Subgroups — C₅×D₃×#478 #14429916

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5009	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4891	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic
13	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic
14	C₅×#4766	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#478	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	—	2	1	no	—
19	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
22	C₄×C₅×#67	—	2	1	no	—
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₅×#893	C₂²	1	1	yes	characteristic
26	C₅×D₃×C₄⋊C₄	—	2	1	no	—
27	C₅×D₃×C₄⋊C₄	—	2	1	no	—
28	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#890	C₂²	1	1	yes	characteristic, complemented
32	C₅×#890	C₂²	1	1	yes	characteristic, complemented
33	C₅×#889	—	2	1	no	—
34	C₅×#889	—	2	1	no	—
35	C₅×#67⋊C₄	—	2	1	no	—
36	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
37	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
38	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
39	C₅×#870	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic
45	C₅×#832	C₂²	1	1	yes	characteristic
46	C₅×#832	C₂²	1	1	yes	characteristic
47	C₅×#821	C₂²	1	1	yes	characteristic
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×#818	C₂²	1	1	yes	characteristic, complemented
50	C₅×#817	C₂²	1	1	yes	characteristic, complemented
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×#809	C₂²	1	1	yes	characteristic
54	C₅×#809	C₂²	1	1	yes	characteristic
55	C₅×#808	C₂²	1	1	yes	characteristic, complemented
56	C₅×#808	C₂²	1	1	yes	characteristic, complemented
57	C₅×#807	C₂²	1	1	yes	characteristic, complemented
58	C₅×#807	C₂²	1	1	yes	characteristic, complemented
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	D₃×#478	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×#125	—	3	1	no	—
62	C₂×C₄×C₅×D₄	—	3	1	no	—
63	C₅×#478	—	3	1	no	—
64	C₅×#478	—	3	1	no	—
65	C₅×#478	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#478	—	3	1	no	—
68	C₅×#478	—	3	1	no	—
69	C₅×#478	—	3	1	no	—
70	C₅×#478	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×C₄⋊C₈	—	3	1	no	—
74	C₂×C₅×#102	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₅×#67	—	2	1	no	—
80	C₂²×C₅×Dic₃	—	2	1	no	—
81	C₅×D₃×D₄	—	2	2	no	—
82	C₅×D₃×D₄	Q₈	1	4	yes	—
83	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
89	C₂×C₄×C₅×D₃	—	4	4	no	—
90	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
91	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₅×#217	—	2	1	no	—
103	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
104	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
105	C₅×C₄⋊Dic₃	—	2	1	no	—
106	C₅×C₄⋊Dic₃	—	2	1	no	—
107	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
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	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
118	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
119	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×D₃×C₈	—	2	2	no	—
123	C₅×D₃×C₈	—	2	2	no	—
124	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
