Subgroups — C₃×C₅×#1545 #14274579

Order 1920.

688 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	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#331	C₂	1	4	yes	maximal, complemented
5	C₅×#1545	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×D₄	—	2	1	no	—
7	C₂²×C₃×C₅×D₄	—	2	1	no	—
8	C₂²×C₃×C₅×D₄	C₄	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	—	2	1	no	—
10	C₃×C₅×#127	—	2	1	no	—
11	C₃×C₅×#127	—	2	1	no	—
12	C₃×C₅×#127	C₄	1	2	yes	—
13	C₃×C₅×#127	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊C₈	—	2	1	no	—
16	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
17	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
18	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
19	C₃×C₄×C₅×C₈	—	2	1	no	—
20	C₃×#1545	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
22	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
23	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#331	C₂×C₃	1	4	yes	complemented
25	C₂⁴×C₃×C₅	—	2	2	no	—
26	C₂×C₃×C₅×D₄	—	2	2	no	—
27	C₂×C₃×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	4	4	no	—
32	C₂×C₃×C₅×D₄	—	4	4	no	—
33	C₂×C₃×C₅×D₄	—	4	2	no	—
34	C₂×C₃×C₅×D₄	—	4	2	no	—
35	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₃×C₅×M₁₆	—	4	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
47	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
48	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
49	C₃×#331	C₂×C₅	1	4	yes	complemented
50	C₂²×C₅×D₄	—	2	1	no	—
51	C₂²×C₅×D₄	—	2	1	no	—
52	C₂²×C₅×D₄	C₃×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₅×#127	—	2	1	no	—
55	C₅×#127	—	2	1	no	—
56	C₅×#127	C₃×C₄	1	2	yes	—
57	C₅×#127	C₂²×C₃	1	2	yes	—
58	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₅×C₄⋊C₈	—	2	1	no	—
60	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
61	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
62	C₅×C₂²⋊C₈	—	2	1	no	—
63	C₄×C₅×C₈	—	2	1	no	—
64	#1545	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	4	no	—
66	C₂³×C₃×C₅	—	4	4	no	—
67	C₂³×C₃×C₅	—	4	4	no	—
68	C₂³×C₃×C₅	—	4	4	no	—
69	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
70	C₃×C₅×D₄	—	4	4	no	—
71	C₃×C₅×D₄	—	4	4	no	—
72	C₃×C₅×D₄	—	4	4	no	—
73	C₃×C₅×D₄	—	4	4	no	—
74	C₃×C₅×D₄	—	4	2	no	—
75	C₃×C₅×D₄	—	4	2	no	—
76	C₃×C₅×D₄	—	4	4	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
83	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
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	C₃×C₅×C₈	—	4	2	no	—
88	C₃×C₅×C₈	—	4	2	no	—
89	C₂²×C₃×D₄	—	2	1	no	—
90	C₂²×C₃×D₄	—	2	1	no	—
91	C₂²×C₃×D₄	C₄×C₅	1	2	yes	—
92	C₂×C₃×M₁₆	—	2	1	no	—
93	C₃×#127	—	2	1	no	—
94	C₃×#127	—	2	1	no	—
95	C₃×#127	C₄×C₅	1	2	yes	—
96	C₃×#127	C₂²×C₅	1	2	yes	—
97	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
98	C₃×C₄⋊C₈	—	2	1	no	—
99	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
100	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
101	C₃×C₂²⋊C₈	—	2	1	no	—
102	C₃×C₄×C₈	—	2	1	no	—
103	C₂⁴×C₅	—	2	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	4	4	no	—
110	C₂×C₅×D₄	—	4	4	no	—
111	C₂×C₅×D₄	—	4	2	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
114	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
117	C₅×M₁₆	—	4	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
122	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
123	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
125	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
126	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
