Subgroups — C₃×C₅×#1816 #14274850

Order 1920.

528 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	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#417	C₂	1	2	yes	maximal
5	C₃×C₅×#343	C₂	1	2	yes	maximal, complemented
6	C₅×#1816	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₃×C₅×#131	—	2	2	no	—
9	C₃×C₅×#131	C₄	1	4	yes	complemented
10	C₂×C₃×C₅×M₁₆	—	2	1	no	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	—	2	1	no	—
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₃×C₅×#108	—	2	2	no	—
17	C₃×C₅×#107	—	2	1	no	—
18	C₃×C₅×#107	—	2	1	no	—
19	C₃×C₅×#103	—	2	2	no	—
20	C₃×C₅×#102	—	2	2	no	—
21	C₃×#1816	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
25	C₅×#417	C₂×C₃	1	2	yes	—
26	C₅×#343	C₂×C₃	1	2	yes	complemented
27	C₃×C₅×#41	—	2	1	no	—
28	C₃×C₅×#41	—	2	1	no	—
29	C₃×C₅×#41	C₂×C₄	1	2	yes	—
30	C₃×C₅×#41	Q₈	1	2	yes	—
31	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₃×C₅×M₁₆	—	2	1	no	—
38	C₃×C₅×M₁₆	—	2	4	no	—
39	C₃×C₅×M₁₆	—	2	2	no	—
40	C₃×C₅×M₁₆	—	2	2	no	—
41	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	4	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
52	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#417	C₂×C₅	1	2	yes	—
55	C₃×#343	C₂×C₅	1	2	yes	complemented
56	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
57	C₅×#131	—	2	2	no	—
58	C₅×#131	C₃×C₄	1	4	yes	complemented
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
61	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₅×#108	—	2	2	no	—
66	C₅×#107	—	2	1	no	—
67	C₅×#107	—	2	1	no	—
68	C₅×#103	—	2	2	no	—
69	C₅×#102	—	2	2	no	—
70	#1816	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³×C₃×C₅	—	2	1	no	—
72	C₂³×C₃×C₅	#41	1	1	yes	characteristic
73	C₃×C₅×Q₈	—	2	1	no	—
74	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
75	C₃×C₅×D₄	—	2	2	no	—
76	C₃×C₅×D₄	—	2	2	no	—
77	C₃×C₅×D₄	—	2	1	no	—
78	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	8	2	no	—
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
90	C₃×C₅×C₈	—	2	2	no	—
91	C₃×C₅×C₈	—	4	2	no	—
92	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
93	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
95	C₃×#131	—	2	2	no	—
96	C₃×#131	C₄×C₅	1	4	yes	complemented
97	C₂×C₃×M₁₆	—	2	1	no	—
98	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
99	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
100	C₂²×C₃×C₈	—	2	1	no	—
101	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
103	C₃×#108	—	2	2	no	—
104	C₃×#107	—	2	1	no	—
105	C₃×#107	—	2	1	no	—
106	C₃×#103	—	2	2	no	—
107	C₃×#102	—	2	2	no	—
108	C₅×#41	—	2	1	no	—
109	C₅×#41	—	2	1	no	—
110	C₅×#41	C₂×C₃×C₄	1	2	yes	—
111	C₅×#41	C₃×Q₈	1	2	yes	—
112	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₅×M₁₆	—	2	1	no	—
119	C₅×M₁₆	—	2	4	no	—
120	C₅×M₁₆	—	2	2	no	—
121	C₅×M₁₆	—	2	2	no	—
122	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	4	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
127	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
133	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	#417	C₂×C₃×C₅	1	2	yes	—
136	#343	C₂×C₃×C₅	1	2	yes	complemented
137	C₂²×C₃×C₅	—	2	1	no	—
138	C₂²×C₃×C₅	—	2	1	no	—
139	C₂²×C₃×C₅	—	2	2	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	1	no	—
142	C₂²×C₃×C₅	#117	1	1	yes	characteristic
143	C₂²×C₃×C₅	#121	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
145	C₃×C₄×C₅	—	2	2	no	—
146	C₃×C₄×C₅	—	8	2	no	—
147	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₃×C₄×C₅	#121	1	1	yes	characteristic
150	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
151	C₃×#41	—	2	1	no	—
152	C₃×#41	—	2	1	no	—
153	C₃×#41	C₂×C₄×C₅	1	2	yes	—
154	C₃×#41	C₅×Q₈	1	2	yes	—
155	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
156	C₂×C₃×D₄	—	2	1	no	—
157	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₃×M₁₆	—	2	1	no	—
162	C₃×M₁₆	—	2	4	no	—
163	C₃×M₁₆	—	2	2	no	—
164	C₃×M₁₆	—	2	2	no	—
165	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
170	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
171	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
172	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₂³×C₅	—	2	1	no	—
176	C₂³×C₅	C₃×#41	1	1	yes	characteristic
177	C₅×Q₈	—	2	1	no	—
178	C₅×Q₈	C₃×C₄⋊C₄	1	2	yes	—
179	C₅×D₄	—	2	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	2	1	no	—
182	C₅×D₄	C₃×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	8	2	no	—
188	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
194	C₅×C₈	—	2	2	no	—
195	C₅×C₈	—	4	2	no	—
196	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
197	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
198	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
199	#131	—	2	2	no	—
200	#131	C₃×C₄×C₅	1	4	yes	complemented
201	C₂×M₁₆	—	2	1	no	—
202	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
203	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	#108	—	2	2	no	—
