Subgroups — D₅×#4130 #13107616

Order 1600.

687 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅²	C₂	1	1	yes	maximal, characteristic
2	#11717425	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4130	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₂²⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
5	#11717339	C₂	1	2	yes	maximal, complemented
6	D₅×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	C₄×D₅×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	#11717325	C₂	1	2	yes	maximal, complemented
9	#11717323	C₂	1	2	yes	maximal, complemented
10	C₂²×D₅²	C₂²	1	1	yes	characteristic
11	C₂×D₅×AGL(1,𝔽₅)	C₂²	1	4	yes	—
12	C₂×C₄×C₅⋊D₅	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×C₅×D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
15	C₂×#6036	C₄	1	1	yes	characteristic, complemented
16	C₂×D₅×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₂×D₅×Dic₅	C₂²	1	1	yes	characteristic
18	C₄×D₅²	C₄	1	1	yes	characteristic, complemented
19	C₄×D₅²	C₄	1	1	yes	characteristic, complemented
20	C₄×D₅²	C₄	1	1	yes	characteristic, complemented
21	C₄×D₅²	C₄	1	1	yes	characteristic, complemented
22	C₄×D₅²	C₂²	1	1	yes	characteristic
23	C₄×D₅²	C₂²	1	1	yes	characteristic
24	C₄×D₅²	C₂²	1	1	yes	characteristic
25	C₄×D₅²	C₂²	1	1	yes	characteristic
26	C₂²⋊#1042	C₂²	1	2	yes	—
27	C₄⋊#1042	C₂²	1	2	yes	complemented
28	C₄×#1042	C₂²	1	2	yes	complemented
29	C₅×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
30	C₅×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
31	C₄×C₅×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
32	#87825	C₂²	1	4	yes	complemented
33	(C₂×AGL(1,𝔽₅))⋊D₅	C₂²	1	4	yes	—
34	Dic₅×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
35	C₂×#4130	—	5	1	no	maximal
36	D₅×#117	—	5	1	no	maximal
37	C₂²×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
40	C₂×D₅²	—	2	4	no	—
41	C₂×D₅²	C₂×C₄	1	1	yes	characteristic
42	C₂×D₅²	C₂×C₄	1	1	yes	characteristic
43	C₂×D₅²	C₂³	1	1	yes	characteristic
44	C₂×D₅²	C₂³	1	1	yes	characteristic
45	C₂×#1042	C₂³	1	4	yes	—
46	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	4	yes	—
47	D₅×AGL(1,𝔽₅)	—	2	8	no	—
48	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×#1039	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
51	C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
52	C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
53	C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
56	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
59	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
60	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
