Subgroups — C₅×#25286 #11948006

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#489	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2545	C₂	1	1	yes	maximal, characteristic
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2067	C₂	1	1	yes	maximal, characteristic
7	C₅×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2042	C₂	1	1	yes	maximal, characteristic
9	C₅×#1983	C₂	1	1	yes	maximal, characteristic
10	C₅×#1983	C₂	1	1	yes	maximal, characteristic
11	C₅×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1925	C₂	1	1	yes	maximal, characteristic
15	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₅×#124	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	—	2	1	no	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₅×#489	—	2	4	no	—
23	C₅×#477	—	2	4	no	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#103	C₂²	1	1	yes	characteristic
34	C₂×C₅×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#103	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×#102	C₂²	1	1	yes	characteristic
40	C₂×C₅×#102	C₂²	1	1	yes	characteristic
41	C₂×C₅×#97	C₂²	1	1	yes	characteristic
42	C₅×#396	—	2	1	no	—
43	C₅×#396	—	2	1	no	—
44	C₅×#391	—	2	1	no	—
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#388	—	2	1	no	—
50	C₅×#388	—	2	1	no	—
51	C₅×#387	—	2	1	no	—
52	C₅×#387	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#25286	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	—	2	1	no	—
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×D₄	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×C₄⋊Q₈	—	2	2	no	—
71	C₅×C₄⋊Q₈	—	2	2	no	—
72	C₅×C₄⋊Q₈	—	4	1	no	—
73	C₅×C₄⋊Q₈	D₄	1	4	yes	—
74	C₅×#124	—	2	2	no	—
75	C₅×#124	—	2	2	no	—
76	C₅×#124	—	2	2	no	—
77	C₅×#124	—	4	1	no	—
78	C₄×C₅×Q₈	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×Q₈	—	4	4	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	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	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	—	2	2	no	—
110	C₅×C₄⋊C₈	—	4	1	no	—
111	C₅×C₄⋊C₈	—	4	1	no	—
112	C₅×#103	—	2	2	no	—
113	C₅×#103	—	2	2	no	—
114	C₅×#103	—	2	2	no	—
115	C₅×#103	—	2	2	no	—
116	C₅×#103	—	2	2	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	4	1	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	4	1	no	—
124	C₅×#97	—	2	2	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	D₄	1	1	yes	characteristic
133	C₅×#95	D₄	1	1	yes	characteristic
134	C₂×#489	C₂×C₅	1	1	yes	characteristic
135	C₂×#477	C₂×C₅	1	1	yes	characteristic, complemented
136	#2545	C₂×C₅	1	1	yes	characteristic
137	#2365	C₂×C₅	1	1	yes	characteristic, complemented
138	#2068	C₂×C₅	1	1	yes	characteristic, complemented
139	#2067	C₂×C₅	1	1	yes	characteristic
140	#2043	C₂×C₅	1	1	yes	characteristic, complemented
141	#2042	C₂×C₅	1	1	yes	characteristic
142	#1983	C₂×C₅	1	1	yes	characteristic
143	#1983	C₂×C₅	1	1	yes	characteristic
144	#1981	C₂×C₅	1	1	yes	characteristic, complemented
145	#1940	C₂×C₅	1	1	yes	characteristic, complemented
146	#1928	C₂×C₅	1	1	yes	characteristic, complemented
147	#1925	C₂×C₅	1	1	yes	characteristic
148	#1763	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂⁴×C₅	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	4	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	4	2	no	—
163	C₂×C₅×Q₈	—	4	2	no	—
164	C₂×C₅×Q₈	#41	1	2	yes	—
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	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	4	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	—	4	2	no	—
208	C₅×C₄⋊C₄	—	4	2	no	—
