Subgroups — D₃×C₈×D₂₀ #14414623

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈×D₅	C₂	1	2	yes	maximal, complemented
2	C₄×D₃×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₈×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#3952	C₂	1	2	yes	maximal, complemented
7	#11748042	C₂	1	2	yes	maximal, complemented
8	C₈×#1202	C₂	1	2	yes	maximal, complemented
9	#11746994	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₂₀	—	3	1	no	maximal, Hall
13	C₂×D₃×D₂₀	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃×D₅	C₂²	1	2	yes	—
15	C₂×C₈×D₁₅	C₂²	1	2	yes	complemented
16	C₄×D₆₀	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
21	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
22	D₃×#685	C₄	1	2	yes	—
23	C₄×#1202	C₂²	1	2	yes	—
24	#91428	C₄	1	1	yes	characteristic
25	D₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
26	Dic₃×D₂₀	C₄	1	1	yes	characteristic
27	#91395	C₄	1	2	yes	—
28	C₂×#6648	C₂²	1	2	yes	complemented
29	C₂×D₃×#168	C₂²	1	2	yes	—
30	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
31	D₃×C₈×D₅	—	2	8	no	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	#91104	C₂²	1	2	yes	complemented
34	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3952	C₂²	1	2	yes	complemented
39	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
40	Dic₃⋊#168	C₂²	1	2	yes	complemented
41	#90957	C₂²	1	2	yes	complemented
42	#90955	C₂²	1	2	yes	complemented
43	D₃×C₈×D₄	—	5	1	no	maximal, Hall
44	C₂²×C₈×D₅	—	3	2	no	—
45	C₂×C₄×D₂₀	—	3	1	no	—
46	C₂×C₄×C₅×C₈	—	3	1	no	—
47	C₂×#3952	—	3	2	no	—
48	C₂×C₄⋊#168	—	3	1	no	—
49	C₈×D₂₀	—	3	2	no	—
50	C₈×D₂₀	—	3	1	no	—
51	C₈×D₂₀	—	3	1	no	—
52	C₈×D₂₀	—	3	2	no	—
53	C₈×D₂₀	—	3	1	no	—
54	C₈×D₂₀	D₃	1	1	yes	characteristic, direct product factor
55	C₂²×D₃×D₅	C₂×C₄	1	2	yes	—
56	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂³	1	2	yes	—
58	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
61	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
63	C₂×#1202	C₂×C₄	1	2	yes	—
64	C₂×#1200	C₂×C₄	1	2	yes	—
65	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
66	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
67	D₃×D₂₀	C₈	1	8	yes	direct product factor
68	C₄×D₃×D₅	—	2	4	no	—
69	C₄×D₃×D₅	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	#6714	C₂×C₄	1	2	yes	—
74	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₈×D₁₅	—	2	4	no	—
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×D₃×C₈	—	2	2	no	—
83	C₅×D₃×C₈	D₄	1	4	yes	complemented
84	C₃×#685	C₂×C₄	1	2	yes	—
85	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₃×C₈×D₅	—	2	4	no	—
