Finite Group Databasebeta

← #14301112

Subgroups — #14301112

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×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#688C211yesmaximal, characteristic
3C2×#91119C211yesmaximal, characteristic, complemented
4#11748785C211yesmaximal, characteristic
5C2×#90964C211yesmaximal, characteristic
6#11745981C211yesmaximal, characteristic, complemented
7#11745967C211yesmaximal, characteristic, complemented
8#10602426—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C5×Q8×Dic3—22no—
14C5×Q8×Dic3—22no—
15C2×C5×C4⋊Dic3—21no—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C2×C4×C5×Dic3—21no—
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C3×#688—22no—
20C2×C3×#688—22no—
21C2×C3×#688C414yescomplemented
22C22×C3×#168C2211yescharacteristic
23C2×#6665—21no—
24C2×#6665—21no—
25#91119—22no—
26#90964—22no—
27#72048—51nomaximal, Hall
28C2×C4×C5×Q8—31no—
29C22×#688D311yescharacteristic
30C2×#3967—31no—
31C2×#3941—31no—
32#65228—31no—
33#64749—31no—
34#64744—31no—
35C23×C3×D5—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C2×C3×C5×Q8D412yes—
41C2×C3×C5×Q8D412yes—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15—21no—
45C22×C5×Dic3—21no—
46C22×C5×Dic3D411yescharacteristic
47C22×C5×Dic3D411yescharacteristic
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20C2×C412yes—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C5×C4⋊Dic3—24no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3D412yes—
62C4×C5×Dic3—24no—
63C4×C5×Dic3—21no—
64C4×C5×Dic3—21no—
65C3×#688—28no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168C2×C412yes—
69#6665—42no—
70#6665—42no—
71C22×C3×SD16—51no—
72C2×Q8×Dic3D511yescharacteristic, complemented
73C2×#835—51no—
74#5221—51no—
75C2×#832—51no—
76#4551—51no—
77#4550—51no—
78C22×C5×Q8C2×D311yescharacteristic
79C22×D20C2×D311yescharacteristic
80C4×C5×Q8—62no—
81C4×C5×Q8—62no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—61no—
84C2×C42×C5—31no—
85C2×C42×C5—61no—
86C2×#688—22no—
87C2×#688—22no—
88C2×#688Dic314yescomplemented
89C2×#685—61no—
90C2×#685—61no—
91C2×C4⋊Dic5—31no—
92C22×#168—31no—
93C22×#168C2×D311yescharacteristic
94#3967—62no—
95#3941—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×C3×D5—22no—
99C22×C3×D5—41no—
100C22×C3×D5—41no—
101C22×C3×D5—41no—
102C22×C3×D5—41no—
103C22×C3×D5—41no—
104C22×C3×D5—41no—
105C3×C5×Q8—22no—
106C3×C5×Q8—22no—
107C3×C5×Q8—22no—
108C3×C5×Q8C22⋊C414yescomplemented
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3SD1612yescomplemented
130C3×D20—22no—
131C3×D20—22no—
132C3×D20—41no—
133C3×D20—41no—
134C3⋊#168—41no—
135C3×#168—22no—
136C22×C3×Q8C2×D511yescharacteristic
137C22×C3×D4—51no—
138C2×C3×SD16—54no—
139C2×C3×SD16—102no—
140C2×C3×SD16—102no—
141C22×C3×C8—51no—
142C2×#217—101no—
143C2×#217—101no—
144Q8×Dic3—22no—
145Q8×Dic3—22no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3—51no—
148C2×C4⋊Dic3C2×D511yescharacteristic
149C2×C4×Dic3—21no—
150C2×C4×Dic3C2×D511yescharacteristic
151C22×C3⋊C8—51no—
152#835—102no—
153#832—102no—
154C23×D5—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8C2×Dic312yes—
159C2×C5×Q8#6712yes—
160C2×C5×Q8#6712yes—
161C22×C4×C5—21no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C22×Dic5—61no—
167C2×D20—21no—
168C2×D20—21no—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20C2×Dic312yes—
173C5×C4⋊C4—32no—
174C5×C4⋊C4—64no—
175C5×C4⋊C4—61no—
176C42×C5—64no—
177C42×C5—61no—
178C42×C5—61no—
179#688—28no—
180#685—122no—
181#685—122no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168C2×Dic312yes—
190C22×SD16—51no—
