Subgroups — C₃×C₅×#1443 #14274477

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#95	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×#1443	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	3	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₅×#95	—	2	6	no	—
9	C₃×C₅×#95	—	2	6	no	—
10	C₃×C₅×#95	C₄	1	4	yes	complemented
11	C₃×#1443	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×#95	C₂×C₃	1	3	yes	—
13	C₂×C₅×#95	C₂×C₃	1	3	yes	—
14	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
15	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₅	—	2	3	no	—
17	C₂²×C₃×C₄×C₅	—	2	3	no	—
18	C₂²×C₃×C₄×C₅	—	2	3	no	—
19	C₂²×C₃×C₄×C₅	—	2	3	no	—
20	C₂²×C₃×C₄×C₅	—	2	3	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	—	2	3	no	—
26	C₂²×C₃×C₄×C₅	—	2	3	no	—
27	C₂²×C₃×C₄×C₅	—	2	3	no	—
28	C₂²×C₃×C₄×C₅	—	2	3	no	—
29	C₂²×C₃×C₄×C₅	—	2	3	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	6	yes	—
31	C₂²×C₃×C₄×C₅	D₄	1	6	yes	—
32	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
33	C₂×C₃×#95	C₂×C₅	1	3	yes	—
34	C₂×C₃×#95	C₂×C₅	1	3	yes	—
35	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
37	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
38	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
39	C₅×#95	—	2	6	no	—
40	C₅×#95	—	2	6	no	—
41	C₅×#95	C₃×C₄	1	4	yes	complemented
42	#1443	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
44	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
45	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
46	C₂³×C₃×C₅	#41	1	3	yes	—
47	C₂³×C₃×C₅	#41	1	3	yes	—
48	C₂³×C₃×C₅	#41	1	3	yes	—
49	C₂³×C₃×C₅	#41	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	—	2	6	no	—
51	C₂×C₃×C₄×C₅	—	2	6	no	—
52	C₂×C₃×C₄×C₅	—	2	6	no	—
53	C₂×C₃×C₄×C₅	—	2	6	no	—
54	C₂×C₃×C₄×C₅	—	2	6	no	—
55	C₂×C₃×C₄×C₅	—	2	6	no	—
56	C₂×C₃×C₄×C₅	—	2	6	no	—
57	C₂×C₃×C₄×C₅	—	4	3	no	—
58	C₂×C₃×C₄×C₅	—	4	3	no	—
59	C₂×C₃×C₄×C₅	—	4	3	no	—
60	C₂×C₃×C₄×C₅	—	4	3	no	—
61	C₂×C₃×C₄×C₅	—	4	3	no	—
62	C₂×C₃×C₄×C₅	—	4	3	no	—
63	C₂×C₃×C₄×C₅	—	4	3	no	—
64	C₂×C₃×C₄×C₅	—	4	1	no	—
65	C₂×C₃×C₄×C₅	—	4	3	no	—
66	C₂×C₃×C₄×C₅	—	4	3	no	—
67	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
68	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
69	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
70	C₃×#95	—	2	6	no	—
71	C₃×#95	—	2	6	no	—
72	C₃×#95	C₄×C₅	1	4	yes	complemented
73	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
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	—	2	3	no	—
