Finite Group Databasebeta

← C5×#68334 #14282964

Subgroups — C5×#68334 #14282964

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5627C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3C5×D3×#95C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6C5×#4470C211yesmaximal, characteristic, complemented
7C5×#4451C211yesmaximal, characteristic, complemented
8C5×#1504—31nomaximal, Hall
9C2×C5×#239C411yescharacteristic, complemented
10C22×C4×C5×D3—21no—
11C22×C4×C5×D3C2211yescharacteristic
12C3×C5×C22⋊Q8C2211yescharacteristic
13C5×#946C411yescharacteristic, complemented
14C5×#930C2211yescharacteristic
15C2×C5×ΓL(1,𝔽25)—21no—
16C5×#895C411yescharacteristic, complemented
17C5×#894—21no—
18C5×#893—21no—
19C5×#892C411yescharacteristic, complemented
20C5×#882—21no—
21C5×#67⋊C4—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24C5×C3⋊#95—21no—
25C5×C3⋊#95C2211yescharacteristic
26C5×#830C2211yescharacteristic
27C5×(C2×D3)⋊C8—21no—
28#68334C511yesmaximal, characteristic, direct product factor, Hall
29C5×#525—31no—
30C5×#407—31no—
31C2×C5×#95—31no—
32C5×#328—31no—
33C5×#328D311yescharacteristic, complemented
34C5×#327—31no—
35C5×#327—31no—
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C5×#67—21no—
41C22×C5×Dic3—21no—
42C22×C5×Dic3D411yescharacteristic
43C5×#239—42no—
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12C2×C411yescharacteristic, complemented
47C2×C4×C5×D3—24no—
48C2×C4×C5×D3—21no—
49C2×C4×C5×D3—42no—
50C2×C4×C5×D3—42no—
51C2×C4×C5×D3—42no—
52C2×C4×C5×D3C2×C411yescharacteristic
53C2×C4×C5×D3C2×C411yescharacteristic
54C2×C4×C5×D3D411yescharacteristic
55C2×C4×C5×D3D411yescharacteristic
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
59C3×C5×C22⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×C4⋊Dic3C2×C411yescharacteristic, complemented
65C5×Dic3⋊C4—21no—
66C4×C5×Dic3—21no—
67C2×C5×C3⋊C8—21no—
68C5×ΓL(1,𝔽25)—42no—
69#5627C2×C511yescharacteristic
70#4726C2×C511yescharacteristic, complemented
71D3×#95C2×C511yescharacteristic, complemented
72C3×#328C2×C511yescharacteristic, complemented
73#4538C2×C511yescharacteristic, complemented
74#4470C2×C511yescharacteristic, complemented
75#4451C2×C511yescharacteristic, complemented
76C2×C5×#41—31no—
77C23×C4×C5—31no—
78C23×C4×C5—61no—
79C2×C5×M16—61no—
80C5×#123—61no—
81C5×C22⋊Q8—31no—
82C5×C22⋊Q8C2×D311yescharacteristic
83C5×#121—31no—
84C5×#121—31no—
85C5×#120—61no—
86C4×C5×D4—61no—
87C4×C5×D4—61no—
88C5×#117—31no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C5×#95—31no—
93C5×#95—61no—
94C5×#95C2×D311yescharacteristic
95#1504—31noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—22no—
100C22×C5×D3—22no—
101C22×C5×D3—21no—
102C22×C5×D3C22⋊C411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C5×#67—41no—
114C5×#67—41no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3C22⋊C411yescharacteristic
121C2×C5×Dic3C22⋊C411yescharacteristic
122C5×D12—41no—
123C5×D12—42no—
124C5×D12—42no—
125C4×C5×D3—22no—
126C4×C5×D3—22no—
127C4×C5×D3—41no—
128C4×C5×D3—41no—
129C4×C5×D3—42no—
130C4×C5×D3—48no—
131C3×C5×C8—41no—
132C5×C3⋊C8—41no—
133C2×#239C4×C511yescharacteristic, complemented
134C22×C4×D3—21no—
135C22×C4×D3C22×C511yescharacteristic
136C3×C22⋊Q8C22×C511yescharacteristic
137#946C4×C511yescharacteristic, complemented
138#930C22×C511yescharacteristic
139C2×ΓL(1,𝔽25)—21no—
140#895C4×C511yescharacteristic, complemented
141#894—21no—
142#893—21no—
143#892C4×C511yescharacteristic, complemented
144#882—21no—
145#67⋊C4—21no—
146C3×C22⋊C8C22×C511yescharacteristic
147C3×#95C22×C511yescharacteristic
148C3⋊#95—21no—
149C3⋊#95C22×C511yescharacteristic
150#830C22×C511yescharacteristic
151(C2×D3)⋊C8—21no—
152C24×C5—31no—
153C5×#41—122no—
154C2×C5×Q8C4×D311yescharacteristic, complemented
155C2×C5×D4—31no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4—61no—
159C22×C4×C5—21no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—61no—
166C22×C4×C5—64no—
167C22×C4×C5—61no—
168C22×C4×C5—122no—
169C22×C4×C5—122no—
170C22×C4×C5—122no—
171C22×C4×C5C22×D311yescharacteristic
172C5×M16—122no—
173C2×C5×C8—21no—
174C2×C5×C8—61no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—31no—
177C5×C4⋊C4—61no—
178C5×C4⋊C4C4×D311yescharacteristic, complemented
179C5×C22⋊C4—21no—
180C5×C22⋊C4—61no—
181C5×C22⋊C4—61no—
182C5×C22⋊C4—61no—
183C5×C22⋊C4—61no—
184C42×C5—61no—
185#525—31no—
186#407—31no—
187C2×#95—31no—
188#328—31no—
189#328C5×D311yescharacteristic, complemented
190#327—31no—
191#327—31no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C5×D3—24no—
198C2×C5×D3—24no—
199C2×C5×D3—21no—
200C2×C5×D3—21no—
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C2×C5×D3—41no—
205C2×C5×D3—41no—
206C2×C5×D3#9912yes—
207C2×C5×D3#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—42no—
211C3×C4×C5—41no—
212C3×C4×C5—41no—
213C5×Dic3—21no—
214C5×Dic3—21no—
215C5×Dic3—42no—
216C5×Dic3—41no—
217C23×D3C5×D411yescharacteristic
218C2×C3×Q8C2×C4×C511yescharacteristic, complemented
219C22×C3×C4—21no—
220C22×C3×C4C23×C511yescharacteristic
221C2×#67—21no—
222C22×Dic3—21no—
223C22×Dic3C5×D411yescharacteristic
224#239—42no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12C2×C4×C511yescharacteristic, complemented
228C2×C4×D3—24no—
