Subgroups — D₅×#4144 #13107820

Order 1600.

1962 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11717517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#4144	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#11717495	C₂	1	4	yes	maximal, complemented
5	C₂×D₅×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
6	#11717479	C₂	1	4	yes	maximal, complemented
7	#11717478	C₂	1	4	yes	maximal, complemented
8	D₅×#711	C₂	1	4	yes	maximal, complemented
9	D₄×D₅²	C₂	1	4	yes	maximal, complemented
10	#11717472	C₂	1	2	yes	maximal, complemented
11	D₅×#709	C₂	1	2	yes	maximal, complemented
12	C₂³×C₅×D₅	C₂²	1	2	yes	complemented
13	C₂²×D₅²	C₂²	1	4	yes	complemented
14	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₂²⋊(C₅⋊D₅)	C₂²	1	4	yes	complemented
16	#87902	C₂²	1	4	yes	complemented
17	D₄×C₅⋊D₅	C₂²	1	4	yes	complemented
18	#87900	C₂²	1	2	yes	complemented
19	C₂×C₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
20	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₅×#711	C₂²	1	4	yes	complemented
22	C₅×D₄×D₅	C₂²	1	4	yes	complemented
23	C₅×D₄×D₅	C₂²	1	4	yes	complemented
24	C₅×D₄×D₅	C₂²	1	4	yes	complemented
25	C₅×#709	C₂²	1	2	yes	complemented
26	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
28	#87886	C₂²	1	8	yes	complemented
29	D₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
30	D₅×C₂²⋊D₅	C₂²	1	8	yes	complemented
31	D₅×C₂²⋊D₅	C₂²	1	8	yes	complemented
32	D₅×C₂²⋊D₅	C₂²	1	8	yes	complemented
33	D₅×C₂²⋊D₅	C₂²	1	8	yes	complemented
34	C₂×#6038	C₂²	1	4	yes	complemented
35	C₂×#6037	C₂²	1	4	yes	complemented
36	#87880	C₂²	1	8	yes	complemented
37	#87879	C₂²	1	4	yes	complemented
38	#87879	C₂²	1	8	yes	complemented
39	C₂×D₅×Dic₅	C₂²	1	4	yes	complemented
40	#87877	C₂²	1	4	yes	complemented
41	D₅×D₂₀	C₂²	1	2	yes	complemented
42	D₅×D₂₀	C₂²	1	4	yes	complemented
43	C₄×D₅²	C₂²	1	4	yes	complemented
44	#87874	C₂²	1	2	yes	complemented
45	#87873	C₂²	1	4	yes	complemented
46	#87871	C₂²	1	4	yes	complemented
47	#87870	C₂²	1	2	yes	complemented
48	#87870	C₂²	1	4	yes	complemented
49	D₅×Dic₁₀	C₂²	1	2	yes	complemented
50	D₅×H(5,𝔽₂)	—	5	1	no	maximal
51	C₂×#4144	—	5	1	no	maximal
52	C₂³×C₅²	C₂³	1	2	yes	complemented
53	C₂²×C₅⋊D₅	C₂³	1	4	yes	complemented
54	C₂²×C₅×D₅	—	4	4	no	—
55	C₂²×C₅×D₅	C₂³	1	4	yes	—
