Subgroups — C₃×C₅×#1581 #14274615

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1581	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	—	2	1	no	—
12	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×#107	C₄	1	1	yes	characteristic
15	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#102	C₄	1	1	yes	characteristic
18	C₃×C₅×#102	C₄	1	1	yes	characteristic
19	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
20	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×#1581	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic
26	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#335	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#322	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₃×C₅×D₈	—	2	2	no	—
37	C₃×C₅×M₁₆	—	4	2	no	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	—	2	1	no	—
40	C₂×C₃×C₅×C₈	—	2	1	no	—
41	C₂×C₃×C₅×C₈	—	4	2	no	—
42	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic
52	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
53	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#335	C₂×C₅	1	1	yes	characteristic, complemented
55	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#322	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
62	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₅×#107	C₃×C₄	1	1	yes	characteristic
64	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
65	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
66	C₅×#102	C₃×C₄	1	1	yes	characteristic
67	C₅×#102	C₃×C₄	1	1	yes	characteristic
68	C₅×C₂²⋊C₈	—	2	1	no	—
69	C₅×C₂²⋊C₈	—	2	1	no	—
70	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
71	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
73	#1581	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₃×C₅×D₄	—	2	1	no	—
77	C₃×C₅×D₄	—	2	1	no	—
78	C₃×C₅×D₄	—	2	1	no	—
79	C₃×C₅×D₄	M₁₆	1	2	yes	complemented
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	4	1	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
89	C₃×C₅×C₈	—	2	1	no	—
90	C₃×C₅×C₈	—	2	1	no	—
91	C₃×C₅×C₈	—	2	1	no	—
92	C₃×C₅×C₈	—	4	1	no	—
93	C₃×C₅×C₈	—	4	1	no	—
94	C₃×C₅×C₈	—	4	1	no	—
95	C₃×C₅×C₈	D₈	1	2	yes	complemented
96	C₂×C₃×D₈	C₄×C₅	1	1	yes	characteristic
97	C₂×C₃×M₁₆	—	2	1	no	—
98	C₂²×C₃×C₈	—	2	1	no	—
99	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
100	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
101	C₃×#107	C₄×C₅	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
103	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
104	C₃×#102	C₄×C₅	1	1	yes	characteristic
105	C₃×#102	C₄×C₅	1	1	yes	characteristic
106	C₃×C₂²⋊C₈	—	2	1	no	—
107	C₃×C₂²⋊C₈	—	2	1	no	—
108	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
112	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₅×D₈	—	2	2	no	—
116	C₅×M₁₆	—	4	2	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	—	4	2	no	—
121	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
125	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
126	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
127	C₅×C₂²⋊C₄	—	2	1	no	—
128	C₅×C₂²⋊C₄	—	2	1	no	—
129	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic
131	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
132	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
133	#335	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
136	#322	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	4	1	no	—
139	C₂²×C₃×C₅	—	4	1	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	1	no	—
142	C₂²×C₃×C₅	—	4	1	no	—
143	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
