Finite Group Databasebeta

← #14427832

Subgroups — #14427832

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×D15C211yesmaximal, characteristic, complemented
2#11754379C212yesmaximal, complemented
3C2×#91279C211yesmaximal, characteristic, complemented
4C5×#5115C211yesmaximal, characteristic, complemented
5C3×#65405C211yesmaximal, characteristic, complemented
6#11748547C212yesmaximal, complemented
7#11748145C212yesmaximal, complemented
8#11747958C211yesmaximal, characteristic, complemented
9#11747933C211yesmaximal, characteristic, complemented
10#11747928C212yesmaximal, complemented
11#11747690C211yesmaximal, characteristic, complemented
12#10612445—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×#6768C2212yes—
15C22×C3×C5×C8C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C8×D15—24no—
18C2×C8×D15C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20C2×C8×D15C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C5×#930C2212yes—
23C2×C5×D24C2211yescharacteristic, complemented
24C3×#4070C2212yes—
25C2×C3×Dic20C2211yescharacteristic, complemented
26#91573—22no—
27#67⋊Dic5—22no—
28#91466C2212yes—
29#91406—22no—
30#91390C2212yes—
31#91355—22no—
32#91347C2212yes—
33C2×#6656C2212yescomplemented
34#91279—24no—
35C5×#821C2212yescomplemented
36C5×#818C2211yescharacteristic, complemented
37C3×#3950C2211yescharacteristic, complemented
38C3×#3948C2212yescomplemented
39#90986C2212yescomplemented
40#90970C2212yescomplemented
41#90966C2212yescomplemented
42#80758—51nomaximal, Hall
43C2×#4058—31no—
44C22×C8×D5—31no—
45#65940—32no—
46C5×#466—31no—
47#65446—31no—
48#65405D311yescharacteristic, complemented
49#65330—32no—
50#65176—31no—
51#65169—31no—
52#65067—32no—
53#65061—32no—
54C23×D15D411yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15D411yescharacteristic
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15D411yescharacteristic
60C2×C4×D15D411yescharacteristic
61C2×C4×D15C2311yescharacteristic
62C2×C4×D15C2311yescharacteristic
63C2×C5×#67—22no—
64C2×C5×D12C2312yes—
65C2×C3×Dic10C2312yes—
66C2×#1203—22no—
67C2×#1203—22no—
68C2×D3×Dic5—22no—
69#6768—24no—
70#6768—24no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2311yescharacteristic
73C2×C3×C5×C8C2311yescharacteristic
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2311yescharacteristic
76C2×C3⋊#168C2311yescharacteristic
77C8×D15—22no—
78C8×D15—22no—
79C8×D15—22no—
80C8×D15D414yescomplemented
81C5×(C2×D3)⋊C4—22no—
82C5×C4⋊Dic3C2312yes—
83C5×D24—22no—
84C3×C22⋊Dic5—22no—
85C3×C4⋊Dic5C2312yes—
86C3×#683—22no—
87C3×Dic20—22no—
88Dic3⋊Dic5—22no—
89#6667—22no—
90#6667—22no—
91(C2×D3)⋊Dic5—22no—
92Dic3×Dic5—22no—
93#6656—24no—
94C2×#919—51no—
95C22×D3×C8—51no—
96#5627—52no—
97C3×#467—51no—
98#5188—51no—
99#5115D511yescharacteristic, complemented
100#5048—52no—
101#4883—51no—
102#4880—51no—
103#4807—52no—
104#4804—52no—
105C2×#711—32no—
106C22×C4×D5—31no—
107C2×C5×D8—31no—
108C22×C5×C8C2×D311yescharacteristic
109C5×#121—32no—
110#4084—32no—
111#4083—62no—
112D4×Dic5—62no—
113C2×#687—32no—
114#4070C2×D312yes—
115C22×#168—31no—
116#4058—64no—
117C2×Dic20C2×D311yescharacteristic, complemented
118C2×C8×D5—31no—
119C2×C8×D5—31no—
120C2×C8×D5—31no—
121C2×C8×D5—31no—
