Subgroups — C₅×#35315 #11958035

Order 1280.

1602 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2857	C₂	1	1	yes	maximal, characteristic
2	C₅×#2855	C₂	1	2	yes	maximal
3	C₅×#2851	C₂	1	1	yes	maximal, characteristic
4	C₅×#2647	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2645	C₂	1	2	yes	maximal, complemented
6	C₅×#2642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2533	C₂	1	4	yes	maximal, complemented
8	C₅×#2528	C₂	1	4	yes	maximal, complemented
9	C₅×#2505	C₂	1	4	yes	maximal
10	C₅×#2493	C₂	1	4	yes	maximal
11	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2320	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
15	C₂×C₅×#376	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#125	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
20	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#401	C₂²	1	4	yes	—
24	C₅×#400	C₂²	1	4	yes	—
25	C₅×#400	C₂²	1	4	yes	—
26	C₅×#400	C₂²	1	4	yes	—
27	C₅×#400	C₂²	1	4	yes	—
28	C₅×#400	C₂²	1	4	yes	—
29	C₅×#400	C₂²	1	4	yes	—
30	C₅×#398	C₂²	1	4	yes	—
31	C₅×#391	C₂²	1	2	yes	—
32	C₅×#391	C₂²	1	2	yes	—
33	C₅×#391	C₂²	1	2	yes	—
34	C₅×#391	C₂²	1	2	yes	—
35	C₅×#389	C₂²	1	4	yes	—
36	C₅×#389	C₂²	1	4	yes	—
37	C₅×#389	C₂²	1	2	yes	—
38	C₅×#389	C₂²	1	2	yes	—
39	C₅×#389	C₂²	1	2	yes	—
40	C₅×#389	C₂²	1	2	yes	—
41	C₅×#387	C₂²	1	4	yes	—
42	C₅×#387	C₂²	1	4	yes	—
43	C₅×#387	C₂²	1	4	yes	—
44	C₅×#387	C₂²	1	4	yes	—
45	C₅×#387	C₂²	1	4	yes	—
46	C₅×#387	C₂²	1	4	yes	—
47	C₅×#387	C₂²	1	4	yes	—
48	C₅×#387	C₂²	1	4	yes	—
49	C₅×#387	C₂²	1	4	yes	—
50	C₅×#385	C₂²	1	4	yes	—
51	C₅×#385	C₂²	1	4	yes	—
52	C₅×#385	C₂²	1	4	yes	—
53	C₅×#384	C₂²	1	1	yes	characteristic
54	C₅×#383	C₂²	1	4	yes	—
55	C₅×#382	C₂²	1	4	yes	—
56	C₅×#382	C₂²	1	1	yes	characteristic
57	C₅×#381	C₂²	1	4	yes	—
58	C₅×#380	C₂²	1	4	yes	—
59	C₅×#380	C₂²	1	2	yes	—
60	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
61	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₅×#376	C₂²	1	2	yes	—
64	C₅×#376	C₂²	1	2	yes	—
65	C₅×#376	C₂²	1	1	yes	characteristic
66	C₅×#376	C₂²	1	1	yes	characteristic
67	C₅×#376	C₂²	1	1	yes	characteristic
68	C₅×#376	C₂²	1	1	yes	characteristic
69	C₂×C₅×#95	C₂²	1	2	yes	—
70	C₂×C₅×#95	C₂²	1	2	yes	—
71	#35315	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂²×C₅×Q₈	C₂³	1	2	yes	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	2	yes	—
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊Q₈	—	2	4	no	—
79	C₅×#125	—	2	4	no	—
80	C₅×C₂²⋊Q₈	—	2	8	no	—
81	C₄×C₅×Q₈	—	2	8	no	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₄²×C₅	—	2	4	no	—
97	C₂×C₄²×C₅	—	2	4	no	—
98	C₂×C₄²×C₅	—	2	4	no	—
99	C₂×C₄²×C₅	C₂³	1	2	yes	—
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	2	yes	—
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₅	C₂³	1	4	yes	—
108	C₂×C₄²×C₅	C₂³	1	4	yes	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₅×#95	C₂³	1	2	yes	—
112	C₅×#95	C₂³	1	2	yes	—
113	C₅×#95	C₂³	1	2	yes	—
