Finite Group Databasebeta

← C5×#68290 #14288530

Subgroups — C5×#68290 #14288530

Order 1920.

576 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5605C211yesmaximal, characteristic
2C5×#5034C211yesmaximal, characteristic, complemented
3C5×#4735C211yesmaximal, characteristic, complemented
4C5×#4677C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic, complemented
6C5×#4468C211yesmaximal, characteristic, complemented
7C5×#4451C211yesmaximal, characteristic, complemented
8C5×#1613—31nomaximal, Hall
9C2×C5×D3×D4—21no—
10C3×C5×#121C2211yescharacteristic
11C5×#939—21no—
12C5×#937—21no—
13C5×#930C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C5×(C2×D3)⋊C4C2211yescharacteristic
16C2×C5×C4⋊Dic3—21no—
17C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
18C5×#894—21no—
19C5×#883—21no—
20C5×#882—21no—
21C3×C5×C22⋊C8C2211yescharacteristic, complemented
22C3×C5×#95C2211yescharacteristic, complemented
23C5×#832—21no—
24C5×#830C2211yescharacteristic, complemented
25C5×#821—21no—
26C5×#817—21no—
27C5×#808—21no—
28#68290C511yesmaximal, characteristic, direct product factor, Hall
29C5×#534—31no—
30C5×#481—31no—
31C5×#481—31no—
32C5×#399—31no—
33C5×#327—31no—
34C5×#327D311yescharacteristic, complemented
35C5×#323—31no—
36C23×C5×D3—21no—
37C23×C5×D3D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C22×C5×Dic3—21no—
46C22×C5×Dic3D411yescharacteristic
47C5×D3×D4—42no—
48C5×D3×D4—42no—
49C2×C5×D12—21no—
50C2×C5×D12D411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—42no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—42no—
64C5×C4⋊Dic3D411yescharacteristic
65C5×Dic3⋊C4—21no—
66C2×C5×C3⋊C8—21no—
67#5605C2×C511yescharacteristic
68#5034C2×C511yescharacteristic, complemented
69#4735C2×C511yescharacteristic, complemented
70#4677C2×C511yescharacteristic, complemented
71C3×#327C2×C511yescharacteristic, complemented
72#4468C2×C511yescharacteristic, complemented
73#4451C2×C511yescharacteristic, complemented
74C22×C5×D4—61no—
75C5×#123—61no—
76C5×#123—61no—
77C5×#121—31no—
78C5×#121—61no—
79C5×#121C2×D311yescharacteristic
80C5×#120—61no—
81C5×#120—61no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—61no—
84C2×C5×C22⋊C4—31no—
85C2×C5×C22⋊C4—61no—
86C5×#106—61no—
87C5×#106—61no—
88C5×#102—61no—
89C5×#102—61no—
90C5×C22⋊C8—31no—
91C5×C22⋊C8C2×D311yescharacteristic, complemented
92C5×#95C2×D311yescharacteristic, complemented
93#1613—31noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—42no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—81no—
103C22×C5×D3—81no—
104C22×C5×D3SD1612yes—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C5×#67—42no—
116C5×#67—41no—
117C5×#67—41no—
118C5×#67—81no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C5×D12—41no—
126C5×D12—42no—
127C4×C5×D3—42no—
128C3×C5×C8—41no—
129C5×C3⋊C8—41no—
130C2×D3×D4—21no—
131C3×#121C22×C511yescharacteristic
132#939—21no—
133#937—21no—
134#930C22×C511yescharacteristic
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4C22×C511yescharacteristic
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3C22×C511yescharacteristic, complemented
139#894—21no—
140#883—21no—
141#882—21no—
142C3×C22⋊C8C22×C511yescharacteristic, complemented
143C3×#95C22×C511yescharacteristic, complemented
144#832—21no—
145#830C22×C511yescharacteristic, complemented
146#821—21no—
147#817—21no—
148#808—21no—
149C24×C5—31no—
150C24×C5—61no—
151C2×C5×D4—21no—
152C2×C5×D4—31no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—61no—
157C2×C5×D4—122no—
158C2×C5×D4—122no—
159C2×C5×D4D1211yescharacteristic
160C22×C4×C5—21no—
161C22×C4×C5—31no—
162C22×C4×C5—61no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C5×C4⋊C4—31no—
168C5×C4⋊C4—61no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—122no—
172C5×C4⋊C4D1211yescharacteristic
173C5×C22⋊C4—21no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4—61no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—122no—
180#534—31no—
181#481—31no—
182#481—31no—
183#399—31no—
184#327—31no—
185#327C5×D311yescharacteristic, complemented
186#323—31no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5#12011yescharacteristic
193C22×C3×C5C2×SD1611yescharacteristic
194C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
195C2×C5×D3—22no—
196C2×C5×D3—41no—
197C2×C5×D3—41no—
198C2×C5×D3—42no—
199C2×C5×D3—41no—
200C2×C5×D3—41no—
201C2×C5×D3—41no—
202C2×C5×D3—81no—
203C2×C5×D3—84no—
204C3×C4×C5—21no—
205C3×C4×C5—21no—
206C3×C4×C5—42no—
207C3×C4×C5—41no—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C5×Dic3—81no—
211C23×D3—21no—
212C23×D3C5×D411yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4C5×D411yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4C23×C511yescharacteristic
217C2×#67—21no—
218C2×#67—21no—
219C2×#67—21no—
220C22×Dic3—21no—
221C22×Dic3C5×D411yescharacteristic
222D3×D4—42no—
223D3×D4—42no—
224C2×D12—21no—
225C2×D12C5×D411yescharacteristic
226C2×C4×D3—21no—
227C2×C3×C8—21no—
228C3×C4⋊C4C5×D411yescharacteristic
229C3×C22⋊C4—21no—