61	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
62	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
64	#6036	C₂×C₄	1	1	yes	characteristic
65	#6036	C₂×C₄	1	1	yes	characteristic
66	#6036	C₂×C₄	1	1	yes	characteristic, complemented
67	#6036	C₂×C₄	1	1	yes	characteristic, complemented
68	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic
69	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic
70	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
71	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
72	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
73	D₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
74	D₅×Dic₅	C₂³	1	1	yes	characteristic
75	D₅×Dic₅	C₂³	1	1	yes	characteristic
76	C₂²×C₄×D₅	—	5	1	no	—
77	C₂²×C₄×D₅	—	5	1	no	—
78	C₂×C₂²⋊AGL(1,𝔽₅)	—	5	2	no	—
79	#4130	—	5	1	no	—
80	#4130	—	5	2	no	—
81	#4130	—	5	2	no	—
82	#4130	—	5	2	no	—
83	#4130	D₅	1	1	yes	characteristic, direct product factor
84	C₂×C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
85	C₂×C₄×AGL(1,𝔽₅)	—	5	2	no	—
86	C₅×#117	—	5	1	no	—
87	#4072	—	5	1	no	—
88	#4038	—	5	2	no	—
89	D₅×C₄⋊C₄	—	5	2	no	—
90	D₅×C₂²⋊C₄	—	5	2	no	—
91	#4023	—	5	2	no	—
92	#4018	—	5	2	no	—
93	C₄²×D₅	—	5	2	no	—
94	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₅⋊D₅	—	2	2	no	—
96	C₂×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₅×D₅	—	2	2	no	—
99	C₂×C₅×D₅	—	2	2	no	—
100	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
104	D₅²	—	2	2	no	—
105	D₅²	—	2	2	no	—
106	D₅²	—	2	2	no	—
107	D₅²	#41	1	4	yes	—
108	#1042	—	2	4	no	—
109	C₅×AGL(1,𝔽₅)	—	2	4	no	—
110	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
111	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
112	#1039	C₂²×C₄	1	1	yes	characteristic
113	#1039	C₂²×C₄	1	1	yes	characteristic
114	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
115	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
116	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₂³×D₅	—	5	1	no	—
119	C₂³×D₅	—	5	1	no	—
120	C₂²×AGL(1,𝔽₅)	—	5	4	no	—
121	C₂²×C₄×C₅	—	5	1	no	—
122	C₂²×C₄×C₅	—	5	1	no	—
123	C₂²×Dic₅	—	5	1	no	—
124	C₂²×Dic₅	—	5	1	no	—
125	C₂×C₄×D₅	—	5	1	no	—
126	C₂×C₄×D₅	—	5	1	no	—
127	C₂×C₄×D₅	—	5	1	no	—
128	C₂×C₄×D₅	—	5	1	no	—
129	C₂×C₄×D₅	—	5	1	no	—
130	C₂×C₄×D₅	—	5	1	no	—
131	C₂×C₄×D₅	—	5	1	no	—
132	C₂×C₄×D₅	—	5	1	no	—
133	C₂×C₄×D₅	—	5	1	no	—
134	C₂×C₄×D₅	—	5	1	no	—
135	C₂×C₄×D₅	—	5	1	no	—
136	C₂×C₄×D₅	—	5	1	no	—
137	C₂×C₄×D₅	—	5	1	no	—
138	C₂×C₄×D₅	—	5	1	no	—
139	C₂×C₄×D₅	—	5	1	no	—
140	C₂×C₄×D₅	—	5	1	no	—
141	C₂×C₄×D₅	—	5	1	no	—
142	C₂×C₄×D₅	—	5	1	no	—
143	C₂×C₄×D₅	—	5	1	no	—
144	C₂×C₄×D₅	—	5	1	no	—
145	C₂×C₄×D₅	—	5	1	no	—
