Subgroups — C₃×C₅×#2483 #14275517

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
2	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#385	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#381	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic
6	C₅×#2483	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
11	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₃×C₅×#95	C₂²	1	4	yes	complemented
17	C₃×C₅×#95	C₂²	1	8	yes	complemented
18	C₃×#2483	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
20	C₅×#397	C₂×C₃	1	4	yes	complemented
21	C₅×#385	C₂×C₃	1	4	yes	complemented
22	C₅×#381	C₂×C₃	1	4	yes	complemented
23	C₅×#379	C₂×C₃	1	1	yes	characteristic
24	C₂⁴×C₃×C₅	—	2	8	no	—
25	C₂⁴×C₃×C₅	—	4	2	no	—
26	C₂⁴×C₃×C₅	D₄	1	4	yes	—
27	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
28	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
29	C₂²×C₃×C₄×C₅	—	2	4	no	—
30	C₂²×C₃×C₄×C₅	—	2	4	no	—
31	C₂²×C₃×C₄×C₅	—	2	8	no	—
32	C₂²×C₃×C₄×C₅	—	4	4	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₃×C₅×C₄⋊C₄	—	4	4	no	—
37	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
38	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
39	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
40	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
41	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
42	C₃×#397	C₂×C₅	1	4	yes	complemented
43	C₃×#385	C₂×C₅	1	4	yes	complemented
44	C₃×#381	C₂×C₅	1	4	yes	complemented
45	C₃×#379	C₂×C₅	1	1	yes	characteristic
46	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
48	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
49	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
50	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
51	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
55	C₅×#95	C₂²×C₃	1	4	yes	complemented
56	C₅×#95	C₂²×C₃	1	8	yes	complemented
57	#2483	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
58	C₂³×C₃×C₅	—	2	4	no	—
59	C₂³×C₃×C₅	—	2	4	no	—
60	C₂³×C₃×C₅	—	2	16	no	—
61	C₂³×C₃×C₅	—	2	4	no	—
62	C₂³×C₃×C₅	—	2	2	no	—
63	C₂³×C₃×C₅	—	4	4	no	—
64	C₂³×C₃×C₅	—	4	16	no	—
65	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
66	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
67	C₂³×C₃×C₅	#41	1	8	yes	—
68	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	—	2	4	no	—
70	C₂×C₃×C₄×C₅	—	2	4	no	—
71	C₂×C₃×C₄×C₅	—	2	8	no	—
72	C₂×C₃×C₄×C₅	—	2	8	no	—
73	C₂×C₃×C₄×C₅	—	2	4	no	—
74	C₂×C₃×C₄×C₅	—	2	8	no	—
75	C₂×C₃×C₄×C₅	—	4	8	no	—
76	C₂×C₃×C₄×C₅	—	4	8	no	—
77	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
79	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
81	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
83	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
84	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
86	C₃×#95	C₂²×C₅	1	4	yes	complemented
87	C₃×#95	C₂²×C₅	1	8	yes	complemented
88	C₂⁴×C₅	—	2	8	no	—
89	C₂⁴×C₅	—	4	2	no	—
90	C₂⁴×C₅	C₃×D₄	1	4	yes	—
91	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
92	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	—	2	4	no	—
95	C₂²×C₄×C₅	—	2	8	no	—
96	C₂²×C₄×C₅	—	4	4	no	—
97	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
98	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
99	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
100	C₅×C₄⋊C₄	—	4	4	no	—
101	C₅×C₂²⋊C₄	—	2	8	no	—
102	C₅×C₂²⋊C₄	—	2	8	no	—
103	C₅×C₂²⋊C₄	—	2	8	no	—
104	C₅×C₂²⋊C₄	—	4	2	no	—
105	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
106	#397	C₂×C₃×C₅	1	4	yes	complemented
107	#385	C₂×C₃×C₅	1	4	yes	complemented