88	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
89	#6667	C₂×C₄	1	2	yes	—
90	#6665	C₂×C₄	1	2	yes	—
91	#6648	—	2	4	no	—
92	D₃×#168	—	2	4	no	—
93	D₅×C₃⋊C₈	—	2	4	no	—
94	C₂²×D₃×C₈	—	5	2	no	—
95	C₄×D₃×D₄	—	5	1	no	—
96	C₃×C₈×D₄	—	5	1	no	—
97	C₈×#67	—	5	2	no	—
98	D₄×C₃⋊C₈	—	5	1	no	—
99	#4834	—	5	1	no	—
100	D₃×C₄⋊C₈	—	5	1	no	—
101	#67⋊C₈	—	5	2	no	—
102	D₃×C₂²⋊C₈	—	5	2	no	—
103	C₈×D₁₂	—	5	1	no	—
104	C₄×D₃×C₈	D₅	1	1	yes	characteristic, complemented
105	C₂²×D₂₀	—	3	1	no	—
106	C₂²×C₄×D₅	—	3	2	no	—
107	C₂²×C₅×C₈	—	3	1	no	—
108	C₂²×C₅×C₈	—	3	1	no	—
109	C₂×C₄²×C₅	—	3	1	no	—
110	C₂×#685	—	3	2	no	—
111	C₂×C₄⋊Dic₅	—	3	1	no	—
112	C₂²×#168	—	3	2	no	—
113	C₂×C₈×D₅	—	3	2	no	—
114	C₂×C₈×D₅	—	3	2	no	—
115	C₂×C₈×D₅	—	3	2	no	—
116	C₂×C₈×D₅	—	6	8	no	—
117	C₂×C₈×D₅	C₂×D₃	1	2	yes	complemented
118	C₄×D₂₀	—	3	1	no	—
119	C₄×D₂₀	—	3	2	no	—
120	C₄×D₂₀	—	3	1	no	—
121	C₄×D₂₀	—	3	2	no	—
122	C₄×D₂₀	—	3	1	no	—
123	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
128	#3952	—	3	2	no	—
129	#3952	—	3	2	no	—
130	#3952	—	3	2	no	—
131	#3952	C₂×D₃	1	2	yes	complemented
132	C₄⋊#168	—	3	1	no	—
133	C₄⋊#168	—	3	2	no	—
134	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
135	C₂×C₈×D₄	—	15	1	no	Sylow
136	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
139	C₂×D₃×D₅	—	2	4	no	—
140	C₂×D₃×D₅	—	2	4	no	—
141	C₂×D₃×D₅	C₂×C₈	1	8	yes	complemented
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
146	D₆₀	C₂×C₈	1	4	yes	complemented
147	C₄×D₁₅	—	2	2	no	—
148	C₄×D₁₅	—	2	2	no	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×C₅×D₃	—	2	2	no	—
153	C₄×C₅×D₃	C₂×C₈	1	4	yes	complemented
154	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
155	C₄×C₅×D₃	#41	1	2	yes	—
156	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
157	C₃×D₂₀	C₂×C₈	1	4	yes	complemented
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×C₄×D₅	—	2	2	no	—
160	#1202	C₂×C₈	1	8	yes	complemented
161	#1200	—	2	4	no	—
162	D₃×Dic₅	—	2	4	no	—
163	D₅×Dic₃	—	2	4	no	—
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
166	C₃⋊#168	—	2	2	no	—
167	C₃×#168	—	2	2	no	—
168	C₅×C₃⋊C₈	—	2	1	no	—
169	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
170	C₂×D₃×D₄	—	5	1	no	—
171	C₂²×C₄×D₃	—	5	2	no	—
172	C₂²×C₃×C₈	—	5	2	no	—
173	C₃×C₄×D₄	—	5	1	no	—
174	D₄×Dic₃	—	5	1	no	—
175	C₄×#67	—	5	2	no	—
176	C₂²×C₃⋊C₈	—	5	2	no	—
177	C₂×D₃×C₈	—	5	2	no	—
178	C₂×D₃×C₈	—	5	2	no	—
179	C₂×D₃×C₈	—	5	2	no	—
180	C₂×D₃×C₈	—	10	8	no	—
181	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
182	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
183	#893	—	5	1	no	—
184	D₃×C₄⋊C₄	—	5	1	no	—
185	#67⋊C₄	—	5	2	no	—
