Subgroups — C₅×#22939 #11945659

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#485	C₂	1	1	yes	maximal, characteristic
2	C₅×#2362	C₂	1	1	yes	maximal, characteristic
3	C₅×#2346	C₂	1	1	yes	maximal, characteristic
4	C₅×#1944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1892	C₂	1	1	yes	maximal, characteristic
10	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1854	C₂	1	1	yes	maximal, characteristic
12	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic
15	C₅×#1735	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#485	C₄	1	8	yes	complemented
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	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	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#389	C₂²	1	1	yes	characteristic
35	C₅×#389	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#388	—	2	1	no	—
38	C₅×#388	—	2	1	no	—
39	C₅×#388	—	2	1	no	—
40	C₅×#388	—	2	1	no	—
41	C₅×#387	—	2	1	no	—
42	C₅×#382	—	2	1	no	—
43	C₅×#380	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	—	2	1	no	—
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×#376	—	2	1	no	—
50	C₅×#340	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#22939	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	—	4	1	no	—
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	C₅×C₂²⋊Q₈	—	2	2	no	—
71	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	—	4	1	no	—
74	C₅×#117	—	2	2	no	—
75	C₅×#117	—	2	2	no	—
76	C₅×#117	—	4	1	no	—
77	C₅×#117	C₂×C₄	1	4	yes	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	—	2	1	no	—
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×#107	—	4	1	no	—
105	C₅×#107	C₂×C₄	1	4	yes	—
106	C₅×#106	—	2	2	no	—
107	C₅×#106	C₂×C₄	1	4	yes	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	—	4	1	no	—
110	C₅×#103	C₂×C₄	1	4	yes	—
111	C₅×#103	C₂×C₄	1	4	yes	—
112	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
113	C₅×#97	—	2	2	no	—
114	C₅×#97	—	4	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	D₄	1	1	yes	characteristic
125	C₅×#95	D₄	1	1	yes	characteristic
126	C₂×#485	C₂×C₅	1	1	yes	characteristic
127	#2362	C₂×C₅	1	1	yes	characteristic
128	#2346	C₂×C₅	1	1	yes	characteristic
129	#1944	C₂×C₅	1	1	yes	characteristic, complemented
130	#1935	C₂×C₅	1	1	yes	characteristic, complemented
131	#1928	C₂×C₅	1	1	yes	characteristic, complemented
132	#1921	C₂×C₅	1	1	yes	characteristic, complemented
133	#1919	C₂×C₅	1	1	yes	characteristic, complemented
134	#1892	C₂×C₅	1	1	yes	characteristic
135	#1865	C₂×C₅	1	1	yes	characteristic, complemented
136	#1854	C₂×C₅	1	1	yes	characteristic
137	#1776	C₂×C₅	1	1	yes	characteristic, complemented
138	#1763	C₂×C₅	1	1	yes	characteristic, complemented
139	#1752	C₂×C₅	1	1	yes	characteristic
140	#1735	C₂×C₅	1	1	yes	characteristic
141	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	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	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	#41	1	2	yes	—
167	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
178	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₅×C₈	#41	1	2	yes	—
181	C₅×C₄⋊C₄	—	2	4	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	4	2	no	—
193	C₅×C₄⋊C₄	—	4	2	no	—
194	C₅×C₄⋊C₄	—	8	1	no	—
195	C₅×C₄⋊C₄	—	8	1	no	—
196	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
197	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
198	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
