Subgroups — C₅×#75474 #14326890

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
3	C₅×#4976	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4951	C₂	1	1	yes	maximal, characteristic
6	C₅×#4945	C₂	1	1	yes	maximal, characteristic
7	C₅×#4944	C₂	1	1	yes	maximal, characteristic
8	C₅×#4942	C₂	1	1	yes	maximal, characteristic
9	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4651	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4651	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4649	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2347	—	3	1	no	maximal, Hall
17	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×#217	C₂²	1	1	yes	characteristic
24	C₂×C₅×#217	C₂²	1	1	yes	characteristic
25	C₂×C₅×#217	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
40	C₅×#877	C₄	1	8	yes	complemented
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
44	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
45	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
46	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
47	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
48	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	#75474	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×#117	—	3	1	no	—
55	C₅×#389	—	3	1	no	—
56	C₅×#389	—	3	1	no	—
57	C₅×#388	—	3	1	no	—
58	C₅×#388	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	D₃	1	1	yes	characteristic
61	C₅×#383	—	3	1	no	—
62	C₅×#383	—	3	1	no	—
63	C₅×#380	—	3	1	no	—
64	C₄×C₅×C₄⋊C₄	—	3	1	no	—
65	C₄×C₅×C₄⋊C₄	—	3	1	no	—
66	C₄×C₅×C₄⋊C₄	—	3	1	no	—
67	C₄×C₅×C₄⋊C₄	—	3	1	no	—
68	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	—	2	2	no	—
77	C₂²×C₅×Dic₃	—	2	2	no	—
78	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
79	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	—	2	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
90	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
91	C₃×C₄²×C₅	—	4	1	no	—
92	C₅×#217	—	2	2	no	—
93	C₅×#217	—	4	1	no	—
94	C₅×#217	C₂×C₄	1	4	yes	—
95	C₅×C₄⋊Dic₃	—	2	2	no	—
96	C₅×Dic₃⋊C₄	—	2	2	no	—
97	C₅×Dic₃⋊C₄	—	2	2	no	—
98	C₅×Dic₃⋊C₄	—	2	2	no	—
99	C₅×Dic₃⋊C₄	—	2	2	no	—
100	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
101	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
102	C₄×C₅×Dic₃	—	2	2	no	—
103	C₄×C₅×Dic₃	—	2	2	no	—
104	C₄×C₅×Dic₃	—	4	1	no	—
105	C₄×C₅×Dic₃	—	4	1	no	—
106	C₄×C₅×Dic₃	—	4	1	no	—
107	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
108	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
109	C₂×#877	C₂×C₅	1	1	yes	characteristic
110	C₃×#388	C₂×C₅	1	1	yes	characteristic
111	#4976	C₂×C₅	1	1	yes	characteristic, complemented
112	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
113	#4951	C₂×C₅	1	1	yes	characteristic
114	#4945	C₂×C₅	1	1	yes	characteristic
115	#4944	C₂×C₅	1	1	yes	characteristic
116	#4942	C₂×C₅	1	1	yes	characteristic
117	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
118	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
119	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
120	#4651	C₂×C₅	1	1	yes	characteristic, complemented
121	#4651	C₂×C₅	1	1	yes	characteristic, complemented
122	#4649	C₂×C₅	1	1	yes	characteristic, complemented
