Finite Group Databasebeta

← #14412573

Subgroups — #14412573

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6766C211yesmaximal, characteristic
2C2×M16×D15C211yesmaximal, characteristic, complemented
3#11754461C211yesmaximal, characteristic, complemented
4C5×#5120C211yesmaximal, characteristic, complemented
5C3×#65420C211yesmaximal, characteristic, complemented
6#11748407C211yesmaximal, characteristic, complemented
7#11748366C211yesmaximal, characteristic, complemented
8#11748142C214yesmaximal, complemented
9#11748141C214yesmaximal, complemented
10#10610687—31nomaximal, Hall
11C22×C4×D15C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×#1202—21no—
15C22×D5×Dic3—21no—
16C2×#6766—21no—
17C2×#6766—21no—
18C2×#6766—24no—
19C2×#6766C418yescomplemented
20C2×#6766C2212yes—
21C2×#6766C2212yes—
22C2×C3×C5×M16C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24M16×D15—24no—
25C2×#6705C2212yescomplemented
26C2×C8×D15C2212yescomplemented
27C5×#926C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29#91561—21no—
30#91532—21no—
31#91437C2212yescomplemented
32C4×#1200—21no—
33#91386—21no—
34#91347C2212yescomplemented
35C5×#816C2214yescomplemented
36C3×#3953C2214yescomplemented
37#90972C2214yescomplemented
38#90964C2214yescomplemented
39#78924—51nomaximal, Hall
40C22×#713—31no—
41C2×D5×M16—31no—
42D5×#117—31no—
43C5×#419—31no—
44#65514—31no—
45#65420D311yescharacteristic, complemented
46#65290—31no—
47#65093—34no—
48#65092—34no—
49C23×D15D411yescharacteristic
50C23×C3×D5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15D411yescharacteristic
53C2×C4×D15C2×C414yes—
54C2×C4×D15D411yescharacteristic
55C2×C4×D15D411yescharacteristic
56C2×C4×D15D414yes—
57C2×C4×D15C2311yescharacteristic
58C2×C4×D15C2311yescharacteristic
59C22×C5×Dic3—21no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6—22no—
62C2×C5×Dic6C2×C414yescomplemented
63C2×C5×Dic6C2312yes—
64C2×C3×D20—21no—
65C2×C3×D20—22no—
66C2×C3×D20C2×C414yescomplemented
67C2×C3×D20C2312yes—
68C2×#1202—28no—
69C2×#1202—22no—
70C2×#1202—22no—
71C2×#1200—22no—
72C2×D5×Dic3—28no—
73C2×D5×Dic3—22no—
74C2×D5×Dic3—22no—
75#6766—28no—
76#6766—28no—
77#6766—24no—
78#6766—24no—
79#6766C2×C418yes—
80#6766C2×C418yescomplemented
81C3×C5×M16—22no—
82C2×C3×C5×C8C2312yes—
83#6710—22no—
84C2×C3⋊#168C2312yes—
85#6705—24no—
86C8×D15—24no—
87C5×#217—21no—
88C5×C4⋊Dic3C2312yes—
89C4×C5×Dic3—21no—
90C3×C22⋊Dic5—21no—
91C3×C4⋊Dic5C2312yes—
92C3×C4×Dic5—21no—
93#6669—22no—
94#6667—22no—
95Dic3×Dic5—22no—
96C22×#237—51no—
97C2×D3×M16—51no—
98D3×#117—51no—
99C3×#418—51no—
100#5215—51no—
101#5120D511yescharacteristic, complemented
102#5004—51no—
103#4772—54no—
104#4771—54no—
105C22×C5×Q8—31no—
106C2×#713—38no—
107C2×#713—32no—
108C2×#713—32no—
109C2×#713—61no—
110C2×#713—61no—
111C2×#713—64no—
112C22×D20—61no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—31no—
115C22×C4×D5—61no—
116C2×C5×M16C2×D311yescharacteristic
117C5×#117—31no—
118#4072C2×D311yescharacteristic
119C2×#681—31no—
120D5×M16—64no—
121C2×#676—32no—
122C2×C8×D5—32no—
123#4038—32no—
124D5×C4⋊C4—32no—
125D5×C22⋊C4—61no—
126#4023—61no—
127#4018—61no—
128C42×D5—61no—
129C5×#103—34no—
130#3967—34no—
131#3953C2×D314yescomplemented
132#3941—34no—
133#2896—151noSylow
