Subgroups — #13034106

Order 1280.

798 conjugacy classes of subgroups.

The subgroup lattice has 626 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	#10603879	C₂	1	1	yes	maximal, characteristic
13	#10603878	C₂	1	1	yes	maximal, characteristic
14	C₈×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
15	#10603840	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×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
22	C₂×C₈×AGL(1,𝔽₅)	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	#65712	C₄	1	2	yes	—
26	#65711	C₄	1	2	yes	—
27	#65711	C₄	1	2	yes	—
28	#65709	C₄	1	2	yes	complemented
29	#65707	C₄	1	2	yes	complemented
30	#65707	C₄	1	2	yes	complemented
31	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
34	#65686	C₂²	1	1	yes	characteristic
35	#65686	C₂²	1	1	yes	characteristic
36	C₄²×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
37	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
38	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
39	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
40	#65676	C₂²	1	1	yes	characteristic
41	#65676	C₂²	1	1	yes	characteristic
42	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×#446	C₄	1	1	yes	characteristic, complemented
44	#65313	C₄	1	1	yes	characteristic, complemented
45	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	#65120	C₄	1	1	yes	characteristic, complemented
49	#65117	C₄	1	1	yes	characteristic, complemented
50	#65117	C₄	1	1	yes	characteristic, complemented
51	D₅×#97	C₂²	1	1	yes	characteristic
52	D₅×#97	C₂²	1	1	yes	characteristic
53	#64990	C₄	1	1	yes	characteristic, complemented
54	#64990	C₄	1	1	yes	characteristic, complemented
55	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
56	#64968	C₄	1	1	yes	characteristic, complemented
57	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
58	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
59	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
60	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
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	#20575	—	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	—	4	1	no	—
120	#3992	—	4	1	no	—
121	C₈×AGL(1,𝔽₅)	—	4	1	no	—
122	C₈×AGL(1,𝔽₅)	—	4	1	no	—
123	C₈×AGL(1,𝔽₅)	—	4	1	no	—
124	C₈×AGL(1,𝔽₅)	—	4	1	no	—
125	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₅×#97	C₂×C₄	1	1	yes	characteristic
129	C₅×#97	C₂×C₄	1	1	yes	characteristic
130	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
131	#3947	C₂×C₄	1	1	yes	characteristic
132	#3947	C₂×C₄	1	1	yes	characteristic
133	#3947	C₂×C₄	1	1	yes	characteristic
134	#3947	C₂×C₄	1	1	yes	characteristic
135	#3946	C₂×C₄	1	1	yes	characteristic
136	#3946	C₂×C₄	1	1	yes	characteristic
137	#3946	C₂×C₄	1	1	yes	characteristic
138	#3946	C₂×C₄	1	1	yes	characteristic
139	#3946	C₂×C₄	1	1	yes	characteristic
140	#3946	C₂×C₄	1	1	yes	characteristic
141	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
142	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
143	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
144	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
145	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
146	#3935	C₂×C₄	1	1	yes	characteristic
147	#3935	C₂×C₄	1	1	yes	characteristic
148	C₄×#168	C₂×C₄	1	1	yes	characteristic
149	C₂×#446	—	5	1	no	—
150	C₂×#446	—	5	1	no	—
151	#2295	—	5	1	no	—
152	#1771	—	5	1	no	—
153	#1771	—	5	1	no	—
154	#1771	—	5	1	no	—
155	#1771	—	5	1	no	—
156	C₈×C₄⋊C₄	—	5	1	no	—
157	C₈×C₄⋊C₄	—	5	1	no	—
158	#1768	—	5	1	no	—
159	#1768	—	5	1	no	—
160	C₄×C₄⋊C₈	—	5	1	no	—
161	#1746	—	5	1	no	—
162	#1746	—	5	1	no	—
163	#1745	—	5	1	no	—
164	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
