Subgroups — C₅×#22589 #11945309

Order 1280.

864 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₅×#1916	C₂	1	2	yes	maximal, complemented
3	C₅×#1916	C₂	1	2	yes	maximal, complemented
4	C₅×#1850	C₂	1	2	yes	maximal
5	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1817	C₂	1	1	yes	maximal, characteristic
8	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₅×#117	C₄	1	1	yes	characteristic
14	C₂×C₅×#117	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
27	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×#376	C₄	1	1	yes	characteristic
30	C₅×#376	C₄	1	1	yes	characteristic
31	C₄³×C₅	C₂²	1	1	yes	characteristic
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	1	yes	characteristic
34	C₅×#336	C₂²	1	1	yes	characteristic
35	C₅×#336	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#22589	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	—	2	4	no	—
48	C₂²×C₅×C₈	—	2	4	no	—
49	C₂²×C₅×C₈	—	4	2	no	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×#117	—	2	4	no	—
55	C₅×#117	C₈	1	8	yes	complemented
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	—	2	4	no	—
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊C₈	—	2	4	no	—
82	C₅×C₄⋊C₈	—	4	2	no	—
83	C₅×C₂²⋊C₈	—	2	4	no	—
84	C₄×C₅×C₈	—	2	4	no	—
85	C₄×C₅×C₈	—	4	2	no	—
86	C₅×#95	C₂×C₄	1	1	yes	characteristic
87	C₅×#95	C₂×C₄	1	1	yes	characteristic
88	C₅×#95	C₂×C₄	1	1	yes	characteristic
89	C₅×#95	C₂×C₄	1	1	yes	characteristic
90	C₅×#95	C₂×C₄	1	1	yes	characteristic
91	C₅×#95	C₂×C₄	1	1	yes	characteristic
92	C₅×#95	C₂×C₄	1	1	yes	characteristic
93	C₅×#95	C₂×C₄	1	1	yes	characteristic
94	C₄×#117	C₂×C₅	1	1	yes	characteristic
95	#1916	C₂×C₅	1	2	yes	complemented
96	#1916	C₂×C₅	1	2	yes	complemented
97	#1850	C₂×C₅	1	2	yes	—
98	#1839	C₂×C₅	1	1	yes	characteristic, complemented
99	#1831	C₂×C₅	1	1	yes	characteristic, complemented
100	#1817	C₂×C₅	1	1	yes	characteristic
101	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
102	C₈×C₂²⋊C₄	C₂×C₅	1	2	yes	—
103	#1744	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#336	C₂×C₅	1	1	yes	characteristic
105	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	4	1	no	—
114	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	4	yes	—
129	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	4	8	no	—
142	C₂×C₅×C₈	#41	1	4	yes	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
146	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
149	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
150	C₅×C₂²⋊C₄	M₁₆	1	4	yes	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	4	1	no	—
166	C₄²×C₅	—	4	1	no	—
167	C₄²×C₅	C₂×C₈	1	4	yes	complemented
168	C₄²×C₅	C₂×C₈	1	4	yes	complemented
169	C₂³×C₈	C₂²×C₅	1	2	yes	—
170	C₂×#117	C₄×C₅	1	1	yes	characteristic
171	C₂×#117	C₄×C₅	1	1	yes	characteristic
172	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
175	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
178	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	#376	C₄×C₅	1	1	yes	characteristic
187	#376	C₄×C₅	1	1	yes	characteristic
188	C₄³	C₂²×C₅	1	1	yes	characteristic
189	C₄³	C₂²×C₅	1	1	yes	characteristic
190	#336	C₂²×C₅	1	1	yes	characteristic
191	#336	C₂²×C₅	1	1	yes	characteristic
192	#336	C₂²×C₅	1	2	yes	—
193	#336	C₂²×C₅	1	1	yes	characteristic
194	#336	C₂²×C₅	1	2	yes	—
195	#336	C₂²×C₅	1	2	yes	—
196	#336	C₂²×C₅	1	2	yes	—
197	#336	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	#117	1	2	yes	—
205	C₂³×C₅	C₂²×C₈	1	2	yes	—
206	C₂³×C₅	C₂×M₁₆	1	2	yes	—
207	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	8	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	#117	1	2	yes	—
242	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
243	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
244	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
245	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
246	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
247	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
248	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
249	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
250	C₂×C₄×C₅	#131	1	2	yes	—
251	C₂×C₄×C₅	C₂×#41	1	2	yes	—
252	C₂×C₄×C₅	C₂×#41	1	2	yes	—
253	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
255	C₅×C₈	—	2	4	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	—	4	2	no	—
258	C₅×C₈	—	4	2	no	—
259	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	—	2	4	no	—
263	C₂²×C₈	—	2	4	no	—
264	C₂²×C₈	—	4	2	no	—
265	C₂²×C₈	C₂³×C₅	1	2	yes	—
266	C₂²×C₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₈	C₂³×C₅	1	2	yes	—
268	C₂²×C₈	C₂³×C₅	1	2	yes	—
269	#117	—	2	4	no	—
270	#117	C₅×C₈	1	8	yes	complemented
271	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
