Subgroups — C₅×#76289 #14320823

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#877	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
4	C₅×#5221	C₂	1	1	yes	maximal, characteristic
5	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4945	C₂	1	2	yes	maximal, complemented
8	C₅×#4944	C₂	1	2	yes	maximal, complemented
9	C₅×Dic₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2293	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₂×C₅×#217	C₂²	1	2	yes	—
21	C₂×C₅×#217	C₂²	1	2	yes	—
22	C₅×D₄×Dic₃	C₄	1	8	yes	complemented
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
32	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
34	C₅×#877	—	2	8	no	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	2	yes	—
38	#76289	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₄×C₅×D₄	—	3	1	no	—
40	C₂×C₅×#117	—	3	2	no	—
41	C₅×#390	—	3	1	no	—
42	C₅×#390	D₃	1	1	yes	characteristic
43	C₅×#389	—	3	1	no	—
44	C₅×#389	—	3	1	no	—
45	C₅×#388	—	3	2	no	—
46	C₅×#388	—	3	2	no	—
47	C₄×C₅×C₄⋊C₄	—	3	1	no	—
48	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
49	C₄³×C₅	—	3	1	no	—
50	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	—	2	4	no	—
59	C₂²×C₅×Dic₃	—	2	4	no	—
60	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
62	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
63	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
64	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
65	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
66	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₅×#217	—	2	4	no	—
72	C₅×#217	—	2	4	no	—
73	C₅×#217	C₂×C₄	1	8	yes	—
74	C₅×C₄⋊Dic₃	—	2	2	no	—
75	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
76	C₅×Dic₃⋊C₄	—	2	4	no	—
77	C₅×Dic₃⋊C₄	—	2	4	no	—
78	C₄×C₅×Dic₃	—	2	2	no	—
79	C₄×C₅×Dic₃	—	2	2	no	—
80	C₄×C₅×Dic₃	—	2	4	no	—
81	C₄×C₅×Dic₃	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
84	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
85	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
86	C₂×#877	C₂×C₅	1	2	yes	complemented
87	C₃×#390	C₂×C₅	1	1	yes	characteristic
88	#5221	C₂×C₅	1	1	yes	characteristic
89	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
90	#4972	C₂×C₅	1	1	yes	characteristic, complemented
91	#4945	C₂×C₅	1	2	yes	complemented
92	#4944	C₂×C₅	1	2	yes	complemented
93	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
94	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
95	#4928	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
97	C₂³×C₄×C₅	—	3	2	no	—
98	C₄×C₅×D₄	—	3	8	no	—
99	C₅×#117	—	6	8	no	—
100	C₂×C₅×C₄⋊C₄	—	3	1	no	—
101	C₂×C₅×C₄⋊C₄	—	3	1	no	—
102	C₂×C₅×C₄⋊C₄	—	3	2	no	—
103	C₂×C₅×C₄⋊C₄	—	3	2	no	—
104	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
106	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
107	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
108	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
109	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
110	C₂×C₄²×C₅	—	3	1	no	—
111	C₂×C₄²×C₅	—	3	1	no	—
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	1	no	—
114	C₂×C₄²×C₅	—	3	1	no	—
115	C₂×C₄²×C₅	—	3	1	no	—
116	C₂×C₄²×C₅	—	3	2	no	—
117	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
118	C₅×#95	—	3	2	no	—
119	C₅×#95	—	3	2	no	—
120	C₅×#95	—	3	2	no	—
121	#2293	—	3	1	no	Sylow
122	C₂³×C₃×C₅	—	2	2	no	—
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
129	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
130	C₃×C₅×D₄	—	2	8	no	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	#41	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	#41	1	2	yes	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	2	1	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	1	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	16	no	—
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	—	2	2	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
156	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