108	#381	C₂×C₃×C₅	1	4	yes	complemented
109	#379	C₂×C₃×C₅	1	1	yes	characteristic
110	C₂²×C₃×C₅	—	2	4	no	—
111	C₂²×C₃×C₅	—	2	4	no	—
112	C₂²×C₃×C₅	—	2	16	no	—
113	C₂²×C₃×C₅	—	2	4	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	—	4	16	no	—
116	C₂²×C₃×C₅	—	4	4	no	—
117	C₂²×C₃×C₅	#123	1	8	yes	—
118	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
119	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
120	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
121	C₃×C₄×C₅	—	4	4	no	—
122	C₃×C₄×C₅	—	4	4	no	—
123	C₃×C₄×C₅	—	4	4	no	—
124	C₂⁴×C₃	—	2	8	no	—
125	C₂⁴×C₃	—	4	2	no	—
126	C₂⁴×C₃	C₅×D₄	1	4	yes	—
127	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
128	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
129	C₂²×C₃×C₄	—	2	4	no	—
130	C₂²×C₃×C₄	—	2	4	no	—
131	C₂²×C₃×C₄	—	2	8	no	—
132	C₂²×C₃×C₄	—	4	4	no	—
133	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
134	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
135	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
136	C₃×C₄⋊C₄	—	4	4	no	—
137	C₃×C₂²⋊C₄	—	2	8	no	—
138	C₃×C₂²⋊C₄	—	2	8	no	—
139	C₃×C₂²⋊C₄	—	2	8	no	—
140	C₃×C₂²⋊C₄	—	4	2	no	—
141	C₂³×C₅	—	2	4	no	—
142	C₂³×C₅	—	2	4	no	—
143	C₂³×C₅	—	2	16	no	—
144	C₂³×C₅	—	2	4	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	—	4	4	no	—
147	C₂³×C₅	—	4	16	no	—
148	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
149	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
150	C₂³×C₅	C₃×#41	1	8	yes	—
151	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
152	C₂×C₄×C₅	—	2	4	no	—
153	C₂×C₄×C₅	—	2	4	no	—
154	C₂×C₄×C₅	—	2	8	no	—
155	C₂×C₄×C₅	—	2	8	no	—
156	C₂×C₄×C₅	—	2	4	no	—
157	C₂×C₄×C₅	—	2	8	no	—
158	C₂×C₄×C₅	—	4	8	no	—
159	C₂×C₄×C₅	—	4	8	no	—
160	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
161	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
162	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
163	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
164	C₂×C₂²⋊C₄	—	2	8	no	—
165	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
166	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
167	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
168	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
169	#95	C₂²×C₃×C₅	1	4	yes	complemented
170	#95	C₂²×C₃×C₅	1	8	yes	complemented
171	C₂×C₃×C₅	—	2	8	no	—
172	C₂×C₃×C₅	—	4	2	no	—
173	C₂×C₃×C₅	C₂×#123	1	2	yes	—
174	C₂×C₃×C₅	#534	1	1	yes	characteristic
175	C₂×C₃×C₅	#551	1	4	yes	—
176	C₂³×C₃	—	2	4	no	—
177	C₂³×C₃	—	2	4	no	—
178	C₂³×C₃	—	2	16	no	—
179	C₂³×C₃	—	2	4	no	—
180	C₂³×C₃	—	2	2	no	—
181	C₂³×C₃	—	4	4	no	—
182	C₂³×C₃	—	4	16	no	—
183	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
184	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
185	C₂³×C₃	C₅×#41	1	8	yes	—
186	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄	—	2	4	no	—
188	C₂×C₃×C₄	—	2	4	no	—
189	C₂×C₃×C₄	—	2	8	no	—
190	C₂×C₃×C₄	—	2	8	no	—
191	C₂×C₃×C₄	—	2	4	no	—
192	C₂×C₃×C₄	—	2	8	no	—
193	C₂×C₃×C₄	—	4	8	no	—
194	C₂×C₃×C₄	—	4	8	no	—
195	C₂²×C₅	—	2	4	no	—
196	C₂²×C₅	—	2	4	no	—
197	C₂²×C₅	—	2	16	no	—
198	C₂²×C₅	—	2	4	no	—
199	C₂²×C₅	—	2	2	no	—
200	C₂²×C₅	—	4	16	no	—
201	C₂²×C₅	—	4	4	no	—
202	C₂²×C₅	C₃×#123	1	8	yes	—
203	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
204	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
205	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
206	C₄×C₅	—	4	4	no	—
207	C₄×C₅	—	4	4	no	—
208	C₄×C₅	—	4	4	no	—
209	C₂⁴	—	2	8	no	—
210	C₂⁴	—	4	2	no	—
211	C₂⁴	C₃×C₅×D₄	1	4	yes	—
212	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
