Subgroups — #13033674

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617046	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	#10604719	C₂	1	2	yes	maximal
5	C₈×C₂²⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
6	#10603842	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	#10603840	C₂	1	2	yes	maximal, complemented
9	#10603838	C₂	1	2	yes	maximal, complemented
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
13	#65765	C₄	1	2	yes	—
14	#65764	C₄	1	2	yes	—
15	C₄×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
16	#65759	C₄	1	2	yes	complemented
17	#65757	C₄	1	2	yes	complemented
18	D₅⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
19	C₂×#3992	C₂²	1	4	yes	—
20	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	4	yes	—
21	#65690	C₄	1	2	yes	—
22	#65689	C₄	1	2	yes	—
23	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
24	#65686	C₂²	1	2	yes	—
25	#65684	C₄	1	2	yes	complemented
26	#65683	C₄	1	2	yes	complemented
27	D₅⋊(C₄⋊C₈)	C₂²	1	2	yes	—
28	#65676	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic, complemented
30	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
31	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
32	C₂×C₄×#168	C₄	1	1	yes	characteristic, complemented
33	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
34	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
35	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
36	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
37	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
41	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	4	yes	—
42	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	4	yes	—
43	#20476	—	5	1	no	maximal, Sylow
44	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
49	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	4	yes	—
50	C₂×D₅⋊C₈	C₂³	1	4	yes	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×#168	C₂×C₄	1	1	yes	characteristic
58	C₂²×#168	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅	—	2	4	no	—
60	C₂×C₈×D₅	—	2	4	no	—
61	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
69	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₅	C₂³	1	1	yes	characteristic
76	C₄²×D₅	C₂³	1	1	yes	characteristic
77	C₂²⋊#170	C₂×C₄	1	4	yes	—
78	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	4	yes	—
79	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	4	yes	—
80	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	4	yes	—
81	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	4	yes	—
82	#4004	C₂×C₄	1	4	yes	—
83	#4003	C₂×C₄	1	4	yes	—
84	#4002	C₂×C₄	1	4	yes	—
85	#4002	C₂×C₄	1	4	yes	—
86	C₄⋊#170	C₂×C₄	1	4	yes	—
87	#3992	—	2	8	no	—
88	C₈×AGL(1,𝔽₅)	—	2	8	no	—
89	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
101	C₄×#168	C₂×C₄	1	1	yes	characteristic
102	C₄×#168	C₂×C₄	1	1	yes	characteristic
103	C₄×#168	C₂×C₄	1	1	yes	characteristic
104	C₄×#168	C₂×C₄	1	1	yes	characteristic
105	C₂×#432	—	5	1	no	—
106	C₂²×C₄×C₈	—	5	1	no	—
107	#2283	—	5	1	no	—
108	#1770	—	5	2	no	—
109	C₈×C₄⋊C₄	—	5	2	no	—
110	#1752	—	5	2	no	—
111	C₈×C₂²⋊C₄	—	5	2	no	—
112	#1746	—	5	2	no	—
113	#1726	—	5	2	no	—
114	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
116	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₅	C₄²	1	1	yes	characteristic
