Subgroups — C₅×#22986 #11945706

Order 1280.

1084 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×#435	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
5	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1924	C₂	1	2	yes	maximal, complemented
8	C₅×#1870	C₂	1	2	yes	maximal, complemented
9	C₅×#1850	C₂	1	2	yes	maximal, complemented
10	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₅×#121	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#435	—	2	8	no	—
19	C₅×C₈×D₄	—	2	4	no	—
20	C₅×#423	—	2	4	no	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#390	C₄	1	1	yes	characteristic
34	C₅×#389	C₄	1	1	yes	characteristic
35	C₅×#388	C₄	1	2	yes	—
36	C₅×#386	C₄	1	2	yes	—
37	C₅×#380	C₄	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	1	yes	characteristic
44	#22986	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
46	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂³	1	2	yes	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	4	no	—
52	C₂×C₅×M₁₆	—	2	4	no	—
53	C₂×C₅×M₁₆	—	4	2	no	—
54	C₂²×C₅×C₈	—	2	4	no	—
55	C₂²×C₅×C₈	—	2	4	no	—
56	C₂²×C₅×C₈	—	4	2	no	—
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	2	yes	—
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₅×#121	—	2	4	no	—
64	C₄×C₅×D₄	—	2	4	no	—
65	C₄×C₅×D₄	—	2	4	no	—
66	C₄×C₅×D₄	—	2	2	no	—
67	C₄×C₅×D₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₅	—	2	2	no	—
78	C₂×C₄²×C₅	—	2	2	no	—
79	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	2	yes	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	—	2	4	no	—
85	C₅×C₄⋊C₈	—	2	4	no	—
86	C₅×C₄⋊C₈	—	2	2	no	—
87	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
88	C₅×C₂²⋊C₈	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	4	no	—
90	C₅×C₂²⋊C₈	—	2	4	no	—
91	C₅×C₂²⋊C₈	—	4	2	no	—
92	C₅×C₂²⋊C₈	D₄	1	4	yes	complemented
93	C₅×#97	—	2	4	no	—
94	C₄×C₅×C₈	—	2	2	no	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₅×#95	C₂×C₄	1	2	yes	—
97	C₅×#95	C₂×C₄	1	2	yes	—
98	C₅×#95	C₂×C₄	1	2	yes	—
99	C₂×#435	C₂×C₅	1	2	yes	complemented
100	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#423	C₂×C₅	1	1	yes	characteristic, complemented
102	C₄×#121	C₂×C₅	1	1	yes	characteristic
103	#1954	C₂×C₅	1	1	yes	characteristic, complemented
104	#1939	C₂×C₅	1	1	yes	characteristic, complemented
105	#1924	C₂×C₅	1	2	yes	complemented
106	#1870	C₂×C₅	1	2	yes	complemented
107	#1850	C₂×C₅	1	2	yes	complemented
108	#1770	C₂×C₅	1	1	yes	characteristic, complemented
109	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₅×D₄	—	2	4	no	—
113	C₂×C₅×D₄	—	2	4	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	M₁₆	1	4	yes	complemented
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	4	1	no	—
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅	#41	1	2	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×M₁₆	—	4	8	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	4	8	no	—
162	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
164	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₅×C₂²⋊C₄	—	2	4	no	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₅×C₂²⋊C₄	—	2	4	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	C₂×D₄	1	2	yes	—
181	C₄²×C₅	#41	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
183	C₂³×C₈	C₂²×C₅	1	2	yes	—
184	C₂×#121	C₄×C₅	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
186	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
188	#435	—	2	8	no	—
189	C₈×D₄	—	2	4	no	—
190	#423	—	2	4	no	—
191	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	C₂×#97	C₂²×C₅	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
203	#390	C₄×C₅	1	1	yes	characteristic
204	#389	C₄×C₅	1	1	yes	characteristic
205	#388	C₄×C₅	1	2	yes	—
206	#386	C₄×C₅	1	2	yes	—
207	#380	C₄×C₅	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
210	#336	C₂²×C₅	1	1	yes	characteristic
211	#336	C₂²×C₅	1	2	yes	—
212	#336	C₂²×C₅	1	2	yes	—
213	#336	C₂²×C₅	1	1	yes	characteristic
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	2	1	no	—
217	C₂³×C₅	—	2	1	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	1	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₄×D₄	1	2	yes	—
227	C₂³×C₅	C₂×M₁₆	1	4	yes	—
228	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₅×D₄	—	2	8	no	—
230	C₅×D₄	—	4	8	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	4	4	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	2	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	4	no	—
259	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
260	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
261	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
262	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
263	C₂×C₄×C₅	#131	1	2	yes	—
264	C₂×C₄×C₅	#131	1	2	yes	—
265	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
271	C₅×C₈	—	2	2	no	—
272	C₅×C₈	—	2	4	no	—
273	C₅×C₈	—	2	2	no	—
274	C₅×C₈	—	4	2	no	—
275	C₅×C₈	—	4	1	no	—
276	C₅×C₈	—	4	1	no	—
277	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
278	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₅	1	2	yes	—
282	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	4	2	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	—	2	4	no	—
288	C₂²×C₈	—	4	2	no	—
289	C₂²×C₈	C₂³×C₅	1	2	yes	—
290	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₅	1	2	yes	—
294	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