144	C₃×C₄×C₅	—	2	1	no	—
145	C₃×C₄×C₅	—	4	1	no	—
146	C₃×C₄×C₅	—	4	1	no	—
147	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
148	C₃×C₄×C₅	#131	1	1	yes	characteristic
149	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
150	C₃×C₄×C₅	#135	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₃×D₈	—	2	2	no	—
156	C₃×M₁₆	—	4	2	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	4	2	no	—
161	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
162	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
163	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
164	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
165	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
166	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₃×C₂²⋊C₄	—	2	1	no	—
168	C₃×C₂²⋊C₄	—	2	1	no	—
169	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
170	C₂³×C₅	—	2	1	no	—
171	C₂³×C₅	—	2	1	no	—
172	C₅×D₄	—	2	1	no	—
173	C₅×D₄	—	2	1	no	—
174	C₅×D₄	—	2	1	no	—
175	C₅×D₄	C₃×M₁₆	1	2	yes	complemented
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
185	C₅×C₈	—	2	1	no	—
186	C₅×C₈	—	2	1	no	—
187	C₅×C₈	—	2	1	no	—
188	C₅×C₈	—	4	1	no	—
189	C₅×C₈	—	4	1	no	—
190	C₅×C₈	—	4	1	no	—
191	C₅×C₈	C₃×D₈	1	2	yes	complemented
192	C₂×D₈	C₃×C₄×C₅	1	1	yes	characteristic
193	C₂×M₁₆	—	2	1	no	—
194	C₂²×C₈	—	2	1	no	—
195	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
197	#107	C₃×C₄×C₅	1	1	yes	characteristic
198	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
199	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
200	#102	C₃×C₄×C₅	1	1	yes	characteristic
201	#102	C₃×C₄×C₅	1	1	yes	characteristic
202	C₂²⋊C₈	—	2	1	no	—
203	C₂²⋊C₈	—	2	1	no	—
204	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
205	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂×C₃×C₅	—	4	2	no	—
208	C₂×C₃×C₅	—	8	1	no	—
209	C₂×C₃×C₅	#435	1	1	yes	characteristic
210	C₂×C₃×C₅	C₄×D₈	1	1	yes	characteristic
211	C₂×C₃×C₅	#444	1	1	yes	characteristic
212	C₂³×C₃	—	2	1	no	—
213	C₂³×C₃	—	2	1	no	—
214	C₃×D₄	—	2	1	no	—
215	C₃×D₄	—	2	1	no	—
216	C₃×D₄	—	2	1	no	—
217	C₃×D₄	C₅×M₁₆	1	2	yes	complemented
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	4	1	no	—
221	C₂×C₃×C₄	—	4	1	no	—
222	C₂×C₃×C₄	—	4	1	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
227	C₃×C₈	—	2	1	no	—
228	C₃×C₈	—	2	1	no	—
229	C₃×C₈	—	2	1	no	—
230	C₃×C₈	—	4	1	no	—
231	C₃×C₈	—	4	1	no	—
232	C₃×C₈	—	4	1	no	—
233	C₃×C₈	C₅×D₈	1	2	yes	complemented
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	4	1	no	—
236	C₂²×C₅	—	4	1	no	—
237	C₂²×C₅	—	4	1	no	—
238	C₂²×C₅	—	4	1	no	—
239	C₂²×C₅	—	4	1	no	—
240	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	4	1	no	—
243	C₄×C₅	—	4	1	no	—
244	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
245	C₄×C₅	C₃×#131	1	1	yes	characteristic
246	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
247	C₄×C₅	C₃×#135	1	1	yes	characteristic
248	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
249	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	D₈	—	2	2	no	—
253	M₁₆	—	4	2	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
259	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
260	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
261	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
262	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
263	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
264	C₂²⋊C₄	—	2	1	no	—
265	C₂²⋊C₄	—	2	1	no	—
266	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₃×C₅	#1581	1	1	yes	characteristic, direct product factor, Hall