120	C₂²×Dic₅	C₄²	1	1	yes	characteristic
121	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	—	2	4	no	—
123	C₂×C₄×D₅	—	2	4	no	—
124	C₂×C₄×D₅	—	2	2	no	—
125	C₂×C₄×D₅	—	2	2	no	—
126	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
127	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
128	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
129	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
138	C₂²⋊AGL(1,𝔽₅)	—	2	8	no	—
139	C₂×#170	C₂²×C₄	1	8	yes	—
140	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
141	C₄×AGL(1,𝔽₅)	—	2	4	no	—
142	C₄×AGL(1,𝔽₅)	—	2	4	no	—
143	D₅⋊C₈	—	2	4	no	—
144	D₅⋊C₈	—	2	4	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₅	C₄²	1	1	yes	characteristic
152	C₄²×C₅	C₄²	1	1	yes	characteristic
153	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₅	C₄²	1	1	yes	characteristic
156	C₄×Dic₅	C₄²	1	1	yes	characteristic
157	C₄×Dic₅	C₄²	1	1	yes	characteristic
158	C₄×Dic₅	C₄²	1	1	yes	characteristic
159	C₄×Dic₅	C₄²	1	1	yes	characteristic
160	C₄×Dic₅	C₄²	1	1	yes	characteristic
161	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×#168	—	2	2	no	—
168	C₂×#168	—	2	2	no	—
169	C₂×#168	C₂²×C₄	1	1	yes	characteristic
170	C₂×#168	C₂²×C₄	1	1	yes	characteristic
171	C₂×#168	C₂²×C₄	1	1	yes	characteristic
172	C₂×#168	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₅	—	2	2	no	—
174	C₈×D₅	—	2	2	no	—
175	C₈×D₅	—	2	2	no	—
176	C₈×D₅	—	2	2	no	—
177	C₈×D₅	—	2	2	no	—
178	C₈×D₅	—	2	2	no	—
179	C₈×D₅	#41	1	4	yes	—
180	C₈×D₅	#41	1	4	yes	—
181	C₂³×C₈	—	5	1	no	—
182	C₂³×C₈	—	5	1	no	—
183	C₂²×C₄²	—	5	1	no	—
184	#432	—	5	2	no	—
185	#432	—	5	2	no	—
186	#432	—	5	2	no	—
187	#432	—	5	2	no	—
188	C₂×C₄⋊C₈	—	5	2	no	—
189	C₂×C₂²⋊C₈	—	5	2	no	—
190	C₂×#97	—	5	2	no	—
191	C₂×#97	—	5	4	no	—
192	C₂×C₄×C₈	—	5	1	no	—
193	C₂×C₄×C₈	—	5	1	no	—
194	C₂×C₄×C₈	—	5	1	no	—
195	C₂×C₄×C₈	—	5	1	no	—
196	C₂×C₄×C₈	—	5	1	no	—
197	C₂×C₄×C₈	—	5	1	no	—
198	C₂×C₄×C₈	—	5	1	no	—
199	C₂×C₄×C₈	—	5	1	no	—
200	C₂×C₄×C₈	—	5	1	no	—
201	C₂×C₄×C₈	—	5	1	no	—
202	C₂×C₄×C₈	—	5	1	no	—
203	C₂×C₄×C₈	—	5	4	no	—
204	C₂×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
205	#383	—	5	2	no	—
206	#382	—	5	2	no	—
207	#381	—	5	2	no	—
208	#380	—	5	2	no	—
209	C₄×C₄⋊C₄	—	5	2	no	—
210	C₄×C₂²⋊C₄	—	5	2	no	—
211	#376	—	5	2	no	—
212	#336	—	5	4	no	—
213	#336	—	5	4	no	—
214	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
215	C₂²×D₅	—	2	2	no	—
216	C₂²×D₅	—	2	2	no	—
217	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
218	C₂²×D₅	#131	1	4	yes	—
219	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
220	C₂×AGL(1,𝔽₅)	—	2	8	no	—
221	C₂×AGL(1,𝔽₅)	—	2	8	no	—
222	C₂×AGL(1,𝔽₅)	—	2	8	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	—	2	2	no	—
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
237	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
238	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
239	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
240	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
241	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
242	C₄×D₅	—	2	2	no	—
243	C₄×D₅	—	2	2	no	—
244	C₄×D₅	—	2	2	no	—
245	C₄×D₅	—	2	2	no	—
246	C₄×D₅	—	2	2	no	—
247	C₄×D₅	—	2	2	no	—
248	C₄×D₅	—	2	1	no	—
249	C₄×D₅	—	2	1	no	—
250	C₄×D₅	—	2	2	no	—
251	C₄×D₅	—	2	2	no	—
252	C₄×D₅	—	2	2	no	—
