Subgroups — C₃×C₅×#2504 #14275538

Order 1920.

1192 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	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#386	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2504	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₃×C₅×#121	—	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×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	8	yes	—
24	C₃×#2504	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×#397	C₂×C₃	1	4	yes	complemented
28	C₅×#390	C₂×C₃	1	2	yes	complemented
29	C₅×#386	C₂×C₃	1	4	yes	complemented
30	C₅×#382	C₂×C₃	1	2	yes	complemented
31	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	8	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	4	4	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
55	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×#397	C₂×C₅	1	4	yes	complemented
57	C₃×#390	C₂×C₅	1	2	yes	complemented
58	C₃×#386	C₂×C₅	1	4	yes	complemented
59	C₃×#382	C₂×C₅	1	2	yes	complemented
60	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
62	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
65	C₅×#121	—	2	4	no	—
66	C₂×C₅×C₄⋊C₄	—	2	4	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
74	C₅×#95	C₂²×C₃	1	2	yes	—
75	C₅×#95	C₂²×C₃	1	8	yes	—
76	#2504	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	#41	1	4	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₃×C₅×D₄	—	4	8	no	—
87	C₃×C₅×D₄	—	4	4	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	8	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	8	no	—
97	C₂×C₃×C₄×C₅	—	4	8	no	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	#41	1	4	yes	—
101	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
102	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
105	C₃×#121	—	2	4	no	—
106	C₂×C₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
114	C₃×#95	C₂²×C₅	1	2	yes	—
115	C₃×#95	C₂²×C₅	1	8	yes	—
116	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
117	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	4	no	—
119	C₂×C₅×D₄	—	2	8	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	—	2	4	no	—
135	C₅×C₂²⋊C₄	—	2	4	no	—
136	C₅×C₂²⋊C₄	—	4	8	no	—
137	C₄²×C₅	—	2	4	no	—
138	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
139	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
140	#397	C₂×C₃×C₅	1	4	yes	complemented
141	#390	C₂×C₃×C₅	1	2	yes	complemented
142	#386	C₂×C₃×C₅	1	4	yes	complemented
143	#382	C₂×C₃×C₅	1	2	yes	complemented
144	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	—	2	8	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	2	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	8	no	—
152	C₂²×C₃×C₅	#124	1	4	yes	—
153	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
155	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
156	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	—	4	4	no	—
160	C₃×C₄×C₅	—	4	4	no	—
161	C₃×C₄×C₅	#123	1	4	yes	—
162	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
163	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
164	C₂×C₃×D₄	—	2	4	no	—
165	C₂×C₃×D₄	—	2	8	no	—
166	C₂×C₃×D₄	—	2	2	no	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	2	4	no	—
170	C₂²×C₃×C₄	—	4	4	no	—
171	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
172	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₃×C₄⋊C₄	—	2	4	no	—
178	C₃×C₄⋊C₄	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	—	2	4	no	—
181	C₃×C₂²⋊C₄	—	2	4	no	—
182	C₃×C₂²⋊C₄	—	4	8	no	—
183	C₃×C₄²	—	2	4	no	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	4	no	—
188	C₂³×C₅	—	2	4	no	—
189	C₂³×C₅	—	2	4	no	—
190	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
191	C₂³×C₅	C₃×#41	1	4	yes	—
192	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
193	C₅×D₄	—	4	8	no	—
194	C₅×D₄	—	4	4	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	8	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	8	no	—
204	C₂×C₄×C₅	—	4	8	no	—
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₂×C₄×C₅	C₃×#41	1	4	yes	—
208	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
209	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
212	#121	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
215	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
216	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
220	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
221	#95	C₂²×C₃×C₅	1	2	yes	—
222	#95	C₂²×C₃×C₅	1	8	yes	—
223	C₂×C₃×C₅	—	2	4	no	—
224	C₂×C₃×C₅	—	8	2	no	—
225	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
226	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
227	C₂×C₃×C₅	#535	1	1	yes	characteristic
228	C₂×C₃×C₅	#553	1	4	yes	—
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	—	2	4	no	—
