Subgroups — C₃×C₅×#2001 #14275035

Order 1920.

784 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	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2001	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
10	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
14	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
18	C₃×C₅×#103	—	2	4	no	—
19	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
20	C₃×#2001	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
23	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
24	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
25	C₅×#340	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
27	C₂×C₃×C₅×Q₈	—	2	2	no	—
28	C₂×C₃×C₅×Q₈	—	2	2	no	—
29	C₂×C₃×C₅×Q₈	—	2	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×Q₁₆	—	2	8	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
46	C₃×C₅×C₄⋊C₄	—	2	8	no	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
51	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
52	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
53	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
54	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
56	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₅×Q₁₆	—	2	4	no	—
58	C₂×C₅×Q₁₆	—	2	2	no	—
59	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₅×C₂²⋊Q₈	—	2	4	no	—
62	C₅×C₂²⋊Q₈	—	2	4	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₅×#103	—	2	4	no	—
67	C₅×C₂²⋊C₈	—	2	2	no	—
68	#2001	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	—	2	1	no	—
71	C₂³×C₃×C₅	—	2	1	no	—
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	Q₁₆	1	2	yes	complemented
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	2	4	no	—
76	C₃×C₅×Q₈	—	2	4	no	—
77	C₃×C₅×Q₈	—	4	2	no	—
78	C₃×C₅×Q₈	—	4	2	no	—
79	C₂×C₃×C₄×C₅	—	2	4	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	4	2	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
94	C₃×C₅×C₈	—	2	2	no	—
95	C₃×C₅×C₈	—	4	1	no	—
96	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
97	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
98	C₂×C₃×Q₁₆	—	2	4	no	—
99	C₂×C₃×Q₁₆	—	2	2	no	—
100	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
101	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
102	C₃×C₂²⋊Q₈	—	2	4	no	—
103	C₃×C₂²⋊Q₈	—	2	4	no	—
104	C₂×C₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
107	C₃×#103	—	2	4	no	—
108	C₃×C₂²⋊C₈	—	2	2	no	—
109	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₅×Q₁₆	—	2	8	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	8	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
132	C₅×C₂²⋊C₄	—	2	8	no	—
133	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
135	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
136	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
137	#340	C₂×C₃×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×C₅	—	2	4	no	—
139	C₂²×C₃×C₅	—	2	2	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	—	4	1	no	—
143	C₂²×C₃×C₅	#120	1	2	yes	—
144	C₂²×C₃×C₅	#121	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
146	C₂²×C₃×C₅	#135	1	1	yes	characteristic
147	C₂²×C₃×C₅	#137	1	2	yes	—
148	C₃×C₄×C₅	—	4	1	no	—
149	C₃×C₄×C₅	—	4	4	no	—
150	C₃×C₄×C₅	—	4	4	no	—
151	C₃×C₄×C₅	#120	1	1	yes	characteristic
152	C₃×C₄×C₅	#121	1	2	yes	—
153	C₃×C₄×C₅	#127	1	1	yes	characteristic
154	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
155	C₂×C₃×Q₈	—	2	2	no	—
156	C₂×C₃×Q₈	—	2	2	no	—
157	C₂×C₃×Q₈	—	2	2	no	—
158	C₂×C₃×Q₈	—	2	2	no	—
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
161	C₂²×C₃×C₄	—	2	2	no	—
162	C₂²×C₃×C₄	—	2	2	no	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₃×Q₁₆	—	2	8	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
174	C₃×C₄⋊C₄	—	2	8	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
177	C₃×C₂²⋊C₄	—	2	8	no	—
178	C₂³×C₅	—	2	2	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	1	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	C₃×Q₁₆	1	2	yes	complemented
183	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₅×Q₈	—	2	4	no	—
185	C₅×Q₈	—	2	4	no	—
186	C₅×Q₈	—	4	2	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
203	C₅×C₈	—	2	2	no	—
204	C₅×C₈	—	4	1	no	—
205	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
206	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂×Q₁₆	—	2	4	no	—
208	C₂×Q₁₆	—	2	2	no	—
209	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂²⋊Q₈	—	2	4	no	—
212	C₂²⋊Q₈	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	#103	—	2	4	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	C₂×C₃×C₅	—	4	2	no	—