122C2×C8×D5—64no—
123#4043—32no—
124#4038—32no—
125#4029—62no—
126#4027—62no—
127C5×#107—31no—
128C5×#102—32no—
129#3964—32no—
130#3950C2×D311yescharacteristic, complemented
131#3948C2×D312yescomplemented
132#3942—32no—
133#3940—32no—
134#3050—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15C2×D411yescharacteristic
140C22×D15C2×D411yescharacteristic
141C22×C5×D3—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15C2×D411yescharacteristic
148C2×Dic15C2×D411yescharacteristic
149C4×D15—22no—
150C4×D15—21no—
151C4×D15—21no—
152C4×D15—22no—
153C4×D15C2×D412yes—
154C4×D15#4112yes—
155C5×#67—44no—
156C2×C5×Dic3—22no—
157C5×D12—22no—
158C5×D12—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C3×Dic10—22no—
162C3×Dic10—22no—
163#1203—44no—
164#1203—44no—
165D3×Dic5—44no—
166C3×C5×C8—21no—
167C3×C5×C8C2×D412yes—
168C3⋊#168—21no—
169C3⋊#168C2×D412yes—
170C2×#239—52no—
171C22×C4×D3—51no—
172C2×C3×Q16—51no—
173C22×C3×C8C2×D511yescharacteristic
174C3×C22⋊Q8—52no—
175#946—52no—
176C2×#215—52no—
177#930C2×D512yes—
178C22×C3⋊C8—51no—
179#919—104no—
180C2×D24C2×D511yescharacteristic, complemented
181C2×D3×C8—51no—
182C2×D3×C8—51no—
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—104no—
186#895—52no—
187#894—102no—
188#893—102no—
189#892—52no—
190#882—102no—
191#67⋊C4—102no—
192C3×#107—51no—
193C3×#103—52no—
194#835—52no—
195#821C2×D512yescomplemented
196#818C2×D511yescharacteristic, complemented
197#809—52no—
198#808—52no—
199C23×D5—31no—
200C2×C5×D4—32no—
201C2×C5×D4—62no—
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—62no—
204C2×C22⋊D5—62no—
205C22×Dic5—31no—
206C22×Dic5—62no—
207#711—64no—
208#711—64no—
209C2×C4×D5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—62no—
214C2×C4×D5—62no—
215C2×Dic10C22×D312yes—
216C5×D8—62no—
217C2×C5×C8—22no—
218C2×C5×C8C22×D311yescharacteristic
219C2×C5×C8C22×D311yescharacteristic
220C5×C4⋊C4—32no—
221C5×C22⋊C4—62no—
222C22⋊Dic5—22no—
223C22⋊Dic5—62no—
224#687—64no—
225#685—62no—
226#685—62no—
227C4⋊Dic5—62no—
228C4⋊Dic5C22×D312yes—
229#683—22no—
230C4×Dic5—62no—
231C2×#168—31no—
232C2×#168—31no—
233C2×#168—62no—
234Dic20—22no—
235C8×D5—34no—
236C8×D5—62no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—151no—
240C23×C8—151no—
241#525—152no—
242#467—51no—
243#467—151no—
244#466—31no—
245#466—151no—
246#465—152no—
247#465—152no—
248#427—151no—
249#416—152no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5#13512yescomplemented
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—28no—
255C2×D15—21no—
256C2×D15—21no—
257C2×D15—21no—
258C2×D15—21no—
259C2×D15#12112yes—
260C2×D15#13512yescomplemented
261C2×C5×D3—42no—
262C2×C5×D3—42no—
263C2×C5×D3—42no—
264C3×C4×C5—21no—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—21no—
268Dic15#12112yes—
269C3×Dic5—42no—
270C3×Dic5—42no—
271C5×Dic3—42no—
272C23×D3—51no—
273C2×C3×Q8—52no—
274C22×C3×C4C22×D511yescharacteristic
275C2×#67—22no—
276C22×Dic3—51no—
277#239—104no—
278#239—104no—
279C2×D12—102no—
280C2×D12—102no—
281C2×D12C22×D512yes—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—51no—
286C2×C4×D3—102no—
287C2×C4×D3—102no—
288C2×C4×D3—102no—
289C3×Q16—102no—
290C2×C3×C8—22no—
291C2×C3×C8C22×D511yescharacteristic