125	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
126	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
127	#5066	C₂×C₅	1	1	yes	characteristic, complemented
128	#5009	C₂×C₅	1	1	yes	characteristic, complemented
129	#4891	C₂×C₅	1	1	yes	characteristic, complemented
130	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
131	#4871	C₂×C₅	1	1	yes	characteristic, complemented
132	D₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
133	#4847	C₂×C₅	1	1	yes	characteristic, complemented
134	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
135	D₃×#102	C₂×C₅	1	1	yes	characteristic
136	D₃×#102	C₂×C₅	1	1	yes	characteristic
137	#4766	C₂×C₅	1	1	yes	characteristic, complemented
138	#4763	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂²×C₅×D₄	—	3	1	no	—
140	C₂³×C₄×C₅	—	6	1	no	—
141	C₂²×C₅×C₈	—	3	1	no	—
142	C₂²×C₅×C₈	—	3	1	no	—
143	C₅×#125	—	3	1	no	—
144	C₅×#125	—	3	1	no	—
145	C₅×#125	—	3	1	no	—
146	C₅×#125	—	6	1	no	—
147	C₅×#125	—	6	1	no	—
148	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
149	C₄×C₅×D₄	—	3	1	no	—
150	C₄×C₅×D₄	—	3	1	no	—
151	C₄×C₅×D₄	—	3	1	no	—
152	C₄×C₅×D₄	—	6	1	no	—
153	C₄×C₅×D₄	—	6	1	no	—
154	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	—	3	1	no	—
156	C₂×C₅×C₄⋊C₄	—	3	1	no	—
157	C₂×C₅×C₄⋊C₄	—	3	1	no	—
158	C₂×C₅×C₄⋊C₄	—	6	1	no	—
159	C₂×C₅×C₄⋊C₄	—	6	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
161	C₂×C₄²×C₅	—	3	1	no	—
162	C₅×#107	—	3	1	no	—
163	C₅×#107	—	3	1	no	—
164	C₅×#107	—	3	1	no	—
165	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
166	C₅×#106	—	3	1	no	—
167	C₅×#106	—	3	1	no	—
168	C₅×#106	—	3	1	no	—
169	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×C₄⋊C₈	—	3	1	no	—
172	C₅×C₄⋊C₈	—	3	1	no	—
173	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×#102	—	3	1	no	—
180	C₅×#102	C₂×D₃	1	1	yes	characteristic
181	C₅×#102	C₂×D₃	1	1	yes	characteristic
182	C₂×#478	—	3	1	no	Sylow
183	C₂³×C₃×C₅	—	2	1	no	—
184	C₂²×C₅×D₃	—	2	1	no	—
185	C₂²×C₅×D₃	—	2	4	no	—
186	C₂²×C₅×D₃	—	4	2	no	—
187	C₂²×C₅×D₃	—	4	2	no	—
188	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
189	C₃×C₅×D₄	—	2	1	no	—
190	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	4	2	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₅×#67	—	2	4	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	4	2	no	—
203	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
206	C₅×D₁₂	—	2	1	no	—
207	C₅×D₁₂	C₂×Q₈	1	2	yes	—
208	C₄×C₅×D₃	—	2	2	no	—
209	C₄×C₅×D₃	—	2	2	no	—
210	C₄×C₅×D₃	—	4	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	C₂×Q₈	1	2	yes	—
216	C₄×C₅×D₃	#41	1	2	yes	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₃×C₅×C₈	—	2	1	no	—
219	C₅×C₃⋊C₈	—	2	1	no	—
220	C₅×C₃⋊C₈	—	2	1	no	—
221	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
222	C₂²×C₄×D₃	—	2	1	no	—
223	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
225	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
226	C₄×#67	—	2	1	no	—
227	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
229	#893	C₂²×C₅	1	1	yes	characteristic
230	D₃×C₄⋊C₄	—	2	1	no	—
231	D₃×C₄⋊C₄	—	2	1	no	—
