Subgroups — C₅×#21590 #11944310

Order 1280.

900 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#482	C₂	1	1	yes	maximal, characteristic
2	C₅×#2324	C₂	1	1	yes	maximal, characteristic
3	C₅×#2274	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1874	C₂	1	1	yes	maximal, characteristic
9	C₅×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1825	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₅×#482	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×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#390	—	2	1	no	—
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#388	—	2	1	no	—
38	C₅×#386	—	2	1	no	—
39	C₅×#385	—	2	1	no	—
40	C₅×#380	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	—	2	1	no	—
42	C₄×C₅×C₄⋊C₄	—	2	1	no	—
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	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₄×C₅×C₂²⋊C₄	—	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	#21590	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂³×C₄×C₅	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	C₅×#121	—	2	2	no	—
71	C₅×#121	C₂×C₄	1	4	yes	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₅×#117	—	2	2	no	—
75	C₅×#117	—	2	2	no	—
76	C₅×#117	—	2	2	no	—
77	C₅×#117	C₂×C₄	1	4	yes	complemented
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₅×C₄⋊C₄	—	2	2	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	—	2	1	no	—
103	C₂×C₄²×C₅	—	2	1	no	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₅×#107	—	2	2	no	—
108	C₅×#107	—	2	2	no	—
109	C₅×#107	C₂×C₄	1	4	yes	complemented
110	C₅×#106	C₂×C₄	1	4	yes	complemented
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	C₂×C₄	1	4	yes	complemented
114	C₅×#102	C₂×C₄	1	4	yes	complemented
115	C₅×C₂²⋊C₈	—	2	2	no	—
116	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
117	C₅×#97	—	2	2	no	—
118	C₄×C₅×C₈	—	2	2	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	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₂×#482	C₂×C₅	1	1	yes	characteristic
127	#2324	C₂×C₅	1	1	yes	characteristic
128	#2274	C₂×C₅	1	1	yes	characteristic, complemented
129	#1925	C₂×C₅	1	1	yes	characteristic, complemented
130	#1925	C₂×C₅	1	1	yes	characteristic, complemented
131	#1921	C₂×C₅	1	1	yes	characteristic, complemented
132	#1919	C₂×C₅	1	1	yes	characteristic, complemented
133	#1874	C₂×C₅	1	1	yes	characteristic
134	#1852	C₂×C₅	1	1	yes	characteristic, complemented
135	#1825	C₂×C₅	1	1	yes	characteristic, complemented
136	#1776	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
138	#1762	C₂×C₅	1	1	yes	characteristic, complemented
139	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
140	#1750	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂⁴×C₅	—	2	1	no	—
142	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×D₄	—	2	4	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	8	1	no	—
150	C₂×C₅×D₄	—	8	1	no	—
151	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	4	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	4	2	no	—
165	C₂²×C₄×C₅	—	8	1	no	—
166	C₂²×C₄×C₅	—	8	1	no	—
167	C₂²×C₄×C₅	—	8	1	no	—
168	C₂²×C₄×C₅	—	8	1	no	—
169	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	#41	1	2	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
188	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
189	C₅×C₄⋊C₄	—	2	4	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	8	1	no	—
202	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
205	C₅×C₄⋊C₄	#41	1	2	yes	—
206	C₅×C₄⋊C₄	#41	1	2	yes	—
207	C₅×C₂²⋊C₄	—	2	4	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	4	2	no	—
212	C₅×C₂²⋊C₄	—	8	1	no	—
213	C₅×C₂²⋊C₄	—	8	1	no	—
214	C₅×C₂²⋊C₄	—	8	1	no	—
215	C₄²×C₅	—	2	4	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	8	1	no	—
219	C₄²×C₅	—	8	1	no	—
220	C₄²×C₅	—	8	1	no	—
221	C₄²×C₅	—	8	1	no	—
222	C₄²×C₅	—	8	1	no	—
223	C₄²×C₅	#41	1	2	yes	—
224	C₄²×C₅	#41	1	2	yes	—
225	C₂×#121	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×#117	C₂²×C₅	1	1	yes	characteristic