292C2×C3×C8C22×D511yescharacteristic
293C3×C4⋊C4—52no—
294C3×C4⋊C4—102no—
295C3×C22⋊C4—102no—
296#215—104no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—102no—
299(C2×D3)⋊C4—102no—
300(C2×D3)⋊C4—102no—
301C4⋊Dic3C22×D512yes—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—102no—
307D24—22no—
308D3×C8—54no—
309D3×C8—102no—
310D3×C8—102no—
311D3×C8—102no—
312C23×C5—62no—
313C23×C5D3×D411yescharacteristic
314C22×D5—31no—
315C22×D5—31no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5—62no—
319C5×D4—62no—
320C5×D4—62no—
321C5×D4—124no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—62no—
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—124no—
328C22⋊D5—124no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—31no—
332C2×Dic5—31no—
333C2×Dic5—62no—
334C2×Dic5—124no—
335C4×D5—32no—
336C4×D5—32no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5—61no—
340C4×D5—61no—
341Dic10—22no—
342Dic10—22no—
343C5×C8—21no—
344C5×C8D3×D412yes—
345#168—32no—
346#168—61no—
347C2×#41—152no—
348C23×C4—151no—
349#135—304no—
350C2×Q16—51no—
351C2×SD16—152no—
352C2×D8—31no—
353C22×C8—151no—
354C22×C8—151no—
355C22×C8—151no—
356C22×C8—151no—
357C22×C8—151no—
358C22×C8—304no—
359C22×C8D3×D511yescharacteristic
360#123—302no—
361C22⋊Q8—52no—
362C22⋊Q8—152no—
363#121—32no—
364#121—152no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—152no—
369#107—31no—
370#107—51no—
371#106—152no—
372#103—52no—
373#103—152no—
374#102—32no—
375#102—152no—
376C2×C3×C5—22no—
377C2×C3×C5C2×#12111yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379C2×C3×C5C2×#13511yescharacteristic
380D15—22no—
381D15—22no—
382C5×D3—82no—
383C23×C3D4×D511yescharacteristic
384C22×D3—22no—
385C22×D3—51no—
386C22×D3—51no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3—102no—
390C3×Q8—102no—
391C3×Q8—102no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—44no—
399C2×Dic3—22no—
400C2×Dic3—51no—
401C2×Dic3—51no—
402C2×Dic3—102no—
403D12—22no—
404D12—22no—
405D12—204no—
406D12—204no—
407C4×D3—52no—
408C4×D3—52no—
409C4×D3—102no—
410C4×D3—102no—
411C4×D3—101no—
412C4×D3—101no—
413C4×D3—204no—
414C3×C8—21no—
415C3×C8D4×D512yes—
416C3⋊C8—52no—
417C3⋊C8—101no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—122no—
421C22×C5—122no—
422C22×C5—122no—
423C22×C5#91912yescomplemented
424C22×C5C2×D3×D411yescharacteristic
425C2×D5—32no—
426C2×D5—32no—
427C2×D5—68no—
428C2×D5—61no—
429C2×D5—61no—
430C2×D5—61no—
431C2×D5—61no—
432C4×C5—21no—
433C4×C5—122no—
434C4×C5C2×D3×D411yescharacteristic
435C4×C5D3×#4111yescharacteristic
436Dic5—32no—
437Dic5—42no—
438Dic5—42no—
439Dic5—61no—
440C24—151no—
441#41—304no—
442#41—304no—
443C2×Q8—52no—
444C2×D4—32no—
445C2×D4—62no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—302no—
454C22×C4—302no—
455C22×C4—302no—
456C22×C4C2×D3×D511yescharacteristic
457Q16—102no—
458SD16—304no—
459D8—62no—
460C2×C8—22no—
461C2×C8—151no—
462C2×C8—154no—
463C2×C8—151no—
464C2×C8—302no—
465C2×C8—302no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8C2×D3×D511yescharacteristic
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—52no—
472C4⋊C4—102no—
473C4⋊C4—302no—
474C22⋊C4—62no—
475C22⋊C4—102no—
