Finite Group Databasebeta

← #14301108

Subgroups — #14301108

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4033C211yesmaximal, characteristic, complemented
2C22×#6658C211yesmaximal, characteristic
3C2×#91093C211yesmaximal, characteristic
4#11748768C211yesmaximal, characteristic
5C2×#90970C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745966C211yesmaximal, characteristic, complemented
8#10599702—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#683—21no—
16C2×C3×C4×Dic5—21no—
17C2×C3×C4×Dic5C2211yescharacteristic
18C3×#4033—22no—
19C3×#4033—22no—
20C2×#6667—21no—
21C2×#6667—21no—
22C2×#6658—22no—
23C2×#6658—22no—
24C2×#6658C414yescomplemented
25#91093—22no—
26#90970—22no—
27#71633—51nomaximal, Hall
28C22×#677—31no—
29C2×#4033D311yescharacteristic, complemented
30#65277—31no—
31C2×#3942—31no—
32C2×#3941—31no—
33C5×#340—31no—
34#64770—31no—
35C23×D15—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60C2×C412yes—
44C22×C5×Dic3—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5D411yescharacteristic
47C22×C3×Dic5D411yescharacteristic
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10C2×C412yes—
52C2×C3×Dic10D412yes—
53C2×C3×Dic10D412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4D412yes—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8C2×C412yes—
64C3×#683—24no—
65C3×C4×Dic5—24no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68#6667—42no—
69#6667—42no—
70#6658—28no—
71C2×C3×C4×Q8—51no—
72C22×#215—51no—
73C2×#835—51no—
74C2×#809—51no—
75#4939—51no—
76#4529D511yescharacteristic, complemented
77#4524—51no—
78C22×D20—31no—
79C22×Dic10C2×D311yescharacteristic
80C22×C5×C8—31no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4C2×D311yescharacteristic
83C2×#685—61no—
84C2×#685—61no—
85C2×#683—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5C2×D311yescharacteristic
88C22×#168—31no—
89C2×#677—34no—
90C2×#677—62no—
91C2×#677—62no—
92#4033—22no—
93#4033—22no—
94#3942—62no—
95#3941—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—22no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15—41no—
104C22×D15—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114D60—22no—
115D60—22no—
116D60—41no—
117D60—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5SD1612yescomplemented
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—22no—
133C3×Dic10C22⋊C414yescomplemented
134C3⋊#168—41no—
135C5×C3⋊C8—22no—
136C22×C3×Q8—51no—
137C22×D12—51no—
138C3×C4×Q8—102no—
139C3×C4×Q8—102no—
140C2×C3×C4⋊C4—101no—
141C2×C3×C4⋊C4C2×D511yescharacteristic
142C2×C3×C42—51no—
143C2×C3×C42—101no—
144C2×#215—54no—
145C2×#215—102no—
146C2×#215—102no—
147C2×(C2×D3)⋊C4—101no—
148C2×(C2×D3)⋊C4—101no—
149C2×C4⋊Dic3C2×D511yescharacteristic
150C22×C3⋊C8—51no—
151C22×C3⋊C8C2×D511yescharacteristic
152#835—102no—
153#809—102no—
154C23×D5—61no—
155C22×C4×C5—21no—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—21no—
159C22×Dic5#6711yescharacteristic
160C22×Dic5#6711yescharacteristic
161C2×D20—32no—
162C2×D20—61no—
163C2×D20—61no—
164C2×D20—61no—
165C2×D20—61no—
166C2×D20—61no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C4×D312yes—
171C2×Dic10D1212yes—
172C2×Dic10#6712yes—
173C2×C5×C8—32no—
174C2×C5×C8—61no—
175C2×C5×C8—61no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—61no—
178C5×C4⋊C4—61no—
179C5×C4⋊C4#6712yes—
180#685—122no—
181#685—122no—
182#683—24no—
183C4×Dic5—24no—
184C4×Dic5—21no—
185C4×Dic5—21no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189#677—68no—
190C22×SD16—151no—
191C2×C4×Q8—51no—
192C2×#103—151no—
193C2×#102—151no—
194#390—151no—
195#340—31no—
196#336—151no—
197C22×C3×C5C4×D411yescharacteristic
