Subgroups — C₃×C₅×#3059 #14276093

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#536	C₂	1	2	yes	maximal
4	C₃×C₅×#470	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#467	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#419	C₂	1	2	yes	maximal, complemented
8	C₅×#3059	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₃×C₅×#131	—	2	4	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
20	C₃×C₅×#124	—	2	2	no	—
21	C₃×C₅×#123	—	2	4	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
23	C₃×C₅×#117	C₂²	1	2	yes	—
24	C₃×C₅×#107	C₂²	1	2	yes	—
25	C₃×C₅×#106	C₂²	1	2	yes	—
26	C₃×C₅×#103	C₂²	1	8	yes	—
27	C₃×#3059	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
30	C₅×#536	C₂×C₃	1	2	yes	—
31	C₅×#470	C₂×C₃	1	4	yes	complemented
32	C₅×#467	C₂×C₃	1	4	yes	complemented
33	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#419	C₂×C₃	1	2	yes	complemented
35	C₃×C₅×#41	—	2	2	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
43	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×Q₁₆	—	2	4	no	—
48	C₃×C₅×Q₁₆	—	2	4	no	—
49	C₃×C₅×M₁₆	—	2	2	no	—
50	C₃×C₅×M₁₆	—	2	4	no	—
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	—	2	8	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
60	C₃×C₄²×C₅	—	2	2	no	—
61	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
63	C₃×#536	C₂×C₅	1	2	yes	—
64	C₃×#470	C₂×C₅	1	4	yes	complemented
65	C₃×#467	C₂×C₅	1	4	yes	complemented
66	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#419	C₂×C₅	1	2	yes	complemented
68	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
70	C₂×C₅×Q₁₆	—	2	4	no	—
71	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
72	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
73	C₅×#131	—	2	4	no	—
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
76	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
77	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₅×C₄⋊Q₈	—	2	2	no	—
79	C₅×#124	—	2	2	no	—
80	C₅×#123	—	2	4	no	—
81	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
82	C₅×#117	C₂²×C₃	1	2	yes	—
83	C₅×#107	C₂²×C₃	1	2	yes	—
84	C₅×#106	C₂²×C₃	1	2	yes	—
85	C₅×#103	C₂²×C₃	1	8	yes	—
86	#3059	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
88	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
89	C₃×C₅×Q₈	—	2	2	no	—
90	C₃×C₅×Q₈	—	2	4	no	—
91	C₃×C₅×Q₈	—	2	4	no	—
92	C₃×C₅×Q₈	—	4	4	no	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	4	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₃×C₅×C₈	—	2	2	no	—
106	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
107	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
108	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
110	C₂×C₃×Q₁₆	—	2	4	no	—
111	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
112	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
113	C₃×#131	—	2	4	no	—
114	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
116	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	—	2	2	no	—
119	C₃×#124	—	2	2	no	—
120	C₃×#123	—	2	4	no	—
121	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
122	C₃×#117	C₂²×C₅	1	2	yes	—
123	C₃×#107	C₂²×C₅	1	2	yes	—
124	C₃×#106	C₂²×C₅	1	2	yes	—
125	C₃×#103	C₂²×C₅	1	8	yes	—
126	C₅×#41	—	2	2	no	—
127	C₅×#41	—	2	2	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	2	4	no	—
130	C₂×C₅×Q₈	—	2	4	no	—
131	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
132	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
133	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
134	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₅×Q₁₆	—	2	4	no	—
139	C₅×Q₁₆	—	2	4	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₅×M₁₆	—	2	4	no	—
142	C₂×C₅×C₈	—	2	4	no	—
143	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
144	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
145	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	8	no	—
148	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	8	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
153	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
154	#536	C₂×C₃×C₅	1	2	yes	—
155	#470	C₂×C₃×C₅	1	4	yes	complemented
156	#467	C₂×C₃×C₅	1	4	yes	complemented
157	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
158	#419	C₂×C₃×C₅	1	2	yes	complemented
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	4	no	—
162	C₂²×C₃×C₅	#121	1	2	yes	—
163	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	—	4	4	no	—
167	C₃×C₄×C₅	#121	1	2	yes	—
168	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
170	C₃×#41	—	2	2	no	—
171	C₃×#41	—	2	2	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	4	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
176	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
177	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
178	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₃×Q₁₆	—	2	4	no	—
183	C₃×Q₁₆	—	2	4	no	—
184	C₃×M₁₆	—	2	2	no	—
185	C₃×M₁₆	—	2	4	no	—
186	C₂×C₃×C₈	—	2	4	no	—
187	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
188	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
189	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
190	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
191	C₃×C₄⋊C₄	—	2	8	no	—
192	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
193	C₃×C₂²⋊C₄	—	2	2	no	—
194	C₃×C₂²⋊C₄	—	2	8	no	—
195	C₃×C₄²	—	2	2	no	—