146	C₂×C₄×D₅	—	5	1	no	—
147	C₂×C₄×D₅	—	5	4	no	—
148	C₂×C₄×D₅	—	20	1	no	—
149	C₂×C₄×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
150	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
151	C₂²⋊AGL(1,𝔽₅)	—	5	2	no	—
152	C₂²⋊AGL(1,𝔽₅)	—	5	4	no	—
153	C₂²⋊AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
154	C₄⋊AGL(1,𝔽₅)	—	5	4	no	—
155	C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
156	C₄⋊AGL(1,𝔽₅)	C₂×D₅	1	2	yes	complemented
157	C₄×AGL(1,𝔽₅)	—	5	4	no	—
158	C₄×AGL(1,𝔽₅)	—	5	2	no	—
159	C₄×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	complemented
160	C₅×C₄⋊C₄	—	5	2	no	—
161	C₅×C₂²⋊C₄	—	5	2	no	—
162	C₄²×C₅	—	5	2	no	—
163	C₂²⋊Dic₅	—	5	2	no	—
164	#685	—	5	4	no	—
165	C₄⋊Dic₅	—	5	2	no	—
166	#683	—	5	4	no	—
167	C₄×Dic₅	—	5	4	no	—
168	C₄×Dic₅	—	5	2	no	—
169	C₂×#117	—	25	1	no	Sylow
170	C₂×C₅²	—	2	1	no	—
171	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
172	C₅⋊D₅	—	2	1	no	—
173	C₅⋊D₅	#117	1	2	yes	complemented
174	C₅×D₅	—	2	1	no	—
175	C₅×D₅	—	2	1	no	—
176	C₅×D₅	#117	1	2	yes	complemented
177	C₅×D₅	C₂×#41	1	2	yes	—
178	C₂³×C₅	—	5	1	no	—
179	C₂³×C₅	—	5	1	no	—
180	C₂²×D₅	—	5	1	no	—
181	C₂²×D₅	—	5	1	no	—
182	C₂²×D₅	—	5	1	no	—
183	C₂²×D₅	—	5	1	no	—
184	C₂²×D₅	—	5	1	no	—
185	C₂²×D₅	—	5	1	no	—
186	C₂²×D₅	—	5	1	no	—
187	C₂²×D₅	—	5	1	no	—
188	C₂²×D₅	—	5	1	no	—
189	C₂²×D₅	—	5	1	no	—
190	C₂²×D₅	—	10	4	no	—
191	C₂²×D₅	—	10	4	no	—
192	C₂²×D₅	—	20	1	no	—
193	C₂²×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
195	C₂×AGL(1,𝔽₅)	—	5	4	no	—
196	C₂×AGL(1,𝔽₅)	—	10	8	no	—
197	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	4	yes	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	5	1	no	—
200	C₂×C₄×C₅	—	5	1	no	—
201	C₂×C₄×C₅	—	5	1	no	—
202	C₂×C₄×C₅	—	5	1	no	—
203	C₂×C₄×C₅	—	5	1	no	—
204	C₂×C₄×C₅	—	5	1	no	—
205	C₂×C₄×C₅	—	5	1	no	—
206	C₂×C₄×C₅	—	5	1	no	—
207	C₂×C₄×C₅	—	5	1	no	—
208	C₂×C₄×C₅	—	5	1	no	—
209	C₂×C₄×C₅	—	5	4	no	—
210	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic, complemented
211	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
212	C₂×Dic₅	—	5	1	no	—
213	C₂×Dic₅	—	5	1	no	—
214	C₂×Dic₅	—	5	1	no	—
215	C₂×Dic₅	—	5	1	no	—
216	C₂×Dic₅	—	5	1	no	—
217	C₂×Dic₅	—	5	1	no	—
218	C₂×Dic₅	—	5	1	no	—
219	C₂×Dic₅	—	5	1	no	—
220	C₂×Dic₅	—	5	1	no	—
221	C₂×Dic₅	—	5	1	no	—
222	C₂×Dic₅	—	5	4	no	—
223	C₂×Dic₅	—	20	1	no	—
224	C₂×Dic₅	C₄×D₅	1	1	yes	characteristic, complemented
225	C₂×Dic₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
226	C₄×D₅	—	5	1	no	—
227	C₄×D₅	—	5	1	no	—
228	C₄×D₅	—	5	1	no	—
229	C₄×D₅	—	5	1	no	—
230	C₄×D₅	—	5	1	no	—
231	C₄×D₅	—	5	1	no	—
232	C₄×D₅	—	5	1	no	—
233	C₄×D₅	—	5	1	no	—
234	C₄×D₅	—	5	1	no	—