229C2×C4×D3—21no—
230C2×C4×D3—42no—
231C2×C4×D3—42no—
232C2×C4×D3—42no—
233C2×C4×D3C2×C4×C511yescharacteristic
234C2×C4×D3C2×C4×C511yescharacteristic
235C2×C4×D3C5×D411yescharacteristic
236C2×C4×D3C5×D411yescharacteristic
237C2×C3×C8—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C2×C4×C511yescharacteristic, complemented
240C3×C22⋊C4—21no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—21no—
245C4⋊Dic3C2×C4×C511yescharacteristic, complemented
246Dic3⋊C4—21no—
247C4×Dic3—21no—
248C2×C3⋊C8—21no—
249ΓL(1,𝔽25)—42no—
250C23×C5—31no—
251C23×C5—31no—
252C23×C5—62no—
253C23×C5—62no—
254C23×C5—61no—
255C23×C5—61no—
256C23×C5—61no—
257C23×C5D3×D411yescharacteristic
258C5×Q8—41no—
259C5×D4—121no—
260C5×D4—122no—
261C5×D4—122no—
262C5×D4—121no—
263C5×D4—121no—
264C2×C4×C5—22no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—31no—
268C2×C4×C5—31no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—61no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5—122no—
279C2×C4×C5—128no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C5×C8—41no—
286C5×C8—121no—
287C2×#41—31no—
288C23×C4—31no—
289C23×C4—61no—
290C2×M16—61no—
291#123—61no—
292C22⋊Q8—31no—
293C22⋊Q8C2×C5×D311yescharacteristic
294#121—31no—
295#121—31no—
296#120—61no—
297C4×D4—61no—
298C4×D4—61no—
299#117—31no—
300C22⋊C8—31no—
301C22⋊C8—61no—
302C22⋊C8C2×C5×D311yescharacteristic
303#95—31no—
304#95—61no—
305#95C2×C5×D311yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311C5×D3—22no—
312C5×D3—22no—
313C5×D3—81no—
314C23×C3C2×C5×D411yescharacteristic
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—21no—
320C22×D3C5×C22⋊C411yescharacteristic
321C22×D3C5×C22⋊C411yescharacteristic
322C3×Q8—41no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4C22×C4×C511yescharacteristic
330C2×C3×C4C2×C5×D411yescharacteristic
331#67—41no—
332#67—41no—
333C2×Dic3—22no—
334C2×Dic3—21no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3C5×C22⋊C411yescharacteristic
339C2×Dic3C5×C22⋊C411yescharacteristic
340D12—41no—
341D12—42no—
342D12—42no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—41no—
346C4×D3—41no—
347C4×D3—42no—
348C4×D3—48no—
349C3×C8—41no—
350C3⋊C8—41no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—64no—
356C22×C5—64no—
357C22×C5—61no—
358C22×C5—61no—
359C22×C5—61no—
360C22×C5—61no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5—121no—
364C22×C5D3×C22⋊C411yescharacteristic
365C22×C5#91411yescharacteristic
366C22×C5#91811yescharacteristic
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—41no—
371C4×C5—41no—
372C4×C5—61no—
373C4×C5—61no—
374C4×C5—122no—
375C4×C5—121no—
376C24—31no—
377#41—122no—
378C2×Q8C4×C5×D311yescharacteristic, complemented
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4—61no—
383C22×C4—21no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—61no—
390C22×C4—64no—
391C22×C4—61no—
392C22×C4—122no—
393C22×C4—122no—
394C22×C4—122no—
395C22×C4C22×C5×D311yescharacteristic
396M16—122no—
397C2×C8—21no—
398C2×C8—61no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—61no—
402C4⋊C4C4×C5×D311yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C42—61no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3C2×C5×C22⋊C411yescharacteristic
413C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
414C22×C3C5×#13711yescharacteristic
415C2×D3—24no—
416C2×D3—24no—
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—41no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3C5×#9912yes—
425C2×D3C5×#10412yes—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—41no—
431Dic3—21no—
432Dic3—21no—
433Dic3—42no—
434Dic3—41no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—62no—
438C2×C5—62no—
439C2×C5—241no—
440C2×C5D3×#9911yescharacteristic
441C2×C5#480311yescharacteristic
442C2×C5D3×#10411yescharacteristic
443C23—31no—
444C23—31no—
445C23—62no—
446C23—62no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23C5×D3×D411yescharacteristic
451Q8—41no—
452D4—121no—
453D4—122no—
454D4—122no—
455D4—121no—
456D4—121no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—122no—
472C2×C4—128no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4C2×C4×C5×D311yescharacteristic
477C2×C4C5×D3×D411yescharacteristic
478C8—41no—
479C8—121no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3C2×C5×#9911yescharacteristic
483C2×C3C5×#41711yescharacteristic
484C2×C3C2×C5×#10411yescharacteristic
485D3—22no—
486D3—22no—
487D3—81no—
488C5#6833411yescharacteristic, direct product factor, Sylow
489C22—21no—
490C22—21no—
491C22—32no—
492C22—32no—
493C22—64no—
494C22—64no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22C5×D3×C22⋊C411yescharacteristic
503C22C5×#91411yescharacteristic
504C22C5×#91811yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—41no—
509C4—41no—
510C4—61no—
511C4—61no—
512C4—122no—
513C4—121no—
514C3C5×#150411yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—62no—
518C2—62no—
519C2—241no—
520C2C5×D3×#9911yescharacteristic
521C2C5×#480311yescharacteristic
522C2C5×D3×#10411yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5627C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#328D3
hypocenterC3C5×#1504
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#328

