Subgroups — C₅×#20441 #11943161

Order 1280.

1138 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#405	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2285	C₂	1	1	yes	maximal, characteristic
5	C₅×#1771	C₂	1	4	yes	maximal, complemented
6	C₅×#1770	C₂	1	2	yes	maximal, complemented
7	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₅×#1729	C₂	1	2	yes	maximal
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₅×#117	C₂²	1	2	yes	—
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₄	1	8	yes	complemented
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₅×#405	—	2	8	no	—
19	C₄×C₅×M₁₆	C₄	1	8	yes	complemented
20	C₂×C₅×#97	C₂²	1	4	yes	—
21	C₂×C₅×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₅×#384	C₄	1	2	yes	—
25	C₅×#382	C₄	1	2	yes	—
26	C₅×#380	C₄	1	2	yes	—
27	C₅×#380	C₄	1	2	yes	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	C₅×#336	C₂²	1	4	yes	—
32	#20441	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×M₁₆	—	2	2	no	—
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
39	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
40	C₂×C₅×M₁₆	D₄	1	4	yes	—
41	C₂×C₅×M₁₆	Q₈	1	4	yes	—
42	C₂²×C₅×C₈	—	2	4	no	—
43	C₂²×C₅×C₈	—	2	4	no	—
44	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₅×#117	—	2	4	no	—
50	C₅×#117	—	2	4	no	—
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₅	C₂³	1	4	yes	—
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
65	C₅×#97	—	2	8	no	—
66	C₅×#97	C₂×C₄	1	8	yes	—
67	C₄×C₅×C₈	—	2	8	no	—
68	C₄×C₅×C₈	C₂×C₄	1	8	yes	—
69	C₅×#95	C₂×C₄	1	4	yes	—
70	C₅×#95	C₂×C₄	1	4	yes	—
71	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
72	C₂×#405	C₂×C₅	1	2	yes	—
73	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
74	#2285	C₂×C₅	1	1	yes	characteristic
75	#1771	C₂×C₅	1	4	yes	complemented
76	#1770	C₂×C₅	1	2	yes	complemented
77	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
78	#1729	C₂×C₅	1	2	yes	—
79	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	—	2	4	no	—
81	C₂²×C₄×C₅	—	4	2	no	—
82	C₂²×C₄×C₅	C₄²	1	4	yes	—
83	C₂²×C₄×C₅	C₄²	1	4	yes	—
84	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
85	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₅	#41	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	2	yes	—
96	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
97	C₅×M₁₆	—	2	8	no	—
98	C₅×M₁₆	C₄⋊C₄	1	16	yes	complemented
99	C₂×C₅×C₈	—	2	16	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
107	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
110	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
111	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
112	C₅×C₄⋊C₄	—	2	8	no	—
113	C₅×C₄⋊C₄	—	2	8	no	—
114	C₅×C₄⋊C₄	—	4	4	no	—
115	C₅×C₂²⋊C₄	—	2	8	no	—
116	C₄²×C₅	—	2	4	no	—
117	C₄²×C₅	—	2	4	no	—
118	C₄²×C₅	C₄²	1	4	yes	—
119	C₄²×C₅	C₄²	1	4	yes	—
120	C₄²×C₅	C₂²×C₄	1	2	yes	—
121	C₄²×C₅	C₂²×C₄	1	2	yes	—
122	C₄²×C₅	C₂²×C₄	1	2	yes	—
123	C₄²×C₅	C₂²×C₄	1	2	yes	—
124	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂³×C₈	C₂²×C₅	1	2	yes	—
127	C₂×#117	C₂²×C₅	1	2	yes	—
128	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄⋊C₈	C₄×C₅	1	8	yes	complemented
130	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
133	#405	—	2	8	no	—
134	C₄×M₁₆	C₄×C₅	1	8	yes	complemented
135	C₂×#97	C₂²×C₅	1	4	yes	—
136	C₂×#97	C₂²×C₅	1	2	yes	—
137	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
138	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
139	#384	C₄×C₅	1	2	yes	—
140	#382	C₄×C₅	1	2	yes	—
141	#380	C₄×C₅	1	2	yes	—
142	#380	C₄×C₅	1	2	yes	—
143	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
144	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
145	#336	C₂²×C₅	1	4	yes	—
146	#336	C₂²×C₅	1	4	yes	—
147	C₂³×C₅	—	2	2	no	—
148	C₂³×C₅	—	2	2	no	—
149	C₂³×C₅	C₂×C₄²	1	2	yes	—
150	C₂³×C₅	C₄×D₄	1	2	yes	—
151	C₂³×C₅	C₄×Q₈	1	2	yes	—
152	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	8	no	—
157	C₂×C₄×C₅	—	2	8	no	—
158	C₂×C₄×C₅	—	2	8	no	—
159	C₂×C₄×C₅	—	2	8	no	—
160	C₂×C₄×C₅	—	4	4	no	—
161	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
162	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
164	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
167	C₂×C₄×C₅	#117	1	4	yes	—
168	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
169	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
171	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₅	#131	1	4	yes	—
173	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
179	C₅×C₈	—	2	4	no	—
180	C₅×C₈	—	2	4	no	—
181	C₅×C₈	—	2	4	no	—
182	C₅×C₈	C₂×C₄⋊C₄	1	8	yes	—
183	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
189	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
190	C₂×M₁₆	C₅×D₄	1	4	yes	—
191	C₂×M₁₆	C₅×Q₈	1	4	yes	—
192	C₂²×C₈	—	2	4	no	—
193	C₂²×C₈	—	2	4	no	—
194	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
195	C₂²×C₈	C₂³×C₅	1	2	yes	—
196	C₂²×C₈	C₂³×C₅	1	2	yes	—
197	C₂²×C₈	C₂³×C₅	1	2	yes	—
198	C₂²×C₈	C₂³×C₅	1	2	yes	—
199	#117	—	2	4	no	—
200	#117	—	2	4	no	—
201	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