295	#121	—	2	4	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₅	1	2	yes	—
314	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
316	C₄⋊C₈	—	2	4	no	—
317	C₄⋊C₈	—	2	4	no	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	4	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	C₂²⋊C₈	—	4	2	no	—
324	C₂²⋊C₈	C₅×D₄	1	4	yes	complemented
325	#97	—	2	4	no	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	C₂×C₄×C₅	1	2	yes	—
329	#95	C₂×C₄×C₅	1	2	yes	—
330	#95	C₂×C₄×C₅	1	2	yes	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	4	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	4	no	—
336	C₂²×C₅	—	2	4	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	4	1	no	—
344	C₂²×C₅	—	4	2	no	—
345	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
346	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₅	#520	1	1	yes	characteristic
348	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
349	C₂²×C₅	C₂×#131	1	1	yes	characteristic
350	C₂²×C₅	C₂×#131	1	1	yes	characteristic
351	C₂²×C₅	#568	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	2	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	4	1	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	#435	1	4	yes	complemented
360	C₄×C₅	D₄²	1	1	yes	characteristic
361	C₄×C₅	#547	1	1	yes	characteristic
362	C₄×C₅	#548	1	1	yes	characteristic
363	C₄×C₅	#553	1	1	yes	characteristic
364	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
365	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	C₅×M₁₆	1	4	yes	complemented
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
391	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
392	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
397	C₂²×C₄	C₅×#41	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
399	M₁₆	—	4	8	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	4	8	no	—
416	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
417	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
418	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×C₅×D₄	1	2	yes	—
435	C₄²	C₅×#41	1	2	yes	—
436	C₂×C₅	—	4	2	no	—
437	C₂×C₅	—	4	4	no	—
438	C₂×C₅	#2361	1	1	yes	characteristic
439	C₂×C₅	C₂×#435	1	1	yes	characteristic
440	C₂×C₅	#2931	1	1	yes	characteristic
441	C₂×C₅	#2933	1	1	yes	characteristic
442	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
443	C₂×C₅	#2990	1	1	yes	characteristic
444	C₂×C₅	#2993	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	2	no	—
457	C₂³	C₄×C₅×D₄	1	2	yes	—
458	C₂³	C₂×C₅×M₁₆	1	4	yes	—
459	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
460	D₄	—	2	8	no	—
461	D₄	—	4	8	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
491	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
492	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
493	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
494	C₂×C₄	C₅×#131	1	2	yes	—
495	C₂×C₄	C₅×#131	1	2	yes	—
496	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
499	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
500	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	4	no	—
504	C₈	—	2	2	no	—
505	C₈	—	4	2	no	—
506	C₈	—	4	1	no	—
507	C₈	—	4	1	no	—
508	C₅	#22986	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	4	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	2	no	—
523	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
524	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
525	C₂²	C₅×#520	1	1	yes	characteristic
526	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
527	C₂²	C₂×C₅×#131	1	1	yes	characteristic
528	C₂²	C₂×C₅×#131	1	1	yes	characteristic
529	C₂²	C₅×#568	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₅×#435	1	4	yes	complemented
538	C₄	C₅×D₄²	1	1	yes	characteristic
539	C₄	C₅×#547	1	1	yes	characteristic
540	C₄	C₅×#548	1	1	yes	characteristic
541	C₄	C₅×#553	1	1	yes	characteristic
542	C₂	—	4	4	no	—
543	C₂	—	4	2	no	—
544	C₂	C₅×#2361	1	1	yes	characteristic
545	C₂	C₂×C₅×#435	1	1	yes	characteristic
546	C₂	C₅×#2931	1	1	yes	characteristic
547	C₂	C₅×#2933	1	1	yes	characteristic
548	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
549	C₂	C₅×#2990	1	1	yes	characteristic
550	C₂	C₅×#2993	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	C₂×C₅×#121	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
1. C₂×C₅×#435	C₂	semidirect
2. C₂×C₅×C₈×D₄	C₂	semidirect
3. C₂×C₅×#423	C₂	semidirect
5. C₅×#1954	C₂	semidirect
6. C₅×#1939	C₂	semidirect
7. C₅×#1924	C₂	semidirect
8. C₅×#1870	C₂	semidirect
9. C₅×#1850	C₂	semidirect
10. C₅×#1770	C₂	semidirect
11. C₄×C₅×C₂²⋊C₈	C₂	semidirect
44. #22986	C₅	direct (N × H)
87. C₅×C₄⋊C₈	D₄	semidirect
92. C₅×C₂²⋊C₈	D₄	semidirect
99. C₂×#435	C₂×C₅	semidirect
100. C₂×C₈×D₄	C₂×C₅	semidirect
101. C₂×#423	C₂×C₅	semidirect
103. #1954	C₂×C₅	semidirect
104. #1939	C₂×C₅	semidirect
105. #1924	C₂×C₅	semidirect
106. #1870	C₂×C₅	semidirect
107. #1850	C₂×C₅	semidirect
108. #1770	C₂×C₅	semidirect
109. C₄×C₂²⋊C₈	C₂×C₅	semidirect
117. C₂×C₅×D₄	M₁₆	semidirect
319. C₄⋊C₈	C₅×D₄	semidirect
324. C₂²⋊C₈	C₅×D₄	semidirect
359. C₄×C₅	#435	semidirect
371. C₂×D₄	C₅×M₁₆	semidirect
508. C₅	#22986	direct (N × H)
537. C₄	C₅×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
C₂×C₅×#423	2
C₄×C₅×#121	2
C₅×#1954	2
C₅×#1939	2
C₅×#1924	2
C₅×#1870	2
C₅×#1850	2
C₅×#1770	2
C₄×C₅×C₂²⋊C₈	2
#22986	5

Subgroups — C5×#22986 #11945706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22986 #11945706