Subgroups — #13033563

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617407	C₂	1	2	yes	maximal
2	C₂×D₅⋊#108	C₂	1	1	yes	maximal, characteristic
3	C₂×#65721	C₂	1	1	yes	maximal, characteristic
4	D₅×#405	C₂	1	1	yes	maximal, characteristic
5	#10604376	C₂	1	2	yes	maximal
6	#10603885	C₂	1	4	yes	maximal, complemented
7	#10603851	C₂	1	4	yes	maximal, complemented
8	C₂×#4130	C₂²	1	2	yes	—
9	C₂×D₅⋊M₁₆	C₂²	1	2	yes	—
10	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
12	D₅×#117	C₂²	1	1	yes	characteristic
13	#65728	—	2	4	no	—
14	M₁₆×AGL(1,𝔽₅)	—	2	4	no	—
15	D₅⋊#108	C₄	1	2	yes	complemented
16	D₅⋊#108	C₄	1	2	yes	complemented
17	D₅⋊#108	C₂²	1	2	yes	—
18	D₅⋊#108	C₂²	1	2	yes	—
19	C₂×#3996	C₄	1	2	yes	complemented
20	C₂×#3995	C₄	1	2	yes	complemented
21	#65721	C₄	1	2	yes	complemented
22	#65721	C₄	1	2	yes	complemented
23	#65721	C₂²	1	2	yes	—
24	#65721	C₂²	1	2	yes	—
25	C₂×#3994	C₄	1	2	yes	complemented
26	C₂×#3993	C₄	1	2	yes	complemented
27	#65718	C₂²	1	8	yes	—
28	C₅×#405	C₄	1	1	yes	characteristic, complemented
29	#65411	C₄	1	1	yes	characteristic, complemented
30	#65390	C₄	1	1	yes	characteristic, complemented
31	#65286	C₄	1	1	yes	characteristic, complemented
32	#64997	C₄	1	2	yes	complemented
33	D₅×#97	C₂²	1	2	yes	—
34	#64978	C₄	1	2	yes	complemented
35	C₄×C₈×D₅	C₂²	1	2	yes	—
36	#64862	C₂²	1	8	yes	—
37	#20446	—	5	1	no	maximal, Sylow
38	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
39	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
40	C₂×#704	—	2	2	no	—
41	#4130	—	2	2	no	—
42	#4130	—	2	2	no	—
43	#4130	C₂×C₄	1	4	yes	—
44	#4130	C₂³	1	4	yes	—
45	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
46	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
47	D₅⋊M₁₆	—	2	2	no	—
48	D₅⋊M₁₆	—	2	2	no	—
49	D₅⋊M₁₆	C₂×C₄	1	4	yes	—
50	D₅⋊M₁₆	C₂³	1	4	yes	—
51	C₂×#700	C₂×C₄	1	4	yes	—
52	C₂×D₅⋊C₈	—	2	2	no	—
53	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#117	C₂×C₄	1	1	yes	characteristic
56	#4072	C₂×C₄	1	1	yes	characteristic
57	C₂×#681	C₂×C₄	1	1	yes	characteristic
58	C₂²×#168	C₂×C₄	1	1	yes	characteristic
59	D₅×M₁₆	D₄	1	2	yes	—
60	D₅×M₁₆	D₄	1	2	yes	—
61	D₅×M₁₆	Q₈	1	2	yes	—
62	D₅×M₁₆	Q₈	1	2	yes	—
63	C₂×#676	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₅	C₂³	1	2	yes	—
77	#4038	—	2	1	no	—
78	D₅×C₄⋊C₄	—	2	1	no	—
79	D₅×C₂²⋊C₄	—	2	1	no	—
80	#4023	—	2	1	no	—
81	#4018	C₂×C₄	1	2	yes	—
82	C₄²×D₅	C₂³	1	2	yes	—
83	#3996	C₂×C₄	1	4	yes	complemented
84	#3996	C₂×C₄	1	4	yes	complemented
85	#3995	C₂×C₄	1	4	yes	complemented
86	#3995	C₂×C₄	1	4	yes	complemented
87	#3994	C₂×C₄	1	4	yes	—
88	#3994	C₂×C₄	1	4	yes	—
89	#3993	C₂×C₄	1	4	yes	—
90	#3993	C₂×C₄	1	4	yes	—
91	#3992	—	2	8	no	—
92	C₈×AGL(1,𝔽₅)	—	2	8	no	—
93	C₅×#97	C₂×C₄	1	2	yes	complemented
94	C₄×C₅×C₈	C₂×C₄	1	2	yes	complemented
95	#3947	C₂×C₄	1	2	yes	complemented
96	#3947	C₂×C₄	1	2	yes	complemented
97	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
98	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
99	#3935	C₂×C₄	1	2	yes	complemented
100	C₄×#168	C₂×C₄	1	2	yes	complemented
101	C₂²×#108	—	5	1	no	—
102	C₂×#427	—	5	1	no	—
103	#2873	—	5	2	no	—
104	C₂×#405	—	5	1	no	—
105	#1773	—	5	4	no	—
106	#1772	—	5	4	no	—
107	#1733	—	5	2	no	—