79	C₂²×C₄×C₅	—	2	3	no	—
80	C₂²×C₄×C₅	—	2	3	no	—
81	C₂²×C₄×C₅	—	2	3	no	—
82	C₂²×C₄×C₅	—	2	3	no	—
83	C₂²×C₄×C₅	—	2	3	no	—
84	C₂²×C₄×C₅	—	2	3	no	—
85	C₂²×C₄×C₅	—	2	3	no	—
86	C₂²×C₄×C₅	—	2	3	no	—
87	C₂²×C₄×C₅	—	2	3	no	—
88	C₂²×C₄×C₅	C₂×C₃×C₄	1	6	yes	—
89	C₂²×C₄×C₅	C₃×D₄	1	6	yes	—
90	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
91	C₂×#95	C₂×C₃×C₅	1	3	yes	—
92	C₂×#95	C₂×C₃×C₅	1	3	yes	—
93	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
94	C₂²×C₃×C₅	#117	1	3	yes	—
95	C₂²×C₃×C₅	C₄×D₄	1	3	yes	—
96	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
97	C₂²×C₃×C₅	#121	1	3	yes	—
98	C₂²×C₃×C₅	C₂²⋊Q₈	1	3	yes	—
99	C₂²×C₃×C₅	#123	1	3	yes	—
100	C₂²×C₃×C₅	#123	1	3	yes	—
101	C₂²×C₃×C₅	#124	1	3	yes	—
102	C₂²×C₃×C₅	#125	1	3	yes	—
103	C₂²×C₃×C₅	#126	1	1	yes	characteristic
104	C₂²×C₃×C₅	#126	1	3	yes	—
105	C₂²×C₃×C₅	#126	1	3	yes	—
106	C₂²×C₃×C₅	#126	1	3	yes	—
107	C₃×C₄×C₅	—	4	6	no	—
108	C₃×C₄×C₅	—	4	2	no	—
109	C₃×C₄×C₅	—	4	6	no	—
110	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
111	C₂²×C₃×C₄	—	2	3	no	—
112	C₂²×C₃×C₄	—	2	3	no	—
113	C₂²×C₃×C₄	—	2	3	no	—
114	C₂²×C₃×C₄	—	2	3	no	—
115	C₂²×C₃×C₄	—	2	3	no	—
116	C₂²×C₃×C₄	—	2	3	no	—
117	C₂²×C₃×C₄	—	2	3	no	—
118	C₂²×C₃×C₄	—	2	3	no	—
119	C₂²×C₃×C₄	—	2	3	no	—
120	C₂²×C₃×C₄	—	2	3	no	—
121	C₂²×C₃×C₄	—	2	3	no	—
122	C₂²×C₃×C₄	—	2	3	no	—
123	C₂²×C₃×C₄	—	2	3	no	—
124	C₂²×C₃×C₄	—	2	3	no	—
125	C₂²×C₃×C₄	C₂×C₄×C₅	1	6	yes	—
126	C₂²×C₃×C₄	C₅×D₄	1	6	yes	—
127	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
128	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
129	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
130	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
131	C₂³×C₅	C₃×#41	1	3	yes	—
132	C₂³×C₅	C₃×#41	1	3	yes	—
133	C₂³×C₅	C₃×#41	1	3	yes	—
134	C₂³×C₅	C₃×#41	1	1	yes	characteristic
135	C₂×C₄×C₅	—	2	6	no	—
136	C₂×C₄×C₅	—	2	6	no	—
137	C₂×C₄×C₅	—	2	6	no	—
138	C₂×C₄×C₅	—	2	6	no	—
139	C₂×C₄×C₅	—	2	6	no	—
140	C₂×C₄×C₅	—	2	6	no	—
141	C₂×C₄×C₅	—	2	6	no	—
142	C₂×C₄×C₅	—	4	3	no	—
143	C₂×C₄×C₅	—	4	3	no	—
144	C₂×C₄×C₅	—	4	3	no	—
145	C₂×C₄×C₅	—	4	3	no	—
146	C₂×C₄×C₅	—	4	3	no	—
147	C₂×C₄×C₅	—	4	3	no	—
148	C₂×C₄×C₅	—	4	3	no	—
149	C₂×C₄×C₅	—	4	1	no	—
150	C₂×C₄×C₅	—	4	3	no	—
151	C₂×C₄×C₅	—	4	3	no	—
152	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
153	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
154	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
155	#95	—	2	6	no	—
156	#95	—	2	6	no	—
157	#95	C₃×C₄×C₅	1	4	yes	complemented
158	C₂×C₃×C₅	#383	1	1	yes	characteristic
