Subgroups — C₅×#22356 #11945076

Order 1280.

642 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2401	C₂	1	1	yes	maximal, characteristic
2	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1924	C₂	1	1	yes	maximal, characteristic
5	C₅×#1923	C₂	1	1	yes	maximal, characteristic
6	C₅×#1923	C₂	1	1	yes	maximal, characteristic
7	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1850	C₂	1	1	yes	maximal, characteristic
11	C₅×#1850	C₂	1	1	yes	maximal, characteristic
12	C₅×#1832	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1752	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊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×#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×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#401	C₄	1	1	yes	characteristic
33	C₅×#400	C₄	1	1	yes	characteristic
34	C₅×#400	C₄	1	1	yes	characteristic
35	C₅×#400	C₄	1	1	yes	characteristic
36	C₅×#397	C₄	1	1	yes	characteristic
37	C₅×#397	C₄	1	1	yes	characteristic
38	C₅×#397	C₄	1	1	yes	characteristic
39	C₅×#396	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×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	C₅×#376	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	#22356	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₂²×C₅×C₈	—	4	1	no	—
63	C₂²×C₅×C₈	—	4	1	no	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	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	C₅×C₄⋊C₈	—	2	2	no	—
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×C₂²⋊C₈	—	2	2	no	—
98	C₅×C₂²⋊C₈	—	4	1	no	—
99	C₅×C₂²⋊C₈	—	4	1	no	—
100	C₅×#97	—	4	1	no	—
101	C₅×#97	—	4	1	no	—
102	C₅×#97	—	4	1	no	—
103	C₄×C₅×C₈	—	2	2	no	—
104	C₄×C₅×C₈	—	4	1	no	—
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	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	C₅×#95	C₂×C₄	1	1	yes	characteristic
121	#2401	C₂×C₅	1	1	yes	characteristic
122	#1940	C₂×C₅	1	1	yes	characteristic, complemented
123	#1940	C₂×C₅	1	1	yes	characteristic, complemented
124	#1924	C₂×C₅	1	1	yes	characteristic
125	#1923	C₂×C₅	1	1	yes	characteristic
126	#1923	C₂×C₅	1	1	yes	characteristic
127	#1917	C₂×C₅	1	1	yes	characteristic, complemented
128	#1916	C₂×C₅	1	1	yes	characteristic, complemented
129	#1916	C₂×C₅	1	1	yes	characteristic, complemented
130	#1850	C₂×C₅	1	1	yes	characteristic
131	#1850	C₂×C₅	1	1	yes	characteristic
132	#1832	C₂×C₅	1	1	yes	characteristic, complemented
133	#1770	C₂×C₅	1	1	yes	characteristic, complemented
134	#1768	C₂×C₅	1	1	yes	characteristic, complemented
135	#1752	C₂×C₅	1	1	yes	characteristic
136	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	4	4	no	—
180	C₂×C₅×C₈	#41	1	2	yes	—
181	C₂×C₅×C₈	#41	1	2	yes	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	4	1	no	—
185	C₅×C₄⋊C₄	—	4	1	no	—
186	C₅×C₄⋊C₄	—	4	1	no	—
187	C₅×C₄⋊C₄	—	4	1	no	—
188	C₅×C₂²⋊C₄	—	2	2	no	—
189	C₅×C₂²⋊C₄	—	2	2	no	—
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	4	1	no	—
193	C₅×C₂²⋊C₄	—	4	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	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₂³×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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	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×#97	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
222	#401	C₄×C₅	1	1	yes	characteristic
223	#400	C₄×C₅	1	1	yes	characteristic
224	#400	C₄×C₅	1	1	yes	characteristic
225	#400	C₄×C₅	1	1	yes	characteristic
226	#397	C₄×C₅	1	1	yes	characteristic
227	#397	C₄×C₅	1	1	yes	characteristic
228	#397	C₄×C₅	1	1	yes	characteristic
229	#396	C₄×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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	#376	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	#336	C₂²×C₅	1	1	yes	characteristic
248	#336	C₂²×C₅	1	1	yes	characteristic
249	C₂³×C₅	—	2	1	no	—
250	C₂³×C₅	—	2	1	no	—
251	C₂³×C₅	—	2	1	no	—
252	C₂³×C₅	—	2	1	no	—
253	C₂³×C₅	—	2	1	no	—
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	#131	1	2	yes	—
256	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	#131	1	2	yes	—
300	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
305	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	2	2	no	—
308	C₅×C₈	—	4	1	no	—
309	C₅×C₈	—	4	1	no	—
310	C₅×C₈	—	4	1	no	—
311	C₅×C₈	—	4	1	no	—
312	C₅×C₈	—	4	1	no	—
313	C₅×C₈	—	4	1	no	—
314	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	4	1	no	—
317	C₂²×C₈	—	4	1	no	—
318	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
