Subgroups — C₃×C₅×#1579 #14274613

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×Q₈	C₂	1	2	yes	maximal
2	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#334	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₃×C₅×#322	C₂	1	1	yes	maximal, characteristic
6	C₅×#1579	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
9	C₃×C₅×#107	C₄	1	1	yes	characteristic
10	C₃×C₅×C₄⋊C₈	—	2	2	no	—
11	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
12	C₃×C₅×#103	C₄	1	2	yes	—
13	C₃×C₄×C₅×C₈	—	2	2	no	—
14	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×#1579	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₅×C₈×Q₈	C₂×C₃	1	2	yes	—
19	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
20	C₅×#334	C₂×C₃	1	1	yes	characteristic
21	C₅×Q₈⋊C₈	C₂×C₃	1	2	yes	—
22	C₅×#322	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
24	C₃×C₅×Q₁₆	C₈	1	4	yes	complemented
25	C₂×C₃×C₅×C₈	—	2	2	no	—
26	C₂×C₃×C₅×C₈	—	2	1	no	—
27	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
30	C₃×C₅×C₄⋊C₄	—	2	2	no	—
31	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₃×C₄²×C₅	—	2	2	no	—
33	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
34	C₃×C₈×Q₈	C₂×C₅	1	2	yes	—
35	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
36	C₃×#334	C₂×C₅	1	1	yes	characteristic
37	C₃×Q₈⋊C₈	C₂×C₅	1	2	yes	—
38	C₃×#322	C₂×C₅	1	1	yes	characteristic
39	C₂×C₅×Q₁₆	C₃×C₄	1	1	yes	characteristic
40	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
41	C₅×#107	C₃×C₄	1	1	yes	characteristic
42	C₅×C₄⋊C₈	—	2	2	no	—
43	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
44	C₅×#103	C₃×C₄	1	2	yes	—
45	C₄×C₅×C₈	—	2	2	no	—
46	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
47	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
49	#1579	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₃×C₅×Q₈	—	2	2	no	—
51	C₃×C₅×Q₈	C₂×C₈	1	4	yes	—
52	C₂×C₃×C₄×C₅	—	2	2	no	—
53	C₂×C₃×C₄×C₅	—	2	2	no	—
54	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
57	C₃×C₅×C₈	—	2	1	no	—
58	C₃×C₅×C₈	—	2	2	no	—
59	C₃×C₅×C₈	—	4	1	no	—
60	C₃×C₅×C₈	—	4	2	no	—
61	C₃×C₅×C₈	C₂×C₈	1	2	yes	—
62	C₂×C₃×Q₁₆	C₄×C₅	1	1	yes	characteristic
63	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
64	C₃×#107	C₄×C₅	1	1	yes	characteristic
65	C₃×C₄⋊C₈	—	2	2	no	—
66	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
67	C₃×#103	C₄×C₅	1	2	yes	—
68	C₃×C₄×C₈	—	2	2	no	—
69	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
70	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
71	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
73	C₅×Q₁₆	C₃×C₈	1	4	yes	complemented
74	C₂×C₅×C₈	—	2	2	no	—
75	C₂×C₅×C₈	—	2	1	no	—
76	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
77	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
78	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
79	C₅×C₄⋊C₄	—	2	2	no	—
80	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
81	C₄²×C₅	—	2	2	no	—
82	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
83	C₈×Q₈	C₂×C₃×C₅	1	2	yes	—
84	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic
85	#334	C₂×C₃×C₅	1	1	yes	characteristic
86	Q₈⋊C₈	C₂×C₃×C₅	1	2	yes	—
87	#322	C₂×C₃×C₅	1	1	yes	characteristic
88	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
89	C₃×C₄×C₅	—	2	4	no	—
90	C₃×C₄×C₅	—	2	1	no	—
91	C₃×C₄×C₅	—	4	2	no	—
92	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
93	C₃×C₄×C₅	#131	1	1	yes	characteristic
94	C₃×C₄×C₅	#137	1	2	yes	—
95	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
96	C₃×Q₁₆	C₅×C₈	1	4	yes	complemented
97	C₂×C₃×C₈	—	2	2	no	—
98	C₂×C₃×C₈	—	2	1	no	—
99	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
100	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
101	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
102	C₃×C₄⋊C₄	—	2	2	no	—
103	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
104	C₃×C₄²	—	2	2	no	—
105	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
106	C₅×Q₈	—	2	2	no	—
107	C₅×Q₈	C₂×C₃×C₈	1	4	yes	—
