Subgroups — C₃×C₅×#2537 #14275571

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	4	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#380	C₂	1	4	yes	maximal, complemented
6	C₅×#2537	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	—
10	C₃×C₅×#121	—	2	16	no	—
11	C₃×C₄×C₅×D₄	—	2	8	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#95	C₂²	1	4	yes	—
19	C₃×#2537	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×#121	C₂×C₃	1	4	yes	complemented
21	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
22	C₅×#394	C₂×C₃	1	4	yes	complemented
23	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#380	C₂×C₃	1	4	yes	complemented
25	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
26	C₂×C₃×C₅×D₄	—	2	16	no	—
27	C₂×C₃×C₅×D₄	—	2	4	no	—
28	C₂×C₃×C₅×D₄	—	2	4	no	—
29	C₂×C₃×C₅×D₄	—	4	4	no	—
30	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
31	C₂²×C₃×C₄×C₅	—	2	8	no	—
32	C₂²×C₃×C₄×C₅	—	2	8	no	—
33	C₂²×C₃×C₄×C₅	—	2	8	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₃×C₅×C₄⋊C₄	—	2	4	no	—
39	C₃×C₅×C₄⋊C₄	—	2	8	no	—
40	C₃×C₅×C₄⋊C₄	—	4	2	no	—
41	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
42	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
43	C₃×C₄²×C₅	D₄	1	4	yes	complemented
44	C₂×C₃×#121	C₂×C₅	1	4	yes	complemented
45	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
46	C₃×#394	C₂×C₅	1	4	yes	complemented
47	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
48	C₃×#380	C₂×C₅	1	4	yes	complemented
49	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
50	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
51	C₂³×C₄×C₅	C₂²×C₃	1	4	yes	—
52	C₅×#121	—	2	16	no	—
53	C₄×C₅×D₄	—	2	8	no	—
54	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
56	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
57	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
58	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
59	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₅×#95	C₂²×C₃	1	4	yes	—
61	#2537	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₂³×C₃×C₅	—	2	4	no	—
63	C₂³×C₃×C₅	—	2	4	no	—
64	C₂³×C₃×C₅	—	2	4	no	—
65	C₂³×C₃×C₅	—	2	4	no	—
66	C₂³×C₃×C₅	—	2	4	no	—
67	C₂³×C₃×C₅	—	2	4	no	—
68	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
69	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
70	C₃×C₅×D₄	—	2	16	no	—
71	C₃×C₅×D₄	—	4	16	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	4	no	—
75	C₂×C₃×C₄×C₅	—	2	4	no	—
76	C₂×C₃×C₄×C₅	—	2	8	no	—
77	C₂×C₃×C₄×C₅	—	2	4	no	—
78	C₂×C₃×C₄×C₅	—	2	4	no	—
79	C₂×C₃×C₄×C₅	—	4	16	no	—
80	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
83	C₂×C₃×C₄×C₅	#41	1	4	yes	—
84	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
85	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
86	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	—
87	C₃×#121	—	2	16	no	—
88	C₃×C₄×D₄	—	2	8	no	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
94	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
95	C₃×#95	C₂²×C₅	1	4	yes	—
96	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
97	C₂×C₅×D₄	—	2	16	no	—
98	C₂×C₅×D₄	—	2	4	no	—
99	C₂×C₅×D₄	—	2	4	no	—
100	C₂×C₅×D₄	—	4	4	no	—
101	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
102	C₂²×C₄×C₅	—	2	8	no	—
103	C₂²×C₄×C₅	—	2	8	no	—
104	C₂²×C₄×C₅	—	2	8	no	—
105	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
106	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
107	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
109	C₅×C₄⋊C₄	—	2	4	no	—
110	C₅×C₄⋊C₄	—	2	8	no	—
111	C₅×C₄⋊C₄	—	4	2	no	—
112	C₅×C₂²⋊C₄	—	2	16	no	—
113	C₅×C₂²⋊C₄	—	2	8	no	—
114	C₄²×C₅	C₃×D₄	1	4	yes	complemented
115	C₂×#121	C₂×C₃×C₅	1	4	yes	complemented
116	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
117	#394	C₂×C₃×C₅	1	4	yes	complemented
118	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
119	#380	C₂×C₃×C₅	1	4	yes	complemented
