Subgroups — C₅×#78866 #14416670

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4817	C₂	1	2	yes	maximal, complemented
9	C₅×#4788	C₂	1	2	yes	maximal, complemented
10	C₅×#4785	C₂	1	2	yes	maximal, complemented
11	C₅×#4756	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×AGL(1,ℤ/8)	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	1	no	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₅×#949	C₄	1	8	yes	complemented
19	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
20	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×#215	C₂²	1	2	yes	—
22	C₅×D₄×Dic₃	—	2	1	no	—
23	C₅×D₄×Dic₃	—	2	1	no	—
24	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#213	C₂²	1	2	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
28	C₅×#926	—	2	1	no	—
29	C₅×#926	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	—	2	1	no	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×#208	C₂²	1	1	yes	characteristic
33	C₅×#893	—	2	1	no	—
34	C₅×#893	—	2	1	no	—
35	C₅×#893	C₂²	1	2	yes	—
36	C₅×#893	C₂²	1	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	complemented
38	C₃×C₅×#102	C₂²	1	2	yes	complemented
39	C₅×#821	C₂²	1	2	yes	—
40	C₅×#821	C₂²	1	2	yes	—
41	C₅×#815	C₂²	1	2	yes	complemented
42	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
43	C₅×#808	C₂²	1	2	yes	complemented
44	C₅×#807	C₂²	1	2	yes	complemented
45	#78866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
47	C₄×C₅×#41	—	3	1	no	—
48	C₂×C₄×C₅×D₄	—	3	1	no	—
49	C₅×#442	—	3	2	no	—
50	C₅×#440	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	2	no	—
52	C₄×C₅×D₈	—	3	2	no	—
53	C₅×#428	—	3	1	no	—
54	C₅×#418	—	3	1	no	—
55	C₅×#417	D₃	1	1	yes	characteristic, complemented
56	C₄×C₅×M₁₆	—	3	1	no	—
57	C₂³×C₅×D₃	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₅×Dic₃	—	2	1	no	—
67	C₂²×C₅×Dic₃	—	2	1	no	—
68	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
70	C₂×C₅×D₁₂	—	2	1	no	—
71	C₂×C₅×D₁₂	—	2	2	no	—
72	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
73	C₂×C₅×D₁₂	C₂³	1	2	yes	—
74	C₂×C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₄×C₅×D₃	—	2	2	no	—
76	C₂×C₄×C₅×D₃	—	4	4	no	—
77	C₃×C₅×M₁₆	—	2	2	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₅×#217	—	2	1	no	—
82	C₅×#217	—	2	1	no	—
83	C₅×#217	—	2	1	no	—
84	C₅×#215	C₂×C₄	1	8	yes	complemented
85	C₅×#213	C₂×C₄	1	8	yes	complemented
86	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
88	C₅×C₄⋊Dic₃	—	2	1	no	—
89	C₅×C₄⋊Dic₃	—	2	1	no	—
90	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
96	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₅×#208	C₂×C₄	1	4	yes	complemented
100	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
101	Dic₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#949	C₂×C₅	1	1	yes	characteristic
103	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
105	#5131	C₂×C₅	1	1	yes	characteristic, complemented
106	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
107	#4964	C₂×C₅	1	1	yes	characteristic, complemented
108	#4817	C₂×C₅	1	2	yes	complemented
109	#4788	C₂×C₅	1	2	yes	complemented
110	#4785	C₂×C₅	1	2	yes	complemented
111	#4756	C₂×C₅	1	2	yes	complemented
112	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
113	C₂²×C₅×D₄	—	3	1	no	—
114	C₂³×C₄×C₅	—	6	1	no	—
115	C₅×AGL(1,ℤ/8)	—	3	8	no	—
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×D₈	—	3	2	no	—
