Subgroups — C₃×D₅×#442 #14416469

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₄×D₅	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65441	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65303	C₂	1	2	yes	maximal, complemented
6	C₃×#65158	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65074	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
10	C₃×#65000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#442	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	—	2	2	no	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
17	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
18	C₂×C₃×#686	C₂²	1	2	yes	—
19	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
20	C₃×D₅×D₈	C₄	1	8	yes	complemented
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	2	yes	complemented
25	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×#4027	—	2	2	no	—
27	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
28	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3964	C₂²	1	2	yes	complemented
34	C₃×#3953	C₂²	1	2	yes	complemented
35	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3941	C₂²	1	2	yes	complemented
39	C₃×#3940	C₂²	1	2	yes	complemented
40	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#442	—	5	1	no	maximal, Hall
42	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
43	C₄×D₄×D₅	C₂×C₃	1	2	yes	complemented
44	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
45	#65441	C₂×C₃	1	1	yes	characteristic, complemented
46	#65303	C₂×C₃	1	2	yes	complemented
47	#65158	C₂×C₃	1	1	yes	characteristic, complemented
48	D₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
49	#65074	C₂×C₃	1	2	yes	complemented
50	D₅×#102	C₂×C₃	1	2	yes	complemented
51	#65000	C₂×C₃	1	1	yes	characteristic, complemented
52	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₃×D₄×D₅	—	2	4	no	—
59	C₃×D₄×D₅	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	—	2	2	no	—
64	C₂×C₃×C₄×D₅	—	4	8	no	—
65	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₂²⋊Dic₅	—	2	2	no	—
74	C₃×#686	C₂×C₄	1	8	yes	complemented
75	C₃×#685	—	2	2	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
78	C₃×#683	—	2	2	no	—
79	C₃×C₄×Dic₅	D₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
84	C₃×C₈×D₅	—	2	2	no	—
85	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
86	C₂²×C₃×D₈	—	5	1	no	—
87	C₂×C₃×C₄×D₄	—	5	2	no	—
88	C₃×#442	—	5	1	no	—
89	C₃×#442	—	5	2	no	—
90	C₃×#442	—	5	1	no	—
91	C₃×#442	—	5	2	no	—
92	C₃×#442	—	5	1	no	—
93	C₃×#442	D₅	1	1	yes	characteristic, direct product factor
94	C₂×C₃×#106	—	5	1	no	—
95	C₂×C₃×#102	—	5	2	no	—
96	C₂×C₃×#97	—	5	1	no	—
97	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
98	C₂²×C₄×D₅	—	2	2	no	—
99	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
101	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
102	C₂×#686	C₂²×C₃	1	2	yes	—
103	C₄×C₂²⋊D₅	—	2	2	no	—
104	D₅×D₈	C₃×C₄	1	8	yes	complemented
105	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
108	#4039	C₂²×C₃	1	2	yes	complemented
109	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	#4027	—	2	2	no	—
111	D₅×C₂²⋊C₄	—	2	2	no	—
112	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
113	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
114	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₅×#102	C₂²×C₃	1	2	yes	complemented
116	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
117	#3964	C₂²×C₃	1	2	yes	complemented
