Subgroups — C₅×#17945 #11940665

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3106	C₂	1	1	yes	maximal, characteristic
2	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1590	C₂	1	2	yes	maximal, complemented
5	C₅×#1589	C₂	1	2	yes	maximal, complemented
6	C₅×#1586	C₂	1	2	yes	maximal, complemented
7	C₅×#1585	C₂	1	2	yes	maximal, complemented
8	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#482	C₄	1	2	yes	—
16	C₅×#477	C₄	1	1	yes	characteristic
17	C₅×#476	C₄	1	1	yes	characteristic
18	C₅×#460	C₄	1	1	yes	characteristic
19	C₅×#459	C₄	1	1	yes	characteristic
20	C₅×#449	C₄	1	2	yes	—
21	C₅×#446	C₂²	1	1	yes	characteristic
22	C₅×#446	C₂²	1	1	yes	characteristic
23	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₅×D₈	C₂²	1	2	yes	—
25	C₅×#436	—	2	1	no	—
26	C₅×#436	C₂²	1	1	yes	characteristic
27	C₅×#436	C₂²	1	1	yes	characteristic
28	C₅×#436	C₂²	1	2	yes	—
29	C₅×#435	—	2	1	no	—
30	C₅×#435	—	2	1	no	—
31	C₅×C₈×D₄	—	2	1	no	—
32	C₅×C₈×D₄	C₂²	1	2	yes	—
33	C₅×#431	—	2	1	no	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₅×#408	—	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	—
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×D₄⋊C₈	C₂²	1	2	yes	—
45	C₅×D₄⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	—
47	C₅×#322	C₂²	1	2	yes	—
48	C₅×C₈²	C₂²	1	2	yes	—
49	#17945	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
54	C₅×#131	—	4	4	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	2	no	—
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₅×#127	C₂×C₄	1	1	yes	characteristic
65	C₅×#124	—	2	1	no	—
66	C₅×#121	—	2	1	no	—
67	C₅×#121	C₂×C₄	1	2	yes	—
68	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂×C₄	1	2	yes	—
81	C₅×#106	C₂×C₄	1	2	yes	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊C₈	C₂³	1	2	yes	—
90	C₅×#103	C₂×C₄	1	2	yes	—
91	C₅×#102	C₂×C₄	1	2	yes	—
92	C₅×#102	C₂×C₄	1	2	yes	—
93	C₅×#102	C₂×C₄	1	2	yes	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×C₂²⋊C₈	—	2	2	no	—
96	C₅×C₂²⋊C₈	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	1	no	—
98	C₅×C₂²⋊C₈	—	2	1	no	—
99	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
100	C₅×#97	—	2	1	no	—
101	C₅×#97	—	2	1	no	—
102	C₅×#97	—	2	1	no	—
103	C₄×C₅×C₈	—	2	1	no	—
104	C₄×C₅×C₈	D₄	1	1	yes	characteristic
105	C₄×C₅×C₈	D₄	1	1	yes	characteristic
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	C₄×C₅×C₈	C₂³	1	2	yes	—
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#3106	C₂×C₅	1	1	yes	characteristic
111	#2965	C₂×C₅	1	1	yes	characteristic, complemented
112	#2931	C₂×C₅	1	1	yes	characteristic, complemented
113	#1590	C₂×C₅	1	2	yes	complemented
114	#1589	C₂×C₅	1	2	yes	complemented
115	#1586	C₂×C₅	1	2	yes	complemented
116	#1585	C₂×C₅	1	2	yes	complemented
117	#1574	C₂×C₅	1	1	yes	characteristic, complemented
118	#1489	C₂×C₅	1	1	yes	characteristic, complemented
119	#1484	C₂×C₅	1	1	yes	characteristic, complemented
120	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	4	1	no	—
122	C₅×#41	—	4	1	no	—
123	C₅×#41	—	4	2	no	—
124	C₅×#41	—	4	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	#41	1	1	yes	characteristic
140	C₅×SD₁₆	—	4	2	no	—
141	C₅×D₈	—	4	2	no	—
142	C₅×M₁₆	—	2	4	no	—
143	C₅×M₁₆	—	4	2	no	—
144	C₅×M₁₆	—	4	2	no	—
145	C₅×M₁₆	—	4	2	no	—
146	C₅×M₁₆	—	4	4	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	4	1	no	—
153	C₂×C₅×C₈	—	4	4	no	—
154	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₅×C₂²⋊C₄	—	2	2	no	—
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	2	2	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	#41	1	1	yes	characteristic
177	C₄²×C₅	C₂⁴	1	1	yes	characteristic
178	C₂×#131	—	2	1	no	—
179	#532	C₂²×C₅	1	1	yes	characteristic
180	C₄×#41	C₂²×C₅	1	1	yes	characteristic
181	#482	C₄×C₅	1	2	yes	—
182	#477	C₄×C₅	1	1	yes	characteristic
183	#476	C₄×C₅	1	1	yes	characteristic
184	#460	C₄×C₅	1	1	yes	characteristic
185	#459	C₄×C₅	1	1	yes	characteristic
186	#449	C₄×C₅	1	2	yes	—
187	#446	C₂²×C₅	1	1	yes	characteristic
188	#446	C₂²×C₅	1	1	yes	characteristic
189	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
190	C₄×D₈	C₂²×C₅	1	2	yes	—
191	#436	—	2	1	no	—
192	#436	C₂²×C₅	1	1	yes	characteristic
193	#436	C₂²×C₅	1	1	yes	characteristic
194	#436	C₂²×C₅	1	2	yes	—
195	#435	—	2	1	no	—
196	#435	—	2	1	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	C₂²×C₅	1	2	yes	—
199	#431	—	2	1	no	—
200	#431	C₂²×C₅	1	1	yes	characteristic
201	#431	C₂²×C₅	1	1	yes	characteristic
202	#423	C₂²×C₅	1	1	yes	characteristic
203	#408	—	2	1	no	—
204	C₄×M₁₆	—	2	1	no	—
205	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
207	#335	C₂²×C₅	1	2	yes	—
208	#334	C₂²×C₅	1	2	yes	—
209	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
210	D₄⋊C₈	C₂²×C₅	1	2	yes	—
211	D₄⋊C₈	C₂²×C₅	1	2	yes	—
212	D₄⋊C₈	C₂²×C₅	1	2	yes	—
213	#322	C₂²×C₅	1	2	yes	—
214	C₈²	C₂²×C₅	1	2	yes	—
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
218	C₅×Q₈	—	2	1	no	—
219	C₅×Q₈	—	2	1	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	2	2	no	—
