Subgroups — #13034702

Order 1280.

894 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617046	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#10604723	C₂	1	2	yes	maximal
4	#10604722	C₂	1	2	yes	maximal
5	#10603849	C₂	1	2	yes	maximal, complemented
6	#10603846	C₂	1	2	yes	maximal, complemented
7	C₄×#3994	C₂	1	2	yes	maximal, complemented
8	C₄×#3993	C₂	1	2	yes	maximal, complemented
9	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
12	#65765	C₂²	1	4	yes	—
13	#65764	—	2	2	no	—
14	C₄×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
15	C₂×#3994	C₂²	1	4	yes	—
16	C₂×#3993	C₂²	1	4	yes	—
17	#65690	—	2	2	no	—
18	#65689	C₂²	1	4	yes	—
19	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
20	#65686	—	2	2	no	—
21	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
23	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×#168	C₄	1	1	yes	characteristic, complemented
25	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
26	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
27	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
28	C₄×C₈×D₅	C₄	1	1	yes	characteristic, complemented
29	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
33	#64893	C₂²	1	4	yes	—
34	#64893	C₂²	1	4	yes	—
35	#20818	—	5	1	no	maximal, Sylow
36	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
38	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
39	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
40	C₂×C₄⋊AGL(1,𝔽₅)	C₂³	1	8	yes	—
41	C₂×C₄×AGL(1,𝔽₅)	—	2	4	no	—
42	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
47	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
48	C₂²×#168	C₂×C₄	1	1	yes	characteristic
49	C₂²×#168	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅	—	2	4	no	—
51	C₂×C₈×D₅	—	2	4	no	—
52	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
60	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅	D₄	1	1	yes	characteristic
63	C₄²×D₅	D₄	1	1	yes	characteristic
64	C₄²×D₅	Q₈	1	1	yes	characteristic
65	C₄²×D₅	Q₈	1	1	yes	characteristic
66	C₄²×D₅	C₂³	1	1	yes	characteristic
67	C₄²×D₅	C₂³	1	1	yes	characteristic
68	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	4	no	—
69	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	4	no	—
70	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	4	no	—
71	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	4	no	—
72	#3994	—	2	8	no	—
73	#3993	—	2	8	no	—
74	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₄×#168	C₂×C₄	1	1	yes	characteristic
87	C₄×#168	C₂×C₄	1	1	yes	characteristic
88	C₄×#168	C₂×C₄	1	1	yes	characteristic
89	C₄×#168	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈	—	5	1	no	—
91	#2283	—	5	2	no	—
92	#1846	—	5	2	no	—
93	#1835	—	5	2	no	—
94	#1808	—	5	2	no	—
95	#1807	—	5	2	no	—
96	C₄×#107	—	5	2	no	—
97	C₄×#106	—	5	2	no	—
98	C₂³×D₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
100	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₅	—	2	4	no	—
107	C₂×C₄×D₅	—	2	4	no	—
108	C₂×C₄×D₅	—	2	2	no	—
109	C₂×C₄×D₅	—	2	2	no	—
110	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
122	C₂²⋊AGL(1,𝔽₅)	—	4	8	no	—
123	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
124	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
125	C₄×AGL(1,𝔽₅)	—	4	8	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
133	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
134	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
138	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
139	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
140	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
141	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
145	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
146	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
