Subgroups — D₂₀×#208 #14415755

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×#208	C₂	1	2	yes	maximal, complemented
3	#11751025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748341	C₂	1	2	yes	maximal, complemented
6	#11747010	C₂	1	2	yes	maximal, complemented
7	#11746991	C₂	1	4	yes	maximal, complemented
8	C₃⋊C₈×D₂₀	C₂	1	2	yes	maximal, complemented
9	M₁₆×D₂₀	—	3	1	no	maximal, Hall
10	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	2	yes	—
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	C₄	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
18	C₃×C₄×D₂₀	C₄	1	2	yes	—
19	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
20	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
21	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
22	C₃×C₄×D₂₀	C₂²	1	2	yes	—
23	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
24	C₂×#6649	C₂²	1	4	yes	complemented
25	D₅×#208	—	2	8	no	—
26	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	complemented
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
28	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
29	C₅×#803	C₂²	1	2	yes	complemented
30	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
31	#90955	C₂²	1	4	yes	complemented
32	#90955	C₂²	1	4	yes	complemented
33	D₄×#208	—	5	1	no	maximal, Hall
34	C₂×D₅×M₁₆	—	3	2	no	—
35	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic
36	C₄×C₅×M₁₆	—	3	1	no	—
37	#65415	—	3	2	no	—
38	#65213	—	3	1	no	—
39	#64995	—	3	4	no	—
40	#64977	—	3	2	no	—
41	C₈×D₂₀	—	3	2	no	—
42	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	—	2	4	no	—
52	C₂×C₃×C₄×D₅	—	2	4	no	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	#6710	—	2	4	no	—
62	C₂×C₃⋊#168	C₂³	1	4	yes	—
63	C₅×#208	—	2	2	no	—
64	C₅×#208	D₄	1	4	yes	complemented
65	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×#685	C₂×C₄	1	2	yes	—
70	C₃×#685	C₂×C₄	1	2	yes	—
71	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
72	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
74	#6649	—	2	8	no	—
75	D₅×C₃⋊C₈	—	2	8	no	—
76	C₂×C₃×C₄×D₄	—	5	1	no	—
77	C₂²×#208	—	5	2	no	—
78	#5207	—	5	2	no	—
79	#5012	—	5	2	no	—
80	#5011	—	5	4	no	—
81	D₄×C₃⋊C₈	—	5	2	no	—
82	#4924	—	5	1	no	—
83	C₄×#208	D₅	1	1	yes	characteristic, complemented
84	C₂²×D₂₀	Dic₃	1	1	yes	characteristic
85	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
86	C₂×C₅×M₁₆	—	3	1	no	—
87	C₂×C₅×M₁₆	—	3	1	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂×#685	Dic₃	1	2	yes	—
90	C₂×C₄⋊Dic₅	Dic₃	1	1	yes	characteristic
91	C₂×#681	—	3	2	no	—
92	D₅×M₁₆	—	6	8	no	—
93	C₂×#676	—	3	4	no	—
94	C₂×C₈×D₅	—	3	4	no	—
95	C₄×D₂₀	Dic₃	1	2	yes	—
96	C₄×D₂₀	Dic₃	1	1	yes	characteristic
97	C₄×D₂₀	Dic₃	1	1	yes	characteristic
98	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
99	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
100	C₄×D₂₀	C₂×D₃	1	2	yes	—
101	C₅×#97	—	3	2	no	—
102	C₄×C₅×C₈	—	3	2	no	—
103	#3952	—	3	4	no	—
104	#3952	—	3	4	no	—
105	C₄⋊#168	—	3	2	no	—
106	C₄⋊#168	—	3	2	no	—
107	D₄×M₁₆	—	15	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×D₅	—	2	4	no	—
110	C₂²×C₃×D₅	—	2	4	no	—
111	C₂²×C₃×D₅	—	4	2	no	—
112	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₃×Dic₅	—	2	4	no	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
127	C₃×D₂₀	—	2	4	no	—
128	C₃×D₂₀	—	2	2	no	—
129	C₃×D₂₀	M₁₆	1	4	yes	complemented
130	C₃×C₄×D₅	—	2	4	no	—
131	C₃×C₄×D₅	—	2	4	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×C₄×D₅	—	2	2	no	—
135	C₃×C₄×D₅	—	2	2	no	—
136	C₃⋊#168	—	2	4	no	—
137	C₅×C₃⋊C₈	—	2	2	no	—
138	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂³×C₃×C₄	—	5	2	no	—
