Finite Group Databasebeta

← #14427874

Subgroups — #14427874

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
1C2×#91801C211yesmaximal, characteristic, complemented
2#11755070C212yesmaximal, complemented
3C2×D3×C8×D5C211yesmaximal, characteristic, complemented
4C5×#5157C211yesmaximal, characteristic, complemented
5C3×#65446C211yesmaximal, characteristic, complemented
6#11749055C212yesmaximal, complemented
7#11749046C212yesmaximal, complemented
8#11748969C212yesmaximal, complemented
9#11747950C211yesmaximal, characteristic, complemented
10#11747943C211yesmaximal, characteristic, complemented
11#11747690C211yesmaximal, characteristic, complemented
12#10612445—31nomaximal, Hall
13C2×#6819C2212yes—
14C2×C4×D3×D5C2211yescharacteristic
15C2×C3×C5×D8C2211yescharacteristic, complemented
16C2×#6716C2212yescomplemented
17#91801—24no—
18C2×Dic60C2211yescharacteristic, complemented
19C2×C8×D15C2211yescharacteristic
20C5×#938C2212yes—
21C2×C5×D3×C8C2211yescharacteristic
22C3×#4084C2212yes—
23C2×C3×C8×D5C2211yescharacteristic
24#91577—22no—
25#91562—22no—
26#67⋊Dic5—22no—
27#91559—22no—
28#91365C2212yes—
29#91360C2212yes—
30#91347C2212yes—
31C2×#6648C2211yescharacteristic
32C2×D3×#168C2211yescharacteristic
33C2×D5×C3⋊C8C2211yescharacteristic
34D3×C8×D5—24no—
35C5×#832C2212yescomplemented
36C5×#818C2211yescharacteristic, complemented
37C3×#3964C2212yescomplemented
38C3×#3950C2211yescharacteristic, complemented
39#90986C2212yescomplemented
40#90975C2212yescomplemented
41#90974C2212yescomplemented
42#80714—51nomaximal, Hall
43C2×#4058—31no—
44C22×C8×D5—31no—
45#65940—32no—
46C5×#466—31no—
47#65446D311yescharacteristic, complemented
48#65405—31no—
49#65330—32no—
50#65176—31no—
51#65169—31no—
52#65067—32no—
53#65061—32no—
54C22×D3×D5D411yescharacteristic
55C2×C3×C5×D4C2312yes—
56C2×#1220—22no—
57C22×Dic15—22no—
58#6819—24no—
59#6819—24no—
60C2×C4×D15C2311yescharacteristic
61C2×Dic30C2312yes—
62C2×C5×#67—22no—
63C2×C4×C5×D3C2311yescharacteristic
64C2×C3×C22⋊D5—22no—
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1200D411yescharacteristic
67C2×D3×Dic5D411yescharacteristic
68C2×D5×Dic3D411yescharacteristic
69C4×D3×D5—22no—
70C4×D3×D5—22no—
71C3×C5×D8—22no—
72C2×C3×C5×C8C2311yescharacteristic
73#6716—24no—
74C2×C3⋊#168C2311yescharacteristic
75Dic60—22no—
76C8×D15D414yescomplemented
77C5×#217—22no—
78C5×C4⋊Dic3C2312yes—
79C2×C5×C3⋊C8C2311yescharacteristic
80C5×D3×C8—22no—
81C3×C22⋊Dic5—22no—
82C3×C4⋊Dic5C2312yes—
83C2×C3×#168C2311yescharacteristic
84C3×C8×D5—22no—
85Dic3⋊Dic5—22no—
86#6668—22no—
87#6667—22no—
88(C2×D3)⋊Dic5—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×#912—51no—
95C22×D3×C8—51no—
96#5606—52no—
97C3×#466—51no—
98#5157D511yescharacteristic, complemented
99#5116—51no—
100#5041—52no—
101#4887—51no—
102#4880—51no—
103#4778—52no—
104#4772—52no—
105C2×#711—32no—
106C22×C4×D5—31no—
107C2×C5×D8C2×D311yescharacteristic, complemented
108C22×C5×C8—31no—
109C5×#121—32no—
110#4084C2×D312yes—
111#4083—62no—
112D4×Dic5—62no—
113C2×#687—32no—
114#4070—32no—
115C22×#168—31no—
116#4058—64no—
117C2×Dic20—31no—
118C2×C8×D5—31no—
119C2×C8×D5—31no—
120C2×C8×D5—31no—
121C2×C8×D5—64no—
122C2×C8×D5C2×D311yescharacteristic