159	C₂×C₃×C₅	#387	1	3	yes	—
160	C₂×C₃×C₅	#388	1	3	yes	—
161	C₂×C₃×C₅	#396	1	1	yes	characteristic
162	C₂×C₃×C₅	#397	1	3	yes	—
163	C₂×C₃×C₅	#400	1	3	yes	—
164	C₂×C₃×C₅	#401	1	1	yes	characteristic
165	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
166	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
167	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
168	C₂³×C₃	C₅×#41	1	3	yes	—
169	C₂³×C₃	C₅×#41	1	3	yes	—
170	C₂³×C₃	C₅×#41	1	3	yes	—
171	C₂³×C₃	C₅×#41	1	1	yes	characteristic
172	C₂×C₃×C₄	—	2	6	no	—
173	C₂×C₃×C₄	—	2	6	no	—
174	C₂×C₃×C₄	—	2	6	no	—
175	C₂×C₃×C₄	—	2	6	no	—
176	C₂×C₃×C₄	—	2	6	no	—
177	C₂×C₃×C₄	—	2	6	no	—
178	C₂×C₃×C₄	—	2	6	no	—
179	C₂×C₃×C₄	—	4	3	no	—
180	C₂×C₃×C₄	—	4	3	no	—
181	C₂×C₃×C₄	—	4	3	no	—
182	C₂×C₃×C₄	—	4	3	no	—
183	C₂×C₃×C₄	—	4	3	no	—
184	C₂×C₃×C₄	—	4	3	no	—
185	C₂×C₃×C₄	—	4	3	no	—
186	C₂×C₃×C₄	—	4	1	no	—
187	C₂×C₃×C₄	—	4	3	no	—
188	C₂×C₃×C₄	—	4	3	no	—
189	C₂²×C₅	C₃×#117	1	3	yes	—
190	C₂²×C₅	C₃×C₄×D₄	1	3	yes	—
191	C₂²×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
192	C₂²×C₅	C₃×#121	1	3	yes	—
193	C₂²×C₅	C₃×C₂²⋊Q₈	1	3	yes	—
194	C₂²×C₅	C₃×#123	1	3	yes	—
195	C₂²×C₅	C₃×#123	1	3	yes	—
196	C₂²×C₅	C₃×#124	1	3	yes	—
197	C₂²×C₅	C₃×#125	1	3	yes	—
198	C₂²×C₅	C₃×#126	1	1	yes	characteristic
199	C₂²×C₅	C₃×#126	1	3	yes	—
200	C₂²×C₅	C₃×#126	1	3	yes	—
201	C₂²×C₅	C₃×#126	1	3	yes	—
202	C₄×C₅	—	4	6	no	—
203	C₄×C₅	—	4	2	no	—
204	C₄×C₅	—	4	6	no	—
205	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
206	C₂²×C₄	—	2	3	no	—
207	C₂²×C₄	—	2	3	no	—
208	C₂²×C₄	—	2	3	no	—
209	C₂²×C₄	—	2	3	no	—
210	C₂²×C₄	—	2	3	no	—
211	C₂²×C₄	—	2	3	no	—
212	C₂²×C₄	—	2	3	no	—
213	C₂²×C₄	—	2	3	no	—
214	C₂²×C₄	—	2	3	no	—
215	C₂²×C₄	—	2	3	no	—
216	C₂²×C₄	—	2	3	no	—
217	C₂²×C₄	—	2	3	no	—
218	C₂²×C₄	—	2	3	no	—
219	C₂²×C₄	—	2	3	no	—
220	C₂²×C₄	C₂×C₃×C₄×C₅	1	6	yes	—
221	C₂²×C₄	C₃×C₅×D₄	1	6	yes	—
222	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
223	C₃×C₅	#1443	1	1	yes	characteristic, direct product factor, Hall
224	C₂²×C₃	C₅×#117	1	3	yes	—
225	C₂²×C₃	C₄×C₅×D₄	1	3	yes	—
226	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
227	C₂²×C₃	C₅×#121	1	3	yes	—
228	C₂²×C₃	C₅×C₂²⋊Q₈	1	3	yes	—
229	C₂²×C₃	C₅×#123	1	3	yes	—
230	C₂²×C₃	C₅×#123	1	3	yes	—
231	C₂²×C₃	C₅×#124	1	3	yes	—
232	C₂²×C₃	C₅×#125	1	3	yes	—
233	C₂²×C₃	C₅×#126	1	1	yes	characteristic
234	C₂²×C₃	C₅×#126	1	3	yes	—
235	C₂²×C₃	C₅×#126	1	3	yes	—
236	C₂²×C₃	C₅×#126	1	3	yes	—
237	C₃×C₄	—	4	6	no	—
238	C₃×C₄	—	4	2	no	—
239	C₃×C₄	—	4	6	no	—
