Subgroups — C₅×D₃×#485 #14431596

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5045	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4996	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4868	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4815	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4814	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
15	C₅×#4723	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#485	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#946	C₂²	1	1	yes	characteristic
22	C₅×#926	C₂²	1	1	yes	characteristic
23	C₅×#924	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
26	C₅×#897	C₂²	1	1	yes	characteristic
27	C₅×#896	—	2	1	no	—
28	C₅×#892	C₂²	1	1	yes	characteristic
29	C₅×#892	C₂²	1	1	yes	characteristic
30	C₅×D₃×C₄⋊C₄	—	2	1	no	—
31	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
35	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
36	C₅×#878	—	2	1	no	—
37	C₅×#877	—	2	1	no	—
38	C₅×#872	—	2	1	no	—
39	C₄²×C₅×D₃	—	2	1	no	—
40	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic, complemented
46	C₅×#835	C₂²	1	1	yes	characteristic, complemented
47	C₅×#830	C₂²	1	1	yes	characteristic
48	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×#818	C₂²	1	1	yes	characteristic, complemented
51	C₅×#817	C₂²	1	1	yes	characteristic, complemented
52	C₅×#816	C₂²	1	1	yes	characteristic, complemented
53	C₅×#816	C₂²	1	1	yes	characteristic, complemented
54	C₅×#810	C₂²	1	1	yes	characteristic, complemented
55	C₅×#810	C₂²	1	1	yes	characteristic, complemented
56	C₅×#808	C₂²	1	1	yes	characteristic, complemented
57	C₅×#808	C₂²	1	1	yes	characteristic, complemented
58	C₅×#807	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	D₃×#485	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
62	C₂×C₅×#117	—	3	1	no	—
63	C₅×#485	—	3	1	no	—
64	C₅×#485	—	3	1	no	—
65	C₅×#485	—	3	1	no	—
66	C₅×#485	—	3	1	no	—
67	C₅×#485	—	3	1	no	—
68	C₅×#485	—	3	1	no	—
69	C₅×#485	—	3	1	no	—
70	C₅×#485	D₃	1	1	yes	characteristic, direct product factor
71	C₂×C₅×#107	—	3	1	no	—
72	C₂×C₅×#106	—	3	1	no	—
73	C₂×C₅×#103	—	3	1	no	—
74	C₂×C₅×#103	—	3	1	no	—
75	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
76	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
80	C₅×D₃×Q₈	—	2	2	no	—
81	C₅×D₃×Q₈	—	2	2	no	—
82	C₂×C₄×C₅×D₃	—	2	2	no	—
83	C₂×C₄×C₅×D₃	—	2	2	no	—
84	C₂×C₄×C₅×D₃	—	2	1	no	—
85	C₂×C₄×C₅×D₃	—	2	1	no	—
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
90	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
92	C₂×C₅×Dic₆	—	2	1	no	—
93	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₃×C₄²×C₅	—	2	1	no	—
103	C₅×#217	—	2	1	no	—
104	C₅×#217	—	2	1	no	—
105	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
106	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
107	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×C₄⋊Dic₃	—	2	1	no	—
110	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₄×C₅×Dic₃	—	2	1	no	—
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×D₃×C₈	—	2	2	no	—
124	C₅×D₃×C₈	—	2	2	no	—