141	C₃×C₄×D₄	—	5	1	no	—
142	C₃×C₄×D₄	—	5	2	no	—
143	C₃×C₄×D₄	—	5	1	no	—
144	C₃×C₄×D₄	—	5	1	no	—
145	C₃×C₄×D₄	—	5	2	no	—
146	C₃×C₄×D₄	—	5	1	no	—
147	C₂×C₃×C₄⋊C₄	—	5	1	no	—
148	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
149	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
150	C₂×#208	—	5	2	no	—
151	C₂×#208	—	5	4	no	—
152	C₂×#208	—	10	8	no	—
153	C₂×#208	C₂×D₅	1	1	yes	characteristic
154	C₂×#208	C₂×D₅	1	1	yes	characteristic
155	C₂²×C₃⋊C₈	—	5	4	no	—
156	#830	—	5	4	no	—
157	#830	—	5	4	no	—
158	C₄⋊(C₃⋊C₈)	—	5	2	no	—
159	C₄⋊(C₃⋊C₈)	—	5	2	no	—
160	#803	C₂×D₅	1	2	yes	complemented
161	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	complemented
162	C₂³×D₅	C₂×Dic₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
167	C₂×D₂₀	—	2	4	no	—
168	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
169	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
170	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
171	C₂×C₄×D₅	—	2	4	no	—
172	C₂×C₄×D₅	—	2	4	no	—
173	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
174	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
175	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
176	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
177	C₅×M₁₆	—	3	4	no	—
178	C₅×M₁₆	—	6	2	no	—
179	C₂×C₅×C₈	—	3	2	no	—
180	C₂×C₅×C₈	—	3	2	no	—
181	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
182	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
183	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
184	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
185	#685	C₂×Dic₃	1	2	yes	—
186	#685	C₂×Dic₃	1	2	yes	—
187	#685	C₂×Dic₃	1	2	yes	—
188	#685	C₂×Dic₃	1	2	yes	—
189	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
190	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
191	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
192	#681	—	6	4	no	—
193	C₂×#168	—	3	4	no	—
194	#676	—	6	8	no	—
195	C₈×D₅	—	6	8	no	—
196	C₂²×M₁₆	—	15	2	no	—
197	C₂×C₄×D₄	—	5	1	no	—
198	#436	—	15	2	no	—
199	#435	—	15	4	no	—
200	C₈×D₄	—	15	2	no	—
201	#423	—	15	1	no	—
202	#407	—	15	2	no	—
203	C₄×M₁₆	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	—	2	2	no	—
211	C₂×C₃×D₅	—	2	2	no	—
212	C₂×C₃×D₅	—	2	2	no	—
213	C₂×C₃×D₅	—	4	8	no	—
214	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₃×Dic₅	—	2	2	no	—
223	C₃×Dic₅	—	2	2	no	—
224	C₂⁴×C₃	—	5	2	no	—
225	C₂×C₃×D₄	—	5	1	no	—
226	C₂×C₃×D₄	—	5	2	no	—
227	C₂×C₃×D₄	—	5	1	no	—
228	C₂×C₃×D₄	—	10	4	no	—
229	C₂²×C₃×C₄	—	5	2	no	—
230	C₂²×C₃×C₄	—	5	2	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	10	4	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₃×C₄⋊C₄	—	5	2	no	—
240	C₃×C₄⋊C₄	—	5	1	no	—
241	C₃×C₄⋊C₄	—	5	1	no	—
242	C₃×C₂²⋊C₄	—	5	2	no	—
243	C₃×C₂²⋊C₄	—	5	2	no	—
244	C₃×C₂²⋊C₄	—	5	2	no	—
245	C₃×C₂²⋊C₄	—	5	2	no	—
246	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
247	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
248	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
249	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
250	#208	—	2	2	no	—
251	#208	—	10	4	no	—
252	#208	—	10	8	no	—
253	#208	D₂₀	1	4	yes	direct product factor
254	C₂×C₃⋊C₈	—	5	4	no	—
255	C₂×C₃⋊C₈	—	10	8	no	—
256	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
257	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
258	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
259	C₂²×D₅	—	2	4	no	—
260	C₂²×D₅	—	2	4	no	—
261	C₂²×D₅	—	4	2	no	—
262	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
263	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
