Subgroups — C₃×#41×D₂₀ #14483058

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65911	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65910	C₂	1	2	yes	maximal, complemented
5	C₃×Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65889	C₂	1	3	yes	maximal, complemented
7	C₃×#65888	C₂	1	6	yes	maximal, complemented
8	C₃×D₄×D₂₀	C₂	1	3	yes	maximal, complemented
9	C₃×#65858	C₂	1	6	yes	maximal, complemented
10	C₃×#65811	C₂	1	3	yes	maximal, complemented
11	C₂×C₃×C₄×D₂₀	C₂	1	3	yes	maximal, complemented
12	#41×D₂₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×D₅×#41	—	2	16	no	—
15	C₂×C₃×#713	C₂²	1	2	yes	complemented
16	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
17	C₂×C₃×#711	C₂²	1	6	yes	complemented
18	C₂×C₃×D₄×D₅	C₂²	1	6	yes	complemented
19	C₂×C₃×#709	C₂²	1	6	yes	complemented
20	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
21	C₂²×C₃×C₄×D₅	C₂²	1	6	yes	complemented
22	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₄	C₂²	1	3	yes	complemented
25	C₃×C₄×C₅×D₄	C₂²	1	3	yes	complemented
26	C₃×C₅×#117	C₂²	1	3	yes	complemented
27	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	complemented
28	C₃×#4076	C₂²	1	6	yes	complemented
29	C₃×#4076	C₂²	1	6	yes	complemented
30	C₂×C₃×#685	C₂²	1	6	yes	complemented
31	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	complemented
32	C₃×#4043	C₂²	1	6	yes	complemented
33	C₃×#4043	C₂²	1	6	yes	complemented
34	C₃×#4041	C₂²	1	6	yes	complemented
35	C₃×#4041	C₂²	1	6	yes	complemented
36	C₃×#4032	C₂²	1	12	yes	complemented
37	C₃×#4028	C₂²	1	12	yes	complemented
38	C₃×#4021	C₂²	1	6	yes	complemented
39	C₃×#4020	C₂²	1	3	yes	complemented
40	C₃×C₄×D₂₀	C₂²	1	3	yes	—
41	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
42	C₃×C₄×D₂₀	C₂²	1	6	yes	complemented
43	C₃×C₄×D₂₀	C₂²	1	6	yes	complemented
44	C₃×C₄×D₂₀	C₂²	1	6	yes	complemented
45	C₃×C₄×D₂₀	C₂²	1	3	yes	complemented
46	C₃×C₄×D₂₀	C₂²	1	3	yes	complemented
47	C₃×#4015	C₂²	1	3	yes	complemented
48	C₃×D₄×#41	—	5	1	no	maximal, Hall
49	C₂×D₅×#41	C₂×C₃	1	2	yes	complemented
50	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
51	#65911	C₂×C₃	1	1	yes	characteristic, complemented
52	#65910	C₂×C₃	1	2	yes	complemented
53	Q₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
54	#65889	C₂×C₃	1	3	yes	complemented
55	#65888	C₂×C₃	1	6	yes	complemented
56	D₄×D₂₀	C₂×C₃	1	3	yes	complemented
57	#65858	C₂×C₃	1	6	yes	complemented
58	#65811	C₂×C₃	1	3	yes	complemented
59	C₂×C₄×D₂₀	C₂×C₃	1	3	yes	complemented
60	C₂³×C₃×D₅	C₂³	1	6	yes	—
61	C₃×C₅×#41	D₄	1	8	yes	complemented
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
67	C₂×C₃×C₂²⋊D₅	C₂³	1	12	yes	—
68	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
69	C₃×#713	—	2	8	no	—
70	C₃×Q₈×D₅	—	2	8	no	—
71	C₃×#711	—	2	24	no	—
72	C₃×D₄×D₅	—	2	24	no	—
73	C₃×#709	—	2	24	no	—
74	C₂×C₃×D₂₀	—	2	12	no	—
75	C₂×C₃×D₂₀	C₂³	1	3	yes	—
76	C₂×C₃×D₂₀	C₂³	1	6	yes	—
