Finite Group Databasebeta

← #14301124

Subgroups — #14301124

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×Dic5×Dic6C211yesmaximal, characteristic, complemented
2C22×#6655C211yesmaximal, characteristic
3C2×C5×#810C211yesmaximal, characteristic, complemented
4C3×#65277C211yesmaximal, characteristic
5C2×#90965C211yesmaximal, characteristic
6#11746350C211yesmaximal, characteristic, complemented
7#11745966C211yesmaximal, characteristic, complemented
8#10601033—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×#685—21no—
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×Dic3⋊Dic5—21no—
19C2×Dic3×Dic5—21no—
20Dic5×Dic6—22no—
21Dic5×Dic6—22no—
22C2×#6655—22no—
23C2×#6655—22no—
24C2×#6655C414yescomplemented
25C5×#810—22no—
26#90965—22no—
27#69660—51nomaximal, Hall
28C2×Q8×Dic5—31no—
29C22×#688—31no—
30C2×C5×#103—31no—
31C2×#3953—31no—
32#65277D311yescharacteristic
33#64770—31no—
34#64749—31no—
35C23×C3×D5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C2×C5×Dic6—21no—
41C2×C5×Dic6—21no—
42C2×C5×Dic6—21no—
43C2×C5×Dic6C2×C412yes—
44C2×C5×Dic6D412yes—
45C2×C5×Dic6D412yes—
46C22×C3×Dic5D411yescharacteristic
47C22×C3×Dic5D411yescharacteristic
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20C2×C412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15D412yes—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168C2×C412yes—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8—21no—
64C3×#685—42no—
65C3×#685—42no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68Dic3⋊Dic5—24no—
69Dic3×Dic5—24no—
70#6655—28no—
71C22×#214—51no—
72C2×C4×Dic6—51no—
73C3×#390—51no—
74C2×#832—51no—
75C2×#810D511yescharacteristic, complemented
76#4529—51no—
77#4524—51no—
78C22×C5×Q8—31no—
79C22×D20C2×D311yescharacteristic
80C22×C5×C8—31no—
81C2×C5×C4⋊C4C2×D311yescharacteristic
82Q8×Dic5—62no—
83Q8×Dic5—62no—
84C2×#688—34no—
85C2×#688—62no—
86C2×#688—62no—
87C2×#685—21no—
88C2×#685—21no—
89C2×C4⋊Dic5—31no—
90C2×C4⋊Dic5—61no—
91C2×C4×Dic5—61no—
92C2×C4×Dic5C2×D311yescharacteristic
93C22×#168—31no—
94C5×#103—62no—
95#3953—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×C5—41no—
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
114C2×Dic15—22no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—22no—
119C2×C5×Dic3—22no—
120C5×Dic6—22no—
121C5×Dic6—22no—
122C5×Dic6—22no—
123C5×Dic6C22⋊C414yescomplemented
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5SD1612yescomplemented
130C3×D20—22no—
131C3×D20—22no—
132C3×D20—41no—
133C3×D20—41no—
134C3⋊#168—22no—
135C5×C3⋊C8—41no—
136C22×C3×D4—51no—
137C22×Dic6C2×D511yescharacteristic
138C2×C3×C4⋊C4C2×D511yescharacteristic
139C2×C3×C22⋊C4—101no—
140C2×C3×C22⋊C4—101no—
141C2×C3×C42—51no—
142C2×#214—54no—
143C2×#214—102no—
144C2×#214—102no—
145C2×C4⋊Dic3—51no—
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—101no—
148C22×C3⋊C8—51no—
149C22×C3⋊C8C2×D511yescharacteristic
150C4×Dic6—102no—
151C4×Dic6—102no—
152#832—102no—
153#810—22no—
154C23×D5—21no—
155C2×C5×Q8—32no—
156C2×C5×Q8—32no—
157C2×C5×Q8—32no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C2×C5×Q8—61no—
161C22×C4×C5—21no—
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C22×Dic5—61no—
165C22×Dic5#6711yescharacteristic
166C22×Dic5#6711yescharacteristic
167C2×D20—21no—
168C2×D20—21no—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20C4×D312yes—
173C2×C5×C8—61no—
174C2×C5×C8—61no—
