Subgroups — C₃×C₅×D₄×D₁₅ #72230733

Order 3600.

560 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₃²×C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#1220	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₅×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₄×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₅×D₄×D₅	—	3	1	no	maximal
8	C₂²×C₃²×C₅²	C₂²	1	2	yes	complemented
9	C₂×C₃×C₅×D₁₅	—	2	4	no	—
10	C₂×C₃×C₅×D₁₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₁₅	C₂²	1	2	yes	complemented
12	C₃²×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
13	C₃×C₅×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
14	C₃×D₄×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
15	C₃×C₅×D₃×D₄	—	5	1	no	maximal
16	C₂²×C₅×D₁₅	C₂×C₃	1	2	yes	complemented
17	C₂²×C₃×C₅×D₅	—	3	2	no	—
18	C₃×C₅²×D₄	—	2	1	no	—
19	C₃×C₅²×D₄	D₃	1	1	yes	characteristic, complemented
20	C₃×C₅²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
21	C₅×#1220	C₂×C₃	1	2	yes	complemented
22	C₅×D₆₀	C₂×C₃	1	1	yes	characteristic, complemented
23	C₄×C₅×D₁₅	C₂×C₃	1	1	yes	characteristic, complemented
24	C₃×C₅×C₂²⋊D₅	—	3	2	no	—
25	C₃×C₅×D₂₀	—	3	1	no	—
26	C₃×C₄×C₅×D₅	—	3	1	no	—
27	C₂×C₃²×C₅²	—	2	2	no	—
28	C₂×C₃²×C₅²	C₂³	1	1	yes	characteristic
29	C₃×C₅×D₁₅	—	2	2	no	—
30	C₃×C₅×D₁₅	D₄	1	2	yes	direct product factor
31	C₅×D₄×D₅	—	3	1	no	Hall
32	C₂²×C₃×D₁₅	C₂×C₅	1	2	yes	complemented
33	C₂²×C₃×C₅×D₃	—	5	2	no	—
34	C₃²×C₅×D₄	—	2	2	no	—
35	C₃²×C₅×D₄	D₅	1	1	yes	characteristic, complemented
36	C₃²×C₅×D₄	C₂×C₅	1	1	yes	characteristic, complemented
37	C₃×#1220	C₂×C₅	1	2	yes	complemented
38	C₃×D₆₀	C₂×C₅	1	1	yes	characteristic, complemented
39	C₃×C₄×D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
40	C₃×C₅×#67	—	5	2	no	—
41	C₃×C₅×D₁₂	—	5	1	no	—
42	C₃×C₄×C₅×D₃	—	5	1	no	—
43	C₂²×C₃×C₅²	—	2	2	no	—
44	C₂²×C₃×C₅²	C₂×D₃	1	2	yes	complemented
45	C₂²×C₃×C₅²	C₂²×C₃	1	2	yes	complemented
46	C₂×C₅×D₁₅	—	2	4	no	—
47	C₂×C₅×D₁₅	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₅×D₁₅	C₂²×C₃	1	2	yes	complemented
49	C₂×C₃×C₅×D₅	—	3	1	no	—
50	C₂×C₃×C₅×D₅	—	3	2	no	—
51	C₂×C₃×C₅×D₅	—	6	4	no	—
52	C₃×C₄×C₅²	—	2	1	no	—
53	C₃×C₄×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
54	C₃×C₄×C₅²	C₂²×C₃	1	1	yes	characteristic, complemented
55	C₅×Dic₁₅	C₂²×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×Dic₅	—	3	1	no	—
57	C₂×C₃×C₅×D₄	—	15	1	no	—
58	D₄×D₁₅	C₃×C₅	1	1	yes	characteristic, direct product factor
