Subgroups — C₅×#71633 #14301083

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
5	C₅×#4939	C₂	1	1	yes	maximal, characteristic
6	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1880	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	—	2	2	no	—
12	C₃×C₄×C₅×Q₈	—	2	2	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#215	—	2	2	no	—
18	C₂×C₅×#215	—	2	2	no	—
19	C₂×C₅×#215	C₄	1	4	yes	complemented
20	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
21	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₅×#835	—	2	2	no	—
26	C₅×#809	—	2	2	no	—
27	#71633	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×SD₁₆	—	3	1	no	—
29	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#103	—	3	1	no	—
31	C₂×C₅×#102	—	3	1	no	—
32	C₅×#390	—	3	1	no	—
33	C₅×#340	—	3	1	no	—
34	C₅×#336	—	3	1	no	—
35	C₂³×C₅×D₃	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	—	2	1	no	—
38	C₂×C₃×C₅×Q₈	—	2	1	no	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
41	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
57	C₃×C₄²×C₅	—	2	4	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₅×#215	—	2	8	no	—
61	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
62	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	—	2	1	no	—
69	C₂×C₅×C₃⋊C₈	—	2	1	no	—
70	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
71	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×#215	C₂×C₅	1	1	yes	characteristic
73	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#809	C₂×C₅	1	1	yes	characteristic
75	#4939	C₂×C₅	1	1	yes	characteristic
76	#4529	C₂×C₅	1	1	yes	characteristic, complemented
77	#4524	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	—	3	1	no	—
80	C₂×C₅×SD₁₆	—	3	4	no	—
81	C₂×C₅×SD₁₆	—	6	2	no	—
82	C₂×C₅×SD₁₆	—	6	2	no	—
83	C₂²×C₅×C₈	—	3	1	no	—
84	C₂²×C₅×C₈	—	3	1	no	—
85	C₄×C₅×Q₈	—	2	2	no	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	3	1	no	—
89	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#103	—	6	2	no	—
95	C₅×#102	—	6	2	no	—
96	#1880	—	3	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	4	1	no	—
100	C₂²×C₅×D₃	—	4	1	no	—
101	C₂²×C₅×D₃	—	4	1	no	—
102	C₂²×C₅×D₃	—	4	1	no	—
103	C₂²×C₅×D₃	—	4	1	no	—
104	C₂²×C₅×D₃	—	4	1	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	2	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	1	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	4	1	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	complemented
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
127	C₂×C₅×Dic₃	—	4	1	no	—
128	C₂×C₅×Dic₃	—	4	1	no	—
129	C₂×C₅×Dic₃	—	4	1	no	—
130	C₅×D₁₂	—	2	2	no	—
131	C₅×D₁₂	—	2	2	no	—
132	C₅×D₁₂	—	4	1	no	—
133	C₅×D₁₂	—	4	1	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₅×C₃⋊C₈	—	4	1	no	—
136	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
137	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
138	C₃×C₄×Q₈	—	2	2	no	—
139	C₃×C₄×Q₈	—	2	2	no	—
140	C₂×C₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄²	—	2	1	no	—
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×#215	—	2	2	no	—
145	C₂×#215	—	2	2	no	—
146	C₂×#215	C₄×C₅	1	4	yes	complemented
147	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
148	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
149	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
150	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	#835	—	2	2	no	—
153	#809	—	2	2	no	—
154	C₂⁴×C₅	—	6	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	C₄×D₃	1	2	yes	—
159	C₂×C₅×Q₈	D₁₂	1	2	yes	—
