Subgroups — AGL(1,𝔽₅)×#444 #13033811

Order 1280.

1022 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊#444	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₅)×#135	C₂	1	1	yes	maximal, characteristic
3	AGL(1,𝔽₅)×#131	C₂	1	2	yes	maximal, complemented
4	D₅×#444	C₂	1	1	yes	maximal, characteristic
5	#10604778	C₂	1	2	yes	maximal, complemented
6	#10604090	C₂	1	1	yes	maximal, characteristic, complemented
7	AGL(1,𝔽₅)×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	#10604006	C₂	1	2	yes	maximal, complemented
9	AGL(1,𝔽₅)×#104	C₂	1	2	yes	maximal, complemented
10	#10603885	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,𝔽₅)×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	D₅⋊#131	C₂²	1	2	yes	—
14	D₅×#135	C₂²	1	1	yes	characteristic
15	D₅×#131	C₂²	1	2	yes	—
16	#65794	C₂²	1	2	yes	—
17	D₅⋊#104	C₂²	1	2	yes	—
18	#65741	C₄	1	2	yes	complemented
19	Q₁₆×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
20	#65737	C₄	1	4	yes	complemented
21	SD₁₆×AGL(1,𝔽₅)	C₄	1	4	yes	complemented
22	#65733	C₄	1	2	yes	complemented
23	D₈×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
24	#65728	—	2	2	no	—
25	#65728	C₂²	1	2	yes	—
26	M₁₆×AGL(1,𝔽₅)	—	2	2	no	—
27	M₁₆×AGL(1,𝔽₅)	C₂²	1	2	yes	—
28	D₅⋊#108	C₂²	1	1	yes	characteristic
29	#65721	C₂²	1	1	yes	characteristic
30	#65718	—	2	2	no	—
31	#65718	C₂²	1	2	yes	—
32	C₂×#3992	C₂²	1	1	yes	characteristic
33	C₂×#3992	C₂²	1	1	yes	characteristic
34	C₂×C₈×AGL(1,𝔽₅)	—	2	2	no	—
35	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
36	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
37	C₄²×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
38	#65676	C₂²	1	1	yes	characteristic
39	C₅×#444	C₄	1	1	yes	characteristic, complemented
40	#65486	C₄	1	1	yes	characteristic, complemented
41	#65434	C₄	1	2	yes	complemented
42	#65183	C₄	1	1	yes	characteristic, complemented
43	D₅×#108	C₂²	1	1	yes	characteristic
44	#65112	C₄	1	2	yes	complemented
45	D₅×#104	C₂²	1	2	yes	—
46	#65006	C₄	1	1	yes	characteristic, complemented
47	D₅×#97	C₂²	1	1	yes	characteristic
48	#64901	C₂²	1	2	yes	—
49	#64900	C₂²	1	2	yes	—
50	#64862	C₂²	1	2	yes	—
51	C₄×#444	—	5	1	no	maximal, Sylow
52	D₅×#41	C₂³	1	2	yes	—
53	Q₈×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
54	#4133	C₂×C₄	1	4	yes	complemented
55	D₄×AGL(1,𝔽₅)	—	2	4	no	—
56	D₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
57	#4131	—	2	4	no	—
58	#4131	C₂×C₄	1	4	yes	complemented
59	#4130	—	2	2	no	—
60	#4130	C₂³	1	2	yes	—
61	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
62	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
