Subgroups — C₃×C₅×#1980 #14275014

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	4	yes	maximal, complemented
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1980	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
7	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	C₃×C₅×#127	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#124	C₄	1	2	yes	complemented
11	C₃×C₅×#121	—	2	1	no	—
12	C₃×C₅×#121	—	2	1	no	—
13	C₃×C₄×C₅×D₄	—	2	1	no	—
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#104	—	2	8	no	—
19	C₃×C₅×#97	—	2	1	no	—
20	C₃×C₄×C₅×C₈	—	2	1	no	—
21	C₃×C₅×#95	—	2	1	no	—
22	C₃×#1980	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#532	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×#104	C₂×C₃	1	4	yes	complemented
25	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×C₅×#41	—	2	4	no	—
28	C₃×C₅×#41	—	2	4	no	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₃×C₅×M₁₆	—	2	2	no	—
40	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	4	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×#532	C₂×C₅	1	1	yes	characteristic
53	C₂×C₃×#104	C₂×C₅	1	4	yes	complemented
54	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
55	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
57	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
58	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
59	C₅×#127	C₃×C₄	1	1	yes	characteristic, complemented
60	C₅×#124	C₃×C₄	1	2	yes	complemented
61	C₅×#121	—	2	1	no	—
62	C₅×#121	—	2	1	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₅×#104	—	2	8	no	—
69	C₅×#97	—	2	1	no	—
70	C₄×C₅×C₈	—	2	1	no	—
71	C₅×#95	—	2	1	no	—
72	#1980	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	—	2	2	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	2	4	no	—
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	—	4	2	no	—
78	C₃×C₅×D₄	—	4	2	no	—
79	C₃×C₅×D₄	—	4	2	no	—
80	C₃×C₅×D₄	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	2	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	—	4	4	no	—
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	2	yes	—
96	C₃×C₅×C₈	—	2	4	no	—
97	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
98	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
99	C₃×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic, complemented
100	C₃×#127	C₄×C₅	1	1	yes	characteristic, complemented
101	C₃×#124	C₄×C₅	1	2	yes	complemented
102	C₃×#121	—	2	1	no	—
103	C₃×#121	—	2	1	no	—
104	C₃×C₄×D₄	—	2	1	no	—
105	C₃×C₄×D₄	—	2	1	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₃×#104	—	2	8	no	—
110	C₃×#97	—	2	1	no	—
111	C₃×C₄×C₈	—	2	1	no	—
112	C₃×#95	—	2	1	no	—
113	C₅×#41	—	2	4	no	—
114	C₅×#41	—	2	4	no	—
115	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₅×M₁₆	—	2	2	no	—
126	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
127	C₂×C₅×C₈	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₂²⋊C₄	—	2	2	no	—
132	C₅×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₅	—	2	4	no	—
134	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
137	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
138	#532	C₂×C₃×C₅	1	1	yes	characteristic
139	C₂×#104	C₂×C₃×C₅	1	4	yes	complemented
140	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
142	C₂²×C₃×C₅	—	2	1	no	—
143	C₂²×C₃×C₅	—	2	1	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	—	4	2	no	—
146	C₂²×C₃×C₅	—	4	2	no	—
147	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	#124	1	1	yes	characteristic
149	C₂²×C₃×C₅	#127	1	1	yes	characteristic
150	C₃×C₄×C₅	—	2	1	no	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	#104	1	2	yes	complemented
156	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
157	C₃×C₄×C₅	#121	1	2	yes	—
158	C₃×#41	—	2	4	no	—
159	C₃×#41	—	2	4	no	—
160	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
161	C₂×C₃×D₄	—	2	2	no	—
162	C₂×C₃×D₄	—	2	1	no	—
163	C₂×C₃×D₄	—	2	1	no	—
164	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₃×M₁₆	—	2	2	no	—
171	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
172	C₂×C₃×C₈	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₂²⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	—	2	2	no	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
180	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
181	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
182	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₅×Q₈	—	2	4	no	—
186	C₅×D₄	—	2	4	no	—
187	C₅×D₄	—	4	2	no	—
188	C₅×D₄	—	4	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₅×D₄	—	4	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₃×#41	1	2	yes	—
206	C₅×C₈	—	2	4	no	—
207	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
208	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
209	C₄⋊Q₈	C₃×C₄×C₅	1	1	yes	characteristic, complemented
210	#127	C₃×C₄×C₅	1	1	yes	characteristic, complemented
211	#124	C₃×C₄×C₅	1	2	yes	complemented