198C22×C3×C5#12011yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5C2×SD1611yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C22×C3×C5#13711yescharacteristic
204C2×D15—42no—
205C2×D15—42no—
206C2×D15—42no—
207C2×D15—81no—
208C2×D15—81no—
209C2×D15—81no—
210C2×D15—81no—
211C3×C4×C5—42no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C3×Dic5—24no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C5×Dic3—81no—
220C23×D3—101no—
221C2×C3×Q8—52no—
222C2×C3×Q8—52no—
223C2×C3×Q8—52no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C22×C3×C4—21no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—101no—
231C22×C3×C4C22×D511yescharacteristic
232C22×Dic3—21no—
233C2×D12—52no—
234C2×D12—101no—
235C2×D12—101no—
236C2×D12—101no—
237C2×D12—101no—
238C2×D12—101no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—104no—
241C3×C4⋊C4D2012yes—
242C3×C42—104no—
243C3×C42—101no—
244C3×C42—101no—
245#215—108no—
246(C2×D3)⋊C4—202no—
247(C2×D3)⋊C4—202no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—101no—
253C2×C3⋊C8—101no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8C4×D512yes—
256C23×C5C2×#6711yescharacteristic
257C22×D5—62no—
258C22×D5—121no—
259C22×D5—121no—
260C22×D5—121no—
261C22×D5—121no—
262C22×D5—121no—
263C22×D5—121no—
264C2×C4×C5—22no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5C2×C4×D311yescharacteristic
271C2×C4×C5C2×D1211yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—22no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5#21512yescomplemented
285D20—62no—
286D20—62no—
287D20—121no—
288D20—121no—
289Dic10—22no—
290Dic10—22no—
291Dic10—22no—
292Dic10(C2×D3)⋊C414yescomplemented
293C5×C8—62no—
294#168—121no—
295C22×Q8—51no—
296C22×D4—151no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—31no—
301C22×C8—151no—
302C4×Q8—102no—
303C4×Q8—102no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—101no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—51no—
310C2×C42—101no—
311#103—302no—
312#102—302no—
313C2×C3×C5#38611yescharacteristic
314C2×C3×C5C4×SD1611yescharacteristic
315C2×C3×C5#44011yescharacteristic
316C2×C3×C5#44811yescharacteristic
317C2×C3×C5#44911yescharacteristic
318C2×C3×C5#46011yescharacteristic
319C2×C3×C5#46411yescharacteristic
320D15—82no—
321C23×C3D4×D511yescharacteristic
322C22×D3—102no—
323C22×D3—201no—
324C22×D3—201no—
325C22×D3—201no—
326C22×D3—201no—
327C22×D3—201no—
328C22×D3—201no—
329C3×Q8—54no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—102no—
333C2×C3×C4—22no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—52no—
337C2×C3×C4—101no—
338C2×C3×C4—102no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4C2×C4×D511yescharacteristic
346C2×C3×C4C2×D2011yescharacteristic
347C2×C3×C4#70911yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4#71311yescharacteristic
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354D12—102no—
355D12—102no—
356D12—201no—
357D12—201no—
358C3⋊C8—22no—
359C3⋊C8—201no—
360C22×C5C4×#6711yescharacteristic
361C22×C5#93011yescharacteristic
362C22×C5C2×#21511yescharacteristic
363C22×C5#94211yescharacteristic
364C22×C5#94911yescharacteristic
365C22×C5#95011yescharacteristic
366C22×C5#95311yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C2×D5—241no—
371C2×D5—241no—
372C2×D5—241no—
373C2×D5—241no—
374C4×C5—42no—
375C4×C5—241no—
376C4×C5C2×(C2×D3)⋊C411yescharacteristic
377C4×C5C4×#6711yescharacteristic
378C4×C5#92911yescharacteristic
379C4×C5#93011yescharacteristic
380Dic5—24no—
381Dic5—22no—
382Dic5—41no—
383C24—301no—
384C2×Q8—52no—
385C2×Q8—52no—
386C2×Q8—52no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×D4—152no—
