Subgroups — C₃×C₅×#2280 #14275314

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#381	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#380	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#379	C₂	1	2	yes	maximal
6	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₅×#2280	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	—	2	8	no	—
10	C₂³×C₃×C₄×C₅	C₄	1	8	yes	complemented
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	—	2	8	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	complemented
20	C₃×C₅×#95	C₂²	1	8	yes	complemented
21	C₃×#2280	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂⁴×C₄×C₅	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×#117	C₂×C₃	1	2	yes	complemented
24	C₅×#381	C₂×C₃	1	2	yes	complemented
25	C₅×#380	C₂×C₃	1	4	yes	complemented
26	C₅×#379	C₂×C₃	1	2	yes	—
27	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
28	C₂⁴×C₃×C₅	—	2	4	no	—
29	C₂⁴×C₃×C₅	—	2	8	no	—
30	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	—
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	32	no	—
35	C₂²×C₃×C₄×C₅	—	2	8	no	—
36	C₂²×C₃×C₄×C₅	—	2	8	no	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	—	2	8	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
49	C₃×C₄²×C₅	—	2	8	no	—
50	C₂⁴×C₃×C₄	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×#117	C₂×C₅	1	2	yes	complemented
52	C₃×#381	C₂×C₅	1	2	yes	complemented
53	C₃×#380	C₂×C₅	1	4	yes	complemented
54	C₃×#379	C₂×C₅	1	2	yes	—
55	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
56	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₂³×C₄×C₅	—	2	8	no	—
58	C₂³×C₄×C₅	C₃×C₄	1	8	yes	complemented
59	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₅×#117	—	2	8	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
65	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	complemented
68	C₅×#95	C₂²×C₃	1	8	yes	complemented
69	#2280	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³×C₃×C₅	—	2	32	no	—
71	C₂³×C₃×C₅	—	2	8	no	—
72	C₂³×C₃×C₅	—	2	16	no	—
73	C₂³×C₃×C₅	—	2	4	no	—
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
79	C₂³×C₃×C₅	#41	1	8	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	—	2	8	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	16	no	—
84	C₂×C₃×C₄×C₅	—	2	16	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	16	no	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
93	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
94	C₂³×C₃×C₄	—	2	8	no	—
95	C₂³×C₃×C₄	C₄×C₅	1	8	yes	complemented
96	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
97	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
98	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
100	C₃×#117	—	2	8	no	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
102	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	complemented
105	C₃×#95	C₂²×C₅	1	8	yes	complemented
106	C₂⁴×C₅	—	2	4	no	—
107	C₂⁴×C₅	—	2	8	no	—
108	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	—
109	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
110	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
111	C₂²×C₄×C₅	—	2	4	no	—
112	C₂²×C₄×C₅	—	2	32	no	—
113	C₂²×C₄×C₅	—	2	8	no	—
114	C₂²×C₄×C₅	—	2	8	no	—
115	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
116	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
118	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
119	C₂²×C₄×C₅	C₃×D₄	1	8	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₅×C₄⋊C₄	—	2	8	no	—
125	C₅×C₂²⋊C₄	—	2	8	no	—
126	C₅×C₂²⋊C₄	—	2	16	no	—
127	C₄²×C₅	—	2	8	no	—
128	C₂⁴×C₄	C₂×C₃×C₅	1	1	yes	characteristic
129	C₂×#117	C₂×C₃×C₅	1	2	yes	complemented
130	#381	C₂×C₃×C₅	1	2	yes	complemented
131	#380	C₂×C₃×C₅	1	4	yes	complemented
132	#379	C₂×C₃×C₅	1	2	yes	—
133	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
134	C₂²×C₃×C₅	—	2	32	no	—
135	C₂²×C₃×C₅	—	2	4	no	—
136	C₂²×C₃×C₅	—	2	4	no	—
137	C₂²×C₃×C₅	—	2	4	no	—
138	C₂²×C₃×C₅	—	2	8	no	—
139	C₂²×C₃×C₅	—	2	16	no	—
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂²×C₃×C₅	#117	1	8	yes	complemented
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
144	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
145	C₃×C₄×C₅	—	2	4	no	—
146	C₃×C₄×C₅	—	4	8	no	—
147	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
148	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂⁴×C₃	—	2	4	no	—
150	C₂⁴×C₃	—	2	8	no	—
151	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	—
152	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
153	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	2	32	no	—
156	C₂²×C₃×C₄	—	2	8	no	—
157	C₂²×C₃×C₄	—	2	8	no	—
158	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
159	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
162	C₂²×C₃×C₄	C₅×D₄	1	8	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₃×C₄⋊C₄	—	2	8	no	—
168	C₃×C₂²⋊C₄	—	2	8	no	—
169	C₃×C₂²⋊C₄	—	2	16	no	—
170	C₃×C₄²	—	2	8	no	—
171	C₂³×C₅	—	2	32	no	—
172	C₂³×C₅	—	2	8	no	—
173	C₂³×C₅	—	2	16	no	—
174	C₂³×C₅	—	2	4	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
178	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
179	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
180	C₂³×C₅	C₃×#41	1	8	yes	—
181	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
182	C₂×C₄×C₅	—	2	8	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	16	no	—
185	C₂×C₄×C₅	—	2	16	no	—
186	C₂×C₄×C₅	—	2	8	no	—
187	C₂×C₄×C₅	—	2	16	no	—
188	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
191	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
194	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
195	C₂³×C₄	—	2	8	no	—
196	C₂³×C₄	C₃×C₄×C₅	1	8	yes	complemented
197	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
198	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
199	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
200	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
201	#117	—	2	8	no	—
202	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
203	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
205	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	complemented
206	#95	C₂²×C₃×C₅	1	8	yes	complemented
207	C₂×C₃×C₅	—	2	4	no	—
208	C₂×C₃×C₅	—	2	8	no	—
209	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₃×C₅	C₂×#117	1	2	yes	—