235	C₄×D₅	—	5	1	no	—
236	C₄×D₅	—	5	1	no	—
237	C₄×D₅	—	5	1	no	—
238	C₄×D₅	—	5	1	no	—
239	C₄×D₅	—	5	1	no	—
240	C₄×D₅	—	5	1	no	—
241	C₄×D₅	—	5	1	no	—
242	C₄×D₅	—	5	1	no	—
243	C₄×D₅	—	5	1	no	—
244	C₄×D₅	—	5	1	no	—
245	C₄×D₅	—	5	1	no	—
246	C₄×D₅	—	5	1	no	—
247	C₄×D₅	—	5	1	no	—
248	C₄×D₅	—	5	1	no	—
249	C₄×D₅	—	5	1	no	—
250	C₄×D₅	—	10	8	no	—
251	C₄×D₅	—	20	1	no	—
252	C₄×D₅	—	20	1	no	—
253	C₄×D₅	—	20	1	no	—
254	C₄×D₅	—	20	1	no	—
255	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
256	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
257	C₄×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
258	C₄×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₄×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
260	C₄×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
261	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
262	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
263	C₂³×C₄	—	25	1	no	—
264	#117	—	5	1	no	—
265	#117	—	25	2	no	—
266	#117	—	25	2	no	—
267	#117	—	25	2	no	—
268	#117	—	25	1	no	—
269	C₂×C₄⋊C₄	—	25	2	no	—
270	C₂×C₂²⋊C₄	—	25	2	no	—
271	C₂×C₄²	—	25	2	no	—
272	C₅²	C₂×#117	1	1	yes	characteristic, complemented, Sylow
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	5	1	no	—
275	C₂²×C₅	—	5	1	no	—
276	C₂²×C₅	—	5	1	no	—
277	C₂²×C₅	—	5	1	no	—
278	C₂²×C₅	—	10	2	no	—
279	C₂²×C₅	—	10	2	no	—
280	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
282	C₂×D₅	—	2	2	no	—
283	C₂×D₅	—	2	2	no	—
284	C₂×D₅	—	5	1	no	—
285	C₂×D₅	—	5	1	no	—
286	C₂×D₅	—	5	4	no	—
287	C₂×D₅	—	5	4	no	—
288	C₂×D₅	—	5	1	no	—
289	C₂×D₅	—	5	1	no	—
290	C₂×D₅	—	10	2	no	—
291	C₂×D₅	—	10	2	no	—
292	C₂×D₅	—	10	2	no	—
293	C₂×D₅	—	10	2	no	—
294	C₂×D₅	—	10	2	no	—
295	C₂×D₅	—	10	2	no	—
296	C₂×D₅	—	10	2	no	—
297	C₂×D₅	—	10	2	no	—
298	C₂×D₅	—	20	1	no	—
299	C₂×D₅	—	20	1	no	—
300	C₂×D₅	—	20	4	no	—
301	C₂×D₅	C₂×C₄×D₅	1	1	yes	characteristic
302	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
303	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
304	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
305	AGL(1,𝔽₅)	—	2	4	no	—
306	AGL(1,𝔽₅)	—	10	4	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	—	4	1	no	—
309	C₄×C₅	—	5	1	no	—
310	C₄×C₅	—	5	1	no	—
311	C₄×C₅	—	5	1	no	—
312	C₄×C₅	—	5	1	no	—
313	C₄×C₅	—	10	4	no	—
314	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
315	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
316	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
318	Dic₅	—	5	1	no	—
319	Dic₅	—	5	1	no	—
320	Dic₅	—	5	1	no	—
321	Dic₅	—	5	1	no	—
322	Dic₅	—	10	4	no	—
323	Dic₅	—	20	1	no	—
324	Dic₅	—	20	1	no	—