127	#331	C₂×C₃×C₅	1	4	yes	complemented
128	C₂²×C₃×C₅	—	2	1	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	—	4	4	no	—
131	C₂²×C₃×C₅	—	4	4	no	—
132	C₂²×C₃×C₅	—	4	4	no	—
133	C₂²×C₃×C₅	—	8	8	no	—
134	C₂²×C₃×C₅	#102	1	2	yes	—
135	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₃×C₄×C₅	—	2	1	no	—
137	C₃×C₄×C₅	—	2	1	no	—
138	C₃×C₄×C₅	#100	1	2	yes	—
139	C₃×C₄×C₅	#102	1	2	yes	—
140	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
141	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
142	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
143	C₂⁴×C₃	—	2	2	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	2	no	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	—	4	4	no	—
150	C₂×C₃×D₄	—	4	4	no	—
151	C₂×C₃×D₄	—	4	2	no	—
152	C₂×C₃×D₄	—	4	2	no	—
153	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
157	C₃×M₁₆	—	4	2	no	—
158	C₂×C₃×C₈	—	2	2	no	—
159	C₂×C₃×C₈	—	2	2	no	—
160	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
161	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
162	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
163	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
164	C₂³×C₅	—	2	4	no	—
165	C₂³×C₅	—	4	4	no	—
166	C₂³×C₅	—	4	4	no	—
167	C₂³×C₅	—	4	4	no	—
168	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
169	C₅×D₄	—	4	4	no	—
170	C₅×D₄	—	4	4	no	—
171	C₅×D₄	—	4	4	no	—
172	C₅×D₄	—	4	4	no	—
173	C₅×D₄	—	4	2	no	—
174	C₅×D₄	—	4	2	no	—
175	C₅×D₄	—	4	4	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₃×D₈	1	2	yes	—
182	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
183	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
186	C₅×C₈	—	4	2	no	—
187	C₅×C₈	—	4	2	no	—
188	C₂²×D₄	—	2	1	no	—
189	C₂²×D₄	—	2	1	no	—
190	C₂²×D₄	C₃×C₄×C₅	1	2	yes	—
191	C₂×M₁₆	—	2	1	no	—
192	#127	—	2	1	no	—
193	#127	—	2	1	no	—
194	#127	C₃×C₄×C₅	1	2	yes	—
195	#127	C₂²×C₃×C₅	1	2	yes	—
196	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₄⋊C₈	—	2	1	no	—
198	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
199	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
200	C₂²⋊C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₂×C₃×C₅	—	2	2	no	—
203	C₂×C₃×C₅	—	8	4	no	—
204	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
206	C₂×C₃×C₅	#418	1	1	yes	characteristic
207	C₂³×C₃	—	2	4	no	—
208	C₂³×C₃	—	4	4	no	—
209	C₂³×C₃	—	4	4	no	—
210	C₂³×C₃	—	4	4	no	—
211	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
212	C₃×D₄	—	4	4	no	—
213	C₃×D₄	—	4	4	no	—
214	C₃×D₄	—	4	2	no	—
215	C₃×D₄	—	4	2	no	—
216	C₃×D₄	—	4	4	no	—
217	C₃×D₄	—	4	4	no	—
218	C₃×D₄	—	4	4	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
225	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
226	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
229	C₃×C₈	—	4	2	no	—
230	C₃×C₈	—	4	2	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	4	4	no	—
234	C₂²×C₅	—	4	4	no	—
235	C₂²×C₅	—	4	4	no	—
236	C₂²×C₅	—	8	8	no	—
237	C₂²×C₅	C₃×#102	1	2	yes	—
238	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	C₃×#100	1	2	yes	—
242	C₄×C₅	C₃×#102	1	2	yes	—
243	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
244	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
245	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
246	C₂⁴	—	2	2	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
257	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
258	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