108	C₂×C₄×C₅	—	2	2	no	—
109	C₂×C₄×C₅	—	2	2	no	—
110	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
111	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
112	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
113	C₅×C₈	—	2	1	no	—
114	C₅×C₈	—	2	2	no	—
115	C₅×C₈	—	4	1	no	—
116	C₅×C₈	—	4	2	no	—
117	C₅×C₈	C₂×C₃×C₈	1	2	yes	—
118	C₂×Q₁₆	C₃×C₄×C₅	1	1	yes	characteristic
119	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
120	#107	C₃×C₄×C₅	1	1	yes	characteristic
121	C₄⋊C₈	—	2	2	no	—
122	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
123	#103	C₃×C₄×C₅	1	2	yes	—
124	C₄×C₈	—	2	2	no	—
125	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
126	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
127	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
128	C₂×C₃×C₅	C₈×D₄	1	1	yes	characteristic
129	C₂×C₃×C₅	#441	1	1	yes	characteristic
130	C₂×C₃×C₅	#444	1	1	yes	characteristic
131	C₃×Q₈	—	2	2	no	—
132	C₃×Q₈	C₂×C₅×C₈	1	4	yes	—
133	C₂×C₃×C₄	—	2	2	no	—
134	C₂×C₃×C₄	—	2	2	no	—
135	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
138	C₃×C₈	—	2	1	no	—
139	C₃×C₈	—	2	2	no	—
140	C₃×C₈	—	4	1	no	—
141	C₃×C₈	—	4	2	no	—
142	C₃×C₈	C₂×C₅×C₈	1	2	yes	—
143	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
144	C₄×C₅	—	2	4	no	—
145	C₄×C₅	—	2	1	no	—
146	C₄×C₅	—	4	2	no	—
147	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
148	C₄×C₅	C₃×#131	1	1	yes	characteristic
149	C₄×C₅	C₃×#137	1	2	yes	—
150	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
151	Q₁₆	C₃×C₅×C₈	1	4	yes	complemented
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
155	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
156	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
159	C₄²	—	2	2	no	—
160	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
161	C₃×C₅	#1579	1	1	yes	characteristic, direct product factor, Hall
162	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
163	C₃×C₄	—	2	4	no	—
164	C₃×C₄	—	2	1	no	—
165	C₃×C₄	—	4	2	no	—
166	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
167	C₃×C₄	C₅×#131	1	1	yes	characteristic
168	C₃×C₄	C₅×#137	1	2	yes	—
169	C₂×C₅	C₃×C₈×D₄	1	1	yes	characteristic
170	C₂×C₅	C₃×#441	1	1	yes	characteristic
171	C₂×C₅	C₃×#444	1	1	yes	characteristic
172	Q₈	—	2	2	no	—
173	Q₈	C₂×C₃×C₅×C₈	1	4	yes	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
177	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
178	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
179	C₈	—	2	1	no	—
180	C₈	—	2	2	no	—
181	C₈	—	4	1	no	—
182	C₈	—	4	2	no	—
183	C₈	C₂×C₃×C₅×C₈	1	2	yes	—
184	C₂×C₃	C₅×C₈×D₄	1	1	yes	characteristic
185	C₂×C₃	C₅×#441	1	1	yes	characteristic
186	C₂×C₃	C₅×#444	1	1	yes	characteristic
187	C₅	C₃×#1579	1	1	yes	characteristic, direct product factor, Sylow
188	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
189	C₄	—	2	4	no	—
190	C₄	—	2	1	no	—
191	C₄	—	4	2	no	—
192	C₄	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
193	C₄	C₃×C₅×#131	1	1	yes	characteristic
194	C₄	C₃×C₅×#137	1	2	yes	—
195	C₃	C₅×#1579	1	1	yes	characteristic, direct product factor, Sylow
196	C₂	C₃×C₅×C₈×D₄	1	1	yes	characteristic
197	C₂	C₃×C₅×#441	1	1	yes	characteristic
198	C₂	C₃×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₄	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₄²	C₂³×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₄×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1579	C₃	direct (N × H)
17. C₃×#1579	C₅	direct (N × H)
24. C₃×C₅×Q₁₆	C₈	semidirect
49. #1579	C₃×C₅	direct (N × H)
73. C₅×Q₁₆	C₃×C₈	semidirect
96. C₃×Q₁₆	C₅×C₈	semidirect
151. Q₁₆	C₃×C₅×C₈	semidirect
161. C₃×C₅	#1579	direct (N × H)
187. C₅	C₃×#1579	direct (N × H)
195. C₃	C₅×#1579	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₈×Q₈	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×#334	2
C₃×C₅×Q₈⋊C₈	2
C₃×C₅×#322	2
C₅×#1579	3
C₃×#1579	5

Subgroups — C3×C5×#1579 #14274613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1579 #14274613