118	C₂×C₅×M₁₆	—	3	1	no	—
119	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
120	C₄×C₅×Q₈	—	3	1	no	—
121	C₄×C₅×Q₈	—	3	1	no	—
122	C₄×C₅×D₄	—	3	1	no	—
123	C₄×C₅×D₄	—	3	1	no	—
124	C₄×C₅×D₄	—	3	2	no	—
125	C₄×C₅×D₄	—	3	2	no	—
126	C₄×C₅×D₄	—	6	1	no	—
127	C₄×C₅×D₄	—	6	1	no	—
128	C₄×C₅×D₄	—	6	1	no	—
129	C₄×C₅×D₄	—	6	1	no	—
130	C₅×#117	—	3	1	no	—
131	C₅×#117	—	6	1	no	—
132	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
134	C₂×C₄²×C₅	—	3	1	no	—
135	C₂×C₄²×C₅	—	6	1	no	—
136	C₅×#107	—	3	2	no	—
137	C₅×#106	—	3	2	no	—
138	C₅×#103	C₂×D₃	1	2	yes	complemented
139	C₅×#102	—	3	2	no	—
140	C₅×#102	—	3	2	no	—
141	C₅×#102	C₂×D₃	1	2	yes	complemented
142	C₅×#97	—	3	2	no	—
143	C₄×C₅×C₈	—	3	2	no	—
144	C₄×AGL(1,ℤ/8)	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₅×D₃	—	2	4	no	—
148	C₂²×C₅×D₃	—	2	2	no	—
149	C₂²×C₅×D₃	—	4	2	no	—
150	C₂²×C₅×D₃	—	4	2	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
153	C₃×C₅×D₄	—	2	4	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	C₂²×C₄	1	2	yes	complemented
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	4	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	4	2	no	—
160	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	#41	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₂×C₅×Dic₃	—	2	2	no	—
165	C₂×C₅×Dic₃	—	2	1	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₂×C₅×Dic₃	—	4	1	no	—
168	C₂×C₅×Dic₃	—	4	2	no	—
169	C₂×C₅×Dic₃	—	4	2	no	—
170	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
174	C₅×D₁₂	—	2	4	no	—
175	C₅×D₁₂	—	2	2	no	—
176	C₅×D₁₂	C₂²×C₄	1	4	yes	—
177	C₄×C₅×D₃	—	4	4	no	—
178	C₄×C₅×D₃	—	4	4	no	—
179	C₃×C₅×C₈	—	2	2	no	—
180	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₄×D₃	—	2	1	no	—
184	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	#949	C₄×C₅	1	8	yes	complemented
187	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
188	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₂×#215	C₂²×C₅	1	2	yes	—
190	D₄×Dic₃	—	2	1	no	—
191	D₄×Dic₃	—	2	1	no	—
192	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
193	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₂×#213	C₂²×C₅	1	2	yes	—
195	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
196	#926	—	2	1	no	—
197	#926	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₄×Dic₃	—	2	1	no	—
199	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
200	C₂×#208	C₂²×C₅	1	1	yes	characteristic
201	#893	—	2	1	no	—
202	#893	—	2	1	no	—
203	#893	C₂²×C₅	1	2	yes	—
204	#893	C₂²×C₅	1	2	yes	—
205	C₃×#103	C₂²×C₅	1	2	yes	complemented
206	C₃×#102	C₂²×C₅	1	2	yes	complemented
207	#821	C₂²×C₅	1	2	yes	—
208	#821	C₂²×C₅	1	2	yes	—
209	#815	C₂²×C₅	1	2	yes	complemented
210	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
211	#808	C₂²×C₅	1	2	yes	complemented
212	#807	C₂²×C₅	1	2	yes	complemented
213	C₂⁴×C₅	—	6	1	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	C₄×D₃	1	4	yes	complemented
216	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	—	3	4	no	—
219	C₂×C₅×D₄	—	3	2	no	—
220	C₂×C₅×D₄	—	6	1	no	—
221	C₂×C₅×D₄	—	6	2	no	—
222	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	6	2	no	—
228	C₂²×C₄×C₅	—	6	2	no	—
229	C₂²×C₄×C₅	—	6	1	no	—
230	C₂²×C₄×C₅	—	6	1	no	—
231	C₂²×C₄×C₅	—	12	4	no	—
232	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₅×SD₁₆	—	3	8	no	—
234	C₅×D₈	—	3	8	no	—