56	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×D₅	C₂³	1	4	yes	complemented
58	C₂²×C₅×D₅	C₂³	1	4	yes	complemented
59	C₂²×C₅×D₅	C₂³	1	2	yes	complemented
60	C₂×D₅²	—	4	8	no	—
61	C₂×D₅²	C₂³	1	4	yes	—
62	C₂×D₅²	C₂³	1	8	yes	complemented
63	C₅²×D₄	C₂³	1	4	yes	complemented
64	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic, complemented
65	C₂²⋊(C₅⋊D₅)	C₂³	1	4	yes	complemented
66	C₂²⋊(C₅⋊D₅)	C₂³	1	8	yes	complemented
67	C₂×#1039	C₂³	1	4	yes	complemented
68	C₄⋊(C₅⋊D₅)	C₂³	1	2	yes	complemented
69	C₄×C₅⋊D₅	C₂³	1	4	yes	complemented
70	#6045	C₂³	1	2	yes	complemented
71	C₅×C₂²⋊D₅	C₂³	1	8	yes	complemented
72	C₅×C₂²⋊D₅	C₂³	1	4	yes	complemented
73	C₅×C₂²⋊D₅	C₂³	1	8	yes	complemented
74	C₂×C₅×Dic₅	C₂³	1	4	yes	complemented
75	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic, complemented
76	C₅×D₂₀	C₂³	1	4	yes	complemented
77	C₅×D₂₀	C₂³	1	2	yes	complemented
78	C₄×C₅×D₅	C₂³	1	2	yes	—
79	C₄×C₅×D₅	C₂³	1	2	yes	complemented
80	C₄×C₅×D₅	C₂³	1	4	yes	complemented
81	C₅×Dic₁₀	C₂³	1	2	yes	complemented
82	#6039	C₂³	1	4	yes	complemented
83	#6038	C₂³	1	8	yes	complemented
84	#6038	C₂³	1	4	yes	complemented
85	#6038	C₂³	1	4	yes	complemented
86	#6037	C₂³	1	4	yes	complemented
87	#6037	C₂³	1	8	yes	complemented
88	#6036	C₂³	1	4	yes	complemented
89	D₅×Dic₅	C₂³	1	4	yes	—
90	D₅×Dic₅	C₂³	1	8	yes	complemented
91	D₅×Dic₅	C₂³	1	4	yes	complemented
92	C₅×H(5,𝔽₂)	—	5	1	no	—
93	C₂²×C₅×D₄	—	5	1	no	—
94	C₂²×C₂²⋊D₅	—	5	4	no	—
95	#4149	—	5	4	no	—
96	#4149	—	5	2	no	—
97	D₅×#41	—	5	4	no	—
98	D₅×#41	—	5	2	no	—
99	#4144	—	5	1	no	—
100	#4144	—	5	1	no	—
101	#4144	—	5	4	no	—
102	#4144	—	5	4	no	—
103	#4144	—	5	4	no	—
104	#4144	—	5	4	no	—
105	#4144	—	5	4	no	—
106	#4144	—	5	2	no	—
107	#4144	—	10	2	no	—
108	#4144	D₅	1	1	yes	characteristic, direct product factor
109	C₂×#711	—	5	4	no	—
110	C₂×D₄×D₅	—	5	4	no	—
111	C₂×D₄×D₅	—	5	4	no	—
112	C₂×D₄×D₅	—	5	4	no	—
113	C₂×D₄×D₅	D₅	1	1	yes	characteristic, complemented
114	C₂×#709	—	5	2	no	—
115	C₂²×C₅²	—	4	2	no	—
116	C₂²×C₅²	C₂⁴	1	4	yes	—
117	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
118	C₂×C₅⋊D₅	—	4	4	no	—
119	C₂×C₅⋊D₅	C₂⁴	1	4	yes	—
120	C₂×C₅×D₅	—	2	8	no	—
121	C₂×C₅×D₅	—	2	2	no	—
122	C₂×C₅×D₅	—	4	4	no	—
123	C₂×C₅×D₅	—	4	4	no	—
124	C₂×C₅×D₅	—	4	2	no	—
125	C₂×C₅×D₅	C₂⁴	1	4	yes	—
126	C₂×C₅×D₅	C₂⁴	1	4	yes	—