123#4043—32no—
124#4038—32no—
125#4029—62no—
126#4027—62no—
127C5×#107—31no—
128C5×#102—32no—
129#3964C2×D312yescomplemented
130#3950C2×D311yescharacteristic, complemented
131#3948—32no—
132#3942—32no—
133#3940—32no—
134#3050—151noSylow
135C23×C3×C5—22no—
136C22×D15C2×D411yescharacteristic
137C22×C5×D3C2×D411yescharacteristic
138C22×C3×D5C2×D411yescharacteristic
139C2×D3×D5—22no—
140C2×D3×D5—22no—
141C2×D3×D5—22no—
142C3×C5×D4—22no—
143C3×C5×D4—22no—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—44no—
146C2×Dic15—22no—
147C2×Dic15—44no—
148C2×Dic15C2×D411yescharacteristic
149C4×D15C2×D412yes—
150C4×D15#4112yes—
151Dic30—22no—
152Dic30—22no—
153C5×#67—44no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3C2×D411yescharacteristic
156C4×C5×D3—21no—
157C4×C5×D3—21no—
158C3×C22⋊D5—44no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C2×D411yescharacteristic
161C3×C4×D5—21no—
162C3×C4×D5—21no—
163#1200—22no—
164D3×Dic5—22no—
165D5×Dic3—22no—
166C3×C5×C8C2×D412yes—
167C3⋊#168C2×D412yes—
168C3×#168—21no—
169C5×C3⋊C8—21no—
170C2×#237—52no—
171C22×C4×D3—51no—
172C2×C3×D8C2×D511yescharacteristic, complemented
173C22×C3×C8—51no—
174C3×#121—52no—
175#938C2×D512yes—
176#937—102no—
177D4×Dic3—102no—
178C2×#214—52no—
179#924—52no—
180C22×C3⋊C8—51no—
181#912—104no—
182C2×Dic12—51no—
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—51no—
186C2×D3×C8—104no—
187C2×D3×C8C2×D511yescharacteristic
188#897—52no—
189#892—52no—
190#883—102no—
191#67⋊C4—102no—
192C3×#107—51no—
193C3×#102—52no—
194#832C2×D512yescomplemented
195#818C2×D511yescharacteristic, complemented
196#816—52no—
197#810—52no—
198#808—52no—
199C23×D5—31no—
200C2×C5×D4—62no—
201C2×C5×D4C22×D312yes—
202C22×C4×C5—31no—
203C2×C22⋊D5—22no—
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—62no—
213C2×C4×D5—62no—
214C2×C4×D5C22×D311yescharacteristic
215C2×Dic10—32no—
216C5×D8—22no—
217C2×C5×C8—31no—
218C2×C5×C8—62no—
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—62no—
230C4×Dic5—62no—
231C2×#168—31no—
232C2×#168—62no—
233C2×#168C22×D311yescharacteristic
234Dic20—62no—
235C8×D5—22no—
236C8×D5—34no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—151no—
240C23×C8—151no—
241#525—152no—
242#467—151no—
243#467—151no—
244#466—31no—
245#466—51no—
246#465—152no—
247#465—152no—
248#427—151no—
249#416—152no—
250C22×C3×C5—42no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—21no—
255C2×D15—21no—
256C2×D15#12112yes—
257C2×C5×D3—21no—
258C2×C5×D3—21no—
259C2×C5×D3#13512yescomplemented
260C2×C3×D5—21no—
261C2×C3×D5—21no—
262C2×C3×D5#13512yescomplemented
263D3×D5—28no—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C2×#4111yescharacteristic
266Dic15—42no—
267Dic15#12112yes—
268C3×Dic5—21no—
269C3×Dic5—42no—
270C5×Dic3—21no—
271C5×Dic3—42no—
272C23×D3—51no—
273C2×C3×D4—102no—
274C2×C3×D4C22×D512yes—
275C22×C3×C4—51no—
276C2×#67—22no—
277C2×#67—102no—
278C22×Dic3—51no—
279C22×Dic3—102no—
280#237—104no—
281#237—104no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—102no—
286C2×C4×D3—102no—
287C2×C4×D3C22×D511yescharacteristic
288C2×Dic6—52no—
289C3×D8—22no—
290C2×C3×C8—51no—
291C2×C3×C8—102no—
292C2×C3×C8C22×D511yescharacteristic
