Subgroups — C₃×C₅×#2089 #14275123

Order 1920.

352 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#428	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#343	C₂	1	2	yes	maximal
5	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic
6	C₅×#2089	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₅×#107	—	2	2	no	—
13	C₃×C₅×#107	—	2	2	no	—
14	C₃×C₅×#106	—	2	2	no	—
15	C₃×C₅×C₄⋊C₈	—	2	2	no	—
16	C₃×#2089	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₅×#428	C₂×C₃	1	2	yes	—
18	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
19	C₅×#424	C₂×C₃	1	1	yes	characteristic
20	C₅×#343	C₂×C₃	1	2	yes	—
21	C₅×#341	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	—	2	2	no	—
23	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₃×C₅×M₁₆	—	2	2	no	—
25	C₃×C₅×M₁₆	—	2	2	no	—
26	C₃×C₅×M₁₆	Q₈	1	4	yes	—
27	C₂×C₃×C₅×C₈	—	2	2	no	—
28	C₂×C₃×C₅×C₈	—	2	2	no	—
29	C₂×C₃×C₅×C₈	—	2	1	no	—
30	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
31	C₃×C₅×C₄⋊C₄	—	2	2	no	—
32	C₃×C₅×C₄⋊C₄	—	2	2	no	—
33	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
35	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
36	C₃×C₄²×C₅	—	2	1	no	—
37	C₃×#428	C₂×C₅	1	2	yes	—
38	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
39	C₃×#424	C₂×C₅	1	1	yes	characteristic
40	C₃×#343	C₂×C₅	1	2	yes	—
41	C₃×#341	C₂×C₅	1	1	yes	characteristic
42	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
44	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
45	C₅×#117	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
47	C₅×#107	—	2	2	no	—
48	C₅×#107	—	2	2	no	—
49	C₅×#106	—	2	2	no	—
50	C₅×C₄⋊C₈	—	2	2	no	—
51	#2089	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³×C₃×C₅	#41	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	—	2	1	no	—
54	C₂×C₃×C₄×C₅	—	2	1	no	—
55	C₂×C₃×C₄×C₅	—	4	2	no	—
56	C₂×C₃×C₄×C₅	—	8	2	no	—
57	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
60	C₂×C₃×C₄×C₅	#41	1	2	yes	—
61	C₃×C₅×C₈	—	2	4	no	—
62	C₃×C₅×C₈	—	2	2	no	—
63	C₃×C₅×C₈	—	4	1	no	—
64	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
65	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
66	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
67	C₃×#117	C₂²×C₅	1	1	yes	characteristic
68	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
69	C₃×#107	—	2	2	no	—
70	C₃×#107	—	2	2	no	—
71	C₃×#106	—	2	2	no	—
72	C₃×C₄⋊C₈	—	2	2	no	—
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
75	C₅×M₁₆	—	2	2	no	—
76	C₅×M₁₆	—	2	2	no	—
77	C₅×M₁₆	C₃×Q₈	1	4	yes	—
78	C₂×C₅×C₈	—	2	2	no	—
79	C₂×C₅×C₈	—	2	2	no	—
80	C₂×C₅×C₈	—	2	1	no	—
81	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
82	C₅×C₄⋊C₄	—	2	2	no	—
83	C₅×C₄⋊C₄	—	2	2	no	—
84	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
85	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
86	C₅×C₂²⋊C₄	—	2	1	no	—
87	C₄²×C₅	—	2	1	no	—
88	#428	C₂×C₃×C₅	1	2	yes	—
89	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
90	#424	C₂×C₃×C₅	1	1	yes	characteristic
91	#343	C₂×C₃×C₅	1	2	yes	—
92	#341	C₂×C₃×C₅	1	1	yes	characteristic
93	C₂²×C₃×C₅	—	2	1	no	—
94	C₂²×C₃×C₅	—	2	1	no	—
95	C₂²×C₃×C₅	#121	1	1	yes	characteristic
96	C₂²×C₃×C₅	#125	1	2	yes	—
97	C₃×C₄×C₅	—	4	1	no	—
98	C₃×C₄×C₅	—	4	1	no	—
99	C₃×C₄×C₅	—	8	2	no	—
100	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
101	C₃×C₄×C₅	#123	1	1	yes	characteristic
102	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
103	C₂²×C₃×C₄	—	2	2	no	—
104	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
105	C₃×M₁₆	—	2	2	no	—
106	C₃×M₁₆	—	2	2	no	—
107	C₃×M₁₆	C₅×Q₈	1	4	yes	—
108	C₂×C₃×C₈	—	2	2	no	—
109	C₂×C₃×C₈	—	2	2	no	—
110	C₂×C₃×C₈	—	2	1	no	—
111	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
112	C₃×C₄⋊C₄	—	2	2	no	—
113	C₃×C₄⋊C₄	—	2	2	no	—
114	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
115	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
116	C₃×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₄²	—	2	1	no	—