230#217—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—42no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3—42no—
239C4⋊Dic3C5×D411yescharacteristic
240Dic3⋊C4—21no—
241C2×C3⋊C8—21no—
242C23×C5—21no—
243C23×C5—32no—
244C23×C5—61no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—121no—
248C23×C5—121no—
249C23×C5—122no—
250C23×C5—241no—
251C23×C5—241no—
252C23×C5D3×D411yescharacteristic
253C5×D4—41no—
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—121no—
257C5×D4—122no—
258C5×D4—122no—
259C5×D4—121no—
260C5×D4—121no—
261C5×D4—241no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—122no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5C2×D1211yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C5×C8—41no—
277C5×C8—121no—
278C22×D4—61no—
279#123—61no—
280#123—61no—
281#121—31no—
282#121—61no—
283#121C2×C5×D311yescharacteristic
284#120—61no—
285#120—61no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—61no—
288C2×C22⋊C4—31no—
289C2×C22⋊C4—61no—
290#106—61no—
291#106—61no—
292#102—61no—
293#102—61no—
294C22⋊C8—31no—
295C22⋊C8C2×C5×D311yescharacteristic, complemented
296#95C2×C5×D311yescharacteristic, complemented
297C2×C3×C5—21no—
298C2×C3×C5—21no—
299C2×C3×C5—81no—
300C2×C3×C5#45011yescharacteristic
301C2×C3×C5#45311yescharacteristic
302C2×C3×C5#45811yescharacteristic
303C5×D3—42no—
304C5×D3—81no—
305C23×C3—21no—
306C23×C3C2×C5×D411yescharacteristic
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—42no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—81no—
314C22×D3—81no—
315C22×D3C5×SD1612yes—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—41no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4C2×C5×D411yescharacteristic
325C2×C3×C4C2×C5×D411yescharacteristic
326#67—42no—
327#67—41no—
328#67—41no—
329#67—81no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336D12—41no—
337D12—42no—
338C4×D3—42no—
339C3×C8—41no—
340C3⋊C8—41no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—41no—
344C22×C5—41no—
345C22×C5—41no—
346C22×C5—62no—
347C22×C5—122no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5—121no—
352C22×C5—121no—
353C22×C5—241no—
354C22×C5—244no—
355C22×C5#88211yescharacteristic
356C22×C5#91111yescharacteristic
357C22×C5D3×SD1611yescharacteristic
358C4×C5—21no—
359C4×C5—21no—
360C4×C5—42no—
361C4×C5—41no—
362C4×C5—121no—
363C4×C5—121no—
364C4×C5—241no—
365C24—31no—
366C24—61no—
367C2×D4—21no—
368C2×D4—31no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—122no—
374C2×D4—122no—
375C2×D4C5×D1211yescharacteristic
376C22×C4—21no—
377C22×C4—31no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4C22×C5×D311yescharacteristic
381C2×C8—21no—
382C2×C8—61no—
383C4⋊C4—31no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—122no—
388C4⋊C4C5×D1211yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—122no—
396C3×C5#161311yescharacteristic, complemented, Hall
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3C5×#12011yescharacteristic
403C22×C3C2×C5×SD1611yescharacteristic
404C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
405C2×D3—22no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—42no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—81no—
413C2×D3—84no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—42no—
417C3×C4—41no—
418Dic3—41no—
419Dic3—41no—
420Dic3—81no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—81no—
424C2×C5—122no—
425C2×C5—241no—
426C2×C5#474211yescharacteristic
427C2×C5#477611yescharacteristic
428C2×C5#482211yescharacteristic
429C23—21no—
430C23—32no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23—121no—
435C23—121no—
436C23—122no—
437C23—241no—
438C23—241no—
439C23C5×D3×D411yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—121no—
444D4—122no—
445D4—122no—
446D4—121no—
447D4—121no—
448D4—241no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—122no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4C2×C5×D1211yescharacteristic
462C2×C4C5×D3×D411yescharacteristic
463C8—41no—
464C8—121no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—81no—
468C2×C3C5×#45011yescharacteristic
469C2×C3C5×#45311yescharacteristic
470C2×C3C5×#45811yescharacteristic
471D3—42no—
472D3—81no—
473C5#6829011yescharacteristic, direct product factor, Sylow
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—62no—
480C22—122no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—121no—
485C22—121no—
486C22—241no—
487C22—244no—
488C22C5×#88211yescharacteristic
489C22C5×#91111yescharacteristic
490C22C5×D3×SD1611yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—41no—
495C4—121no—
496C4—121no—
497C4—241no—
498C3C5×#161311yescharacteristic, complemented, Sylow
499C2—21no—
500C2—21no—
501C2—81no—
502C2—122no—
503C2—241no—
504C2C5×#474211yescharacteristic
505C2C5×#477611yescharacteristic
506C2C5×#482211yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC5×#5605C2
hypercenterC5×#327D3
hypocenterC3C5×#1613
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

