Subgroups — C₅×#22080 #11944800

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#482	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
3	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1875	C₂	1	1	yes	maximal, characteristic
11	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1825	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	—	2	1	no	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#482	C₄	1	8	yes	complemented
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#106	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×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#388	—	2	1	no	—
42	C₅×#386	—	2	1	no	—
43	C₅×#385	—	2	1	no	—
44	C₅×#385	—	2	1	no	—
45	C₅×#380	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	—	2	1	no	—
47	C₄×C₅×C₄⋊C₄	—	2	1	no	—
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	#22080	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₅×#121	—	2	2	no	—
72	C₅×#121	C₂×C₄	1	4	yes	—
73	C₄×C₅×D₄	—	4	1	no	—
74	C₄×C₅×D₄	—	4	1	no	—
75	C₄×C₅×D₄	—	4	4	no	—
76	C₅×#117	—	2	2	no	—
77	C₅×#117	—	4	1	no	—
78	C₅×#117	—	4	1	no	—
79	C₅×#117	C₂×C₄	1	4	yes	complemented
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	—	4	1	no	—
103	C₂×C₄²×C₅	—	4	1	no	—
104	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#107	—	4	1	no	—
109	C₅×#107	C₂×C₄	1	4	yes	complemented
110	C₅×#106	—	4	1	no	—
111	C₅×#106	C₂×C₄	1	4	yes	complemented
112	C₅×#102	—	4	1	no	—
113	C₅×#102	—	4	1	no	—
114	C₅×#102	C₂×C₄	1	4	yes	complemented
115	C₅×#102	C₂×C₄	1	4	yes	complemented
116	C₅×C₂²⋊C₈	—	2	2	no	—
117	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
118	C₄×C₅×C₈	—	4	1	no	—
119	C₄×C₅×C₈	—	4	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	C₂×#482	C₂×C₅	1	1	yes	characteristic
128	C₄×#121	C₂×C₅	1	1	yes	characteristic
129	#2296	C₂×C₅	1	1	yes	characteristic, complemented
130	#1942	C₂×C₅	1	1	yes	characteristic, complemented
131	#1941	C₂×C₅	1	1	yes	characteristic, complemented
132	#1934	C₂×C₅	1	1	yes	characteristic, complemented
133	#1934	C₂×C₅	1	1	yes	characteristic, complemented
134	#1921	C₂×C₅	1	1	yes	characteristic, complemented
135	#1919	C₂×C₅	1	1	yes	characteristic, complemented
136	#1875	C₂×C₅	1	1	yes	characteristic
137	#1864	C₂×C₅	1	1	yes	characteristic, complemented
138	#1862	C₂×C₅	1	1	yes	characteristic, complemented
139	#1854	C₂×C₅	1	1	yes	characteristic, complemented
140	#1825	C₂×C₅	1	1	yes	characteristic, complemented
141	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	—	4	2	no	—
152	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	—	2	2	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	4	1	no	—
168	C₂²×C₄×C₅	—	4	1	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	—	4	2	no	—
171	C₂²×C₄×C₅	—	4	2	no	—
172	C₂²×C₄×C₅	—	4	2	no	—
173	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	#41	1	2	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	4	2	no	—
205	C₅×C₄⋊C₄	—	4	2	no	—
206	C₅×C₄⋊C₄	—	4	2	no	—
207	C₅×C₄⋊C₄	—	4	2	no	—
208	C₅×C₄⋊C₄	—	4	2	no	—
209	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
210	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
211	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₅×C₂²⋊C₄	—	4	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	—	4	2	no	—
217	C₅×C₂²⋊C₄	—	4	2	no	—
218	C₅×C₂²⋊C₄	—	4	2	no	—
219	C₄²×C₅	—	2	4	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	4	1	no	—
225	C₄²×C₅	—	4	1	no	—
226	C₄²×C₅	—	4	2	no	—
227	C₄²×C₅	—	4	2	no	—
228	C₂×#121	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×#117	C₂²×C₅	1	1	yes	characteristic
232	C₂×#117	C₂²×C₅	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
