Finite Group Databasebeta

← #14417397

Subgroups — #14417397

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D40C211yesmaximal, characteristic
2#11753839C212yesmaximal, complemented
3#11750973C211yesmaximal, characteristic, complemented
4C5×#4880C211yesmaximal, characteristic, complemented
5C3×#65161C211yesmaximal, characteristic, complemented
6#11747809C211yesmaximal, characteristic, complemented
7#11747766C211yesmaximal, characteristic, complemented
8#11747653C211yesmaximal, characteristic, complemented
9#11747477C212yesmaximal, complemented
10#11747469C212yesmaximal, complemented
11#11747229C212yesmaximal, complemented
12#10610898—31nomaximal, Hall
13C2×D3×D20C2212yes—
14C2×D120C2211yescharacteristic
15#91782C2212yescomplemented
16C2×C5×D3×C8C2211yescharacteristic
17C5×#892C2212yes—
18C2×C3×D40C2211yescharacteristic
19C3×#4039C2212yescomplemented
20#91473—22no—
21D5×(C2×D3)⋊C4—22no—
22C4×#1202—22no—
23#91434C2212yescomplemented
24#91418C2212yescomplemented
25#91395—22no—
26#91371C2211yescharacteristic
27C2×#6653C2212yes—
28C2×#6650C2211yescharacteristic
29D3×D40C418yescomplemented
30C3×C5×#107C2211yescharacteristic, complemented
31C8×Dic15C2211yescharacteristic, complemented
32#91093C2212yescomplemented
33C5×#818C2211yescharacteristic, complemented
34C5×#808C2212yescomplemented
35C3×C8×Dic5C2211yescharacteristic, complemented
36C3×#3941C2212yescomplemented
37#90969C2212yescomplemented
38#90964C2212yescomplemented
39#90954C2211yescharacteristic, complemented
40#90952C2211yescharacteristic, complemented
41#79588—51nomaximal, Hall
42C22×D40—31no—
43#65855—32no—
44C5×#427—31no—
45#65390—31no—
46#65290—32no—
47#65161—31no—
48#65161—31no—
49#65161—31no—
50#65161D311yescharacteristic, complemented
51#65158—32no—
52#65158—32no—
53C22×D3×D5—22no—
54C2×D60C2312yes—
55C2×C4×D15—22no—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C3×D20C2312yes—
58C2×C3×C4×D5—22no—
59C2×#1202—22no—
60C2×#1200—22no—
61C2×D5×Dic3—22no—
62D3×D20—24no—
63D3×D20C2×C418yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C3×C5×C4⋊C4C2312yes—
66#6714—22no—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69D120C2×C414yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3—22no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C5×D3×C8C2×C414yescomplemented
75C3×#685—22no—
76C3×C4×Dic5C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78C3×D40C2×C414yescomplemented
79Dic3⋊Dic5D411yescharacteristic
80Dic3⋊Dic5D411yescharacteristic
81#6667—22no—
82(C2×D3)⋊Dic5D411yescharacteristic
83(C2×D3)⋊Dic5D411yescharacteristic
84#6665—22no—
85#6653C2×C418yescomplemented
86#6650—22no—
87C2×D3×D8—51no—
88#5545—52no—
89C3×C4×D8—51no—
90Dic3×D8—51no—
91#5014—52no—
92#4880D511yescharacteristic, complemented
93#4872—51no—
94#4785—52no—
95#4770—52no—
96C4×D24—51no—
97#4689—51no—
98C22×D20—32no—
99C22×C5×C8—31no—
100C5×#117—32no—
101#4072—31no—
102C2×#681—31no—
103C2×D40—32no—
104C2×D40—31no—
105C2×D40—38no—
106C2×D40C2×D311yescharacteristic
107#4039—32no—
108#4039—32no—
109#4039—32no—
110#4039C2×D312yescomplemented
111D5×C22⋊C4—62no—
112D5×C22⋊C4—62no—
113C4×D20—62no—
114C4×D20—62no—
115C5×#107—31no—