123	#4647	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂³×C₄×C₅	—	3	1	no	—
125	C₅×#117	—	3	8	no	—
126	C₂×C₅×C₄⋊C₄	—	3	1	no	—
127	C₂×C₅×C₄⋊C₄	—	3	1	no	—
128	C₂×C₅×C₄⋊C₄	—	3	1	no	—
129	C₂×C₅×C₄⋊C₄	—	3	1	no	—
130	C₂×C₅×C₄⋊C₄	—	3	1	no	—
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	1	no	—
133	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
135	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
136	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
137	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
140	C₂×C₄²×C₅	—	3	1	no	—
141	C₂×C₄²×C₅	—	3	1	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₂×C₄²×C₅	—	3	1	no	—
144	C₂×C₄²×C₅	—	3	1	no	—
145	C₂×C₄²×C₅	—	3	1	no	—
146	C₂×C₄²×C₅	—	3	1	no	—
147	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
148	C₅×#95	—	3	1	no	—
149	C₅×#95	—	3	1	no	—
150	C₅×#95	—	3	1	no	—
151	C₅×#95	—	3	1	no	—
152	C₅×#95	—	3	1	no	—
153	C₅×#95	—	3	1	no	—
154	C₅×#95	—	3	1	no	—
155	C₅×#95	—	3	1	no	—
156	C₅×#95	—	3	1	no	—
157	C₅×#95	—	3	1	no	—
158	C₅×#95	C₂×D₃	1	1	yes	characteristic
159	C₅×#95	C₂×D₃	1	1	yes	characteristic
160	#2347	—	3	1	no	Sylow
161	C₂³×C₃×C₅	—	2	1	no	—
162	C₂³×C₃×C₅	—	2	1	no	—
163	C₂³×C₃×C₅	—	2	1	no	—
164	C₂³×C₃×C₅	—	2	1	no	—
165	C₂³×C₃×C₅	—	2	1	no	—
166	C₂³×C₃×C₅	—	2	1	no	—
167	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
168	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
185	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
186	C₂×C₃×C₄×C₅	#41	1	2	yes	—
187	C₂×C₅×Dic₃	—	2	1	no	—
188	C₂×C₅×Dic₃	—	2	1	no	—
189	C₂×C₅×Dic₃	—	2	1	no	—
190	C₂×C₅×Dic₃	—	2	1	no	—
191	C₂×C₅×Dic₃	—	2	1	no	—
192	C₂×C₅×Dic₃	—	2	1	no	—
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	8	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	—	2	1	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
206	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
207	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
208	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
209	C₂×C₅×Dic₃	#41	1	2	yes	—
210	C₂×C₅×Dic₃	#41	1	2	yes	—
211	C₂×C₅×Dic₃	#41	1	2	yes	—
212	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
218	C₂×#217	C₂²×C₅	1	1	yes	characteristic
219	C₂×#217	C₂²×C₅	1	1	yes	characteristic
220	C₂×#217	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
222	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	#877	C₄×C₅	1	8	yes	complemented
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃×#95	C₂²×C₅	1	1	yes	characteristic
238	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
239	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
240	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
241	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
242	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
243	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
244	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
245	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
246	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
247	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
248	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
249	C₂²×C₄×C₅	—	3	1	no	—
250	C₂²×C₄×C₅	—	3	4	no	—