165	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
166	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
167	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
168	C₂×C₅×Q₈	C₄²	1	1	yes	characteristic
169	Q₈×D₅	—	4	2	no	—
170	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
178	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
179	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
180	C₂×#170	C₂²×C₄	1	2	yes	—
181	C₂×#170	C₂²×C₄	1	2	yes	—
182	C₂×#170	C₂²×C₄	1	2	yes	—
183	C₂×#170	C₂²×C₄	1	2	yes	—
184	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
185	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
186	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
187	C₄×AGL(1,𝔽₅)	—	2	4	no	—
188	C₄×AGL(1,𝔽₅)	—	2	1	no	—
189	C₄×AGL(1,𝔽₅)	—	2	1	no	—
190	C₄×AGL(1,𝔽₅)	—	2	1	no	—
191	C₄×AGL(1,𝔽₅)	—	2	1	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)	—	4	2	no	—
197	D₅⋊C₈	—	2	1	no	—
198	D₅⋊C₈	—	2	1	no	—
199	D₅⋊C₈	—	2	1	no	—
200	D₅⋊C₈	—	2	1	no	—
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	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
212	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
215	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
216	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
217	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
218	#683	C₄²	1	1	yes	characteristic
219	#683	C₄²	1	1	yes	characteristic
220	#683	C₄²	1	1	yes	characteristic
221	#683	C₄²	1	1	yes	characteristic
222	#683	C₄²	1	1	yes	characteristic
223	#683	C₄²	1	1	yes	characteristic
224	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
225	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
226	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₅	C₂²×C₄	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	C₂×#168	C₂²×C₄	1	1	yes	characteristic
234	C₂×#168	C₂²×C₄	1	1	yes	characteristic
235	C₂×#168	C₂²×C₄	1	1	yes	characteristic
236	C₂×#168	C₂²×C₄	1	1	yes	characteristic
237	C₈×D₅	—	2	1	no	—
238	C₈×D₅	—	2	1	no	—
239	C₈×D₅	—	2	1	no	—
240	C₈×D₅	—	2	1	no	—
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	C₂×C₄×Q₈	—	5	1	no	—
246	#446	—	5	2	no	—
247	#446	—	5	2	no	—
248	#446	—	5	2	no	—
249	#446	—	5	2	no	—
250	#446	—	5	1	no	—
251	#446	—	5	1	no	—
252	#446	—	5	1	no	—
253	#446	—	5	1	no	—
254	#446	—	5	1	no	—
255	#446	—	5	1	no	—
256	#446	—	5	1	no	—
257	#446	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
258	C₂×C₄⋊C₈	—	5	1	no	—
259	C₂×C₄⋊C₈	—	5	1	no	—
260	C₂×C₄⋊C₈	—	5	1	no	—
261	C₂×C₄⋊C₈	—	5	1	no	—
262	C₂×C₄⋊C₈	—	5	1	no	—
263	C₂×C₄⋊C₈	—	5	1	no	—
264	C₂×#97	—	5	1	no	—
265	C₂×#97	—	5	1	no	—
266	C₂×#97	—	5	1	no	—
267	C₂×#97	—	5	1	no	—
268	C₂×#97	—	5	1	no	—
269	C₂×#97	—	5	1	no	—
270	C₂×C₄×C₈	—	5	1	no	—
271	C₂×C₄×C₈	—	5	1	no	—
272	C₂×C₄×C₈	—	5	1	no	—
273	C₂×C₄×C₈	—	5	1	no	—
274	C₂×C₄×C₈	—	5	1	no	—
275	C₂×C₄×C₈	—	5	1	no	—
276	#391	—	5	2	no	—
277	#389	—	5	2	no	—
278	#387	—	5	2	no	—
279	#387	—	5	2	no	—
280	C₄×C₄⋊C₄	—	5	1	no	—
281	C₄×C₄⋊C₄	—	5	1	no	—
282	C₄×C₄⋊C₄	—	5	1	no	—
283	#376	—	5	1	no	—
284	#376	—	5	1	no	—
285	C₄³	—	5	1	no	—
286	#336	—	5	1	no	—
287	#336	—	5	1	no	—
288	#336	—	5	1	no	—
289	#336	—	5	1	no	—
290	#336	—	5	1	no	—
291	#336	—	5	1	no	—
292	#336	—	5	1	no	—
293	#336	—	5	1	no	—
294	#336	—	5	1	no	—
295	#336	—	5	1	no	—
296	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
297	C₂×AGL(1,𝔽₅)	—	2	2	no	—
298	C₂×AGL(1,𝔽₅)	—	2	2	no	—
299	C₂×AGL(1,𝔽₅)	—	2	2	no	—
300	C₂×AGL(1,𝔽₅)	—	2	2	no	—
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)	#131	1	4	yes	—
309	C₅×Q₈	—	4	1	no	—
310	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
317	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
318	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