77	C₂×C₃×D₂₀	C₂³	1	6	yes	—
78	C₂×C₃×D₂₀	C₂³	1	6	yes	—
79	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	—	2	24	no	—
81	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
82	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
83	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
84	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
85	C₂×C₃×Dic₁₀	C₂³	1	6	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₃×C₄²×C₅	C₂³	1	3	yes	—
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×C₄²×C₅	C₂³	1	3	yes	—
92	C₃×C₄²×C₅	C₂³	1	3	yes	—
93	C₃×#685	C₂³	1	2	yes	—
94	C₃×#685	C₂³	1	6	yes	—
95	C₃×#685	C₂³	1	6	yes	—
96	C₃×#685	C₂³	1	6	yes	—
97	C₃×#685	C₂³	1	12	yes	—
98	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
99	C₃×C₄⋊Dic₅	C₂³	1	6	yes	—
100	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
101	C₃×C₄⋊Dic₅	C₂³	1	6	yes	—
102	C₂²×C₃×#41	—	5	2	no	—
103	C₃×#550	—	5	1	no	—
104	C₃×D₄×Q₈	—	5	1	no	—
105	C₃×#548	—	5	2	no	—
106	C₃×#547	—	5	3	no	—
107	C₃×#546	—	5	6	no	—
108	C₃×D₄²	—	5	3	no	—
109	C₃×#532	—	5	3	no	—
110	C₃×#525	—	5	6	no	—
111	C₃×C₄×#41	D₅	1	1	yes	characteristic, complemented
112	C₂×C₃×C₄×D₄	—	5	3	no	—
113	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
114	D₅×#41	—	2	16	no	—
115	C₂×#713	C₂²×C₃	1	2	yes	complemented
116	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
117	C₂×#711	C₂²×C₃	1	6	yes	complemented
118	C₂×D₄×D₅	C₂²×C₃	1	6	yes	complemented
119	C₂×#709	C₂²×C₃	1	6	yes	complemented
120	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
121	C₂²×C₄×D₅	C₂²×C₃	1	6	yes	complemented
122	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₄×C₅×D₄	C₂²×C₃	1	3	yes	complemented
125	C₄×C₅×D₄	C₂²×C₃	1	3	yes	complemented
126	C₅×#117	C₂²×C₃	1	3	yes	complemented
127	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	complemented
128	#4076	C₂²×C₃	1	6	yes	complemented
129	#4076	C₂²×C₃	1	6	yes	complemented
130	C₂×#685	C₂²×C₃	1	6	yes	complemented
131	C₂×C₄⋊Dic₅	C₂²×C₃	1	3	yes	complemented
132	#4043	C₂²×C₃	1	6	yes	complemented
133	#4043	C₂²×C₃	1	6	yes	complemented
134	#4041	C₂²×C₃	1	6	yes	complemented
135	#4041	C₂²×C₃	1	6	yes	complemented
136	#4032	C₂²×C₃	1	12	yes	complemented
137	#4028	C₂²×C₃	1	12	yes	complemented
138	#4021	C₂²×C₃	1	6	yes	complemented
139	#4020	C₂²×C₃	1	3	yes	complemented
140	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
141	C₄×D₂₀	C₂²×C₃	1	3	yes	—
142	C₄×D₂₀	C₂²×C₃	1	3	yes	complemented
143	C₄×D₂₀	C₂²×C₃	1	6	yes	complemented
144	C₄×D₂₀	C₂²×C₃	1	6	yes	complemented
145	C₄×D₂₀	C₂²×C₃	1	3	yes	complemented
146	C₄×D₂₀	C₂²×C₃	1	6	yes	complemented
147	#4015	C₂²×C₃	1	3	yes	complemented
148	D₄×#41	—	5	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
150	C₂²×C₃×D₅	—	2	12	no	—
151	C₂²×C₃×D₅	—	2	12	no	—
152	C₂²×C₃×D₅	—	4	6	no	—
153	C₂²×C₃×D₅	C₂⁴	1	6	yes	—
154	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
155	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
