Subgroups — C₃×C₅×#2013 #14275047

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2013	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
10	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
11	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#103	—	2	4	no	—
19	C₃×#2013	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×SD₁₆	C₂×C₃	1	2	yes	—
21	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
23	C₅×#390	C₂×C₃	1	1	yes	characteristic
24	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂⁴×C₃×C₅	—	2	1	no	—
26	C₂×C₃×C₅×Q₈	—	2	2	no	—
27	C₂×C₃×C₅×Q₈	—	2	2	no	—
28	C₂×C₃×C₅×Q₈	—	2	2	no	—
29	C₂×C₃×C₅×Q₈	—	2	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₃×C₅×SD₁₆	—	2	16	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
44	C₃×C₅×C₄⋊C₄	—	2	8	no	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
47	C₃×C₄²×C₅	—	2	2	no	—
48	C₂²×C₃×SD₁₆	C₂×C₅	1	2	yes	—
49	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
51	C₃×#390	C₂×C₅	1	1	yes	characteristic
52	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
54	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	—	2	4	no	—
56	C₂×C₅×SD₁₆	—	2	4	no	—
57	C₂×C₅×SD₁₆	—	2	4	no	—
58	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₅×#103	—	2	4	no	—
65	#2013	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³×C₃×C₅	—	2	2	no	—
67	C₂³×C₃×C₅	—	4	1	no	—
68	C₂³×C₃×C₅	—	4	1	no	—
69	C₂³×C₃×C₅	—	4	2	no	—
70	C₂³×C₃×C₅	—	4	2	no	—
71	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
72	C₃×C₅×Q₈	—	2	4	no	—
73	C₃×C₅×Q₈	—	2	4	no	—
74	C₃×C₅×Q₈	—	4	2	no	—
75	C₃×C₅×Q₈	—	4	2	no	—
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	—	4	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	4	2	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
90	C₃×C₅×C₈	—	2	4	no	—
91	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
92	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×SD₁₆	—	2	4	no	—
94	C₂×C₃×SD₁₆	—	2	4	no	—
95	C₂×C₃×SD₁₆	—	2	4	no	—
96	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
97	C₃×C₄⋊Q₈	—	2	4	no	—
98	C₂×C₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
100	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₃×#103	—	2	4	no	—
103	C₂⁴×C₅	—	2	1	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₅×SD₁₆	—	2	16	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
122	C₅×C₄⋊C₄	—	2	8	no	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₂²⋊C₄	—	4	4	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₂²×SD₁₆	C₂×C₃×C₅	1	2	yes	—
127	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
128	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
129	#390	C₂×C₃×C₅	1	1	yes	characteristic
130	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₃×C₅	—	4	2	no	—
132	C₂²×C₃×C₅	—	4	4	no	—
133	C₂²×C₃×C₅	—	8	2	no	—
134	C₂²×C₃×C₅	—	8	1	no	—
135	C₂²×C₃×C₅	—	8	1	no	—
136	C₂²×C₃×C₅	#120	1	1	yes	characteristic
137	C₂²×C₃×C₅	#121	1	1	yes	characteristic
138	C₂²×C₃×C₅	#127	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
140	C₂²×C₃×C₅	#137	1	2	yes	—
141	C₃×C₄×C₅	—	2	4	no	—
142	C₃×C₄×C₅	—	4	4	no	—
143	C₃×C₄×C₅	—	8	1	no	—
144	C₃×C₄×C₅	#120	1	2	yes	—
145	C₃×C₄×C₅	#121	1	2	yes	—
146	C₂⁴×C₃	—	2	1	no	—
147	C₂×C₃×Q₈	—	2	2	no	—
148	C₂×C₃×Q₈	—	2	2	no	—
149	C₂×C₃×Q₈	—	2	2	no	—
150	C₂×C₃×Q₈	—	2	2	no	—
151	C₂×C₃×Q₈	—	2	2	no	—
152	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
153	C₂×C₃×D₄	—	2	2	no	—
154	C₂×C₃×D₄	—	2	2	no	—
155	C₂×C₃×D₄	—	2	1	no	—
156	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₃×SD₁₆	—	2	16	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
165	C₃×C₄⋊C₄	—	2	8	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₂²⋊C₄	—	4	4	no	—
168	C₃×C₄²	—	2	2	no	—
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	—	4	1	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
175	C₅×Q₈	—	2	4	no	—
176	C₅×Q₈	—	2	4	no	—
177	C₅×Q₈	—	4	2	no	—
178	C₅×Q₈	—	4	2	no	—
179	C₅×D₄	—	2	4	no	—
180	C₅×D₄	—	4	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
189	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
193	C₅×C₈	—	2	4	no	—
194	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
195	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₂×SD₁₆	—	2	4	no	—
197	C₂×SD₁₆	—	2	4	no	—
198	C₂×SD₁₆	—	2	4	no	—
199	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
200	C₄⋊Q₈	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
205	#103	—	2	4	no	—
206	C₂×C₃×C₅	—	8	2	no	—
207	C₂×C₃×C₅	#392	1	1	yes	characteristic
