Subgroups — C₃×C₅×#1444 #14274478

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	3	yes	maximal
2	C₂×C₃×C₅×#95	C₂	1	3	yes	maximal
3	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
4	C₅×#1444	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
8	C₂×C₃×C₅×C₄⋊C₄	—	2	12	no	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	6	no	—
10	C₃×C₅×#95	—	2	6	no	—
11	C₃×C₅×#95	C₄	1	4	yes	complemented
12	C₃×#1444	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	3	yes	—
14	C₂×C₅×#95	C₂×C₃	1	3	yes	—
15	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
16	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₅	—	2	6	no	—
18	C₂²×C₃×C₄×C₅	—	2	6	no	—
19	C₂²×C₃×C₄×C₅	—	2	6	no	—
20	C₂²×C₃×C₄×C₅	—	2	6	no	—
21	C₂²×C₃×C₄×C₅	—	2	3	no	—
22	C₂²×C₃×C₄×C₅	—	2	3	no	—
23	C₂²×C₃×C₄×C₅	—	2	3	no	—
24	C₂²×C₃×C₄×C₅	—	2	3	no	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	6	yes	—
26	C₂²×C₃×C₄×C₅	D₄	1	6	yes	—
27	C₂²×C₃×C₄×C₅	D₄	1	6	yes	—
28	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
29	C₂²×C₃×C₄×C₅	Q₈	1	6	yes	—
30	C₃×C₅×C₄⋊C₄	—	2	24	no	—
31	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	3	yes	—
32	C₂×C₃×#95	C₂×C₅	1	3	yes	—
33	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
35	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
37	C₂×C₅×C₄⋊C₄	—	2	12	no	—
38	C₂×C₅×C₄⋊C₄	—	2	6	no	—
39	C₅×#95	—	2	6	no	—
40	C₅×#95	C₃×C₄	1	4	yes	complemented
41	#1444	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
43	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
44	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
45	C₂³×C₃×C₅	C₂×Q₈	1	3	yes	—
46	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
47	C₂³×C₃×C₅	#41	1	3	yes	—
48	C₂³×C₃×C₅	#41	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	—	2	12	no	—
50	C₂×C₃×C₄×C₅	—	2	6	no	—
51	C₂×C₃×C₄×C₅	—	2	12	no	—
52	C₂×C₃×C₄×C₅	—	2	6	no	—
53	C₂×C₃×C₄×C₅	—	2	12	no	—
54	C₂×C₃×C₄×C₅	—	2	6	no	—
55	C₂×C₃×C₄×C₅	—	2	6	no	—
56	C₂×C₃×C₄×C₅	—	4	3	no	—
57	C₂×C₃×C₄×C₅	—	4	6	no	—
58	C₂×C₃×C₄×C₅	—	4	3	no	—
59	C₂×C₃×C₄×C₅	—	4	3	no	—
60	C₂×C₃×C₄×C₅	—	4	1	no	—
61	C₂×C₃×C₄×C₅	C₄⋊C₄	1	12	yes	complemented
62	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
63	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
64	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
65	C₂×C₃×C₄⋊C₄	—	2	12	no	—
66	C₂×C₃×C₄⋊C₄	—	2	6	no	—
67	C₃×#95	—	2	6	no	—
68	C₃×#95	C₄×C₅	1	4	yes	complemented
69	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
70	C₂²×C₄×C₅	—	2	6	no	—
71	C₂²×C₄×C₅	—	2	6	no	—
72	C₂²×C₄×C₅	—	2	6	no	—
