Subgroups — #13033844

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617209	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#446	C₂	1	1	yes	maximal, characteristic
3	D₅×#446	C₂	1	1	yes	maximal, characteristic
4	#10604035	C₂	1	1	yes	maximal, characteristic
5	#10604035	C₂	1	1	yes	maximal, characteristic
6	#10604033	C₂	1	1	yes	maximal, characteristic
7	#10604029	C₂	1	1	yes	maximal, characteristic
8	#10604029	C₂	1	1	yes	maximal, characteristic
9	AGL(1,𝔽₅)×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
10	#10603880	C₂	1	1	yes	maximal, characteristic
11	#10603880	C₂	1	1	yes	maximal, characteristic
12	#10603877	C₂	1	1	yes	maximal, characteristic
13	AGL(1,𝔽₅)×#97	C₂	1	1	yes	maximal, characteristic
14	C₈×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
15	#10603838	C₂	1	1	yes	maximal, characteristic
16	C₄×Q₈×D₅	C₂²	1	1	yes	characteristic
17	(C₂×AGL(1,𝔽₅))⋊Q₈	C₄	1	2	yes	—
18	#65788	C₄	1	2	yes	complemented
19	C₂×#3992	C₂²	1	1	yes	characteristic
20	C₂×#3992	C₂²	1	1	yes	characteristic
21	C₂×#3992	C₂²	1	1	yes	characteristic
22	C₂×#3992	C₂²	1	1	yes	characteristic
23	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
24	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
25	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
26	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
27	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
28	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
29	#65712	C₄	1	2	yes	—
30	#65711	C₄	1	2	yes	—
31	#65711	C₄	1	2	yes	—
32	#65709	C₄	1	2	yes	complemented
33	#65707	C₄	1	2	yes	complemented
34	#65707	C₄	1	2	yes	complemented
35	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
38	#65686	C₂²	1	1	yes	characteristic
39	#65686	C₂²	1	1	yes	characteristic
40	C₄²×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
41	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
42	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
43	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
44	#65676	C₂²	1	1	yes	characteristic
45	#65676	C₂²	1	1	yes	characteristic
46	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×#446	C₄	1	1	yes	characteristic, complemented
48	#65313	C₄	1	1	yes	characteristic, complemented
49	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	#65120	C₄	1	1	yes	characteristic, complemented
53	#65117	C₄	1	1	yes	characteristic, complemented
54	#65117	C₄	1	1	yes	characteristic, complemented
55	D₅×#97	C₂²	1	1	yes	characteristic
56	D₅×#97	C₂²	1	1	yes	characteristic
57	#64990	C₄	1	1	yes	characteristic, complemented
58	#64990	C₄	1	1	yes	characteristic, complemented
59	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
60	#64968	C₄	1	1	yes	characteristic, complemented
61	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
62	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
63	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
64	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
65	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
66	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
67	#20519	—	5	1	no	maximal, Sylow
68	C₂×Q₈×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
