Subgroups — C₅×#73760 #14322701

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4987	C₂	1	1	yes	maximal, characteristic
4	C₅×#4987	C₂	1	1	yes	maximal, characteristic
5	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4940	C₂	1	2	yes	maximal
8	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4933	C₂	1	2	yes	maximal, complemented
10	C₅×#4669	C₂	1	2	yes	maximal
11	C₅×#4652	C₂	1	2	yes	maximal, complemented
12	C₅×#2314	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₅×#872	C₄	1	8	yes	complemented
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₅×C₃⋊#95	C₂²	1	2	yes	—
33	C₅×C₃⋊#95	C₂²	1	2	yes	—
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	#73760	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×#117	—	3	1	no	—
39	C₅×#388	—	3	2	no	—
40	C₅×#388	—	3	2	no	—
41	C₅×#387	—	3	2	no	—
42	C₅×#387	—	3	2	no	—
43	C₅×#384	—	3	1	no	—
44	C₅×#382	—	3	1	no	—
45	C₅×#380	—	3	1	no	—
46	C₅×#380	—	3	1	no	—
47	C₄×C₅×C₄⋊C₄	—	3	1	no	—
48	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
49	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₄²×C₅	—	4	2	no	—
66	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
67	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
68	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
69	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
71	C₅×C₄⋊Dic₃	—	2	2	no	—
72	C₅×C₄⋊Dic₃	—	2	2	no	—
73	C₅×Dic₃⋊C₄	—	4	2	no	—
74	C₅×Dic₃⋊C₄	—	4	2	no	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
76	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
77	C₄×C₅×Dic₃	—	4	2	no	—
78	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
79	C₂×#872	C₂×C₅	1	1	yes	characteristic
80	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
81	#4987	C₂×C₅	1	1	yes	characteristic
82	#4987	C₂×C₅	1	1	yes	characteristic
83	#4977	C₂×C₅	1	1	yes	characteristic, complemented
84	#4975	C₂×C₅	1	1	yes	characteristic, complemented
85	#4940	C₂×C₅	1	2	yes	—
86	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
87	#4933	C₂×C₅	1	2	yes	complemented
88	#4669	C₂×C₅	1	2	yes	—
89	#4652	C₂×C₅	1	2	yes	complemented
90	C₂³×C₄×C₅	—	3	1	no	—
91	C₅×#117	—	3	8	no	—
92	C₂×C₅×C₄⋊C₄	—	3	1	no	—
93	C₂×C₅×C₄⋊C₄	—	3	1	no	—
94	C₂×C₅×C₄⋊C₄	—	3	1	no	—
95	C₂×C₅×C₄⋊C₄	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	—	3	2	no	—
97	C₂×C₅×C₄⋊C₄	—	3	2	no	—
98	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
103	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
104	C₂×C₄²×C₅	—	3	1	no	—
105	C₂×C₄²×C₅	—	3	2	no	—
106	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
107	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
108	C₅×#95	—	3	2	no	—
109	C₅×#95	—	3	2	no	—
110	C₅×#95	—	3	2	no	—
111	C₅×#95	—	3	2	no	—
112	C₅×#95	—	3	2	no	—
113	C₅×#95	C₂×D₃	1	2	yes	—
114	#2314	—	3	1	no	Sylow
115	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
116	C₂²×C₅×D₃	—	2	1	no	—
117	C₂²×C₅×D₃	—	2	1	no	—
118	C₂²×C₅×D₃	—	2	1	no	—
119	C₂²×C₅×D₃	—	2	1	no	—
120	C₂²×C₅×D₃	—	2	1	no	—
121	C₂²×C₅×D₃	—	2	1	no	—
122	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	#41	1	2	yes	—
137	C₂×C₃×C₄×C₅	#41	1	2	yes	—
138	C₂×C₅×Dic₃	—	2	1	no	—
139	C₂×C₅×Dic₃	—	2	1	no	—
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	1	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
151	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
152	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
153	C₄×C₅×D₃	—	2	8	no	—
154	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
159	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
165	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
