Subgroups — C₄×D₅×D₂₀ #13105084

Order 1600.

946 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×D₅×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₅²	C₂	1	2	yes	maximal, complemented
3	C₄×C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×#685	C₂	1	2	yes	maximal, complemented
7	C₄×#6038	C₂	1	2	yes	maximal, complemented
8	#11717013	C₂	1	1	yes	maximal, characteristic, complemented
9	Dic₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
11	#11716998	C₂	1	2	yes	maximal, complemented
12	C₂²×D₅²	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅⋊D₅	C₂²	1	2	yes	complemented
15	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₅	C₂²	1	2	yes	complemented
20	C₂×#6038	C₂²	1	2	yes	—
21	C₂×#6036	C₂²	1	2	yes	complemented
22	C₂×D₅×Dic₅	C₂²	1	2	yes	—
23	C₂×D₅×Dic₅	C₂²	1	2	yes	complemented
24	D₅×D₂₀	C₄	1	8	yes	direct product factor
25	C₄×D₅²	—	2	8	no	—
26	C₄²×C₅²	C₂²	1	1	yes	characteristic, complemented
27	#87808	C₂²	1	2	yes	complemented
28	C₄⋊#1039	C₂²	1	1	yes	characteristic, complemented
29	C₅×#685	C₂²	1	2	yes	complemented
30	C₅×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
34	#87780	C₂²	1	2	yes	complemented
35	#87779	C₂²	1	2	yes	complemented
36	#87778	C₂²	1	2	yes	complemented
37	C₄×D₄×D₅	—	5	1	no	maximal
38	C₂×C₄×D₂₀	—	5	1	no	maximal
39	C₂²×C₅⋊D₅	C₂³	1	2	yes	—
40	C₂²×C₅×D₅	C₂³	1	2	yes	—
41	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
42	C₂×D₅²	—	2	4	no	—
43	C₂×D₅²	—	2	4	no	—
44	C₂×D₅²	C₂×C₄	1	8	yes	complemented
45	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
46	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
47	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
48	C₂×#1039	C₂³	1	2	yes	—
49	C₄⋊(C₅⋊D₅)	C₂×C₄	1	4	yes	complemented
50	C₄×C₅⋊D₅	—	2	4	no	—
51	C₂×C₅×Dic₅	C₂³	1	2	yes	—
52	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
55	C₅×D₂₀	C₂×C₄	1	4	yes	complemented
56	C₄×C₅×D₅	—	2	2	no	—
57	C₄×C₅×D₅	—	2	4	no	—
58	C₄×C₅×D₅	C₂×C₄	1	4	yes	complemented
59	C₄×C₅×D₅	D₄	1	4	yes	complemented
60	#6038	C₂×C₄	1	8	yes	complemented
61	#6036	—	2	4	no	—
62	D₅×Dic₅	—	2	4	no	—
63	D₅×Dic₅	—	2	4	no	—
64	C₂×D₄×D₅	—	5	1	no	—
65	C₂²×D₂₀	—	5	1	no	—
66	C₂²×C₄×D₅	—	5	2	no	—
67	C₂²×C₄×D₅	—	5	2	no	—
68	C₄×C₅×D₄	—	5	1	no	—
69	C₂×C₄²×C₅	—	5	1	no	—
70	D₄×Dic₅	—	5	1	no	—
71	C₄×C₂²⋊D₅	—	5	2	no	—
72	C₂×#685	—	5	2	no	—
73	C₂×C₄⋊Dic₅	—	5	1	no	—
74	#4039	—	5	1	no	—
75	D₅×C₄⋊C₄	—	5	1	no	—
76	#4027	—	5	2	no	—
77	D₅×C₂²⋊C₄	—	5	2	no	—
78	C₄×D₂₀	—	5	1	no	—
79	C₄×D₂₀	—	5	2	no	—
80	C₄×D₂₀	—	5	1	no	—
81	C₄×D₂₀	—	5	1	no	—
82	C₄×D₂₀	—	5	2	no	—
83	C₄×D₂₀	—	5	1	no	—
84	C₄×D₂₀	—	10	2	no	—
