Finite Group Databasebeta

← #14301113

Subgroups — #14301113

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×Q8×Dic15C211yesmaximal, characteristic, complemented
2C22×C5×#215C211yesmaximal, characteristic
3C2×C3×#3967C211yesmaximal, characteristic, complemented
4#11748797C211yesmaximal, characteristic
5C2×#90967C211yesmaximal, characteristic
6#11745980C211yesmaximal, characteristic, complemented
7#11745968C211yesmaximal, characteristic, complemented
8#10602841—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11Q8×Dic15—22no—
12Q8×Dic15—22no—
13C2×C4⋊Dic15—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×Dic15—21no—
16C2×C4×Dic15C2211yescharacteristic
17C2×C5×#215—22no—
18C2×C5×#215—22no—
19C2×C5×#215C414yescomplemented
20C22×C5×C3⋊C8C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23C2×(C2×D3)⋊Dic5—21no—
24C2×(C2×D3)⋊Dic5—21no—
25C3×#3967—22no—
26#90967—22no—
27#70240—51nomaximal, Hall
28C22×C5×SD16—31no—
29C2×Q8×Dic5—31no—
30C2×#3967D311yescharacteristic, complemented
31#65510—31no—
32C2×#3964—31no—
33#64771—31no—
34#64770—31no—
35C23×C5×D3—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×Dic15D411yescharacteristic
46C22×Dic15D411yescharacteristic
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12C2×C412yes—
53C22×C3×Dic5—21no—
54C4⋊Dic15—24no—
55C4⋊Dic15—21no—
56C4⋊Dic15D412yes—
57C4×Dic15—24no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C5×#215—28no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8C2×C412yes—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168—21no—
69(C2×D3)⋊Dic5—42no—
70(C2×D3)⋊Dic5—42no—
71C2×Q8×Dic3—51no—
72C22×#215D511yescharacteristic
73C2×C3×#103—51no—
74C2×#821—51no—
75#4988—51no—
76#4550—51no—
77#4529—51no—
78C22×C5×Q8C2×D311yescharacteristic
79C22×C5×D4—31no—
80C2×C5×SD16—34no—
81C2×C5×SD16—62no—
82C2×C5×SD16—62no—
83C22×C5×C8—31no—
84C2×C22⋊Dic5—61no—
85C2×C22⋊Dic5—61no—
86Q8×Dic5—62no—
87Q8×Dic5—62no—
88C2×C4⋊Dic5—31no—
89C2×C4⋊Dic5—61no—
90C2×C4⋊Dic5C2×D311yescharacteristic
91C2×C4×Dic5—31no—
92C2×C4×Dic5—61no—
93C22×#168C2×D311yescharacteristic
94#3967—22no—
95#3964—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×C5×D3—22no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C5×D3—41no—
104C22×C5×D3—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—21no—
119C2×Dic15—21no—
120C2×Dic15—21no—
121C2×Dic15—22no—
122C2×Dic15—21no—
123C2×Dic15—21no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×Dic15SD1612yescomplemented
127C5×D12—22no—
128C5×D12—22no—
129C5×D12—41no—
130C5×D12—41no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C3×#168—41no—
135C5×C3⋊C8—22no—
136C22×C3×Q8C2×D511yescharacteristic
137C22×D12C2×D511yescharacteristic
138C22×C3×C8—51no—
139C2×C3×C4⋊C4—51no—
140Q8×Dic3—102no—
141Q8×Dic3—102no—
142C2×#215—22no—
143C2×#215—22no—
144C2×#215Dic514yescomplemented
145C2×(C2×D3)⋊C4—101no—
146C2×(C2×D3)⋊C4—101no—
147C2×C4⋊Dic3—51no—
148C2×C4⋊Dic3—101no—
149C2×C4×Dic3—51no—
150C2×C4×Dic3—101no—
151C22×C3⋊C8C2×D511yescharacteristic
152C3×#103—102no—
153#821—102no—
154C24×C5—61no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8C4×D312yes—
159C2×C5×Q8D1212yes—
160C2×C5×Q8#6712yes—
161C2×C5×D4—32no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C22×C4×C5—21no—
168C22×C4×C5C22×D311yescharacteristic
169C22×Dic5—21no—
170C22×Dic5—31no—
171C22×Dic5—31no—
172C22×Dic5—61no—
173C5×SD16—68no—
174C2×C5×C8—32no—
175C2×C5×C8—61no—
176C2×C5×C8—61no—
177C22⋊Dic5—122no—
178C22⋊Dic5—122no—
179C4⋊Dic5—21no—
180C4⋊Dic5—21no—
181C4⋊Dic5—32no—
182C4⋊Dic5—64no—
183C4⋊Dic5—61no—
184C4×Dic5—64no—
185C4×Dic5—61no—
