Subgroups — D₅×#4095 #13106542

Order 1600.

664 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#11717269	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4095	C₂	1	1	yes	maximal, characteristic, complemented
5	#11717057	C₂	1	2	yes	maximal, complemented
6	D₅×#688	C₂	1	2	yes	maximal, complemented
7	#11717043	C₂	1	2	yes	maximal, complemented
8	D₅×#686	C₂	1	2	yes	maximal, complemented
9	#11716943	C₂	1	1	yes	maximal, characteristic, complemented
10	#11716941	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₅²	—	2	1	no	—
13	C₅²×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
15	C₅×#713	C₂²	1	1	yes	characteristic, complemented
16	C₅×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
17	C₅×#711	—	2	1	no	—
18	C₅×#711	C₂²	1	1	yes	characteristic, complemented
19	C₅×D₄×D₅	—	2	1	no	—
20	C₅×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
21	C₅×#709	—	2	1	no	—
22	C₅×#709	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×C₅×D₅	—	2	1	no	—
25	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
26	C₂×#6038	—	2	1	no	—
27	D₅×D₂₀	—	2	1	no	—
28	D₅×D₂₀	—	2	1	no	—
29	D₅×D₂₀	C₂²	1	2	yes	—
30	D₅×D₂₀	C₂²	1	2	yes	complemented
31	#87811	C₂²	1	2	yes	complemented
32	#87809	C₂²	1	2	yes	complemented
33	#87804	C₂²	1	1	yes	characteristic, complemented
34	C₅×#688	C₂²	1	2	yes	complemented
35	C₅×#686	C₂²	1	2	yes	complemented
36	C₅×#681	C₂²	1	1	yes	characteristic, complemented
37	#87774	C₂²	1	2	yes	complemented
38	#87772	C₂²	1	2	yes	complemented
39	#87771	C₂²	1	2	yes	complemented
40	#87770	C₂²	1	2	yes	complemented
41	#87768	C₂²	1	2	yes	complemented
42	D₅×#168	C₂²	1	2	yes	complemented
43	C₂×#4095	—	5	1	no	maximal
44	D₅×AGL(1,ℤ/8)	—	5	1	no	maximal
45	C₂²×C₅⋊D₅	—	2	1	no	—
46	C₂²×C₅×D₅	—	2	1	no	—
47	C₂²×C₅×D₅	—	2	1	no	—
48	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
49	C₂×D₅²	—	2	2	no	—
50	C₂×D₅²	—	2	2	no	—
51	C₂×D₅²	—	4	4	no	—
52	C₅²×Q₈	C₂³	1	1	yes	characteristic, complemented
53	C₅²×D₄	—	2	1	no	—
54	C₅²×D₄	C₂³	1	1	yes	characteristic, complemented
55	C₂×C₄×C₅²	—	2	1	no	—
56	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
57	C₄⋊(C₅⋊D₅)	—	2	1	no	—
58	C₄⋊(C₅⋊D₅)	C₂³	1	2	yes	—
59	C₅×C₂²⋊D₅	—	2	1	no	—
60	C₅×C₂²⋊D₅	—	2	1	no	—
61	C₅×C₂²⋊D₅	—	2	1	no	—
62	C₂×C₅×Dic₅	—	2	1	no	—
63	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
64	C₅×D₂₀	—	2	1	no	—
65	C₅×D₂₀	—	2	1	no	—
66	C₅×D₂₀	C₂³	1	2	yes	—
67	C₅×D₂₀	C₂³	1	1	yes	characteristic, complemented
68	C₄×C₅×D₅	—	2	1	no	—
69	C₄×C₅×D₅	—	2	1	no	—