125	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
126	D₃×#117	C₂×C₅	1	1	yes	characteristic
127	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
128	#5045	C₂×C₅	1	1	yes	characteristic, complemented
129	#4996	C₂×C₅	1	1	yes	characteristic, complemented
130	#4888	C₂×C₅	1	1	yes	characteristic, complemented
131	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
132	#4868	C₂×C₅	1	1	yes	characteristic, complemented
133	D₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
134	#4815	C₂×C₅	1	1	yes	characteristic, complemented
135	#4814	C₂×C₅	1	1	yes	characteristic, complemented
136	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
137	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
138	D₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
139	#4723	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×Q₈	—	3	1	no	—
141	C₂³×C₄×C₅	—	3	1	no	—
142	C₂²×C₅×C₈	—	3	1	no	—
143	C₂²×C₅×C₈	—	3	1	no	—
144	C₅×C₂²⋊Q₈	—	3	1	no	—
145	C₅×C₂²⋊Q₈	—	3	1	no	—
146	C₅×C₂²⋊Q₈	—	3	1	no	—
147	C₅×C₂²⋊Q₈	—	6	1	no	—
148	C₅×C₂²⋊Q₈	—	6	1	no	—
149	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
150	C₅×#117	—	3	1	no	—
151	C₅×#117	—	3	1	no	—
152	C₅×#117	—	3	1	no	—
153	C₅×#117	—	6	1	no	—
154	C₅×#117	—	6	1	no	—
155	C₅×#117	C₂×D₃	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	—	3	1	no	—
157	C₂×C₅×C₄⋊C₄	—	3	1	no	—
158	C₂×C₅×C₄⋊C₄	—	3	1	no	—
159	C₂×C₅×C₄⋊C₄	—	6	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
161	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
162	C₂×C₄²×C₅	—	6	1	no	—
163	C₅×#107	—	3	1	no	—
164	C₅×#107	—	3	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
167	C₅×#106	—	3	1	no	—
168	C₅×#106	—	3	1	no	—
169	C₅×#106	—	3	1	no	—
170	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
171	C₅×#103	—	3	1	no	—
172	C₅×#103	—	3	1	no	—
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	—	3	1	no	—
176	C₅×#103	—	3	1	no	—
177	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
178	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
179	C₅×C₂²⋊C₈	—	3	1	no	—
180	C₅×C₂²⋊C₈	—	3	1	no	—
181	C₅×C₂²⋊C₈	—	3	1	no	—
182	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
183	C₂×#485	—	3	1	no	Sylow
184	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₅×D₃	—	2	2	no	—
186	C₂²×C₅×D₃	—	2	2	no	—
187	C₂²×C₅×D₃	—	2	2	no	—
188	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₂×C₅×Dic₃	—	2	2	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
207	C₄×C₅×D₃	—	2	2	no	—
208	C₄×C₅×D₃	—	2	1	no	—
209	C₄×C₅×D₃	—	2	1	no	—
210	C₄×C₅×D₃	—	2	2	no	—
211	C₄×C₅×D₃	—	4	2	no	—
212	C₄×C₅×D₃	—	4	2	no	—
213	C₄×C₅×D₃	—	4	2	no	—
214	C₄×C₅×D₃	—	4	2	no	—
215	C₄×C₅×D₃	#41	1	2	yes	—
216	C₄×C₅×D₃	#41	1	2	yes	—
217	C₅×Dic₆	—	2	1	no	—
218	C₅×Dic₆	—	2	1	no	—
219	C₅×Dic₆	—	4	2	no	—
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
225	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
226	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₃×#117	C₂²×C₅	1	1	yes	characteristic
228	#946	C₂²×C₅	1	1	yes	characteristic
229	#926	C₂²×C₅	1	1	yes	characteristic
230	#924	C₂²×C₅	1	1	yes	characteristic