127	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
128	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
129	D₅²	—	2	8	no	—
130	D₅²	—	4	8	no	—
131	C₄×C₅²	C₂⁴	1	2	yes	—
132	#1039	C₂⁴	1	4	yes	—
133	C₅×Dic₅	C₂⁴	1	4	yes	—
134	C₅×Dic₅	C₂⁴	1	2	yes	—
135	C₂⁴×C₅	—	5	2	no	—
136	C₂³×D₅	—	5	4	no	—
137	C₂³×D₅	—	5	4	no	—
138	C₂³×D₅	C₂×D₅	1	2	yes	complemented
139	C₅×#41	—	5	4	no	—
140	C₅×#41	—	5	2	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	—	5	4	no	—
143	C₂×C₅×D₄	—	5	2	no	—
144	C₂×C₅×D₄	—	5	4	no	—
145	C₂×C₅×D₄	—	5	4	no	—
146	C₂×C₅×D₄	—	5	4	no	—
147	C₂×C₅×D₄	—	5	1	no	—
148	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
149	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
150	C₂²×C₄×C₅	—	5	1	no	—
151	C₂×C₂²⋊D₅	—	5	4	no	—
152	C₂×C₂²⋊D₅	—	5	4	no	—
153	C₂×C₂²⋊D₅	—	5	4	no	—
154	C₂×C₂²⋊D₅	—	5	4	no	—
155	C₂×C₂²⋊D₅	—	5	4	no	—
156	C₂×C₂²⋊D₅	—	5	8	no	—
157	C₂×C₂²⋊D₅	—	5	8	no	—
158	C₂×C₂²⋊D₅	—	5	8	no	—
159	C₂×C₂²⋊D₅	—	5	8	no	—
160	C₂×C₂²⋊D₅	—	5	4	no	—
161	C₂×C₂²⋊D₅	—	10	8	no	—
162	C₂×C₂²⋊D₅	C₂×D₅	1	2	yes	complemented
163	C₂×C₂²⋊D₅	C₂×D₅	1	4	yes	complemented
164	C₂²×Dic₅	—	5	4	no	—
165	#713	—	5	4	no	—
166	#713	—	5	2	no	—
167	Q₈×D₅	—	5	2	no	—
168	#711	—	5	4	no	—
169	#711	—	5	4	no	—
170	#711	—	5	8	no	—
171	#711	—	5	8	no	—
172	#711	—	5	8	no	—
173	#711	—	5	4	no	—
174	#711	—	5	4	no	—
175	#711	—	5	2	no	—
176	#711	—	5	4	no	—
177	#711	—	10	8	no	—
178	#711	C₂×D₅	1	4	yes	complemented
179	D₄×D₅	—	5	8	no	—
180	D₄×D₅	—	5	4	no	—
181	D₄×D₅	—	5	8	no	—
182	D₄×D₅	—	5	8	no	—
183	D₄×D₅	—	5	8	no	—
184	D₄×D₅	—	5	4	no	—
185	D₄×D₅	—	5	4	no	—
186	D₄×D₅	—	5	8	no	—
187	D₄×D₅	—	5	8	no	—
188	D₄×D₅	—	5	4	no	—
189	D₄×D₅	—	5	4	no	—
190	D₄×D₅	—	5	2	no	—
191	D₄×D₅	—	5	4	no	—
192	D₄×D₅	—	10	8	no	—
193	D₄×D₅	C₂×D₅	1	4	yes	complemented
194	D₄×D₅	C₂×D₅	1	4	yes	complemented
195	D₄×D₅	C₂×D₅	1	4	yes	complemented
196	#709	—	5	2	no	—
197	#709	—	5	2	no	—
198	#709	—	5	4	no	—
199	#709	—	5	8	no	—
200	#709	—	5	2	no	—
201	#709	—	5	4	no	—
202	#709	—	5	4	no	—
203	#709	—	5	4	no	—
204	#709	—	5	2	no	—
205	#709	—	10	4	no	—
206	#709	C₂×D₅	1	2	yes	complemented
207	C₂×D₂₀	—	5	4	no	—
208	C₂×D₂₀	—	5	2	no	—
209	C₂×D₂₀	—	5	4	no	—
210	C₂×D₂₀	C₂×D₅	1	1	yes	characteristic, complemented
211	C₂×C₄×D₅	—	5	4	no	—
212	C₂×C₄×D₅	—	5	4	no	—
213	C₂×C₄×D₅	—	5	4	no	—
