Subgroups — C₃×C₅×#1851 #14274885

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#336	C₂	1	2	yes	maximal, complemented
6	C₅×#1851	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	—	2	2	no	—
9	C₂×C₃×C₅×M₁₆	—	2	4	no	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊C₈	—	2	4	no	—
16	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
17	C₃×C₅×#95	C₄	1	1	yes	characteristic
18	C₃×C₅×#95	C₄	1	1	yes	characteristic
19	C₃×#1851	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
22	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₅×#336	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₃×C₅×M₁₆	—	2	8	no	—
35	C₂×C₃×C₅×C₈	—	2	2	no	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
42	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
43	C₃×C₄²×C₅	—	2	2	no	—
44	C₃×C₄²×C₅	—	2	2	no	—
45	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
46	C₂×C₃×C₄⋊C₈	C₂×C₅	1	2	yes	complemented
47	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
48	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
49	C₃×#336	C₂×C₅	1	2	yes	complemented
50	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	—	2	4	no	—
53	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
57	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
58	C₅×C₄⋊C₈	—	2	4	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₅×#95	C₃×C₄	1	1	yes	characteristic
61	C₅×#95	C₃×C₄	1	1	yes	characteristic
62	#1851	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
63	C₂³×C₃×C₅	—	2	2	no	—
64	C₂³×C₃×C₅	—	2	2	no	—
65	C₂³×C₃×C₅	—	2	1	no	—
66	C₂³×C₃×C₅	—	2	1	no	—
67	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
68	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	—	2	2	no	—
70	C₂×C₃×C₄×C₅	—	2	2	no	—
71	C₂×C₃×C₄×C₅	—	2	2	no	—
72	C₂×C₃×C₄×C₅	—	2	2	no	—
73	C₂×C₃×C₄×C₅	—	2	4	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
80	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	#41	1	2	yes	—
84	C₃×C₅×C₈	—	2	4	no	—
85	C₃×C₅×C₈	—	4	1	no	—
86	C₃×C₅×C₈	—	4	1	no	—
87	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
88	C₂×C₃×M₁₆	—	2	2	no	—
89	C₂×C₃×M₁₆	—	2	4	no	—
90	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
91	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
94	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
95	C₃×C₄⋊C₈	—	2	4	no	—
96	C₃×C₂²⋊C₈	—	2	2	no	—
97	C₃×#95	C₄×C₅	1	1	yes	characteristic
98	C₃×#95	C₄×C₅	1	1	yes	characteristic
99	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
106	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
107	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₅×M₁₆	—	2	8	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
116	C₅×C₂²⋊C₄	—	2	4	no	—
117	C₄²×C₅	—	2	2	no	—
118	C₄²×C₅	—	2	2	no	—
119	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic
120	C₂×C₄⋊C₈	C₂×C₃×C₅	1	2	yes	complemented
121	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
122	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
123	#336	C₂×C₃×C₅	1	2	yes	complemented
124	C₂²×C₃×C₅	—	2	2	no	—
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	2	2	no	—
127	C₂²×C₃×C₅	—	4	2	no	—
128	C₂²×C₃×C₅	—	4	2	no	—
129	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
131	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
132	C₂²×C₃×C₅	#131	1	1	yes	characteristic
133	C₂²×C₃×C₅	#131	1	1	yes	characteristic
134	C₃×C₄×C₅	—	2	2	no	—
135	C₃×C₄×C₅	—	2	4	no	—
136	C₃×C₄×C₅	—	4	2	no	—
137	C₃×C₄×C₅	#120	1	1	yes	characteristic
138	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
139	C₃×C₄×C₅	#123	1	1	yes	characteristic
140	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	2	2	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
144	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
146	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
147	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
148	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
149	C₃×M₁₆	—	2	8	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
157	C₃×C₂²⋊C₄	—	2	4	no	—
158	C₃×C₄²	—	2	2	no	—
159	C₃×C₄²	—	2	2	no	—
160	C₂³×C₅	—	2	2	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	2	1	no	—
163	C₂³×C₅	—	2	1	no	—
164	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
165	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	4	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
177	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
178	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	C₃×#41	1	2	yes	—
181	C₅×C₈	—	2	4	no	—
182	C₅×C₈	—	4	1	no	—
183	C₅×C₈	—	4	1	no	—
184	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	4	no	—
187	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
188	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
189	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
190	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	2	yes	—
191	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
192	C₄⋊C₈	—	2	4	no	—
193	C₂²⋊C₈	—	2	2	no	—
194	#95	C₃×C₄×C₅	1	1	yes	characteristic
