Subgroups — C₅×#25960 #11948680

Order 1280.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#102	C₂	1	1	yes	maximal, characteristic
3	C₅×#2442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1807	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₂²⋊C₄	—	2	1	no	—
23	C₅×#478	—	2	4	no	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#106	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#102	—	2	4	no	—
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×#400	—	2	1	no	—
41	C₅×#398	—	2	1	no	—
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic, complemented
45	C₅×#389	C₂²	1	1	yes	characteristic, complemented
46	C₅×#386	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#385	—	2	1	no	—
49	C₅×#382	C₂²	1	1	yes	characteristic, complemented
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₅×#379	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic, complemented
56	C₅×#340	C₂²	1	1	yes	characteristic, complemented
57	C₅×#340	C₂²	1	1	yes	characteristic, complemented
58	C₅×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅×#336	C₂²	1	1	yes	characteristic, complemented
60	C₅×#336	C₂²	1	1	yes	characteristic, complemented
61	#25960	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₅	—	2	1	no	—
63	C₂²×C₅×D₄	—	2	2	no	—
64	C₂²×C₅×D₄	—	2	2	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	—	2	2	no	—
67	C₂²×C₅×D₄	—	4	1	no	—
68	C₂²×C₅×D₄	—	4	1	no	—
69	C₂²×C₅×D₄	Q₈	1	4	yes	—
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅	—	2	1	no	—
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	—	2	2	no	—
77	C₂²×C₅×C₈	—	2	2	no	—
78	C₂²×C₅×C₈	—	4	1	no	—
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₅×#125	—	2	2	no	—
84	C₅×#125	—	4	1	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	4	1	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	2	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	4	1	no	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
111	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₅×#107	—	2	2	no	—
116	C₅×#107	—	4	1	no	—
117	C₅×#106	—	2	2	no	—
118	C₅×#106	—	4	1	no	—
119	C₅×C₄⋊C₈	—	2	2	no	—
120	C₅×C₄⋊C₈	—	4	1	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#102	—	4	1	no	—
127	C₅×#102	—	4	1	no	—
128	C₅×#102	D₄	1	4	yes	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	D₄	1	1	yes	characteristic
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₂×#478	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂²×#102	C₂×C₅	1	1	yes	characteristic
140	#2442	C₂×C₅	1	1	yes	characteristic, complemented
141	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
142	#2092	C₂×C₅	1	1	yes	characteristic, complemented
143	#2067	C₂×C₅	1	1	yes	characteristic, complemented
144	#2065	C₂×C₅	1	1	yes	characteristic, complemented
145	#2025	C₂×C₅	1	1	yes	characteristic, complemented
146	#1864	C₂×C₅	1	1	yes	characteristic, complemented
147	#1862	C₂×C₅	1	1	yes	characteristic, complemented
148	#1852	C₂×C₅	1	1	yes	characteristic, complemented
149	#1850	C₂×C₅	1	1	yes	characteristic, complemented
150	#1807	C₂×C₅	1	1	yes	characteristic, complemented
151	#1804	C₂×C₅	1	1	yes	characteristic, complemented
152	#1786	C₂×C₅	1	1	yes	characteristic
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	4	no	—
156	C₂⁴×C₅	—	4	2	no	—
157	C₂⁴×C₅	—	4	2	no	—
158	C₂⁴×C₅	—	4	2	no	—
159	C₂⁴×C₅	—	4	2	no	—
160	C₂⁴×C₅	—	8	1	no	—
161	C₂⁴×C₅	—	8	1	no	—
162	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	8	no	—
164	C₂×C₅×D₄	—	2	4	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	4	4	no	—
174	C₂×C₅×D₄	—	4	4	no	—
175	C₂×C₅×D₄	—	4	4	no	—
176	C₂×C₅×D₄	—	4	2	no	—
177	C₂×C₅×D₄	—	4	2	no	—
178	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
180	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
