Subgroups — C₅×#22120 #11944840

Order 1280.

784 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×#478	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2293	C₂	1	1	yes	maximal, characteristic
4	C₅×#1989	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1936	C₂	1	1	yes	maximal, characteristic
9	C₅×#1936	C₂	1	1	yes	maximal, characteristic
10	C₅×#1926	C₂	1	1	yes	maximal, characteristic
11	C₅×#1925	C₂	1	1	yes	maximal, characteristic
12	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1804	C₂	1	1	yes	maximal, characteristic
15	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	—	2	1	no	—
19	C₅×#478	C₄	1	8	yes	complemented
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×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₅×#390	C₂²	1	1	yes	characteristic
33	C₅×#390	C₂²	1	1	yes	characteristic
34	C₅×#389	C₂²	1	1	yes	characteristic
35	C₅×#389	C₂²	1	1	yes	characteristic
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×#387	—	2	1	no	—
41	C₅×#387	—	2	1	no	—
42	C₅×#382	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₄⋊C₄	—	2	1	no	—
44	C₄×C₅×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
49	C₄³×C₅	C₂²	1	1	yes	characteristic
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	#22120	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₅×#125	—	2	2	no	—
68	C₅×#125	C₂×C₄	1	4	yes	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
71	C₅×#117	—	4	4	no	—
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	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	—	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	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#107	—	4	1	no	—
101	C₅×#107	C₂×C₄	1	4	yes	—
102	C₅×#106	—	4	1	no	—
103	C₅×#106	C₂×C₄	1	4	yes	—
104	C₅×C₄⋊C₈	—	2	2	no	—
105	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
106	C₅×#102	—	4	1	no	—
107	C₅×#102	—	4	1	no	—
108	C₅×#102	C₂×C₄	1	4	yes	—
109	C₅×#102	C₂×C₄	1	4	yes	—
110	C₅×#97	—	4	1	no	—
111	C₅×#97	—	4	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	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₂×#478	C₂×C₅	1	1	yes	characteristic
122	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
123	#2293	C₂×C₅	1	1	yes	characteristic
124	#1989	C₂×C₅	1	1	yes	characteristic, complemented
125	#1949	C₂×C₅	1	1	yes	characteristic, complemented
126	#1944	C₂×C₅	1	1	yes	characteristic, complemented
127	#1943	C₂×C₅	1	1	yes	characteristic, complemented
128	#1936	C₂×C₅	1	1	yes	characteristic
129	#1936	C₂×C₅	1	1	yes	characteristic
130	#1926	C₂×C₅	1	1	yes	characteristic
131	#1925	C₂×C₅	1	1	yes	characteristic
132	#1919	C₂×C₅	1	1	yes	characteristic, complemented
133	#1918	C₂×C₅	1	1	yes	characteristic, complemented
134	#1804	C₂×C₅	1	1	yes	characteristic
135	#1767	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂⁴×C₅	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	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	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	4	2	no	—
152	C₂²×C₄×C₅	—	4	2	no	—
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
171	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
186	C₅×C₄⋊C₄	—	4	2	no	—
187	C₅×C₄⋊C₄	—	4	2	no	—
188	C₅×C₄⋊C₄	—	4	2	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×C₂²⋊C₄	—	2	4	no	—
193	C₅×C₂²⋊C₄	—	4	2	no	—
194	C₅×C₂²⋊C₄	—	4	2	no	—
195	C₅×C₂²⋊C₄	—	4	2	no	—
196	C₅×C₂²⋊C₄	—	4	2	no	—
197	C₄²×C₅	—	2	2	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	1	no	—
203	C₄²×C₅	—	4	1	no	—
204	C₄²×C₅	—	4	1	no	—
205	C₄²×C₅	—	4	2	no	—
206	C₄²×C₅	—	4	2	no	—
207	C₄²×C₅	—	4	2	no	—
208	C₄²×C₅	C₂²×C₄	1	2	yes	—
209	C₄²×C₅	#41	1	2	yes	—
210	C₂×#125	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
212	C₂×#117	—	2	1	no	—
213	#478	C₄×C₅	1	8	yes	complemented
214	C₂×#107	C₂²×C₅	1	1	yes	characteristic
215	C₂×#107	C₂²×C₅	1	1	yes	characteristic
216	C₂×#106	C₂²×C₅	1	1	yes	characteristic
217	C₂×#106	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×#102	C₂²×C₅	1	1	yes	characteristic
221	C₂×#102	C₂²×C₅	1	1	yes	characteristic
222	C₂×#102	C₂²×C₅	1	1	yes	characteristic
223	C₂×#102	C₂²×C₅	1	1	yes	characteristic
224	C₂×#97	C₂²×C₅	1	1	yes	characteristic
225	C₂×#97	C₂²×C₅	1	1	yes	characteristic
226	#390	C₂²×C₅	1	1	yes	characteristic
227	#390	C₂²×C₅	1	1	yes	characteristic
228	#389	C₂²×C₅	1	1	yes	characteristic
229	#389	C₂²×C₅	1	1	yes	characteristic
230	#389	C₂²×C₅	1	1	yes	characteristic
231	#389	C₂²×C₅	1	1	yes	characteristic
232	#388	—	2	1	no	—
233	#388	—	2	1	no	—
234	#387	—	2	1	no	—
235	#387	—	2	1	no	—
236	#382	C₂²×C₅	1	1	yes	characteristic
237	C₄×C₄⋊C₄	—	2	1	no	—
238	C₄×C₄⋊C₄	—	2	1	no	—
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	C₄³	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	#340	C₂²×C₅	1	1	yes	characteristic
252	#336	C₂²×C₅	1	1	yes	characteristic
253	#336	C₂²×C₅	1	1	yes	characteristic
254	C₂³×C₅	—	2	2	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	—	4	1	no	—
261	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
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	1	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	—	4	8	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	—	4	1	no	—
303	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
304	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