114	C₅×#95	C₂³	1	2	yes	—
115	C₅×#95	C₂³	1	2	yes	—
116	C₅×#95	C₂³	1	2	yes	—
117	C₅×#95	C₂³	1	2	yes	—
118	C₅×#95	C₂³	1	2	yes	—
119	C₅×#95	C₂³	1	4	yes	—
120	C₅×#95	C₂³	1	4	yes	—
121	C₅×#95	C₂³	1	4	yes	—
122	C₅×#95	C₂³	1	4	yes	—
123	C₅×#95	C₂³	1	4	yes	—
124	C₅×#95	C₂³	1	4	yes	—
125	C₅×#95	C₂³	1	4	yes	—
126	C₅×#95	C₂³	1	4	yes	—
127	C₅×#95	C₂³	1	4	yes	—
128	C₅×#95	C₂³	1	4	yes	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	4	yes	—
131	C₅×#95	C₂³	1	4	yes	—
132	C₅×#95	C₂³	1	4	yes	—
133	C₅×#95	C₂³	1	4	yes	—
134	#2857	C₂×C₅	1	1	yes	characteristic
135	#2855	C₂×C₅	1	2	yes	—
136	#2851	C₂×C₅	1	1	yes	characteristic
137	#2647	C₂×C₅	1	1	yes	characteristic, complemented
138	#2645	C₂×C₅	1	2	yes	complemented
139	#2642	C₂×C₅	1	1	yes	characteristic, complemented
140	#2533	C₂×C₅	1	4	yes	complemented
141	#2528	C₂×C₅	1	4	yes	complemented
142	#2505	C₂×C₅	1	4	yes	—
143	#2493	C₂×C₅	1	4	yes	—
144	#2330	C₂×C₅	1	1	yes	characteristic, complemented
145	#2327	C₂×C₅	1	1	yes	characteristic, complemented
146	#2320	C₂×C₅	1	2	yes	complemented
147	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
148	C₂×#376	C₂×C₅	1	1	yes	characteristic
149	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
150	C₂×C₅×Q₈	—	2	4	no	—
151	C₂×C₅×Q₈	—	2	4	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	2	4	no	—
159	C₂²×C₄×C₅	—	2	4	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	—	4	2	no	—
164	C₂²×C₄×C₅	—	4	2	no	—
165	C₂²×C₄×C₅	#41	1	4	yes	—
166	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
180	C₅×C₄⋊C₄	—	2	4	no	—
181	C₅×C₄⋊C₄	—	2	8	no	—
182	C₅×C₄⋊C₄	—	2	4	no	—
183	C₅×C₄⋊C₄	—	2	8	no	—
184	C₅×C₄⋊C₄	—	2	8	no	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	2	8	no	—
187	C₅×C₄⋊C₄	—	4	4	no	—
188	C₅×C₄⋊C₄	—	4	4	no	—
189	C₅×C₄⋊C₄	—	4	4	no	—
190	C₅×C₄⋊C₄	—	4	4	no	—
191	C₅×C₄⋊C₄	—	4	4	no	—
192	C₅×C₂²⋊C₄	—	2	8	no	—
193	C₅×C₂²⋊C₄	—	2	8	no	—
194	C₄²×C₅	—	2	4	no	—
195	C₄²×C₅	—	2	4	no	—
196	C₄²×C₅	—	2	2	no	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	2	8	no	—
203	C₄²×C₅	—	4	4	no	—
204	C₄²×C₅	#41	1	4	yes	—
205	C₄²×C₅	#41	1	4	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
207	C₂×#125	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
210	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
213	#401	C₂²×C₅	1	4	yes	—
214	#400	C₂²×C₅	1	4	yes	—
215	#400	C₂²×C₅	1	4	yes	—
216	#400	C₂²×C₅	1	4	yes	—
217	#400	C₂²×C₅	1	4	yes	—
218	#400	C₂²×C₅	1	4	yes	—
219	#400	C₂²×C₅	1	4	yes	—
220	#398	C₂²×C₅	1	4	yes	—
221	#391	C₂²×C₅	1	2	yes	—
222	#391	C₂²×C₅	1	2	yes	—
223	#391	C₂²×C₅	1	2	yes	—
224	#391	C₂²×C₅	1	2	yes	—
225	#389	C₂²×C₅	1	2	yes	—
226	#389	C₂²×C₅	1	2	yes	—
227	#389	C₂²×C₅	1	2	yes	—
228	#389	C₂²×C₅	1	4	yes	—
229	#389	C₂²×C₅	1	4	yes	—
230	#389	C₂²×C₅	1	2	yes	—
231	#387	C₂²×C₅	1	4	yes	—
232	#387	C₂²×C₅	1	4	yes	—
233	#387	C₂²×C₅	1	4	yes	—
234	#387	C₂²×C₅	1	4	yes	—
235	#387	C₂²×C₅	1	4	yes	—
236	#387	C₂²×C₅	1	4	yes	—
237	#387	C₂²×C₅	1	4	yes	—
