Subgroups — C₅×#69645 #14304708

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
4	C₅×#4928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1936	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₅×#832	—	2	2	no	—
20	C₅×#832	C₄	1	4	yes	complemented
21	C₅×C₃⋊#95	—	2	1	no	—
22	C₅×#803	—	2	2	no	—
23	#69645	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#102	—	3	1	no	—
25	C₂×C₅×#102	—	3	1	no	—
26	C₂×C₅×#97	—	3	1	no	—
27	C₅×#390	D₃	1	1	yes	characteristic
28	C₅×#389	—	3	1	no	—
29	C₅×#340	—	3	1	no	—
30	C₅×#340	—	3	1	no	—
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
47	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
54	C₅×Dic₃⋊C₄	—	4	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
61	C₃×#390	C₂×C₅	1	1	yes	characteristic
62	C₂×#832	C₂×C₅	1	1	yes	characteristic
63	C₂×#832	C₂×C₅	1	1	yes	characteristic
64	#4928	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
66	#4529	C₂×C₅	1	1	yes	characteristic, complemented
67	#4529	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	—	3	1	no	—
71	C₂×C₅×C₄⋊C₄	—	3	1	no	—
72	C₂×C₅×C₄⋊C₄	—	3	1	no	—
73	C₂×C₅×C₄⋊C₄	—	6	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
78	C₅×#102	—	3	4	no	—
79	C₅×#102	—	6	2	no	—
80	C₅×#97	—	6	2	no	—
81	C₅×#95	—	6	1	no	—
82	#1936	—	3	1	no	Sylow
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	—	4	1	no	—
85	C₂³×C₃×C₅	—	4	1	no	—
86	C₂³×C₃×C₅	—	4	1	no	—
87	C₂³×C₃×C₅	—	4	1	no	—
88	C₂³×C₃×C₅	—	4	1	no	—
89	C₂³×C₃×C₅	—	4	1	no	—
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₃×C₅×D₄	—	2	2	no	—
92	C₃×C₅×D₄	—	2	2	no	—
93	C₃×C₅×D₄	—	4	1	no	—
94	C₃×C₅×D₄	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₂×C₅×Dic₃	—	4	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₅×C₃⋊C₈	—	2	2	no	—
117	C₅×C₃⋊C₈	—	2	2	no	—
118	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂×Dic₃⋊C₄	—	2	1	no	—
126	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
128	#832	—	2	2	no	—
129	#832	C₄×C₅	1	4	yes	complemented
130	C₃⋊#95	—	2	1	no	—
131	#803	—	2	2	no	—
132	C₂⁴×C₅	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	6	1	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	#67	1	1	yes	characteristic
143	C₂²×C₄×C₅	#67	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	3	2	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	—	6	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	3	2	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₄⋊C₄	—	12	2	no	—
158	C₅×C₂²⋊C₄	—	4	2	no	—
159	C₅×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₂×#102	—	3	1	no	—
163	C₂×#102	—	3	1	no	—
164	C₂×#97	—	3	1	no	—
165	#390	C₅×D₃	1	1	yes	characteristic
166	#389	—	3	1	no	—
167	#340	—	3	1	no	—
168	#340	—	3	1	no	—
169	C₂²×C₃×C₅	—	4	2	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	8	1	no	—
173	C₂²×C₃×C₅	—	8	1	no	—
174	C₂²×C₃×C₅	—	8	1	no	—
175	C₂²×C₃×C₅	—	8	1	no	—
176	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	#121	1	1	yes	characteristic
178	C₂²×C₃×C₅	#124	1	1	yes	characteristic
179	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂²×C₃×C₅	#137	1	1	yes	characteristic
183	C₃×C₄×C₅	—	4	1	no	—
184	C₃×C₄×C₅	—	4	1	no	—
185	C₃×C₄×C₅	—	8	1	no	—
186	C₃×C₄×C₅	#117	1	1	yes	characteristic
187	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	#123	1	1	yes	characteristic
189	C₃×C₄×C₅	#126	1	1	yes	characteristic
190	C₅×Dic₃	—	4	2	no	—
191	C₅×Dic₃	—	8	1	no	—
192	C₂⁴×C₃	—	2	1	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	—	2	1	no	—
198	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×Dic₃	—	2	1	no	—
204	C₂²×Dic₃	—	2	1	no	—