118	#3953	C₂²×C₃	1	2	yes	complemented
119	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
120	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
121	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
122	#3941	C₂²×C₃	1	2	yes	complemented
123	#3940	C₂²×C₃	1	2	yes	complemented
124	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×#442	—	5	1	no	Sylow
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂²×C₃×D₅	—	2	2	no	—
128	C₂²×C₃×D₅	—	2	8	no	—
129	C₂²×C₃×D₅	—	4	4	no	—
130	C₂²×C₃×D₅	—	4	4	no	—
131	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	4	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₂²⋊D₅	—	2	8	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	4	4	no	—
141	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
143	C₃×D₂₀	—	2	2	no	—
144	C₃×D₂₀	C₂²×C₄	1	4	yes	complemented
145	C₃×C₄×D₅	—	2	4	no	—
146	C₃×C₄×D₅	—	4	4	no	—
147	C₃×C₄×D₅	—	4	4	no	—
148	C₃×C₄×D₅	—	4	4	no	—
149	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
150	C₃×C₄×D₅	#41	1	2	yes	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
153	C₃×#168	—	2	1	no	—
154	C₃×#168	C₂²×C₄	1	2	yes	complemented
155	C₂²×C₃×D₄	—	5	2	no	—
156	C₂³×C₃×C₄	—	10	2	no	—
157	C₂×C₃×D₈	—	5	2	no	—
158	C₂×C₃×D₈	—	5	8	no	—
159	C₂×C₃×D₈	—	5	1	no	—
160	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
161	C₂²×C₃×C₈	—	5	1	no	—
162	C₂²×C₃×C₈	—	5	1	no	—
163	C₃×C₄×D₄	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	—	10	2	no	—
167	C₃×C₄×D₄	—	10	2	no	—
168	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
169	C₂×C₃×C₄⋊C₄	—	5	2	no	—
170	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
171	C₂×C₃×C₄²	—	5	1	no	—
172	C₃×#106	—	5	1	no	—
173	C₃×#106	—	5	2	no	—
174	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
175	C₃×#102	—	5	2	no	—
176	C₃×#102	—	5	2	no	—
177	C₃×#102	—	5	2	no	—
178	C₃×#102	C₂×D₅	1	2	yes	complemented
179	C₃×#97	—	5	1	no	—
180	C₃×#97	—	5	1	no	—
181	C₃×#97	—	5	1	no	—
182	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
183	C₂³×D₅	—	2	2	no	—
184	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂×C₂²⋊D₅	—	2	2	no	—
187	C₂²×Dic₅	—	2	2	no	—
188	D₄×D₅	—	2	4	no	—
189	D₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
190	C₂×D₂₀	C₂³×C₃	1	2	yes	—
191	C₂×C₄×D₅	—	2	2	no	—
192	C₂×C₄×D₅	—	2	2	no	—
193	C₂×C₄×D₅	—	2	2	no	—
194	C₂×C₄×D₅	—	4	8	no	—
195	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
196	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
197	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
198	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	—	2	2	no	—
204	#686	C₂×C₃×C₄	1	8	yes	complemented
205	#685	—	2	2	no	—
206	#685	—	2	2	no	—
207	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
208	#683	—	2	2	no	—
209	C₄×Dic₅	C₃×D₄	1	2	yes	—
210	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	C₂×#168	C₂³×C₃	1	1	yes	characteristic
213	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
214	C₈×D₅	—	2	2	no	—
215	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
216	C₂²×D₈	—	5	1	no	—
217	C₂×C₄×D₄	—	5	2	no	—
218	#442	—	5	1	no	—
219	#442	—	5	2	no	—
220	#442	—	5	1	no	—
221	#442	—	5	2	no	—
222	#442	—	5	1	no	—
223	#442	C₃×D₅	1	1	yes	characteristic, direct product factor
224	C₂×#106	—	5	1	no	—
225	C₂×#102	—	5	2	no	—
226	C₂×#97	—	5	1	no	—
227	C₂²×C₃×C₅	—	2	4	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₃×D₅	—	2	4	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₂×C₃×D₅	—	4	2	no	—