231	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
233	#897	C₂²×C₅	1	1	yes	characteristic
234	#896	—	2	1	no	—
235	#892	C₂²×C₅	1	1	yes	characteristic
236	#892	C₂²×C₅	1	1	yes	characteristic
237	D₃×C₄⋊C₄	—	2	1	no	—
238	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	D₃×C₂²⋊C₄	—	2	1	no	—
242	D₃×C₂²⋊C₄	—	2	1	no	—
243	#878	—	2	1	no	—
244	#877	—	2	1	no	—
245	#872	—	2	1	no	—
246	C₄²×D₃	—	2	1	no	—
247	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	#835	C₂²×C₅	1	1	yes	characteristic, complemented
253	#835	C₂²×C₅	1	1	yes	characteristic, complemented
254	#830	C₂²×C₅	1	1	yes	characteristic
255	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	#818	C₂²×C₅	1	1	yes	characteristic, complemented
258	#817	C₂²×C₅	1	1	yes	characteristic, complemented
259	#816	C₂²×C₅	1	1	yes	characteristic, complemented
260	#816	C₂²×C₅	1	1	yes	characteristic, complemented
261	#810	C₂²×C₅	1	1	yes	characteristic, complemented
262	#810	C₂²×C₅	1	1	yes	characteristic, complemented
263	#808	C₂²×C₅	1	1	yes	characteristic, complemented
264	#808	C₂²×C₅	1	1	yes	characteristic, complemented
265	#807	C₂²×C₅	1	1	yes	characteristic, complemented
266	#807	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	—	3	1	no	—
268	C₂×C₅×Q₈	—	3	1	no	—
269	C₂×C₅×Q₈	—	6	1	no	—
270	C₂×C₅×Q₈	—	6	2	no	—
271	C₂×C₅×Q₈	—	6	2	no	—
272	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	3	1	no	—
275	C₂²×C₄×C₅	—	3	1	no	—
276	C₂²×C₄×C₅	—	3	1	no	—
277	C₂²×C₄×C₅	—	3	1	no	—
278	C₂²×C₄×C₅	—	6	2	no	—
279	C₂²×C₄×C₅	—	6	2	no	—
280	C₂²×C₄×C₅	—	6	1	no	—
281	C₂²×C₄×C₅	—	6	1	no	—
282	C₂²×C₄×C₅	—	6	1	no	—
283	C₂²×C₄×C₅	—	6	1	no	—
284	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
285	C₂×C₅×C₈	—	3	1	no	—
286	C₂×C₅×C₈	—	3	1	no	—
287	C₂×C₅×C₈	—	6	2	no	—
288	C₂×C₅×C₈	—	6	2	no	—
289	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	3	1	no	—
293	C₅×C₄⋊C₄	—	3	1	no	—
294	C₅×C₄⋊C₄	—	3	1	no	—
295	C₅×C₄⋊C₄	—	6	1	no	—
296	C₅×C₄⋊C₄	—	6	1	no	—
297	C₅×C₄⋊C₄	—	6	1	no	—
298	C₅×C₄⋊C₄	—	6	1	no	—
299	C₅×C₄⋊C₄	—	6	1	no	—
300	C₅×C₄⋊C₄	—	6	1	no	—
301	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
302	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
303	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	6	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₅×C₂²⋊C₄	—	6	1	no	—
309	C₅×C₂²⋊C₄	—	6	1	no	—
310	C₅×C₂²⋊C₄	—	6	1	no	—
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	6	1	no	—
314	C₄²×C₅	—	6	1	no	—
315	C₄²×C₅	—	6	1	no	—
316	C₂×C₂²⋊Q₈	—	3	1	no	—
317	C₂×#117	—	3	1	no	—
318	#485	—	3	1	no	—
319	#485	—	3	1	no	—
320	#485	—	3	1	no	—
321	#485	—	3	1	no	—
322	#485	—	3	1	no	—
323	#485	—	3	1	no	—
324	#485	—	3	1	no	—
325	#485	C₅×D₃	1	1	yes	characteristic, direct product factor
326	C₂×#107	—	3	1	no	—
327	C₂×#106	—	3	1	no	—
328	C₂×#103	—	3	1	no	—
329	C₂×#103	—	3	1	no	—
330	C₂×C₂²⋊C₈	—	3	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	1	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₅×D₃	—	2	1	no	—
336	C₂×C₅×D₃	—	2	1	no	—
337	C₂×C₅×D₃	—	2	1	no	—
338	C₂×C₅×D₃	—	4	4	no	—
339	C₂×C₅×D₃	#123	1	2	yes	—
340	C₂×C₅×D₃	#135	1	2	yes	—