156	C₃×C₅×D₄	C₂×D₄	1	12	yes	complemented
157	C₂×C₃×C₄×C₅	—	2	6	no	—
158	C₂×C₃×C₄×C₅	—	4	3	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	complemented
160	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₃×C₂²⋊D₅	—	2	24	no	—
167	C₂×C₃×Dic₅	—	2	12	no	—
168	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
169	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
170	C₃×D₂₀	—	2	12	no	—
171	C₃×D₂₀	—	2	12	no	—
172	C₃×D₂₀	—	2	6	no	—
173	C₃×D₂₀	—	4	6	no	—
174	C₃×D₂₀	#41	1	4	yes	direct product factor
175	C₃×C₄×D₅	—	2	4	no	—
176	C₃×C₄×D₅	—	2	12	no	—
177	C₃×C₄×D₅	—	2	12	no	—
178	C₃×C₄×D₅	—	2	12	no	—
179	C₃×Dic₁₀	—	2	12	no	—
180	C₂×C₃×#41	—	5	2	no	—
181	C₂×C₃×#41	—	5	6	no	—
182	C₂×C₃×#41	—	5	6	no	—
183	C₂×C₃×#41	—	10	16	no	—
184	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
185	C₂²×C₃×Q₈	—	5	2	no	—
186	C₂²×C₃×D₄	—	5	6	no	—
187	C₂²×C₃×D₄	—	5	3	no	—
188	C₂³×C₃×C₄	—	5	6	no	—
189	C₃×C₄⋊Q₈	—	5	3	no	—
190	C₃×#127	—	5	3	no	—
191	C₃×#124	—	5	6	no	—
192	C₃×#123	—	5	12	no	—
193	C₃×C₂²⋊Q₈	—	5	6	no	—
194	C₃×C₂²⋊Q₈	—	5	6	no	—
195	C₃×#121	—	5	6	no	—
196	C₃×#121	—	5	6	no	—
197	C₃×#121	—	5	6	no	—
198	C₃×#121	—	5	6	no	—
199	C₃×#120	—	5	12	no	—
200	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
201	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
202	C₃×C₄×D₄	—	5	1	no	—
203	C₃×C₄×D₄	—	5	3	no	—
204	C₃×C₄×D₄	—	5	6	no	—
205	C₃×C₄×D₄	—	5	3	no	—
206	C₃×C₄×D₄	—	5	6	no	—
207	C₃×C₄×D₄	—	5	3	no	—
208	C₃×C₄×D₄	—	5	6	no	—
209	C₃×C₄×D₄	C₂×D₅	1	3	yes	complemented
210	C₃×C₄×D₄	C₂×D₅	1	3	yes	complemented
211	C₃×#117	C₂×D₅	1	3	yes	complemented
212	C₂×C₃×C₄⋊C₄	—	5	3	no	—
213	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
214	C₂×C₃×C₄²	C₂×D₅	1	3	yes	complemented
215	C₂³×D₅	C₂³×C₃	1	6	yes	—
216	C₅×#41	C₃×D₄	1	8	yes	complemented
217	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×D₄	C₂³×C₃	1	3	yes	—
219	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
220	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
221	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
222	C₂×C₂²⋊D₅	C₂³×C₃	1	12	yes	—
223	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
224	#713	—	2	8	no	—
225	Q₈×D₅	—	2	8	no	—
226	#711	—	2	24	no	—
227	D₄×D₅	—	2	24	no	—
228	#709	—	2	24	no	—
229	C₂×D₂₀	—	2	12	no	—
230	C₂×D₂₀	C₂³×C₃	1	3	yes	—
231	C₂×D₂₀	C₂³×C₃	1	6	yes	—
232	C₂×D₂₀	C₂³×C₃	1	6	yes	—
233	C₂×D₂₀	C₂³×C₃	1	6	yes	—
234	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₄×D₅	—	2	24	no	—
236	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
237	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
238	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
239	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
240	C₂×Dic₁₀	C₂³×C₃	1	6	yes	—
241	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
243	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
244	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₄²×C₅	C₂³×C₃	1	3	yes	—