305	C₂×C₄×C₅	AGL(1,ℤ/8)	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	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₅	2₋¹⁺⁴	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	—	4	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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	#125	—	2	2	no	—
323	#125	C₂×C₄×C₅	1	4	yes	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
326	#117	—	4	4	no	—
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	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
349	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
350	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
351	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
355	#107	—	4	1	no	—
356	#107	C₂×C₄×C₅	1	4	yes	—
357	#106	—	4	1	no	—
358	#106	C₂×C₄×C₅	1	4	yes	—
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
361	#102	—	4	1	no	—
362	#102	—	4	1	no	—
363	#102	C₂×C₄×C₅	1	4	yes	—
364	#102	C₂×C₄×C₅	1	4	yes	—
365	#97	—	4	1	no	—
366	#97	—	4	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	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	C₂²×C₅	—	4	2	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	2	no	—
379	C₂²×C₅	—	8	1	no	—
380	C₂²×C₅	—	8	1	no	—
381	C₂²×C₅	—	8	1	no	—
382	C₂²×C₅	—	8	1	no	—
383	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
384	C₂²×C₅	#536	1	1	yes	characteristic
385	C₂²×C₅	#537	1	1	yes	characteristic
386	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₂²×C₅	#575	1	1	yes	characteristic
388	C₂²×C₅	#575	1	1	yes	characteristic
389	C₂²×C₅	#575	1	1	yes	characteristic
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	2	2	no	—
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	—	4	2	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	—	4	2	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	8	1	no	—
400	C₄×C₅	—	8	1	no	—
401	C₄×C₅	—	8	1	no	—
402	C₄×C₅	—	8	1	no	—
403	C₄×C₅	#519	1	1	yes	characteristic
404	C₄×C₅	#520	1	1	yes	characteristic
405	C₄×C₅	#541	1	1	yes	characteristic
406	C₄×C₅	#542	1	1	yes	characteristic
407	C₂⁴	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
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	C₂²×C₄×C₅	1	2	yes	—
442	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	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	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	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	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	2	no	—
477	C₄²	—	4	2	no	—
478	C₄²	—	4	2	no	—
479	C₄²	C₂²×C₄×C₅	1	2	yes	—
480	C₄²	C₅×#41	1	2	yes	—
481	C₂×C₅	—	8	2	no	—
482	C₂×C₅	#2323	1	1	yes	characteristic
483	C₂×C₅	#2943	1	1	yes	characteristic
484	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂×C₅	#3234	1	1	yes	characteristic
486	C₂×C₅	#3240	1	1	yes	characteristic
487	C₂×C₅	#3251	1	1	yes	characteristic
488	C₂×C₅	#3256	1	1	yes	characteristic
489	C₂³	—	2	2	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	—	4	1	no	—
496	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
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	1	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	—	4	8	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	—	4	1	no	—
538	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
539	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
540	C₂×C₄	C₅×AGL(1,ℤ/8)	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	C₅×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂×C₄	C₅×2₋¹⁺⁴	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	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₅	#22120	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×#536	1	1	yes	characteristic
561	C₂²	C₅×#537	1	1	yes	characteristic
562	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
563	C₂²	C₅×#575	1	1	yes	characteristic
564	C₂²	C₅×#575	1	1	yes	characteristic
565	C₂²	C₅×#575	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	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	C₅×#519	1	1	yes	characteristic
580	C₄	C₅×#520	1	1	yes	characteristic
581	C₄	C₅×#541	1	1	yes	characteristic
582	C₄	C₅×#542	1	1	yes	characteristic
583	C₂	—	8	2	no	—
584	C₂	C₅×#2323	1	1	yes	characteristic
585	C₂	C₅×#2943	1	1	yes	characteristic
586	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
587	C₂	C₅×#3234	1	1	yes	characteristic
588	C₂	C₅×#3240	1	1	yes	characteristic
589	C₂	C₅×#3251	1	1	yes	characteristic
590	C₂	C₅×#3256	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 ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#125	C₂	semidirect
4. C₅×#1989	C₂	semidirect
5. C₅×#1949	C₂	semidirect
6. C₅×#1944	C₂	semidirect
7. C₅×#1943	C₂	semidirect
12. C₅×#1919	C₂	semidirect
13. C₅×#1918	C₂	semidirect
15. C₅×#1767	C₂	semidirect
19. C₅×#478	C₄	semidirect
60. #22120	C₅	direct (N × H)
122. C₄×#125	C₂×C₅	semidirect
124. #1989	C₂×C₅	semidirect
125. #1949	C₂×C₅	semidirect
126. #1944	C₂×C₅	semidirect
127. #1943	C₂×C₅	semidirect
132. #1919	C₂×C₅	semidirect
133. #1918	C₂×C₅	semidirect
135. #1767	C₂×C₅	semidirect
213. #478	C₄×C₅	semidirect
551. C₅	#22120	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×#478	2
C₄×C₅×#125	2
C₅×#2293	2
C₅×#1989	2
C₅×#1949	2
C₅×#1944	2
C₅×#1943	2
C₅×#1936	2
C₅×#1926	2
C₅×#1925	2
C₅×#1919	2
C₅×#1918	2
C₅×#1804	2
C₅×#1767	2
#22120	5

Subgroups — C5×#22120 #11944840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22120 #11944840