Subgroups — C₃×C₅×#2071 #14275105

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal
2	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#340	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2071	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#102	—	2	4	no	—
17	C₃×#2071	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₅×#102	C₂×C₃	1	2	yes	—
19	C₅×#390	C₂×C₃	1	1	yes	characteristic
20	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
21	C₅×#340	C₂×C₃	1	2	yes	complemented
22	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂⁴×C₃×C₅	—	2	1	no	—
24	C₂×C₃×C₅×D₄	—	2	2	no	—
25	C₂×C₃×C₅×D₄	—	2	2	no	—
26	C₂×C₃×C₅×D₄	—	2	1	no	—
27	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
28	C₂²×C₃×C₄×C₅	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₅×C₈	—	2	2	no	—
34	C₂×C₃×C₅×C₈	—	2	2	no	—
35	C₂×C₃×C₅×C₈	—	2	2	no	—
36	C₃×C₅×C₄⋊C₄	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	—	4	2	no	—
40	C₃×C₅×C₄⋊C₄	—	4	2	no	—
41	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
42	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
43	C₃×C₄²×C₅	—	2	2	no	—
44	C₂×C₃×#102	C₂×C₅	1	2	yes	—
45	C₃×#390	C₂×C₅	1	1	yes	characteristic
46	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
47	C₃×#340	C₂×C₅	1	2	yes	complemented
48	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₅×#102	—	2	4	no	—
59	#2071	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
60	C₂³×C₃×C₅	—	2	2	no	—
61	C₂³×C₃×C₅	—	4	1	no	—
62	C₂³×C₃×C₅	—	4	1	no	—
63	C₂³×C₃×C₅	—	4	1	no	—
64	C₂³×C₃×C₅	—	4	1	no	—
65	C₂³×C₃×C₅	—	4	1	no	—
66	C₂³×C₃×C₅	—	4	1	no	—
67	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
68	C₃×C₅×D₄	—	2	4	no	—
69	C₃×C₅×D₄	—	4	2	no	—
70	C₂×C₃×C₄×C₅	—	2	1	no	—
71	C₂×C₃×C₄×C₅	—	2	1	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	4	1	no	—
76	C₂×C₃×C₄×C₅	—	4	1	no	—
77	C₂×C₃×C₄×C₅	—	4	2	no	—
78	C₂×C₃×C₄×C₅	—	4	1	no	—
79	C₂×C₃×C₄×C₅	—	4	2	no	—
80	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
81	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	#41	1	2	yes	—
84	C₂×C₃×C₄×C₅	#41	1	2	yes	—
85	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
86	C₃×C₅×C₈	—	4	2	no	—
87	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
88	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
96	C₃×#102	—	2	4	no	—
97	C₂⁴×C₅	—	2	1	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	1	no	—
101	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₅×C₄⋊C₄	—	2	2	no	—
111	C₅×C₄⋊C₄	—	2	2	no	—
112	C₅×C₄⋊C₄	—	2	2	no	—
113	C₅×C₄⋊C₄	—	4	2	no	—
114	C₅×C₄⋊C₄	—	4	2	no	—
115	C₅×C₂²⋊C₄	—	4	2	no	—
116	C₅×C₂²⋊C₄	—	4	2	no	—
117	C₄²×C₅	—	2	2	no	—
118	C₂×#102	C₂×C₃×C₅	1	2	yes	—
119	#390	C₂×C₃×C₅	1	1	yes	characteristic
120	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
121	#340	C₂×C₃×C₅	1	2	yes	complemented
122	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
123	C₂²×C₃×C₅	—	4	2	no	—
124	C₂²×C₃×C₅	—	4	2	no	—
125	C₂²×C₃×C₅	—	4	2	no	—
126	C₂²×C₃×C₅	—	8	1	no	—
127	C₂²×C₃×C₅	—	8	1	no	—
128	C₂²×C₃×C₅	—	8	1	no	—
129	C₂²×C₃×C₅	—	8	1	no	—
130	C₂²×C₃×C₅	#121	1	1	yes	characteristic
131	C₂²×C₃×C₅	#123	1	1	yes	characteristic
132	C₂²×C₃×C₅	#124	1	1	yes	characteristic
133	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