246	C₄²×C₅	C₂³×C₃	1	3	yes	—
247	C₄²×C₅	C₂³×C₃	1	3	yes	—
248	#685	C₂³×C₃	1	2	yes	—
249	#685	C₂³×C₃	1	6	yes	—
250	#685	C₂³×C₃	1	6	yes	—
251	#685	C₂³×C₃	1	6	yes	—
252	#685	C₂³×C₃	1	12	yes	—
253	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
254	C₄⋊Dic₅	C₂³×C₃	1	6	yes	—
255	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
256	C₄⋊Dic₅	C₂³×C₃	1	6	yes	—
257	C₂²×#41	—	5	2	no	—
258	#550	—	5	1	no	—
259	D₄×Q₈	—	5	1	no	—
260	#548	—	5	2	no	—
261	#547	—	5	3	no	—
262	#546	—	5	6	no	—
263	D₄²	—	5	3	no	—
264	#532	—	5	3	no	—
265	#525	—	5	6	no	—
266	C₄×#41	C₃×D₅	1	1	yes	characteristic, complemented
267	C₂×C₄×D₄	—	5	3	no	—
268	C₂²×C₃×C₅	—	2	3	no	—
269	C₂²×C₃×C₅	—	2	3	no	—
270	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
271	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
272	C₂×C₃×D₅	—	2	2	no	—
273	C₂×C₃×D₅	—	2	2	no	—
274	C₂×C₃×D₅	—	2	6	no	—
275	C₂×C₃×D₅	—	2	6	no	—
276	C₂×C₃×D₅	—	2	6	no	—
277	C₂×C₃×D₅	—	4	24	no	—
278	C₂×C₃×D₅	C₂×#41	1	4	yes	complemented
279	C₃×C₄×C₅	—	2	3	no	—
280	C₃×C₄×C₅	—	2	3	no	—
281	C₃×C₄×C₅	—	2	1	no	—
282	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
283	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
284	C₃×C₄×C₅	C₂×#41	1	2	yes	complemented
285	C₃×Dic₅	—	2	6	no	—
286	C₃×Dic₅	—	2	2	no	—
287	C₂⁴×C₃	—	5	6	no	—
288	C₃×#41	—	10	8	no	—
289	C₃×#41	—	10	24	no	—
290	C₃×#41	—	10	24	no	—
291	C₃×#41	D₂₀	1	8	yes	direct product factor
292	C₂×C₃×Q₈	—	5	6	no	—
293	C₂×C₃×Q₈	—	10	8	no	—
294	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₃×D₄	—	5	12	no	—
296	C₂×C₃×D₄	—	5	1	no	—
297	C₂×C₃×D₄	—	5	6	no	—
298	C₂×C₃×D₄	—	5	3	no	—
299	C₂×C₃×D₄	—	5	6	no	—
300	C₂×C₃×D₄	—	5	6	no	—
301	C₂×C₃×D₄	—	10	12	no	—
302	C₂×C₃×D₄	—	10	24	no	—
303	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
304	C₂²×C₃×C₄	—	5	6	no	—
305	C₂²×C₃×C₄	—	5	6	no	—
306	C₂²×C₃×C₄	—	5	6	no	—
307	C₂²×C₃×C₄	—	5	2	no	—
308	C₂²×C₃×C₄	—	5	6	no	—
309	C₂²×C₃×C₄	—	10	24	no	—
310	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
311	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
312	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
313	C₃×C₄⋊C₄	—	5	1	no	—
314	C₃×C₄⋊C₄	—	5	3	no	—
315	C₃×C₄⋊C₄	—	5	6	no	—
316	C₃×C₄⋊C₄	—	5	6	no	—
317	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
318	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	—	5	6	no	—
321	C₃×C₂²⋊C₄	—	5	6	no	—
322	C₃×C₂²⋊C₄	—	5	6	no	—
323	C₃×C₂²⋊C₄	—	5	12	no	—
324	C₃×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
325	C₃×C₄²	C₂²×D₅	1	3	yes	—
326	C₃×C₄²	C₂²×D₅	1	3	yes	—
327	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
328	C₃×C₄²	C₂²×D₅	1	3	yes	—
329	C₂³×C₅	C₂⁴×C₃	1	3	yes	—
330	C₂²×D₅	—	2	12	no	—
331	C₂²×D₅	—	2	12	no	—
332	C₂²×D₅	—	4	6	no	—
333	C₂²×D₅	C₂⁴×C₃	1	6	yes	—
334	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
335	C₅×Q₈	C₂×C₃×D₄	1	4	yes	complemented
336	C₅×D₄	C₂×C₃×D₄	1	12	yes	complemented