223	C₅×D₄	—	2	2	no	—
224	C₅×D₄	—	2	1	no	—
225	C₅×D₄	—	4	2	no	—
226	C₅×D₄	—	4	2	no	—
227	C₅×D₄	—	4	4	no	—
228	C₅×D₄	—	4	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	2	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	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	4	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	—	2	1	no	—
255	C₅×C₈	—	2	1	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	—	4	1	no	—
258	C₅×C₈	—	4	1	no	—
259	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
260	C₂×#41	—	2	1	no	—
261	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
262	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
263	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
264	#131	—	4	4	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
273	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
274	#127	C₂×C₄×C₅	1	1	yes	characteristic
275	#124	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	C₂×C₄×C₅	1	2	yes	—
278	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
279	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
285	C₄×D₄	C₂³×C₅	1	2	yes	—
286	#117	—	2	1	no	—
287	#117	C₂×C₄×C₅	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	#107	C₂×C₄×C₅	1	2	yes	—
291	#106	C₂×C₄×C₅	1	2	yes	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
297	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₅	1	2	yes	—
300	#103	C₂×C₄×C₅	1	2	yes	—
301	#102	C₂×C₄×C₅	1	2	yes	—
302	#102	C₂×C₄×C₅	1	2	yes	—
303	#102	C₂×C₄×C₅	1	2	yes	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
310	#97	—	2	1	no	—
311	#97	—	2	1	no	—
312	#97	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₅×D₄	1	1	yes	characteristic
315	C₄×C₈	C₅×D₄	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₅	1	2	yes	—
317	C₄×C₈	C₂³×C₅	1	2	yes	—
318	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	4	1	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	4	2	no	—
326	C₂²×C₅	—	4	1	no	—
327	C₂²×C₅	—	4	1	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	4	1	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	—	4	1	no	—
337	C₄×C₅	#443	1	2	yes	—
338	C₄×C₅	#568	1	1	yes	characteristic
339	C₄×C₅	#568	1	1	yes	characteristic
340	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₄×C₅	#575	1	1	yes	characteristic
342	#41	—	4	1	no	—
343	#41	—	4	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
353	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₅×#41	1	1	yes	characteristic
361	SD₁₆	—	4	2	no	—
362	D₈	—	4	2	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	4	2	no	—
366	M₁₆	—	4	4	no	—
367	M₁₆	—	4	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
377	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
385	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
386	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
397	C₄²	C₅×#41	1	1	yes	characteristic
398	C₄²	C₂⁴×C₅	1	1	yes	characteristic
399	C₂×C₅	—	4	1	no	—
400	C₂×C₅	—	8	1	no	—
401	C₂×C₅	—	8	2	no	—
402	C₂×C₅	#2930	1	1	yes	characteristic
403	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂×C₅	C₂×#443	1	1	yes	characteristic
405	C₂³	—	2	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
408	Q₈	—	2	1	no	—
409	Q₈	—	2	1	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	2	1	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
435	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
436	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
450	C₅	#17945	1	1	yes	characteristic, direct product factor, Sylow
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	C₅×#443	1	2	yes	—
469	C₄	C₅×#568	1	1	yes	characteristic
470	C₄	C₅×#568	1	1	yes	characteristic
471	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₄	C₅×#575	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	8	1	no	—
475	C₂	—	8	2	no	—
476	C₂	C₅×#2930	1	1	yes	characteristic
477	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂	C₂×C₅×#443	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	C₅×#3106	C₂
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
2. C₅×#2965	C₂	semidirect
3. C₅×#2931	C₂	semidirect
4. C₅×#1590	C₂	semidirect
5. C₅×#1589	C₂	semidirect
6. C₅×#1586	C₂	semidirect
7. C₅×#1585	C₂	semidirect
8. C₅×#1574	C₂	semidirect
9. C₅×#1489	C₂	semidirect
10. C₅×#1484	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
49. #17945	C₅	direct (N × H)
111. #2965	C₂×C₅	semidirect
112. #2931	C₂×C₅	semidirect
113. #1590	C₂×C₅	semidirect
114. #1589	C₂×C₅	semidirect
115. #1586	C₂×C₅	semidirect
116. #1585	C₂×C₅	semidirect
117. #1574	C₂×C₅	semidirect
118. #1489	C₂×C₅	semidirect
119. #1484	C₂×C₅	semidirect
120. C₈×M₁₆	C₂×C₅	semidirect
450. C₅	#17945	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×#3106	2
C₅×#2965	2
C₅×#2931	2
C₅×#1590	2
C₅×#1589	2
C₅×#1586	2
C₅×#1585	2
C₅×#1574	2
C₅×#1489	2
C₅×#1484	2
C₅×C₈×M₁₆	2
#17945	5

Subgroups — C5×#17945 #11940665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17945 #11940665