Finite Group Databasebeta

← #14302011

Subgroups — #14302011

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
1C2×C3×#4018C211yesmaximal, characteristic, complemented
2#11754564C211yesmaximal, characteristic
3C2×#91089C211yesmaximal, characteristic, complemented
4C2×#90981C211yesmaximal, characteristic, complemented
5#11748341C211yesmaximal, characteristic, complemented
6C5×#4523C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10599550—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×#683—21no—
17C2×C3×C4×Dic5C2211yescharacteristic
18C3×#4018—22no—
19C3×#4018—22no—
20#91564—21no—
21#91546—21no—
22#91450C412yescomplemented
23C4×#1202—22no—
24#91360C412yescomplemented
25#91089—22no—
26#90981—22no—
27#90955—22no—
28#71591—51nomaximal, Hall
29#65858—31no—
30C2×#4018D311yescharacteristic, complemented
31C2×#3957—31no—
32#65415—31no—
33C2×#3937—31no—
34C5×#339—31no—
35#64752—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40#6817—21no—
41#6817—21no—
42#6817—21no—
43#6817—21no—
44C2×D60C2×C411yescharacteristic
45C2×C4×D15—21no—
46C2×Dic30C2×C411yescharacteristic
47C22×C3×Dic5—21no—
48C22×C3×Dic5D411yescharacteristic
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5C2×C412yes—
54C2×C3×C4×D5D412yes—
55C2×#1202—22no—
56C3×C42×C5—21no—
57C3×C42×C5D412yescomplemented
58#6710—21no—
59#6710—21no—
60C2×C3⋊#168—21no—
61C5×#217—21no—
62C5×C4⋊Dic3C2×C412yes—
63C4×C5×Dic3—21no—
64C5×#208—21no—
65C5×#208—21no—
66C2×C5×C3⋊C8—21no—
67C3×#685—24no—
68C3×#683—24no—
69C3×C4×Dic5—21no—
70C3×C4×Dic5D412yescomplemented
71Dic3⋊Dic5—22no—
72#6667—22no—
73#6665—22no—
74C2×C3×#117—51no—
75#5791—51no—
76#5207—51no—
77C2×#805—51no—
78C2×#805—51no—
79#4523—51no—
80#4523D511yescharacteristic, complemented
81C2×#709—31no—
82C22×C4×D5C2×D311yescharacteristic
83C2×C5×M16—31no—
84C5×#117—31no—
85C2×C42×C5C2×D311yescharacteristic
86C2×#685—21no—
87C2×#683—21no—
88C2×C4×Dic5C2×D311yescharacteristic
89C2×#681—31no—
90#4043—32no—
91#4041—32no—
92#4032—61no—
93#4028—61no—
94C4×D20—62no—
95#4018—22no—
96#4018—22no—
97#3957—62no—
98#3952—62no—
99#3937—62no—
100#1897—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C22×C3×D5—42no—
106C22×C3×D5C22⋊C412yes—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115#1220—41no—
116#1220—41no—
117C2×Dic15—21no—
118D60—21no—
119D60—21no—
120C4×D15—41no—
121C4×D15—41no—
122Dic30—21no—
123Dic30—21no—
124C2×C5×Dic3—22no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—42no—
129C2×C3×Dic5C22⋊C412yes—
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134#1202—44no—
135C3⋊#168—41no—
136C5×C3⋊C8—41no—
137C23×C3×C4—51no—
138C2×#235—51no—
139C3×#117—102no—
140C3×#117—102no—
141C2×C3×C4⋊C4—101no—
142C2×C3×C22⋊C4—101no—
143C2×C3×C42—51no—
144C2×C3×C42C2×D511yescharacteristic
145#953—101no—
146#930—52no—
147#929—101no—
148C4×#67—102no—
149#926C2×D511yescharacteristic
150#924—52no—
151C2×#208—51no—
152C2×#208C2×D511yescharacteristic
153#830—102no—
154#805—102no—
155#805—102no—
156C23×D5#6711yescharacteristic
157C22×C4×C5—21no—
158C22×C4×C5C22×D311yescharacteristic
159C2×C22⋊D5—61no—
160C22×Dic5—21no—
161C22×Dic5#6711yescharacteristic
162#709—61no—
163#709—61no—
164#709—61no—
165#709—61no—
166C2×D20—31no—
167C2×D20—62no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—61no—
173C2×C4×D5C4×D312yes—
174C2×C4×D5D1212yes—
175C2×Dic10—31no—
176C5×M16—61no—
177C5×M16—61no—
178C2×C5×C8—61no—
179C5×C4⋊C4—32no—
180C5×C22⋊C4—61no—
181C42×C5—21no—
182C42×C5—61no—
