Subgroups — C₅×#19168 #11941888

Order 1280.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3141	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3100	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1703	C₂	1	2	yes	maximal, complemented
6	C₅×#1697	C₂	1	2	yes	maximal, complemented
7	C₅×#1683	C₂	1	2	yes	maximal, complemented
8	C₅×#1677	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	—	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×#489	—	2	2	no	—
17	C₅×#487	C₂²	1	2	yes	complemented
18	C₅×#486	C₂²	1	2	yes	complemented
19	C₅×#480	—	2	1	no	—
20	C₅×#476	—	2	1	no	—
21	C₅×#476	—	2	1	no	—
22	C₅×#476	C₂²	1	2	yes	—
23	C₅×#476	C₂²	1	2	yes	—
24	C₅×#474	C₂²	1	1	yes	characteristic
25	C₅×#474	C₂²	1	1	yes	characteristic
26	C₅×#459	C₂²	1	1	yes	characteristic
27	C₅×#459	C₂²	1	1	yes	characteristic
28	C₅×#447	—	2	1	no	—
29	C₄×C₅×D₈	—	2	1	no	—
30	C₄×C₅×D₈	—	2	1	no	—
31	C₅×#436	C₂²	1	2	yes	—
32	C₅×#435	—	2	2	no	—
33	C₅×C₈×D₄	C₂²	1	2	yes	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₂×C₅×#106	—	2	1	no	—
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#417	—	2	1	no	—
39	C₅×#417	—	2	1	no	—
40	C₂×C₅×#102	—	2	1	no	—
41	C₅×#407	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
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×#333	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19168	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×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	4	4	no	—
59	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
60	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	—	2	1	no	—
65	C₅×C₄⋊Q₈	—	2	1	no	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₅×#127	C₂³	1	1	yes	characteristic
69	C₅×#124	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₅×#121	—	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	—	2	1	no	—
76	C₄×C₅×D₄	D₄	1	1	yes	characteristic
77	C₄×C₅×D₄	D₄	1	1	yes	characteristic
78	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	1	no	—
86	C₅×#107	—	2	1	no	—
87	C₅×#106	—	2	2	no	—
88	C₅×#106	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×#103	—	2	2	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×#97	D₄	1	2	yes	—
109	C₄×C₅×C₈	—	2	1	no	—
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3141	C₂×C₅	1	1	yes	characteristic, complemented
112	#3100	C₂×C₅	1	1	yes	characteristic
113	C₂×#476	C₂×C₅	1	1	yes	characteristic, complemented
114	D₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
115	#1703	C₂×C₅	1	2	yes	complemented
116	#1697	C₂×C₅	1	2	yes	complemented
117	#1683	C₂×C₅	1	2	yes	complemented
118	#1677	C₂×C₅	1	2	yes	complemented
119	#1565	C₂×C₅	1	1	yes	characteristic, complemented
120	#1548	C₂×C₅	1	1	yes	characteristic, complemented
121	#1547	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	2	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	—	2	2	no	—
127	C₂×C₅×Q₈	—	4	1	no	—
128	C₂×C₅×Q₈	—	8	2	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	2	no	—
144	C₂²×C₄×C₅	—	4	2	no	—
145	C₂²×C₄×C₅	—	4	1	no	—
146	C₂²×C₄×C₅	—	4	1	no	—
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	#41	1	1	yes	characteristic
150	C₅×D₈	—	4	2	no	—
151	C₅×D₈	—	4	2	no	—
152	C₅×M₁₆	—	2	2	no	—
153	C₅×M₁₆	—	2	2	no	—
154	C₅×M₁₆	—	4	4	no	—
155	C₅×M₁₆	—	4	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	4	4	no	—
161	C₂×C₅×C₈	—	4	2	no	—
162	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	4	1	no	—
170	C₅×C₄⋊C₄	—	4	1	no	—
171	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	4	1	no	—
178	C₅×C₂²⋊C₄	—	4	1	no	—
