Subgroups — C₅×#22027 #11944747

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2295	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	1	yes	maximal, characteristic
3	C₅×#1984	C₂	1	1	yes	maximal, characteristic
4	C₅×#1940	C₂	1	1	yes	maximal, characteristic
5	C₅×#1939	C₂	1	1	yes	maximal, characteristic
6	C₅×#1917	C₂	1	1	yes	maximal, characteristic
7	C₅×#1917	C₂	1	1	yes	maximal, characteristic
8	C₅×#1916	C₂	1	1	yes	maximal, characteristic
9	C₅×#1916	C₂	1	1	yes	maximal, characteristic
10	C₅×#1840	C₂	1	1	yes	maximal, characteristic
11	C₅×#1839	C₂	1	1	yes	maximal, characteristic
12	C₅×#1832	C₂	1	1	yes	maximal, characteristic
13	C₅×#1831	C₂	1	1	yes	maximal, characteristic
14	C₅×#1768	C₂	1	1	yes	maximal, characteristic
15	C₅×#1746	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#391	C₄	1	1	yes	characteristic
28	C₅×#391	C₄	1	1	yes	characteristic
29	C₅×#389	C₄	1	1	yes	characteristic
30	C₅×#389	C₄	1	1	yes	characteristic
31	C₅×#387	C₄	1	1	yes	characteristic
32	C₅×#387	C₄	1	1	yes	characteristic
33	C₅×#387	C₄	1	1	yes	characteristic
34	C₅×#387	C₄	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#376	C₂²	1	1	yes	characteristic
39	C₅×#376	C₂²	1	1	yes	characteristic
40	C₄³×C₅	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	1	yes	characteristic
43	C₅×#336	C₂²	1	1	yes	characteristic
44	C₅×#336	C₂²	1	1	yes	characteristic
45	C₅×#336	C₂²	1	1	yes	characteristic
46	C₅×#336	C₂²	1	1	yes	characteristic
47	C₅×#336	C₂²	1	1	yes	characteristic
48	C₅×#336	C₂²	1	1	yes	characteristic
49	C₅×#336	C₂²	1	1	yes	characteristic
50	C₅×#336	C₂²	1	1	yes	characteristic
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	C₅×#336	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#22027	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×Q₈	—	2	2	no	—
70	C₄×C₅×Q₈	—	2	2	no	—
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×C₄⋊C₈	—	2	2	no	—
93	C₅×C₄⋊C₈	—	4	1	no	—
94	C₅×C₄⋊C₈	—	4	1	no	—
95	C₅×C₄⋊C₈	—	4	1	no	—
96	C₅×C₄⋊C₈	—	4	1	no	—
97	C₅×#97	—	2	2	no	—
98	C₅×#97	—	4	1	no	—
99	C₄×C₅×C₈	—	2	2	no	—
100	C₄×C₅×C₈	—	4	1	no	—
101	C₅×#95	C₂×C₄	1	1	yes	characteristic
102	C₅×#95	C₂×C₄	1	1	yes	characteristic
103	C₅×#95	C₂×C₄	1	1	yes	characteristic
104	C₅×#95	C₂×C₄	1	1	yes	characteristic
105	C₅×#95	C₂×C₄	1	1	yes	characteristic
106	C₅×#95	C₂×C₄	1	1	yes	characteristic
107	C₅×#95	C₂×C₄	1	1	yes	characteristic
108	C₅×#95	C₂×C₄	1	1	yes	characteristic
109	C₅×#95	C₂×C₄	1	1	yes	characteristic
110	C₅×#95	C₂×C₄	1	1	yes	characteristic
111	C₅×#95	C₂×C₄	1	1	yes	characteristic
112	C₅×#95	C₂×C₄	1	1	yes	characteristic
113	C₅×#95	C₂×C₄	1	1	yes	characteristic
114	C₅×#95	C₂×C₄	1	1	yes	characteristic
115	#2295	C₂×C₅	1	1	yes	characteristic
116	#1985	C₂×C₅	1	1	yes	characteristic
117	#1984	C₂×C₅	1	1	yes	characteristic
118	#1940	C₂×C₅	1	1	yes	characteristic
119	#1939	C₂×C₅	1	1	yes	characteristic
120	#1917	C₂×C₅	1	1	yes	characteristic
121	#1917	C₂×C₅	1	1	yes	characteristic
122	#1916	C₂×C₅	1	1	yes	characteristic
123	#1916	C₂×C₅	1	1	yes	characteristic
124	#1840	C₂×C₅	1	1	yes	characteristic
125	#1839	C₂×C₅	1	1	yes	characteristic
126	#1832	C₂×C₅	1	1	yes	characteristic
127	#1831	C₂×C₅	1	1	yes	characteristic
128	#1768	C₂×C₅	1	1	yes	characteristic
129	#1746	C₂×C₅	1	1	yes	characteristic
