Subgroups — C₅×#26113 #11948833

Order 1280.

666 conjugacy classes of subgroups.

The subgroup lattice has 416 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
2	C₅×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#2101	C₂	1	2	yes	maximal
4	C₅×#2088	C₂	1	2	yes	maximal
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic
7	C₅×#1865	C₂	1	2	yes	maximal
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic
9	C₅×#1805	C₂	1	2	yes	maximal
10	C₅×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#106	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×#103	C₂²	1	1	yes	characteristic
18	C₂×C₅×#103	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₅×#400	—	2	2	no	—
22	C₅×#389	—	2	2	no	—
23	C₅×#389	—	2	1	no	—
24	C₅×#389	C₂²	1	2	yes	—
25	C₅×#389	C₂²	1	2	yes	—
26	C₅×#384	—	2	1	no	—
27	C₅×#384	C₂²	1	1	yes	characteristic
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#382	—	2	1	no	—
30	C₅×#382	C₂²	1	2	yes	—
31	C₄×C₅×C₄⋊C₄	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#340	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#26113	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₄×C₅×Q₈	—	2	2	no	—
47	C₄×C₅×Q₈	—	2	4	no	—
48	C₄×C₅×Q₈	—	4	2	no	—
49	C₄×C₅×Q₈	Q₈	1	4	yes	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	—	2	1	no	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#106	—	4	2	no	—
71	C₅×C₄⋊C₈	—	2	2	no	—
72	C₅×C₄⋊C₈	—	4	2	no	—
73	C₅×#103	—	2	2	no	—
74	C₅×#103	—	2	2	no	—
75	C₅×#103	—	2	4	no	—
76	C₄×C₅×C₈	—	2	2	no	—
77	C₅×#95	—	2	2	no	—
78	C₅×#95	—	2	1	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	D₄	1	2	yes	—
83	#2571	C₂×C₅	1	1	yes	characteristic
84	Q₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
85	#2101	C₂×C₅	1	2	yes	—
86	#2088	C₂×C₅	1	2	yes	—
87	#1948	C₂×C₅	1	1	yes	characteristic
88	#1939	C₂×C₅	1	1	yes	characteristic
89	#1865	C₂×C₅	1	2	yes	—
90	#1834	C₂×C₅	1	1	yes	characteristic
91	#1805	C₂×C₅	1	2	yes	—
92	#1803	C₂×C₅	1	1	yes	characteristic
93	C₄×#103	C₂×C₅	1	1	yes	characteristic
94	C₂×C₅×Q₈	—	2	1	no	—
95	C₂×C₅×Q₈	—	2	1	no	—
96	C₂×C₅×Q₈	—	2	1	no	—
97	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
98	C₂×C₅×Q₈	#41	1	2	yes	—
99	C₂×C₅×Q₈	#41	1	2	yes	—
100	C₂²×C₄×C₅	—	2	1	no	—
101	C₂²×C₄×C₅	—	2	1	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	1	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₅×C₄⋊C₄	—	2	4	no	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	4	4	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₄⋊C₄	—	4	2	no	—
135	C₅×C₄⋊C₄	—	8	1	no	—
136	C₅×C₄⋊C₄	—	8	1	no	—
137	C₅×C₄⋊C₄	—	8	2	no	—
138	C₅×C₄⋊C₄	—	8	2	no	—
139	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
140	C₄²×C₅	—	2	4	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	4	4	no	—
144	C₄²×C₅	—	4	2	no	—
145	C₄²×C₅	C₂×Q₈	1	2	yes	—
146	C₄²×C₅	#41	1	2	yes	—
147	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
148	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×#106	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
152	C₂×#103	C₂²×C₅	1	2	yes	—
153	C₂×#103	C₂²×C₅	1	1	yes	characteristic
154	C₂×#103	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
156	#400	—	2	2	no	—
157	#389	—	2	1	no	—
158	#389	—	2	2	no	—
159	#389	C₂²×C₅	1	2	yes	—
160	#389	C₂²×C₅	1	2	yes	—
161	#384	—	2	1	no	—
162	#384	C₂²×C₅	1	1	yes	characteristic
163	#384	C₂²×C₅	1	1	yes	characteristic
164	#382	—	2	1	no	—
165	#382	C₂²×C₅	1	2	yes	—
166	C₄×C₄⋊C₄	—	2	1	no	—
167	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	#340	C₂²×C₅	1	2	yes	—
170	#340	C₂²×C₅	1	2	yes	—
171	#340	C₂²×C₅	1	2	yes	—
172	#340	C₂²×C₅	1	1	yes	characteristic
173	#340	C₂²×C₅	1	2	yes	—
174	#340	C₂²×C₅	1	1	yes	characteristic
175	#336	C₂²×C₅	1	2	yes	—
176	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