209	C₅×C₄⋊C₄	—	4	2	no	—
210	C₅×C₄⋊C₄	—	4	2	no	—
211	C₅×C₄⋊C₄	—	4	2	no	—
212	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
213	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
214	C₅×C₄⋊C₄	#41	1	2	yes	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	—	4	2	no	—
217	C₅×C₂²⋊C₄	—	4	2	no	—
218	C₅×C₂²⋊C₄	—	4	2	no	—
219	C₅×C₂²⋊C₄	—	4	2	no	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	4	2	no	—
226	C₄²×C₅	—	4	2	no	—
227	C₄²×C₅	—	4	2	no	—
228	C₄²×C₅	—	4	2	no	—
229	C₄²×C₅	C₂×D₄	1	2	yes	—
230	C₄²×C₅	#41	1	2	yes	—
231	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×#124	C₂²×C₅	1	1	yes	characteristic
234	C₂×#124	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄×Q₈	—	2	1	no	—
236	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
237	#489	—	2	4	no	—
238	#477	—	2	4	no	—
239	C₂×#107	C₂²×C₅	1	1	yes	characteristic
240	C₂×#107	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×#103	C₂²×C₅	1	1	yes	characteristic
245	C₂×#103	C₂²×C₅	1	1	yes	characteristic
246	C₂×#103	C₂²×C₅	1	1	yes	characteristic
247	C₂×#103	C₂²×C₅	1	1	yes	characteristic
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅	1	1	yes	characteristic
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#103	C₂²×C₅	1	1	yes	characteristic
252	C₂×#102	C₂²×C₅	1	1	yes	characteristic
253	C₂×#102	C₂²×C₅	1	1	yes	characteristic
254	C₂×#102	C₂²×C₅	1	1	yes	characteristic
255	C₂×#102	C₂²×C₅	1	1	yes	characteristic
256	C₂×#97	C₂²×C₅	1	1	yes	characteristic
257	#396	—	2	1	no	—
258	#396	—	2	1	no	—
259	#391	—	2	1	no	—
260	#391	C₂²×C₅	1	1	yes	characteristic
261	#390	C₂²×C₅	1	1	yes	characteristic
262	#389	C₂²×C₅	1	1	yes	characteristic
263	#389	C₂²×C₅	1	1	yes	characteristic
264	#388	—	2	1	no	—
265	#388	—	2	1	no	—
266	#387	—	2	1	no	—
267	#387	—	2	1	no	—
268	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	#340	C₂²×C₅	1	1	yes	characteristic
273	#340	C₂²×C₅	1	1	yes	characteristic
274	#336	C₂²×C₅	1	1	yes	characteristic
275	#336	C₂²×C₅	1	1	yes	characteristic
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	—	4	1	no	—
283	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	4	8	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	4	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	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	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	#121	1	2	yes	—
334	C₂×C₄×C₅	#121	1	2	yes	—
335	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
336	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₅×C₈	—	4	1	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	4	1	no	—
357	C₄⋊Q₈	C₅×D₄	1	4	yes	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#124	—	4	1	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	4	4	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#107	—	2	2	no	—
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	4	1	no	—
395	C₄⋊C₈	—	4	1	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#103	—	2	2	no	—
402	#103	—	2	2	no	—
403	#103	—	4	1	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#102	—	4	1	no	—
408	#97	—	2	2	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	C₅×D₄	1	1	yes	characteristic
417	#95	C₅×D₄	1	1	yes	characteristic
418	C₂²×C₅	—	8	1	no	—
419	C₂²×C₅	—	8	1	no	—
420	C₂²×C₅	—	8	1	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	—	8	1	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	C₂×#121	1	1	yes	characteristic
426	C₂²×C₅	#546	1	1	yes	characteristic
427	C₂²×C₅	#548	1	1	yes	characteristic
428	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂²×C₅	#575	1	1	yes	characteristic