134C23×C3×C5C2×D411yescharacteristic
135C22×D15—42no—
136C22×D15C22⋊C414yes—
137C22×D15C2×D411yescharacteristic
138C22×D15C2×D411yescharacteristic
139C22×C3×D5—24no—
140C22×C3×D5—22no—
141C22×C3×D5—44no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C22⋊C414yes—
147C2×Dic15C2×D411yescharacteristic
148C2×Dic15C2×D411yescharacteristic
149C4×D15C22⋊C414yes—
150C4×D15C22⋊C414yes—
151C4×D15C22×C412yes—
152C4×D15C22×C412yes—
153C4×D15C2×D412yes—
154C4×D15C2×D412yes—
155C2×C5×Dic3—24no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C5×Dic6—24no—
159C5×Dic6—22no—
160C5×Dic6C22×C414yes—
161C2×C3×Dic5—22no—
162C3×D20—24no—
163C3×D20—22no—
164C3×D20C22×C414yes—
165#1202—28no—
166#1202—28no—
167#1200—44no—
168D5×Dic3—28no—
169D5×Dic3—28no—
170C3×C5×C8—22no—
171C3⋊#168—22no—
172C22×C3×D4—51no—
173C22×#67—101no—
174C23×Dic3—101no—
175C2×#237—58no—
176C2×#237—52no—
177C2×#237—52no—
178C2×#237—101no—
179C2×#237—101no—
180C2×#237—104no—
181C22×C4×D3—51no—
182C22×Dic6C2×D511yescharacteristic
183C2×C3×M16C2×D511yescharacteristic
184C3×#117—51no—
185#926C2×D511yescharacteristic
186C2×#208—51no—
187D3×M16—104no—
188C2×ΓL(1,𝔽25)—52no—
189C2×D3×C8—52no—
190#892—52no—
191D3×C4⋊C4—52no—
192D3×C22⋊C4—101no—
193#877—101no—
194#872—101no—
195C42×D3—101no—
196C3×#102—54no—
197#832—54no—
198#816C2×D514yescomplemented
199#810—54no—
200C23×D5—21no—
201C23×D5—31no—
202C2×C5×Q8—34no—
203C2×C5×Q8—32no—
204C2×C5×Q8—61no—
205C2×C5×Q8—62no—
206C22×C4×C5—61no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—31no—
209#713—38no—
210#713—38no—
211#713—68no—
212#713—68no—
213#713—64no—
214#713—64no—
215C2×D20—21no—
216C2×D20—22no—
217C2×D20—68no—
218C2×D20—62no—
219C2×D20—62no—
220C2×D20C4×D314yescomplemented
221C2×D20C22×D312yes—
222C2×C4×D5—34no—
223C2×C4×D5—31no—
224C2×C4×D5—31no—
225C2×C4×D5—34no—
226C2×C4×D5—31no—
227C2×C4×D5—31no—
228C2×C4×D5—68no—
229C2×C4×D5—62no—
230C2×C4×D5—62no—
231C2×C4×D5—62no—
232C5×M16—22no—
233C2×C5×C8C22×D312yes—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237C22⋊Dic5—21no—
238#685—62no—
239C4⋊Dic5C22×D312yes—
240#683—62no—
241C4×Dic5—21no—
242C4×Dic5—62no—
243#681—62no—
244C2×#168—32no—
245#676—64no—
246C8×D5—64no—
247C22×#41—151no—
248C22×M16—151no—
249C2×#117—151no—
250#419—31no—
251#419—151no—
252#418—51no—
253#418—151no—
254#417—154no—
255#416—154no—
256C22×C3×C5—22no—
257C22×C3×C5C2×C22⋊C412yes—
258C22×C3×C5C22×D411yescharacteristic
259C2×D15—22no—
260C2×D15—22no—
261C2×D15—44no—
262C2×D15C2×C22⋊C412yes—
263C2×D15C2×C22⋊C412yes—
264C2×C3×D5—24no—
265C2×C3×D5—48no—
266C2×C3×D5—44no—
267C3×C4×C5C2×C22⋊C412yes—
268C3×C4×C5C23×C411yescharacteristic
269C3×C4×C5C22×D411yescharacteristic
270Dic15C2×C22⋊C412yes—
271Dic15C2×C22⋊C412yes—
272C3×Dic5—42no—
273C5×Dic3—24no—
274C5×Dic3—42no—
275C24×C3—101no—
276C23×D3—51no—
277C2×C3×D4—54no—
278C2×C3×D4—52no—
279C2×C3×D4—101no—
280C2×C3×D4—102no—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—102no—
283C2×#67—102no—
284C2×#67—108no—
285C22×Dic3—21no—
286C22×Dic3—51no—
287C22×Dic3—102no—
288C22×Dic3—102no—
289C22×Dic3—108no—
290#237—58no—
291#237—58no—
292#237—104no—
293#237—104no—
294#237—108no—
295#237—108no—
296C2×C4×D3—54no—
297C2×C4×D3—51no—
298C2×C4×D3—51no—
299C2×C4×D3—54no—
300C2×C4×D3—51no—
301C2×C4×D3—51no—
