Subgroups — C₅×#23083 #11945803

Order 1280.

1040 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
4	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1954	C₂	1	2	yes	maximal, complemented
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1923	C₂	1	2	yes	maximal, complemented
8	C₅×#1869	C₂	1	2	yes	maximal, complemented
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₅×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₅×C₈×D₄	—	2	4	no	—
18	C₅×#431	—	2	4	no	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
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×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
32	C₅×#390	C₄	1	1	yes	characteristic
33	C₅×#389	C₄	1	1	yes	characteristic
34	C₅×#388	C₄	1	2	yes	—
35	C₅×#386	C₄	1	2	yes	—
36	C₅×#380	C₄	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	1	yes	characteristic
43	#23083	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂³	1	2	yes	—
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	—	2	4	no	—
51	C₂²×C₅×C₈	—	2	4	no	—
52	C₂²×C₅×C₈	—	4	2	no	—
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×#121	C₈	1	8	yes	complemented
60	C₄×C₅×D₄	—	2	2	no	—
61	C₄×C₅×D₄	—	2	2	no	—
62	C₄×C₅×D₄	—	4	2	no	—
63	C₄×C₅×D₄	—	4	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	2	yes	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	4	2	no	—
82	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
83	C₅×C₂²⋊C₈	—	2	4	no	—
84	C₅×C₂²⋊C₈	—	2	4	no	—
85	C₅×C₂²⋊C₈	—	2	2	no	—
86	C₅×C₂²⋊C₈	—	2	2	no	—
87	C₅×C₂²⋊C₈	—	2	4	no	—
88	C₅×C₂²⋊C₈	—	4	2	no	—
89	C₄×C₅×C₈	—	2	4	no	—
90	C₄×C₅×C₈	—	2	2	no	—
91	C₄×C₅×C₈	—	2	2	no	—
92	C₄×C₅×C₈	—	4	2	no	—
93	C₅×#95	C₂×C₄	1	2	yes	—
94	C₅×#95	C₂×C₄	1	2	yes	—
95	C₅×#95	C₂×C₄	1	2	yes	—
96	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×#121	C₂×C₅	1	1	yes	characteristic
99	#1954	C₂×C₅	1	1	yes	characteristic, complemented
100	#1954	C₂×C₅	1	2	yes	complemented
101	#1939	C₂×C₅	1	1	yes	characteristic, complemented
102	#1923	C₂×C₅	1	2	yes	complemented
103	#1869	C₂×C₅	1	2	yes	complemented
104	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
105	C₈×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
106	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	4	2	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
114	C₂×C₅×D₄	C₂×C₈	1	8	yes	complemented
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	2	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	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	4	1	no	—
132	C₂²×C₄×C₅	C₂×C₈	1	4	yes	complemented
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	4	8	no	—
158	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
159	C₂×C₅×C₈	#41	1	2	yes	—
160	C₂×C₅×C₈	#41	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	4	2	no	—
164	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₅×C₂²⋊C₄	—	4	2	no	—
168	C₅×C₂²⋊C₄	—	4	2	no	—
169	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	2	2	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	C₂×D₄	1	2	yes	—
177	C₄²×C₅	#41	1	2	yes	—
178	C₂³×C₈	C₂²×C₅	1	2	yes	—
179	C₂×#121	C₄×C₅	1	1	yes	characteristic
180	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
182	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
183	C₈×D₄	—	2	4	no	—
184	#431	—	2	4	no	—
185	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
198	#390	C₄×C₅	1	1	yes	characteristic
199	#389	C₄×C₅	1	1	yes	characteristic
200	#388	C₄×C₅	1	2	yes	—
201	#386	C₄×C₅	1	2	yes	—
202	#380	C₄×C₅	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
205	#336	C₂²×C₅	1	2	yes	—
206	#336	C₂²×C₅	1	2	yes	—
207	#336	C₂²×C₅	1	1	yes	characteristic
208	#336	C₂²×C₅	1	1	yes	characteristic
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	—	2	1	no	—
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	C₂²×C₈	1	4	yes	—
222	C₂³×C₅	C₂²×C₈	1	2	yes	—
223	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₅×D₄	—	2	8	no	—
225	C₅×D₄	—	4	8	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	4	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
255	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
256	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
257	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
258	C₂×C₄×C₅	#131	1	2	yes	—
259	C₂×C₄×C₅	#131	1	2	yes	—
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	2	4	no	—
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
274	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₅	1	2	yes	—
277	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	4	2	no	—
281	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₅	1	2	yes	—
284	C₂²×C₈	C₂³×C₅	1	2	yes	—
285	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
287	#121	C₅×C₈	1	8	yes	complemented
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	4	2	no	—
291	C₄×D₄	—	4	2	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
304	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₅	1	2	yes	—
306	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	4	2	no	—
310	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
311	C₂²⋊C₈	—	2	4	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	4	2	no	—
317	C₄×C₈	—	2	4	no	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	4	2	no	—