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	4	1	no	—
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
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	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	—	4	1	no	—
179	C₅×C₄⋊C₄	—	4	1	no	—
180	C₅×C₄⋊C₄	—	4	1	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	2	2	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	—	2	1	no	—
185	C₄²×C₅	—	2	1	no	—
186	C₄²×C₅	—	2	1	no	—
187	C₄²×C₅	—	2	1	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₄²×C₅	—	2	1	no	—
191	C₄²×C₅	—	2	1	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₄²×C₅	—	4	1	no	—
196	C₄²×C₅	—	4	1	no	—
197	C₄²×C₅	#41	1	2	yes	—
198	C₄²×C₅	#41	1	2	yes	—
199	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×#97	C₂²×C₅	1	1	yes	characteristic
207	C₂×#97	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
210	#391	C₄×C₅	1	1	yes	characteristic
211	#391	C₄×C₅	1	1	yes	characteristic
212	#389	C₄×C₅	1	1	yes	characteristic
213	#389	C₄×C₅	1	1	yes	characteristic
214	#387	C₄×C₅	1	1	yes	characteristic
215	#387	C₄×C₅	1	1	yes	characteristic
216	#387	C₄×C₅	1	1	yes	characteristic
217	#387	C₄×C₅	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	#376	C₂²×C₅	1	1	yes	characteristic
222	#376	C₂²×C₅	1	1	yes	characteristic
223	C₄³	C₂²×C₅	1	1	yes	characteristic
224	#336	C₂²×C₅	1	1	yes	characteristic
225	#336	C₂²×C₅	1	1	yes	characteristic
226	#336	C₂²×C₅	1	1	yes	characteristic
227	#336	C₂²×C₅	1	1	yes	characteristic
228	#336	C₂²×C₅	1	1	yes	characteristic
229	#336	C₂²×C₅	1	1	yes	characteristic
230	#336	C₂²×C₅	1	1	yes	characteristic
231	#336	C₂²×C₅	1	1	yes	characteristic
232	#336	C₂²×C₅	1	1	yes	characteristic
233	#336	C₂²×C₅	1	1	yes	characteristic
234	#336	C₂²×C₅	1	1	yes	characteristic
235	#336	C₂²×C₅	1	1	yes	characteristic
236	#336	C₂²×C₅	1	1	yes	characteristic
237	#336	C₂²×C₅	1	1	yes	characteristic
238	#336	C₂²×C₅	1	1	yes	characteristic
239	#336	C₂²×C₅	1	1	yes	characteristic
240	#336	C₂²×C₅	1	1	yes	characteristic
241	#336	C₂²×C₅	1	1	yes	characteristic
242	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₅×Q₈	—	4	4	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	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	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	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	#117	1	2	yes	—
283	C₂×C₄×C₅	#117	1	2	yes	—
284	C₂×C₄×C₅	#131	1	2	yes	—
285	C₂×C₄×C₅	#131	1	2	yes	—
286	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
290	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
291	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
292	C₅×C₈	—	4	1	no	—
293	C₅×C₈	—	4	1	no	—
294	C₅×C₈	—	4	1	no	—
295	C₅×C₈	—	4	1	no	—
296	C₅×C₈	—	4	1	no	—
297	C₅×C₈	—	4	1	no	—
298	C₅×C₈	—	4	1	no	—
299	C₅×C₈	—	4	1	no	—
300	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	4	1	no	—
334	C₄⋊C₈	—	4	1	no	—
335	C₄⋊C₈	—	4	1	no	—
336	C₄⋊C₈	—	4	1	no	—
337	#97	—	2	2	no	—
338	#97	—	4	1	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	4	1	no	—
341	#95	C₂×C₄×C₅	1	1	yes	characteristic
342	#95	C₂×C₄×C₅	1	1	yes	characteristic
343	#95	C₂×C₄×C₅	1	1	yes	characteristic
344	#95	C₂×C₄×C₅	1	1	yes	characteristic
345	#95	C₂×C₄×C₅	1	1	yes	characteristic
346	#95	C₂×C₄×C₅	1	1	yes	characteristic