186C4×Dic5—61no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168—21no—
190C22×SD16—31no—
191C2×C4×Q8—151no—
192C2×#103—51no—
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×C5×D3—42no—
205C2×C5×D3—42no—
206C2×C5×D3—42no—
207C2×C5×D3—81no—
208C2×C5×D3—81no—
209C2×C5×D3—81no—
210C2×C5×D3—81no—
211C3×C4×C5—24no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—22no—
217Dic15—41no—
218Dic15—42no—
219C3×Dic5—81no—
220C23×D3—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C2×Dic512yes—
225C2×C3×Q8C22⋊D512yes—
226C2×C3×Q8C22⋊D512yes—
227C22×C3×C4—21no—
228C22×C3×C4—101no—
229C22×C3×C4C22×D511yescharacteristic
230C22×Dic3—51no—
231C22×Dic3—51no—
232C22×Dic3—101no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12C2×Dic512yes—
239C2×C3×C8—101no—
240C2×C3×C8—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—101no—
243C3×C4⋊C4—101no—
244#215—28no—
245(C2×D3)⋊C4—202no—
246(C2×D3)⋊C4—202no—
247C4⋊Dic3—52no—
248C4⋊Dic3—104no—
249C4⋊Dic3—101no—
250C4×Dic3—104no—
251C4×Dic3—101no—
252C4×Dic3—101no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8C2×Dic512yes—
256C23×C5—62no—
257C23×C5—121no—
258C23×C5—121no—
259C23×C5—121no—
260C23×C5—121no—
261C23×C5—121no—
262C23×C5—121no—
263C23×C5D3×D411yescharacteristic
264C5×Q8—22no—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8(C2×D3)⋊C414yescomplemented
268C5×D4—62no—
269C5×D4—62no—
270C5×D4—121no—
271C5×D4—121no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5C2×C4×D311yescharacteristic
276C2×C4×C5C2×D1211yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5#23711yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×C4×C5C2×#6711yescharacteristic
281C2×Dic5—32no—
282C2×Dic5—41no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—62no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291C2×Dic5—121no—
292C2×Dic5—121no—
293C5×C8—62no—
294#168—41no—
295C22×Q8D3×D511yescharacteristic
296C22×D4—31no—
297C2×SD16—34no—
298C2×SD16—62no—
299C2×SD16—62no—
300C22×C8—31no—
301C22×C8—51no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42—301no—
311#103—102no—
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
320C5×D3—82no—
321C23×C3D4×D511yescharacteristic
322C22×D3—22no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8C22⋊Dic514yescomplemented
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4—201no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71111yescharacteristic
341C2×C3×C4#71111yescharacteristic
342C2×C3×C4C22×Dic511yescharacteristic
343C2×C3×C4C2×C22⋊D511yescharacteristic
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350C2×Dic3—102no—
351C2×Dic3—101no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354D12—22no—
355D12—22no—
356D12—41no—
357D12—41no—
358C3×C8—201no—
359C3⋊C8—22no—
360C22×C5—122no—
361C22×C5—122no—
362C22×C5—122no—
363C22×C5—241no—
364C22×C5—241no—
365C22×C5—241no—
366C22×C5—241no—
367C22×C5#67⋊C411yescharacteristic
368C22×C5#88211yescharacteristic
369C22×C5D3×SD1611yescharacteristic
370C22×C5#91411yescharacteristic
371C22×C5#91811yescharacteristic
372C22×C5#91911yescharacteristic
373C22×C5#93911yescharacteristic
374C4×C5—24no—
375C4×C5#67⋊C411yescharacteristic
376C4×C5#88611yescharacteristic
377C4×C5C2×(C2×D3)⋊C411yescharacteristic
378C4×C5#93911yescharacteristic
379Dic5—62no—
380Dic5—81no—
381Dic5—121no—
382Dic5—122no—
383C24—61no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8D3×Dic512yes—
388C2×Q8#120112yes—
389C2×Q8#120312yes—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C22×C4—21no—
397C22×C4—101no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—68no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—101no—
