Subgroups — C₅×D₅×AGL(1,ℤ/8) #13106926

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

	subgroup	G/H
center	C₂×C₅	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₅
Fitting	C₅²×AGL(1,ℤ/8)	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₅×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₂×C₅×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×#41	C₂	semidirect
2. C₂×C₅×D₄×D₅	C₂	semidirect
3. C₅²×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#4095	C₂	semidirect
5. C₅×#4078	C₂	semidirect
6. C₅×#4060	C₂	semidirect
7. C₅×D₅×SD₁₆	C₂	semidirect
8. C₅×#4057	C₂	semidirect
9. C₅×D₅×D₈	C₂	semidirect
10. C₅×#4054	C₂	semidirect
11. C₅×D₅×M₁₆	C₂	semidirect
13. C₅²×#41	C₂²	semidirect
14. C₂×C₅²×D₄	C₂²	semidirect
16. C₅×#713	C₂²	semidirect
17. C₅×Q₈×D₅	C₂²	semidirect
19. C₅×#711	C₂²	semidirect
24. C₅×D₄×D₅	C₂²	semidirect
25. C₅×D₄×D₅	C₂²	semidirect
27. C₅×#709	C₂²	semidirect
28. C₂×C₅×D₂₀	C₂²	semidirect
31. C₅²×SD₁₆	C₂²	semidirect
32. C₅²×D₈	C₂²	semidirect
33. C₅²×M₁₆	C₂²	semidirect
34. C₅×#688	C₂²	semidirect
35. C₅×#687	C₂²	semidirect
36. C₅×#686	C₂²	semidirect
37. C₅×#686	C₂²	semidirect
38. C₅×#681	C₂²	semidirect
39. C₅×D₄₀	C₂²	semidirect
40. C₅×#677	C₂²	semidirect
41. C₅×#676	C₂²	semidirect
42. C₅×C₈×D₅	C₂²	semidirect
44. D₅×AGL(1,ℤ/8)	C₅	direct (N × H)
52. C₅²×Q₈	C₂³	semidirect
56. C₅²×D₄	C₂³	semidirect
69. C₅×D₂₀	C₂³	semidirect
78. C₅×Dic₁₀	C₂³	semidirect
79. C₅²×C₈	C₂³	semidirect
80. C₅×#168	C₂³	semidirect
83. D₅×#41	C₂×C₅	semidirect
84. C₂×D₄×D₅	C₂×C₅	semidirect
91. C₅×AGL(1,ℤ/8)	D₅	direct (N × H)
92. C₅×AGL(1,ℤ/8)	C₂×C₅	semidirect
96. #4095	C₂×C₅	semidirect
97. #4078	C₂×C₅	semidirect
98. #4060	C₂×C₅	semidirect
99. D₅×SD₁₆	C₂×C₅	semidirect
100. #4057	C₂×C₅	semidirect
101. D₅×D₈	C₂×C₅	semidirect
102. #4054	C₂×C₅	semidirect
103. D₅×M₁₆	C₂×C₅	semidirect
131. C₅×#41	C₂×D₅	semidirect
132. C₅×#41	C₂²×C₅	semidirect
143. C₂×C₅×D₄	C₂×D₅	semidirect
144. C₂×C₅×D₄	C₂²×C₅	semidirect
148. #713	C₂²×C₅	semidirect
149. Q₈×D₅	C₂²×C₅	semidirect
151. #711	C₂²×C₅	semidirect
156. D₄×D₅	C₂²×C₅	semidirect
157. D₄×D₅	C₂²×C₅	semidirect
159. #709	C₂²×C₅	semidirect
160. C₂×D₂₀	C₂²×C₅	semidirect
167. C₅×SD₁₆	C₂×D₅	semidirect
168. C₅×SD₁₆	C₂²×C₅	semidirect
173. C₅×D₈	C₂×D₅	semidirect
174. C₅×D₈	C₂²×C₅	semidirect
178. C₅×M₁₆	C₂×D₅	semidirect
179. C₅×M₁₆	C₂²×C₅	semidirect
181. #688	C₂²×C₅	semidirect
182. #687	C₂²×C₅	semidirect
183. #686	C₂²×C₅	semidirect
184. #686	C₂²×C₅	semidirect
185. #681	C₂²×C₅	semidirect
186. D₄₀	C₂²×C₅	semidirect
187. #677	C₂²×C₅	semidirect
188. #676	C₂²×C₅	semidirect
189. C₈×D₅	C₂²×C₅	semidirect
198. C₅×D₅	AGL(1,ℤ/8)	direct (N × H)
217. C₅×Q₈	C₂²×D₅	semidirect
218. C₅×Q₈	C₂³×C₅	semidirect
237. C₅×D₄	C₂²×D₅	semidirect
239. C₅×D₄	C₂³×C₅	semidirect
265. D₂₀	C₂³×C₅	semidirect
274. Dic₁₀	C₂³×C₅	semidirect
277. C₅×C₈	C₂²×D₅	semidirect
278. C₅×C₈	C₂³×C₅	semidirect
279. #168	C₂³×C₅	semidirect
287. AGL(1,ℤ/8)	C₅×D₅	direct (N × H)
291. C₅²	C₂×AGL(1,ℤ/8)	semidirect
343. #41	C₂×C₅×D₅	semidirect
353. C₂×D₄	C₂×C₅×D₅	semidirect
359. SD₁₆	C₂×C₅×D₅	semidirect
363. D₈	C₂×C₅×D₅	semidirect
366. M₁₆	C₂×C₅×D₅	semidirect
387. D₅	C₅×AGL(1,ℤ/8)	direct (N × H)
397. Q₈	C₂²×C₅×D₅	semidirect
410. D₄	C₂²×C₅×D₅	semidirect
423. C₈	C₂²×C₅×D₅	semidirect
425. C₅	D₅×AGL(1,ℤ/8)	direct (N × H)
426. C₅	C₂×C₅×AGL(1,ℤ/8)	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×C₅×D₄×D₅	2
C₅²×AGL(1,ℤ/8)	2
C₅×#4095	2
C₅×#4078	2
C₅×#4060	2
C₅×D₅×SD₁₆	2
C₅×#4057	2
C₅×D₅×D₈	2
C₅×#4054	2
C₅×D₅×M₁₆	2
C₂×C₅×AGL(1,ℤ/8)	5
D₅×AGL(1,ℤ/8)	5

Subgroups — C5×D5×AGL(1,ℤ/8) #13106926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×AGL(1,ℤ/8) #13106926