59	C₅×D₃×D₄	—	5	1	no	—
60	C₃×D₄×D₅	—	3	1	no	—
61	C₃²×C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₅×D₅	—	3	2	no	—
63	C₅²×D₄	C₃×D₃	1	1	yes	characteristic, complemented
64	C₅×C₂²⋊D₅	—	3	2	no	—
65	C₅×D₂₀	—	3	1	no	—
66	C₄×C₅×D₅	—	3	1	no	—
67	C₂²×C₃²×C₅	—	2	4	no	—
68	C₂²×C₃²×C₅	C₂×D₅	1	2	yes	complemented
69	C₂²×C₃²×C₅	C₂²×C₅	1	2	yes	complemented
70	C₂×C₃×D₁₅	—	2	4	no	—
71	C₂×C₃×D₁₅	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₃×D₁₅	C₂²×C₅	1	2	yes	complemented
73	C₂×C₃×C₅×D₃	—	5	1	no	—
74	C₂×C₃×C₅×D₃	—	5	2	no	—
75	C₂×C₃×C₅×D₃	—	10	4	no	—
76	C₃²×C₄×C₅	—	2	2	no	—
77	C₃²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
78	C₃²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
79	C₃×Dic₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
80	C₃×C₅×Dic₃	—	5	1	no	—
81	C₂×C₃×C₅²	—	2	2	no	—
82	C₂×C₃×C₅²	—	2	2	no	—
83	C₂×C₃×C₅²	—	2	1	no	—
84	C₂×C₃×C₅²	—	4	2	no	—
85	C₂×C₃×C₅²	C₂²×D₃	1	1	yes	characteristic
86	C₂×C₃×C₅²	C₂³×C₃	1	1	yes	characteristic
87	C₅×D₁₅	—	2	2	no	—
88	C₅×D₁₅	C₃×D₄	1	2	yes	direct product factor
89	C₃×C₅×D₅	—	3	2	no	—
90	C₃×C₅×D₅	—	6	2	no	—
91	C₃×D₃×D₄	—	5	1	no	Hall
92	C₂³×C₃×C₅	—	15	2	no	—
93	C₂²×D₁₅	C₂×C₃×C₅	1	2	yes	complemented
94	C₂²×C₅×D₃	—	5	2	no	—
95	C₂²×C₃×D₅	—	3	2	no	—
96	C₃×C₅×D₄	—	2	4	no	—
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	15	2	no	—
102	C₃×C₅×D₄	—	15	1	no	—
103	C₃×C₅×D₄	C₅×D₃	1	1	yes	characteristic, complemented
104	C₃×C₅×D₄	C₃×D₅	1	1	yes	characteristic, complemented
105	C₃×C₅×D₄	D₁₅	1	1	yes	characteristic, direct product factor
106	C₃×C₅×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
107	C₂×C₃×C₄×C₅	—	15	1	no	—
108	#1220	C₂×C₃×C₅	1	2	yes	complemented
109	D₆₀	C₂×C₃×C₅	1	1	yes	characteristic, complemented
110	C₄×D₁₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
111	C₅×#67	—	5	2	no	—
112	C₅×D₁₂	—	5	1	no	—
113	C₄×C₅×D₃	—	5	1	no	—
114	C₃×C₂²⋊D₅	—	3	2	no	—
115	C₃×D₂₀	—	3	1	no	—
116	C₃×C₄×D₅	—	3	1	no	—
117	C₂²×C₅²	C₂×C₃×D₃	1	2	yes	complemented
118	C₂×C₅×D₅	—	3	1	no	—
119	C₂×C₅×D₅	—	3	2	no	—
120	C₂×C₅×D₅	—	6	4	no	—
121	C₄×C₅²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
122	C₅×Dic₅	—	3	1	no	—
123	C₂×C₃²×C₅	—	2	2	no	—
124	C₂×C₃²×C₅	—	2	2	no	—
125	C₂×C₃²×C₅	—	2	2	no	—
126	C₂×C₃²×C₅	—	4	4	no	—
127	C₂×C₃²×C₅	C₂²×D₅	1	1	yes	characteristic
128	C₂×C₃²×C₅	C₂³×C₅	1	1	yes	characteristic
129	C₃×D₁₅	—	2	2	no	—
130	C₃×D₁₅	C₅×D₄	1	2	yes	direct product factor