166	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
167	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
170	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
171	#872	C₄×C₅	1	8	yes	complemented
172	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃⋊#95	C₂²×C₅	1	2	yes	—
174	C₃⋊#95	C₂²×C₅	1	2	yes	—
175	C₃⋊#95	C₂²×C₅	1	2	yes	—
176	C₃⋊#95	C₂²×C₅	1	2	yes	—
177	C₃⋊#95	C₂²×C₅	1	2	yes	—
178	C₂⁴×C₅	—	3	1	no	—
179	C₂²×C₄×C₅	—	3	1	no	—
180	C₂²×C₄×C₅	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	4	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	—	6	2	no	—
187	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	3	4	no	—
195	C₅×C₄⋊C₄	—	3	4	no	—
196	C₅×C₄⋊C₄	—	6	2	no	—
197	C₅×C₄⋊C₄	—	6	2	no	—
198	C₅×C₄⋊C₄	—	12	2	no	—
199	C₅×C₄⋊C₄	—	12	2	no	—
200	C₅×C₂²⋊C₄	—	3	4	no	—
201	C₅×C₂²⋊C₄	—	3	4	no	—
202	C₅×C₂²⋊C₄	—	12	2	no	—
203	C₅×C₂²⋊C₄	—	12	2	no	—
204	C₄²×C₅	—	3	4	no	—
205	C₄²×C₅	—	4	2	no	—
206	C₄²×C₅	—	12	2	no	—
207	C₄²×C₅	C₄×D₃	1	4	yes	—
208	C₂×#117	—	3	1	no	—
209	#388	—	3	2	no	—
210	#388	—	3	2	no	—
211	#387	—	3	2	no	—
212	#387	—	3	2	no	—
213	#384	—	3	1	no	—
214	#382	—	3	1	no	—
215	#380	—	3	1	no	—
216	#380	—	3	1	no	—
217	C₄×C₄⋊C₄	—	3	1	no	—
218	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
219	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
222	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
225	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂×C₅×D₃	—	2	2	no	—
227	C₂×C₅×D₃	—	2	2	no	—
228	C₂×C₅×D₃	—	2	2	no	—
229	C₂×C₅×D₃	—	4	1	no	—
230	C₂×C₅×D₃	—	4	1	no	—
231	C₂×C₅×D₃	—	4	1	no	—
232	C₂×C₅×D₃	—	4	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	2	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	#117	1	4	yes	—
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	2	2	no	—
240	C₅×Dic₃	—	2	2	no	—
241	C₅×Dic₃	—	4	2	no	—
242	C₅×Dic₃	—	4	2	no	—
243	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
250	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
251	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
252	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
253	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₄×D₃	—	2	2	no	—
255	C₂×C₄×D₃	—	2	2	no	—
256	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄²	—	4	2	no	—
260	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
261	(C₂×D₃)⋊C₄	—	4	2	no	—
262	(C₂×D₃)⋊C₄	—	4	2	no	—
263	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
264	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
265	C₄⋊Dic₃	—	2	2	no	—
266	C₄⋊Dic₃	—	2	2	no	—
267	Dic₃⋊C₄	—	4	2	no	—
268	Dic₃⋊C₄	—	4	2	no	—
269	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
270	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
271	C₄×Dic₃	—	4	2	no	—
272	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
273	C₂³×C₅	—	3	2	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₂³×C₅	—	6	1	no	—
276	C₂³×C₅	—	6	1	no	—
277	C₂³×C₅	—	6	1	no	—
278	C₂³×C₅	—	6	1	no	—
279	C₂³×C₅	—	6	1	no	—
280	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	3	2	no	—
294	C₂×C₄×C₅	—	6	1	no	—
295	C₂×C₄×C₅	—	6	1	no	—
296	C₂×C₄×C₅	—	6	1	no	—
297	C₂×C₄×C₅	—	6	1	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	1	no	—
300	C₂×C₄×C₅	—	6	8	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	2	no	—
303	C₂×C₄×C₅	—	6	2	no	—
304	C₂×C₄×C₅	—	6	2	no	—
305	C₂×C₄×C₅	—	6	2	no	—
306	C₂×C₄×C₅	—	6	2	no	—
307	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
308	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
310	C₂×C₄×C₅	#235	1	2	yes	—
311	C₂×C₄×C₅	#235	1	2	yes	—
312	C₂³×C₄	—	3	1	no	—
313	#117	—	3	8	no	—
314	C₂×C₄⋊C₄	—	3	1	no	—
315	C₂×C₄⋊C₄	—	3	1	no	—
