Subgroups — C₅×#21717 #11944437

Order 1280.

766 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#446	C₂	1	2	yes	maximal
2	C₅×#2399	C₂	1	1	yes	maximal, characteristic
3	C₅×#1984	C₂	1	2	yes	maximal
4	C₅×#1940	C₂	1	1	yes	maximal, characteristic
5	C₅×#1940	C₂	1	1	yes	maximal, characteristic
6	C₅×#1939	C₂	1	2	yes	maximal
7	C₅×#1843	C₂	1	1	yes	maximal, characteristic
8	C₅×#1771	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	C₅×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
13	C₅×#446	—	2	8	no	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×#97	C₂²	1	2	yes	—
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₅×#398	C₄	1	2	yes	—
29	C₅×#398	C₄	1	2	yes	—
30	C₅×#395	C₄	1	2	yes	—
31	C₅×#395	C₄	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₅×#376	C₂²	1	1	yes	characteristic
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	#21717	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
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	C₄×C₅×Q₈	—	2	4	no	—
49	C₄×C₅×Q₈	—	2	4	no	—
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
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	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	2	yes	—
58	C₂×C₄²×C₅	C₂³	1	2	yes	—
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊C₈	—	2	4	no	—
63	C₅×C₄⋊C₈	—	2	4	no	—
64	C₅×C₄⋊C₈	—	2	4	no	—
65	C₅×C₄⋊C₈	—	2	4	no	—
66	C₅×C₄⋊C₈	—	2	2	no	—
67	C₅×C₄⋊C₈	—	2	2	no	—
68	C₅×#97	—	2	4	no	—
69	C₅×#97	—	2	2	no	—
70	C₅×#97	D₄	1	4	yes	—
71	C₅×#97	Q₈	1	4	yes	complemented
72	C₄×C₅×C₈	—	2	4	no	—
73	C₄×C₅×C₈	—	2	2	no	—
74	C₄×C₅×C₈	—	2	2	no	—
75	C₄×C₅×C₈	Q₈	1	4	yes	complemented
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₅×#95	C₂×C₄	1	2	yes	—
78	C₅×#95	C₂×C₄	1	1	yes	characteristic
79	C₅×#95	C₂×C₄	1	2	yes	—
80	C₅×#95	C₂×C₄	1	1	yes	characteristic
81	C₅×#95	C₂×C₄	1	1	yes	characteristic
82	C₅×#95	C₂×C₄	1	1	yes	characteristic
83	C₅×#95	C₂×C₄	1	2	yes	—
84	C₂×#446	C₂×C₅	1	2	yes	—
85	#2399	C₂×C₅	1	1	yes	characteristic
86	#1984	C₂×C₅	1	2	yes	—
87	#1940	C₂×C₅	1	1	yes	characteristic
88	#1940	C₂×C₅	1	1	yes	characteristic
89	#1939	C₂×C₅	1	2	yes	—
90	#1843	C₂×C₅	1	1	yes	characteristic
91	#1771	C₂×C₅	1	2	yes	—
92	#1770	C₂×C₅	1	1	yes	characteristic
93	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
94	#1726	C₂×C₅	1	1	yes	characteristic
95	C₂×C₅×Q₈	—	2	4	no	—
96	C₂×C₅×Q₈	—	2	4	no	—
97	C₂×C₅×Q₈	—	4	2	no	—
98	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	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	—	2	2	no	—
119	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
122	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
123	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
124	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	—	4	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	C₂×D₄	1	2	yes	—
137	C₄²×C₅	C₂×Q₈	1	2	yes	—
138	C₄²×C₅	C₂×Q₈	1	2	yes	—
139	C₄²×C₅	#41	1	2	yes	—
140	C₄²×C₅	#41	1	2	yes	—
141	C₄²×C₅	#41	1	2	yes	—
142	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
143	#446	—	2	8	no	—
144	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
145	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
146	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
149	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×#97	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×C₄×C₈	C₂²×C₅	1	2	yes	—
155	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
158	#398	C₄×C₅	1	2	yes	—
159	#398	C₄×C₅	1	2	yes	—
160	#395	C₄×C₅	1	2	yes	—
161	#395	C₄×C₅	1	2	yes	—
162	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
163	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	#376	C₂²×C₅	1	1	yes	characteristic
166	#336	C₂²×C₅	1	2	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	2	yes	—
170	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₅×Q₈	—	4	8	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
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	2	no	—
185	C₂×C₄×C₅	—	2	2	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	C₄×D₄	1	4	yes	—