251	C₂²×C₄×C₅	—	3	1	no	—
252	C₂²×C₄×C₅	—	3	1	no	—
253	C₂²×C₄×C₅	—	3	1	no	—
254	C₂²×C₄×C₅	—	3	1	no	—
255	C₂²×C₄×C₅	—	3	1	no	—
256	C₂²×C₄×C₅	—	3	1	no	—
257	C₂²×C₄×C₅	—	3	1	no	—
258	C₂²×C₄×C₅	—	6	2	no	—
259	C₂²×C₄×C₅	—	6	2	no	—
260	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
266	C₅×C₄⋊C₄	—	2	2	no	—
267	C₅×C₄⋊C₄	—	3	4	no	—
268	C₅×C₄⋊C₄	—	3	4	no	—
269	C₅×C₄⋊C₄	—	6	2	no	—
270	C₅×C₄⋊C₄	—	6	2	no	—
271	C₅×C₄⋊C₄	—	6	2	no	—
272	C₅×C₄⋊C₄	—	6	2	no	—
273	C₅×C₄⋊C₄	—	6	2	no	—
274	C₅×C₂²⋊C₄	—	2	2	no	—
275	C₅×C₂²⋊C₄	—	3	4	no	—
276	C₅×C₂²⋊C₄	—	4	1	no	—
277	C₅×C₂²⋊C₄	—	6	2	no	—
278	C₅×C₂²⋊C₄	—	12	1	no	—
279	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	—
280	C₄²×C₅	—	3	4	no	—
281	C₄²×C₅	—	3	4	no	—
282	C₄²×C₅	—	4	1	no	—
283	C₄²×C₅	—	6	2	no	—
284	C₄²×C₅	—	6	2	no	—
285	C₄²×C₅	—	12	1	no	—
286	C₄²×C₅	—	12	1	no	—
287	C₄²×C₅	—	12	1	no	—
288	C₂×#117	—	3	1	no	—
289	#389	—	3	1	no	—
290	#389	—	3	1	no	—
291	#388	—	3	1	no	—
292	#388	—	3	1	no	—
293	#388	—	3	1	no	—
294	#388	C₅×D₃	1	1	yes	characteristic
295	#383	—	3	1	no	—
296	#383	—	3	1	no	—
297	#380	—	3	1	no	—
298	C₄×C₄⋊C₄	—	3	1	no	—
299	C₄×C₄⋊C₄	—	3	1	no	—
300	C₄×C₄⋊C₄	—	3	1	no	—
301	C₄×C₄⋊C₄	—	3	1	no	—
302	C₄×C₂²⋊C₄	—	3	1	no	—
303	C₂²×C₃×C₅	—	2	2	no	—
304	C₂²×C₃×C₅	—	2	2	no	—
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	4	1	no	—
307	C₂²×C₃×C₅	—	4	1	no	—
308	C₂²×C₃×C₅	—	4	1	no	—
309	C₂²×C₃×C₅	—	4	1	no	—
310	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
311	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
312	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
313	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
314	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
315	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	—	2	2	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	4	1	no	—
321	C₃×C₄×C₅	—	4	1	no	—
322	C₃×C₄×C₅	—	4	1	no	—
323	C₅×Dic₃	—	2	2	no	—
324	C₅×Dic₃	—	2	2	no	—
325	C₅×Dic₃	—	2	2	no	—
326	C₅×Dic₃	—	2	2	no	—
327	C₅×Dic₃	—	4	1	no	—
328	C₅×Dic₃	—	4	1	no	—
329	C₅×Dic₃	—	4	1	no	—
330	C₅×Dic₃	#117	1	4	yes	—
331	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×Dic₃	—	2	2	no	—
339	C₂²×Dic₃	—	2	2	no	—
340	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
341	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
342	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
343	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
344	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
345	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
346	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
347	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
348	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
349	C₃×C₄⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	2	no	—
351	C₃×C₂²⋊C₄	—	4	1	no	—
352	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
353	C₃×C₄²	—	4	1	no	—
354	#217	—	2	2	no	—
355	#217	—	4	1	no	—
356	#217	C₂×C₄×C₅	1	4	yes	—
357	C₄⋊Dic₃	—	2	2	no	—
358	Dic₃⋊C₄	—	2	2	no	—
359	Dic₃⋊C₄	—	2	2	no	—
360	Dic₃⋊C₄	—	2	2	no	—
361	Dic₃⋊C₄	—	2	2	no	—
362	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
363	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
364	C₄×Dic₃	—	2	2	no	—