337	C₂×C₄×C₅	—	2	6	no	—
338	C₂×C₄×C₅	—	4	3	no	—
339	C₂×C₄×C₅	C₂×C₃×D₄	1	12	yes	complemented
340	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
341	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
342	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
345	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₂²⋊D₅	—	2	24	no	—
347	C₂×Dic₅	—	2	12	no	—
348	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
349	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
350	D₂₀	—	2	12	no	—
351	D₂₀	—	2	12	no	—
352	D₂₀	—	2	6	no	—
353	D₂₀	—	4	6	no	—
354	D₂₀	C₃×#41	1	4	yes	direct product factor
355	C₄×D₅	—	2	4	no	—
356	C₄×D₅	—	2	12	no	—
357	C₄×D₅	—	2	12	no	—
358	C₄×D₅	—	2	12	no	—
359	Dic₁₀	—	2	12	no	—
360	C₂×#41	—	5	2	no	—
361	C₂×#41	—	5	6	no	—
362	C₂×#41	—	5	6	no	—
363	C₂×#41	—	10	16	no	—
364	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
365	C₂²×Q₈	—	5	2	no	—
366	C₂²×D₄	—	5	6	no	—
367	C₂²×D₄	—	5	3	no	—
368	C₂³×C₄	—	5	6	no	—
369	C₄⋊Q₈	—	5	3	no	—
370	#127	—	5	3	no	—
371	#124	—	5	6	no	—
372	#123	—	5	12	no	—
373	C₂²⋊Q₈	—	5	6	no	—
374	C₂²⋊Q₈	—	5	6	no	—
375	#121	—	5	6	no	—
376	#121	—	5	6	no	—
377	#121	—	5	6	no	—
378	#121	—	5	6	no	—
379	#120	—	5	12	no	—
380	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
381	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	6	no	—
384	C₄×D₄	—	5	3	no	—
385	C₄×D₄	—	5	3	no	—
386	C₄×D₄	—	5	6	no	—
387	C₄×D₄	—	5	3	no	—
388	C₄×D₄	—	5	6	no	—
389	C₄×D₄	C₂×C₃×D₅	1	3	yes	complemented
390	C₄×D₄	C₂×C₃×D₅	1	3	yes	complemented
391	#117	C₂×C₃×D₅	1	3	yes	complemented
392	C₂×C₄⋊C₄	—	5	3	no	—
393	C₂×C₂²⋊C₄	—	5	6	no	—
394	C₂×C₄²	C₂×C₃×D₅	1	3	yes	complemented
395	C₂×C₃×C₅	—	2	6	no	—
396	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
397	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
398	C₂×C₃×C₅	#585	1	1	yes	characteristic
399	C₃×D₅	—	2	4	no	—
400	C₃×D₅	—	4	6	no	—
401	C₂³×C₃	—	5	2	no	—
402	C₂³×C₃	—	5	6	no	—
403	C₂³×C₃	—	10	12	no	—
404	C₂³×C₃	—	10	12	no	—
405	C₂³×C₃	—	20	6	no	—
406	C₂³×C₃	C₂³×D₅	1	3	yes	—
407	C₃×Q₈	—	10	12	no	—
408	C₃×Q₈	C₂×D₂₀	1	4	yes	complemented
409	C₃×D₄	—	5	4	no	—
410	C₃×D₄	—	10	12	no	—
411	C₃×D₄	—	10	24	no	—
412	C₃×D₄	—	10	12	no	—
413	C₃×D₄	—	10	6	no	—
414	C₃×D₄	—	20	6	no	—
415	C₃×D₄	C₂×D₂₀	1	12	yes	complemented
416	C₂×C₃×C₄	—	2	6	no	—
417	C₂×C₃×C₄	—	4	3	no	—
418	C₂×C₃×C₄	—	5	2	no	—
419	C₂×C₃×C₄	—	5	6	no	—
420	C₂×C₃×C₄	—	10	12	no	—
421	C₂×C₃×C₄	—	10	4	no	—
422	C₂×C₃×C₄	—	10	12	no	—
423	C₂×C₃×C₄	—	10	12	no	—
424	C₂×C₃×C₄	—	10	12	no	—
425	C₂×C₃×C₄	C₂×D₂₀	1	12	yes	complemented
426	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
428	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
429	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
430	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
432	C₂²×C₅	—	2	3	no	—
433	C₂²×C₅	—	2	3	no	—
434	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