186	D₃×C₂²⋊C₄	—	5	2	no	—
187	C₄×D₁₂	—	5	1	no	—
188	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
189	C₃×C₄⋊C₈	—	5	1	no	—
190	C₃×C₂²⋊C₈	—	5	2	no	—
191	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
192	#830	—	5	2	no	—
193	(C₂×D₃)⋊C₈	—	5	2	no	—
194	(C₂×D₃)⋊C₈	—	5	2	no	—
195	Dic₃⋊C₈	—	5	2	no	—
196	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
197	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
198	C₄⋊(C₃⋊C₈)	—	5	1	no	—
199	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
200	C₂³×D₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	3	1	no	—
202	C₂²×C₄×C₅	—	3	1	no	—
203	C₂²×C₄×C₅	—	3	1	no	—
204	C₂²×Dic₅	—	3	2	no	—
205	C₂×D₂₀	—	3	2	no	—
206	C₂×D₂₀	—	3	1	no	—
207	C₂×D₂₀	—	3	8	no	—
208	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
209	C₂×C₄×D₅	—	3	2	no	—
210	C₂×C₄×D₅	—	3	2	no	—
211	C₂×C₄×D₅	—	3	2	no	—
212	C₂×C₄×D₅	—	6	4	no	—
213	C₂×C₄×D₅	—	6	4	no	—
214	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
215	C₂×C₅×C₈	—	3	1	no	—
216	C₂×C₅×C₈	—	3	4	no	—
217	C₂×C₅×C₈	—	3	1	no	—
218	C₂×C₅×C₈	—	6	2	no	—
219	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
221	C₄²×C₅	—	3	1	no	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
225	#685	—	3	2	no	—
226	#685	—	3	2	no	—
227	#685	—	3	2	no	—
228	#685	C₄×D₃	1	2	yes	—
229	C₄⋊Dic₅	—	3	1	no	—
230	C₄⋊Dic₅	—	3	2	no	—
231	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
232	C₂×#168	—	3	2	no	—
233	C₂×#168	—	6	4	no	—
234	C₂×#168	C₂²×D₃	1	2	yes	—
235	C₈×D₅	—	2	4	no	—
236	C₈×D₅	—	6	4	no	—
237	C₈×D₅	—	6	4	no	—
238	C₈×D₅	—	6	4	no	—
239	C₂³×C₈	—	15	2	no	—
240	C₂×C₄×D₄	—	15	1	no	—
241	C₈×D₄	—	5	1	no	—
242	C₈×D₄	—	15	2	no	—
243	C₈×D₄	—	15	1	no	—
244	C₈×D₄	—	15	1	no	—
245	C₈×D₄	—	15	2	no	—
246	C₈×D₄	—	15	1	no	—
247	C₂×C₄⋊C₈	—	15	1	no	—
248	C₂×C₂²⋊C₈	—	15	2	no	—
249	C₂×C₄×C₈	—	3	1	no	—
250	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂×D₁₅	—	2	2	no	—
252	C₂×D₁₅	—	2	2	no	—
253	C₂×D₁₅	C₂²×C₈	1	4	yes	complemented
254	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
255	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
256	C₂×C₅×D₃	#131	1	2	yes	—
257	C₂×C₃×D₅	—	2	2	no	—
258	C₂×C₃×D₅	—	2	2	no	—
259	C₂×C₃×D₅	C₂²×C₈	1	4	yes	complemented
260	D₃×D₅	—	2	16	no	—
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	C₂²×C₈	1	2	yes	complemented
263	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	Dic₁₅	—	2	2	no	—
266	C₃×Dic₅	—	2	2	no	—
267	C₅×Dic₃	—	2	1	no	—
268	C₅×Dic₃	C₄×D₄	1	2	yes	—
269	C₅×Dic₃	C₂²×C₈	1	2	yes	complemented
270	C₂³×D₃	—	5	2	no	—
271	C₂×C₃×D₄	—	5	1	no	—
272	C₂²×C₃×C₄	—	5	2	no	—
273	C₂×#67	—	5	2	no	—