365	C₄×Dic₃	—	2	2	no	—
366	C₄×Dic₃	—	4	1	no	—
367	C₄×Dic₃	—	4	1	no	—
368	C₄×Dic₃	—	4	1	no	—
369	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
370	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
371	C₂³×C₅	—	2	1	no	—
372	C₂³×C₅	—	2	1	no	—
373	C₂³×C₅	—	2	1	no	—
374	C₂³×C₅	—	2	1	no	—
375	C₂³×C₅	—	2	1	no	—
376	C₂³×C₅	—	2	1	no	—
377	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
378	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	3	2	no	—
395	C₂×C₄×C₅	—	3	2	no	—
396	C₂×C₄×C₅	—	3	2	no	—
397	C₂×C₄×C₅	—	3	2	no	—
398	C₂×C₄×C₅	—	3	2	no	—
399	C₂×C₄×C₅	—	3	2	no	—
400	C₂×C₄×C₅	—	3	2	no	—
401	C₂×C₄×C₅	—	6	8	no	—
402	C₂×C₄×C₅	—	6	1	no	—
403	C₂×C₄×C₅	—	6	1	no	—
404	C₂×C₄×C₅	—	6	1	no	—
405	C₂×C₄×C₅	—	6	1	no	—
406	C₂×C₄×C₅	—	6	1	no	—
407	C₂×C₄×C₅	—	6	1	no	—
408	C₂×C₄×C₅	—	6	1	no	—
409	C₂×C₄×C₅	—	6	1	no	—
410	C₂×C₄×C₅	—	6	1	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
420	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
421	C₂×C₄×C₅	#237	1	2	yes	—
422	C₂³×C₄	—	3	1	no	—
423	#117	—	3	8	no	—
424	C₂×C₄⋊C₄	—	3	1	no	—
425	C₂×C₄⋊C₄	—	3	1	no	—
426	C₂×C₄⋊C₄	—	3	1	no	—
427	C₂×C₄⋊C₄	—	3	1	no	—
428	C₂×C₄⋊C₄	—	3	1	no	—
429	C₂×C₄⋊C₄	—	3	1	no	—
430	C₂×C₄⋊C₄	—	3	1	no	—
431	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	3	1	no	—
433	C₂×C₂²⋊C₄	—	3	1	no	—
434	C₂×C₂²⋊C₄	—	3	1	no	—
435	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
438	C₂×C₄²	—	3	1	no	—
439	C₂×C₄²	—	3	1	no	—
440	C₂×C₄²	—	3	1	no	—
441	C₂×C₄²	—	3	1	no	—
442	C₂×C₄²	—	3	1	no	—
443	C₂×C₄²	—	3	1	no	—
444	C₂×C₄²	—	3	1	no	—
445	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
446	#95	—	3	1	no	—
447	#95	—	3	1	no	—
448	#95	—	3	1	no	—
449	#95	—	3	1	no	—
450	#95	—	3	1	no	—
451	#95	—	3	1	no	—
452	#95	—	3	1	no	—
453	#95	—	3	1	no	—
454	#95	—	3	1	no	—
455	#95	—	3	1	no	—
456	#95	C₂×C₅×D₃	1	1	yes	characteristic
457	#95	C₂×C₅×D₃	1	1	yes	characteristic
458	C₂×C₃×C₅	—	4	2	no	—
459	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
460	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
461	C₂×C₃×C₅	#520	1	1	yes	characteristic
462	C₂×C₃×C₅	#553	1	1	yes	characteristic
463	C₂×C₃×C₅	#553	1	1	yes	characteristic
464	C₂×C₃×C₅	#556	1	1	yes	characteristic
465	C₂×C₃×C₅	#556	1	1	yes	characteristic
466	C₂³×C₃	—	2	1	no	—
467	C₂³×C₃	—	2	1	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	1	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	2	1	no	—
472	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
473	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
490	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
491	C₂×C₃×C₄	C₅×#41	1	2	yes	—
492	C₂×Dic₃	—	2	1	no	—
493	C₂×Dic₃	—	2	1	no	—
494	C₂×Dic₃	—	2	1	no	—
495	C₂×Dic₃	—	2	1	no	—
496	C₂×Dic₃	—	2	1	no	—
497	C₂×Dic₃	—	2	1	no	—
498	C₂×Dic₃	—	2	1	no	—
499	C₂×Dic₃	—	2	1	no	—
500	C₂×Dic₃	—	2	8	no	—
501	C₂×Dic₃	—	2	1	no	—
502	C₂×Dic₃	—	2	1	no	—
503	C₂×Dic₃	—	2	1	no	—
504	C₂×Dic₃	—	2	1	no	—
505	C₂×Dic₃	—	2	1	no	—
506	C₂×Dic₃	—	2	1	no	—
507	C₂×Dic₃	—	2	1	no	—
508	C₂×Dic₃	—	2	1	no	—
509	C₂×Dic₃	—	2	1	no	—
510	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
511	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
512	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