72	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
73	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
74	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
75	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
76	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
77	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
78	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
83	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
85	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
88	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	#4033	C₂×C₄	1	1	yes	characteristic
92	#4033	C₂×C₄	1	1	yes	characteristic
93	#4033	C₂×C₄	1	1	yes	characteristic
94	C₄²×D₅	C₂³	1	1	yes	characteristic
95	C₄²×D₅	C₂³	1	1	yes	characteristic
96	C₄²×D₅	C₂³	1	1	yes	characteristic
97	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
100	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
101	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
105	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
106	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
107	#4004	C₂×C₄	1	2	yes	—
108	#4004	C₂×C₄	1	2	yes	—
109	#4004	C₂×C₄	1	2	yes	—
110	#4002	C₂×C₄	1	2	yes	—
111	#4002	C₂×C₄	1	2	yes	—
112	#4002	C₂×C₄	1	2	yes	—
113	#4002	C₂×C₄	1	2	yes	—
114	C₄⋊#170	C₂×C₄	1	2	yes	—
115	C₄⋊#170	C₂×C₄	1	2	yes	—
116	C₄⋊#170	C₂×C₄	1	2	yes	—
117	C₄×#170	C₂×C₄	1	2	yes	—
118	C₄×#170	C₂×C₄	1	2	yes	—
119	#3992	—	2	2	no	—
120	#3992	—	2	2	no	—
121	#3992	—	2	2	no	—
122	#3992	Q₈	1	4	yes	complemented
123	C₈×AGL(1,𝔽₅)	—	2	2	no	—
124	C₈×AGL(1,𝔽₅)	—	2	2	no	—
125	C₈×AGL(1,𝔽₅)	—	2	2	no	—
126	C₈×AGL(1,𝔽₅)	—	2	2	no	—
127	C₈×AGL(1,𝔽₅)	—	2	2	no	—
128	C₈×AGL(1,𝔽₅)	—	2	2	no	—
129	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₅×#97	C₂×C₄	1	1	yes	characteristic
133	C₅×#97	C₂×C₄	1	1	yes	characteristic
134	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
135	#3947	C₂×C₄	1	1	yes	characteristic
136	#3947	C₂×C₄	1	1	yes	characteristic
137	#3947	C₂×C₄	1	1	yes	characteristic
138	#3947	C₂×C₄	1	1	yes	characteristic
139	#3946	C₂×C₄	1	1	yes	characteristic
140	#3946	C₂×C₄	1	1	yes	characteristic
141	#3946	C₂×C₄	1	1	yes	characteristic
142	#3946	C₂×C₄	1	1	yes	characteristic
143	#3946	C₂×C₄	1	1	yes	characteristic
144	#3946	C₂×C₄	1	1	yes	characteristic
145	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
146	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
147	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
149	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
150	#3935	C₂×C₄	1	1	yes	characteristic
151	#3935	C₂×C₄	1	1	yes	characteristic
152	C₄×#168	C₂×C₄	1	1	yes	characteristic
153	C₂×#446	—	5	1	no	—
154	C₂×#446	—	5	1	no	—
155	#2295	—	5	1	no	—
156	#1771	—	5	1	no	—
157	#1771	—	5	1	no	—
158	#1771	—	5	1	no	—
159	#1771	—	5	1	no	—
160	C₈×C₄⋊C₄	—	5	1	no	—
161	C₈×C₄⋊C₄	—	5	1	no	—
162	#1768	—	5	1	no	—
163	#1768	—	5	1	no	—
164	C₄×C₄⋊C₈	—	5	1	no	—
165	#1726	—	5	1	no	—
166	#1726	—	5	1	no	—
167	C₄×#97	—	5	1	no	—
168	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
169	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
170	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
171	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
