Subgroups — C₃×C₅×#3140 #14276174

Order 1920.

800 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×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#489	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#488	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#419	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#418	C₂	1	2	yes	maximal
7	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3140	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
13	C₃×C₅×#125	C₂²	1	2	yes	complemented
14	C₃×C₅×#124	—	2	2	no	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×#124	C₂²	1	2	yes	—
17	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
18	C₃×C₄×C₅×Q₈	—	2	2	no	—
19	C₃×C₅×#117	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#103	C₂²	1	8	yes	complemented
23	C₃×C₅×#102	C₂²	1	8	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	complemented
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
26	C₃×#3140	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
29	C₅×#489	C₂×C₃	1	4	yes	complemented
30	C₅×#488	C₂×C₃	1	4	yes	complemented
31	C₅×#419	C₂×C₃	1	2	yes	complemented
32	C₅×#418	C₂×C₃	1	2	yes	—
33	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×M₁₆	—	2	4	no	—
46	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
50	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₄²×C₅	—	2	2	no	—
54	C₃×C₄²×C₅	D₄	1	2	yes	—
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
59	C₃×#489	C₂×C₅	1	4	yes	complemented
60	C₃×#488	C₂×C₅	1	4	yes	complemented
61	C₃×#419	C₂×C₅	1	2	yes	complemented
62	C₃×#418	C₂×C₅	1	2	yes	—
63	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
67	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
68	C₅×#125	C₂²×C₃	1	2	yes	complemented
69	C₅×#124	—	2	2	no	—
70	C₅×#124	C₂²×C₃	1	2	yes	—
71	C₅×#124	C₂²×C₃	1	2	yes	—
72	C₅×C₂²⋊Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₅×#117	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×#103	C₂²×C₃	1	8	yes	complemented
78	C₅×#102	C₂²×C₃	1	8	yes	—
79	C₅×#97	C₂²×C₃	1	2	yes	complemented
80	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
81	#3140	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	—	4	2	no	—
85	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
86	C₃×C₅×Q₈	—	2	4	no	—
87	C₃×C₅×Q₈	—	4	4	no	—
88	C₃×C₅×Q₈	—	4	2	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×C₈	—	2	4	no	—
101	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
104	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
105	C₃×#125	C₂²×C₅	1	2	yes	complemented
106	C₃×#124	—	2	2	no	—
107	C₃×#124	C₂²×C₅	1	2	yes	—
108	C₃×#124	C₂²×C₅	1	2	yes	—
109	C₃×C₂²⋊Q₈	—	2	2	no	—
110	C₃×C₄×Q₈	—	2	2	no	—
111	C₃×#117	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₃×#103	C₂²×C₅	1	8	yes	complemented
115	C₃×#102	C₂²×C₅	1	8	yes	—
116	C₃×#97	C₂²×C₅	1	2	yes	complemented
117	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
118	C₂⁴×C₅	—	2	1	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	4	no	—
122	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	4	no	—
125	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₅×M₁₆	—	2	4	no	—
130	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₅×C₂²⋊C₄	—	2	4	no	—
136	C₅×C₂²⋊C₄	—	2	4	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	C₃×D₄	1	2	yes	—
139	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
141	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
142	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
143	#489	C₂×C₃×C₅	1	4	yes	complemented
144	#488	C₂×C₃×C₅	1	4	yes	complemented
145	#419	C₂×C₃×C₅	1	2	yes	complemented
146	#418	C₂×C₃×C₅	1	2	yes	—
147	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	4	2	no	—
150	C₂²×C₃×C₅	—	4	4	no	—
151	C₂²×C₃×C₅	—	8	4	no	—
152	C₂²×C₃×C₅	#124	1	2	yes	—
153	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
154	C₃×C₄×C₅	—	2	2	no	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	4	2	no	—
157	C₃×C₄×C₅	—	4	4	no	—
158	C₃×C₄×C₅	#124	1	2	yes	—
159	C₃×C₄×C₅	C₂×#41	1	2	yes	—
160	C₂⁴×C₃	—	2	1	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
165	C₂×C₃×D₄	—	2	1	no	—
166	C₂×C₃×D₄	—	2	4	no	—
167	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₃×M₁₆	—	2	4	no	—
172	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
176	C₃×C₂²⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₂²⋊C₄	—	2	4	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	C₅×D₄	1	2	yes	—
181	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
182	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	4	4	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₅×Q₈	—	2	4	no	—
188	C₅×Q₈	—	4	4	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×D₄	—	2	4	no	—
191	C₅×D₄	—	4	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₃×#41	1	4	yes	—
200	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
201	C₅×C₈	—	2	4	no	—
202	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
