Subgroups — C₃×C₅×#1445 #14274479

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 368 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	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#95	C₂	1	4	yes	maximal
3	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
5	C₅×#1445	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
11	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	4	yes	complemented
13	C₃×C₅×#95	—	2	8	no	—
14	C₃×C₅×#95	—	2	2	no	—
15	C₃×C₅×#95	—	2	2	no	—
16	C₃×#1445	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
18	C₂×C₅×#95	C₂×C₃	1	4	yes	—
19	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
20	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
21	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	—	2	4	no	—
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	—	2	2	no	—
25	C₂²×C₃×C₄×C₅	—	2	4	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	4	no	—
29	C₂²×C₃×C₄×C₅	—	2	4	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	4	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
41	C₃×C₅×C₄⋊C₄	—	2	8	no	—
42	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
43	C₂×C₃×#95	C₂×C₅	1	4	yes	—
44	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
45	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
47	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
48	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
49	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	C₃×C₄	1	4	yes	complemented
53	C₅×#95	—	2	8	no	—
54	C₅×#95	—	2	2	no	—
55	C₅×#95	—	2	2	no	—
56	#1445	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
58	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
59	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
60	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
61	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
62	C₂³×C₃×C₅	#41	1	4	yes	—
63	C₂³×C₃×C₅	#41	1	2	yes	—
64	C₂³×C₃×C₅	#41	1	2	yes	—
65	C₂×C₃×C₄×C₅	—	2	4	no	—
66	C₂×C₃×C₄×C₅	—	2	4	no	—
67	C₂×C₃×C₄×C₅	—	2	4	no	—
68	C₂×C₃×C₄×C₅	—	2	4	no	—
69	C₂×C₃×C₄×C₅	—	2	8	no	—
70	C₂×C₃×C₄×C₅	—	2	4	no	—
71	C₂×C₃×C₄×C₅	—	2	8	no	—
72	C₂×C₃×C₄×C₅	—	2	4	no	—
73	C₂×C₃×C₄×C₅	—	2	8	no	—
74	C₂×C₃×C₄×C₅	—	4	4	no	—
75	C₂×C₃×C₄×C₅	—	4	2	no	—
76	C₂×C₃×C₄×C₅	—	4	2	no	—
77	C₂×C₃×C₄×C₅	—	4	4	no	—
78	C₂×C₃×C₄×C₅	—	4	2	no	—
79	C₂×C₃×C₄×C₅	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	4	4	no	—
81	C₂×C₃×C₄×C₅	—	4	2	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
84	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
85	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
86	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
87	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₃×C₄⋊C₄	C₄×C₅	1	4	yes	complemented
91	C₃×#95	—	2	8	no	—
92	C₃×#95	—	2	2	no	—
93	C₃×#95	—	2	2	no	—
94	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
95	C₂²×C₄×C₅	—	2	4	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	4	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	4	no	—
102	C₂²×C₄×C₅	—	2	4	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	4	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	2	4	no	—
108	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
109	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
110	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
111	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
112	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
113	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
114	C₅×C₄⋊C₄	—	2	8	no	—
115	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
116	C₂×#95	C₂×C₃×C₅	1	4	yes	—
117	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
118	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₃×C₅	#117	1	2	yes	—
121	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
122	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
123	C₂²×C₃×C₅	#121	1	2	yes	—
124	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
125	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
126	C₂²×C₃×C₅	#123	1	2	yes	—
127	C₂²×C₃×C₅	#123	1	2	yes	—
128	C₂²×C₃×C₅	#123	1	4	yes	—
129	C₂²×C₃×C₅	#124	1	1	yes	characteristic
130	C₂²×C₃×C₅	#124	1	1	yes	characteristic
131	C₂²×C₃×C₅	#125	1	4	yes	—
132	C₂²×C₃×C₅	#126	1	4	yes	—
133	C₂²×C₃×C₅	#127	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
135	C₃×C₄×C₅	—	2	4	no	—
136	C₃×C₄×C₅	—	4	4	no	—
137	C₃×C₄×C₅	—	4	4	no	—
138	C₃×C₄×C₅	—	4	4	no	—
139	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
140	C₂²×C₃×C₄	—	2	4	no	—
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	4	no	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	4	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	4	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
155	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
156	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
159	C₃×C₄⋊C₄	—	2	8	no	—
160	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
161	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
163	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
164	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
165	C₂³×C₅	C₃×#41	1	4	yes	—
166	C₂³×C₅	C₃×#41	1	2	yes	—
167	C₂³×C₅	C₃×#41	1	2	yes	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	4	no	—
170	C₂×C₄×C₅	—	2	4	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	2	8	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	8	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	8	no	—
177	C₂×C₄×C₅	—	4	4	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	—	4	2	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	4	4	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
187	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
188	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