321	#95	C₂×C₄×C₅	1	2	yes	—
322	#95	C₂×C₄×C₅	1	2	yes	—
323	#95	C₂×C₄×C₅	1	2	yes	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	4	no	—
326	C₂²×C₅	—	2	4	no	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	4	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	4	1	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
339	C₂²×C₅	C₄×#41	1	1	yes	characteristic
340	C₂²×C₅	#518	1	1	yes	characteristic
341	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
342	C₂²×C₅	C₂×#131	1	1	yes	characteristic
343	C₂²×C₅	C₂×#131	1	1	yes	characteristic
344	C₂²×C₅	#568	1	1	yes	characteristic
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	2	4	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	4	2	no	—
352	C₄×C₅	C₈×D₄	1	4	yes	—
353	C₄×C₅	#546	1	1	yes	characteristic
354	C₄×C₅	#550	1	1	yes	characteristic
355	C₄×C₅	#553	1	1	yes	characteristic
356	C₄×C₅	#555	1	1	yes	characteristic
357	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
358	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
364	C₂×D₄	C₂×C₅×C₈	1	8	yes	complemented
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	C₂×C₅×C₈	1	4	yes	complemented
383	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
385	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
389	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	4	8	no	—
408	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
409	C₂×C₈	C₅×#41	1	2	yes	—
410	C₂×C₈	C₅×#41	1	2	yes	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	complemented
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×C₅×D₄	1	2	yes	—
427	C₄²	C₅×#41	1	2	yes	—
428	C₂×C₅	—	4	2	no	—
429	C₂×C₅	—	4	4	no	—
430	C₂×C₅	#2363	1	1	yes	characteristic
431	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
432	C₂×C₅	#2933	1	1	yes	characteristic
433	C₂×C₅	C₈×#41	1	1	yes	characteristic
434	C₂×C₅	#2969	1	1	yes	characteristic
435	C₂×C₅	#2972	1	1	yes	characteristic
436	C₂×C₅	#2979	1	1	yes	characteristic
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	2	no	—
449	C₂³	C₂²×C₅×C₈	1	4	yes	—
450	C₂³	C₂²×C₅×C₈	1	2	yes	—
451	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
452	D₄	—	2	8	no	—
453	D₄	—	4	8	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
482	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
483	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
484	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
485	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
486	C₂×C₄	C₅×#131	1	2	yes	—
487	C₂×C₄	C₅×#131	1	2	yes	—
488	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
491	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
492	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
494	C₈	—	2	2	no	—
495	C₈	—	2	4	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	1	no	—
498	C₈	—	4	2	no	—
499	C₈	—	4	1	no	—
500	C₅	#23083	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
516	C₂²	C₄×C₅×#41	1	1	yes	characteristic
517	C₂²	C₅×#518	1	1	yes	characteristic
518	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
519	C₂²	C₂×C₅×#131	1	1	yes	characteristic
520	C₂²	C₂×C₅×#131	1	1	yes	characteristic
521	C₂²	C₅×#568	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	4	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₅×C₈×D₄	1	4	yes	—
530	C₄	C₅×#546	1	1	yes	characteristic
531	C₄	C₅×#550	1	1	yes	characteristic
532	C₄	C₅×#553	1	1	yes	characteristic
533	C₄	C₅×#555	1	1	yes	characteristic
534	C₂	—	4	2	no	—
535	C₂	—	4	4	no	—
536	C₂	C₅×#2363	1	1	yes	characteristic
537	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
538	C₂	C₅×#2933	1	1	yes	characteristic
539	C₂	C₅×C₈×#41	1	1	yes	characteristic
540	C₂	C₅×#2969	1	1	yes	characteristic
541	C₂	C₅×#2972	1	1	yes	characteristic
542	C₂	C₅×#2979	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂×C₅×#121	C₄
LCS	G ▷ C₂² ▷ 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×C₈×D₄	C₂	semidirect
2. C₂×C₅×#431	C₂	semidirect
4. C₅×#1954	C₂	semidirect
5. C₅×#1954	C₂	semidirect
6. C₅×#1939	C₂	semidirect
7. C₅×#1923	C₂	semidirect
8. C₅×#1869	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
10. C₅×C₈×C₂²⋊C₄	C₂	semidirect
11. C₄×C₅×C₂²⋊C₈	C₂	semidirect
43. #23083	C₅	direct (N × H)
59. C₅×#121	C₈	semidirect
82. C₅×C₄⋊C₈	D₄	semidirect
96. C₂×C₈×D₄	C₂×C₅	semidirect
97. C₂×#431	C₂×C₅	semidirect
99. #1954	C₂×C₅	semidirect
100. #1954	C₂×C₅	semidirect
101. #1939	C₂×C₅	semidirect
102. #1923	C₂×C₅	semidirect
103. #1869	C₂×C₅	semidirect
104. C₈×C₄⋊C₄	C₂×C₅	semidirect
105. C₈×C₂²⋊C₄	C₂×C₅	semidirect
106. C₄×C₂²⋊C₈	C₂×C₅	semidirect
114. C₂×C₅×D₄	C₂×C₈	semidirect
132. C₂²×C₄×C₅	C₂×C₈	semidirect
164. C₅×C₄⋊C₄	C₂×C₈	semidirect
169. C₅×C₂²⋊C₄	C₂×C₈	semidirect
287. #121	C₅×C₈	semidirect
310. C₄⋊C₈	C₅×D₄	semidirect
364. C₂×D₄	C₂×C₅×C₈	semidirect
382. C₂²×C₄	C₂×C₅×C₈	semidirect
414. C₄⋊C₄	C₂×C₅×C₈	semidirect
419. C₂²⋊C₄	C₂×C₅×C₈	semidirect
500. C₅	#23083	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×D₄	2
C₂×C₅×#431	2
C₄×C₅×#121	2
C₅×#1954	2
C₅×#1939	2
C₅×#1923	2
C₅×#1869	2
C₅×C₈×C₄⋊C₄	2
C₅×C₈×C₂²⋊C₄	2
C₄×C₅×C₂²⋊C₈	2
#23083	5

Subgroups — C5×#23083 #11945803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23083 #11945803