302C2×C4×D3—102no—
303C2×Dic6—21no—
304C2×Dic6—22no—
305C2×Dic6C4×D514yescomplemented
306C2×Dic6C22×D512yes—
307C3×M16—22no—
308C2×C3×C8C22×D512yes—
309C3×C4⋊C4—52no—
310C3×C22⋊C4—101no—
311C3×C42—101no—
312#217—21no—
313(C2×D3)⋊C4—102no—
314C4⋊Dic3C22×D512yes—
315Dic3⋊C4—102no—
316C4×Dic3—21no—
317C4×Dic3—102no—
318#208—102no—
319C2×C3⋊C8—52no—
320ΓL(1,𝔽25)—104no—
321D3×C8—104no—
322C23×C5D3×D411yescharacteristic
323C22×D5—24no—
324C22×D5—22no—
325C22×D5—31no—
326C22×D5—31no—
327C22×D5—34no—
328C22×D5—44no—
329C22×D5—122no—
330C5×Q8—34no—
331C5×Q8—64no—
332C5×Q8—62no—
333C2×C4×C5—64no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5C2×C4×D312yes—
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5D3×D412yes—
339C2×C4×C5C23×D311yescharacteristic
340C2×Dic5—22no—
341C2×Dic5—34no—
342C2×Dic5—31no—
343C2×Dic5—31no—
344D20—24no—
345D20—22no—
346D20—68no—
347D20—68no—
348D20C2×C4×D314yes—
349C4×D5—34no—
350C4×D5—34no—
351C4×D5—32no—
352C4×D5—32no—
353C4×D5—32no—
354C4×D5—32no—
355C4×D5—68no—
356C4×D5—68no—
357C4×D5—124no—
358C5×C8—22no—
359#168—62no—
360C2×#41—152no—
361C2×#41—152no—
362C2×#41—158no—
363C2×#41—301no—
364C2×#41—301no—
365C2×#41—304no—
366C22×Q8—31no—
367C22×D4—51no—
368C22×D4—301no—
369C23×C4—151no—
370C23×C4—301no—
371C2×M16—151no—
372C2×M16—152no—
373C2×M16—304no—
374C2×M16D3×D511yescharacteristic
375C22×C8—152no—
376#117—31no—
377#117—51no—
378#117—152no—
379#117—301no—
380#117—301no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—301no—
383C2×C42—301no—
384#103—34no—
385#103—154no—
386#102—54no—
387#102—154no—
388C2×C3×C5—22no—
389C2×C3×C5C22×C22⋊C411yescharacteristic
390C2×C3×C5#57512yes—
391D15—22no—
392D15—22no—
393C3×D5—44no—
394C23×C3—102no—
395C23×C3—104no—
396C23×C3—204no—
397C23×C3D4×D511yescharacteristic
398C22×D3—51no—
399C22×D3—51no—
400C22×D3—54no—
401C22×D3—202no—
402C3×D4—54no—
403C3×D4—102no—
404C3×D4—104no—
405C2×C3×C4—102no—
406C2×C3×C4C2×C4×D512yes—
407C2×C3×C4D4×D511yescharacteristic
408C2×C3×C4D4×D512yes—
409C2×C3×C4C23×D511yescharacteristic
410#67—108no—
411#67—108no—
412C2×Dic3—22no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415C2×Dic3—51no—
416C2×Dic3—51no—
417C2×Dic3—54no—
418C2×Dic3—108no—
419C2×Dic3—108no—
420C4×D3—52no—
421C4×D3—52no—
422C4×D3—52no—
423C4×D3—52no—
424C4×D3—54no—
425C4×D3—54no—
426C4×D3—204no—
427Dic6—22no—
428Dic6—24no—
429Dic6C2×C4×D514yes—
430C3×C8—22no—
431C3⋊C8—102no—
432C22×C5—22no—
433C22×C5D3×C22⋊C412yes—
434C22×C5C2×D3×D411yescharacteristic
435C2×D5—24no—
436C2×D5—32no—
437C2×D5—32no—
438C2×D5—48no—
439C2×D5—44no—
440C2×D5—62no—
441C2×D5—62no—
442C2×D5—124no—
443C4×C5—64no—
444C4×C5—122no—
445C4×C5D3×C22⋊C412yes—
446C4×C5C22×C4×D311yescharacteristic
447C4×C5C2×D3×D411yescharacteristic
448Dic5—32no—
449Dic5—32no—
450Dic5—42no—
451C24—101no—
452C24—151no—
453#41—158no—
454#41—158no—
455#41—308no—
456#41—308no—
457#41—304no—
458#41—304no—
459C2×Q8—34no—
460C2×Q8—32no—
461C2×Q8—61no—
462C2×Q8—62no—
463C2×D4—54no—
464C2×D4—52no—
465C2×D4—101no—
466C2×D4—102no—
467C2×D4—308no—
468C2×D4—302no—
469C2×D4—302no—
470C22×C4—61no—
471C22×C4—151no—
472C22×C4—154no—
473C22×C4—151no—
474C22×C4—151no—
475C22×C4—154no—
476C22×C4—151no—
477C22×C4—151no—
478C22×C4—302no—
479C22×C4—308no—
480C22×C4—302no—