266	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	#237	1	2	yes	—
268	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₂×Dic₅	—	2	4	no	—
275	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
276	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
277	D₂₀	—	2	4	no	—
278	D₂₀	—	2	2	no	—
279	D₂₀	#208	1	4	yes	direct product factor
280	C₄×D₅	—	2	4	no	—
281	C₄×D₅	—	2	4	no	—
282	C₄×D₅	—	2	2	no	—
283	C₄×D₅	—	2	2	no	—
284	C₄×D₅	—	2	2	no	—
285	C₄×D₅	—	2	2	no	—
286	C₅×C₈	—	3	4	no	—
287	C₅×C₈	—	6	2	no	—
288	#168	—	6	4	no	—
289	C₂²×D₄	—	5	1	no	—
290	C₂³×C₄	—	5	2	no	—
291	C₂×M₁₆	—	3	1	no	—
292	C₂×M₁₆	—	3	1	no	—
293	C₂×M₁₆	—	15	4	no	—
294	C₂×M₁₆	—	15	2	no	—
295	C₂×M₁₆	—	30	8	no	—
296	C₂²×C₈	—	15	4	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	2	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	1	no	—
301	C₄×D₄	—	5	2	no	—
302	C₄×D₄	—	5	1	no	—
303	C₂×C₄⋊C₄	—	5	1	no	—
304	C₂×C₂²⋊C₄	—	5	2	no	—
305	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
306	C₄⋊C₈	—	15	2	no	—
307	C₄⋊C₈	—	15	2	no	—
308	C₂²⋊C₈	—	15	4	no	—
309	C₂²⋊C₈	—	15	4	no	—
310	#97	—	3	2	no	—
311	C₄×C₈	—	3	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	C₃×D₅	—	2	4	no	—
317	C₃×D₅	—	4	2	no	—
318	C₂³×C₃	—	5	2	no	—
319	C₂³×C₃	—	5	2	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	—	10	4	no	—
322	C₂³×C₃	—	20	2	no	—
323	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
324	C₃×D₄	—	5	4	no	—
325	C₃×D₄	—	10	4	no	—
326	C₃×D₄	—	10	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	1	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	10	4	no	—
332	C₂×C₃×C₄	—	10	2	no	—
333	C₂×C₃×C₄	—	10	2	no	—
334	C₂×C₃×C₄	—	10	2	no	—
335	C₂×C₃×C₄	—	10	2	no	—
336	C₂×C₃×C₄	—	10	4	no	—
337	C₂×C₃×C₄	—	10	4	no	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
344	C₂×C₃×C₄	#709	1	2	yes	—
345	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
346	C₃⋊C₈	—	2	2	no	—
347	C₃⋊C₈	—	10	4	no	—
348	C₃⋊C₈	C₂×D₂₀	1	4	yes	complemented
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	D₄×Dic₃	1	2	yes	—
352	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
353	C₂×D₅	—	2	2	no	—
354	C₂×D₅	—	2	2	no	—
355	C₂×D₅	—	2	2	no	—
356	C₂×D₅	—	2	2	no	—
357	C₂×D₅	—	2	2	no	—
358	C₂×D₅	—	4	8	no	—
359	C₂×D₅	C₂×#208	1	4	yes	complemented
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	C₂×#208	1	2	yes	complemented
364	C₄×C₅	D₄×Dic₃	1	2	yes	—
365	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₄×C₅	C₂×#237	1	1	yes	characteristic
367	Dic₅	—	2	2	no	—
368	Dic₅	—	2	2	no	—
369	C₂⁴	—	5	2	no	—
370	C₂×D₄	—	5	1	no	—
371	C₂×D₄	—	5	2	no	—
372	C₂×D₄	—	5	1	no	—
373	C₂×D₄	—	10	4	no	—
374	C₂²×C₄	—	5	2	no	—
375	C₂²×C₄	—	5	2	no	—
376	C₂²×C₄	—	5	2	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	10	4	no	—
380	C₂²×C₄	—	10	4	no	—
381	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
382	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
384	M₁₆	—	3	4	no	—
385	M₁₆	—	6	2	no	—
386	M₁₆	—	30	8	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	3	2	no	—
389	C₂×C₈	—	3	2	no	—
390	C₂×C₈	—	15	4	no	—
391	C₂×C₈	—	30	8	no	—
392	C₄⋊C₄	—	5	2	no	—
393	C₄⋊C₄	—	5	1	no	—
394	C₄⋊C₄	—	5	1	no	—
395	C₂²⋊C₄	—	5	2	no	—
396	C₂²⋊C₄	—	5	2	no	—
397	C₂²⋊C₄	—	5	2	no	—
398	C₂²⋊C₄	—	5	2	no	—
399	C₄²	D₅×Dic₃	1	1	yes	characteristic
400	C₄²	D₅×Dic₃	1	1	yes	characteristic
401	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
402	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	5	4	no	—
407	C₂²×C₃	—	10	2	no	—
408	C₂²×C₃	—	10	2	no	—
409	C₂²×C₃	—	10	2	no	—
410	C₂²×C₃	—	10	2	no	—
411	C₂²×C₃	—	10	2	no	—
