Subgroups — C₅×#26769 #11949489

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2366	C₂	1	1	yes	maximal, characteristic
3	C₅×#2071	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2041	C₂	1	1	yes	maximal, characteristic
6	C₅×#2041	C₂	1	1	yes	maximal, characteristic
7	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#127	C₂²	1	1	yes	characteristic
17	C₂×C₅×#125	—	2	1	no	—
18	C₂×C₄×C₅×D₄	—	2	1	no	—
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	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×#102	C₂²	1	1	yes	characteristic
25	C₂×C₅×#102	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×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₅×#400	—	2	1	no	—
34	C₅×#398	—	2	1	no	—
35	C₅×#390	—	2	1	no	—
36	C₅×#390	C₂²	1	1	yes	characteristic
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#389	C₂²	1	1	yes	characteristic
42	C₅×#387	—	2	1	no	—
43	C₅×#386	—	2	1	no	—
44	C₅×#386	—	2	1	no	—
45	C₅×#384	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#26769	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	—	2	1	no	—
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂³×C₄×C₅	—	2	1	no	—
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×#127	—	2	2	no	—
71	C₅×#127	—	2	2	no	—
72	C₅×#125	—	4	4	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₄×C₅×D₄	—	2	2	no	—
75	C₄×C₅×D₄	—	4	1	no	—
76	C₄×C₅×D₄	—	4	1	no	—
77	C₄×C₅×D₄	—	4	4	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₅×#106	—	2	2	no	—
104	C₅×#106	—	2	2	no	—
105	C₅×C₄⋊C₈	—	4	1	no	—
106	C₅×#102	—	2	2	no	—
107	C₅×#102	—	2	2	no	—
108	C₅×#102	—	2	2	no	—
109	C₅×#102	—	2	2	no	—
110	C₅×#102	—	2	2	no	—
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	4	1	no	—
113	C₅×#102	—	4	1	no	—
114	C₅×#97	—	4	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	D₄	1	1	yes	characteristic
122	C₅×#95	D₄	1	1	yes	characteristic
123	#2506	C₂×C₅	1	1	yes	characteristic, complemented
124	#2366	C₂×C₅	1	1	yes	characteristic
125	#2071	C₂×C₅	1	1	yes	characteristic, complemented
126	#2065	C₂×C₅	1	1	yes	characteristic, complemented
127	#2041	C₂×C₅	1	1	yes	characteristic
128	#2041	C₂×C₅	1	1	yes	characteristic
129	#1936	C₂×C₅	1	1	yes	characteristic, complemented
130	#1926	C₂×C₅	1	1	yes	characteristic, complemented
131	#1919	C₂×C₅	1	1	yes	characteristic, complemented
132	#1919	C₂×C₅	1	1	yes	characteristic, complemented
133	#1917	C₂×C₅	1	1	yes	characteristic, complemented
134	#1864	C₂×C₅	1	1	yes	characteristic, complemented
135	#1864	C₂×C₅	1	1	yes	characteristic, complemented
136	#1802	C₂×C₅	1	1	yes	characteristic, complemented
137	#1762	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	—	2	1	no	—
139	C₂⁴×C₅	—	2	1	no	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂×C₅×D₄	—	2	4	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	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	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	4	2	no	—
153	C₂×C₅×D₄	—	4	2	no	—
154	C₂×C₅×D₄	—	8	1	no	—
155	C₂×C₅×D₄	—	8	1	no	—
156	C₂×C₅×D₄	#41	1	2	yes	—
157	C₂×C₅×D₄	#41	1	2	yes	—
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	1	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	—	4	2	no	—
166	C₂²×C₄×C₅	—	4	2	no	—
167	C₂²×C₄×C₅	—	4	2	no	—
168	C₂²×C₄×C₅	—	8	1	no	—
169	C₂²×C₄×C₅	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
202	C₅×C₄⋊C₄	—	4	2	no	—
203	C₅×C₄⋊C₄	—	4	2	no	—
204	C₅×C₄⋊C₄	—	4	2	no	—
205	C₅×C₄⋊C₄	—	4	2	no	—
206	C₅×C₄⋊C₄	—	4	2	no	—
207	C₅×C₄⋊C₄	#41	1	2	yes	—
208	C₅×C₄⋊C₄	#41	1	2	yes	—
209	C₅×C₂²⋊C₄	—	4	2	no	—
210	C₅×C₂²⋊C₄	—	4	2	no	—
211	C₅×C₂²⋊C₄	—	4	2	no	—
212	C₅×C₂²⋊C₄	—	4	2	no	—
213	C₅×C₂²⋊C₄	—	8	1	no	—
214	C₅×C₂²⋊C₄	—	8	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	4	2	no	—
222	C₄²×C₅	—	4	2	no	—