190	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
191	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
192	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
193	C₂×C₄×C₅	#131	1	4	yes	—
194	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
200	C₅×C₈	—	2	2	no	—
201	C₅×C₈	—	2	2	no	—
202	C₅×C₈	—	2	2	no	—
203	C₅×C₈	—	4	2	no	—
204	C₅×C₈	—	4	2	no	—
205	C₅×C₈	C₄⋊Q₈	1	4	yes	—
206	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
207	C₂²×C₈	C₂³×C₅	1	2	yes	—
208	C₂²×C₈	C₂³×C₅	1	2	yes	—
209	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
213	C₄×Q₈	—	2	4	no	—
214	C₄×Q₈	—	2	4	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₄²	C₂³×C₅	1	2	yes	—
223	C₂×C₄²	C₂³×C₅	1	2	yes	—
224	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
227	C₄⋊C₈	—	2	4	no	—
228	C₄⋊C₈	—	2	4	no	—
229	C₄⋊C₈	—	2	4	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	2	no	—
233	#97	—	2	4	no	—
234	#97	—	2	2	no	—
235	#97	C₅×D₄	1	4	yes	—
236	#97	C₅×Q₈	1	4	yes	complemented
237	C₄×C₈	—	2	4	no	—
238	C₄×C₈	—	2	2	no	—
239	C₄×C₈	—	2	2	no	—
240	C₄×C₈	C₅×Q₈	1	4	yes	complemented
241	#95	C₂×C₄×C₅	1	2	yes	—
242	#95	C₂×C₄×C₅	1	2	yes	—
243	#95	C₂×C₄×C₅	1	1	yes	characteristic
244	#95	C₂×C₄×C₅	1	2	yes	—
245	#95	C₂×C₄×C₅	1	1	yes	characteristic
246	#95	C₂×C₄×C₅	1	2	yes	—
247	#95	C₂×C₄×C₅	1	1	yes	characteristic
248	#95	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
251	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
252	C₂²×C₅	C₂×#131	1	2	yes	—
253	C₂²×C₅	#568	1	2	yes	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	2	4	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	4	2	no	—
260	C₄×C₅	—	4	2	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
263	C₄×C₅	#532	1	1	yes	characteristic
264	C₄×C₅	#533	1	1	yes	characteristic
265	C₄×C₅	#533	1	1	yes	characteristic
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
291	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
292	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
293	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
294	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
295	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂×C₅×D₄	1	2	yes	—
308	C₄²	C₂×C₅×Q₈	1	2	yes	—
309	C₄²	C₂×C₅×Q₈	1	2	yes	—
310	C₄²	C₅×#41	1	2	yes	—
311	C₄²	C₅×#41	1	2	yes	—
312	C₄²	C₅×#41	1	2	yes	—
313	C₂×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic
314	C₂×C₅	#2933	1	2	yes	—
315	C₂×C₅	#2960	1	1	yes	characteristic
316	C₂×C₅	#2961	1	1	yes	characteristic
317	C₂×C₅	#2962	1	2	yes	—
318	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
319	Q₈	—	4	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
338	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
339	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
340	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
341	C₂×C₄	C₅×#131	1	4	yes	—
342	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	2	no	—
353	C₈	C₅×C₄⋊Q₈	1	4	yes	—
354	C₅	#21717	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
356	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
357	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
358	C₂²	C₂×C₅×#131	1	2	yes	—
359	C₂²	C₅×#568	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
369	C₄	C₅×#532	1	1	yes	characteristic
370	C₄	C₅×#533	1	1	yes	characteristic
371	C₄	C₅×#533	1	1	yes	characteristic
372	C₂	C₄×C₅×C₄⋊Q₈	1	1	yes	characteristic
373	C₂	C₅×#2933	1	2	yes	—
374	C₂	C₅×#2960	1	1	yes	characteristic
375	C₂	C₅×#2961	1	1	yes	characteristic
376	C₂	C₅×#2962	1	2	yes	—

	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
40. #21717	C₅	direct (N × H)
71. C₅×#97	Q₈	semidirect
75. C₄×C₅×C₈	Q₈	semidirect
236. #97	C₅×Q₈	semidirect
240. C₄×C₈	C₅×Q₈	semidirect
354. C₅	#21717	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×#446	2
C₅×#2399	2
C₅×#1984	2
C₅×#1940	2
C₅×#1939	2
C₅×#1843	2
C₅×#1771	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1726	2
#21717	5

Subgroups — C5×#21717 #11944437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21717 #11944437