Subgroups — C₅×#26103 #11948823

Order 1280.

672 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2571	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2357	C₂	1	1	yes	maximal, characteristic
3	C₅×#2092	C₂	1	1	yes	maximal, characteristic
4	C₅×#2092	C₂	1	1	yes	maximal, characteristic
5	C₅×#2067	C₂	1	1	yes	maximal, characteristic
6	C₅×#2065	C₂	1	1	yes	maximal, characteristic
7	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1802	C₂	1	1	yes	maximal, characteristic
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×#107	C₂²	1	1	yes	characteristic
18	C₂×C₅×#107	C₂²	1	1	yes	characteristic
19	C₂×C₅×#107	C₂²	1	1	yes	characteristic
20	C₂×C₅×#106	C₂²	1	1	yes	characteristic
21	C₂×C₅×#106	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
31	C₅×#400	—	2	1	no	—
32	C₅×#400	—	2	1	no	—
33	C₅×#390	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#389	—	2	1	no	—
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#388	—	2	1	no	—
39	C₅×#388	—	2	1	no	—
40	C₅×#384	C₂²	1	1	yes	characteristic
41	C₅×#382	—	2	1	no	—
42	C₅×#382	C₂²	1	1	yes	characteristic
43	C₅×#382	C₂²	1	1	yes	characteristic
44	C₅×#382	C₂²	1	1	yes	characteristic
45	C₅×#381	—	2	1	no	—
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
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×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#26103	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₅	—	2	1	no	—
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×D₄	—	2	2	no	—
67	C₄×C₅×D₄	Q₈	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₅×#107	—	2	2	no	—
93	C₅×#107	—	4	1	no	—
94	C₅×#107	—	4	1	no	—
95	C₅×#106	—	2	2	no	—
96	C₅×#106	—	4	1	no	—
97	C₅×#106	—	4	1	no	—
98	C₅×C₄⋊C₈	—	2	2	no	—
99	C₅×C₄⋊C₈	—	2	2	no	—
100	C₅×C₄⋊C₈	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	4	1	no	—
104	C₅×#102	—	4	1	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#95	—	2	1	no	—
107	C₅×#95	—	2	1	no	—
108	C₅×#95	—	2	1	no	—
109	C₅×#95	—	2	1	no	—
110	C₅×#95	—	2	1	no	—
111	C₅×#95	—	2	1	no	—
112	C₅×#95	—	2	1	no	—
113	C₅×#95	—	2	1	no	—
114	C₅×#95	—	2	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	D₄	1	1	yes	characteristic
118	C₅×#95	D₄	1	1	yes	characteristic
119	#2571	C₂×C₅	1	1	yes	characteristic, complemented
120	#2357	C₂×C₅	1	1	yes	characteristic
121	#2092	C₂×C₅	1	1	yes	characteristic
122	#2092	C₂×C₅	1	1	yes	characteristic
123	#2067	C₂×C₅	1	1	yes	characteristic
124	#2065	C₂×C₅	1	1	yes	characteristic
125	#1949	C₂×C₅	1	1	yes	characteristic, complemented
126	#1949	C₂×C₅	1	1	yes	characteristic, complemented
127	#1949	C₂×C₅	1	1	yes	characteristic, complemented
128	#1940	C₂×C₅	1	1	yes	characteristic, complemented
129	#1920	C₂×C₅	1	1	yes	characteristic, complemented
130	#1918	C₂×C₅	1	1	yes	characteristic, complemented
131	#1847	C₂×C₅	1	1	yes	characteristic, complemented
132	#1802	C₂×C₅	1	1	yes	characteristic
133	#1762	C₂×C₅	1	1	yes	characteristic
134	C₂⁴×C₅	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	8	1	no	—
150	C₂²×C₄×C₅	—	8	1	no	—
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	#41	1	2	yes	—
169	C₂×C₅×C₈	#41	1	2	yes	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	4	1	no	—
184	C₅×C₄⋊C₄	—	4	1	no	—
185	C₅×C₄⋊C₄	—	4	2	no	—
186	C₅×C₄⋊C₄	—	8	1	no	—
187	C₅×C₄⋊C₄	—	8	1	no	—