73	C₂²×C₄×C₅	—	2	6	no	—
74	C₂²×C₄×C₅	—	2	3	no	—
75	C₂²×C₄×C₅	—	2	3	no	—
76	C₂²×C₄×C₅	—	2	3	no	—
77	C₂²×C₄×C₅	—	2	3	no	—
78	C₂²×C₄×C₅	C₂×C₃×C₄	1	6	yes	—
79	C₂²×C₄×C₅	C₃×D₄	1	6	yes	—
80	C₂²×C₄×C₅	C₃×D₄	1	6	yes	—
81	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
82	C₂²×C₄×C₅	C₃×Q₈	1	6	yes	—
83	C₅×C₄⋊C₄	—	2	24	no	—
84	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	3	yes	—
85	C₂×#95	C₂×C₃×C₅	1	3	yes	—
86	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
87	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	3	yes	—
88	C₂²×C₃×C₅	C₄×D₄	1	3	yes	—
89	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
90	C₂²×C₃×C₅	#120	1	3	yes	—
91	C₂²×C₃×C₅	#121	1	3	yes	—
92	C₂²×C₃×C₅	C₂²⋊Q₈	1	6	yes	—
93	C₂²×C₃×C₅	C₂²⋊Q₈	1	3	yes	—
94	C₂²×C₃×C₅	#123	1	3	yes	—
95	C₂²×C₃×C₅	#125	1	3	yes	—
96	C₂²×C₃×C₅	#127	1	1	yes	characteristic
97	C₂²×C₃×C₅	C₄⋊Q₈	1	3	yes	—
98	C₂²×C₃×C₅	C₄⋊Q₈	1	3	yes	—
99	C₃×C₄×C₅	—	2	12	no	—
100	C₃×C₄×C₅	—	4	6	no	—
101	C₃×C₄×C₅	—	4	2	no	—
102	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₄	—	2	6	no	—
104	C₂²×C₃×C₄	—	2	6	no	—
105	C₂²×C₃×C₄	—	2	3	no	—
106	C₂²×C₃×C₄	—	2	3	no	—
107	C₂²×C₃×C₄	—	2	6	no	—
108	C₂²×C₃×C₄	—	2	6	no	—
109	C₂²×C₃×C₄	—	2	3	no	—
110	C₂²×C₃×C₄	—	2	3	no	—
111	C₂²×C₃×C₄	C₂×C₄×C₅	1	6	yes	—
112	C₂²×C₃×C₄	C₅×D₄	1	6	yes	—
113	C₂²×C₃×C₄	C₅×D₄	1	6	yes	—
114	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
115	C₂²×C₃×C₄	C₅×Q₈	1	6	yes	—
116	C₃×C₄⋊C₄	—	2	24	no	—
117	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
118	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
119	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
120	C₂³×C₅	C₂×C₃×Q₈	1	3	yes	—
121	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
122	C₂³×C₅	C₃×#41	1	3	yes	—
123	C₂³×C₅	C₃×#41	1	1	yes	characteristic
124	C₂×C₄×C₅	—	2	12	no	—
125	C₂×C₄×C₅	—	2	6	no	—
126	C₂×C₄×C₅	—	2	12	no	—
127	C₂×C₄×C₅	—	2	6	no	—
128	C₂×C₄×C₅	—	2	12	no	—
129	C₂×C₄×C₅	—	2	6	no	—
130	C₂×C₄×C₅	—	2	6	no	—
131	C₂×C₄×C₅	—	4	3	no	—
132	C₂×C₄×C₅	—	4	6	no	—
133	C₂×C₄×C₅	—	4	3	no	—
134	C₂×C₄×C₅	—	4	3	no	—
135	C₂×C₄×C₅	—	4	1	no	—
136	C₂×C₄×C₅	C₃×C₄⋊C₄	1	12	yes	complemented
137	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
138	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
139	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
140	C₂×C₄⋊C₄	—	2	12	no	—
141	C₂×C₄⋊C₄	—	2	6	no	—
142	#95	—	2	6	no	—
143	#95	C₃×C₄×C₅	1	4	yes	complemented
144	C₂×C₃×C₅	#384	1	1	yes	characteristic
145	C₂×C₃×C₅	#385	1	3	yes	—
146	C₂×C₃×C₅	#389	1	3	yes	—
147	C₂×C₃×C₅	#392	1	1	yes	characteristic
