Subgroups — C₃×C₅×#2484 #14275518

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#387	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	2	yes	maximal
7	C₃×C₅×#381	C₂	1	2	yes	maximal
8	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
9	C₅×#2484	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2484	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#400	C₂×C₃	1	2	yes	complemented
32	C₅×#398	C₂×C₃	1	2	yes	complemented
33	C₅×#387	C₂×C₃	1	4	yes	complemented
34	C₅×#385	C₂×C₃	1	2	yes	—
35	C₅×#381	C₂×C₃	1	1	yes	characteristic
36	C₅×#381	C₂×C₃	1	2	yes	—
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	8	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
60	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
61	C₃×#400	C₂×C₅	1	2	yes	complemented
62	C₃×#398	C₂×C₅	1	2	yes	complemented
63	C₃×#387	C₂×C₅	1	4	yes	complemented
64	C₃×#385	C₂×C₅	1	2	yes	—
65	C₃×#381	C₂×C₅	1	1	yes	characteristic
66	C₃×#381	C₂×C₅	1	2	yes	—
67	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₅×#117	—	2	4	no	—
71	C₂×C₅×C₄⋊C₄	—	2	4	no	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
80	C₅×#95	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	4	yes	—
82	C₅×#95	C₂²×C₃	1	4	yes	—
83	C₅×#95	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	4	yes	—
85	#2484	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
89	C₂³×C₃×C₅	#41	1	4	yes	—
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	—	2	8	no	—
92	C₂×C₃×C₄×C₅	—	2	8	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	4	4	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	4	yes	—
110	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
112	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
113	C₃×#117	—	2	4	no	—
114	C₂×C₃×C₄⋊C₄	—	2	4	no	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
123	C₃×#95	C₂²×C₅	1	2	yes	—
124	C₃×#95	C₂²×C₅	1	4	yes	—
125	C₃×#95	C₂²×C₅	1	4	yes	—
126	C₃×#95	C₂²×C₅	1	2	yes	—
127	C₃×#95	C₂²×C₅	1	4	yes	—
128	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	4	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	4	no	—
134	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
142	C₅×C₄⋊C₄	—	2	4	no	—
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	8	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	2	4	no	—
149	C₄²×C₅	—	2	4	no	—
150	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
151	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
152	#400	C₂×C₃×C₅	1	2	yes	complemented
153	#398	C₂×C₃×C₅	1	2	yes	complemented
154	#387	C₂×C₃×C₅	1	4	yes	complemented
155	#385	C₂×C₃×C₅	1	2	yes	—
156	#381	C₂×C₃×C₅	1	1	yes	characteristic
157	#381	C₂×C₃×C₅	1	2	yes	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	8	no	—
161	C₂²×C₃×C₅	#123	1	4	yes	—
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
164	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
165	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	4	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	—	4	2	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	4	no	—
173	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	2	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	8	no	—
192	C₃×C₂²⋊C₄	—	2	4	no	—
193	C₃×C₂²⋊C₄	—	2	4	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂³×C₅	C₃×#41	1	4	yes	—
199	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
200	C₂×C₄×C₅	—	2	8	no	—
201	C₂×C₄×C₅	—	2	8	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	4	4	no	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	4	yes	—
219	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
222	#117	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
232	#95	C₂²×C₃×C₅	1	2	yes	—
233	#95	C₂²×C₃×C₅	1	4	yes	—
234	#95	C₂²×C₃×C₅	1	4	yes	—
235	#95	C₂²×C₃×C₅	1	2	yes	—
236	#95	C₂²×C₃×C₅	1	4	yes	—
237	C₂×C₃×C₅	—	2	4	no	—
238	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
239	C₂×C₃×C₅	#525	1	1	yes	characteristic
240	C₂×C₃×C₅	#536	1	1	yes	characteristic
241	C₂×C₃×C₅	#552	1	4	yes	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
245	C₂³×C₃	C₅×#41	1	4	yes	—
246	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄	—	2	8	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₅×#41	1	4	yes	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	2	8	no	—
269	C₂²×C₅	C₃×#123	1	4	yes	—
270	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
271	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
272	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
273	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	4	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	4	no	—
281	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
288	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
289	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
290	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
291	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
292	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	8	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₃×C₅	#2484	1	1	yes	characteristic, direct product factor, Hall
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	C₅×#123	1	4	yes	—
308	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
310	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
311	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	4	no	—
315	C₃×C₄	—	4	2	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	4	no	—
319	C₂×C₅	—	2	4	no	—
320	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
321	C₂×C₅	C₃×#525	1	1	yes	characteristic
322	C₂×C₅	C₃×#536	1	1	yes	characteristic
323	C₂×C₅	C₃×#552	1	4	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
327	C₂³	C₃×C₅×#41	1	4	yes	—
328	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
347	C₂×C₄	C₃×C₅×#41	1	4	yes	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
350	C₂×C₃	C₅×#525	1	1	yes	characteristic
351	C₂×C₃	C₅×#536	1	1	yes	characteristic
352	C₂×C₃	C₅×#552	1	4	yes	—
353	C₅	C₃×#2484	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	8	no	—
357	C₂²	C₃×C₅×#123	1	4	yes	—
358	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
359	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
360	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
361	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	4	no	—
369	C₃	C₅×#2484	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	4	no	—
371	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
372	C₂	C₃×C₅×#525	1	1	yes	characteristic
373	C₂	C₃×C₅×#536	1	1	yes	characteristic
374	C₂	C₃×C₅×#552	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
9. C₅×#2484	C₃	direct (N × H)
28. C₃×#2484	C₅	direct (N × H)
31. C₅×#400	C₂×C₃	semidirect
32. C₅×#398	C₂×C₃	semidirect
33. C₅×#387	C₂×C₃	semidirect
61. C₃×#400	C₂×C₅	semidirect
62. C₃×#398	C₂×C₅	semidirect
63. C₃×#387	C₂×C₅	semidirect
85. #2484	C₃×C₅	direct (N × H)
152. #400	C₂×C₃×C₅	semidirect
153. #398	C₂×C₃×C₅	semidirect
154. #387	C₂×C₃×C₅	semidirect
303. C₃×C₅	#2484	direct (N × H)
353. C₅	C₃×#2484	direct (N × H)
369. C₃	C₅×#2484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₅×#2484	3
C₃×#2484	5

Subgroups — C3×C5×#2484 #14275518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2484 #14275518