Subgroups — C₅×#17891 #11940611

Order 1280.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	2	yes	maximal, complemented
5	C₅×#1592	C₂	1	2	yes	maximal, complemented
6	C₅×#1590	C₂	1	2	yes	maximal, complemented
7	C₅×#1589	C₂	1	2	yes	maximal, complemented
8	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	—	2	1	no	—
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#446	C₂²	1	1	yes	characteristic, complemented
17	C₅×#446	C₂²	1	1	yes	characteristic, complemented
18	C₅×#442	C₄	1	2	yes	—
19	C₅×#440	C₄	1	2	yes	—
20	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₅×D₈	C₂²	1	2	yes	—
22	C₅×#436	—	2	1	no	—
23	C₅×#436	—	2	1	no	—
24	C₅×#436	C₂²	1	2	yes	—
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#436	C₂²	1	1	yes	characteristic, complemented
27	C₅×#436	C₂²	1	1	yes	characteristic, complemented
28	C₅×#435	—	2	1	no	—
29	C₅×#435	—	2	1	no	—
30	C₅×#431	—	2	1	no	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#428	C₄	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₅×#418	C₄	1	1	yes	characteristic
36	C₅×#417	C₄	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	complemented
42	C₅×#334	C₂²	1	2	yes	complemented
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₅×D₄⋊C₈	C₂²	1	2	yes	—
45	C₅×D₄⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₅×#322	C₂²	1	2	yes	complemented
48	C₅×C₈²	C₂²	1	2	yes	complemented
49	#17891	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₅×AGL(1,ℤ/8)	—	2	4	no	—
54	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂×C₅×M₁₆	—	4	4	no	—
61	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
67	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
73	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	2	yes	—
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₅×#117	—	2	1	no	—
77	C₅×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	C₂×C₄	1	2	yes	—
83	C₅×#106	C₂×C₄	1	2	yes	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	—	2	1	no	—
86	C₅×C₄⋊C₈	—	2	1	no	—
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×#103	C₂×C₄	1	2	yes	—
92	C₅×#102	C₂×C₄	1	2	yes	—
93	C₅×#102	C₂×C₄	1	2	yes	—
94	C₅×#102	C₂×C₄	1	2	yes	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	—	2	2	no	—
98	C₅×C₂²⋊C₈	—	2	2	no	—
99	C₅×C₂²⋊C₈	—	2	1	no	—
100	C₅×C₂²⋊C₈	—	2	1	no	—
101	C₅×#97	—	2	1	no	—
102	C₅×#97	—	2	1	no	—
103	C₅×#97	C₂×C₄	1	2	yes	—
104	C₄×C₅×C₈	—	2	1	no	—
105	C₄×C₅×C₈	D₄	1	1	yes	characteristic
106	C₄×C₅×C₈	D₄	1	1	yes	characteristic
107	C₄×C₅×C₈	C₂³	1	2	yes	—
108	C₄×C₅×C₈	C₂³	1	2	yes	—
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	#2965	C₂×C₅	1	1	yes	characteristic, complemented
112	C₄×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
113	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
114	#1594	C₂×C₅	1	2	yes	complemented
115	#1592	C₂×C₅	1	2	yes	complemented
116	#1590	C₂×C₅	1	2	yes	complemented
117	#1589	C₂×C₅	1	2	yes	complemented
118	#1565	C₂×C₅	1	1	yes	characteristic, complemented
119	#1478	C₂×C₅	1	1	yes	characteristic, complemented
120	#1477	C₂×C₅	1	1	yes	characteristic, complemented
121	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	2	1	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	2	2	no	—
125	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	1	no	—
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	4	2	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	#41	1	1	yes	characteristic
143	C₅×SD₁₆	—	2	4	no	—
144	C₅×D₈	—	2	4	no	—
145	C₅×M₁₆	—	2	2	no	—
146	C₅×M₁₆	—	4	2	no	—
147	C₅×M₁₆	—	4	4	no	—
148	C₅×M₁₆	—	4	2	no	—
149	C₅×M₁₆	—	4	4	no	—
150	C₅×M₁₆	M₁₆	1	4	yes	complemented
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	4	1	no	—
157	C₂×C₅×C₈	—	4	2	no	—