148	C₂×C₃×C₅	#395	1	3	yes	—
149	C₂×C₃×C₅	#398	1	3	yes	—
150	C₂×C₃×C₅	#399	1	1	yes	characteristic
151	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
152	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
153	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
154	C₂³×C₃	C₂×C₅×Q₈	1	3	yes	—
155	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
156	C₂³×C₃	C₅×#41	1	3	yes	—
157	C₂³×C₃	C₅×#41	1	1	yes	characteristic
158	C₂×C₃×C₄	—	2	12	no	—
159	C₂×C₃×C₄	—	2	6	no	—
160	C₂×C₃×C₄	—	2	12	no	—
161	C₂×C₃×C₄	—	2	6	no	—
162	C₂×C₃×C₄	—	2	12	no	—
163	C₂×C₃×C₄	—	2	6	no	—
164	C₂×C₃×C₄	—	2	6	no	—
165	C₂×C₃×C₄	—	4	3	no	—
166	C₂×C₃×C₄	—	4	6	no	—
167	C₂×C₃×C₄	—	4	3	no	—
168	C₂×C₃×C₄	—	4	3	no	—
169	C₂×C₃×C₄	—	4	1	no	—
170	C₂×C₃×C₄	C₅×C₄⋊C₄	1	12	yes	complemented
171	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	3	yes	—
172	C₂²×C₅	C₃×C₄×D₄	1	3	yes	—
173	C₂²×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
174	C₂²×C₅	C₃×#120	1	3	yes	—
175	C₂²×C₅	C₃×#121	1	3	yes	—
176	C₂²×C₅	C₃×C₂²⋊Q₈	1	6	yes	—
177	C₂²×C₅	C₃×C₂²⋊Q₈	1	3	yes	—
178	C₂²×C₅	C₃×#123	1	3	yes	—
179	C₂²×C₅	C₃×#125	1	3	yes	—
180	C₂²×C₅	C₃×#127	1	1	yes	characteristic
181	C₂²×C₅	C₃×C₄⋊Q₈	1	3	yes	—
182	C₂²×C₅	C₃×C₄⋊Q₈	1	3	yes	—
183	C₄×C₅	—	2	12	no	—
184	C₄×C₅	—	4	6	no	—
185	C₄×C₅	—	4	2	no	—
186	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	—	2	6	no	—
189	C₂²×C₄	—	2	3	no	—
190	C₂²×C₄	—	2	3	no	—
191	C₂²×C₄	—	2	6	no	—
192	C₂²×C₄	—	2	6	no	—
193	C₂²×C₄	—	2	3	no	—
194	C₂²×C₄	—	2	3	no	—
195	C₂²×C₄	C₂×C₃×C₄×C₅	1	6	yes	—
196	C₂²×C₄	C₃×C₅×D₄	1	6	yes	—
197	C₂²×C₄	C₃×C₅×D₄	1	6	yes	—
198	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
199	C₂²×C₄	C₃×C₅×Q₈	1	6	yes	—
200	C₄⋊C₄	—	2	24	no	—
201	C₃×C₅	#1444	1	1	yes	characteristic, direct product factor, Hall
202	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	3	yes	—
203	C₂²×C₃	C₄×C₅×D₄	1	3	yes	—
204	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
205	C₂²×C₃	C₅×#120	1	3	yes	—
206	C₂²×C₃	C₅×#121	1	3	yes	—
207	C₂²×C₃	C₅×C₂²⋊Q₈	1	6	yes	—
208	C₂²×C₃	C₅×C₂²⋊Q₈	1	3	yes	—
209	C₂²×C₃	C₅×#123	1	3	yes	—
210	C₂²×C₃	C₅×#125	1	3	yes	—
211	C₂²×C₃	C₅×#127	1	1	yes	characteristic
212	C₂²×C₃	C₅×C₄⋊Q₈	1	3	yes	—
213	C₂²×C₃	C₅×C₄⋊Q₈	1	3	yes	—
214	C₃×C₄	—	2	12	no	—
215	C₃×C₄	—	4	6	no	—
216	C₃×C₄	—	4	2	no	—
217	C₂×C₅	C₃×#384	1	1	yes	characteristic
218	C₂×C₅	C₃×#385	1	3	yes	—
219	C₂×C₅	C₃×#389	1	3	yes	—
220	C₂×C₅	C₃×#392	1	1	yes	characteristic
221	C₂×C₅	C₃×#395	1	3	yes	—
222	C₂×C₅	C₃×#398	1	3	yes	—
223	C₂×C₅	C₃×#399	1	1	yes	characteristic
