Subgroups — C₅×#21987 #11944707

Order 1280.

902 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	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#384	C₂	1	1	yes	maximal, characteristic
3	C₅×#2283	C₂	1	1	yes	maximal, characteristic
4	C₅×#1948	C₂	1	2	yes	maximal, complemented
5	C₅×#1947	C₂	1	2	yes	maximal, complemented
6	C₅×#1853	C₂	1	2	yes	maximal
7	C₅×#1852	C₂	1	2	yes	maximal
8	C₅×#1847	C₂	1	2	yes	maximal, complemented
9	C₅×#1836	C₂	1	2	yes	maximal, complemented
10	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
12	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#432	C₄	1	8	yes	complemented
15	C₂×C₅×#107	C₂²	1	4	yes	—
16	C₂×C₅×#106	C₂²	1	4	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₅×#384	—	2	1	no	—
21	C₅×#384	—	2	1	no	—
22	C₅×#384	C₂²	1	2	yes	—
23	C₅×#384	C₂²	1	2	yes	—
24	C₅×#383	—	2	1	no	—
25	C₅×#382	C₂²	1	1	yes	characteristic
26	C₅×#382	C₂²	1	1	yes	characteristic
27	C₅×#381	—	2	1	no	—
28	C₅×#380	C₂²	1	1	yes	characteristic
29	C₅×#380	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
33	C₅×#376	—	2	1	no	—
34	C₅×#340	C₂²	1	4	yes	—
35	C₅×#340	C₂²	1	4	yes	—
36	#21987	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂³×C₄×C₅	—	2	2	no	—
38	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂³	1	4	yes	—
42	C₂×C₅×C₄⋊C₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	—	2	2	no	—
44	C₂×C₅×C₄⋊C₄	—	2	2	no	—
45	C₂×C₅×C₄⋊C₄	—	2	2	no	—
46	C₂×C₅×C₄⋊C₄	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	—	4	4	no	—
48	C₂×C₅×C₄⋊C₄	—	4	4	no	—
49	C₂×C₅×C₄⋊C₄	—	4	4	no	—
50	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
53	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
55	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₄²×C₅	—	2	1	no	—
58	C₂×C₄²×C₅	—	2	1	no	—
59	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	Q₈	1	4	yes	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₅×#107	—	4	4	no	—
66	C₅×#106	—	4	4	no	—
67	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
68	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
69	C₅×#97	C₂×C₄	1	8	yes	complemented
70	C₅×#95	—	2	1	no	—
71	C₅×#95	—	2	1	no	—
72	C₅×#95	—	2	1	no	—
73	C₅×#95	—	2	1	no	—
74	C₅×#95	—	2	1	no	—
75	C₅×#95	—	2	1	no	—
76	C₅×#95	—	2	1	no	—
77	C₅×#95	—	2	1	no	—
78	C₂×#432	C₂×C₅	1	1	yes	characteristic
79	C₂×#384	C₂×C₅	1	1	yes	characteristic
80	#2283	C₂×C₅	1	1	yes	characteristic
81	#1948	C₂×C₅	1	2	yes	complemented
82	#1947	C₂×C₅	1	2	yes	complemented
83	#1853	C₂×C₅	1	2	yes	—
84	#1852	C₂×C₅	1	2	yes	—
85	#1847	C₂×C₅	1	2	yes	complemented
86	#1836	C₂×C₅	1	2	yes	complemented
87	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	—	2	1	no	—
98	C₂²×C₄×C₅	—	2	4	no	—
99	C₂²×C₄×C₅	—	4	4	no	—
100	C₂²×C₄×C₅	—	4	4	no	—
101	C₂²×C₄×C₅	—	4	4	no	—
102	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
103	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₂×C₅×C₈	—	2	4	no	—
113	C₂×C₅×C₈	—	2	4	no	—
114	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	2	4	no	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	—	4	4	no	—
122	C₅×C₄⋊C₄	—	4	4	no	—
123	C₅×C₄⋊C₄	—	4	4	no	—
124	C₅×C₄⋊C₄	—	4	4	no	—
125	C₅×C₄⋊C₄	—	4	4	no	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₄²×C₅	—	4	2	no	—
129	C₄²×C₅	—	4	2	no	—
130	C₄²×C₅	C₄⋊C₄	1	4	yes	—
131	C₄²×C₅	C₄⋊C₄	1	4	yes	—
132	C₄²×C₅	C₂²×C₄	1	2	yes	—
133	C₄²×C₅	C₂²×C₄	1	2	yes	—
134	C₄²×C₅	C₂×Q₈	1	2	yes	—
135	C₄²×C₅	C₂×Q₈	1	2	yes	—
136	C₂²×C₄⋊C₄	—	2	1	no	—
137	C₂²×C₄⋊C₄	—	2	1	no	—
138	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
140	#432	C₄×C₅	1	8	yes	complemented
141	C₂×#107	C₂²×C₅	1	4	yes	—
142	C₂×#106	C₂²×C₅	1	4	yes	—
143	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
144	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
145	C₂×#97	C₂²×C₅	1	2	yes	—
146	#384	—	2	1	no	—
147	#384	—	2	1	no	—
148	#384	C₂²×C₅	1	2	yes	—
149	#384	C₂²×C₅	1	2	yes	—
150	#383	—	2	1	no	—
151	#382	C₂²×C₅	1	1	yes	characteristic
152	#382	C₂²×C₅	1	1	yes	characteristic
153	#381	—	2	1	no	—
154	#380	C₂²×C₅	1	1	yes	characteristic
155	#380	C₂²×C₅	1	1	yes	characteristic
156	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₄×C₂²⋊C₄	—	2	1	no	—
159	#376	—	2	1	no	—
160	#340	C₂²×C₅	1	4	yes	—
161	#340	C₂²×C₅	1	4	yes	—
162	C₂³×C₅	—	2	1	no	—
163	C₂³×C₅	—	2	1	no	—
164	C₂³×C₅	—	2	1	no	—
165	C₂³×C₅	—	2	1	no	—
166	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
167	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
168	C₂³×C₅	#137	1	2	yes	—
169	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	1	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	8	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	2	8	no	—
182	C₂×C₄×C₅	—	4	4	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	1	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	—	4	1	no	—
188	C₂×C₄×C₅	—	4	1	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	4	no	—
192	C₂×C₄×C₅	—	4	4	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	—	8	8	no	—