513	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
514	C₂×Dic₃	C₅×#41	1	2	yes	—
515	C₂×Dic₃	C₅×#41	1	2	yes	—
516	C₂×Dic₃	C₅×#41	1	2	yes	—
517	C₂²×C₅	—	2	2	no	—
518	C₂²×C₅	—	2	2	no	—
519	C₂²×C₅	—	2	2	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
525	C₂²×C₅	C₂×#237	1	1	yes	characteristic
526	C₂²×C₅	#1004	1	1	yes	characteristic
527	C₂²×C₅	D₃×#41	1	1	yes	characteristic
528	C₂²×C₅	D₃×#41	1	1	yes	characteristic
529	C₂²×C₅	D₃×#41	1	1	yes	characteristic
530	C₂²×C₅	#1010	1	1	yes	characteristic
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	2	2	no	—
534	C₄×C₅	—	3	4	no	—
535	C₄×C₅	—	4	1	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	6	2	no	—
539	C₄×C₅	—	6	2	no	—
540	C₄×C₅	—	6	2	no	—
541	C₄×C₅	—	6	2	no	—
542	C₄×C₅	—	12	1	no	—
543	C₄×C₅	—	12	1	no	—
544	C₄×C₅	—	12	1	no	—
545	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	—	3	4	no	—
548	C₂²×C₄	—	3	1	no	—
549	C₂²×C₄	—	3	1	no	—
550	C₂²×C₄	—	3	1	no	—
551	C₂²×C₄	—	3	1	no	—
552	C₂²×C₄	—	3	1	no	—
553	C₂²×C₄	—	3	1	no	—
554	C₂²×C₄	—	3	1	no	—
555	C₂²×C₄	—	6	2	no	—
556	C₂²×C₄	—	6	2	no	—
557	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
562	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	3	4	no	—
565	C₄⋊C₄	—	3	4	no	—
566	C₄⋊C₄	—	6	2	no	—
567	C₄⋊C₄	—	6	2	no	—
568	C₄⋊C₄	—	6	2	no	—
569	C₄⋊C₄	—	6	2	no	—
570	C₄⋊C₄	—	6	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	3	4	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	6	2	no	—
575	C₂²⋊C₄	—	12	1	no	—
576	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	—
577	C₄²	—	3	4	no	—
578	C₄²	—	3	4	no	—
579	C₄²	—	4	1	no	—
580	C₄²	—	6	2	no	—
581	C₄²	—	6	2	no	—
582	C₄²	—	12	1	no	—
583	C₄²	—	12	1	no	—
584	C₄²	—	12	1	no	—
585	C₃×C₅	#2347	1	1	yes	characteristic, complemented, Hall
586	C₂²×C₃	—	2	2	no	—
587	C₂²×C₃	—	2	2	no	—
588	C₂²×C₃	—	2	2	no	—
589	C₂²×C₃	—	4	1	no	—
590	C₂²×C₃	—	4	1	no	—
591	C₂²×C₃	—	4	1	no	—
592	C₂²×C₃	—	4	1	no	—
593	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
594	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
595	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
596	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
597	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
598	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
600	C₃×C₄	—	2	2	no	—
601	C₃×C₄	—	2	2	no	—
602	C₃×C₄	—	2	2	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	1	no	—
606	Dic₃	—	2	2	no	—
607	Dic₃	—	2	2	no	—
608	Dic₃	—	2	2	no	—
609	Dic₃	—	2	2	no	—
610	Dic₃	—	4	1	no	—
611	Dic₃	—	4	1	no	—
612	Dic₃	—	4	1	no	—
613	Dic₃	C₅×#117	1	4	yes	—
614	C₂×C₅	—	4	2	no	—
615	C₂×C₅	D₃×#117	1	1	yes	characteristic
616	C₂×C₅	C₄×#237	1	1	yes	characteristic
617	C₂×C₅	#5546	1	1	yes	characteristic
618	C₂×C₅	#5601	1	1	yes	characteristic
619	C₂×C₅	#5661	1	1	yes	characteristic
620	C₂×C₅	#5671	1	1	yes	characteristic
621	C₂×C₅	#5702	1	1	yes	characteristic
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
629	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	3	2	no	—
646	C₂×C₄	—	3	2	no	—
647	C₂×C₄	—	3	2	no	—
648	C₂×C₄	—	3	2	no	—
649	C₂×C₄	—	3	2	no	—
650	C₂×C₄	—	3	2	no	—
651	C₂×C₄	—	3	2	no	—
652	C₂×C₄	—	6	8	no	—
653	C₂×C₄	—	6	1	no	—
654	C₂×C₄	—	6	1	no	—
655	C₂×C₄	—	6	1	no	—