183C42×C5#6712yescomplemented
184#685—24no—
185#685—62no—
186#685—62no—
187C4⋊Dic5—62no—
188#683—24no—
189C4×Dic5—21no—
190C4×Dic5#6712yescomplemented
191#681—61no—
192#681—61no—
193C2×#168—61no—
194#525—151no—
195C2×#117—51no—
196C2×#104—151no—
197C2×#104—151no—
198#407—151no—
199#339—31no—
200#339—151no—
201C22×C3×C5—22no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5#12011yescharacteristic
204C22×C3×C5#12311yescharacteristic
205C2×D15—41no—
206C2×D15—42no—
207C2×C3×D5—22no—
208C2×C3×D5—22no—
209C2×C3×D5—22no—
210C2×C3×D5—42no—
211C2×C3×D5—42no—
212C3×C4×C5—42no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12111yescharacteristic
217Dic15—41no—
218C3×Dic5—22no—
219C3×Dic5—42no—
220C5×Dic3—42no—
221C24×C3—51no—
222C22×C3×C4—21no—
223C22×C3×C4—51no—
224C22×C3×C4—52no—
225C22×C3×C4—52no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C22×C3×C4—101no—
229C22×C3×C4—101no—
230C22×C3×C4—101no—
231C22×C3×C4C22×D511yescharacteristic
232C2×#67—102no—
233C2×#67—101no—
234#235—101no—
235#235—101no—
236#235—101no—
237#235—101no—
238C2×D12—51no—
239C2×C4×D3—101no—
240C2×Dic6—51no—
241C3×C4⋊C4—104no—
242C3×C22⋊C4—104no—
243C3×C42—21no—
244C3×C42—52no—
245C3×C42—101no—
246C3×C42D2012yescomplemented
247#217—21no—
248#217—102no—
249(C2×D3)⋊C4—102no—
250C4⋊Dic3C4×D512yes—
251Dic3⋊C4—102no—
252C4×Dic3—21no—
253#208—21no—
254#208—21no—
255#208—101no—
256#208—101no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—101no—
259C23×C5C2×#6711yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—42no—
263C22×D5—61no—
264C22×D5(C2×D3)⋊C412yes—
265C2×C4×C5—22no—
266C2×C4×C5—42no—
267C2×C4×C5—62no—
268C2×C4×C5C2×C4×D311yescharacteristic
269C2×C4×C5C2×D1211yescharacteristic
270C2×C4×C5#23511yescharacteristic
271C2×C4×C5#23511yescharacteristic
272C2×C4×C5C2×#6711yescharacteristic
273C2×C4×C5C2×#6711yescharacteristic
274C22⋊D5—121no—
275C22⋊D5—121no—
276C2×Dic5—21no—
277C2×Dic5—21no—
278C2×Dic5—22no—
279C2×Dic5—42no—
280C2×Dic5—61no—
281C2×Dic5(C2×D3)⋊C412yes—
282D20—61no—
283D20—61no—
284D20—124no—
285C4×D5—22no—
286C4×D5—22no—
287C4×D5—22no—
288C4×D5—22no—
289C4×D5—121no—
290C4×D5—121no—
291Dic10—61no—
292Dic10—61no—
293C5×C8—121no—
294#168—121no—
295C2×#41—151no—
296C23×C4—51no—
297C2×M16—31no—
298C2×M16—151no—
299#123—301no—
300C22⋊Q8—152no—
301#121—152no—
302#120—301no—
303C4×D4—302no—
304#117—31no—
305#117—102no—
306#117—102no—
307C2×C4⋊C4—101no—
308C2×C22⋊C4—101no—
309C2×C42—51no—
310C2×C42D3×D511yescharacteristic
311#104—302no—
312#104—302no—
313C22⋊C8—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C2×C3×C5#42112yes—
318D15—81no—
319C3×D5—42no—
320C23×C3—52no—
321C23×C3—101no—
322C23×C3—101no—
323C23×C3—202no—
324C23×C3D4×D511yescharacteristic
325C22×D3—101no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—52no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4—102no—
336C2×C3×C4—202no—
337C2×C3×C4C2×C4×D511yescharacteristic
338C2×C3×C4C2×D2011yescharacteristic
339C2×C3×C4#70911yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4#71311yescharacteristic
343#67—204no—
344#67—201no—
345#67—201no—
346C2×Dic3—22no—
347C2×Dic3—101no—
348D12—101no—
349D12—101no—
350C4×D3—201no—
351C4×D3—201no—
352Dic6—101no—
353Dic6—101no—
354C3⋊C8—41no—
355C3⋊C8—201no—
356C22×C5—22no—
357C22×C5C2×(C2×D3)⋊C411yescharacteristic
358C22×C5#92911yescharacteristic
359C22×C5#95311yescharacteristic
360C2×D5—22no—
361C2×D5—22no—
362C2×D5—22no—
363C2×D5—42no—
364C2×D5—42no—
365C2×D5—121no—
366C2×D5—122no—
367C4×C5—42no—
