Subgroups — C₅×#68882 #14301756

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4987	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1892	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	—	2	2	no	—
20	C₂×C₅×D₃×C₈	—	2	2	no	—
21	C₂×C₅×D₃×C₈	—	2	2	no	—
22	C₅×#897	—	2	2	no	—
23	C₅×#897	C₄	1	4	yes	complemented
24	C₅×C₃⋊#95	—	2	1	no	—
25	C₅×#816	—	2	2	no	—
26	C₅×#810	—	2	2	no	—
27	#68882	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂³×C₅×C₈	—	3	1	no	—
29	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
30	C₂×C₅×#103	—	3	1	no	—
31	C₂×C₅×#103	—	3	1	no	—
32	C₅×#380	—	3	1	no	—
33	C₅×#340	—	3	1	no	—
34	C₅×#340	D₃	1	1	yes	characteristic, complemented
35	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₄×C₅×D₃	—	2	1	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
47	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
48	C₂×C₅×Dic₆	—	2	1	no	—
49	C₂×C₅×Dic₆	—	2	1	no	—
50	C₂×C₅×Dic₆	—	2	1	no	—
51	C₂×C₅×Dic₆	—	2	1	no	—
52	C₂×C₅×Dic₆	—	2	1	no	—
53	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
63	C₅×C₄⋊Dic₃	—	2	4	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
69	C₅×D₃×C₈	—	2	8	no	—
70	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic
71	C₂×#897	C₂×C₅	1	1	yes	characteristic
72	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
73	#4987	C₂×C₅	1	1	yes	characteristic
74	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
76	#4529	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×C₅×Q₈	—	3	1	no	—
78	C₂³×C₄×C₅	—	3	1	no	—
79	C₂²×C₅×C₈	—	3	1	no	—
80	C₂²×C₅×C₈	—	6	2	no	—
81	C₂²×C₅×C₈	—	6	2	no	—
82	C₂²×C₅×C₈	—	6	2	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₅×C₂²⋊Q₈	—	3	4	no	—
85	C₅×C₂²⋊Q₈	—	6	2	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	—	6	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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	C₅×#103	—	6	2	no	—
93	C₅×#103	—	6	2	no	—
94	C₅×#95	—	6	1	no	—
95	#1892	—	3	1	no	Sylow
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	1	no	—
98	C₂²×C₅×D₃	—	2	1	no	—
99	C₂²×C₅×D₃	—	2	1	no	—
100	C₂²×C₅×D₃	—	2	1	no	—
101	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₅×D₃	SD₁₆	1	2	yes	—
103	C₂²×C₅×D₃	Q₁₆	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	4	1	no	—
108	C₂×C₃×C₄×C₅	—	4	1	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₂×C₅×Dic₃	—	2	1	no	—
117	C₂×C₅×Dic₃	—	2	1	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	4	1	no	—
120	C₂×C₅×Dic₃	—	4	1	no	—
121	C₂×C₅×Dic₃	—	4	1	no	—
122	C₂×C₅×Dic₃	—	4	1	no	—
123	C₂×C₅×Dic₃	—	4	1	no	—
124	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
125	C₄×C₅×D₃	—	2	2	no	—
126	C₄×C₅×D₃	—	2	2	no	—
127	C₄×C₅×D₃	—	2	2	no	—
128	C₄×C₅×D₃	—	2	2	no	—
129	C₅×Dic₆	—	2	2	no	—
130	C₅×Dic₆	—	2	2	no	—
131	C₅×Dic₆	—	4	1	no	—
132	C₅×Dic₆	—	4	1	no	—
133	C₃×C₅×C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