316	C₂×C₄⋊C₄	—	3	1	no	—
317	C₂×C₄⋊C₄	—	3	1	no	—
318	C₂×C₄⋊C₄	—	3	2	no	—
319	C₂×C₄⋊C₄	—	3	2	no	—
320	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	3	1	no	—
323	C₂×C₂²⋊C₄	—	3	1	no	—
324	C₂×C₂²⋊C₄	—	3	2	no	—
325	C₂×C₂²⋊C₄	—	3	2	no	—
326	C₂×C₄²	—	3	1	no	—
327	C₂×C₄²	—	3	2	no	—
328	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
329	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
330	#95	—	3	2	no	—
331	#95	—	3	2	no	—
332	#95	—	3	2	no	—
333	#95	—	3	2	no	—
334	#95	—	3	2	no	—
335	#95	C₂×C₅×D₃	1	2	yes	—
336	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
337	C₂×C₃×C₅	#520	1	1	yes	characteristic
338	C₂×C₃×C₅	#520	1	1	yes	characteristic
339	C₂×C₃×C₅	#540	1	1	yes	characteristic
340	C₂×C₃×C₅	#541	1	1	yes	characteristic
341	C₂×C₃×C₅	#542	1	1	yes	characteristic
342	C₂×C₃×C₅	#542	1	1	yes	characteristic
343	C₅×D₃	—	4	2	no	—
344	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
345	C₂²×D₃	—	2	1	no	—
346	C₂²×D₃	—	2	1	no	—
347	C₂²×D₃	—	2	1	no	—
348	C₂²×D₃	—	2	1	no	—
349	C₂²×D₃	—	2	1	no	—
350	C₂²×D₃	—	2	1	no	—
351	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
364	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
365	C₂×C₃×C₄	C₅×#41	1	2	yes	—
366	C₂×C₃×C₄	C₅×#41	1	2	yes	—
367	C₂×Dic₃	—	2	1	no	—
368	C₂×Dic₃	—	2	1	no	—
369	C₂×Dic₃	—	2	1	no	—
370	C₂×Dic₃	—	2	1	no	—
371	C₂×Dic₃	—	2	1	no	—
372	C₂×Dic₃	—	2	1	no	—
373	C₂×Dic₃	—	2	2	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	2	2	no	—
376	C₂×Dic₃	—	2	2	no	—
377	C₂×Dic₃	—	2	2	no	—
378	C₂×Dic₃	—	2	2	no	—
379	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
380	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
381	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
382	C₄×D₃	—	2	8	no	—
383	C₂²×C₅	—	6	2	no	—
384	C₂²×C₅	—	6	2	no	—
385	C₂²×C₅	—	6	2	no	—
386	C₂²×C₅	—	12	1	no	—
387	C₂²×C₅	—	12	1	no	—
388	C₂²×C₅	—	12	1	no	—
389	C₂²×C₅	—	12	1	no	—
390	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
391	C₂²×C₅	C₂×#235	1	1	yes	characteristic
392	C₂²×C₅	C₂×#235	1	1	yes	characteristic
393	C₂²×C₅	#1004	1	1	yes	characteristic
394	C₂²×C₅	#1007	1	1	yes	characteristic
395	C₂²×C₅	#1009	1	1	yes	characteristic
396	C₂²×C₅	#1010	1	1	yes	characteristic
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	—	6	2	no	—
402	C₄×C₅	—	6	2	no	—
403	C₄×C₅	—	6	2	no	—
404	C₄×C₅	—	12	2	no	—
405	C₄×C₅	—	12	2	no	—
406	C₄×C₅	#872	1	4	yes	—
407	C₂⁴	—	3	1	no	—
408	C₂²×C₄	—	3	1	no	—
409	C₂²×C₄	—	3	1	no	—
410	C₂²×C₄	—	3	1	no	—
411	C₂²×C₄	—	3	4	no	—
412	C₂²×C₄	—	3	2	no	—
413	C₂²×C₄	—	3	2	no	—
414	C₂²×C₄	—	6	2	no	—
415	C₂²×C₄	—	6	2	no	—
416	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
417	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
418	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	3	4	no	—
424	C₄⋊C₄	—	3	4	no	—
425	C₄⋊C₄	—	6	2	no	—
426	C₄⋊C₄	—	6	2	no	—
427	C₄⋊C₄	—	12	2	no	—
428	C₄⋊C₄	—	12	2	no	—
429	C₂²⋊C₄	—	3	4	no	—
430	C₂²⋊C₄	—	3	4	no	—
431	C₂²⋊C₄	—	12	2	no	—
432	C₂²⋊C₄	—	12	2	no	—
433	C₄²	—	3	4	no	—
434	C₄²	—	4	2	no	—
435	C₄²	—	12	2	no	—
436	C₄²	C₄×C₅×D₃	1	4	yes	—
437	C₃×C₅	#2314	1	1	yes	characteristic, complemented, Hall
438	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
439	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
440	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
441	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂×D₃	—	2	2	no	—
446	C₂×D₃	—	2	2	no	—
447	C₂×D₃	—	2	2	no	—
448	C₂×D₃	—	4	1	no	—
449	C₂×D₃	—	4	1	no	—
450	C₂×D₃	—	4	1	no	—
451	C₂×D₃	—	4	1	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	2	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	C₅×#117	1	4	yes	—