205	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
206	#125	C₂²×C₃×C₅	1	2	yes	complemented
207	#124	—	2	2	no	—
208	#124	C₂²×C₃×C₅	1	2	yes	—
209	#124	C₂²×C₃×C₅	1	2	yes	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₄×Q₈	—	2	2	no	—
212	#117	C₂²×C₃×C₅	1	2	yes	—
213	C₂×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
215	#103	C₂²×C₃×C₅	1	8	yes	complemented
216	#102	C₂²×C₃×C₅	1	8	yes	—
217	#97	C₂²×C₃×C₅	1	2	yes	complemented
218	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
219	C₂×C₃×C₅	—	2	2	no	—
220	C₂×C₃×C₅	—	8	2	no	—
221	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
222	C₂×C₃×C₅	#575	1	2	yes	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	4	4	no	—
225	C₂³×C₃	—	4	2	no	—
226	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
227	C₃×Q₈	—	2	4	no	—
228	C₃×Q₈	—	4	4	no	—
229	C₃×Q₈	—	4	2	no	—
230	C₃×D₄	—	2	4	no	—
231	C₃×D₄	—	4	2	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	4	2	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₅×#41	1	4	yes	—
240	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
241	C₃×C₈	—	2	4	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	4	4	no	—
244	C₂²×C₅	—	4	2	no	—
245	C₂²×C₅	—	8	4	no	—
246	C₂²×C₅	C₃×#124	1	2	yes	—
247	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	C₃×#124	1	2	yes	—
253	C₄×C₅	C₂×C₃×#41	1	2	yes	—
254	C₂⁴	—	2	1	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	M₁₆	—	2	4	no	—
266	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
270	C₂²⋊C₄	—	2	2	no	—
271	C₂²⋊C₄	—	2	4	no	—
272	C₂²⋊C₄	—	2	4	no	—
273	C₄²	—	2	2	no	—
274	C₄²	C₃×C₅×D₄	1	2	yes	—
275	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
276	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
277	C₃×C₅	#3140	1	1	yes	characteristic, direct product factor, Hall
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	4	2	no	—
280	C₂²×C₃	—	4	4	no	—
281	C₂²×C₃	—	8	4	no	—
282	C₂²×C₃	C₅×#124	1	2	yes	—
283	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	—	4	4	no	—
288	C₃×C₄	C₅×#124	1	2	yes	—
289	C₃×C₄	C₂×C₅×#41	1	2	yes	—
290	C₂×C₅	—	2	2	no	—
291	C₂×C₅	—	8	2	no	—
292	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
293	C₂×C₅	C₃×#575	1	2	yes	—
294	C₂³	—	2	2	no	—
295	C₂³	—	4	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
298	Q₈	—	2	4	no	—
299	Q₈	—	4	4	no	—
300	Q₈	—	4	2	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
308	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
309	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
310	C₂×C₄	C₃×C₅×#41	1	4	yes	—
311	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
312	C₈	—	2	4	no	—
313	C₂×C₃	—	2	2	no	—
314	C₂×C₃	—	8	2	no	—
315	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
316	C₂×C₃	C₅×#575	1	2	yes	—
317	C₅	C₃×#3140	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	8	4	no	—
322	C₂²	C₃×C₅×#124	1	2	yes	—
323	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	4	no	—
328	C₄	C₃×C₅×#124	1	2	yes	—
329	C₄	C₂×C₃×C₅×#41	1	2	yes	—
330	C₃	C₅×#3140	1	1	yes	characteristic, direct product factor, Sylow
331	C₂	—	2	2	no	—
332	C₂	—	8	2	no	—
333	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
334	C₂	C₃×C₅×#575	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#488	C₂	semidirect
5. C₃×C₅×#419	C₂	semidirect
7. C₃×C₄×C₅×M₁₆	C₂	semidirect
8. C₅×#3140	C₃	direct (N × H)
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
13. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₅×#103	C₂²	semidirect
24. C₃×C₅×#97	C₂²	semidirect
25. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₃×#3140	C₅	direct (N × H)
27. C₅×#533	C₂×C₃	semidirect
29. C₅×#489	C₂×C₃	semidirect
30. C₅×#488	C₂×C₃	semidirect
31. C₅×#419	C₂×C₃	semidirect
33. C₄×C₅×M₁₆	C₂×C₃	semidirect
57. C₃×#533	C₂×C₅	semidirect
59. C₃×#489	C₂×C₅	semidirect
60. C₃×#488	C₂×C₅	semidirect
61. C₃×#419	C₂×C₅	semidirect
63. C₃×C₄×M₁₆	C₂×C₅	semidirect
67. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
68. C₅×#125	C₂²×C₃	semidirect
77. C₅×#103	C₂²×C₃	semidirect
79. C₅×#97	C₂²×C₃	semidirect
80. C₄×C₅×C₈	C₂²×C₃	semidirect
81. #3140	C₃×C₅	direct (N × H)
104. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
105. C₃×#125	C₂²×C₅	semidirect
114. C₃×#103	C₂²×C₅	semidirect
116. C₃×#97	C₂²×C₅	semidirect
117. C₃×C₄×C₈	C₂²×C₅	semidirect
141. #533	C₂×C₃×C₅	semidirect
143. #489	C₂×C₃×C₅	semidirect
144. #488	C₂×C₃×C₅	semidirect
145. #419	C₂×C₃×C₅	semidirect
147. C₄×M₁₆	C₂×C₃×C₅	semidirect
205. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
206. #125	C₂²×C₃×C₅	semidirect
215. #103	C₂²×C₃×C₅	semidirect
217. #97	C₂²×C₃×C₅	semidirect
218. C₄×C₈	C₂²×C₃×C₅	semidirect
277. C₃×C₅	#3140	direct (N × H)
317. C₅	C₃×#3140	direct (N × H)
330. C₃	C₅×#3140	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
C₂×C₃×C₅×#124	2
C₃×C₅×#489	2
C₃×C₅×#488	2
C₃×C₅×#419	2
C₃×C₅×#418	2
C₃×C₄×C₅×M₁₆	2
C₅×#3140	3
C₃×#3140	5

Subgroups — C3×C5×#3140 #14276174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3140 #14276174