160	C₂×C₅×Q₈	#67	1	2	yes	—
161	C₂×C₅×D₄	—	3	2	no	—
162	C₂×C₅×D₄	—	6	1	no	—
163	C₂×C₅×D₄	—	6	1	no	—
164	C₂×C₅×D₄	—	6	1	no	—
165	C₂×C₅×D₄	—	6	1	no	—
166	C₂×C₅×D₄	—	6	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	6	1	no	—
170	C₂²×C₄×C₅	#67	1	1	yes	characteristic
171	C₂²×C₄×C₅	#67	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₅×SD₁₆	—	6	8	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	6	1	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₂×C₅×C₈	—	6	1	no	—
178	C₂×C₅×C₈	—	6	1	no	—
179	C₂×C₅×C₈	—	6	1	no	—
180	C₅×C₄⋊C₄	—	2	4	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	6	1	no	—
183	C₅×C₄⋊C₄	—	6	1	no	—
184	C₅×C₄⋊C₄	#67	1	2	yes	—
185	C₅×C₂²⋊C₄	—	12	2	no	—
186	C₅×C₂²⋊C₄	—	12	2	no	—
187	C₄²×C₅	—	2	4	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₂²×SD₁₆	—	3	1	no	—
191	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
192	C₂×#103	—	3	1	no	—
193	C₂×#102	—	3	1	no	—
194	#390	—	3	1	no	—
195	#340	—	3	1	no	—
196	#336	—	3	1	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	#120	1	1	yes	characteristic
199	C₂²×C₃×C₅	#121	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₃×C₅	#137	1	1	yes	characteristic
204	C₂×C₅×D₃	—	4	2	no	—
205	C₂×C₅×D₃	—	4	2	no	—
206	C₂×C₅×D₃	—	4	2	no	—
207	C₂×C₅×D₃	—	8	1	no	—
208	C₂×C₅×D₃	—	8	1	no	—
209	C₂×C₅×D₃	—	8	1	no	—
210	C₂×C₅×D₃	—	8	1	no	—
211	C₃×C₄×C₅	—	2	4	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	4	1	no	—
214	C₃×C₄×C₅	—	4	2	no	—
215	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
217	C₃×C₄×C₅	#121	1	1	yes	characteristic
218	C₃×C₄×C₅	#123	1	1	yes	characteristic
219	C₅×Dic₃	—	8	1	no	—
220	C₂³×D₃	—	2	1	no	—
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	—	2	1	no	—
223	C₂×C₃×Q₈	—	2	1	no	—
224	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
226	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×Dic₃	—	2	1	no	—
233	C₂×D₁₂	—	2	1	no	—
234	C₂×D₁₂	—	2	1	no	—
235	C₂×D₁₂	—	2	1	no	—
236	C₂×D₁₂	—	2	1	no	—
237	C₂×D₁₂	—	2	1	no	—
238	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
239	C₃×C₄⋊C₄	—	2	4	no	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
242	C₃×C₄²	—	2	4	no	—
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	2	1	no	—
245	#215	—	2	8	no	—
246	(C₂×D₃)⋊C₄	—	4	2	no	—
247	(C₂×D₃)⋊C₄	—	4	2	no	—
248	C₄⋊Dic₃	—	2	1	no	—
249	C₄⋊Dic₃	—	2	1	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	—	2	1	no	—
252	C₂×C₃⋊C₈	—	2	1	no	—
253	C₂×C₃⋊C₈	—	2	1	no	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
256	C₂³×C₅	—	6	2	no	—
257	C₂³×C₅	—	12	1	no	—
258	C₂³×C₅	—	12	1	no	—
259	C₂³×C₅	—	12	1	no	—
260	C₂³×C₅	—	12	1	no	—
261	C₂³×C₅	—	12	1	no	—
262	C₂³×C₅	—	12	1	no	—
263	C₂³×C₅	C₂×#67	1	1	yes	characteristic
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
268	C₅×D₄	—	6	2	no	—
269	C₅×D₄	—	6	2	no	—
270	C₅×D₄	—	12	1	no	—
271	C₅×D₄	—	12	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	12	1	no	—
284	C₂×C₄×C₅	—	12	1	no	—
285	C₂×C₄×C₅	—	12	1	no	—
286	C₂×C₄×C₅	#215	1	2	yes	complemented
287	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
289	C₂×C₄×C₅	#235	1	1	yes	characteristic
290	C₂×C₄×C₅	#235	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
293	C₅×C₈	—	6	2	no	—
294	C₅×C₈	—	12	1	no	—
295	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
296	C₂²×D₄	—	3	1	no	—
297	C₂×SD₁₆	—	3	4	no	—
298	C₂×SD₁₆	—	6	2	no	—
299	C₂×SD₁₆	—	6	2	no	—
300	C₂²×C₈	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	3	1	no	—
306	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	6	1	no	—
