Finite Group Databasebeta

← C5×#70383 #14301981

Subgroups — C5×#70383 #14301981

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5828C211yesmaximal, characteristic
2C2×C5×#872C211yesmaximal, characteristic, complemented
3C2×C3×C5×#104C211yesmaximal, characteristic, complemented
4C2×C5×#837C211yesmaximal, characteristic, complemented
5C5×#5126C211yesmaximal, characteristic, complemented
6C5×#4555C211yesmaximal, characteristic, complemented
7C5×#4523C211yesmaximal, characteristic, complemented
8C5×#1897—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C5×#946C412yescomplemented
14C5×#938C412yescomplemented
15C5×#937—21no—
16C5×#935—21no—
17C4×C5×#67—22no—
18C2×C5×(C2×D3)⋊C4—21no—
19C5×#926C2211yescharacteristic
20C2×C5×Dic3⋊C4—21no—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C5×#872—22no—
24C5×#872—22no—
25C3×C5×#104—22no—
26C5×#837—22no—
27C5×(C2×D3)⋊C8—22no—
28#70383C511yesmaximal, characteristic, direct product factor, Hall
29C5×#525—31no—
30C2×C5×#117—31no—
31C2×C5×#104—31no—
32C2×C5×#104D311yescharacteristic, complemented
33C5×#407—31no—
34C5×#339—31no—
35C5×#339—31no—
36C23×C5×D3D411yescharacteristic
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C2×C3×C5×Q8C2×C411yescharacteristic
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4C2×C411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×C5×#67—22no—
48C22×C5×Dic3—21no—
49C22×C5×Dic3D411yescharacteristic
50C2×C4×C5×D3—21no—
51C2×C4×C5×D3—21no—
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3C2×C412yes—
55C2×C4×C5×D3D412yes—
56C3×C5×M16—21no—
57C3×C5×M16—21no—
58C2×C3×C5×C8—21no—
59C3×C42×C5—21no—
60C3×C42×C5D412yescomplemented
61C5×#217—21no—
62C5×#217—22no—
63C5×(C2×D3)⋊C4—24no—
64C5×(C2×D3)⋊C4—22no—
65C5×C4⋊Dic3C2×C412yes—
66C5×Dic3⋊C4—24no—
67C5×Dic3⋊C4—22no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3—21no—
70C4×C5×Dic3D412yescomplemented
71C5×#208—21no—
72C5×#208—21no—
73C2×C5×C3⋊C8—21no—
74#5828C2×C511yescharacteristic
75C2×#872C2×C511yescharacteristic, complemented
76C2×C3×#104C2×C511yescharacteristic, complemented
77C2×#837C2×C511yescharacteristic, complemented
78#5126C2×C511yescharacteristic, complemented
79#4555C2×C511yescharacteristic, complemented
80#4523C2×C511yescharacteristic, complemented
81C2×C5×#41C2×D311yescharacteristic
82C23×C4×C5—31no—
83C2×C5×M16—31no—
84C2×C5×M16C2×D311yescharacteristic
85C5×#123—61no—
86C5×C22⋊Q8—32no—
87C5×#121—32no—
88C5×#120—61no—
89C4×C5×D4—62no—
90C5×#117—31no—
91C5×#117—62no—
92C5×#117—62no—
93C2×C5×C4⋊C4—61no—
94C2×C5×C22⋊C4—61no—
95C2×C42×C5—31no—
96C2×C42×C5C2×D311yescharacteristic
97C5×#104—22no—
98C5×#104—62no—
99C5×C22⋊C8—62no—
100#1897—31noSylow
101C23×C3×C5—21no—
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—42no—
106C22×C5×D3C22⋊C412yes—
107C3×C5×Q8—21no—
108C3×C5×Q8—21no—
109C3×C5×D4—21no—
110C3×C5×D4—21no—
111C3×C5×D4—41no—
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—42no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5C22×C411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5#4111yescharacteristic
123C2×C3×C4×C5#4111yescharacteristic
124C5×#67—44no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—42no—
130C2×C5×Dic3C22⋊C412yes—
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—22no—
134C4×C5×D3—22no—
135C3×C5×C8—41no—
136C5×C3⋊C8—41no—
137C2×C3×#41C22×C511yescharacteristic
138C22×C4×D3C22×C511yescharacteristic
139C2×C3×M16C22×C511yescharacteristic
140C2×C3×C42C22×C511yescharacteristic
141#946C4×C512yescomplemented
142#938C4×C512yescomplemented
143#937—21no—
144#935—21no—
145C4×#67—22no—
146C2×(C2×D3)⋊C4—21no—
147#926C22×C511yescharacteristic
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3C22×C511yescharacteristic
150C2×#208C22×C511yescharacteristic
151#872—22no—
152#872—22no—
153C3×#104—22no—
154#837—22no—
155(C2×D3)⋊C8—22no—
156C24×C5—31no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—21no—
161C2×C5×Q8C4×D311yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4—62no—
164C2×C5×D4C4×D311yescharacteristic
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—31no—
168C22×C4×C5—32no—
169C22×C4×C5—32no—
170C22×C4×C5—61no—
171C22×C4×C5—61no—
172C22×C4×C5—61no—
173C22×C4×C5—61no—
174C22×C4×C5—61no—
175C22×C4×C5C22×D311yescharacteristic
176C5×M16—21no—
177C5×M16—21no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—21no—
181C2×C5×C8—61no—
182C5×C4⋊C4—32no—
183C5×C4⋊C4—62no—
184C5×C4⋊C4—64no—
185C5×C22⋊C4—62no—
186C5×C22⋊C4—64no—
187C5×C22⋊C4—62no—
188C5×C22⋊C4—61no—
189C42×C5—21no—
190C42×C5—32no—
191C42×C5—61no—
192C42×C5—61no—
193C42×C5#6712yescomplemented
194#525—31no—
195C2×#117—31no—
196C2×#104—31no—
197C2×#104C5×D311yescharacteristic, complemented
198#407—31no—
199#339—31no—
200#339—31no—
201C22×C3×C5—22no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12311yescharacteristic
207C2×C5×D3—22no—
208C2×C5×D3—22no—
209C2×C5×D3—22no—
210C2×C5×D3—42no—
211C2×C5×D3—42no—
212C3×C4×C5—42no—
213C3×C4×C5—41no—
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5C4×D411yescharacteristic
216C3×C4×C5#12111yescharacteristic
217C3×C4×C5#12111yescharacteristic
218C5×Dic3—22no—
219C5×Dic3—42no—
220C5×Dic3—42no—
221C23×D3C5×D411yescharacteristic
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—21no—
226C2×C3×Q8C2×C4×C511yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4C2×C4×C511yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C23×C511yescharacteristic