63	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
64	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
65	D₅⋊M₁₆	—	2	2	no	—
66	D₅⋊M₁₆	C₂³	1	2	yes	—
67	C₂×D₅⋊C₈	—	2	2	no	—
68	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
70	C₅×#135	C₂×C₄	1	1	yes	characteristic
71	C₅×#131	C₂×C₄	1	2	yes	complemented
72	#4096	C₂×C₄	1	2	yes	—
73	#4094	C₂×C₄	1	2	yes	complemented
74	#4065	C₂×C₄	1	1	yes	characteristic
75	D₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
76	#4062	C₂×C₄	1	2	yes	—
77	D₅×SD₁₆	C₂×C₄	1	2	yes	—
78	#4058	C₂×C₄	1	1	yes	characteristic
79	D₅×D₈	C₂×C₄	1	1	yes	characteristic
80	#4053	—	2	2	no	—
81	#4053	C₂×C₄	1	2	yes	complemented
82	D₅×M₁₆	—	2	2	no	—
83	D₅×M₁₆	C₂³	1	2	yes	—
84	#4050	C₂×C₄	1	1	yes	characteristic
85	#4047	—	2	2	no	—
86	#4047	C₂×C₄	1	2	yes	complemented
87	C₂×C₈×D₅	—	2	2	no	—
88	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
90	C₄²×D₅	C₂³	1	1	yes	characteristic
91	#4010	C₂×C₄	1	4	yes	complemented
92	#4009	C₂×C₄	1	4	yes	—
93	#4008	C₂×C₄	1	4	yes	complemented
94	#4007	C₂×C₄	1	4	yes	—
95	#4002	—	2	2	no	—
96	#3996	C₂×C₄	1	2	yes	complemented
97	#3995	C₂×C₄	1	2	yes	complemented
98	#3994	C₂×C₄	1	2	yes	—
99	#3993	C₂×C₄	1	2	yes	—
100	#3992	—	2	2	no	—
101	#3992	—	2	2	no	—
102	#3992	—	2	2	no	—
103	#3992	—	2	2	no	—
104	#3992	C₂×C₄	1	2	yes	complemented
105	#3992	C₂×C₄	1	2	yes	complemented
106	C₈×AGL(1,𝔽₅)	—	2	2	no	—
107	C₈×AGL(1,𝔽₅)	—	2	2	no	—
108	C₈×AGL(1,𝔽₅)	—	2	2	no	—
109	C₈×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
110	C₈×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
111	C₈×AGL(1,𝔽₅)	D₄	1	2	yes	—
112	C₈×AGL(1,𝔽₅)	D₄	1	2	yes	—
113	C₅×#108	C₂×C₄	1	1	yes	characteristic, complemented
114	C₅×#104	C₂×C₄	1	2	yes	complemented
115	C₅×#97	C₂×C₄	1	1	yes	characteristic, complemented
116	#3969	C₂×C₄	1	2	yes	complemented
117	#3957	C₂×C₄	1	2	yes	complemented
118	#3954	C₂×C₄	1	2	yes	complemented
119	#3951	C₂×C₄	1	1	yes	characteristic, complemented
120	#3947	C₂×C₄	1	1	yes	characteristic, complemented
121	#3947	C₂×C₄	1	1	yes	characteristic, complemented
122	#3937	C₂×C₄	1	2	yes	complemented
123	#3935	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂×#444	—	5	1	no	—
125	C₂×#444	—	5	1	no	—
126	C₄×#135	—	5	1	no	—
127	C₄×#131	—	5	2	no	—
128	C₄×#108	—	5	1	no	—
129	#1773	—	5	1	no	—
130	#1773	—	5	1	no	—
131	#1765	—	5	2	no	—
132	#1765	—	5	2	no	—
133	C₄×#104	—	5	2	no	—
134	C₄×#97	—	5	1	no	—
135	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
136	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
137	C₂²×AGL(1,𝔽₅)	#41	1	2	yes	—