287	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
288	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
296	C₄⋊C₈	—	2	4	no	—
297	C₄⋊C₈	—	4	2	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₄×C₈	—	2	4	no	—
300	C₄×C₈	—	4	2	no	—
301	#95	C₂×C₄×C₅	1	1	yes	characteristic
302	#95	C₂×C₄×C₅	1	1	yes	characteristic
303	#95	C₂×C₄×C₅	1	1	yes	characteristic
304	#95	C₂×C₄×C₅	1	1	yes	characteristic
305	#95	C₂×C₄×C₅	1	1	yes	characteristic
306	#95	C₂×C₄×C₅	1	1	yes	characteristic
307	#95	C₂×C₄×C₅	1	1	yes	characteristic
308	#95	C₂×C₄×C₅	1	1	yes	characteristic
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	#431	1	4	yes	—
316	C₂²×C₅	C₂×#117	1	1	yes	characteristic
317	C₂²×C₅	C₄×#41	1	1	yes	characteristic
318	C₂²×C₅	#520	1	1	yes	characteristic
319	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
320	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
321	C₂²×C₅	C₂×#131	1	1	yes	characteristic
322	C₂²×C₅	#568	1	1	yes	characteristic
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	2	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	2	2	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	4	1	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	#551	1	2	yes	—
337	C₄×C₅	#552	1	2	yes	—
338	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₅×#41	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	8	no	—
375	C₂×C₈	C₅×#41	1	4	yes	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
379	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
382	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
383	C₂²⋊C₄	C₅×M₁₆	1	4	yes	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	C₂×C₅×C₈	1	4	yes	complemented
401	C₄²	C₂×C₅×C₈	1	4	yes	complemented
402	C₂×C₅	—	2	4	no	—
403	C₂×C₅	#2343	1	1	yes	characteristic
404	C₂×C₅	C₂×#431	1	1	yes	characteristic
405	C₂×C₅	#2924	1	1	yes	characteristic
406	C₂×C₅	C₈×#41	1	1	yes	characteristic
407	C₂×C₅	#2970	1	1	yes	characteristic
408	C₂×C₅	#2988	1	1	yes	characteristic
409	C₂×C₅	#2990	1	1	yes	characteristic
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	C₅×#117	1	2	yes	—
415	C₂³	C₂²×C₅×C₈	1	2	yes	—
416	C₂³	C₂×C₅×M₁₆	1	2	yes	—
417	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	C₅×#117	1	2	yes	—
452	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
453	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
454	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
455	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
456	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
457	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
458	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
459	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
460	C₂×C₄	C₅×#131	1	2	yes	—
461	C₂×C₄	C₂×C₅×#41	1	2	yes	—
462	C₂×C₄	C₂×C₅×#41	1	2	yes	—
463	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
465	C₈	—	2	4	no	—
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₅	#22589	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	C₅×#431	1	4	yes	—
477	C₂²	C₂×C₅×#117	1	1	yes	characteristic
478	C₂²	C₄×C₅×#41	1	1	yes	characteristic
479	C₂²	C₅×#520	1	1	yes	characteristic
480	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
481	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
482	C₂²	C₂×C₅×#131	1	1	yes	characteristic
483	C₂²	C₅×#568	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	C₅×#551	1	2	yes	—
498	C₄	C₅×#552	1	2	yes	—
499	C₂	—	2	4	no	—
500	C₂	C₅×#2343	1	1	yes	characteristic
501	C₂	C₂×C₅×#431	1	1	yes	characteristic
502	C₂	C₅×#2924	1	1	yes	characteristic
503	C₂	C₅×C₈×#41	1	1	yes	characteristic
504	C₂	C₅×#2970	1	1	yes	characteristic
505	C₂	C₅×#2988	1	1	yes	characteristic
506	C₂	C₅×#2990	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1916	C₂	semidirect
3. C₅×#1916	C₂	semidirect
5. C₅×#1839	C₂	semidirect
6. C₅×#1831	C₂	semidirect
8. C₄×C₅×C₄⋊C₈	C₂	semidirect
10. C₅×#1744	C₂	semidirect
43. #22589	C₅	direct (N × H)
55. C₅×#117	C₈	semidirect
95. #1916	C₂×C₅	semidirect
96. #1916	C₂×C₅	semidirect
98. #1839	C₂×C₅	semidirect
99. #1831	C₂×C₅	semidirect
101. C₄×C₄⋊C₈	C₂×C₅	semidirect
103. #1744	C₂×C₅	semidirect
145. C₅×C₄⋊C₄	C₂×C₈	semidirect
146. C₅×C₄⋊C₄	C₂×C₈	semidirect
167. C₄²×C₅	C₂×C₈	semidirect
168. C₄²×C₅	C₂×C₈	semidirect
270. #117	C₅×C₈	semidirect
378. C₄⋊C₄	C₂×C₅×C₈	semidirect
379. C₄⋊C₄	C₂×C₅×C₈	semidirect
400. C₄²	C₂×C₅×C₈	semidirect
401. C₄²	C₂×C₅×C₈	semidirect
469. C₅	#22589	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×#117	2
C₅×#1916	2
C₅×#1850	2
C₅×#1839	2
C₅×#1831	2
C₅×#1817	2
C₄×C₅×C₄⋊C₈	2
C₅×C₈×C₂²⋊C₄	2
C₅×#1744	2
C₂×C₅×#336	2
#22589	5

Subgroups — C5×#22589 #11945309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22589 #11945309