Subgroups — C₅×#68813 #14298493

Order 1920.

600 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	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#4987	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4551	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×#1825	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	—	2	1	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₅×#892	—	2	2	no	—
20	C₅×#892	C₄	1	4	yes	complemented
21	C₅×C₃⋊#95	—	2	1	no	—
22	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
23	#68813	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#117	—	3	1	no	—
25	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
26	C₅×#380	—	3	1	no	—
27	C₅×#340	—	3	1	no	—
28	C₅×#340	—	3	1	no	—
29	C₅×#340	—	3	1	no	—
30	C₅×#340	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	—	2	1	no	—
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
52	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
57	C₄×C₅×Dic₃	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×#892	C₂×C₅	1	1	yes	characteristic
62	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic
63	#4987	C₂×C₅	1	1	yes	characteristic
64	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
65	#4551	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	C₂³×C₄×C₅	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
71	C₅×#117	—	3	4	no	—
72	C₅×#117	—	6	2	no	—
73	C₂×C₅×C₄⋊C₄	—	3	1	no	—
74	C₂×C₅×C₄⋊C₄	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
78	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
79	C₂×C₄²×C₅	—	6	1	no	—
80	C₅×C₂²⋊C₈	—	6	2	no	—
81	C₅×#95	—	6	1	no	—
82	#1825	—	3	1	no	Sylow
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₅×D₃	—	2	1	no	—
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₂²×C₅×D₃	—	2	1	no	—
89	C₂²×C₅×D₃	—	2	1	no	—
90	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	4	1	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₂×C₅×Dic₃	—	4	1	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₄×Dic₃	—	2	1	no	—
127	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
128	#892	—	2	2	no	—
129	#892	C₄×C₅	1	4	yes	complemented
130	C₃⋊#95	—	2	1	no	—
131	(C₂×D₃)⋊C₈	—	2	2	no	—
132	C₂⁴×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	3	1	no	—
136	C₂²×C₄×C₅	—	3	2	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	—	6	1	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₂²×C₄×C₅	—	6	1	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	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	—	2	1	no	—
154	C₅×C₄⋊C₄	—	3	2	no	—
155	C₅×C₄⋊C₄	—	6	1	no	—
156	C₅×C₄⋊C₄	—	6	1	no	—
157	C₅×C₄⋊C₄	—	6	1	no	—
158	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
159	C₅×C₂²⋊C₄	—	6	4	no	—
160	C₅×C₂²⋊C₄	—	12	2	no	—
161	C₄²×C₅	—	6	4	no	—
162	C₂×#117	—	3	1	no	—
163	C₂×C₂²⋊C₈	—	3	1	no	—
164	#380	—	3	1	no	—
165	#340	—	3	1	no	—
166	#340	—	3	1	no	—
167	#340	—	3	1	no	—
168	#340	C₅×D₃	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	#123	1	1	yes	characteristic
171	C₂²×C₃×C₅	#123	1	1	yes	characteristic
172	C₂²×C₃×C₅	#135	1	1	yes	characteristic
173	C₂²×C₃×C₅	#135	1	1	yes	characteristic
174	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂²×C₃×C₅	#137	1	1	yes	characteristic
176	C₂×C₅×D₃	—	2	2	no	—
177	C₂×C₅×D₃	—	2	2	no	—
178	C₂×C₅×D₃	—	2	2	no	—
179	C₂×C₅×D₃	—	4	1	no	—
180	C₂×C₅×D₃	—	4	1	no	—
181	C₂×C₅×D₃	—	4	1	no	—
182	C₂×C₅×D₃	—	4	1	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	8	1	no	—
185	C₃×C₄×C₅	#117	1	1	yes	characteristic
186	C₃×C₄×C₅	#117	1	1	yes	characteristic
187	C₃×C₄×C₅	#123	1	1	yes	characteristic
188	C₃×C₄×C₅	#123	1	1	yes	characteristic
189	C₅×Dic₃	—	2	2	no	—
190	C₅×Dic₃	—	4	2	no	—
191	C₅×Dic₃	—	8	1	no	—
192	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×Dic₃	—	2	1	no	—
197	C₂²×Dic₃	—	2	1	no	—
198	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
199	C₂×C₄×D₃	—	2	1	no	—
200	C₂×C₄×D₃	—	2	1	no	—
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	2	1	no	—
