Subgroups — C₅×#22305 #11945025

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₅×#1940	C₂	1	1	yes	maximal, characteristic
3	C₅×#1940	C₂	1	1	yes	maximal, characteristic
4	C₅×#1940	C₂	1	1	yes	maximal, characteristic
5	C₅×#1940	C₂	1	1	yes	maximal, characteristic
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic
7	C₅×#1939	C₂	1	1	yes	maximal, characteristic
8	C₅×#1917	C₂	1	1	yes	maximal, characteristic
9	C₅×#1917	C₂	1	1	yes	maximal, characteristic
10	C₅×#1916	C₂	1	1	yes	maximal, characteristic
11	C₅×#1916	C₂	1	1	yes	maximal, characteristic
12	C₅×#1842	C₂	1	1	yes	maximal, characteristic
13	C₅×#1771	C₂	1	1	yes	maximal, characteristic
14	C₅×#1771	C₂	1	1	yes	maximal, characteristic
15	C₅×#1745	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×#125	C₄	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×C₄⋊C₈	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×#97	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×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#389	C₄	1	1	yes	characteristic
34	C₅×#389	C₄	1	1	yes	characteristic
35	C₅×#387	C₄	1	1	yes	characteristic
36	C₅×#387	C₄	1	1	yes	characteristic
37	C₅×#387	C₄	1	1	yes	characteristic
38	C₅×#387	C₄	1	1	yes	characteristic
39	C₅×#382	C₄	1	1	yes	characteristic
40	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	C₄³×C₅	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	#22305	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×C₈	C₂³	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	C₅×#125	—	2	4	no	—
69	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₅×C₄⋊C₄	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	C₂×C₄	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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊C₈	—	2	2	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	—	4	1	no	—
95	C₅×C₄⋊C₈	—	4	1	no	—
96	C₅×C₄⋊C₈	—	4	1	no	—
97	C₅×C₄⋊C₈	—	4	1	no	—
98	C₅×C₄⋊C₈	—	4	1	no	—
99	C₅×C₄⋊C₈	—	4	1	no	—
100	C₅×C₄⋊C₈	—	4	1	no	—
101	C₅×C₄⋊C₈	—	4	1	no	—
102	C₅×#97	—	2	2	no	—
103	C₅×#97	—	4	1	no	—
104	C₅×#97	—	4	1	no	—
105	C₅×#97	Q₈	1	4	yes	—
106	C₄×C₅×C₈	—	4	1	no	—
107	C₄×C₅×C₈	—	4	1	no	—
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	C₅×#95	C₂×C₄	1	1	yes	characteristic
116	C₅×#95	C₂×C₄	1	1	yes	characteristic
117	C₅×#95	C₂×C₄	1	1	yes	characteristic
118	C₅×#95	C₂×C₄	1	1	yes	characteristic
119	C₅×#95	C₂×C₄	1	1	yes	characteristic
120	C₄×#125	C₂×C₅	1	1	yes	characteristic
121	#1940	C₂×C₅	1	1	yes	characteristic
122	#1940	C₂×C₅	1	1	yes	characteristic
123	#1940	C₂×C₅	1	1	yes	characteristic
124	#1940	C₂×C₅	1	1	yes	characteristic
125	#1939	C₂×C₅	1	1	yes	characteristic
126	#1939	C₂×C₅	1	1	yes	characteristic
127	#1917	C₂×C₅	1	1	yes	characteristic
128	#1917	C₂×C₅	1	1	yes	characteristic
129	#1916	C₂×C₅	1	1	yes	characteristic
130	#1916	C₂×C₅	1	1	yes	characteristic
131	#1842	C₂×C₅	1	1	yes	characteristic
132	#1771	C₂×C₅	1	1	yes	characteristic
133	#1771	C₂×C₅	1	1	yes	characteristic
134	#1745	C₂×C₅	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	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
173	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
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	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	—	2	2	no	—
181	C₅×C₄⋊C₄	—	4	1	no	—
182	C₅×C₄⋊C₄	—	4	1	no	—
183	C₅×C₄⋊C₄	—	4	1	no	—
184	C₅×C₄⋊C₄	—	4	1	no	—
185	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	—	2	2	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	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	4	1	no	—
201	C₄²×C₅	—	4	1	no	—
202	C₄²×C₅	C₂×Q₈	1	2	yes	—
203	C₄²×C₅	#41	1	2	yes	—
204	C₂×#125	C₄×C₅	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₈	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	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
215	C₂×#97	C₂²×C₅	1	1	yes	characteristic
216	C₂×#97	C₂²×C₅	1	1	yes	characteristic
217	C₂×#97	C₂²×C₅	1	1	yes	characteristic
218	C₂×#97	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
221	#389	C₄×C₅	1	1	yes	characteristic
222	#389	C₄×C₅	1	1	yes	characteristic
223	#387	C₄×C₅	1	1	yes	characteristic
224	#387	C₄×C₅	1	1	yes	characteristic
225	#387	C₄×C₅	1	1	yes	characteristic
226	#387	C₄×C₅	1	1	yes	characteristic
227	#382	C₄×C₅	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₄³	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	#336	C₂²×C₅	1	1	yes	characteristic
243	#336	C₂²×C₅	1	1	yes	characteristic
244	#336	C₂²×C₅	1	1	yes	characteristic
245	#336	C₂²×C₅	1	1	yes	characteristic
246	#336	C₂²×C₅	1	1	yes	characteristic