208	C₂×C₃×C₅	#448	1	2	yes	—
209	C₂×C₃×C₅	#461	1	2	yes	—
210	C₂×C₃×C₅	#492	1	1	yes	characteristic
211	C₂×C₃×C₅	#497	1	1	yes	characteristic
212	C₂³×C₃	—	2	2	no	—
213	C₂³×C₃	—	4	1	no	—
214	C₂³×C₃	—	4	1	no	—
215	C₂³×C₃	—	4	2	no	—
216	C₂³×C₃	—	4	2	no	—
217	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
218	C₃×Q₈	—	2	4	no	—
219	C₃×Q₈	—	2	4	no	—
220	C₃×Q₈	—	4	2	no	—
221	C₃×Q₈	—	4	2	no	—
222	C₃×D₄	—	2	4	no	—
223	C₃×D₄	—	4	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
232	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
236	C₃×C₈	—	2	4	no	—
237	C₂²×C₅	—	4	2	no	—
238	C₂²×C₅	—	4	4	no	—
239	C₂²×C₅	—	8	2	no	—
240	C₂²×C₅	—	8	1	no	—
241	C₂²×C₅	—	8	1	no	—
242	C₂²×C₅	C₃×#120	1	1	yes	characteristic
243	C₂²×C₅	C₃×#121	1	1	yes	characteristic
244	C₂²×C₅	C₃×#127	1	1	yes	characteristic
245	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
246	C₂²×C₅	C₃×#137	1	2	yes	—
247	C₄×C₅	—	2	4	no	—
248	C₄×C₅	—	4	4	no	—
249	C₄×C₅	—	8	1	no	—
250	C₄×C₅	C₃×#120	1	2	yes	—
251	C₄×C₅	C₃×#121	1	2	yes	—
252	C₂⁴	—	2	1	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	SD₁₆	—	2	16	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₂²⋊C₄	—	4	4	no	—
274	C₄²	—	2	2	no	—
275	C₃×C₅	#2013	1	1	yes	characteristic, direct product factor, Hall
276	C₂²×C₃	—	4	2	no	—
277	C₂²×C₃	—	4	4	no	—
278	C₂²×C₃	—	8	2	no	—
279	C₂²×C₃	—	8	1	no	—
280	C₂²×C₃	—	8	1	no	—
281	C₂²×C₃	C₅×#120	1	1	yes	characteristic
282	C₂²×C₃	C₅×#121	1	1	yes	characteristic
283	C₂²×C₃	C₅×#127	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
285	C₂²×C₃	C₅×#137	1	2	yes	—
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	4	4	no	—
288	C₃×C₄	—	8	1	no	—
289	C₃×C₄	C₅×#120	1	2	yes	—
290	C₃×C₄	C₅×#121	1	2	yes	—
291	C₂×C₅	—	8	2	no	—
292	C₂×C₅	C₃×#392	1	1	yes	characteristic
293	C₂×C₅	C₃×#448	1	2	yes	—
294	C₂×C₅	C₃×#461	1	2	yes	—
295	C₂×C₅	C₃×#492	1	1	yes	characteristic
296	C₂×C₅	C₃×#497	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	—	4	1	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
303	Q₈	—	2	4	no	—
304	Q₈	—	2	4	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	4	2	no	—
307	D₄	—	2	4	no	—
308	D₄	—	4	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	complemented
317	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
319	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
320	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
321	C₈	—	2	4	no	—
322	C₂×C₃	—	8	2	no	—
323	C₂×C₃	C₅×#392	1	1	yes	characteristic
324	C₂×C₃	C₅×#448	1	2	yes	—
325	C₂×C₃	C₅×#461	1	2	yes	—
326	C₂×C₃	C₅×#492	1	1	yes	characteristic
327	C₂×C₃	C₅×#497	1	1	yes	characteristic
328	C₅	C₃×#2013	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	—	4	4	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	8	1	no	—
332	C₂²	—	8	1	no	—
333	C₂²	—	8	2	no	—
334	C₂²	C₃×C₅×#120	1	1	yes	characteristic
335	C₂²	C₃×C₅×#121	1	1	yes	characteristic
336	C₂²	C₃×C₅×#127	1	1	yes	characteristic
337	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
338	C₂²	C₃×C₅×#137	1	2	yes	—
339	C₄	—	2	4	no	—
340	C₄	—	4	4	no	—
341	C₄	—	8	1	no	—
342	C₄	C₃×C₅×#120	1	2	yes	—
343	C₄	C₃×C₅×#121	1	2	yes	—
344	C₃	C₅×#2013	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	—	8	2	no	—
346	C₂	C₃×C₅×#392	1	1	yes	characteristic
347	C₂	C₃×C₅×#448	1	2	yes	—
348	C₂	C₃×C₅×#461	1	2	yes	—
349	C₂	C₃×C₅×#492	1	1	yes	characteristic
350	C₂	C₃×C₅×#497	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×C₅×#103	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2013	C₃	direct (N × H)
19. C₃×#2013	C₅	direct (N × H)
21. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
22. C₂×C₅×#103	C₂×C₃	semidirect
24. C₅×#336	C₂×C₃	semidirect
49. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
50. C₂×C₃×#103	C₂×C₅	semidirect
52. C₃×#336	C₂×C₅	semidirect
65. #2013	C₃×C₅	direct (N × H)
85. C₂×C₃×C₄×C₅	SD₁₆	semidirect
127. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
128. C₂×#103	C₂×C₃×C₅	semidirect
130. #336	C₂×C₃×C₅	semidirect
188. C₂×C₄×C₅	C₃×SD₁₆	semidirect
231. C₂×C₃×C₄	C₅×SD₁₆	semidirect
275. C₃×C₅	#2013	direct (N × H)
316. C₂×C₄	C₃×C₅×SD₁₆	semidirect
328. C₅	C₃×#2013	direct (N × H)
344. C₃	C₅×#2013	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×SD₁₆	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×C₅×#103	2
C₃×C₅×#390	2
C₃×C₅×#336	2
C₅×#2013	3
C₃×#2013	5

Subgroups — C3×C5×#2013 #14275047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2013 #14275047