235	C₅×M₁₆	—	2	2	no	—
236	C₅×M₁₆	—	3	4	no	—
237	C₂×C₅×C₈	—	3	2	no	—
238	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	3	1	no	—
241	C₅×C₄⋊C₄	—	3	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	—	6	1	no	—
244	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
245	C₅×C₂²⋊C₄	—	6	2	no	—
246	C₅×C₂²⋊C₄	—	6	2	no	—
247	C₅×C₂²⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₅×C₂²⋊C₄	—	6	1	no	—
250	C₄²×C₅	—	3	1	no	—
251	C₄²×C₅	—	3	1	no	—
252	C₄²×C₅	—	3	1	no	—
253	C₄²×C₅	—	3	1	no	—
254	C₄²×C₅	—	6	1	no	—
255	C₄²×C₅	—	6	1	no	—
256	C₄²×C₅	—	6	1	no	—
257	C₂×AGL(1,ℤ/8)	—	3	1	no	—
258	C₄×#41	—	3	1	no	—
259	C₂×C₄×D₄	—	3	1	no	—
260	#442	—	3	2	no	—
261	#440	—	3	2	no	—
262	C₄×SD₁₆	—	3	2	no	—
263	C₄×D₈	—	3	2	no	—
264	#428	—	3	1	no	—
265	#418	—	3	1	no	—
266	#417	C₅×D₃	1	1	yes	characteristic, complemented
267	C₄×M₁₆	—	3	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	1	no	—
270	C₂²×C₃×C₅	—	2	2	no	—
271	C₂²×C₃×C₅	—	4	1	no	—
272	C₂²×C₃×C₅	—	4	1	no	—
273	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
274	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₅×D₃	—	2	4	no	—
276	C₂×C₅×D₃	—	4	8	no	—
277	C₂×C₅×D₃	—	4	2	no	—
278	C₂×C₅×D₃	—	4	2	no	—
279	C₃×C₄×C₅	—	2	2	no	—
280	C₃×C₄×C₅	—	4	2	no	—
281	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
282	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
283	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
284	C₅×Dic₃	—	2	1	no	—
285	C₅×Dic₃	—	2	1	no	—
286	C₅×Dic₃	—	2	1	no	—
287	C₅×Dic₃	—	4	1	no	—
288	C₅×Dic₃	—	4	1	no	—
289	C₅×Dic₃	AGL(1,ℤ/8)	1	2	yes	complemented
290	C₂³×D₃	—	2	1	no	—
291	C₃×#41	—	2	2	no	—
292	C₃×#41	C₂×C₄×C₅	1	4	yes	complemented
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂²×Dic₃	—	2	1	no	—
300	C₂²×Dic₃	—	2	1	no	—
301	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
302	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
303	C₂×D₁₂	—	2	1	no	—
304	C₂×D₁₂	—	2	2	no	—
305	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
306	C₂×D₁₂	C₂³×C₅	1	2	yes	—
307	C₂×C₄×D₃	—	2	2	no	—
308	C₂×C₄×D₃	—	2	2	no	—
309	C₂×C₄×D₃	—	4	4	no	—
310	C₃×M₁₆	—	2	2	no	—
311	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
312	C₃×C₄⋊C₄	—	2	1	no	—
313	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
314	#217	—	2	1	no	—
315	#217	—	2	1	no	—
316	#217	—	2	1	no	—
317	#215	C₂×C₄×C₅	1	8	yes	complemented
318	#213	C₂×C₄×C₅	1	8	yes	complemented
319	(C₂×D₃)⋊C₄	—	2	2	no	—
320	(C₂×D₃)⋊C₄	—	2	2	no	—
321	C₄⋊Dic₃	—	2	1	no	—
322	C₄⋊Dic₃	—	2	1	no	—
323	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
324	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
325	C₄×Dic₃	—	2	1	no	—
326	C₄×Dic₃	—	2	1	no	—
327	C₄×Dic₃	—	2	1	no	—
328	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
329	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
330	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
331	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
332	#208	C₂×C₄×C₅	1	4	yes	complemented
333	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
334	C₂³×C₅	—	2	1	no	—
335	C₂³×C₅	—	6	4	no	—
336	C₂³×C₅	—	6	2	no	—
337	C₂³×C₅	—	12	2	no	—
338	C₂³×C₅	—	12	2	no	—
339	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
340	C₅×Q₈	—	2	1	no	—
341	C₅×Q₈	C₂×C₄×D₃	1	2	yes	complemented
342	C₅×D₄	—	2	4	no	—
343	C₅×D₄	—	2	1	no	—
344	C₅×D₄	—	3	4	no	—