274	C₂²×Dic₃	—	5	2	no	—
275	D₃×D₄	—	5	8	no	—
276	C₂×D₁₂	—	5	1	no	—
277	C₂×C₄×D₃	—	5	2	no	—
278	C₂×C₄×D₃	—	5	2	no	—
279	C₂×C₄×D₃	—	5	2	no	—
280	C₂×C₄×D₃	—	10	4	no	—
281	C₂×C₄×D₃	—	10	4	no	—
282	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
283	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
285	C₂×C₃×C₈	—	5	2	no	—
286	C₂×C₃×C₈	—	10	4	no	—
287	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	—	5	1	no	—
290	C₃×C₂²⋊C₄	—	5	2	no	—
291	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
292	#217	—	5	2	no	—
293	(C₂×D₃)⋊C₄	—	5	2	no	—
294	(C₂×D₃)⋊C₄	—	5	2	no	—
295	C₄⋊Dic₃	—	5	1	no	—
296	Dic₃⋊C₄	—	5	2	no	—
297	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
298	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
299	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
300	C₂×C₃⋊C₈	—	5	2	no	—
301	C₂×C₃⋊C₈	—	10	4	no	—
302	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
304	D₃×C₈	—	2	2	no	—
305	D₃×C₈	—	10	4	no	—
306	D₃×C₈	—	10	4	no	—
307	D₃×C₈	—	10	4	no	—
308	D₃×C₈	D₂₀	1	4	yes	direct product factor
309	C₂³×C₅	—	3	1	no	—
310	C₂²×D₅	—	3	2	no	—
311	C₂²×D₅	—	3	8	no	—
312	C₂²×D₅	—	6	4	no	—
313	C₂²×D₅	—	6	4	no	—
314	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
315	C₂×C₄×C₅	—	3	1	no	—
316	C₂×C₄×C₅	—	3	1	no	—
317	C₂×C₄×C₅	—	3	4	no	—
318	C₂×C₄×C₅	—	3	2	no	—
319	C₂×C₄×C₅	—	3	2	no	—
320	C₂×C₄×C₅	—	3	1	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₂×Dic₅	—	3	2	no	—
326	C₂×Dic₅	—	6	4	no	—
327	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
328	D₂₀	—	3	8	no	—
329	D₂₀	—	3	4	no	—
330	D₂₀	D₃×C₈	1	4	yes	direct product factor
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	6	4	no	—
334	C₄×D₅	—	6	4	no	—
335	C₄×D₅	—	6	2	no	—
336	C₄×D₅	—	6	2	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	3	2	no	—
339	C₅×C₈	—	6	1	no	—
340	C₅×C₈	D₃×D₄	1	2	yes	complemented
341	#168	—	2	2	no	—
342	#168	—	6	2	no	—
343	C₂²×D₄	—	15	1	no	—
344	C₂³×C₄	—	15	2	no	—
345	C₂²×C₈	—	3	1	no	—
346	C₂²×C₈	—	3	1	no	—
347	C₂²×C₈	—	5	2	no	—
348	C₂²×C₈	—	15	2	no	—
349	C₂²×C₈	—	15	2	no	—
350	C₂²×C₈	—	15	2	no	—
351	C₂²×C₈	—	15	2	no	—
352	C₂²×C₈	—	30	8	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	15	2	no	—
355	C₄×D₄	—	15	1	no	—
356	C₄×D₄	—	15	2	no	—
357	C₄×D₄	—	15	1	no	—
358	C₄×D₄	—	15	1	no	—
359	C₂×C₄⋊C₄	—	15	1	no	—
360	C₂×C₂²⋊C₄	—	15	2	no	—
361	C₂×C₄²	—	3	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	—	15	2	no	—
364	C₄⋊C₈	—	15	1	no	—
365	C₂²⋊C₈	—	5	2	no	—
366	C₂²⋊C₈	—	15	2	no	—
367	C₂²⋊C₈	—	15	2	no	—
368	C₂²⋊C₈	—	15	2	no	—
369	C₄×C₈	—	3	1	no	—
370	C₄×C₈	—	3	1	no	—
371	C₄×C₈	—	3	1	no	—