228	C₂×#117	C₂²×C₅	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	#482	C₄×C₅	1	8	yes	complemented
231	C₂×#107	C₂²×C₅	1	1	yes	characteristic
232	C₂×#107	C₂²×C₅	1	1	yes	characteristic
233	C₂×#107	C₂²×C₅	1	1	yes	characteristic
234	C₂×#106	C₂²×C₅	1	1	yes	characteristic
235	C₂×#102	C₂²×C₅	1	1	yes	characteristic
236	C₂×#102	C₂²×C₅	1	1	yes	characteristic
237	C₂×#102	C₂²×C₅	1	1	yes	characteristic
238	C₂×#102	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×#97	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
243	#390	—	2	1	no	—
244	#390	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#388	—	2	1	no	—
247	#386	—	2	1	no	—
248	#385	—	2	1	no	—
249	#380	C₂²×C₅	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	—	2	1	no	—
252	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	—	2	1	no	—
258	C₄×C₂²⋊C₄	—	2	1	no	—
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#340	C₂²×C₅	1	1	yes	characteristic
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#340	C₂²×C₅	1	1	yes	characteristic
265	#340	C₂²×C₅	1	1	yes	characteristic
266	#340	C₂²×C₅	1	1	yes	characteristic
267	#336	C₂²×C₅	1	1	yes	characteristic
268	#336	C₂²×C₅	1	1	yes	characteristic
269	C₂³×C₅	—	2	1	no	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	4	1	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	C₄×D₄	1	2	yes	—
283	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₅×D₄	—	2	2	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	1	no	—
288	C₅×D₄	—	8	4	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	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	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	—	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	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	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	—	8	4	no	—
327	C₂×C₄×C₅	—	8	4	no	—
328	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
329	C₂×C₄×C₅	#123	1	2	yes	—
330	C₂×C₄×C₅	#123	1	2	yes	—
331	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
337	C₅×C₈	—	2	2	no	—
338	C₅×C₈	—	2	2	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
350	#121	—	2	2	no	—
351	#121	C₂×C₄×C₅	1	4	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	#117	C₂×C₄×C₅	1	4	yes	complemented
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
387	#107	—	2	2	no	—
388	#107	—	2	2	no	—
389	#107	C₂×C₄×C₅	1	4	yes	complemented
390	#106	C₂×C₄×C₅	1	4	yes	complemented
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	C₂×C₄×C₅	1	4	yes	complemented
394	#102	C₂×C₄×C₅	1	4	yes	complemented
395	C₂²⋊C₈	—	2	2	no	—
396	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
397	#97	—	2	2	no	—
398	C₄×C₈	—	2	2	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	—	2	2	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	2	no	—
414	C₂²×C₅	—	4	2	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	8	1	no	—
417	C₂²×C₅	—	8	1	no	—
418	C₂²×C₅	—	8	1	no	—
419	C₂²×C₅	—	8	1	no	—
420	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₅	C₂×#123	1	1	yes	characteristic
422	C₂²×C₅	#525	1	1	yes	characteristic
423	C₂²×C₅	#576	1	1	yes	characteristic
424	C₂²×C₅	#576	1	1	yes	characteristic
425	C₂²×C₅	#577	1	1	yes	characteristic
426	C₂²×C₅	#578	1	1	yes	characteristic
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	4	2	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	8	1	no	—
438	C₄×C₅	—	8	1	no	—
439	C₄×C₅	C₄×#41	1	1	yes	characteristic
440	C₄×C₅	C₄×#41	1	1	yes	characteristic
441	C₄×C₅	#529	1	1	yes	characteristic
442	C₄×C₅	#529	1	1	yes	characteristic
443	C₂⁴	—	2	1	no	—
444	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	8	1	no	—
452	C₂×D₄	—	8	1	no	—
453	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	8	1	no	—
468	C₂²×C₄	—	8	1	no	—
469	C₂²×C₄	—	8	1	no	—
470	C₂²×C₄	—	8	1	no	—
471	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
472	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