234	C₂×C₃×D₅	—	4	16	no	—
235	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
236	C₂×C₃×D₅	AGL(1,ℤ/8)	1	4	yes	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	—	4	2	no	—
243	C₃×Dic₅	C₄×D₄	1	2	yes	—
244	C₂⁴×C₃	—	10	2	no	—
245	C₂×C₃×D₄	—	5	8	no	—
246	C₂×C₃×D₄	—	5	2	no	—
247	C₂×C₃×D₄	—	10	4	no	—
248	C₂×C₃×D₄	—	10	2	no	—
249	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	5	1	no	—
252	C₂²×C₃×C₄	—	5	2	no	—
253	C₂²×C₃×C₄	—	10	2	no	—
254	C₂²×C₃×C₄	—	10	2	no	—
255	C₂²×C₃×C₄	—	10	2	no	—
256	C₂²×C₃×C₄	—	10	2	no	—
257	C₂²×C₃×C₄	—	20	8	no	—
258	C₃×D₈	—	5	8	no	—
259	C₃×D₈	—	5	4	no	—
260	C₃×D₈	C₄×D₅	1	4	yes	complemented
261	C₂×C₃×C₈	—	5	1	no	—
262	C₂×C₃×C₈	—	5	4	no	—
263	C₂×C₃×C₈	—	5	1	no	—
264	C₂×C₃×C₈	—	10	2	no	—
265	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
267	C₃×C₄⋊C₄	—	5	2	no	—
268	C₃×C₄⋊C₄	—	10	2	no	—
269	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	10	2	no	—
272	C₃×C₂²⋊C₄	—	10	2	no	—
273	C₃×C₂²⋊C₄	—	10	2	no	—
274	C₃×C₄²	—	5	2	no	—
275	C₃×C₄²	—	5	1	no	—
276	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
277	C₂³×C₅	—	2	2	no	—
278	C₂²×D₅	—	2	2	no	—
279	C₂²×D₅	—	2	8	no	—
280	C₂²×D₅	—	4	4	no	—
281	C₂²×D₅	—	4	4	no	—
282	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	C₂²×C₃×C₄	1	4	yes	complemented
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	4	4	no	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	2	8	no	—
290	C₂×Dic₅	—	2	2	no	—
291	C₂×Dic₅	—	4	4	no	—
292	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
293	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
294	D₂₀	—	2	2	no	—
295	D₂₀	C₂²×C₃×C₄	1	4	yes	complemented
296	C₄×D₅	—	2	4	no	—
297	C₄×D₅	—	4	4	no	—
298	C₄×D₅	—	4	4	no	—
299	C₄×D₅	—	4	4	no	—
300	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
301	C₄×D₅	C₃×#41	1	2	yes	—
302	C₅×C₈	—	2	1	no	—
303	C₅×C₈	C₂²×C₃×C₄	1	2	yes	complemented
304	#168	—	2	1	no	—
305	#168	C₂²×C₃×C₄	1	2	yes	complemented
306	C₂²×D₄	—	5	2	no	—
307	C₂³×C₄	—	10	2	no	—
308	C₂×D₈	—	5	2	no	—
309	C₂×D₈	—	5	8	no	—
310	C₂×D₈	—	5	1	no	—
311	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
312	C₂²×C₈	—	5	1	no	—
313	C₂²×C₈	—	5	1	no	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	2	no	—
316	C₄×D₄	—	5	2	no	—
317	C₄×D₄	—	10	2	no	—
318	C₄×D₄	—	10	2	no	—
319	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
320	C₂×C₄⋊C₄	—	5	2	no	—
321	C₂×C₂²⋊C₄	—	10	2	no	—
322	C₂×C₄²	—	5	1	no	—
323	#106	—	5	1	no	—
324	#106	—	5	2	no	—
325	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
326	#102	—	5	2	no	—
327	#102	—	5	2	no	—
328	#102	—	5	2	no	—
329	#102	C₂×C₃×D₅	1	2	yes	complemented
330	#97	—	5	1	no	—
331	#97	—	5	1	no	—
332	#97	—	5	1	no	—
333	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
337	C₃×D₅	—	4	4	no	—
338	C₃×D₅	#442	1	4	yes	direct product factor
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	5	1	no	—
341	C₂³×C₃	—	10	8	no	—
342	C₂³×C₃	—	10	2	no	—
343	C₂³×C₃	—	20	4	no	—
344	C₂³×C₃	—	20	4	no	—
345	C₃×D₄	—	2	2	no	—
346	C₃×D₄	—	5	4	no	—
347	C₃×D₄	—	10	8	no	—
348	C₃×D₄	—	10	2	no	—
349	C₃×D₄	C₂×C₄×D₅	1	4	yes	complemented
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	4	4	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	5	2	no	—
354	C₂×C₃×C₄	—	5	2	no	—
355	C₂×C₃×C₄	—	5	2	no	—
356	C₂×C₃×C₄	—	10	4	no	—
357	C₂×C₃×C₄	—	10	2	no	—
358	C₂×C₃×C₄	—	20	4	no	—
359	C₂×C₃×C₄	—	20	4	no	—
360	C₂×C₃×C₄	—	20	4	no	—
361	C₂×C₃×C₄	—	20	4	no	—