172	C₂×C₅×Q₈	C₄²	1	1	yes	characteristic
173	Q₈×D₅	—	4	2	no	—
174	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
182	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
183	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
184	C₂×#170	C₂²×C₄	1	2	yes	—
185	C₂×#170	C₂²×C₄	1	2	yes	—
186	C₂×#170	C₂²×C₄	1	2	yes	—
187	C₂×#170	C₂²×C₄	1	2	yes	—
188	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
189	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
190	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
191	C₄×AGL(1,𝔽₅)	—	2	4	no	—
192	C₄×AGL(1,𝔽₅)	—	2	1	no	—
193	C₄×AGL(1,𝔽₅)	—	2	1	no	—
194	C₄×AGL(1,𝔽₅)	—	2	1	no	—
195	C₄×AGL(1,𝔽₅)	—	2	1	no	—
196	C₄×AGL(1,𝔽₅)	—	2	1	no	—
197	C₄×AGL(1,𝔽₅)	—	2	1	no	—
198	C₄×AGL(1,𝔽₅)	—	4	2	no	—
199	C₄×AGL(1,𝔽₅)	C₂×Q₈	1	2	yes	—
200	C₄×AGL(1,𝔽₅)	#41	1	2	yes	—
201	D₅⋊C₈	—	2	1	no	—
202	D₅⋊C₈	—	2	1	no	—
203	D₅⋊C₈	—	2	1	no	—
204	D₅⋊C₈	—	2	1	no	—
205	D₅⋊C₈	—	2	1	no	—
206	D₅⋊C₈	—	2	1	no	—
207	D₅⋊C₈	C₂×Q₈	1	2	yes	—
208	D₅⋊C₈	#41	1	2	yes	—
209	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
216	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
220	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
221	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
222	#683	C₄²	1	1	yes	characteristic
223	#683	C₄²	1	1	yes	characteristic
224	#683	C₄²	1	1	yes	characteristic
225	#683	C₄²	1	1	yes	characteristic
226	#683	C₄²	1	1	yes	characteristic
227	#683	C₄²	1	1	yes	characteristic
228	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
230	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
231	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
232	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
233	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
234	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
235	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
236	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
237	C₂×#168	C₂²×C₄	1	1	yes	characteristic
238	C₂×#168	C₂²×C₄	1	1	yes	characteristic
239	C₂×#168	C₂²×C₄	1	1	yes	characteristic
240	C₂×#168	C₂²×C₄	1	1	yes	characteristic
241	C₈×D₅	—	2	1	no	—
242	C₈×D₅	—	2	1	no	—
243	C₈×D₅	—	2	1	no	—
244	C₈×D₅	—	2	1	no	—
245	C₈×D₅	—	2	1	no	—
246	C₈×D₅	—	2	1	no	—
247	C₈×D₅	C₂×Q₈	1	2	yes	—
248	C₈×D₅	#41	1	2	yes	—
249	C₂×C₄×Q₈	—	5	1	no	—
250	#446	—	5	2	no	—
251	#446	—	5	2	no	—
252	#446	—	5	2	no	—
253	#446	—	5	2	no	—
254	#446	—	5	1	no	—
255	#446	—	5	1	no	—
256	#446	—	5	1	no	—
257	#446	—	5	1	no	—
258	#446	—	5	1	no	—
259	#446	—	5	1	no	—
260	#446	—	5	1	no	—
261	#446	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
262	C₂×C₄⋊C₈	—	5	1	no	—
263	C₂×C₄⋊C₈	—	5	1	no	—
264	C₂×C₄⋊C₈	—	5	1	no	—
265	C₂×C₄⋊C₈	—	5	1	no	—
266	C₂×C₄⋊C₈	—	5	1	no	—
267	C₂×C₄⋊C₈	—	5	1	no	—
268	C₂×#97	—	5	1	no	—
269	C₂×#97	—	5	1	no	—
270	C₂×#97	—	5	1	no	—
271	C₂×#97	—	5	1	no	—
272	C₂×#97	—	5	1	no	—
273	C₂×#97	—	5	1	no	—
274	C₂×#97	—	5	1	no	—
275	C₂×#97	—	5	1	no	—
276	C₂×C₄×C₈	—	5	1	no	—
277	C₂×C₄×C₈	—	5	1	no	—
278	C₂×C₄×C₈	—	5	1	no	—
279	C₂×C₄×C₈	—	5	1	no	—
280	C₂×C₄×C₈	—	5	1	no	—
281	C₂×C₄×C₈	—	5	1	no	—
282	C₂×C₄×C₈	—	5	1	no	—
283	C₂×C₄×C₈	—	5	1	no	—
284	#391	—	5	2	no	—
285	#389	—	5	2	no	—
286	#387	—	5	2	no	—
