Subgroups — C₅×#19462 #11942182

Order 1280.

680 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3109	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2974	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	2	yes	maximal, complemented
6	C₅×#1691	C₂	1	2	yes	maximal, complemented
7	C₅×#1681	C₂	1	2	yes	maximal, complemented
8	C₅×#1671	C₂	1	2	yes	maximal, complemented
9	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	—	2	1	no	—
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#498	C₂²	1	2	yes	complemented
17	C₅×#486	C₂²	1	2	yes	complemented
18	C₅×#481	—	2	1	no	—
19	C₅×#481	—	2	1	no	—
20	C₅×#481	—	2	1	no	—
21	C₅×#476	—	2	2	no	—
22	C₅×#476	C₂²	1	1	yes	characteristic
23	C₅×#476	C₂²	1	1	yes	characteristic
24	C₅×#461	—	2	1	no	—
25	C₅×#461	—	2	1	no	—
26	C₅×#461	C₂²	1	2	yes	—
27	C₅×#461	C₂²	1	2	yes	—
28	C₅×#459	C₂²	1	1	yes	characteristic
29	C₅×#459	C₂²	1	1	yes	characteristic
30	C₅×#447	—	2	1	no	—
31	C₅×#442	—	2	1	no	—
32	C₅×#442	—	2	1	no	—
33	C₅×#436	C₂²	1	2	yes	—
34	C₅×#435	—	2	2	no	—
35	C₅×C₈×D₄	C₂²	1	2	yes	—
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#432	C₂²	1	1	yes	characteristic
38	C₅×#431	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	—	2	1	no	—
41	C₅×#407	—	2	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#333	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19462	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₅	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	4	4	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	—	2	1	no	—
65	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×#127	C₂³	1	1	yes	characteristic
68	C₅×#124	—	2	1	no	—
69	C₅×#121	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	D₄	1	1	yes	characteristic
76	C₄×C₅×D₄	D₄	1	1	yes	characteristic
77	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#106	—	2	2	no	—
85	C₅×#106	—	2	2	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×C₄⋊C₈	—	2	1	no	—
89	C₅×C₄⋊C₈	D₄	1	2	yes	—
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#102	—	2	1	no	—
97	C₅×#102	—	2	1	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
108	C₅×#97	—	2	1	no	—
109	C₅×#97	—	2	1	no	—
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3227	C₂×C₅	1	1	yes	characteristic, complemented
112	#3109	C₂×C₅	1	1	yes	characteristic
113	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
114	#2974	C₂×C₅	1	1	yes	characteristic, complemented
115	#1701	C₂×C₅	1	2	yes	complemented
116	#1691	C₂×C₅	1	2	yes	complemented
117	#1681	C₂×C₅	1	2	yes	complemented
118	#1671	C₂×C₅	1	2	yes	complemented
119	#1573	C₂×C₅	1	1	yes	characteristic, complemented
120	#1556	C₂×C₅	1	1	yes	characteristic, complemented
121	#1551	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	2	1	no	—
123	C₅×#41	—	8	2	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	4	2	no	—
127	C₂×C₅×Q₈	—	4	2	no	—
128	C₂×C₅×Q₈	—	4	1	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	4	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	4	1	no	—
144	C₂²×C₄×C₅	—	4	1	no	—
145	C₂²×C₄×C₅	—	8	2	no	—
146	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	1	yes	characteristic
149	C₅×SD₁₆	—	4	4	no	—
150	C₅×SD₁₆	—	4	4	no	—
151	C₅×D₈	—	4	2	no	—
152	C₅×D₈	—	4	2	no	—
153	C₅×M₁₆	—	8	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	4	2	no	—
159	C₂×C₅×C₈	—	8	2	no	—
160	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	4	1	no	—
168	C₅×C₄⋊C₄	—	4	1	no	—
169	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	2	1	no	—