234	#482	C₄×C₅	1	8	yes	complemented
235	C₂×#107	C₂²×C₅	1	1	yes	characteristic
236	C₂×#107	C₂²×C₅	1	1	yes	characteristic
237	C₂×#106	C₂²×C₅	1	1	yes	characteristic
238	C₂×#106	C₂²×C₅	1	1	yes	characteristic
239	C₂×#102	C₂²×C₅	1	1	yes	characteristic
240	C₂×#102	C₂²×C₅	1	1	yes	characteristic
241	C₂×#102	C₂²×C₅	1	1	yes	characteristic
242	C₂×#102	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
247	#390	C₂²×C₅	1	1	yes	characteristic
248	#389	C₂²×C₅	1	1	yes	characteristic
249	#389	C₂²×C₅	1	1	yes	characteristic
250	#389	C₂²×C₅	1	1	yes	characteristic
251	#389	C₂²×C₅	1	1	yes	characteristic
252	#389	C₂²×C₅	1	1	yes	characteristic
253	#388	—	2	1	no	—
254	#386	—	2	1	no	—
255	#385	—	2	1	no	—
256	#385	—	2	1	no	—
257	#380	C₂²×C₅	1	1	yes	characteristic
258	C₄×C₄⋊C₄	—	2	1	no	—
259	C₄×C₄⋊C₄	—	2	1	no	—
260	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₄×C₂²⋊C₄	—	2	1	no	—
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#340	C₂²×C₅	1	1	yes	characteristic
265	#340	C₂²×C₅	1	1	yes	characteristic
266	#340	C₂²×C₅	1	1	yes	characteristic
267	#340	C₂²×C₅	1	1	yes	characteristic
268	#340	C₂²×C₅	1	1	yes	characteristic
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#336	C₂²×C₅	1	1	yes	characteristic
271	#336	C₂²×C₅	1	1	yes	characteristic
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	2	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	C₄×D₄	1	2	yes	—
286	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	4	8	no	—
290	C₅×D₄	—	4	1	no	—
291	C₅×D₄	—	4	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	4	4	no	—
311	C₂×C₄×C₅	—	4	4	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	8	4	no	—
331	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
332	C₂×C₄×C₅	#135	1	2	yes	—
333	C₂×C₄×C₅	#135	1	2	yes	—
334	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
335	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
340	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	2	2	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
349	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	#121	—	2	2	no	—
356	#121	C₂×C₄×C₅	1	4	yes	—
357	C₄×D₄	—	4	1	no	—
358	C₄×D₄	—	4	1	no	—
359	C₄×D₄	—	4	4	no	—
360	#117	—	2	2	no	—
361	#117	—	4	1	no	—
362	#117	—	4	1	no	—
363	#117	C₂×C₄×C₅	1	4	yes	complemented
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	4	1	no	—
387	C₂×C₄²	—	4	1	no	—
388	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
389	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	#107	—	4	1	no	—
393	#107	C₂×C₄×C₅	1	4	yes	complemented
394	#106	—	4	1	no	—
395	#106	C₂×C₄×C₅	1	4	yes	complemented
396	#102	—	4	1	no	—
397	#102	—	4	1	no	—
398	#102	C₂×C₄×C₅	1	4	yes	complemented
399	#102	C₂×C₄×C₅	1	4	yes	complemented
400	C₂²⋊C₈	—	2	2	no	—
401	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
402	C₄×C₈	—	4	1	no	—
403	C₄×C₈	—	4	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	4	1	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	—	8	1	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
426	C₂²×C₅	#534	1	1	yes	characteristic
427	C₂²×C₅	#536	1	1	yes	characteristic
428	C₂²×C₅	C₂×#135	1	1	yes	characteristic
429	C₂²×C₅	C₂×#135	1	1	yes	characteristic
430	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂²×C₅	#575	1	1	yes	characteristic
432	C₄×C₅	—	2	2	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	2	no	—
440	C₄×C₅	—	8	1	no	—
441	C₄×C₅	—	8	1	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	#520	1	1	yes	characteristic
445	C₄×C₅	#520	1	1	yes	characteristic
446	C₄×C₅	#539	1	1	yes	characteristic
447	C₄×C₅	#539	1	1	yes	characteristic
448	C₂⁴	—	2	1	no	—
449	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