120	C₂²×C₃×C₅	—	2	8	no	—
121	C₂²×C₃×C₅	—	2	8	no	—
122	C₂²×C₃×C₅	—	2	8	no	—
123	C₂²×C₃×C₅	—	4	4	no	—
124	C₂²×C₃×C₅	—	4	4	no	—
125	C₂²×C₃×C₅	—	4	4	no	—
126	C₂²×C₃×C₅	—	4	4	no	—
127	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
128	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
129	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
130	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
131	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
132	C₃×C₄×C₅	—	2	2	no	—
133	C₃×C₄×C₅	—	4	4	no	—
134	C₃×C₄×C₅	—	4	4	no	—
135	C₃×C₄×C₅	#121	1	8	yes	complemented
136	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
137	C₂×C₃×D₄	—	2	16	no	—
138	C₂×C₃×D₄	—	2	4	no	—
139	C₂×C₃×D₄	—	2	4	no	—
140	C₂×C₃×D₄	—	4	4	no	—
141	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
142	C₂²×C₃×C₄	—	2	8	no	—
143	C₂²×C₃×C₄	—	2	8	no	—
144	C₂²×C₃×C₄	—	2	8	no	—
145	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
146	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
147	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
149	C₃×C₄⋊C₄	—	2	4	no	—
150	C₃×C₄⋊C₄	—	2	8	no	—
151	C₃×C₄⋊C₄	—	4	2	no	—
152	C₃×C₂²⋊C₄	—	2	16	no	—
153	C₃×C₂²⋊C₄	—	2	8	no	—
154	C₃×C₄²	C₅×D₄	1	4	yes	complemented
155	C₂³×C₅	—	2	4	no	—
156	C₂³×C₅	—	2	4	no	—
157	C₂³×C₅	—	2	4	no	—
158	C₂³×C₅	—	2	4	no	—
159	C₂³×C₅	—	2	4	no	—
160	C₂³×C₅	—	2	4	no	—
161	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
162	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
163	C₅×D₄	—	2	16	no	—
164	C₅×D₄	—	4	16	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	8	no	—
170	C₂×C₄×C₅	—	2	4	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	4	16	no	—
173	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
174	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
175	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
176	C₂×C₄×C₅	C₃×#41	1	4	yes	—
177	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
178	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
179	C₂³×C₄	C₂²×C₃×C₅	1	4	yes	—
180	#121	—	2	16	no	—
181	C₄×D₄	—	2	8	no	—
182	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
184	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
186	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
187	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
188	#95	C₂²×C₃×C₅	1	4	yes	—
189	C₂×C₃×C₅	—	4	8	no	—
190	C₂×C₃×C₅	C₂×#121	1	2	yes	—
191	C₂×C₃×C₅	#537	1	1	yes	characteristic
192	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
193	C₂×C₃×C₅	#547	1	2	yes	—
194	C₂×C₃×C₅	#555	1	1	yes	characteristic
195	C₂³×C₃	—	2	4	no	—
196	C₂³×C₃	—	2	4	no	—
197	C₂³×C₃	—	2	4	no	—
198	C₂³×C₃	—	2	4	no	—
199	C₂³×C₃	—	2	4	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
202	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
203	C₃×D₄	—	2	16	no	—
204	C₃×D₄	—	4	16	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	4	16	no	—
213	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
214	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
215	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
216	C₂×C₃×C₄	C₅×#41	1	4	yes	—
217	C₂²×C₅	—	2	8	no	—
218	C₂²×C₅	—	2	8	no	—
219	C₂²×C₅	—	2	8	no	—
220	C₂²×C₅	—	4	4	no	—
221	C₂²×C₅	—	4	4	no	—
222	C₂²×C₅	—	4	4	no	—
223	C₂²×C₅	—	4	4	no	—
224	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
225	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
226	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
227	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
229	C₄×C₅	—	2	2	no	—
230	C₄×C₅	—	4	4	no	—
231	C₄×C₅	—	4	4	no	—
232	C₄×C₅	C₃×#121	1	8	yes	complemented
233	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
234	C₂×D₄	—	2	16	no	—
235	C₂×D₄	—	2	4	no	—
236	C₂×D₄	—	2	4	no	—
237	C₂×D₄	—	4	4	no	—
238	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
243	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