308	C₂×C₂²⋊C₄	—	6	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
311	#103	—	6	2	no	—
312	#102	—	6	2	no	—
313	C₂×C₃×C₅	#386	1	1	yes	characteristic
314	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#440	1	1	yes	characteristic
316	C₂×C₃×C₅	#448	1	1	yes	characteristic
317	C₂×C₃×C₅	#449	1	1	yes	characteristic
318	C₂×C₃×C₅	#460	1	1	yes	characteristic
319	C₂×C₃×C₅	#464	1	1	yes	characteristic
320	C₅×D₃	—	8	2	no	—
321	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	—	4	1	no	—
324	C₂²×D₃	—	4	1	no	—
325	C₂²×D₃	—	4	1	no	—
326	C₂²×D₃	—	4	1	no	—
327	C₂²×D₃	—	4	1	no	—
328	C₂²×D₃	—	4	1	no	—
329	C₃×Q₈	—	2	2	no	—
330	C₃×Q₈	—	2	2	no	—
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	C₅×C₂²⋊C₄	1	4	yes	complemented
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	4	1	no	—
343	C₂×C₃×C₄	—	4	1	no	—
344	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	complemented
345	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
350	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
351	C₂×Dic₃	—	4	1	no	—
352	C₂×Dic₃	—	4	1	no	—
353	C₂×Dic₃	—	4	1	no	—
354	D₁₂	—	2	2	no	—
355	D₁₂	—	2	2	no	—
356	D₁₂	—	4	1	no	—
357	D₁₂	—	4	1	no	—
358	C₃⋊C₈	—	2	2	no	—
359	C₃⋊C₈	—	4	1	no	—
360	C₂²×C₅	—	12	2	no	—
361	C₂²×C₅	—	12	2	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	24	1	no	—
364	C₂²×C₅	—	24	1	no	—
365	C₂²×C₅	—	24	1	no	—
366	C₂²×C₅	—	24	1	no	—
367	C₂²×C₅	C₄×#67	1	1	yes	characteristic
368	C₂²×C₅	#930	1	1	yes	characteristic
369	C₂²×C₅	C₂×#215	1	1	yes	characteristic
370	C₂²×C₅	#942	1	1	yes	characteristic
371	C₂²×C₅	#949	1	1	yes	characteristic
372	C₂²×C₅	#950	1	1	yes	characteristic
373	C₂²×C₅	#953	1	1	yes	characteristic
374	C₄×C₅	—	2	4	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	—	24	1	no	—
379	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
380	C₄×C₅	C₄×#67	1	1	yes	characteristic
381	C₄×C₅	#929	1	1	yes	characteristic
382	C₄×C₅	#930	1	1	yes	characteristic
383	C₂⁴	—	6	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	C₄×C₅×D₃	1	2	yes	—
388	C₂×Q₈	C₅×D₁₂	1	2	yes	—
389	C₂×Q₈	C₅×#67	1	2	yes	—
390	C₂×D₄	—	3	2	no	—
391	C₂×D₄	—	6	1	no	—
392	C₂×D₄	—	6	1	no	—
393	C₂×D₄	—	6	1	no	—
394	C₂×D₄	—	6	1	no	—
395	C₂×D₄	—	6	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	6	1	no	—
399	C₂²×C₄	C₅×#67	1	1	yes	characteristic
400	C₂²×C₄	C₅×#67	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
402	SD₁₆	—	6	8	no	—
403	C₂×C₈	—	3	2	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	—	6	1	no	—
406	C₂×C₈	—	6	1	no	—
407	C₂×C₈	—	6	1	no	—
408	C₂×C₈	—	6	1	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	6	1	no	—
412	C₄⋊C₄	—	6	1	no	—
413	C₄⋊C₄	C₅×#67	1	2	yes	—
414	C₂²⋊C₄	—	12	2	no	—
415	C₂²⋊C₄	—	12	2	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₃×C₅	#1880	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₃	C₅×#120	1	1	yes	characteristic
422	C₂²×C₃	C₅×#121	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
424	C₂²×C₃	C₅×#135	1	1	yes	characteristic
425	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂²×C₃	C₅×#137	1	1	yes	characteristic
427	C₂×D₃	—	4	2	no	—
428	C₂×D₃	—	4	2	no	—
429	C₂×D₃	—	4	2	no	—
430	C₂×D₃	—	8	1	no	—
431	C₂×D₃	—	8	1	no	—
432	C₂×D₃	—	8	1	no	—
433	C₂×D₃	—	8	1	no	—
434	C₃×C₄	—	2	4	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
439	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
440	C₃×C₄	C₅×#121	1	1	yes	characteristic
441	C₃×C₄	C₅×#123	1	1	yes	characteristic
442	Dic₃	—	8	1	no	—
443	C₂×C₅	—	24	2	no	—
444	C₂×C₅	C₄×#215	1	1	yes	characteristic
445	C₂×C₅	#5026	1	1	yes	characteristic
