Subgroups — C₃×C₅×#552 #11756641

Order 960.

428 conjugacy classes of subgroups.

The subgroup lattice has 292 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	2	yes	maximal, complemented
3	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#123	C₂	1	2	yes	maximal
5	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#117	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#552	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	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
27	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄²×C₅	C₂²	1	2	yes	—
34	C₃×C₄²×C₅	C₂²	1	2	yes	—
35	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₃×#552	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	2	yes	complemented
39	C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#123	C₂×C₃	1	2	yes	—
41	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
43	C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
45	C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#117	C₂×C₃	1	2	yes	complemented
47	C₂×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
49	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×Q₈	—	2	2	no	—
51	C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₄×C₅	—	2	4	no	—
53	C₂×C₃×C₄×C₅	—	2	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×#126	C₂×C₅	1	2	yes	complemented
65	C₃×#125	C₂×C₅	1	2	yes	complemented
66	C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#123	C₂×C₅	1	2	yes	—
68	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
72	C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#117	C₂×C₅	1	2	yes	complemented
74	C₂×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	—
78	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
89	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
94	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₄²×C₅	C₂²×C₃	1	2	yes	—
96	C₄²×C₅	C₂²×C₃	1	2	yes	—
97	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	#552	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂²×C₃×C₅	—	2	1	no	—
100	C₂²×C₃×C₅	—	2	1	no	—
101	C₂²×C₃×C₅	—	2	1	no	—
102	C₂²×C₃×C₅	—	2	1	no	—
103	C₂²×C₃×C₅	—	2	1	no	—
104	C₂²×C₃×C₅	#41	1	2	yes	—
105	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₃×C₄×C₅	—	2	2	no	—
107	C₃×C₄×C₅	—	2	2	no	—
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	2	no	—
112	C₃×C₄×C₅	—	2	1	no	—
113	C₃×C₄×C₅	—	2	2	no	—
114	C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	—
118	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
129	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
130	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
134	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
135	C₃×C₄²	C₂²×C₅	1	2	yes	—
136	C₃×C₄²	C₂²×C₅	1	2	yes	—
137	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₅×Q₈	—	2	2	no	—
141	C₅×D₄	—	2	2	no	—
142	C₂×C₄×C₅	—	2	4	no	—
143	C₂×C₄×C₅	—	2	2	no	—
144	C₂×C₄×C₅	—	2	2	no	—
145	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
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	2	yes	—
153	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	#126	C₂×C₃×C₅	1	2	yes	complemented
155	#125	C₂×C₃×C₅	1	2	yes	complemented
156	#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
157	#123	C₂×C₃×C₅	1	2	yes	—
158	C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
161	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
162	#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	#117	C₂×C₃×C₅	1	2	yes	complemented
164	C₂×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	C₂×C₃×C₅	—	2	2	no	—
166	C₂×C₃×C₅	—	4	1	no	—
167	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
168	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
169	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
172	C₃×Q₈	—	2	2	no	—
173	C₃×D₄	—	2	2	no	—
174	C₂×C₃×C₄	—	2	4	no	—
175	C₂×C₃×C₄	—	2	2	no	—
176	C₂×C₃×C₄	—	2	2	no	—
177	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
180	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
181	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
185	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×C₅	—	2	1	no	—
187	C₂²×C₅	—	2	1	no	—
188	C₂²×C₅	—	2	1	no	—
189	C₂²×C₅	—	2	1	no	—
190	C₂²×C₅	—	2	1	no	—
191	C₂²×C₅	C₃×#41	1	2	yes	—
192	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
193	C₄×C₅	—	2	2	no	—
194	C₄×C₅	—	2	2	no	—
195	C₄×C₅	—	2	1	no	—
196	C₄×C₅	—	2	1	no	—
197	C₄×C₅	—	2	1	no	—
198	C₄×C₅	—	2	2	no	—
199	C₄×C₅	—	2	1	no	—
200	C₄×C₅	—	2	2	no	—
201	C₄×C₅	C₃×#41	1	2	yes	—
202	C₂×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	—
