Subgroups — C₃×C₅×#3164 #14276198

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#544	C₂	1	2	yes	maximal
2	C₃×C₅×#501	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#500	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#499	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#428	C₂	1	2	yes	maximal
6	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic
9	C₅×#3164	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
14	C₃×C₅×#125	—	2	2	no	—
15	C₃×C₅×#125	C₂²	1	4	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
17	C₃×C₅×#117	C₂²	1	2	yes	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₅×#107	C₂²	1	1	yes	characteristic
21	C₃×C₅×#107	C₂²	1	2	yes	—
22	C₃×C₅×#107	C₂²	1	1	yes	characteristic
23	C₃×C₅×#107	C₂²	1	4	yes	—
24	C₃×C₅×#107	C₂²	1	2	yes	—
25	C₃×C₅×#106	C₂²	1	4	yes	—
26	C₃×C₅×#106	C₂²	1	2	yes	—
27	C₃×C₅×#97	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
29	C₃×#3164	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₅×#544	C₂×C₃	1	2	yes	—
31	C₅×#501	C₂×C₃	1	4	yes	complemented
32	C₅×#500	C₂×C₃	1	2	yes	complemented
33	C₅×#499	C₂×C₃	1	2	yes	complemented
34	C₅×#428	C₂×C₃	1	2	yes	—
35	C₅×#427	C₂×C₃	1	1	yes	characteristic
36	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
37	C₅×#405	C₂×C₃	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×M₁₆	Q₈	1	4	yes	complemented
42	C₂×C₃×C₅×C₈	Q₈	1	4	yes	complemented
43	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
46	C₃×C₅×C₄⋊C₄	—	2	2	no	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
57	C₃×C₄²×C₅	—	2	2	no	—
58	C₃×C₄²×C₅	C₂³	1	2	yes	—
59	C₃×#544	C₂×C₅	1	2	yes	—
60	C₃×#501	C₂×C₅	1	4	yes	complemented
61	C₃×#500	C₂×C₅	1	2	yes	complemented
62	C₃×#499	C₂×C₅	1	2	yes	complemented
63	C₃×#428	C₂×C₅	1	2	yes	—
64	C₃×#427	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
66	C₃×#405	C₂×C₅	1	1	yes	characteristic
67	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₅×C₄⋊Q₈	—	2	2	no	—
70	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
71	C₅×#125	—	2	2	no	—
72	C₅×#125	C₂²×C₃	1	4	yes	—
73	C₅×C₂²⋊Q₈	—	2	4	no	—
74	C₅×#117	C₂²×C₃	1	2	yes	—
75	C₅×#117	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₅×#107	C₂²×C₃	1	2	yes	—
78	C₅×#107	C₂²×C₃	1	2	yes	—
79	C₅×#107	C₂²×C₃	1	1	yes	characteristic
80	C₅×#107	C₂²×C₃	1	1	yes	characteristic
81	C₅×#107	C₂²×C₃	1	4	yes	—
82	C₅×#106	C₂²×C₃	1	2	yes	—
83	C₅×#106	C₂²×C₃	1	4	yes	—
84	C₅×#97	C₂²×C₃	1	2	yes	—
85	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
86	#3164	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×Q₈	—	8	4	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	8	2	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
100	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
101	C₃×C₅×C₈	C₂×Q₈	1	4	yes	—
102	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₃×C₄⋊Q₈	—	2	2	no	—
105	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
106	C₃×#125	—	2	2	no	—
107	C₃×#125	C₂²×C₅	1	4	yes	—
108	C₃×C₂²⋊Q₈	—	2	4	no	—
109	C₃×#117	C₂²×C₅	1	2	yes	—
110	C₃×#117	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
112	C₃×#107	C₂²×C₅	1	2	yes	—
113	C₃×#107	C₂²×C₅	1	2	yes	—
114	C₃×#107	C₂²×C₅	1	1	yes	characteristic
115	C₃×#107	C₂²×C₅	1	1	yes	characteristic
116	C₃×#107	C₂²×C₅	1	4	yes	—
117	C₃×#106	C₂²×C₅	1	2	yes	—
118	C₃×#106	C₂²×C₅	1	4	yes	—
119	C₃×#97	C₂²×C₅	1	2	yes	—
120	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
121	C₂×C₅×Q₈	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₅×M₁₆	C₃×Q₈	1	4	yes	complemented
125	C₂×C₅×C₈	C₃×Q₈	1	4	yes	complemented
126	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	4	no	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
