Finite Group Databasebeta

← #14417354

Subgroups — #14417354

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×D8×D15C211yesmaximal, characteristic
2#11754922C212yesmaximal, complemented
3C5×Dic3×D8C211yesmaximal, characteristic, complemented
4C3×D8×Dic5C211yesmaximal, characteristic, complemented
5#11748989C212yesmaximal, complemented
6#11748979C212yesmaximal, complemented
7#11748972C212yesmaximal, complemented
8#11747793C211yesmaximal, characteristic, complemented
9#11747766C211yesmaximal, characteristic, complemented
10#11747690C211yesmaximal, characteristic, complemented
11#11747657C211yesmaximal, characteristic, complemented
12#10611319—31nomaximal, Hall
13C2×D4×D15C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15C2×#6715C2212yes—
16D8×D15C418yescomplemented
17C2×D120C2211yescharacteristic
18C2×C8×D15C2211yescharacteristic
19C5×D4×Dic3C2212yescomplemented
20C3×D4×Dic5C2212yescomplemented
21#91561—22no—
22#91556—22no—
23#91552—22no—
24C2×#6667—22no—
25#91428C2212yescomplemented
26#91418C2212yescomplemented
27#91386C2211yescharacteristic
28#91347C2212yes—
29C2×#6651C2211yescharacteristic
30C5×#832C2212yescomplemented
31C5×#818C2211yescharacteristic, complemented
32C5×C8×Dic3C2211yescharacteristic, complemented
33C3×#3964C2212yescomplemented
34C3×#3950C2211yescharacteristic, complemented
35C3×C8×Dic5C2211yescharacteristic, complemented
36#90986C2212yescomplemented
37#90969C2212yescomplemented
38#90968C2212yescomplemented
39#90953C2211yescharacteristic, complemented
40#90952C2211yescharacteristic, complemented
41#79588—51nomaximal, Hall
42C2×D5×D8—31no—
43#65879—32no—
44C4×C5×D8—31no—
45D8×Dic5D311yescharacteristic, complemented
46#65303—32no—
47#65169—31no—
48#65161—31no—
49#65074—32no—
50#65059—32no—
51C4×D40—31no—
52#64978—31no—
53C23×D15—22no—
54C2×C3×C5×D4C2312yes—
55C2×#1220—22no—
56D4×D15—24no—
57D4×D15C2×C418yescomplemented
58C2×D60C2312yes—
59C2×C4×D15C2311yescharacteristic
60C22×C5×Dic3—22no—
61C22×C3×Dic5—22no—
62C2×#1200—22no—
63C2×#1200—22no—
64C3×C5×D8C2×C414yescomplemented
65C2×C3×C5×C8C2311yescharacteristic
66#6715C2×C418yescomplemented
67C2×C3⋊#168C2311yescharacteristic
68D120C2×C414yescomplemented
69C8×D15C2×C414yescomplemented
70C5×#217—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×C22⋊Dic5—22no—
75C3×C4⋊Dic5C2312yes—
76C3×C4×Dic5C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78#6669D411yescharacteristic
79#6669D411yescharacteristic
80#6667—22no—
81#6667—22no—
82#6667—22no—
83#6667D411yescharacteristic
84#6667D411yescharacteristic
85Dic3×Dic5—22no—
86#6651—22no—
87C2×D3×D8—51no—
88#5545—52no—
89C3×C4×D8—51no—
90Dic3×D8D511yescharacteristic, complemented
91#5014—52no—
92#4880—51no—
93#4872—51no—
94#4785—52no—
95#4770—52no—
96C4×D24—51no—
97#4689—51no—
98C2×D4×D5—32no—
99C2×C5×D8C2×D311yescharacteristic
100C4×C5×D4—32no—
101D4×Dic5C2×D312yescomplemented
102C2×#686—32no—
103C4×C22⋊D5—62no—
104C2×#685—62no—
105D5×D8—38no—
106C2×D40—31no—
107C2×#676—31no—
108C2×C8×D5—31no—
109#4039—32no—
110#4038—32no—
111#4027—62no—
112D5×C22⋊C4—62no—
113C4×D20—32no—
114#4018—31no—
115C5×#107—31no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964C2×D312yescomplemented
