Subgroups — C₅×#22028 #11944748

Order 1280.

1238 conjugacy classes of subgroups.

The subgroup lattice has 562 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	C₂²×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#120	C₂	1	1	yes	maximal, characteristic
4	C₅×#1954	C₂	1	2	yes	maximal, complemented
5	C₅×#1923	C₂	1	2	yes	maximal, complemented
6	C₅×#1923	C₂	1	2	yes	maximal, complemented
7	C₅×#1869	C₂	1	2	yes	maximal, complemented
8	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1779	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₅×#120	C₄	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
19	C₅×C₈×D₄	—	2	4	no	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊C₈	—	2	4	no	—
23	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
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, complemented
30	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
33	C₅×#386	C₄	1	1	yes	characteristic
34	C₅×#386	C₄	1	2	yes	—
35	C₅×#385	C₄	1	1	yes	characteristic
36	C₅×#385	C₄	1	2	yes	—
37	C₅×#379	C₄	1	1	yes	characteristic
38	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	complemented
41	C₅×#336	C₂²	1	2	yes	complemented
42	C₅×#336	C₂²	1	2	yes	complemented
43	#22028	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₅	—	2	2	no	—
48	C₂³×C₄×C₅	—	2	2	no	—
49	C₂³×C₄×C₅	—	4	2	no	—
50	C₂³×C₄×C₅	—	4	2	no	—
51	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₅	C₂³	1	2	yes	—
54	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	—	2	2	no	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₂²×C₅×C₈	—	4	2	no	—
59	C₂²×C₅×C₈	—	4	2	no	—
60	C₂²×C₅×C₈	—	4	2	no	—
61	C₂²×C₅×C₈	D₄	1	4	yes	complemented
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	2	yes	—
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₅×#120	C₈	1	8	yes	complemented
69	C₄×C₅×D₄	—	2	2	no	—
70	C₄×C₅×D₄	—	2	2	no	—
71	C₄×C₅×D₄	—	4	2	no	—
72	C₄×C₅×D₄	—	4	2	no	—
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	2	yes	—
85	C₅×C₄⋊C₈	—	2	2	no	—
86	C₅×C₄⋊C₈	—	4	2	no	—
87	C₅×C₂²⋊C₈	—	2	2	no	—
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	—	2	2	no	—
92	C₅×C₂²⋊C₈	—	4	2	no	—
93	C₅×C₂²⋊C₈	—	4	2	no	—
94	C₅×C₂²⋊C₈	—	4	2	no	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	—	4	2	no	—
97	C₅×#95	C₂×C₄	1	2	yes	—
98	C₅×#95	C₂×C₄	1	2	yes	—
99	C₅×#95	C₂×C₄	1	2	yes	—
100	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
102	C₄×#120	C₂×C₅	1	1	yes	characteristic
103	#1954	C₂×C₅	1	2	yes	complemented
104	#1923	C₂×C₅	1	2	yes	complemented
105	#1923	C₂×C₅	1	2	yes	complemented
106	#1869	C₂×C₅	1	1	yes	characteristic, complemented
107	#1869	C₂×C₅	1	2	yes	complemented
108	#1850	C₂×C₅	1	1	yes	characteristic, complemented
109	#1779	C₂×C₅	1	1	yes	characteristic, complemented
110	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	2	no	—
112	C₂⁴×C₅	—	2	2	no	—
113	C₂⁴×C₅	—	4	2	no	—
114	C₂⁴×C₅	—	4	2	no	—
115	C₂⁴×C₅	C₂×C₈	1	4	yes	complemented
116	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
117	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	4	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
124	C₂×C₅×D₄	C₂×C₈	1	8	yes	complemented
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	4	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	—	4	2	no	—
141	C₂²×C₄×C₅	—	4	2	no	—
142	C₂²×C₄×C₅	—	4	4	no	—
143	C₂²×C₄×C₅	—	4	4	no	—
144	C₂²×C₄×C₅	—	4	8	no	—
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₅	#41	1	2	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	4	4	no	—
168	C₂×C₅×C₈	—	4	4	no	—
169	C₂×C₅×C₈	—	4	4	no	—
170	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	4	2	no	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	4	2	no	—
178	C₅×C₂²⋊C₄	—	4	2	no	—
179	C₅×C₂²⋊C₄	—	4	2	no	—
180	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
181	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	—	2	2	no	—
185	C₄²×C₅	—	2	2	no	—
186	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
189	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₂×#120	C₄×C₅	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
193	C₈×D₄	—	2	4	no	—
194	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
196	C₂×C₂²⋊C₈	—	2	4	no	—
197	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
205	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
207	#386	C₄×C₅	1	2	yes	—
208	#386	C₄×C₅	1	1	yes	characteristic
209	#385	C₄×C₅	1	1	yes	characteristic
210	#385	C₄×C₅	1	2	yes	—
211	#379	C₄×C₅	1	1	yes	characteristic
212	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
214	#336	C₂²×C₅	1	2	yes	complemented
215	#336	C₂²×C₅	1	2	yes	complemented
216	#336	C₂²×C₅	1	2	yes	complemented
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	1	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	8	no	—
230	C₂³×C₅	—	4	8	no	—
231	C₂³×C₅	—	4	4	no	—
232	C₂³×C₅	—	4	4	no	—
233	C₂³×C₅	—	4	8	no	—
234	C₂³×C₅	C₄×D₄	1	2	yes	—
235	C₂³×C₅	C₂²×C₈	1	4	yes	—
236	C₂³×C₅	C₂²×C₈	1	2	yes	—
237	C₂³×C₅	C₂²×C₈	1	2	yes	—
238	C₂³×C₅	#131	1	2	yes	—
239	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₅×D₄	—	2	8	no	—
241	C₅×D₄	—	4	8	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	4	8	no	—
