Subgroups — #13033819

Order 1280.

1014 conjugacy classes of subgroups.

The subgroup lattice has 540 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	#10617439	C₂	1	1	yes	maximal, characteristic
3	#10617415	C₂	1	2	yes	maximal, complemented
4	D₅×#443	C₂	1	1	yes	maximal, characteristic
5	#10604778	C₂	1	2	yes	maximal, complemented
6	#10604090	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604086	C₂	1	1	yes	maximal, characteristic, complemented
8	#10604005	C₂	1	2	yes	maximal, complemented
9	AGL(1,𝔽₅)×#104	C₂	1	2	yes	maximal, complemented
10	#10603851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#3992	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	#65739	C₄	1	2	yes	complemented
20	#65737	C₄	1	4	yes	complemented
21	#65735	C₄	1	4	yes	complemented
22	#65733	C₄	1	2	yes	complemented
23	#65731	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	—	2	2	no	—
33	C₂×#3992	C₂²	1	1	yes	characteristic
34	C₂×#3992	C₂²	1	1	yes	characteristic
35	C₂×#3992	C₂²	1	1	yes	characteristic
36	C₂×#3992	C₂²	1	1	yes	characteristic
37	C₄²×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
38	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#443	C₄	1	1	yes	characteristic, complemented
40	#65485	C₄	1	1	yes	characteristic, complemented
41	#65433	C₄	1	2	yes	complemented
42	#65184	C₄	1	1	yes	characteristic, complemented
43	D₅×#108	C₂²	1	1	yes	characteristic
44	#65113	C₄	1	2	yes	complemented
45	D₅×#104	C₂²	1	2	yes	—
46	#64989	C₄	1	1	yes	characteristic, complemented
47	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
48	#64901	C₂²	1	2	yes	—
49	#64900	C₂²	1	2	yes	—
50	#64862	C₂²	1	2	yes	—
51	#20512	—	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	C₄×#170	—	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	1	no	—
104	#3992	—	2	1	no	—
105	#3992	C₂×C₄	1	2	yes	—
106	#3992	C₂×C₄	1	2	yes	—
107	#3992	C₂×C₄	1	2	yes	complemented
108	#3992	C₂×C₄	1	2	yes	complemented
109	#3992	D₄	1	2	yes	—
110	#3992	D₄	1	2	yes	—
111	C₈×AGL(1,𝔽₅)	—	2	2	no	—
112	C₈×AGL(1,𝔽₅)	—	2	2	no	—
113	C₈×AGL(1,𝔽₅)	—	2	2	no	—
114	C₅×#108	C₂×C₄	1	1	yes	characteristic, complemented
115	C₅×#104	C₂×C₄	1	2	yes	complemented
116	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
117	#3969	C₂×C₄	1	2	yes	complemented
118	#3957	C₂×C₄	1	2	yes	complemented
119	#3954	C₂×C₄	1	2	yes	complemented
120	#3951	C₂×C₄	1	1	yes	characteristic, complemented
121	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
122	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
123	#3937	C₂×C₄	1	2	yes	complemented
124	C₄×#168	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#444	—	5	1	no	—
126	C₂×#443	—	5	1	no	—
127	#2943	—	5	1	no	—
128	#2875	—	5	2	no	—
129	#1778	—	5	1	no	—
130	#1773	—	5	1	no	—
131	#1772	—	5	1	no	—
132	#1765	—	5	2	no	—
133	#1764	—	5	2	no	—
134	C₄×#104	—	5	2	no	—