345	C₅×D₄	—	6	4	no	—
346	C₅×D₄	—	6	2	no	—
347	C₅×D₄	C₂×C₄×D₃	1	2	yes	complemented
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	4	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	3	1	no	—
352	C₂×C₄×C₅	—	3	1	no	—
353	C₂×C₄×C₅	—	3	1	no	—
354	C₂×C₄×C₅	—	3	1	no	—
355	C₂×C₄×C₅	—	4	2	no	—
356	C₂×C₄×C₅	—	6	2	no	—
357	C₂×C₄×C₅	—	6	1	no	—
358	C₂×C₄×C₅	—	6	1	no	—
359	C₂×C₄×C₅	—	12	4	no	—
360	C₂×C₄×C₅	—	12	2	no	—
361	C₂×C₄×C₅	—	12	4	no	—
362	C₂×C₄×C₅	—	12	1	no	—
363	C₂×C₄×C₅	—	12	2	no	—
364	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
365	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
366	C₂×C₄×C₅	#237	1	2	yes	—
367	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
368	C₅×C₈	—	2	2	no	—
369	C₅×C₈	—	3	4	no	—
370	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
371	C₂²×D₄	—	3	1	no	—
372	C₂³×C₄	—	6	1	no	—
373	AGL(1,ℤ/8)	—	3	8	no	—
374	C₂×SD₁₆	—	3	2	no	—
375	C₂×D₈	—	3	2	no	—
376	C₂×M₁₆	—	3	1	no	—
377	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
378	C₄×Q₈	—	3	1	no	—
379	C₄×Q₈	—	3	1	no	—
380	C₄×D₄	—	3	1	no	—
381	C₄×D₄	—	3	1	no	—
382	C₄×D₄	—	3	2	no	—
383	C₄×D₄	—	3	2	no	—
384	C₄×D₄	—	6	1	no	—
385	C₄×D₄	—	6	1	no	—
386	C₄×D₄	—	6	1	no	—
387	C₄×D₄	—	6	1	no	—
388	#117	—	3	1	no	—
389	#117	—	6	1	no	—
390	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	6	1	no	—
392	C₂×C₄²	—	3	1	no	—
393	C₂×C₄²	—	6	1	no	—
394	#107	—	3	2	no	—
395	#106	—	3	2	no	—
396	#103	C₂×C₅×D₃	1	2	yes	complemented
397	#102	—	3	2	no	—
398	#102	—	3	2	no	—
399	#102	C₂×C₅×D₃	1	2	yes	complemented
400	#97	—	3	2	no	—
401	C₄×C₈	—	3	2	no	—
402	C₂×C₃×C₅	—	2	2	no	—
403	C₂×C₃×C₅	—	4	2	no	—
404	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
405	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂×C₃×C₅	#575	1	1	yes	characteristic
407	C₅×D₃	—	4	4	no	—
408	C₂³×C₃	—	2	1	no	—
409	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²×D₃	—	2	4	no	—
411	C₂²×D₃	—	2	2	no	—
412	C₂²×D₃	—	4	2	no	—
413	C₂²×D₃	—	4	2	no	—
414	C₃×Q₈	—	2	1	no	—
415	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	complemented
416	C₃×D₄	—	2	4	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	C₂²×C₄×C₅	1	2	yes	complemented
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	2	no	—
422	C₂×C₃×C₄	—	4	2	no	—
423	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₅×#41	1	2	yes	—
426	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	—	2	1	no	—
430	C₂×Dic₃	—	4	1	no	—
431	C₂×Dic₃	—	4	2	no	—
432	C₂×Dic₃	—	4	2	no	—
433	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
434	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
437	D₁₂	—	2	4	no	—
438	D₁₂	—	2	2	no	—
439	D₁₂	C₂²×C₄×C₅	1	4	yes	—
440	C₄×D₃	—	4	4	no	—
441	C₄×D₃	—	4	4	no	—
442	C₃×C₈	—	2	2	no	—
443	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	complemented
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	2	2	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	—	4	1	no	—
449	C₂²×C₅	—	6	4	no	—
450	C₂²×C₅	—	12	8	no	—
451	C₂²×C₅	—	12	2	no	—
452	C₂²×C₅	—	12	2	no	—
453	C₂²×C₅	#67⋊C₄	1	2	yes	—
454	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
455	C₄×C₅	—	2	2	no	—
456	C₄×C₅	—	3	2	no	—
457	C₄×C₅	—	4	2	no	—
458	C₄×C₅	—	6	1	no	—
459	C₄×C₅	—	6	1	no	—
460	C₄×C₅	—	6	1	no	—
461	C₄×C₅	—	12	1	no	—
462	C₄×C₅	—	12	1	no	—
463	C₄×C₅	#67⋊C₄	1	2	yes	—