108	C₂³×D₅	#41	1	1	yes	characteristic
109	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₅	#41	1	1	yes	characteristic
112	C₂×C₄×D₅	—	2	2	no	—
113	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₄×D₅	#41	1	1	yes	characteristic
123	C₂×C₄×D₅	#41	1	1	yes	characteristic
124	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
125	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
126	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
127	#704	—	2	4	no	—
128	#704	—	2	4	no	—
129	C₂×#170	—	2	4	no	—
130	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
131	C₄⋊AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
132	C₄×AGL(1,𝔽₅)	—	2	4	no	—
133	C₄×AGL(1,𝔽₅)	—	2	4	no	—
134	#700	—	2	4	no	—
135	#700	C₂²×C₄	1	8	yes	—
136	D₅⋊C₈	—	2	4	no	—
137	D₅⋊C₈	—	2	4	no	—
138	C₅×M₁₆	C₄⋊C₄	1	2	yes	—
139	C₅×M₁₆	C₄⋊C₄	1	2	yes	—
140	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
141	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
142	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
143	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₂²⋊C₄	—	2	1	no	—
149	C₄²×C₅	C₂²×C₄	1	2	yes	—
150	C₂²⋊Dic₅	—	2	1	no	—
151	#685	—	2	2	no	—
152	C₄⋊Dic₅	—	2	1	no	—
153	#683	—	2	2	no	—
154	C₄×Dic₅	—	2	2	no	—
155	C₄×Dic₅	C₂²×C₄	1	2	yes	—
156	#681	C₄⋊C₄	1	2	yes	—
157	#681	C₄⋊C₄	1	2	yes	—
158	C₂×#168	C₄²	1	1	yes	characteristic
159	C₂×#168	C₄²	1	1	yes	characteristic
160	C₂×#168	C₄²	1	1	yes	characteristic
161	C₂×#168	C₄²	1	1	yes	characteristic
162	C₂×#168	C₂²×C₄	1	1	yes	characteristic
163	C₂×#168	C₂²×C₄	1	1	yes	characteristic
164	C₂×#168	C₂²×C₄	1	2	yes	—
165	#676	C₄⋊C₄	1	4	yes	—
166	#676	C₄⋊C₄	1	4	yes	—
167	C₈×D₅	C₄²	1	1	yes	characteristic
168	C₈×D₅	C₄²	1	1	yes	characteristic
169	C₈×D₅	C₄²	1	1	yes	characteristic
170	C₈×D₅	C₄²	1	1	yes	characteristic
171	C₈×D₅	C₄²	1	1	yes	characteristic
172	C₈×D₅	C₄²	1	1	yes	characteristic
173	C₈×D₅	C₄²	1	1	yes	characteristic
174	C₈×D₅	C₄²	1	1	yes	characteristic
175	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
176	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
177	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
178	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
179	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
180	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
181	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
183	C₈×D₅	C₂×D₄	1	4	yes	—
184	C₈×D₅	C₂×Q₈	1	4	yes	—
185	C₂²×M₁₆	—	5	1	no	—
186	C₂²×M₁₆	—	5	2	no	—
187	C₂³×C₈	—	5	1	no	—
188	C₂×#117	—	5	1	no	—
189	C₂×#117	—	5	2	no	—
190	C₂×#108	—	5	2	no	—
191	C₂×#108	—	5	2	no	—
192	C₂×#108	—	5	2	no	—
193	C₂×#108	—	5	2	no	—
194	C₂×#108	—	5	2	no	—
195	C₂×#108	—	5	2	no	—
196	#427	—	5	2	no	—
197	#427	—	5	2	no	—
198	#427	—	5	2	no	—
199	#427	—	5	2	no	—
200	C₂×#107	—	5	2	no	—
201	C₂×#106	—	5	2	no	—
202	#405	—	5	1	no	—
203	#405	—	5	1	no	—
204	#405	—	5	1	no	—
205	#405	—	5	2	no	—
206	#405	—	5	2	no	—
207	#405	—	5	8	no	—
208	#405	—	10	4	no	—
209	#405	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
210	C₄×M₁₆	—	10	4	no	—
211	C₂×#97	—	5	2	no	—
212	C₂×C₄×C₈	—	5	2	no	—
213	#339	—	5	8	no	—
214	C₂³×C₅	#117	1	1	yes	characteristic
215	C₂²×D₅	—	4	2	no	—
216	C₂²×D₅	#117	1	1	yes	characteristic
