Subgroups — C₃×C₅×#542 #11756631

Order 960.

432 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#542	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
25	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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×#542	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#126	C₂×C₃	1	2	yes	complemented
39	C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#124	C₂×C₃	1	2	yes	complemented
41	C₅×#123	C₂×C₃	1	2	yes	complemented
42	C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
43	C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#121	C₂×C₃	1	1	yes	characteristic
45	C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
49	C₂³×C₃×C₅	C₂³	1	2	yes	—
50	C₃×C₅×Q₈	—	2	2	no	—
51	C₃×C₅×Q₈	—	4	2	no	—
52	C₃×C₅×D₄	—	2	2	no	—
53	C₃×C₅×D₄	—	4	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	—	4	2	no	—
56	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
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	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×#126	C₂×C₅	1	2	yes	complemented
67	C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#124	C₂×C₅	1	2	yes	complemented
69	C₃×#123	C₂×C₅	1	2	yes	complemented
70	C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
71	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#121	C₂×C₅	1	1	yes	characteristic
73	C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×Q₈	C₂²×C₃	1	2	yes	—
78	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×D₄	C₂²×C₃	1	2	yes	—
80	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	—
82	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
94	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₄²×C₅	C₂²×C₃	1	2	yes	—
99	#542	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
100	C₂²×C₃×C₅	—	2	1	no	—
101	C₂²×C₃×C₅	—	2	2	no	—
102	C₂²×C₃×C₅	—	2	2	no	—
103	C₂²×C₃×C₅	—	2	1	no	—
104	C₂²×C₃×C₅	—	2	1	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
107	C₃×C₄×C₅	—	2	1	no	—
108	C₃×C₄×C₅	—	2	2	no	—
109	C₃×C₄×C₅	—	2	1	no	—
110	C₃×C₄×C₅	—	2	2	no	—
111	C₃×C₄×C₅	—	2	2	no	—
112	C₃×C₄×C₅	—	2	1	no	—
113	C₃×C₄×C₅	—	2	1	no	—
114	C₃×C₄×C₅	—	2	1	no	—
115	C₃×C₄×C₅	#41	1	2	yes	—
116	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₃×Q₈	C₂²×C₅	1	2	yes	—
118	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
120	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	—
122	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
129	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
134	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
135	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
136	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₃×C₄²	C₂²×C₅	1	2	yes	—
139	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂³×C₅	C₂³×C₃	1	2	yes	—
141	C₅×Q₈	—	2	2	no	—
142	C₅×Q₈	—	4	2	no	—
143	C₅×D₄	—	2	2	no	—
144	C₅×D₄	—	4	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	4	2	no	—
147	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
157	#126	C₂×C₃×C₅	1	2	yes	complemented
158	#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	#124	C₂×C₃×C₅	1	2	yes	complemented
160	#123	C₂×C₃×C₅	1	2	yes	complemented
161	C₂²⋊Q₈	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	#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	C₂×C₃×C₅	—	4	1	no	—
168	C₂×C₃×C₅	—	4	2	no	—
169	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
170	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
173	C₂³×C₃	C₂³×C₅	1	2	yes	—
174	C₃×Q₈	—	2	2	no	—
175	C₃×Q₈	—	4	2	no	—
176	C₃×D₄	—	2	2	no	—
177	C₃×D₄	—	4	2	no	—
178	C₂×C₃×C₄	—	2	2	no	—
179	C₂×C₃×C₄	—	4	2	no	—
180	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
181	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
189	C₂²×C₅	—	2	1	no	—
190	C₂²×C₅	—	2	2	no	—
191	C₂²×C₅	—	2	2	no	—
192	C₂²×C₅	—	2	1	no	—
193	C₂²×C₅	—	2	1	no	—
194	C₂²×C₅	—	2	2	no	—
195	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
196	C₄×C₅	—	2	1	no	—
197	C₄×C₅	—	2	2	no	—
198	C₄×C₅	—	2	1	no	—
199	C₄×C₅	—	2	2	no	—
200	C₄×C₅	—	2	2	no	—
201	C₄×C₅	—	2	1	no	—
202	C₄×C₅	—	2	1	no	—
203	C₄×C₅	—	2	1	no	—
204	C₄×C₅	C₃×#41	1	2	yes	—
205	C₂×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂×Q₈	C₂²×C₃×C₅	1	2	yes	—