70	C₄×C₅×D₅	—	2	1	no	—
71	C₄×C₅×D₅	D₄	1	1	yes	characteristic
72	C₄×C₅×D₅	D₄	1	1	yes	characteristic
73	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
75	C₅×Dic₁₀	—	2	1	no	—
76	C₅×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
77	#6038	—	2	2	no	—
78	#6038	—	2	2	no	—
79	#6029	C₂³	1	2	yes	complemented
80	C₅×#168	C₂³	1	2	yes	complemented
81	C₂×C₅×#41	—	5	1	no	—
82	D₅×#41	D₅	1	1	yes	characteristic, complemented
83	C₂×D₄×D₅	—	5	1	no	—
84	C₂²×D₂₀	—	5	1	no	—
85	C₅×AGL(1,ℤ/8)	—	5	1	no	—
86	#4095	—	5	1	no	—
87	#4095	—	5	1	no	—
88	#4095	—	5	1	no	—
89	#4095	—	5	2	no	—
90	#4095	—	5	2	no	—
91	#4095	—	5	1	no	—
92	#4095	—	10	2	no	—
93	#4095	D₅	1	1	yes	characteristic, direct product factor
94	C₂×#688	—	5	2	no	—
95	#4078	—	5	1	no	—
96	C₂×#686	—	5	2	no	—
97	C₂×#681	—	5	1	no	—
98	#4060	—	5	2	no	—
99	D₅×SD₁₆	—	5	2	no	—
100	#4057	—	5	2	no	—
101	D₅×D₈	—	5	2	no	—
102	#4054	—	5	1	no	—
103	D₅×M₁₆	—	5	1	no	—
104	C₂²×C₅²	—	2	1	no	—
105	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
106	C₂×C₅⋊D₅	—	2	2	no	—
107	C₂×C₅⋊D₅	—	4	2	no	—
108	C₂×C₅×D₅	—	2	2	no	—
109	C₂×C₅×D₅	—	2	2	no	—
110	C₂×C₅×D₅	—	2	1	no	—
111	C₂×C₅×D₅	—	4	2	no	—
112	C₂×C₅×D₅	—	4	2	no	—
113	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
115	D₅²	—	4	4	no	—
116	D₅²	—	4	4	no	—
117	C₄×C₅²	—	2	1	no	—
118	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
119	C₄×C₅²	C₂⁴	1	1	yes	characteristic
120	C₅×Dic₅	—	2	1	no	—
121	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
122	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
123	C₂³×D₅	—	10	1	no	—
124	C₂³×D₅	—	10	1	no	—
125	C₅×#41	—	2	2	no	—
126	C₅×#41	—	5	1	no	—
127	C₅×#41	—	5	1	no	—
128	C₅×#41	—	5	1	no	—
129	C₅×#41	—	10	1	no	—
130	C₅×#41	—	10	1	no	—
131	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
132	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
133	C₂×C₅×Q₈	—	5	1	no	—
134	C₂×C₅×D₄	—	5	1	no	—
135	C₂×C₅×D₄	—	5	1	no	—
136	C₂×C₅×D₄	—	10	1	no	—
137	C₂²×C₄×C₅	—	5	1	no	—
138	C₂²×C₄×C₅	—	10	1	no	—
139	C₂×C₂²⋊D₅	—	10	1	no	—
140	#713	C₂×D₅	1	1	yes	characteristic, complemented
141	Q₈×D₅	C₂×D₅	1	1	yes	characteristic, complemented
142	#711	—	2	1	no	—
143	#711	C₂×D₅	1	1	yes	characteristic, complemented
144	D₄×D₅	—	2	1	no	—
145	D₄×D₅	—	5	2	no	—
146	D₄×D₅	—	5	2	no	—
147	D₄×D₅	—	10	1	no	—
148	D₄×D₅	—	10	1	no	—
149	D₄×D₅	C₂×D₅	1	1	yes	characteristic, complemented
150	#709	—	2	1	no	—
151	#709	C₂×D₅	1	1	yes	characteristic, complemented
152	C₂×D₂₀	—	5	1	no	—
153	C₂×D₂₀	—	5	1	no	—