131	C₃×C₅×D₃	—	5	2	no	—
132	C₃×C₅×D₃	—	10	2	no	—
133	C₂×C₅×D₄	—	15	1	no	—
134	D₄×D₅	—	3	1	no	—
135	C₃×C₅²	—	2	1	no	—
136	C₃×C₅²	D₃×D₄	1	1	yes	characteristic, complemented
137	C₃×C₅²	C₂×C₃×D₄	1	1	yes	characteristic, complemented
138	C₂²×C₃×D₃	—	5	2	no	—
139	C₃²×D₄	C₅×D₅	1	1	yes	characteristic, complemented
140	C₃×#67	—	5	2	no	—
141	C₃×D₁₂	—	5	1	no	—
142	C₃×C₄×D₃	—	5	1	no	—
143	C₂²×C₃×C₅	—	2	8	no	—
144	C₂²×C₃×C₅	—	2	2	no	—
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	—	2	4	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	15	1	no	—
149	C₂²×C₃×C₅	—	15	2	no	—
150	C₂²×C₃×C₅	—	30	4	no	—
151	C₂²×C₃×C₅	C₂×C₃×D₅	1	2	yes	complemented
152	C₂²×C₃×C₅	C₂×C₅×D₃	1	2	yes	complemented
153	C₂²×C₃×C₅	C₂×D₁₅	1	2	yes	complemented
154	C₂²×C₃×C₅	C₂²×C₃×C₅	1	2	yes	complemented
155	C₂×D₁₅	—	2	4	no	—
156	C₂×D₁₅	C₂²×C₃×C₅	1	1	yes	characteristic
157	C₂×D₁₅	C₂²×C₃×C₅	1	2	yes	complemented
158	C₂×C₅×D₃	—	5	1	no	—
159	C₂×C₅×D₃	—	5	2	no	—
160	C₂×C₅×D₃	—	10	4	no	—
161	C₂×C₃×D₅	—	3	1	no	—
162	C₂×C₃×D₅	—	3	2	no	—
163	C₂×C₃×D₅	—	6	4	no	—
164	C₃×C₄×C₅	—	2	4	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	15	1	no	—
170	C₃×C₄×C₅	C₂×C₃×D₅	1	1	yes	characteristic, complemented
171	C₃×C₄×C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
172	C₃×C₄×C₅	C₂×D₁₅	1	1	yes	characteristic, complemented
173	C₃×C₄×C₅	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
174	Dic₁₅	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
175	C₃×Dic₅	—	3	1	no	—
176	C₅×Dic₃	—	5	1	no	—
177	C₂×C₅²	—	2	2	no	—
178	C₂×C₅²	C₂²×C₃×D₃	1	1	yes	characteristic
179	C₅×D₅	—	3	2	no	—
180	C₅×D₅	—	6	2	no	—
181	C₂×C₃×D₄	—	15	1	no	—
182	D₃×D₄	—	5	1	no	—
183	C₃²×C₅	—	2	2	no	—
184	C₃²×C₅	D₄×D₅	1	1	yes	characteristic, complemented
185	C₃²×C₅	C₂×C₅×D₄	1	1	yes	characteristic, complemented
186	C₂³×C₅	—	15	2	no	—
187	C₂²×D₅	—	3	2	no	—
188	C₅×D₄	—	2	2	no	—
189	C₅×D₄	—	15	2	no	—
190	C₅×D₄	—	15	1	no	—
191	C₅×D₄	C₃×C₅×D₃	1	1	yes	characteristic, complemented
192	C₅×D₄	C₃×D₁₅	1	1	yes	characteristic, direct product factor
193	C₂×C₄×C₅	—	15	1	no	—
194	C₂²⋊D₅	—	3	2	no	—
195	D₂₀	—	3	1	no	—
196	C₄×D₅	—	3	1	no	—
197	C₂²×C₃²	C₂×C₅×D₅	1	2	yes	complemented
198	C₂×C₃×D₃	—	5	1	no	—
199	C₂×C₃×D₃	—	5	2	no	—
200	C₂×C₃×D₃	—	10	4	no	—
201	C₃²×C₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
202	C₃×Dic₃	—	5	1	no	—
203	C₂×C₃×C₅	—	2	4	no	—
204	C₂×C₃×C₅	—	2	2	no	—
205	C₂×C₃×C₅	—	2	2	no	—
206	C₂×C₃×C₅	—	2	2	no	—
207	C₂×C₃×C₅	—	2	2	no	—