480	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
485	C₂²×C₄	C₅×#41	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
498	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
516	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
517	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	4	1	no	—
531	C₄²	—	4	1	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	4	2	no	—
534	C₂×C₅	—	4	2	no	—
535	C₂×C₅	—	8	2	no	—
536	C₂×C₅	#2322	1	1	yes	characteristic
537	C₂×C₅	C₄×#135	1	1	yes	characteristic
538	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
539	C₂×C₅	#3188	1	1	yes	characteristic
540	C₂×C₅	#3191	1	1	yes	characteristic
541	C₂×C₅	#3228	1	1	yes	characteristic
542	C₂×C₅	#3233	1	1	yes	characteristic
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	C₄×C₅×D₄	1	2	yes	—
557	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	4	8	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
603	C₂×C₄	C₅×#135	1	2	yes	—
604	C₂×C₄	C₅×#135	1	2	yes	—
605	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
607	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
608	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
611	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₅	#22080	1	1	yes	characteristic, direct product factor, Sylow
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
632	C₂²	C₅×#534	1	1	yes	characteristic
633	C₂²	C₅×#536	1	1	yes	characteristic
634	C₂²	C₂×C₅×#135	1	1	yes	characteristic
635	C₂²	C₂×C₅×#135	1	1	yes	characteristic
636	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
637	C₂²	C₅×#575	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	C₅×#520	1	1	yes	characteristic
651	C₄	C₅×#520	1	1	yes	characteristic
652	C₄	C₅×#539	1	1	yes	characteristic
653	C₄	C₅×#539	1	1	yes	characteristic
654	C₂	—	4	2	no	—
655	C₂	—	8	2	no	—
656	C₂	C₅×#2322	1	1	yes	characteristic
657	C₂	C₄×C₅×#135	1	1	yes	characteristic
658	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
659	C₂	C₅×#3188	1	1	yes	characteristic
660	C₂	C₅×#3191	1	1	yes	characteristic
661	C₂	C₅×#3228	1	1	yes	characteristic
662	C₂	C₅×#3233	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	C₂×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2296	C₂	semidirect
4. C₅×#1942	C₂	semidirect
5. C₅×#1941	C₂	semidirect
6. C₅×#1934	C₂	semidirect
7. C₅×#1934	C₂	semidirect
8. C₅×#1921	C₂	semidirect
9. C₅×#1919	C₂	semidirect
11. C₅×#1864	C₂	semidirect
12. C₅×#1862	C₂	semidirect
13. C₅×#1854	C₂	semidirect
14. C₅×#1825	C₂	semidirect
15. C₄×C₅×C₂²⋊C₈	C₂	semidirect
22. C₅×#482	C₄	semidirect
60. #22080	C₅	direct (N × H)
79. C₅×#117	C₂×C₄	semidirect
109. C₅×#107	C₂×C₄	semidirect
111. C₅×#106	C₂×C₄	semidirect
114. C₅×#102	C₂×C₄	semidirect
115. C₅×#102	C₂×C₄	semidirect
117. C₅×C₂²⋊C₈	C₂×C₄	semidirect
129. #2296	C₂×C₅	semidirect
130. #1942	C₂×C₅	semidirect
131. #1941	C₂×C₅	semidirect
132. #1934	C₂×C₅	semidirect
133. #1934	C₂×C₅	semidirect
134. #1921	C₂×C₅	semidirect
135. #1919	C₂×C₅	semidirect
137. #1864	C₂×C₅	semidirect
138. #1862	C₂×C₅	semidirect
139. #1854	C₂×C₅	semidirect
140. #1825	C₂×C₅	semidirect
141. C₄×C₂²⋊C₈	C₂×C₅	semidirect
234. #482	C₄×C₅	semidirect
363. #117	C₂×C₄×C₅	semidirect
393. #107	C₂×C₄×C₅	semidirect
395. #106	C₂×C₄×C₅	semidirect
398. #102	C₂×C₄×C₅	semidirect
399. #102	C₂×C₄×C₅	semidirect
401. C₂²⋊C₈	C₂×C₄×C₅	semidirect
616. C₅	#22080	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×#482	2
C₄×C₅×#121	2
C₅×#2296	2
C₅×#1942	2
C₅×#1941	2
C₅×#1934	2
C₅×#1921	2
C₅×#1919	2
C₅×#1875	2
C₅×#1864	2
C₅×#1862	2
C₅×#1854	2
C₅×#1825	2
C₄×C₅×C₂²⋊C₈	2
#22080	5

Subgroups — C5×#22080 #11944800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22080 #11944800