Finite Group Databasebeta

← #14300888

Subgroups — #14300888

Order 1920.

804 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91428C211yesmaximal, characteristic
2C22×#6658C211yesmaximal, characteristic
3C2×#91105C211yesmaximal, characteristic
4C2×C3×#3948C211yesmaximal, characteristic, complemented
5#11748609C211yesmaximal, characteristic, complemented
6C5×#4550C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10599465—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×#1200—21no—
12C22×C3×C5×C8C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×#6667—21no—
18#91428—22no—
19#91428—22no—
20C2×#6658—22no—
21C2×#6658—22no—
22C2×#6658C414yescomplemented
23#91105—22no—
24C3×#3948—22no—
25#90994—21no—
26#90994—21no—
27#70276—51nomaximal, Hall
28C22×#677—31no—
29C2×C4×D20—31no—
30C2×#3953—31no—
31C2×#3948D311yescharacteristic, complemented
32#65218—31no—
33C5×#336—31no—
34#64771—31no—
35C23×D15—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60C2×C412yes—
42C2×D60D412yes—
43C2×D60D412yes—
44C22×C5×Dic3D411yescharacteristic
45C22×C5×Dic3D411yescharacteristic
46C22×C3×Dic5—21no—
47C22×C3×Dic5—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2×C412yescomplemented
54C2×#1200—24no—
55C2×#1200—42no—
56C2×#1200—42no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C4⋊Dic15—21no—
61C4⋊Dic15—21no—
62C4×C5×Dic3—21no—
63C4×C5×Dic3—21no—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8C2×C412yescomplemented
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5D412yes—
69#6667—24no—
70#6658—28no—
71C22×#215—51no—
72C2×#893—51no—
73C2×C3×#103—51no—
74#5229—51no—
75C2×#821—51no—
76#4550D511yescharacteristic, complemented
77#4529—51no—
78C22×D20—31no—
79C22×C4×D5—61no—
80C22×Dic10C2×D311yescharacteristic
81C22×C5×C8—31no—
82C22×C5×C8C2×D311yescharacteristic
83C2×C42×C5—31no—
84C2×#685—61no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C2×#677—34no—
88C2×#677—62no—
89C2×#677—62no—
90C4×D20—62no—
91C4×D20—62no—
92#3963—61no—
93#3963—61no—
94#3953—62no—
95#3948—22no—
96#1877—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—22no—
99C22×D15—22no—
100C22×D15—22no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15—41no—
104C22×D15—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114D60—22no—
115D60—22no—
116D60—22no—
117D60C22⋊C414yes—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3SD1612yescomplemented
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—41no—
133C3×Dic10—41no—
134#1200—48no—
135C3×C5×C8—41no—
136C5×C3⋊C8—22no—
137C22×C3×Q8—51no—
138C22×D12—51no—
139C22×C4×D3—101no—
140C22×C3×C8C2×D511yescharacteristic
141C2×C3×C4⋊C4—51no—
142C2×#215—54no—
143C2×#215—102no—
144C2×#215—102no—
145C2×(C2×D3)⋊C4—101no—
146C2×C4⋊Dic3—51no—
147C2×C4×Dic3C2×D511yescharacteristic
148C22×C3⋊C8C2×D511yescharacteristic
149#893—102no—
150#893—102no—
151C3×#103—102no—
152C3⋊#95—101no—
153C3⋊#95—101no—
154#821—102no—
155C23×D5—61no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5C22×D311yescharacteristic
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—61no—
162C2×D20—32no—
163C2×D20—32no—
164C2×D20—32no—
165C2×D20—61no—
166C2×D20—61no—
167C2×D20—61no—
168C2×C4×D5—64no—
169C2×C4×D5—122no—
170C2×C4×D5—122no—
171C2×Dic10—21no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10—21no—
175C2×Dic10—21no—
176C2×Dic10C4×D312yescomplemented
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—32no—
181C2×C5×C8—61no—
182C2×C5×C8—61no—
183C42×C5—61no—
184C42×C5—61no—
185#685—64no—
186C4⋊Dic5—21no—
187C4⋊Dic5—61no—
188C4⋊Dic5—61no—
189C4⋊Dic5#6712yes—
190#677—68no—
191C22×SD16—151no—
192C2×C4×D4—151no—
193C2×#103—51no—
194C2×#102—151no—
195#391—151no—
196#340—151no—
