Finite Group Databasebeta

← #14417104

Subgroups — #14417104

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91838C211yesmaximal, characteristic
2C5×#5827C211yesmaximal, characteristic, complemented
3#11754515C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5#11749235C212yesmaximal, complemented
6#11749232C212yesmaximal, complemented
7#11748989C212yesmaximal, complemented
8#11748986C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10C2×#90969C211yesmaximal, characteristic, complemented
11#11748323C211yesmaximal, characteristic, complemented
12#10614295—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15#91838C418yescomplemented
16C2×#6717C2212yes—
17C2×#6715C2212yes—
18C2×#6710C2211yescharacteristic
19C5×Q8×Dic3C2212yescomplemented
20C5×D4×Dic3—22no—
21C5×D4×Dic3C2212yescomplemented
22C5×#926—21no—
23C5×#926C2211yescharacteristic
24C2×C5×C4⋊Dic3—21no—
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C3×#4072C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28#91561—22no—
29#91428C2212yes—
30#91428C2212yes—
31#91418—21no—
32#91418—21no—
33C3×#3967C2211yescharacteristic, complemented
34C3×#3967C2211yescharacteristic, complemented
35C3×#3964C2211yescharacteristic, complemented
36C3×#3964C2211yescharacteristic, complemented
37#90989C2212yescomplemented
38#90986C2212yescomplemented
39#90969C2212yes—
40#90969C2212yes—
41#90953C2212yescomplemented
42Dic3×#168C2212yescomplemented
43#78820—51nomaximal, Hall
44C5×#520—31no—
45C2×#4095—31no—
46#65855—31no—
47#65522D311yescharacteristic, complemented
48#65315—32no—
49C4×#688—32no—
50#65303—32no—
51C4×#686—32no—
52#65286—31no—
53C2×#3941—31no—
54#65253—31no—
55C23×D15—21no—
56C3×C5×#41—22no—
57C3×C5×#41C2×C414yescomplemented
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×D60—21no—
64C2×D60—22no—
65C2×D60C2×C414yescomplemented
66C2×D60C2312yes—
67C22×C5×Dic3—21no—
68C22×C5×Dic3—22no—
69C2×#1200—22no—
70C2×#1200—22no—
71#6717C2×C418yescomplemented
72#6715C2×C418yescomplemented
73#6710C2×C414yescomplemented
74C2×C3⋊#168C2312yes—
75C5×#217—22no—
76C5×#217D412yes—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3—22no—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3D411yescharacteristic
81C5×C4⋊Dic3C2312yes—
82C4×C5×Dic3—22no—
83C4×C5×Dic3C2312yes—
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4×Dic5—21no—
88C2×C3×#168—22no—
89C2×C3×#168C2311yescharacteristic
90C2×C3×#168C2311yescharacteristic
91#6667—22no—
92#6667—22no—
93#5827D511yescharacteristic, complemented
94C2×#949—51no—
95#5521—51no—
96C3×#416—51no—
97C2×#821—51no—
98#5101—51no—
99#4995—51no—
100#4817—52no—
101#4788—52no—
102#4785—52no—
103#4756—52no—
104C2×C5×#41C2×D311yescharacteristic
105C22×D20—31no—
106C4×C5×Q8—32no—
107C4×C5×D4—32no—
108C4×C5×D4—62no—
109C5×#117—31no—
110C5×#117—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113#4095—38no—
114C2×#688—32no—
115C2×#686—32no—
116#4072C2×D311yescharacteristic
117C2×#681—31no—
118C22×#168C2×D311yescharacteristic
119#4039—61no—
120#4039—61no—
121D5×C22⋊C4—62no—
122C4×D20—32no—
123C4×D20—32no—
124#3967C2×D311yescharacteristic, complemented
125#3967C2×D311yescharacteristic, complemented