464	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
465	C₄×C₅	C₂×#237	1	1	yes	characteristic
466	C₂⁴	—	6	1	no	—
467	#41	—	2	2	no	—
468	#41	C₄×C₅×D₃	1	4	yes	complemented
469	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	3	4	no	—
472	C₂×D₄	—	3	2	no	—
473	C₂×D₄	—	6	1	no	—
474	C₂×D₄	—	6	2	no	—
475	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	1	no	—
480	C₂²×C₄	—	6	2	no	—
481	C₂²×C₄	—	6	2	no	—
482	C₂²×C₄	—	6	1	no	—
483	C₂²×C₄	—	6	1	no	—
484	C₂²×C₄	—	12	4	no	—
485	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	SD₁₆	—	3	8	no	—
487	D₈	—	3	8	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	3	4	no	—
490	C₂×C₈	—	3	2	no	—
491	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	3	1	no	—
494	C₄⋊C₄	—	3	1	no	—
495	C₄⋊C₄	—	6	1	no	—
496	C₄⋊C₄	—	6	1	no	—
497	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
498	C₂²⋊C₄	—	6	2	no	—
499	C₂²⋊C₄	—	6	2	no	—
500	C₂²⋊C₄	—	6	1	no	—
501	C₂²⋊C₄	—	6	1	no	—
502	C₂²⋊C₄	—	6	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	6	1	no	—
508	C₄²	—	6	1	no	—
509	C₄²	—	6	1	no	—
510	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
517	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
518	C₂×D₃	—	2	4	no	—
519	C₂×D₃	—	4	8	no	—
520	C₂×D₃	—	4	2	no	—
521	C₂×D₃	—	4	2	no	—
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	4	2	no	—
524	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
525	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
526	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
527	Dic₃	—	2	1	no	—
528	Dic₃	—	2	1	no	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	4	1	no	—
531	Dic₃	—	4	1	no	—
532	Dic₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
533	C₂×C₅	—	2	2	no	—
534	C₂×C₅	—	4	2	no	—
535	C₂×C₅	—	12	4	no	—
536	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
537	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂×C₅	#5777	1	1	yes	characteristic
539	C₂³	—	2	1	no	—
540	C₂³	—	6	4	no	—
541	C₂³	—	6	2	no	—
542	C₂³	—	12	2	no	—
543	C₂³	—	12	2	no	—
544	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
545	Q₈	—	2	1	no	—
546	Q₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
547	D₄	—	2	4	no	—
548	D₄	—	2	1	no	—
549	D₄	—	3	4	no	—
550	D₄	—	6	4	no	—
551	D₄	—	6	2	no	—
552	D₄	C₂×C₄×C₅×D₃	1	2	yes	complemented
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	3	1	no	—
557	C₂×C₄	—	3	1	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	6	2	no	—
562	C₂×C₄	—	6	1	no	—
563	C₂×C₄	—	6	1	no	—
564	C₂×C₄	—	12	4	no	—
565	C₂×C₄	—	12	2	no	—
566	C₂×C₄	—	12	4	no	—
567	C₂×C₄	—	12	1	no	—
568	C₂×C₄	—	12	2	no	—
569	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
570	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
571	C₂×C₄	C₅×#237	1	2	yes	—
572	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	3	4	no	—
575	C₂×C₃	—	2	2	no	—
576	C₂×C₃	—	4	2	no	—
577	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
578	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂×C₃	C₅×#575	1	1	yes	characteristic
580	D₃	—	4	4	no	—
581	C₅	#78866	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	6	4	no	—
588	C₂²	—	12	8	no	—
589	C₂²	—	12	2	no	—
590	C₂²	—	12	2	no	—
591	C₂²	C₅×#67⋊C₄	1	2	yes	—
592	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	3	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	6	1	no	—
597	C₄	—	6	1	no	—
598	C₄	—	6	1	no	—