214	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic, complemented
215	C₂×Dic₁₀	—	5	2	no	—
216	C₂×H(5,𝔽₂)	—	25	1	no	Sylow
217	C₂×C₅²	—	2	4	no	—
218	C₂×C₅²	—	2	1	no	—
219	C₂×C₅²	C₂⁵	1	1	yes	characteristic
220	C₅⋊D₅	—	2	4	no	—
221	C₅×D₅	—	2	4	no	—
222	C₅×D₅	—	2	4	no	—
223	C₅×D₅	—	2	1	no	—
224	C₅×D₅	H(5,𝔽₂)	1	2	yes	complemented
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	5	4	no	—
227	C₂³×C₅	—	5	1	no	—
228	C₂³×C₅	—	5	2	no	—
229	C₂³×C₅	—	5	4	no	—
230	C₂³×C₅	—	5	4	no	—
231	C₂³×C₅	—	20	4	no	—
232	C₂³×C₅	C₂²×D₅	1	2	yes	complemented
233	C₂³×C₅	C₂²×D₅	1	2	yes	complemented
234	C₂²×D₅	—	4	4	no	—
235	C₂²×D₅	—	5	4	no	—
236	C₂²×D₅	—	5	4	no	—
237	C₂²×D₅	—	5	4	no	—
238	C₂²×D₅	—	5	4	no	—
239	C₂²×D₅	—	5	8	no	—
240	C₂²×D₅	—	5	8	no	—
241	C₂²×D₅	—	10	8	no	—
242	C₂²×D₅	—	20	8	no	—
243	C₂²×D₅	—	20	8	no	—
244	C₂²×D₅	C₂²×D₅	1	4	yes	—
245	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
246	C₂²×D₅	C₂²×D₅	1	4	yes	complemented
247	C₂²×D₅	C₂²×D₅	1	2	yes	complemented
248	C₂²×D₅	C₂²×D₅	1	4	yes	complemented
249	C₅×Q₈	—	5	2	no	—
250	C₅×D₄	—	2	8	no	—
251	C₅×D₄	—	5	8	no	—
252	C₅×D₄	—	5	4	no	—
253	C₅×D₄	—	5	8	no	—
254	C₅×D₄	—	5	2	no	—
255	C₅×D₄	—	5	4	no	—
256	C₅×D₄	C₂²×D₅	1	4	yes	complemented
257	C₅×D₄	C₂²×D₅	1	4	yes	complemented
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	5	4	no	—
260	C₂×C₄×C₅	—	5	1	no	—
261	C₂×C₄×C₅	—	5	2	no	—
262	C₂×C₄×C₅	—	5	4	no	—
263	C₂×C₄×C₅	—	5	2	no	—
264	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic, complemented
265	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic, complemented
266	C₂²⋊D₅	—	5	4	no	—
267	C₂²⋊D₅	—	5	8	no	—
268	C₂²⋊D₅	—	5	4	no	—
269	C₂²⋊D₅	—	5	8	no	—
270	C₂²⋊D₅	—	5	4	no	—
271	C₂²⋊D₅	—	5	8	no	—
272	C₂²⋊D₅	—	5	4	no	—
273	C₂²⋊D₅	—	5	8	no	—
274	C₂²⋊D₅	—	5	4	no	—
275	C₂²⋊D₅	—	5	4	no	—
276	C₂²⋊D₅	—	5	8	no	—
277	C₂²⋊D₅	—	10	8	no	—
278	C₂²⋊D₅	—	10	16	no	—
279	C₂²⋊D₅	C₂²×D₅	1	4	yes	complemented
280	C₂²⋊D₅	C₂²×D₅	1	8	yes	complemented
281	C₂²⋊D₅	C₂²×D₅	1	8	yes	complemented
282	C₂×Dic₅	—	5	4	no	—
283	C₂×Dic₅	—	5	4	no	—
284	C₂×Dic₅	—	5	4	no	—
285	C₂×Dic₅	—	5	4	no	—
286	C₂×Dic₅	—	5	8	no	—
287	C₂×Dic₅	—	10	8	no	—
288	C₂×Dic₅	C₂²×D₅	1	1	yes	characteristic, complemented
289	C₂×Dic₅	C₂²×D₅	1	4	yes	complemented
290	D₂₀	—	5	8	no	—
291	D₂₀	—	5	4	no	—
292	D₂₀	—	5	4	no	—
293	D₂₀	—	5	2	no	—
