Subgroups — C₃×C₅×#2082 #14275116

Order 1920.

368 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#430	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₅×#2082	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₃×C₅×#108	—	2	2	no	—
17	C₃×C₅×#103	—	2	2	no	—
18	C₃×C₅×#103	—	2	2	no	—
19	C₃×C₅×#101	—	2	2	no	—
20	C₃×#2082	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₅×#430	C₂×C₃	1	1	yes	characteristic
22	C₅×#419	C₂×C₃	1	1	yes	characteristic
23	C₅×#419	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic
25	C₅×#344	C₂×C₃	1	1	yes	characteristic
26	C₅×#344	C₂×C₃	1	1	yes	characteristic
27	C₅×H(3,ℤ/4)	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	2	1	no	—
30	C₂×C₃×C₅×Q₈	—	2	1	no	—
31	C₂×C₃×C₅×Q₈	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₃×C₅×M₁₆	—	2	1	no	—
37	C₃×C₅×M₁₆	—	2	1	no	—
38	C₃×C₅×M₁₆	—	2	1	no	—
39	C₃×C₅×M₁₆	—	2	1	no	—
40	C₃×C₅×M₁₆	—	2	1	no	—
41	C₃×C₅×M₁₆	—	2	1	no	—
42	C₃×C₅×M₁₆	—	2	1	no	—
43	C₃×C₅×M₁₆	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×#430	C₂×C₅	1	1	yes	characteristic
55	C₃×#419	C₂×C₅	1	1	yes	characteristic
56	C₃×#419	C₂×C₅	1	1	yes	characteristic
57	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic
58	C₃×#344	C₂×C₅	1	1	yes	characteristic
59	C₃×#344	C₂×C₅	1	1	yes	characteristic
60	C₃×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
66	C₅×#117	C₂²×C₃	1	1	yes	characteristic
67	C₅×#117	C₂²×C₃	1	1	yes	characteristic
68	C₅×#108	—	2	2	no	—
69	C₅×#103	—	2	2	no	—
70	C₅×#103	—	2	2	no	—
71	C₅×#101	—	2	2	no	—
72	#2082	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	#41	1	1	yes	characteristic
74	C₃×C₅×Q₈	—	2	2	no	—
75	C₃×C₅×Q₈	—	2	2	no	—
76	C₃×C₅×Q₈	—	4	1	no	—
77	C₃×C₅×Q₈	—	4	1	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	4	1	no	—
81	C₂×C₃×C₄×C₅	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	4	1	no	—
83	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
89	C₃×C₅×C₈	—	2	2	no	—
90	C₃×C₅×C₈	—	4	1	no	—
91	C₃×C₅×C₈	—	4	1	no	—
92	C₃×C₅×C₈	—	4	1	no	—
93	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
96	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
97	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
98	C₃×#117	C₂²×C₅	1	1	yes	characteristic
99	C₃×#117	C₂²×C₅	1	1	yes	characteristic
100	C₃×#108	—	2	2	no	—
101	C₃×#103	—	2	2	no	—
102	C₃×#103	—	2	2	no	—
103	C₃×#101	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
112	C₅×M₁₆	—	2	1	no	—
113	C₅×M₁₆	—	2	1	no	—
114	C₅×M₁₆	—	2	1	no	—
115	C₅×M₁₆	—	2	1	no	—
116	C₅×M₁₆	—	2	1	no	—
117	C₅×M₁₆	—	2	1	no	—
118	C₅×M₁₆	—	2	1	no	—
119	C₅×M₁₆	—	2	1	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
124	C₅×C₄⋊C₄	—	2	1	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₂²⋊C₄	—	2	1	no	—
127	C₅×C₂²⋊C₄	—	2	1	no	—
128	C₄²×C₅	—	2	1	no	—
129	C₄²×C₅	—	2	1	no	—
130	#430	C₂×C₃×C₅	1	1	yes	characteristic
131	#419	C₂×C₃×C₅	1	1	yes	characteristic
132	#419	C₂×C₃×C₅	1	1	yes	characteristic