138	C₅×#41	C₂²×C₄	1	2	yes	—
139	#713	C₂²×C₄	1	2	yes	—
140	Q₈×D₅	C₂²×C₄	1	2	yes	—
141	#711	—	2	2	no	—
142	#711	C₂²×C₄	1	2	yes	—
143	D₄×D₅	—	2	2	no	—
144	D₄×D₅	C₂²×C₄	1	2	yes	—
145	#709	—	2	2	no	—
146	#709	C₂²×C₄	1	2	yes	—
147	C₂×C₄×D₅	—	2	2	no	—
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
150	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
151	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
152	#704	—	2	2	no	—
153	#704	—	2	4	no	—
154	C₂×#170	—	2	1	no	—
155	C₂×#170	—	2	4	no	—
156	C₂×#170	#41	1	2	yes	—
157	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
158	C₄⋊AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
159	C₄×AGL(1,𝔽₅)	—	2	4	no	—
160	C₄×AGL(1,𝔽₅)	—	2	2	no	—
161	C₄×AGL(1,𝔽₅)	—	2	1	no	—
162	C₄×AGL(1,𝔽₅)	—	4	4	no	—
163	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
164	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
165	C₄×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
166	C₄×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
167	#700	—	2	4	no	—
168	#700	C₂²×C₄	1	4	yes	—
169	D₅⋊C₈	—	2	2	no	—
170	D₅⋊C₈	—	2	1	no	—
171	D₅⋊C₈	—	2	4	no	—
172	D₅⋊C₈	C₂²×C₄	1	2	yes	—
173	D₅⋊C₈	C₂²×C₄	1	2	yes	—
174	D₅⋊C₈	C₂×D₄	1	2	yes	—
175	C₅×Q₁₆	C₄²	1	1	yes	characteristic, complemented
176	C₅×SD₁₆	C₄²	1	2	yes	complemented
177	C₅×D₈	C₄²	1	1	yes	characteristic, complemented
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	C₂²×C₄	1	2	yes	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
184	#689	C₄²	1	2	yes	complemented
185	#688	C₄²	1	2	yes	complemented
186	#687	C₄²	1	2	yes	complemented
187	#686	C₄²	1	2	yes	complemented
188	C₄×Dic₅	—	2	1	no	—
189	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
190	#681	—	2	2	no	—
191	#681	C₂²×C₄	1	2	yes	—
192	C₂×#168	—	2	2	no	—
193	C₂×#168	C₂²×C₄	1	1	yes	characteristic
194	C₂×#168	C₂²×C₄	1	1	yes	characteristic
195	Dic₂₀	C₄²	1	1	yes	characteristic, complemented
196	D₄₀	C₄²	1	1	yes	characteristic, complemented
197	#677	C₄²	1	2	yes	complemented
198	#676	—	2	2	no	—
199	#676	—	2	2	no	—
200	#676	—	2	2	no	—
201	C₈×D₅	—	2	2	no	—
202	C₈×D₅	—	2	2	no	—
203	C₈×D₅	—	2	2	no	—
204	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
205	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
206	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
207	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
208	C₈×D₅	C₂×D₄	1	2	yes	—
209	C₈×D₅	#41	1	2	yes	—
210	C₂×#135	—	5	1	no	—
211	C₂×#131	—	5	2	no	—
212	C₂×#131	—	5	2	no	—
213	C₄×#41	—	5	2	no	—
214	#444	—	5	2	no	—
215	#444	—	5	4	no	—
216	#444	—	5	2	no	—
217	#444	—	5	1	no	—
218	#444	—	5	2	no	—
