Subgroups — C₅×#26092 #11948812

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2552	C₂	1	1	yes	maximal, characteristic
2	C₅×#2355	C₂	1	1	yes	maximal, characteristic
3	C₅×#2095	C₂	1	2	yes	maximal
4	C₅×#2068	C₂	1	2	yes	maximal
5	C₅×#1947	C₂	1	1	yes	maximal, characteristic
6	C₅×#1947	C₂	1	2	yes	maximal
7	C₅×#1939	C₂	1	1	yes	maximal, characteristic
8	C₅×#1921	C₂	1	2	yes	maximal
9	C₅×#1845	C₂	1	1	yes	maximal, characteristic
10	C₅×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#125	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#107	C₂²	1	2	yes	—
15	C₂×C₅×#107	C₂²	1	2	yes	—
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	1	yes	characteristic
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#398	—	2	2	no	—
24	C₅×#391	C₂²	1	2	yes	—
25	C₅×#389	—	2	1	no	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#387	—	2	2	no	—
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#384	C₂²	1	2	yes	—
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#382	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#26092	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	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₅×#125	—	4	4	no	—
47	C₄×C₅×Q₈	—	2	2	no	—
48	C₄×C₅×Q₈	Q₈	1	4	yes	—
49	C₂×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	2	no	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#107	—	2	4	no	—
70	C₅×#107	—	4	2	no	—
71	C₅×#107	—	4	2	no	—
72	C₅×C₄⋊C₈	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	2	no	—
74	C₅×#103	—	2	2	no	—
75	C₅×#103	—	2	2	no	—
76	C₅×#103	—	4	2	no	—
77	C₄×C₅×C₈	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	1	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	D₄	1	2	yes	—
84	#2552	C₂×C₅	1	1	yes	characteristic
85	#2355	C₂×C₅	1	1	yes	characteristic
86	#2095	C₂×C₅	1	2	yes	—
87	#2068	C₂×C₅	1	2	yes	—
88	#1947	C₂×C₅	1	2	yes	—
89	#1947	C₂×C₅	1	1	yes	characteristic
90	#1939	C₂×C₅	1	1	yes	characteristic
91	#1921	C₂×C₅	1	2	yes	—
92	#1845	C₂×C₅	1	1	yes	characteristic
93	#1803	C₂×C₅	1	1	yes	characteristic
94	C₄×#103	C₂×C₅	1	1	yes	characteristic
95	C₂×C₅×Q₈	—	2	1	no	—
96	C₂×C₅×Q₈	—	2	1	no	—
97	C₂×C₅×Q₈	—	2	1	no	—
98	C₂×C₅×Q₈	—	2	1	no	—
99	C₂×C₅×Q₈	—	2	1	no	—
100	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₅	—	2	1	no	—
102	C₂²×C₄×C₅	—	2	1	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	—	2	2	no	—
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	2	yes	—
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	#41	1	2	yes	—
120	C₂×C₅×C₈	#41	1	2	yes	—
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	2	1	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	2	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	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	4	4	no	—
133	C₅×C₄⋊C₄	—	4	4	no	—
134	C₅×C₄⋊C₄	—	4	2	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	8	2	no	—
137	C₅×C₄⋊C₄	—	8	1	no	—
138	C₅×C₄⋊C₄	—	8	1	no	—
139	C₅×C₄⋊C₄	Q₁₆	1	4	yes	—
140	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
141	C₄²×C₅	—	2	4	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	4	2	no	—
145	C₄²×C₅	—	8	2	no	—
146	C₄²×C₅	C₂×Q₈	1	2	yes	—
147	C₄²×C₅	#41	1	2	yes	—
148	C₂×#125	—	2	1	no	—
149	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×#107	C₂²×C₅	1	2	yes	—
151	C₂×#107	C₂²×C₅	1	2	yes	—
152	C₂×#107	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
155	C₂×#103	C₂²×C₅	1	1	yes	characteristic
156	C₂×#103	C₂²×C₅	1	1	yes	characteristic
157	C₂×#103	C₂²×C₅	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	#398	—	2	2	no	—
160	#391	C₂²×C₅	1	2	yes	—
161	#389	—	2	1	no	—
162	#389	C₂²×C₅	1	2	yes	—
163	#387	—	2	2	no	—
164	#384	C₂²×C₅	1	1	yes	characteristic
165	#384	C₂²×C₅	1	2	yes	—
166	#384	C₂²×C₅	1	1	yes	characteristic
167	#382	—	2	1	no	—
168	C₄×C₄⋊C₄	—	2	1	no	—
169	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
170	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	#340	C₂²×C₅	1	2	yes	—
173	#340	C₂²×C₅	1	2	yes	—
174	#340	C₂²×C₅	1	1	yes	characteristic
175	#340	C₂²×C₅	1	1	yes	characteristic
176	#336	C₂²×C₅	1	2	yes	—
177	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₅×Q₈	—	2	2	no	—
179	C₅×Q₈	—	2	2	no	—
180	C₅×Q₈	—	4	1	no	—