141	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
142	C₂×C₄⋊Dic₃	—	2	1	no	—
143	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×D₃×C₈	—	2	2	no	—
146	C₂×D₃×C₈	—	2	2	no	—
147	C₂×D₃×C₈	—	2	2	no	—
148	#897	—	2	2	no	—
149	#897	C₄×C₅	1	4	yes	complemented
150	C₃⋊#95	—	2	1	no	—
151	#816	—	2	2	no	—
152	#810	—	2	2	no	—
153	C₂⁴×C₅	—	3	1	no	—
154	C₂×C₅×Q₈	—	3	2	no	—
155	C₂×C₅×Q₈	—	6	1	no	—
156	C₂×C₅×Q₈	—	6	1	no	—
157	C₂×C₅×Q₈	—	6	1	no	—
158	C₂×C₅×Q₈	—	6	1	no	—
159	C₂×C₅×Q₈	—	6	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	—	6	1	no	—
166	C₂²×C₄×C₅	—	6	1	no	—
167	C₂²×C₄×C₅	—	6	1	no	—
168	C₂²×C₄×C₅	—	6	1	no	—
169	C₂²×C₄×C₅	—	6	1	no	—
170	C₂²×C₄×C₅	—	6	1	no	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	6	8	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₂×C₅×C₈	—	6	1	no	—
178	C₂×C₅×C₈	D₁₂	1	2	yes	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	6	4	no	—
183	C₅×C₄⋊C₄	—	6	1	no	—
184	C₅×C₄⋊C₄	—	6	1	no	—
185	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
186	C₅×C₂²⋊C₄	—	6	4	no	—
187	C₅×C₂²⋊C₄	—	12	2	no	—
188	C₂³×C₈	—	3	1	no	—
189	C₂×C₂²⋊Q₈	—	3	1	no	—
190	C₂×#103	—	3	1	no	—
191	C₂×#103	—	3	1	no	—
192	#380	—	3	1	no	—
193	#340	—	3	1	no	—
194	#340	C₅×D₃	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	#121	1	1	yes	characteristic
197	C₂²×C₃×C₅	#121	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
200	C₂²×C₃×C₅	#135	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂×C₅×D₃	—	2	2	no	—
203	C₂×C₅×D₃	—	2	2	no	—
204	C₂×C₅×D₃	—	2	2	no	—
205	C₂×C₅×D₃	—	2	2	no	—
206	C₂×C₅×D₃	—	2	2	no	—
207	C₂×C₅×D₃	—	2	2	no	—
208	C₂×C₅×D₃	#103	1	4	yes	complemented
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	—	8	1	no	—
211	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
212	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	#120	1	1	yes	characteristic
214	C₃×C₄×C₅	#123	1	1	yes	characteristic
215	C₅×Dic₃	—	2	2	no	—
216	C₅×Dic₃	—	4	2	no	—
217	C₅×Dic₃	—	8	1	no	—
218	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	2	1	no	—
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂²×Dic₃	—	2	1	no	—
223	C₂²×Dic₃	—	2	1	no	—
224	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
225	C₂×C₄×D₃	—	2	1	no	—
226	C₂×C₄×D₃	—	2	1	no	—
227	C₂×C₄×D₃	—	2	1	no	—
228	C₂×C₄×D₃	—	2	1	no	—
229	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
231	C₂×Dic₆	—	2	1	no	—
232	C₂×Dic₆	—	2	1	no	—
233	C₂×Dic₆	—	2	1	no	—
234	C₂×Dic₆	—	2	1	no	—
235	C₂×Dic₆	—	2	1	no	—
236	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₃×C₈	—	2	1	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
244	(C₂×D₃)⋊C₄	—	2	4	no	—
245	(C₂×D₃)⋊C₄	—	4	2	no	—
246	C₄⋊Dic₃	—	2	4	no	—
247	C₄⋊Dic₃	—	2	1	no	—
248	C₄⋊Dic₃	—	2	1	no	—
249	C₂×C₃⋊C₈	—	2	1	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
252	D₃×C₈	—	2	8	no	—
253	C₂³×C₅	—	3	2	no	—
254	C₂³×C₅	—	3	2	no	—
255	C₂³×C₅	—	3	2	no	—
256	C₂³×C₅	—	6	1	no	—
