Subgroups — C₅×#23008 #11945728

Order 1280.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	—	2	1	no	—
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₅×#459	C₄	1	8	yes	complemented
26	C₅×#442	—	2	4	no	—
27	C₄×C₅×D₈	—	2	4	no	—
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#106	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₅×#390	—	2	1	no	—
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#385	—	2	1	no	—
51	C₅×#382	C₂²	1	1	yes	characteristic
52	C₅×#380	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×#95	—	2	1	no	—
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	#23008	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂³×C₄×C₅	—	2	1	no	—
71	C₂³×C₄×C₅	—	2	1	no	—
72	C₂³×C₄×C₅	—	2	1	no	—
73	C₂×C₅×D₈	—	2	2	no	—
74	C₂×C₅×D₈	—	2	2	no	—
75	C₂×C₅×D₈	—	2	2	no	—
76	C₂×C₅×D₈	—	2	2	no	—
77	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
78	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
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×#127	—	2	2	no	—
84	C₅×#127	C₂×C₄	1	4	yes	complemented
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₄×C₅×D₄	—	4	1	no	—
92	C₄×C₅×D₄	—	4	1	no	—
93	C₄×C₅×D₄	—	4	1	no	—
94	C₄×C₅×D₄	—	4	4	no	—
95	C₄×C₅×D₄	C₂×C₄	1	4	yes	complemented
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#107	—	2	2	no	—
119	C₅×#106	—	2	2	no	—
120	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	4	1	no	—
125	C₅×#102	—	4	1	no	—
126	C₅×#102	C₂×C₄	1	4	yes	complemented
127	C₅×#102	C₂×C₄	1	4	yes	complemented
128	C₅×#102	D₄	1	4	yes	complemented
129	C₅×#97	—	2	2	no	—
130	C₅×#97	—	2	2	no	—
131	C₄×C₅×C₈	—	2	2	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	—	2	1	no	—
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#459	C₂×C₅	1	1	yes	characteristic
140	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
142	#2366	C₂×C₅	1	1	yes	characteristic, complemented
143	#2349	C₂×C₅	1	1	yes	characteristic, complemented
144	#1961	C₂×C₅	1	1	yes	characteristic, complemented
145	#1949	C₂×C₅	1	1	yes	characteristic, complemented
146	#1936	C₂×C₅	1	1	yes	characteristic, complemented
147	#1934	C₂×C₅	1	1	yes	characteristic, complemented
148	#1879	C₂×C₅	1	1	yes	characteristic, complemented
149	#1879	C₂×C₅	1	1	yes	characteristic, complemented
150	#1864	C₂×C₅	1	1	yes	characteristic, complemented
151	#1862	C₂×C₅	1	1	yes	characteristic, complemented
152	#1771	C₂×C₅	1	1	yes	characteristic, complemented
153	#1762	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	—	2	1	no	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	4	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	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	—	4	2	no	—
173	C₂×C₅×D₄	—	4	2	no	—
174	C₂×C₅×D₄	—	8	1	no	—
175	C₂×C₅×D₄	—	8	1	no	—
176	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
177	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
178	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
179	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
180	C₂×C₅×D₄	#41	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	4	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	—	4	2	no	—
188	C₂²×C₄×C₅	—	4	2	no	—
189	C₂²×C₄×C₅	—	4	2	no	—
190	C₂²×C₄×C₅	—	4	2	no	—
191	C₂²×C₄×C₅	—	4	2	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	—	8	1	no	—
196	C₂²×C₄×C₅	—	8	1	no	—
197	C₂²×C₄×C₅	—	8	1	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×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₅×D₈	—	2	8	no	—
209	C₅×D₈	—	2	8	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	C₂²×C₄	1	2	yes	—
220	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
221	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
222	C₅×C₄⋊C₄	—	2	2	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	—	4	1	no	—
232	C₅×C₄⋊C₄	—	8	1	no	—
233	C₅×C₄⋊C₄	—	8	1	no	—
234	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
235	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
236	C₅×C₂²⋊C₄	—	2	4	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₅×C₂²⋊C₄	—	4	2	no	—
240	C₅×C₂²⋊C₄	—	4	2	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	8	1	no	—
244	C₅×C₂²⋊C₄	—	8	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	4	2	no	—
250	C₄²×C₅	C₂²×C₄	1	2	yes	—
251	C₄²×C₅	#41	1	2	yes	—
252	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
253	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
254	C₂×#127	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×D₄	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
261	#459	C₄×C₅	1	8	yes	complemented
262	#442	—	2	4	no	—
263	C₄×D₈	—	2	4	no	—
264	C₂×#107	C₂²×C₅	1	1	yes	characteristic