362	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
363	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	5	2	no	—
366	C₃×C₈	—	10	1	no	—
367	C₃×C₈	C₂×C₄×D₅	1	2	yes	complemented
368	C₂²×C₅	—	2	4	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
372	C₂×D₅	—	2	4	no	—
373	C₂×D₅	—	4	2	no	—
374	C₂×D₅	—	4	2	no	—
375	C₂×D₅	—	4	16	no	—
376	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
377	C₂×D₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
381	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
382	Dic₅	—	2	2	no	—
383	Dic₅	—	4	2	no	—
384	Dic₅	C₃×C₄×D₄	1	2	yes	—
385	C₂⁴	—	10	2	no	—
386	C₂×D₄	—	5	8	no	—
387	C₂×D₄	—	5	2	no	—
388	C₂×D₄	—	10	4	no	—
389	C₂×D₄	—	10	2	no	—
390	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	5	2	no	—
394	C₂²×C₄	—	10	2	no	—
395	C₂²×C₄	—	10	2	no	—
396	C₂²×C₄	—	10	2	no	—
397	C₂²×C₄	—	10	2	no	—
398	C₂²×C₄	—	20	8	no	—
399	D₈	—	5	8	no	—
400	D₈	—	5	4	no	—
401	D₈	C₃×C₄×D₅	1	4	yes	complemented
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	4	no	—
404	C₂×C₈	—	5	1	no	—
405	C₂×C₈	—	10	2	no	—
406	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
408	C₄⋊C₄	—	5	2	no	—
409	C₄⋊C₄	—	10	2	no	—
410	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	10	2	no	—
413	C₂²⋊C₄	—	10	2	no	—
414	C₂²⋊C₄	—	10	2	no	—
415	C₄²	—	5	2	no	—
416	C₄²	—	5	1	no	—
417	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
418	C₃×C₅	C₂×#442	1	1	yes	characteristic, complemented, Hall
419	C₂²×C₃	—	2	4	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	—	5	4	no	—
423	C₂²×C₃	—	5	2	no	—
424	C₂²×C₃	—	10	4	no	—
425	C₂²×C₃	—	20	16	no	—
426	C₂²×C₃	—	20	2	no	—
427	C₂²×C₃	—	20	2	no	—
428	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	5	2	no	—
432	C₃×C₄	—	10	2	no	—
433	C₃×C₄	—	20	2	no	—
434	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
435	C₃×C₄	D₅×#41	1	1	yes	characteristic
436	C₂×C₅	—	4	4	no	—
437	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
438	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
439	D₅	—	4	4	no	—
440	D₅	C₃×#442	1	4	yes	direct product factor
441	C₂³	—	2	2	no	—
442	C₂³	—	5	1	no	—
443	C₂³	—	10	8	no	—
444	C₂³	—	10	2	no	—
445	C₂³	—	20	4	no	—
446	C₂³	—	20	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	5	4	no	—
449	D₄	—	10	8	no	—
450	D₄	—	10	2	no	—
451	D₄	C₂×C₃×C₄×D₅	1	4	yes	complemented
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	2	no	—
457	C₂×C₄	—	5	2	no	—
458	C₂×C₄	—	10	4	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	20	4	no	—
461	C₂×C₄	—	20	4	no	—
462	C₂×C₄	—	20	4	no	—
463	C₂×C₄	—	20	4	no	—
464	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
465	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	5	2	no	—
468	C₈	—	10	1	no	—
469	C₈	C₂×C₃×C₄×D₅	1	2	yes	complemented
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	—	5	4	no	—
472	C₂×C₃	—	20	4	no	—
473	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
474	C₂×C₃	D₅×AGL(1,ℤ/8)	1	2	yes	—
475	C₅	C₂×C₃×#442	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	2	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	5	4	no	—
480	C₂²	—	5	2	no	—
481	C₂²	—	10	4	no	—
482	C₂²	—	20	16	no	—
483	C₂²	—	20	2	no	—
484	C₂²	—	20	2	no	—
485	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	5	2	no	—
489	C₄	—	10	2	no	—
490	C₄	—	20	2	no	—
491	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
492	C₄	C₃×D₅×#41	1	1	yes	characteristic