240	C₂×C₅	C₃×#383	1	1	yes	characteristic
241	C₂×C₅	C₃×#387	1	3	yes	—
242	C₂×C₅	C₃×#388	1	3	yes	—
243	C₂×C₅	C₃×#396	1	1	yes	characteristic
244	C₂×C₅	C₃×#397	1	3	yes	—
245	C₂×C₅	C₃×#400	1	3	yes	—
246	C₂×C₅	C₃×#401	1	1	yes	characteristic
247	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
248	C₂³	C₂×C₃×C₅×D₄	1	3	yes	—
249	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
250	C₂³	C₃×C₅×#41	1	3	yes	—
251	C₂³	C₃×C₅×#41	1	3	yes	—
252	C₂³	C₃×C₅×#41	1	3	yes	—
253	C₂³	C₃×C₅×#41	1	1	yes	characteristic
254	C₂×C₄	—	2	6	no	—
255	C₂×C₄	—	2	6	no	—
256	C₂×C₄	—	2	6	no	—
257	C₂×C₄	—	2	6	no	—
258	C₂×C₄	—	2	6	no	—
259	C₂×C₄	—	2	6	no	—
260	C₂×C₄	—	2	6	no	—
261	C₂×C₄	—	4	3	no	—
262	C₂×C₄	—	4	3	no	—
263	C₂×C₄	—	4	3	no	—
264	C₂×C₄	—	4	3	no	—
265	C₂×C₄	—	4	3	no	—
266	C₂×C₄	—	4	3	no	—
267	C₂×C₄	—	4	3	no	—
268	C₂×C₄	—	4	1	no	—
269	C₂×C₄	—	4	3	no	—
270	C₂×C₄	—	4	3	no	—
271	C₂×C₃	C₅×#383	1	1	yes	characteristic
272	C₂×C₃	C₅×#387	1	3	yes	—
273	C₂×C₃	C₅×#388	1	3	yes	—
274	C₂×C₃	C₅×#396	1	1	yes	characteristic
275	C₂×C₃	C₅×#397	1	3	yes	—
276	C₂×C₃	C₅×#400	1	3	yes	—
277	C₂×C₃	C₅×#401	1	1	yes	characteristic
278	C₅	C₃×#1443	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²	C₃×C₅×#117	1	3	yes	—
280	C₂²	C₃×C₄×C₅×D₄	1	3	yes	—
281	C₂²	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
282	C₂²	C₃×C₅×#121	1	3	yes	—
283	C₂²	C₃×C₅×C₂²⋊Q₈	1	3	yes	—
284	C₂²	C₃×C₅×#123	1	3	yes	—
285	C₂²	C₃×C₅×#123	1	3	yes	—
286	C₂²	C₃×C₅×#124	1	3	yes	—
287	C₂²	C₃×C₅×#125	1	3	yes	—
288	C₂²	C₃×C₅×#126	1	1	yes	characteristic
289	C₂²	C₃×C₅×#126	1	3	yes	—
290	C₂²	C₃×C₅×#126	1	3	yes	—
291	C₂²	C₃×C₅×#126	1	3	yes	—
292	C₄	—	4	6	no	—
293	C₄	—	4	2	no	—
294	C₄	—	4	6	no	—
295	C₃	C₅×#1443	1	1	yes	characteristic, direct product factor, Sylow
296	C₂	C₃×C₅×#383	1	1	yes	characteristic
297	C₂	C₃×C₅×#387	1	3	yes	—
298	C₂	C₃×C₅×#388	1	3	yes	—
299	C₂	C₃×C₅×#396	1	1	yes	characteristic
300	C₂	C₃×C₅×#397	1	3	yes	—
301	C₂	C₃×C₅×#400	1	3	yes	—
302	C₂	C₃×C₅×#401	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×#1443	C₃	direct (N × H)
10. C₃×C₅×#95	C₄	semidirect
11. C₃×#1443	C₅	direct (N × H)
41. C₅×#95	C₃×C₄	semidirect
42. #1443	C₃×C₅	direct (N × H)
72. C₃×#95	C₄×C₅	semidirect
157. #95	C₃×C₄×C₅	semidirect
223. C₃×C₅	#1443	direct (N × H)
278. C₅	C₃×#1443	direct (N × H)
295. C₃	C₅×#1443	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×C₅×#95	2
C₅×#1443	3
C₃×#1443	5

Subgroups — C3×C5×#1443 #14274477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1443 #14274477