157	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
158	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
159	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
160	C₂×C₅×Dic₃	#41	1	2	yes	—
161	C₂×C₅×Dic₃	#41	1	2	yes	—
162	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
163	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
167	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
168	C₂×#217	C₂²×C₅	1	2	yes	—
169	C₂×#217	C₂²×C₅	1	2	yes	—
170	C₂×#217	C₂²×C₅	1	2	yes	—
171	D₄×Dic₃	C₄×C₅	1	8	yes	complemented
172	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
181	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
183	#877	—	2	8	no	—
184	C₃⋊#95	C₂²×C₅	1	2	yes	—
185	C₃⋊#95	C₂²×C₅	1	2	yes	—
186	C₃⋊#95	C₂²×C₅	1	2	yes	—
187	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
188	C₂×C₅×D₄	—	2	2	no	—
189	C₂×C₅×D₄	—	2	2	no	—
190	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	3	8	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	3	2	no	—
197	C₂²×C₄×C₅	—	3	2	no	—
198	C₂²×C₄×C₅	—	6	4	no	—
199	C₂²×C₄×C₅	—	6	4	no	—
200	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
201	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	3	4	no	—
206	C₅×C₄⋊C₄	—	6	4	no	—
207	C₅×C₄⋊C₄	—	6	4	no	—
208	C₅×C₄⋊C₄	—	6	2	no	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	3	8	no	—
212	C₅×C₂²⋊C₄	—	6	4	no	—
213	C₅×C₂²⋊C₄	—	6	4	no	—
214	C₄²×C₅	—	2	2	no	—
215	C₄²×C₅	—	3	4	no	—
216	C₄²×C₅	—	3	4	no	—
217	C₄²×C₅	—	6	4	no	—
218	C₄²×C₅	—	6	2	no	—
219	C₄²×C₅	—	6	2	no	—
220	C₄²×C₅	—	6	2	no	—
221	C₄²×C₅	—	6	2	no	—
222	C₂×C₄×D₄	—	3	1	no	—
223	C₂×#117	—	3	2	no	—
224	#390	—	3	1	no	—
225	#390	C₅×D₃	1	1	yes	characteristic
226	#389	—	3	1	no	—
227	#389	—	3	1	no	—
228	#388	—	3	2	no	—
229	#388	—	3	2	no	—
230	C₄×C₄⋊C₄	—	3	1	no	—
231	C₄×C₂²⋊C₄	—	3	2	no	—
232	C₄³	—	3	1	no	—
233	C₂²×C₃×C₅	—	2	4	no	—
234	C₂²×C₃×C₅	—	2	4	no	—
235	C₂²×C₃×C₅	—	2	4	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
243	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
244	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
245	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
247	C₃×C₄×C₅	—	2	2	no	—
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	—	4	2	no	—
250	C₃×C₄×C₅	#117	1	4	yes	complemented
251	C₅×Dic₃	—	2	4	no	—
252	C₅×Dic₃	—	2	2	no	—
253	C₅×Dic₃	—	2	2	no	—
254	C₅×Dic₃	—	2	2	no	—
255	C₅×Dic₃	—	4	2	no	—
256	C₅×Dic₃	C₄×D₄	1	4	yes	—
257	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
261	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×Dic₃	—	2	4	no	—
266	C₂²×Dic₃	—	2	4	no	—
267	C₂²×Dic₃	C₂×C₄×C₅	1	8	yes	—
268	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
269	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
270	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
271	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
274	C₃×C₄⋊C₄	—	2	2	no	—
275	C₃×C₂²⋊C₄	—	2	4	no	—
276	C₃×C₂²⋊C₄	—	2	4	no	—
277	C₃×C₄²	—	2	2	no	—
278	#217	—	2	4	no	—
279	#217	—	2	4	no	—
280	#217	C₂×C₄×C₅	1	8	yes	—
281	C₄⋊Dic₃	—	2	2	no	—
282	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
283	Dic₃⋊C₄	—	2	4	no	—
284	Dic₃⋊C₄	—	2	4	no	—
285	C₄×Dic₃	—	2	2	no	—
286	C₄×Dic₃	—	2	2	no	—
287	C₄×Dic₃	—	2	4	no	—
288	C₄×Dic₃	—	2	2	no	—
289	C₄×Dic₃	—	2	2	no	—
290	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
291	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
292	C₂³×C₅	—	2	2	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
299	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
300	C₅×D₄	—	2	8	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	3	2	no	—
311	C₂×C₄×C₅	—	3	2	no	—
312	C₂×C₄×C₅	—	3	4	no	—
313	C₂×C₄×C₅	—	3	2	no	—
314	C₂×C₄×C₅	—	3	2	no	—
315	C₂×C₄×C₅	—	6	16	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	1	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	1	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	6	2	no	—
326	C₂×C₄×C₅	—	6	2	no	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