116C5×#107C2×D311yescharacteristic, complemented
117C5×#106—32no—
118#3947—31no—
119#3947—31no—
120C8×Dic5—31no—
121C8×Dic5C2×D311yescharacteristic, complemented
122#3941—32no—
123#3941—32no—
124#3941—32no—
125#3941C2×D312yescomplemented
126#2948—151noSylow
127C22×D15—22no—
128C22×C5×D3C2×D411yescharacteristic
129C22×C3×D5—22no—
130C2×D3×D5—28no—
131C2×D3×D5—82no—
132C2×D3×D5—82no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15C2×D411yescharacteristic
136C2×Dic15C2×D411yescharacteristic
137D60—22no—
138D60C22×C414yes—
139C4×D15—82no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3C2×D411yescharacteristic
142C4×C5×D3C22×C412yes—
143C4×C5×D3#4112yes—
144C2×C3×Dic5C2×D411yescharacteristic
145C2×C3×Dic5C2×D411yescharacteristic
146C3×D20—22no—
147C3×D20C22×C414yes—
148C3×C4×D5—82no—
149#1202—28no—
150#1200—82no—
151D5×Dic3—82no—
152C3×C5×C8C22×C412yes—
153C3⋊#168—21no—
154C3×#168—21no—
155C5×C3⋊C8C22×C412yes—
156C2×D3×D4—52no—
157C2×C3×D8—51no—
158C3×C4×D4—52no—
159D4×Dic3—52no—
160C2×#213—52no—
161C4×#67—102no—
162C2×(C2×D3)⋊C4—102no—
163D3×D8—58no—
164C2×D24—51no—
165C2×ΓL(1,𝔽25)—51no—
166C2×D3×C8C2×D511yescharacteristic
167#893—52no—
168#892C2×D512yes—
169#67⋊C4—102no—
170D3×C22⋊C4—102no—
171C4×D12—52no—
172#872—51no—
173C3×#107C2×D511yescharacteristic, complemented
174C3×#102—52no—
175C3×C4×C8—51no—
176#832—52no—
177#821—52no—
178#818C2×D511yescharacteristic, complemented
179#815—51no—
180C8×Dic3—51no—
181#809—52no—
182#808C2×D512yescomplemented
183#803—51no—
184C23×D5—62no—
185C22×C4×C5—31no—
186C2×D20—32no—
187C2×D20—38no—
188C2×D20—64no—
189C2×D20—62no—
190C2×D20C22×D312yes—
191C2×C4×D5—22no—
192C2×C4×D5—62no—
193C2×C4×D5—62no—
194C2×C4×D5—62no—
195C2×C5×C8—31no—
196C2×C5×C8—34no—
197C2×C5×C8C22×D311yescharacteristic
198C5×C4⋊C4—32no—
199C5×C4⋊C4C22×D312yes—
200C5×C22⋊C4—62no—
201C42×C5—62no—
202C22⋊Dic5—31no—
203C22⋊Dic5—31no—
204#685—22no—
205#685—62no—
206#685—62no—
207#685—62no—
208C4⋊Dic5—31no—
209C4⋊Dic5—31no—
210C4×Dic5—31no—
211C4×Dic5C22×D311yescharacteristic
212#681—62no—
213C2×#168—31no—
214C2×#168C22×D311yescharacteristic
215D40—38no—
216D40—34no—
217D40C4×D314yescomplemented
218C22×D8—151no—
219#518—152no—
220#442—152no—
221#442—152no—
222C4×D8—51no—
223C4×D8—151no—
224C4×D8—151no—
225C4×D8—151no—
226#427—31no—
227#418—152no—
228#405—151no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—24no—
231C2×D15—42no—
232C2×D15—42no—
233C2×C5×D3—21no—
234C2×C5×D3—21no—
235C2×C5×D3C4×D412yes—
236C2×C3×D5—24no—
237C2×C3×D5—42no—
238C2×C3×D5—42no—
239D3×D5—88no—
240C3×C4×C5—42no—
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C2×#4111yescharacteristic
243Dic15—21no—
244Dic15—21no—
245C3×Dic5—21no—
246C3×Dic5—21no—
247C5×Dic3—42no—
248C5×Dic3C4×D412yes—
249C23×D3—102no—
250C2×C3×D4—52no—
251C22×C3×C4—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254D3×D4—58no—
255D3×D4—104no—
256C2×D12—52no—
257C2×C4×D3—102no—
258C2×C4×D3—102no—
259C2×C4×D3C22×D511yescharacteristic
260C3×D8—54no—
261C2×C3×C8—51no—
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—102no—
265C3×C42—51no—
266#217—102no—
267#213—58no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—51no—