294	D₂₀	—	5	2	no	—
295	D₂₀	—	10	4	no	—
296	D₂₀	C₂²×D₅	1	4	yes	complemented
297	D₂₀	C₂²×D₅	1	2	yes	complemented
298	C₄×D₅	—	5	4	no	—
299	C₄×D₅	—	5	4	no	—
300	C₄×D₅	—	5	8	no	—
301	C₄×D₅	—	5	4	no	—
302	C₄×D₅	—	5	4	no	—
303	C₄×D₅	—	5	4	no	—
304	C₄×D₅	—	5	4	no	—
305	C₄×D₅	—	10	8	no	—
306	C₄×D₅	C₂²×D₅	1	2	yes	—
307	C₄×D₅	C₂²×D₅	1	4	yes	complemented
308	C₄×D₅	C₂²×D₅	1	2	yes	complemented
309	Dic₁₀	—	5	2	no	—
310	Dic₁₀	—	5	2	no	—
311	Dic₁₀	—	5	4	no	—
312	Dic₁₀	—	5	4	no	—
313	Dic₁₀	—	10	4	no	—
314	Dic₁₀	C₂²×D₅	1	2	yes	complemented
315	H(5,𝔽₂)	—	5	1	no	—
316	H(5,𝔽₂)	—	25	4	no	—
317	H(5,𝔽₂)	—	25	4	no	—
318	H(5,𝔽₂)	—	25	4	no	—
319	H(5,𝔽₂)	—	25	2	no	—
320	H(5,𝔽₂)	—	25	1	no	—
321	C₂×#41	—	25	2	no	—
322	C₂×#41	—	25	4	no	—
323	C₂²×D₄	—	5	1	no	—
324	C₂²×D₄	—	25	4	no	—
325	C₂²×D₄	—	25	4	no	—
326	C₅²	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
327	C₂²×C₅	—	2	8	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	5	1	no	—
332	C₂²×C₅	—	5	4	no	—
333	C₂²×C₅	—	5	4	no	—
334	C₂²×C₅	—	5	1	no	—
335	C₂²×C₅	—	8	4	no	—
336	C₂²×C₅	—	10	8	no	—
337	C₂²×C₅	—	10	2	no	—
338	C₂²×C₅	—	20	4	no	—
339	C₂²×C₅	—	20	4	no	—
340	C₂²×C₅	—	20	2	no	—
341	C₂²×C₅	C₂³×D₅	1	4	yes	—
342	C₂²×C₅	C₂³×D₅	1	4	yes	—
343	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
344	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
345	C₂×D₅	—	2	2	no	—
346	C₂×D₅	—	2	8	no	—
347	C₂×D₅	—	4	4	no	—
348	C₂×D₅	—	4	2	no	—
349	C₂×D₅	—	4	4	no	—
350	C₂×D₅	—	5	4	no	—
351	C₂×D₅	—	5	4	no	—
352	C₂×D₅	—	10	8	no	—
353	C₂×D₅	—	10	8	no	—
354	C₂×D₅	—	10	8	no	—
355	C₂×D₅	—	20	8	no	—
356	C₂×D₅	—	20	8	no	—
357	C₂×D₅	—	20	4	no	—
358	C₂×D₅	—	20	4	no	—
359	C₂×D₅	—	40	8	no	—
360	C₂×D₅	C₂³×D₅	1	4	yes	—
361	C₂×D₅	C₂³×D₅	1	4	yes	—
362	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
363	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
364	C₄×C₅	—	2	4	no	—
365	C₄×C₅	—	5	2	no	—
366	C₄×C₅	—	5	4	no	—
367	C₄×C₅	C₂³×D₅	1	2	yes	—
368	C₄×C₅	C₂³×D₅	1	2	yes	—
369	Dic₅	—	5	4	no	—
370	Dic₅	—	5	4	no	—
371	Dic₅	—	10	8	no	—
372	Dic₅	C₂³×D₅	1	2	yes	—
373	Dic₅	C₂³×D₅	1	4	yes	—
374	C₂⁴	—	5	2	no	—
375	C₂⁴	—	25	4	no	—
376	#41	—	5	4	no	—
377	#41	—	5	2	no	—
378	#41	—	25	4	no	—
379	#41	—	25	4	no	—
380	#41	—	25	8	no	—
381	#41	—	25	2	no	—
382	#41	—	25	4	no	—
383	#41	—	25	2	no	—
384	#41	—	25	8	no	—
385	#41	—	25	4	no	—