217	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
218	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
219	C₂²×D₅	C₄×Q₈	1	1	yes	characteristic
220	C₂²×D₅	C₄×Q₈	1	1	yes	characteristic
221	C₂²×D₅	C₂×#41	1	1	yes	characteristic
222	C₂×AGL(1,𝔽₅)	—	2	8	no	—
223	C₂×AGL(1,𝔽₅)	—	8	4	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	#117	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	#117	1	1	yes	characteristic
233	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
234	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
235	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
236	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
237	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
238	C₄×D₅	—	4	4	no	—
239	C₄×D₅	C₂×C₄²	1	1	yes	characteristic
240	C₄×D₅	C₂×C₄²	1	1	yes	characteristic
241	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₄×D₅	C₄×D₄	1	1	yes	characteristic
244	C₄×D₅	C₄×D₄	1	1	yes	characteristic
245	C₄×D₅	C₄×D₄	1	1	yes	characteristic
246	C₄×D₅	C₄×D₄	1	1	yes	characteristic
247	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
248	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
249	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
250	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
251	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
252	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
253	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
254	C₄×D₅	C₂²×Q₈	1	1	yes	characteristic
255	#170	—	2	8	no	—
256	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
257	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
258	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
259	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
260	C₅×C₈	C₂×C₄⋊C₄	1	4	yes	—
261	#168	C₂×C₄²	1	1	yes	characteristic
262	#168	C₂×C₄²	1	1	yes	characteristic
263	#168	C₂×C₄²	1	1	yes	characteristic
264	#168	C₂×C₄²	1	1	yes	characteristic
265	#168	C₂×C₄⋊C₄	1	4	yes	—
266	C₂³×C₄	—	5	1	no	—
267	C₂×M₁₆	—	5	1	no	—
268	C₂×M₁₆	—	5	2	no	—
269	C₂×M₁₆	—	5	2	no	—
270	C₂×M₁₆	—	5	2	no	—
271	C₂×M₁₆	—	5	2	no	—
272	C₂×M₁₆	—	5	2	no	—
273	C₂×M₁₆	—	5	4	no	—
274	C₂×M₁₆	—	5	4	no	—
275	C₂×M₁₆	—	5	4	no	—
276	C₂×M₁₆	—	10	2	no	—
277	C₂×M₁₆	—	10	2	no	—
278	C₂×M₁₆	—	10	2	no	—
279	C₂×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
280	C₂²×C₈	—	5	1	no	—
281	C₂²×C₈	—	5	1	no	—
282	C₂²×C₈	—	5	1	no	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	5	1	no	—
286	C₂²×C₈	—	5	1	no	—
287	C₂²×C₈	—	5	1	no	—
288	C₂²×C₈	—	5	1	no	—
289	C₂²×C₈	—	5	1	no	—
290	C₂²×C₈	—	5	1	no	—
291	C₂²×C₈	—	5	1	no	—
292	C₂²×C₈	—	5	1	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₂²×C₈	—	10	2	no	—
295	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
296	#117	—	5	1	no	—
297	#117	—	5	2	no	—
298	#117	—	5	4	no	—
299	#117	—	5	4	no	—
300	#117	—	10	1	no	—
301	#117	—	10	1	no	—
302	#117	—	10	2	no	—
303	#117	—	10	2	no	—
304	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
305	C₂×C₄⋊C₄	—	5	4	no	—
306	C₂×C₄⋊C₄	—	10	1	no	—
307	C₂×C₂²⋊C₄	—	10	1	no	—
308	C₂×C₂²⋊C₄	—	10	2	no	—
309	C₂×C₄²	—	5	2	no	—
310	C₂×C₄²	—	10	2	no	—
311	#108	—	5	4	no	—
312	#108	—	5	4	no	—
313	#108	—	5	4	no	—
314	#108	—	5	4	no	—