219	C₂×C₃×C₅	#392	1	1	yes	characteristic
220	C₂×C₃×C₅	#451	1	2	yes	—
221	C₂×C₃×C₅	#452	1	2	yes	—
222	C₂×C₃×C₅	#467	1	1	yes	characteristic
223	C₂×C₃×C₅	#470	1	1	yes	characteristic
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	2	1	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	C₅×Q₁₆	1	2	yes	complemented
229	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	2	4	no	—
232	C₃×Q₈	—	4	2	no	—
233	C₃×Q₈	—	4	2	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
248	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
249	C₃×C₈	—	2	2	no	—
250	C₃×C₈	—	4	1	no	—
251	C₂²×C₅	—	2	4	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	4	1	no	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	4	1	no	—
256	C₂²×C₅	C₃×#120	1	2	yes	—
257	C₂²×C₅	C₃×#121	1	1	yes	characteristic
258	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
259	C₂²×C₅	C₃×#135	1	1	yes	characteristic
260	C₂²×C₅	C₃×#137	1	2	yes	—
261	C₄×C₅	—	4	1	no	—
262	C₄×C₅	—	4	4	no	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	C₃×#120	1	1	yes	characteristic
265	C₄×C₅	C₃×#121	1	2	yes	—
266	C₄×C₅	C₃×#127	1	1	yes	characteristic
267	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
282	Q₁₆	—	2	8	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
287	C₄⋊C₄	—	2	8	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
290	C₂²⋊C₄	—	2	8	no	—
291	C₃×C₅	#2001	1	1	yes	characteristic, direct product factor, Hall
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	4	1	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	1	no	—
297	C₂²×C₃	C₅×#120	1	2	yes	—
298	C₂²×C₃	C₅×#121	1	1	yes	characteristic
299	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
300	C₂²×C₃	C₅×#135	1	1	yes	characteristic
301	C₂²×C₃	C₅×#137	1	2	yes	—
302	C₃×C₄	—	4	1	no	—
303	C₃×C₄	—	4	4	no	—
304	C₃×C₄	—	4	4	no	—
305	C₃×C₄	C₅×#120	1	1	yes	characteristic
306	C₃×C₄	C₅×#121	1	2	yes	—
307	C₃×C₄	C₅×#127	1	1	yes	characteristic
308	C₂×C₅	—	4	2	no	—
309	C₂×C₅	C₃×#392	1	1	yes	characteristic
310	C₂×C₅	C₃×#451	1	2	yes	—
311	C₂×C₅	C₃×#452	1	2	yes	—
312	C₂×C₅	C₃×#467	1	1	yes	characteristic
313	C₂×C₅	C₃×#470	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	2	no	—
318	C₂³	C₃×C₅×Q₁₆	1	2	yes	complemented
319	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	2	4	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
336	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
338	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	4	1	no	—
341	C₂×C₃	—	4	2	no	—
342	C₂×C₃	C₅×#392	1	1	yes	characteristic
343	C₂×C₃	C₅×#451	1	2	yes	—
344	C₂×C₃	C₅×#452	1	2	yes	—
345	C₂×C₃	C₅×#467	1	1	yes	characteristic
346	C₂×C₃	C₅×#470	1	1	yes	characteristic
347	C₅	C₃×#2001	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²	—	2	4	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	C₃×C₅×#120	1	2	yes	—
354	C₂²	C₃×C₅×#121	1	1	yes	characteristic
355	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
356	C₂²	C₃×C₅×#135	1	1	yes	characteristic
357	C₂²	C₃×C₅×#137	1	2	yes	—
358	C₄	—	4	4	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	4	no	—
361	C₄	C₃×C₅×#120	1	1	yes	characteristic
362	C₄	C₃×C₅×#121	1	2	yes	—
363	C₄	C₃×C₅×#127	1	1	yes	characteristic
364	C₃	C₅×#2001	1	1	yes	characteristic, direct product factor, Sylow
365	C₂	—	4	2	no	—
366	C₂	C₃×C₅×#392	1	1	yes	characteristic
367	C₂	C₃×C₅×#451	1	2	yes	—
368	C₂	C₃×C₅×#452	1	2	yes	—
369	C₂	C₃×C₅×#467	1	1	yes	characteristic
370	C₂	C₃×C₅×#470	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂⁴×C₃×C₅	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₂×C₃×C₅×#103	C₂	semidirect
5. C₃×C₅×#340	C₂	semidirect
6. C₅×#2001	C₃	direct (N × H)
20. C₃×#2001	C₅	direct (N × H)
21. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
23. C₂×C₅×#103	C₂×C₃	semidirect
25. C₅×#340	C₂×C₃	semidirect
50. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
52. C₂×C₃×#103	C₂×C₅	semidirect
54. C₃×#340	C₂×C₅	semidirect
68. #2001	C₃×C₅	direct (N × H)
73. C₂³×C₃×C₅	Q₁₆	semidirect
133. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
135. C₂×#103	C₂×C₃×C₅	semidirect
137. #340	C₂×C₃×C₅	semidirect
182. C₂³×C₅	C₃×Q₁₆	semidirect
228. C₂³×C₃	C₅×Q₁₆	semidirect
291. C₃×C₅	#2001	direct (N × H)
318. C₂³	C₃×C₅×Q₁₆	semidirect
347. C₅	C₃×#2001	direct (N × H)
364. C₃	C₅×#2001	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×C₂²⋊Q₈	2
C₂×C₃×C₅×#103	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₅×#340	2
C₅×#2001	3
C₃×#2001	5

Subgroups — C3×C5×#2001 #14275035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2001 #14275035