232	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	#890	C₂²×C₅	1	1	yes	characteristic, complemented
236	#890	C₂²×C₅	1	1	yes	characteristic, complemented
237	#889	—	2	1	no	—
238	#889	—	2	1	no	—
239	#67⋊C₄	—	2	1	no	—
240	D₃×C₂²⋊C₄	—	2	1	no	—
241	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
242	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
243	#870	C₂²×C₅	1	1	yes	characteristic, complemented
244	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₃×#102	C₂²×C₅	1	1	yes	characteristic
248	C₃×#102	C₂²×C₅	1	1	yes	characteristic
249	#832	C₂²×C₅	1	1	yes	characteristic
250	#832	C₂²×C₅	1	1	yes	characteristic
251	#821	C₂²×C₅	1	1	yes	characteristic
252	#821	C₂²×C₅	1	1	yes	characteristic
253	#818	C₂²×C₅	1	1	yes	characteristic, complemented
254	#817	C₂²×C₅	1	1	yes	characteristic, complemented
255	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
257	#809	C₂²×C₅	1	1	yes	characteristic
258	#809	C₂²×C₅	1	1	yes	characteristic
259	#808	C₂²×C₅	1	1	yes	characteristic, complemented
260	#808	C₂²×C₅	1	1	yes	characteristic, complemented
261	#807	C₂²×C₅	1	1	yes	characteristic, complemented
262	#807	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂⁴×C₅	—	6	1	no	—
265	C₂×C₅×D₄	—	3	4	no	—
266	C₂×C₅×D₄	—	3	1	no	—
267	C₂×C₅×D₄	—	6	2	no	—
268	C₂×C₅×D₄	—	6	1	no	—
269	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
270	C₂²×C₄×C₅	—	2	1	no	—
271	C₂²×C₄×C₅	—	3	1	no	—
272	C₂²×C₄×C₅	—	3	1	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	6	1	no	—
275	C₂²×C₄×C₅	—	6	1	no	—
276	C₂²×C₄×C₅	—	6	1	no	—
277	C₂²×C₄×C₅	—	6	1	no	—
278	C₂²×C₄×C₅	—	6	1	no	—
279	C₂²×C₄×C₅	—	6	1	no	—
280	C₂²×C₄×C₅	—	12	4	no	—
281	C₂×C₅×C₈	—	3	1	no	—
282	C₂×C₅×C₈	—	3	1	no	—
283	C₂×C₅×C₈	—	6	2	no	—
284	C₂×C₅×C₈	—	6	2	no	—
285	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
286	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	2	1	no	—
289	C₅×C₄⋊C₄	—	3	1	no	—
290	C₅×C₄⋊C₄	—	3	1	no	—
291	C₅×C₄⋊C₄	—	3	1	no	—
292	C₅×C₄⋊C₄	—	6	1	no	—
293	C₅×C₄⋊C₄	—	6	1	no	—
294	C₅×C₄⋊C₄	—	6	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	—	6	1	no	—
306	C₅×C₂²⋊C₄	—	6	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₄²×C₅	—	3	1	no	—
309	C₄²×C₅	—	3	1	no	—
310	C₄²×C₅	—	3	1	no	—
311	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
312	C₂×#125	—	3	1	no	—
313	C₂×C₄×D₄	—	3	1	no	—
314	#478	—	3	1	no	—
315	#478	—	3	1	no	—
316	#478	—	3	1	no	—
317	#478	—	3	1	no	—
318	#478	—	3	1	no	—
319	#478	—	3	1	no	—
320	#478	—	3	1	no	—
321	#478	C₅×D₃	1	1	yes	characteristic, direct product factor
322	C₂×#107	—	3	1	no	—
323	C₂×#106	—	3	1	no	—
324	C₂×C₄⋊C₈	—	3	1	no	—
325	C₂×#102	—	3	1	no	—
326	C₂×#102	—	3	1	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	4	1	no	—
329	C₂²×C₃×C₅	—	4	1	no	—
330	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₅×D₃	—	2	2	no	—
332	C₂×C₅×D₃	—	4	1	no	—
333	C₂×C₅×D₃	—	4	1	no	—
334	C₂×C₅×D₃	—	4	8	no	—
335	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
336	C₂×C₅×D₃	#135	1	2	yes	—
337	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	1	no	—
340	C₃×C₄×C₅	—	4	1	no	—
341	C₃×C₄×C₅	—	4	1	no	—