435	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
436	C₂×D₅	—	2	2	no	—
437	C₂×D₅	—	2	2	no	—
438	C₂×D₅	—	2	6	no	—
439	C₂×D₅	—	2	6	no	—
440	C₂×D₅	—	2	6	no	—
441	C₂×D₅	—	4	24	no	—
442	C₂×D₅	C₂×C₃×#41	1	4	yes	complemented
443	C₄×C₅	—	2	3	no	—
444	C₄×C₅	—	2	3	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
447	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
448	C₄×C₅	C₂×C₃×#41	1	2	yes	complemented
449	Dic₅	—	2	6	no	—
450	Dic₅	—	2	2	no	—
451	C₂⁴	—	5	6	no	—
452	#41	—	10	8	no	—
453	#41	—	10	24	no	—
454	#41	—	10	24	no	—
455	#41	C₃×D₂₀	1	8	yes	direct product factor
456	C₂×Q₈	—	5	6	no	—
457	C₂×Q₈	—	10	8	no	—
458	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
459	C₂×D₄	—	5	12	no	—
460	C₂×D₄	—	5	1	no	—
461	C₂×D₄	—	5	6	no	—
462	C₂×D₄	—	5	3	no	—
463	C₂×D₄	—	5	6	no	—
464	C₂×D₄	—	5	6	no	—
465	C₂×D₄	—	10	12	no	—
466	C₂×D₄	—	10	24	no	—
467	C₂×D₄	C₂²×C₃×D₅	1	3	yes	—
468	C₂²×C₄	—	5	6	no	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	6	no	—
471	C₂²×C₄	—	5	6	no	—
472	C₂²×C₄	—	5	6	no	—
473	C₂²×C₄	—	10	24	no	—
474	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
475	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
476	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
477	C₄⋊C₄	—	5	1	no	—
478	C₄⋊C₄	—	5	3	no	—
479	C₄⋊C₄	—	5	6	no	—
480	C₄⋊C₄	—	5	6	no	—
481	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
482	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
483	C₂²⋊C₄	—	5	2	no	—
484	C₂²⋊C₄	—	5	6	no	—
485	C₂²⋊C₄	—	5	6	no	—
486	C₂²⋊C₄	—	5	6	no	—
487	C₂²⋊C₄	—	5	12	no	—
488	C₂²⋊C₄	C₂²×C₃×D₅	1	6	yes	—
489	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
490	C₄²	C₂²×C₃×D₅	1	3	yes	—
491	C₄²	C₂²×C₃×D₅	1	3	yes	—
492	C₄²	C₂²×C₃×D₅	1	3	yes	—
493	C₃×C₅	D₄×#41	1	1	yes	characteristic, complemented, Hall
494	C₂²×C₃	—	2	3	no	—
495	C₂²×C₃	—	2	3	no	—
496	C₂²×C₃	—	5	4	no	—
497	C₂²×C₃	—	10	2	no	—
498	C₂²×C₃	—	10	2	no	—
499	C₂²×C₃	—	10	6	no	—
500	C₂²×C₃	—	10	6	no	—
501	C₂²×C₃	—	10	6	no	—
502	C₂²×C₃	—	20	24	no	—
503	C₂²×C₃	C₂²×D₂₀	1	6	yes	—
504	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
505	C₃×C₄	—	2	3	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	3	no	—
508	C₃×C₄	—	10	2	no	—
509	C₃×C₄	—	10	6	no	—
510	C₃×C₄	C₂²×D₂₀	1	2	yes	—
511	C₃×C₄	C₂²×D₂₀	1	6	yes	—
512	C₃×C₄	D₅×#41	1	2	yes	complemented
513	C₂×C₅	—	2	6	no	—
514	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
515	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
516	C₂×C₅	C₃×#585	1	1	yes	characteristic
517	D₅	—	2	4	no	—
518	D₅	—	4	6	no	—
519	C₂³	—	5	2	no	—
520	C₂³	—	5	6	no	—
521	C₂³	—	10	12	no	—
522	C₂³	—	10	12	no	—
523	C₂³	—	20	6	no	—
524	C₂³	C₂³×C₃×D₅	1	3	yes	—
525	Q₈	—	10	12	no	—
526	Q₈	C₂×C₃×D₂₀	1	4	yes	complemented
527	D₄	—	5	4	no	—
528	D₄	—	10	12	no	—
529	D₄	—	10	24	no	—
530	D₄	—	10	12	no	—
531	D₄	—	10	6	no	—
532	D₄	—	20	6	no	—
533	D₄	C₂×C₃×D₂₀	1	12	yes	complemented
534	C₂×C₄	—	2	6	no	—
535	C₂×C₄	—	4	3	no	—
536	C₂×C₄	—	5	2	no	—
