Subgroups — C₅×#23079 #11945799

Order 1280.

778 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic
2	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2357	C₂	1	1	yes	maximal, characteristic
4	C₅×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1936	C₂	1	1	yes	maximal, characteristic
7	C₅×#1934	C₂	1	1	yes	maximal, characteristic
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic
9	C₅×#1925	C₂	1	1	yes	maximal, characteristic
10	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#474	C₄	1	8	yes	complemented
19	C₂×C₅×#107	C₂²	1	1	yes	characteristic
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	1	yes	characteristic
25	C₂×C₅×#102	C₂²	1	1	yes	characteristic
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#391	—	2	1	no	—
32	C₅×#391	—	2	1	no	—
33	C₅×#390	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#389	—	2	1	no	—
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#388	—	2	1	no	—
39	C₅×#388	—	2	1	no	—
40	C₅×#382	C₂²	1	1	yes	characteristic
41	C₅×#381	—	2	1	no	—
42	C₄×C₅×C₄⋊C₄	—	2	1	no	—
43	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
50	C₅×#340	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#23079	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊Q₈	—	2	2	no	—
69	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
70	C₄×C₅×D₄	—	2	2	no	—
71	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₅	—	2	1	no	—
90	C₂×C₄²×C₅	—	2	1	no	—
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	—	2	1	no	—
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₅×#107	—	2	2	no	—
98	C₅×#107	C₂×C₄	1	4	yes	—
99	C₅×#107	C₂×C₄	1	4	yes	—
100	C₅×#106	—	2	2	no	—
101	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	2	2	no	—
104	C₅×#102	C₂×C₄	1	4	yes	—
105	C₅×#102	C₂×C₄	1	4	yes	—
106	C₅×#97	—	2	2	no	—
107	C₅×#97	—	2	2	no	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₅×#95	—	2	1	no	—
110	C₅×#95	—	2	1	no	—
111	C₅×#95	—	2	1	no	—
112	C₅×#95	—	2	1	no	—
113	C₅×#95	—	2	1	no	—
114	C₅×#95	—	2	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	D₄	1	1	yes	characteristic
119	C₅×#95	D₄	1	1	yes	characteristic
120	C₂×#474	C₂×C₅	1	1	yes	characteristic
121	#2369	C₂×C₅	1	1	yes	characteristic, complemented
122	#2357	C₂×C₅	1	1	yes	characteristic
123	#1993	C₂×C₅	1	1	yes	characteristic, complemented
124	#1949	C₂×C₅	1	1	yes	characteristic, complemented
125	#1936	C₂×C₅	1	1	yes	characteristic
126	#1934	C₂×C₅	1	1	yes	characteristic
127	#1926	C₂×C₅	1	1	yes	characteristic
128	#1925	C₂×C₅	1	1	yes	characteristic
129	#1921	C₂×C₅	1	1	yes	characteristic, complemented
130	#1918	C₂×C₅	1	1	yes	characteristic, complemented
131	#1776	C₂×C₅	1	1	yes	characteristic, complemented
132	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
133	#1771	C₂×C₅	1	1	yes	characteristic, complemented
134	#1762	C₂×C₅	1	1	yes	characteristic
135	C₂⁴×C₅	—	2	1	no	—
136	C₂×C₅×Q₈	—	2	4	no	—
137	C₂×C₅×Q₈	—	8	1	no	—
138	C₂×C₅×Q₈	—	8	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	4	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	8	1	no	—
154	C₂²×C₄×C₅	—	8	1	no	—
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₅×C₈	#41	1	2	yes	—
174	C₅×C₄⋊C₄	—	2	4	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	4	1	no	—
187	C₅×C₄⋊C₄	—	8	1	no	—
188	C₅×C₄⋊C₄	—	8	1	no	—
189	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
190	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
191	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
192	C₅×C₄⋊C₄	#41	1	2	yes	—
193	C₅×C₂²⋊C₄	—	2	4	no	—
194	C₅×C₂²⋊C₄	—	4	2	no	—
195	C₅×C₂²⋊C₄	—	4	2	no	—
196	C₅×C₂²⋊C₄	—	8	1	no	—