342	C₃×C₄×C₅	—	4	1	no	—
343	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
344	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	C₅×Dic₃	—	2	1	no	—
346	C₅×Dic₃	—	2	1	no	—
347	C₅×Dic₃	—	4	1	no	—
348	C₅×Dic₃	—	4	1	no	—
349	C₅×Dic₃	—	4	1	no	—
350	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
351	C₂³×D₃	—	2	1	no	—
352	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂×#67	—	2	1	no	—
355	C₂²×Dic₃	—	2	1	no	—
356	D₃×D₄	—	2	2	no	—
357	D₃×D₄	C₅×Q₈	1	4	yes	—
358	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄×D₃	—	2	1	no	—
360	C₂×C₄×D₃	—	2	1	no	—
361	C₂×C₄×D₃	—	2	1	no	—
362	C₂×C₄×D₃	—	2	1	no	—
363	C₂×C₄×D₃	—	2	1	no	—
364	C₂×C₄×D₃	—	4	4	no	—
365	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
366	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
367	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
370	C₃×C₄⋊C₄	—	2	1	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
373	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₃×C₂²⋊C₄	—	2	1	no	—
376	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
377	#217	—	2	1	no	—
378	(C₂×D₃)⋊C₄	—	2	1	no	—
379	(C₂×D₃)⋊C₄	—	2	1	no	—
380	C₄⋊Dic₃	—	2	1	no	—
381	C₄⋊Dic₃	—	2	1	no	—
382	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
383	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
384	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
385	Dic₃⋊C₄	—	2	1	no	—
386	Dic₃⋊C₄	—	2	1	no	—
387	Dic₃⋊C₄	—	2	1	no	—
388	Dic₃⋊C₄	—	2	1	no	—
389	Dic₃⋊C₄	—	2	1	no	—
390	Dic₃⋊C₄	—	2	1	no	—
391	Dic₃⋊C₄	—	2	1	no	—
392	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
393	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
394	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
397	D₃×C₈	—	2	2	no	—
398	D₃×C₈	—	2	2	no	—
399	C₂³×C₅	—	2	1	no	—
400	C₂³×C₅	—	3	1	no	—
401	C₂³×C₅	—	6	4	no	—
402	C₂³×C₅	—	6	1	no	—
403	C₂³×C₅	—	12	2	no	—
404	C₂³×C₅	—	12	2	no	—
405	C₅×D₄	—	2	1	no	—
406	C₅×D₄	—	3	2	no	—
407	C₅×D₄	—	6	4	no	—
408	C₅×D₄	—	6	1	no	—
409	C₅×D₄	D₃×Q₈	1	2	yes	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	3	1	no	—
414	C₂×C₄×C₅	—	3	2	no	—
415	C₂×C₄×C₅	—	3	2	no	—
416	C₂×C₄×C₅	—	3	1	no	—
417	C₂×C₄×C₅	—	3	1	no	—
418	C₂×C₄×C₅	—	4	2	no	—
419	C₂×C₄×C₅	—	6	2	no	—
420	C₂×C₄×C₅	—	6	2	no	—
421	C₂×C₄×C₅	—	6	1	no	—
422	C₂×C₄×C₅	—	6	1	no	—
423	C₂×C₄×C₅	—	6	1	no	—
424	C₂×C₄×C₅	—	12	2	no	—
425	C₂×C₄×C₅	—	12	2	no	—
426	C₂×C₄×C₅	—	12	2	no	—
427	C₂×C₄×C₅	—	12	2	no	—
428	C₂×C₄×C₅	—	12	2	no	—
429	C₂×C₄×C₅	—	12	2	no	—
430	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
431	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
432	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
433	C₅×C₈	—	2	1	no	—
434	C₅×C₈	—	2	1	no	—
435	C₅×C₈	—	6	1	no	—
436	C₅×C₈	—	6	1	no	—
437	C₂²×D₄	—	3	1	no	—
438	C₂³×C₄	—	6	1	no	—
439	C₂²×C₈	—	3	1	no	—
440	C₂²×C₈	—	3	1	no	—
441	#125	—	3	1	no	—
442	#125	—	3	1	no	—
443	#125	—	3	1	no	—
444	#125	—	6	1	no	—
445	#125	—	6	1	no	—
446	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
447	C₄×D₄	—	3	1	no	—
448	C₄×D₄	—	3	1	no	—
449	C₄×D₄	—	3	1	no	—
450	C₄×D₄	—	6	1	no	—
451	C₄×D₄	—	6	1	no	—