223	C₂×#127	C₂²×C₅	1	1	yes	characteristic
224	C₂×#125	—	2	1	no	—
225	C₂×C₄×D₄	—	2	1	no	—
226	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×#106	C₂²×C₅	1	1	yes	characteristic
229	C₂×#106	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×#102	C₂²×C₅	1	1	yes	characteristic
232	C₂×#102	C₂²×C₅	1	1	yes	characteristic
233	C₂×#102	C₂²×C₅	1	1	yes	characteristic
234	C₂×#102	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×#97	C₂²×C₅	1	1	yes	characteristic
240	#400	—	2	1	no	—
241	#398	—	2	1	no	—
242	#390	—	2	1	no	—
243	#390	C₂²×C₅	1	1	yes	characteristic
244	#390	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#389	C₂²×C₅	1	1	yes	characteristic
247	#389	C₂²×C₅	1	1	yes	characteristic
248	#389	C₂²×C₅	1	1	yes	characteristic
249	#387	—	2	1	no	—
250	#386	—	2	1	no	—
251	#386	—	2	1	no	—
252	#384	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	#340	C₂²×C₅	1	1	yes	characteristic
257	#340	C₂²×C₅	1	1	yes	characteristic
258	#340	C₂²×C₅	1	1	yes	characteristic
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	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	4	1	no	—
269	C₂³×C₅	—	4	1	no	—
270	C₂³×C₅	—	4	1	no	—
271	C₂³×C₅	—	4	1	no	—
272	C₂³×C₅	—	4	1	no	—
273	C₂³×C₅	—	4	1	no	—
274	C₂³×C₅	—	4	1	no	—
275	C₂³×C₅	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	2	2	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	2	2	no	—
285	C₅×D₄	—	4	8	no	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	1	no	—
288	C₅×D₄	—	4	1	no	—
289	C₅×D₄	—	4	1	no	—
290	C₅×D₄	—	8	4	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	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	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	1	no	—
309	C₂×C₄×C₅	—	4	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	—	8	4	no	—
326	C₂×C₄×C₅	—	8	4	no	—
327	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
328	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂²×C₈	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	#127	—	2	2	no	—
350	#127	—	2	2	no	—
351	#125	—	4	4	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	4	1	no	—
355	C₄×D₄	—	4	1	no	—
356	C₄×D₄	—	4	4	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₅×D₄	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×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
382	#106	—	2	2	no	—
383	#106	—	2	2	no	—
384	C₄⋊C₈	—	4	1	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	4	1	no	—
392	#102	—	4	1	no	—
393	#97	—	4	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	C₅×D₄	1	1	yes	characteristic
401	#95	C₅×D₄	1	1	yes	characteristic
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	—	4	2	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	8	1	no	—
409	C₂²×C₅	—	8	1	no	—
410	C₂²×C₅	—	8	1	no	—
411	C₂²×C₅	—	8	1	no	—
412	C₂²×C₅	—	8	1	no	—
413	C₂²×C₅	—	8	1	no	—
414	C₂²×C₅	—	8	1	no	—
415	C₂²×C₅	—	8	1	no	—
416	C₂²×C₅	#525	1	1	yes	characteristic
417	C₂²×C₅	#546	1	1	yes	characteristic
418	C₂²×C₅	#548	1	1	yes	characteristic
419	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂²×C₅	#577	1	1	yes	characteristic
422	C₂²×C₅	#577	1	1	yes	characteristic
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	—	4	2	no	—
431	C₄×C₅	—	8	1	no	—
432	C₄×C₅	—	8	1	no	—
433	C₄×C₅	—	8	1	no	—
434	C₄×C₅	—	8	1	no	—
435	C₄×C₅	#529	1	1	yes	characteristic
436	C₄×C₅	#539	1	1	yes	characteristic
437	C₄×C₅	#552	1	1	yes	characteristic
438	C₄×C₅	#553	1	1	yes	characteristic
439	C₂⁴	—	2	1	no	—
440	C₂⁴	—	2	1	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	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	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	8	1	no	—
456	C₂×D₄	—	8	1	no	—
457	C₂×D₄	C₅×#41	1	2	yes	—
458	C₂×D₄	C₅×#41	1	2	yes	—