656	C₂×C₄	—	6	1	no	—
657	C₂×C₄	—	6	1	no	—
658	C₂×C₄	—	6	1	no	—
659	C₂×C₄	—	6	1	no	—
660	C₂×C₄	—	6	1	no	—
661	C₂×C₄	—	6	1	no	—
662	C₂×C₄	—	6	1	no	—
663	C₂×C₄	—	6	1	no	—
664	C₂×C₄	—	6	1	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	6	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	—	6	1	no	—
670	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
671	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
672	C₂×C₄	C₅×#237	1	2	yes	—
673	C₂×C₃	—	4	2	no	—
674	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
675	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
676	C₂×C₃	C₅×#520	1	1	yes	characteristic
677	C₂×C₃	C₅×#553	1	1	yes	characteristic
678	C₂×C₃	C₅×#553	1	1	yes	characteristic
679	C₂×C₃	C₅×#556	1	1	yes	characteristic
680	C₂×C₃	C₅×#556	1	1	yes	characteristic
681	C₅	#75474	1	1	yes	characteristic, direct product factor, Sylow
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
690	C₂²	C₂×C₅×#237	1	1	yes	characteristic
691	C₂²	C₅×#1004	1	1	yes	characteristic
692	C₂²	C₅×D₃×#41	1	1	yes	characteristic
693	C₂²	C₅×D₃×#41	1	1	yes	characteristic
694	C₂²	C₅×D₃×#41	1	1	yes	characteristic
695	C₂²	C₅×#1010	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	3	4	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	6	2	no	—
704	C₄	—	6	2	no	—
705	C₄	—	6	2	no	—
706	C₄	—	6	2	no	—
707	C₄	—	12	1	no	—
708	C₄	—	12	1	no	—
709	C₄	—	12	1	no	—
710	C₃	C₅×#2347	1	1	yes	characteristic, complemented, Sylow
711	C₂	—	4	2	no	—
712	C₂	C₅×D₃×#117	1	1	yes	characteristic
713	C₂	C₄×C₅×#237	1	1	yes	characteristic
714	C₂	C₅×#5546	1	1	yes	characteristic
715	C₂	C₅×#5601	1	1	yes	characteristic
716	C₂	C₅×#5661	1	1	yes	characteristic
717	C₂	C₅×#5671	1	1	yes	characteristic
718	C₂	C₅×#5702	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×#388	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#388	D₃
hypocenter	C₃	C₅×#2347
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#388

Complements

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

N	H ≅ G/N	type
3. C₅×#4976	C₂	semidirect
4. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
10. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
11. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
12. C₅×#4651	C₂	semidirect
13. C₅×#4651	C₂	semidirect
14. C₅×#4649	C₂	semidirect
15. C₅×#4647	C₂	semidirect
40. C₅×#877	C₄	semidirect
53. #75474	C₅	direct (N × H)
111. #4976	C₂×C₅	semidirect
112. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
118. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
119. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
120. #4651	C₂×C₅	semidirect
121. #4651	C₂×C₅	semidirect
122. #4649	C₂×C₅	semidirect
123. #4647	C₂×C₅	semidirect
235. #877	C₄×C₅	semidirect
585. C₃×C₅	#2347	semidirect
681. C₅	#75474	direct (N × H)
710. C₃	C₅×#2347	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#877	2
C₃×C₅×#388	2
C₅×#4976	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4951	2
C₅×#4945	2
C₅×#4944	2
C₅×#4942	2
C₅×Dic₃×C₂²⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4651	2
C₅×#4649	2
C₅×#4647	2
C₅×#2347	3
#75474	5

Subgroups — C5×#75474 #14326890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75474 #14326890