189	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
190	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	C₃×C₄×C₅	1	4	yes	complemented
194	#95	—	2	8	no	—
195	#95	—	2	2	no	—
196	#95	—	2	2	no	—
197	C₂×C₃×C₅	#381	1	1	yes	characteristic
198	C₂×C₃×C₅	#387	1	4	yes	—
199	C₂×C₃×C₅	#390	1	1	yes	characteristic
200	C₂×C₃×C₅	#391	1	1	yes	characteristic
201	C₂×C₃×C₅	#397	1	2	yes	—
202	C₂×C₃×C₅	#398	1	2	yes	—
203	C₂×C₃×C₅	#399	1	2	yes	—
204	C₂×C₃×C₅	#400	1	2	yes	—
205	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
206	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
208	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
209	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
210	C₂³×C₃	C₅×#41	1	4	yes	—
211	C₂³×C₃	C₅×#41	1	2	yes	—
212	C₂³×C₃	C₅×#41	1	2	yes	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	8	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	8	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	4	4	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	4	2	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	4	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
232	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₅	C₃×#117	1	2	yes	—
234	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
235	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
236	C₂²×C₅	C₃×#121	1	2	yes	—
237	C₂²×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
238	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
239	C₂²×C₅	C₃×#123	1	2	yes	—
240	C₂²×C₅	C₃×#123	1	2	yes	—
241	C₂²×C₅	C₃×#123	1	4	yes	—
242	C₂²×C₅	C₃×#124	1	1	yes	characteristic
243	C₂²×C₅	C₃×#124	1	1	yes	characteristic
244	C₂²×C₅	C₃×#125	1	4	yes	—
245	C₂²×C₅	C₃×#126	1	4	yes	—
246	C₂²×C₅	C₃×#127	1	1	yes	characteristic
247	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
248	C₄×C₅	—	2	4	no	—
249	C₄×C₅	—	4	4	no	—
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	—	4	4	no	—
252	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
267	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
268	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
269	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
270	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
271	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
272	C₄⋊C₄	—	2	8	no	—
273	C₃×C₅	#1445	1	1	yes	characteristic, direct product factor, Hall
274	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₃	C₅×#117	1	2	yes	—
276	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
277	C₂²×C₃	C₄×C₅×Q₈	1	2	yes	—
278	C₂²×C₃	C₅×#121	1	2	yes	—
279	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
280	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
281	C₂²×C₃	C₅×#123	1	2	yes	—
282	C₂²×C₃	C₅×#123	1	2	yes	—
283	C₂²×C₃	C₅×#123	1	4	yes	—
284	C₂²×C₃	C₅×#124	1	1	yes	characteristic
285	C₂²×C₃	C₅×#124	1	1	yes	characteristic
286	C₂²×C₃	C₅×#125	1	4	yes	—
287	C₂²×C₃	C₅×#126	1	4	yes	—
288	C₂²×C₃	C₅×#127	1	1	yes	characteristic
289	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	4	4	no	—
292	C₃×C₄	—	4	4	no	—
293	C₃×C₄	—	4	4	no	—
294	C₂×C₅	C₃×#381	1	1	yes	characteristic
295	C₂×C₅	C₃×#387	1	4	yes	—
296	C₂×C₅	C₃×#390	1	1	yes	characteristic
297	C₂×C₅	C₃×#391	1	1	yes	characteristic
298	C₂×C₅	C₃×#397	1	2	yes	—
299	C₂×C₅	C₃×#398	1	2	yes	—
300	C₂×C₅	C₃×#399	1	2	yes	—
301	C₂×C₅	C₃×#400	1	2	yes	—
302	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
303	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
304	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
305	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
306	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
307	C₂³	C₃×C₅×#41	1	4	yes	—
308	C₂³	C₃×C₅×#41	1	2	yes	—
309	C₂³	C₃×C₅×#41	1	2	yes	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	4	yes	—
329	C₂×C₃	C₅×#381	1	1	yes	characteristic
330	C₂×C₃	C₅×#387	1	4	yes	—
331	C₂×C₃	C₅×#390	1	1	yes	characteristic
332	C₂×C₃	C₅×#391	1	1	yes	characteristic
333	C₂×C₃	C₅×#397	1	2	yes	—
334	C₂×C₃	C₅×#398	1	2	yes	—
335	C₂×C₃	C₅×#399	1	2	yes	—
336	C₂×C₃	C₅×#400	1	2	yes	—
337	C₅	C₃×#1445	1	1	yes	characteristic, direct product factor, Sylow
338	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²	C₃×C₅×#117	1	2	yes	—
340	C₂²	C₃×C₄×C₅×D₄	1	2	yes	—
341	C₂²	C₃×C₄×C₅×Q₈	1	2	yes	—
342	C₂²	C₃×C₅×#121	1	2	yes	—
343	C₂²	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
344	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
345	C₂²	C₃×C₅×#123	1	2	yes	—
346	C₂²	C₃×C₅×#123	1	2	yes	—
347	C₂²	C₃×C₅×#123	1	4	yes	—
348	C₂²	C₃×C₅×#124	1	1	yes	characteristic
349	C₂²	C₃×C₅×#124	1	1	yes	characteristic
350	C₂²	C₃×C₅×#125	1	4	yes	—
351	C₂²	C₃×C₅×#126	1	4	yes	—
352	C₂²	C₃×C₅×#127	1	1	yes	characteristic
353	C₂²	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	4	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	4	no	—
358	C₃	C₅×#1445	1	1	yes	characteristic, direct product factor, Sylow
359	C₂	C₃×C₅×#381	1	1	yes	characteristic
360	C₂	C₃×C₅×#387	1	4	yes	—
361	C₂	C₃×C₅×#390	1	1	yes	characteristic
362	C₂	C₃×C₅×#391	1	1	yes	characteristic
363	C₂	C₃×C₅×#397	1	2	yes	—
364	C₂	C₃×C₅×#398	1	2	yes	—
365	C₂	C₃×C₅×#399	1	2	yes	—
366	C₂	C₃×C₅×#400	1	2	yes	—

	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
5. C₅×#1445	C₃	direct (N × H)
12. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
16. C₃×#1445	C₅	direct (N × H)
52. C₂×C₅×C₄⋊C₄	C₃×C₄	semidirect
56. #1445	C₃×C₅	direct (N × H)
90. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
193. C₂×C₄⋊C₄	C₃×C₄×C₅	semidirect
273. C₃×C₅	#1445	direct (N × H)
337. C₅	C₃×#1445	direct (N × H)
358. C₃	C₅×#1445	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×#1445	3
C₃×#1445	5

Subgroups — C3×C5×#1445 #14274479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1445 #14274479