181	C₂×C₅×D₄	#41	1	2	yes	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	4	2	no	—
193	C₂²×C₄×C₅	—	4	2	no	—
194	C₂²×C₄×C₅	—	4	2	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	—	8	1	no	—
199	C₂²×C₄×C₅	—	8	1	no	—
200	C₂²×C₄×C₅	—	8	1	no	—
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
207	C₂²×C₄×C₅	#41	1	2	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	4	4	no	—
221	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	4	2	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	8	1	no	—
237	C₅×C₄⋊C₄	—	8	1	no	—
238	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	2	2	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	4	2	no	—
244	C₅×C₂²⋊C₄	—	4	2	no	—
245	C₅×C₂²⋊C₄	—	4	2	no	—
246	C₅×C₂²⋊C₄	—	4	2	no	—
247	C₅×C₂²⋊C₄	—	8	1	no	—
248	C₅×C₂²⋊C₄	—	8	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
255	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	—	2	1	no	—
260	#478	—	2	4	no	—
261	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×#106	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂×#106	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂×#102	—	2	4	no	—
268	C₂×#102	C₂²×C₅	1	1	yes	characteristic
269	C₂×#102	C₂²×C₅	1	1	yes	characteristic
270	C₂×#102	C₂²×C₅	1	1	yes	characteristic
271	C₂×#102	C₂²×C₅	1	1	yes	characteristic
272	C₂×#102	C₂²×C₅	1	1	yes	characteristic
273	C₂×#102	C₂²×C₅	1	1	yes	characteristic
274	C₂×#102	C₂²×C₅	1	1	yes	characteristic
275	C₂×#102	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	#400	—	2	1	no	—
278	#398	—	2	1	no	—
279	#390	C₂²×C₅	1	1	yes	characteristic
280	#390	C₂²×C₅	1	1	yes	characteristic
281	#389	C₂²×C₅	1	1	yes	characteristic, complemented
282	#389	C₂²×C₅	1	1	yes	characteristic, complemented
283	#386	—	2	1	no	—
284	#386	—	2	1	no	—
285	#385	—	2	1	no	—
286	#382	C₂²×C₅	1	1	yes	characteristic, complemented
287	#380	—	2	1	no	—
288	#380	C₂²×C₅	1	1	yes	characteristic
289	#380	C₂²×C₅	1	1	yes	characteristic
290	#379	—	2	1	no	—
291	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	#340	C₂²×C₅	1	1	yes	characteristic, complemented
293	#340	C₂²×C₅	1	1	yes	characteristic, complemented
294	#340	C₂²×C₅	1	1	yes	characteristic, complemented
295	#340	C₂²×C₅	1	1	yes	characteristic, complemented
296	#336	C₂²×C₅	1	1	yes	characteristic, complemented
297	#336	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	4	8	no	—
307	C₂³×C₅	—	4	1	no	—
308	C₂³×C₅	—	4	1	no	—
309	C₂³×C₅	—	4	1	no	—
310	C₂³×C₅	—	4	1	no	—
311	C₂³×C₅	—	4	1	no	—
312	C₂³×C₅	—	4	1	no	—
313	C₂³×C₅	—	4	1	no	—
314	C₂³×C₅	—	4	1	no	—
315	C₂³×C₅	—	4	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	8	no	—
318	C₂³×C₅	—	8	4	no	—
319	C₂³×C₅	—	8	4	no	—
320	C₂³×C₅	—	8	4	no	—
321	C₂³×C₅	—	8	4	no	—
322	C₂³×C₅	—	8	4	no	—
323	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
324	C₂³×C₅	#135	1	2	yes	—
325	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
326	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
327	C₅×D₄	—	2	2	no	—
328	C₅×D₄	—	2	2	no	—
329	C₅×D₄	—	2	2	no	—
330	C₅×D₄	—	2	2	no	—
331	C₅×D₄	—	2	2	no	—
332	C₅×D₄	—	4	8	no	—
333	C₅×D₄	—	4	1	no	—
334	C₅×D₄	—	4	1	no	—
335	C₅×D₄	C₂²⋊Q₈	1	4	yes	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	8	4	no	—
373	C₂×C₄×C₅	—	8	4	no	—
374	C₂×C₄×C₅	—	8	4	no	—
375	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
376	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
381	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
382	C₅×C₈	—	2	2	no	—
383	C₅×C₈	—	4	1	no	—
384	C₅×C₈	—	4	1	no	—
385	C₅×C₈	—	4	1	no	—
386	C₂⁵	—	2	1	no	—
387	C₂²×D₄	—	2	2	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	4	1	no	—
392	C₂²×D₄	—	4	1	no	—
393	C₂²×D₄	C₅×Q₈	1	4	yes	—
394	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	—	2	2	no	—
401	C₂²×C₈	—	2	2	no	—