247	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
285	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
286	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
287	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
288	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
289	C₂×C₄×C₅	#131	1	2	yes	—
290	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	4	1	no	—
299	C₅×C₈	—	4	1	no	—
300	C₅×C₈	—	4	1	no	—
301	C₅×C₈	—	4	1	no	—
302	C₅×C₈	—	4	1	no	—
303	C₅×C₈	—	4	1	no	—
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	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
312	#125	—	2	4	no	—
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×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	4	1	no	—
339	C₄⋊C₈	—	4	1	no	—
340	C₄⋊C₈	—	4	1	no	—
341	C₄⋊C₈	—	4	1	no	—
342	C₄⋊C₈	—	4	1	no	—
343	C₄⋊C₈	—	4	1	no	—
344	C₄⋊C₈	—	4	1	no	—
345	C₄⋊C₈	—	4	1	no	—
346	#97	—	2	2	no	—
347	#97	—	4	1	no	—
348	#97	—	4	1	no	—
349	#97	C₅×Q₈	1	4	yes	—
350	C₄×C₈	—	4	1	no	—
351	C₄×C₈	—	4	1	no	—
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	#95	C₂×C₄×C₅	1	1	yes	characteristic
356	#95	C₂×C₄×C₅	1	1	yes	characteristic
357	#95	C₂×C₄×C₅	1	1	yes	characteristic
358	#95	C₂×C₄×C₅	1	1	yes	characteristic
359	#95	C₂×C₄×C₅	1	1	yes	characteristic
360	#95	C₂×C₄×C₅	1	1	yes	characteristic
361	#95	C₂×C₄×C₅	1	1	yes	characteristic
362	#95	C₂×C₄×C₅	1	1	yes	characteristic
363	#95	C₂×C₄×C₅	1	1	yes	characteristic
364	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
365	C₂²×C₅	#520	1	1	yes	characteristic
366	C₂²×C₅	#520	1	1	yes	characteristic
367	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
368	C₂²×C₅	C₂×#131	1	1	yes	characteristic
369	C₂²×C₅	#568	1	1	yes	characteristic
370	C₂²×C₅	#568	1	1	yes	characteristic
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	—	2	2	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	—	4	1	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	1	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	4	1	no	—
385	C₄×C₅	#540	1	1	yes	characteristic
386	C₄×C₅	#541	1	1	yes	characteristic
387	C₄×C₅	#544	1	1	yes	characteristic
388	C₄×C₅	#544	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	C₂²×C₄×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
427	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	4	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	4	1	no	—
455	C₄²	—	4	1	no	—
456	C₄²	C₂×C₅×Q₈	1	2	yes	—
457	C₄²	C₅×#41	1	2	yes	—
458	C₂×C₅	#2330	1	1	yes	characteristic
459	C₂×C₅	#2962	1	1	yes	characteristic
460	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
461	C₂×C₅	#2989	1	1	yes	characteristic
462	C₂×C₅	#2990	1	1	yes	characteristic
463	C₂×C₅	#2992	1	1	yes	characteristic
464	C₂×C₅	#2995	1	1	yes	characteristic
465	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
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	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
503	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
504	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
505	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
506	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
507	C₂×C₄	C₅×#131	1	2	yes	—
508	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
509	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
510	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
513	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₅	#22305	1	1	yes	characteristic, direct product factor, Sylow
523	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
524	C₂²	C₅×#520	1	1	yes	characteristic
525	C₂²	C₅×#520	1	1	yes	characteristic
526	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
527	C₂²	C₂×C₅×#131	1	1	yes	characteristic
528	C₂²	C₅×#568	1	1	yes	characteristic
529	C₂²	C₅×#568	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	C₅×#540	1	1	yes	characteristic
545	C₄	C₅×#541	1	1	yes	characteristic
546	C₄	C₅×#544	1	1	yes	characteristic
547	C₄	C₅×#544	1	1	yes	characteristic
548	C₂	C₅×#2330	1	1	yes	characteristic
549	C₂	C₅×#2962	1	1	yes	characteristic
550	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic
551	C₂	C₅×#2989	1	1	yes	characteristic
552	C₂	C₅×#2990	1	1	yes	characteristic
553	C₂	C₅×#2992	1	1	yes	characteristic
554	C₂	C₅×#2995	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. #22305	C₅	direct (N × H)
522. C₅	#22305	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#125	2
C₅×#1940	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1842	2
C₅×#1771	2
C₅×#1745	2
#22305	5

Subgroups — C5×#22305 #11945025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22305 #11945025