293C3×C4⋊C4—52no—
294C3×C22⋊C4—102no—
295#217—22no—
296#217—102no—
297#214—104no—
298(C2×D3)⋊C4—102no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—102no—
301C4⋊Dic3C22×D512yes—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—102no—
308D3×C8—22no—
309D3×C8—54no—
310D3×C8—102no—
311D3×C8—102no—
312C23×C5—22no—
313C23×C5—31no—
314C22×D5—31no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5D3×D411yescharacteristic
319C5×D4—22no—
320C5×D4—22no—
321C5×D4—124no—
322C2×C4×C5—31no—
323C2×C4×C5—61no—
324C2×C4×C5—61no—
325C2×C4×C5—62no—
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—44no—
328C22⋊D5—124no—
329C2×Dic5—22no—
330C2×Dic5—31no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—124no—
334C2×Dic5D3×D411yescharacteristic
335C4×D5—21no—
336C4×D5—21no—
337C4×D5—32no—
338C4×D5—32no—
339C4×D5—62no—
340C4×D5—62no—
341Dic10—62no—
342Dic10—62no—
343C5×C8—61no—
344C5×C8D3×D412yes—
345#168—21no—
346#168—32no—
347C2×#41—152no—
348C23×C4—151no—
349#135—304no—
350C2×Q16—151no—
351C2×SD16—152no—
352C2×D8D3×D511yescharacteristic, complemented
353C22×C8—31no—
354C22×C8—51no—
355C22×C8—151no—
356C22×C8—151no—
357C22×C8—151no—
358C22×C8—151no—
359C22×C8—304no—
360#123—302no—
361C22⋊Q8—152no—
362C22⋊Q8—152no—
363#121—32no—
364#121—52no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—152no—
369#107—31no—
370#107—51no—
371#106—152no—
372#103—152no—
373#103—152no—
374#102—32no—
375#102—52no—
376C2×C3×C5—82no—
377C2×C3×C5C2×#12111yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379C2×C3×C5C2×#13511yescharacteristic
380D15—22no—
381C3×D5—22no—
382C5×D3—22no—
383C23×C3—22no—
384C23×C3—51no—
385C22×D3—51no—
386C22×D3—102no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3D4×D511yescharacteristic
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—204no—
393C2×C3×C4—51no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4—102no—
397C2×C3×C4C23×D511yescharacteristic
398#67—44no—
399#67—204no—
400C2×Dic3—22no—
401C2×Dic3—51no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—204no—
405C2×Dic3D4×D511yescharacteristic
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—52no—
409C4×D3—52no—
410C4×D3—102no—
411C4×D3—102no—
412Dic6—102no—
413Dic6—102no—
414C3×C8—101no—
415C3×C8D4×D512yes—
416C3⋊C8—21no—
417C3⋊C8—52no—
418C22×C5—32no—
419C22×C5—42no—
420C22×C5—42no—
421C22×C5—42no—
422C22×C5—61no—
423C22×C5—61no—
424C22×C5C2×D3×D411yescharacteristic
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—32no—
428C2×D5—68no—
429C2×D5—61no—
430C2×D5—61no—
431C2×D5#91212yescomplemented
432C4×C5—61no—
433C4×C5—122no—
434C4×C5C2×D3×D411yescharacteristic
435C4×C5D3×#4111yescharacteristic
436Dic5—21no—
437Dic5—32no—
438Dic5—42no—
439Dic5—122no—
440C24—151no—
441#41—304no—
442#41—304no—
443C2×Q8—152no—
444C2×D4—62no—
445C2×D4—102no—
446C2×D4—302no—
447C2×D4C2×D3×D512yes—
448C22×C4—31no—
449C22×C4—51no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—302no—
455C22×C4—302no—
456C22×C4—302no—
457Q16—302no—
458SD16—304no—
459D8—22no—
460C2×C8—31no—
461C2×C8—51no—
462C2×C8—62no—
463C2×C8—102no—
464C2×C8—151no—
465C2×C8—154no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—52no—
472C4⋊C4—302no—