430	C₂²×C₅	#578	1	1	yes	characteristic
431	C₂²×C₅	#578	1	1	yes	characteristic
432	C₄×C₅	—	2	2	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	4	2	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	—	8	1	no	—
445	C₄×C₅	#529	1	1	yes	characteristic
446	C₄×C₅	#542	1	1	yes	characteristic
447	C₄×C₅	#548	1	1	yes	characteristic
448	C₄×C₅	#550	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	C₅×#41	1	2	yes	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	2	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	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
513	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
514	C₄⋊C₄	C₅×#41	1	2	yes	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	4	2	no	—
526	C₄²	—	4	2	no	—
527	C₄²	—	4	2	no	—
528	C₄²	—	4	2	no	—
529	C₄²	C₂×C₅×D₄	1	2	yes	—
530	C₄²	C₅×#41	1	2	yes	—
531	C₂×C₅	—	16	1	no	—
532	C₂×C₅	#2426	1	1	yes	characteristic
533	C₂×C₅	#3036	1	1	yes	characteristic
534	C₂×C₅	#3044	1	1	yes	characteristic
535	C₂×C₅	#3308	1	1	yes	characteristic
536	C₂×C₅	#3313	1	1	yes	characteristic
537	C₂×C₅	#3367	1	1	yes	characteristic
538	C₂×C₅	#3377	1	1	yes	characteristic
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	4	8	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	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	—	2	1	no	—
578	C₂×C₄	—	2	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	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	C₅×#121	1	2	yes	—
597	C₂×C₄	C₅×#121	1	2	yes	—
598	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
599	C₂×C₄	C₂²×C₅×D₄	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	C₅×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₅	#25286	1	1	yes	characteristic, direct product factor, Sylow
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	C₂×C₅×#121	1	1	yes	characteristic
618	C₂²	C₅×#546	1	1	yes	characteristic
619	C₂²	C₅×#548	1	1	yes	characteristic
620	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
621	C₂²	C₅×#575	1	1	yes	characteristic
622	C₂²	C₅×#578	1	1	yes	characteristic
623	C₂²	C₅×#578	1	1	yes	characteristic
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₅×#529	1	1	yes	characteristic
638	C₄	C₅×#542	1	1	yes	characteristic
639	C₄	C₅×#548	1	1	yes	characteristic
640	C₄	C₅×#550	1	1	yes	characteristic
641	C₂	—	16	1	no	—
642	C₂	C₅×#2426	1	1	yes	characteristic
643	C₂	C₅×#3036	1	1	yes	characteristic
644	C₂	C₅×#3044	1	1	yes	characteristic
645	C₂	C₅×#3308	1	1	yes	characteristic
646	C₂	C₅×#3313	1	1	yes	characteristic
647	C₂	C₅×#3367	1	1	yes	characteristic
648	C₂	C₅×#3377	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×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×#477	C₂	semidirect
4. C₅×#2365	C₂	semidirect
5. C₅×#2068	C₂	semidirect
7. C₅×#2043	C₂	semidirect
11. C₅×#1981	C₂	semidirect
12. C₅×#1940	C₂	semidirect
13. C₅×#1928	C₂	semidirect
15. C₅×#1763	C₂	semidirect
61. #25286	C₅	direct (N × H)
135. C₂×#477	C₂×C₅	semidirect
137. #2365	C₂×C₅	semidirect
138. #2068	C₂×C₅	semidirect
140. #2043	C₂×C₅	semidirect
144. #1981	C₂×C₅	semidirect
145. #1940	C₂×C₅	semidirect
146. #1928	C₂×C₅	semidirect
148. #1763	C₂×C₅	semidirect
609. C₅	#25286	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×#489	2
C₂×C₅×#477	2
C₅×#2545	2
C₅×#2365	2
C₅×#2068	2
C₅×#2067	2
C₅×#2043	2
C₅×#2042	2
C₅×#1983	2
C₅×#1981	2
C₅×#1940	2
C₅×#1928	2
C₅×#1925	2
C₅×#1763	2
#25286	5

Subgroups — C5×#25286 #11948006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25286 #11948006