253	C₄×D₅	#131	1	4	yes	—
254	C₄×D₅	C₂×#41	1	2	yes	—
255	C₄×D₅	C₂×#41	1	2	yes	—
256	#170	—	2	8	no	—
257	C₅×C₈	—	2	1	no	—
258	C₅×C₈	—	2	1	no	—
259	C₅×C₈	#117	1	2	yes	—
260	C₅×C₈	#117	1	2	yes	—
261	#168	—	2	1	no	—
262	#168	—	2	1	no	—
263	#168	#117	1	2	yes	—
264	#168	#117	1	2	yes	—
265	C₂³×C₄	—	5	1	no	—
266	C₂³×C₄	—	5	1	no	—
267	C₂³×C₄	—	5	1	no	—
268	C₂²×C₈	—	5	1	no	—
269	C₂²×C₈	—	5	1	no	—
270	C₂²×C₈	—	5	4	no	—
271	C₂²×C₈	—	5	1	no	—
272	C₂²×C₈	—	5	1	no	—
273	C₂²×C₈	—	5	1	no	—
274	C₂²×C₈	—	5	1	no	—
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	5	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	10	4	no	—
280	C₂²×C₈	—	10	4	no	—
281	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
282	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	5	4	no	—
284	C₂×C₂²⋊C₄	—	5	4	no	—
285	C₂×C₄²	—	5	1	no	—
286	C₂×C₄²	—	5	1	no	—
287	C₂×C₄²	—	5	1	no	—
288	C₂×C₄²	—	5	1	no	—
289	C₂×C₄²	—	5	1	no	—
290	C₂×C₄²	—	5	1	no	—
291	C₂×C₄²	—	5	1	no	—
292	C₂×C₄²	—	5	1	no	—
293	C₂×C₄²	—	5	1	no	—
294	C₂×C₄²	—	5	1	no	—
295	C₂×C₄²	—	5	1	no	—
296	C₂×C₄²	—	5	4	no	—
297	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₄⋊C₈	—	5	4	no	—
299	C₄⋊C₈	—	5	4	no	—
300	C₂²⋊C₈	—	5	4	no	—
301	C₂²⋊C₈	—	5	4	no	—
302	#97	—	5	4	no	—
303	#97	—	5	4	no	—
304	#97	—	10	8	no	—
305	C₄×C₈	—	5	1	no	—
306	C₄×C₈	—	5	1	no	—
307	C₄×C₈	—	5	1	no	—
308	C₄×C₈	—	5	1	no	—
309	C₄×C₈	—	5	1	no	—
310	C₄×C₈	—	5	1	no	—
311	C₄×C₈	—	5	1	no	—
312	C₄×C₈	—	5	1	no	—
313	C₄×C₈	—	5	1	no	—
314	C₄×C₈	—	5	1	no	—
315	C₄×C₈	—	5	1	no	—
316	C₄×C₈	—	5	1	no	—
317	C₄×C₈	—	10	8	no	—
318	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
319	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
322	#95	—	5	4	no	—
323	#95	—	5	4	no	—
324	#95	—	5	4	no	—
325	#95	—	5	4	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	#405	1	2	yes	—
329	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
330	C₂×D₅	—	2	1	no	—
331	C₂×D₅	—	2	1	no	—
332	C₂×D₅	—	2	8	no	—
333	C₂×D₅	#405	1	2	yes	—
334	C₂×D₅	C₄×#41	1	2	yes	—
335	C₂×D₅	C₂×#131	1	2	yes	—
336	C₂×D₅	C₂×#131	1	2	yes	—
337	AGL(1,𝔽₅)	—	4	8	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	#405	1	2	yes	—
343	C₄×C₅	C₂×#117	1	1	yes	characteristic
344	C₄×C₅	C₂×#117	1	1	yes	characteristic
345	Dic₅	—	2	1	no	—
346	Dic₅	—	2	1	no	—
347	Dic₅	—	2	1	no	—
348	Dic₅	—	2	1	no	—
349	Dic₅	#405	1	2	yes	—
350	Dic₅	C₄×#41	1	2	yes	—
351	C₂⁴	—	5	1	no	—
352	C₂²×C₄	—	5	1	no	—
353	C₂²×C₄	—	5	1	no	—
354	C₂²×C₄	—	5	1	no	—
355	C₂²×C₄	—	5	1	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	1	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	5	1	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	—	5	1	no	—
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	8	no	—
368	C₂²×C₄	—	10	2	no	—
369	C₂²×C₄	—	10	2	no	—
370	C₂²×C₄	—	10	4	no	—
371	C₂²×C₄	—	10	4	no	—
372	C₂²×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₂²×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	5	1	no	—
378	C₂×C₈	—	5	1	no	—
379	C₂×C₈	—	5	4	no	—
380	C₂×C₈	—	5	4	no	—
381	C₂×C₈	—	5	8	no	—
382	C₂×C₈	—	5	1	no	—
383	C₂×C₈	—	5	1	no	—
384	C₂×C₈	—	10	2	no	—
385	C₂×C₈	—	10	2	no	—
386	C₂×C₈	—	10	2	no	—
387	C₂×C₈	—	10	2	no	—
388	C₂×C₈	—	10	2	no	—
389	C₂×C₈	—	10	2	no	—
390	C₂×C₈	—	10	4	no	—
391	C₂×C₈	—	10	4	no	—
392	C₂×C₈	—	10	2	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₄⋊C₄	—	10	8	no	—