219	#444	—	5	1	no	—
220	#444	—	5	2	no	—
221	#444	—	5	1	no	—
222	#444	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
223	C₄×Q₁₆	—	5	2	no	—
224	C₄×SD₁₆	—	5	4	no	—
225	C₄×D₈	—	5	2	no	—
226	C₂×#108	—	5	1	no	—
227	C₂×#108	—	5	1	no	—
228	#427	—	5	1	no	—
229	C₂×#104	—	5	2	no	—
230	C₂×#104	—	5	2	no	—
231	#416	—	5	2	no	—
232	#405	—	5	2	no	—
233	#405	—	5	2	no	—
234	#405	—	10	2	no	—
235	#405	—	10	2	no	—
236	C₄×M₁₆	—	5	2	no	—
237	C₄×M₁₆	—	10	2	no	—
238	C₂×#97	—	5	1	no	—
239	C₂×#97	—	5	1	no	—
240	C₂×#97	—	5	1	no	—
241	C₂×#97	—	5	1	no	—
242	C₂×C₄×C₈	—	5	1	no	—
243	C₂×C₄×C₈	—	5	1	no	—
244	C₂×C₄×C₈	—	10	2	no	—
245	C₄³	—	5	1	no	—
246	#341	—	5	2	no	—
247	#339	—	5	2	no	—
248	#339	—	5	2	no	—
249	C₂²×D₅	—	2	2	no	—
250	C₂²×D₅	C₂×#41	1	1	yes	characteristic
251	C₂×AGL(1,𝔽₅)	—	2	4	no	—
252	C₂×AGL(1,𝔽₅)	—	2	4	no	—
253	C₂×AGL(1,𝔽₅)	—	2	2	no	—
254	C₂×AGL(1,𝔽₅)	—	4	2	no	—
255	C₂×AGL(1,𝔽₅)	—	4	8	no	—
256	C₂×AGL(1,𝔽₅)	C₄×D₄	1	2	yes	—
257	C₂×AGL(1,𝔽₅)	C₄×D₄	1	2	yes	—
258	C₅×Q₈	C₂×C₄²	1	2	yes	—
259	C₅×D₄	—	2	2	no	—
260	C₅×D₄	C₂×C₄²	1	2	yes	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₂²⋊D₅	—	2	2	no	—
265	C₂²⋊D₅	—	2	2	no	—
266	C₂²⋊D₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	—	2	1	no	—
269	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
270	D₂₀	—	2	2	no	—
271	D₂₀	C₂×C₄²	1	2	yes	—
272	C₄×D₅	—	2	2	no	—
273	C₄×D₅	—	2	2	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	4	2	no	—
276	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
277	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
278	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
279	C₄×D₅	C₂×#41	1	1	yes	characteristic
280	Dic₁₀	—	2	2	no	—
281	Dic₁₀	C₂×C₄²	1	2	yes	—
282	#170	—	2	4	no	—
283	#170	—	2	2	no	—
284	#170	C₄×D₄	1	4	yes	—
285	C₅×C₈	—	2	2	no	—
286	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
287	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
288	C₅×C₈	C₄×D₄	1	2	yes	—
289	#168	—	2	2	no	—
290	#168	C₂×C₄²	1	1	yes	characteristic
291	#168	C₂×C₄²	1	1	yes	characteristic
292	#168	C₄×D₄	1	2	yes	—
293	C₂×#41	—	5	2	no	—
294	#135	—	5	2	no	—
295	#135	—	5	1	no	—
296	#135	—	5	2	no	—
297	#135	—	5	1	no	—
298	#135	—	5	1	no	—
299	#135	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₂×Q₁₆	—	5	1	no	—
301	C₂×SD₁₆	—	5	2	no	—
302	C₂×D₈	—	5	1	no	—
303	#131	—	5	4	no	—
304	#131	—	5	4	no	—
305	#131	—	5	2	no	—
306	#131	—	5	2	no	—
307	#131	—	5	2	no	—
308	#131	—	10	2	no	—
309	#131	—	10	2	no	—
310	#131	—	10	4	no	—
311	#131	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
312	C₂×M₁₆	—	5	2	no	—
313	C₂×M₁₆	—	5	2	no	—