197#336—31no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12011yescharacteristic
200C22×C3×C5#12111yescharacteristic
201C22×C3×C5C2×SD1611yescharacteristic
202C22×C3×C5#13511yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C22×C3×C5#13711yescharacteristic
205C2×D15—24no—
206C2×D15—42no—
207C2×D15—42no—
208C2×D15—42no—
209C2×D15—42no—
210C2×D15—42no—
211C2×D15—42no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—81no—
217C3×Dic5—42no—
218C3×Dic5—42no—
219C5×Dic3—22no—
220C5×Dic3—41no—
221C23×D3—101no—
222C2×C3×Q8—52no—
223C2×C3×Q8—101no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C2×C3×Q8—101no—
228C22×C3×C4—101no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—101no—
232C22×Dic3D2011yescharacteristic
233C22×Dic3D2011yescharacteristic
234C2×D12—52no—
235C2×D12—52no—
236C2×D12—52no—
237C2×D12—101no—
238C2×D12—101no—
239C2×D12—101no—
240C2×C4×D3—104no—
241C2×C4×D3—202no—
242C2×C4×D3—202no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C3×C4⋊C4—52no—
247C3×C4⋊C4—101no—
248#215—108no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252C4×Dic3—21no—
253C4×Dic3—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8C4×D512yescomplemented
257C23×C5D3×D411yescharacteristic
258C22×D5—62no—
259C22×D5—62no—
260C22×D5—62no—
261C22×D5—121no—
262C22×D5—121no—
263C22×D5—121no—
264C22×D5—121no—
265C2×C4×C5—32no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—41no—
280C2×Dic5—41no—
281C2×Dic5—41no—
282C2×Dic5—41no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285C2×Dic5—121no—
286D20—34no—
287D20—62no—
288D20—62no—
289D20—62no—
290C4×D5—128no—
291Dic10—22no—
292Dic10—22no—
293Dic10—41no—
294Dic10—41no—
295C5×C8—41no—
296C5×C8—62no—
297C22×Q8—51no—
298C22×D4—151no—
299C23×C4—301no—
300C2×SD16—154no—
301C2×SD16—302no—
302C2×SD16—302no—
303C22×C8—31no—
304C22×C8D3×D511yescharacteristic
305C4×D4—302no—
306C4×D4—302no—
307C2×C4⋊C4—51no—
308C2×C4⋊C4—151no—
309C2×C22⋊C4—301no—
310C2×C42—31no—
311#103—102no—
312#102—302no—
313#95—301no—
314#95—301no—
315C2×C3×C5#38611yescharacteristic
316C2×C3×C5C4×SD1611yescharacteristic
317C2×C3×C5#44011yescharacteristic
318C2×C3×C5#45011yescharacteristic
319C2×C3×C5#45211yescharacteristic
320C2×C3×C5#46111yescharacteristic
321C2×C3×C5#46311yescharacteristic
322D15—44no—
323C23×C3C2×D2011yescharacteristic
324C22×D3—102no—
325C22×D3—102no—
326C22×D3—102no—
327C22×D3—201no—
328C22×D3—201no—
329C22×D3—201no—
330C22×D3—201no—
331C3×Q8—102no—
332C3×Q8—102no—
333C3×Q8—201no—
334C3×Q8—201no—
335C2×C3×C4—102no—
336C2×C3×C4—102no—
337C2×C3×C4—201no—
338C2×C3×C4—201no—
339C2×C3×C4—201no—
340C2×C3×C4—201no—
341C2×C3×C4C2×C4×D511yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4#71311yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354C2×Dic3—201no—
355C2×Dic3#67712yescomplemented
356D12—54no—
357D12—102no—
358D12—102no—
359D12—102no—
360C4×D3—208no—
361C3×C8—41no—
362C3⋊C8—22no—
363C22×C5#67⋊C411yescharacteristic
364C22×C5#88411yescharacteristic
365C22×C5D3×SD1611yescharacteristic
366C22×C5#91411yescharacteristic
367C22×C5#91811yescharacteristic
368C22×C5#91911yescharacteristic
369C22×C5#93711yescharacteristic
370C2×D5—64no—
371C2×D5—122no—
372C2×D5—122no—
373C2×D5—122no—
374C2×D5—122no—
375C2×D5—122no—
376C2×D5—122no—
377C4×C5—62no—
378C4×C5—121no—
379C4×C5D3×C22⋊C411yescharacteristic
380C4×C5#88311yescharacteristic
381C4×C5C4×#6711yescharacteristic
382C4×C5#93811yescharacteristic
383Dic5—42no—
384Dic5—42no—
385Dic5—241no—
386C24—301no—
387C2×Q8—52no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×Q8—101no—
391C2×Q8—101no—
392C2×Q8—101no—
393C2×D4—152no—
394C2×D4—152no—
395C2×D4—152no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—301no—
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—101no—