154	C₂×D₂₀	—	5	2	no	—
155	C₂×D₂₀	—	5	2	no	—
156	C₂×D₂₀	—	10	2	no	—
157	C₂×D₂₀	—	10	1	no	—
158	C₂×D₂₀	—	10	1	no	—
159	C₂×D₂₀	—	10	1	no	—
160	C₂×D₂₀	C₂×D₅	1	1	yes	characteristic, complemented
161	C₂×C₄×D₅	—	2	1	no	—
162	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
163	C₅×SD₁₆	—	5	2	no	—
164	C₅×D₈	—	5	2	no	—
165	C₅×M₁₆	—	5	1	no	—
166	#688	—	5	2	no	—
167	#688	—	5	2	no	—
168	#688	—	5	2	no	—
169	#688	—	5	2	no	—
170	#688	—	10	4	no	—
171	#688	C₂×D₅	1	2	yes	complemented
172	#687	—	5	2	no	—
173	#686	—	5	2	no	—
174	#686	—	5	2	no	—
175	#686	—	5	2	no	—
176	#686	—	5	2	no	—
177	#686	—	5	2	no	—
178	#686	—	10	4	no	—
179	#686	C₂×D₅	1	2	yes	complemented
180	#681	—	5	1	no	—
181	#681	—	5	1	no	—
182	#681	—	5	2	no	—
183	#681	—	10	2	no	—
184	#681	C₂×D₅	1	1	yes	characteristic, complemented
185	C₂×#168	—	5	2	no	—
186	D₄₀	—	5	2	no	—
187	#677	—	5	2	no	—
188	#676	—	5	2	no	—
189	C₈×D₅	—	5	2	no	—
190	C₂×AGL(1,ℤ/8)	—	25	1	no	Sylow
191	C₂×C₅²	—	2	1	no	—
192	C₂×C₅²	—	4	1	no	—
193	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
194	C₅⋊D₅	—	4	2	no	—
195	C₅×D₅	—	2	1	no	—
196	C₅×D₅	—	4	2	no	—
197	C₅×D₅	—	4	1	no	—
198	C₅×D₅	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂³×C₅	—	5	1	no	—
200	C₂³×C₅	—	10	1	no	—
201	C₂³×C₅	—	10	1	no	—
202	C₂²×D₅	—	2	1	no	—
203	C₂²×D₅	—	2	1	no	—
204	C₂²×D₅	—	10	2	no	—
205	C₂²×D₅	—	10	2	no	—
206	C₂²×D₅	—	10	1	no	—
207	C₂²×D₅	—	10	1	no	—
208	C₂²×D₅	—	10	2	no	—
209	C₂²×D₅	—	10	2	no	—
210	C₂²×D₅	—	20	2	no	—
211	C₂²×D₅	—	20	4	no	—
212	C₂²×D₅	—	20	4	no	—
213	C₂²×D₅	C₂²⋊D₅	1	1	yes	characteristic
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	5	1	no	—
216	C₅×Q₈	—	10	1	no	—
217	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
218	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
219	C₅×D₄	—	2	1	no	—
220	C₅×D₄	—	2	1	no	—
221	C₅×D₄	—	2	2	no	—
222	C₅×D₄	—	4	2	no	—
223	C₅×D₄	—	5	2	no	—
224	C₅×D₄	—	5	1	no	—
225	C₅×D₄	—	10	1	no	—
226	C₅×D₄	—	10	1	no	—
227	C₅×D₄	—	10	1	no	—
228	C₅×D₄	—	10	1	no	—
229	C₅×D₄	—	10	1	no	—
230	C₅×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
231	C₅×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	5	1	no	—
237	C₂×C₄×C₅	—	5	1	no	—
238	C₂×C₄×C₅	—	5	1	no	—
239	C₂×C₄×C₅	—	5	1	no	—
240	C₂×C₄×C₅	—	5	1	no	—
241	C₂×C₄×C₅	—	10	1	no	—
242	C₂×C₄×C₅	—	10	1	no	—
243	C₂×C₄×C₅	—	10	1	no	—
244	C₂×C₄×C₅	—	10	1	no	—
245	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
247	C₂²⋊D₅	—	2	1	no	—
248	C₂²⋊D₅	—	2	1	no	—
249	C₂²⋊D₅	—	2	1	no	—