147	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
148	C₂×#168	—	2	2	no	—
149	C₂×#168	—	2	2	no	—
150	C₂×#168	C₂²×C₄	1	1	yes	characteristic
151	C₂×#168	C₂²×C₄	1	1	yes	characteristic
152	C₂×#168	C₂²×C₄	1	1	yes	characteristic
153	C₂×#168	C₂²×C₄	1	1	yes	characteristic
154	C₈×D₅	—	2	2	no	—
155	C₈×D₅	—	2	2	no	—
156	C₈×D₅	—	2	2	no	—
157	C₈×D₅	—	2	2	no	—
158	C₈×D₅	—	2	2	no	—
159	C₈×D₅	—	2	2	no	—
160	C₈×D₅	#41	1	4	yes	—
161	C₈×D₅	#41	1	4	yes	—
162	C₂³×C₈	—	5	1	no	—
163	C₂³×C₈	—	5	1	no	—
164	C₂²×C₄²	—	5	1	no	—
165	C₂×#107	—	5	4	no	—
166	C₂×#106	—	5	4	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	C₂×C₄×C₈	—	5	1	no	—
169	C₂×C₄×C₈	—	5	1	no	—
170	C₂×C₄×C₈	—	5	1	no	—
171	C₂×C₄×C₈	—	5	1	no	—
172	C₂×C₄×C₈	—	5	1	no	—
173	C₂×C₄×C₈	—	5	1	no	—
174	C₂×C₄×C₈	—	5	1	no	—
175	C₂×C₄×C₈	—	5	1	no	—
176	C₂×C₄×C₈	—	5	1	no	—
177	C₂×C₄×C₈	—	5	1	no	—
178	C₂×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
179	#383	—	10	2	no	—
180	#382	—	5	4	no	—
181	#381	—	10	2	no	—
182	#380	—	5	4	no	—
183	C₄×C₄⋊C₄	—	5	4	no	—
184	C₄×C₂²⋊C₄	—	10	2	no	—
185	#376	—	10	2	no	—
186	#340	—	5	4	no	—
187	#340	—	5	4	no	—
188	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×D₅	—	2	2	no	—
190	C₂²×D₅	—	2	2	no	—
191	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×D₅	#135	1	4	yes	—
193	C₂²×D₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×AGL(1,𝔽₅)	—	4	8	no	—
195	C₂×AGL(1,𝔽₅)	—	4	8	no	—
196	C₂×AGL(1,𝔽₅)	—	4	8	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₂×Dic₅	—	2	2	no	—
208	C₂×Dic₅	—	2	2	no	—
209	C₂×Dic₅	—	2	2	no	—
210	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×Dic₅	C₂²×Q₈	1	1	yes	characteristic
216	C₄×D₅	—	2	2	no	—
217	C₄×D₅	—	2	2	no	—
218	C₄×D₅	—	2	2	no	—
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	2	2	no	—
221	C₄×D₅	—	2	2	no	—
222	C₄×D₅	—	2	1	no	—
223	C₄×D₅	—	2	1	no	—
224	C₄×D₅	—	2	2	no	—
225	C₄×D₅	—	2	2	no	—
226	C₄×D₅	—	2	2	no	—
227	C₄×D₅	#135	1	4	yes	—
228	C₄×D₅	C₂×#41	1	2	yes	—
229	C₄×D₅	C₂×#41	1	2	yes	—
230	C₅×C₈	—	2	1	no	—
231	C₅×C₈	—	2	1	no	—
232	C₅×C₈	#117	1	2	yes	—
233	C₅×C₈	#117	1	2	yes	—
234	#168	—	2	1	no	—
235	#168	—	2	1	no	—
236	#168	#117	1	2	yes	—
237	#168	#117	1	2	yes	—
238	C₂³×C₄	—	5	1	no	—
239	C₂³×C₄	—	5	1	no	—
240	C₂³×C₄	—	5	1	no	—
241	C₂²×C₈	—	5	1	no	—
242	C₂²×C₈	—	5	1	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	5	1	no	—
246	C₂²×C₈	—	5	1	no	—
247	C₂²×C₈	—	5	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	5	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	10	4	no	—
252	C₂²×C₈	—	10	4	no	—
253	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
254	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	5	8	no	—
256	C₂×C₂²⋊C₄	—	10	4	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	—	5	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	5	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	C₂×C₄²	—	5	1	no	—
267	C₂×C₄²	—	5	1	no	—
268	C₂×C₄²	—	10	4	no	—
269	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
270	#107	—	10	8	no	—
271	#106	—	10	8	no	—
272	C₄×C₈	—	5	1	no	—
273	C₄×C₈	—	5	1	no	—
274	C₄×C₈	—	5	1	no	—
275	C₄×C₈	—	5	1	no	—
276	C₄×C₈	—	5	1	no	—
277	C₄×C₈	—	5	1	no	—
278	C₄×C₈	—	5	1	no	—
279	C₄×C₈	—	5	1	no	—
280	C₄×C₈	—	5	1	no	—
281	C₄×C₈	—	5	1	no	—
282	C₄×C₈	—	5	1	no	—
283	C₄×C₈	—	5	1	no	—
284	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
286	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
288	#95	—	10	4	no	—
289	#95	—	10	4	no	—
290	#95	—	10	4	no	—
291	#95	—	10	4	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	#427	1	2	yes	—
295	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
296	C₂×D₅	—	2	1	no	—
297	C₂×D₅	—	2	1	no	—
298	C₂×D₅	—	2	8	no	—
299	C₂×D₅	#427	1	2	yes	—
300	C₂×D₅	#532	1	2	yes	—
301	C₂×D₅	C₂×#135	1	2	yes	—
302	C₂×D₅	C₂×#135	1	2	yes	—