257	C₂³×C₅	—	6	1	no	—
258	C₂³×C₅	—	6	1	no	—
259	C₂³×C₅	—	6	1	no	—
260	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
261	C₅×Q₈	—	6	2	no	—
262	C₅×Q₈	—	6	2	no	—
263	C₅×Q₈	—	12	1	no	—
264	C₅×Q₈	—	12	1	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	3	2	no	—
267	C₂×C₄×C₅	—	4	1	no	—
268	C₂×C₄×C₅	—	4	1	no	—
269	C₂×C₄×C₅	—	4	1	no	—
270	C₂×C₄×C₅	—	4	1	no	—
271	C₂×C₄×C₅	—	4	1	no	—
272	C₂×C₄×C₅	—	6	1	no	—
273	C₂×C₄×C₅	—	6	1	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	6	2	no	—
276	C₂×C₄×C₅	—	6	2	no	—
277	C₂×C₄×C₅	—	6	2	no	—
278	C₂×C₄×C₅	—	6	2	no	—
279	C₂×C₄×C₅	—	12	1	no	—
280	C₂×C₄×C₅	—	12	1	no	—
281	C₂×C₄×C₅	—	12	1	no	—
282	C₂×C₄×C₅	—	12	1	no	—
283	C₂×C₄×C₅	—	12	1	no	—
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
286	C₂×C₄×C₅	#235	1	1	yes	characteristic
287	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	#239	1	1	yes	characteristic
290	C₅×C₈	—	2	2	no	—
291	C₅×C₈	—	6	2	no	—
292	C₂²×Q₈	—	3	1	no	—
293	C₂³×C₄	—	3	1	no	—
294	C₂²×C₈	—	3	1	no	—
295	C₂²×C₈	—	6	2	no	—
296	C₂²×C₈	—	6	2	no	—
297	C₂²×C₈	—	6	2	no	—
298	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
299	C₂²⋊Q₈	—	3	4	no	—
300	C₂²⋊Q₈	—	6	2	no	—
301	C₂×C₄⋊C₄	—	3	1	no	—
302	C₂×C₄⋊C₄	—	6	1	no	—
303	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	6	1	no	—
306	C₂×C₂²⋊C₄	—	6	1	no	—
307	#103	—	6	2	no	—
308	#103	—	6	2	no	—
309	#95	—	6	1	no	—
310	C₂×C₃×C₅	#386	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
312	C₂×C₃×C₅	#416	1	1	yes	characteristic
313	C₂×C₃×C₅	#465	1	1	yes	characteristic
314	C₂×C₃×C₅	#465	1	1	yes	characteristic
315	C₂×C₃×C₅	#467	1	1	yes	characteristic
316	C₂×C₃×C₅	#467	1	1	yes	characteristic
317	C₅×D₃	—	2	4	no	—
318	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂²×D₃	—	2	1	no	—
320	C₂²×D₃	—	2	1	no	—
321	C₂²×D₃	—	2	1	no	—
322	C₂²×D₃	—	2	1	no	—
323	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
324	C₂²×D₃	C₅×SD₁₆	1	2	yes	—
325	C₂²×D₃	C₅×Q₁₆	1	2	yes	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	4	1	no	—
328	C₂×C₃×C₄	—	4	1	no	—
329	C₂×C₃×C₄	—	4	1	no	—
330	C₂×C₃×C₄	—	4	1	no	—
331	C₂×C₃×C₄	—	4	1	no	—
332	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
337	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
338	C₂×Dic₃	—	2	1	no	—
339	C₂×Dic₃	—	2	1	no	—
340	C₂×Dic₃	—	2	2	no	—
341	C₂×Dic₃	—	4	1	no	—
342	C₂×Dic₃	—	4	1	no	—
343	C₂×Dic₃	—	4	1	no	—
344	C₂×Dic₃	—	4	1	no	—
345	C₂×Dic₃	—	4	1	no	—
346	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
347	C₄×D₃	—	2	2	no	—
348	C₄×D₃	—	2	2	no	—
349	C₄×D₃	—	2	2	no	—
350	C₄×D₃	—	2	2	no	—
351	Dic₆	—	2	2	no	—
352	Dic₆	—	2	2	no	—
353	Dic₆	—	4	1	no	—
354	Dic₆	—	4	1	no	—
355	C₃×C₈	—	2	2	no	—
356	C₃⋊C₈	—	2	2	no	—
357	C₂²×C₅	—	3	4	no	—
358	C₂²×C₅	—	6	2	no	—
359	C₂²×C₅	—	6	2	no	—
360	C₂²×C₅	—	6	2	no	—
361	C₂²×C₅	—	6	2	no	—
362	C₂²×C₅	—	6	2	no	—
363	C₂²×C₅	—	6	2	no	—
364	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₅	#884	1	1	yes	characteristic