175C2×C5×C8—61no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178#688—68no—
179#685—42no—
180#685—42no—
181C4⋊Dic5—32no—
182C4⋊Dic5—64no—
183C4⋊Dic5—61no—
184C4×Dic5—21no—
185C4×Dic5—21no—
186C4×Dic5—64no—
187C2×#168—32no—
188C2×#168—61no—
189C2×#168—61no—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—31no—
193C2×#102—151no—
194#390—51no—
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—81no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—42no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C5×Dic3—24no—
220C24×C3—101no—
221C2×C3×D4—52no—
222C2×C3×D4—101no—
223C2×C3×D4—101no—
224C2×C3×D4—101no—
225C2×C3×D4—101no—
226C2×C3×D4—101no—
227C22×C3×C4—21no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—101no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6C4×D512yes—
237C2×Dic6D2012yes—
238C2×Dic6C22⋊D512yes—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C22⋊C4—202no—
242C3×C22⋊C4—202no—
243C3×C42—101no—
244C3×C42—101no—
245#214—108no—
246C4⋊Dic3—52no—
247C4⋊Dic3—101no—
248Dic3⋊C4—104no—
249C4×Dic3—104no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—52no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8—101no—
256C23×C5C2×#6711yescharacteristic
257C22×D5—22no—
258C22×D5—41no—
259C22×D5—41no—
260C22×D5—41no—
261C22×D5—41no—
262C22×D5—41no—
263C22×D5—41no—
264C5×Q8—34no—
265C5×Q8—62no—
266C5×Q8—62no—
267C5×Q8—62no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—62no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5C2×C4×D311yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—62no—
286C2×Dic5—121no—
287C2×Dic5—121no—
288C2×Dic5#21412yescomplemented
289D20—22no—
290D20—22no—
291D20—41no—
292D20—41no—
293C5×C8—121no—
294#168—62no—
295C22×Q8—31no—
296C22×D4—51no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—31no—
301C22×C8—151no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—301no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C22⋊C4—101no—
308C2×C22⋊C4—101no—
309C2×C42—51no—
310C2×C42—301no—
311#103—62no—
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×D4—102no—
330C3×D4—102no—
331C3×D4—201no—
332C3×D4—201no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—52no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—101no—
341C2×C3×C4—101no—
342C2×C3×C4C2×C4×D511yescharacteristic
343C2×C3×C4C2×D2011yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71111yescharacteristic
346C2×C3×C4#71111yescharacteristic
347C2×C3×C4C2×C22⋊D511yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—102no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354Dic6—22no—
355Dic6—22no—
356Dic6—22no—
357Dic6#68514yescomplemented
358C3⋊C8—41no—
359C3⋊C8—102no—
360C22×C5C4×#6711yescharacteristic
361C22×C5#93211yescharacteristic
362C22×C5C2×#21411yescharacteristic
363C22×C5#93711yescharacteristic
364C22×C5#93811yescharacteristic
365C22×C5#95011yescharacteristic
366C22×C5#95111yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C2×D5—81no—
371C2×D5—81no—
372C2×D5—81no—
373C2×D5—81no—
374C4×C5—64no—
375C4×C5—81no—
376C4×C5D3×C22⋊C411yescharacteristic
377C4×C5#67⋊C411yescharacteristic
378C4×C5#88311yescharacteristic
379C4×C5#88411yescharacteristic
380Dic5—22no—
381Dic5—41no—
382Dic5—122no—
383C24—101no—
384C2×Q8—32no—
385C2×Q8—32no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×D4—52no—
391C2×D4—101no—
392C2×D4—101no—
393C2×D4—101no—
394C2×D4—101no—