118	C₂³×C₅	C₃×#41	1	1	yes	characteristic
119	C₂×C₄×C₅	—	2	1	no	—
120	C₂×C₄×C₅	—	2	1	no	—
121	C₂×C₄×C₅	—	4	2	no	—
122	C₂×C₄×C₅	—	8	2	no	—
123	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
124	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
125	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
126	C₂×C₄×C₅	C₃×#41	1	2	yes	—
127	C₅×C₈	—	2	4	no	—
128	C₅×C₈	—	2	2	no	—
129	C₅×C₈	—	4	1	no	—
130	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
131	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
132	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
133	#117	C₂²×C₃×C₅	1	1	yes	characteristic
134	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
135	#107	—	2	2	no	—
136	#107	—	2	2	no	—
137	#106	—	2	2	no	—
138	C₄⋊C₈	—	2	2	no	—
139	C₂×C₃×C₅	—	2	2	no	—
140	C₂×C₃×C₅	#398	1	1	yes	characteristic
141	C₂×C₃×C₅	#472	1	1	yes	characteristic
142	C₂×C₃×C₅	#473	1	1	yes	characteristic
143	C₂³×C₃	C₅×#41	1	1	yes	characteristic
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	—	8	2	no	—
148	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
151	C₂×C₃×C₄	C₅×#41	1	2	yes	—
152	C₃×C₈	—	2	4	no	—
153	C₃×C₈	—	2	2	no	—
154	C₃×C₈	—	4	1	no	—
155	C₂²×C₅	—	2	1	no	—
156	C₂²×C₅	—	2	1	no	—
157	C₂²×C₅	C₃×#121	1	1	yes	characteristic
158	C₂²×C₅	C₃×#125	1	2	yes	—
159	C₄×C₅	—	4	1	no	—
160	C₄×C₅	—	4	1	no	—
161	C₄×C₅	—	8	2	no	—
162	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
163	C₄×C₅	C₃×#123	1	1	yes	characteristic
164	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
167	M₁₆	—	2	2	no	—
168	M₁₆	—	2	2	no	—
169	M₁₆	C₃×C₅×Q₈	1	4	yes	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
177	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
178	C₂²⋊C₄	—	2	1	no	—
179	C₄²	—	2	1	no	—
180	C₃×C₅	#2089	1	1	yes	characteristic, direct product factor, Hall
181	C₂²×C₃	—	2	1	no	—
182	C₂²×C₃	—	2	1	no	—
183	C₂²×C₃	C₅×#121	1	1	yes	characteristic
184	C₂²×C₃	C₅×#125	1	2	yes	—
185	C₃×C₄	—	4	1	no	—
186	C₃×C₄	—	4	1	no	—
187	C₃×C₄	—	8	2	no	—
188	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
189	C₃×C₄	C₅×#123	1	1	yes	characteristic
190	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
191	C₂×C₅	—	2	2	no	—
192	C₂×C₅	C₃×#398	1	1	yes	characteristic
193	C₂×C₅	C₃×#472	1	1	yes	characteristic
194	C₂×C₅	C₃×#473	1	1	yes	characteristic
195	C₂³	C₃×C₅×#41	1	1	yes	characteristic
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	2	no	—
200	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
201	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
202	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
203	C₂×C₄	C₃×C₅×#41	1	2	yes	—
204	C₈	—	2	4	no	—
205	C₈	—	2	2	no	—
206	C₈	—	4	1	no	—
207	C₂×C₃	—	2	2	no	—
208	C₂×C₃	C₅×#398	1	1	yes	characteristic
209	C₂×C₃	C₅×#472	1	1	yes	characteristic
210	C₂×C₃	C₅×#473	1	1	yes	characteristic
211	C₅	C₃×#2089	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²	—	2	1	no	—
213	C₂²	—	2	1	no	—
214	C₂²	C₃×C₅×#121	1	1	yes	characteristic
215	C₂²	C₃×C₅×#125	1	2	yes	—
216	C₄	—	4	1	no	—
217	C₄	—	4	1	no	—
218	C₄	—	8	2	no	—
219	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
220	C₄	C₃×C₅×#123	1	1	yes	characteristic
221	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
222	C₃	C₅×#2089	1	1	yes	characteristic, direct product factor, Sylow
223	C₂	—	2	2	no	—
224	C₂	C₃×C₅×#398	1	1	yes	characteristic
225	C₂	C₃×C₅×#472	1	1	yes	characteristic
226	C₂	C₃×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2089	C₃	direct (N × H)
16. C₃×#2089	C₅	direct (N × H)
51. #2089	C₃×C₅	direct (N × H)
180. C₃×C₅	#2089	direct (N × H)
211. C₅	C₃×#2089	direct (N × H)
222. C₃	C₅×#2089	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×#428	2
C₂×C₃×C₅×#107	2
C₃×C₅×#424	2
C₃×C₅×#343	2
C₃×C₅×#341	2
C₅×#2089	3
C₃×#2089	5

Subgroups — C3×C5×#2089 #14275123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2089 #14275123