493	C₃	D₅×#442	1	1	yes	characteristic, direct product factor, Sylow
494	C₂	—	4	4	no	—
495	C₂	—	5	4	no	—
496	C₂	—	20	4	no	—
497	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
498	C₂	C₃×D₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#442	D₅
hypocenter	C₅	C₂×C₃×#442
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#442

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₄×D₅	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₃×#65441	C₂	semidirect
5. C₃×#65303	C₂	semidirect
6. C₃×#65158	C₂	semidirect
7. C₃×D₅×#106	C₂	semidirect
8. C₃×#65074	C₂	semidirect
9. C₃×D₅×#102	C₂	semidirect
10. C₃×#65000	C₂	semidirect
11. C₃×D₅×#97	C₂	semidirect
12. D₅×#442	C₃	direct (N × H)
16. C₃×C₄×C₅×D₄	C₂²	semidirect
17. C₃×D₄×Dic₅	C₂²	semidirect
20. C₃×D₅×D₈	C₄	semidirect
24. C₃×#4039	C₂²	semidirect
28. C₃×C₄×D₂₀	C₂²	semidirect
30. C₃×C₅×#106	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#97	C₂²	semidirect
33. C₃×#3964	C₂²	semidirect
34. C₃×#3953	C₂²	semidirect
35. C₃×#3949	C₂²	semidirect
36. C₃×#3947	C₂²	semidirect
37. C₃×#3947	C₂²	semidirect
38. C₃×#3941	C₂²	semidirect
39. C₃×#3940	C₂²	semidirect
40. C₃×#3935	C₂²	semidirect
43. C₄×D₄×D₅	C₂×C₃	semidirect
44. C₅×#442	C₂×C₃	semidirect
45. #65441	C₂×C₃	semidirect
46. #65303	C₂×C₃	semidirect
47. #65158	C₂×C₃	semidirect
48. D₅×#106	C₂×C₃	semidirect
49. #65074	C₂×C₃	semidirect
50. D₅×#102	C₂×C₃	semidirect
51. #65000	C₂×C₃	semidirect
52. D₅×#97	C₂×C₃	semidirect
59. C₃×D₄×D₅	C₂×C₄	semidirect
67. C₃×C₅×D₈	C₂×C₄	semidirect
74. C₃×#686	C₂×C₄	semidirect
83. C₃×D₄₀	C₂×C₄	semidirect
85. C₃×C₈×D₅	C₂×C₄	semidirect
93. C₃×#442	D₅	direct (N × H)
100. C₄×C₅×D₄	C₂²×C₃	semidirect
101. D₄×Dic₅	C₂²×C₃	semidirect
104. D₅×D₈	C₃×C₄	semidirect
108. #4039	C₂²×C₃	semidirect
112. C₄×D₂₀	C₂²×C₃	semidirect
114. C₅×#106	C₂²×C₃	semidirect
115. C₅×#102	C₂²×C₃	semidirect
116. C₅×#97	C₂²×C₃	semidirect
117. #3964	C₂²×C₃	semidirect
118. #3953	C₂²×C₃	semidirect
119. #3949	C₂²×C₃	semidirect
120. #3947	C₂²×C₃	semidirect
121. #3947	C₂²×C₃	semidirect
122. #3941	C₂²×C₃	semidirect
123. #3940	C₂²×C₃	semidirect
124. #3935	C₂²×C₃	semidirect
133. C₃×C₅×D₄	C₂²×C₄	semidirect
144. C₃×D₂₀	C₂²×C₄	semidirect
152. C₃×C₅×C₈	C₂²×C₄	semidirect
154. C₃×#168	C₂²×C₄	semidirect
168. C₃×C₄×D₄	C₂×D₅	semidirect
174. C₃×#106	C₂×D₅	semidirect
178. C₃×#102	C₂×D₅	semidirect
182. C₃×#97	C₂×D₅	semidirect
189. D₄×D₅	C₂×C₃×C₄	semidirect
197. C₅×D₈	C₂×C₃×C₄	semidirect
204. #686	C₂×C₃×C₄	semidirect
213. D₄₀	C₂×C₃×C₄	semidirect
215. C₈×D₅	C₂×C₃×C₄	semidirect
223. #442	C₃×D₅	direct (N × H)
260. C₃×D₈	C₄×D₅	semidirect
284. C₅×D₄	C₂²×C₃×C₄	semidirect
295. D₂₀	C₂²×C₃×C₄	semidirect
303. C₅×C₈	C₂²×C₃×C₄	semidirect
305. #168	C₂²×C₃×C₄	semidirect
319. C₄×D₄	C₂×C₃×D₅	semidirect
325. #106	C₂×C₃×D₅	semidirect
329. #102	C₂×C₃×D₅	semidirect
333. #97	C₂×C₃×D₅	semidirect
338. C₃×D₅	#442	direct (N × H)
349. C₃×D₄	C₂×C₄×D₅	semidirect
367. C₃×C₈	C₂×C₄×D₅	semidirect
401. D₈	C₃×C₄×D₅	semidirect
418. C₃×C₅	C₂×#442	semidirect
440. D₅	C₃×#442	direct (N × H)
451. D₄	C₂×C₃×C₄×D₅	semidirect
469. C₈	C₂×C₃×C₄×D₅	semidirect
475. C₅	C₂×C₃×#442	semidirect
493. C₃	D₅×#442	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×D₈	2
C₃×C₄×D₄×D₅	2
C₃×C₅×#442	2
C₃×#65441	2
C₃×#65303	2
C₃×#65158	2
C₃×D₅×#106	2
C₃×#65074	2
C₃×D₅×#102	2
C₃×#65000	2
C₃×D₅×#97	2
D₅×#442	3
C₂×C₃×#442	5

Subgroups — C3×D5×#442 #14416469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#442 #14416469