224	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
225	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
226	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
227	C₂³	C₂×C₃×C₅×Q₈	1	3	yes	—
228	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
229	C₂³	C₃×C₅×#41	1	3	yes	—
230	C₂³	C₃×C₅×#41	1	1	yes	characteristic
231	C₂×C₄	—	2	12	no	—
232	C₂×C₄	—	2	6	no	—
233	C₂×C₄	—	2	12	no	—
234	C₂×C₄	—	2	6	no	—
235	C₂×C₄	—	2	12	no	—
236	C₂×C₄	—	2	6	no	—
237	C₂×C₄	—	2	6	no	—
238	C₂×C₄	—	4	3	no	—
239	C₂×C₄	—	4	6	no	—
240	C₂×C₄	—	4	3	no	—
241	C₂×C₄	—	4	3	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	C₃×C₅×C₄⋊C₄	1	12	yes	complemented
244	C₂×C₃	C₅×#384	1	1	yes	characteristic
245	C₂×C₃	C₅×#385	1	3	yes	—
246	C₂×C₃	C₅×#389	1	3	yes	—
247	C₂×C₃	C₅×#392	1	1	yes	characteristic
248	C₂×C₃	C₅×#395	1	3	yes	—
249	C₂×C₃	C₅×#398	1	3	yes	—
250	C₂×C₃	C₅×#399	1	1	yes	characteristic
251	C₅	C₃×#1444	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	3	yes	—
253	C₂²	C₃×C₄×C₅×D₄	1	3	yes	—
254	C₂²	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
255	C₂²	C₃×C₅×#120	1	3	yes	—
256	C₂²	C₃×C₅×#121	1	3	yes	—
257	C₂²	C₃×C₅×C₂²⋊Q₈	1	6	yes	—
258	C₂²	C₃×C₅×C₂²⋊Q₈	1	3	yes	—
259	C₂²	C₃×C₅×#123	1	3	yes	—
260	C₂²	C₃×C₅×#125	1	3	yes	—
261	C₂²	C₃×C₅×#127	1	1	yes	characteristic
262	C₂²	C₃×C₅×C₄⋊Q₈	1	3	yes	—
263	C₂²	C₃×C₅×C₄⋊Q₈	1	3	yes	—
264	C₄	—	2	12	no	—
265	C₄	—	4	6	no	—
266	C₄	—	4	2	no	—
267	C₃	C₅×#1444	1	1	yes	characteristic, direct product factor, Sylow
268	C₂	C₃×C₅×#384	1	1	yes	characteristic
269	C₂	C₃×C₅×#385	1	3	yes	—
270	C₂	C₃×C₅×#389	1	3	yes	—
271	C₂	C₃×C₅×#392	1	1	yes	characteristic
272	C₂	C₃×C₅×#395	1	3	yes	—
273	C₂	C₃×C₅×#398	1	3	yes	—
274	C₂	C₃×C₅×#399	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃×C₅	C₂³
commutator	C₂³	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂⁴	C₂³×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1444	C₃	direct (N × H)
11. C₃×C₅×#95	C₄	semidirect
12. C₃×#1444	C₅	direct (N × H)
40. C₅×#95	C₃×C₄	semidirect
41. #1444	C₃×C₅	direct (N × H)
61. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
68. C₃×#95	C₄×C₅	semidirect
136. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
143. #95	C₃×C₄×C₅	semidirect
170. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
201. C₃×C₅	#1444	direct (N × H)
243. C₂×C₄	C₃×C₅×C₄⋊C₄	semidirect
251. C₅	C₃×#1444	direct (N × H)
267. C₃	C₅×#1444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#1444	3
C₃×#1444	5

Subgroups — C3×C5×#1444 #14274478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1444 #14274478