135	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂²×C₃×C₅	#137	1	1	yes	characteristic
137	C₃×C₄×C₅	—	2	2	no	—
138	C₃×C₄×C₅	—	2	2	no	—
139	C₃×C₄×C₅	—	8	2	no	—
140	C₃×C₄×C₅	—	8	1	no	—
141	C₃×C₄×C₅	#123	1	2	yes	—
142	C₃×C₄×C₅	#126	1	2	yes	—
143	C₂⁴×C₃	—	2	1	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	1	no	—
147	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₃×C₄⋊C₄	—	2	2	no	—
157	C₃×C₄⋊C₄	—	2	2	no	—
158	C₃×C₄⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₄	—	4	2	no	—
160	C₃×C₄⋊C₄	—	4	2	no	—
161	C₃×C₂²⋊C₄	—	4	2	no	—
162	C₃×C₂²⋊C₄	—	4	2	no	—
163	C₃×C₄²	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	—	4	1	no	—
166	C₂³×C₅	—	4	1	no	—
167	C₂³×C₅	—	4	1	no	—
168	C₂³×C₅	—	4	1	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
172	C₅×D₄	—	2	4	no	—
173	C₅×D₄	—	4	2	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	C₃×D₈	1	2	yes	—
185	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
186	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₃×#41	1	2	yes	—
188	C₂×C₄×C₅	C₃×#41	1	2	yes	—
189	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
190	C₅×C₈	—	4	2	no	—
191	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
197	C₂×C₂²⋊C₄	—	2	1	no	—
198	C₂×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
200	#102	—	2	4	no	—
201	C₂×C₃×C₅	—	8	2	no	—
202	C₂×C₃×C₅	#397	1	1	yes	characteristic
203	C₂×C₃×C₅	#459	1	1	yes	characteristic
204	C₂×C₃×C₅	#461	1	1	yes	characteristic
205	C₂×C₃×C₅	#480	1	1	yes	characteristic
206	C₂×C₃×C₅	#481	1	1	yes	characteristic
207	C₂×C₃×C₅	#486	1	1	yes	characteristic
208	C₂×C₃×C₅	#489	1	1	yes	characteristic
209	C₂³×C₃	—	2	2	no	—
210	C₂³×C₃	—	4	1	no	—
211	C₂³×C₃	—	4	1	no	—
212	C₂³×C₃	—	4	1	no	—
213	C₂³×C₃	—	4	1	no	—
214	C₂³×C₃	—	4	1	no	—
215	C₂³×C₃	—	4	1	no	—
216	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
217	C₃×D₄	—	2	4	no	—
218	C₃×D₄	—	4	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	4	1	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
230	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₅×#41	1	2	yes	—
233	C₂×C₃×C₄	C₅×#41	1	2	yes	—
234	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
235	C₃×C₈	—	4	2	no	—
236	C₂²×C₅	—	4	2	no	—
237	C₂²×C₅	—	4	2	no	—
238	C₂²×C₅	—	4	2	no	—
239	C₂²×C₅	—	8	1	no	—
240	C₂²×C₅	—	8	1	no	—
241	C₂²×C₅	—	8	1	no	—
242	C₂²×C₅	—	8	1	no	—
243	C₂²×C₅	C₃×#121	1	1	yes	characteristic
244	C₂²×C₅	C₃×#123	1	1	yes	characteristic
245	C₂²×C₅	C₃×#124	1	1	yes	characteristic
246	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
247	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
248	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₅	C₃×#137	1	1	yes	characteristic
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	2	2	no	—
252	C₄×C₅	—	8	2	no	—
253	C₄×C₅	—	8	1	no	—
254	C₄×C₅	C₃×#123	1	2	yes	—
255	C₄×C₅	C₃×#126	1	2	yes	—
256	C₂⁴	—	2	1	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	4	2	no	—
273	C₄⋊C₄	—	4	2	no	—
274	C₂²⋊C₄	—	4	2	no	—
275	C₂²⋊C₄	—	4	2	no	—
276	C₄²	—	2	2	no	—
277	C₃×C₅	#2071	1	1	yes	characteristic, direct product factor, Hall
278	C₂²×C₃	—	4	2	no	—
279	C₂²×C₃	—	4	2	no	—
280	C₂²×C₃	—	4	2	no	—
281	C₂²×C₃	—	8	1	no	—
282	C₂²×C₃	—	8	1	no	—
283	C₂²×C₃	—	8	1	no	—
284	C₂²×C₃	—	8	1	no	—