207	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×D₄	C₂²×C₃×C₅	1	2	yes	—
209	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	—
211	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
212	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
218	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂²⋊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	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
226	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₄²	C₂²×C₃×C₅	1	2	yes	—
228	C₃×C₅	#542	1	1	yes	characteristic, direct product factor, Hall
229	C₂²×C₃	—	2	1	no	—
230	C₂²×C₃	—	2	2	no	—
231	C₂²×C₃	—	2	2	no	—
232	C₂²×C₃	—	2	1	no	—
233	C₂²×C₃	—	2	1	no	—
234	C₂²×C₃	—	2	2	no	—
235	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
236	C₃×C₄	—	2	1	no	—
237	C₃×C₄	—	2	2	no	—
238	C₃×C₄	—	2	1	no	—
239	C₃×C₄	—	2	2	no	—
240	C₃×C₄	—	2	2	no	—
241	C₃×C₄	—	2	1	no	—
242	C₃×C₄	—	2	1	no	—
243	C₃×C₄	—	2	1	no	—
244	C₃×C₄	C₅×#41	1	2	yes	—
245	C₂×C₅	—	4	1	no	—
246	C₂×C₅	—	4	2	no	—
247	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
248	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
250	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
251	C₂³	C₂³×C₃×C₅	1	2	yes	—
252	Q₈	—	2	2	no	—
253	Q₈	—	4	2	no	—
254	D₄	—	2	2	no	—
255	D₄	—	4	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
259	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
261	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
262	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
264	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
266	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₂×C₃	—	4	1	no	—
268	C₂×C₃	—	4	2	no	—
269	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
270	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
271	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
272	C₅	C₃×#542	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²	—	2	1	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	2	no	—
279	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
280	C₄	—	2	1	no	—
281	C₄	—	2	2	no	—
282	C₄	—	2	1	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	2	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	C₃×C₅×#41	1	2	yes	—
289	C₃	C₅×#542	1	1	yes	characteristic, direct product factor, Sylow
290	C₂	—	4	1	no	—
291	C₂	—	4	2	no	—
292	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
293	C₂	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
294	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	C₃×C₅×#121	C₂
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×C₄⋊Q₈	C₂	semidirect
2. C₃×C₅×#126	C₂	semidirect
3. C₃×C₅×#124	C₂	semidirect
4. C₃×C₅×#124	C₂	semidirect
5. C₃×C₅×#123	C₂	semidirect
6. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
7. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
9. C₃×C₄×C₅×Q₈	C₂	semidirect
10. C₃×C₄×C₅×D₄	C₂	semidirect
11. C₃×C₅×#117	C₂	semidirect
12. C₅×#542	C₃	direct (N × H)
36. C₃×#542	C₅	direct (N × H)
37. C₅×C₄⋊Q₈	C₂×C₃	semidirect
38. C₅×#126	C₂×C₃	semidirect
39. C₅×#124	C₂×C₃	semidirect
40. C₅×#124	C₂×C₃	semidirect
41. C₅×#123	C₂×C₃	semidirect
42. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
43. C₅×C₂²⋊Q₈	C₂×C₃	semidirect
45. C₄×C₅×Q₈	C₂×C₃	semidirect
46. C₄×C₅×D₄	C₂×C₃	semidirect
47. C₅×#117	C₂×C₃	semidirect
65. C₃×C₄⋊Q₈	C₂×C₅	semidirect
66. C₃×#126	C₂×C₅	semidirect
67. C₃×#124	C₂×C₅	semidirect
68. C₃×#124	C₂×C₅	semidirect
69. C₃×#123	C₂×C₅	semidirect
70. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
71. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
73. C₃×C₄×Q₈	C₂×C₅	semidirect
74. C₃×C₄×D₄	C₂×C₅	semidirect
75. C₃×#117	C₂×C₅	semidirect
99. #542	C₃×C₅	direct (N × H)
156. C₄⋊Q₈	C₂×C₃×C₅	semidirect
157. #126	C₂×C₃×C₅	semidirect
158. #124	C₂×C₃×C₅	semidirect
159. #124	C₂×C₃×C₅	semidirect
160. #123	C₂×C₃×C₅	semidirect
161. C₂²⋊Q₈	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. #117	C₂×C₃×C₅	semidirect
228. C₃×C₅	#542	direct (N × H)
272. C₅	C₃×#542	direct (N × H)
289. C₃	C₅×#542	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×C₄⋊Q₈	2
C₃×C₅×#126	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
C₅×#542	3
C₃×#542	5

Subgroups — C3×C5×#542 #11756631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#542 #11756631