341	C₂×C₅×D₃	#137	1	2	yes	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	4	1	no	—
344	C₃×C₄×C₅	—	4	1	no	—
345	C₃×C₄×C₅	—	4	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₅×Dic₃	—	2	1	no	—
350	C₅×Dic₃	—	4	1	no	—
351	C₅×Dic₃	—	4	1	no	—
352	C₅×Dic₃	—	4	1	no	—
353	C₅×Dic₃	—	4	1	no	—
354	C₅×Dic₃	#123	1	2	yes	—
355	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
356	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
359	D₃×Q₈	—	2	2	no	—
360	D₃×Q₈	—	2	2	no	—
361	C₂×C₄×D₃	—	2	2	no	—
362	C₂×C₄×D₃	—	2	2	no	—
363	C₂×C₄×D₃	—	2	1	no	—
364	C₂×C₄×D₃	—	2	1	no	—
365	C₂×C₄×D₃	—	2	1	no	—
366	C₂×C₄×D₃	—	2	1	no	—
367	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
368	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
369	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
371	C₂×Dic₆	—	2	1	no	—
372	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₃×C₄⋊C₄	—	2	1	no	—
376	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₃×C₂²⋊C₄	—	2	1	no	—
380	C₃×C₂²⋊C₄	—	2	1	no	—
381	C₃×C₄²	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	—	2	1	no	—
384	(C₂×D₃)⋊C₄	—	2	1	no	—
385	(C₂×D₃)⋊C₄	—	2	1	no	—
386	(C₂×D₃)⋊C₄	—	2	1	no	—
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	C₄⋊Dic₃	—	2	1	no	—
389	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
390	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
391	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
392	Dic₃⋊C₄	—	2	1	no	—
393	Dic₃⋊C₄	—	2	1	no	—
394	Dic₃⋊C₄	—	2	1	no	—
395	Dic₃⋊C₄	—	2	1	no	—
396	Dic₃⋊C₄	—	2	1	no	—
397	C₄×Dic₃	—	2	1	no	—
398	C₄×Dic₃	—	2	1	no	—
399	C₄×Dic₃	—	2	1	no	—
400	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
402	D₃×C₈	—	2	2	no	—
403	D₃×C₈	—	2	2	no	—
404	C₂³×C₅	—	3	1	no	—
405	C₂³×C₅	—	3	1	no	—
406	C₂³×C₅	—	6	2	no	—
407	C₂³×C₅	—	6	2	no	—
408	C₂³×C₅	—	6	2	no	—
409	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
410	C₅×Q₈	—	2	1	no	—
411	C₅×Q₈	—	2	1	no	—
412	C₅×Q₈	—	6	1	no	—
413	C₅×Q₈	—	6	1	no	—
414	C₅×Q₈	—	12	2	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	3	1	no	—
422	C₂×C₄×C₅	—	3	2	no	—
423	C₂×C₄×C₅	—	3	2	no	—
424	C₂×C₄×C₅	—	3	1	no	—
425	C₂×C₄×C₅	—	6	2	no	—
426	C₂×C₄×C₅	—	6	2	no	—
427	C₂×C₄×C₅	—	6	2	no	—
428	C₂×C₄×C₅	—	6	1	no	—
429	C₂×C₄×C₅	—	6	1	no	—
430	C₂×C₄×C₅	—	6	1	no	—
431	C₂×C₄×C₅	—	6	1	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	12	2	no	—
435	C₂×C₄×C₅	—	12	2	no	—
436	C₂×C₄×C₅	—	12	2	no	—
437	C₂×C₄×C₅	—	12	2	no	—
438	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
440	C₅×C₈	—	2	1	no	—
441	C₅×C₈	—	2	1	no	—
442	C₅×C₈	—	6	1	no	—
443	C₅×C₈	—	6	1	no	—
444	C₂²×Q₈	—	3	1	no	—
445	C₂³×C₄	—	3	1	no	—
446	C₂²×C₈	—	3	1	no	—
447	C₂²×C₈	—	3	1	no	—
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	—	6	1	no	—
452	C₂²⋊Q₈	—	6	1	no	—
453	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
454	#117	—	3	1	no	—
455	#117	—	3	1	no	—
456	#117	—	3	1	no	—
457	#117	—	6	1	no	—
458	#117	—	6	1	no	—
459	#117	C₂×C₅×D₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	—	3	1	no	—
461	C₂×C₄⋊C₄	—	3	1	no	—
462	C₂×C₄⋊C₄	—	3	1	no	—