386	#41	—	25	4	no	—
387	#41	—	25	2	no	—
388	C₂×Q₈	—	25	2	no	—
389	C₂×D₄	—	5	2	no	—
390	C₂×D₄	—	5	4	no	—
391	C₂×D₄	—	5	4	no	—
392	C₂×D₄	—	5	4	no	—
393	C₂×D₄	—	5	4	no	—
394	C₂×D₄	—	5	1	no	—
395	C₂×D₄	—	25	2	no	—
396	C₂×D₄	—	25	4	no	—
397	C₂×D₄	—	25	4	no	—
398	C₂×D₄	—	25	8	no	—
399	C₂×D₄	—	25	4	no	—
400	C₂×D₄	—	25	4	no	—
401	C₂×D₄	—	25	8	no	—
402	C₂×D₄	—	25	8	no	—
403	C₂×D₄	—	25	8	no	—
404	C₂×D₄	—	25	8	no	—
405	C₂×D₄	—	25	4	no	—
406	C₂×D₄	—	25	4	no	—
407	C₂×D₄	—	25	4	no	—
408	C₂×D₄	D₅²	1	1	yes	characteristic, complemented
409	C₂²×C₄	—	5	1	no	—
410	C₂²×C₄	—	25	4	no	—
411	C₂²×C₄	—	25	4	no	—
412	C₂×C₅	—	2	1	no	—
413	C₂×C₅	—	2	4	no	—
414	C₂×C₅	—	2	4	no	—
415	C₂×C₅	—	2	1	no	—
416	C₂×C₅	—	2	2	no	—
417	C₂×C₅	—	4	8	no	—
418	C₂×C₅	—	4	2	no	—
419	C₂×C₅	—	5	2	no	—
420	C₂×C₅	—	10	4	no	—
421	C₂×C₅	—	10	4	no	—
422	C₂×C₅	—	10	1	no	—
423	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
424	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
425	D₅	—	2	1	no	—
426	D₅	—	2	4	no	—
427	D₅	—	2	4	no	—
428	D₅	—	10	4	no	—
429	D₅	—	10	4	no	—
430	D₅	—	20	8	no	—
431	D₅	#4144	1	2	yes	direct product factor
432	C₂³	—	5	1	no	—
433	C₂³	—	5	4	no	—
434	C₂³	—	5	4	no	—
435	C₂³	—	5	4	no	—
436	C₂³	—	5	2	no	—
437	C₂³	—	20	4	no	—
438	C₂³	—	25	4	no	—
439	C₂³	—	25	8	no	—
440	C₂³	—	25	4	no	—
441	C₂³	—	100	8	no	—
442	C₂³	C₂×D₅²	1	2	yes	complemented
443	Q₈	—	5	2	no	—
444	Q₈	—	25	4	no	—
445	Q₈	—	25	2	no	—
446	D₄	—	5	8	no	—
447	D₄	—	5	8	no	—
448	D₄	—	5	4	no	—
449	D₄	—	5	4	no	—
450	D₄	—	5	2	no	—
451	D₄	—	25	4	no	—
452	D₄	—	25	4	no	—
453	D₄	—	25	8	no	—
454	D₄	—	25	4	no	—
455	D₄	—	25	8	no	—
456	D₄	—	25	8	no	—
457	D₄	—	25	4	no	—
458	D₄	—	25	2	no	—
459	D₄	C₂×D₅²	1	4	yes	complemented
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	4	no	—
462	C₂×C₄	—	5	2	no	—
463	C₂×C₄	—	5	2	no	—
464	C₂×C₄	—	5	4	no	—
465	C₂×C₄	—	25	4	no	—
466	C₂×C₄	—	25	4	no	—
467	C₂×C₄	—	25	4	no	—
468	C₂×C₄	—	25	8	no	—
469	C₂×C₄	—	25	4	no	—
470	C₂×C₄	—	25	4	no	—
471	C₂×C₄	C₂×D₅²	1	1	yes	characteristic, complemented
472	C₅	—	2	2	no	—
473	C₅	C₂×#4144	1	1	yes	characteristic, complemented
474	C₅	D₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented
475	C₂²	—	4	2	no	—
476	C₂²	—	5	1	no	—
477	C₂²	—	5	1	no	—
478	C₂²	—	5	4	no	—
479	C₂²	—	5	4	no	—
480	C₂²	—	10	2	no	—
481	C₂²	—	10	8	no	—