372	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
373	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
376	D₁₅	—	2	4	no	—
377	C₃×D₅	—	2	4	no	—
378	C₅×D₃	C₈×D₄	1	4	yes	complemented
379	C₂³×C₃	—	5	2	no	—
380	C₂²×D₃	—	5	2	no	—
381	C₂²×D₃	—	5	8	no	—
382	C₂²×D₃	—	10	4	no	—
383	C₂²×D₃	—	10	4	no	—
384	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
385	C₃×D₄	—	5	4	no	—
386	C₂×C₃×C₄	—	5	2	no	—
387	C₂×C₃×C₄	—	10	2	no	—
388	C₂×C₃×C₄	—	10	2	no	—
389	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
392	#67	—	5	8	no	—
393	C₂×Dic₃	—	5	2	no	—
394	C₂×Dic₃	—	10	4	no	—
395	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
396	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
397	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
398	D₁₂	—	5	4	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	10	4	no	—
401	C₄×D₃	—	10	2	no	—
402	C₄×D₃	—	10	2	no	—
403	C₄×D₃	—	10	4	no	—
404	C₄×D₃	C₈×D₅	1	4	yes	complemented
405	C₄×D₃	C₂×D₂₀	1	2	yes	—
406	C₄×D₃	#709	1	2	yes	—
407	C₃×C₈	—	2	1	no	—
408	C₃×C₈	—	10	2	no	—
409	C₃×C₈	C₂×D₂₀	1	2	yes	complemented
410	C₃⋊C₈	—	2	1	no	—
411	C₃⋊C₈	—	10	2	no	—
412	C₃⋊C₈	C₂×D₂₀	1	2	yes	complemented
413	C₂²×C₅	—	3	2	no	—
414	C₂²×C₅	—	3	2	no	—
415	C₂²×C₅	—	3	2	no	—
416	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₂×D₅	—	2	2	no	—
418	C₂×D₅	—	2	2	no	—
419	C₂×D₅	—	3	4	no	—
420	C₂×D₅	—	6	16	no	—
421	C₂×D₅	—	6	2	no	—
422	C₂×D₅	—	6	2	no	—
423	C₂×D₅	C₂×D₃×C₈	1	4	yes	complemented
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	3	2	no	—
426	C₄×C₅	—	3	2	no	—
427	C₄×C₅	—	6	1	no	—
428	C₄×C₅	C₂×D₃×C₈	1	2	yes	complemented
429	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
430	C₄×C₅	D₃×#41	1	1	yes	characteristic
431	Dic₅	—	2	2	no	—
432	Dic₅	—	6	2	no	—
433	C₂⁴	—	15	2	no	—
434	C₂×D₄	—	5	1	no	—
435	C₂×D₄	—	15	8	no	—
436	C₂×D₄	—	15	2	no	—
437	C₂×D₄	—	15	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	5	2	no	—
442	C₂²×C₄	—	15	2	no	—
443	C₂²×C₄	—	15	2	no	—
444	C₂²×C₄	—	15	2	no	—
445	C₂²×C₄	—	15	2	no	—
446	C₂²×C₄	—	30	4	no	—
447	C₂²×C₄	—	30	4	no	—
448	C₂×C₈	—	3	1	no	—
449	C₂×C₈	—	3	4	no	—
450	C₂×C₈	—	3	1	no	—
451	C₂×C₈	—	5	2	no	—
452	C₂×C₈	—	6	2	no	—
453	C₂×C₈	—	10	4	no	—
454	C₂×C₈	—	15	2	no	—
455	C₂×C₈	—	30	4	no	—
456	C₂×C₈	—	30	4	no	—
457	C₂×C₈	—	30	4	no	—
458	C₂×C₈	—	30	4	no	—
459	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
460	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	—	15	2	no	—
463	C₄⋊C₄	—	15	1	no	—
464	C₂²⋊C₄	—	5	2	no	—
465	C₂²⋊C₄	—	15	2	no	—
466	C₂²⋊C₄	—	15	2	no	—
467	C₂²⋊C₄	—	15	2	no	—
468	C₄²	—	3	1	no	—
469	C₄²	—	3	1	no	—