463	C₂×C₄⋊C₄	—	6	1	no	—
464	C₂×C₂²⋊C₄	—	6	1	no	—
465	C₂×C₂²⋊C₄	—	6	1	no	—
466	C₂×C₄²	—	6	1	no	—
467	#107	—	3	1	no	—
468	#107	—	3	1	no	—
469	#107	—	3	1	no	—
470	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
471	#106	—	3	1	no	—
472	#106	—	3	1	no	—
473	#106	—	3	1	no	—
474	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
475	#103	—	3	1	no	—
476	#103	—	3	1	no	—
477	#103	—	3	1	no	—
478	#103	—	3	1	no	—
479	#103	—	3	1	no	—
480	#103	—	3	1	no	—
481	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
482	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
483	C₂²⋊C₈	—	3	1	no	—
484	C₂²⋊C₈	—	3	1	no	—
485	C₂²⋊C₈	—	3	1	no	—
486	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
487	C₂×C₃×C₅	—	4	1	no	—
488	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
489	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
490	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
491	C₅×D₃	—	4	1	no	—
492	C₅×D₃	#485	1	4	yes	direct product factor
493	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂²×D₃	—	2	2	no	—
495	C₂²×D₃	—	2	2	no	—
496	C₂²×D₃	—	2	2	no	—
497	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₃×Q₈	—	2	1	no	—
500	C₃×Q₈	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	C₂×Dic₃	—	2	2	no	—
510	C₂×Dic₃	—	2	1	no	—
511	C₂×Dic₃	—	2	1	no	—
512	C₂×Dic₃	—	2	1	no	—
513	C₂×Dic₃	—	2	1	no	—
514	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
515	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
516	C₄×D₃	—	2	2	no	—
517	C₄×D₃	—	2	1	no	—
518	C₄×D₃	—	2	1	no	—
519	C₄×D₃	—	2	2	no	—
520	C₄×D₃	—	4	2	no	—
521	C₄×D₃	—	4	2	no	—
522	C₄×D₃	—	4	2	no	—
523	C₄×D₃	—	4	2	no	—
524	C₄×D₃	C₅×#41	1	2	yes	—
525	C₄×D₃	C₅×#41	1	2	yes	—
526	Dic₆	—	2	1	no	—
527	Dic₆	—	2	1	no	—
528	Dic₆	—	4	2	no	—
529	C₃×C₈	—	2	1	no	—
530	C₃×C₈	—	2	1	no	—
531	C₃⋊C₈	—	2	1	no	—
532	C₃⋊C₈	—	2	1	no	—
533	C₂²×C₅	—	2	1	no	—
534	C₂²×C₅	—	2	1	no	—
535	C₂²×C₅	—	2	1	no	—
536	C₂²×C₅	—	3	2	no	—
537	C₂²×C₅	—	3	2	no	—
538	C₂²×C₅	—	3	2	no	—
539	C₂²×C₅	—	6	1	no	—
540	C₂²×C₅	—	6	1	no	—
541	C₂²×C₅	—	6	1	no	—
542	C₂²×C₅	—	12	4	no	—
543	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
544	C₄×C₅	—	2	1	no	—
545	C₄×C₅	—	3	2	no	—
546	C₄×C₅	—	4	1	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	—	4	1	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	6	1	no	—
551	C₄×C₅	—	12	1	no	—
552	C₄×C₅	—	12	1	no	—
553	C₄×C₅	—	12	1	no	—
554	C₄×C₅	—	12	1	no	—
555	C₄×C₅	D₃×#41	1	1	yes	characteristic
556	C₄×C₅	D₃×#41	1	1	yes	characteristic
557	C₂⁴	—	3	1	no	—
558	C₂×Q₈	—	3	1	no	—
559	C₂×Q₈	—	6	1	no	—
560	C₂×Q₈	—	6	2	no	—
561	C₂×Q₈	—	6	2	no	—
562	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
563	C₂²×C₄	—	3	1	no	—
564	C₂²×C₄	—	3	1	no	—
565	C₂²×C₄	—	3	1	no	—
566	C₂²×C₄	—	3	1	no	—
567	C₂²×C₄	—	3	1	no	—
568	C₂²×C₄	—	6	2	no	—
569	C₂²×C₄	—	6	2	no	—
570	C₂²×C₄	—	6	1	no	—
571	C₂²×C₄	—	6	1	no	—
572	C₂²×C₄	—	6	1	no	—
573	C₂²×C₄	—	6	1	no	—
574	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
575	C₂×C₈	—	3	1	no	—
576	C₂×C₈	—	3	1	no	—
577	C₂×C₈	—	6	2	no	—
578	C₂×C₈	—	6	2	no	—
579	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
