Finite Group Databasebeta

← #14427835

Subgroups — #14427835

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#11754373C212yesmaximal, complemented
3C2×#91277C211yesmaximal, characteristic, complemented
4C5×#5116C211yesmaximal, characteristic, complemented
5C3×#65404C211yesmaximal, characteristic, complemented
6#11748545C212yesmaximal, complemented
7#11748141C212yesmaximal, complemented
8#11747956C211yesmaximal, characteristic, complemented
9#11747932C211yesmaximal, characteristic, complemented
10#11747926C212yesmaximal, complemented
11#11747690C211yesmaximal, characteristic, complemented
12#10612489—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×#6766C2212yes—
15C22×C3×C5×C8C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C8×D15—24no—
18C2×C8×D15C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20C2×C8×D15C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C5×#924C2212yes—
23C2×C5×Dic12C2211yescharacteristic, complemented
24C3×#4076C2212yes—
25C2×C3×D40C2211yescharacteristic, complemented
26#91572—22no—
27#91559—22no—
28#91465C2212yes—
29#91396—22no—
30#91383C2212yes—
31#91354—22no—
32#91347C2212yes—
33C2×#6655C2212yescomplemented
34#91277—24no—
35C5×#818C2211yescharacteristic, complemented
36C5×#816C2212yescomplemented
37C3×#3953C2212yescomplemented
38C3×#3950C2211yescharacteristic, complemented
39#90986C2212yescomplemented
40#90972C2212yescomplemented
41#90964C2212yescomplemented
42#80714—51nomaximal, Hall
43C2×#4065—31no—
44C22×C8×D5—31no—
45#65961—32no—
46C5×#467—31no—
47#65477—31no—
48#65404D311yescharacteristic, complemented
49#65337—32no—
50#65172—31no—
51#65169—31no—
52#65096—32no—
53#65093—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×Dic6C2312yes—
64C2×C3×C22⋊D5—22no—
65C2×C3×D20C2312yes—
66C2×#1202—22no—
67C2×#1202—22no—
68C2×D5×Dic3—22no—
69#6766—24no—
70#6766—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×#217—22no—
82C5×C4⋊Dic3C2312yes—
83C5×Dic3⋊C4—22no—
84C5×Dic12—22no—
85C3×#685—22no—
86C3×C4⋊Dic5C2312yes—
87C3×D40—22no—
88#6668—22no—
89#6667—22no—
90#6667—22no—
91#6665—22no—
92Dic3×Dic5—22no—
93#6655—24no—
94C2×#912—51no—
95C22×D3×C8—51no—
96#5606—52no—
97C3×#466—51no—
98#5157—51no—
99#5116D511yescharacteristic, complemented
100#5041—52no—
101#4887—51no—
102#4880—51no—
103#4778—52no—
104#4772—52no—
105C2×#713—32no—
106C22×C4×D5—31no—
107C2×C5×Q16—31no—
108C22×C5×C8C2×D311yescharacteristic
109C5×C22⋊Q8—32no—
110#4092—32no—
111C2×#688—32no—
112#4076C2×D312yes—
113C22×#168—31no—
114#4065—64no—
115C2×D40C2×D311yescharacteristic, complemented
116C2×C8×D5—31no—
117C2×C8×D5—31no—
118C2×C8×D5—31no—
119C2×C8×D5—31no—
120C2×C8×D5—64no—
121#4041—32no—
122#4040—62no—
123#4039—62no—
124#4038—32no—
125#4028—62no—
126#4027—62no—
127C5×#107—31no—
128C5×#103—32no—
129#3967—32no—
130#3953C2×D312yescomplemented
131#3950C2×D311yescharacteristic, complemented
132#3941—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×C3×D5—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—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C5×Dic6—22no—
158C5×Dic6—22no—
159C3×C22⋊D5—44no—
160C2×C3×Dic5—22no—
161C3×D20—22no—
162C3×D20—22no—
163#1202—44no—
164#1202—44no—
165D5×Dic3—44no—
166C3×C5×C8—21no—
167C3×C5×C8C2×D412yes—
168C3⋊#168—21no—
169C3⋊#168C2×D412yes—
170C2×#237—52no—
171C22×C4×D3—51no—
172C2×C3×D8—51no—
173C22×C3×C8C2×D511yescharacteristic
174C3×#121—52no—
175#938—52no—
176#937—102no—
177D4×Dic3—102no—
178C2×#214—52no—
179#924C2×D512yes—
180C22×C3⋊C8—51no—
181#912—104no—