197	C₅×C₂²⋊C₄	—	8	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	4	2	no	—
203	C₄²×C₅	—	8	1	no	—
204	C₄²×C₅	—	8	1	no	—
205	C₄²×C₅	—	8	1	no	—
206	C₄²×C₅	—	8	1	no	—
207	C₄²×C₅	C₂²×C₄	1	2	yes	—
208	C₄²×C₅	#41	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
211	#474	C₄×C₅	1	8	yes	complemented
212	C₂×#107	C₂²×C₅	1	1	yes	characteristic
213	C₂×#107	C₂²×C₅	1	1	yes	characteristic
214	C₂×#107	C₂²×C₅	1	1	yes	characteristic
215	C₂×#106	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×#102	C₂²×C₅	1	1	yes	characteristic
218	C₂×#102	C₂²×C₅	1	1	yes	characteristic
219	C₂×#102	C₂²×C₅	1	1	yes	characteristic
220	C₂×#102	C₂²×C₅	1	1	yes	characteristic
221	C₂×#97	C₂²×C₅	1	1	yes	characteristic
222	C₂×#97	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
224	#391	—	2	1	no	—
225	#391	—	2	1	no	—
226	#390	C₂²×C₅	1	1	yes	characteristic
227	#390	C₂²×C₅	1	1	yes	characteristic
228	#389	—	2	1	no	—
229	#389	C₂²×C₅	1	1	yes	characteristic
230	#389	C₂²×C₅	1	1	yes	characteristic
231	#388	—	2	1	no	—
232	#388	—	2	1	no	—
233	#382	C₂²×C₅	1	1	yes	characteristic
234	#381	—	2	1	no	—
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	2	1	no	—
243	#340	C₂²×C₅	1	1	yes	characteristic
244	#340	C₂²×C₅	1	1	yes	characteristic
245	#340	C₂²×C₅	1	1	yes	characteristic
246	#340	C₂²×C₅	1	1	yes	characteristic
247	#340	C₂²×C₅	1	1	yes	characteristic
248	#340	C₂²×C₅	1	1	yes	characteristic
249	#340	C₂²×C₅	1	1	yes	characteristic
250	#340	C₂²×C₅	1	1	yes	characteristic
251	#336	C₂²×C₅	1	1	yes	characteristic
252	#336	C₂²×C₅	1	1	yes	characteristic
253	C₂³×C₅	—	2	2	no	—
254	C₂³×C₅	—	4	1	no	—
255	C₂³×C₅	—	4	1	no	—
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	—	4	1	no	—
259	C₂³×C₅	—	4	1	no	—
260	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₅×Q₈	—	8	4	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	4	1	no	—
265	C₅×D₄	—	4	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	8	4	no	—
303	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
304	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
305	C₂×C₄×C₅	#137	1	2	yes	—
306	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
312	C₅×C₈	—	2	2	no	—
313	C₅×C₈	—	2	2	no	—
314	C₅×C₈	—	2	2	no	—
315	C₅×C₈	—	4	1	no	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
352	#107	—	2	2	no	—
353	#107	C₂×C₄×C₅	1	4	yes	—
354	#107	C₂×C₄×C₅	1	4	yes	—
355	#106	—	2	2	no	—
356	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
357	#102	—	2	2	no	—
358	#102	—	2	2	no	—
359	#102	C₂×C₄×C₅	1	4	yes	—
360	#102	C₂×C₄×C₅	1	4	yes	—
361	#97	—	2	2	no	—
362	#97	—	2	2	no	—
363	C₄×C₈	—	2	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	C₅×D₄	1	1	yes	characteristic
374	#95	C₅×D₄	1	1	yes	characteristic
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	4	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	8	1	no	—
379	C₂²×C₅	—	8	1	no	—
380	C₂²×C₅	—	8	1	no	—
381	C₂²×C₅	—	8	1	no	—
382	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
383	C₂²×C₅	#547	1	1	yes	characteristic
384	C₂²×C₅	#548	1	1	yes	characteristic
385	C₂²×C₅	C₂×#137	1	1	yes	characteristic
386	C₂²×C₅	#575	1	1	yes	characteristic
387	C₂²×C₅	#576	1	1	yes	characteristic
388	C₂²×C₅	#576	1	1	yes	characteristic
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	2	2	no	—
392	C₄×C₅	—	4	1	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	2	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	4	2	no	—
398	C₄×C₅	—	4	2	no	—
399	C₄×C₅	—	8	1	no	—
400	C₄×C₅	—	8	1	no	—
401	C₄×C₅	—	8	1	no	—
402	C₄×C₅	C₄×#41	1	1	yes	characteristic
403	C₄×C₅	#519	1	1	yes	characteristic
404	C₄×C₅	#552	1	1	yes	characteristic