303	AGL(1,𝔽₅)	—	8	8	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	2	1	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	#427	1	2	yes	—
309	C₄×C₅	C₂×#117	1	1	yes	characteristic
310	C₄×C₅	C₂×#117	1	1	yes	characteristic
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	2	1	no	—
314	Dic₅	—	2	1	no	—
315	Dic₅	#427	1	2	yes	—
316	Dic₅	#533	1	2	yes	—
317	C₂⁴	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	10	2	no	—
334	C₂²×C₄	—	10	2	no	—
335	C₂²×C₄	—	10	4	no	—
336	C₂²×C₄	—	10	4	no	—
337	C₂²×C₄	—	10	8	no	—
338	C₂²×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
339	C₂²×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
340	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	4	no	—
346	C₂×C₈	—	5	4	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	10	2	no	—
350	C₂×C₈	—	10	2	no	—
351	C₂×C₈	—	10	2	no	—
352	C₂×C₈	—	10	2	no	—
353	C₂×C₈	—	10	2	no	—
354	C₂×C₈	—	10	2	no	—
355	C₂×C₈	—	10	2	no	—
356	C₂×C₈	—	10	2	no	—
357	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₄⋊C₄	—	10	8	no	—
362	C₄⋊C₄	—	10	8	no	—
363	C₂²⋊C₄	—	20	8	no	—
364	C₄²	—	5	1	no	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	—	5	1	no	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	1	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	5	1	no	—
373	C₄²	—	5	1	no	—
374	C₄²	—	5	1	no	—
375	C₄²	—	5	1	no	—
376	C₄²	—	20	8	no	—
377	C₄²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₄²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
380	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₂×C₅	—	2	2	no	—
382	C₂×C₅	#2285	1	1	yes	characteristic
383	C₂×C₅	C₂×#427	1	1	yes	characteristic
384	C₂×C₅	C₂×#427	1	1	yes	characteristic
385	D₅	—	2	2	no	—
386	D₅	#3168	1	4	yes	—
387	C₂³	—	5	1	no	—
388	C₂³	—	5	4	no	—
389	C₂³	—	5	1	no	—
390	C₂³	—	10	2	no	—
391	C₂³	—	10	2	no	—
392	C₂³	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	2	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	10	2	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	10	1	no	—
419	C₂×C₄	—	10	1	no	—
420	C₂×C₄	—	20	8	no	—
421	C₂×C₄	—	20	8	no	—
422	C₂×C₄	—	20	8	no	—
423	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	5	2	no	—
432	C₈	—	5	2	no	—
433	C₈	—	10	1	no	—
434	C₈	—	10	1	no	—
435	C₈	#4130	1	2	yes	—
436	C₈	#4130	1	2	yes	—
437	C₅	#20818	1	1	yes	characteristic, complemented, Sylow
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	5	2	no	—
441	C₂²	—	5	2	no	—
442	C₂²	—	5	2	no	—
443	C₂²	—	5	2	no	—
444	C₂²	—	10	8	no	—
445	C₂²	—	10	1	no	—
446	C₂²	—	10	1	no	—
447	C₂²	#65721	1	2	yes	—
448	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	5	2	no	—
454	C₄	—	5	2	no	—
455	C₄	—	10	1	no	—
456	C₄	—	10	1	no	—
457	C₄	—	10	1	no	—
458	C₄	—	10	1	no	—
459	C₄	—	40	8	no	—
460	C₄	#65721	1	2	yes	—
461	C₄	C₂×#4130	1	1	yes	characteristic
462	C₄	C₂×#4130	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	5	4	no	—
465	C₂	—	10	2	no	—
466	C₂	#10617048	1	1	yes	characteristic
467	C₂	C₂×#65721	1	1	yes	characteristic
468	C₂	C₂×#65721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₈	C₄
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₂×D₄
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂×C₄×C₈	AGL(1,𝔽₅)
hypocenter	C₅	#20818
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #10603849	C₂	semidirect
6. #10603846	C₂	semidirect
7. C₄×#3994	C₂	semidirect
8. C₄×#3993	C₂	semidirect
21. C₂×C₄×C₅×C₈	C₄	semidirect
22. C₂×C₈×Dic₅	C₄	semidirect
23. C₂×C₈×Dic₅	C₄	semidirect
24. C₂×C₄×#168	C₄	semidirect
25. C₄×C₈×D₅	C₄	semidirect
26. C₄×C₈×D₅	C₄	semidirect
27. C₄×C₈×D₅	C₄	semidirect
28. C₄×C₈×D₅	C₄	semidirect
178. C₂×C₄×C₈	AGL(1,𝔽₅)	semidirect
437. C₅	#20818	semidirect

Maximal subgroups

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

subgroup	index
#10617046	2
C₂×C₄×C₈×D₅	2
#10604723	2
#10604722	2
#10603849	2
#10603846	2
C₄×#3994	2
C₄×#3993	2
#20818	5