476C22⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C42—302no—
480C3×C5#305011yescharacteristic, complemented, Hall
481C22×C3—21no—
482C22×C3—21no—
483C22×C3#405812yescomplemented
484C22×C3C2×D4×D511yescharacteristic
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—52no—
489C2×D3—52no—
490C2×D3—108no—
491C2×D3—101no—
492C2×D3—101no—
493C2×D3—101no—
494C2×D3—101no—
495C3×C4—21no—
496C3×C4—202no—
497C3×C4—202no—
498C3×C4C2×D4×D511yescharacteristic
499C3×C4D5×#4111yescharacteristic
500Dic3—42no—
501Dic3—52no—
502Dic3—101no—
503C2×C5—22no—
504C2×C5—242no—
505C2×C5D3×#12111yescharacteristic
506C2×C5C2×#91911yescharacteristic
507C2×C5D3×#13511yescharacteristic
508D5—62no—
509D5—62no—
510C23—62no—
511C23—151no—
512C23—151no—
513C23—302no—
514C23—302no—
515C23—302no—
516C23#677711yescharacteristic
517Q8—102no—
518Q8—102no—
519D4—62no—
520D4—62no—
521D4—124no—
522D4—604no—
523D4—604no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—62no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—151no—
530C2×C4—152no—
531C2×C4—152no—
532C2×C4—151no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—604no—
539C2×C4#677711yescharacteristic
540C2×C4C22×D3×D511yescharacteristic
541C8—21no—
542C8—152no—
543C8—301no—
544C8#679012yes—
545C2×C3—22no—
546C2×C3D5×#12111yescharacteristic
547C2×C3C2×#405811yescharacteristic
548C2×C3D5×#13511yescharacteristic
549D3—82no—
550D3—102no—
551D3—102no—
552C5#8075811yescharacteristic, complemented, Sylow
553C22—21no—
554C22—21no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—152no—
559C22—152no—
560C22—308no—
561C22—301no—
562C22—301no—
563C22—301no—
564C22—301no—
565C22#9127912yescomplemented
566C22C2×#677711yescharacteristic
567C4—21no—
568C4—122no—
569C4—152no—
570C4—202no—
571C4—202no—
572C4—301no—
573C4#9201611yescharacteristic
574C4C2×#679011yescharacteristic
575C3#1061244511yescharacteristic, complemented, Sylow
576C2—22no—
577C2—242no—
578C2—302no—
579C2—302no—
580C2#1175397811yescharacteristic
581C2C2×#9127911yescharacteristic
582C2#1175467011yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×D15C2semidirect
2. #11754379C2semidirect
3. C2×#91279C2semidirect
4. C5×#5115C2semidirect
5. C3×#65405C2semidirect
6. #11748547C2semidirect
7. #11748145C2semidirect
8. #11747958C2semidirect
9. #11747933C2semidirect
10. #11747928C2semidirect
11. #11747690C2semidirect
23. C2×C5×D24C22semidirect
25. C2×C3×Dic20C22semidirect
33. C2×#6656C22semidirect
35. C5×#821C22semidirect
36. C5×#818C22semidirect
37. C3×#3950C22semidirect
38. C3×#3948C22semidirect
39. #90986C22semidirect
40. #90970C22semidirect
41. #90966C22semidirect
48. #65405D3semidirect
80. C8×D15D4semidirect
99. #5115D5semidirect
117. C2×Dic20C2×D3semidirect
130. #3950C2×D3semidirect
131. #3948C2×D3semidirect
180. C2×D24C2×D5semidirect
195. #821C2×D5semidirect
196. #818C2×D5semidirect
252. C22×C3×C5#135semidirect
260. C2×D15#135semidirect
423. C22×C5#919semidirect
480. C3×C5#3050semidirect
483. C22×C3#4058semidirect
552. C5#80758semidirect
565. C22#91279semidirect
575. C3#10612445semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D152
#117543792
C2×#912792
C5×#51152
C3×#654052
#117485472
#117481452
#117479582
#117479332
#117479282
#117476902
#106124453
#807585