135	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
136	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
137	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	C₂³×C₃	1	2	yes	—
142	#544	C₂×C₃×C₅	1	2	yes	—
143	#501	C₂×C₃×C₅	1	4	yes	complemented
144	#500	C₂×C₃×C₅	1	2	yes	complemented
145	#499	C₂×C₃×C₅	1	2	yes	complemented
146	#428	C₂×C₃×C₅	1	2	yes	—
147	#427	C₂×C₃×C₅	1	1	yes	characteristic
148	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
149	#405	C₂×C₃×C₅	1	1	yes	characteristic
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	C₄⋊Q₈	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	4	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
160	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₃×Q₈	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₃×M₁₆	C₅×Q₈	1	4	yes	complemented
166	C₂×C₃×C₈	C₅×Q₈	1	4	yes	complemented
167	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
169	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
176	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
177	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
178	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
179	C₃×C₂²⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
181	C₃×C₄²	—	2	2	no	—
182	C₃×C₄²	C₂³×C₅	1	2	yes	—
183	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₅×Q₈	—	8	4	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	8	2	no	—
189	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
190	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
193	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
194	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
195	C₅×C₈	C₂×C₃×Q₈	1	2	yes	—
196	C₅×C₈	C₂×C₃×Q₈	1	2	yes	—
197	C₅×C₈	C₂×C₃×Q₈	1	4	yes	—
198	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
200	C₄⋊Q₈	—	2	2	no	—
201	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
202	#125	—	2	2	no	—
203	#125	C₂²×C₃×C₅	1	4	yes	—
204	C₂²⋊Q₈	—	2	4	no	—
205	#117	C₂²×C₃×C₅	1	2	yes	—
206	#117	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	#107	C₂²×C₃×C₅	1	2	yes	—
209	#107	C₂²×C₃×C₅	1	2	yes	—
210	#107	C₂²×C₃×C₅	1	1	yes	characteristic
211	#107	C₂²×C₃×C₅	1	1	yes	characteristic
212	#107	C₂²×C₃×C₅	1	4	yes	—
213	#106	C₂²×C₃×C₅	1	2	yes	—
214	#106	C₂²×C₃×C₅	1	4	yes	—
215	#97	C₂²×C₃×C₅	1	2	yes	—
216	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
217	C₂×C₃×C₅	—	2	2	no	—
218	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
219	C₂×C₃×C₅	#576	1	1	yes	characteristic
220	C₂×C₃×C₅	#578	1	1	yes	characteristic
221	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
222	C₃×Q₈	—	8	4	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	8	2	no	—
227	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
228	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
229	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
232	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
233	C₃×C₈	C₂×C₅×Q₈	1	2	yes	—
234	C₃×C₈	C₂×C₅×Q₈	1	2	yes	—
235	C₃×C₈	C₂×C₅×Q₈	1	4	yes	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	C₃×C₄⋊Q₈	1	2	yes	—
239	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
240	C₄×C₅	—	2	2	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	4	4	no	—
243	C₄×C₅	—	4	2	no	—
244	C₄×C₅	—	4	2	no	—
245	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
246	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
247	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
248	C₂×Q₈	—	2	4	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
251	M₁₆	C₃×C₅×Q₈	1	4	yes	complemented
252	C₂×C₈	C₃×C₅×Q₈	1	4	yes	complemented