325	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
326	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
327	Dic₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
328	Dic₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
329	C₂⁴	—	25	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	25	1	no	—
333	C₂²×C₄	—	25	1	no	—
334	C₂²×C₄	—	25	1	no	—
335	C₂²×C₄	—	25	1	no	—
336	C₂²×C₄	—	25	1	no	—
337	C₂²×C₄	—	25	1	no	—
338	C₂²×C₄	—	25	1	no	—
339	C₂²×C₄	—	25	1	no	—
340	C₂²×C₄	—	25	1	no	—
341	C₂²×C₄	—	25	1	no	—
342	C₂²×C₄	—	25	1	no	—
343	C₂²×C₄	—	25	4	no	—
344	C₂²×C₄	—	25	1	no	—
345	C₄⋊C₄	—	5	2	no	—
346	C₄⋊C₄	—	25	4	no	—
347	C₄⋊C₄	—	25	2	no	—
348	C₂²⋊C₄	—	5	2	no	—
349	C₂²⋊C₄	—	25	4	no	—
350	C₂²⋊C₄	—	25	2	no	—
351	C₄²	—	5	2	no	—
352	C₄²	—	25	2	no	—
353	C₄²	—	25	4	no	—
354	C₂×C₅	—	2	1	no	—
355	C₂×C₅	—	2	1	no	—
356	C₂×C₅	—	4	2	no	—
357	C₂×C₅	—	4	1	no	—
358	C₂×C₅	—	5	2	no	—
359	C₂×C₅	—	5	2	no	—
360	C₂×C₅	—	10	1	no	—
361	C₂×C₅	—	10	1	no	—
362	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
363	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
364	D₅	—	2	1	no	—
365	D₅	—	2	1	no	—
366	D₅	—	5	2	no	—
367	D₅	—	5	2	no	—
368	D₅	—	10	1	no	—
369	D₅	—	10	1	no	—
370	D₅	—	20	2	no	—
371	D₅	—	20	2	no	—
372	D₅	#4130	1	2	yes	direct product factor
373	D₅	D₅×#41	1	2	yes	—
374	C₂³	—	5	1	no	—
375	C₂³	—	5	1	no	—
376	C₂³	—	25	1	no	—
377	C₂³	—	25	1	no	—
378	C₂³	—	25	1	no	—
379	C₂³	—	25	1	no	—
380	C₂³	—	25	1	no	—
381	C₂³	—	50	4	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	4	no	—
393	C₂×C₄	—	25	1	no	—
394	C₂×C₄	—	25	1	no	—
395	C₂×C₄	—	25	1	no	—
396	C₂×C₄	—	25	1	no	—
397	C₂×C₄	—	25	1	no	—
398	C₂×C₄	—	25	1	no	—
399	C₂×C₄	—	25	1	no	—
400	C₂×C₄	—	25	1	no	—
401	C₂×C₄	—	25	1	no	—
402	C₂×C₄	—	25	1	no	—
403	C₂×C₄	—	25	1	no	—
404	C₂×C₄	—	25	1	no	—
405	C₂×C₄	—	25	1	no	—
406	C₂×C₄	—	25	1	no	—
407	C₂×C₄	—	25	1	no	—
408	C₂×C₄	—	25	1	no	—
409	C₂×C₄	—	25	1	no	—
410	C₂×C₄	—	25	4	no	—
411	C₂×C₄	—	50	8	no	—
412	C₂×C₄	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
413	C₅	—	4	1	no	—
414	C₅	D₅×#117	1	1	yes	characteristic, complemented
415	C₅	C₂×#4130	1	1	yes	characteristic, complemented
416	C₂²	—	5	1	no	—
417	C₂²	—	5	1	no	—
418	C₂²	—	5	1	no	—
419	C₂²	—	5	1	no	—
420	C₂²	—	10	2	no	—
421	C₂²	—	10	2	no	—
422	C₂²	—	25	4	no	—
423	C₂²	—	25	1	no	—
424	C₂²	—	25	1	no	—
425	C₂²	—	50	2	no	—
426	C₂²	—	50	2	no	—
427	C₂²	—	50	2	no	—
428	C₂²	—	50	2	no	—
429	C₂²	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
430	C₄	—	5	1	no	—
431	C₄	—	5	1	no	—
432	C₄	—	5	1	no	—
433	C₄	—	5	1	no	—
434	C₄	—	10	4	no	—
435	C₄	—	25	1	no	—
436	C₄	—	25	1	no	—
437	C₄	—	50	4	no	—
