Subgroups — C₅×#22391 #11945111

Order 1280.

768 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1870	C₂	1	1	yes	maximal, characteristic
9	C₅×#1869	C₂	1	1	yes	maximal, characteristic
10	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	C₄	1	1	yes	characteristic
36	C₅×#390	C₄	1	1	yes	characteristic
37	C₅×#388	C₄	1	1	yes	characteristic
38	C₅×#388	C₄	1	1	yes	characteristic
39	C₅×#388	C₄	1	1	yes	characteristic
40	C₅×#388	C₄	1	1	yes	characteristic
41	C₅×#382	C₄	1	1	yes	characteristic
42	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₂²⋊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	#22391	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	4	1	no	—
66	C₂×C₅×M₁₆	—	4	1	no	—
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₂²×C₅×C₈	—	4	1	no	—
69	C₂²×C₅×C₈	—	4	1	no	—
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₅×#124	—	2	4	no	—
79	C₄×C₅×Q₈	—	4	1	no	—
80	C₄×C₅×Q₈	—	4	1	no	—
81	C₄×C₅×D₄	—	4	1	no	—
82	C₄×C₅×D₄	—	4	1	no	—
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	2	no	—
108	C₅×C₄⋊C₈	—	4	1	no	—
109	C₅×C₄⋊C₈	—	4	1	no	—
110	C₅×C₂²⋊C₈	—	2	2	no	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×C₂²⋊C₈	—	4	1	no	—
113	C₅×C₂²⋊C₈	—	4	1	no	—
114	C₅×C₂²⋊C₈	—	4	1	no	—
115	C₅×C₂²⋊C₈	—	4	1	no	—
116	C₅×#97	—	4	1	no	—
117	C₅×#97	—	4	1	no	—
118	C₅×#97	—	4	1	no	—
119	C₄×C₅×C₈	—	4	1	no	—
120	C₅×#95	C₂×C₄	1	1	yes	characteristic
121	C₅×#95	C₂×C₄	1	1	yes	characteristic
122	C₅×#95	C₂×C₄	1	1	yes	characteristic
123	C₅×#95	C₂×C₄	1	1	yes	characteristic
124	C₅×#95	C₂×C₄	1	1	yes	characteristic
125	C₅×#95	C₂×C₄	1	1	yes	characteristic
126	C₅×#95	C₂×C₄	1	1	yes	characteristic
127	C₅×#95	C₂×C₄	1	1	yes	characteristic
128	C₄×#124	C₂×C₅	1	1	yes	characteristic
129	#1985	C₂×C₅	1	1	yes	characteristic, complemented
130	#1984	C₂×C₅	1	1	yes	characteristic, complemented
131	#1924	C₂×C₅	1	1	yes	characteristic, complemented
132	#1924	C₂×C₅	1	1	yes	characteristic, complemented
133	#1924	C₂×C₅	1	1	yes	characteristic, complemented
134	#1923	C₂×C₅	1	1	yes	characteristic, complemented
135	#1870	C₂×C₅	1	1	yes	characteristic
136	#1869	C₂×C₅	1	1	yes	characteristic
137	#1851	C₂×C₅	1	1	yes	characteristic, complemented
138	#1850	C₂×C₅	1	1	yes	characteristic, complemented
139	#1839	C₂×C₅	1	1	yes	characteristic, complemented
140	#1767	C₂×C₅	1	1	yes	characteristic, complemented
141	#1753	C₂×C₅	1	1	yes	characteristic, complemented
142	#1752	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂×C₅×Q₈	—	4	1	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	—	4	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
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	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
176	C₅×M₁₆	—	4	4	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
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	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	4	4	no	—
200	C₂×C₅×C₈	#41	1	2	yes	—
201	C₂×C₅×C₈	#41	1	2	yes	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	4	1	no	—
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
216	C₄²×C₅	—	2	2	no	—
217	C₄²×C₅	—	2	2	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	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	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	4	1	no	—
229	C₄²×C₅	—	4	1	no	—
230	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×#124	C₄×C₅	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	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×#97	C₂²×C₅	1	1	yes	characteristic