135	C₄×#97	—	5	1	no	—
136	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
137	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
138	C₂²×AGL(1,𝔽₅)	#41	1	2	yes	—
139	C₅×#41	C₂²×C₄	1	2	yes	—
140	#713	C₂²×C₄	1	2	yes	—
141	Q₈×D₅	C₂²×C₄	1	2	yes	—
142	#711	—	2	2	no	—
143	#711	C₂²×C₄	1	2	yes	—
144	D₄×D₅	—	2	2	no	—
145	D₄×D₅	C₂²×C₄	1	2	yes	—
146	#709	—	2	2	no	—
147	#709	C₂²×C₄	1	2	yes	—
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	—	2	2	no	—
150	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
151	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
152	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
153	#704	—	2	2	no	—
154	#704	—	2	4	no	—
155	C₂×#170	—	2	1	no	—
156	C₂×#170	—	2	4	no	—
157	C₂×#170	#41	1	2	yes	—
158	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
159	C₄⋊AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
160	C₄×AGL(1,𝔽₅)	—	2	4	no	—
161	C₄×AGL(1,𝔽₅)	—	2	2	no	—
162	C₄×AGL(1,𝔽₅)	—	2	1	no	—
163	C₄×AGL(1,𝔽₅)	—	4	4	no	—
164	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
165	C₄×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
166	C₄×AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
209	C₈×D₅	C₂×D₄	1	1	yes	characteristic
210	C₈×D₅	#41	1	1	yes	characteristic
211	C₈×D₅	#41	1	1	yes	characteristic
212	C₂×#135	—	5	1	no	—
213	C₂×#131	—	5	2	no	—
214	C₂×#131	—	5	2	no	—
215	C₄×#41	—	5	2	no	—
216	#444	—	5	2	no	—
217	#444	—	5	4	no	—
218	#444	—	5	2	no	—
219	#443	—	5	1	no	—
220	#443	—	5	2	no	—
221	#443	—	5	1	no	—
222	#443	—	5	2	no	—
223	#443	—	5	1	no	—
224	#443	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
225	#442	—	5	2	no	—
226	#441	—	5	2	no	—
227	#440	—	5	4	no	—
228	C₂×#108	—	5	1	no	—
229	C₂×#108	—	5	1	no	—
230	#427	—	5	1	no	—
231	C₂×#104	—	5	2	no	—
232	C₂×#104	—	5	2	no	—
233	#416	—	5	2	no	—
234	#405	—	5	2	no	—
235	#405	—	5	2	no	—
236	#405	—	10	2	no	—
237	#405	—	10	2	no	—
238	C₄×M₁₆	—	5	2	no	—
239	C₄×M₁₆	—	10	2	no	—
240	C₂×#97	—	5	1	no	—
241	C₂×#97	—	5	1	no	—
242	C₂×#97	—	5	1	no	—
243	C₂×#97	—	5	1	no	—
244	C₂×#97	—	10	2	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₂×C₄×C₈	—	5	1	no	—
247	C₄³	—	5	1	no	—
248	#341	—	5	2	no	—
249	#339	—	5	2	no	—
250	#339	—	5	2	no	—
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	C₂×#41	1	1	yes	characteristic
253	C₂×AGL(1,𝔽₅)	—	2	4	no	—
254	C₂×AGL(1,𝔽₅)	—	2	2	no	—
255	C₂×AGL(1,𝔽₅)	—	4	2	no	—
256	C₂×AGL(1,𝔽₅)	—	4	2	no	—
257	C₂×AGL(1,𝔽₅)	—	8	4	no	—
258	C₂×AGL(1,𝔽₅)	C₄×D₄	1	4	yes	—
259	C₅×Q₈	C₂×C₄²	1	2	yes	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	C₂×C₄²	1	2	yes	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
265	C₂²⋊D₅	—	2	2	no	—
266	C₂²⋊D₅	—	2	2	no	—
267	C₂²⋊D₅	—	2	2	no	—
268	C₂×Dic₅	—	2	1	no	—
269	C₂×Dic₅	—	2	2	no	—
270	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
271	D₂₀	—	2	2	no	—
272	D₂₀	C₂×C₄²	1	2	yes	—