250	C₂²⋊D₅	—	10	2	no	—
251	C₂²⋊D₅	—	10	2	no	—
252	C₂×Dic₅	—	2	1	no	—
253	C₂×Dic₅	C₂²⋊D₅	1	1	yes	characteristic
254	D₂₀	—	2	1	no	—
255	D₂₀	—	2	1	no	—
256	D₂₀	—	5	2	no	—
257	D₂₀	—	5	2	no	—
258	D₂₀	—	10	4	no	—
259	D₂₀	—	10	2	no	—
260	D₂₀	—	10	2	no	—
261	D₂₀	—	10	1	no	—
262	D₂₀	—	10	1	no	—
263	D₂₀	—	20	2	no	—
264	D₂₀	C₂²×D₅	1	2	yes	—
265	D₂₀	C₂²×D₅	1	1	yes	characteristic, complemented
266	C₄×D₅	—	2	1	no	—
267	C₄×D₅	—	2	1	no	—
268	C₄×D₅	—	2	1	no	—
269	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
270	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
271	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
272	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
273	Dic₁₀	—	2	1	no	—
274	Dic₁₀	C₂²×D₅	1	1	yes	characteristic, complemented
275	C₅×C₈	—	5	2	no	—
276	#168	—	5	2	no	—
277	#168	—	5	2	no	—
278	#168	—	10	4	no	—
279	#168	C₂²×D₅	1	2	yes	complemented
280	C₂×#41	—	5	1	no	—
281	C₂²×D₄	—	25	1	no	—
282	AGL(1,ℤ/8)	—	5	1	no	—
283	AGL(1,ℤ/8)	—	25	1	no	—
284	AGL(1,ℤ/8)	—	25	2	no	—
285	AGL(1,ℤ/8)	—	25	2	no	—
286	AGL(1,ℤ/8)	—	25	1	no	—
287	AGL(1,ℤ/8)	—	25	1	no	—
288	C₂×SD₁₆	—	25	2	no	—
289	C₂×D₈	—	25	2	no	—
290	C₂×M₁₆	—	25	1	no	—
291	C₅²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	5	1	no	—
297	C₂²×C₅	—	5	1	no	—
298	C₂²×C₅	—	10	2	no	—
299	C₂²×C₅	—	10	1	no	—
300	C₂²×C₅	—	10	2	no	—
301	C₂²×C₅	—	20	2	no	—
302	C₂²×C₅	—	20	2	no	—
303	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
304	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
305	C₂×D₅	—	2	2	no	—
306	C₂×D₅	—	2	2	no	—
307	C₂×D₅	—	2	1	no	—
308	C₂×D₅	—	4	2	no	—
309	C₂×D₅	—	4	2	no	—
310	C₂×D₅	—	10	2	no	—
311	C₂×D₅	—	10	2	no	—
312	C₂×D₅	—	20	4	no	—
313	C₂×D₅	—	20	4	no	—
314	C₂×D₅	—	20	4	no	—
315	C₂×D₅	—	20	4	no	—
316	C₂×D₅	—	20	2	no	—
317	C₂×D₅	—	20	2	no	—
318	C₂×D₅	—	20	4	no	—
319	C₂×D₅	—	40	4	no	—
320	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
321	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	5	1	no	—
328	C₄×C₅	—	5	1	no	—
329	C₄×C₅	—	10	1	no	—
330	C₄×C₅	D₄×D₅	1	1	yes	characteristic
331	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
332	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
333	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
334	Dic₅	—	2	1	no	—
335	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
336	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
337	C₂⁴	—	50	1	no	—
338	#41	—	5	1	no	—
339	#41	—	5	1	no	—
340	#41	—	5	1	no	—
341	#41	—	10	1	no	—
342	#41	—	10	1	no	—