203	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
204	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
212	(C₂×D₃)⋊C₄	—	2	4	no	—
213	(C₂×D₃)⋊C₄	—	4	2	no	—
214	C₄⋊Dic₃	—	2	1	no	—
215	C₄⋊Dic₃	—	2	1	no	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
218	C₄×Dic₃	—	2	4	no	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	—	2	1	no	—
221	C₂×C₃⋊C₈	—	2	1	no	—
222	C₂³×C₅	—	3	2	no	—
223	C₂³×C₅	—	6	1	no	—
224	C₂³×C₅	—	6	1	no	—
225	C₂³×C₅	—	6	1	no	—
226	C₂³×C₅	—	6	1	no	—
227	C₂³×C₅	—	6	1	no	—
228	C₂³×C₅	—	6	1	no	—
229	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	3	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	6	2	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	2	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	#235	1	1	yes	characteristic
252	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	1	yes	characteristic
254	C₂×C₄×C₅	#239	1	1	yes	characteristic
255	C₅×C₈	—	4	1	no	—
256	C₅×C₈	—	12	1	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₂²×C₈	—	3	1	no	—
259	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
260	#117	—	3	4	no	—
261	#117	—	6	2	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₄⋊C₄	—	3	1	no	—
264	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	6	1	no	—
267	C₂×C₂²⋊C₄	—	6	1	no	—
268	C₂×C₄²	—	6	1	no	—
269	C₂²⋊C₈	—	6	2	no	—
270	#95	—	6	1	no	—
271	C₂×C₃×C₅	#381	1	1	yes	characteristic
272	C₂×C₃×C₅	#416	1	1	yes	characteristic
273	C₂×C₃×C₅	#417	1	1	yes	characteristic
274	C₂×C₃×C₅	#482	1	1	yes	characteristic
275	C₂×C₃×C₅	#482	1	1	yes	characteristic
276	C₂×C₃×C₅	#485	1	1	yes	characteristic
277	C₂×C₃×C₅	#485	1	1	yes	characteristic
278	C₅×D₃	—	4	2	no	—
279	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂²×D₃	—	2	1	no	—
281	C₂²×D₃	—	2	1	no	—
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	—	2	1	no	—
284	C₂²×D₃	—	2	1	no	—
285	C₂²×D₃	—	2	1	no	—
286	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	1	no	—
289	C₂×C₃×C₄	—	4	1	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	—	4	1	no	—
293	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
297	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
298	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
299	C₂×Dic₃	—	2	1	no	—
300	C₂×Dic₃	—	2	1	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	4	1	no	—
303	C₂×Dic₃	—	4	1	no	—
304	C₂×Dic₃	—	4	1	no	—
305	C₂×Dic₃	—	4	1	no	—
306	C₂×Dic₃	—	4	1	no	—
307	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
308	C₄×D₃	—	2	2	no	—
309	C₄×D₃	—	2	2	no	—
310	C₄×D₃	—	2	2	no	—
311	C₄×D₃	—	2	2	no	—
312	C₃×C₈	—	4	1	no	—
313	C₃⋊C₈	—	4	1	no	—
314	C₂²×C₅	—	6	2	no	—
315	C₂²×C₅	—	6	2	no	—
316	C₂²×C₅	—	6	2	no	—
317	C₂²×C₅	—	12	1	no	—
318	C₂²×C₅	—	12	1	no	—
319	C₂²×C₅	—	12	1	no	—
320	C₂²×C₅	—	12	1	no	—
321	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₅	#883	1	1	yes	characteristic
323	C₂²×C₅	#894	1	1	yes	characteristic
324	C₂²×C₅	#911	1	1	yes	characteristic
325	C₂²×C₅	#915	1	1	yes	characteristic
326	C₂²×C₅	#916	1	1	yes	characteristic
327	C₂²×C₅	#919	1	1	yes	characteristic
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	—	6	2	no	—
330	C₄×C₅	—	8	1	no	—
331	C₄×C₅	—	12	2	no	—
332	C₄×C₅	—	24	1	no	—
333	C₄×C₅	#872	1	1	yes	characteristic
334	C₄×C₅	#883	1	1	yes	characteristic
335	C₄×C₅	#892	1	1	yes	characteristic
336	C₄×C₅	#894	1	1	yes	characteristic
337	C₂⁴	—	3	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	2	no	—
342	C₂²×C₄	—	3	2	no	—
343	C₂²×C₄	—	6	1	no	—
344	C₂²×C₄	—	6	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	—	6	1	no	—
348	C₂²×C₄	—	6	1	no	—
349	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	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	—	2	1	no	—
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₄⋊C₄	—	6	1	no	—
362	C₄⋊C₄	—	6	1	no	—
363	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
364	C₂²⋊C₄	—	6	4	no	—
365	C₂²⋊C₄	—	12	2	no	—
366	C₄²	—	6	4	no	—