270(C2×D3)⋊C4—51no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—102no—
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—51no—
275Dic3⋊C4—51no—
276C4×Dic3—22no—
277C4×Dic3—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D511yescharacteristic
280D24—54no—
281ΓL(1,𝔽25)—102no—
282D3×C8C4×D514yescomplemented
283C23×C5—31no—
284C22×D5—22no—
285C22×D5—68no—
286C22×D5—62no—
287C22×D5—242no—
288C22×D5—242no—
289C2×C4×C5—22no—
290C2×C4×C5—31no—
291C2×C4×C5—32no—
292C2×C4×C5—32no—
293C2×C4×C5—62no—
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—31no—
296C2×Dic5—31no—
297C2×Dic5D3×D411yescharacteristic
298C2×Dic5D3×D411yescharacteristic
299D20—22no—
300D20—34no—
301D20—68no—
302D20—62no—
303D20C2×C4×D314yes—
304C4×D5—82no—
305C4×D5—242no—
306C4×D5—242no—
307C4×D5—242no—
308C5×C8—32no—
309C5×C8C2×C4×D312yes—
310#168—21no—
311#168—61no—
312C22×D4—152no—
313C2×D8—51no—
314C2×D8—158no—
315C2×D8—152no—
316C2×D8—151no—
317C2×M16—151no—
318C22×C8—31no—
319C4×D4—52no—
320C4×D4—152no—
321C4×D4—152no—
322C4×D4—152no—
323C4×D4—302no—
324C4×D4—302no—
325#117—32no—
326#117—151no—
327C2×C22⋊C4—302no—
328C2×C22⋊C4—302no—
329#107—31no—
330#107D3×D511yescharacteristic, complemented
331#106—32no—
332#102—52no—
333#102—152no—
334#102—152no—
335#102—152no—
336#97—151no—
337#97—151no—
338C4×C8—51no—
339C4×C8—151no—
340C2×C3×C5C2×C4×D411yescharacteristic
341C2×C3×C5#57611yescharacteristic
342C2×C3×C5#57611yescharacteristic
343D15—44no—
344C3×D5—44no—
345C5×D3—22no—
346C23×C3—102no—
347C22×D3—102no—
348C22×D3—108no—
349C22×D3—402no—
350C22×D3—402no—
351C22×D3D4×D511yescharacteristic
352C3×D4—54no—
353C3×D4—102no—
354C2×C3×C4—22no—
355C2×C3×C4—51no—
356C2×C3×C4—51no—
357C2×C3×C4—402no—
358C2×C3×C4C23×D511yescharacteristic
359#67—108no—
360C2×Dic3—22no—
361C2×Dic3—51no—
362C2×Dic3—51no—
363C2×Dic3—402no—
364C2×Dic3D4×D511yescharacteristic
365D12—54no—
366D12—102no—
367C4×D3—402no—
368C4×D3—402no—
369C4×D3C2×C4×D512yes—
370C4×D3#71312yes—
371C3×C8—101no—
372C3×C8C2×C4×D512yes—
373C3⋊C8—101no—
374C3⋊C8C2×C4×D512yes—
375C22×C5—32no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5C2×D3×D411yescharacteristic
379C2×D5—24no—
380C2×D5—42no—
381C2×D5—42no—
382C2×D5—64no—
383C2×D5—122no—
384C2×D5—122no—
385C2×D5—248no—
386C4×C5—32no—
387C4×C5—42no—
388C4×C5—122no—
389C4×C5C22×C4×D311yescharacteristic
390C4×C5D3×#4111yescharacteristic
391Dic5—21no—
392Dic5—21no—
393Dic5—61no—
394Dic5—61no—
395C24—302no—
396C2×D4—52no—
397C2×D4—158no—
398C2×D4—152no—
399C2×D4—304no—
400C2×D4—302no—
401C22×C4—31no—
402C22×C4—102no—
403C22×C4—302no—
404C22×C4—302no—
405C22×C4—302no—
406D8—54no—
407D8—158no—
408D8—154no—
409M16—302no—
410C2×C8—31no—
411C2×C8—34no—
412C2×C8—51no—
413C2×C8—151no—
414C2×C8C2×D3×D511yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—151no—
417C4⋊C4—151no—
418C4⋊C4C2×D3×D512yes—
419C22⋊C4—62no—
420C22⋊C4—102no—
421C22⋊C4—151no—
422C22⋊C4—151no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4—302no—
426C42—51no—
427C42—62no—
428C42—151no—
429C3×C5#294811yescharacteristic, complemented, Hall
430C22×C3—104no—
431C22×C3—202no—
432C22×C3—202no—