261	C₂×C₄×C₅	—	4	4	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	4	1	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	4	2	no	—
269	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
271	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
272	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
276	C₅×C₈	—	2	2	no	—
277	C₅×C₈	—	2	2	no	—
278	C₅×C₈	—	4	1	no	—
279	C₅×C₈	—	4	1	no	—
280	C₅×C₈	—	4	2	no	—
281	C₅×C₈	—	4	2	no	—
282	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	4	2	no	—
288	C₂³×C₄	—	4	2	no	—
289	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
291	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₅	1	2	yes	—
293	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	4	2	no	—
297	C₂²×C₈	—	4	2	no	—
298	C₂²×C₈	—	4	2	no	—
299	C₂²×C₈	C₅×D₄	1	4	yes	complemented
300	C₂²×C₈	C₂³×C₅	1	2	yes	—
301	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₅	1	2	yes	—
303	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
306	#120	C₅×C₈	1	8	yes	complemented
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	4	2	no	—
310	C₄×D₄	—	4	2	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₅	1	2	yes	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	4	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	4	no	—
328	C₂²⋊C₈	—	2	4	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	4	2	no	—
331	C₂²⋊C₈	—	4	2	no	—
332	C₂²⋊C₈	—	4	2	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	4	2	no	—
335	#95	C₂×C₄×C₅	1	2	yes	—
336	#95	C₂×C₄×C₅	1	2	yes	—
337	#95	C₂×C₄×C₅	1	2	yes	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	—	2	4	no	—
341	C₂²×C₅	—	2	4	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	4	no	—
344	C₂²×C₅	—	2	4	no	—
345	C₂²×C₅	—	2	4	no	—
346	C₂²×C₅	—	2	4	no	—
347	C₂²×C₅	—	4	16	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	—	4	1	no	—
350	C₂²×C₅	—	4	1	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	4	2	no	—
355	C₂²×C₅	C₈×D₄	1	4	yes	—
356	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂²×C₅	#518	1	2	yes	—
358	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
359	C₂²×C₅	C₂×#131	1	1	yes	characteristic
360	C₂²×C₅	#568	1	2	yes	—
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	2	4	no	—
364	C₄×C₅	—	4	1	no	—
365	C₄×C₅	—	4	2	no	—
366	C₄×C₅	—	4	1	no	—
367	C₄×C₅	—	4	2	no	—
368	C₄×C₅	#534	1	1	yes	characteristic
369	C₄×C₅	#535	1	1	yes	characteristic
370	C₄×C₅	#538	1	2	yes	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	—	4	2	no	—
375	C₂⁴	C₂×C₅×C₈	1	4	yes	complemented
376	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
377	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
378	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
384	C₂×D₄	C₂×C₅×C₈	1	8	yes	complemented
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	4	8	no	—
405	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
407	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
408	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
410	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
412	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
413	C₂²×C₄	C₅×#41	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	4	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	—	4	4	no	—
430	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
431	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	complemented
441	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₂×C₅	—	2	4	no	—
447	C₂×C₅	—	4	2	no	—
448	C₂×C₅	—	4	4	no	—
449	C₂×C₅	#2321	1	1	yes	characteristic
450	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
451	C₂×C₅	#2930	1	1	yes	characteristic
452	C₂×C₅	#2972	1	2	yes	—
453	C₂×C₅	#2976	1	2	yes	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	8	no	—
471	C₂³	C₄×C₅×D₄	1	2	yes	—
472	C₂³	C₂²×C₅×C₈	1	4	yes	—
473	C₂³	C₂²×C₅×C₈	1	2	yes	—
474	C₂³	C₂²×C₅×C₈	1	2	yes	—
475	C₂³	C₅×#131	1	2	yes	—
476	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
477	D₄	—	2	8	no	—
478	D₄	—	4	8	no	—
479	C₂×C₄	—	2	1	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	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
507	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
508	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
509	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
511	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
512	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
513	C₈	—	2	2	no	—
514	C₈	—	2	2	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	2	no	—
519	C₅	#22028	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	16	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	C₅×C₈×D₄	1	4	yes	—
538	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
539	C₂²	C₅×#518	1	2	yes	—
540	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
541	C₂²	C₂×C₅×#131	1	1	yes	characteristic
542	C₂²	C₅×#568	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	C₅×#534	1	1	yes	characteristic
551	C₄	C₅×#535	1	1	yes	characteristic
552	C₄	C₅×#538	1	2	yes	—
553	C₂	—	2	4	no	—
554	C₂	—	4	4	no	—
555	C₂	—	4	2	no	—
556	C₂	C₅×#2321	1	1	yes	characteristic
557	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
558	C₂	C₅×#2930	1	1	yes	characteristic
559	C₂	C₅×#2972	1	2	yes	—
560	C₂	C₅×#2976	1	2	yes	—

