Subgroups — C₃×C₅×#529 #11756618

Order 960.

468 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#117	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#529	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	—
20	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₃×C₄²×C₅	C₂²	1	2	yes	—
36	C₃×#529	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#126	C₂×C₃	1	2	yes	complemented
38	C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#123	C₂×C₃	1	2	yes	complemented
41	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#121	C₂×C₃	1	1	yes	characteristic
43	C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
46	C₅×#117	C₂×C₃	1	2	yes	complemented
47	C₂×C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×C₅	C₂³	1	2	yes	—
49	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×Q₈	—	2	2	no	—
51	C₃×C₅×D₄	—	2	4	no	—
52	C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₄×C₅	—	2	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	—	2	4	no	—
56	C₂×C₃×C₄×C₅	—	2	2	no	—
57	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₃×#126	C₂×C₅	1	2	yes	complemented
67	C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#123	C₂×C₅	1	2	yes	complemented
70	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#121	C₂×C₅	1	1	yes	characteristic
72	C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
75	C₃×#117	C₂×C₅	1	2	yes	complemented
76	C₂×C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×D₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	—
84	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₄²×C₅	C₂²×C₃	1	2	yes	—
100	#529	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
101	C₂²×C₃×C₅	—	2	1	no	—
102	C₂²×C₃×C₅	—	2	1	no	—
103	C₂²×C₃×C₅	—	2	2	no	—
104	C₂²×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	#41	1	2	yes	—
107	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₄×C₅	—	2	1	no	—
109	C₃×C₄×C₅	—	2	1	no	—
110	C₃×C₄×C₅	—	2	1	no	—
111	C₃×C₄×C₅	—	2	1	no	—
112	C₃×C₄×C₅	—	2	2	no	—
113	C₃×C₄×C₅	—	2	2	no	—
114	C₃×C₄×C₅	—	2	2	no	—
115	C₃×C₄×C₅	#41	1	2	yes	—
116	C₃×C₄×C₅	#41	1	2	yes	—
117	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	—
124	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
125	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
126	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
127	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
130	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
132	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
133	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
135	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
136	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
139	C₃×C₄²	C₂²×C₅	1	2	yes	—
140	C₂³×C₅	C₂³×C₃	1	2	yes	—
141	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₅×Q₈	—	2	2	no	—
143	C₅×D₄	—	2	4	no	—
144	C₅×D₄	—	2	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	2	2	no	—
147	C₂×C₄×C₅	—	2	4	no	—
148	C₂×C₄×C₅	—	2	2	no	—
149	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	#126	C₂×C₃×C₅	1	2	yes	complemented
159	#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
161	#123	C₂×C₃×C₅	1	2	yes	complemented
162	C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	#121	C₂×C₃×C₅	1	1	yes	characteristic
164	C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
167	#117	C₂×C₃×C₅	1	2	yes	complemented
168	C₂×C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	C₂×C₃×C₅	—	2	2	no	—
170	C₂×C₃×C₅	—	4	2	no	—
171	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
172	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
173	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
174	C₂³×C₃	C₂³×C₅	1	2	yes	—
175	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
176	C₃×Q₈	—	2	2	no	—
177	C₃×D₄	—	2	4	no	—
178	C₃×D₄	—	2	2	no	—
179	C₂×C₃×C₄	—	2	2	no	—
180	C₂×C₃×C₄	—	2	2	no	—
181	C₂×C₃×C₄	—	2	4	no	—
182	C₂×C₃×C₄	—	2	2	no	—
183	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
188	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
189	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
190	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₅	—	2	1	no	—
193	C₂²×C₅	—	2	1	no	—
194	C₂²×C₅	—	2	2	no	—
195	C₂²×C₅	—	2	2	no	—
196	C₂²×C₅	—	2	2	no	—
197	C₂²×C₅	C₃×#41	1	2	yes	—
198	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
199	C₄×C₅	—	2	1	no	—
200	C₄×C₅	—	2	1	no	—
201	C₄×C₅	—	2	1	no	—
202	C₄×C₅	—	2	1	no	—
203	C₄×C₅	—	2	2	no	—
204	C₄×C₅	—	2	2	no	—
205	C₄×C₅	—	2	2	no	—
206	C₄×C₅	C₃×#41	1	2	yes	—
207	C₄×C₅	C₃×#41	1	2	yes	—