85	C₄×D₂₀	D₅	1	1	yes	characteristic, direct product factor
86	C₄²×D₅	D₅	1	1	yes	characteristic, complemented
87	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
88	C₂×C₅⋊D₅	—	2	2	no	—
89	C₂×C₅⋊D₅	—	2	2	no	—
90	C₂×C₅⋊D₅	C₂²×C₄	1	4	yes	complemented
91	C₂×C₅×D₅	—	2	2	no	—
92	C₂×C₅×D₅	—	2	2	no	—
93	C₂×C₅×D₅	C₂²×C₄	1	2	yes	—
94	C₂×C₅×D₅	C₂²×C₄	1	4	yes	complemented
95	C₂×C₅×D₅	C₂×D₄	1	2	yes	—
96	C₂×C₅×D₅	#41	1	2	yes	—
97	D₅²	—	2	16	no	—
98	C₄×C₅²	—	2	1	no	—
99	C₄×C₅²	C₂²×C₄	1	2	yes	complemented
100	C₄×C₅²	C₂×D₄	1	2	yes	complemented
101	#1039	—	2	2	no	—
102	C₅×Dic₅	—	2	2	no	—
103	C₅×Dic₅	—	2	1	no	—
104	C₅×Dic₅	C₂²×C₄	1	2	yes	complemented
105	C₅×Dic₅	C₂×D₄	1	2	yes	complemented
106	C₂³×D₅	—	5	2	no	—
107	C₂³×D₅	—	5	2	no	—
108	C₂×C₅×D₄	—	5	1	no	—
109	C₂²×C₄×C₅	—	5	1	no	—
110	C₂²×C₄×C₅	—	5	1	no	—
111	C₂²×C₄×C₅	—	5	1	no	—
112	C₂²×C₄×C₅	—	5	2	no	—
113	C₂×C₂²⋊D₅	—	5	2	no	—
114	C₂²×Dic₅	—	5	2	no	—
115	C₂²×Dic₅	—	5	2	no	—
116	D₄×D₅	—	5	8	no	—
117	C₂×D₂₀	—	5	2	no	—
118	C₂×D₂₀	—	5	1	no	—
119	C₂×D₂₀	—	5	1	no	—
120	C₂×D₂₀	—	5	8	no	—
121	C₂×D₂₀	—	10	2	no	—
122	C₂×D₂₀	C₂×D₅	1	1	yes	characteristic
123	C₂×C₄×D₅	—	5	2	no	—
124	C₂×C₄×D₅	—	5	2	no	—
125	C₂×C₄×D₅	—	5	2	no	—
126	C₂×C₄×D₅	—	5	2	no	—
127	C₂×C₄×D₅	—	5	2	no	—
128	C₂×C₄×D₅	—	5	2	no	—
129	C₂×C₄×D₅	—	10	4	no	—
130	C₂×C₄×D₅	—	10	8	no	—
131	C₂×C₄×D₅	—	10	8	no	—
132	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂×D₅	1	2	yes	complemented
136	C₅×C₄⋊C₄	—	5	1	no	—
137	C₅×C₂²⋊C₄	—	5	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	5	1	no	—
140	C₄²×C₅	—	5	1	no	—
141	C₄²×C₅	—	5	1	no	—
142	C₄²×C₅	C₂×D₅	1	1	yes	characteristic, complemented
143	C₄²×C₅	C₂×D₅	1	1	yes	characteristic, complemented
144	C₂²⋊Dic₅	—	5	2	no	—
145	#685	—	5	2	no	—
146	#685	—	5	2	no	—
147	#685	—	5	2	no	—
148	#685	—	5	2	no	—
149	#685	—	5	2	no	—
150	#685	—	10	4	no	—
151	#685	C₂×D₅	1	2	yes	complemented
152	C₄⋊Dic₅	—	5	1	no	—
153	C₄⋊Dic₅	—	5	1	no	—
154	C₄⋊Dic₅	—	5	2	no	—
155	C₄⋊Dic₅	—	10	2	no	—
156	C₄⋊Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
157	#683	—	5	2	no	—
158	C₄×Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
159	C₄×Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
160	C₄×Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
161	C₂×C₄×D₄	—	25	1	no	Sylow
162	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₅²	C₂×#41	1	1	yes	characteristic
165	C₅⋊D₅	—	2	4	no	—
166	C₅×D₅	—	2	4	no	—
167	C₅×D₅	C₄×D₄	1	4	yes	complemented
168	C₂³×C₅	—	5	1	no	—
169	C₂³×C₅	—	5	2	no	—
170	C₂²×D₅	—	5	2	no	—
171	C₂²×D₅	—	5	2	no	—
172	C₂²×D₅	—	5	8	no	—
173	C₂²×D₅	—	5	8	no	—
174	C₂²×D₅	—	10	4	no	—