Complements

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

NH ≅ G/Ntype
2. C5×#5034C2semidirect
3. C5×#4735C2semidirect
4. C5×#4677C2semidirect
5. C3×C5×#327C2semidirect
6. C5×#4468C2semidirect
7. C5×#4451C2semidirect
17. C2×C5×C4⋊Dic3C22semidirect
21. C3×C5×C22⋊C8C22semidirect
22. C3×C5×#95C22semidirect
24. C5×#830C22semidirect
28. #68290C5direct (N × H)
34. C5×#327D3semidirect
68. #5034C2×C5semidirect
69. #4735C2×C5semidirect
70. #4677C2×C5semidirect
71. C3×#327C2×C5semidirect
72. #4468C2×C5semidirect
73. #4451C2×C5semidirect
91. C5×C22⋊C8C2×D3semidirect
92. C5×#95C2×D3semidirect
138. C2×C4⋊Dic3C22×C5semidirect
142. C3×C22⋊C8C22×C5semidirect
143. C3×#95C22×C5semidirect
145. #830C22×C5semidirect
185. #327C5×D3semidirect
295. C22⋊C8C2×C5×D3semidirect
296. #95C2×C5×D3semidirect
396. C3×C5#1613semidirect
473. C5#68290direct (N × H)
498. C3C5×#1613semidirect

Maximal subgroups

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

subgroupindex
C5×#56052
C5×#50342
C5×#47352
C5×#46772
C3×C5×#3272
C5×#44682
C5×#44512
C5×#16133
#682905