366	C₂²×C₅	#895	1	1	yes	characteristic
367	C₂²×C₅	#912	1	1	yes	characteristic
368	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
369	C₂²×C₅	#916	1	1	yes	characteristic
370	C₂²×C₅	D₃×Q₁₆	1	1	yes	characteristic
371	C₄×C₅	—	4	2	no	—
372	C₄×C₅	—	6	2	no	—
373	C₄×C₅	—	8	1	no	—
374	C₄×C₅	—	12	2	no	—
375	C₄×C₅	—	24	1	no	—
376	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
377	C₄×C₅	#882	1	1	yes	characteristic
378	C₄×C₅	#893	1	1	yes	characteristic
379	C₄×C₅	#894	1	1	yes	characteristic
380	C₂⁴	—	3	1	no	—
381	C₂×Q₈	—	3	2	no	—
382	C₂×Q₈	—	6	1	no	—
383	C₂×Q₈	—	6	1	no	—
384	C₂×Q₈	—	6	1	no	—
385	C₂×Q₈	—	6	1	no	—
386	C₂×Q₈	—	6	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	3	2	no	—
391	C₂²×C₄	—	3	2	no	—
392	C₂²×C₄	—	6	1	no	—
393	C₂²×C₄	—	6	1	no	—
394	C₂²×C₄	—	6	1	no	—
395	C₂²×C₄	—	6	1	no	—
396	C₂²×C₄	—	6	1	no	—
397	C₂²×C₄	—	6	1	no	—
398	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	3	2	no	—
402	C₂×C₈	—	6	8	no	—
403	C₂×C₈	—	6	1	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	C₅×D₁₂	1	2	yes	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	6	4	no	—
410	C₄⋊C₄	—	6	1	no	—
411	C₄⋊C₄	—	6	1	no	—
412	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
413	C₂²⋊C₄	—	6	4	no	—
414	C₂²⋊C₄	—	12	2	no	—
415	C₃×C₅	#1892	1	1	yes	characteristic, complemented, Hall
416	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²×C₃	C₅×#121	1	1	yes	characteristic
418	C₂²×C₃	C₅×#121	1	1	yes	characteristic
419	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
420	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
421	C₂²×C₃	C₅×#135	1	1	yes	characteristic
422	C₂²×C₃	C₅×#135	1	1	yes	characteristic
423	C₂×D₃	—	2	2	no	—
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	C₅×#103	1	4	yes	complemented
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	8	1	no	—
432	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
433	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
434	C₃×C₄	C₅×#120	1	1	yes	characteristic
435	C₃×C₄	C₅×#123	1	1	yes	characteristic
436	Dic₃	—	2	2	no	—
437	Dic₃	—	4	2	no	—
438	Dic₃	—	8	1	no	—
439	C₂×C₅	—	6	4	no	—
440	C₂×C₅	#4665	1	1	yes	characteristic
441	C₂×C₅	#4772	1	1	yes	characteristic
442	C₂×C₅	#4778	1	1	yes	characteristic
443	C₂×C₅	D₃×#103	1	1	yes	characteristic
444	C₂×C₅	#4813	1	1	yes	characteristic
445	C₂×C₅	#4864	1	1	yes	characteristic
446	C₂×C₅	#4887	1	1	yes	characteristic
447	C₂³	—	3	2	no	—
448	C₂³	—	3	2	no	—
449	C₂³	—	3	2	no	—
450	C₂³	—	6	1	no	—
451	C₂³	—	6	1	no	—
452	C₂³	—	6	1	no	—
453	C₂³	—	6	1	no	—
454	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
455	Q₈	—	6	2	no	—
456	Q₈	—	6	2	no	—
457	Q₈	—	12	1	no	—
458	Q₈	—	12	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	6	1	no	—
467	C₂×C₄	—	6	1	no	—
468	C₂×C₄	—	6	2	no	—
469	C₂×C₄	—	6	2	no	—
470	C₂×C₄	—	6	2	no	—
471	C₂×C₄	—	6	2	no	—
472	C₂×C₄	—	6	2	no	—
