Subgroups — C₃×C₅×#3170 #14276204

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	2	yes	maximal
2	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#487	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#467	C₂	1	4	yes	maximal
6	C₃×C₄×C₅×Q₁₆	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
8	C₅×#3170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₃×C₅×#125	—	2	2	no	—
14	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
15	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₃×C₄×C₅×Q₈	—	2	2	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
18	C₃×C₅×#117	—	2	2	no	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#107	C₂²	1	4	yes	—
21	C₃×C₅×#103	C₂²	1	8	yes	—
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₃×#3170	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₅×#533	C₂×C₃	1	2	yes	—
27	C₅×#500	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#494	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#487	C₂×C₃	1	2	yes	complemented
30	C₅×#467	C₂×C₃	1	4	yes	—
31	C₄×C₅×Q₁₆	C₂×C₃	1	4	yes	complemented
32	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₃×C₅×Q₁₆	—	2	8	no	—
39	C₂×C₃×C₅×C₈	—	2	4	no	—
40	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
41	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
48	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
49	C₃×C₄²×C₅	—	2	4	no	—
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₃×#533	C₂×C₅	1	2	yes	—
55	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#487	C₂×C₅	1	2	yes	complemented
58	C₃×#467	C₂×C₅	1	4	yes	—
59	C₃×C₄×Q₁₆	C₂×C₅	1	4	yes	complemented
60	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
61	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
62	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
63	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
64	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
65	C₅×#125	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
68	C₄×C₅×Q₈	—	2	2	no	—
69	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
70	C₅×#117	—	2	2	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₅×#107	C₂²×C₃	1	4	yes	—
73	C₅×#103	C₂²×C₃	1	8	yes	—
74	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
75	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
77	#3170	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₃×C₅×Q₈	—	2	8	no	—
80	C₃×C₅×Q₈	—	4	4	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	complemented
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×C₈	—	2	2	no	—
93	C₃×C₅×C₈	#41	1	4	yes	—
94	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
95	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
96	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
97	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
98	C₃×#125	—	2	2	no	—
99	C₃×C₂²⋊Q₈	—	2	2	no	—
100	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
101	C₃×C₄×Q₈	—	2	2	no	—
102	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
103	C₃×#117	—	2	2	no	—
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	C₃×#107	C₂²×C₅	1	4	yes	—
106	C₃×#103	C₂²×C₅	1	8	yes	—
107	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
108	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
112	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
115	C₅×Q₁₆	—	2	8	no	—
116	C₂×C₅×C₈	—	2	4	no	—
117	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
118	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	4	no	—
123	C₅×C₄⋊C₄	—	2	4	no	—
124	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
125	C₅×C₂²⋊C₄	—	2	4	no	—
126	C₄²×C₅	—	2	4	no	—
127	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
128	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
129	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
131	#533	C₂×C₃×C₅	1	2	yes	—
132	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
133	#494	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	#487	C₂×C₃×C₅	1	2	yes	complemented
135	#467	C₂×C₃×C₅	1	4	yes	—
136	C₄×Q₁₆	C₂×C₃×C₅	1	4	yes	complemented
137	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
138	C₂²×C₃×C₅	—	2	1	no	—
139	C₂²×C₃×C₅	—	2	1	no	—
140	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
141	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	—	4	4	no	—
145	C₃×C₄×C₅	—	4	4	no	—
146	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
147	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
148	C₃×C₄×C₅	#135	1	2	yes	—
149	C₃×C₄×C₅	C₂×#41	1	2	yes	—
150	C₂×C₃×Q₈	—	2	2	no	—
151	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
152	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
155	C₃×Q₁₆	—	2	8	no	—
156	C₂×C₃×C₈	—	2	4	no	—
157	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
158	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
159	C₃×C₄⋊C₄	—	2	2	no	—
160	C₃×C₄⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₄	—	2	2	no	—
162	C₃×C₄⋊C₄	—	2	4	no	—
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
165	C₃×C₂²⋊C₄	—	2	4	no	—
166	C₃×C₄²	—	2	4	no	—
167	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
168	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
169	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
170	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
171	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
172	C₅×Q₈	—	2	8	no	—
173	C₅×Q₈	—	4	4	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	complemented
179	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
185	C₅×C₈	—	2	2	no	—
