Subgroups — C₅×#21675 #11944395

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₅×#1939	C₂	1	1	yes	maximal, characteristic
3	C₅×#1939	C₂	1	1	yes	maximal, characteristic
4	C₅×#1917	C₂	1	2	yes	maximal
5	C₅×#1917	C₂	1	2	yes	maximal
6	C₅×#1831	C₂	1	1	yes	maximal, characteristic
7	C₅×#1771	C₂	1	2	yes	maximal
8	C₅×#1770	C₂	1	2	yes	maximal
9	C₅×#1770	C₂	1	1	yes	maximal, characteristic
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#125	C₄	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×#97	C₂²	1	2	yes	—
18	C₂×C₅×#97	C₂²	1	1	yes	characteristic
19	C₂×C₅×#97	C₂²	1	1	yes	characteristic
20	C₂×C₅×#97	C₂²	1	1	yes	characteristic
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#389	C₄	1	1	yes	characteristic
26	C₅×#389	C₄	1	1	yes	characteristic
27	C₅×#387	C₄	1	2	yes	—
28	C₅×#387	C₄	1	2	yes	—
29	C₅×#382	C₄	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₅	C₂²	1	1	yes	characteristic
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#21675	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×#125	—	2	4	no	—
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊C₈	—	2	4	no	—
67	C₅×C₄⋊C₈	—	2	4	no	—
68	C₅×C₄⋊C₈	—	2	2	no	—
69	C₅×C₄⋊C₈	—	2	2	no	—
70	C₅×#97	—	2	2	no	—
71	C₅×#97	—	2	2	no	—
72	C₅×#97	—	2	2	no	—
73	C₅×#97	—	2	2	no	—
74	C₅×#97	—	2	4	no	—
75	C₄×C₅×C₈	—	2	4	no	—
76	C₄×C₅×C₈	—	2	2	no	—
77	C₄×C₅×C₈	Q₈	1	4	yes	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	C₅×#95	C₂×C₄	1	2	yes	—
80	C₅×#95	C₂×C₄	1	2	yes	—
81	C₅×#95	C₂×C₄	1	2	yes	—
82	C₅×#95	C₂×C₄	1	2	yes	—
83	C₅×#95	C₂×C₄	1	2	yes	—
84	C₄×#125	C₂×C₅	1	1	yes	characteristic
85	#1939	C₂×C₅	1	1	yes	characteristic
86	#1939	C₂×C₅	1	1	yes	characteristic
87	#1917	C₂×C₅	1	2	yes	—
88	#1917	C₂×C₅	1	2	yes	—
89	#1831	C₂×C₅	1	1	yes	characteristic
90	#1771	C₂×C₅	1	2	yes	—
91	#1770	C₂×C₅	1	2	yes	—
92	#1770	C₂×C₅	1	1	yes	characteristic
93	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
94	C₄×#97	C₂×C₅	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₅×C₈	—	2	1	no	—
107	C₂×C₅×C₈	—	2	1	no	—
108	C₂×C₅×C₈	—	2	1	no	—
109	C₂×C₅×C₈	—	2	1	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
119	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
120	C₂×C₅×C₈	#41	1	2	yes	—
121	C₂×C₅×C₈	#41	1	2	yes	—
122	C₂×C₅×C₈	#41	1	2	yes	—
123	C₂×C₅×C₈	#41	1	2	yes	—
124	C₅×C₄⋊C₄	—	2	4	no	—
125	C₅×C₄⋊C₄	—	2	4	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	—	4	2	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	4	1	no	—
143	C₄²×C₅	—	4	1	no	—
144	C₄²×C₅	C₂×Q₈	1	2	yes	—
145	C₄²×C₅	#41	1	2	yes	—
146	C₂×#125	C₄×C₅	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂×#97	C₂²×C₅	1	1	yes	characteristic
152	C₂×#97	C₂²×C₅	1	1	yes	characteristic
153	C₂×#97	C₂²×C₅	1	1	yes	characteristic
154	C₂×#97	C₂²×C₅	1	1	yes	characteristic
155	C₂×#97	C₂²×C₅	1	2	yes	—
156	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	#389	C₄×C₅	1	1	yes	characteristic
160	#389	C₄×C₅	1	1	yes	characteristic
161	#387	C₄×C₅	1	2	yes	—
162	#387	C₄×C₅	1	2	yes	—
163	#382	C₄×C₅	1	1	yes	characteristic
164	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
165	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
166	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₄³	C₂²×C₅	1	1	yes	characteristic
169	#336	C₂²×C₅	1	2	yes	—
170	#336	C₂²×C₅	1	2	yes	—
171	#336	C₂²×C₅	1	2	yes	—
172	#336	C₂²×C₅	1	2	yes	—
173	#336	C₂²×C₅	1	2	yes	—
174	#336	C₂²×C₅	1	2	yes	—
175	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	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	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
202	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
203	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
204	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
205	C₂×C₄×C₅	#131	1	2	yes	—
206	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	—	2	2	no	—