212	#121	—	2	1	no	—
213	#121	—	2	1	no	—
214	C₄×D₄	—	2	1	no	—
215	C₄×D₄	—	2	1	no	—
216	C₂×C₄⋊C₄	—	2	1	no	—
217	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
218	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
219	#104	—	2	8	no	—
220	#97	—	2	1	no	—
221	C₄×C₈	—	2	1	no	—
222	#95	—	2	1	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	—	2	1	no	—
225	C₂×C₃×C₅	—	8	2	no	—
226	C₂×C₃×C₅	#390	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
228	C₂×C₃×C₅	#421	1	1	yes	characteristic
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
231	C₃×Q₈	—	2	4	no	—
232	C₃×D₄	—	2	4	no	—
233	C₃×D₄	—	4	2	no	—
234	C₃×D₄	—	4	2	no	—
235	C₃×D₄	—	4	2	no	—
236	C₃×D₄	—	4	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₅×#41	1	2	yes	—
252	C₃×C₈	—	2	4	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₅	C₃×#124	1	1	yes	characteristic
260	C₂²×C₅	C₃×#127	1	1	yes	characteristic
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	4	4	no	—
265	C₄×C₅	—	4	2	no	—
266	C₄×C₅	C₃×#104	1	2	yes	complemented
267	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
268	C₄×C₅	C₃×#121	1	2	yes	—
269	#41	—	2	4	no	—
270	#41	—	2	4	no	—
271	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
279	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
281	M₁₆	—	2	2	no	—
282	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
283	C₂×C₈	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₄²	—	2	4	no	—
290	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
291	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
292	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
293	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
294	C₃×C₅	#1980	1	1	yes	characteristic, direct product factor, Hall
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	4	2	no	—
300	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	C₅×#124	1	1	yes	characteristic
302	C₂²×C₃	C₅×#127	1	1	yes	characteristic
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	—	4	2	no	—
308	C₃×C₄	C₅×#104	1	2	yes	complemented
309	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
310	C₃×C₄	C₅×#121	1	2	yes	—
311	C₂×C₅	—	2	1	no	—
312	C₂×C₅	—	2	1	no	—
313	C₂×C₅	—	8	2	no	—
314	C₂×C₅	C₃×#390	1	1	yes	characteristic
315	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
316	C₂×C₅	C₃×#421	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
319	Q₈	—	2	4	no	—
320	D₄	—	2	4	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
337	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
338	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
339	C₂×C₄	C₃×C₅×#41	1	2	yes	—
340	C₈	—	2	4	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	8	2	no	—
344	C₂×C₃	C₅×#390	1	1	yes	characteristic
345	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
346	C₂×C₃	C₅×#421	1	1	yes	characteristic
347	C₅	C₃×#1980	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²	C₃×C₅×#124	1	1	yes	characteristic
355	C₂²	C₃×C₅×#127	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	C₃×C₅×#104	1	2	yes	complemented
362	C₄	C₃×C₄×C₅×D₄	1	2	yes	—
363	C₄	C₃×C₅×#121	1	2	yes	—
364	C₃	C₅×#1980	1	1	yes	characteristic, direct product factor, Sylow
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	—	8	2	no	—
368	C₂	C₃×C₅×#390	1	1	yes	characteristic
369	C₂	C₂×C₃×C₅×#104	1	1	yes	characteristic
370	C₂	C₃×C₅×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#104	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#1980	C₃	direct (N × H)
8. C₃×C₅×C₄⋊Q₈	C₄	semidirect
9. C₃×C₅×#127	C₄	semidirect
10. C₃×C₅×#124	C₄	semidirect
22. C₃×#1980	C₅	direct (N × H)
24. C₂×C₅×#104	C₂×C₃	semidirect
25. C₄×C₅×M₁₆	C₂×C₃	semidirect
26. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
40. C₃×C₅×M₁₆	D₄	semidirect
53. C₂×C₃×#104	C₂×C₅	semidirect
54. C₃×C₄×M₁₆	C₂×C₅	semidirect
55. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
58. C₅×C₄⋊Q₈	C₃×C₄	semidirect
59. C₅×#127	C₃×C₄	semidirect
60. C₅×#124	C₃×C₄	semidirect
72. #1980	C₃×C₅	direct (N × H)
99. C₃×C₄⋊Q₈	C₄×C₅	semidirect
100. C₃×#127	C₄×C₅	semidirect
101. C₃×#124	C₄×C₅	semidirect
126. C₅×M₁₆	C₃×D₄	semidirect
139. C₂×#104	C₂×C₃×C₅	semidirect
140. C₄×M₁₆	C₂×C₃×C₅	semidirect
141. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
155. C₃×C₄×C₅	#104	semidirect
171. C₃×M₁₆	C₅×D₄	semidirect
209. C₄⋊Q₈	C₃×C₄×C₅	semidirect
210. #127	C₃×C₄×C₅	semidirect
211. #124	C₃×C₄×C₅	semidirect
266. C₄×C₅	C₃×#104	semidirect
282. M₁₆	C₃×C₅×D₄	semidirect
294. C₃×C₅	#1980	direct (N × H)
308. C₃×C₄	C₅×#104	semidirect
347. C₅	C₃×#1980	direct (N × H)
361. C₄	C₃×C₅×#104	semidirect
364. C₃	C₅×#1980	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×#532	2
C₂×C₃×C₅×#104	2
C₃×C₄×C₅×M₁₆	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#1980	3
C₃×#1980	5

Subgroups — C3×C5×#1980 #14275014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1980 #14275014