287	#387	—	5	2	no	—
288	C₄×C₄⋊C₄	—	5	1	no	—
289	C₄×C₄⋊C₄	—	5	1	no	—
290	C₄×C₄⋊C₄	—	5	1	no	—
291	#376	—	5	1	no	—
292	#376	—	5	1	no	—
293	C₄³	—	5	1	no	—
294	#336	—	5	1	no	—
295	#336	—	5	1	no	—
296	#336	—	5	1	no	—
297	#336	—	5	1	no	—
298	#336	—	5	1	no	—
299	#336	—	5	1	no	—
300	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
301	C₂×AGL(1,𝔽₅)	—	2	2	no	—
302	C₂×AGL(1,𝔽₅)	—	2	2	no	—
303	C₂×AGL(1,𝔽₅)	—	2	2	no	—
304	C₂×AGL(1,𝔽₅)	—	2	2	no	—
305	C₂×AGL(1,𝔽₅)	—	2	2	no	—
306	C₂×AGL(1,𝔽₅)	—	2	2	no	—
307	C₂×AGL(1,𝔽₅)	—	2	2	no	—
308	C₂×AGL(1,𝔽₅)	—	2	2	no	—
309	C₂×AGL(1,𝔽₅)	—	2	2	no	—
310	C₂×AGL(1,𝔽₅)	—	2	2	no	—
311	C₂×AGL(1,𝔽₅)	C₄×Q₈	1	4	yes	—
312	C₂×AGL(1,𝔽₅)	#131	1	4	yes	—
313	C₅×Q₈	—	4	1	no	—
314	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
321	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
322	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
323	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
324	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
325	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
326	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
327	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	2	2	no	—
330	C₄×D₅	—	2	2	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	2	2	no	—
334	C₄×D₅	C₂²×Q₈	1	1	yes	characteristic
335	C₄×D₅	C₂×#41	1	1	yes	characteristic
336	C₄×D₅	C₂×#41	1	1	yes	characteristic
337	C₄×D₅	C₂×#41	1	1	yes	characteristic
338	Dic₁₀	—	4	1	no	—
339	Dic₁₀	—	4	1	no	—
340	Dic₁₀	—	4	1	no	—
341	#170	—	2	2	no	—
342	#170	—	2	2	no	—
343	#170	—	2	2	no	—
344	#170	C₄×Q₈	1	4	yes	—
345	C₅×C₈	—	2	1	no	—
346	C₅×C₈	—	2	1	no	—
347	C₅×C₈	—	2	1	no	—
348	C₅×C₈	C₄×Q₈	1	2	yes	—
349	#168	—	2	1	no	—
350	#168	—	2	1	no	—
351	#168	—	2	1	no	—
352	#168	C₄×Q₈	1	2	yes	—
353	C₂²×Q₈	—	5	1	no	—
354	C₂²×C₈	—	5	1	no	—
355	C₂²×C₈	—	5	1	no	—
356	C₂²×C₈	—	5	1	no	—
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	5	1	no	—
359	C₂²×C₈	—	5	1	no	—
360	C₂²×C₈	—	5	1	no	—
361	C₂²×C₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	—	5	1	no	—
369	C₄×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	5	1	no	—
371	C₂×C₄⋊C₄	—	5	1	no	—
372	C₂×C₄⋊C₄	—	5	1	no	—
373	C₂×C₄⋊C₄	—	5	2	no	—
374	C₂×C₄⋊C₄	—	5	2	no	—
375	C₂×C₄⋊C₄	—	5	2	no	—
376	C₂×C₄²	—	5	1	no	—
377	C₂×C₄²	—	5	1	no	—
378	C₂×C₄²	—	5	1	no	—
379	C₂×C₄²	—	5	1	no	—
380	C₂×C₄²	—	5	2	no	—
381	C₂×C₄²	—	5	1	no	—
382	C₂×C₄²	—	5	1	no	—
383	C₂×C₄²	—	5	1	no	—
384	C₂×C₄²	—	5	2	no	—
385	C₄⋊C₈	—	5	2	no	—
386	C₄⋊C₈	—	5	2	no	—
387	C₄⋊C₈	—	5	2	no	—
388	C₄⋊C₈	—	5	2	no	—
389	C₄⋊C₈	—	5	2	no	—
390	C₄⋊C₈	—	5	2	no	—
391	C₄⋊C₈	—	5	1	no	—
392	C₄⋊C₈	—	5	1	no	—
393	C₄⋊C₈	—	5	1	no	—
394	C₄⋊C₈	—	5	1	no	—
395	C₄⋊C₈	—	5	1	no	—
396	C₄⋊C₈	—	5	1	no	—
397	C₄⋊C₈	—	5	1	no	—
398	C₄⋊C₈	—	5	1	no	—
399	C₄⋊C₈	—	5	1	no	—
400	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
401	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
402	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
403	#97	—	5	4	no	—
404	#97	—	5	2	no	—
405	#97	—	5	2	no	—
406	#97	—	5	2	no	—
407	#97	—	5	2	no	—
408	#97	—	5	1	no	—
409	#97	—	5	1	no	—
410	#97	—	5	1	no	—
411	#97	—	5	1	no	—
412	#97	—	5	1	no	—
413	#97	—	5	1	no	—
414	#97	—	10	2	no	—
415	#97	—	10	2	no	—
416	#97	—	10	2	no	—