246	C₂×#97	C₂²×C₅	1	1	yes	characteristic
247	C₂×#97	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
249	#391	C₄×C₅	1	1	yes	characteristic
250	#390	C₄×C₅	1	1	yes	characteristic
251	#388	C₄×C₅	1	1	yes	characteristic
252	#388	C₄×C₅	1	1	yes	characteristic
253	#388	C₄×C₅	1	1	yes	characteristic
254	#388	C₄×C₅	1	1	yes	characteristic
255	#382	C₄×C₅	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₄³	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	#336	C₂²×C₅	1	1	yes	characteristic
268	#336	C₂²×C₅	1	1	yes	characteristic
269	#336	C₂²×C₅	1	1	yes	characteristic
270	#336	C₂²×C₅	1	1	yes	characteristic
271	#336	C₂²×C₅	1	1	yes	characteristic
272	#336	C₂²×C₅	1	1	yes	characteristic
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	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	C₂×M₁₆	1	2	yes	—
287	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
288	C₅×Q₈	—	4	4	no	—
289	C₅×D₄	—	4	4	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	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	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	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	—	4	1	no	—
331	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
332	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
333	C₂×C₄×C₅	#131	1	2	yes	—
334	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₅	H(5,𝔽₂)	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	C₅×C₈	—	2	2	no	—
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₅×C₈	—	4	1	no	—
346	C₅×C₈	—	4	1	no	—
347	C₅×C₈	—	4	1	no	—
348	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
349	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	—	4	1	no	—
354	C₂×M₁₆	—	4	1	no	—
355	C₂²×C₈	—	2	2	no	—
356	C₂²×C₈	—	4	1	no	—
357	C₂²×C₈	—	4	1	no	—
358	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
366	#124	—	2	4	no	—
367	C₄×Q₈	—	4	1	no	—
368	C₄×Q₈	—	4	1	no	—
369	C₄×D₄	—	4	1	no	—
370	C₄×D₄	—	4	1	no	—
371	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
387	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
388	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	—	4	1	no	—
397	C₄⋊C₈	—	4	1	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	4	1	no	—
401	C₂²⋊C₈	—	4	1	no	—
402	C₂²⋊C₈	—	4	1	no	—
403	C₂²⋊C₈	—	4	1	no	—
404	#97	—	4	1	no	—
405	#97	—	4	1	no	—
406	#97	—	4	1	no	—
407	C₄×C₈	—	4	1	no	—
408	#95	C₂×C₄×C₅	1	1	yes	characteristic
409	#95	C₂×C₄×C₅	1	1	yes	characteristic
410	#95	C₂×C₄×C₅	1	1	yes	characteristic
411	#95	C₂×C₄×C₅	1	1	yes	characteristic
412	#95	C₂×C₄×C₅	1	1	yes	characteristic
413	#95	C₂×C₄×C₅	1	1	yes	characteristic
414	#95	C₂×C₄×C₅	1	1	yes	characteristic
415	#95	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	C₄×#41	1	1	yes	characteristic
431	C₂²×C₅	#518	1	1	yes	characteristic
432	C₂²×C₅	#520	1	1	yes	characteristic
433	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
434	C₂²×C₅	C₂×#131	1	1	yes	characteristic
435	C₂²×C₅	#568	1	1	yes	characteristic
436	C₂²×C₅	#568	1	1	yes	characteristic
437	C₄×C₅	—	2	2	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	1	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	#538	1	1	yes	characteristic
450	C₄×C₅	#538	1	1	yes	characteristic
451	C₄×C₅	#542	1	1	yes	characteristic
452	C₄×C₅	#542	1	1	yes	characteristic
453	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