208	C₂×C₃×C₅	—	2	1	no	—
209	C₂×C₃×C₅	—	2	1	no	—
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	—	2	2	no	—
212	C₂×C₃×C₅	—	4	4	no	—
213	C₂×C₃×C₅	—	4	4	no	—
214	C₂×C₃×C₅	—	4	2	no	—
215	C₂×C₃×C₅	—	4	2	no	—
216	C₂×C₃×C₅	—	4	8	no	—
217	C₂×C₃×C₅	—	15	2	no	—
218	C₂×C₃×C₅	—	30	2	no	—
219	C₂×C₃×C₅	C₂²×C₃×D₅	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
221	C₂×C₃×C₅	C₂²×D₁₅	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂³×C₃×C₅	1	1	yes	characteristic
223	D₁₅	—	2	2	no	—
224	D₁₅	C₃×C₅×D₄	1	2	yes	direct product factor
225	C₃×D₅	—	3	2	no	—
226	C₃×D₅	—	6	2	no	—
227	C₅×D₃	—	5	2	no	—
228	C₅×D₃	—	10	2	no	—
229	C₅²	C₃×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	15	2	no	—
231	C₂²×D₃	—	5	2	no	—
232	C₃×D₄	—	2	1	no	—
233	C₃×D₄	—	15	2	no	—
234	C₃×D₄	—	15	1	no	—
235	C₃×D₄	C₃×C₅×D₅	1	1	yes	characteristic, complemented
236	C₃×D₄	C₅×D₁₅	1	1	yes	characteristic, direct product factor
237	C₂×C₃×C₄	—	15	1	no	—
238	#67	—	5	2	no	—
239	D₁₂	—	5	1	no	—
240	C₄×D₃	—	5	1	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	15	1	no	—
243	C₂²×C₅	—	15	2	no	—
244	C₂²×C₅	—	30	4	no	—
245	C₂²×C₅	C₂×C₃×C₅×D₃	1	2	yes	complemented
246	C₂²×C₅	C₂×C₃×D₁₅	1	2	yes	complemented
247	C₂×D₅	—	3	1	no	—
248	C₂×D₅	—	3	2	no	—
249	C₂×D₅	—	6	4	no	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	15	1	no	—
252	C₄×C₅	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented
253	C₄×C₅	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented
254	Dic₅	—	3	1	no	—
255	C₂×C₃²	—	2	2	no	—
256	C₂×C₃²	C₂²×C₅×D₅	1	1	yes	characteristic
257	C₃×D₃	—	5	2	no	—
258	C₃×D₃	—	10	2	no	—
259	C₂×D₄	—	15	1	no	Sylow
260	C₃×C₅	—	2	4	no	—
261	C₃×C₅	—	2	1	no	—
262	C₃×C₅	—	2	1	no	—
263	C₃×C₅	—	2	2	no	—
264	C₃×C₅	—	2	2	no	—
265	C₃×C₅	C₃×D₄×D₅	1	1	yes	characteristic, complemented
266	C₃×C₅	C₅×D₃×D₄	1	1	yes	characteristic, complemented
267	C₃×C₅	D₄×D₁₅	1	1	yes	characteristic, direct product factor
268	C₃×C₅	C₂×C₃×C₅×D₄	1	1	yes	characteristic, complemented
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	15	1	no	—
271	C₂²×C₃	—	15	2	no	—
272	C₂²×C₃	—	30	4	no	—
273	C₂²×C₃	C₂×C₃×C₅×D₅	1	2	yes	complemented
274	C₂²×C₃	C₂×C₅×D₁₅	1	2	yes	complemented
275	C₂×D₃	—	5	1	no	—
276	C₂×D₃	—	5	2	no	—
277	C₂×D₃	—	10	4	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	15	1	no	—
280	C₃×C₄	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented
281	C₃×C₄	C₂×C₅×D₁₅	1	1	yes	characteristic, complemented