481C22×C4—302no—
482C22×C4C2×D3×D511yescharacteristic
483M16—22no—
484M16—304no—
485M16—302no—
486C2×C8—152no—
487C2×C8—304no—
488C2×C8C2×D3×D512yes—
489C4⋊C4—32no—
490C4⋊C4—52no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—101no—
494C22⋊C4—302no—
495C42—61no—
496C42—101no—
497C42—302no—
498C3×C5#289611yescharacteristic, complemented, Hall
499C22×C3—22no—
500C22×C3—104no—
501C22×C3—208no—
502C22×C3—204no—
503C22×C3D5×C22⋊C412yes—
504C22×C3C2×D4×D511yescharacteristic
505C2×D3—52no—
506C2×D3—52no—
507C2×D3—102no—
508C2×D3—102no—
509C2×D3—204no—
510C3×C4—202no—
511C3×C4D5×C22⋊C412yes—
512C3×C4C22×C4×D511yescharacteristic
513C3×C4C2×D4×D511yescharacteristic
514Dic3—24no—
515Dic3—42no—
516Dic3—52no—
517Dic3—52no—
518C2×C5—22no—
519C2×C5C2×D3×C22⋊C411yescharacteristic
520C2×C5#577312yes—
521D5—44no—
522D5—62no—
523D5—62no—
524C23—104no—
525C23—102no—
526C23—151no—
527C23—151no—
528C23—154no—
529C23—204no—
530C23—602no—
531C23#677711yescharacteristic
532Q8—34no—
533Q8—64no—
534Q8—62no—
535D4—54no—
536D4—104no—
537D4—102no—
538D4—308no—
539D4—308no—
540C2×C4—64no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—102no—
544C2×C4—154no—
545C2×C4—151no—
546C2×C4—151no—
547C2×C4—154no—
548C2×C4—154no—
549C2×C4—152no—
550C2×C4—152no—
551C2×C4—152no—
552C2×C4—152no—
553C2×C4—308no—
554C2×C4—308no—
555C2×C4—604no—
556C2×C4C4×D3×D512yes—
557C2×C4#677711yescharacteristic
558C2×C4#679012yes—
559C2×C4C22×D3×D511yescharacteristic
560C8—22no—
561C8—302no—
562C2×C3—22no—
563C2×C3—204no—
564C2×C3C2×D5×C22⋊C411yescharacteristic
565C2×C3#6611112yes—
566D3—102no—
567D3—102no—
568C5#7892411yescharacteristic, complemented, Sylow
569C22—22no—
570C22—104no—
571C22—152no—
572C22—152no—
573C22—208no—
574C22—204no—
575C22—302no—
576C22—302no—
577C22—604no—
578C22#9147312yes—
579C22C2×#677711yescharacteristic
580C4—64no—
581C4—122no—
582C4—152no—
583C4—152no—
584C4—202no—
585C4#9147312yes—
586C4C2×C4×D3×D511yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061068711yescharacteristic, complemented, Sylow
589C2—22no—
590C2—204no—
591C2—302no—
592C2—302no—
593C2#1175403612yes—
594C2C2×#9147311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC22×#6766C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2896
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×M16×D15C2semidirect
3. #11754461C2semidirect
4. C5×#5120C2semidirect
5. C3×#65420C2semidirect
6. #11748407C2semidirect
7. #11748366C2semidirect
8. #11748142C2semidirect
9. #11748141C2semidirect
19. C2×#6766C4semidirect
25. C2×#6705C22semidirect
26. C2×C8×D15C22semidirect
31. #91437C22semidirect
34. #91347C22semidirect
35. C5×#816C22semidirect
36. C3×#3953C22semidirect
37. #90972C22semidirect
38. #90964C22semidirect
45. #65420D3semidirect
62. C2×C5×Dic6C2×C4semidirect
66. C2×C3×D20C2×C4semidirect
80. #6766C2×C4semidirect
101. #5120D5semidirect
131. #3953C2×D3semidirect
198. #816C2×D5semidirect
220. C2×D20C4×D3semidirect
305. C2×Dic6C4×D5semidirect
498. C3×C5#2896semidirect
568. C5#78924semidirect
588. C3#10610687semidirect

Maximal subgroups

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

subgroupindex
C22×#67662
C2×M16×D152
#117544612
C5×#51202
C3×#654202
#117484072
#117483662
#117481422
#117481412
#106106873
#789245