188	C₅×C₄⋊C₄	—	8	1	no	—
189	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
190	C₅×C₂²⋊C₄	—	2	4	no	—
191	C₅×C₂²⋊C₄	—	4	2	no	—
192	C₅×C₂²⋊C₄	—	4	2	no	—
193	C₅×C₂²⋊C₄	—	8	1	no	—
194	C₅×C₂²⋊C₄	—	8	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	4	2	no	—
200	C₄²×C₅	—	8	1	no	—
201	C₄²×C₅	—	8	1	no	—
202	C₄²×C₅	C₂×Q₈	1	2	yes	—
203	C₄²×C₅	#41	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
205	C₂×#107	C₂²×C₅	1	1	yes	characteristic
206	C₂×#107	C₂²×C₅	1	1	yes	characteristic
207	C₂×#107	C₂²×C₅	1	1	yes	characteristic
208	C₂×#106	C₂²×C₅	1	1	yes	characteristic
209	C₂×#106	C₂²×C₅	1	1	yes	characteristic
210	C₂×#106	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
214	C₂×#102	C₂²×C₅	1	1	yes	characteristic
215	C₂×#102	C₂²×C₅	1	1	yes	characteristic
216	C₂×#102	C₂²×C₅	1	1	yes	characteristic
217	C₂×#102	C₂²×C₅	1	1	yes	characteristic
218	C₂×#97	C₂²×C₅	1	1	yes	characteristic
219	#400	—	2	1	no	—
220	#400	—	2	1	no	—
221	#390	C₂²×C₅	1	1	yes	characteristic
222	#390	C₂²×C₅	1	1	yes	characteristic
223	#389	—	2	1	no	—
224	#389	C₂²×C₅	1	1	yes	characteristic
225	#389	C₂²×C₅	1	1	yes	characteristic
226	#388	—	2	1	no	—
227	#388	—	2	1	no	—
228	#384	C₂²×C₅	1	1	yes	characteristic
229	#382	—	2	1	no	—
230	#382	C₂²×C₅	1	1	yes	characteristic
231	#382	C₂²×C₅	1	1	yes	characteristic
232	#382	C₂²×C₅	1	1	yes	characteristic
233	#381	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	—	2	1	no	—
239	#340	C₂²×C₅	1	1	yes	characteristic
240	#340	C₂²×C₅	1	1	yes	characteristic
241	#340	C₂²×C₅	1	1	yes	characteristic
242	#340	C₂²×C₅	1	1	yes	characteristic
243	#340	C₂²×C₅	1	1	yes	characteristic
244	#340	C₂²×C₅	1	1	yes	characteristic
245	#336	C₂²×C₅	1	1	yes	characteristic
246	#336	C₂²×C₅	1	1	yes	characteristic
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	4	1	no	—
249	C₂³×C₅	—	4	1	no	—
250	C₂³×C₅	—	4	1	no	—
251	C₂³×C₅	—	4	1	no	—
252	C₂³×C₅	—	4	1	no	—
253	C₂³×C₅	—	4	1	no	—
254	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	2	2	no	—
257	C₅×D₄	—	4	1	no	—
258	C₅×D₄	—	4	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	4	1	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	8	4	no	—
297	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
298	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
299	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	4	1	no	—
308	C₅×C₈	—	4	1	no	—
309	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	C₅×Q₈	1	4	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#107	—	4	1	no	—
343	#107	—	4	1	no	—
344	#106	—	2	2	no	—
345	#106	—	4	1	no	—
346	#106	—	4	1	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	2	no	—
350	#102	—	2	2	no	—
351	#102	—	2	2	no	—
352	#102	—	4	1	no	—
353	#102	—	4	1	no	—
354	#97	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	C₅×D₄	1	1	yes	characteristic
367	#95	C₅×D₄	1	1	yes	characteristic
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	8	1	no	—
372	C₂²×C₅	—	8	1	no	—
373	C₂²×C₅	—	8	1	no	—
374	C₂²×C₅	—	8	1	no	—
375	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
376	C₂²×C₅	#547	1	1	yes	characteristic
377	C₂²×C₅	#550	1	1	yes	characteristic
378	C₂²×C₅	#575	1	1	yes	characteristic
379	C₂²×C₅	#575	1	1	yes	characteristic
380	C₂²×C₅	#576	1	1	yes	characteristic
381	C₂²×C₅	#577	1	1	yes	characteristic