158	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₅×C₂²⋊C₄	—	2	1	no	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₅	#41	1	1	yes	characteristic
181	C₄²×C₅	C₂⁴	1	1	yes	characteristic
182	C₂×AGL(1,ℤ/8)	C₄×C₅	1	1	yes	characteristic
183	C₂²×M₁₆	—	2	1	no	—
184	C₄×#41	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
186	#446	C₂²×C₅	1	1	yes	characteristic, complemented
187	#446	C₂²×C₅	1	1	yes	characteristic, complemented
188	#442	C₄×C₅	1	2	yes	—
189	#440	C₄×C₅	1	2	yes	—
190	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
191	C₄×D₈	C₂²×C₅	1	2	yes	—
192	#436	—	2	1	no	—
193	#436	—	2	1	no	—
194	#436	C₂²×C₅	1	2	yes	—
195	#436	C₂²×C₅	1	2	yes	—
196	#436	C₂²×C₅	1	1	yes	characteristic, complemented
197	#436	C₂²×C₅	1	1	yes	characteristic, complemented
198	#435	—	2	1	no	—
199	#435	—	2	1	no	—
200	#431	—	2	1	no	—
201	#431	C₂²×C₅	1	1	yes	characteristic
202	#431	C₂²×C₅	1	1	yes	characteristic
203	#428	C₄×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	#418	C₄×C₅	1	1	yes	characteristic
206	#417	C₄×C₅	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	—	2	1	no	—
208	C₄×M₁₆	—	2	1	no	—
209	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
211	#335	C₂²×C₅	1	2	yes	complemented
212	#334	C₂²×C₅	1	2	yes	complemented
213	Q₈⋊C₈	C₂²×C₅	1	2	yes	complemented
214	D₄⋊C₈	C₂²×C₅	1	2	yes	—
215	D₄⋊C₈	C₂²×C₅	1	2	yes	—
216	D₄⋊C₈	C₂²×C₅	1	2	yes	complemented
217	#322	C₂²×C₅	1	2	yes	complemented
218	C₈²	C₂²×C₅	1	2	yes	complemented
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	—	2	1	no	—
227	C₅×D₄	—	2	1	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	2	2	no	—
230	C₅×D₄	—	2	1	no	—
231	C₅×D₄	—	4	2	no	—
232	C₅×D₄	—	4	2	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	4	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
252	C₂×C₄×C₅	#131	1	2	yes	—
253	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	2	1	no	—
258	C₅×C₈	—	2	1	no	—
259	C₅×C₈	—	2	1	no	—
260	C₅×C₈	—	4	2	no	—
261	C₅×C₈	—	4	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₅×C₈	—	4	1	no	—
264	C₅×C₈	C₂×M₁₆	1	4	yes	complemented
265	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
266	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
267	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	AGL(1,ℤ/8)	—	2	4	no	—
270	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
271	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	4	4	no	—
277	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
281	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
282	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
289	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
290	C₄×D₄	C₂³×C₅	1	2	yes	—
291	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
298	#107	C₂×C₄×C₅	1	2	yes	—
299	#106	C₂×C₄×C₅	1	2	yes	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₅	1	2	yes	—
307	#103	C₂×C₄×C₅	1	2	yes	—
308	#102	C₂×C₄×C₅	1	2	yes	—
309	#102	C₂×C₄×C₅	1	2	yes	—
310	#102	C₂×C₄×C₅	1	2	yes	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	#97	—	2	1	no	—
318	#97	—	2	1	no	—
319	#97	C₂×C₄×C₅	1	2	yes	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	C₅×D₄	1	1	yes	characteristic
322	C₄×C₈	C₅×D₄	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₅	1	2	yes	—
324	C₄×C₈	C₂³×C₅	1	2	yes	—
325	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	1	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	8	4	no	—
336	C₂²×C₅	#436	1	2	yes	—
337	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	4	1	no	—
342	C₄×C₅	—	4	1	no	—
343	C₄×C₅	—	4	2	no	—
344	C₄×C₅	—	4	1	no	—
345	C₄×C₅	#436	1	2	yes	—
346	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
347	C₄×C₅	C₂×#131	1	1	yes	characteristic