273	C₄×D₅	—	2	4	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
278	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
279	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
280	C₄×D₅	C₂×#41	1	1	yes	characteristic
281	Dic₁₀	—	2	2	no	—
282	Dic₁₀	C₂×C₄²	1	2	yes	—
283	#170	—	2	4	no	—
284	#170	—	2	2	no	—
285	#170	C₄×D₄	1	4	yes	—
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
288	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
289	C₅×C₈	C₄×D₄	1	1	yes	characteristic
290	C₅×C₈	C₄×D₄	1	1	yes	characteristic
291	#168	—	2	2	no	—
292	#168	C₂×C₄²	1	1	yes	characteristic
293	#168	C₂×C₄²	1	1	yes	characteristic
294	#168	C₄×D₄	1	1	yes	characteristic
295	#168	C₄×D₄	1	1	yes	characteristic
296	C₂×#41	—	5	2	no	—
297	#135	—	5	2	no	—
298	#135	—	5	1	no	—
299	#135	—	5	2	no	—
300	#135	—	5	1	no	—
301	#135	—	5	1	no	—
302	#135	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
303	C₂×Q₁₆	—	5	1	no	—
304	C₂×SD₁₆	—	5	2	no	—
305	C₂×D₈	—	5	1	no	—
306	#131	—	5	4	no	—
307	#131	—	5	4	no	—
308	#131	—	5	2	no	—
309	#131	—	5	2	no	—
310	#131	—	5	2	no	—
311	#131	—	10	2	no	—
312	#131	—	10	2	no	—
313	#131	—	10	4	no	—
314	#131	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
315	C₂×M₁₆	—	5	2	no	—
316	C₂×M₁₆	—	5	2	no	—
317	C₂×M₁₆	—	10	2	no	—
318	C₂×M₁₆	—	10	2	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	5	1	no	—
321	C₂²×C₈	—	5	1	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	10	2	no	—
324	C₂²×C₈	—	10	2	no	—
325	C₄×Q₈	—	5	4	no	—
326	C₄×D₄	—	5	4	no	—
327	C₄×D₄	—	10	4	no	—
328	#117	—	5	2	no	—
329	#117	—	10	2	no	—
330	C₂×C₄²	—	5	1	no	—
331	C₂×C₄²	—	5	1	no	—
332	C₂×C₄²	—	5	1	no	—
333	C₂×C₄²	—	10	2	no	—
334	C₂×C₄²	—	10	2	no	—
335	#108	—	5	2	no	—
336	#108	—	5	2	no	—
337	#108	—	5	2	no	—
338	#108	—	5	1	no	—
339	#108	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
340	#107	—	5	2	no	—
341	#106	—	5	2	no	—
342	#104	—	5	4	no	—
343	#104	—	5	4	no	—
344	#104	—	5	2	no	—
345	#104	—	5	2	no	—
346	#104	—	5	2	no	—
347	#104	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
348	#103	—	5	4	no	—
349	#102	—	5	4	no	—
350	#97	—	5	2	no	—
351	#97	—	5	2	no	—
352	#97	—	5	2	no	—
353	#97	—	5	2	no	—
354	#97	—	5	2	no	—
355	#97	—	5	2	no	—
356	#97	—	10	2	no	—
357	#97	—	10	1	no	—
358	#97	—	10	1	no	—
359	#97	—	10	2	no	—
360	#97	—	10	2	no	—
361	C₄×C₈	—	5	1	no	—
362	C₄×C₈	—	5	1	no	—
363	C₄×C₈	—	5	1	no	—
364	C₄×C₈	—	10	2	no	—
365	C₄×C₈	—	10	2	no	—
366	C₄×C₈	—	10	2	no	—
367	C₄×C₈	—	10	2	no	—
368	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	C₄×#41	1	1	yes	characteristic
371	C₂×D₅	—	2	2	no	—
372	C₂×D₅	—	2	2	no	—
373	C₂×D₅	—	4	4	no	—
374	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×D₅	C₄×#41	1	1	yes	characteristic
376	AGL(1,𝔽₅)	—	2	4	no	—
377	AGL(1,𝔽₅)	—	4	2	no	—
378	AGL(1,𝔽₅)	—	4	4	no	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