213	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	8	no	—
217	C₂²×C₄	—	4	4	no	—
218	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
219	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
220	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
221	C₄⋊C₄	—	4	4	no	—
222	C₂²⋊C₄	—	2	8	no	—
223	C₂²⋊C₄	—	2	8	no	—
224	C₂²⋊C₄	—	2	8	no	—
225	C₂²⋊C₄	—	4	2	no	—
226	C₃×C₅	#2483	1	1	yes	characteristic, direct product factor, Hall
227	C₂²×C₃	—	2	4	no	—
228	C₂²×C₃	—	2	4	no	—
229	C₂²×C₃	—	2	16	no	—
230	C₂²×C₃	—	2	4	no	—
231	C₂²×C₃	—	2	2	no	—
232	C₂²×C₃	—	4	16	no	—
233	C₂²×C₃	—	4	4	no	—
234	C₂²×C₃	C₅×#123	1	8	yes	—
235	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
236	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
237	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
238	C₃×C₄	—	4	4	no	—
239	C₃×C₄	—	4	4	no	—
240	C₃×C₄	—	4	4	no	—
241	C₂×C₅	—	2	8	no	—
242	C₂×C₅	—	4	2	no	—
243	C₂×C₅	C₂×C₃×#123	1	2	yes	—
244	C₂×C₅	C₃×#534	1	1	yes	characteristic
245	C₂×C₅	C₃×#551	1	4	yes	—
246	C₂³	—	2	4	no	—
247	C₂³	—	2	4	no	—
248	C₂³	—	2	4	no	—
249	C₂³	—	2	16	no	—
250	C₂³	—	2	2	no	—
251	C₂³	—	4	4	no	—
252	C₂³	—	4	16	no	—
253	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
254	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
255	C₂³	C₃×C₅×#41	1	8	yes	—
256	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	8	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	4	8	no	—
264	C₂×C₄	—	4	8	no	—
265	C₂×C₃	—	2	8	no	—
266	C₂×C₃	—	4	2	no	—
267	C₂×C₃	C₂×C₅×#123	1	2	yes	—
268	C₂×C₃	C₅×#534	1	1	yes	characteristic
269	C₂×C₃	C₅×#551	1	4	yes	—
270	C₅	C₃×#2483	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²	—	2	4	no	—
272	C₂²	—	2	4	no	—
273	C₂²	—	2	16	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	4	16	no	—
277	C₂²	—	4	4	no	—
278	C₂²	C₃×C₅×#123	1	8	yes	—
279	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
280	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
281	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
282	C₄	—	4	4	no	—
283	C₄	—	4	4	no	—
284	C₄	—	4	4	no	—
285	C₃	C₅×#2483	1	1	yes	characteristic, direct product factor, Sylow
286	C₂	—	2	8	no	—
287	C₂	—	4	2	no	—
288	C₂	C₂×C₃×C₅×#123	1	2	yes	—
289	C₂	C₃×C₅×#534	1	1	yes	characteristic
290	C₂	C₃×C₅×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#397	C₂	semidirect
3. C₃×C₅×#385	C₂	semidirect
4. C₃×C₅×#381	C₂	semidirect
6. C₅×#2483	C₃	direct (N × H)
10. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
16. C₃×C₅×#95	C₂²	semidirect
17. C₃×C₅×#95	C₂²	semidirect
18. C₃×#2483	C₅	direct (N × H)
20. C₅×#397	C₂×C₃	semidirect
21. C₅×#385	C₂×C₃	semidirect
22. C₅×#381	C₂×C₃	semidirect
42. C₃×#397	C₂×C₅	semidirect
43. C₃×#385	C₂×C₅	semidirect
44. C₃×#381	C₂×C₅	semidirect
49. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
55. C₅×#95	C₂²×C₃	semidirect
56. C₅×#95	C₂²×C₃	semidirect
57. #2483	C₃×C₅	direct (N × H)
80. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
86. C₃×#95	C₂²×C₅	semidirect
87. C₃×#95	C₂²×C₅	semidirect
106. #397	C₂×C₃×C₅	semidirect
107. #385	C₂×C₃×C₅	semidirect
108. #381	C₂×C₃×C₅	semidirect
163. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
169. #95	C₂²×C₃×C₅	semidirect
170. #95	C₂²×C₃×C₅	semidirect
226. C₃×C₅	#2483	direct (N × H)
270. C₅	C₃×#2483	direct (N × H)
285. C₃	C₅×#2483	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×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₃×C₅×#379	2
C₅×#2483	3
C₃×#2483	5

Subgroups — C3×C5×#2483 #14275517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2483 #14275517