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	4	1	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅	#41	1	1	yes	characteristic
180	C₄²×C₅	C₂⁴	1	1	yes	characteristic
181	C₂²×SD₁₆	—	2	1	no	—
182	#532	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
185	#498	C₂²×C₅	1	2	yes	complemented
186	#486	C₂²×C₅	1	2	yes	complemented
187	#481	—	2	1	no	—
188	#481	—	2	1	no	—
189	#481	—	2	1	no	—
190	#476	—	2	2	no	—
191	#476	C₂²×C₅	1	1	yes	characteristic
192	#476	C₂²×C₅	1	1	yes	characteristic
193	#461	—	2	1	no	—
194	#461	—	2	1	no	—
195	#461	C₂²×C₅	1	2	yes	—
196	#461	C₂²×C₅	1	2	yes	—
197	#459	C₂²×C₅	1	1	yes	characteristic
198	#459	C₂²×C₅	1	1	yes	characteristic
199	#447	—	2	1	no	—
200	#442	—	2	1	no	—
201	#442	—	2	1	no	—
202	#436	C₂²×C₅	1	2	yes	—
203	#435	—	2	2	no	—
204	C₈×D₄	C₂²×C₅	1	2	yes	—
205	#432	C₂²×C₅	1	1	yes	characteristic
206	#432	C₂²×C₅	1	1	yes	characteristic
207	#431	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
209	C₂×#103	—	2	1	no	—
210	#407	—	2	1	no	—
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	#335	C₂²×C₅	1	2	yes	complemented
213	#334	C₂²×C₅	1	2	yes	complemented
214	#333	C₂²×C₅	1	2	yes	complemented
215	#332	C₂²×C₅	1	2	yes	complemented
216	#332	C₂²×C₅	1	2	yes	complemented
217	#331	C₂²×C₅	1	2	yes	complemented
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	4	2	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	—	8	1	no	—
224	C₂³×C₅	#121	1	1	yes	characteristic
225	C₅×Q₈	—	4	2	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	8	1	no	—
228	C₅×Q₈	—	8	2	no	—
229	C₅×D₄	—	2	1	no	—
230	C₅×D₄	—	2	1	no	—
231	C₅×D₄	—	2	1	no	—
232	C₅×D₄	—	4	2	no	—
233	C₅×D₄	—	4	1	no	—
234	C₅×D₄	—	4	1	no	—
235	C₅×D₄	—	4	2	no	—
236	C₅×D₄	—	8	1	no	—
237	C₅×D₄	—	8	2	no	—
238	C₅×D₄	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₅	—	2	2	no	—
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	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	8	1	no	—
250	C₂×C₄×C₅	—	8	1	no	—
251	C₂×C₄×C₅	—	8	2	no	—
252	C₂×C₄×C₅	—	8	1	no	—
253	C₂×C₄×C₅	—	8	2	no	—
254	C₂×C₄×C₅	#121	1	1	yes	characteristic
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	#121	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₅×C₈	—	2	2	no	—
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	2	no	—
263	C₅×C₈	—	4	1	no	—
264	C₅×C₈	—	4	1	no	—
265	C₅×C₈	—	4	2	no	—
266	C₂×#41	—	2	1	no	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	4	4	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
282	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
283	#127	C₂³×C₅	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	C₅×D₄	1	1	yes	characteristic
292	C₄×D₄	C₅×D₄	1	1	yes	characteristic
293	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
300	#106	—	2	2	no	—
301	#106	—	2	2	no	—
302	#106	—	2	1	no	—
303	#106	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₅×D₄	1	2	yes	—
306	C₄⋊C₈	C₂³×C₅	1	2	yes	—
307	C₄⋊C₈	C₂³×C₅	1	2	yes	—
308	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	1	no	—
313	#102	—	2	1	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	1	no	—
317	#102	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
323	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
324	#97	—	2	1	no	—
325	#97	—	2	1	no	—
326	C₄×C₈	C₂³×C₅	1	2	yes	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	4	1	no	—
331	C₂²×C₅	—	4	1	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	1	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	8	4	no	—