395C2×D4—101no—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—61no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—152no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—152no—
412C4⋊C4—304no—
413C4⋊C4—301no—
414C22⋊C4—202no—
415C22⋊C4—202no—
416C42—101no—
417C42—101no—
418C42—304no—
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#402711yescharacteristic
428C22×C3#402811yescharacteristic
429C22×C3D5×SD1611yescharacteristic
430C22×C3#406011yescharacteristic
431C22×C3#406411yescharacteristic
432C22×C3#406511yescharacteristic
433C22×C3#408511yescharacteristic
434C3×C4—81no—
435C3×C4—102no—
436C3×C4—201no—
437C3×C4#402711yescharacteristic
438C3×C4#403211yescharacteristic
439C3×C4C2×#68511yescharacteristic
440C3×C4#408511yescharacteristic
441Dic3—24no—
442Dic3—202no—
443C2×C5#495611yescharacteristic
444C2×C5C4×#21411yescharacteristic
445C2×C5#501811yescharacteristic
446C2×C5#503711yescharacteristic
447C2×C5#504011yescharacteristic
448C2×C5#505411yescharacteristic
449C2×C5#507511yescharacteristic
450D5—82no—
451C23—102no—
452C23—201no—
453C23—201no—
454C23—201no—
455C23—201no—
456C23—201no—
457C23—201no—
458C23D5×#6711yescharacteristic
459Q8—34no—
460Q8—62no—
461Q8—62no—
462Q8—62no—
463D4—102no—
464D4—102no—
465D4—201no—
466D4—201no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—52no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—101no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—101no—
479C2×C4—302no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4#677211yescharacteristic
483C2×C4C4×D3×D511yescharacteristic
484C2×C4D3×D2011yescharacteristic
485C2×C4#677711yescharacteristic
486C2×C4#678011yescharacteristic
487C2×C4D3×C22⋊D511yescharacteristic
488C8—121no—
489C8—302no—
490C2×C3—402no—
491C2×C3#6507711yescharacteristic
492C2×C3#6509511yescharacteristic
493C2×C3#6510011yescharacteristic
494C2×C3#6510611yescharacteristic
495C2×C3#6524711yescharacteristic
496C2×C3#6545211yescharacteristic
497C2×C3#6547411yescharacteristic
498C5#6966011yescharacteristic, complemented, Sylow
499C22—202no—
500C22—202no—
501C22—202no—
502C22—401no—
503C22—401no—
504C22—401no—
505C22—401no—
506C22#9144011yescharacteristic
507C22#9147411yescharacteristic
508C22D5×#21411yescharacteristic
509C22#9149111yescharacteristic
510C22#9150811yescharacteristic
511C22#9151611yescharacteristic
512C22#9156511yescharacteristic
513C4—64no—
514C4—81no—
515C4—102no—
516C4—201no—
517C4—602no—
518C4#9144211yescharacteristic
519C4#9145311yescharacteristic
520C4#9145711yescharacteristic
521C4D3×#68511yescharacteristic
522C3#1060103311yescharacteristic, complemented, Sylow
523C2—402no—
524C2#1174726111yescharacteristic
525C2#1174747111yescharacteristic
526C2#1174749311yescharacteristic
527C2#1174751211yescharacteristic
528C2#1174891111yescharacteristic
529C2#1174899911yescharacteristic
530C2#1174924911yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
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×Dic5×Dic6C2semidirect
3. C2×C5×#810C2semidirect
6. #11746350C2semidirect
7. #11745966C2semidirect
24. C2×#6655C4semidirect
75. C2×#810D5semidirect
123. C5×Dic6C22⋊C4semidirect
129. C2×C3×Dic5SD16semidirect
288. C2×Dic5#214semidirect
357. Dic6#685semidirect
419. C3×C5#1880semidirect
498. C5#69660semidirect
522. C3#10601033semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×Dic62
C22×#66552
C2×C5×#8102
C3×#652772
C2×#909652
#117463502
#117459662
#106010333
#696605