C₄×C₅×Dic₃	C₂×C₄	semidirect
33. C₃×#376	C₂×C₅	semidirect
34. #4932	C₂×C₅	semidirect
36. #4648	C₂×C₅	semidirect
62. C₄²×D₃	C₄×C₅	semidirect
75. C₄²×C₅	C₄×D₃	semidirect
79. #376	C₅×D₃	direct (N × H)
97. C₃×C₄²	C₂×C₄×C₅	semidirect
98. C₄×Dic₃	C₂×C₄×C₅	semidirect
99. C₄×Dic₃	C₂×C₄×C₅	semidirect
121. C₅×D₃	#376	direct (N × H)
151. C₄²	C₄×C₅×D₃	semidirect
152. C₃×C₅	C₂×#376	semidirect
177. D₃	C₅×#376	direct (N × H)
178. C₅	D₃×#376	direct (N × H)
187. C₃	C₂×C₅×#376	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₅×#376	2
C₅×#4932	2
C₅×D₃×#95	2
C₅×#4648	2
C₂×C₅×#376	3
D₃×#376	5

Subgroups — C5×D3×#376 #14319346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#376 #14319346