457	Dic₃	—	2	2	no	—
458	Dic₃	—	2	2	no	—
459	Dic₃	—	2	2	no	—
460	Dic₃	—	4	2	no	—
461	Dic₃	—	4	2	no	—
462	C₂×C₅	—	12	2	no	—
463	C₂×C₅	C₂×#872	1	1	yes	characteristic
464	C₂×C₅	#5504	1	1	yes	characteristic
465	C₂×C₅	#5523	1	1	yes	characteristic
466	C₂×C₅	#5561	1	1	yes	characteristic
467	C₂×C₅	#5562	1	1	yes	characteristic
468	C₂×C₅	#5582	1	1	yes	characteristic
469	C₂×C₅	#5583	1	1	yes	characteristic
470	C₂³	—	3	2	no	—
471	C₂³	—	6	1	no	—
472	C₂³	—	6	1	no	—
473	C₂³	—	6	1	no	—
474	C₂³	—	6	1	no	—
475	C₂³	—	6	1	no	—
476	C₂³	—	6	1	no	—
477	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	3	2	no	—
489	C₂×C₄	—	3	2	no	—
490	C₂×C₄	—	3	2	no	—
491	C₂×C₄	—	6	1	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	1	no	—
494	C₂×C₄	—	6	1	no	—
495	C₂×C₄	—	6	1	no	—
496	C₂×C₄	—	6	1	no	—
497	C₂×C₄	—	6	8	no	—
498	C₂×C₄	—	6	2	no	—
499	C₂×C₄	—	6	2	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	6	2	no	—
502	C₂×C₄	—	6	2	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
505	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
506	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
507	C₂×C₄	C₅×#235	1	2	yes	—
508	C₂×C₄	C₅×#235	1	2	yes	—
509	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
510	C₂×C₃	C₅×#520	1	1	yes	characteristic
511	C₂×C₃	C₅×#520	1	1	yes	characteristic
512	C₂×C₃	C₅×#540	1	1	yes	characteristic
513	C₂×C₃	C₅×#541	1	1	yes	characteristic
514	C₂×C₃	C₅×#542	1	1	yes	characteristic
515	C₂×C₃	C₅×#542	1	1	yes	characteristic
516	D₃	—	4	2	no	—
517	C₅	#73760	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²	—	6	2	no	—
519	C₂²	—	6	2	no	—
520	C₂²	—	6	2	no	—
521	C₂²	—	12	1	no	—
522	C₂²	—	12	1	no	—
523	C₂²	—	12	1	no	—
524	C₂²	—	12	1	no	—
525	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
526	C₂²	C₂×C₅×#235	1	1	yes	characteristic
527	C₂²	C₂×C₅×#235	1	1	yes	characteristic
528	C₂²	C₅×#1004	1	1	yes	characteristic
529	C₂²	C₅×#1007	1	1	yes	characteristic
530	C₂²	C₅×#1009	1	1	yes	characteristic
531	C₂²	C₅×#1010	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	6	2	no	—
537	C₄	—	6	2	no	—
538	C₄	—	6	2	no	—
539	C₄	—	12	2	no	—
540	C₄	—	12	2	no	—
541	C₄	C₅×#872	1	4	yes	—
542	C₃	C₅×#2314	1	1	yes	characteristic, complemented, Sylow
543	C₂	—	12	2	no	—
544	C₂	C₂×C₅×#872	1	1	yes	characteristic
545	C₂	C₅×#5504	1	1	yes	characteristic
546	C₂	C₅×#5523	1	1	yes	characteristic
547	C₂	C₅×#5561	1	1	yes	characteristic
548	C₂	C₅×#5562	1	1	yes	characteristic
549	C₂	C₅×#5582	1	1	yes	characteristic
550	C₂	C₅×#5583	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×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2314
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#4977	C₂	semidirect
6. C₅×#4975	C₂	semidirect
8. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
9. C₅×#4933	C₂	semidirect
11. C₅×#4652	C₂	semidirect
30. C₅×#872	C₄	semidirect
37. #73760	C₅	direct (N × H)
48. C₄×C₅×C₄⋊C₄	D₃	semidirect
80. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
83. #4977	C₂×C₅	semidirect
84. #4975	C₂×C₅	semidirect
86. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
87. #4933	C₂×C₅	semidirect
89. #4652	C₂×C₅	semidirect
171. #872	C₄×C₅	semidirect
218. C₄×C₄⋊C₄	C₅×D₃	semidirect
437. C₃×C₅	#2314	semidirect
517. C₅	#73760	direct (N × H)
542. C₃	C₅×#2314	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#872	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4987	2
C₅×#4977	2
C₅×#4975	2
C₅×#4940	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4933	2
C₅×#4669	2
C₅×#4652	2
C₅×#2314	3
#73760	5

Subgroups — C5×#73760 #14322701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73760 #14322701