205	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
209	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
210	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
211	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
212	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
213	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₄⋊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	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
219	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
220	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₄²	C₂²×C₃×C₅	1	2	yes	—
223	C₄²	C₂²×C₃×C₅	1	2	yes	—
224	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₃×C₅	#552	1	1	yes	characteristic, direct product factor, Hall
226	C₂²×C₃	—	2	1	no	—
227	C₂²×C₃	—	2	1	no	—
228	C₂²×C₃	—	2	1	no	—
229	C₂²×C₃	—	2	1	no	—
230	C₂²×C₃	—	2	1	no	—
231	C₂²×C₃	C₅×#41	1	2	yes	—
232	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
233	C₃×C₄	—	2	2	no	—
234	C₃×C₄	—	2	2	no	—
235	C₃×C₄	—	2	1	no	—
236	C₃×C₄	—	2	1	no	—
237	C₃×C₄	—	2	1	no	—
238	C₃×C₄	—	2	2	no	—
239	C₃×C₄	—	2	1	no	—
240	C₃×C₄	—	2	2	no	—
241	C₃×C₄	C₅×#41	1	2	yes	—
242	C₂×C₅	—	2	2	no	—
243	C₂×C₅	—	4	1	no	—
244	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
245	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
246	C₂×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
247	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
248	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
249	Q₈	—	2	2	no	—
250	D₄	—	2	2	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
255	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
256	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
257	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
258	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
259	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
261	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
262	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	C₂×C₃	—	2	2	no	—
264	C₂×C₃	—	4	1	no	—
265	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
266	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
267	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
268	C₅	C₃×#552	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²	—	2	1	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	C₃×C₅×#41	1	2	yes	—
275	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	1	no	—
281	C₄	—	2	2	no	—
282	C₄	—	2	1	no	—
283	C₄	—	2	2	no	—
284	C₄	C₃×C₅×#41	1	2	yes	—
285	C₃	C₅×#552	1	1	yes	characteristic, direct product factor, Sylow
286	C₂	—	2	2	no	—
287	C₂	—	4	1	no	—
288	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
289	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
290	C₂	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×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×#125	C₂	semidirect
5. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
6. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
7. C₃×C₄×C₅×Q₈	C₂	semidirect
9. C₃×C₅×#117	C₂	semidirect
10. C₃×C₅×#117	C₂	semidirect
11. C₂×C₃×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#552	C₃	direct (N × H)
36. C₃×#552	C₅	direct (N × H)
37. C₅×#126	C₂×C₃	semidirect
38. C₅×#125	C₂×C₃	semidirect
39. C₅×#125	C₂×C₃	semidirect
41. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
42. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
43. C₄×C₅×Q₈	C₂×C₃	semidirect
45. C₅×#117	C₂×C₃	semidirect
46. C₅×#117	C₂×C₃	semidirect
47. C₂×C₅×C₄⋊C₄	C₂×C₃	semidirect
64. C₃×#126	C₂×C₅	semidirect
65. C₃×#125	C₂×C₅	semidirect
66. C₃×#125	C₂×C₅	semidirect
68. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
69. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
70. C₃×C₄×Q₈	C₂×C₅	semidirect
72. C₃×#117	C₂×C₅	semidirect
73. C₃×#117	C₂×C₅	semidirect
74. C₂×C₃×C₄⋊C₄	C₂×C₅	semidirect
98. #552	C₃×C₅	direct (N × H)
154. #126	C₂×C₃×C₅	semidirect
155. #125	C₂×C₃×C₅	semidirect
156. #125	C₂×C₃×C₅	semidirect
158. C₂²⋊Q₈	C₂×C₃×C₅	semidirect
159. C₂²⋊Q₈	C₂×C₃×C₅	semidirect
160. C₄×Q₈	C₂×C₃×C₅	semidirect
162. #117	C₂×C₃×C₅	semidirect
163. #117	C₂×C₃×C₅	semidirect
164. C₂×C₄⋊C₄	C₂×C₃×C₅	semidirect
225. C₃×C₅	#552	direct (N × H)
268. C₅	C₃×#552	direct (N × H)
285. C₃	C₅×#552	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×#123	2
C₃×C₅×C₂²⋊Q₈	2
C₃×C₄×C₅×Q₈	2
C₃×C₄×C₅×D₄	2
C₃×C₅×#117	2
C₂×C₃×C₅×C₄⋊C₄	2
C₅×#552	3
C₃×#552	5

Subgroups — C3×C5×#552 #11756641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#552 #11756641