452	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	—	3	1	no	—
454	C₂×C₄⋊C₄	—	3	1	no	—
455	C₂×C₄⋊C₄	—	3	1	no	—
456	C₂×C₄⋊C₄	—	6	1	no	—
457	C₂×C₄⋊C₄	—	6	1	no	—
458	C₂×C₂²⋊C₄	—	6	1	no	—
459	C₂×C₄²	—	3	1	no	—
460	#107	—	3	1	no	—
461	#107	—	3	1	no	—
462	#107	—	3	1	no	—
463	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
464	#106	—	3	1	no	—
465	#106	—	3	1	no	—
466	#106	—	3	1	no	—
467	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
468	C₄⋊C₈	—	3	1	no	—
469	C₄⋊C₈	—	3	1	no	—
470	C₄⋊C₈	—	3	1	no	—
471	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
472	#102	—	3	1	no	—
473	#102	—	3	1	no	—
474	#102	—	3	1	no	—
475	#102	—	3	1	no	—
476	#102	—	3	1	no	—
477	#102	—	3	1	no	—
478	#102	C₂×C₅×D₃	1	1	yes	characteristic
479	#102	C₂×C₅×D₃	1	1	yes	characteristic
480	C₂×C₃×C₅	—	4	2	no	—
481	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
483	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
484	C₅×D₃	—	4	2	no	—
485	C₅×D₃	#478	1	4	yes	direct product factor
486	C₂³×C₃	—	2	1	no	—
487	C₂²×D₃	—	2	1	no	—
488	C₂²×D₃	—	2	4	no	—
489	C₂²×D₃	—	4	2	no	—
490	C₂²×D₃	—	4	2	no	—
491	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
492	C₃×D₄	—	2	1	no	—
493	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	4	2	no	—
498	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
501	#67	—	2	4	no	—
502	C₂×Dic₃	—	2	1	no	—
503	C₂×Dic₃	—	2	1	no	—
504	C₂×Dic₃	—	2	1	no	—
505	C₂×Dic₃	—	4	2	no	—
506	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
509	D₁₂	—	2	1	no	—
510	D₁₂	C₂×C₅×Q₈	1	2	yes	—
511	C₄×D₃	—	2	2	no	—
512	C₄×D₃	—	2	2	no	—
513	C₄×D₃	—	4	2	no	—
514	C₄×D₃	—	4	2	no	—
515	C₄×D₃	—	4	2	no	—
516	C₄×D₃	—	4	2	no	—
517	C₄×D₃	—	4	2	no	—
518	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
519	C₄×D₃	C₅×#41	1	2	yes	—
520	C₃×C₈	—	2	1	no	—
521	C₃×C₈	—	2	1	no	—
522	C₃⋊C₈	—	2	1	no	—
523	C₃⋊C₈	—	2	1	no	—
524	C₂²×C₅	—	2	2	no	—
525	C₂²×C₅	—	3	2	no	—
526	C₂²×C₅	—	3	2	no	—
527	C₂²×C₅	—	3	2	no	—
528	C₂²×C₅	—	4	1	no	—
529	C₂²×C₅	—	4	1	no	—
530	C₂²×C₅	—	6	2	no	—
531	C₂²×C₅	—	12	8	no	—
532	C₂²×C₅	—	12	1	no	—
533	C₂²×C₅	—	12	1	no	—
534	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	—	2	1	no	—
537	C₄×C₅	—	3	2	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	—	6	1	no	—
542	C₄×C₅	—	6	1	no	—
543	C₄×C₅	—	12	1	no	—
544	C₄×C₅	—	12	1	no	—
545	C₄×C₅	—	12	1	no	—
546	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
547	C₄×C₅	D₃×#41	1	1	yes	characteristic
548	C₂⁴	—	6	1	no	—
549	C₂×D₄	—	3	4	no	—
550	C₂×D₄	—	3	1	no	—
551	C₂×D₄	—	6	2	no	—
552	C₂×D₄	—	6	1	no	—
553	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	3	1	no	—
556	C₂²×C₄	—	3	1	no	—
557	C₂²×C₄	—	3	1	no	—
558	C₂²×C₄	—	6	1	no	—
559	C₂²×C₄	—	6	1	no	—
560	C₂²×C₄	—	6	1	no	—
561	C₂²×C₄	—	6	1	no	—
562	C₂²×C₄	—	6	1	no	—
563	C₂²×C₄	—	6	1	no	—
564	C₂²×C₄	—	12	4	no	—
565	C₂×C₈	—	3	1	no	—
566	C₂×C₈	—	3	1	no	—
567	C₂×C₈	—	6	2	no	—
568	C₂×C₈	—	6	2	no	—
569	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
570	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	3	1	no	—
574	C₄⋊C₄	—	3	1	no	—
575	C₄⋊C₄	—	3	1	no	—
576	C₄⋊C₄	—	6	1	no	—