	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×#120	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. C₂²×C₅×C₂²⋊C₈	C₂	semidirect
4. C₅×#1954	C₂	semidirect
5. C₅×#1923	C₂	semidirect
6. C₅×#1923	C₂	semidirect
7. C₅×#1869	C₂	semidirect
8. C₅×#1869	C₂	semidirect
9. C₅×#1850	C₂	semidirect
10. C₅×#1779	C₂	semidirect
11. C₅×C₈×C₂²⋊C₄	C₂	semidirect
15. C₂³×C₅×C₈	C₂²	semidirect
20. C₂×C₅×C₄⋊C₈	C₂²	semidirect
21. C₂×C₅×C₄⋊C₈	C₂²	semidirect
29. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
30. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
31. C₂×C₄×C₅×C₈	C₂²	semidirect
32. C₂×C₄×C₅×C₈	C₂²	semidirect
40. C₅×#336	C₂²	semidirect
41. C₅×#336	C₂²	semidirect
42. C₅×#336	C₂²	semidirect
43. #22028	C₅	direct (N × H)
61. C₂²×C₅×C₈	D₄	semidirect
68. C₅×#120	C₈	semidirect
100. C₂×C₈×D₄	C₂×C₅	semidirect
101. C₂²×C₂²⋊C₈	C₂×C₅	semidirect
103. #1954	C₂×C₅	semidirect
104. #1923	C₂×C₅	semidirect
105. #1923	C₂×C₅	semidirect
106. #1869	C₂×C₅	semidirect
107. #1869	C₂×C₅	semidirect
108. #1850	C₂×C₅	semidirect
109. #1779	C₂×C₅	semidirect
110. C₈×C₂²⋊C₄	C₂×C₅	semidirect
115. C₂⁴×C₅	C₂×C₈	semidirect
124. C₂×C₅×D₄	C₂×C₈	semidirect
180. C₅×C₂²⋊C₄	C₂×C₈	semidirect
181. C₅×C₂²⋊C₄	C₂×C₈	semidirect
189. C₂³×C₈	C₂²×C₅	semidirect
194. C₂×C₄⋊C₈	C₂²×C₅	semidirect
195. C₂×C₄⋊C₈	C₂²×C₅	semidirect
203. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
204. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
205. C₂×C₄×C₈	C₂²×C₅	semidirect
206. C₂×C₄×C₈	C₂²×C₅	semidirect
214. #336	C₂²×C₅	semidirect
215. #336	C₂²×C₅	semidirect
216. #336	C₂²×C₅	semidirect
299. C₂²×C₈	C₅×D₄	semidirect
306. #120	C₅×C₈	semidirect
375. C₂⁴	C₂×C₅×C₈	semidirect
384. C₂×D₄	C₂×C₅×C₈	semidirect
440. C₂²⋊C₄	C₂×C₅×C₈	semidirect
441. C₂²⋊C₄	C₂×C₅×C₈	semidirect
519. C₅	#22028	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
C₂²×C₅×C₂²⋊C₈	2
C₄×C₅×#120	2
C₅×#1954	2
C₅×#1923	2
C₅×#1869	2
C₅×#1850	2
C₅×#1779	2
C₅×C₈×C₂²⋊C₄	2
#22028	5

Subgroups — C5×#22028 #11944748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22028 #11944748