382	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
383	Dic₅	—	2	2	no	—
384	Dic₅	—	2	2	no	—
385	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
386	Dic₅	C₄×#41	1	1	yes	characteristic
387	#41	—	5	2	no	—
388	#41	—	5	2	no	—
389	#41	—	5	2	no	—
390	#41	—	10	2	no	—
391	#41	—	10	2	no	—
392	#41	C₂²×AGL(1,𝔽₅)	1	2	yes	—
393	C₂×Q₈	—	5	2	no	—
394	C₂×D₄	—	5	2	no	—
395	C₂×D₄	—	10	2	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	5	2	no	—
398	C₂²×C₄	—	10	2	no	—
399	C₂²×C₄	—	10	1	no	—
400	C₂²×C₄	—	10	4	no	—
401	C₂²×C₄	—	10	1	no	—
402	Q₁₆	—	5	2	no	—
403	Q₁₆	—	5	1	no	—
404	Q₁₆	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
405	SD₁₆	—	5	2	no	—
406	SD₁₆	—	5	2	no	—
407	SD₁₆	—	5	2	no	—
408	SD₁₆	C₄×AGL(1,𝔽₅)	1	2	yes	complemented
409	D₈	—	5	2	no	—
410	D₈	—	5	1	no	—
411	D₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
412	M₁₆	—	2	2	no	—
413	M₁₆	—	5	4	no	—
414	M₁₆	—	5	2	no	—
415	M₁₆	—	10	2	no	—
416	M₁₆	—	10	2	no	—
417	M₁₆	—	10	2	no	—
418	M₁₆	—	10	4	no	—
419	M₁₆	—	10	4	no	—
420	M₁₆	—	10	2	no	—
421	M₁₆	—	10	2	no	—
422	M₁₆	C₂²×AGL(1,𝔽₅)	1	2	yes	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	5	2	no	—
425	C₂×C₈	—	5	2	no	—
426	C₂×C₈	—	5	2	no	—
427	C₂×C₈	—	5	1	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	1	no	—
431	C₂×C₈	—	5	1	no	—
432	C₂×C₈	—	5	1	no	—
433	C₂×C₈	—	5	1	no	—
434	C₂×C₈	—	5	1	no	—
435	C₂×C₈	—	5	1	no	—
436	C₂×C₈	—	5	1	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	10	2	no	—
439	C₂×C₈	—	10	2	no	—
440	C₂×C₈	—	10	2	no	—
441	C₂×C₈	—	10	4	no	—
442	C₂×C₈	—	10	4	no	—
443	C₂×C₈	—	10	2	no	—
444	C₂×C₈	—	10	1	no	—
445	C₂×C₈	—	10	1	no	—
446	C₂×C₈	—	10	2	no	—
447	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
448	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₄⋊C₄	—	5	4	no	—
450	C₄⋊C₄	—	10	4	no	—
451	C₂²⋊C₄	—	10	4	no	—
452	C₂²⋊C₄	—	10	2	no	—
453	C₄²	—	5	2	no	—
454	C₄²	—	5	2	no	—
455	C₄²	—	5	2	no	—
456	C₄²	—	5	1	no	—
457	C₄²	—	10	1	no	—
458	C₄²	—	10	2	no	—
459	C₄²	—	10	1	no	—
460	C₄²	—	10	4	no	—
461	C₄²	—	20	4	no	—
462	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
463	C₂×C₅	—	2	1	no	—
464	C₂×C₅	—	4	2	no	—
465	C₂×C₅	C₄²×D₄	1	1	yes	characteristic
466	D₅	—	2	1	no	—
467	D₅	—	4	2	no	—
468	D₅	#2956	1	2	yes	—
469	C₂³	—	5	1	no	—
470	C₂³	—	10	2	no	—
471	Q₈	—	5	2	no	—
472	Q₈	—	10	2	no	—
473	Q₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	5	2	no	—
476	D₄	—	10	2	no	—
477	D₄	—	10	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	2	no	—
480	D₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	5	1	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	1	no	—
486	C₂×C₄	—	5	1	no	—
487	C₂×C₄	—	5	1	no	—
488	C₂×C₄	—	5	4	no	—
489	C₂×C₄	—	10	2	no	—
490	C₂×C₄	—	10	2	no	—
491	C₂×C₄	—	10	4	no	—
492	C₂×C₄	—	10	2	no	—
493	C₂×C₄	—	10	1	no	—
494	C₂×C₄	—	10	2	no	—
495	C₂×C₄	—	10	2	no	—