181	C₅×Q₈	—	4	1	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	—	4	1	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	1	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	C₂×Q₁₆	1	4	yes	—
210	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
211	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₅	C₂²×Q₈	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	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	4	2	no	—
221	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
225	#125	—	4	4	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	C₅×Q₈	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	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	1	yes	characteristic
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	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	C₂³×C₅	1	2	yes	—
247	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
248	#107	—	2	4	no	—
249	#107	—	4	2	no	—
250	#107	—	4	2	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	#103	—	2	2	no	—
254	#103	—	2	2	no	—
255	#103	—	4	2	no	—
256	C₄×C₈	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	1	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	C₅×D₄	1	2	yes	—
263	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂²×C₅	#547	1	1	yes	characteristic
265	C₂²×C₅	#550	1	1	yes	characteristic
266	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
267	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂²×C₅	#576	1	1	yes	characteristic
269	C₂²×C₅	#578	1	1	yes	characteristic
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	8	1	no	—
276	C₄×C₅	—	8	1	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	—	8	2	no	—
279	C₄×C₅	#477	1	4	yes	—
280	C₄×C₅	#533	1	1	yes	characteristic
281	C₄×C₅	#544	1	1	yes	characteristic
282	C₄×C₅	#552	1	1	yes	characteristic
283	C₄×C₅	#553	1	1	yes	characteristic
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₅×#41	1	2	yes	—
309	C₂×C₈	C₅×#41	1	2	yes	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	—	8	1	no	—
327	C₄⋊C₄	—	8	1	no	—
328	C₄⋊C₄	C₅×Q₁₆	1	4	yes	—
329	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	2	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂×C₅×Q₈	1	2	yes	—
336	C₄²	C₅×#41	1	2	yes	—
337	C₂×C₅	#2441	1	1	yes	characteristic
338	C₂×C₅	C₂×#477	1	1	yes	characteristic
339	C₂×C₅	#3083	1	1	yes	characteristic
340	C₂×C₅	#3338	1	1	yes	characteristic
341	C₂×C₅	#3353	1	1	yes	characteristic
342	C₂×C₅	#3395	1	1	yes	characteristic
343	C₂×C₅	#3399	1	1	yes	characteristic
344	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	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	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
375	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
376	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
377	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
378	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
379	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
383	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	2	no	—
388	C₅	#26092	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂²	C₅×#547	1	1	yes	characteristic
391	C₂²	C₅×#550	1	1	yes	characteristic
392	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
393	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²	C₅×#576	1	1	yes	characteristic
395	C₂²	C₅×#578	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₅×#477	1	4	yes	—
406	C₄	C₅×#533	1	1	yes	characteristic
407	C₄	C₅×#544	1	1	yes	characteristic
408	C₄	C₅×#552	1	1	yes	characteristic
409	C₄	C₅×#553	1	1	yes	characteristic
410	C₂	C₅×#2441	1	1	yes	characteristic
411	C₂	C₂×C₅×#477	1	1	yes	characteristic
412	C₂	C₅×#3083	1	1	yes	characteristic
413	C₂	C₅×#3338	1	1	yes	characteristic
414	C₂	C₅×#3353	1	1	yes	characteristic
415	C₂	C₅×#3395	1	1	yes	characteristic
416	C₂	C₅×#3399	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. #26092	C₅	direct (N × H)
388. C₅	#26092	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×#2552	2
C₅×#2355	2
C₅×#2095	2
C₅×#2068	2
C₅×#1947	2
C₅×#1939	2
C₅×#1921	2
C₅×#1845	2
C₅×#1803	2
C₄×C₅×#103	2
#26092	5

Subgroups — C5×#26092 #11948812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26092 #11948812