198	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
202	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
203	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₅	#137	1	2	yes	—
205	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
208	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
209	C₅×C₈	—	2	8	no	—
210	C₂³×C₄	—	2	2	no	—
211	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
212	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₅	1	4	yes	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	4	4	no	—
221	C₂×C₄⋊C₄	—	4	4	no	—
222	C₂×C₄⋊C₄	—	4	4	no	—
223	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
224	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₄²	—	2	1	no	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
233	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
234	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
235	C₂×C₄²	C₅×Q₈	1	4	yes	—
236	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
238	#107	—	4	4	no	—
239	#106	—	4	4	no	—
240	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
241	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
242	#97	C₂×C₄×C₅	1	8	yes	complemented
243	#95	—	2	1	no	—
244	#95	—	2	1	no	—
245	#95	—	2	1	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	#428	1	4	yes	—
258	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₅	#535	1	1	yes	characteristic
260	C₂²×C₅	#536	1	1	yes	characteristic
261	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₅	C₂×#137	1	1	yes	characteristic
264	C₂²×C₅	C₂×#137	1	1	yes	characteristic
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	8	1	no	—
270	C₄×C₅	—	8	4	no	—
271	C₄×C₅	—	8	1	no	—
272	C₄×C₅	—	8	1	no	—
273	C₄×C₅	—	8	1	no	—
274	C₄×C₅	#428	1	4	yes	—
275	C₄×C₅	#520	1	2	yes	—
276	C₄×C₅	#544	1	2	yes	—
277	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
293	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
294	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
295	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	4	2	no	—
319	C₄²	—	4	2	no	—
320	C₄²	C₅×C₄⋊C₄	1	4	yes	—
321	C₄²	C₅×C₄⋊C₄	1	4	yes	—
322	C₄²	C₂²×C₄×C₅	1	2	yes	—
323	C₄²	C₂²×C₄×C₅	1	2	yes	—
324	C₄²	C₂×C₅×Q₈	1	2	yes	—
325	C₄²	C₂×C₅×Q₈	1	2	yes	—
326	C₂×C₅	—	2	4	no	—
327	C₂×C₅	#2317	1	1	yes	characteristic
328	C₂×C₅	C₂×#428	1	1	yes	characteristic
329	C₂×C₅	C₂×#428	1	1	yes	characteristic
330	C₂×C₅	#3217	1	1	yes	characteristic
331	C₂×C₅	#3218	1	1	yes	characteristic
332	C₂×C₅	#3238	1	1	yes	characteristic
333	C₂×C₅	#3239	1	1	yes	characteristic
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
339	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
340	C₂³	C₅×#137	1	2	yes	—
341	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	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	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	8	no	—
370	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
371	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
372	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
373	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
374	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
375	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
376	C₂×C₄	C₅×#137	1	2	yes	—
377	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
379	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
381	C₈	—	2	8	no	—
382	C₅	#21987	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	C₅×#428	1	4	yes	—
390	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
391	C₂²	C₅×#535	1	1	yes	characteristic
392	C₂²	C₅×#536	1	1	yes	characteristic
393	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₂²	C₂×C₅×#137	1	1	yes	characteristic
396	C₂²	C₂×C₅×#137	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	4	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	1	no	—
406	C₄	C₅×#428	1	4	yes	—
407	C₄	C₅×#520	1	2	yes	—
408	C₄	C₅×#544	1	2	yes	—
409	C₂	—	2	4	no	—
410	C₂	C₅×#2317	1	1	yes	characteristic
411	C₂	C₂×C₅×#428	1	1	yes	characteristic
412	C₂	C₂×C₅×#428	1	1	yes	characteristic
413	C₂	C₅×#3217	1	1	yes	characteristic
414	C₂	C₅×#3218	1	1	yes	characteristic
415	C₂	C₅×#3238	1	1	yes	characteristic
416	C₂	C₅×#3239	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1948	C₂	semidirect
5. C₅×#1947	C₂	semidirect
8. C₅×#1847	C₂	semidirect
9. C₅×#1836	C₂	semidirect
14. C₅×#432	C₄	semidirect
36. #21987	C₅	direct (N × H)
67. C₅×C₄⋊C₈	C₂×C₄	semidirect
69. C₅×#97	C₂×C₄	semidirect
81. #1948	C₂×C₅	semidirect
82. #1947	C₂×C₅	semidirect
85. #1847	C₂×C₅	semidirect
86. #1836	C₂×C₅	semidirect
140. #432	C₄×C₅	semidirect
240. C₄⋊C₈	C₂×C₄×C₅	semidirect
242. #97	C₂×C₄×C₅	semidirect
382. C₅	#21987	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#432	2
C₂×C₅×#384	2
C₅×#2283	2
C₅×#1948	2
C₅×#1947	2
C₅×#1853	2
C₅×#1852	2
C₅×#1847	2
C₅×#1836	2
#21987	5

Subgroups — C5×#21987 #11944707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21987 #11944707