182C2×Dic12C2×D511yescharacteristic, complemented
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—51no—
186C2×D3×C8—51no—
187C2×D3×C8—104no—
188#897—52no—
189#892—52no—
190#883—102no—
191#67⋊C4—102no—
192C3×#107—51no—
193C3×#102—52no—
194#832—52no—
195#818C2×D511yescharacteristic, complemented
196#816C2×D512yescomplemented
197#810—52no—
198#808—52no—
199C23×D5—31no—
200C2×C5×Q8—32no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—22no—
203C22×Dic5—31no—
204#713—64no—
205#713—64no—
206C2×D20—62no—
207C2×D20—62no—
208C2×D20C22×D312yes—
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×C4×D5—62no—
216C5×Q16—62no—
217C2×C5×C8—22no—
218C2×C5×C8C22×D311yescharacteristic
219C2×C5×C8C22×D311yescharacteristic
220C5×C4⋊C4—32no—
221C5×C4⋊C4—62no—
222C5×C22⋊C4—62no—
223#688—64no—
224#685—22no—
225#685—62no—
226#685—62no—
227#685—62no—
228C4⋊Dic5C22×D312yes—
229#683—62no—
230C4×Dic5—62no—
231C2×#168—31no—
232C2×#168—31no—
233C2×#168—62no—
234D40—22no—
235C8×D5—34no—
236C8×D5—62no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—151no—
240C23×C8—151no—
241#525—152no—
242#467—31no—
243#467—151no—
244#466—51no—
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×C3×D5—42no—
262C2×C3×D5—42no—
263C2×C3×D5—42no—
264C3×C4×C5—21no—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—21no—
268Dic15#12112yes—
269C3×Dic5—42no—
270C5×Dic3—42no—
271C5×Dic3—42no—
272C23×D3—51no—
273C2×C3×D4—52no—
274C2×C3×D4—102no—
275C22×C3×C4C22×D511yescharacteristic
276C2×#67—102no—
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—51no—
286C2×C4×D3—102no—
287C2×C4×D3—102no—
288C2×Dic6C22×D512yes—
289C3×D8—102no—
290C2×C3×C8—22no—
291C2×C3×C8C22×D511yescharacteristic
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—22no—
303C4×Dic3—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—102no—
307Dic12—22no—
308D3×C8—54no—
309D3×C8—102no—
310D3×C8—102no—
311D3×C8—102no—
312C23×C5D3×D411yescharacteristic
313C22×D5—22no—
314C22×D5—31no—
315C22×D5—31no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5—62no—
319C5×Q8—62no—
320C5×Q8—62no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—62no—
324C2×C4×C5—62no—
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—44no—
328C2×Dic5—22no—
329C2×Dic5—31no—
330C2×Dic5—31no—
331C2×Dic5—62no—
332D20—22no—
333D20—22no—
334D20—124no—
335D20—124no—
336C4×D5—32no—
337C4×D5—32no—
338C4×D5—62no—
339C4×D5—62no—
340C4×D5—61no—
341C4×D5—61no—
342C4×D5—124no—
343C5×C8—21no—
344C5×C8D3×D412yes—
345#168—32no—
346#168—61no—
347C2×#41—152no—
348C23×C4—151no—
349#135—304no—
350C2×Q16—31no—
351C2×SD16—152no—
352C2×D8—51no—
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—32no—
362C22⋊Q8—152no—
363#121—52no—
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—32no—
373#103—152no—
374#102—52no—
375#102—152no—
376C2×C3×C5—22no—
377C2×C3×C5C2×#12111yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379C2×C3×C5C2×#13511yescharacteristic
380D15—22no—
381D15—22no—
382C3×D5—82no—
383C23×C3—102no—
384C23×C3D4×D511yescharacteristic
385C22×D3—51no—
386C22×D3—51no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3—102no—
390C3×D4—102no—
391C3×D4—102no—
392C3×D4—204no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—102no—
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—204no—
399#67—204no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—51no—
403C2×Dic3—51no—
404C2×Dic3—102no—
405C2×Dic3—204no—
406C4×D3—52no—
407C4×D3—52no—
408C4×D3—102no—
409C4×D3—102no—
410C4×D3—101no—
411C4×D3—101no—
412Dic6—22no—