343	#41	D₅²	1	1	yes	characteristic, complemented
344	C₂×Q₈	—	5	1	no	—
345	C₂×D₄	—	5	1	no	—
346	C₂×D₄	—	5	1	no	—
347	C₂×D₄	—	10	1	no	—
348	C₂×D₄	—	25	2	no	—
349	C₂×D₄	—	25	2	no	—
350	C₂×D₄	—	25	1	no	—
351	C₂×D₄	—	50	1	no	—
352	C₂×D₄	—	50	1	no	—
353	C₂×D₄	—	50	1	no	—
354	C₂²×C₄	—	5	1	no	—
355	C₂²×C₄	—	10	1	no	—
356	SD₁₆	—	5	2	no	—
357	SD₁₆	—	25	2	no	—
358	SD₁₆	—	25	2	no	—
359	SD₁₆	—	25	2	no	—
360	D₈	—	5	2	no	—
361	D₈	—	25	2	no	—
362	D₈	—	25	2	no	—
363	D₈	—	25	2	no	—
364	M₁₆	—	5	1	no	—
365	M₁₆	—	25	2	no	—
366	M₁₆	—	25	1	no	—
367	C₂×C₈	—	25	2	no	—
368	C₂×C₅	—	2	1	no	—
369	C₂×C₅	—	2	1	no	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	—	4	2	no	—
372	C₂×C₅	—	4	1	no	—
373	C₂×C₅	—	4	1	no	—
374	C₂×C₅	—	5	2	no	—
375	C₂×C₅	—	8	2	no	—
376	C₂×C₅	—	10	1	no	—
377	C₂×C₅	—	20	1	no	—
378	C₂×C₅	—	20	2	no	—
379	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
380	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
381	D₅	—	2	1	no	—
382	D₅	—	4	2	no	—
383	D₅	—	4	1	no	—
384	D₅	—	20	2	no	—
385	D₅	—	20	2	no	—
386	D₅	—	40	4	no	—
387	D₅	#4095	1	2	yes	direct product factor
388	C₂³	—	5	1	no	—
389	C₂³	—	10	1	no	—
390	C₂³	—	10	1	no	—
391	C₂³	—	50	2	no	—
392	C₂³	—	50	2	no	—
393	C₂³	—	50	1	no	—
394	C₂³	—	100	4	no	—
395	Q₈	—	5	1	no	—
396	Q₈	—	10	1	no	—
397	Q₈	C₂×D₅²	1	1	yes	characteristic, complemented
398	D₄	—	2	1	no	—
399	D₄	—	5	2	no	—
400	D₄	—	5	1	no	—
401	D₄	—	10	1	no	—
402	D₄	—	10	1	no	—
403	D₄	—	10	1	no	—
404	D₄	—	10	1	no	—
405	D₄	—	10	1	no	—
406	D₄	—	25	2	no	—
407	D₄	—	50	2	no	—
408	D₄	—	50	2	no	—
409	D₄	—	50	1	no	—
410	D₄	C₂×D₅²	1	1	yes	characteristic, complemented
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	5	1	no	—
417	C₂×C₄	—	10	1	no	—
418	C₂×C₄	—	10	1	no	—
419	C₂×C₄	—	10	1	no	—
420	C₂×C₄	—	10	1	no	—
421	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
422	C₈	—	5	2	no	—
423	C₈	—	25	2	no	—
424	C₅	—	2	2	no	—
425	C₅	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
426	C₅	C₂×#4095	1	1	yes	characteristic, complemented
427	C₂²	—	2	1	no	—
428	C₂²	—	5	1	no	—
429	C₂²	—	5	1	no	—
430	C₂²	—	10	2	no	—
431	C₂²	—	10	1	no	—
432	C₂²	—	10	2	no	—
433	C₂²	—	20	2	no	—
434	C₂²	—	20	2	no	—
435	C₂²	—	50	2	no	—
436	C₂²	—	100	2	no	—
437	C₂²	—	100	4	no	—
438	C₂²	—	100	4	no	—
439	C₂²	D₅×C₂²⋊D₅	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	5	1	no	—
442	C₄	—	5	1	no	—
443	C₄	—	10	1	no	—
444	C₄	D₅×C₂²⋊D₅	1	1	yes	characteristic
445	C₄	C₂²×D₅²	1	1	yes	characteristic
446	C₂	—	2	1	no	—
447	C₂	—	4	1	no	—