319	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
320	C₂×Dic₅	C₂×C₄²	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	C₂³×C₄	1	1	yes	characteristic
324	C₄×D₅	—	2	2	no	—
325	C₄×D₅	—	2	2	no	—
326	C₄×D₅	—	2	2	no	—
327	C₄×D₅	—	2	2	no	—
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	2	2	no	—
330	C₄×D₅	H(5,𝔽₂)	1	1	yes	characteristic
331	C₄×D₅	2₋¹⁺⁴	1	1	yes	characteristic
332	C₄×D₅	2₋¹⁺⁴	1	1	yes	characteristic
333	C₄×D₅	2₋¹⁺⁴	1	1	yes	characteristic
334	Dic₁₀	—	4	1	no	—
335	Dic₁₀	—	4	1	no	—
336	Dic₁₀	—	4	1	no	—
337	#170	—	2	2	no	—
338	#170	—	2	2	no	—
339	#170	—	2	2	no	—
340	#170	—	2	2	no	—
341	C₅×C₈	—	2	1	no	—
342	C₅×C₈	—	2	1	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	2	1	no	—
345	#168	—	2	1	no	—
346	#168	—	2	1	no	—
347	#168	—	2	1	no	—
348	#168	—	2	1	no	—
349	C₂²×Q₈	—	5	1	no	—
350	C₂²×C₈	—	5	1	no	—
351	C₂²×C₈	—	5	1	no	—
352	C₂²×C₈	—	5	1	no	—
353	C₂²×C₈	—	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	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	5	1	no	—
367	C₂×C₄⋊C₄	—	5	1	no	—
368	C₂×C₄⋊C₄	—	5	1	no	—
369	C₂×C₄⋊C₄	—	5	2	no	—
370	C₂×C₄⋊C₄	—	5	2	no	—
371	C₂×C₄⋊C₄	—	5	2	no	—
372	C₂×C₄²	—	5	1	no	—
373	C₂×C₄²	—	5	1	no	—
374	C₂×C₄²	—	5	1	no	—
375	C₂×C₄²	—	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	C₄⋊C₈	—	5	2	no	—
382	C₄⋊C₈	—	5	2	no	—
383	C₄⋊C₈	—	5	2	no	—
384	C₄⋊C₈	—	5	2	no	—
385	C₄⋊C₈	—	5	2	no	—
386	C₄⋊C₈	—	5	2	no	—
387	C₄⋊C₈	—	5	1	no	—
388	C₄⋊C₈	—	5	1	no	—
389	C₄⋊C₈	—	5	1	no	—
390	C₄⋊C₈	—	5	1	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	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
399	#97	—	5	2	no	—
400	#97	—	5	2	no	—
401	#97	—	5	2	no	—
402	#97	—	5	2	no	—
403	#97	—	5	1	no	—
404	#97	—	5	1	no	—
405	#97	—	5	1	no	—
406	#97	—	5	1	no	—
407	#97	—	5	1	no	—
408	#97	—	5	1	no	—
409	#97	—	20	1	no	—
410	#97	—	20	1	no	—
411	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
412	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₄×C₈	—	5	2	no	—
414	C₄×C₈	—	5	2	no	—
415	C₄×C₈	—	5	1	no	—
416	C₄×C₈	—	5	1	no	—
417	C₄×C₈	—	5	1	no	—
418	C₄×C₈	—	20	1	no	—
419	C₄×C₈	—	20	1	no	—
420	C₄×C₈	—	20	1	no	—
421	C₄×C₈	—	20	1	no	—
422	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
423	#95	—	5	2	no	—
424	#95	—	5	2	no	—
425	#95	—	5	2	no	—
426	#95	—	5	2	no	—
427	#95	—	5	2	no	—
428	#95	—	5	2	no	—
429	#95	—	5	2	no	—
430	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
431	C₂×D₅	#519	1	1	yes	characteristic
432	C₂×D₅	#520	1	1	yes	characteristic
433	C₂×D₅	C₂×#131	1	2	yes	—
434	C₂×D₅	#568	1	2	yes	—
435	AGL(1,𝔽₅)	—	2	4	no	—
436	AGL(1,𝔽₅)	—	4	2	no	—
437	AGL(1,𝔽₅)	—	4	2	no	—
438	AGL(1,𝔽₅)	—	4	2	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	#519	1	1	yes	characteristic
446	C₄×C₅	#520	1	1	yes	characteristic
447	Dic₅	—	2	1	no	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	1	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	#519	1	1	yes	characteristic
454	Dic₅	#520	1	1	yes	characteristic
455	C₂×Q₈	—	5	1	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	1	no	—
458	C₂×Q₈	—	20	2	no	—
459	C₂×Q₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	5	1	no	—
465	C₂²×C₄	—	5	1	no	—
466	C₂²×C₄	—	5	1	no	—
467	C₂²×C₄	—	5	1	no	—
468	C₂²×C₄	—	5	2	no	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	2	no	—
471	C₂×C₈	—	5	2	no	—
472	C₂×C₈	—	5	2	no	—
473	C₂×C₈	—	5	2	no	—
474	C₂×C₈	—	5	2	no	—
475	C₂×C₈	—	5	1	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	10	1	no	—
480	C₂×C₈	—	10	1	no	—
481	C₂×C₈	—	10	1	no	—
482	C₂×C₈	—	10	1	no	—
483	C₂×C₈	—	10	1	no	—
484	C₂×C₈	—	10	1	no	—
485	C₂×C₈	—	10	1	no	—
486	C₂×C₈	—	10	1	no	—
487	C₂×C₈	—	10	1	no	—
488	C₂×C₈	—	10	1	no	—
489	C₂×C₈	—	10	1	no	—