265	C₂×#106	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×#102	C₂²×C₅	1	1	yes	characteristic
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×#97	C₂²×C₅	1	1	yes	characteristic
276	C₂×#97	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
278	#390	—	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
282	#389	C₂²×C₅	1	1	yes	characteristic
283	#386	—	2	1	no	—
284	#386	—	2	1	no	—
285	#385	—	2	1	no	—
286	#385	—	2	1	no	—
287	#382	C₂²×C₅	1	1	yes	characteristic
288	#380	—	2	1	no	—
289	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×#95	—	2	1	no	—
292	#340	C₂²×C₅	1	1	yes	characteristic
293	#340	C₂²×C₅	1	1	yes	characteristic
294	#340	C₂²×C₅	1	1	yes	characteristic
295	#340	C₂²×C₅	1	1	yes	characteristic
296	#336	C₂²×C₅	1	1	yes	characteristic
297	#336	C₂²×C₅	1	1	yes	characteristic
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	—	4	1	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	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	2	2	no	—
327	C₅×D₄	—	4	8	no	—
328	C₅×D₄	—	4	1	no	—
329	C₅×D₄	—	4	1	no	—
330	C₅×D₄	—	4	1	no	—
331	C₅×D₄	—	4	1	no	—
332	C₅×D₄	—	8	4	no	—
333	C₅×D₄	C₄×D₄	1	4	yes	complemented
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	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	—	8	4	no	—
365	C₂×C₄×C₅	—	8	4	no	—
366	C₂×C₄×C₅	—	8	4	no	—
367	C₂×C₄×C₅	—	8	4	no	—
368	C₂×C₄×C₅	—	8	4	no	—
369	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
370	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
371	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
372	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
376	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
378	C₅×C₈	—	2	2	no	—
379	C₅×C₈	—	2	2	no	—
380	C₅×C₈	—	2	2	no	—
381	C₅×C₈	—	4	1	no	—
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×D₈	—	2	2	no	—
394	C₂×D₈	—	2	2	no	—
395	C₂×D₈	—	2	2	no	—
396	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
397	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
398	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
402	#127	—	2	2	no	—
403	#127	C₂×C₄×C₅	1	4	yes	complemented
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	4	1	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	C₄×D₄	—	4	1	no	—
413	C₄×D₄	—	4	4	no	—
414	C₄×D₄	C₂×C₄×C₅	1	4	yes	complemented
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
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×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
437	#107	—	2	2	no	—
438	#106	—	2	2	no	—
439	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	4	1	no	—
444	#102	—	4	1	no	—
445	#102	C₂×C₄×C₅	1	4	yes	complemented
446	#102	C₂×C₄×C₅	1	4	yes	complemented
447	#102	C₅×D₄	1	4	yes	complemented
448	#97	—	2	2	no	—
449	#97	—	2	2	no	—
450	C₄×C₈	—	2	2	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	C₅×D₄	1	1	yes	characteristic
457	#95	C₅×D₄	1	1	yes	characteristic
458	C₂²×C₅	—	2	4	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	4	2	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	4	2	no	—
469	C₂²×C₅	—	4	2	no	—
470	C₂²×C₅	—	4	2	no	—
471	C₂²×C₅	—	8	1	no	—
472	C₂²×C₅	—	8	1	no	—
473	C₂²×C₅	—	8	1	no	—
474	C₂²×C₅	—	8	1	no	—
475	C₂²×C₅	—	8	1	no	—
476	C₂²×C₅	—	8	1	no	—
477	C₂²×C₅	—	8	1	no	—
478	C₂²×C₅	—	8	1	no	—
479	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
480	C₂²×C₅	D₄²	1	1	yes	characteristic
481	C₂²×C₅	#548	1	1	yes	characteristic
482	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
483	C₂²×C₅	#575	1	1	yes	characteristic
484	C₂²×C₅	#576	1	1	yes	characteristic
485	C₂²×C₅	#576	1	1	yes	characteristic
486	C₄×C₅	—	2	2	no	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	2	2	no	—
489	C₄×C₅	—	4	2	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	4	2	no	—
492	C₄×C₅	—	4	1	no	—
493	C₄×C₅	—	4	1	no	—
494	C₄×C₅	—	8	1	no	—
495	C₄×C₅	—	8	1	no	—
496	C₄×C₅	—	8	1	no	—
497	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
498	C₄×C₅	#520	1	1	yes	characteristic
499	C₄×C₅	#547	1	1	yes	characteristic
500	C₄×C₅	#553	1	1	yes	characteristic
501	C₂⁴	—	2	1	no	—
502	C₂⁴	—	2	1	no	—
503	C₂⁴	—	2	1	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	8	1	no	—
522	C₂×D₄	—	8	1	no	—
523	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
524	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
525	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
526	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
527	C₂×D₄	C₅×#41	1	2	yes	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	8	1	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	—	8	1	no	—
548	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