344	C₄⋊C₈	—	2	2	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	—	2	2	no	—
347	C₄⋊C₈	—	4	1	no	—
348	C₄⋊C₈	—	4	1	no	—
349	C₄⋊C₈	—	4	1	no	—
350	C₄⋊C₈	—	4	1	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	C₂²⋊C₈	—	4	1	no	—
353	C₂²⋊C₈	—	4	1	no	—
354	#97	—	4	1	no	—
355	#97	—	4	1	no	—
356	#97	—	4	1	no	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	—	4	1	no	—
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	#95	C₂×C₄×C₅	1	1	yes	characteristic
365	#95	C₂×C₄×C₅	1	1	yes	characteristic
366	#95	C₂×C₄×C₅	1	1	yes	characteristic
367	#95	C₂×C₄×C₅	1	1	yes	characteristic
368	#95	C₂×C₄×C₅	1	1	yes	characteristic
369	#95	C₂×C₄×C₅	1	1	yes	characteristic
370	#95	C₂×C₄×C₅	1	1	yes	characteristic
371	#95	C₂×C₄×C₅	1	1	yes	characteristic
372	#95	C₂×C₄×C₅	1	1	yes	characteristic
373	#95	C₂×C₄×C₅	1	1	yes	characteristic
374	#95	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	2	2	no	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	1	no	—
382	C₂²×C₅	C₄×#41	1	1	yes	characteristic
383	C₂²×C₅	#520	1	1	yes	characteristic
384	C₂²×C₅	#520	1	1	yes	characteristic
385	C₂²×C₅	C₂×#131	1	1	yes	characteristic
386	C₂²×C₅	C₂×#131	1	1	yes	characteristic
387	C₂²×C₅	#568	1	1	yes	characteristic
388	C₂²×C₅	#568	1	1	yes	characteristic
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	—	4	1	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	#538	1	1	yes	characteristic
403	C₄×C₅	#539	1	1	yes	characteristic
404	C₄×C₅	#541	1	1	yes	characteristic
405	C₄×C₅	#542	1	1	yes	characteristic
406	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
414	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
418	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
419	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
421	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	4	4	no	—
450	C₂×C₈	C₅×#41	1	2	yes	—
451	C₂×C₈	C₅×#41	1	2	yes	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₂×C₅	—	4	2	no	—
477	C₂×C₅	#2334	1	1	yes	characteristic
478	C₂×C₅	#2968	1	1	yes	characteristic
479	C₂×C₅	#2968	1	1	yes	characteristic
480	C₂×C₅	#2992	1	1	yes	characteristic
481	C₂×C₅	#2993	1	1	yes	characteristic
482	C₂×C₅	#2994	1	1	yes	characteristic
483	C₂×C₅	#2995	1	1	yes	characteristic
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	C₅×#131	1	2	yes	—
491	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
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	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	C₅×#131	1	2	yes	—
535	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
536	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
537	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
540	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	2	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₅	#22356	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	C₄×C₅×#41	1	1	yes	characteristic
558	C₂²	C₅×#520	1	1	yes	characteristic
559	C₂²	C₅×#520	1	1	yes	characteristic
560	C₂²	C₂×C₅×#131	1	1	yes	characteristic
561	C₂²	C₂×C₅×#131	1	1	yes	characteristic
562	C₂²	C₅×#568	1	1	yes	characteristic
563	C₂²	C₅×#568	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	C₅×#538	1	1	yes	characteristic
578	C₄	C₅×#539	1	1	yes	characteristic
579	C₄	C₅×#541	1	1	yes	characteristic
580	C₄	C₅×#542	1	1	yes	characteristic
581	C₂	—	4	2	no	—
582	C₂	C₅×#2334	1	1	yes	characteristic
583	C₂	C₅×#2968	1	1	yes	characteristic
584	C₂	C₅×#2968	1	1	yes	characteristic
585	C₂	C₅×#2992	1	1	yes	characteristic
586	C₂	C₅×#2993	1	1	yes	characteristic
587	C₂	C₅×#2994	1	1	yes	characteristic
588	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	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×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×#1940	C₂	semidirect
3. C₅×#1940	C₂	semidirect
7. C₅×#1917	C₂	semidirect
8. C₅×#1916	C₂	semidirect
9. C₅×#1916	C₂	semidirect
12. C₅×#1832	C₂	semidirect
13. C₅×#1770	C₂	semidirect
14. C₅×#1768	C₂	semidirect
59. #22356	C₅	direct (N × H)
122. #1940	C₂×C₅	semidirect
123. #1940	C₂×C₅	semidirect
127. #1917	C₂×C₅	semidirect
128. #1916	C₂×C₅	semidirect
129. #1916	C₂×C₅	semidirect
132. #1832	C₂×C₅	semidirect
133. #1770	C₂×C₅	semidirect
134. #1768	C₂×C₅	semidirect
549. C₅	#22356	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×#2401	2
C₅×#1940	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1850	2
C₅×#1832	2
C₅×#1770	2
C₅×#1768	2
C₅×#1752	2
#22356	5

Subgroups — C5×#22356 #11945076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22356 #11945076