537	C₂×C₄	—	5	6	no	—
538	C₂×C₄	—	10	12	no	—
539	C₂×C₄	—	10	4	no	—
540	C₂×C₄	—	10	12	no	—
541	C₂×C₄	—	10	12	no	—
542	C₂×C₄	—	10	12	no	—
543	C₂×C₄	C₂×C₃×D₂₀	1	12	yes	complemented
544	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
545	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
546	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
547	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
548	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
549	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
550	C₂×C₃	—	2	6	no	—
551	C₂×C₃	—	10	4	no	—
552	C₂×C₃	—	20	6	no	—
553	C₂×C₃	C₂³×D₂₀	1	1	yes	characteristic
554	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
555	C₂×C₃	#66283	1	1	yes	characteristic
556	C₅	C₃×D₄×#41	1	1	yes	characteristic, complemented, Sylow
557	C₂²	—	2	3	no	—
558	C₂²	—	2	3	no	—
559	C₂²	—	5	4	no	—
560	C₂²	—	10	2	no	—
561	C₂²	—	10	2	no	—
562	C₂²	—	10	6	no	—
563	C₂²	—	10	6	no	—
564	C₂²	—	10	6	no	—
565	C₂²	—	20	24	no	—
566	C₂²	C₂²×C₃×D₂₀	1	6	yes	—
567	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
568	C₄	—	2	3	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	3	no	—
571	C₄	—	10	2	no	—
572	C₄	—	10	6	no	—
573	C₄	C₂²×C₃×D₂₀	1	2	yes	—
574	C₄	C₂²×C₃×D₂₀	1	6	yes	—
575	C₄	C₃×D₅×#41	1	2	yes	complemented
576	C₃	#41×D₂₀	1	1	yes	characteristic, direct product factor, Sylow
577	C₂	—	2	6	no	—
578	C₂	—	10	4	no	—
579	C₂	—	20	6	no	—
580	C₂	C₂³×C₃×D₂₀	1	1	yes	characteristic
581	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
582	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×D₄×#41
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×#41	C₂	semidirect
2. C₃×C₄×C₅×#41	C₂	semidirect
3. C₃×#65911	C₂	semidirect
4. C₃×#65910	C₂	semidirect
5. C₃×Q₈×D₂₀	C₂	semidirect
6. C₃×#65889	C₂	semidirect
7. C₃×#65888	C₂	semidirect
8. C₃×D₄×D₂₀	C₂	semidirect
9. C₃×#65858	C₂	semidirect
10. C₃×#65811	C₂	semidirect
11. C₂×C₃×C₄×D₂₀	C₂	semidirect
12. #41×D₂₀	C₃	direct (N × H)
15. C₂×C₃×#713	C₂²	semidirect
16. C₂×C₃×Q₈×D₅	C₂²	semidirect
17. C₂×C₃×#711	C₂²	semidirect
18. C₂×C₃×D₄×D₅	C₂²	semidirect
19. C₂×C₃×#709	C₂²	semidirect
21. C₂²×C₃×C₄×D₅	C₂²	semidirect
22. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
25. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×C₅×#117	C₂²	semidirect
27. C₂×C₃×C₄²×C₅	C₂²	semidirect
28. C₃×#4076	C₂²	semidirect
29. C₃×#4076	C₂²	semidirect
30. C₂×C₃×#685	C₂²	semidirect
31. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
32. C₃×#4043	C₂²	semidirect
33. C₃×#4043	C₂²	semidirect
34. C₃×#4041	C₂²	semidirect
35. C₃×#4041	C₂²	semidirect
36. C₃×#4032	C₂²	semidirect
37. C₃×#4028	C₂²	semidirect
38. C₃×#4021	C₂²	semidirect
39. C₃×#4020	C₂²	semidirect
42. C₃×C₄×D₂₀	C₂²	semidirect
43. C₃×C₄×D₂₀	C₂²	semidirect
44. C₃×C₄×D₂₀	C₂²	semidirect
45. C₃×C₄×D₂₀	C₂²	semidirect
46. C₃×C₄×D₂₀	C₂²	semidirect
47. C₃×#4015	C₂²	semidirect