328	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
329	C₂×C₄×C₅	#237	1	2	yes	—
330	C₂×C₄×C₅	#237	1	2	yes	—
331	C₂×C₄×C₅	#237	1	2	yes	—
332	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂³×C₄	—	3	2	no	—
334	C₄×D₄	—	3	8	no	—
335	#117	—	6	8	no	—
336	C₂×C₄⋊C₄	—	3	1	no	—
337	C₂×C₄⋊C₄	—	3	2	no	—
338	C₂×C₄⋊C₄	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	1	no	—
340	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	3	2	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	2	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	3	1	no	—
352	C₂×C₄²	—	3	1	no	—
353	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
354	#95	—	3	2	no	—
355	#95	—	3	2	no	—
356	#95	—	3	2	no	—
357	C₂×C₃×C₅	—	4	4	no	—
358	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
359	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
360	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
361	C₂×C₃×C₅	#529	1	1	yes	characteristic
362	C₂×C₃×C₅	#529	1	1	yes	characteristic
363	C₂×C₃×C₅	#532	1	1	yes	characteristic
364	C₂×C₃×C₅	#532	1	1	yes	characteristic
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
372	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
373	C₃×D₄	—	2	8	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₃×C₄	C₅×#41	1	2	yes	—
384	C₂×C₃×C₄	C₅×#41	1	2	yes	—
385	C₂×C₃×C₄	C₅×#41	1	2	yes	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	2	1	no	—
389	C₂×Dic₃	—	2	1	no	—
390	C₂×Dic₃	—	2	1	no	—
391	C₂×Dic₃	—	2	1	no	—
392	C₂×Dic₃	—	2	1	no	—
393	C₂×Dic₃	—	2	2	no	—
394	C₂×Dic₃	—	2	16	no	—
395	C₂×Dic₃	—	2	2	no	—
396	C₂×Dic₃	—	2	2	no	—
397	C₂×Dic₃	—	2	2	no	—
398	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
399	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
400	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
401	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
402	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
403	C₂×Dic₃	C₅×#41	1	2	yes	—
404	C₂×Dic₃	C₅×#41	1	2	yes	—
405	C₂²×C₅	—	2	4	no	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	2	4	no	—
408	C₂²×C₅	—	4	2	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	2	no	—
412	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
413	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
414	C₂²×C₅	C₂×#237	1	1	yes	characteristic
415	C₂²×C₅	C₂×#237	1	1	yes	characteristic
416	C₂²×C₅	C₂×#237	1	1	yes	characteristic
417	C₂²×C₅	D₃×#41	1	1	yes	characteristic
418	C₂²×C₅	D₃×#41	1	1	yes	characteristic
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	3	4	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	6	2	no	—
424	C₄×C₅	—	6	2	no	—
425	C₄×C₅	—	6	2	no	—
426	C₄×C₅	—	6	4	no	—
427	C₄×C₅	—	12	2	no	—
428	C₄×C₅	#877	1	4	yes	complemented
429	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	8	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	6	4	no	—
441	C₂²×C₄	—	6	4	no	—
442	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
443	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	3	4	no	—
448	C₄⋊C₄	—	6	4	no	—
449	C₄⋊C₄	—	6	4	no	—
450	C₄⋊C₄	—	6	2	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	3	8	no	—
454	C₂²⋊C₄	—	6	4	no	—
455	C₂²⋊C₄	—	6	4	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	3	4	no	—
458	C₄²	—	3	4	no	—
459	C₄²	—	6	4	no	—
460	C₄²	—	6	2	no	—
461	C₄²	—	6	2	no	—
462	C₄²	—	6	2	no	—
463	C₄²	—	6	2	no	—
464	C₃×C₅	#2293	1	1	yes	characteristic, complemented, Hall
465	C₂²×C₃	—	2	4	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	2	4	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	—	4	2	no	—
471	C₂²×C₃	—	4	2	no	—
472	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
473	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
474	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
475	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
476	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
477	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
478	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	4	2	no	—