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	4	1	no	—
270	C₂²×C₃	—	4	1	no	—
271	C₂²×C₃	—	4	1	no	—
272	C₂²×C₃	—	4	1	no	—
273	C₂²×C₃	—	4	1	no	—
274	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	4	1	no	—
277	C₃×C₄	—	4	1	no	—
278	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
279	C₃×C₄	C₅×#131	1	1	yes	characteristic
280	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
281	C₃×C₄	C₅×#135	1	1	yes	characteristic
282	C₂×C₅	—	4	2	no	—
283	C₂×C₅	—	8	1	no	—
284	C₂×C₅	C₃×#435	1	1	yes	characteristic
285	C₂×C₅	C₃×C₄×D₈	1	1	yes	characteristic
286	C₂×C₅	C₃×#444	1	1	yes	characteristic
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	D₄	—	2	1	no	—
290	D₄	—	2	1	no	—
291	D₄	—	2	1	no	—
292	D₄	C₃×C₅×M₁₆	1	2	yes	complemented
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
300	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
301	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
302	C₈	—	2	1	no	—
303	C₈	—	2	1	no	—
304	C₈	—	2	1	no	—
305	C₈	—	4	1	no	—
306	C₈	—	4	1	no	—
307	C₈	—	4	1	no	—
308	C₈	C₃×C₅×D₈	1	2	yes	complemented
309	C₂×C₃	—	4	2	no	—
310	C₂×C₃	—	8	1	no	—
311	C₂×C₃	C₅×#435	1	1	yes	characteristic
312	C₂×C₃	C₄×C₅×D₈	1	1	yes	characteristic
313	C₂×C₃	C₅×#444	1	1	yes	characteristic
314	C₅	C₃×#1581	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²	—	2	2	no	—
316	C₂²	—	4	1	no	—
317	C₂²	—	4	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	1	no	—
320	C₂²	—	4	1	no	—
321	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	4	1	no	—
324	C₄	—	4	1	no	—
325	C₄	C₂×C₃×C₅×M₁₆	1	1	yes	characteristic
326	C₄	C₃×C₅×#131	1	1	yes	characteristic
327	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
328	C₄	C₃×C₅×#135	1	1	yes	characteristic
329	C₃	C₅×#1581	1	1	yes	characteristic, direct product factor, Sylow
330	C₂	—	4	2	no	—
331	C₂	—	8	1	no	—
332	C₂	C₃×C₅×#435	1	1	yes	characteristic
333	C₂	C₃×C₄×C₅×D₈	1	1	yes	characteristic
334	C₂	C₃×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₄²	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×D₈	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₃×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#436	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. C₃×C₅×#335	C₂	semidirect
5. C₃×C₅×D₄⋊C₈	C₂	semidirect
6. C₃×C₅×D₄⋊C₈	C₂	semidirect
7. C₃×C₅×#322	C₂	semidirect
8. C₅×#1581	C₃	direct (N × H)
24. C₃×#1581	C₅	direct (N × H)
26. C₅×#436	C₂×C₃	semidirect
27. C₅×C₈×D₄	C₂×C₃	semidirect
28. C₅×#335	C₂×C₃	semidirect
29. C₅×D₄⋊C₈	C₂×C₃	semidirect
30. C₅×D₄⋊C₈	C₂×C₃	semidirect
31. C₅×#322	C₂×C₃	semidirect
52. C₃×#436	C₂×C₅	semidirect
53. C₃×C₈×D₄	C₂×C₅	semidirect
54. C₃×#335	C₂×C₅	semidirect
55. C₃×D₄⋊C₈	C₂×C₅	semidirect
56. C₃×D₄⋊C₈	C₂×C₅	semidirect
57. C₃×#322	C₂×C₅	semidirect
73. #1581	C₃×C₅	direct (N × H)
79. C₃×C₅×D₄	M₁₆	semidirect
95. C₃×C₅×C₈	D₈	semidirect
131. #436	C₂×C₃×C₅	semidirect
132. C₈×D₄	C₂×C₃×C₅	semidirect
133. #335	C₂×C₃×C₅	semidirect
134. D₄⋊C₈	C₂×C₃×C₅	semidirect
135. D₄⋊C₈	C₂×C₃×C₅	semidirect
136. #322	C₂×C₃×C₅	semidirect
175. C₅×D₄	C₃×M₁₆	semidirect
191. C₅×C₈	C₃×D₈	semidirect
217. C₃×D₄	C₅×M₁₆	semidirect
233. C₃×C₈	C₅×D₈	semidirect
267. C₃×C₅	#1581	direct (N × H)
292. D₄	C₃×C₅×M₁₆	semidirect
308. C₈	C₃×C₅×D₈	semidirect
314. C₅	C₃×#1581	direct (N × H)
329. C₃	C₅×#1581	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×D₈	2
C₃×C₅×#436	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#335	2
C₃×C₅×D₄⋊C₈	2
C₃×C₅×#322	2
C₅×#1581	3
C₃×#1581	5

Subgroups — C3×C5×#1581 #14274615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1581 #14274615