417	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
418	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₄×C₈	—	5	2	no	—
420	C₄×C₈	—	5	2	no	—
421	C₄×C₈	—	5	1	no	—
422	C₄×C₈	—	5	1	no	—
423	C₄×C₈	—	5	1	no	—
424	C₄×C₈	—	10	2	no	—
425	C₄×C₈	—	10	2	no	—
426	C₄×C₈	—	10	2	no	—
427	C₄×C₈	—	10	2	no	—
428	C₄×C₈	—	10	2	no	—
429	C₄×C₈	—	10	2	no	—
430	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
431	#95	—	5	2	no	—
432	#95	—	5	2	no	—
433	#95	—	5	2	no	—
434	#95	—	5	2	no	—
435	#95	—	5	2	no	—
436	#95	—	5	2	no	—
437	#95	—	5	2	no	—
438	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
439	C₂×D₅	C₂×C₄×Q₈	1	1	yes	characteristic
440	C₂×D₅	C₄×#41	1	1	yes	characteristic
441	C₂×D₅	C₂×#131	1	2	yes	—
442	C₂×D₅	#568	1	2	yes	—
443	AGL(1,𝔽₅)	—	2	4	no	—
444	AGL(1,𝔽₅)	—	2	4	no	—
445	AGL(1,𝔽₅)	—	4	2	no	—
446	AGL(1,𝔽₅)	—	4	2	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	—	2	1	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
454	C₄×C₅	C₄×#41	1	1	yes	characteristic
455	Dic₅	—	2	1	no	—
456	Dic₅	—	2	1	no	—
457	Dic₅	—	2	1	no	—
458	Dic₅	—	2	1	no	—
459	Dic₅	—	2	1	no	—
460	Dic₅	—	2	1	no	—
461	Dic₅	C₂×C₄×Q₈	1	1	yes	characteristic
462	Dic₅	C₄×#41	1	1	yes	characteristic
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	1	no	—
465	C₂×Q₈	—	5	1	no	—
466	C₂×Q₈	—	20	2	no	—
467	C₂×Q₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
468	C₂²×C₄	—	5	1	no	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	2	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	5	1	no	—
473	C₂²×C₄	—	5	1	no	—
474	C₂²×C₄	—	5	1	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	2	no	—
478	C₂²×C₄	—	5	2	no	—
479	C₂×C₈	—	5	2	no	—
480	C₂×C₈	—	5	2	no	—
481	C₂×C₈	—	5	2	no	—
482	C₂×C₈	—	5	1	no	—
483	C₂×C₈	—	5	2	no	—
484	C₂×C₈	—	5	2	no	—
485	C₂×C₈	—	5	2	no	—
486	C₂×C₈	—	5	2	no	—
487	C₂×C₈	—	5	2	no	—
488	C₂×C₈	—	5	1	no	—
489	C₂×C₈	—	5	1	no	—
490	C₂×C₈	—	5	1	no	—
491	C₂×C₈	—	10	1	no	—
492	C₂×C₈	—	10	1	no	—
493	C₂×C₈	—	10	1	no	—
494	C₂×C₈	—	10	1	no	—
495	C₂×C₈	—	10	1	no	—
496	C₂×C₈	—	10	1	no	—
497	C₂×C₈	—	10	1	no	—
498	C₂×C₈	—	10	1	no	—
499	C₂×C₈	—	10	1	no	—
500	C₂×C₈	—	10	1	no	—
501	C₂×C₈	—	10	1	no	—
502	C₂×C₈	—	10	1	no	—
503	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
504	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
506	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₄⋊C₄	—	5	1	no	—
508	C₄⋊C₄	—	5	1	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	1	no	—
511	C₄⋊C₄	—	5	1	no	—
512	C₄⋊C₄	—	5	1	no	—
513	C₄⋊C₄	—	5	1	no	—
514	C₄⋊C₄	—	5	1	no	—
515	C₄⋊C₄	—	5	1	no	—
516	C₄⋊C₄	—	10	4	no	—
517	C₄⋊C₄	—	10	4	no	—
518	C₄⋊C₄	—	20	2	no	—
519	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
520	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
521	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
522	C₄²	—	5	2	no	—
523	C₄²	—	5	2	no	—
524	C₄²	—	5	1	no	—
525	C₄²	—	5	1	no	—
526	C₄²	—	5	1	no	—
527	C₄²	—	5	1	no	—
528	C₄²	—	5	1	no	—
529	C₄²	—	5	1	no	—
530	C₄²	—	5	1	no	—
531	C₄²	—	5	1	no	—
532	C₄²	—	5	1	no	—
533	C₄²	—	10	1	no	—
534	C₄²	—	10	1	no	—
535	C₄²	—	10	1	no	—
536	C₄²	—	10	1	no	—
537	C₄²	—	10	1	no	—
538	C₄²	—	10	1	no	—
539	C₄²	—	10	4	no	—
540	C₄²	—	20	2	no	—