433C22×C3C2×D4×D511yescharacteristic
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—104no—
437C2×D3—202no—
438C2×D3—202no—
439C2×D3—408no—
440C2×D3#403912yes—
441C3×C4—42no—
442C3×C4—101no—
443C3×C4—101no—
444C3×C4C22×C4×D511yescharacteristic
445C3×C4C2×#71311yescharacteristic
446Dic3—42no—
447Dic3—101no—
448Dic3—101no—
449Dic3#403912yes—
450C2×C5—62no—
451C2×C5C4×D3×D411yescharacteristic
452C2×C5#575711yescharacteristic
453C2×C5#576911yescharacteristic
454D5—44no—
455D5—124no—
456C23—31no—
457C23—102no—
458C23—308no—
459C23—302no—
460C23—1202no—
461C23—1202no—
462D4—54no—
463D4—102no—
464D4—154no—
465D4—308no—
466D4—302no—
467C2×C4—22no—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—62no—
474C2×C4—151no—
475C2×C4—151no—
476C2×C4—402no—
477C2×C4—1202no—
478C2×C4—1202no—
479C2×C4—1202no—
480C2×C4C22×D3×D511yescharacteristic
481C8—32no—
482C8—101no—
483C8—301no—
484C8C4×D3×D512yes—
485C2×C3—204no—
486C2×C3C2×#403911yescharacteristic
487C2×C3#6610311yescharacteristic
488C2×C3#6610311yescharacteristic
489D3—22no—
490D3—204no—
491C5#7958811yescharacteristic, complemented, Sylow
492C22—32no—
493C22—61no—
494C22—61no—
495C22—104no—
496C22—202no—
497C22—202no—
498C22—304no—
499C22—602no—
500C22—602no—
501C22—1208no—
502C22D3×D4×D511yescharacteristic
503C4—32no—
504C4—42no—
505C4—101no—
506C4—101no—
507C4—122no—
508C4—301no—
509C4—301no—
510C4C2×C4×D3×D511yescharacteristic
511C4D3×#71311yescharacteristic
512C3#1061089811yescharacteristic, complemented, Sylow
513C2—62no—
514C2—204no—
515C2—604no—
516C2D3×#403911yescharacteristic
517C2#1175405811yescharacteristic
518C2#1175411511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×D40C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2948
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11753839C2semidirect
3. #11750973C2semidirect
4. C5×#4880C2semidirect
5. C3×#65161C2semidirect
6. #11747809C2semidirect
7. #11747766C2semidirect
8. #11747653C2semidirect
9. #11747477C2semidirect
10. #11747469C2semidirect
11. #11747229C2semidirect
15. #91782C22semidirect
19. C3×#4039C22semidirect
23. #91434C22semidirect
24. #91418C22semidirect
29. D3×D40C4semidirect
30. C3×C5×#107C22semidirect
31. C8×Dic15C22semidirect
32. #91093C22semidirect
33. C5×#818C22semidirect
34. C5×#808C22semidirect
35. C3×C8×Dic5C22semidirect
36. C3×#3941C22semidirect
37. #90969C22semidirect
38. #90964C22semidirect
39. #90954C22semidirect
40. #90952C22semidirect
50. #65161D3semidirect
63. D3×D20C2×C4semidirect
69. D120C2×C4semidirect
74. C5×D3×C8C2×C4semidirect
78. C3×D40C2×C4semidirect
85. #6653C2×C4semidirect
92. #4880D5semidirect
110. #4039C2×D3semidirect
116. C5×#107C2×D3semidirect
121. C8×Dic5C2×D3semidirect
125. #3941C2×D3semidirect
173. C3×#107C2×D5semidirect
178. #818C2×D5semidirect
182. #808C2×D5semidirect
217. D40C4×D3semidirect
282. D3×C8C4×D5semidirect
330. #107D3×D5semidirect
429. C3×C5#2948semidirect
491. C5#79588semidirect
512. C3#10610898semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D402
#117538392
#117509732
C5×#48802
C3×#651612
#117478092
#117477662
#117476532
#117474772
#117474692
#117472292
#106108983
#795885