Finite Group Databasebeta

← #14301133

Subgroups — #14301133

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
1C22×C3×#677C211yesmaximal, characteristic
2C2×#91331C211yesmaximal, characteristic, complemented
3#11748796C211yesmaximal, characteristic
4C2×#90970C211yesmaximal, characteristic, complemented
5C2×#90964C211yesmaximal, characteristic
6#11746371C211yesmaximal, characteristic, complemented
7C5×#4551C211yesmaximal, characteristic, complemented
8#10599702—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C3×#677—22no—
17C2×C3×#677—22no—
18C2×C3×#677C414yescomplemented
19C2×#6668—21no—
20C2×#6665—21no—
21C2×#6665—21no—
22C2×Dic3×Dic5—21no—
23#91331—22no—
24#91331—22no—
25#90970—22no—
26#90964—22no—
27#72048—51nomaximal, Hall
28C22×#677D311yescharacteristic
29C2×#4033—31no—
30#65277—31no—
31C2×#3942—31no—
32C2×#3941—31no—
33C5×#340—31no—
34#64770—31no—
35C23×C3×D5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15D411yescharacteristic
38C22×Dic15D411yescharacteristic
39C22×C5×Dic3—21no—
40C22×C5×Dic3—21no—
41C22×C3×Dic5—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20C2×C412yes—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10C2×C412yes—
52C2×C3×Dic10D412yes—
53C2×C3×Dic10D412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8C2×C412yes—
57C4×Dic15—21no—
58C4×Dic15—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—21no—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3D412yes—
66C3×#677—28no—
67#6668—24no—
68#6665—42no—
69#6665—42no—
70Dic3×Dic5—24no—
71C22×C3×SD16—51no—
72C2×Q8×Dic3—51no—
73C2×#835—51no—
74#5221—51no—
75C2×#832—51no—
76#4551D511yescharacteristic, complemented
77#4550—51no—
78C22×D20C2×D311yescharacteristic
79C22×Dic10C2×D311yescharacteristic
80C22×C5×C8C2×D311yescharacteristic
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4—31no—
83C2×#685—61no—
84C2×#685—61no—
85C2×#683—61no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—61no—
88C22×#168—31no—
89C2×#677—22no—
90C2×#677—22no—
91C2×#677Dic314yescomplemented
92#4033—62no—
93#4033—62no—
94#3942—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—
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—21no—
112C2×Dic15—21no—
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15SD1612yescomplemented
117C2×C5×Dic3—22no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C3×D20—22no—
127C3×D20—22no—
128C3×D20—41no—
129C3×D20—41no—
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—22no—
133C3×Dic10C22⋊C414yescomplemented
134C3×C5×C8—22no—
135C3⋊#168—41no—
136C22×C3×Q8—51no—
137C22×C3×D4—51no—
138C2×C3×SD16—54no—
139C2×C3×SD16—102no—
140C2×C3×SD16—102no—
141C22×C3×C8C2×D511yescharacteristic
142C2×#217—101no—
143C2×#217—101no—
144Q8×Dic3—102no—
145Q8×Dic3—102no—
146C2×C4⋊Dic3—101no—
147C2×C4⋊Dic3C2×D511yescharacteristic
148C2×C4⋊Dic3C2×D511yescharacteristic
149C2×C4×Dic3—51no—
150C2×C4×Dic3—101no—
151C22×C3⋊C8—51no—
152#835—102no—
153#832—102no—
154C23×D5—21no—
155C22×C4×C5—61no—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—21no—
159C22×Dic5—31no—
160C22×Dic5—31no—
161C2×D20—21no—
162C2×D20—21no—
163C2×D20—21no—
164C2×D20—21no—
165C2×D20—21no—
166C2×D20C2×Dic312yes—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C2×Dic312yes—
171C2×Dic10#6712yes—
172C2×Dic10#6712yes—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8C2×Dic312yes—
176C5×C4⋊C4—32no—
177C5×C4⋊C4—61no—
178C5×C4⋊C4—61no—
179C5×C4⋊C4—61no—
180#685—122no—
181#685—122no—
182#683—64no—
183C4×Dic5—64no—
184C4×Dic5—61no—
185C4×Dic5—61no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189#677—28no—
190C22×SD16—51no—
191C2×C4×Q8—151no—
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×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×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—22no—
216Dic15—41no—
217C3×Dic5—24no—
218C5×Dic3—42no—
219C5×Dic3—81no—
220C24×C3—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—
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—101no—
234C22×C3×C4C22×D511yescharacteristic
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—51no—
238C22×Dic3—51no—
239C3×SD16—108no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8C4×D512yes—
243#217—202no—
244#217—202no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—104no—
249C4⋊Dic3D2012yes—
250C4×Dic3—104no—
251C4×Dic3—101no—
252C4×Dic3—101no—
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—
264C2×C4×C5—62no—
265C2×C4×C5—121no—
266C2×C4×C5—121no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5#23711yescharacteristic
272C2×C4×C5#23711yescharacteristic
