Subgroups — C₅×#21024 #11943744

Order 1280.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 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	1	yes	maximal, characteristic
3	C₅×#2296	C₂	1	1	yes	maximal, characteristic
4	C₅×#1917	C₂	1	4	yes	maximal, complemented
5	C₅×#1916	C₂	1	4	yes	maximal, complemented
6	C₅×#1729	C₂	1	1	yes	maximal, characteristic
7	C₅×#1729	C₂	1	1	yes	maximal, characteristic
8	C₅×#1729	C₂	1	1	yes	maximal, characteristic
9	C₅×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	—	2	4	no	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₅×#405	—	2	4	no	—
21	C₂×C₅×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₅×#389	C₄	1	2	yes	—
24	C₅×#389	C₄	1	2	yes	—
25	C₅×#385	C₄	1	2	yes	—
26	C₅×#385	C₄	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
28	C₅×#336	C₂²	1	2	yes	—
29	C₅×#336	C₂²	1	4	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	C₅×#336	C₂²	1	4	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	#21024	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	2	2	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	—	2	2	no	—
42	C₂×C₅×M₁₆	Q₈	1	4	yes	—
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	—	2	2	no	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	D₄	1	4	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₅×#117	—	2	2	no	—
57	C₅×#117	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₅×C₄⋊C₈	—	2	4	no	—
72	C₅×C₄⋊C₈	—	2	4	no	—
73	C₅×#97	—	2	4	no	—
74	C₄×C₅×C₈	—	2	4	no	—
75	C₅×#95	C₂×C₄	1	4	yes	—
76	C₅×#95	C₂×C₄	1	4	yes	—
77	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
78	C₂×#405	C₂×C₅	1	1	yes	characteristic
79	#2296	C₂×C₅	1	1	yes	characteristic
80	#1917	C₂×C₅	1	4	yes	complemented
81	#1916	C₂×C₅	1	4	yes	complemented
82	#1729	C₂×C₅	1	1	yes	characteristic
83	#1729	C₂×C₅	1	1	yes	characteristic
84	#1729	C₂×C₅	1	1	yes	characteristic
85	#1728	C₂×C₅	1	1	yes	characteristic
86	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	4	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₅	#41	1	2	yes	—
100	C₂²×C₄×C₅	#41	1	2	yes	—
101	C₂²×C₄×C₅	#41	1	2	yes	—
102	C₂²×C₄×C₅	#41	1	2	yes	—
103	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₅×M₁₆	—	2	8	no	—
105	C₅×M₁₆	—	4	4	no	—
106	C₂×C₅×C₈	—	2	8	no	—
107	C₂×C₅×C₈	—	2	2	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	—	2	2	no	—
119	C₂×C₅×C₈	—	4	4	no	—
120	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
122	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
123	C₅×C₄⋊C₄	—	2	4	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	8	no	—
127	C₅×C₄⋊C₄	—	4	4	no	—
128	C₅×C₂²⋊C₄	—	2	4	no	—
129	C₅×C₂²⋊C₄	—	2	4	no	—
130	C₄²×C₅	—	2	4	no	—
131	C₄²×C₅	—	2	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	—	2	2	no	—
137	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
138	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
139	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
141	C₂×#117	C₂²×C₅	1	1	yes	characteristic
142	C₂×#117	C₂²×C₅	1	1	yes	characteristic
143	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₄⋊C₈	—	2	4	no	—
145	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
146	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
147	#405	—	2	4	no	—
148	C₂×#97	C₂²×C₅	1	2	yes	—
149	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
150	#389	C₄×C₅	1	2	yes	—
151	#389	C₄×C₅	1	2	yes	—
152	#385	C₄×C₅	1	2	yes	—
153	#385	C₄×C₅	1	2	yes	—
154	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
155	#336	C₂²×C₅	1	2	yes	—
156	#336	C₂²×C₅	1	4	yes	—
157	#336	C₂²×C₅	1	4	yes	—
158	#336	C₂²×C₅	1	4	yes	—
159	#336	C₂²×C₅	1	2	yes	—
160	C₂³×C₅	—	2	2	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	#117	1	2	yes	—
163	C₂³×C₅	C₄×D₄	1	2	yes	—
164	C₂³×C₅	C₄×Q₈	1	2	yes	—
165	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	—	2	8	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	4	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	4	4	no	—
180	C₂×C₄×C₅	#117	1	2	yes	—
181	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
183	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₅	#123	1	4	yes	—
185	C₂×C₄×C₅	#125	1	4	yes	—
186	C₂×C₄×C₅	#126	1	4	yes	—
187	C₂×C₄×C₅	#131	1	4	yes	—