552	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
555	D₈	—	2	8	no	—
556	D₈	—	2	8	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
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	C₂²×C₄×C₅	1	2	yes	—
567	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
568	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	1	no	—
579	C₄⋊C₄	—	8	1	no	—
580	C₄⋊C₄	—	8	1	no	—
581	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
582	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	8	1	no	—
591	C₂²⋊C₄	—	8	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	4	2	no	—
597	C₄²	C₂²×C₄×C₅	1	2	yes	—
598	C₄²	C₅×#41	1	2	yes	—
599	C₂×C₅	—	4	4	no	—
600	C₂×C₅	—	8	2	no	—
601	C₂×C₅	—	8	2	no	—
602	C₂×C₅	#2361	1	1	yes	characteristic
603	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
604	C₂×C₅	#2948	1	1	yes	characteristic
605	C₂×C₅	#3264	1	1	yes	characteristic
606	C₂×C₅	#3268	1	1	yes	characteristic
607	C₂×C₅	#3366	1	1	yes	characteristic
608	C₂×C₅	#3370	1	1	yes	characteristic
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
631	D₄	—	2	2	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	2	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	4	8	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	8	4	no	—
644	D₄	C₄×C₅×D₄	1	4	yes	complemented
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
681	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
682	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
684	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
685	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
686	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
687	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
689	C₈	—	2	2	no	—
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	—	4	1	no	—
693	C₅	#23008	1	1	yes	characteristic, direct product factor, Sylow
694	C₂²	—	2	4	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
716	C₂²	C₅×D₄²	1	1	yes	characteristic
717	C₂²	C₅×#548	1	1	yes	characteristic
718	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
719	C₂²	C₅×#575	1	1	yes	characteristic
720	C₂²	C₅×#576	1	1	yes	characteristic
721	C₂²	C₅×#576	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	8	1	no	—
731	C₄	—	8	1	no	—
732	C₄	—	8	1	no	—
733	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
734	C₄	C₅×#520	1	1	yes	characteristic
735	C₄	C₅×#547	1	1	yes	characteristic
736	C₄	C₅×#553	1	1	yes	characteristic
737	C₂	—	4	4	no	—
738	C₂	—	8	2	no	—
739	C₂	—	8	2	no	—
740	C₂	C₅×#2361	1	1	yes	characteristic
741	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
742	C₂	C₅×#2948	1	1	yes	characteristic
743	C₂	C₅×#3264	1	1	yes	characteristic
744	C₂	C₅×#3268	1	1	yes	characteristic
745	C₂	C₅×#3366	1	1	yes	characteristic
746	C₂	C₅×#3370	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×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#442	C₂	semidirect
3. C₂×C₄×C₅×D₈	C₂	semidirect
4. C₅×#2366	C₂	semidirect
5. C₅×#2349	C₂	semidirect
6. C₅×#1961	C₂	semidirect
7. C₅×#1949	C₂	semidirect
8. C₅×#1936	C₂	semidirect
9. C₅×#1934	C₂	semidirect
10. C₅×#1879	C₂	semidirect
11. C₅×#1879	C₂	semidirect
12. C₅×#1864	C₂	semidirect
13. C₅×#1862	C₂	semidirect
14. C₅×#1771	C₂	semidirect
15. C₅×#1762	C₂	semidirect
25. C₅×#459	C₄	semidirect
62. #23008	C₅	direct (N × H)
77. C₂×C₅×D₈	C₂×C₄	semidirect
78. C₂×C₅×D₈	C₂×C₄	semidirect
84. C₅×#127	C₂×C₄	semidirect
95. C₄×C₅×D₄	C₂×C₄	semidirect
120. C₅×C₄⋊C₈	C₂×C₄	semidirect
126. C₅×#102	C₂×C₄	semidirect
127. C₅×#102	C₂×C₄	semidirect
128. C₅×#102	D₄	semidirect
140. C₂×#442	C₂×C₅	semidirect
141. C₂×C₄×D₈	C₂×C₅	semidirect
142. #2366	C₂×C₅	semidirect
143. #2349	C₂×C₅	semidirect
144. #1961	C₂×C₅	semidirect
145. #1949	C₂×C₅	semidirect
146. #1936	C₂×C₅	semidirect
147. #1934	C₂×C₅	semidirect
148. #1879	C₂×C₅	semidirect
149. #1879	C₂×C₅	semidirect
150. #1864	C₂×C₅	semidirect
151. #1862	C₂×C₅	semidirect
152. #1771	C₂×C₅	semidirect
153. #1762	C₂×C₅	semidirect
261. #459	C₄×C₅	semidirect
333. C₅×D₄	C₄×D₄	semidirect
396. C₂×D₈	C₂×C₄×C₅	semidirect
397. C₂×D₈	C₂×C₄×C₅	semidirect
403. #127	C₂×C₄×C₅	semidirect
414. C₄×D₄	C₂×C₄×C₅	semidirect
439. C₄⋊C₈	C₂×C₄×C₅	semidirect
445. #102	C₂×C₄×C₅	semidirect
446. #102	C₂×C₄×C₅	semidirect
447. #102	C₅×D₄	semidirect
644. D₄	C₄×C₅×D₄	semidirect
693. C₅	#23008	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×#459	2
C₂×C₅×#442	2
C₂×C₄×C₅×D₈	2
C₅×#2366	2
C₅×#2349	2
C₅×#1961	2
C₅×#1949	2
C₅×#1936	2
C₅×#1934	2
C₅×#1879	2
C₅×#1864	2
C₅×#1862	2
C₅×#1771	2
C₅×#1762	2
#23008	5

Subgroups — C5×#23008 #11945728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23008 #11945728