211	C₂×C₃×C₅	#525	1	4	yes	—
212	C₂³×C₃	—	2	32	no	—
213	C₂³×C₃	—	2	8	no	—
214	C₂³×C₃	—	2	16	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
219	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
220	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
221	C₂³×C₃	C₅×#41	1	8	yes	—
222	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	16	no	—
226	C₂×C₃×C₄	—	2	16	no	—
227	C₂×C₃×C₄	—	2	8	no	—
228	C₂×C₃×C₄	—	2	16	no	—
229	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
230	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
232	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
234	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
235	C₂²×C₅	—	2	32	no	—
236	C₂²×C₅	—	2	4	no	—
237	C₂²×C₅	—	2	4	no	—
238	C₂²×C₅	—	2	4	no	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	—	2	16	no	—
241	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
242	C₂²×C₅	C₃×#117	1	8	yes	complemented
243	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
244	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
245	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
246	C₄×C₅	—	2	4	no	—
247	C₄×C₅	—	4	8	no	—
248	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
249	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	—
253	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
254	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
260	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
261	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
262	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
263	C₂²×C₄	C₃×C₅×D₄	1	8	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
265	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
268	C₄⋊C₄	—	2	8	no	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₂²⋊C₄	—	2	16	no	—
271	C₄²	—	2	8	no	—
272	C₃×C₅	#2280	1	1	yes	characteristic, direct product factor, Hall
273	C₂²×C₃	—	2	32	no	—
274	C₂²×C₃	—	2	4	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	8	no	—
278	C₂²×C₃	—	2	16	no	—
279	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
280	C₂²×C₃	C₅×#117	1	8	yes	complemented
281	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
282	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
283	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	4	8	no	—
286	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
287	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
288	C₂×C₅	—	2	4	no	—
289	C₂×C₅	—	2	8	no	—
290	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₅	C₂×C₃×#117	1	2	yes	—
292	C₂×C₅	C₃×#525	1	4	yes	—
293	C₂³	—	2	32	no	—
294	C₂³	—	2	8	no	—
295	C₂³	—	2	16	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
300	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
301	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
302	C₂³	C₃×C₅×#41	1	8	yes	—
303	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	16	yes	complemented
311	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
312	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
313	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
314	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
315	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
316	C₂×C₃	—	2	4	no	—
317	C₂×C₃	—	2	8	no	—
318	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₃	C₂×C₅×#117	1	2	yes	—
320	C₂×C₃	C₅×#525	1	4	yes	—
321	C₅	C₃×#2280	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	2	32	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	2	16	no	—
328	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	—
329	C₂²	C₃×C₅×#117	1	8	yes	complemented
330	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
331	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
332	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
333	C₄	—	2	4	no	—
334	C₄	—	4	8	no	—
335	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	—
336	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	—
337	C₃	C₅×#2280	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	2	4	no	—
339	C₂	—	2	8	no	—
340	C₂	C₂²×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂	C₂×C₃×C₅×#117	1	2	yes	—
342	C₂	C₃×C₅×#525	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁵×C₃×C₅	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₃×C₅×#381	C₂	semidirect
4. C₃×C₅×#380	C₂	semidirect
6. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
7. C₅×#2280	C₃	direct (N × H)
10. C₂³×C₃×C₄×C₅	C₄	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₂×C₃×C₄²×C₅	C₂²	semidirect
20. C₃×C₅×#95	C₂²	semidirect
21. C₃×#2280	C₅	direct (N × H)
23. C₂×C₅×#117	C₂×C₃	semidirect
24. C₅×#381	C₂×C₃	semidirect
25. C₅×#380	C₂×C₃	semidirect
27. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
51. C₂×C₃×#117	C₂×C₅	semidirect
52. C₃×#381	C₂×C₅	semidirect
53. C₃×#380	C₂×C₅	semidirect
55. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
58. C₂³×C₄×C₅	C₃×C₄	semidirect
64. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
67. C₂×C₄²×C₅	C₂²×C₃	semidirect
68. C₅×#95	C₂²×C₃	semidirect
69. #2280	C₃×C₅	direct (N × H)
87. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
95. C₂³×C₃×C₄	C₄×C₅	semidirect
101. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
104. C₂×C₃×C₄²	C₂²×C₅	semidirect
105. C₃×#95	C₂²×C₅	semidirect
129. C₂×#117	C₂×C₃×C₅	semidirect
130. #381	C₂×C₃×C₅	semidirect
131. #380	C₂×C₃×C₅	semidirect
133. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
141. C₂²×C₃×C₅	#117	semidirect
188. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
196. C₂³×C₄	C₃×C₄×C₅	semidirect
202. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
205. C₂×C₄²	C₂²×C₃×C₅	semidirect
206. #95	C₂²×C₃×C₅	semidirect
229. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
242. C₂²×C₅	C₃×#117	semidirect
272. C₃×C₅	#2280	direct (N × H)
280. C₂²×C₃	C₅×#117	semidirect
310. C₂×C₄	C₃×C₅×C₂²⋊C₄	semidirect
321. C₅	C₃×#2280	direct (N × H)
329. C₂²	C₃×C₅×#117	semidirect
337. C₃	C₅×#2280	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₃×C₄×C₅	2
C₂×C₃×C₅×#117	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2280	3
C₃×#2280	5

Subgroups — C3×C5×#2280 #14275314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2280 #14275314