175	C₂²×D₅	—	10	4	no	—
176	C₂²×D₅	—	10	4	no	—
177	C₂²×D₅	—	10	4	no	—
178	C₂²×D₅	—	10	4	no	—
179	C₂²×D₅	C₂²×D₅	1	2	yes	—
180	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
181	C₅×D₄	—	5	4	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	—	5	1	no	—
186	C₂×C₄×C₅	—	5	1	no	—
187	C₂×C₄×C₅	—	5	4	no	—
188	C₂×C₄×C₅	—	5	4	no	—
189	C₂×C₄×C₅	—	5	2	no	—
190	C₂×C₄×C₅	—	5	1	no	—
191	C₂×C₄×C₅	—	10	2	no	—
192	C₂×C₄×C₅	—	10	4	no	—
193	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
199	C₂²⋊D₅	—	5	8	no	—
200	C₂×Dic₅	—	5	2	no	—
201	C₂×Dic₅	—	5	2	no	—
202	C₂×Dic₅	—	10	4	no	—
203	C₂×Dic₅	—	10	4	no	—
204	C₂×Dic₅	—	10	4	no	—
205	C₂×Dic₅	C₂²×D₅	1	1	yes	characteristic
206	C₂×Dic₅	C₂²×D₅	1	2	yes	—
207	C₂×Dic₅	C₂²×D₅	1	1	yes	characteristic
208	C₂×Dic₅	C₂²×D₅	1	1	yes	characteristic
209	D₂₀	—	5	8	no	—
210	D₂₀	—	5	4	no	—
211	D₂₀	—	5	4	no	—
212	D₂₀	—	10	8	no	—
213	D₂₀	C₄×D₅	1	4	yes	direct product factor
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	—	2	4	no	—
216	C₄×D₅	—	10	4	no	—
217	C₄×D₅	—	10	4	no	—
218	C₄×D₅	—	10	4	no	—
219	C₄×D₅	—	10	4	no	—
220	C₄×D₅	—	10	4	no	—
221	C₄×D₅	—	10	4	no	—
222	C₄×D₅	—	20	8	no	—
223	C₄×D₅	C₄×D₅	1	4	yes	complemented
224	C₄×D₅	D₂₀	1	4	yes	direct product factor
225	C₂²×D₄	—	25	1	no	—
226	C₂³×C₄	—	25	2	no	—
227	C₄×D₄	—	5	1	no	—
228	C₄×D₄	—	25	2	no	—
229	C₄×D₄	—	25	1	no	—
230	C₄×D₄	—	25	2	no	—
231	C₄×D₄	—	25	1	no	—
232	C₄×D₄	—	25	1	no	—
233	C₂×C₄⋊C₄	—	25	1	no	—
234	C₂×C₂²⋊C₄	—	25	2	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₅²	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	5	2	no	—
239	C₂²×C₅	—	5	2	no	—
240	C₂²×C₅	—	5	2	no	—
241	C₂²×C₅	—	5	4	no	—
242	C₂²×C₅	—	10	2	no	—
243	C₂²×C₅	—	10	2	no	—
244	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
245	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
246	C₂×D₅	—	2	2	no	—
247	C₂×D₅	—	2	2	no	—
248	C₂×D₅	—	5	4	no	—
249	C₂×D₅	—	5	4	no	—
250	C₂×D₅	—	10	8	no	—
251	C₂×D₅	—	10	16	no	—
252	C₂×D₅	—	10	2	no	—
253	C₂×D₅	—	10	2	no	—
254	C₂×D₅	—	10	2	no	—
255	C₂×D₅	—	10	2	no	—
256	C₂×D₅	—	10	16	no	—
257	C₂×D₅	—	20	4	no	—
258	C₂×D₅	—	20	4	no	—
259	C₂×D₅	C₂×C₄×D₅	1	2	yes	—
260	C₂×D₅	C₂×C₄×D₅	1	4	yes	complemented
261	C₂×D₅	C₂×D₂₀	1	2	yes	—
262	C₂×D₅	#709	1	2	yes	—
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	4	no	—
266	C₄×C₅	—	2	4	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	5	2	no	—
269	C₄×C₅	—	5	2	no	—
270	C₄×C₅	—	10	2	no	—
271	C₄×C₅	—	10	1	no	—
272	C₄×C₅	C₂×C₄×D₅	1	2	yes	complemented
273	C₄×C₅	C₂×C₄×D₅	1	2	yes	complemented
274	C₄×C₅	C₂×D₂₀	1	2	yes	complemented
275	C₄×C₅	D₄×D₅	1	2	yes	complemented