473	C₂×C₄	—	12	1	no	—
474	C₂×C₄	—	12	1	no	—
475	C₂×C₄	—	12	1	no	—
476	C₂×C₄	—	12	1	no	—
477	C₂×C₄	—	12	1	no	—
478	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
479	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
480	C₂×C₄	C₅×#235	1	1	yes	characteristic
481	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
482	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
483	C₂×C₄	C₅×#239	1	1	yes	characteristic
484	C₈	—	2	2	no	—
485	C₈	—	6	2	no	—
486	C₂×C₃	C₅×#386	1	1	yes	characteristic
487	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
488	C₂×C₃	C₅×#416	1	1	yes	characteristic
489	C₂×C₃	C₅×#465	1	1	yes	characteristic
490	C₂×C₃	C₅×#465	1	1	yes	characteristic
491	C₂×C₃	C₅×#467	1	1	yes	characteristic
492	C₂×C₃	C₅×#467	1	1	yes	characteristic
493	D₃	—	2	4	no	—
494	C₅	#68882	1	1	yes	characteristic, direct product factor, Sylow
495	C₂²	—	3	4	no	—
496	C₂²	—	6	2	no	—
497	C₂²	—	6	2	no	—
498	C₂²	—	6	2	no	—
499	C₂²	—	6	2	no	—
500	C₂²	—	6	2	no	—
501	C₂²	—	6	2	no	—
502	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
503	C₂²	C₅×#884	1	1	yes	characteristic
504	C₂²	C₅×#895	1	1	yes	characteristic
505	C₂²	C₅×#912	1	1	yes	characteristic
506	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
507	C₂²	C₅×#916	1	1	yes	characteristic
508	C₂²	C₅×D₃×Q₁₆	1	1	yes	characteristic
509	C₄	—	4	2	no	—
510	C₄	—	6	2	no	—
511	C₄	—	8	1	no	—
512	C₄	—	12	2	no	—
513	C₄	—	24	1	no	—
514	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
515	C₄	C₅×#882	1	1	yes	characteristic
516	C₄	C₅×#893	1	1	yes	characteristic
517	C₄	C₅×#894	1	1	yes	characteristic
518	C₃	C₅×#1892	1	1	yes	characteristic, complemented, Sylow
519	C₂	—	6	4	no	—
520	C₂	C₅×#4665	1	1	yes	characteristic
521	C₂	C₅×#4772	1	1	yes	characteristic
522	C₂	C₅×#4778	1	1	yes	characteristic
523	C₂	C₅×D₃×#103	1	1	yes	characteristic
524	C₂	C₅×#4813	1	1	yes	characteristic
525	C₂	C₅×#4864	1	1	yes	characteristic
526	C₂	C₅×#4887	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#340	D₃
hypocenter	C₃	C₅×#1892
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#340

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#816	C₂	semidirect
5. C₂×C₅×#810	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. C₅×#4529	C₂	semidirect
23. C₅×#897	C₄	semidirect
27. #68882	C₅	direct (N × H)
34. C₅×#340	D₃	semidirect
72. C₂×#816	C₂×C₅	semidirect
74. C₂×#810	C₂×C₅	semidirect
75. C₃×#340	C₂×C₅	semidirect
76. #4529	C₂×C₅	semidirect
149. #897	C₄×C₅	semidirect
194. #340	C₅×D₃	semidirect
208. C₂×C₅×D₃	#103	semidirect
415. C₃×C₅	#1892	semidirect
429. C₂×D₃	C₅×#103	semidirect
494. C₅	#68882	direct (N × H)
518. C₃	C₅×#1892	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃×C₈	2
C₂×C₅×#897	2
C₂×C₅×#816	2
C₅×#4987	2
C₂×C₅×#810	2
C₃×C₅×#340	2
C₅×#4529	2
C₅×#1892	3
#68882	5

Subgroups — C5×#68882 #14301756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68882 #14301756