177	C₅×Q₈	—	2	2	no	—
178	C₅×Q₈	—	2	2	no	—
179	C₅×Q₈	—	2	2	no	—
180	C₅×Q₈	#125	1	4	yes	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₅	#135	1	2	yes	—
210	C₂×C₄×C₅	#137	1	2	yes	—
211	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
217	C₅×C₈	—	4	1	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	—	4	2	no	—
220	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₄×Q₈	—	2	2	no	—
225	C₄×Q₈	—	2	4	no	—
226	C₄×Q₈	—	4	2	no	—
227	C₄×Q₈	C₅×Q₈	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	C₂³×C₅	1	2	yes	—
247	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
248	#106	—	4	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	4	2	no	—
251	#103	—	2	4	no	—
252	#103	—	2	2	no	—
253	#103	—	2	2	no	—
254	C₄×C₈	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	1	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	C₅×D₄	1	2	yes	—
261	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₅	#546	1	1	yes	characteristic
263	C₂²×C₅	#548	1	1	yes	characteristic
264	C₂²×C₅	C₂×#135	1	1	yes	characteristic
265	C₂²×C₅	C₂×#137	1	1	yes	characteristic
266	C₂²×C₅	#577	1	1	yes	characteristic
267	C₂²×C₅	#577	1	1	yes	characteristic
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	2	4	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	8	1	no	—
274	C₄×C₅	—	8	2	no	—
275	C₄×C₅	—	8	1	no	—
276	C₄×C₅	—	8	2	no	—
277	C₄×C₅	#479	1	4	yes	—
278	C₄×C₅	C₂×#125	1	1	yes	characteristic
279	C₄×C₅	#544	1	1	yes	characteristic
280	C₄×C₅	#552	1	1	yes	characteristic
281	C₄×C₅	#553	1	1	yes	characteristic
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
286	C₂×Q₈	C₅×#41	1	2	yes	—
287	C₂×Q₈	C₅×#41	1	2	yes	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	8	1	no	—
324	C₄⋊C₄	—	8	1	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	4	4	no	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×C₅×Q₈	1	2	yes	—
334	C₄²	C₅×#41	1	2	yes	—
335	C₂×C₅	#2442	1	1	yes	characteristic
336	C₂×C₅	C₂×#479	1	1	yes	characteristic
337	C₂×C₅	#3084	1	1	yes	characteristic
338	C₂×C₅	#3304	1	1	yes	characteristic
339	C₂×C₅	#3329	1	1	yes	characteristic
340	C₂×C₅	#3365	1	1	yes	characteristic
341	C₂×C₅	#3369	1	1	yes	characteristic
342	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	2	2	no	—
345	Q₈	—	2	2	no	—
346	Q₈	C₅×#125	1	4	yes	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
374	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
375	C₂×C₄	C₅×#135	1	2	yes	—
376	C₂×C₄	C₅×#137	1	2	yes	—
377	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	2	no	—
386	C₅	#26113	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
388	C₂²	C₅×#546	1	1	yes	characteristic
389	C₂²	C₅×#548	1	1	yes	characteristic
390	C₂²	C₂×C₅×#135	1	1	yes	characteristic
391	C₂²	C₂×C₅×#137	1	1	yes	characteristic
392	C₂²	C₅×#577	1	1	yes	characteristic
393	C₂²	C₅×#577	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	1	no	—
403	C₄	C₅×#479	1	4	yes	—
404	C₄	C₂×C₅×#125	1	1	yes	characteristic
405	C₄	C₅×#544	1	1	yes	characteristic
406	C₄	C₅×#552	1	1	yes	characteristic
407	C₄	C₅×#553	1	1	yes	characteristic
408	C₂	C₅×#2442	1	1	yes	characteristic
409	C₂	C₂×C₅×#479	1	1	yes	characteristic
410	C₂	C₅×#3084	1	1	yes	characteristic
411	C₂	C₅×#3304	1	1	yes	characteristic
412	C₂	C₅×#3329	1	1	yes	characteristic
413	C₂	C₅×#3365	1	1	yes	characteristic
414	C₂	C₅×#3369	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
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
41. #26113	C₅	direct (N × H)
386. C₅	#26113	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×Q₈×C₄⋊C₄	2
C₅×#2101	2
C₅×#2088	2
C₅×#1948	2
C₅×#1939	2
C₅×#1865	2
C₅×#1834	2
C₅×#1805	2
C₅×#1803	2
C₄×C₅×#103	2
#26113	5

Subgroups — C5×#26113 #11948833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26113 #11948833