314	C₂×M₁₆	—	10	2	no	—
315	C₂×M₁₆	—	10	2	no	—
316	C₂²×C₈	—	5	1	no	—
317	C₂²×C₈	—	5	1	no	—
318	C₂²×C₈	—	5	1	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	10	2	no	—
321	C₂²×C₈	—	10	2	no	—
322	C₄×Q₈	—	5	4	no	—
323	C₄×D₄	—	5	4	no	—
324	C₄×D₄	—	10	4	no	—
325	#117	—	5	2	no	—
326	#117	—	10	2	no	—
327	C₂×C₄²	—	5	1	no	—
328	C₂×C₄²	—	5	1	no	—
329	C₂×C₄²	—	5	1	no	—
330	C₂×C₄²	—	10	2	no	—
331	C₂×C₄²	—	10	2	no	—
332	#108	—	5	2	no	—
333	#108	—	5	2	no	—
334	#108	—	5	2	no	—
335	#108	—	5	1	no	—
336	#108	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
337	#107	—	5	2	no	—
338	#106	—	5	2	no	—
339	#104	—	5	4	no	—
340	#104	—	5	4	no	—
341	#104	—	5	2	no	—
342	#104	—	5	2	no	—
343	#104	—	5	2	no	—
344	#104	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
345	#103	—	5	4	no	—
346	#102	—	5	4	no	—
347	#97	—	5	2	no	—
348	#97	—	5	2	no	—
349	#97	—	5	1	no	—
350	#97	—	5	1	no	—
351	#97	—	5	1	no	—
352	#97	—	10	2	no	—
353	#97	—	10	2	no	—
354	#97	—	10	2	no	—
355	#97	—	10	2	no	—
356	#97	—	10	2	no	—
357	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
358	C₄×C₈	—	5	2	no	—
359	C₄×C₈	—	5	2	no	—
360	C₄×C₈	—	5	2	no	—
361	C₄×C₈	—	5	2	no	—
362	C₄×C₈	—	10	2	no	—
363	C₄×C₈	—	10	2	no	—
364	C₄×C₈	—	10	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	C₄×#41	1	1	yes	characteristic
367	C₂×D₅	—	2	2	no	—
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	—	4	4	no	—
370	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
371	C₂×D₅	C₄×#41	1	1	yes	characteristic
372	AGL(1,𝔽₅)	—	2	2	no	—
373	AGL(1,𝔽₅)	—	4	2	no	—
374	AGL(1,𝔽₅)	—	4	4	no	—
375	AGL(1,𝔽₅)	#444	1	4	yes	direct product factor
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
379	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
380	Dic₅	—	2	2	no	—
381	Dic₅	—	4	1	no	—
382	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
383	Dic₅	C₄×#41	1	1	yes	characteristic
384	#41	—	5	2	no	—
385	#41	—	5	2	no	—
386	#41	—	5	2	no	—
387	#41	—	10	2	no	—
388	#41	—	10	2	no	—
389	#41	C₂²×AGL(1,𝔽₅)	1	2	yes	—
390	C₂×Q₈	—	5	2	no	—
391	C₂×D₄	—	5	2	no	—
392	C₂×D₄	—	10	2	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	2	no	—
395	C₂²×C₄	—	10	2	no	—
396	C₂²×C₄	—	10	1	no	—
397	C₂²×C₄	—	10	4	no	—
398	C₂²×C₄	—	10	1	no	—
399	Q₁₆	—	5	2	no	—
400	Q₁₆	—	5	1	no	—
401	Q₁₆	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
402	SD₁₆	—	5	2	no	—
403	SD₁₆	—	5	2	no	—
404	SD₁₆	—	5	2	no	—
405	SD₁₆	C₄×AGL(1,𝔽₅)	1	2	yes	complemented
406	D₈	—	5	2	no	—
407	D₈	—	5	1	no	—
408	D₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
409	M₁₆	—	2	2	no	—
410	M₁₆	—	5	4	no	—