577	C₄⋊C₄	—	6	1	no	—
578	C₄⋊C₄	—	6	1	no	—
579	C₄⋊C₄	—	6	1	no	—
580	C₄⋊C₄	—	6	1	no	—
581	C₄⋊C₄	—	6	1	no	—
582	C₄⋊C₄	—	6	1	no	—
583	C₄⋊C₄	—	6	1	no	—
584	C₄⋊C₄	—	6	1	no	—
585	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	6	1	no	—
590	C₂²⋊C₄	—	6	1	no	—
591	C₂²⋊C₄	—	6	1	no	—
592	C₄²	—	3	1	no	—
593	C₄²	—	3	1	no	—
594	C₄²	—	3	1	no	—
595	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
596	C₃×C₅	C₂×#478	1	1	yes	characteristic, complemented, Hall
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	4	1	no	—
599	C₂²×C₃	—	4	1	no	—
600	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
601	C₂×D₃	—	2	2	no	—
602	C₂×D₃	—	4	1	no	—
603	C₂×D₃	—	4	1	no	—
604	C₂×D₃	—	4	8	no	—
605	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
606	C₂×D₃	C₅×#135	1	2	yes	—
607	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
608	C₃×C₄	—	2	1	no	—
609	C₃×C₄	—	2	1	no	—
610	C₃×C₄	—	4	1	no	—
611	C₃×C₄	—	4	1	no	—
612	C₃×C₄	—	4	1	no	—
613	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
614	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
615	Dic₃	—	2	1	no	—
616	Dic₃	—	2	1	no	—
617	Dic₃	—	4	1	no	—
618	Dic₃	—	4	1	no	—
619	Dic₃	—	4	1	no	—
620	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
621	C₂×C₅	—	3	4	no	—
622	C₂×C₅	—	4	2	no	—
623	C₂×C₅	—	12	2	no	—
624	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
625	C₂×C₅	D₃×#135	1	1	yes	characteristic
626	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
627	C₂³	—	2	1	no	—
628	C₂³	—	3	1	no	—
629	C₂³	—	6	4	no	—
630	C₂³	—	6	1	no	—
631	C₂³	—	12	2	no	—
632	C₂³	—	12	2	no	—
633	D₄	—	2	1	no	—
634	D₄	—	3	2	no	—
635	D₄	—	6	4	no	—
636	D₄	—	6	1	no	—
637	D₄	C₅×D₃×Q₈	1	2	yes	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	3	1	no	—
642	C₂×C₄	—	3	2	no	—
643	C₂×C₄	—	3	2	no	—
644	C₂×C₄	—	3	1	no	—
645	C₂×C₄	—	3	1	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	6	2	no	—
648	C₂×C₄	—	6	2	no	—
649	C₂×C₄	—	6	1	no	—
650	C₂×C₄	—	6	1	no	—
651	C₂×C₄	—	6	1	no	—
652	C₂×C₄	—	12	2	no	—
653	C₂×C₄	—	12	2	no	—
654	C₂×C₄	—	12	2	no	—
655	C₂×C₄	—	12	2	no	—
656	C₂×C₄	—	12	2	no	—
657	C₂×C₄	—	12	2	no	—
658	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
659	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
661	C₈	—	2	1	no	—
662	C₈	—	2	1	no	—
663	C₈	—	6	1	no	—
664	C₈	—	6	1	no	—
665	C₂×C₃	—	4	2	no	—
666	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
667	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
668	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
669	D₃	—	4	2	no	—
670	D₃	C₅×#478	1	4	yes	direct product factor
671	C₅	D₃×#478	1	1	yes	characteristic, direct product factor, Sylow
672	C₂²	—	2	2	no	—
673	C₂²	—	3	2	no	—
674	C₂²	—	3	2	no	—
675	C₂²	—	3	2	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	6	2	no	—
679	C₂²	—	12	8	no	—
680	C₂²	—	12	1	no	—
681	C₂²	—	12	1	no	—
682	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	3	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	6	1	no	—
690	C₄	—	6	1	no	—
691	C₄	—	12	1	no	—
692	C₄	—	12	1	no	—
693	C₄	—	12	1	no	—
694	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