446	C₂×C₅	#5027	1	1	yes	characteristic
447	C₂×C₅	#5028	1	1	yes	characteristic
448	C₂×C₅	#5213	1	1	yes	characteristic
449	C₂×C₅	#5227	1	1	yes	characteristic
450	C₂×C₅	#5238	1	1	yes	characteristic
451	C₂³	—	6	2	no	—
452	C₂³	—	12	1	no	—
453	C₂³	—	12	1	no	—
454	C₂³	—	12	1	no	—
455	C₂³	—	12	1	no	—
456	C₂³	—	12	1	no	—
457	C₂³	—	12	1	no	—
458	C₂³	C₂×C₅×#67	1	1	yes	characteristic
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	C₅×(C₂×D₃)⋊C₄	1	4	yes	complemented
463	D₄	—	6	2	no	—
464	D₄	—	6	2	no	—
465	D₄	—	12	1	no	—
466	D₄	—	12	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	12	1	no	—
479	C₂×C₄	—	12	1	no	—
480	C₂×C₄	—	12	1	no	—
481	C₂×C₄	C₅×#215	1	2	yes	complemented
482	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
483	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
484	C₂×C₄	C₅×#235	1	1	yes	characteristic
485	C₂×C₄	C₅×#235	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
487	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
488	C₈	—	6	2	no	—
489	C₈	—	12	1	no	—
490	C₂×C₃	C₅×#386	1	1	yes	characteristic
491	C₂×C₃	C₄×C₅×SD₁₆	1	1	yes	characteristic
492	C₂×C₃	C₅×#440	1	1	yes	characteristic
493	C₂×C₃	C₅×#448	1	1	yes	characteristic
494	C₂×C₃	C₅×#449	1	1	yes	characteristic
495	C₂×C₃	C₅×#460	1	1	yes	characteristic
496	C₂×C₃	C₅×#464	1	1	yes	characteristic
497	D₃	—	8	2	no	—
498	C₅	#71633	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	12	2	no	—
500	C₂²	—	12	2	no	—
501	C₂²	—	12	2	no	—
502	C₂²	—	24	1	no	—
503	C₂²	—	24	1	no	—
504	C₂²	—	24	1	no	—
505	C₂²	—	24	1	no	—
506	C₂²	C₄×C₅×#67	1	1	yes	characteristic
507	C₂²	C₅×#930	1	1	yes	characteristic
508	C₂²	C₂×C₅×#215	1	1	yes	characteristic
509	C₂²	C₅×#942	1	1	yes	characteristic
510	C₂²	C₅×#949	1	1	yes	characteristic
511	C₂²	C₅×#950	1	1	yes	characteristic
512	C₂²	C₅×#953	1	1	yes	characteristic
513	C₄	—	2	4	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	24	1	no	—
518	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
519	C₄	C₄×C₅×#67	1	1	yes	characteristic
520	C₄	C₅×#929	1	1	yes	characteristic
521	C₄	C₅×#930	1	1	yes	characteristic
522	C₃	C₅×#1880	1	1	yes	characteristic, complemented, Sylow
523	C₂	—	24	2	no	—
524	C₂	C₄×C₅×#215	1	1	yes	characteristic
525	C₂	C₅×#5026	1	1	yes	characteristic
526	C₂	C₅×#5027	1	1	yes	characteristic
527	C₂	C₅×#5028	1	1	yes	characteristic
528	C₂	C₅×#5213	1	1	yes	characteristic
529	C₂	C₅×#5227	1	1	yes	characteristic
530	C₂	C₅×#5238	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₅×#1880
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₂×C₅×#835	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. C₅×#4524	C₂	semidirect
19. C₂×C₅×#215	C₄	semidirect
27. #71633	C₅	direct (N × H)
29. C₂×C₄×C₅×Q₈	D₃	semidirect
71. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
73. C₂×#835	C₂×C₅	semidirect
76. #4529	C₂×C₅	semidirect
77. #4524	C₂×C₅	semidirect
108. C₃×C₅×Q₈	C₂²⋊C₄	semidirect
120. C₂×C₃×C₄×C₅	SD₁₆	semidirect
146. C₂×#215	C₄×C₅	semidirect
191. C₂×C₄×Q₈	C₅×D₃	semidirect
267. C₅×Q₈	(C₂×D₃)⋊C₄	semidirect
286. C₂×C₄×C₅	#215	semidirect
332. C₃×Q₈	C₅×C₂²⋊C₄	semidirect
344. C₂×C₃×C₄	C₅×SD₁₆	semidirect
419. C₃×C₅	#1880	semidirect
462. Q₈	C₅×(C₂×D₃)⋊C₄	semidirect
481. C₂×C₄	C₅×#215	semidirect
498. C₅	#71633	direct (N × H)
522. C₃	C₅×#1880	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×Q₈	2
C₂²×C₅×#215	2
C₂×C₅×#835	2
C₂×C₅×#809	2
C₅×#4939	2
C₅×#4529	2
C₅×#4524	2
C₅×#1880	3
#71633	5

Subgroups — C5×#71633 #14301083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71633 #14301083