391C2×D4—301no—
392C2×D4—301no—
393C2×D4—301no—
394C2×D4—301no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—61no—
400C22×C4—101no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—21no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—104no—
413C4⋊C4#120212yes—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—104no—
417C42—101no—
418C42—101no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3#402811yescharacteristic
421C22×C3#403011yescharacteristic
422C22×C3#403911yescharacteristic
423C22×C3#405711yescharacteristic
424C22×C3D5×SD1611yescharacteristic
425C22×C3#406211yescharacteristic
426C22×C3#406411yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C2×D3—401no—
431C2×D3—401no—
432C2×D3—401no—
433C2×D3—401no—
434C3×C4—42no—
435C3×C4—102no—
436C3×C4—104no—
437C3×C4—201no—
438C3×C4C4×D2011yescharacteristic
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#404011yescharacteristic
441C3×C4#404111yescharacteristic
442Dic3—81no—
443C2×C5C4×#21511yescharacteristic
444C2×C5#502611yescharacteristic
445C2×C5#502711yescharacteristic
446C2×C5#502811yescharacteristic
447C2×C5#521311yescharacteristic
448C2×C5#522711yescharacteristic
449C2×C5#523811yescharacteristic
450D5—242no—
451C23—302no—
452C23—601no—
453C23—601no—
454C23—601no—
455C23—601no—
456C23—601no—
457C23—601no—
458C23D5×#6711yescharacteristic
459Q8—54no—
460Q8—102no—
461Q8—102no—
462Q8—102no—
463D4—302no—
464D4—302no—
465D4—601no—
466D4—601no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—52no—
471C2×C4—102no—
472C2×C4—102no—
473C2×C4—101no—
474C2×C4—101no—
475C2×C4—102no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—101no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4#677111yescharacteristic
483C2×C4#677311yescharacteristic
484C2×C4C4×D3×D511yescharacteristic
485C2×C4D5×D1211yescharacteristic
486C2×C4C2×#120211yescharacteristic
487C2×C4D5×#6711yescharacteristic
488C8—62no—
489C8—601no—
490C2×C3#6495411yescharacteristic
491C2×C3#6505111yescharacteristic
492C2×C3#6507011yescharacteristic
493C2×C3#6508711yescharacteristic
494C2×C3#6509511yescharacteristic
495C2×C3#6514111yescharacteristic
496C2×C3#6517811yescharacteristic
497D3—402no—
498C5#7163311yescharacteristic, complemented, Sylow
499C22—602no—
500C22—602no—
501C22—602no—
502C22—1201no—
503C22—1201no—
504C22—1201no—
505C22—1201no—
506C22#9144411yescharacteristic
507C22#9144811yescharacteristic
508C22#9147811yescharacteristic
509C22#9149211yescharacteristic
510C22D5×#21511yescharacteristic
511C22#9151511yescharacteristic
512C22#9156411yescharacteristic
513C4—42no—
514C4—104no—
515C4—102no—
516C4—201no—
517C4—241no—
518C4#9134811yescharacteristic
519C4C4×#120211yescharacteristic
520C4#9145011yescharacteristic
521C4D5×(C2×D3)⋊C411yescharacteristic
522C3#1059970211yescharacteristic, complemented, Sylow
523C2—1202no—
524C2#1174722411yescharacteristic
525C2#1174722511yescharacteristic
526C2#1174737211yescharacteristic
527C2#1174740011yescharacteristic
528C2#1174890711yescharacteristic
529C2#1174902611yescharacteristic
530C2#1174926811yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4033C2semidirect
5. C2×#90970C2semidirect
6. C5×#4529C2semidirect
7. #11745966C2semidirect
24. C2×#6658C4semidirect
29. C2×#4033D3semidirect
76. #4529D5semidirect
129. C2×C3×Dic5SD16semidirect
133. C3×Dic10C22⋊C4semidirect
284. C2×Dic5#215semidirect
292. Dic10(C2×D3)⋊C4semidirect
419. C3×C5#1880semidirect
498. C5#71633semidirect
522. C3#10599702semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40332
C22×#66582
C2×#910932
#117487682
C2×#909702
C5×#45292
#117459662
#105997023
#716335