470	C₄²	—	3	1	no	—
471	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
472	C₃×C₅	C₂×C₈×D₄	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	5	4	no	—
474	C₂²×C₃	—	10	2	no	—
475	C₂²×C₃	—	10	2	no	—
476	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
477	C₂×D₃	—	5	4	no	—
478	C₂×D₃	—	10	2	no	—
479	C₂×D₃	—	10	2	no	—
480	C₂×D₃	—	10	16	no	—
481	C₂×D₃	C₄×D₂₀	1	2	yes	—
482	C₂×D₃	C₂×C₈×D₅	1	2	yes	—
483	C₂×D₃	#4047	1	2	yes	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	10	2	no	—
486	C₃×C₄	C₂×C₈×D₅	1	2	yes	complemented
487	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
488	C₃×C₄	C₂×#709	1	1	yes	characteristic
489	Dic₃	—	2	1	no	—
490	Dic₃	—	10	2	no	—
491	Dic₃	C₄×D₂₀	1	2	yes	—
492	Dic₃	C₂×C₈×D₅	1	2	yes	complemented
493	C₂×C₅	—	3	4	no	—
494	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
495	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
496	C₂×C₅	D₃×#131	1	1	yes	characteristic
497	D₅	—	2	4	no	—
498	D₅	—	6	4	no	—
499	C₂³	—	3	1	no	—
500	C₂³	—	5	2	no	—
501	C₂³	—	15	8	no	—
502	C₂³	—	15	2	no	—
503	C₂³	—	30	4	no	—
504	C₂³	—	30	4	no	—
505	D₄	—	5	4	no	—
506	D₄	—	15	8	no	—
507	D₄	—	15	4	no	—
508	C₂×C₄	—	3	1	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	4	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	5	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	10	2	no	—
517	C₂×C₄	—	10	2	no	—
518	C₂×C₄	—	15	2	no	—
519	C₂×C₄	—	30	4	no	—
520	C₂×C₄	—	30	4	no	—
521	C₂×C₄	—	30	4	no	—
522	C₂×C₄	—	30	2	no	—
523	C₂×C₄	—	30	2	no	—
524	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
525	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	3	2	no	—
529	C₈	—	6	1	no	—
530	C₈	—	10	2	no	—
531	C₈	—	30	2	no	—
532	C₈	D₃×D₂₀	1	2	yes	direct product factor
533	C₂×C₃	—	10	4	no	—
534	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
535	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
536	C₂×C₃	C₂×#4047	1	1	yes	characteristic
537	D₃	—	10	4	no	—
538	D₃	C₈×D₂₀	1	4	yes	direct product factor
539	C₅	D₃×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	3	2	no	—
541	C₂²	—	3	2	no	—
542	C₂²	—	3	2	no	—
543	C₂²	—	5	4	no	—
544	C₂²	—	10	2	no	—
545	C₂²	—	10	2	no	—
546	C₂²	—	15	4	no	—
547	C₂²	—	30	16	no	—
548	C₂²	—	30	2	no	—
549	C₂²	—	30	2	no	—
550	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	3	2	no	—
553	C₄	—	3	2	no	—
554	C₄	—	6	1	no	—
555	C₄	—	10	2	no	—
556	C₄	—	30	2	no	—
557	C₄	D₃×C₈×D₅	1	2	yes	complemented
558	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
559	C₄	D₃×#709	1	1	yes	characteristic
560	C₃	C₂×C₈×D₂₀	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	3	4	no	—
