Subgroups — C₅×#22372 #11945092

Order 1280.

716 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2395	C₂	1	1	yes	maximal, characteristic
2	C₅×#1955	C₂	1	1	yes	maximal, characteristic
3	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1869	C₂	1	1	yes	maximal, characteristic
11	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₅×#400	C₄	1	1	yes	characteristic
37	C₅×#399	C₄	1	1	yes	characteristic
38	C₅×#398	C₄	1	1	yes	characteristic
39	C₅×#397	C₄	1	1	yes	characteristic
40	C₅×#397	C₄	1	1	yes	characteristic
41	C₅×#397	C₄	1	1	yes	characteristic
42	C₅×#394	C₄	1	1	yes	characteristic
43	C₅×#394	C₄	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×#336	C₂²	1	1	yes	characteristic
50	C₅×#336	C₂²	1	1	yes	characteristic
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	C₅×#336	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#22372	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	—	4	1	no	—
65	C₂²×C₅×C₈	—	4	1	no	—
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	—	4	1	no	—
75	C₄×C₅×D₄	—	4	1	no	—
76	C₅×#117	—	4	1	no	—
77	C₅×#117	—	4	1	no	—
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	2	no	—
101	C₅×C₄⋊C₈	—	4	1	no	—
102	C₅×C₄⋊C₈	—	4	1	no	—
103	C₅×C₄⋊C₈	—	4	1	no	—
104	C₅×C₄⋊C₈	—	4	1	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	—	4	1	no	—
109	C₅×C₂²⋊C₈	—	4	1	no	—
110	C₅×C₂²⋊C₈	—	4	1	no	—
111	C₅×C₂²⋊C₈	—	4	1	no	—
112	C₅×#97	—	4	1	no	—
113	C₅×#97	—	4	1	no	—
114	C₅×#97	—	4	1	no	—
115	C₄×C₅×C₈	—	2	2	no	—
116	C₄×C₅×C₈	—	4	1	no	—
117	C₅×#95	C₂×C₄	1	1	yes	characteristic
118	C₅×#95	C₂×C₄	1	1	yes	characteristic
119	C₅×#95	C₂×C₄	1	1	yes	characteristic
120	C₅×#95	C₂×C₄	1	1	yes	characteristic
121	C₅×#95	C₂×C₄	1	1	yes	characteristic
122	C₅×#95	C₂×C₄	1	1	yes	characteristic
123	C₅×#95	C₂×C₄	1	1	yes	characteristic
124	C₅×#95	C₂×C₄	1	1	yes	characteristic
125	C₅×#95	C₂×C₄	1	1	yes	characteristic
126	C₅×#95	C₂×C₄	1	1	yes	characteristic
127	#2395	C₂×C₅	1	1	yes	characteristic
128	#1955	C₂×C₅	1	1	yes	characteristic
129	#1940	C₂×C₅	1	1	yes	characteristic, complemented
130	#1924	C₂×C₅	1	1	yes	characteristic, complemented
131	#1923	C₂×C₅	1	1	yes	characteristic, complemented
132	#1923	C₂×C₅	1	1	yes	characteristic, complemented
133	#1923	C₂×C₅	1	1	yes	characteristic, complemented
134	#1917	C₂×C₅	1	1	yes	characteristic, complemented
135	#1916	C₂×C₅	1	1	yes	characteristic, complemented
136	#1869	C₂×C₅	1	1	yes	characteristic
137	#1850	C₂×C₅	1	1	yes	characteristic, complemented
138	#1798	C₂×C₅	1	1	yes	characteristic, complemented
139	#1770	C₂×C₅	1	1	yes	characteristic, complemented
140	#1752	C₂×C₅	1	1	yes	characteristic, complemented
141	#1750	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	4	1	no	—
146	C₂×C₅×D₄	—	4	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	4	4	no	—
195	C₂×C₅×C₈	#41	1	2	yes	—
196	C₂×C₅×C₈	#41	1	2	yes	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	4	1	no	—
199	C₅×C₄⋊C₄	—	4	1	no	—
200	C₅×C₄⋊C₄	—	4	1	no	—
201	C₅×C₄⋊C₄	—	4	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₂²⋊C₄	—	2	2	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	4	1	no	—
209	C₅×C₂²⋊C₄	—	4	1	no	—
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×#117	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×#97	C₂²×C₅	1	1	yes	characteristic
240	C₂×#97	C₂²×C₅	1	1	yes	characteristic
241	C₂×#97	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
244	#400	C₄×C₅	1	1	yes	characteristic
245	#399	C₄×C₅	1	1	yes	characteristic
246	#398	C₄×C₅	1	1	yes	characteristic
247	#397	C₄×C₅	1	1	yes	characteristic
248	#397	C₄×C₅	1	1	yes	characteristic
249	#397	C₄×C₅	1	1	yes	characteristic
250	#394	C₄×C₅	1	1	yes	characteristic
251	#394	C₄×C₅	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	#336	C₂²×C₅	1	1	yes	characteristic
258	#336	C₂²×C₅	1	1	yes	characteristic
259	#336	C₂²×C₅	1	1	yes	characteristic
260	#336	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	—	2	1	no	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	#131	1	2	yes	—
281	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
282	C₅×D₄	—	4	4	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	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	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	#131	1	2	yes	—
327	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	C₅×C₈	—	2	2	no	—
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	4	1	no	—
346	C₂²×C₈	—	4	1	no	—
347	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	C₄×D₄	—	4	1	no	—