482	C₂²	—	20	2	no	—
483	C₂²	—	20	4	no	—
484	C₂²	—	20	4	no	—
485	C₂²	—	25	4	no	—
486	C₂²	—	50	8	no	—
487	C₂²	—	100	4	no	—
488	C₂²	—	100	8	no	—
489	C₂²	C₂²×D₅²	1	4	yes	—
490	C₂²	C₂²×D₅²	1	1	yes	characteristic
491	C₄	—	5	2	no	—
492	C₄	—	5	4	no	—
493	C₄	—	25	4	no	—
494	C₄	C₂²×D₅²	1	2	yes	—
495	C₂	—	2	1	no	—
496	C₂	—	2	4	no	—
497	C₂	—	5	2	no	—
498	C₂	—	10	1	no	—
499	C₂	—	10	4	no	—
500	C₂	—	10	4	no	—
501	C₂	—	50	4	no	—
502	C₂	C₂³×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₅²
commutator, socle, cosocle	C₂×C₅²	C₂⁵
Fitting	C₂×C₅²×D₄	C₂²
hypercenter	C₂×D₄	D₅²
hypocenter	C₅²	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #11717517	C₂	semidirect
2. C₅×#4144	C₂	semidirect
3. C₂×C₅×D₄×D₅	C₂	semidirect
4. #11717495	C₂	semidirect
5. C₂×D₅×C₂²⋊D₅	C₂	semidirect
6. #11717479	C₂	semidirect
7. #11717478	C₂	semidirect
8. D₅×#711	C₂	semidirect
9. D₄×D₅²	C₂	semidirect
10. #11717472	C₂	semidirect
11. D₅×#709	C₂	semidirect
12. C₂³×C₅×D₅	C₂²	semidirect
13. C₂²×D₅²	C₂²	semidirect
14. C₂×C₅²×D₄	C₂²	semidirect
15. C₂×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
16. #87902	C₂²	semidirect
17. D₄×C₅⋊D₅	C₂²	semidirect
18. #87900	C₂²	semidirect
19. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
20. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₅×#711	C₂²	semidirect
22. C₅×D₄×D₅	C₂²	semidirect
23. C₅×D₄×D₅	C₂²	semidirect
24. C₅×D₄×D₅	C₂²	semidirect
25. C₅×#709	C₂²	semidirect
26. C₂×C₅×D₂₀	C₂²	semidirect
27. C₂×C₄×C₅×D₅	C₂²	semidirect
28. #87886	C₂²	semidirect
29. D₅×C₂²⋊D₅	C₂²	semidirect
30. D₅×C₂²⋊D₅	C₂²	semidirect
31. D₅×C₂²⋊D₅	C₂²	semidirect
32. D₅×C₂²⋊D₅	C₂²	semidirect
33. D₅×C₂²⋊D₅	C₂²	semidirect
34. C₂×#6038	C₂²	semidirect
35. C₂×#6037	C₂²	semidirect
36. #87880	C₂²	semidirect
37. #87879	C₂²	semidirect
38. #87879	C₂²	semidirect
39. C₂×D₅×Dic₅	C₂²	semidirect
40. #87877	C₂²	semidirect
41. D₅×D₂₀	C₂²	semidirect
42. D₅×D₂₀	C₂²	semidirect
43. C₄×D₅²	C₂²	semidirect
44. #87874	C₂²	semidirect
45. #87873	C₂²	semidirect
46. #87871	C₂²	semidirect
47. #87870	C₂²	semidirect
48. #87870	C₂²	semidirect
49. D₅×Dic₁₀	C₂²	semidirect
52. C₂³×C₅²	C₂³	semidirect
53. C₂²×C₅⋊D₅	C₂³	semidirect
57. C₂²×C₅×D₅	C₂³	semidirect
58. C₂²×C₅×D₅	C₂³	semidirect
59. C₂²×C₅×D₅	C₂³	semidirect
62. C₂×D₅²	C₂³	semidirect