282	Dic₃	—	5	1	no	—
283	C₂×C₅	—	2	2	no	—
284	C₂×C₅	—	2	2	no	—
285	C₂×C₅	—	2	2	no	—
286	C₂×C₅	—	4	4	no	—
287	C₂×C₅	—	15	2	no	—
288	C₂×C₅	—	30	2	no	—
289	C₂×C₅	C₂²×C₃×C₅×D₃	1	1	yes	characteristic
290	C₂×C₅	C₂²×C₃×D₁₅	1	1	yes	characteristic
291	D₅	—	3	2	no	—
292	D₅	—	6	2	no	—
293	C₃²	C₅×D₄×D₅	1	1	yes	characteristic, complemented, Sylow
294	C₂³	—	15	2	no	—
295	D₄	—	15	2	no	—
296	D₄	—	15	1	no	—
297	D₄	C₃×C₅×D₁₅	1	1	yes	characteristic, direct product factor
298	C₂×C₄	—	15	1	no	—
299	C₂×C₃	—	2	2	no	—
300	C₂×C₃	—	2	2	no	—
301	C₂×C₃	—	2	1	no	—
302	C₂×C₃	—	4	2	no	—
303	C₂×C₃	—	15	2	no	—
304	C₂×C₃	—	30	2	no	—
305	C₂×C₃	C₂²×C₃×C₅×D₅	1	1	yes	characteristic
306	C₂×C₃	C₂²×C₅×D₁₅	1	1	yes	characteristic
307	D₃	—	5	2	no	—
308	D₃	—	10	2	no	—
309	C₅	—	2	2	no	—
310	C₅	C₃×C₅×D₃×D₄	1	1	yes	characteristic, complemented
311	C₅	C₃×D₄×D₁₅	1	1	yes	characteristic, direct product factor
312	C₂²	—	15	1	no	—
313	C₂²	—	15	2	no	—
314	C₂²	—	30	4	no	—
315	C₂²	C₂×C₃×C₅×D₁₅	1	2	yes	complemented
316	C₄	—	15	1	no	—
317	C₄	C₂×C₃×C₅×D₁₅	1	1	yes	characteristic, complemented
318	C₃	—	2	1	no	—
319	C₃	C₃×C₅×D₄×D₅	1	1	yes	characteristic, complemented
320	C₃	C₅×D₄×D₁₅	1	1	yes	characteristic, direct product factor
321	C₂	—	2	2	no	—
322	C₂	—	15	2	no	—
323	C₂	—	30	2	no	—
324	C₂	C₂²×C₃×C₅×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₅	C₂²×D₁₅
commutator, cosocle	C₂×C₃×C₅	C₂³×C₃×C₅
Frattini	C₂	C₂²×C₃×C₅×D₁₅
Fitting	C₃²×C₅²×D₄	C₂
socle	C₂×C₃²×C₅²	C₂³
hypercenter	C₃×C₅×D₄	D₁₅
hypocenter	C₃×C₅	C₂×C₃×C₅×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₁₅	C₂	semidirect
2. C₃²×C₅²×D₄	C₂	semidirect
3. C₃×C₅×#1220	C₂	semidirect
4. C₃×C₅×D₆₀	C₂	semidirect
5. C₃×C₄×C₅×D₁₅	C₂	semidirect
6. C₅×D₄×D₁₅	C₃	direct (N × H)
8. C₂²×C₃²×C₅²	C₂²	semidirect
11. C₂×C₃×C₅×D₁₅	C₂²	semidirect
12. C₃²×C₄×C₅²	C₂²	semidirect
13. C₃×C₅×Dic₁₅	C₂²	semidirect
14. C₃×D₄×D₁₅	C₅	direct (N × H)
16. C₂²×C₅×D₁₅	C₂×C₃	semidirect
19. C₃×C₅²×D₄	D₃	semidirect
20. C₃×C₅²×D₄	C₂×C₃	semidirect
21. C₅×#1220	C₂×C₃	semidirect
22. C₅×D₆₀	C₂×C₃	semidirect
23. C₄×C₅×D₁₅	C₂×C₃	semidirect
30. C₃×C₅×D₁₅	D₄	direct (N × H)
32. C₂²×C₃×D₁₅	C₂×C₅	semidirect
35. C₃²×C₅×D₄	D₅	semidirect
36. C₃²×C₅×D₄	C₂×C₅	semidirect
37. C₃×#1220	C₂×C₅	semidirect
38. C₃×D₆₀	C₂×C₅	semidirect
39. C₃×C₄×D₁₅	C₂×C₅	semidirect
44. C₂²×C₃×C₅²	C₂×D₃	semidirect
45. C₂²×C₃×C₅²	C₂²×C₃	semidirect
48. C₂×C₅×D₁₅	C₂²×C₃	semidirect
53. C₃×C₄×C₅²	C₂×D₃	semidirect
