Subgroups — C₅×#71640 #14282159

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#4926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4535	C₂	1	2	yes	maximal, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
6	C₅×#1488	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₅×D₄	—	2	1	no	—
11	C₃×C₄×C₅×D₄	—	2	1	no	—
12	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#830	—	2	1	no	—
19	C₅×#830	—	2	1	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
22	C₅×#803	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#71640	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	D₃	1	1	yes	characteristic
26	C₅×#432	—	3	1	no	—
27	C₅×#431	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
58	#4926	C₂×C₅	1	1	yes	characteristic, complemented
59	#4925	C₂×C₅	1	1	yes	characteristic, complemented
60	#4535	C₂×C₅	1	2	yes	complemented
61	D₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	Dic₃	1	1	yes	characteristic
63	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic
64	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
68	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
69	C₅×#117	—	2	1	no	—
70	C₅×#117	Dic₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	3	2	no	—
74	C₅×C₄⋊C₈	—	6	1	no	—
75	C₅×C₂²⋊C₈	—	6	1	no	—
76	C₅×C₂²⋊C₈	—	6	1	no	—
77	C₅×#97	—	6	1	no	—
78	C₄×C₅×C₈	—	3	2	no	—
79	#1488	—	3	1	no	Sylow
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	1	no	—
83	C₃×C₅×Q₈	M₁₆	1	2	yes	—
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	1	no	—
86	C₃×C₅×D₄	M₁₆	1	2	yes	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₅×C₃⋊C₈	—	4	2	no	—
104	C₅×C₃⋊C₈	—	4	2	no	—
105	C₂×C₃×#41	C₄×C₅	1	1	yes	characteristic
106	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
107	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	—	2	1	no	—
110	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
111	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
112	C₃×#117	—	2	1	no	—
113	C₃×#117	C₄×C₅	1	1	yes	characteristic
114	C₂×C₃×C₄²	—	2	1	no	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	#830	—	2	1	no	—
117	#830	—	2	1	no	—
118	C₄⋊(C₃⋊C₈)	—	2	1	no	—
119	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
120	#803	—	2	1	no	—
121	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	2	2	no	—
124	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	#67	1	1	yes	characteristic
132	C₂²×C₄×C₅	#67	1	1	yes	characteristic
133	C₂×C₅×C₈	—	6	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
138	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
139	C₅×C₂²⋊C₄	—	2	1	no	—
140	C₅×C₂²⋊C₄	—	2	1	no	—
141	C₅×C₂²⋊C₄	—	2	1	no	—
142	C₄²×C₅	—	2	1	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
146	C₄²×C₅	#67	1	1	yes	characteristic
147	C₄²×C₅	#67	1	1	yes	characteristic
148	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₄×#41	C₅×D₃	1	1	yes	characteristic
150	#432	—	3	1	no	—
151	#431	—	3	1	no	—
152	Q₈⋊C₈	—	3	2	no	—
153	D₄⋊C₈	—	3	2	no	—
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	4	1	no	—
159	C₂²×C₃×C₅	—	4	1	no	—
160	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
170	C₃×C₄×C₅	#135	1	2	yes	—
171	C₃×#41	—	2	2	no	—
172	C₃×#41	—	2	2	no	—
173	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	2	1	no	—
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
193	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
194	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
195	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
196	C₂×C₃⋊C₈	—	2	2	no	—
197	C₂×C₃⋊C₈	—	2	2	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	#217	1	1	yes	characteristic
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	#208	1	2	yes	—
202	C₅×D₄	—	2	4	no	—
203	C₅×D₄	—	2	1	no	—
204	C₅×D₄	#208	1	2	yes	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	#217	1	1	yes	characteristic
216	C₂×C₄×C₅	#217	1	1	yes	characteristic
217	C₂×C₄×C₅	#217	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	12	2	no	—