405	C₄×C₅	#556	1	1	yes	characteristic
406	C₂⁴	—	2	1	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	8	1	no	—
409	C₂×Q₈	—	8	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	8	1	no	—
425	C₂²×C₄	—	8	1	no	—
426	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
443	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
444	C₂×C₈	C₅×#41	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	8	1	no	—
459	C₄⋊C₄	—	8	1	no	—
460	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
461	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
462	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
463	C₄⋊C₄	C₅×#41	1	2	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	8	1	no	—
468	C₂²⋊C₄	—	8	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	4	2	no	—
474	C₄²	—	8	1	no	—
475	C₄²	—	8	1	no	—
476	C₄²	—	8	1	no	—
477	C₄²	—	8	1	no	—
478	C₄²	C₂²×C₄×C₅	1	2	yes	—
479	C₄²	C₅×#41	1	2	yes	—
480	C₂×C₅	—	8	2	no	—
481	C₂×C₅	#2362	1	1	yes	characteristic
482	C₂×C₅	C₄×#137	1	1	yes	characteristic
483	C₂×C₅	#2948	1	1	yes	characteristic
484	C₂×C₅	#3346	1	1	yes	characteristic
485	C₂×C₅	#3347	1	1	yes	characteristic
486	C₂×C₅	#3370	1	1	yes	characteristic
487	C₂×C₅	#3375	1	1	yes	characteristic
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
496	Q₈	—	8	4	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
539	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
540	C₂×C₄	C₅×#137	1	2	yes	—
541	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
542	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
543	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
544	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
545	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
546	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	—	2	2	no	—
550	C₈	—	4	1	no	—
551	C₅	#23079	1	1	yes	characteristic, direct product factor, Sylow
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
560	C₂²	C₅×#547	1	1	yes	characteristic
561	C₂²	C₅×#548	1	1	yes	characteristic
562	C₂²	C₂×C₅×#137	1	1	yes	characteristic
563	C₂²	C₅×#575	1	1	yes	characteristic
564	C₂²	C₅×#576	1	1	yes	characteristic
565	C₂²	C₅×#576	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	C₄×C₅×#41	1	1	yes	characteristic
580	C₄	C₅×#519	1	1	yes	characteristic
581	C₄	C₅×#552	1	1	yes	characteristic
582	C₄	C₅×#556	1	1	yes	characteristic
583	C₂	—	8	2	no	—
584	C₂	C₅×#2362	1	1	yes	characteristic
585	C₂	C₄×C₅×#137	1	1	yes	characteristic
586	C₂	C₅×#2948	1	1	yes	characteristic
587	C₂	C₅×#3346	1	1	yes	characteristic
588	C₂	C₅×#3347	1	1	yes	characteristic
589	C₂	C₅×#3370	1	1	yes	characteristic
590	C₂	C₅×#3375	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#2369	C₂	semidirect
4. C₅×#1993	C₂	semidirect
5. C₅×#1949	C₂	semidirect
10. C₅×#1921	C₂	semidirect
11. C₅×#1918	C₂	semidirect
12. C₅×#1776	C₂	semidirect
13. C₄×C₅×#107	C₂	semidirect
14. C₅×#1771	C₂	semidirect
18. C₅×#474	C₄	semidirect
60. #23079	C₅	direct (N × H)
121. #2369	C₂×C₅	semidirect
123. #1993	C₂×C₅	semidirect
124. #1949	C₂×C₅	semidirect
129. #1921	C₂×C₅	semidirect
130. #1918	C₂×C₅	semidirect
131. #1776	C₂×C₅	semidirect
132. C₄×#107	C₂×C₅	semidirect
133. #1771	C₂×C₅	semidirect
211. #474	C₄×C₅	semidirect
551. C₅	#23079	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×C₅×#474	2
C₅×#2369	2
C₅×#2357	2
C₅×#1993	2
C₅×#1949	2
C₅×#1936	2
C₅×#1934	2
C₅×#1926	2
C₅×#1925	2
C₅×#1921	2
C₅×#1918	2
C₅×#1776	2
C₄×C₅×#107	2
C₅×#1771	2
C₅×#1762	2
#23079	5

Subgroups — C5×#23079 #11945799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23079 #11945799