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	—	4	1	no	—
386	C₄×C₅	—	4	1	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	8	1	no	—
390	C₄×C₅	—	8	1	no	—
391	C₄×C₅	—	8	1	no	—
392	C₄×C₅	—	8	1	no	—
393	C₄×C₅	—	8	1	no	—
394	C₄×C₅	—	8	1	no	—
395	C₄×C₅	#533	1	1	yes	characteristic
396	C₄×C₅	#544	1	1	yes	characteristic
397	C₄×C₅	#552	1	1	yes	characteristic
398	C₄×C₅	#553	1	1	yes	characteristic
399	C₂⁴	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	8	1	no	—
415	C₂²×C₄	—	8	1	no	—
416	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	C₅×#41	1	2	yes	—
434	C₂×C₈	C₅×#41	1	2	yes	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	8	1	no	—
452	C₄⋊C₄	—	8	1	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	8	1	no	—
459	C₂²⋊C₄	—	8	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	4	2	no	—
465	C₄²	—	8	1	no	—
466	C₄²	—	8	1	no	—
467	C₄²	C₂×C₅×Q₈	1	2	yes	—
468	C₄²	C₅×#41	1	2	yes	—
469	C₂×C₅	—	8	2	no	—
470	C₂×C₅	#2441	1	1	yes	characteristic
471	C₂×C₅	#3080	1	1	yes	characteristic
472	C₂×C₅	#3081	1	1	yes	characteristic
473	C₂×C₅	#3347	1	1	yes	characteristic
474	C₂×C₅	#3350	1	1	yes	characteristic
475	C₂×C₅	#3401	1	1	yes	characteristic
476	C₂×C₅	#3403	1	1	yes	characteristic
477	C₂³	—	2	2	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	8	4	no	—
527	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
528	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
529	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
530	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
531	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
532	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
533	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₅	#26103	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
548	C₂²	C₅×#547	1	1	yes	characteristic
549	C₂²	C₅×#550	1	1	yes	characteristic
550	C₂²	C₅×#575	1	1	yes	characteristic
551	C₂²	C₅×#575	1	1	yes	characteristic
552	C₂²	C₅×#576	1	1	yes	characteristic
553	C₂²	C₅×#577	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₅×#533	1	1	yes	characteristic
568	C₄	C₅×#544	1	1	yes	characteristic
569	C₄	C₅×#552	1	1	yes	characteristic
570	C₄	C₅×#553	1	1	yes	characteristic
571	C₂	—	8	2	no	—
572	C₂	C₅×#2441	1	1	yes	characteristic
573	C₂	C₅×#3080	1	1	yes	characteristic
574	C₂	C₅×#3081	1	1	yes	characteristic
575	C₂	C₅×#3347	1	1	yes	characteristic
576	C₂	C₅×#3350	1	1	yes	characteristic
577	C₂	C₅×#3401	1	1	yes	characteristic
578	C₂	C₅×#3403	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
1. C₅×#2571	C₂	semidirect
7. C₅×#1949	C₂	semidirect
8. C₅×#1949	C₂	semidirect
9. C₅×#1949	C₂	semidirect
10. C₅×#1940	C₂	semidirect
11. C₅×#1920	C₂	semidirect
12. C₅×#1918	C₂	semidirect
13. C₅×#1847	C₂	semidirect
59. #26103	C₅	direct (N × H)
119. #2571	C₂×C₅	semidirect
125. #1949	C₂×C₅	semidirect
126. #1949	C₂×C₅	semidirect
127. #1949	C₂×C₅	semidirect
128. #1940	C₂×C₅	semidirect
129. #1920	C₂×C₅	semidirect
130. #1918	C₂×C₅	semidirect
131. #1847	C₂×C₅	semidirect
539. C₅	#26103	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2571	2
C₅×#2357	2
C₅×#2092	2
C₅×#2067	2
C₅×#2065	2
C₅×#1949	2
C₅×#1940	2
C₅×#1920	2
C₅×#1918	2
C₅×#1847	2
C₅×#1802	2
C₅×#1762	2
#26103	5

Subgroups — C5×#26103 #11948823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26103 #11948823