208	#107	—	2	1	no	—
209	#107	—	2	1	no	—
210	#103	—	2	2	no	—
211	#102	—	2	2	no	—
212	C₂×C₃×C₅	—	2	1	no	—
213	C₂×C₃×C₅	—	2	1	no	—
214	C₂×C₃×C₅	—	4	2	no	—
215	C₂×C₃×C₅	#380	1	1	yes	characteristic
216	C₂×C₃×C₅	#472	1	1	yes	characteristic
217	C₂×C₃×C₅	#473	1	1	yes	characteristic
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	C₅×#41	1	1	yes	characteristic
220	C₃×Q₈	—	2	1	no	—
221	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	—
222	C₃×D₄	—	2	2	no	—
223	C₃×D₄	—	2	2	no	—
224	C₃×D₄	—	2	1	no	—
225	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	8	2	no	—
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
236	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
237	C₃×C₈	—	2	2	no	—
238	C₃×C₈	—	4	2	no	—
239	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
240	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	C₃×#117	1	1	yes	characteristic
247	C₂²×C₅	C₃×#121	1	1	yes	characteristic
248	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	8	2	no	—
251	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
253	C₄×C₅	C₃×#121	1	1	yes	characteristic
254	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
255	#41	—	2	1	no	—
256	#41	—	2	1	no	—
257	#41	C₂×C₃×C₄×C₅	1	2	yes	—
258	#41	C₃×C₅×Q₈	1	2	yes	—
259	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	M₁₆	—	2	1	no	—
266	M₁₆	—	2	4	no	—
267	M₁₆	—	2	2	no	—
268	M₁₆	—	2	2	no	—
269	M₁₆	C₂×C₃×C₄×C₅	1	2	yes	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
274	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
275	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
276	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₃×C₅	#1816	1	1	yes	characteristic, direct product factor, Hall
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	4	1	no	—
284	C₂²×C₃	—	4	1	no	—
285	C₂²×C₃	C₅×#117	1	1	yes	characteristic
286	C₂²×C₃	C₅×#121	1	1	yes	characteristic
287	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	8	2	no	—
290	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
291	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
292	C₃×C₄	C₅×#121	1	1	yes	characteristic
293	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
294	C₂×C₅	—	2	1	no	—
295	C₂×C₅	—	2	1	no	—
296	C₂×C₅	—	4	2	no	—
297	C₂×C₅	C₃×#380	1	1	yes	characteristic
298	C₂×C₅	C₃×#472	1	1	yes	characteristic
299	C₂×C₅	C₃×#473	1	1	yes	characteristic
300	C₂³	—	2	1	no	—
301	C₂³	C₃×C₅×#41	1	1	yes	characteristic
302	Q₈	—	2	1	no	—
303	Q₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
304	D₄	—	2	2	no	—
305	D₄	—	2	2	no	—
306	D₄	—	2	1	no	—
307	D₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	2	no	—
313	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
314	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
315	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
316	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
317	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
318	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	—	4	2	no	—
321	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
322	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	4	2	no	—
326	C₂×C₃	C₅×#380	1	1	yes	characteristic
327	C₂×C₃	C₅×#472	1	1	yes	characteristic
328	C₂×C₃	C₅×#473	1	1	yes	characteristic
329	C₅	C₃×#1816	1	1	yes	characteristic, direct product factor, Sylow
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	C₃×C₅×#117	1	1	yes	characteristic
336	C₂²	C₃×C₅×#121	1	1	yes	characteristic
337	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	8	2	no	—
340	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
342	C₄	C₃×C₅×#121	1	1	yes	characteristic
343	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
344	C₃	C₅×#1816	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	—	2	1	no	—
346	C₂	—	2	1	no	—
347	C₂	—	4	2	no	—
348	C₂	C₃×C₅×#380	1	1	yes	characteristic
349	C₂	C₃×C₅×#472	1	1	yes	characteristic
350	C₂	C₃×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
3. C₂×C₃×C₅×#107	C₂	semidirect
5. C₃×C₅×#343	C₂	semidirect
6. C₅×#1816	C₃	direct (N × H)
9. C₃×C₅×#131	C₄	semidirect
21. C₃×#1816	C₅	direct (N × H)
23. C₂×C₅×#108	C₂×C₃	semidirect
24. C₂×C₅×#107	C₂×C₃	semidirect
26. C₅×#343	C₂×C₃	semidirect
52. C₂×C₃×#108	C₂×C₅	semidirect
53. C₂×C₃×#107	C₂×C₅	semidirect
55. C₃×#343	C₂×C₅	semidirect
58. C₅×#131	C₃×C₄	semidirect
70. #1816	C₃×C₅	direct (N × H)
96. C₃×#131	C₄×C₅	semidirect
133. C₂×#108	C₂×C₃×C₅	semidirect
134. C₂×#107	C₂×C₃×C₅	semidirect
136. #343	C₂×C₃×C₅	semidirect
200. #131	C₃×C₄×C₅	semidirect
279. C₃×C₅	#1816	direct (N × H)
329. C₅	C₃×#1816	direct (N × H)
344. C₃	C₅×#1816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#131	2
C₂×C₃×C₅×#108	2
C₂×C₃×C₅×#107	2
C₃×C₅×#417	2
C₃×C₅×#343	2
C₅×#1816	3
C₃×#1816	5

Subgroups — C3×C5×#1816 #14274850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1816 #14274850