205	C₃×C₄⋊C₄	—	2	1	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₂²⋊C₄	—	4	2	no	—
208	C₃×C₂²⋊C₄	—	4	2	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	—	2	1	no	—
211	C₄⋊Dic₃	—	2	1	no	—
212	C₄⋊Dic₃	—	2	1	no	—
213	C₄⋊Dic₃	—	2	1	no	—
214	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
215	Dic₃⋊C₄	—	4	2	no	—
216	C₂×C₃⋊C₈	—	2	1	no	—
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	2	1	no	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	4	1	no	—
224	C₂³×C₅	—	4	1	no	—
225	C₂³×C₅	—	4	1	no	—
226	C₂³×C₅	—	4	1	no	—
227	C₂³×C₅	—	4	1	no	—
228	C₂³×C₅	—	4	1	no	—
229	C₂³×C₅	C₂×#67	1	1	yes	characteristic
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	4	1	no	—
233	C₅×D₄	—	4	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	12	1	no	—
245	C₂×C₄×C₅	—	12	1	no	—
246	C₂×C₄×C₅	—	12	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	—	12	1	no	—
249	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
250	C₂×C₄×C₅	#235	1	1	yes	characteristic
251	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	#237	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	1	yes	characteristic
254	C₂×C₄×C₅	#237	1	1	yes	characteristic
255	C₅×C₈	—	6	2	no	—
256	C₅×C₈	—	6	2	no	—
257	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
258	C₂²×C₈	—	3	1	no	—
259	C₂²×C₈	—	3	1	no	—
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₄⋊C₄	—	3	1	no	—
262	C₂×C₄⋊C₄	—	6	1	no	—
263	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
267	#102	—	3	4	no	—
268	#102	—	6	2	no	—
269	#97	—	6	2	no	—
270	#95	—	6	1	no	—
271	C₂×C₃×C₅	—	8	2	no	—
272	C₂×C₃×C₅	#388	1	1	yes	characteristic
273	C₂×C₃×C₅	#440	1	1	yes	characteristic
274	C₂×C₃×C₅	#442	1	1	yes	characteristic
275	C₂×C₃×C₅	#468	1	1	yes	characteristic
276	C₂×C₃×C₅	#469	1	1	yes	characteristic
277	C₂×C₃×C₅	#489	1	1	yes	characteristic
278	C₂×C₃×C₅	#490	1	1	yes	characteristic
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	4	1	no	—
281	C₂³×C₃	—	4	1	no	—
282	C₂³×C₃	—	4	1	no	—
283	C₂³×C₃	—	4	1	no	—
284	C₂³×C₃	—	4	1	no	—
285	C₂³×C₃	—	4	1	no	—
286	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	4	1	no	—
290	C₃×D₄	—	4	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	4	1	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	4	1	no	—
308	C₂×Dic₃	—	4	1	no	—
309	C₂×Dic₃	—	4	1	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₃⋊C₈	—	2	2	no	—
313	C₃⋊C₈	—	2	2	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	2	no	—
317	C₂²×C₅	—	8	1	no	—
318	C₂²×C₅	—	8	1	no	—
319	C₂²×C₅	—	8	1	no	—
320	C₂²×C₅	—	8	1	no	—
321	C₂²×C₅	C₄×#67	1	1	yes	characteristic
322	C₂²×C₅	#932	1	1	yes	characteristic
323	C₂²×C₅	#932	1	1	yes	characteristic
324	C₂²×C₅	#936	1	1	yes	characteristic
325	C₂²×C₅	#939	1	1	yes	characteristic
326	C₂²×C₅	#949	1	1	yes	characteristic
327	C₂²×C₅	#951	1	1	yes	characteristic
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	8	1	no	—
331	C₄×C₅	—	12	2	no	—
332	C₄×C₅	—	24	1	no	—
333	C₄×C₅	#877	1	1	yes	characteristic
334	C₄×C₅	#879	1	1	yes	characteristic
335	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
336	C₄×C₅	#883	1	1	yes	characteristic
337	C₂⁴	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	C₅×#67	1	1	yes	characteristic
348	C₂²×C₄	C₅×#67	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₂×C₈	—	3	2	no	—
351	C₂×C₈	—	3	2	no	—
352	C₂×C₈	—	6	1	no	—
353	C₂×C₈	—	6	1	no	—
354	C₂×C₈	—	6	1	no	—
355	C₂×C₈	—	6	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₄⋊C₄	—	6	1	no	—
362	C₄⋊C₄	—	12	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₃×C₅	#1936	1	1	yes	characteristic, complemented, Hall