348	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₄×C₅	#575	1	1	yes	characteristic
350	C₂⁴	—	2	1	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₅×#41	1	1	yes	characteristic
371	SD₁₆	—	2	4	no	—
372	D₈	—	2	4	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	4	4	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	2	no	—
378	M₁₆	C₅×M₁₆	1	4	yes	complemented
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	4	2	no	—
386	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
387	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
388	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
407	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
408	C₄²	C₅×#41	1	1	yes	characteristic
409	C₄²	C₂⁴×C₅	1	1	yes	characteristic
410	C₂×C₅	—	2	2	no	—
411	C₂×C₅	—	8	1	no	—
412	C₂×C₅	—	8	2	no	—
413	C₂×C₅	C₂×#436	1	1	yes	characteristic
414	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂×C₅	#2955	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
422	Q₈	—	2	1	no	—
423	Q₈	—	2	1	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	1	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
446	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
447	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
449	C₂×C₄	C₅×#131	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₈	C₂×C₅×M₁₆	1	4	yes	complemented
462	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
463	C₅	#17891	1	1	yes	characteristic, direct product factor, Sylow
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	8	4	no	—
473	C₂²	C₅×#436	1	2	yes	—
474	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	C₅×#436	1	2	yes	—
483	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
484	C₄	C₂×C₅×#131	1	1	yes	characteristic
485	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	C₅×#575	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	2	no	—
489	C₂	—	8	1	no	—
490	C₂	C₂×C₅×#436	1	1	yes	characteristic
491	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×AGL(1,ℤ/8)	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2965	C₂	semidirect
3. C₂×C₅×#436	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1592	C₂	semidirect
6. C₅×#1590	C₂	semidirect
7. C₅×#1589	C₂	semidirect
8. C₅×#1565	C₂	semidirect
9. C₅×#1478	C₂	semidirect
10. C₅×#1477	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
16. C₅×#446	C₂²	semidirect
17. C₅×#446	C₂²	semidirect
26. C₅×#436	C₂²	semidirect
27. C₅×#436	C₂²	semidirect
41. C₅×#335	C₂²	semidirect
42. C₅×#334	C₂²	semidirect
43. C₅×Q₈⋊C₈	C₂²	semidirect
46. C₅×D₄⋊C₈	C₂²	semidirect
47. C₅×#322	C₂²	semidirect
48. C₅×C₈²	C₂²	semidirect
49. #17891	C₅	direct (N × H)
111. #2965	C₂×C₅	semidirect
113. C₂×#436	C₂×C₅	semidirect
114. #1594	C₂×C₅	semidirect
115. #1592	C₂×C₅	semidirect
116. #1590	C₂×C₅	semidirect
117. #1589	C₂×C₅	semidirect
118. #1565	C₂×C₅	semidirect
119. #1478	C₂×C₅	semidirect
120. #1477	C₂×C₅	semidirect
121. C₈×M₁₆	C₂×C₅	semidirect
150. C₅×M₁₆	M₁₆	semidirect
186. #446	C₂²×C₅	semidirect
187. #446	C₂²×C₅	semidirect
196. #436	C₂²×C₅	semidirect
197. #436	C₂²×C₅	semidirect
211. #335	C₂²×C₅	semidirect
212. #334	C₂²×C₅	semidirect
213. Q₈⋊C₈	C₂²×C₅	semidirect
216. D₄⋊C₈	C₂²×C₅	semidirect
217. #322	C₂²×C₅	semidirect
218. C₈²	C₂²×C₅	semidirect
264. C₅×C₈	C₂×M₁₆	semidirect
265. C₅×C₈	AGL(1,ℤ/8)	semidirect
378. M₁₆	C₅×M₁₆	semidirect
461. C₈	C₂×C₅×M₁₆	semidirect
462. C₈	C₅×AGL(1,ℤ/8)	semidirect
463. C₅	#17891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2965	2
C₄×C₅×AGL(1,ℤ/8)	2
C₂×C₅×#436	2
C₅×#1594	2
C₅×#1592	2
C₅×#1590	2
C₅×#1589	2
C₅×#1565	2
C₅×#1478	2
C₅×#1477	2
C₅×C₈×M₁₆	2
#17891	5

Subgroups — C5×#17891 #11940611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17891 #11940611