202	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
205	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
209	C₂×C₄²	C₂³×C₅	1	4	yes	—
210	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
212	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
213	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
214	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
215	#97	—	2	8	no	—
216	#97	C₂×C₄×C₅	1	8	yes	—
217	C₄×C₈	—	2	8	no	—
218	C₄×C₈	C₂×C₄×C₅	1	8	yes	—
219	#95	C₂×C₄×C₅	1	4	yes	—
220	#95	C₂×C₄×C₅	1	4	yes	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	4	no	—
224	C₂²×C₅	—	2	4	no	—
225	C₂²×C₅	C₄×C₄⋊C₄	1	4	yes	—
226	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
227	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₂²×C₅	C₂×#131	1	2	yes	—
230	C₂²×C₅	#568	1	2	yes	—
231	C₄×C₅	—	2	2	no	—
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	4	8	no	—
235	C₄×C₅	C₄×C₄⋊C₄	1	4	yes	—
236	C₄×C₅	#405	1	4	yes	complemented
237	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₅	C₂×#117	1	1	yes	characteristic
239	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
241	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	C₄²×C₅	1	4	yes	—
245	C₂²×C₄	C₄²×C₅	1	4	yes	—
246	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
247	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
254	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
256	C₂²×C₄	C₅×#41	1	2	yes	—
257	C₂²×C₄	C₅×#41	1	2	yes	—
258	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	M₁₆	—	2	8	no	—
260	M₁₆	C₅×C₄⋊C₄	1	16	yes	complemented
261	C₂×C₈	—	2	16	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
269	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
270	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
272	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
273	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₂²⋊C₄	—	2	8	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	C₄²×C₅	1	4	yes	—
281	C₄²	C₄²×C₅	1	4	yes	—
282	C₄²	C₂²×C₄×C₅	1	2	yes	—
283	C₄²	C₂²×C₄×C₅	1	2	yes	—
284	C₄²	C₂²×C₄×C₅	1	2	yes	—
285	C₄²	C₂²×C₄×C₅	1	2	yes	—
286	C₂×C₅	—	2	4	no	—
287	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₅	C₂×#405	1	1	yes	characteristic
289	C₂×C₅	#2873	1	1	yes	characteristic
290	C₂×C₅	#2935	1	2	yes	—
291	C₂×C₅	#2962	1	2	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×C₄²×C₅	1	2	yes	—
295	C₂³	C₄×C₅×D₄	1	2	yes	—
296	C₂³	C₄×C₅×Q₈	1	2	yes	—
297	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
307	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
308	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
309	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
310	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
311	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
312	C₂×C₄	C₅×#117	1	4	yes	—
313	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
314	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
315	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
316	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
317	C₂×C₄	C₅×#131	1	4	yes	—
318	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
319	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
321	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
322	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
323	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₈	—	2	4	no	—
326	C₈	—	2	4	no	—
327	C₈	C₂×C₅×C₄⋊C₄	1	8	yes	—
328	C₅	#20441	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	C₄×C₅×C₄⋊C₄	1	4	yes	—
334	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
335	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
336	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
337	C₂²	C₂×C₅×#131	1	2	yes	—
338	C₂²	C₅×#568	1	2	yes	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	4	8	no	—
343	C₄	C₄×C₅×C₄⋊C₄	1	4	yes	—
344	C₄	C₅×#405	1	4	yes	complemented
345	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
346	C₄	C₂×C₅×#117	1	1	yes	characteristic
347	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
348	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	C₂×C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₂	C₂×C₅×#405	1	1	yes	characteristic
352	C₂	C₅×#2873	1	1	yes	characteristic
353	C₂	C₅×#2935	1	2	yes	—
354	C₂	C₅×#2962	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₅×#1771	C₂	semidirect
6. C₅×#1770	C₂	semidirect
7. C₅×C₈×C₄⋊C₄	C₂	semidirect
14. C₂×C₅×C₄⋊C₈	C₄	semidirect
19. C₄×C₅×M₁₆	C₄	semidirect
32. #20441	C₅	direct (N × H)
75. #1771	C₂×C₅	semidirect
76. #1770	C₂×C₅	semidirect
77. C₈×C₄⋊C₄	C₂×C₅	semidirect
98. C₅×M₁₆	C₄⋊C₄	semidirect
129. C₂×C₄⋊C₈	C₄×C₅	semidirect
134. C₄×M₁₆	C₄×C₅	semidirect
236. C₄×C₅	#405	semidirect
260. M₁₆	C₅×C₄⋊C₄	semidirect
328. C₅	#20441	direct (N × H)
344. C₄	C₅×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₄⋊C₈	2
C₂×C₅×#405	2
C₂×C₄×C₅×M₁₆	2
C₅×#2285	2
C₅×#1771	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1729	2
#20441	5

Subgroups — C5×#20441 #11943161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20441 #11943161