244	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	2	8	no	—
248	C₄⋊C₄	—	4	2	no	—
249	C₂²⋊C₄	—	2	16	no	—
250	C₂²⋊C₄	—	2	8	no	—
251	C₄²	C₃×C₅×D₄	1	4	yes	complemented
252	C₃×C₅	#2537	1	1	yes	characteristic, direct product factor, Hall
253	C₂²×C₃	—	2	8	no	—
254	C₂²×C₃	—	2	8	no	—
255	C₂²×C₃	—	2	8	no	—
256	C₂²×C₃	—	4	4	no	—
257	C₂²×C₃	—	4	4	no	—
258	C₂²×C₃	—	4	4	no	—
259	C₂²×C₃	—	4	4	no	—
260	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
261	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
262	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
263	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
265	C₃×C₄	—	2	2	no	—
266	C₃×C₄	—	4	4	no	—
267	C₃×C₄	—	4	4	no	—
268	C₃×C₄	C₅×#121	1	8	yes	complemented
269	C₂×C₅	—	4	8	no	—
270	C₂×C₅	C₂×C₃×#121	1	2	yes	—
271	C₂×C₅	C₃×#537	1	1	yes	characteristic
272	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
273	C₂×C₅	C₃×#547	1	2	yes	—
274	C₂×C₅	C₃×#555	1	1	yes	characteristic
275	C₂³	—	2	4	no	—
276	C₂³	—	2	4	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
282	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
283	D₄	—	2	16	no	—
284	D₄	—	4	16	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
294	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
295	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
296	C₂×C₄	C₃×C₅×#41	1	4	yes	—
297	C₂×C₃	—	4	8	no	—
298	C₂×C₃	C₂×C₅×#121	1	2	yes	—
299	C₂×C₃	C₅×#537	1	1	yes	characteristic
300	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
301	C₂×C₃	C₅×#547	1	2	yes	—
302	C₂×C₃	C₅×#555	1	1	yes	characteristic
303	C₅	C₃×#2537	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²	—	2	8	no	—
305	C₂²	—	2	8	no	—
306	C₂²	—	2	8	no	—
307	C₂²	—	4	4	no	—
308	C₂²	—	4	4	no	—
309	C₂²	—	4	4	no	—
310	C₂²	—	4	4	no	—
311	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
312	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
313	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
314	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
316	C₄	—	2	2	no	—
317	C₄	—	4	4	no	—
318	C₄	—	4	4	no	—
319	C₄	C₃×C₅×#121	1	8	yes	complemented
320	C₃	C₅×#2537	1	1	yes	characteristic, direct product factor, Sylow
321	C₂	—	4	8	no	—
322	C₂	C₂×C₃×C₅×#121	1	2	yes	—
323	C₂	C₃×C₅×#537	1	1	yes	characteristic
324	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
325	C₂	C₃×C₅×#547	1	2	yes	—
326	C₂	C₃×C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#394	C₂	semidirect
4. C₃×C₅×#384	C₂	semidirect
5. C₃×C₅×#380	C₂	semidirect
6. C₅×#2537	C₃	direct (N × H)
19. C₃×#2537	C₅	direct (N × H)
20. C₂×C₅×#121	C₂×C₃	semidirect
21. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
22. C₅×#394	C₂×C₃	semidirect
23. C₅×#384	C₂×C₃	semidirect
24. C₅×#380	C₂×C₃	semidirect
30. C₂×C₃×C₅×D₄	D₄	semidirect
43. C₃×C₄²×C₅	D₄	semidirect
44. C₂×C₃×#121	C₂×C₅	semidirect
45. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
46. C₃×#394	C₂×C₅	semidirect
47. C₃×#384	C₂×C₅	semidirect
48. C₃×#380	C₂×C₅	semidirect
61. #2537	C₃×C₅	direct (N × H)
101. C₂×C₅×D₄	C₃×D₄	semidirect
114. C₄²×C₅	C₃×D₄	semidirect
115. C₂×#121	C₂×C₃×C₅	semidirect
116. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
117. #394	C₂×C₃×C₅	semidirect
118. #384	C₂×C₃×C₅	semidirect
119. #380	C₂×C₃×C₅	semidirect
135. C₃×C₄×C₅	#121	semidirect
141. C₂×C₃×D₄	C₅×D₄	semidirect
154. C₃×C₄²	C₅×D₄	semidirect
232. C₄×C₅	C₃×#121	semidirect
238. C₂×D₄	C₃×C₅×D₄	semidirect
251. C₄²	C₃×C₅×D₄	semidirect
252. C₃×C₅	#2537	direct (N × H)
268. C₃×C₄	C₅×#121	semidirect
303. C₅	C₃×#2537	direct (N × H)
319. C₄	C₃×C₅×#121	semidirect
320. C₃	C₅×#2537	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×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#394	2
C₃×C₅×#384	2
C₃×C₅×#380	2
C₅×#2537	3
C₃×#2537	5

Subgroups — C3×C5×#2537 #14275571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2537 #14275571