186	C₅×C₈	C₃×#41	1	4	yes	—
187	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
188	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
189	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
190	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
191	#125	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
194	C₄×Q₈	—	2	2	no	—
195	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
196	#117	—	2	2	no	—
197	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
198	#107	C₂²×C₃×C₅	1	4	yes	—
199	#103	C₂²×C₃×C₅	1	8	yes	—
200	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
201	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
202	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂×C₃×C₅	—	2	2	no	—
204	C₂×C₃×C₅	#532	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
206	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
208	C₃×Q₈	—	2	8	no	—
209	C₃×Q₈	—	4	4	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	C₅×Q₁₆	1	4	yes	complemented
215	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
221	C₃×C₈	—	2	2	no	—
222	C₃×C₈	C₅×#41	1	4	yes	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	1	no	—
225	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
226	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
227	C₄×C₅	—	2	1	no	—
228	C₄×C₅	—	2	1	no	—
229	C₄×C₅	—	4	4	no	—
230	C₄×C₅	—	4	4	no	—
231	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	—
232	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	—
233	C₄×C₅	C₃×#135	1	2	yes	—
234	C₄×C₅	C₂×C₃×#41	1	2	yes	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
237	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
238	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
239	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
240	Q₁₆	—	2	8	no	—
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
243	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	2	4	no	—
248	C₄⋊C₄	—	2	4	no	—
249	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₄²	—	2	4	no	—
252	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
253	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
254	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
255	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
256	C₃×C₅	#3170	1	1	yes	characteristic, direct product factor, Hall
257	C₂²×C₃	—	2	1	no	—
258	C₂²×C₃	—	2	1	no	—
259	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
260	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
261	C₃×C₄	—	2	1	no	—
262	C₃×C₄	—	2	1	no	—
263	C₃×C₄	—	4	4	no	—
264	C₃×C₄	—	4	4	no	—
265	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	—
266	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	—
267	C₃×C₄	C₅×#135	1	2	yes	—
268	C₃×C₄	C₂×C₅×#41	1	2	yes	—
269	C₂×C₅	—	2	2	no	—
270	C₂×C₅	C₃×#532	1	1	yes	characteristic
271	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
272	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
273	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
274	Q₈	—	2	8	no	—
275	Q₈	—	4	4	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	C₃×C₅×Q₁₆	1	4	yes	complemented
281	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
282	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
283	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
284	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
285	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
286	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
287	C₈	—	2	2	no	—
288	C₈	C₃×C₅×#41	1	4	yes	—
289	C₂×C₃	—	2	2	no	—
290	C₂×C₃	C₅×#532	1	1	yes	characteristic
291	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
292	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
293	C₅	C₃×#3170	1	1	yes	characteristic, direct product factor, Sylow
294	C₂²	—	2	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
297	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	4	4	no	—
301	C₄	—	4	4	no	—
302	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	—
303	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	—
304	C₄	C₃×C₅×#135	1	2	yes	—
305	C₄	C₂×C₃×C₅×#41	1	2	yes	—
306	C₃	C₅×#3170	1	1	yes	characteristic, direct product factor, Sylow
307	C₂	—	2	2	no	—
308	C₂	C₃×C₅×#532	1	1	yes	characteristic
309	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
310	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₃×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#500	C₂	semidirect
3. C₃×C₅×#494	C₂	semidirect
4. C₃×C₅×#487	C₂	semidirect
6. C₃×C₄×C₅×Q₁₆	C₂	semidirect
8. C₅×#3170	C₃	direct (N × H)
25. C₃×#3170	C₅	direct (N × H)
27. C₅×#500	C₂×C₃	semidirect
28. C₅×#494	C₂×C₃	semidirect
29. C₅×#487	C₂×C₃	semidirect
31. C₄×C₅×Q₁₆	C₂×C₃	semidirect
55. C₃×#500	C₂×C₅	semidirect
56. C₃×#494	C₂×C₅	semidirect
57. C₃×#487	C₂×C₅	semidirect
59. C₃×C₄×Q₁₆	C₂×C₅	semidirect
77. #3170	C₃×C₅	direct (N × H)
85. C₂×C₃×C₄×C₅	Q₁₆	semidirect
132. #500	C₂×C₃×C₅	semidirect
133. #494	C₂×C₃×C₅	semidirect
134. #487	C₂×C₃×C₅	semidirect
136. C₄×Q₁₆	C₂×C₃×C₅	semidirect
178. C₂×C₄×C₅	C₃×Q₁₆	semidirect
214. C₂×C₃×C₄	C₅×Q₁₆	semidirect
256. C₃×C₅	#3170	direct (N × H)
280. C₂×C₄	C₃×C₅×Q₁₆	semidirect
293. C₅	C₃×#3170	direct (N × H)
306. C₃	C₅×#3170	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×#533	2
C₃×C₅×#500	2
C₃×C₅×#494	2
C₃×C₅×#487	2
C₃×C₅×#467	2
C₃×C₄×C₅×Q₁₆	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#3170	3
C₃×#3170	5

Subgroups — C3×C5×#3170 #14276204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3170 #14276204