Subgroups — C₃×D₅×#367 #14314563

Order 1920.

336 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×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×#107	C₂	1	2	yes	maximal
3	C₃×C₅×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64725	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64710	C₂	1	2	yes	maximal, complemented
6	D₅×#367	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
8	C₃×D₅×C₄⋊C₄	—	2	2	no	—
9	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	C₃×C₅×#107	C₂²	1	2	yes	—
11	C₃×#3950	C₂²	1	2	yes	—
12	C₂×C₃×#672	C₂²	1	1	yes	characteristic
13	C₃×#3939	—	2	2	no	—
14	C₃×D₅×C₁₆	C₄	1	4	yes	complemented
15	C₂×C₃×#367	—	5	1	no	maximal, Hall
16	C₂×D₅×C₁₆	C₂×C₃	1	1	yes	characteristic
17	D₅×#107	C₂×C₃	1	2	yes	—
18	C₅×#367	C₂×C₃	1	1	yes	characteristic, complemented
19	#64725	C₂×C₃	1	1	yes	characteristic, complemented
20	#64710	C₂×C₃	1	2	yes	complemented
21	C₂×C₃×C₄×D₅	—	4	2	no	—
22	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
23	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
24	C₃×C₅×C₄⋊C₄	—	2	2	no	—
25	C₃×C₄⋊Dic₅	—	2	2	no	—
26	C₃×#683	—	4	2	no	—
27	C₂×C₃×#168	D₄	1	1	yes	characteristic
28	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
29	C₃×C₈×D₅	Q₈	1	2	yes	—
30	C₃×C₅×C₁₆	C₂×C₄	1	2	yes	complemented
31	C₃×#672	C₂×C₄	1	2	yes	complemented
32	C₂²×C₃×C₁₆	—	5	1	no	—
33	C₂×C₃×#107	—	5	2	no	—
34	C₃×#367	—	5	1	no	—
35	C₃×#367	—	5	2	no	—
36	C₃×#367	D₅	1	1	yes	characteristic, direct product factor
37	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
38	D₅×C₄⋊C₄	—	2	2	no	—
39	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
40	C₅×#107	C₂²×C₃	1	2	yes	—
41	#3950	C₂²×C₃	1	2	yes	—
42	C₂×#672	C₂²×C₃	1	1	yes	characteristic
43	#3939	—	2	2	no	—
44	D₅×C₁₆	C₃×C₄	1	4	yes	complemented
45	C₂×#367	—	5	1	no	Sylow
46	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
47	C₂×C₃×C₄×C₅	—	4	2	no	—
48	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃×Dic₅	—	4	2	no	—
50	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
51	C₃×C₄×D₅	—	8	4	no	—
52	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
53	C₃×C₄×D₅	Q₁₆	1	2	yes	—
54	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
55	C₃×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
56	C₃×#168	C₄⋊C₄	1	2	yes	—
57	C₂²×C₃×C₈	—	5	1	no	—
58	C₂×C₃×C₄⋊C₄	—	10	2	no	—
59	C₂×C₃×C₁₆	—	5	1	no	—
60	C₂×C₃×C₁₆	—	5	4	no	—
61	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
62	C₃×#107	—	5	2	no	—
63	C₃×#107	—	10	2	no	—
64	C₃×#107	C₂×D₅	1	2	yes	—
65	C₂×C₄×D₅	—	4	2	no	—
66	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
67	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
68	C₅×C₄⋊C₄	—	2	2	no	—
69	C₄⋊Dic₅	—	2	2	no	—
70	#683	—	4	2	no	—
71	C₂×#168	C₃×D₄	1	1	yes	characteristic
72	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
73	C₈×D₅	C₃×Q₈	1	2	yes	—
74	C₅×C₁₆	C₂×C₃×C₄	1	2	yes	complemented
75	#672	C₂×C₃×C₄	1	2	yes	complemented
76	C₂²×C₁₆	—	5	1	no	—
77	C₂×#107	—	5	2	no	—
78	#367	—	5	1	no	—
79	#367	—	5	2	no	—
80	#367	C₃×D₅	1	1	yes	characteristic, direct product factor
81	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
82	C₂×C₃×D₅	#107	1	2	yes	—
83	C₂×C₃×D₅	SD₃₂	1	4	yes	—
84	C₃×C₄×C₅	—	8	2	no	—
85	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₃×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
87	C₃×Dic₅	—	8	2	no	—
88	C₃×Dic₅	#107	1	2	yes	—
89	C₂²×C₃×C₄	—	5	1	no	—
90	C₂²×C₃×C₄	—	20	2	no	—
91	C₂×C₃×C₈	—	5	1	no	—
92	C₂×C₃×C₈	—	5	2	no	—
93	C₂×C₃×C₈	—	5	2	no	—
94	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
95	C₃×C₄⋊C₄	—	2	2	no	—
96	C₃×C₄⋊C₄	—	10	2	no	—
97	C₃×C₄⋊C₄	—	20	2	no	—
98	C₃×C₁₆	—	5	2	no	—
99	C₃×C₁₆	C₄×D₅	1	2	yes	complemented
100	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
101	C₂×C₄×C₅	—	4	2	no	—
102	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
103	C₂×Dic₅	—	4	2	no	—
104	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
105	C₄×D₅	—	8	4	no	—
106	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
107	C₄×D₅	C₃×Q₁₆	1	2	yes	—
108	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
109	C₅×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
110	#168	C₃×C₄⋊C₄	1	2	yes	—
111	C₂²×C₈	—	5	1	no	—
112	C₂×C₄⋊C₄	—	10	2	no	—
113	C₂×C₁₆	—	5	1	no	—
114	C₂×C₁₆	—	5	4	no	—
115	C₂×C₁₆	C₂×C₃×D₅	1	1	yes	characteristic
116	#107	—	5	2	no	—
117	#107	—	10	2	no	—
118	#107	C₂×C₃×D₅	1	2	yes	—
119	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
120	C₂×C₃×C₅	C₂×SD₃₂	1	2	yes	—
121	C₃×D₅	#367	1	4	yes	direct product factor
122	C₂³×C₃	—	5	1	no	—
123	C₂×C₃×C₄	—	4	2	no	—
124	C₂×C₃×C₄	—	5	1	no	—
125	C₂×C₃×C₄	—	5	2	no	—
126	C₂×C₃×C₄	—	5	2	no	—
127	C₂×C₃×C₄	—	20	2	no	—
128	C₂×C₃×C₄	—	40	4	no	—
129	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
130	C₃×C₈	—	5	2	no	—
131	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
132	C₃×C₈	Q₈×D₅	1	1	yes	characteristic
133	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
134	C₂×D₅	C₃×#107	1	2	yes	—
135	C₂×D₅	C₃×SD₃₂	1	4	yes	—
136	C₄×C₅	—	8	2	no	—
137	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
138	C₄×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
139	Dic₅	—	8	2	no	—
140	Dic₅	C₃×#107	1	2	yes	—
141	C₂²×C₄	—	5	1	no	—
142	C₂²×C₄	—	20	2	no	—
143	C₂×C₈	—	5	1	no	—
144	C₂×C₈	—	5	2	no	—
145	C₂×C₈	—	5	2	no	—
146	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
147	C₄⋊C₄	—	2	2	no	—
148	C₄⋊C₄	—	10	2	no	—
149	C₄⋊C₄	—	20	2	no	—
150	C₁₆	—	5	2	no	—
151	C₁₆	C₃×C₄×D₅	1	2	yes	complemented
152	C₃×C₅	C₂×#367	1	1	yes	characteristic, complemented, Hall
153	C₂²×C₃	—	5	2	no	—
154	C₂²×C₃	—	5	4	no	—
155	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
156	C₃×C₄	—	5	2	no	—
157	C₃×C₄	—	8	2	no	—
158	C₃×C₄	—	40	2	no	—
159	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
160	C₃×C₄	D₅×Q₁₆	1	1	yes	characteristic
161	C₂×C₅	C₂×C₃×#107	1	1	yes	characteristic
162	C₂×C₅	C₂×C₃×SD₃₂	1	2	yes	—
163	D₅	C₃×#367	1	4	yes	direct product factor
164	C₂³	—	5	1	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	5	1	no	—
167	C₂×C₄	—	5	2	no	—
168	C₂×C₄	—	5	2	no	—
169	C₂×C₄	—	20	2	no	—
170	C₂×C₄	—	40	4	no	—
171	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
172	C₈	—	5	2	no	—
173	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
174	C₈	C₃×Q₈×D₅	1	1	yes	characteristic
175	C₂×C₃	—	5	4	no	—
176	C₂×C₃	D₅×#107	1	1	yes	characteristic
177	C₂×C₃	D₅×SD₃₂	1	2	yes	—
178	C₅	C₂×C₃×#367	1	1	yes	characteristic, complemented, Sylow
179	C₂²	—	5	2	no	—
180	C₂²	—	5	4	no	—
181	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
182	C₄	—	5	2	no	—
183	C₄	—	8	2	no	—
184	C₄	—	40	2	no	—
185	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
186	C₄	C₃×D₅×Q₁₆	1	1	yes	characteristic
187	C₃	D₅×#367	1	1	yes	characteristic, direct product factor, Sylow
188	C₂	—	5	4	no	—
189	C₂	C₃×D₅×#107	1	1	yes	characteristic
190	C₂	C₃×D₅×SD₃₂	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	D₅×D₈
commutator	C₅×C₈	C₂²×C₃×C₄
Frattini	C₂×C₈	C₂²×C₃×D₅
Fitting	C₃×C₅×#367	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂²×C₃×D₅	D₈
cosocle	C₂×C₅×C₈	C₂³×C₃
hypercenter	C₃×#367	D₅
hypocenter	C₅	C₂×C₃×#367
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#367