367	C₃×C₅	#1825	1	1	yes	characteristic, complemented, Hall
368	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
369	C₂²×C₃	C₅×#123	1	1	yes	characteristic
370	C₂²×C₃	C₅×#123	1	1	yes	characteristic
371	C₂²×C₃	C₅×#135	1	1	yes	characteristic
372	C₂²×C₃	C₅×#135	1	1	yes	characteristic
373	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂²×C₃	C₅×#137	1	1	yes	characteristic
375	C₂×D₃	—	2	2	no	—
376	C₂×D₃	—	2	2	no	—
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	4	1	no	—
379	C₂×D₃	—	4	1	no	—
380	C₂×D₃	—	4	1	no	—
381	C₂×D₃	—	4	1	no	—
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	—	8	1	no	—
384	C₃×C₄	C₅×#117	1	1	yes	characteristic
385	C₃×C₄	C₅×#117	1	1	yes	characteristic
386	C₃×C₄	C₅×#123	1	1	yes	characteristic
387	C₃×C₄	C₅×#123	1	1	yes	characteristic
388	Dic₃	—	2	2	no	—
389	Dic₃	—	4	2	no	—
390	Dic₃	—	8	1	no	—
391	C₂×C₅	—	12	2	no	—
392	C₂×C₅	#4664	1	1	yes	characteristic
393	C₂×C₅	#4771	1	1	yes	characteristic
394	C₂×C₅	#4779	1	1	yes	characteristic
395	C₂×C₅	#4804	1	1	yes	characteristic
396	C₂×C₅	#4814	1	1	yes	characteristic
397	C₂×C₅	#4868	1	1	yes	characteristic
398	C₂×C₅	#4885	1	1	yes	characteristic
399	C₂³	—	3	2	no	—
400	C₂³	—	6	1	no	—
401	C₂³	—	6	1	no	—
402	C₂³	—	6	1	no	—
403	C₂³	—	6	1	no	—
404	C₂³	—	6	1	no	—
405	C₂³	—	6	1	no	—
406	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	6	1	no	—
415	C₂×C₄	—	6	1	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	2	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×#235	1	1	yes	characteristic
429	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
430	C₂×C₄	C₅×#237	1	1	yes	characteristic
431	C₂×C₄	C₅×#239	1	1	yes	characteristic
432	C₈	—	4	1	no	—
433	C₈	—	12	1	no	—
434	C₂×C₃	C₅×#381	1	1	yes	characteristic
435	C₂×C₃	C₅×#416	1	1	yes	characteristic
436	C₂×C₃	C₅×#417	1	1	yes	characteristic
437	C₂×C₃	C₅×#482	1	1	yes	characteristic
438	C₂×C₃	C₅×#482	1	1	yes	characteristic
439	C₂×C₃	C₅×#485	1	1	yes	characteristic
440	C₂×C₃	C₅×#485	1	1	yes	characteristic
441	D₃	—	4	2	no	—
442	C₅	#68813	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	6	2	no	—
444	C₂²	—	6	2	no	—
445	C₂²	—	6	2	no	—
446	C₂²	—	12	1	no	—
447	C₂²	—	12	1	no	—
448	C₂²	—	12	1	no	—
449	C₂²	—	12	1	no	—
450	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
451	C₂²	C₅×#883	1	1	yes	characteristic
452	C₂²	C₅×#894	1	1	yes	characteristic
453	C₂²	C₅×#911	1	1	yes	characteristic
454	C₂²	C₅×#915	1	1	yes	characteristic
455	C₂²	C₅×#916	1	1	yes	characteristic
456	C₂²	C₅×#919	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	6	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	12	2	no	—
461	C₄	—	24	1	no	—
462	C₄	C₅×#872	1	1	yes	characteristic
463	C₄	C₅×#883	1	1	yes	characteristic
464	C₄	C₅×#892	1	1	yes	characteristic
465	C₄	C₅×#894	1	1	yes	characteristic
466	C₃	C₅×#1825	1	1	yes	characteristic, complemented, Sylow
467	C₂	—	12	2	no	—
468	C₂	C₅×#4664	1	1	yes	characteristic
469	C₂	C₅×#4771	1	1	yes	characteristic
470	C₂	C₅×#4779	1	1	yes	characteristic
471	C₂	C₅×#4804	1	1	yes	characteristic
472	C₂	C₅×#4814	1	1	yes	characteristic
473	C₂	C₅×#4868	1	1	yes	characteristic
474	C₂	C₅×#4885	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1825
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#340	C₂	semidirect
5. C₅×#4551	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. C₅×#4529	C₂	semidirect
20. C₅×#892	C₄	semidirect
23. #68813	C₅	direct (N × H)
30. C₅×#340	D₃	semidirect
64. C₃×#340	C₂×C₅	semidirect
65. #4551	C₂×C₅	semidirect
66. #4529	C₂×C₅	semidirect
67. #4529	C₂×C₅	semidirect
129. #892	C₄×C₅	semidirect
168. #340	C₅×D₃	semidirect
367. C₃×C₅	#1825	semidirect
442. C₅	#68813	direct (N × H)
466. C₃	C₅×#1825	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#892	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₅×#4987	2
C₃×C₅×#340	2
C₅×#4551	2
C₅×#4529	2
C₅×#1825	3
#68813	5

Subgroups — C5×#68813 #14298493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68813 #14298493