438	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
439	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂	—	2	1	no	—
441	C₂	—	5	2	no	—
442	C₂	—	5	2	no	—
443	C₂	—	10	1	no	—
444	C₂	—	10	1	no	—
445	C₂	—	25	2	no	—
446	C₂	—	50	1	no	—
447	C₂	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₅×AGL(1,𝔽₅)
commutator, socle	C₂×C₅²	C₂³×C₄
Frattini	C₂	C₂²×D₅×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅²	C₂×C₄
prime radical	C₂²×D₅²	C₂²
cosocle	C₂×C₅×D₅	C₂⁴
hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
hypocenter	C₅²	C₂×#117
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11717425	C₂	semidirect
3. C₅×#4130	C₂	semidirect
5. #11717339	C₂	semidirect
6. D₅×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
7. C₄×D₅×AGL(1,𝔽₅)	C₂	semidirect
8. #11717325	C₂	semidirect
9. #11717323	C₂	semidirect
12. C₂×C₄×C₅⋊D₅	C₄	semidirect
13. C₂×C₄×C₅×D₅	C₄	semidirect
15. C₂×#6036	C₄	semidirect
16. C₂×D₅×Dic₅	C₄	semidirect
18. C₄×D₅²	C₄	semidirect
19. C₄×D₅²	C₄	semidirect
20. C₄×D₅²	C₄	semidirect
21. C₄×D₅²	C₄	semidirect
27. C₄⋊#1042	C₂²	semidirect
28. C₄×#1042	C₂²	semidirect
30. C₅×C₄⋊AGL(1,𝔽₅)	C₂²	semidirect
31. C₄×C₅×AGL(1,𝔽₅)	C₂²	semidirect
32. #87825	C₂²	semidirect
34. Dic₅×AGL(1,𝔽₅)	C₂²	semidirect
48. C₂×C₄×C₅²	C₂×C₄	semidirect
49. C₂×#1039	C₂×C₄	semidirect
52. C₄×C₅⋊D₅	C₂×C₄	semidirect
53. C₄×C₅⋊D₅	C₂×C₄	semidirect
54. C₂×C₅×Dic₅	C₂×C₄	semidirect
55. C₂×C₅×Dic₅	C₂×C₄	semidirect
58. C₄×C₅×D₅	C₂×C₄	semidirect
59. C₄×C₅×D₅	C₂×C₄	semidirect
60. C₄×C₅×D₅	C₂×C₄	semidirect
61. C₄×C₅×D₅	C₂×C₄	semidirect
66. #6036	C₂×C₄	semidirect
67. #6036	C₂×C₄	semidirect
70. D₅×Dic₅	C₂×C₄	semidirect
71. D₅×Dic₅	C₂×C₄	semidirect
72. D₅×Dic₅	C₂×C₄	semidirect
73. D₅×Dic₅	C₂×C₄	semidirect
83. #4130	D₅	direct (N × H)
149. C₂×C₄×D₅	AGL(1,𝔽₅)	semidirect
156. C₄⋊AGL(1,𝔽₅)	C₂×D₅	semidirect
159. C₄×AGL(1,𝔽₅)	C₂×D₅	semidirect
173. C₅⋊D₅	#117	semidirect
176. C₅×D₅	#117	semidirect
210. C₂×C₄×C₅	C₄×D₅	semidirect
211. C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
224. C₂×Dic₅	C₄×D₅	semidirect
225. C₂×Dic₅	C₂×AGL(1,𝔽₅)	semidirect
255. C₄×D₅	C₄×D₅	semidirect
256. C₄×D₅	C₄×D₅	semidirect
259. C₄×D₅	C₂×AGL(1,𝔽₅)	semidirect
260. C₄×D₅	C₂×AGL(1,𝔽₅)	semidirect
272. C₅²	C₂×#117	semidirect
372. D₅	#4130	direct (N × H)
412. C₂×C₄	D₅×AGL(1,𝔽₅)	semidirect
414. C₅	D₅×#117	semidirect
415. C₅	C₂×#4130	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅²	2
#11717425	2
C₅×#4130	2
D₅×C₂²⋊AGL(1,𝔽₅)	2
#11717339	2
D₅×C₄⋊AGL(1,𝔽₅)	2
C₄×D₅×AGL(1,𝔽₅)	2
#11717325	2
#11717323	2
C₂×#4130	5
D₅×#117	5

Subgroups — D5×#4130 #13107616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4130 #13107616