238	#387	C₂²×C₅	1	4	yes	—
239	#387	C₂²×C₅	1	4	yes	—
240	#385	C₂²×C₅	1	4	yes	—
241	#385	C₂²×C₅	1	4	yes	—
242	#385	C₂²×C₅	1	4	yes	—
243	#384	C₂²×C₅	1	1	yes	characteristic
244	#383	C₂²×C₅	1	4	yes	—
245	#382	C₂²×C₅	1	4	yes	—
246	#382	C₂²×C₅	1	1	yes	characteristic
247	#381	C₂²×C₅	1	4	yes	—
248	#380	C₂²×C₅	1	2	yes	—
249	#380	C₂²×C₅	1	4	yes	—
250	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
252	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
253	#376	C₂²×C₅	1	1	yes	characteristic
254	#376	C₂²×C₅	1	1	yes	characteristic
255	#376	C₂²×C₅	1	1	yes	characteristic
256	#376	C₂²×C₅	1	1	yes	characteristic
257	#376	C₂²×C₅	1	2	yes	—
258	#376	C₂²×C₅	1	2	yes	—
259	C₂×#95	C₂²×C₅	1	2	yes	—
260	C₂×#95	C₂²×C₅	1	2	yes	—
261	C₂³×C₅	—	2	1	no	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	C₂×#41	1	2	yes	—
265	C₂³×C₅	2₋¹⁺⁴	1	4	yes	—
266	C₂³×C₅	C₂⁵	1	1	yes	characteristic
267	C₅×Q₈	—	4	8	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	8	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	4	no	—
282	C₂×C₄×C₅	—	2	4	no	—
283	C₂×C₄×C₅	—	2	4	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	4	no	—
286	C₂×C₄×C₅	—	2	4	no	—
287	C₂×C₄×C₅	—	2	4	no	—
288	C₂×C₄×C₅	—	2	4	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	2	4	no	—
295	C₂×C₄×C₅	—	2	4	no	—
296	C₂×C₄×C₅	—	2	4	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	4	8	no	—
302	C₂×C₄×C₅	—	4	8	no	—
303	C₂×C₄×C₅	—	4	4	no	—
304	C₂×C₄×C₅	—	4	4	no	—
305	C₂×C₄×C₅	C₂×#41	1	4	yes	—
306	C₂×C₄×C₅	C₂×#41	1	2	yes	—
307	C₂×C₄×C₅	C₂×#41	1	4	yes	—
308	C₂×C₄×C₅	C₂×#41	1	2	yes	—
309	C₂×C₄×C₅	C₂×#41	1	2	yes	—
310	C₂×C₄×C₅	C₂×#41	1	2	yes	—
311	C₂²×Q₈	C₂³×C₅	1	2	yes	—
312	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₅	1	2	yes	—
314	C₂³×C₄	C₂³×C₅	1	2	yes	—
315	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	4	no	—
318	#125	—	2	4	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	C₄×Q₈	—	2	8	no	—
321	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
335	C₂×C₄²	—	2	4	no	—
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	C₂³×C₅	1	4	yes	—
339	C₂×C₄²	C₂³×C₅	1	2	yes	—
340	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₅	1	2	yes	—
343	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₅	1	4	yes	—
348	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
350	#95	C₂³×C₅	1	2	yes	—
351	#95	C₂³×C₅	1	2	yes	—
352	#95	C₂³×C₅	1	2	yes	—
353	#95	C₂³×C₅	1	2	yes	—
354	#95	C₂³×C₅	1	2	yes	—
355	#95	C₂³×C₅	1	2	yes	—
356	#95	C₂³×C₅	1	2	yes	—
357	#95	C₂³×C₅	1	2	yes	—
358	#95	C₂³×C₅	1	4	yes	—
359	#95	C₂³×C₅	1	4	yes	—
360	#95	C₂³×C₅	1	4	yes	—
361	#95	C₂³×C₅	1	4	yes	—
362	#95	C₂³×C₅	1	4	yes	—
363	#95	C₂³×C₅	1	4	yes	—
364	#95	C₂³×C₅	1	4	yes	—
365	#95	C₂³×C₅	1	4	yes	—
366	#95	C₂³×C₅	1	4	yes	—
367	#95	C₂³×C₅	1	4	yes	—
368	#95	C₂³×C₅	1	4	yes	—
369	#95	C₂³×C₅	1	4	yes	—
370	#95	C₂³×C₅	1	4	yes	—
371	#95	C₂³×C₅	1	4	yes	—
372	#95	C₂³×C₅	1	4	yes	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	#541	1	4	yes	—