179	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₅	#41	1	1	yes	characteristic
182	C₄²×C₅	C₂⁴	1	1	yes	characteristic
183	C₂²×M₁₆	—	2	1	no	—
184	#532	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
187	#489	—	2	2	no	—
188	#487	C₂²×C₅	1	2	yes	complemented
189	#486	C₂²×C₅	1	2	yes	complemented
190	#480	—	2	1	no	—
191	#476	—	2	1	no	—
192	#476	—	2	1	no	—
193	#476	C₂²×C₅	1	2	yes	—
194	#476	C₂²×C₅	1	2	yes	—
195	#474	C₂²×C₅	1	1	yes	characteristic
196	#474	C₂²×C₅	1	1	yes	characteristic
197	#459	C₂²×C₅	1	1	yes	characteristic
198	#459	C₂²×C₅	1	1	yes	characteristic
199	#447	—	2	1	no	—
200	C₄×D₈	—	2	1	no	—
201	C₄×D₈	—	2	1	no	—
202	#436	C₂²×C₅	1	2	yes	—
203	#435	—	2	2	no	—
204	C₈×D₄	C₂²×C₅	1	2	yes	—
205	#431	C₂²×C₅	1	1	yes	characteristic
206	C₂×#106	—	2	1	no	—
207	#423	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
209	#417	—	2	1	no	—
210	#417	—	2	1	no	—
211	C₂×#102	—	2	1	no	—
212	#407	—	2	1	no	—
213	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
214	#335	C₂²×C₅	1	2	yes	complemented
215	#334	C₂²×C₅	1	2	yes	complemented
216	#333	C₂²×C₅	1	2	yes	complemented
217	#333	C₂²×C₅	1	2	yes	complemented
218	#332	C₂²×C₅	1	2	yes	complemented
219	#331	C₂²×C₅	1	2	yes	complemented
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	1	no	—
225	C₂³×C₅	—	8	1	no	—
226	C₂³×C₅	#121	1	1	yes	characteristic
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	4	1	no	—
229	C₅×Q₈	—	8	2	no	—
230	C₅×Q₈	—	8	2	no	—
231	C₅×D₄	—	2	1	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	—	2	1	no	—
234	C₅×D₄	—	4	2	no	—
235	C₅×D₄	—	4	1	no	—
236	C₅×D₄	—	4	1	no	—
237	C₅×D₄	—	4	1	no	—
238	C₅×D₄	—	4	1	no	—
239	C₅×D₄	—	8	1	no	—
240	C₅×D₄	—	8	2	no	—
241	C₅×D₄	#137	1	2	yes	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	2	no	—
256	C₂×C₄×C₅	—	8	2	no	—
257	C₂×C₄×C₅	—	8	2	no	—
258	C₂×C₄×C₅	#121	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	#121	1	1	yes	characteristic
261	C₂×C₄×C₅	#135	1	2	yes	—
262	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	2	2	no	—
268	C₅×C₈	—	4	2	no	—
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂×D₈	—	2	1	no	—
277	C₂×D₈	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	4	4	no	—
281	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
282	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
290	#127	C₂³×C₅	1	1	yes	characteristic
291	#124	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	C₅×D₄	1	1	yes	characteristic
299	C₄×D₄	C₅×D₄	1	1	yes	characteristic
300	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
301	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
307	#107	—	2	1	no	—
308	#107	—	2	1	no	—
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂³×C₅	1	2	yes	—
314	C₄⋊C₈	C₂³×C₅	1	2	yes	—
315	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	1	no	—
322	#102	—	2	1	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	1	no	—
326	#102	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	#97	C₅×D₄	1	2	yes	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	C₂³×C₅	1	2	yes	—
333	C₂²×C₅	—	2	1	no	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	1	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	8	4	no	—
342	C₂²×C₅	—	8	1	no	—
343	C₂²×C₅	—	8	1	no	—
344	C₂²×C₅	—	8	1	no	—
345	C₂²×C₅	#463	1	2	yes	—
346	C₂²×C₅	C₂×#121	1	1	yes	characteristic
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	8	1	no	—
353	C₄×C₅	—	8	2	no	—
354	C₄×C₅	#463	1	2	yes	—
355	C₄×C₅	C₂×#135	1	1	yes	characteristic
356	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₄×C₅	C₂×#137	1	1	yes	characteristic