411	M₁₆	—	5	2	no	—
412	M₁₆	—	10	2	no	—
413	M₁₆	—	10	2	no	—
414	M₁₆	—	10	2	no	—
415	M₁₆	—	10	4	no	—
416	M₁₆	—	10	4	no	—
417	M₁₆	—	10	2	no	—
418	M₁₆	—	10	2	no	—
419	M₁₆	C₂²×AGL(1,𝔽₅)	1	2	yes	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	5	2	no	—
422	C₂×C₈	—	5	2	no	—
423	C₂×C₈	—	5	2	no	—
424	C₂×C₈	—	5	1	no	—
425	C₂×C₈	—	5	1	no	—
426	C₂×C₈	—	5	1	no	—
427	C₂×C₈	—	5	1	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	—	5	2	no	—
432	C₂×C₈	—	5	2	no	—
433	C₂×C₈	—	10	2	no	—
434	C₂×C₈	—	10	2	no	—
435	C₂×C₈	—	10	2	no	—
436	C₂×C₈	—	10	4	no	—
437	C₂×C₈	—	10	4	no	—
438	C₂×C₈	—	10	2	no	—
439	C₂×C₈	—	10	1	no	—
440	C₂×C₈	—	10	1	no	—
441	C₂×C₈	—	10	2	no	—
442	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
443	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
444	C₄⋊C₄	—	5	4	no	—
445	C₄⋊C₄	—	10	4	no	—
446	C₂²⋊C₄	—	10	4	no	—
447	C₂²⋊C₄	—	10	2	no	—
448	C₄²	—	5	1	no	—
449	C₄²	—	5	1	no	—
450	C₄²	—	5	2	no	—
451	C₄²	—	5	2	no	—
452	C₄²	—	5	1	no	—
453	C₄²	—	10	1	no	—
454	C₄²	—	10	2	no	—
455	C₄²	—	10	1	no	—
456	C₄²	—	10	4	no	—
457	C₄²	—	20	4	no	—
458	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	4	2	no	—
461	C₂×C₅	C₄²×D₄	1	1	yes	characteristic
462	D₅	—	2	1	no	—
463	D₅	—	4	2	no	—
464	D₅	C₂×#444	1	2	yes	—
465	C₂³	—	5	1	no	—
466	C₂³	—	10	2	no	—
467	Q₈	—	5	2	no	—
468	Q₈	—	10	2	no	—
469	Q₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
470	D₄	—	2	2	no	—
471	D₄	—	5	2	no	—
472	D₄	—	10	2	no	—
473	D₄	—	10	2	no	—
474	D₄	—	10	2	no	—
475	D₄	—	10	2	no	—
476	D₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	5	2	no	—
480	C₂×C₄	—	5	1	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	1	no	—
483	C₂×C₄	—	5	1	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	2	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	10	4	no	—
490	C₂×C₄	—	10	2	no	—
491	C₂×C₄	—	10	2	no	—
492	C₂×C₄	—	10	4	no	—
493	C₂×C₄	—	10	1	no	—
494	C₂×C₄	—	20	2	no	—
495	C₂×C₄	—	20	8	no	—
496	C₂×C₄	—	20	2	no	—
497	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	5	4	no	—
500	C₈	—	5	1	no	—
501	C₈	—	5	1	no	—
502	C₈	—	5	2	no	—
503	C₈	—	10	2	no	—
504	C₈	—	10	4	no	—
505	C₈	—	10	2	no	—
506	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₈	D₄×AGL(1,𝔽₅)	1	2	yes	—
509	C₅	C₄×#444	1	1	yes	characteristic, complemented, Sylow
510	C₂²	—	2	2	no	—
511	C₂²	—	5	1	no	—
512	C₂²	—	5	1	no	—
513	C₂²	—	10	2	no	—
514	C₂²	—	10	2	no	—
515	C₂²	—	20	4	no	—
516	C₂²	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	5	4	no	—
520	C₄	—	5	1	no	—
521	C₄	—	5	1	no	—
522	C₄	—	10	2	no	—
523	C₄	—	10	2	no	—
524	C₄	—	20	1	no	—
525	C₄	—	20	4	no	—