191C2×C4×Q8—31no—
192C2×#103—151no—
193C2×#102—151no—
194#390—151no—
195#340—151no—
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×C3×D5—42no—
205C2×C3×D5—42no—
206C2×C3×D5—42no—
207C2×C3×D5—81no—
208C2×C3×D5—81no—
209C2×C3×D5—81no—
210C2×C3×D5—81no—
211C3×C4×C5—24no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—81no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3—42no—
220C24×C3—101no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C4×D512yes—
225C2×C3×Q8D2012yes—
226C2×C3×Q8C22⋊D512yes—
227C2×C3×D4—52no—
228C2×C3×D4—101no—
229C2×C3×D4—101no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C22×C3×C4—21no—
234C22×C3×C4C22×D511yescharacteristic
235C22×Dic3—21no—
236C22×Dic3—101no—
237C22×Dic3C22⋊D511yescharacteristic
238C22×Dic3C22⋊D511yescharacteristic
239C3×SD16—108no—
240C2×C3×C8—52no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243#217—202no—
244#217—202no—
245C4⋊Dic3—24no—
246C4⋊Dic3—21no—
247C4⋊Dic3—101no—
248C4⋊Dic3—101no—
249C4⋊Dic3C22⋊D512yes—
250C4×Dic3—24no—
251C4×Dic3—21no—
252C4×Dic3—21no—
253C2×C3⋊C8—101no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8—101no—
256C23×C5D3×D411yescharacteristic
257C22×D5—22no—
258C22×D5—41no—
259C22×D5—41no—
260C22×D5—41no—
261C22×D5—41no—
262C22×D5—41no—
263C22×D5—41no—
264C5×Q8—22no—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8#21714yescomplemented
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—32no—
272C2×C4×C5—61no—
273C2×C4×C5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—62no—
277C2×C4×C5—61no—
278C2×C4×C5—121no—
279C2×C4×C5—121no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23711yescharacteristic
282C2×C4×C5#23711yescharacteristic
283C2×C4×C5C22×Dic311yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C2×#6711yescharacteristic
286C2×Dic5—121no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289D20—22no—
290D20—22no—
291D20—41no—
292D20—41no—
293#168—22no—
294#168—121no—
295C22×Q8D3×D511yescharacteristic
296C22×D4—51no—
297C2×SD16—54no—
298C2×SD16—102no—
299C2×SD16—102no—
300C22×C8—51no—
301C22×C8—151no—
302C4×Q8—62no—
303C4×Q8—62no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4—151no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—31no—
310C2×C42—61no—
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
320C3×D5—82no—
321C23×C3—102no—
322C23×C3—201no—
323C23×C3—201no—
324C23×C3—201no—
325C23×C3—201no—
326C23×C3—201no—
327C23×C3—201no—
328C23×C3C2×C22⋊D511yescharacteristic
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8#68514yescomplemented
333C3×D4—102no—
334C3×D4—102no—
335C3×D4—201no—
336C3×D4—201no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4#70911yescharacteristic
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—201no—
355C2×Dic3—201no—
356C2×Dic3—201no—
357C2×Dic3#68812yescomplemented
358C3×C8—102no—
359C3⋊C8—201no—
360C22×C5D3×SD1611yescharacteristic
361C22×C5#91411yescharacteristic
362C22×C5#91511yescharacteristic
363C22×C5#91611yescharacteristic
364C22×C5D4×Dic311yescharacteristic
365C22×C5#93711yescharacteristic
366C22×C5#93911yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C2×D5—81no—
371C2×D5—81no—
372C2×D5—81no—
373C2×D5—81no—
374C4×C5—24no—
375C4×C5—62no—
376C4×C5—121no—
377C4×C5—122no—
378C4×C5D4×Dic311yescharacteristic
379C4×C5#93511yescharacteristic
380C4×C5#93911yescharacteristic
381C4×C5C2×#21711yescharacteristic
382Dic5—241no—
383C24—101no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8D5×Dic312yes—
388C2×Q8#120112yes—
389C2×Q8#120212yes—
390C2×D4—52no—
391C2×D4—101no—
392C2×D4—101no—
393C2×D4—101no—