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	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	8	1	no	—
470	C₂²×C₄	—	8	1	no	—
471	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
478	C₂×C₈	—	2	1	no	—
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	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	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	—	4	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	C₅×#41	1	2	yes	—
509	C₄⋊C₄	C₅×#41	1	2	yes	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	8	1	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	4	2	no	—
523	C₄²	—	4	2	no	—
524	C₂×C₅	—	8	2	no	—
525	C₂×C₅	—	8	2	no	—
526	C₂×C₅	#2460	1	1	yes	characteristic
527	C₂×C₅	#3109	1	1	yes	characteristic
528	C₂×C₅	#3123	1	1	yes	characteristic
529	C₂×C₅	#3310	1	1	yes	characteristic
530	C₂×C₅	#3332	1	1	yes	characteristic
531	C₂×C₅	#3368	1	1	yes	characteristic
532	C₂×C₅	#3373	1	1	yes	characteristic
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
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	—	4	1	no	—
547	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	8	4	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	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	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	4	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	—	8	4	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
595	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
596	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
597	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
598	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
600	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₅	#26769	1	1	yes	characteristic, direct product factor, Sylow
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	C₅×#525	1	1	yes	characteristic
622	C₂²	C₅×#546	1	1	yes	characteristic
623	C₂²	C₅×#548	1	1	yes	characteristic
624	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
625	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
626	C₂²	C₅×#577	1	1	yes	characteristic
627	C₂²	C₅×#577	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	C₅×#529	1	1	yes	characteristic
641	C₄	C₅×#539	1	1	yes	characteristic
642	C₄	C₅×#552	1	1	yes	characteristic
643	C₄	C₅×#553	1	1	yes	characteristic
644	C₂	—	8	2	no	—
645	C₂	—	8	2	no	—
646	C₂	C₅×#2460	1	1	yes	characteristic
647	C₂	C₅×#3109	1	1	yes	characteristic
648	C₂	C₅×#3123	1	1	yes	characteristic
649	C₂	C₅×#3310	1	1	yes	characteristic
650	C₂	C₅×#3332	1	1	yes	characteristic
651	C₂	C₅×#3368	1	1	yes	characteristic
652	C₂	C₅×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
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×#2506	C₂	semidirect
3. C₅×#2071	C₂	semidirect
4. C₅×#2065	C₂	semidirect
7. C₅×#1936	C₂	semidirect
8. C₅×#1926	C₂	semidirect
9. C₅×#1919	C₂	semidirect
10. C₅×#1919	C₂	semidirect
11. C₅×#1917	C₂	semidirect
12. C₅×#1864	C₂	semidirect
13. C₅×#1864	C₂	semidirect
14. C₅×#1802	C₂	semidirect
15. C₅×#1762	C₂	semidirect
59. #26769	C₅	direct (N × H)
123. #2506	C₂×C₅	semidirect
125. #2071	C₂×C₅	semidirect
126. #2065	C₂×C₅	semidirect
129. #1936	C₂×C₅	semidirect
130. #1926	C₂×C₅	semidirect
131. #1919	C₂×C₅	semidirect
132. #1919	C₂×C₅	semidirect
133. #1917	C₂×C₅	semidirect
134. #1864	C₂×C₅	semidirect
135. #1864	C₂×C₅	semidirect
136. #1802	C₂×C₅	semidirect
137. #1762	C₂×C₅	semidirect
606. C₅	#26769	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×#2506	2
C₅×#2366	2
C₅×#2071	2
C₅×#2065	2
C₅×#2041	2
C₅×#1936	2
C₅×#1926	2
C₅×#1919	2
C₅×#1917	2
C₅×#1864	2
C₅×#1802	2
C₅×#1762	2
#26769	5

Subgroups — C5×#26769 #11949489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26769 #11949489