188	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	C₅×C₈	—	2	4	no	—
195	C₅×C₈	—	2	2	no	—
196	C₅×C₈	—	2	2	no	—
197	C₅×C₈	—	4	2	no	—
198	C₅×C₈	—	4	2	no	—
199	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	—	2	2	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	C₅×Q₈	1	4	yes	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	—	2	2	no	—
210	C₂²×C₈	—	2	2	no	—
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	C₅×D₄	1	4	yes	—
214	C₂²×C₈	C₂³×C₅	1	2	yes	—
215	C₂²×C₈	C₂³×C₅	1	2	yes	—
216	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₅	1	2	yes	—
219	#117	—	2	2	no	—
220	#117	—	2	2	no	—
221	#117	—	2	2	no	—
222	#117	—	2	2	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
233	C₂×C₄²	C₂³×C₅	1	2	yes	—
234	C₂×C₄²	C₂³×C₅	1	2	yes	—
235	C₂×C₄²	C₂³×C₅	1	2	yes	—
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	4	no	—
238	#97	—	2	4	no	—
239	C₄×C₈	—	2	4	no	—
240	#95	C₂×C₄×C₅	1	4	yes	—
241	#95	C₂×C₄×C₅	1	4	yes	—
242	C₂²×C₅	—	2	4	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	#387	1	4	yes	—
247	C₂²×C₅	C₂×#117	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
250	C₂²×C₅	C₂×#131	1	2	yes	—
251	C₂²×C₅	#568	1	2	yes	—
252	C₄×C₅	—	2	4	no	—
253	C₄×C₅	—	4	4	no	—
254	C₄×C₅	—	4	2	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	—	4	2	no	—
257	C₄×C₅	#387	1	4	yes	—
258	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
259	C₄×C₅	C₂×#123	1	1	yes	characteristic
260	C₄×C₅	C₂×#125	1	1	yes	characteristic
261	C₄×C₅	C₂×#126	1	1	yes	characteristic
262	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
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	1	yes	characteristic
273	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
275	C₂²×C₄	C₅×#41	1	2	yes	—
276	C₂²×C₄	C₅×#41	1	2	yes	—
277	C₂²×C₄	C₅×#41	1	2	yes	—
278	C₂²×C₄	C₅×#41	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
280	M₁₆	—	2	8	no	—
281	M₁₆	—	4	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
297	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
298	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₂×C₅	—	2	4	no	—
314	C₂×C₅	C₂×#387	1	1	yes	characteristic
315	C₂×C₅	#2925	1	2	yes	—
316	C₂×C₅	#2929	1	1	yes	characteristic
317	C₂×C₅	#2930	1	1	yes	characteristic
318	C₂×C₅	#2962	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₅×#117	1	2	yes	—
322	C₂³	C₄×C₅×D₄	1	2	yes	—
323	C₂³	C₄×C₅×Q₈	1	2	yes	—
324	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	C₅×#117	1	2	yes	—
340	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
341	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
342	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
343	C₂×C₄	C₅×#123	1	4	yes	—
344	C₂×C₄	C₅×#125	1	4	yes	—
345	C₂×C₄	C₅×#126	1	4	yes	—
346	C₂×C₄	C₅×#131	1	4	yes	—
347	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
351	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₅	#21024	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	4	no	—
363	C₂²	C₅×#387	1	4	yes	—
364	C₂²	C₂×C₅×#117	1	1	yes	characteristic
365	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
366	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
367	C₂²	C₂×C₅×#131	1	2	yes	—
368	C₂²	C₅×#568	1	2	yes	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	C₅×#387	1	4	yes	—
375	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
376	C₄	C₂×C₅×#123	1	1	yes	characteristic
377	C₄	C₂×C₅×#125	1	1	yes	characteristic
378	C₄	C₂×C₅×#126	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	C₂×C₅×#387	1	1	yes	characteristic
381	C₂	C₅×#2925	1	2	yes	—
382	C₂	C₅×#2929	1	1	yes	characteristic
383	C₂	C₅×#2930	1	1	yes	characteristic
384	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	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×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
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
33. #21024	C₅	direct (N × H)
80. #1917	C₂×C₅	semidirect
81. #1916	C₂×C₅	semidirect
358. C₅	#21024	direct (N × H)

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
C₅×#2296	2
C₅×#1917	2
C₅×#1916	2
C₅×#1729	2
C₅×#1728	2
#21024	5

Subgroups — C5×#21024 #11943744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21024 #11943744