541	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
542	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
543	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
544	C₂×C₅	C₄²×Q₈	1	1	yes	characteristic
545	C₂×C₅	#2873	1	1	yes	characteristic
546	C₂×C₅	C₄×#131	1	1	yes	characteristic
547	D₅	#2962	1	2	yes	—
548	D₅	#2968	1	2	yes	—
549	C₂³	—	5	1	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	20	1	no	—
552	Q₈	—	20	1	no	—
553	Q₈	—	20	1	no	—
554	C₂×C₄	—	5	1	no	—
555	C₂×C₄	—	5	1	no	—
556	C₂×C₄	—	5	1	no	—
557	C₂×C₄	—	5	1	no	—
558	C₂×C₄	—	5	1	no	—
559	C₂×C₄	—	5	4	no	—
560	C₂×C₄	—	5	4	no	—
561	C₂×C₄	—	5	1	no	—
562	C₂×C₄	—	5	1	no	—
563	C₂×C₄	—	5	1	no	—
564	C₂×C₄	—	5	1	no	—
565	C₂×C₄	—	5	1	no	—
566	C₂×C₄	—	5	1	no	—
567	C₂×C₄	—	10	2	no	—
568	C₂×C₄	—	10	2	no	—
569	C₂×C₄	—	10	2	no	—
570	C₂×C₄	—	10	2	no	—
571	C₂×C₄	—	10	2	no	—
572	C₂×C₄	—	10	2	no	—
573	C₂×C₄	—	10	2	no	—
574	C₂×C₄	—	10	2	no	—
575	C₂×C₄	—	10	2	no	—
576	C₂×C₄	—	10	2	no	—
577	C₂×C₄	—	10	2	no	—
578	C₂×C₄	—	10	2	no	—
579	C₂×C₄	—	10	2	no	—
580	C₂×C₄	—	10	2	no	—
581	C₂×C₄	—	10	2	no	—
582	C₂×C₄	—	10	2	no	—
583	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
584	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
586	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
587	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
588	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
589	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	5	4	no	—
594	C₈	—	5	2	no	—
595	C₈	—	10	2	no	—
596	C₈	—	10	2	no	—
597	C₈	—	10	2	no	—
598	C₈	—	10	1	no	—
599	C₈	—	10	1	no	—
600	C₈	—	10	1	no	—
601	C₈	Q₈×AGL(1,𝔽₅)	1	2	yes	—
602	C₅	#20519	1	1	yes	characteristic, complemented, Sylow
603	C₂²	—	5	2	no	—
604	C₂²	—	5	2	no	—
605	C₂²	—	5	1	no	—
606	C₂²	—	5	1	no	—
607	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	5	1	no	—
615	C₄	—	5	1	no	—
616	C₄	—	10	4	no	—
617	C₄	—	10	4	no	—
618	C₄	—	10	1	no	—
619	C₄	—	10	1	no	—
620	C₄	—	10	1	no	—
621	C₄	—	10	1	no	—
622	C₄	—	10	1	no	—
623	C₄	—	10	1	no	—
624	C₄	—	20	2	no	—
625	C₄	—	20	2	no	—
626	C₄	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
627	C₄	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
628	C₂	—	5	2	no	—
629	C₂	—	5	2	no	—
630	C₂	C₄×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
631	C₂	#10617407	1	1	yes	characteristic
632	C₂	AGL(1,𝔽₅)×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#446	C₄
prime radical	C₂²×D₅	C₂³×C₄
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#446	AGL(1,𝔽₅)
hypocenter	C₅	#20519
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
18. #65788	C₄	semidirect
32. #65709	C₄	semidirect
33. #65707	C₄	semidirect
34. #65707	C₄	semidirect
47. C₅×#446	C₄	semidirect
48. #65313	C₄	semidirect
52. #65120	C₄	semidirect
53. #65117	C₄	semidirect
54. #65117	C₄	semidirect
57. #64990	C₄	semidirect
58. #64990	C₄	semidirect
60. #64968	C₄	semidirect
122. #3992	Q₈	semidirect
261. #446	AGL(1,𝔽₅)	semidirect
602. C₅	#20519	semidirect

Maximal subgroups

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

subgroup	index
#10617209	2
D₅⋊#446	2
D₅×#446	2
#10604035	2
#10604033	2
#10604029	2
AGL(1,𝔽₅)×C₄⋊C₈	2
#10603880	2
#10603877	2
AGL(1,𝔽₅)×#97	2
C₈×C₄⋊AGL(1,𝔽₅)	2
#10603838	2
#20519	5