482	C₃×C₄	C₅×#117	1	4	yes	complemented
483	Dic₃	—	2	4	no	—
484	Dic₃	—	2	2	no	—
485	Dic₃	—	2	2	no	—
486	Dic₃	—	2	2	no	—
487	Dic₃	—	4	2	no	—
488	Dic₃	C₄×C₅×D₄	1	4	yes	—
489	C₂×C₅	—	4	4	no	—
490	C₂×C₅	C₂×#877	1	1	yes	characteristic
491	C₂×C₅	C₄×#237	1	1	yes	characteristic
492	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
493	C₂×C₅	#5596	1	1	yes	characteristic
494	C₂×C₅	#5600	1	1	yes	characteristic
495	C₂×C₅	#5680	1	1	yes	characteristic
496	C₂×C₅	#5716	1	1	yes	characteristic
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
504	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
505	D₄	—	2	8	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	2	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	3	2	no	—
517	C₂×C₄	—	3	4	no	—
518	C₂×C₄	—	3	2	no	—
519	C₂×C₄	—	3	2	no	—
520	C₂×C₄	—	6	16	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	1	no	—
523	C₂×C₄	—	6	1	no	—
524	C₂×C₄	—	6	1	no	—
525	C₂×C₄	—	6	1	no	—
526	C₂×C₄	—	6	1	no	—
527	C₂×C₄	—	6	1	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	—	6	2	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	—	6	2	no	—
532	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
533	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
534	C₂×C₄	C₅×#237	1	2	yes	—
535	C₂×C₄	C₅×#237	1	2	yes	—
536	C₂×C₄	C₅×#237	1	2	yes	—
537	C₂×C₃	—	4	4	no	—
538	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
539	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
540	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
541	C₂×C₃	C₅×#529	1	1	yes	characteristic
542	C₂×C₃	C₅×#529	1	1	yes	characteristic
543	C₂×C₃	C₅×#532	1	1	yes	characteristic
544	C₂×C₃	C₅×#532	1	1	yes	characteristic
545	C₅	#76289	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
554	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
555	C₂²	C₂×C₅×#237	1	1	yes	characteristic
556	C₂²	C₂×C₅×#237	1	1	yes	characteristic
557	C₂²	C₂×C₅×#237	1	1	yes	characteristic
558	C₂²	C₅×D₃×#41	1	1	yes	characteristic
559	C₂²	C₅×D₃×#41	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	3	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	6	2	no	—
565	C₄	—	6	2	no	—
566	C₄	—	6	2	no	—
567	C₄	—	6	4	no	—
568	C₄	—	12	2	no	—
569	C₄	C₅×#877	1	4	yes	complemented
570	C₃	C₅×#2293	1	1	yes	characteristic, complemented, Sylow
571	C₂	—	4	4	no	—
572	C₂	C₂×C₅×#877	1	1	yes	characteristic
573	C₂	C₄×C₅×#237	1	1	yes	characteristic
574	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
575	C₂	C₅×#5596	1	1	yes	characteristic
576	C₂	C₅×#5600	1	1	yes	characteristic
577	C₂	C₅×#5680	1	1	yes	characteristic
578	C₂	C₅×#5716	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₅×#2293
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#877	C₂	semidirect
5. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
6. C₅×#4972	C₂	semidirect
7. C₅×#4945	C₂	semidirect
8. C₅×#4944	C₂	semidirect
9. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
10. C₄²×C₅×Dic₃	C₂	semidirect
11. C₅×#4928	C₂	semidirect
22. C₅×D₄×Dic₃	C₄	semidirect
38. #76289	C₅	direct (N × H)
84. C₄×C₅×Dic₃	D₄	semidirect
86. C₂×#877	C₂×C₅	semidirect
89. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
90. #4972	C₂×C₅	semidirect
91. #4945	C₂×C₅	semidirect
92. #4944	C₂×C₅	semidirect
93. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
94. C₄²×Dic₃	C₂×C₅	semidirect
95. #4928	C₂×C₅	semidirect
171. D₄×Dic₃	C₄×C₅	semidirect
250. C₃×C₄×C₅	#117	semidirect
291. C₄×Dic₃	C₅×D₄	semidirect
428. C₄×C₅	#877	semidirect
464. C₃×C₅	#2293	semidirect
482. C₃×C₄	C₅×#117	semidirect
545. C₅	#76289	direct (N × H)
569. C₄	C₅×#877	semidirect
570. C₃	C₅×#2293	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#877	2
C₃×C₅×#390	2
C₅×#5221	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4972	2
C₅×#4945	2
C₅×#4944	2
C₅×Dic₃×C₂²⋊C₄	2
C₄²×C₅×Dic₃	2
C₅×#4928	2
C₅×#2293	3
#76289	5

Subgroups — C5×#76289 #14320823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76289 #14320823