54. C₃×C₄×C₅²	C₂²×C₃	semidirect
55. C₅×Dic₁₅	C₂²×C₃	semidirect
58. D₄×D₁₅	C₃×C₅	direct (N × H)
61. C₃²×C₅²	C₂×D₄	semidirect
63. C₅²×D₄	C₃×D₃	semidirect
68. C₂²×C₃²×C₅	C₂×D₅	semidirect
69. C₂²×C₃²×C₅	C₂²×C₅	semidirect
72. C₂×C₃×D₁₅	C₂²×C₅	semidirect
77. C₃²×C₄×C₅	C₂×D₅	semidirect
78. C₃²×C₄×C₅	C₂²×C₅	semidirect
79. C₃×Dic₁₅	C₂²×C₅	semidirect
88. C₅×D₁₅	C₃×D₄	direct (N × H)
93. C₂²×D₁₅	C₂×C₃×C₅	semidirect
103. C₃×C₅×D₄	C₅×D₃	semidirect
104. C₃×C₅×D₄	C₃×D₅	semidirect
105. C₃×C₅×D₄	D₁₅	direct (N × H)
106. C₃×C₅×D₄	C₂×C₃×C₅	semidirect
108. #1220	C₂×C₃×C₅	semidirect
109. D₆₀	C₂×C₃×C₅	semidirect
110. C₄×D₁₅	C₂×C₃×C₅	semidirect
117. C₂²×C₅²	C₂×C₃×D₃	semidirect
121. C₄×C₅²	C₂×C₃×D₃	semidirect
130. C₃×D₁₅	C₅×D₄	direct (N × H)
136. C₃×C₅²	D₃×D₄	semidirect
137. C₃×C₅²	C₂×C₃×D₄	semidirect
139. C₃²×D₄	C₅×D₅	semidirect
151. C₂²×C₃×C₅	C₂×C₃×D₅	semidirect
152. C₂²×C₃×C₅	C₂×C₅×D₃	semidirect
153. C₂²×C₃×C₅	C₂×D₁₅	semidirect
154. C₂²×C₃×C₅	C₂²×C₃×C₅	semidirect
157. C₂×D₁₅	C₂²×C₃×C₅	semidirect
170. C₃×C₄×C₅	C₂×C₃×D₅	semidirect
171. C₃×C₄×C₅	C₂×C₅×D₃	semidirect
172. C₃×C₄×C₅	C₂×D₁₅	semidirect
173. C₃×C₄×C₅	C₂²×C₃×C₅	semidirect
174. Dic₁₅	C₂²×C₃×C₅	semidirect
184. C₃²×C₅	D₄×D₅	semidirect
185. C₃²×C₅	C₂×C₅×D₄	semidirect
191. C₅×D₄	C₃×C₅×D₃	semidirect
192. C₅×D₄	C₃×D₁₅	direct (N × H)
197. C₂²×C₃²	C₂×C₅×D₅	semidirect
201. C₃²×C₄	C₂×C₅×D₅	semidirect
224. D₁₅	C₃×C₅×D₄	direct (N × H)
229. C₅²	C₃×D₃×D₄	semidirect
235. C₃×D₄	C₃×C₅×D₅	semidirect
236. C₃×D₄	C₅×D₁₅	direct (N × H)
245. C₂²×C₅	C₂×C₃×C₅×D₃	semidirect
246. C₂²×C₅	C₂×C₃×D₁₅	semidirect
252. C₄×C₅	C₂×C₃×C₅×D₃	semidirect
253. C₄×C₅	C₂×C₃×D₁₅	semidirect
265. C₃×C₅	C₃×D₄×D₅	semidirect
266. C₃×C₅	C₅×D₃×D₄	semidirect
267. C₃×C₅	D₄×D₁₅	direct (N × H)
268. C₃×C₅	C₂×C₃×C₅×D₄	semidirect
273. C₂²×C₃	C₂×C₃×C₅×D₅	semidirect
274. C₂²×C₃	C₂×C₅×D₁₅	semidirect
280. C₃×C₄	C₂×C₃×C₅×D₅	semidirect
281. C₃×C₄	C₂×C₅×D₁₅	semidirect
293. C₃²	C₅×D₄×D₅	semidirect
297. D₄	C₃×C₅×D₁₅	direct (N × H)
310. C₅	C₃×C₅×D₃×D₄	semidirect
311. C₅	C₃×D₄×D₁₅	direct (N × H)
315. C₂²	C₂×C₃×C₅×D₁₅	semidirect
317. C₄	C₂×C₃×C₅×D₁₅	semidirect
319. C₃	C₃×C₅×D₄×D₅	semidirect
320. C₃	C₅×D₄×D₁₅	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×D₁₅	2
C₃²×C₅²×D₄	2
C₃×C₅×#1220	2
C₃×C₅×D₆₀	2
C₃×C₄×C₅×D₁₅	2
C₅×D₄×D₁₅	3
C₃×C₅×D₄×D₅	3
C₃×D₄×D₁₅	5
C₃×C₅×D₃×D₄	5

Subgroups — C3×C5×D4×D15 #72230733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₄×D₁₅ #72230733