233	C₂³×C₃	—	2	4	no	—
234	C₂³×C₃	—	2	4	no	—
235	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
236	C₂³×C₃	C₅×#41	1	4	yes	—
237	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
238	C₃×D₄	—	4	8	no	—
239	C₃×D₄	—	4	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	8	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	4	8	no	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
252	C₂×C₃×C₄	C₅×#41	1	4	yes	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	8	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	4	8	no	—
260	C₂²×C₅	C₃×#124	1	4	yes	—
261	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
262	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
263	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
264	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	4	2	no	—
267	C₄×C₅	—	4	4	no	—
268	C₄×C₅	—	4	4	no	—
269	C₄×C₅	C₃×#123	1	4	yes	—
270	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
271	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
280	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
281	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
282	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
283	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	4	no	—
289	C₂²⋊C₄	—	2	4	no	—
290	C₂²⋊C₄	—	4	8	no	—
291	C₄²	—	2	4	no	—
292	C₃×C₅	#2504	1	1	yes	characteristic, direct product factor, Hall
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	8	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	4	8	no	—
300	C₂²×C₃	C₅×#124	1	4	yes	—
301	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
303	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
304	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	—	4	4	no	—
308	C₃×C₄	—	4	4	no	—
309	C₃×C₄	C₅×#123	1	4	yes	—
310	C₂×C₅	—	2	4	no	—
311	C₂×C₅	—	8	2	no	—
312	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
313	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
314	C₂×C₅	C₃×#535	1	1	yes	characteristic
315	C₂×C₅	C₃×#553	1	4	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
323	C₂³	C₃×C₅×#41	1	4	yes	—
324	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
325	D₄	—	4	8	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
338	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
339	C₂×C₄	C₃×C₅×#41	1	4	yes	—
340	C₂×C₃	—	2	4	no	—
341	C₂×C₃	—	8	2	no	—
342	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
343	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
344	C₂×C₃	C₅×#535	1	1	yes	characteristic
345	C₂×C₃	C₅×#553	1	4	yes	—
346	C₅	C₃×#2504	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	8	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	8	no	—
354	C₂²	C₃×C₅×#124	1	4	yes	—
355	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
356	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
357	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
358	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	4	4	no	—
363	C₄	C₃×C₅×#123	1	4	yes	—
364	C₃	C₅×#2504	1	1	yes	characteristic, direct product factor, Sylow
365	C₂	—	2	4	no	—
366	C₂	—	8	2	no	—
367	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
368	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
369	C₂	C₃×C₅×#535	1	1	yes	characteristic
370	C₂	C₃×C₅×#553	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#121	C₂
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
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#386	C₂	semidirect
6. C₃×C₅×#382	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2504	C₃	direct (N × H)
24. C₃×#2504	C₅	direct (N × H)
26. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
27. C₅×#397	C₂×C₃	semidirect
28. C₅×#390	C₂×C₃	semidirect
29. C₅×#386	C₂×C₃	semidirect
30. C₅×#382	C₂×C₃	semidirect
31. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
55. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
56. C₃×#397	C₂×C₅	semidirect
57. C₃×#390	C₂×C₅	semidirect
58. C₃×#386	C₂×C₅	semidirect
59. C₃×#382	C₂×C₅	semidirect
60. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
76. #2504	C₃×C₅	direct (N × H)
139. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
140. #397	C₂×C₃×C₅	semidirect
141. #390	C₂×C₃×C₅	semidirect
142. #386	C₂×C₃×C₅	semidirect
143. #382	C₂×C₃×C₅	semidirect
144. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
292. C₃×C₅	#2504	direct (N × H)
346. C₅	C₃×#2504	direct (N × H)
364. C₃	C₅×#2504	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×#121	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#390	2
C₃×C₅×#386	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2504	3
C₃×#2504	5

Subgroups — C3×C5×#2504 #14275538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2504 #14275538