368C4×C5—122no—
369C4×C5C4×#6711yescharacteristic
370C4×C5C4×#6711yescharacteristic
371C4×C5#93011yescharacteristic
372C4×C5#93011yescharacteristic
373Dic5—22no—
374Dic5—42no—
375Dic5—121no—
376C24—51no—
377#41—301no—
378#41—301no—
379#41—301no—
380#41—301no—
381C2×Q8—151no—
382C2×D4—151no—
383C2×D4—302no—
384C2×D4—301no—
385C22×C4—21no—
386C22×C4—51no—
387C22×C4—52no—
388C22×C4—52no—
389C22×C4—101no—
390C22×C4—101no—
391C22×C4—101no—
392C22×C4—101no—
393C22×C4—101no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—61no—
397M16—61no—
398M16—301no—
399M16—301no—
400C2×C8—61no—
401C2×C8—301no—
402C4⋊C4—32no—
403C4⋊C4—104no—
404C4⋊C4—302no—
405C22⋊C4—61no—
406C22⋊C4—104no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—21no—
410C42—52no—
411C42—61no—
412C42—101no—
413C42#120212yescomplemented
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3—102no—
417C22×C3—102no—
418C22×C3—102no—
419C22×C3—202no—
420C22×C3—202no—
421C22×C3D5×C22⋊C411yescharacteristic
422C22×C3#402811yescharacteristic
423C22×C3#404011yescharacteristic
424C2×D3—202no—
425C2×D3—201no—
426C3×C4—42no—
427C3×C4—102no—
428C3×C4—202no—
429C3×C4C4×D2011yescharacteristic
430C3×C4#403011yescharacteristic
431C3×C4#403911yescharacteristic
432C3×C4#404111yescharacteristic
433Dic3—42no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#500512yes—
438C2×C5#521311yescharacteristic
439D5—42no—
440D5—241no—
441C23—52no—
442C23—101no—
443C23—101no—
444C23—202no—
445C23—301no—
446C23D5×#6711yescharacteristic
447Q8—301no—
448Q8—301no—
449D4—301no—
450D4—301no—
451D4—604no—
452D4—601no—
453D4—601no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—52no—
457C2×C4—62no—
458C2×C4—101no—
459C2×C4—101no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—202no—
466C2×C4—301no—
467C2×C4—601no—
468C2×C4—601no—
469C2×C4#677111yescharacteristic
470C2×C4#677311yescharacteristic
471C2×C4C4×D3×D511yescharacteristic
472C2×C4D5×D1211yescharacteristic
473C2×C4C2×#120211yescharacteristic
474C2×C4D5×#6711yescharacteristic
475C8—121no—
476C8—601no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—202no—
480C2×C3#6495411yescharacteristic
481C2×C3#6511012yes—
482D3—401no—
483C5#7159111yescharacteristic, complemented, Sylow
484C22—22no—
485C22—102no—
486C22—102no—
487C22—102no—
488C22—202no—
489C22—202no—
490C22—602no—
491C22—601no—
492C22#9134811yescharacteristic
493C22D5×(C2×D3)⋊C411yescharacteristic
494C22#9156411yescharacteristic
495C4—42no—
496C4—102no—
497C4—122no—
498C4—202no—
499C4—601no—
500C4C4×#120211yescharacteristic
501C4#9144411yescharacteristic
502C4#9144811yescharacteristic
503C4#9145011yescharacteristic
504C3#1059955011yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—202no—
508C2—1201no—
509C2#1174710912yes—
510C2#1174890711yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754564C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4018C2semidirect
3. C2×#91089C2semidirect
4. C2×#90981C2semidirect
5. #11748341C2semidirect
6. C5×#4523C2semidirect
7. #11745977C2semidirect
22. #91450C4semidirect
24. #91360C4semidirect
30. C2×#4018D3semidirect
57. C3×C42×C5D4semidirect
70. C3×C4×Dic5D4semidirect
80. #4523D5semidirect
183. C42×C5#67semidirect
190. C4×Dic5#67semidirect
246. C3×C42D20semidirect
413. C42#1202semidirect
414. C3×C5#1897semidirect
483. C5#71591semidirect
504. C3#10599550semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
#117545642
C2×#910892
C2×#909812
#117483412
C5×#45232
#117459772
#105995503
#715915