119#3953—32no—
120#3950C2×D311yescharacteristic, complemented
121#3947—31no—
122C8×Dic5C2×D311yescharacteristic, complemented
123#3941—32no—
124#3940—32no—
125#3935—31no—
126#2948—151noSylow
127C23×C3×C5—22no—
128C22×D15—22no—
129C22×D15—28no—
130C22×D15—82no—
131C22×D15—82no—
132C22×D15C2×D411yescharacteristic
133C3×C5×D4—22no—
134C3×C5×D4C22×C414yes—
135C2×C3×C4×C5C2411yescharacteristic
136#1220—28no—
137C2×Dic15C2×D411yescharacteristic
138D60—22no—
139D60C22×C414yes—
140C4×D15C22×C412yes—
141C4×D15#4112yes—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—82no—
144C2×C5×Dic3C2×D411yescharacteristic
145C2×C5×Dic3C2×D411yescharacteristic
146C2×C3×Dic5—22no—
147C2×C3×Dic5—82no—
148C2×C3×Dic5C2×D411yescharacteristic
149C2×C3×Dic5C2×D411yescharacteristic
150#1200—82no—
151#1200—82no—
152C3×C5×C8C22×C412yes—
153C3⋊#168C22×C412yes—
154C3×#168—21no—
155C5×C3⋊C8—21no—
156C2×D3×D4—52no—
157C2×C3×D8C2×D511yescharacteristic
158C3×C4×D4—52no—
159D4×Dic3C2×D512yescomplemented
160C2×#213—52no—
161C4×#67—102no—
162C2×(C2×D3)⋊C4—102no—
163D3×D8—58no—
164C2×D24—51no—
165C2×ΓL(1,𝔽25)—51no—
166C2×D3×C8—51no—
167#893—52no—
168#892—52no—
169#67⋊C4—102no—
170D3×C22⋊C4—102no—
171C4×D12—52no—
172#872—51no—
173C3×#107—51no—
174C3×#102—52no—
175C3×C4×C8—51no—
176#832C2×D512yescomplemented
177#821—52no—
178#818C2×D511yescharacteristic, complemented
179#815—51no—
180C8×Dic3C2×D511yescharacteristic, complemented
181#809—52no—
182#808—52no—
183#803—51no—
184C23×D5—62no—
185C2×C5×D4C22×D312yes—
186C22×C4×C5—62no—
187C2×C22⋊D5—62no—
188C22×Dic5—22no—
189D4×D5—38no—
190D4×D5—64no—
191C2×D20—32no—
192C2×C4×D5—31no—
193C2×C4×D5—62no—
194C2×C4×D5—62no—
195C5×D8C4×D314yescomplemented
196C2×C5×C8—31no—
197C2×C5×C8C22×D311yescharacteristic
198C5×C4⋊C4—32no—
199C5×C22⋊C4—62no—
200C42×C5—31no—
201C22⋊Dic5—22no—
202#686—38no—
203#685—31no—
204#685—31no—
205#685—62no—
206#685—62no—
207#685—62no—
208C4⋊Dic5C22×D312yes—
209#683—31no—
210#683—31no—
211C4×Dic5—62no—
212C4×Dic5C22×D311yescharacteristic
213C2×#168—31no—
214C2×#168C22×D311yescharacteristic
215D40—34no—
216#676—62no—
217C8×D5—34no—
218C22×D8—151no—
219#518—152no—
220#442—152no—
221#442—152no—
222C4×D8—31no—
223C4×D8—51no—
224C4×D8—151no—
225C4×D8—151no—
226#427—151no—
227#418—152no—
228#405—151no—
229C22×C3×C5—24no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—21no—
234C2×D15—21no—
235C2×D15—24no—
236C2×D15—42no—
237C2×D15—42no—
238C2×D15—88no—
239C2×D15C4×D412yes—
240C3×C4×C5C23×C411yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15C4×D412yes—
243C3×Dic5—21no—
244C3×Dic5—21no—
245C3×Dic5—42no—
246C5×Dic3—21no—
247C5×Dic3—21no—
248C5×Dic3—42no—
249C23×D3—102no—
250C2×C3×D4C22×D512yes—
251C22×C3×C4—102no—
252C2×#67—102no—
253C22×Dic3—22no—
254D3×D4—58no—
255D3×D4—104no—
256C2×D12—52no—
257C2×C4×D3—51no—
258C2×C4×D3—102no—
259C2×C4×D3—102no—
260C3×D8C4×D514yescomplemented
261C2×C3×C8—51no—
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—52no—
264C3×C22⋊C4—102no—
265C3×C42—51no—
266#217—22no—
267#213—58no—
268(C2×D3)⋊C4—51no—
269(C2×D3)⋊C4—51no—
270(C2×D3)⋊C4—102no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—102no—