394C2×D4—101no—
395C2×D4—101no—
396C22×C4—21no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—61no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—108no—
403C2×C8—52no—
404C2×C8—101no—
405C2×C8—101no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—32no—
410C4⋊C4—64no—
411C4⋊C4—61no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—64no—
417C42—61no—
418C42—61no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—202no—
421C22×C3—202no—
422C22×C3—202no—
423C22×C3—401no—
424C22×C3—401no—
425C22×C3—401no—
426C22×C3—401no—
427C22×C3C4×C22⋊D511yescharacteristic
428C22×C3#407611yescharacteristic
429C22×C3C2×#68811yescharacteristic
430C22×C3#408811yescharacteristic
431C22×C3#409511yescharacteristic
432C22×C3#409611yescharacteristic
433C22×C3#409911yescharacteristic
434C3×C4—24no—
435C3×C4C2×#68511yescharacteristic
436C3×C4C4×C22⋊D511yescharacteristic
437C3×C4#407511yescharacteristic
438C3×C4#407611yescharacteristic
439Dic3—22no—
440Dic3—41no—
441Dic3—42no—
442Dic3—401no—
443C2×C5Dic3×SD1611yescharacteristic
444C2×C5#516311yescharacteristic
445C2×C5#516411yescharacteristic
446C2×C5#516611yescharacteristic
447C2×C5#517011yescharacteristic
448C2×C5#517211yescharacteristic
449C2×C5#522011yescharacteristic
450D5—82no—
451C23—102no—
452C23—201no—
453C23—201no—
454C23—201no—
455C23—201no—
456C23—201no—
457C23—201no—
458C23D3×C22⋊D511yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—22no—
462Q8#666514yescomplemented
463D4—102no—
464D4—102no—
465D4—201no—
466D4—201no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—601no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4C2×D5×Dic311yescharacteristic
483C2×C4#677911yescharacteristic
484C2×C4#677911yescharacteristic
485C2×C4C2×#120111yescharacteristic
486C2×C4C2×#120211yescharacteristic
487C2×C4D3×C22⋊D511yescharacteristic
488C8—102no—
489C8—601no—
490C2×C3—402no—
491C2×C3C4×#68811yescharacteristic
492C2×C3#6531511yescharacteristic
493C2×C3#6531611yescharacteristic
494C2×C3#6531711yescharacteristic
495C2×C3#6550211yescharacteristic
496C2×C3#6551611yescharacteristic
497C2×C3#6552711yescharacteristic
498C5#7204811yescharacteristic, complemented, Sylow
499C22—202no—
500C22—202no—
501C22—202no—
502C22—401no—
503C22—401no—
504C22—401no—
505C22—401no—
506C22D3×#68811yescharacteristic
507C22#9150411yescharacteristic
508C22#9151711yescharacteristic
509C22#9151811yescharacteristic
510C22Dic3×C22⋊D511yescharacteristic
511C22#9156811yescharacteristic
512C22#9156911yescharacteristic
513C4—24no—
514C4—62no—
515C4—121no—
516C4—122no—
517C4—1201no—
518C4C2×#666511yescharacteristic
519C4#9153611yescharacteristic
520C4Dic3×C22⋊D511yescharacteristic
521C4#9156911yescharacteristic
522C3#1060242611yescharacteristic, complemented, Sylow
523C2—402no—
524C2Dic3×#68811yescharacteristic
525C2#1174923411yescharacteristic
526C2#1174927811yescharacteristic
527C2#1174928111yescharacteristic
528C2#1174932511yescharacteristic
529C2#1174934511yescharacteristic
530C2#1174949511yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q8×Dic3C2semidirect
3. C2×#91119C2semidirect
6. #11745981C2semidirect
7. #11745967C2semidirect
21. C2×C3×#688C4semidirect
72. C2×Q8×Dic3D5semidirect
88. C2×#688Dic3semidirect
108. C3×C5×Q8C22⋊C4semidirect
129. C2×C5×Dic3SD16semidirect
267. C5×Q8#217semidirect
332. C3×Q8#685semidirect
357. C2×Dic3#688semidirect
419. C3×C5#1880semidirect
462. Q8#6665semidirect
498. C5#72048semidirect
522. C3#10602426semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×Dic32
C22×C3×#6882
C2×#911192
#117487852
C2×#909642
#117459812
#117459672
#106024263
#720485