402C22×C4—101no—
403C22×C4—304no—
404C22×C4—301no—
405C22×C4—602no—
406C22×C4—602no—
407C22×C4C2×D3×D511yescharacteristic
408SD16—308no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—32no—
413C2×C8—61no—
414C2×C8—61no—
415C4⋊C4—52no—
416C4⋊C4—101no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C22⋊C4—304no—
420C42—61no—
421C42—61no—
422C3×C5#187711yescharacteristic, complemented, Hall
423C22×C3C4×D2011yescharacteristic
424C22×C3#402811yescharacteristic
425C22×C3#404111yescharacteristic
426C22×C3C2×#67711yescharacteristic
427C22×C3#405011yescharacteristic
428C22×C3#405411yescharacteristic
429C22×C3#405511yescharacteristic
430C2×D3—104no—
431C2×D3—202no—
432C2×D3—202no—
433C2×D3—202no—
434C2×D3—202no—
435C2×D3—202no—
436C2×D3—202no—
437C3×C4—202no—
438C3×C4—202no—
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#403011yescharacteristic
441C3×C4#403911yescharacteristic
442C3×C4#404011yescharacteristic
443Dic3—22no—
444Dic3—41no—
445Dic3—401no—
446C2×C5#478811yescharacteristic
447C2×C5#481711yescharacteristic
448C2×C5#481811yescharacteristic
449C2×C5#481911yescharacteristic
450C2×C5#495611yescharacteristic
451C2×C5#516911yescharacteristic
452C2×C5#518711yescharacteristic
453D5—124no—
454C23—302no—
455C23—302no—
456C23—302no—
457C23—601no—
458C23—601no—
459C23—601no—
460C23—601no—
461C23D3×D2011yescharacteristic
462Q8—102no—
463Q8—102no—
464Q8—201no—
465Q8—201no—
466D4—154no—
467D4—302no—
468D4—302no—
469D4—302no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—201no—
479C2×C4—201no—
480C2×C4—201no—
481C2×C4—201no—
482C2×C4—608no—
483C2×C4—601no—
484C2×C4—601no—
485C2×C4—601no—
486C2×C4#677311yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4#677711yescharacteristic
489C2×C4#677911yescharacteristic
490C2×C4D5×#6711yescharacteristic
491C2×C4#679011yescharacteristic
492C8—41no—
493C8—62no—
494C2×C3#6495411yescharacteristic
495C2×C3C4×#67711yescharacteristic
496C2×C3#6499911yescharacteristic
497C2×C3#6502011yescharacteristic
498C2×C3#6502211yescharacteristic
499C2×C3#6513011yescharacteristic
500C2×C3#6513311yescharacteristic
501D3—204no—
502C5#7027611yescharacteristic, complemented, Sylow
503C22—304no—
504C22—602no—
505C22—602no—
506C22—602no—
507C22—602no—
508C22—602no—
509C22—602no—
510C22D3×#67711yescharacteristic
511C22#9125311yescharacteristic
512C22#9126311yescharacteristic
513C22#9127511yescharacteristic
514C22#9139511yescharacteristic
515C22#9145911yescharacteristic
516C22#9147411yescharacteristic
517C4—62no—
518C4—121no—
519C4—202no—
520C4—202no—
521C4—1201no—
522C4#9135611yescharacteristic
523C4#9144411yescharacteristic
524C4#9147311yescharacteristic
525C4#9153311yescharacteristic
526C3#1059946511yescharacteristic, complemented, Sylow
527C2—604no—
528C2#1174774311yescharacteristic
529C2#1174779111yescharacteristic
530C2#1174779811yescharacteristic
531C2#1174783011yescharacteristic
532C2#1174811011yescharacteristic
533C2#1174815211yescharacteristic
534C2#1174870011yescharacteristic
subgroupG/H
centerC23D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1877
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3948C2semidirect
5. #11748609C2semidirect
6. C5×#4550C2semidirect
7. #11745980C2semidirect
22. C2×#6658C4semidirect
31. C2×#3948D3semidirect
53. C2×C3×Dic10C2×C4semidirect
66. C2×C5×C3⋊C8C2×C4semidirect
76. #4550D5semidirect
123. C2×C5×Dic3SD16semidirect
176. C2×Dic10C4×D3semidirect
256. C2×C3⋊C8C4×D5semidirect
355. C2×Dic3#677semidirect
422. C3×C5#1877semidirect
502. C5#70276semidirect
526. C3#10599465semidirect

Maximal subgroups

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

subgroupindex
C2×#914282
C22×#66582
C2×#911052
C2×C3×#39482
#117486092
C5×#45502
#117459802
#105994653
#702765