336	C₂²×C₅	—	8	1	no	—
337	C₂²×C₅	—	8	1	no	—
338	C₂²×C₅	—	8	1	no	—
339	C₂²×C₅	#471	1	2	yes	—
340	C₂²×C₅	C₂×#121	1	1	yes	characteristic
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	4	1	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	8	2	no	—
348	C₄×C₅	—	8	1	no	—
349	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₄×C₅	#575	1	1	yes	characteristic
351	C₄×C₅	#577	1	2	yes	—
352	C₂⁴	—	2	1	no	—
353	#41	—	8	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₅×#41	1	1	yes	characteristic
379	SD₁₆	—	4	4	no	—
380	SD₁₆	—	4	4	no	—
381	D₈	—	4	2	no	—
382	D₈	—	4	2	no	—
383	M₁₆	—	8	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	8	2	no	—
390	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
391	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₂²⋊C₄	—	4	1	no	—
407	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
408	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
409	C₄²	C₅×#41	1	1	yes	characteristic
410	C₄²	C₂⁴×C₅	1	1	yes	characteristic
411	C₂×C₅	—	2	2	no	—
412	C₂×C₅	—	4	2	no	—
413	C₂×C₅	—	8	1	no	—
414	C₂×C₅	—	16	1	no	—
415	C₂×C₅	#3042	1	1	yes	characteristic
416	C₂×C₅	#3055	1	1	yes	characteristic
417	C₂×C₅	C₂×#471	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	8	1	no	—
424	C₂³	C₅×#121	1	1	yes	characteristic
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	8	1	no	—
428	Q₈	—	8	2	no	—
429	D₄	—	2	1	no	—
430	D₄	—	2	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	8	1	no	—
437	D₄	—	8	2	no	—
438	D₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	C₅×#121	1	1	yes	characteristic
455	C₂×C₄	C₅×#121	1	1	yes	characteristic
456	C₂×C₄	C₅×#121	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₅	#19462	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₅×#471	1	2	yes	—
480	C₂²	C₂×C₅×#121	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	1	no	—
489	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
490	C₄	C₅×#575	1	1	yes	characteristic
491	C₄	C₅×#577	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	16	1	no	—
496	C₂	C₅×#3042	1	1	yes	characteristic
497	C₂	C₅×#3055	1	1	yes	characteristic
498	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3109	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3227	C₂	semidirect
3. C₂×C₅×#461	C₂	semidirect
4. C₅×#2974	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1691	C₂	semidirect
7. C₅×#1681	C₂	semidirect
8. C₅×#1671	C₂	semidirect
9. C₅×#1573	C₂	semidirect
10. C₅×#1556	C₂	semidirect
11. C₅×#1551	C₂	semidirect
16. C₅×#498	C₂²	semidirect
17. C₅×#486	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19462	C₅	direct (N × H)
111. #3227	C₂×C₅	semidirect
113. C₂×#461	C₂×C₅	semidirect
114. #2974	C₂×C₅	semidirect
115. #1701	C₂×C₅	semidirect
116. #1691	C₂×C₅	semidirect
117. #1681	C₂×C₅	semidirect
118. #1671	C₂×C₅	semidirect
119. #1573	C₂×C₅	semidirect
120. #1556	C₂×C₅	semidirect
121. #1551	C₂×C₅	semidirect
185. #498	C₂²×C₅	semidirect
186. #486	C₂²×C₅	semidirect
212. #335	C₂²×C₅	semidirect
213. #334	C₂²×C₅	semidirect
214. #333	C₂²×C₅	semidirect
215. #332	C₂²×C₅	semidirect
216. #332	C₂²×C₅	semidirect
217. #331	C₂²×C₅	semidirect
466. C₅	#19462	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×#3227	2
C₅×#3109	2
C₂×C₅×#461	2
C₅×#2974	2
C₅×#1701	2
C₅×#1691	2
C₅×#1681	2
C₅×#1671	2
C₅×#1573	2
C₅×#1556	2
C₅×#1551	2
#19462	5

Subgroups — C5×#19462 #11942182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19462 #11942182