276	Dic₅	—	2	1	no	—
277	Dic₅	—	2	2	no	—
278	Dic₅	—	10	2	no	—
279	Dic₅	—	10	2	no	—
280	Dic₅	—	20	4	no	—
281	Dic₅	C₂×C₄×D₅	1	2	yes	complemented
282	Dic₅	C₂×D₂₀	1	2	yes	complemented
283	C₂⁴	—	25	2	no	—
284	C₂×D₄	—	5	1	no	—
285	C₂×D₄	—	25	8	no	—
286	C₂×D₄	—	25	2	no	—
287	C₂×D₄	—	25	1	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	—	5	1	no	—
290	C₂²×C₄	—	5	1	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	25	2	no	—
293	C₂²×C₄	—	25	2	no	—
294	C₂²×C₄	—	25	2	no	—
295	C₂²×C₄	—	25	2	no	—
296	C₂²×C₄	—	50	8	no	—
297	C₄⋊C₄	—	5	1	no	—
298	C₄⋊C₄	—	25	2	no	—
299	C₄⋊C₄	—	25	1	no	—
300	C₂²⋊C₄	—	5	2	no	—
301	C₂²⋊C₄	—	25	2	no	—
302	C₂²⋊C₄	—	25	2	no	—
303	C₂²⋊C₄	—	25	2	no	—
304	C₄²	—	5	1	no	—
305	C₄²	—	5	1	no	—
306	C₄²	—	5	1	no	—
307	C₄²	D₅²	1	1	yes	characteristic, complemented
308	C₂×C₅	—	2	2	no	—
309	C₂×C₅	—	2	2	no	—
310	C₂×C₅	—	2	2	no	—
311	C₂×C₅	—	5	4	no	—
312	C₂×C₅	—	10	4	no	—
313	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
314	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
315	C₂×C₅	C₂²×D₂₀	1	1	yes	characteristic
316	C₂×C₅	C₂×#709	1	1	yes	characteristic
317	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
318	C₂×C₅	D₅×#41	1	1	yes	characteristic
319	D₅	—	2	4	no	—
320	D₅	—	10	4	no	—
321	D₅	—	10	4	no	—
322	D₅	—	20	8	no	—
323	D₅	C₄×D₂₀	1	4	yes	direct product factor
324	C₂³	—	5	1	no	—
325	C₂³	—	5	2	no	—
326	C₂³	—	25	8	no	—
327	C₂³	—	25	2	no	—
328	C₂³	—	50	4	no	—
329	C₂³	—	50	4	no	—
330	D₄	—	5	4	no	—
331	D₄	—	25	8	no	—
332	D₄	—	25	4	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	5	1	no	—
335	C₂×C₄	—	5	4	no	—
336	C₂×C₄	—	5	4	no	—
337	C₂×C₄	—	5	1	no	—
338	C₂×C₄	—	5	2	no	—
339	C₂×C₄	—	10	2	no	—
340	C₂×C₄	—	10	4	no	—
341	C₂×C₄	—	25	2	no	—
342	C₂×C₄	—	50	4	no	—
343	C₂×C₄	—	50	4	no	—
344	C₂×C₄	—	50	4	no	—
345	C₂×C₄	—	50	4	no	—
346	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
347	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
348	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
349	C₅	—	2	2	no	—
350	C₅	C₂×C₄×D₂₀	1	1	yes	characteristic, complemented
351	C₅	C₄×D₄×D₅	1	1	yes	characteristic, complemented
352	C₂²	—	5	2	no	—
353	C₂²	—	5	2	no	—
354	C₂²	—	5	2	no	—
355	C₂²	—	5	4	no	—
356	C₂²	—	10	2	no	—
357	C₂²	—	10	2	no	—
358	C₂²	—	25	4	no	—
359	C₂²	—	50	16	no	—
360	C₂²	—	50	2	no	—
361	C₂²	—	50	2	no	—
362	C₂²	C₂²×D₅²	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	5	2	no	—
365	C₄	—	5	2	no	—
366	C₄	—	10	2	no	—
367	C₄	—	10	1	no	—
368	C₄	—	50	2	no	—
369	C₄	C₄×D₅²	1	2	yes	complemented
370	C₄	D₅×D₂₀	1	2	yes	direct product factor
371	C₂	—	5	4	no	—
372	C₂	—	10	4	no	—
373	C₂	—	50	4	no	—