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	4	2	no	—
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	#125	1	4	yes	complemented
218	C₂²×C₈	C₂³×C₅	1	2	yes	—
219	C₂²×C₈	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	#125	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₅	1	2	yes	—
240	C₂×C₄²	C₂³×C₅	1	2	yes	—
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₄⋊C₈	—	2	4	no	—
243	C₄⋊C₈	—	2	4	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	#97	—	2	2	no	—
247	#97	—	2	2	no	—
248	#97	—	2	2	no	—
249	#97	—	2	2	no	—
250	#97	—	2	4	no	—
251	C₄×C₈	—	2	4	no	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	C₅×Q₈	1	4	yes	—
254	#95	C₂×C₄×C₅	1	2	yes	—
255	#95	C₂×C₄×C₅	1	2	yes	—
256	#95	C₂×C₄×C₅	1	2	yes	—
257	#95	C₂×C₄×C₅	1	2	yes	—
258	#95	C₂×C₄×C₅	1	2	yes	—
259	#95	C₂×C₄×C₅	1	2	yes	—
260	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
261	C₂²×C₅	C₄×#41	1	1	yes	characteristic
262	C₂²×C₅	C₄×#41	1	1	yes	characteristic
263	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
264	C₂²×C₅	C₂×#131	1	1	yes	characteristic
265	C₂²×C₅	#568	1	1	yes	characteristic
266	C₂²×C₅	#568	1	1	yes	characteristic
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	2	4	no	—
269	C₄×C₅	—	4	1	no	—
270	C₄×C₅	—	4	1	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	1	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	#446	1	4	yes	—
277	C₄×C₅	C₂×#125	1	1	yes	characteristic
278	C₄×C₅	#529	1	1	yes	characteristic
279	C₄×C₅	#529	1	1	yes	characteristic
280	C₄×C₅	#533	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
305	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
306	C₂×C₈	C₅×#41	1	2	yes	—
307	C₂×C₈	C₅×#41	1	2	yes	—
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	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂×C₅×Q₈	1	2	yes	—
331	C₄²	C₅×#41	1	2	yes	—
332	C₂×C₅	C₄×#125	1	1	yes	characteristic
333	C₂×C₅	C₂×#446	1	1	yes	characteristic
334	C₂×C₅	#2961	1	1	yes	characteristic
335	C₂×C₅	#2969	1	1	yes	characteristic
336	C₂×C₅	#2969	1	1	yes	characteristic
337	C₂×C₅	#2970	1	1	yes	characteristic
338	C₂×C₅	#2971	1	1	yes	characteristic
339	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	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	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
366	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
367	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
368	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
369	C₂×C₄	C₅×#131	1	2	yes	—
370	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	C₅×#125	1	4	yes	complemented
382	C₅	#21675	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
384	C₂²	C₄×C₅×#41	1	1	yes	characteristic
385	C₂²	C₄×C₅×#41	1	1	yes	characteristic
386	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
387	C₂²	C₂×C₅×#131	1	1	yes	characteristic
388	C₂²	C₅×#568	1	1	yes	characteristic
389	C₂²	C₅×#568	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	C₅×#446	1	4	yes	—
400	C₄	C₂×C₅×#125	1	1	yes	characteristic
401	C₄	C₅×#529	1	1	yes	characteristic
402	C₄	C₅×#529	1	1	yes	characteristic
403	C₄	C₅×#533	1	1	yes	characteristic
404	C₂	C₄×C₅×#125	1	1	yes	characteristic
405	C₂	C₂×C₅×#446	1	1	yes	characteristic
406	C₂	C₅×#2961	1	1	yes	characteristic
407	C₂	C₅×#2969	1	1	yes	characteristic
408	C₂	C₅×#2969	1	1	yes	characteristic
409	C₂	C₅×#2970	1	1	yes	characteristic
410	C₂	C₅×#2971	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
41. #21675	C₅	direct (N × H)
217. C₅×C₈	#125	semidirect
381. C₈	C₅×#125	semidirect
382. C₅	#21675	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#125	2
C₅×#1939	2
C₅×#1917	2
C₅×#1831	2
C₅×#1771	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#97	2
#21675	5

Subgroups — C5×#21675 #11944395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21675 #11944395