412	C₂²×C₃	—	20	8	no	—
413	C₂²×C₃	C₄×D₂₀	1	2	yes	—
414	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	10	2	no	—
419	C₃×C₄	—	10	2	no	—
420	C₃×C₄	C₄×D₂₀	1	2	yes	—
421	C₃×C₄	D₅×M₁₆	1	2	yes	complemented
422	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
423	C₃×C₄	C₂×#709	1	1	yes	characteristic
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	C₂²×#208	1	1	yes	characteristic
426	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
427	C₂×C₅	#5819	1	1	yes	characteristic
428	D₅	—	2	4	no	—
429	D₅	—	4	2	no	—
430	C₂³	—	5	2	no	—
431	C₂³	—	5	2	no	—
432	C₂³	—	10	4	no	—
433	C₂³	—	10	4	no	—
434	C₂³	—	20	2	no	—
435	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
436	D₄	—	5	4	no	—
437	D₄	—	10	4	no	—
438	D₄	—	10	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	5	2	no	—
442	C₂×C₄	—	5	2	no	—
443	C₂×C₄	—	10	4	no	—
444	C₂×C₄	—	10	4	no	—
445	C₂×C₄	—	10	4	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	#6765	1	2	yes	—
451	C₂×C₄	D₃×D₂₀	1	2	yes	—
452	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
453	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
454	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
455	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
456	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
458	C₈	—	3	4	no	—
459	C₈	—	6	2	no	—
460	C₈	—	30	4	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	10	4	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
465	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
466	C₂×C₃	#66079	1	1	yes	characteristic
467	C₅	D₄×#208	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	5	4	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	—	10	2	no	—
474	C₂²	—	10	2	no	—
475	C₂²	—	10	2	no	—
476	C₂²	—	20	8	no	—
477	C₂²	Dic₃×D₂₀	1	2	yes	—
478	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	10	2	no	—
483	C₄	—	10	2	no	—
484	C₄	D₅×#208	1	2	yes	complemented
485	C₄	Dic₃×D₂₀	1	2	yes	—
486	C₄	C₂×#6765	1	1	yes	characteristic
487	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
488	C₃	M₁₆×D₂₀	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	10	4	no	—
491	C₂	—	20	2	no	—
492	C₂	C₂×D₅×#208	1	1	yes	characteristic
493	C₂	#11754120	1	1	yes	characteristic
494	C₂	C₂×Dic₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₂²×C₃×D₂₀	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×D₅×#208	C₂	semidirect
3. #11751025	C₂	semidirect
4. C₄×C₅×#208	C₂	semidirect
5. #11748341	C₂	semidirect
6. #11747010	C₂	semidirect
7. #11746991	C₂	semidirect
8. C₃⋊C₈×D₂₀	C₂	semidirect
24. C₂×#6649	C₂²	semidirect
26. C₂×D₅×C₃⋊C₈	C₂²	semidirect
27. C₄⋊(C₃⋊#168)	C₂²	semidirect
28. C₄⋊(C₃⋊#168)	C₂²	semidirect
29. C₅×#803	C₂²	semidirect
30. C₄×C₅×C₃⋊C₈	C₂²	semidirect
31. #90955	C₂²	semidirect
32. #90955	C₂²	semidirect
64. C₅×#208	D₄	semidirect
83. C₄×#208	D₅	semidirect
129. C₃×D₂₀	M₁₆	semidirect
138. C₅×C₃⋊C₈	C₂×D₄	semidirect
160. #803	C₂×D₅	semidirect
161. C₄×C₃⋊C₈	C₂×D₅	semidirect
214. C₂×C₃×D₅	C₂×M₁₆	semidirect
219. C₃×C₄×C₅	C₂×M₁₆	semidirect
253. #208	D₂₀	direct (N × H)
279. D₂₀	#208	direct (N × H)
348. C₃⋊C₈	C₂×D₂₀	semidirect
359. C₂×D₅	C₂×#208	semidirect
363. C₄×C₅	C₂×#208	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
421. C₃×C₄	D₅×M₁₆	semidirect
467. C₅	D₄×#208	semidirect
484. C₄	D₅×#208	semidirect
488. C₃	M₁₆×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₂₀	2
C₂×D₅×#208	2
#11751025	2
C₄×C₅×#208	2
#11748341	2
#11747010	2
#11746991	2
C₃⋊C₈×D₂₀	2
M₁₆×D₂₀	3
D₄×#208	5

Subgroups — D20×#208 #14415755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₀×#208 #14415755