562	C₂	—	10	4	no	—
563	C₂	—	30	4	no	—
564	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
565	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
566	C₂	D₃×#4047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×D₃×D₂₀	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₈×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×C₈×D₅	C₂	semidirect
3. C₈×D₆₀	C₂	semidirect
4. C₄×C₅×D₃×C₈	C₂	semidirect
5. C₃×C₈×D₂₀	C₂	semidirect
6. D₃×#3952	C₂	semidirect
7. #11748042	C₂	semidirect
8. C₈×#1202	C₂	semidirect
9. #11746994	C₂	semidirect
10. D₃×C₄⋊#168	C₂	semidirect
11. C₃⋊C₈×D₂₀	C₂	semidirect
15. C₂×C₈×D₁₅	C₂²	semidirect
20. C₂×C₃×C₈×D₅	C₂²	semidirect
28. C₂×#6648	C₂²	semidirect
30. C₂×D₅×C₃⋊C₈	C₂²	semidirect
32. C₃×C₄×C₅×C₈	C₂²	semidirect
33. #91104	C₂²	semidirect
34. C₄⋊(C₃⋊#168)	C₂²	semidirect
35. C₅×C₈×Dic₃	C₂²	semidirect
36. C₅×C₈×Dic₃	C₂²	semidirect
37. C₄×C₅×C₃⋊C₈	C₂²	semidirect
38. C₃×#3952	C₂²	semidirect
39. C₃×C₄⋊#168	C₂²	semidirect
40. Dic₃⋊#168	C₂²	semidirect
41. #90957	C₂²	semidirect
42. #90955	C₂²	semidirect
54. C₈×D₂₀	D₃	direct (N × H)
67. D₃×D₂₀	C₈	direct (N × H)
83. C₅×D₃×C₈	D₄	semidirect
104. C₄×D₃×C₈	D₅	semidirect
117. C₂×C₈×D₅	C₂×D₃	semidirect
127. C₄×C₅×C₈	C₂×D₃	semidirect
131. #3952	C₂×D₃	semidirect
134. C₄⋊#168	C₂×D₃	semidirect
141. C₂×D₃×D₅	C₂×C₈	semidirect
146. D₆₀	C₂×C₈	semidirect
153. C₄×C₅×D₃	C₂×C₈	semidirect
157. C₃×D₂₀	C₂×C₈	semidirect
160. #1202	C₂×C₈	semidirect
165. C₃×C₅×C₈	C₂×D₄	semidirect
169. C₅×C₃⋊C₈	C₂×D₄	semidirect
191. C₃×C₄×C₈	C₂×D₅	semidirect
196. C₈×Dic₃	C₂×D₅	semidirect
197. C₈×Dic₃	C₂×D₅	semidirect
199. C₄×C₃⋊C₈	C₂×D₅	semidirect
253. C₂×D₁₅	C₂²×C₈	semidirect
259. C₂×C₃×D₅	C₂²×C₈	semidirect
262. C₃×C₄×C₅	C₂²×C₈	semidirect
269. C₅×Dic₃	C₂²×C₈	semidirect
308. D₃×C₈	D₂₀	direct (N × H)
330. D₂₀	D₃×C₈	direct (N × H)
340. C₅×C₈	D₃×D₄	semidirect
372. C₄×C₈	D₃×D₅	semidirect
378. C₅×D₃	C₈×D₄	semidirect
404. C₄×D₃	C₈×D₅	semidirect
409. C₃×C₈	C₂×D₂₀	semidirect
412. C₃⋊C₈	C₂×D₂₀	semidirect
423. C₂×D₅	C₂×D₃×C₈	semidirect
428. C₄×C₅	C₂×D₃×C₈	semidirect
472. C₃×C₅	C₂×C₈×D₄	semidirect
486. C₃×C₄	C₂×C₈×D₅	semidirect
492. Dic₃	C₂×C₈×D₅	semidirect
532. C₈	D₃×D₂₀	direct (N × H)
538. D₃	C₈×D₂₀	direct (N × H)
539. C₅	D₃×C₈×D₄	semidirect
557. C₄	D₃×C₈×D₅	semidirect
560. C₃	C₂×C₈×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈×D₅	2
C₄×D₃×D₂₀	2
C₈×D₆₀	2
C₄×C₅×D₃×C₈	2
C₃×C₈×D₂₀	2
D₃×#3952	2
#11748042	2
C₈×#1202	2
#11746994	2
D₃×C₄⋊#168	2
C₃⋊C₈×D₂₀	2
C₂×C₈×D₂₀	3
D₃×C₈×D₄	5

Subgroups — D3×C8×D20 #14414623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₈×D₂₀ #14414623