580	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	3	1	no	—
583	C₄⋊C₄	—	3	1	no	—
584	C₄⋊C₄	—	3	1	no	—
585	C₄⋊C₄	—	6	1	no	—
586	C₄⋊C₄	—	6	1	no	—
587	C₄⋊C₄	—	6	1	no	—
588	C₄⋊C₄	—	6	1	no	—
589	C₄⋊C₄	—	6	1	no	—
590	C₄⋊C₄	—	6	1	no	—
591	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
592	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
593	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	6	1	no	—
597	C₂²⋊C₄	—	6	1	no	—
598	C₂²⋊C₄	—	6	1	no	—
599	C₂²⋊C₄	—	6	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₂²⋊C₄	—	6	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	6	1	no	—
604	C₄²	—	6	1	no	—
605	C₄²	—	6	1	no	—
606	C₃×C₅	C₂×#485	1	1	yes	characteristic, complemented, Hall
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	2	1	no	—
610	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
611	C₂×D₃	—	2	1	no	—
612	C₂×D₃	—	2	1	no	—
613	C₂×D₃	—	2	1	no	—
614	C₂×D₃	—	4	4	no	—
615	C₂×D₃	C₅×#123	1	2	yes	—
616	C₂×D₃	C₅×#135	1	2	yes	—
617	C₂×D₃	C₅×#137	1	2	yes	—
618	C₃×C₄	—	2	1	no	—
619	C₃×C₄	—	4	1	no	—
620	C₃×C₄	—	4	1	no	—
621	C₃×C₄	—	4	1	no	—
622	C₃×C₄	—	4	1	no	—
623	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
624	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
625	Dic₃	—	2	1	no	—
626	Dic₃	—	4	1	no	—
627	Dic₃	—	4	1	no	—
628	Dic₃	—	4	1	no	—
629	Dic₃	—	4	1	no	—
630	Dic₃	C₅×#123	1	2	yes	—
631	C₂×C₅	—	3	4	no	—
632	C₂×C₅	—	4	1	no	—
633	C₂×C₅	—	12	1	no	—
634	C₂×C₅	D₃×#123	1	1	yes	characteristic
635	C₂×C₅	D₃×#135	1	1	yes	characteristic
636	C₂×C₅	D₃×#137	1	1	yes	characteristic
637	C₂³	—	3	1	no	—
638	C₂³	—	3	1	no	—
639	C₂³	—	6	2	no	—
640	C₂³	—	6	2	no	—
641	C₂³	—	6	2	no	—
642	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
643	Q₈	—	2	1	no	—
644	Q₈	—	2	1	no	—
645	Q₈	—	6	1	no	—
646	Q₈	—	6	1	no	—
647	Q₈	—	12	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	3	1	no	—
655	C₂×C₄	—	3	2	no	—
656	C₂×C₄	—	3	2	no	—
657	C₂×C₄	—	3	1	no	—
658	C₂×C₄	—	6	2	no	—
659	C₂×C₄	—	6	2	no	—
660	C₂×C₄	—	6	2	no	—
661	C₂×C₄	—	6	1	no	—
662	C₂×C₄	—	6	1	no	—
663	C₂×C₄	—	6	1	no	—
664	C₂×C₄	—	6	1	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	12	2	no	—
668	C₂×C₄	—	12	2	no	—
669	C₂×C₄	—	12	2	no	—
670	C₂×C₄	—	12	2	no	—
671	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
672	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
673	C₈	—	2	1	no	—
674	C₈	—	2	1	no	—
675	C₈	—	6	1	no	—
676	C₈	—	6	1	no	—
677	C₂×C₃	—	4	1	no	—
678	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
679	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
680	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
681	D₃	—	4	1	no	—
682	D₃	C₅×#485	1	4	yes	direct product factor
683	C₅	D₃×#485	1	1	yes	characteristic, direct product factor, Sylow
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	3	2	no	—
688	C₂²	—	3	2	no	—
689	C₂²	—	3	2	no	—
690	C₂²	—	6	1	no	—
691	C₂²	—	6	1	no	—
692	C₂²	—	6	1	no	—
693	C₂²	—	12	4	no	—
694	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	3	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	6	1	no	—
702	C₄	—	12	1	no	—