378	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
382	C₂²×C₅	#585	1	2	yes	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	—	2	4	no	—
385	C₄×C₅	—	2	4	no	—
386	C₄×C₅	—	4	4	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	4	4	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	—	4	4	no	—
393	C₄×C₅	—	4	4	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	—	4	2	no	—
396	C₄×C₅	#529	1	4	yes	—
397	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	C₅×#41	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	4	4	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	8	no	—
451	C₄²	—	4	4	no	—
452	C₄²	C₅×#41	1	4	yes	—
453	C₄²	C₅×#41	1	4	yes	—
454	C₂×C₅	—	2	4	no	—
455	C₂×C₅	C₂×#529	1	1	yes	characteristic
456	C₂×C₅	C₂×#541	1	1	yes	characteristic
457	C₂×C₅	#3455	1	1	yes	characteristic
458	C₂×C₅	#3495	1	2	yes	—
459	C₂×C₅	#3495	1	2	yes	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×C₅×#41	1	2	yes	—
464	C₂³	C₅×2₋¹⁺⁴	1	4	yes	—
465	C₂³	C₂⁵×C₅	1	1	yes	characteristic
466	Q₈	—	4	8	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	C₂×C₅×#41	1	4	yes	—
505	C₂×C₄	C₂×C₅×#41	1	2	yes	—
506	C₂×C₄	C₂×C₅×#41	1	4	yes	—
507	C₂×C₄	C₂×C₅×#41	1	2	yes	—
508	C₂×C₄	C₂×C₅×#41	1	2	yes	—
509	C₂×C₄	C₂×C₅×#41	1	2	yes	—
510	C₅	#35315	1	1	yes	characteristic, direct product factor, Sylow
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	C₅×#541	1	4	yes	—
516	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
517	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
518	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
519	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
520	C₂²	C₅×#585	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	2	4	no	—
523	C₄	—	2	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	4	no	—
534	C₄	C₅×#529	1	4	yes	—
535	C₂	—	2	4	no	—
536	C₂	C₂×C₅×#529	1	1	yes	characteristic
537	C₂	C₂×C₅×#541	1	1	yes	characteristic
538	C₂	C₅×#3455	1	1	yes	characteristic
539	C₂	C₅×#3495	1	2	yes	—
540	C₂	C₅×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2647	C₂	semidirect
5. C₅×#2645	C₂	semidirect
6. C₅×#2642	C₂	semidirect
7. C₅×#2533	C₂	semidirect
8. C₅×#2528	C₂	semidirect
11. C₅×#2330	C₂	semidirect
12. C₅×#2327	C₂	semidirect
13. C₅×#2320	C₂	semidirect
71. #35315	C₅	direct (N × H)
137. #2647	C₂×C₅	semidirect
138. #2645	C₂×C₅	semidirect
139. #2642	C₂×C₅	semidirect
140. #2533	C₂×C₅	semidirect
141. #2528	C₂×C₅	semidirect
144. #2330	C₂×C₅	semidirect
145. #2327	C₂×C₅	semidirect
146. #2320	C₂×C₅	semidirect
510. C₅	#35315	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×#2857	2
C₅×#2855	2
C₅×#2851	2
C₅×#2647	2
C₅×#2645	2
C₅×#2642	2
C₅×#2533	2
C₅×#2528	2
C₅×#2505	2
C₅×#2493	2
C₅×#2330	2
C₅×#2327	2
C₅×#2320	2
C₄×C₅×C₂²⋊Q₈	2
C₂×C₅×#376	2
#35315	5

Subgroups — C5×#35315 #11958035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35315 #11958035