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#367	C₂	semidirect
4. C₃×#64725	C₂	semidirect
5. C₃×#64710	C₂	semidirect
6. D₅×#367	C₃	direct (N × H)
14. C₃×D₅×C₁₆	C₄	semidirect
18. C₅×#367	C₂×C₃	semidirect
19. #64725	C₂×C₃	semidirect
20. #64710	C₂×C₃	semidirect
30. C₃×C₅×C₁₆	C₂×C₄	semidirect
31. C₃×#672	C₂×C₄	semidirect
36. C₃×#367	D₅	direct (N × H)
44. D₅×C₁₆	C₃×C₄	semidirect
74. C₅×C₁₆	C₂×C₃×C₄	semidirect
75. #672	C₂×C₃×C₄	semidirect
80. #367	C₃×D₅	direct (N × H)
99. C₃×C₁₆	C₄×D₅	semidirect
121. C₃×D₅	#367	direct (N × H)
151. C₁₆	C₃×C₄×D₅	semidirect
152. C₃×C₅	C₂×#367	semidirect
163. D₅	C₃×#367	direct (N × H)
178. C₅	C₂×C₃×#367	semidirect
187. C₃	D₅×#367	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×D₅×C₁₆	2
C₃×D₅×#107	2
C₃×C₅×#367	2
C₃×#64725	2
C₃×#64710	2
D₅×#367	3
C₂×C₃×#367	5

Subgroups — C3×D5×#367 #14314563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#367 #14314563