49. C₂×D₅×#41	C₂×C₃	semidirect
50. C₄×C₅×#41	C₂×C₃	semidirect
51. #65911	C₂×C₃	semidirect
52. #65910	C₂×C₃	semidirect
53. Q₈×D₂₀	C₂×C₃	semidirect
54. #65889	C₂×C₃	semidirect
55. #65888	C₂×C₃	semidirect
56. D₄×D₂₀	C₂×C₃	semidirect
57. #65858	C₂×C₃	semidirect
58. #65811	C₂×C₃	semidirect
59. C₂×C₄×D₂₀	C₂×C₃	semidirect
61. C₃×C₅×#41	D₄	semidirect
111. C₃×C₄×#41	D₅	semidirect
115. C₂×#713	C₂²×C₃	semidirect
116. C₂×Q₈×D₅	C₂²×C₃	semidirect
117. C₂×#711	C₂²×C₃	semidirect
118. C₂×D₄×D₅	C₂²×C₃	semidirect
119. C₂×#709	C₂²×C₃	semidirect
121. C₂²×C₄×D₅	C₂²×C₃	semidirect
122. C₄×C₅×Q₈	C₂²×C₃	semidirect
123. C₄×C₅×Q₈	C₂²×C₃	semidirect
124. C₄×C₅×D₄	C₂²×C₃	semidirect
125. C₄×C₅×D₄	C₂²×C₃	semidirect
126. C₅×#117	C₂²×C₃	semidirect
127. C₂×C₄²×C₅	C₂²×C₃	semidirect
128. #4076	C₂²×C₃	semidirect
129. #4076	C₂²×C₃	semidirect
130. C₂×#685	C₂²×C₃	semidirect
131. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
132. #4043	C₂²×C₃	semidirect
133. #4043	C₂²×C₃	semidirect
134. #4041	C₂²×C₃	semidirect
135. #4041	C₂²×C₃	semidirect
136. #4032	C₂²×C₃	semidirect
137. #4028	C₂²×C₃	semidirect
138. #4021	C₂²×C₃	semidirect
139. #4020	C₂²×C₃	semidirect
142. C₄×D₂₀	C₂²×C₃	semidirect
143. C₄×D₂₀	C₂²×C₃	semidirect
144. C₄×D₂₀	C₂²×C₃	semidirect
145. C₄×D₂₀	C₂²×C₃	semidirect
146. C₄×D₂₀	C₂²×C₃	semidirect
147. #4015	C₂²×C₃	semidirect
155. C₃×C₅×Q₈	C₂×D₄	semidirect
156. C₃×C₅×D₄	C₂×D₄	semidirect
159. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
174. C₃×D₂₀	#41	direct (N × H)
200. C₃×C₄×Q₈	C₂×D₅	semidirect
201. C₃×C₄×Q₈	C₂×D₅	semidirect
209. C₃×C₄×D₄	C₂×D₅	semidirect
210. C₃×C₄×D₄	C₂×D₅	semidirect
211. C₃×#117	C₂×D₅	semidirect
214. C₂×C₃×C₄²	C₂×D₅	semidirect
216. C₅×#41	C₃×D₄	semidirect
266. C₄×#41	C₃×D₅	semidirect
278. C₂×C₃×D₅	C₂×#41	semidirect
284. C₃×C₄×C₅	C₂×#41	semidirect
291. C₃×#41	D₂₀	direct (N × H)
335. C₅×Q₈	C₂×C₃×D₄	semidirect
336. C₅×D₄	C₂×C₃×D₄	semidirect
339. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
354. D₂₀	C₃×#41	direct (N × H)
380. C₄×Q₈	C₂×C₃×D₅	semidirect
381. C₄×Q₈	C₂×C₃×D₅	semidirect
389. C₄×D₄	C₂×C₃×D₅	semidirect
390. C₄×D₄	C₂×C₃×D₅	semidirect
391. #117	C₂×C₃×D₅	semidirect
394. C₂×C₄²	C₂×C₃×D₅	semidirect
408. C₃×Q₈	C₂×D₂₀	semidirect
415. C₃×D₄	C₂×D₂₀	semidirect
425. C₂×C₃×C₄	C₂×D₂₀	semidirect
442. C₂×D₅	C₂×C₃×#41	semidirect
448. C₄×C₅	C₂×C₃×#41	semidirect
455. #41	C₃×D₂₀	direct (N × H)
493. C₃×C₅	D₄×#41	semidirect
512. C₃×C₄	D₅×#41	semidirect
526. Q₈	C₂×C₃×D₂₀	semidirect
533. D₄	C₂×C₃×D₂₀	semidirect
543. C₂×C₄	C₂×C₃×D₂₀	semidirect
556. C₅	C₃×D₄×#41	semidirect
575. C₄	C₃×D₅×#41	semidirect
576. C₃	#41×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×C₃×D₅×#41	2
C₃×C₄×C₅×#41	2
C₃×#65911	2
C₃×#65910	2
C₃×Q₈×D₂₀	2
C₃×#65889	2
C₃×#65888	2
C₃×D₄×D₂₀	2
C₃×#65858	2
C₃×#65811	2
C₂×C₃×C₄×D₂₀	2
#41×D₂₀	3
C₃×D₄×#41	5

Subgroups — C3×#41×D20 #14483058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41×D₂₀ #14483058