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	—	8	1	no	—
372	C₂²×C₃	—	8	1	no	—
373	C₂²×C₃	—	8	1	no	—
374	C₂²×C₃	—	8	1	no	—
375	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₃	C₅×#121	1	1	yes	characteristic
377	C₂²×C₃	C₅×#124	1	1	yes	characteristic
378	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₂²×C₃	C₅×#137	1	1	yes	characteristic
382	C₃×C₄	—	4	1	no	—
383	C₃×C₄	—	4	1	no	—
384	C₃×C₄	—	8	1	no	—
385	C₃×C₄	C₅×#117	1	1	yes	characteristic
386	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
387	C₃×C₄	C₅×#123	1	1	yes	characteristic
388	C₃×C₄	C₅×#126	1	1	yes	characteristic
389	Dic₃	—	4	2	no	—
390	Dic₃	—	8	1	no	—
391	C₂×C₅	—	8	2	no	—
392	C₂×C₅	#4945	1	1	yes	characteristic
393	C₂×C₅	#5014	1	1	yes	characteristic
394	C₂×C₅	#5018	1	1	yes	characteristic
395	C₂×C₅	#5039	1	1	yes	characteristic
396	C₂×C₅	#5042	1	1	yes	characteristic
397	C₂×C₅	#5055	1	1	yes	characteristic
398	C₂×C₅	#5071	1	1	yes	characteristic
399	C₂³	—	2	2	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	C₂×C₅×#67	1	1	yes	characteristic
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	6	2	no	—
421	C₂×C₄	—	12	1	no	—
422	C₂×C₄	—	12	1	no	—
423	C₂×C₄	—	12	1	no	—
424	C₂×C₄	—	12	1	no	—
425	C₂×C₄	—	12	1	no	—
426	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
427	C₂×C₄	C₅×#235	1	1	yes	characteristic
428	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
429	C₂×C₄	C₅×#237	1	1	yes	characteristic
430	C₂×C₄	C₅×#237	1	1	yes	characteristic
431	C₂×C₄	C₅×#237	1	1	yes	characteristic
432	C₈	—	6	2	no	—
433	C₈	—	6	2	no	—
434	C₂×C₃	—	8	2	no	—
435	C₂×C₃	C₅×#388	1	1	yes	characteristic
436	C₂×C₃	C₅×#440	1	1	yes	characteristic
437	C₂×C₃	C₅×#442	1	1	yes	characteristic
438	C₂×C₃	C₅×#468	1	1	yes	characteristic
439	C₂×C₃	C₅×#469	1	1	yes	characteristic
440	C₂×C₃	C₅×#489	1	1	yes	characteristic
441	C₂×C₃	C₅×#490	1	1	yes	characteristic
442	C₅	#69645	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₄×C₅×#67	1	1	yes	characteristic
451	C₂²	C₅×#932	1	1	yes	characteristic
452	C₂²	C₅×#932	1	1	yes	characteristic
453	C₂²	C₅×#936	1	1	yes	characteristic
454	C₂²	C₅×#939	1	1	yes	characteristic
455	C₂²	C₅×#949	1	1	yes	characteristic
456	C₂²	C₅×#951	1	1	yes	characteristic
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	12	2	no	—
461	C₄	—	24	1	no	—
462	C₄	C₅×#877	1	1	yes	characteristic
463	C₄	C₅×#879	1	1	yes	characteristic
464	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
465	C₄	C₅×#883	1	1	yes	characteristic
466	C₃	C₅×#1936	1	1	yes	characteristic, complemented, Sylow
467	C₂	—	8	2	no	—
468	C₂	C₅×#4945	1	1	yes	characteristic
469	C₂	C₅×#5014	1	1	yes	characteristic
470	C₂	C₅×#5018	1	1	yes	characteristic
471	C₂	C₅×#5039	1	1	yes	characteristic
472	C₂	C₅×#5042	1	1	yes	characteristic
473	C₂	C₅×#5055	1	1	yes	characteristic
474	C₂	C₅×#5071	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₅×#1936
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
4. C₅×#4928	C₂	semidirect
5. C₂×C₅×#803	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. C₅×#4529	C₂	semidirect
20. C₅×#832	C₄	semidirect
23. #69645	C₅	direct (N × H)
64. #4928	C₂×C₅	semidirect
65. C₂×#803	C₂×C₅	semidirect
66. #4529	C₂×C₅	semidirect
67. #4529	C₂×C₅	semidirect
129. #832	C₄×C₅	semidirect
367. C₃×C₅	#1936	semidirect
442. C₅	#69645	direct (N × H)
466. C₃	C₅×#1936	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#390	2
C₂×C₅×#832	2
C₅×#4928	2
C₂×C₅×#803	2
C₅×#4529	2
C₅×#1936	3
#69645	5

Subgroups — C5×#69645 #14304708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69645 #14304708