222	C₅×C₈	—	12	2	no	—
223	C₂×#41	C₅×Dic₃	1	1	yes	characteristic
224	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic
225	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
229	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
230	#117	—	2	1	no	—
231	#117	C₅×Dic₃	1	1	yes	characteristic
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
234	C₄⋊C₈	—	3	2	no	—
235	C₄⋊C₈	—	6	1	no	—
236	C₂²⋊C₈	—	6	1	no	—
237	C₂²⋊C₈	—	6	1	no	—
238	#97	—	6	1	no	—
239	C₄×C₈	—	3	2	no	—
240	C₂×C₃×C₅	—	4	1	no	—
241	C₂×C₃×C₅	—	4	2	no	—
242	C₂×C₃×C₅	#407	1	1	yes	characteristic
243	C₂×C₃×C₅	#416	1	1	yes	characteristic
244	C₂×C₃×C₅	#421	1	1	yes	characteristic
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₃×Q₈	—	2	1	no	—
248	C₃×Q₈	C₅×M₁₆	1	2	yes	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	1	no	—
251	C₃×D₄	C₅×M₁₆	1	2	yes	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₃⋊C₈	—	4	2	no	—
269	C₃⋊C₈	—	4	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	4	1	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	C₂×#217	1	1	yes	characteristic
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	C₂×#208	1	1	yes	characteristic
285	C₄×C₅	C₂×#208	1	1	yes	characteristic
286	C₄×C₅	#950	1	2	yes	—
287	#41	—	2	2	no	—
288	#41	—	2	2	no	—
289	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
296	C₂²×C₄	C₅×#67	1	1	yes	characteristic
297	C₂²×C₄	C₅×#67	1	1	yes	characteristic
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	—	6	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
303	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
311	C₄²	C₅×#67	1	1	yes	characteristic
312	C₄²	C₅×#67	1	1	yes	characteristic
313	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
314	C₃×C₅	#1488	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	4	1	no	—
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
330	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
331	C₃×C₄	C₅×#135	1	2	yes	—
332	C₂×C₅	—	4	1	no	—
333	C₂×C₅	—	4	2	no	—
334	C₂×C₅	#5207	1	1	yes	characteristic
335	C₂×C₅	#5233	1	1	yes	characteristic
336	C₂×C₅	#5236	1	1	yes	characteristic
337	C₂³	—	2	1	no	—
338	C₂³	C₅×#217	1	1	yes	characteristic
339	Q₈	—	2	1	no	—
340	Q₈	C₅×#208	1	2	yes	—
341	D₄	—	2	4	no	—
342	D₄	—	2	1	no	—
343	D₄	C₅×#208	1	2	yes	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₅×#217	1	1	yes	characteristic
355	C₂×C₄	C₅×#217	1	1	yes	characteristic
356	C₂×C₄	C₅×#217	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
360	C₈	—	12	2	no	—
361	C₈	—	12	2	no	—
362	C₂×C₃	—	4	1	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	C₅×#407	1	1	yes	characteristic
365	C₂×C₃	C₅×#416	1	1	yes	characteristic
366	C₂×C₃	C₅×#421	1	1	yes	characteristic
367	C₅	#71640	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	2	1	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	C₂×C₅×#217	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	C₂×C₅×#208	1	1	yes	characteristic
383	C₄	C₂×C₅×#208	1	1	yes	characteristic
384	C₄	C₅×#950	1	2	yes	—
385	C₃	C₅×#1488	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	4	1	no	—
387	C₂	—	4	2	no	—
388	C₂	C₅×#5207	1	1	yes	characteristic
389	C₂	C₅×#5233	1	1	yes	characteristic
390	C₂	C₅×#5236	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#1488
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#4926	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4535	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
24. #71640	C₅	direct (N × H)
58. #4926	C₂×C₅	semidirect
59. #4925	C₂×C₅	semidirect
60. #4535	C₂×C₅	semidirect
61. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
314. C₃×C₅	#1488	semidirect
367. C₅	#71640	direct (N × H)
385. C₃	C₅×#1488	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#4926	2
C₅×#4925	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1488	3
#71640	5

Subgroups — C5×#71640 #14282159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71640 #14282159