599	C₄	—	12	1	no	—
600	C₄	—	12	1	no	—
601	C₄	C₅×#67⋊C₄	1	2	yes	—
602	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
603	C₄	C₂×C₅×#237	1	1	yes	characteristic
604	C₃	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
605	C₂	—	2	2	no	—
606	C₂	—	4	2	no	—
607	C₂	—	12	4	no	—
608	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
609	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
610	C₂	C₅×#5777	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#949	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#417	D₃
hypocenter	C₃	C₄×C₅×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#417

Complements

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

N	H ≅ G/N	type
1. C₅×Dic₃×#41	C₂	semidirect
3. C₂×C₅×#893	C₂	semidirect
4. C₃×C₅×#417	C₂	semidirect
5. C₅×#5131	C₂	semidirect
6. C₅×Dic₃×M₁₆	C₂	semidirect
7. C₅×#4964	C₂	semidirect
8. C₅×#4817	C₂	semidirect
9. C₅×#4788	C₂	semidirect
10. C₅×#4785	C₂	semidirect
11. C₅×#4756	C₂	semidirect
18. C₅×#949	C₄	semidirect
19. C₅×Q₈×Dic₃	C₂²	semidirect
20. C₅×Q₈×Dic₃	C₂²	semidirect
24. C₅×D₄×Dic₃	C₂²	semidirect
25. C₅×D₄×Dic₃	C₂²	semidirect
37. C₃×C₅×#103	C₂²	semidirect
38. C₃×C₅×#102	C₂²	semidirect
41. C₅×#815	C₂²	semidirect
42. C₅×C₈×Dic₃	C₂²	semidirect
43. C₅×#808	C₂²	semidirect
44. C₅×#807	C₂²	semidirect
45. #78866	C₅	direct (N × H)
55. C₅×#417	D₃	semidirect
59. C₃×C₅×#41	C₂×C₄	semidirect
72. C₂×C₅×D₁₂	C₂×C₄	semidirect
84. C₅×#215	C₂×C₄	semidirect
85. C₅×#213	C₂×C₄	semidirect
99. C₅×#208	C₂×C₄	semidirect
101. Dic₃×#41	C₂×C₅	semidirect
103. C₂×#893	C₂×C₅	semidirect
104. C₃×#417	C₂×C₅	semidirect
105. #5131	C₂×C₅	semidirect
106. Dic₃×M₁₆	C₂×C₅	semidirect
107. #4964	C₂×C₅	semidirect
108. #4817	C₂×C₅	semidirect
109. #4788	C₂×C₅	semidirect
110. #4785	C₂×C₅	semidirect
111. #4756	C₂×C₅	semidirect
138. C₅×#103	C₂×D₃	semidirect
141. C₅×#102	C₂×D₃	semidirect
152. C₃×C₅×Q₈	C₂²×C₄	semidirect
155. C₃×C₅×D₄	C₂²×C₄	semidirect
180. C₅×C₃⋊C₈	C₂²×C₄	semidirect
186. #949	C₄×C₅	semidirect
187. Q₈×Dic₃	C₂²×C₅	semidirect
188. Q₈×Dic₃	C₂²×C₅	semidirect
192. D₄×Dic₃	C₂²×C₅	semidirect
193. D₄×Dic₃	C₂²×C₅	semidirect
205. C₃×#103	C₂²×C₅	semidirect
206. C₃×#102	C₂²×C₅	semidirect
209. #815	C₂²×C₅	semidirect
210. C₈×Dic₃	C₂²×C₅	semidirect
211. #808	C₂²×C₅	semidirect
212. #807	C₂²×C₅	semidirect
215. C₅×#41	C₄×D₃	semidirect
266. #417	C₅×D₃	semidirect
289. C₅×Dic₃	AGL(1,ℤ/8)	semidirect
292. C₃×#41	C₂×C₄×C₅	semidirect
305. C₂×D₁₂	C₂×C₄×C₅	semidirect
317. #215	C₂×C₄×C₅	semidirect
318. #213	C₂×C₄×C₅	semidirect
332. #208	C₂×C₄×C₅	semidirect
341. C₅×Q₈	C₂×C₄×D₃	semidirect
347. C₅×D₄	C₂×C₄×D₃	semidirect
396. #103	C₂×C₅×D₃	semidirect
399. #102	C₂×C₅×D₃	semidirect
415. C₃×Q₈	C₂²×C₄×C₅	semidirect
418. C₃×D₄	C₂²×C₄×C₅	semidirect
443. C₃⋊C₈	C₂²×C₄×C₅	semidirect
468. #41	C₄×C₅×D₃	semidirect
510. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
532. Dic₃	C₅×AGL(1,ℤ/8)	semidirect
546. Q₈	C₂×C₄×C₅×D₃	semidirect
552. D₄	C₂×C₄×C₅×D₃	semidirect
581. C₅	#78866	direct (N × H)
604. C₃	C₄×C₅×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₃×#41	2
C₂×C₅×#949	2
C₂×C₅×#893	2
C₃×C₅×#417	2
C₅×#5131	2
C₅×Dic₃×M₁₆	2
C₅×#4964	2
C₅×#4817	2
C₅×#4788	2
C₅×#4785	2
C₅×#4756	2
C₄×C₅×AGL(1,ℤ/8)	3
#78866	5

Subgroups — C5×#78866 #14416670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78866 #14416670