477	C₂²×C₄	C₅×#41	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
490	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
505	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
506	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
507	C₄⋊C₄	C₅×#41	1	2	yes	—
508	C₄⋊C₄	C₅×#41	1	2	yes	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	8	1	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₂²⋊C₄	—	8	1	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	8	1	no	—
521	C₄²	—	8	1	no	—
522	C₄²	—	8	1	no	—
523	C₄²	—	8	1	no	—
524	C₄²	—	8	1	no	—
525	C₄²	C₅×#41	1	2	yes	—
526	C₄²	C₅×#41	1	2	yes	—
527	C₂×C₅	—	4	2	no	—
528	C₂×C₅	—	8	2	no	—
529	C₂×C₅	C₄×#123	1	1	yes	characteristic
530	C₂×C₅	#2946	1	1	yes	characteristic
531	C₂×C₅	#2951	1	1	yes	characteristic
532	C₂×C₅	#3096	1	1	yes	characteristic
533	C₂×C₅	#3098	1	1	yes	characteristic
534	C₂×C₅	#3121	1	1	yes	characteristic
535	C₂×C₅	#3122	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	C₄×C₅×D₄	1	2	yes	—
550	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	8	4	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	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	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
596	C₂×C₄	C₅×#123	1	2	yes	—
597	C₂×C₄	C₅×#123	1	2	yes	—
598	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
599	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
601	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
602	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
603	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₅	#21590	1	1	yes	characteristic, direct product factor, Sylow
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
624	C₂²	C₂×C₅×#123	1	1	yes	characteristic
625	C₂²	C₅×#525	1	1	yes	characteristic
626	C₂²	C₅×#576	1	1	yes	characteristic
627	C₂²	C₅×#576	1	1	yes	characteristic
628	C₂²	C₅×#577	1	1	yes	characteristic
629	C₂²	C₅×#578	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	C₄×C₅×#41	1	1	yes	characteristic
643	C₄	C₄×C₅×#41	1	1	yes	characteristic
644	C₄	C₅×#529	1	1	yes	characteristic
645	C₄	C₅×#529	1	1	yes	characteristic
646	C₂	—	4	2	no	—
647	C₂	—	8	2	no	—
648	C₂	C₄×C₅×#123	1	1	yes	characteristic
649	C₂	C₅×#2946	1	1	yes	characteristic
650	C₂	C₅×#2951	1	1	yes	characteristic
651	C₂	C₅×#3096	1	1	yes	characteristic
652	C₂	C₅×#3098	1	1	yes	characteristic
653	C₂	C₅×#3121	1	1	yes	characteristic
654	C₂	C₅×#3122	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	C₂×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2274	C₂	semidirect
4. C₅×#1925	C₂	semidirect
5. C₅×#1925	C₂	semidirect
6. C₅×#1921	C₂	semidirect
7. C₅×#1919	C₂	semidirect
9. C₅×#1852	C₂	semidirect
10. C₅×#1825	C₂	semidirect
11. C₅×#1776	C₂	semidirect
12. C₄×C₅×#107	C₂	semidirect
13. C₅×#1762	C₂	semidirect
14. C₄×C₅×#102	C₂	semidirect
15. C₅×#1750	C₂	semidirect
21. C₅×#482	C₄	semidirect
60. #21590	C₅	direct (N × H)
77. C₅×#117	C₂×C₄	semidirect
109. C₅×#107	C₂×C₄	semidirect
110. C₅×#106	C₂×C₄	semidirect
113. C₅×#102	C₂×C₄	semidirect
114. C₅×#102	C₂×C₄	semidirect
116. C₅×C₂²⋊C₈	C₂×C₄	semidirect
128. #2274	C₂×C₅	semidirect
129. #1925	C₂×C₅	semidirect
130. #1925	C₂×C₅	semidirect
131. #1921	C₂×C₅	semidirect
132. #1919	C₂×C₅	semidirect
134. #1852	C₂×C₅	semidirect
135. #1825	C₂×C₅	semidirect
136. #1776	C₂×C₅	semidirect
137. C₄×#107	C₂×C₅	semidirect
138. #1762	C₂×C₅	semidirect
139. C₄×#102	C₂×C₅	semidirect
140. #1750	C₂×C₅	semidirect
230. #482	C₄×C₅	semidirect
357. #117	C₂×C₄×C₅	semidirect
389. #107	C₂×C₄×C₅	semidirect
390. #106	C₂×C₄×C₅	semidirect
393. #102	C₂×C₄×C₅	semidirect
394. #102	C₂×C₄×C₅	semidirect
396. C₂²⋊C₈	C₂×C₄×C₅	semidirect
608. C₅	#21590	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×#482	2
C₅×#2324	2
C₅×#2274	2
C₅×#1925	2
C₅×#1921	2
C₅×#1919	2
C₅×#1874	2
C₅×#1852	2
C₅×#1825	2
C₅×#1776	2
C₄×C₅×#107	2
C₅×#1762	2
C₄×C₅×#102	2
C₅×#1750	2
#21590	5

Subgroups — C5×#21590 #11944310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21590 #11944310