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—51no—
275Dic3⋊C4—51no—
276C4×Dic3—102no—
277C4×Dic3C22×D511yescharacteristic
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D511yescharacteristic
280D24—54no—
281ΓL(1,𝔽25)—102no—
282D3×C8—54no—
283C23×C5—22no—
284C22×D5—31no—
285C22×D5—68no—
286C22×D5—62no—
287C22×D5—242no—
288C22×D5—242no—
289C5×D4—22no—
290C5×D4C2×C4×D314yes—
291C2×C4×C5—31no—
292C2×C4×C5—31no—
293C2×C4×C5—62no—
294C2×C4×C5—242no—
295C2×C4×C5C23×D311yescharacteristic
296C22⋊D5—68no—
297C2×Dic5—22no—
298C2×Dic5—31no—
299C2×Dic5—82no—
300C2×Dic5D3×D411yescharacteristic
301C2×Dic5D3×D411yescharacteristic
302D20—34no—
303D20—62no—
304C4×D5—32no—
305C4×D5—32no—
306C4×D5—242no—
307C4×D5—242no—
308C5×C8—61no—
309C5×C8C2×C4×D312yes—
310#168—21no—
311#168—32no—
312C22×D4—152no—
313C2×D8—152no—
314C2×D8—158no—
315C2×D8—151no—
316C2×D8D3×D511yescharacteristic
317C2×M16—151no—
318C22×C8—151no—
319C4×D4—32no—
320C4×D4—52no—
321C4×D4—152no—
322C4×D4—152no—
323C4×D4—302no—
324C4×D4—302no—
325#117—151no—
326#117—152no—
327C2×C22⋊C4—302no—
328C2×C22⋊C4—302no—
329#107—31no—
330#107—51no—
331#106—152no—
332#102—32no—
333#102—52no—
334#102—152no—
335#102—152no—
336#97—151no—
337#97—151no—
338C4×C8—31no—
339C4×C8—51no—
340C2×C3×C5—44no—
341C2×C3×C5C2×C4×D411yescharacteristic
342C2×C3×C5#57611yescharacteristic
343C2×C3×C5#57611yescharacteristic
344D15—22no—
345D15—44no—
346C23×C3—22no—
347C22×D3—51no—
348C22×D3—108no—
349C22×D3—102no—
350C22×D3—402no—
351C22×D3—402no—
352C3×D4—22no—
353C3×D4C2×C4×D514yes—
354C2×C3×C4—51no—
355C2×C3×C4—51no—
356C2×C3×C4—102no—
357C2×C3×C4—402no—
358C2×C3×C4C23×D511yescharacteristic
359#67—108no—
360C2×Dic3—22no—
361C2×Dic3—51no—
362C2×Dic3—82no—
363C2×Dic3D4×D511yescharacteristic
364C2×Dic3D4×D511yescharacteristic
365D12—54no—
366D12—102no—
367C4×D3—52no—
368C4×D3—52no—
369C4×D3—402no—
370C4×D3—402no—
371C3×C8—101no—
372C3×C8C2×C4×D512yes—
373C3⋊C8—21no—
374C3⋊C8—52no—
375C22×C5—24no—
376C22×C5—42no—
377C22×C5—42no—
378C22×C5C2×D3×D411yescharacteristic
379C2×D5—32no—
380C2×D5—61no—
381C2×D5—61no—
382C2×D5—64no—
383C2×D5—122no—
384C2×D5—122no—
385C2×D5—248no—
386C4×C5—61no—
387C4×C5—61no—
388C4×C5—122no—
389C4×C5C22×C4×D311yescharacteristic
390C4×C5D3×#4111yescharacteristic
391Dic5—21no—
392Dic5—21no—
393Dic5—32no—
394Dic5—42no—
395C24—302no—
396C2×D4—158no—
397C2×D4—152no—
398C2×D4—304no—
399C2×D4—302no—
400C2×D4C2×D3×D512yes—
401C22×C4—62no—
402C22×C4—102no—
403C22×C4—151no—
404C22×C4—302no—
405C22×C4—302no—
406D8—158no—
407D8—154no—
408D8#120014yescomplemented
409M16—302no—
410C2×C8—31no—
411C2×C8—51no—
412C2×C8—151no—
413C2×C8—154no—
414C2×C8C2×D3×D511yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—52no—
417C4⋊C4—151no—
418C4⋊C4—151no—
419C22⋊C4—62no—
420C22⋊C4—102no—
421C22⋊C4—151no—
422C22⋊C4—151no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4—302no—
426C42—31no—
427C42—51no—
428C42—302no—
429C3×C5#294811yescharacteristic, complemented, Hall
430C22×C3—24no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3C2×D4×D511yescharacteristic
434C2×D3—52no—
435C2×D3—101no—