402	C₂²×C₈	—	4	1	no	—
403	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
407	#125	—	2	2	no	—
408	#125	—	4	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	4	1	no	—
412	C₄×D₄	—	4	1	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	4	1	no	—
420	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	4	4	no	—
435	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
439	#107	—	2	2	no	—
440	#107	—	4	1	no	—
441	#106	—	2	2	no	—
442	#106	—	4	1	no	—
443	C₄⋊C₈	—	2	2	no	—
444	C₄⋊C₈	—	4	1	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	4	1	no	—
451	#102	—	4	1	no	—
452	#102	C₅×D₄	1	4	yes	—
453	C₂²⋊C₈	—	2	2	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	C₅×D₄	1	1	yes	characteristic
461	#95	C₅×D₄	1	1	yes	characteristic
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	2	no	—
465	C₂²×C₅	—	2	2	no	—
466	C₂²×C₅	—	2	2	no	—
467	C₂²×C₅	—	2	2	no	—
468	C₂²×C₅	—	2	4	no	—
469	C₂²×C₅	—	4	2	no	—
470	C₂²×C₅	—	4	2	no	—
471	C₂²×C₅	—	4	2	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	2	no	—
474	C₂²×C₅	—	4	2	no	—
475	C₂²×C₅	—	4	2	no	—
476	C₂²×C₅	—	4	2	no	—
477	C₂²×C₅	—	4	2	no	—
478	C₂²×C₅	—	8	16	no	—
479	C₂²×C₅	—	8	1	no	—
480	C₂²×C₅	—	8	1	no	—
481	C₂²×C₅	—	8	1	no	—
482	C₂²×C₅	—	8	1	no	—
483	C₂²×C₅	#478	1	4	yes	complemented
484	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
485	C₂²×C₅	D₄²	1	1	yes	characteristic
486	C₂²×C₅	#546	1	1	yes	characteristic
487	C₂²×C₅	C₂×#135	1	1	yes	characteristic
488	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₂²×C₅	#576	1	1	yes	characteristic
490	C₂²×C₅	#577	1	1	yes	characteristic
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	4	1	no	—
493	C₄×C₅	—	4	2	no	—
494	C₄×C₅	—	4	1	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	8	1	no	—
498	C₄×C₅	—	8	1	no	—
499	C₄×C₅	—	8	1	no	—
500	C₄×C₅	—	8	1	no	—
501	C₄×C₅	—	8	1	no	—
502	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
503	C₄×C₅	#543	1	1	yes	characteristic
504	C₄×C₅	#546	1	1	yes	characteristic
505	C₄×C₅	#551	1	1	yes	characteristic
506	C₂⁴	—	2	1	no	—
507	C₂⁴	—	2	1	no	—
508	C₂⁴	—	2	4	no	—
509	C₂⁴	—	4	2	no	—
510	C₂⁴	—	4	2	no	—
511	C₂⁴	—	4	2	no	—
512	C₂⁴	—	4	2	no	—
513	C₂⁴	—	8	1	no	—
514	C₂⁴	—	8	1	no	—
515	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
516	C₂×D₄	—	2	8	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
532	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
533	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
534	C₂×D₄	C₅×#41	1	2	yes	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	8	1	no	—
552	C₂²×C₄	—	8	1	no	—
553	C₂²×C₄	—	8	1	no	—
554	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
560	C₂²×C₄	C₅×#41	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	4	4	no	—
574	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	8	1	no	—
590	C₄⋊C₄	—	8	1	no	—
591	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	8	1	no	—
601	C₂²⋊C₄	—	8	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₂×C₅	—	2	4	no	—
607	C₂×C₅	—	4	4	no	—
608	C₂×C₅	—	8	2	no	—
609	C₂×C₅	#2437	1	1	yes	characteristic
610	C₂×C₅	C₂×#478	1	1	yes	characteristic
611	C₂×C₅	#3081	1	1	yes	characteristic
612	C₂×C₅	#3264	1	1	yes	characteristic
613	C₂×C₅	#3282	1	1	yes	characteristic
614	C₂×C₅	#3297	1	1	yes	characteristic
615	C₂×C₅	#3310	1	1	yes	characteristic
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	8	4	no	—
637	C₂³	—	8	4	no	—
638	C₂³	—	8	4	no	—
639	C₂³	—	8	4	no	—
640	C₂³	—	8	4	no	—
641	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
642	C₂³	C₅×#135	1	2	yes	—
643	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
644	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	4	8	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	C₅×C₂²⋊Q₈	1	4	yes	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