358	C₄×C₅	#575	1	1	yes	characteristic
359	C₂⁴	—	2	1	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	4	1	no	—
365	C₂×Q₈	—	8	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₅×#41	1	1	yes	characteristic
387	D₈	—	4	2	no	—
388	D₈	—	4	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	4	4	no	—
392	M₁₆	—	4	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	4	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
400	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
417	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
418	C₄²	C₅×#41	1	1	yes	characteristic
419	C₄²	C₂⁴×C₅	1	1	yes	characteristic
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	4	2	no	—
422	C₂×C₅	—	8	1	no	—
423	C₂×C₅	—	16	1	no	—
424	C₂×C₅	C₂×#463	1	1	yes	characteristic
425	C₂×C₅	#3056	1	1	yes	characteristic
426	C₂×C₅	#3068	1	1	yes	characteristic
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	8	1	no	—
433	C₂³	C₅×#121	1	1	yes	characteristic
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	8	2	no	—
437	Q₈	—	8	2	no	—
438	D₄	—	2	1	no	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	8	1	no	—
447	D₄	—	8	2	no	—
448	D₄	C₅×#137	1	2	yes	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	8	2	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	C₅×#121	1	1	yes	characteristic
466	C₂×C₄	C₅×#121	1	1	yes	characteristic
467	C₂×C₄	C₅×#121	1	1	yes	characteristic
468	C₂×C₄	C₅×#135	1	2	yes	—
469	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
470	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	1	no	—
479	C₅	#19168	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	C₅×#463	1	2	yes	—
493	C₂²	C₂×C₅×#121	1	1	yes	characteristic
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	2	no	—
501	C₄	C₅×#463	1	2	yes	—
502	C₄	C₂×C₅×#135	1	1	yes	characteristic
503	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₄	C₂×C₅×#137	1	1	yes	characteristic
505	C₄	C₅×#575	1	1	yes	characteristic
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	8	1	no	—
509	C₂	—	16	1	no	—
510	C₂	C₂×C₅×#463	1	1	yes	characteristic
511	C₂	C₅×#3056	1	1	yes	characteristic
512	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3100	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×#3141	C₂	semidirect
3. C₂×C₅×#476	C₂	semidirect
4. C₅×D₄×M₁₆	C₂	semidirect
5. C₅×#1703	C₂	semidirect
6. C₅×#1697	C₂	semidirect
7. C₅×#1683	C₂	semidirect
8. C₅×#1677	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₅×#1548	C₂	semidirect
11. C₅×#1547	C₂	semidirect
17. C₅×#487	C₂²	semidirect
18. C₅×#486	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#333	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19168	C₅	direct (N × H)
111. #3141	C₂×C₅	semidirect
113. C₂×#476	C₂×C₅	semidirect
114. D₄×M₁₆	C₂×C₅	semidirect
115. #1703	C₂×C₅	semidirect
116. #1697	C₂×C₅	semidirect
117. #1683	C₂×C₅	semidirect
118. #1677	C₂×C₅	semidirect
119. #1565	C₂×C₅	semidirect
120. #1548	C₂×C₅	semidirect
121. #1547	C₂×C₅	semidirect
188. #487	C₂²×C₅	semidirect
189. #486	C₂²×C₅	semidirect
214. #335	C₂²×C₅	semidirect
215. #334	C₂²×C₅	semidirect
216. #333	C₂²×C₅	semidirect
217. #333	C₂²×C₅	semidirect
218. #332	C₂²×C₅	semidirect
219. #331	C₂²×C₅	semidirect
479. C₅	#19168	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×#3141	2
C₅×#3100	2
C₂×C₅×#476	2
C₅×D₄×M₁₆	2
C₅×#1703	2
C₅×#1697	2
C₅×#1683	2
C₅×#1677	2
C₅×#1565	2
C₅×#1548	2
C₅×#1547	2
#19168	5

Subgroups — C5×#19168 #11941888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19168 #11941888