232C2×#67—22no—
233C22×Dic3—21no—
234C22×Dic3C5×D411yescharacteristic
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3C2×C4×C512yes—
240C2×C4×D3C5×D412yes—
241C3×M16—21no—
242C3×M16—21no—
243C2×C3×C8—21no—
244C3×C42—21no—
245C3×C42C5×D412yescomplemented
246#217—21no—
247#217—22no—
248(C2×D3)⋊C4—24no—
249(C2×D3)⋊C4—22no—
250C4⋊Dic3C2×C4×C512yes—
251Dic3⋊C4—24no—
252Dic3⋊C4—22no—
253C4×Dic3—21no—
254C4×Dic3—21no—
255C4×Dic3C5×D412yescomplemented
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C23×C5—21no—
260C23×C5—32no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—122no—
264C23×C5D3×D411yescharacteristic
265C5×Q8—21no—
266C5×Q8—21no—
267C5×D4—21no—
268C5×D4—21no—
269C5×D4—41no—
270C5×D4—41no—
271C5×D4—124no—
272C2×C4×C5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—32no—
275C2×C4×C5—42no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—62no—
284C2×C4×C5—62no—
285C2×C4×C5—62no—
286C2×C4×C5—122no—
287C2×C4×C5C2×C4×D311yescharacteristic
288C2×C4×C5#23511yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5#23711yescharacteristic
292C2×C4×C5C2×#6711yescharacteristic
293C5×C8—41no—
294C5×C8—121no—
295C2×#41C2×C5×D311yescharacteristic
296C23×C4—31no—
297C2×M16—31no—
298C2×M16C2×C5×D311yescharacteristic
299#123—61no—
300C22⋊Q8—32no—
301#121—32no—
302#120—61no—
303C4×D4—62no—
304#117—31no—
305#117—62no—
306#117—62no—
307C2×C4⋊C4—61no—
308C2×C22⋊C4—61no—
309C2×C42—31no—
310C2×C42C2×C5×D311yescharacteristic
311#104—22no—
312#104—62no—
313C22⋊C8—62no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318C2×C3×C5#42112yes—
319C5×D3—42no—
320C23×C3—21no—
321C23×C3C2×C5×D411yescharacteristic
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—42no—
325C22×D3C5×C22⋊C412yes—
326C3×Q8—21no—
327C3×Q8—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—41no—
331C3×D4—41no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4C22×C4×C511yescharacteristic
338C2×C3×C4C2×C5×D411yescharacteristic
339C2×C3×C4C2×C5×D411yescharacteristic
340C2×C3×C4C2×C5×D411yescharacteristic
341C2×C3×C4C5×#4111yescharacteristic
342C2×C3×C4C5×#4111yescharacteristic
343#67—44no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—42no—
349C2×Dic3C5×C22⋊C412yes—
350C4×D3—22no—
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—22no—
354C3×C8—41no—
355C3⋊C8—41no—
356C22×C5—22no—
357C22×C5—41no—
358C22×C5—42no—
359C22×C5—62no—
360C22×C5—62no—
361C22×C5—62no—
362C22×C5—122no—
363C22×C5—122no—
364C22×C5D3×C22⋊C411yescharacteristic
365C22×C5#88311yescharacteristic
366C22×C5#93711yescharacteristic
367C4×C5—42no—
368C4×C5—41no—
369C4×C5—62no—
370C4×C5—122no—
371C4×C5—122no—
372C4×C5#67⋊C411yescharacteristic
373C4×C5#88411yescharacteristic
374C4×C5C4×#6711yescharacteristic
375C4×C5#93811yescharacteristic
376C24—31no—
377#41—21no—
378#41—21no—
379#41—21no—
380#41—21no—
381C2×Q8C4×C5×D311yescharacteristic
382C2×D4—21no—
383C2×D4—62no—
384C2×D4C4×C5×D311yescharacteristic
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4C22×C5×D311yescharacteristic
396M16—21no—
397M16—21no—
398M16—61no—
399M16—61no—
400C2×C8—21no—
401C2×C8—61no—
402C4⋊C4—32no—
403C4⋊C4—62no—
404C4⋊C4—64no—
405C22⋊C4—62no—
406C22⋊C4—64no—
407C22⋊C4—62no—
408C22⋊C4—61no—
409C42—21no—
410C42—32no—
411C42—61no—
412C42—61no—
413C42C5×#6712yescomplemented
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3—41no—
417C22×C3—42no—
418C22×C3C2×C5×C22⋊C411yescharacteristic
419C22×C3C5×#12011yescharacteristic
420C22×C3C5×#12311yescharacteristic
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—22no—
424C2×D3—42no—
425C2×D3—42no—
426C3×C4—42no—
427C3×C4—41no—
428C3×C4C4×C5×D411yescharacteristic
429C3×C4C4×C5×D411yescharacteristic
430C3×C4C5×#12111yescharacteristic
431C3×C4C5×#12111yescharacteristic
432Dic3—22no—
433Dic3—42no—
434Dic3—42no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—81no—
438C2×C5—122no—
439C2×C5#482112yes—
440C2×C5#495611yescharacteristic
441C23—21no—
442C23—32no—
443C23—61no—
444C23—61no—
445C23—122no—
446C23C5×D3×D411yescharacteristic
447Q8—21no—
448Q8—21no—
449D4—21no—
450D4—21no—
451D4—41no—
452D4—41no—
453D4—124no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—32no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—122no—
469C2×C4C2×C4×C5×D311yescharacteristic
470C2×C4C5×#23511yescharacteristic
471C2×C4C5×D3×D411yescharacteristic
472C2×C4C5×D3×D411yescharacteristic
473C2×C4C5×#23711yescharacteristic
474C2×C4C2×C5×#6711yescharacteristic
475C8—41no—
476C8—121no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—81no—
480C2×C3C5×#38611yescharacteristic
481C2×C3C5×#42112yes—
482D3—42no—
483C5#7038311yescharacteristic, direct product factor, Sylow
484C22—22no—
485C22—41no—
486C22—42no—
487C22—62no—
488C22—62no—
489C22—62no—
490C22—122no—
491C22—122no—
492C22C5×D3×C22⋊C411yescharacteristic
493C22C5×#88311yescharacteristic
494C22C5×#93711yescharacteristic
495C4—42no—
496C4—41no—
497C4—62no—
498C4—122no—
499C4—122no—
500C4C5×#67⋊C411yescharacteristic
501C4C5×#88411yescharacteristic
502C4C4×C5×#6711yescharacteristic
503C4C5×#93811yescharacteristic
504C3C5×#189711yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—81no—
508C2—122no—
509C2C5×#482112yes—
510C2C5×#495611yescharacteristic
subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5828C2
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#104D3
hypocenterC3C5×#1897
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#104