374	C₂	C₂×C₄×D₅²	1	1	yes	characteristic
375	C₂	C₂×D₅×D₂₀	1	1	yes	characteristic
376	C₂	D₅×#709	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₅²
commutator	C₂×C₅²	C₂³×C₄
Frattini	C₂²	C₂²×D₅²
Fitting	C₄²×C₅²	C₂²
socle, cosocle	C₂²×C₅²	C₂⁴
prime radical	C₂×D₅×D₂₀	C₂
hypercenter	C₄²	D₅²
hypocenter	C₅²	C₂×C₄×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₅²	C₂	semidirect
3. C₄×C₄⋊(C₅⋊D₅)	C₂	semidirect
4. C₄×C₅×D₂₀	C₂	semidirect
5. C₄²×C₅×D₅	C₂	semidirect
6. D₅×#685	C₂	semidirect
7. C₄×#6038	C₂	semidirect
8. #11717013	C₂	semidirect
9. Dic₅×D₂₀	C₂	semidirect
10. D₅×C₄⋊Dic₅	C₂	semidirect
11. #11716998	C₂	semidirect
14. C₂×C₄×C₅⋊D₅	C₂²	semidirect
19. C₂×C₄×C₅×D₅	C₂²	semidirect
21. C₂×#6036	C₂²	semidirect
23. C₂×D₅×Dic₅	C₂²	semidirect
24. D₅×D₂₀	C₄	direct (N × H)
26. C₄²×C₅²	C₂²	semidirect
27. #87808	C₂²	semidirect
28. C₄⋊#1039	C₂²	semidirect
29. C₅×#685	C₂²	semidirect
30. C₅×C₄⋊Dic₅	C₂²	semidirect
31. C₄×C₅×Dic₅	C₂²	semidirect
32. C₄×C₅×Dic₅	C₂²	semidirect
33. C₄×C₅×Dic₅	C₂²	semidirect
34. #87780	C₂²	semidirect
35. #87779	C₂²	semidirect
36. #87778	C₂²	semidirect
44. C₂×D₅²	C₂×C₄	semidirect
49. C₄⋊(C₅⋊D₅)	C₂×C₄	semidirect
55. C₅×D₂₀	C₂×C₄	semidirect
58. C₄×C₅×D₅	C₂×C₄	semidirect
59. C₄×C₅×D₅	D₄	semidirect
60. #6038	C₂×C₄	semidirect
85. C₄×D₂₀	D₅	direct (N × H)
86. C₄²×D₅	D₅	semidirect
90. C₂×C₅⋊D₅	C₂²×C₄	semidirect
94. C₂×C₅×D₅	C₂²×C₄	semidirect
99. C₄×C₅²	C₂²×C₄	semidirect
100. C₄×C₅²	C₂×D₄	semidirect
104. C₅×Dic₅	C₂²×C₄	semidirect
105. C₅×Dic₅	C₂×D₄	semidirect
135. C₂×C₄×D₅	C₂×D₅	semidirect
142. C₄²×C₅	C₂×D₅	semidirect
143. C₄²×C₅	C₂×D₅	semidirect
151. #685	C₂×D₅	semidirect
156. C₄⋊Dic₅	C₂×D₅	semidirect
158. C₄×Dic₅	C₂×D₅	semidirect
159. C₄×Dic₅	C₂×D₅	semidirect
160. C₄×Dic₅	C₂×D₅	semidirect
167. C₅×D₅	C₄×D₄	semidirect
213. D₂₀	C₄×D₅	direct (N × H)
223. C₄×D₅	C₄×D₅	semidirect
224. C₄×D₅	D₂₀	direct (N × H)
236. C₅²	C₂×C₄×D₄	semidirect
260. C₂×D₅	C₂×C₄×D₅	semidirect
272. C₄×C₅	C₂×C₄×D₅	semidirect
273. C₄×C₅	C₂×C₄×D₅	semidirect
274. C₄×C₅	C₂×D₂₀	semidirect
275. C₄×C₅	D₄×D₅	semidirect
281. Dic₅	C₂×C₄×D₅	semidirect
282. Dic₅	C₂×D₂₀	semidirect
307. C₄²	D₅²	semidirect
323. D₅	C₄×D₂₀	direct (N × H)
350. C₅	C₂×C₄×D₂₀	semidirect
351. C₅	C₄×D₄×D₅	semidirect
369. C₄	C₄×D₅²	semidirect
370. C₄	D₅×D₂₀	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×D₅×D₂₀	2
C₂×C₄×D₅²	2
C₄×C₄⋊(C₅⋊D₅)	2
C₄×C₅×D₂₀	2
C₄²×C₅×D₅	2
D₅×#685	2
C₄×#6038	2
#11717013	2
Dic₅×D₂₀	2
D₅×C₄⋊Dic₅	2
#11716998	2
C₄×D₄×D₅	5
C₂×C₄×D₂₀	5

Subgroups — C4×D5×D20 #13105084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅×D₂₀ #13105084