260	M₁₆	—	4	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
264	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
265	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
266	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₃×C₅	#1545	1	1	yes	characteristic, direct product factor, Hall
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	4	4	no	—
271	C₂²×C₃	—	4	4	no	—
272	C₂²×C₃	—	4	4	no	—
273	C₂²×C₃	—	8	8	no	—
274	C₂²×C₃	C₅×#102	1	2	yes	—
275	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
276	C₃×C₄	—	2	1	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	C₅×#100	1	2	yes	—
279	C₃×C₄	C₅×#102	1	2	yes	—
280	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
281	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
282	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
283	C₂×C₅	—	2	2	no	—
284	C₂×C₅	—	8	4	no	—
285	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
286	C₂×C₅	C₂×C₃×#102	1	1	yes	characteristic
287	C₂×C₅	C₃×#418	1	1	yes	characteristic
288	C₂³	—	2	4	no	—
289	C₂³	—	4	4	no	—
290	C₂³	—	4	4	no	—
291	C₂³	—	4	4	no	—
292	C₂³	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
293	D₄	—	4	4	no	—
294	D₄	—	4	4	no	—
295	D₄	—	4	2	no	—
296	D₄	—	4	2	no	—
297	D₄	—	4	4	no	—
298	D₄	—	4	4	no	—
299	D₄	—	4	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄	C₃×C₅×D₈	1	2	yes	—
306	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
307	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
308	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
309	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
310	C₈	—	4	2	no	—
311	C₈	—	4	2	no	—
312	C₂×C₃	—	2	2	no	—
313	C₂×C₃	—	8	4	no	—
314	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
315	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
316	C₂×C₃	C₅×#418	1	1	yes	characteristic
317	C₅	C₃×#1545	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	8	8	no	—
324	C₂²	C₃×C₅×#102	1	2	yes	—
325	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	C₃×C₅×#100	1	2	yes	—
329	C₄	C₃×C₅×#102	1	2	yes	—
330	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
331	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
332	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
333	C₃	C₅×#1545	1	1	yes	characteristic, direct product factor, Sylow
334	C₂	—	2	2	no	—
335	C₂	—	8	4	no	—
336	C₂	C₂×C₃×C₅×#100	1	1	yes	characteristic
337	C₂	C₂×C₃×C₅×#102	1	1	yes	characteristic
338	C₂	C₃×C₅×#418	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₃×C₅×#423	C₂	semidirect
4. C₃×C₅×#331	C₂	semidirect
5. C₅×#1545	C₃	direct (N × H)
16. C₃×C₅×C₄⋊C₈	C₂²	semidirect
17. C₃×C₅×C₄⋊C₈	C₂²	semidirect
20. C₃×#1545	C₅	direct (N × H)
22. C₅×#431	C₂×C₃	semidirect
23. C₅×#423	C₂×C₃	semidirect
24. C₅×#331	C₂×C₃	semidirect
47. C₃×#431	C₂×C₅	semidirect
48. C₃×#423	C₂×C₅	semidirect
49. C₃×#331	C₂×C₅	semidirect
60. C₅×C₄⋊C₈	C₂²×C₃	semidirect
61. C₅×C₄⋊C₈	C₂²×C₃	semidirect
64. #1545	C₃×C₅	direct (N × H)
99. C₃×C₄⋊C₈	C₂²×C₅	semidirect
100. C₃×C₄⋊C₈	C₂²×C₅	semidirect
125. #431	C₂×C₃×C₅	semidirect
126. #423	C₂×C₃×C₅	semidirect
127. #331	C₂×C₃×C₅	semidirect
198. C₄⋊C₈	C₂²×C₃×C₅	semidirect
199. C₄⋊C₈	C₂²×C₃×C₅	semidirect
267. C₃×C₅	#1545	direct (N × H)
317. C₅	C₃×#1545	direct (N × H)
333. C₃	C₅×#1545	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×#127	2
C₃×C₅×#431	2
C₃×C₅×#423	2
C₃×C₅×#331	2
C₅×#1545	3
C₃×#1545	5

Subgroups — C3×C5×#1545 #14274579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1545 #14274579