199	C₅×C₄⋊C₄	#41	1	2	yes	—
200	C₅×C₂²⋊C₄	—	2	4	no	—
201	C₅×C₂²⋊C₄	—	2	4	no	—
202	C₅×C₂²⋊C₄	—	4	1	no	—
203	C₅×C₂²⋊C₄	—	4	1	no	—
204	C₅×C₂²⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	8	1	no	—
206	C₄²×C₅	—	2	4	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	4	2	no	—
212	C₄²×C₅	—	4	2	no	—
213	C₄²×C₅	—	4	2	no	—
214	C₄²×C₅	—	4	2	no	—
215	C₄²×C₅	—	4	2	no	—
216	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×#117	C₂²×C₅	1	1	yes	characteristic
220	C₂×#117	C₂²×C₅	1	1	yes	characteristic
221	#485	C₄×C₅	1	8	yes	complemented
222	C₂×#107	C₂²×C₅	1	1	yes	characteristic
223	C₂×#107	C₂²×C₅	1	1	yes	characteristic
224	C₂×#106	C₂²×C₅	1	1	yes	characteristic
225	C₂×#106	C₂²×C₅	1	1	yes	characteristic
226	C₂×#103	C₂²×C₅	1	1	yes	characteristic
227	C₂×#103	C₂²×C₅	1	1	yes	characteristic
228	C₂×#103	C₂²×C₅	1	1	yes	characteristic
229	C₂×#103	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×#97	C₂²×C₅	1	1	yes	characteristic
232	C₂×#97	C₂²×C₅	1	1	yes	characteristic
233	#391	C₂²×C₅	1	1	yes	characteristic
234	#389	C₂²×C₅	1	1	yes	characteristic
235	#389	C₂²×C₅	1	1	yes	characteristic
236	#389	C₂²×C₅	1	1	yes	characteristic
237	#388	—	2	1	no	—
238	#388	—	2	1	no	—
239	#388	—	2	1	no	—
240	#388	—	2	1	no	—
241	#387	—	2	1	no	—
242	#382	—	2	1	no	—
243	#380	C₂²×C₅	1	1	yes	characteristic
244	C₄×C₄⋊C₄	—	2	1	no	—
245	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	#376	—	2	1	no	—
250	#340	C₂²×C₅	1	1	yes	characteristic
251	#340	C₂²×C₅	1	1	yes	characteristic
252	#340	C₂²×C₅	1	1	yes	characteristic
253	#340	C₂²×C₅	1	1	yes	characteristic
254	#340	C₂²×C₅	1	1	yes	characteristic
255	#340	C₂²×C₅	1	1	yes	characteristic
256	#340	C₂²×C₅	1	1	yes	characteristic
257	#340	C₂²×C₅	1	1	yes	characteristic
258	#336	C₂²×C₅	1	1	yes	characteristic
259	#336	C₂²×C₅	1	1	yes	characteristic
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	—	2	1	no	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	1	no	—
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	C₄×D₄	1	2	yes	—
267	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	2	2	no	—
270	C₅×Q₈	—	4	1	no	—
271	C₅×Q₈	—	4	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	2	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	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
321	C₅×C₈	—	2	2	no	—
322	C₅×C₈	—	2	2	no	—
323	C₅×C₈	—	2	2	no	—
324	C₅×C₈	—	4	1	no	—
325	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	4	1	no	—
330	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	4	1	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	#117	—	4	1	no	—
341	#117	C₂×C₄×C₅	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
368	#107	—	4	1	no	—
369	#107	C₂×C₄×C₅	1	4	yes	—
370	#106	—	2	2	no	—
371	#106	C₂×C₄×C₅	1	4	yes	—
372	#103	—	2	2	no	—
373	#103	—	4	1	no	—
374	#103	C₂×C₄×C₅	1	4	yes	—
375	#103	C₂×C₄×C₅	1	4	yes	—
376	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
377	#97	—	2	2	no	—
378	#97	—	4	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	C₅×D₄	1	1	yes	characteristic
389	#95	C₅×D₄	1	1	yes	characteristic
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	4	1	no	—
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
398	C₂²×C₅	#546	1	1	yes	characteristic
399	C₂²×C₅	#547	1	1	yes	characteristic
400	C₂²×C₅	#575	1	1	yes	characteristic
401	C₂²×C₅	#575	1	1	yes	characteristic
402	C₂²×C₅	#577	1	1	yes	characteristic
403	C₂²×C₅	#578	1	1	yes	characteristic