448	C₂	—	5	2	no	—
449	C₂	—	10	1	no	—
450	C₂	—	20	2	no	—
451	C₂	—	20	1	no	—
452	C₂	—	100	2	no	—
453	C₂	C₂×D₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₅×C₂²⋊D₅
commutator, cosocle	C₄×C₅²	C₂⁴
Frattini	C₄	C₂²×D₅²
Fitting	C₅²×#41	C₂²
socle	C₂×C₅²	C₂²×D₄
hypercenter	#41	D₅²
hypocenter	C₅²	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×#41	C₂	semidirect
2. C₂×D₅×D₂₀	C₂	semidirect
3. #11717269	C₂	semidirect
4. C₅×#4095	C₂	semidirect
5. #11717057	C₂	semidirect
6. D₅×#688	C₂	semidirect
7. #11717043	C₂	semidirect
8. D₅×#686	C₂	semidirect
9. #11716943	C₂	semidirect
10. #11716941	C₂	semidirect
11. D₅×#681	C₂	semidirect
13. C₅²×#41	C₂²	semidirect
14. C₂×C₄⋊(C₅⋊D₅)	C₂²	semidirect
15. C₅×#713	C₂²	semidirect
16. C₅×Q₈×D₅	C₂²	semidirect
18. C₅×#711	C₂²	semidirect
20. C₅×D₄×D₅	C₂²	semidirect
22. C₅×#709	C₂²	semidirect
23. C₂×C₅×D₂₀	C₂²	semidirect
30. D₅×D₂₀	C₂²	semidirect
31. #87811	C₂²	semidirect
32. #87809	C₂²	semidirect
33. #87804	C₂²	semidirect
34. C₅×#688	C₂²	semidirect
35. C₅×#686	C₂²	semidirect
36. C₅×#681	C₂²	semidirect
37. #87774	C₂²	semidirect
38. #87772	C₂²	semidirect
39. #87771	C₂²	semidirect
40. #87770	C₂²	semidirect
41. #87768	C₂²	semidirect
42. D₅×#168	C₂²	semidirect
52. C₅²×Q₈	C₂³	semidirect
54. C₅²×D₄	C₂³	semidirect
67. C₅×D₂₀	C₂³	semidirect
76. C₅×Dic₁₀	C₂³	semidirect
79. #6029	C₂³	semidirect
80. C₅×#168	C₂³	semidirect
82. D₅×#41	D₅	semidirect
93. #4095	D₅	direct (N × H)
131. C₅×#41	C₂×D₅	semidirect
132. C₅×#41	C₂×D₅	semidirect
140. #713	C₂×D₅	semidirect
141. Q₈×D₅	C₂×D₅	semidirect
143. #711	C₂×D₅	semidirect
149. D₄×D₅	C₂×D₅	semidirect
151. #709	C₂×D₅	semidirect
160. C₂×D₂₀	C₂×D₅	semidirect
171. #688	C₂×D₅	semidirect
179. #686	C₂×D₅	semidirect
184. #681	C₂×D₅	semidirect
198. C₅×D₅	AGL(1,ℤ/8)	semidirect
217. C₅×Q₈	C₂²×D₅	semidirect
218. C₅×Q₈	C₂²×D₅	semidirect
230. C₅×D₄	C₂²×D₅	semidirect
231. C₅×D₄	C₂²×D₅	semidirect
265. D₂₀	C₂²×D₅	semidirect
274. Dic₁₀	C₂²×D₅	semidirect
279. #168	C₂²×D₅	semidirect
291. C₅²	C₂×AGL(1,ℤ/8)	semidirect
343. #41	D₅²	semidirect
387. D₅	#4095	direct (N × H)
397. Q₈	C₂×D₅²	semidirect
410. D₄	C₂×D₅²	semidirect
425. C₅	D₅×AGL(1,ℤ/8)	semidirect
426. C₅	C₂×#4095	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×#41	2
C₂×D₅×D₂₀	2
#11717269	2
C₅×#4095	2
#11717057	2
D₅×#688	2
#11717043	2
D₅×#686	2
#11716943	2
#11716941	2
D₅×#681	2
C₂×#4095	5
D₅×AGL(1,ℤ/8)	5

Subgroups — D5×#4095 #13106542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4095 #13106542