703	C₄	—	12	1	no	—
704	C₄	—	12	1	no	—
705	C₄	—	12	1	no	—
706	C₄	C₅×D₃×#41	1	1	yes	characteristic
707	C₄	C₅×D₃×#41	1	1	yes	characteristic
708	C₃	C₂×C₅×#485	1	1	yes	characteristic, complemented, Sylow
709	C₂	—	3	4	no	—
710	C₂	—	4	1	no	—
711	C₂	—	12	1	no	—
712	C₂	C₅×D₃×#123	1	1	yes	characteristic
713	C₂	C₅×D₃×#135	1	1	yes	characteristic
714	C₂	C₅×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#485	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₅×D₃	D₄
hypercenter	C₅×#485	D₃
hypocenter	C₃	C₂×C₅×#485
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#485

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#485	C₂	semidirect
4. C₅×#5045	C₂	semidirect
5. C₅×#4996	C₂	semidirect
6. C₅×#4888	C₂	semidirect
7. C₅×D₃×#107	C₂	semidirect
8. C₅×#4868	C₂	semidirect
9. C₅×D₃×#106	C₂	semidirect
10. C₅×#4815	C₂	semidirect
11. C₅×#4814	C₂	semidirect
12. C₅×D₃×#103	C₂	semidirect
13. C₅×D₃×#103	C₂	semidirect
15. C₅×#4723	C₂	semidirect
40. C₃×C₅×#107	C₂²	semidirect
41. C₃×C₅×#106	C₂²	semidirect
42. C₃×C₅×#103	C₂²	semidirect
43. C₃×C₅×#103	C₂²	semidirect
45. C₅×#835	C₂²	semidirect
46. C₅×#835	C₂²	semidirect
50. C₅×#818	C₂²	semidirect
51. C₅×#817	C₂²	semidirect
52. C₅×#816	C₂²	semidirect
53. C₅×#816	C₂²	semidirect
54. C₅×#810	C₂²	semidirect
55. C₅×#810	C₂²	semidirect
56. C₅×#808	C₂²	semidirect
57. C₅×#808	C₂²	semidirect
58. C₅×#807	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. D₃×#485	C₅	direct (N × H)
70. C₅×#485	D₃	direct (N × H)
127. C₃×#485	C₂×C₅	semidirect
128. #5045	C₂×C₅	semidirect
129. #4996	C₂×C₅	semidirect
130. #4888	C₂×C₅	semidirect
131. D₃×#107	C₂×C₅	semidirect
132. #4868	C₂×C₅	semidirect
133. D₃×#106	C₂×C₅	semidirect
134. #4815	C₂×C₅	semidirect
135. #4814	C₂×C₅	semidirect
136. D₃×#103	C₂×C₅	semidirect
137. D₃×#103	C₂×C₅	semidirect
139. #4723	C₂×C₅	semidirect
166. C₅×#107	C₂×D₃	semidirect
170. C₅×#106	C₂×D₃	semidirect
177. C₅×#103	C₂×D₃	semidirect
178. C₅×#103	C₂×D₃	semidirect
247. C₃×#107	C₂²×C₅	semidirect
248. C₃×#106	C₂²×C₅	semidirect
249. C₃×#103	C₂²×C₅	semidirect
250. C₃×#103	C₂²×C₅	semidirect
252. #835	C₂²×C₅	semidirect
253. #835	C₂²×C₅	semidirect
257. #818	C₂²×C₅	semidirect
258. #817	C₂²×C₅	semidirect
259. #816	C₂²×C₅	semidirect
260. #816	C₂²×C₅	semidirect
261. #810	C₂²×C₅	semidirect
262. #810	C₂²×C₅	semidirect
263. #808	C₂²×C₅	semidirect
264. #808	C₂²×C₅	semidirect
265. #807	C₂²×C₅	semidirect
266. #807	C₂²×C₅	semidirect
325. #485	C₅×D₃	direct (N × H)
470. #107	C₂×C₅×D₃	semidirect
474. #106	C₂×C₅×D₃	semidirect
481. #103	C₂×C₅×D₃	semidirect
482. #103	C₂×C₅×D₃	semidirect
492. C₅×D₃	#485	direct (N × H)
606. C₃×C₅	C₂×#485	semidirect
682. D₃	C₅×#485	direct (N × H)
683. C₅	D₃×#485	direct (N × H)
708. C₃	C₂×C₅×#485	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₂²⋊Q₈	2
C₅×D₃×#117	2
C₃×C₅×#485	2
C₅×#5045	2
C₅×#4996	2
C₅×#4888	2
C₅×D₃×#107	2
C₅×#4868	2
C₅×D₃×#106	2
C₅×#4815	2
C₅×#4814	2
C₅×D₃×#103	2
C₅×D₃×C₂²⋊C₈	2
C₅×#4723	2
C₂×C₅×#485	3
D₃×#485	5

Subgroups — C5×D3×#485 #14431596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#485 #14431596