399	C₂²⋊C₄	—	10	8	no	—
400	C₄²	—	5	1	no	—
401	C₄²	—	5	1	no	—
402	C₄²	—	5	1	no	—
403	C₄²	—	5	1	no	—
404	C₄²	—	5	1	no	—
405	C₄²	—	5	1	no	—
406	C₄²	—	5	1	no	—
407	C₄²	—	5	1	no	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	5	1	no	—
412	C₄²	—	10	4	no	—
413	C₄²	—	10	4	no	—
414	C₄²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₄²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
417	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
418	C₂×C₅	—	2	2	no	—
419	C₂×C₅	C₄×#117	1	1	yes	characteristic
420	C₂×C₅	C₂×#405	1	1	yes	characteristic
421	C₂×C₅	C₂×#405	1	1	yes	characteristic
422	D₅	—	2	2	no	—
423	D₅	#2966	1	4	yes	—
424	C₂³	—	5	1	no	—
425	C₂³	—	5	4	no	—
426	C₂³	—	5	1	no	—
427	C₂³	—	10	2	no	—
428	C₂³	—	10	2	no	—
429	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	5	1	no	—
435	C₂×C₄	—	5	1	no	—
436	C₂×C₄	—	5	4	no	—
437	C₂×C₄	—	5	2	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	5	1	no	—
440	C₂×C₄	—	5	1	no	—
441	C₂×C₄	—	5	1	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	10	2	no	—
444	C₂×C₄	—	10	2	no	—
445	C₂×C₄	—	10	2	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	10	2	no	—
455	C₂×C₄	—	10	1	no	—
456	C₂×C₄	—	10	1	no	—
457	C₂×C₄	—	10	8	no	—
458	C₂×C₄	—	10	8	no	—
459	C₂×C₄	—	10	8	no	—
460	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
461	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
463	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
465	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₈	—	5	2	no	—
469	C₈	—	5	2	no	—
470	C₈	—	10	8	no	—
471	C₈	—	10	1	no	—
472	C₈	—	10	1	no	—
473	C₈	#4130	1	2	yes	—
474	C₈	#4130	1	2	yes	—
475	C₅	#20476	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	5	2	no	—
479	C₂²	—	5	2	no	—
480	C₂²	—	5	2	no	—
481	C₂²	—	5	2	no	—
482	C₂²	—	10	8	no	—
483	C₂²	—	10	1	no	—
484	C₂²	—	10	1	no	—
485	C₂²	#65718	1	2	yes	—
486	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	5	2	no	—
492	C₄	—	5	2	no	—
493	C₄	—	10	1	no	—
494	C₄	—	10	1	no	—
495	C₄	—	10	1	no	—
496	C₄	—	10	1	no	—
497	C₄	—	20	8	no	—
498	C₄	#65718	1	2	yes	—
499	C₄	C₂×#4130	1	1	yes	characteristic
500	C₄	C₂×#4130	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	5	4	no	—
503	C₂	—	10	2	no	—
504	C₂	C₄×#4130	1	1	yes	characteristic
505	C₂	C₂×#65718	1	1	yes	characteristic
506	C₂	C₂×#65718	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₈	C₄
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂×C₄×C₈	AGL(1,𝔽₅)
hypocenter	C₅	#20476
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10603842	C₂	semidirect
7. C₈×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
8. #10603840	C₂	semidirect
9. #10603838	C₂	semidirect
16. #65759	C₄	semidirect
17. #65757	C₄	semidirect
25. #65684	C₄	semidirect
26. #65683	C₄	semidirect
29. C₂×C₄×C₅×C₈	C₄	semidirect
30. C₂×C₈×Dic₅	C₄	semidirect
31. C₂×C₈×Dic₅	C₄	semidirect
32. C₂×C₄×#168	C₄	semidirect
33. C₄×C₈×D₅	C₄	semidirect
34. C₄×C₈×D₅	C₄	semidirect
35. C₄×C₈×D₅	C₄	semidirect
36. C₄×C₈×D₅	C₄	semidirect
204. C₂×C₄×C₈	AGL(1,𝔽₅)	semidirect
475. C₅	#20476	semidirect

Maximal subgroups

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

subgroup	index
#10617046	2
D₅⋊#432	2
C₂×C₄×C₈×D₅	2
#10604719	2
C₈×C₂²⋊AGL(1,𝔽₅)	2
#10603842	2
C₈×C₄⋊AGL(1,𝔽₅)	2
#10603840	2
#10603838	2
#20476	5