195	#95	C₃×C₄×C₅	1	1	yes	characteristic
196	C₂×C₃×C₅	—	4	2	no	—
197	C₂×C₃×C₅	#385	1	1	yes	characteristic
198	C₂×C₃×C₅	#423	1	1	yes	characteristic
199	C₂×C₃×C₅	#424	1	1	yes	characteristic
200	C₂×C₃×C₅	#435	1	2	yes	—
201	C₂×C₃×C₅	#436	1	2	yes	—
202	C₂³×C₃	—	2	2	no	—
203	C₂³×C₃	—	2	2	no	—
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	2	1	no	—
206	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
207	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
218	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
219	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
220	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
222	C₂×C₃×C₄	C₅×#41	1	2	yes	—
223	C₃×C₈	—	2	4	no	—
224	C₃×C₈	—	4	1	no	—
225	C₃×C₈	—	4	1	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	2	no	—
229	C₂²×C₅	—	4	2	no	—
230	C₂²×C₅	—	4	2	no	—
231	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
233	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
234	C₂²×C₅	C₃×#131	1	1	yes	characteristic
235	C₂²×C₅	C₃×#131	1	1	yes	characteristic
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	4	no	—
238	C₄×C₅	—	4	2	no	—
239	C₄×C₅	C₃×#120	1	1	yes	characteristic
240	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
241	C₄×C₅	C₃×#123	1	1	yes	characteristic
242	C₂⁴	C₂×C₃×C₄×C₅	1	1	yes	characteristic
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
246	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
247	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
248	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
249	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
250	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
251	M₁₆	—	2	8	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₃×C₅	#1851	1	1	yes	characteristic, direct product factor, Hall
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	2	2	no	—
266	C₂²×C₃	—	4	2	no	—
267	C₂²×C₃	—	4	2	no	—
268	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
270	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
271	C₂²×C₃	C₅×#131	1	1	yes	characteristic
272	C₂²×C₃	C₅×#131	1	1	yes	characteristic
273	C₃×C₄	—	2	2	no	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	4	2	no	—
276	C₃×C₄	C₅×#120	1	1	yes	characteristic
277	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
278	C₃×C₄	C₅×#123	1	1	yes	characteristic
279	C₂×C₅	—	4	2	no	—
280	C₂×C₅	C₃×#385	1	1	yes	characteristic
281	C₂×C₅	C₃×#423	1	1	yes	characteristic
282	C₂×C₅	C₃×#424	1	1	yes	characteristic
283	C₂×C₅	C₃×#435	1	2	yes	—
284	C₂×C₅	C₃×#436	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	C₃×C₅×C₄⋊C₄	1	2	yes	—
290	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
301	C₂×C₄	C₃×C₅×M₁₆	1	4	yes	complemented
302	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
303	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
304	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
305	C₂×C₄	C₃×C₅×#41	1	2	yes	—
306	C₈	—	2	4	no	—
307	C₈	—	4	1	no	—
308	C₈	—	4	1	no	—
309	C₂×C₃	—	4	2	no	—
310	C₂×C₃	C₅×#385	1	1	yes	characteristic
311	C₂×C₃	C₅×#423	1	1	yes	characteristic
312	C₂×C₃	C₅×#424	1	1	yes	characteristic
313	C₂×C₃	C₅×#435	1	2	yes	—
314	C₂×C₃	C₅×#436	1	2	yes	—
315	C₅	C₃×#1851	1	1	yes	characteristic, direct product factor, Sylow
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
322	C₂²	C₃×C₄×C₅×D₄	1	2	yes	—
323	C₂²	C₂×C₃×C₅×M₁₆	1	2	yes	—
324	C₂²	C₃×C₅×#131	1	1	yes	characteristic
325	C₂²	C₃×C₅×#131	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	4	no	—
328	C₄	—	4	2	no	—
329	C₄	C₃×C₅×#120	1	1	yes	characteristic
330	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
331	C₄	C₃×C₅×#123	1	1	yes	characteristic
332	C₃	C₅×#1851	1	1	yes	characteristic, direct product factor, Sylow
333	C₂	—	4	2	no	—
334	C₂	C₃×C₅×#385	1	1	yes	characteristic
335	C₂	C₃×C₅×#423	1	1	yes	characteristic
336	C₂	C₃×C₅×#424	1	1	yes	characteristic
337	C₂	C₃×C₅×#435	1	2	yes	—
338	C₂	C₃×C₅×#436	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂³	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ 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×C₄⋊C₈	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#1851	C₃	direct (N × H)
19. C₃×#1851	C₅	direct (N × H)
21. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
24. C₅×#336	C₂×C₃	semidirect
46. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
49. C₃×#336	C₂×C₅	semidirect
62. #1851	C₃×C₅	direct (N × H)
79. C₂×C₃×C₄×C₅	M₁₆	semidirect
120. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
123. #336	C₂×C₃×C₅	semidirect
176. C₂×C₄×C₅	C₃×M₁₆	semidirect
218. C₂×C₃×C₄	C₅×M₁₆	semidirect
262. C₃×C₅	#1851	direct (N × H)
301. C₂×C₄	C₃×C₅×M₁₆	semidirect
315. C₅	C₃×#1851	direct (N × H)
332. C₃	C₅×#1851	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×M₁₆	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#336	2
C₅×#1851	3
C₃×#1851	5

Subgroups — C3×C5×#1851 #14274885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1851 #14274885