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	2	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	—	4	2	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	8	1	no	—
415	C₄×C₅	—	8	1	no	—
416	C₄×C₅	—	8	1	no	—
417	C₄×C₅	C₄×#41	1	1	yes	characteristic
418	C₄×C₅	#520	1	1	yes	characteristic
419	C₄×C₅	#551	1	1	yes	characteristic
420	C₄×C₅	#552	1	1	yes	characteristic
421	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
441	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₅×#41	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	4	4	no	—
458	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
459	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
460	C₂×C₈	C₅×#41	1	2	yes	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	8	1	no	—
475	C₄⋊C₄	—	8	1	no	—
476	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
477	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
478	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
479	C₄⋊C₄	C₅×#41	1	2	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	8	1	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	4	2	no	—
492	C₄²	—	4	2	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	4	2	no	—
496	C₂×C₅	—	4	2	no	—
497	C₂×C₅	#2359	1	1	yes	characteristic
498	C₂×C₅	#2943	1	1	yes	characteristic
499	C₂×C₅	#2947	1	1	yes	characteristic
500	C₂×C₅	#3315	1	1	yes	characteristic
501	C₂×C₅	#3321	1	1	yes	characteristic
502	C₂×C₅	#3348	1	1	yes	characteristic
503	C₂×C₅	#3349	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	C₄×C₅×D₄	1	2	yes	—
511	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
559	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
563	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	4	1	no	—
569	C₅	#22939	1	1	yes	characteristic, direct product factor, Sylow
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
578	C₂²	C₅×#546	1	1	yes	characteristic
579	C₂²	C₅×#547	1	1	yes	characteristic
580	C₂²	C₅×#575	1	1	yes	characteristic
581	C₂²	C₅×#575	1	1	yes	characteristic
582	C₂²	C₅×#577	1	1	yes	characteristic
583	C₂²	C₅×#578	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₄×C₅×#41	1	1	yes	characteristic
598	C₄	C₅×#520	1	1	yes	characteristic
599	C₄	C₅×#551	1	1	yes	characteristic
600	C₄	C₅×#552	1	1	yes	characteristic
601	C₂	—	4	2	no	—
602	C₂	C₅×#2359	1	1	yes	characteristic
603	C₂	C₅×#2943	1	1	yes	characteristic
604	C₂	C₅×#2947	1	1	yes	characteristic
605	C₂	C₅×#3315	1	1	yes	characteristic
606	C₂	C₅×#3321	1	1	yes	characteristic
607	C₂	C₅×#3348	1	1	yes	characteristic
608	C₂	C₅×#3349	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1944	C₂	semidirect
5. C₅×#1935	C₂	semidirect
6. C₅×#1928	C₂	semidirect
7. C₅×#1921	C₂	semidirect
8. C₅×#1919	C₂	semidirect
10. C₅×#1865	C₂	semidirect
12. C₅×#1776	C₂	semidirect
13. C₅×#1763	C₂	semidirect
21. C₅×#485	C₄	semidirect
60. #22939	C₅	direct (N × H)
129. #1944	C₂×C₅	semidirect
130. #1935	C₂×C₅	semidirect
131. #1928	C₂×C₅	semidirect
132. #1921	C₂×C₅	semidirect
133. #1919	C₂×C₅	semidirect
135. #1865	C₂×C₅	semidirect
137. #1776	C₂×C₅	semidirect
138. #1763	C₂×C₅	semidirect
221. #485	C₄×C₅	semidirect
569. C₅	#22939	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#485	2
C₅×#2362	2
C₅×#2346	2
C₅×#1944	2
C₅×#1935	2
C₅×#1928	2
C₅×#1921	2
C₅×#1919	2
C₅×#1892	2
C₅×#1865	2
C₅×#1854	2
C₅×#1776	2
C₅×#1763	2
C₅×#1752	2
C₅×#1735	2
#22939	5

Subgroups — C5×#22939 #11945659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22939 #11945659