413Dic6—22no—
414C3×C8—21no—
415C3×C8D4×D512yes—
416C3⋊C8—52no—
417C3⋊C8—101no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5#91212yescomplemented
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—32no—
423C2×D5—32no—
424C2×D5—42no—
425C2×D5—42no—
426C2×D5—42no—
427C2×D5—68no—
428C2×D5—61no—
429C2×D5—61no—
430C2×D5—61no—
431C2×D5—61no—
432C4×C5—21no—
433C4×C5—122no—
434C4×C5—122no—
435C4×C5C2×D3×D411yescharacteristic
436C4×C5D3×#4111yescharacteristic
437Dic5—32no—
438Dic5—42no—
439Dic5—61no—
440C24—151no—
441#41—304no—
442#41—304no—
443C2×Q8—32no—
444C2×D4—52no—
445C2×D4—102no—
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—62no—
458SD16—304no—
459D8—102no—
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—62no—
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—202no—
484C22×C3—202no—
485C22×C3—202no—
486C22×C3#406512yescomplemented
487C22×C3C2×D4×D511yescharacteristic
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×C4C2×D4×D511yescharacteristic
498C3×C4D5×#4111yescharacteristic
499Dic3—42no—
500Dic3—42no—
501Dic3—52no—
502Dic3—101no—
503C2×C5—22no—
504C2×C5D3×#12111yescharacteristic
505C2×C5C2×#91211yescharacteristic
506C2×C5D3×#13511yescharacteristic
507D5—62no—
508D5—62no—
509D5—82no—
510C23—102no—
511C23—151no—
512C23—151no—
513C23—302no—
514C23—302no—
515C23—302no—
516C23#677711yescharacteristic
517Q8—62no—
518Q8—62no—
519D4—102no—
520D4—102no—
521D4—204no—
522D4—604no—
523D4—604no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—62no—
527C2×C4—62no—
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×C3—402no—
547C2×C3D5×#12111yescharacteristic
548C2×C3C2×#406511yescharacteristic
549C2×C3D5×#13511yescharacteristic
550D3—102no—
551D3—102no—
552C5#8071411yescharacteristic, complemented, Sylow
553C22—21no—
554C22—21no—
555C22—152no—
556C22—152no—
557C22—202no—
558C22—202no—
559C22—202no—
560C22—308no—
561C22—301no—
562C22—301no—
563C22—301no—
564C22—301no—
565C22#9127712yescomplemented
566C22C2×#677711yescharacteristic
567C4—21no—
568C4—122no—
569C4—122no—
570C4—152no—
571C4—202no—
572C4—301no—
573C4#9201611yescharacteristic
574C4C2×#679011yescharacteristic
575C3#1061248911yescharacteristic, complemented, Sylow
576C2—22no—
577C2—302no—
578C2—302no—
579C2—402no—
580C2#1175397811yescharacteristic
581C2C2×#9127711yescharacteristic
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. #11754373C2semidirect
3. C2×#91277C2semidirect
4. C5×#5116C2semidirect
5. C3×#65404C2semidirect
6. #11748545C2semidirect
7. #11748141C2semidirect
8. #11747956C2semidirect
9. #11747932C2semidirect
10. #11747926C2semidirect
11. #11747690C2semidirect
23. C2×C5×Dic12C22semidirect
25. C2×C3×D40C22semidirect
33. C2×#6655C22semidirect
35. C5×#818C22semidirect
36. C5×#816C22semidirect
37. C3×#3953C22semidirect
38. C3×#3950C22semidirect
39. #90986C22semidirect
40. #90972C22semidirect
41. #90964C22semidirect
48. #65404D3semidirect
80. C8×D15D4semidirect
99. #5116D5semidirect
115. C2×D40C2×D3semidirect
130. #3953C2×D3semidirect
131. #3950C2×D3semidirect
182. C2×Dic12C2×D5semidirect
195. #818C2×D5semidirect
196. #816C2×D5semidirect
252. C22×C3×C5#135semidirect
260. C2×D15#135semidirect
420. C22×C5#912semidirect
480. C3×C5#3050semidirect
486. C22×C3#4065semidirect
552. C5#80714semidirect
565. C22#91277semidirect
575. C3#10612489semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D152
#117543732
C2×#912772
C5×#51162
C3×#654042
#117485452
#117481412
#117479562
#117479322
#117479262
#117476902
#106124893
#807145