356	C₄×D₄	—	4	1	no	—
357	#117	—	4	1	no	—
358	#117	—	4	1	no	—
359	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₄⋊C₈	—	2	2	no	—
382	C₄⋊C₈	—	4	1	no	—
383	C₄⋊C₈	—	4	1	no	—
384	C₄⋊C₈	—	4	1	no	—
385	C₄⋊C₈	—	4	1	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	4	1	no	—
390	C₂²⋊C₈	—	4	1	no	—
391	C₂²⋊C₈	—	4	1	no	—
392	C₂²⋊C₈	—	4	1	no	—
393	#97	—	4	1	no	—
394	#97	—	4	1	no	—
395	#97	—	4	1	no	—
396	C₄×C₈	—	2	2	no	—
397	C₄×C₈	—	4	1	no	—
398	#95	C₂×C₄×C₅	1	1	yes	characteristic
399	#95	C₂×C₄×C₅	1	1	yes	characteristic
400	#95	C₂×C₄×C₅	1	1	yes	characteristic
401	#95	C₂×C₄×C₅	1	1	yes	characteristic
402	#95	C₂×C₄×C₅	1	1	yes	characteristic
403	#95	C₂×C₄×C₅	1	1	yes	characteristic
404	#95	C₂×C₄×C₅	1	1	yes	characteristic
405	#95	C₂×C₄×C₅	1	1	yes	characteristic
406	#95	C₂×C₄×C₅	1	1	yes	characteristic
407	#95	C₂×C₄×C₅	1	1	yes	characteristic
408	C₂²×C₅	—	2	2	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	—	4	1	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	C₄×#41	1	1	yes	characteristic
423	C₂²×C₅	#518	1	1	yes	characteristic
424	C₂²×C₅	#520	1	1	yes	characteristic
425	C₂²×C₅	C₂×#131	1	1	yes	characteristic
426	C₂²×C₅	C₂×#131	1	1	yes	characteristic
427	C₂²×C₅	#568	1	1	yes	characteristic
428	C₂²×C₅	#568	1	1	yes	characteristic
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	#538	1	1	yes	characteristic
442	C₄×C₅	#539	1	1	yes	characteristic
443	C₄×C₅	#540	1	1	yes	characteristic
444	C₄×C₅	#542	1	1	yes	characteristic
445	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
446	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	4	4	no	—
498	C₂×C₈	C₅×#41	1	2	yes	—
499	C₂×C₈	C₅×#41	1	2	yes	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₂×C₅	—	4	2	no	—
528	C₂×C₅	—	8	1	no	—
529	C₂×C₅	#2335	1	1	yes	characteristic
530	C₂×C₅	#2968	1	1	yes	characteristic
531	C₂×C₅	#2968	1	1	yes	characteristic
532	C₂×C₅	#2976	1	1	yes	characteristic
533	C₂×C₅	#2981	1	1	yes	characteristic
534	C₂×C₅	#2994	1	1	yes	characteristic
535	C₂×C₅	#2995	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	C₅×#131	1	2	yes	—
550	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
551	D₄	—	4	4	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	C₅×#131	1	2	yes	—
596	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
597	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
598	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	2	2	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₅	#22372	1	1	yes	characteristic, direct product factor, Sylow
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	C₄×C₅×#41	1	1	yes	characteristic
626	C₂²	C₅×#518	1	1	yes	characteristic
627	C₂²	C₅×#520	1	1	yes	characteristic
628	C₂²	C₂×C₅×#131	1	1	yes	characteristic
629	C₂²	C₂×C₅×#131	1	1	yes	characteristic
630	C₂²	C₅×#568	1	1	yes	characteristic
631	C₂²	C₅×#568	1	1	yes	characteristic
632	C₄	—	2	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	C₅×#538	1	1	yes	characteristic
645	C₄	C₅×#539	1	1	yes	characteristic
646	C₄	C₅×#540	1	1	yes	characteristic
647	C₄	C₅×#542	1	1	yes	characteristic
648	C₂	—	4	2	no	—
649	C₂	—	8	1	no	—
650	C₂	C₅×#2335	1	1	yes	characteristic
651	C₂	C₅×#2968	1	1	yes	characteristic
652	C₂	C₅×#2968	1	1	yes	characteristic
653	C₂	C₅×#2976	1	1	yes	characteristic
654	C₂	C₅×#2981	1	1	yes	characteristic
655	C₂	C₅×#2994	1	1	yes	characteristic
656	C₂	C₅×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1940	C₂	semidirect
4. C₅×#1924	C₂	semidirect
5. C₅×#1923	C₂	semidirect
6. C₅×#1923	C₂	semidirect
7. C₅×#1923	C₂	semidirect
8. C₅×#1917	C₂	semidirect
9. C₅×#1916	C₂	semidirect
11. C₅×#1850	C₂	semidirect
12. C₅×#1798	C₂	semidirect
13. C₅×#1770	C₂	semidirect
14. C₅×#1752	C₂	semidirect
15. C₅×#1750	C₂	semidirect
59. #22372	C₅	direct (N × H)
129. #1940	C₂×C₅	semidirect
130. #1924	C₂×C₅	semidirect
131. #1923	C₂×C₅	semidirect
132. #1923	C₂×C₅	semidirect
133. #1923	C₂×C₅	semidirect
134. #1917	C₂×C₅	semidirect
135. #1916	C₂×C₅	semidirect
137. #1850	C₂×C₅	semidirect
138. #1798	C₂×C₅	semidirect
139. #1770	C₂×C₅	semidirect
140. #1752	C₂×C₅	semidirect
141. #1750	C₂×C₅	semidirect
610. C₅	#22372	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2395	2
C₅×#1955	2
C₅×#1940	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1869	2
C₅×#1850	2
C₅×#1798	2
C₅×#1770	2
C₅×#1752	2
C₅×#1750	2
#22372	5

Subgroups — C5×#22372 #11945092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22372 #11945092