454	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	4	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	4	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	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	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	C₂²×C₄×C₅	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
486	M₁₆	—	4	4	no	—
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	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	4	4	no	—
510	C₂×C₈	C₅×#41	1	2	yes	—
511	C₂×C₈	C₅×#41	1	2	yes	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	4	1	no	—
539	C₄²	—	4	1	no	—
540	C₂×C₅	—	4	2	no	—
541	C₂×C₅	—	8	1	no	—
542	C₂×C₅	#2337	1	1	yes	characteristic
543	C₂×C₅	#2969	1	1	yes	characteristic
544	C₂×C₅	#2970	1	1	yes	characteristic
545	C₂×C₅	#2974	1	1	yes	characteristic
546	C₂×C₅	#2980	1	1	yes	characteristic
547	C₂×C₅	#2989	1	1	yes	characteristic
548	C₂×C₅	#2993	1	1	yes	characteristic
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	C₂×C₅×M₁₆	1	2	yes	—
563	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
564	Q₈	—	4	4	no	—
565	D₄	—	4	4	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	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
608	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
609	C₂×C₄	C₅×#131	1	2	yes	—
610	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
611	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
612	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	2	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₅	#22391	1	1	yes	characteristic, direct product factor, Sylow
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₄×C₅×#41	1	1	yes	characteristic
640	C₂²	C₅×#518	1	1	yes	characteristic
641	C₂²	C₅×#520	1	1	yes	characteristic
642	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
643	C₂²	C₂×C₅×#131	1	1	yes	characteristic
644	C₂²	C₅×#568	1	1	yes	characteristic
645	C₂²	C₅×#568	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	C₅×#538	1	1	yes	characteristic
659	C₄	C₅×#538	1	1	yes	characteristic
660	C₄	C₅×#542	1	1	yes	characteristic
661	C₄	C₅×#542	1	1	yes	characteristic
662	C₂	—	4	2	no	—
663	C₂	—	8	1	no	—
664	C₂	C₅×#2337	1	1	yes	characteristic
665	C₂	C₅×#2969	1	1	yes	characteristic
666	C₂	C₅×#2970	1	1	yes	characteristic
667	C₂	C₅×#2974	1	1	yes	characteristic
668	C₂	C₅×#2980	1	1	yes	characteristic
669	C₂	C₅×#2989	1	1	yes	characteristic
670	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	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×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
2. C₅×#1985	C₂	semidirect
3. C₅×#1984	C₂	semidirect
4. C₅×#1924	C₂	semidirect
5. C₅×#1924	C₂	semidirect
6. C₅×#1924	C₂	semidirect
7. C₅×#1923	C₂	semidirect
10. C₅×#1851	C₂	semidirect
11. C₅×#1850	C₂	semidirect
12. C₅×#1839	C₂	semidirect
13. C₅×#1767	C₂	semidirect
14. C₅×#1753	C₂	semidirect
15. C₅×#1752	C₂	semidirect
59. #22391	C₅	direct (N × H)
129. #1985	C₂×C₅	semidirect
130. #1984	C₂×C₅	semidirect
131. #1924	C₂×C₅	semidirect
132. #1924	C₂×C₅	semidirect
133. #1924	C₂×C₅	semidirect
134. #1923	C₂×C₅	semidirect
137. #1851	C₂×C₅	semidirect
138. #1850	C₂×C₅	semidirect
139. #1839	C₂×C₅	semidirect
140. #1767	C₂×C₅	semidirect
141. #1753	C₂×C₅	semidirect
142. #1752	C₂×C₅	semidirect
215. C₅×C₂²⋊C₄	M₁₆	semidirect
525. C₂²⋊C₄	C₅×M₁₆	semidirect
624. C₅	#22391	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×#124	2
C₅×#1985	2
C₅×#1984	2
C₅×#1924	2
C₅×#1923	2
C₅×#1870	2
C₅×#1869	2
C₅×#1851	2
C₅×#1850	2
C₅×#1839	2
C₅×#1767	2
C₅×#1753	2
C₅×#1752	2
#22391	5

Subgroups — C5×#22391 #11945111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22391 #11945111