208	C₂×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
209	C₂×D₄	C₂²×C₃×C₅	1	2	yes	—
210	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
212	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	—
215	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
216	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
217	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
219	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
221	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
225	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₄²	C₂²×C₃×C₅	1	2	yes	—
231	C₃×C₅	#529	1	1	yes	characteristic, direct product factor, Hall
232	C₂²×C₃	—	2	1	no	—
233	C₂²×C₃	—	2	1	no	—
234	C₂²×C₃	—	2	2	no	—
235	C₂²×C₃	—	2	2	no	—
236	C₂²×C₃	—	2	2	no	—
237	C₂²×C₃	C₅×#41	1	2	yes	—
238	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
239	C₃×C₄	—	2	1	no	—
240	C₃×C₄	—	2	1	no	—
241	C₃×C₄	—	2	1	no	—
242	C₃×C₄	—	2	1	no	—
243	C₃×C₄	—	2	2	no	—
244	C₃×C₄	—	2	2	no	—
245	C₃×C₄	—	2	2	no	—
246	C₃×C₄	C₅×#41	1	2	yes	—
247	C₃×C₄	C₅×#41	1	2	yes	—
248	C₂×C₅	—	2	2	no	—
249	C₂×C₅	—	4	2	no	—
250	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
251	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
252	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
253	C₂³	C₂³×C₃×C₅	1	2	yes	—
254	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
255	Q₈	—	2	2	no	—
256	D₄	—	2	4	no	—
257	D₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	4	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
264	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
266	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
267	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
268	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
270	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
271	C₂×C₃	—	2	2	no	—
272	C₂×C₃	—	4	2	no	—
273	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
274	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
275	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
276	C₅	C₃×#529	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	2	2	no	—
280	C₂²	—	2	2	no	—
281	C₂²	—	2	2	no	—
282	C₂²	C₃×C₅×#41	1	2	yes	—
283	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	—	2	2	no	—
289	C₄	—	2	2	no	—
290	C₄	—	2	2	no	—
291	C₄	C₃×C₅×#41	1	2	yes	—
292	C₄	C₃×C₅×#41	1	2	yes	—
293	C₃	C₅×#529	1	1	yes	characteristic, direct product factor, Sylow
294	C₂	—	2	2	no	—
295	C₂	—	4	2	no	—
296	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
297	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
298	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₃×C₅×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#126	C₂	semidirect
2. C₃×C₅×#125	C₂	semidirect
3. C₃×C₅×#124	C₂	semidirect
4. C₃×C₅×#123	C₂	semidirect
5. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
7. C₃×C₄×C₅×Q₈	C₂	semidirect
8. C₃×C₄×C₅×D₄	C₂	semidirect
9. C₃×C₄×C₅×D₄	C₂	semidirect
10. C₃×C₅×#117	C₂	semidirect
11. C₂×C₃×C₄²×C₅	C₂	semidirect
12. C₅×#529	C₃	direct (N × H)
36. C₃×#529	C₅	direct (N × H)
37. C₅×#126	C₂×C₃	semidirect
38. C₅×#125	C₂×C₃	semidirect
39. C₅×#124	C₂×C₃	semidirect
40. C₅×#123	C₂×C₃	semidirect
41. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
43. C₄×C₅×Q₈	C₂×C₃	semidirect
44. C₄×C₅×D₄	C₂×C₃	semidirect
45. C₄×C₅×D₄	C₂×C₃	semidirect
46. C₅×#117	C₂×C₃	semidirect
47. C₂×C₄²×C₅	C₂×C₃	semidirect
66. C₃×#126	C₂×C₅	semidirect
67. C₃×#125	C₂×C₅	semidirect
68. C₃×#124	C₂×C₅	semidirect
69. C₃×#123	C₂×C₅	semidirect
70. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
72. C₃×C₄×Q₈	C₂×C₅	semidirect
73. C₃×C₄×D₄	C₂×C₅	semidirect
74. C₃×C₄×D₄	C₂×C₅	semidirect
75. C₃×#117	C₂×C₅	semidirect
76. C₂×C₃×C₄²	C₂×C₅	semidirect
100. #529	C₃×C₅	direct (N × H)
158. #126	C₂×C₃×C₅	semidirect
159. #125	C₂×C₃×C₅	semidirect
160. #124	C₂×C₃×C₅	semidirect
161. #123	C₂×C₃×C₅	semidirect
162. C₂²⋊Q₈	C₂×C₃×C₅	semidirect
164. C₄×Q₈	C₂×C₃×C₅	semidirect
165. C₄×D₄	C₂×C₃×C₅	semidirect
166. C₄×D₄	C₂×C₃×C₅	semidirect
167. #117	C₂×C₃×C₅	semidirect
168. C₂×C₄²	C₂×C₃×C₅	semidirect
231. C₃×C₅	#529	direct (N × H)
276. C₅	C₃×#529	direct (N × H)
293. C₃	C₅×#529	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×C₅×#126	2
C₃×C₅×#125	2
C₃×C₅×#124	2
C₃×C₅×#123	2
C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#121	2
C₃×C₄×C₅×Q₈	2
C₃×C₄×C₅×D₄	2
C₃×C₅×#117	2
C₂×C₃×C₄²×C₅	2
C₅×#529	3
C₃×#529	5

Subgroups — C3×C5×#529 #11756618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#529 #11756618