273C2×C4×C5C22×Dic311yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—32no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285D20—22no—
286D20—22no—
287D20—41no—
288D20—41no—
289Dic10—22no—
290Dic10—22no—
291Dic10—22no—
292Dic10#21714yescomplemented
293C5×C8—22no—
294#168—121no—
295C22×Q8—51no—
296C22×D4—51no—
297C2×SD16—54no—
298C2×SD16—102no—
299C2×SD16—102no—
300C22×C8—151no—
301C22×C8D3×D511yescharacteristic
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42—301no—
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×C3D4×D511yescharacteristic
329C3×Q8—54no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—102no—
333C3×D4—102no—
334C3×D4—102no—
335C3×D4—201no—
336C3×D4—201no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4—102no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71311yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—52no—
353C2×Dic3—101no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C3×C8—22no—
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—122no—
375C4×C5—241no—
376C4×C5D4×Dic311yescharacteristic
377C4×C5#93511yescharacteristic
378C4×C5#93911yescharacteristic
379C4×C5C2×#21711yescharacteristic
380Dic5—24no—
381Dic5—62no—
382Dic5—121no—
383C24—101no—
384C2×Q8—52no—
385C2×Q8—52no—
386C2×Q8—52no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×D4—52no—
391C2×D4—101no—
392C2×D4—101no—
393C2×D4—101no—
394C2×D4—101no—
395C2×D4—101no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—101no—
399C22×C4—151no—
400C22×C4—151no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—108no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—301no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8D5×Dic312yes—
409C4⋊C4—32no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—304no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—304no—
417C42—301no—
418C42—301no—
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×C3#402811yescharacteristic
428C22×C3#403011yescharacteristic
429C22×C3#403911yescharacteristic
430C22×C3#405711yescharacteristic
431C22×C3D5×SD1611yescharacteristic
432C22×C3#406211yescharacteristic
433C22×C3#406411yescharacteristic
434C3×C4—104no—
435C3×C4C4×D2011yescharacteristic
436C3×C4D5×C22⋊C411yescharacteristic
437C3×C4#404011yescharacteristic
438C3×C4#404111yescharacteristic
439Dic3—42no—
440Dic3—81no—
441Dic3—102no—
442Dic3—201no—
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—
458C23#677711yescharacteristic
459Q8—54no—
460Q8—102no—
461Q8—102no—
462Q8—102no—
463D4—102no—
464D4—102no—
465D4—201no—
466D4—201no—
467C2×C4—62no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—152no—
477C2×C4—301no—
478C2×C4—301no—
479C2×C4—301no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4#676511yescharacteristic
483C2×C4#676611yescharacteristic
484C2×C4D3×D2011yescharacteristic
485C2×C4C2×D5×Dic311yescharacteristic
486C2×C4D5×#6711yescharacteristic
487C2×C4D5×#6711yescharacteristic
488C8—22no—
489C8—601no—
490C2×C3—402no—
491C2×C3#6495411yescharacteristic
492C2×C3#6505111yescharacteristic
493C2×C3#6507011yescharacteristic
494C2×C3#6508711yescharacteristic
495C2×C3#6509511yescharacteristic
496C2×C3#6514111yescharacteristic
497C2×C3#6517811yescharacteristic
498C5#7204811yescharacteristic, complemented, Sylow
499C22—202no—
500C22—202no—
501C22—202no—
502C22—401no—
503C22—401no—
504C22—401no—
505C22—401no—
506C22#9125511yescharacteristic
507C22#9125711yescharacteristic
508C22#9127611yescharacteristic
509C22#9127811yescharacteristic
510C22#9140811yescharacteristic
511C22#9143411yescharacteristic
512C22#9147411yescharacteristic
513C4—104no—
514C4—122no—
515C4—241no—
516C4—302no—
517C4—601no—
518C4#9140711yescharacteristic
519C4#9140911yescharacteristic
520C4Dic3×D2011yescharacteristic
521C4D5×#21711yescharacteristic
522C3#1059970211yescharacteristic, complemented, Sylow
523C2—402no—
524C2#1174780611yescharacteristic
525C2#1174781211yescharacteristic
526C2#1174783611yescharacteristic
527C2#1174788911yescharacteristic
528C2#1174789111yescharacteristic
529C2#1174799311yescharacteristic
530C2#1174889611yescharacteristic
subgroupG/H
centerC23#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1880
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
2. C2×#91331C2semidirect
4. C2×#90970C2semidirect
6. #11746371C2semidirect
7. C5×#4551C2semidirect
18. C2×C3×#677C4semidirect
76. #4551D5semidirect
91. C2×#677Dic3semidirect
116. C2×Dic15SD16semidirect
133. C3×Dic10C22⋊C4semidirect
292. Dic10#217semidirect
419. C3×C5#1880semidirect
498. C5#72048semidirect
522. C3#10599702semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6772
C2×#913312
#117487962
C2×#909702
C2×#909642
#117463712
C5×#45512
#105997023
#720485