Complements

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

NH ≅ G/Ntype
2. C2×C5×#872C2semidirect
3. C2×C3×C5×#104C2semidirect
4. C2×C5×#837C2semidirect
5. C5×#5126C2semidirect
6. C5×#4555C2semidirect
7. C5×#4523C2semidirect
13. C5×#946C4semidirect
14. C5×#938C4semidirect
28. #70383C5direct (N × H)
32. C2×C5×#104D3semidirect
60. C3×C42×C5D4semidirect
70. C4×C5×Dic3D4semidirect
75. C2×#872C2×C5semidirect
76. C2×C3×#104C2×C5semidirect
77. C2×#837C2×C5semidirect
78. #5126C2×C5semidirect
79. #4555C2×C5semidirect
80. #4523C2×C5semidirect
141. #946C4×C5semidirect
142. #938C4×C5semidirect
193. C42×C5#67semidirect
197. C2×#104C5×D3semidirect
245. C3×C42C5×D4semidirect
255. C4×Dic3C5×D4semidirect
413. C42C5×#67semidirect
414. C3×C5#1897semidirect
483. C5#70383direct (N × H)
504. C3C5×#1897semidirect

Maximal subgroups

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

subgroupindex
C5×#58282
C2×C5×#8722
C2×C3×C5×#1042
C2×C5×#8372
C5×#51262
C5×#45552
C5×#45232
C5×#18973
#703835