63. C₅²×D₄	C₂³	semidirect
64. C₂×C₄×C₅²	C₂³	semidirect
65. C₂²⋊(C₅⋊D₅)	C₂³	semidirect
66. C₂²⋊(C₅⋊D₅)	C₂³	semidirect
67. C₂×#1039	C₂³	semidirect
68. C₄⋊(C₅⋊D₅)	C₂³	semidirect
69. C₄×C₅⋊D₅	C₂³	semidirect
70. #6045	C₂³	semidirect
71. C₅×C₂²⋊D₅	C₂³	semidirect
72. C₅×C₂²⋊D₅	C₂³	semidirect
73. C₅×C₂²⋊D₅	C₂³	semidirect
74. C₂×C₅×Dic₅	C₂³	semidirect
75. C₂×C₅×Dic₅	C₂³	semidirect
76. C₅×D₂₀	C₂³	semidirect
77. C₅×D₂₀	C₂³	semidirect
79. C₄×C₅×D₅	C₂³	semidirect
80. C₄×C₅×D₅	C₂³	semidirect
81. C₅×Dic₁₀	C₂³	semidirect
82. #6039	C₂³	semidirect
83. #6038	C₂³	semidirect
84. #6038	C₂³	semidirect
85. #6038	C₂³	semidirect
86. #6037	C₂³	semidirect
87. #6037	C₂³	semidirect
88. #6036	C₂³	semidirect
90. D₅×Dic₅	C₂³	semidirect
91. D₅×Dic₅	C₂³	semidirect
108. #4144	D₅	direct (N × H)
113. C₂×D₄×D₅	D₅	semidirect
138. C₂³×D₅	C₂×D₅	semidirect
148. C₂×C₅×D₄	C₂×D₅	semidirect
149. C₂×C₅×D₄	C₂×D₅	semidirect
162. C₂×C₂²⋊D₅	C₂×D₅	semidirect
163. C₂×C₂²⋊D₅	C₂×D₅	semidirect
178. #711	C₂×D₅	semidirect
193. D₄×D₅	C₂×D₅	semidirect
194. D₄×D₅	C₂×D₅	semidirect
195. D₄×D₅	C₂×D₅	semidirect
206. #709	C₂×D₅	semidirect
210. C₂×D₂₀	C₂×D₅	semidirect
214. C₂×C₄×D₅	C₂×D₅	semidirect
224. C₅×D₅	H(5,𝔽₂)	semidirect
232. C₂³×C₅	C₂²×D₅	semidirect
233. C₂³×C₅	C₂²×D₅	semidirect
246. C₂²×D₅	C₂²×D₅	semidirect
247. C₂²×D₅	C₂²×D₅	semidirect
248. C₂²×D₅	C₂²×D₅	semidirect
256. C₅×D₄	C₂²×D₅	semidirect
257. C₅×D₄	C₂²×D₅	semidirect
264. C₂×C₄×C₅	C₂²×D₅	semidirect
265. C₂×C₄×C₅	C₂²×D₅	semidirect
279. C₂²⋊D₅	C₂²×D₅	semidirect
280. C₂²⋊D₅	C₂²×D₅	semidirect
281. C₂²⋊D₅	C₂²×D₅	semidirect
288. C₂×Dic₅	C₂²×D₅	semidirect
289. C₂×Dic₅	C₂²×D₅	semidirect
296. D₂₀	C₂²×D₅	semidirect
297. D₂₀	C₂²×D₅	semidirect
307. C₄×D₅	C₂²×D₅	semidirect
308. C₄×D₅	C₂²×D₅	semidirect
314. Dic₁₀	C₂²×D₅	semidirect
326. C₅²	C₂×H(5,𝔽₂)	semidirect
408. C₂×D₄	D₅²	semidirect
431. D₅	#4144	direct (N × H)
442. C₂³	C₂×D₅²	semidirect
459. D₄	C₂×D₅²	semidirect
471. C₂×C₄	C₂×D₅²	semidirect
473. C₅	C₂×#4144	semidirect
474. C₅	D₅×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#11717517	2
C₅×#4144	2
C₂×C₅×D₄×D₅	2
#11717495	2
C₂×D₅×C₂²⋊D₅	2
#11717479	2
#11717478	2
D₅×#711	2
D₄×D₅²	2
#11717472	2
D₅×#709	2
D₅×H(5,𝔽₂)	5
C₂×#4144	5

Subgroups — D5×#4144 #13107820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4144 #13107820