315	#107	—	5	4	no	—
316	#107	—	5	4	no	—
317	#106	—	5	4	no	—
318	#106	—	5	4	no	—
319	#97	—	5	2	no	—
320	#97	—	5	2	no	—
321	#97	—	5	2	no	—
322	#97	—	10	8	no	—
323	#97	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
324	C₄×C₈	—	5	2	no	—
325	C₄×C₈	—	5	2	no	—
326	C₄×C₈	—	5	2	no	—
327	C₄×C₈	—	10	8	no	—
328	C₄×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
331	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
332	C₂²×C₅	C₂×#117	1	1	yes	characteristic
333	C₂×D₅	—	2	2	no	—
334	C₂×D₅	—	2	2	no	—
335	C₂×D₅	—	2	2	no	—
336	C₂×D₅	—	4	1	no	—
337	C₂×D₅	—	4	1	no	—
338	C₂×D₅	—	4	1	no	—
339	C₂×D₅	C₄×C₄⋊C₄	1	1	yes	characteristic
340	C₂×D₅	C₄×C₄⋊C₄	1	1	yes	characteristic
341	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂×D₅	C₂×C₄×Q₈	1	1	yes	characteristic
343	AGL(1,𝔽₅)	—	4	8	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
346	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
347	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
348	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
349	Dic₅	—	4	2	no	—
350	Dic₅	C₄×C₄⋊C₄	1	1	yes	characteristic
351	Dic₅	C₄×C₄⋊C₄	1	1	yes	characteristic
352	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
353	Dic₅	C₂×C₄×Q₈	1	1	yes	characteristic
354	C₂⁴	—	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	1	no	—
368	C₂²×C₄	—	10	2	no	—
369	C₂²×C₄	—	10	4	no	—
370	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
371	M₁₆	—	5	2	no	—
372	M₁₆	—	5	2	no	—
373	M₁₆	—	5	4	no	—
374	M₁₆	—	5	4	no	—
375	M₁₆	—	5	8	no	—
376	M₁₆	—	10	4	no	—
377	M₁₆	—	10	4	no	—
378	M₁₆	—	10	4	no	—
379	M₁₆	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
380	M₁₆	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
381	C₂×C₈	—	5	1	no	—
382	C₂×C₈	—	5	1	no	—
383	C₂×C₈	—	5	1	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	—	5	2	no	—
387	C₂×C₈	—	5	1	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	5	1	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	5	1	no	—
395	C₂×C₈	—	5	1	no	—
396	C₂×C₈	—	5	1	no	—
397	C₂×C₈	—	5	1	no	—
398	C₂×C₈	—	5	1	no	—
399	C₂×C₈	—	5	1	no	—
400	C₂×C₈	—	5	1	no	—
401	C₂×C₈	—	5	1	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	1	no	—
404	C₂×C₈	—	5	4	no	—
405	C₂×C₈	—	5	4	no	—
406	C₂×C₈	—	10	4	no	—
407	C₂×C₈	—	10	4	no	—
408	C₂×C₈	—	10	4	no	—
409	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
410	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
412	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	5	8	no	—
418	C₄⋊C₄	—	10	2	no	—
419	C₄⋊C₄	—	10	4	no	—
420	C₄⋊C₄	—	10	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	10	2	no	—
423	C₂²⋊C₄	—	10	4	no	—
424	C₂²⋊C₄	—	10	4	no	—
425	C₂²⋊C₄	—	10	1	no	—
426	C₄²	—	5	2	no	—
427	C₄²	—	10	2	no	—
428	C₄²	—	10	4	no	—
429	C₄²	—	10	4	no	—
430	C₄²	C₂²×AGL(1,𝔽₅)	1	2	yes	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	—	2	1	no	—
433	C₂×C₅	—	2	1	no	—
434	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
435	D₅	—	2	1	no	—
436	D₅	—	2	1	no	—
437	D₅	—	2	1	no	—
438	D₅	#2957	1	2	yes	—
439	C₂³	—	5	1	no	—
440	C₂³	—	5	1	no	—
441	C₂³	—	5	1	no	—
442	C₂³	—	5	1	no	—
443	C₂³	—	5	1	no	—
444	C₂³	—	5	1	no	—
445	C₂³	—	20	2	no	—
446	C₂³	#4130	1	1	yes	characteristic