526	C₄	—	20	2	no	—
527	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
528	C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	5	2	no	—
532	C₂	—	10	1	no	—
533	C₂	—	20	2	no	—
534	C₂	C₄×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#444	C₄
socle	C₂×C₅	C₄²×D₄
prime radical	D₅×#135	C₂²
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#444	AGL(1,𝔽₅)
hypocenter	C₅	C₄×#444
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
3. AGL(1,𝔽₅)×#131	C₂	semidirect
5. #10604778	C₂	semidirect
6. #10604090	C₂	semidirect
7. AGL(1,𝔽₅)×#108	C₂	semidirect
8. #10604006	C₂	semidirect
9. AGL(1,𝔽₅)×#104	C₂	semidirect
10. #10603885	C₂	semidirect
11. AGL(1,𝔽₅)×#97	C₂	semidirect
18. #65741	C₄	semidirect
19. Q₁₆×AGL(1,𝔽₅)	C₄	semidirect
20. #65737	C₄	semidirect
21. SD₁₆×AGL(1,𝔽₅)	C₄	semidirect
22. #65733	C₄	semidirect
23. D₈×AGL(1,𝔽₅)	C₄	semidirect
39. C₅×#444	C₄	semidirect
40. #65486	C₄	semidirect
41. #65434	C₄	semidirect
42. #65183	C₄	semidirect
44. #65112	C₄	semidirect
46. #65006	C₄	semidirect
54. #4133	C₂×C₄	semidirect
58. #4131	C₂×C₄	semidirect
71. C₅×#131	C₂×C₄	semidirect
73. #4094	C₂×C₄	semidirect
81. #4053	C₂×C₄	semidirect
86. #4047	C₂×C₄	semidirect
91. #4010	C₂×C₄	semidirect
93. #4008	C₂×C₄	semidirect
96. #3996	C₂×C₄	semidirect
97. #3995	C₂×C₄	semidirect
104. #3992	C₂×C₄	semidirect
105. #3992	C₂×C₄	semidirect
113. C₅×#108	C₂×C₄	semidirect
114. C₅×#104	C₂×C₄	semidirect
115. C₅×#97	C₂×C₄	semidirect
116. #3969	C₂×C₄	semidirect
117. #3957	C₂×C₄	semidirect
118. #3954	C₂×C₄	semidirect
119. #3951	C₂×C₄	semidirect
120. #3947	C₂×C₄	semidirect
121. #3947	C₂×C₄	semidirect
122. #3937	C₂×C₄	semidirect
123. #3935	C₂×C₄	semidirect
175. C₅×Q₁₆	C₄²	semidirect
176. C₅×SD₁₆	C₄²	semidirect
177. C₅×D₈	C₄²	semidirect
184. #689	C₄²	semidirect
185. #688	C₄²	semidirect
186. #687	C₄²	semidirect
187. #686	C₄²	semidirect
195. Dic₂₀	C₄²	semidirect
196. D₄₀	C₄²	semidirect
197. #677	C₄²	semidirect
222. #444	AGL(1,𝔽₅)	direct (N × H)
311. #131	C₂×AGL(1,𝔽₅)	semidirect
336. #108	C₂×AGL(1,𝔽₅)	semidirect
344. #104	C₂×AGL(1,𝔽₅)	semidirect
357. #97	C₂×AGL(1,𝔽₅)	semidirect
375. AGL(1,𝔽₅)	#444	direct (N × H)
401. Q₁₆	C₄×AGL(1,𝔽₅)	semidirect
405. SD₁₆	C₄×AGL(1,𝔽₅)	semidirect
408. D₈	C₄×AGL(1,𝔽₅)	semidirect
509. C₅	C₄×#444	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊#444	2
AGL(1,𝔽₅)×#135	2
AGL(1,𝔽₅)×#131	2
D₅×#444	2
#10604778	2
#10604090	2
AGL(1,𝔽₅)×#108	2
#10604006	2
AGL(1,𝔽₅)×#104	2
#10603885	2
AGL(1,𝔽₅)×#97	2
C₄×#444	5

Subgroups — AGL(1,𝔽5)×#444 #13033811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#444 #13033811