133	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic
134	#344	C₂×C₃×C₅	1	1	yes	characteristic
135	#344	C₂×C₃×C₅	1	1	yes	characteristic
136	H(3,ℤ/4)	C₂×C₃×C₅	1	1	yes	characteristic
137	C₂²×C₃×C₅	—	4	1	no	—
138	C₂²×C₃×C₅	#123	1	1	yes	characteristic
139	C₂²×C₃×C₅	#124	1	1	yes	characteristic
140	C₂²×C₃×C₅	#126	1	1	yes	characteristic
141	C₃×C₄×C₅	—	4	2	no	—
142	C₃×C₄×C₅	—	8	1	no	—
143	C₃×C₄×C₅	—	8	1	no	—
144	C₃×C₄×C₅	#121	1	1	yes	characteristic
145	C₃×C₄×C₅	#123	1	1	yes	characteristic
146	C₃×C₄×C₅	#123	1	1	yes	characteristic
147	C₃×C₄×C₅	#126	1	1	yes	characteristic
148	C₂×C₃×Q₈	—	2	1	no	—
149	C₂×C₃×Q₈	—	2	1	no	—
150	C₂×C₃×Q₈	—	2	1	no	—
151	C₂×C₃×Q₈	—	2	1	no	—
152	C₂×C₃×Q₈	—	2	1	no	—
153	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
156	C₃×M₁₆	—	2	1	no	—
157	C₃×M₁₆	—	2	1	no	—
158	C₃×M₁₆	—	2	1	no	—
159	C₃×M₁₆	—	2	1	no	—
160	C₃×M₁₆	—	2	1	no	—
161	C₃×M₁₆	—	2	1	no	—
162	C₃×M₁₆	—	2	1	no	—
163	C₃×M₁₆	—	2	1	no	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	2	1	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	—	2	1	no	—
170	C₃×C₂²⋊C₄	—	2	1	no	—
171	C₃×C₂²⋊C₄	—	2	1	no	—
172	C₃×C₄²	—	2	1	no	—
173	C₃×C₄²	—	2	1	no	—
174	C₂³×C₅	C₃×#41	1	1	yes	characteristic
175	C₅×Q₈	—	2	2	no	—
176	C₅×Q₈	—	2	2	no	—
177	C₅×Q₈	—	4	1	no	—
178	C₅×Q₈	—	4	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
187	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
188	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
189	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
190	C₅×C₈	—	2	2	no	—
191	C₅×C₈	—	4	1	no	—
192	C₅×C₈	—	4	1	no	—
193	C₅×C₈	—	4	1	no	—
194	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
195	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
198	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
199	#117	C₂²×C₃×C₅	1	1	yes	characteristic
200	#117	C₂²×C₃×C₅	1	1	yes	characteristic
201	#108	—	2	2	no	—
202	#103	—	2	2	no	—
203	#103	—	2	2	no	—
204	#101	—	2	2	no	—
205	C₂×C₃×C₅	—	2	1	no	—
206	C₂×C₃×C₅	—	2	1	no	—
207	C₂×C₃×C₅	—	2	1	no	—
208	C₂×C₃×C₅	#397	1	1	yes	characteristic
209	C₂³×C₃	C₅×#41	1	1	yes	characteristic
210	C₃×Q₈	—	2	2	no	—
211	C₃×Q₈	—	2	2	no	—
212	C₃×Q₈	—	4	1	no	—
213	C₃×Q₈	—	4	1	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	4	1	no	—
216	C₂×C₃×C₄	—	4	1	no	—
217	C₂×C₃×C₄	—	4	1	no	—
218	C₂×C₃×C₄	—	4	1	no	—
219	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
222	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
223	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
224	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
225	C₃×C₈	—	2	2	no	—
226	C₃×C₈	—	4	1	no	—
227	C₃×C₈	—	4	1	no	—
228	C₃×C₈	—	4	1	no	—
229	C₂²×C₅	—	4	1	no	—
230	C₂²×C₅	C₃×#123	1	1	yes	characteristic
231	C₂²×C₅	C₃×#124	1	1	yes	characteristic
232	C₂²×C₅	C₃×#126	1	1	yes	characteristic
233	C₄×C₅	—	4	2	no	—
234	C₄×C₅	—	8	1	no	—
235	C₄×C₅	—	8	1	no	—
236	C₄×C₅	C₃×#121	1	1	yes	characteristic
237	C₄×C₅	C₃×#123	1	1	yes	characteristic