496	C₂×C₄	—	10	4	no	—
497	C₂×C₄	—	20	2	no	—
498	C₂×C₄	—	20	2	no	—
499	C₂×C₄	—	40	4	no	—
500	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	5	4	no	—
503	C₈	—	5	1	no	—
504	C₈	—	5	1	no	—
505	C₈	—	5	1	no	—
506	C₈	—	5	1	no	—
507	C₈	—	10	2	no	—
508	C₈	—	10	4	no	—
509	C₈	—	10	2	no	—
510	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
511	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₈	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
513	C₈	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
514	C₅	#20512	1	1	yes	characteristic, complemented, Sylow
515	C₂²	—	2	2	no	—
516	C₂²	—	5	1	no	—
517	C₂²	—	5	1	no	—
518	C₂²	—	10	2	no	—
519	C₂²	—	10	2	no	—
520	C₂²	—	20	4	no	—
521	C₂²	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	5	1	no	—
525	C₄	—	5	1	no	—
526	C₄	—	10	2	no	—
527	C₄	—	10	4	no	—
528	C₄	—	10	2	no	—
529	C₄	—	20	4	no	—
530	C₄	—	20	2	no	—
531	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
532	C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
533	C₂	—	2	1	no	—
534	C₂	—	4	2	no	—
535	C₂	—	5	2	no	—
536	C₂	—	10	1	no	—
537	C₂	—	20	2	no	—
538	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×#443	C₄
socle	C₂×C₅	C₄²×D₄
prime radical	D₅×#135	C₂²
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#443	AGL(1,𝔽₅)
hypocenter	C₅	#20512
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #10617415	C₂	semidirect
5. #10604778	C₂	semidirect
6. #10604090	C₂	semidirect
7. #10604086	C₂	semidirect
8. #10604005	C₂	semidirect
9. AGL(1,𝔽₅)×#104	C₂	semidirect
10. #10603851	C₂	semidirect
11. C₄×#3992	C₂	semidirect
18. #65741	C₄	semidirect
19. #65739	C₄	semidirect
20. #65737	C₄	semidirect
21. #65735	C₄	semidirect
22. #65733	C₄	semidirect
23. #65731	C₄	semidirect
39. C₅×#443	C₄	semidirect
40. #65485	C₄	semidirect
41. #65433	C₄	semidirect
42. #65184	C₄	semidirect
44. #65113	C₄	semidirect
46. #64989	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
107. #3992	C₂×C₄	semidirect
108. #3992	C₂×C₄	semidirect
114. C₅×#108	C₂×C₄	semidirect
115. C₅×#104	C₂×C₄	semidirect
116. C₄×C₅×C₈	C₂×C₄	semidirect
117. #3969	C₂×C₄	semidirect
118. #3957	C₂×C₄	semidirect
119. #3954	C₂×C₄	semidirect
120. #3951	C₂×C₄	semidirect
121. C₈×Dic₅	C₂×C₄	semidirect
122. C₈×Dic₅	C₂×C₄	semidirect
123. #3937	C₂×C₄	semidirect
124. C₄×#168	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
224. #443	AGL(1,𝔽₅)	semidirect
314. #131	C₂×AGL(1,𝔽₅)	semidirect
339. #108	C₂×AGL(1,𝔽₅)	semidirect
347. #104	C₂×AGL(1,𝔽₅)	semidirect
368. C₄×C₈	C₂×AGL(1,𝔽₅)	semidirect
404. Q₁₆	C₄×AGL(1,𝔽₅)	semidirect
408. SD₁₆	C₄×AGL(1,𝔽₅)	semidirect
411. D₈	C₄×AGL(1,𝔽₅)	semidirect
514. C₅	#20512	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
#10617439	2
#10617415	2
D₅×#443	2
#10604778	2
#10604090	2
#10604086	2
#10604005	2
AGL(1,𝔽₅)×#104	2
#10603851	2
C₄×#3992	2
#20512	5