407C2×C8—101no—
408C2×C8—101no—
409C4⋊C4—101no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—304no—
413C4⋊C4—301no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—304no—
417C42—301no—
418C42—301no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3D5×SD1611yescharacteristic
421C22×C3#406011yescharacteristic
422C22×C3#406111yescharacteristic
423C22×C3#406211yescharacteristic
424C22×C3D4×Dic511yescharacteristic
425C22×C3#408311yescharacteristic
426C22×C3#408511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—81no—
431C2×D3—81no—
432C2×D3—81no—
433C2×D3—81no—
434C3×C4—24no—
435C3×C4—401no—
436C3×C4D4×Dic511yescharacteristic
437C3×C4#408111yescharacteristic
438C3×C4#408511yescharacteristic
439C3×C4C2×C22⋊Dic511yescharacteristic
440Dic3—102no—
441Dic3—201no—
442Dic3—202no—
443C2×C5—242no—
444C2×C5#478811yescharacteristic
445C2×C5#480611yescharacteristic
446C2×C5#481011yescharacteristic
447C2×C5#481711yescharacteristic
448C2×C5#495811yescharacteristic
449C2×C5#516311yescharacteristic
450C2×C5#518511yescharacteristic
451C23—62no—
452C23—121no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23#679011yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—22no—
462Q8(C2×D3)⋊Dic514yescomplemented
463D4—62no—
464D4—62no—
465D4—121no—
466D4—121no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—152no—
471C2×C4—201no—
472C2×C4—201no—
473C2×C4—201no—
474C2×C4—301no—
475C2×C4—301no—
476C2×C4—301no—
477C2×C4—301no—
478C2×C4—302no—
479C2×C4—301no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4#678011yescharacteristic
483C2×C4#678011yescharacteristic
484C2×C4C2×D3×Dic511yescharacteristic
485C2×C4C2×#120111yescharacteristic
486C2×C4C2×#120311yescharacteristic
487C2×C4#679011yescharacteristic
488C8—62no—
489C8—201no—
490C2×C3SD16×Dic511yescharacteristic
491C2×C3#6545211yescharacteristic
492C2×C3#6545311yescharacteristic
493C2×C3#6545511yescharacteristic
494C2×C3#6545911yescharacteristic
495C2×C3#6546111yescharacteristic
496C2×C3#6550911yescharacteristic
497D3—82no—
498C5#7024011yescharacteristic, complemented, Sylow
499C22—122no—
500C22—122no—
501C22—122no—
502C22—241no—
503C22—241no—
504C22—241no—
505C22—241no—
506C22#9150511yescharacteristic
507C22#9150611yescharacteristic
508C22#9152311yescharacteristic
509C22#9152411yescharacteristic
510C22#67⋊Dic511yescharacteristic
511C22#9157111yescharacteristic
512C22#9157311yescharacteristic
513C4—24no—
514C4—302no—
515C4—401no—
516C4—601no—
517C4—602no—
518C4C2×(C2×D3)⋊Dic511yescharacteristic
519C4#9154311yescharacteristic
520C4#67⋊Dic511yescharacteristic
521C4#9157111yescharacteristic
522C3#1060284111yescharacteristic, complemented, Sylow
523C2—242no—
524C2#1174924011yescharacteristic
525C2#1174924211yescharacteristic
526C2#1174928711yescharacteristic
527C2#1174928911yescharacteristic
528C2#1174932811yescharacteristic
529C2#1174934611yescharacteristic
530C2#1174950111yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
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×Q8×Dic15C2semidirect
3. C2×C3×#3967C2semidirect
6. #11745980C2semidirect
7. #11745968C2semidirect
19. C2×C5×#215C4semidirect
30. C2×#3967D3semidirect
108. C3×C5×Q8C22⋊C4semidirect
126. C2×Dic15SD16semidirect
144. C2×#215Dic5semidirect
267. C5×Q8(C2×D3)⋊C4semidirect
332. C3×Q8C22⋊Dic5semidirect
419. C3×C5#1880semidirect
462. Q8(C2×D3)⋊Dic5semidirect
498. C5#70240semidirect
522. C3#10602841semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
C22×C5×#2152
C2×C3×#39672
#117487972
C2×#909672
#117459802
#117459682
#106028413
#702405