347	#95	C₂×C₄×C₅	1	1	yes	characteristic
348	#95	C₂×C₄×C₅	1	1	yes	characteristic
349	#95	C₂×C₄×C₅	1	1	yes	characteristic
350	#95	C₂×C₄×C₅	1	1	yes	characteristic
351	#95	C₂×C₄×C₅	1	1	yes	characteristic
352	#95	C₂×C₄×C₅	1	1	yes	characteristic
353	#95	C₂×C₄×C₅	1	1	yes	characteristic
354	#95	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂²×C₅	C₂×#117	1	1	yes	characteristic
356	C₂²×C₅	#519	1	1	yes	characteristic
357	C₂²×C₅	#520	1	1	yes	characteristic
358	C₂²×C₅	C₂×#131	1	1	yes	characteristic
359	C₂²×C₅	C₂×#131	1	1	yes	characteristic
360	C₂²×C₅	#568	1	1	yes	characteristic
361	C₂²×C₅	#568	1	1	yes	characteristic
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	4	1	no	—
367	C₄×C₅	—	4	1	no	—
368	C₄×C₅	—	4	1	no	—
369	C₄×C₅	—	4	1	no	—
370	C₄×C₅	—	4	1	no	—
371	C₄×C₅	—	4	1	no	—
372	C₄×C₅	—	4	1	no	—
373	C₄×C₅	—	4	1	no	—
374	C₄×C₅	—	4	1	no	—
375	C₄×C₅	—	4	1	no	—
376	C₄×C₅	#541	1	1	yes	characteristic
377	C₄×C₅	#541	1	1	yes	characteristic
378	C₄×C₅	#542	1	1	yes	characteristic
379	C₄×C₅	#542	1	1	yes	characteristic
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	4	1	no	—
446	C₄²	—	4	1	no	—
447	C₄²	C₅×#41	1	2	yes	—
448	C₄²	C₅×#41	1	2	yes	—
449	C₂×C₅	#2320	1	1	yes	characteristic
450	C₂×C₅	#2924	1	1	yes	characteristic
451	C₂×C₅	#2925	1	1	yes	characteristic
452	C₂×C₅	#2986	1	1	yes	characteristic
453	C₂×C₅	#2987	1	1	yes	characteristic
454	C₂×C₅	#2992	1	1	yes	characteristic
455	C₂×C₅	#2993	1	1	yes	characteristic
456	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
457	Q₈	—	4	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	C₅×#117	1	2	yes	—
497	C₂×C₄	C₅×#117	1	2	yes	—
498	C₂×C₄	C₅×#131	1	2	yes	—
499	C₂×C₄	C₅×#131	1	2	yes	—
500	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
501	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
502	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
504	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
506	C₈	—	4	1	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	1	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₅	#22027	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²	C₂×C₅×#117	1	1	yes	characteristic
516	C₂²	C₅×#519	1	1	yes	characteristic
517	C₂²	C₅×#520	1	1	yes	characteristic
518	C₂²	C₂×C₅×#131	1	1	yes	characteristic
519	C₂²	C₂×C₅×#131	1	1	yes	characteristic
520	C₂²	C₅×#568	1	1	yes	characteristic
521	C₂²	C₅×#568	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	C₅×#541	1	1	yes	characteristic
537	C₄	C₅×#541	1	1	yes	characteristic
538	C₄	C₅×#542	1	1	yes	characteristic
539	C₄	C₅×#542	1	1	yes	characteristic
540	C₂	C₅×#2320	1	1	yes	characteristic
541	C₂	C₅×#2924	1	1	yes	characteristic
542	C₂	C₅×#2925	1	1	yes	characteristic
543	C₂	C₅×#2986	1	1	yes	characteristic
544	C₂	C₅×#2987	1	1	yes	characteristic
545	C₂	C₅×#2992	1	1	yes	characteristic
546	C₂	C₅×#2993	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
59. #22027	C₅	direct (N × H)
514. C₅	#22027	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2295	2
C₅×#1985	2
C₅×#1984	2
C₅×#1940	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1840	2
C₅×#1839	2
C₅×#1832	2
C₅×#1831	2
C₅×#1768	2
C₅×#1746	2
#22027	5

Subgroups — C5×#22027 #11944747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22027 #11944747