Complements

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

NH ≅ G/Ntype
2. C5×#4726C2semidirect
3. C5×D3×#95C2semidirect
4. C3×C5×#328C2semidirect
5. C5×#4538C2semidirect
6. C5×#4470C2semidirect
7. C5×#4451C2semidirect
9. C2×C5×#239C4semidirect
13. C5×#946C4semidirect
16. C5×#895C4semidirect
19. C5×#892C4semidirect
28. #68334C5direct (N × H)
33. C5×#328D3semidirect
37. C2×C3×C5×Q8C2×C4semidirect
46. C2×C5×D12C2×C4semidirect
58. C3×C5×C4⋊C4C2×C4semidirect
64. C5×C4⋊Dic3C2×C4semidirect
70. #4726C2×C5semidirect
71. D3×#95C2×C5semidirect
72. C3×#328C2×C5semidirect
73. #4538C2×C5semidirect
74. #4470C2×C5semidirect
75. #4451C2×C5semidirect
133. C2×#239C4×C5semidirect
137. #946C4×C5semidirect
140. #895C4×C5semidirect
143. #892C4×C5semidirect
154. C2×C5×Q8C4×D3semidirect
178. C5×C4⋊C4C4×D3semidirect
189. #328C5×D3semidirect
218. C2×C3×Q8C2×C4×C5semidirect
227. C2×D12C2×C4×C5semidirect
239. C3×C4⋊C4C2×C4×C5semidirect
245. C4⋊Dic3C2×C4×C5semidirect
378. C2×Q8C4×C5×D3semidirect
402. C4⋊C4C4×C5×D3semidirect
409. C3×C5#1504semidirect
488. C5#68334direct (N × H)
514. C3C5×#1504semidirect

Maximal subgroups

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

subgroupindex
C5×#56272
C5×#47262
C5×D3×#952
C3×C5×#3282
C5×#45382
C5×#44702
C5×#44512
C5×#15043
#683345