490	C₂×C₈	—	10	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	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
496	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
497	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
498	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
499	C₄⋊C₄	—	5	1	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	1	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	5	1	no	—
508	C₄⋊C₄	—	10	4	no	—
509	C₄⋊C₄	—	10	4	no	—
510	C₄⋊C₄	—	20	2	no	—
511	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
513	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
514	C₄²	—	5	1	no	—
515	C₄²	—	5	1	no	—
516	C₄²	—	5	1	no	—
517	C₄²	—	5	1	no	—
518	C₄²	—	5	1	no	—
519	C₄²	—	5	1	no	—
520	C₄²	—	5	1	no	—
521	C₄²	—	5	1	no	—
522	C₄²	—	5	1	no	—
523	C₄²	—	10	1	no	—
524	C₄²	—	10	1	no	—
525	C₄²	—	10	1	no	—
526	C₄²	—	10	1	no	—
527	C₄²	—	10	1	no	—
528	C₄²	—	10	1	no	—
529	C₄²	—	10	1	no	—
530	C₄²	—	10	1	no	—
531	C₄²	—	10	4	no	—
532	C₄²	—	20	2	no	—
533	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
534	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
535	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
536	C₂×C₅	#2276	1	1	yes	characteristic
537	C₂×C₅	#2873	1	1	yes	characteristic
538	C₂×C₅	C₄×#131	1	1	yes	characteristic
539	D₅	#2985	1	2	yes	—
540	D₅	#2992	1	2	yes	—
541	C₂³	—	5	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	20	1	no	—
544	Q₈	—	20	1	no	—
545	Q₈	—	20	1	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	1	no	—
548	C₂×C₄	—	5	1	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	1	no	—
551	C₂×C₄	—	5	4	no	—
552	C₂×C₄	—	5	1	no	—
553	C₂×C₄	—	5	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	—	10	2	no	—
559	C₂×C₄	—	10	2	no	—
560	C₂×C₄	—	10	2	no	—
561	C₂×C₄	—	10	2	no	—
562	C₂×C₄	—	10	2	no	—
563	C₂×C₄	—	10	2	no	—
564	C₂×C₄	—	10	2	no	—
565	C₂×C₄	—	10	2	no	—
566	C₂×C₄	—	10	2	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	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
576	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
577	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
578	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
579	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
580	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
581	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	10	2	no	—
587	C₈	—	10	2	no	—
588	C₈	—	10	2	no	—
589	C₈	—	10	2	no	—
590	C₈	—	10	1	no	—
591	C₈	—	10	1	no	—
592	C₈	—	10	1	no	—
593	C₈	—	10	1	no	—
594	C₅	#20575	1	1	yes	characteristic, complemented, Sylow
595	C₂²	—	5	2	no	—
596	C₂²	—	5	2	no	—
597	C₂²	—	5	1	no	—
598	C₂²	—	5	1	no	—
599	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	5	1	no	—
607	C₄	—	5	1	no	—
608	C₄	—	10	4	no	—
609	C₄	—	10	1	no	—
610	C₄	—	10	1	no	—
611	C₄	—	10	1	no	—
612	C₄	—	10	1	no	—
613	C₄	—	10	1	no	—
614	C₄	—	10	1	no	—
615	C₄	—	20	2	no	—
616	C₄	—	20	2	no	—
617	C₄	—	20	2	no	—
618	C₄	#66262	1	1	yes	characteristic
619	C₄	#66266	1	1	yes	characteristic
620	C₂	—	5	2	no	—
621	C₂	—	5	2	no	—
622	C₂	#10617208	1	1	yes	characteristic
623	C₂	#10617407	1	1	yes	characteristic
624	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	#20575
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
28. #65709	C₄	semidirect
29. #65707	C₄	semidirect
30. #65707	C₄	semidirect
43. C₅×#446	C₄	semidirect
44. #65313	C₄	semidirect
48. #65120	C₄	semidirect
49. #65117	C₄	semidirect
50. #65117	C₄	semidirect
53. #64990	C₄	semidirect
54. #64990	C₄	semidirect
56. #64968	C₄	semidirect
257. #446	AGL(1,𝔽₅)	semidirect
594. C₅	#20575	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
#10603879	2
#10603878	2
C₈×C₄⋊AGL(1,𝔽₅)	2
#10603840	2
#20575	5