196	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
198	C₅×Q₈	—	2	2	no	—
199	C₅×Q₈	—	2	4	no	—
200	C₅×Q₈	—	2	4	no	—
201	C₅×Q₈	—	4	4	no	—
202	C₅×D₄	—	2	4	no	—
203	C₅×D₄	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	4	4	no	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₃×#41	1	2	yes	—
213	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
216	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
217	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
219	C₂×Q₁₆	—	2	4	no	—
220	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
221	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
222	#131	—	2	4	no	—
223	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
225	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
226	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	2	no	—
228	#124	—	2	2	no	—
229	#123	—	2	4	no	—
230	C₂²⋊Q₈	C₂²×C₃×C₅	1	8	yes	—
231	#117	C₂²×C₃×C₅	1	2	yes	—
232	#107	C₂²×C₃×C₅	1	2	yes	—
233	#106	C₂²×C₃×C₅	1	2	yes	—
234	#103	C₂²×C₃×C₅	1	8	yes	—
235	C₂×C₃×C₅	—	2	2	no	—
236	C₂×C₃×C₅	—	4	2	no	—
237	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
238	C₂×C₃×C₅	#578	1	2	yes	—
239	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
240	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
241	C₃×Q₈	—	2	2	no	—
242	C₃×Q₈	—	2	4	no	—
243	C₃×Q₈	—	2	4	no	—
244	C₃×Q₈	—	4	4	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	4	4	no	—
252	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₅×#41	1	2	yes	—
256	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
257	C₃×C₈	—	2	2	no	—
258	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
259	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	2	4	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	C₃×#121	1	2	yes	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	4	4	no	—
267	C₄×C₅	—	4	4	no	—
268	C₄×C₅	C₃×#121	1	2	yes	—
269	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
277	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
278	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
279	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
282	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
283	Q₁₆	—	2	4	no	—
284	Q₁₆	—	2	4	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
289	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
290	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
291	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₄²	—	2	2	no	—
297	C₃×C₅	#3059	1	1	yes	characteristic, direct product factor, Hall
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	4	no	—
301	C₂²×C₃	C₅×#121	1	2	yes	—
302	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	4	4	no	—
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	C₅×#121	1	2	yes	—
307	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
309	C₂×C₅	—	2	2	no	—
310	C₂×C₅	—	4	2	no	—
311	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
312	C₂×C₅	C₃×#578	1	2	yes	—
313	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
314	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
315	Q₈	—	2	2	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	2	4	no	—
318	Q₈	—	4	4	no	—
319	D₄	—	2	4	no	—
320	D₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
327	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
328	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
329	C₂×C₄	C₃×C₅×#41	1	2	yes	—
330	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
331	C₈	—	2	2	no	—
332	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
333	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
334	C₂×C₃	—	2	2	no	—
335	C₂×C₃	—	4	2	no	—
336	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
337	C₂×C₃	C₅×#578	1	2	yes	—
338	C₅	C₃×#3059	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	C₃×C₅×#121	1	2	yes	—
343	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	4	4	no	—
346	C₄	—	4	4	no	—
347	C₄	C₃×C₅×#121	1	2	yes	—
348	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
349	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
350	C₃	C₅×#3059	1	1	yes	characteristic, direct product factor, Sylow
351	C₂	—	2	2	no	—
352	C₂	—	4	2	no	—
353	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
354	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#470	C₂	semidirect
5. C₃×C₅×#467	C₂	semidirect
6. C₃×C₅×#427	C₂	semidirect
7. C₃×C₅×#419	C₂	semidirect
8. C₅×#3059	C₃	direct (N × H)
27. C₃×#3059	C₅	direct (N × H)
28. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
31. C₅×#470	C₂×C₃	semidirect
32. C₅×#467	C₂×C₃	semidirect
33. C₅×#427	C₂×C₃	semidirect
34. C₅×#419	C₂×C₃	semidirect
61. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
64. C₃×#470	C₂×C₅	semidirect
65. C₃×#467	C₂×C₅	semidirect
66. C₃×#427	C₂×C₅	semidirect
67. C₃×#419	C₂×C₅	semidirect
86. #3059	C₃×C₅	direct (N × H)
152. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
155. #470	C₂×C₃×C₅	semidirect
156. #467	C₂×C₃×C₅	semidirect
157. #427	C₂×C₃×C₅	semidirect
158. #419	C₂×C₃×C₅	semidirect
297. C₃×C₅	#3059	direct (N × H)
338. C₅	C₃×#3059	direct (N × H)
350. C₃	C₅×#3059	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×Q₁₆	2
C₂×C₃×C₅×#131	2
C₃×C₅×#536	2
C₃×C₅×#470	2
C₃×C₅×#467	2
C₃×C₅×#427	2
C₃×C₅×#419	2
C₅×#3059	3
C₃×#3059	5

Subgroups — C3×C5×#3059 #14276093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3059 #14276093