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	5	1	no	—
451	C₂×C₄	—	5	1	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	1	no	—
462	C₂×C₄	—	5	1	no	—
463	C₂×C₄	—	5	1	no	—
464	C₂×C₄	—	5	1	no	—
465	C₂×C₄	—	5	1	no	—
466	C₂×C₄	—	5	1	no	—
467	C₂×C₄	—	5	1	no	—
468	C₂×C₄	—	5	1	no	—
469	C₂×C₄	—	5	1	no	—
470	C₂×C₄	—	10	8	no	—
471	C₂×C₄	—	10	2	no	—
472	C₂×C₄	—	20	4	no	—
473	C₂×C₄	—	40	4	no	—
474	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₂×C₄	#4130	1	1	yes	characteristic
479	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₈	—	5	1	no	—
481	C₈	—	5	1	no	—
482	C₈	—	5	1	no	—
483	C₈	—	5	1	no	—
484	C₈	—	5	4	no	—
485	C₈	—	10	8	no	—
486	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
487	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
488	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
489	C₈	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
490	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
491	C₅	#20446	1	1	yes	characteristic, complemented, Sylow
492	C₂²	—	4	1	no	—
493	C₂²	—	5	1	no	—
494	C₂²	—	5	1	no	—
495	C₂²	—	5	1	no	—
496	C₂²	—	5	1	no	—
497	C₂²	—	10	2	no	—
498	C₂²	—	10	2	no	—
499	C₂²	—	10	2	no	—
500	C₂²	—	20	1	no	—
501	C₂²	—	20	1	no	—
502	C₂²	—	20	1	no	—
503	C₂²	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
504	C₂²	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₂²	C₂×#4130	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	5	1	no	—
508	C₄	—	5	1	no	—
509	C₄	—	5	1	no	—
510	C₄	—	5	1	no	—
511	C₄	—	20	2	no	—
512	C₄	—	20	8	no	—
513	C₄	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
514	C₄	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
515	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
516	C₄	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	5	2	no	—
521	C₂	—	10	1	no	—
522	C₂	—	10	1	no	—
523	C₂	—	10	1	no	—
524	C₂	C₂×C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#405	C₄
socle	C₂×C₅	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₅	#41
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#405	AGL(1,𝔽₅)
hypocenter	C₅	#20446
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
6. #10603885	C₂	semidirect
7. #10603851	C₂	semidirect
15. D₅⋊#108	C₄	semidirect
16. D₅⋊#108	C₄	semidirect
19. C₂×#3996	C₄	semidirect
20. C₂×#3995	C₄	semidirect
21. #65721	C₄	semidirect
22. #65721	C₄	semidirect
25. C₂×#3994	C₄	semidirect
26. C₂×#3993	C₄	semidirect
28. C₅×#405	C₄	semidirect
29. #65411	C₄	semidirect
30. #65390	C₄	semidirect
31. #65286	C₄	semidirect
32. #64997	C₄	semidirect
34. #64978	C₄	semidirect
83. #3996	C₂×C₄	semidirect
84. #3996	C₂×C₄	semidirect
85. #3995	C₂×C₄	semidirect
86. #3995	C₂×C₄	semidirect
93. C₅×#97	C₂×C₄	semidirect
94. C₄×C₅×C₈	C₂×C₄	semidirect
95. #3947	C₂×C₄	semidirect
96. #3947	C₂×C₄	semidirect
97. C₈×Dic₅	C₂×C₄	semidirect
98. C₈×Dic₅	C₂×C₄	semidirect
99. #3935	C₂×C₄	semidirect
100. C₄×#168	C₂×C₄	semidirect
209. #405	AGL(1,𝔽₅)	semidirect
323. #97	C₂×AGL(1,𝔽₅)	semidirect
328. C₄×C₈	C₂×AGL(1,𝔽₅)	semidirect
491. C₅	#20446	semidirect

Maximal subgroups

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

subgroup	index
#10617407	2
C₂×D₅⋊#108	2
C₂×#65721	2
D₅×#405	2
#10604376	2
#10603885	2
#10603851	2
#20446	5