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—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—52no—
485C22×C3—101no—
486C22×C3—101no—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—21no—
489C2×D3—21no—
490C2×D3—52no—
491C2×D3—108no—
492C2×D3—101no—
493C2×D3—101no—
494C2×D3#405812yescomplemented
495C3×C4—101no—
496C3×C4—202no—
497C3×C4C2×D4×D511yescharacteristic
498C3×C4D5×#4111yescharacteristic
499Dic3—21no—
500Dic3—42no—
501Dic3—52no—
502Dic3—202no—
503C2×C5—62no—
504C2×C5—82no—
505C2×C5D3×#12111yescharacteristic
506C2×C5C2×#91211yescharacteristic
507C2×C5D3×#13511yescharacteristic
508D5—22no—
509D5—62no—
510C23—22no—
511C23—31no—
512C23—51no—
513C23—151no—
514C23—302no—
515C23—302no—
516C23—302no—
517Q8—302no—
518Q8—302no—
519D4—22no—
520D4—22no—
521D4—124no—
522D4—204no—
523D4—604no—
524C2×C4—31no—
525C2×C4—51no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—102no—
532C2×C4—151no—
533C2×C4—152no—
534C2×C4—152no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4—604no—
540C2×C4C22×D3×D511yescharacteristic
541C8—61no—
542C8—101no—
543C8—152no—
544C8#679012yes—
545C2×C3—82no—
546C2×C3—102no—
547C2×C3D5×#12111yescharacteristic
548C2×C3C2×#405811yescharacteristic
549C2×C3D5×#13511yescharacteristic
550D3—22no—
551D3—102no—
552C5#8071411yescharacteristic, complemented, Sylow
553C22—32no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—52no—
558C22—61no—
559C22—61no—
560C22—101no—
561C22—101no—
562C22—152no—
563C22—308no—
564C22—301no—
565C22—301no—
566C22D3×D4×D511yescharacteristic
567C4—61no—
568C4—101no—
569C4—122no—
570C4—152no—
571C4—202no—
572C4—602no—
573C4#9202411yescharacteristic
574C4C2×#679011yescharacteristic
575C3#1061244511yescharacteristic, complemented, Sylow
576C2—62no—
577C2—82no—
578C2—102no—
579C2—302no—
580C2D5×#91211yescharacteristic
581C2D3×#405811yescharacteristic
582C2#1175502611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
hypercenterC2×D8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#91801C2semidirect
2. #11755070C2semidirect
3. C2×D3×C8×D5C2semidirect
4. C5×#5157C2semidirect
5. C3×#65446C2semidirect
6. #11749055C2semidirect
7. #11749046C2semidirect
8. #11748969C2semidirect
9. #11747950C2semidirect
10. #11747943C2semidirect
11. #11747690C2semidirect
15. C2×C3×C5×D8C22semidirect
16. C2×#6716C22semidirect
18. C2×Dic60C22semidirect
35. C5×#832C22semidirect
36. C5×#818C22semidirect
37. C3×#3964C22semidirect
38. C3×#3950C22semidirect
39. #90986C22semidirect
40. #90975C22semidirect
41. #90974C22semidirect
47. #65446D3semidirect
76. C8×D15D4semidirect
98. #5157D5semidirect
107. C2×C5×D8C2×D3semidirect
129. #3964C2×D3semidirect
130. #3950C2×D3semidirect
172. C2×C3×D8C2×D5semidirect
194. #832C2×D5semidirect
195. #818C2×D5semidirect
259. C2×C5×D3#135semidirect
262. C2×C3×D5#135semidirect
352. C2×D8D3×D5semidirect
431. C2×D5#912semidirect
480. C3×C5#3050semidirect
494. C2×D3#4058semidirect
552. C5#80714semidirect
575. C3#10612445semidirect

Maximal subgroups

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

subgroupindex
C2×#918012
#117550702
C2×D3×C8×D52
C5×#51572
C3×#654462
#117490552
#117490462
#117489692
#117479502
#117479432
#117476902
#106124453
#807145