436C2×D3—101no—
437C2×D3—104no—
438C2×D3—202no—
439C2×D3—202no—
440C2×D3—408no—
441C3×C4—101no—
442C3×C4—101no—
443C3×C4—202no—
444C3×C4C22×C4×D511yescharacteristic
445C3×C4D5×#4111yescharacteristic
446Dic3—21no—
447Dic3—21no—
448Dic3—42no—
449Dic3—52no—
450C2×C5—44no—
451C2×C5C4×D3×D411yescharacteristic
452C2×C5#575711yescharacteristic
453C2×C5#576911yescharacteristic
454D5—62no—
455D5—124no—
456C23—22no—
457C23—151no—
458C23—308no—
459C23—302no—
460C23—1202no—
461C23—1202no—
462D4—22no—
463D4—154no—
464D4—308no—
465D4—302no—
466D4C2×#120014yes—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—51no—
470C2×C4—51no—
471C2×C4—62no—
472C2×C4—102no—
473C2×C4—151no—
474C2×C4—152no—
475C2×C4—152no—
476C2×C4—242no—
477C2×C4—402no—
478C2×C4—1202no—
479C2×C4—1202no—
480C2×C4C22×D3×D511yescharacteristic
481C8—61no—
482C8—101no—
483C8—152no—
484C8C2×#120012yes—
485C2×C3—44no—
486C2×C3C4×D4×D511yescharacteristic
487C2×C3#6609111yescharacteristic
488C2×C3#6610311yescharacteristic
489D3—102no—
490D3—204no—
491C5#7958811yescharacteristic, complemented, Sylow
492C22—24no—
493C22—42no—
494C22—42no—
495C22—152no—
496C22—301no—
497C22—301no—
498C22—304no—
499C22—602no—
500C22—602no—
501C22—1208no—
502C22D3×D4×D511yescharacteristic
503C4—61no—
504C4—61no—
505C4—101no—
506C4—101no—
507C4—122no—
508C4—152no—
509C4—202no—
510C4#9202411yescharacteristic
511C4C22×#120011yescharacteristic
512C3#1061131911yescharacteristic, complemented, Sylow
513C2—44no—
514C2—302no—
515C2—604no—
516C2#1175405811yescharacteristic
517C2#1175406111yescharacteristic
518C2D4×#120011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×D8×D15C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2948
LCSG ▷ 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
2. #11754922C2semidirect
3. C5×Dic3×D8C2semidirect
4. C3×D8×Dic5C2semidirect
5. #11748989C2semidirect
6. #11748979C2semidirect
7. #11748972C2semidirect
8. #11747793C2semidirect
9. #11747766C2semidirect
10. #11747690C2semidirect
11. #11747657C2semidirect
16. D8×D15C4semidirect
19. C5×D4×Dic3C22semidirect
20. C3×D4×Dic5C22semidirect
25. #91428C22semidirect
26. #91418C22semidirect
30. C5×#832C22semidirect
31. C5×#818C22semidirect
32. C5×C8×Dic3C22semidirect
33. C3×#3964C22semidirect
34. C3×#3950C22semidirect
35. C3×C8×Dic5C22semidirect
36. #90986C22semidirect
37. #90969C22semidirect
38. #90968C22semidirect
39. #90953C22semidirect
40. #90952C22semidirect
45. D8×Dic5D3semidirect
57. D4×D15C2×C4semidirect
64. C3×C5×D8C2×C4semidirect
66. #6715C2×C4semidirect
68. D120C2×C4semidirect
69. C8×D15C2×C4semidirect
90. Dic3×D8D5semidirect
101. D4×Dic5C2×D3semidirect
118. #3964C2×D3semidirect
120. #3950C2×D3semidirect
122. C8×Dic5C2×D3semidirect
159. D4×Dic3C2×D5semidirect
176. #832C2×D5semidirect
178. #818C2×D5semidirect
180. C8×Dic3C2×D5semidirect
195. C5×D8C4×D3semidirect
260. C3×D8C4×D5semidirect
408. D8#1200semidirect
429. C3×C5#2948semidirect
491. C5#79588semidirect
512. C3#10611319semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D152
#117549222
C5×Dic3×D82
C3×D8×Dic52
#117489892
#117489792
#117489722
#117477932
#117477662
#117476902
#117476572
#106113193
#795885