285	C₂²×C₃	C₅×#121	1	1	yes	characteristic
286	C₂²×C₃	C₅×#123	1	1	yes	characteristic
287	C₂²×C₃	C₅×#124	1	1	yes	characteristic
288	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
289	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
290	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₂²×C₃	C₅×#137	1	1	yes	characteristic
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	8	2	no	—
295	C₃×C₄	—	8	1	no	—
296	C₃×C₄	C₅×#123	1	2	yes	—
297	C₃×C₄	C₅×#126	1	2	yes	—
298	C₂×C₅	—	8	2	no	—
299	C₂×C₅	C₃×#397	1	1	yes	characteristic
300	C₂×C₅	C₃×#459	1	1	yes	characteristic
301	C₂×C₅	C₃×#461	1	1	yes	characteristic
302	C₂×C₅	C₃×#480	1	1	yes	characteristic
303	C₂×C₅	C₃×#481	1	1	yes	characteristic
304	C₂×C₅	C₃×#486	1	1	yes	characteristic
305	C₂×C₅	C₃×#489	1	1	yes	characteristic
306	C₂³	—	2	2	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
314	D₄	—	2	4	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	C₃×C₅×D₈	1	2	yes	—
327	C₂×C₄	C₃×C₅×SD₁₆	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	C₃×C₅×#41	1	2	yes	—
331	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
332	C₈	—	4	2	no	—
333	C₂×C₃	—	8	2	no	—
334	C₂×C₃	C₅×#397	1	1	yes	characteristic
335	C₂×C₃	C₅×#459	1	1	yes	characteristic
336	C₂×C₃	C₅×#461	1	1	yes	characteristic
337	C₂×C₃	C₅×#480	1	1	yes	characteristic
338	C₂×C₃	C₅×#481	1	1	yes	characteristic
339	C₂×C₃	C₅×#486	1	1	yes	characteristic
340	C₂×C₃	C₅×#489	1	1	yes	characteristic
341	C₅	C₃×#2071	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	8	1	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	1	no	—
349	C₂²	C₃×C₅×#121	1	1	yes	characteristic
350	C₂²	C₃×C₅×#123	1	1	yes	characteristic
351	C₂²	C₃×C₅×#124	1	1	yes	characteristic
352	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
353	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
354	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₂²	C₃×C₅×#137	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	1	no	—
360	C₄	C₃×C₅×#123	1	2	yes	—
361	C₄	C₃×C₅×#126	1	2	yes	—
362	C₃	C₅×#2071	1	1	yes	characteristic, direct product factor, Sylow
363	C₂	—	8	2	no	—
364	C₂	C₃×C₅×#397	1	1	yes	characteristic
365	C₂	C₃×C₅×#459	1	1	yes	characteristic
366	C₂	C₃×C₅×#461	1	1	yes	characteristic
367	C₂	C₃×C₅×#480	1	1	yes	characteristic
368	C₂	C₃×C₅×#481	1	1	yes	characteristic
369	C₂	C₃×C₅×#486	1	1	yes	characteristic
370	C₂	C₃×C₅×#489	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#384	C₂	semidirect
4. C₃×C₅×#340	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2071	C₃	direct (N × H)
17. C₃×#2071	C₅	direct (N × H)
20. C₅×#384	C₂×C₃	semidirect
21. C₅×#340	C₂×C₃	semidirect
22. C₅×#336	C₂×C₃	semidirect
46. C₃×#384	C₂×C₅	semidirect
47. C₃×#340	C₂×C₅	semidirect
48. C₃×#336	C₂×C₅	semidirect
59. #2071	C₃×C₅	direct (N × H)
120. #384	C₂×C₃×C₅	semidirect
121. #340	C₂×C₃×C₅	semidirect
122. #336	C₂×C₃×C₅	semidirect
277. C₃×C₅	#2071	direct (N × H)
341. C₅	C₃×#2071	direct (N × H)
362. C₃	C₅×#2071	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×#102	2
C₃×C₅×#390	2
C₃×C₅×#384	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#2071	3
C₃×#2071	5

Subgroups — C3×C5×#2071 #14275105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2071 #14275105