253	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
254	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
255	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
261	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
262	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
263	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
264	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
265	C₂²⋊C₄	—	2	2	no	—
266	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
267	C₄²	—	2	2	no	—
268	C₄²	C₂³×C₃×C₅	1	2	yes	—
269	C₃×C₅	#3164	1	1	yes	characteristic, direct product factor, Hall
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	C₅×C₄⋊Q₈	1	2	yes	—
273	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
274	C₃×C₄	—	2	2	no	—
275	C₃×C₄	—	2	2	no	—
276	C₃×C₄	—	4	4	no	—
277	C₃×C₄	—	4	2	no	—
278	C₃×C₄	—	4	2	no	—
279	C₃×C₄	C₅×C₄⋊Q₈	1	2	yes	—
280	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
281	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
282	C₂×C₅	—	2	2	no	—
283	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
284	C₂×C₅	C₃×#576	1	1	yes	characteristic
285	C₂×C₅	C₃×#578	1	1	yes	characteristic
286	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
287	Q₈	—	8	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	8	2	no	—
292	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
293	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
294	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
295	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
296	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
297	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
298	C₈	C₂×C₃×C₅×Q₈	1	2	yes	—
299	C₈	C₂×C₃×C₅×Q₈	1	2	yes	—
300	C₈	C₂×C₃×C₅×Q₈	1	4	yes	—
301	C₂×C₃	—	2	2	no	—
302	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
303	C₂×C₃	C₅×#576	1	1	yes	characteristic
304	C₂×C₃	C₅×#578	1	1	yes	characteristic
305	C₅	C₃×#3164	1	1	yes	characteristic, direct product factor, Sylow
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	C₃×C₅×C₄⋊Q₈	1	2	yes	—
309	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
310	C₄	—	2	2	no	—
311	C₄	—	2	2	no	—
312	C₄	—	4	4	no	—
313	C₄	—	4	2	no	—
314	C₄	—	4	2	no	—
315	C₄	C₃×C₅×C₄⋊Q₈	1	2	yes	—
316	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
317	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
318	C₃	C₅×#3164	1	1	yes	characteristic, direct product factor, Sylow
319	C₂	—	2	2	no	—
320	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
321	C₂	C₃×C₅×#576	1	1	yes	characteristic
322	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#501	C₂	semidirect
3. C₃×C₅×#500	C₂	semidirect
4. C₃×C₅×#499	C₂	semidirect
9. C₅×#3164	C₃	direct (N × H)
29. C₃×#3164	C₅	direct (N × H)
31. C₅×#501	C₂×C₃	semidirect
32. C₅×#500	C₂×C₃	semidirect
33. C₅×#499	C₂×C₃	semidirect
41. C₃×C₅×M₁₆	Q₈	semidirect
42. C₂×C₃×C₅×C₈	Q₈	semidirect
60. C₃×#501	C₂×C₅	semidirect
61. C₃×#500	C₂×C₅	semidirect
62. C₃×#499	C₂×C₅	semidirect
86. #3164	C₃×C₅	direct (N × H)
124. C₅×M₁₆	C₃×Q₈	semidirect
125. C₂×C₅×C₈	C₃×Q₈	semidirect
143. #501	C₂×C₃×C₅	semidirect
144. #500	C₂×C₃×C₅	semidirect
145. #499	C₂×C₃×C₅	semidirect
165. C₃×M₁₆	C₅×Q₈	semidirect
166. C₂×C₃×C₈	C₅×Q₈	semidirect
251. M₁₆	C₃×C₅×Q₈	semidirect
252. C₂×C₈	C₃×C₅×Q₈	semidirect
269. C₃×C₅	#3164	direct (N × H)
305. C₅	C₃×#3164	direct (N × H)
318. C₃	C₅×#3164	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×#544	2
C₃×C₅×#501	2
C₃×C₅×#500	2
C₃×C₅×#499	2
C₃×C₅×#428	2
C₃×C₅×#427	2
C₂×C₃×C₅×#107	2
C₃×C₅×#405	2
C₅×#3164	3
C₃×#3164	5

Subgroups — C3×C5×#3164 #14276198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3164 #14276198