694	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
695	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
696	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
697	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
698	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
700	C₈	—	2	2	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₅	#25960	1	1	yes	characteristic, direct product factor, Sylow
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	8	16	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	—	8	1	no	—
726	C₂²	C₅×#478	1	4	yes	complemented
727	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
728	C₂²	C₅×D₄²	1	1	yes	characteristic
729	C₂²	C₅×#546	1	1	yes	characteristic
730	C₂²	C₂×C₅×#135	1	1	yes	characteristic
731	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
732	C₂²	C₅×#576	1	1	yes	characteristic
733	C₂²	C₅×#577	1	1	yes	characteristic
734	C₄	—	2	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	—	8	1	no	—
743	C₄	—	8	1	no	—
744	C₄	—	8	1	no	—
745	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
746	C₄	C₅×#543	1	1	yes	characteristic
747	C₄	C₅×#546	1	1	yes	characteristic
748	C₄	C₅×#551	1	1	yes	characteristic
749	C₂	—	2	4	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	2	no	—
752	C₂	C₅×#2437	1	1	yes	characteristic
753	C₂	C₂×C₅×#478	1	1	yes	characteristic
754	C₂	C₅×#3081	1	1	yes	characteristic
755	C₂	C₅×#3264	1	1	yes	characteristic
756	C₂	C₅×#3282	1	1	yes	characteristic
757	C₂	C₅×#3297	1	1	yes	characteristic
758	C₂	C₅×#3310	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂²×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
1. C₂×C₅×#478	C₂	semidirect
3. C₅×#2442	C₂	semidirect
5. C₅×#2092	C₂	semidirect
6. C₅×#2067	C₂	semidirect
7. C₅×#2065	C₂	semidirect
8. C₅×#2025	C₂	semidirect
9. C₅×#1864	C₂	semidirect
10. C₅×#1862	C₂	semidirect
11. C₅×#1852	C₂	semidirect
12. C₅×#1850	C₂	semidirect
13. C₅×#1807	C₂	semidirect
14. C₅×#1804	C₂	semidirect
18. C₂×C₅×#125	C₂²	semidirect
24. C₂×C₅×#107	C₂²	semidirect
25. C₂×C₅×#107	C₂²	semidirect
26. C₂×C₅×#106	C₂²	semidirect
27. C₂×C₅×#106	C₂²	semidirect
28. C₂×C₅×C₄⋊C₈	C₂²	semidirect
29. C₂×C₅×C₄⋊C₈	C₂²	semidirect
44. C₅×#389	C₂²	semidirect
45. C₅×#389	C₂²	semidirect
49. C₅×#382	C₂²	semidirect
55. C₅×#340	C₂²	semidirect
56. C₅×#340	C₂²	semidirect
57. C₅×#340	C₂²	semidirect
58. C₅×#340	C₂²	semidirect
59. C₅×#336	C₂²	semidirect
60. C₅×#336	C₂²	semidirect
61. #25960	C₅	direct (N × H)
138. C₂×#478	C₂×C₅	semidirect
140. #2442	C₂×C₅	semidirect
142. #2092	C₂×C₅	semidirect
143. #2067	C₂×C₅	semidirect
144. #2065	C₂×C₅	semidirect
145. #2025	C₂×C₅	semidirect
146. #1864	C₂×C₅	semidirect
147. #1862	C₂×C₅	semidirect
148. #1852	C₂×C₅	semidirect
149. #1850	C₂×C₅	semidirect
150. #1807	C₂×C₅	semidirect
151. #1804	C₂×C₅	semidirect
255. C₂×#125	C₂²×C₅	semidirect
261. C₂×#107	C₂²×C₅	semidirect
262. C₂×#107	C₂²×C₅	semidirect
263. C₂×#106	C₂²×C₅	semidirect
264. C₂×#106	C₂²×C₅	semidirect
265. C₂×C₄⋊C₈	C₂²×C₅	semidirect
266. C₂×C₄⋊C₈	C₂²×C₅	semidirect
281. #389	C₂²×C₅	semidirect
282. #389	C₂²×C₅	semidirect
286. #382	C₂²×C₅	semidirect
292. #340	C₂²×C₅	semidirect
293. #340	C₂²×C₅	semidirect
294. #340	C₂²×C₅	semidirect
295. #340	C₂²×C₅	semidirect
296. #336	C₂²×C₅	semidirect
297. #336	C₂²×C₅	semidirect
483. C₂²×C₅	#478	semidirect
704. C₅	#25960	direct (N × H)
726. C₂²	C₅×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#478	2
C₂²×C₅×#102	2
C₅×#2442	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2092	2
C₅×#2067	2
C₅×#2065	2
C₅×#2025	2
C₅×#1864	2
C₅×#1862	2
C₅×#1852	2
C₅×#1850	2
C₅×#1807	2
C₅×#1804	2
C₅×#1786	2
#25960	5

Subgroups — C5×#25960 #11948680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25960 #11948680