238	C₄×C₅	C₃×#123	1	1	yes	characteristic
239	C₄×C₅	C₃×#126	1	1	yes	characteristic
240	C₂×Q₈	—	2	1	no	—
241	C₂×Q₈	—	2	1	no	—
242	C₂×Q₈	—	2	1	no	—
243	C₂×Q₈	—	2	1	no	—
244	C₂×Q₈	—	2	1	no	—
245	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
248	M₁₆	—	2	1	no	—
249	M₁₆	—	2	1	no	—
250	M₁₆	—	2	1	no	—
251	M₁₆	—	2	1	no	—
252	M₁₆	—	2	1	no	—
253	M₁₆	—	2	1	no	—
254	M₁₆	—	2	1	no	—
255	M₁₆	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
260	C₄⋊C₄	—	2	1	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₂²⋊C₄	—	2	1	no	—
263	C₂²⋊C₄	—	2	1	no	—
264	C₄²	—	2	1	no	—
265	C₄²	—	2	1	no	—
266	C₃×C₅	#2082	1	1	yes	characteristic, direct product factor, Hall
267	C₂²×C₃	—	4	1	no	—
268	C₂²×C₃	C₅×#123	1	1	yes	characteristic
269	C₂²×C₃	C₅×#124	1	1	yes	characteristic
270	C₂²×C₃	C₅×#126	1	1	yes	characteristic
271	C₃×C₄	—	4	2	no	—
272	C₃×C₄	—	8	1	no	—
273	C₃×C₄	—	8	1	no	—
274	C₃×C₄	C₅×#121	1	1	yes	characteristic
275	C₃×C₄	C₅×#123	1	1	yes	characteristic
276	C₃×C₄	C₅×#123	1	1	yes	characteristic
277	C₃×C₄	C₅×#126	1	1	yes	characteristic
278	C₂×C₅	—	2	1	no	—
279	C₂×C₅	—	2	1	no	—
280	C₂×C₅	—	2	1	no	—
281	C₂×C₅	C₃×#397	1	1	yes	characteristic
282	C₂³	C₃×C₅×#41	1	1	yes	characteristic
283	Q₈	—	2	2	no	—
284	Q₈	—	2	2	no	—
285	Q₈	—	4	1	no	—
286	Q₈	—	4	1	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	1	no	—
292	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
293	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
294	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
295	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
296	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
297	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
298	C₈	—	2	2	no	—
299	C₈	—	4	1	no	—
300	C₈	—	4	1	no	—
301	C₈	—	4	1	no	—
302	C₂×C₃	—	2	1	no	—
303	C₂×C₃	—	2	1	no	—
304	C₂×C₃	—	2	1	no	—
305	C₂×C₃	C₅×#397	1	1	yes	characteristic
306	C₅	C₃×#2082	1	1	yes	characteristic, direct product factor, Sylow
307	C₂²	—	4	1	no	—
308	C₂²	C₃×C₅×#123	1	1	yes	characteristic
309	C₂²	C₃×C₅×#124	1	1	yes	characteristic
310	C₂²	C₃×C₅×#126	1	1	yes	characteristic
311	C₄	—	4	2	no	—
312	C₄	—	8	1	no	—
313	C₄	—	8	1	no	—
314	C₄	C₃×C₅×#121	1	1	yes	characteristic
315	C₄	C₃×C₅×#123	1	1	yes	characteristic
316	C₄	C₃×C₅×#123	1	1	yes	characteristic
317	C₄	C₃×C₅×#126	1	1	yes	characteristic
318	C₃	C₅×#2082	1	1	yes	characteristic, direct product factor, Sylow
319	C₂	—	2	1	no	—
320	C₂	—	2	1	no	—
321	C₂	—	2	1	no	—
322	C₂	C₃×C₅×#397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#2082	C₃	direct (N × H)
20. C₃×#2082	C₅	direct (N × H)
72. #2082	C₃×C₅	direct (N × H)
266. C₃×C₅	#2082	direct (N × H)
306. C₅	C₃×#2082	direct (N × H)
318. C₃	C₅×#2082	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×#430	2
C₃×C₅×#419	2
C₂×C₃×C₅×#101	2
C₃×C₅×#344	2
C₃×C₅×H(3,ℤ/4)	2
C₅×#2082	3
C₃×#2082	5

Subgroups — C3×C5×#2082 #14275116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2082 #14275116