695	C₄	C₅×D₃×#41	1	1	yes	characteristic
696	C₃	C₂×C₅×#478	1	1	yes	characteristic, complemented, Sylow
697	C₂	—	3	4	no	—
698	C₂	—	4	2	no	—
699	C₂	—	12	2	no	—
700	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
701	C₂	C₅×D₃×#135	1	1	yes	characteristic
702	C₂	C₅×D₃×AGL(1,ℤ/8)	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×#478	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#478	D₃
hypocenter	C₃	C₂×C₅×#478
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#478

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×#125	C₂	semidirect
3. C₃×C₅×#478	C₂	semidirect
4. C₅×#5066	C₂	semidirect
5. C₅×#5009	C₂	semidirect
6. C₅×#4891	C₂	semidirect
7. C₅×D₃×#107	C₂	semidirect
8. C₅×#4871	C₂	semidirect
9. C₅×D₃×#106	C₂	semidirect
10. C₅×#4847	C₂	semidirect
11. C₅×D₃×C₄⋊C₈	C₂	semidirect
14. C₅×#4766	C₂	semidirect
15. C₅×#4763	C₂	semidirect
19. C₃×C₅×#125	C₂²	semidirect
31. C₅×#890	C₂²	semidirect
32. C₅×#890	C₂²	semidirect
39. C₅×#870	C₂²	semidirect
40. C₃×C₅×#107	C₂²	semidirect
41. C₃×C₅×#106	C₂²	semidirect
42. C₃×C₅×C₄⋊C₈	C₂²	semidirect
49. C₅×#818	C₂²	semidirect
50. C₅×#817	C₂²	semidirect
51. C₅×Dic₃⋊C₈	C₂²	semidirect
52. C₅×Dic₃⋊C₈	C₂²	semidirect
55. C₅×#808	C₂²	semidirect
56. C₅×#808	C₂²	semidirect
57. C₅×#807	C₂²	semidirect
58. C₅×#807	C₂²	semidirect
59. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
60. D₃×#478	C₅	direct (N × H)
70. C₅×#478	D₃	direct (N × H)
124. D₃×#125	C₂×C₅	semidirect
126. C₃×#478	C₂×C₅	semidirect
127. #5066	C₂×C₅	semidirect
128. #5009	C₂×C₅	semidirect
129. #4891	C₂×C₅	semidirect
130. D₃×#107	C₂×C₅	semidirect
131. #4871	C₂×C₅	semidirect
132. D₃×#106	C₂×C₅	semidirect
133. #4847	C₂×C₅	semidirect
134. D₃×C₄⋊C₈	C₂×C₅	semidirect
137. #4766	C₂×C₅	semidirect
138. #4763	C₂×C₅	semidirect
148. C₅×#125	C₂×D₃	semidirect
165. C₅×#107	C₂×D₃	semidirect
169. C₅×#106	C₂×D₃	semidirect
173. C₅×C₄⋊C₈	C₂×D₃	semidirect
223. C₃×#125	C₂²×C₅	semidirect
235. #890	C₂²×C₅	semidirect
236. #890	C₂²×C₅	semidirect
243. #870	C₂²×C₅	semidirect
244. C₃×#107	C₂²×C₅	semidirect
245. C₃×#106	C₂²×C₅	semidirect
246. C₃×C₄⋊C₈	C₂²×C₅	semidirect
253. #818	C₂²×C₅	semidirect
254. #817	C₂²×C₅	semidirect
255. Dic₃⋊C₈	C₂²×C₅	semidirect
256. Dic₃⋊C₈	C₂²×C₅	semidirect
259. #808	C₂²×C₅	semidirect
260. #808	C₂²×C₅	semidirect
261. #807	C₂²×C₅	semidirect
262. #807	C₂²×C₅	semidirect
263. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
321. #478	C₅×D₃	direct (N × H)
446. #125	C₂×C₅×D₃	semidirect
463. #107	C₂×C₅×D₃	semidirect
467. #106	C₂×C₅×D₃	semidirect
471. C₄⋊C₈	C₂×C₅×D₃	semidirect
485. C₅×D₃	#478	direct (N × H)
596. C₃×C₅	C₂×#478	semidirect
670. D₃	C₅×#478	direct (N × H)
671. C₅	D₃×#478	direct (N × H)
696. C₃	C₂×C₅×#478	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#125	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#478	2
C₅×#5066	2
C₅×#5009	2
C₅×#4891	2
C₅×D₃×#107	2
C₅×#4871	2
C₅×D₃×#106	2
C₅×#4847	2
C₅×D₃×C₄⋊C₈	2
C₅×D₃×#102	2
C₅×#4766	2
C₅×#4763	2
C₂×C₅×#478	3
D₃×#478	5

Subgroups — C5×D3×#478 #14429916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#478 #14429916