126#3964C2×D311yescharacteristic, complemented
127#3964C2×D311yescharacteristic, complemented
128#3941—32no—
129#3941—32no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2946—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C22×D15—22no—
138C22×D15—24no—
139C22×D15—81no—
140C22×D15—81no—
141C3×C5×Q8—21no—
142C3×C5×Q8C22×C412yes—
143C3×C5×D4—24no—
144C3×C5×D4—21no—
145C3×C5×D4C22×C412yes—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—24no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5C2411yescharacteristic
152D60—24no—
153D60—22no—
154D60C22×C414yes—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—82no—
157C2×C5×Dic3—81no—
158C2×C5×Dic3C2×D412yes—
159C2×C5×Dic3C2×D412yes—
160C2×C3×Dic5—21no—
161C2×C3×Dic5—21no—
162#1200—82no—
163#1200—82no—
164C3⋊#168C22×C414yes—
165C3×#168—21no—
166C3×#168—21no—
167C2×C3×#41C2×D511yescharacteristic
168C22×D12—51no—
169C22×C3×C8—51no—
170C3×#117—51no—
171#949—58no—
172Q8×Dic3C2×D512yescomplemented
173C2×#215—52no—
174D4×Dic3—22no—
175D4×Dic3C2×D512yescomplemented
176C2×#213—52no—
177#926—21no—
178#926C2×D511yescharacteristic
179C2×C4⋊Dic3—21no—
180C2×C4⋊Dic3C2×D511yescharacteristic
181C2×#208—51no—
182#893—52no—
183#893—52no—
184D3×C22⋊C4—102no—
185C4×D12—101no—
186C4×D12—101no—
187C3×#103—51no—
188C3×#103—51no—
189C3×#102—51no—
190C3×#102—51no—
191#821—52no—
192#821—52no—
193#815—52no—
194C8×Dic3—52no—
195#808—52no—
196#807—52no—
197C23×D5—61no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—62no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×D20—34no—
208C2×D20—32no—
209C2×D20—61no—
210C2×D20—62no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4—32no—
216C5×C4⋊C4—62no—
217C5×C4⋊C4—61no—
218C5×C22⋊C4—32no—
219C5×C22⋊C4—62no—
220C42×C5—32no—
221C42×C5—62no—
222C22⋊Dic5—21no—
223#688—38no—
224#686—38no—
225#685—62no—
226#685—62no—
227C4⋊Dic5C22×D311yescharacteristic
228C4⋊Dic5C22×D311yescharacteristic
229C4×Dic5—21no—
230#681—34no—
231C2×#168—22no—
232C2×#168—32no—
233C2×#168C22×D311yescharacteristic
234C2×#168C22×D311yescharacteristic
235C2×AGL(1,ℤ/8)—151no—
236#520—31no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—51no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5C4×D412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—24no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—84no—
257C3×C4×C5—22no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261C3×Dic5—41no—
262C3×Dic5—41no—
263C5×Dic3—22no—
264C5×Dic3—22no—
265C5×Dic3—42no—
266C23×D3—101no—
267C3×#41—22no—
268C3×#41C4×D514yescomplemented
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4C22×D511yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4C22×D511yescharacteristic
274C22×Dic3—21no—
275C22×Dic3—22no—
276C2×D12—54no—
277C2×D12—52no—
278C2×D12—102no—
279C2×D12—101no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C2×C3×C8—51no—
283C2×C3×C8—51no—
284C2×C3×C8—102no—
285C3×C4⋊C4—51no—
286C3×C4⋊C4—51no—
287C3×C22⋊C4—101no—
288C3×C42—101no—
289#217—22no—
290#217C22⋊D512yes—
291#215—58no—
292#213—58no—
293(C2×D3)⋊C4—102no—
294(C2×D3)⋊C4—102no—
295C4⋊Dic3—21no—
296C4⋊Dic3—22no—
297C4⋊Dic3C22⋊D511yescharacteristic
298C4⋊Dic3C22⋊D511yescharacteristic
299C4⋊Dic3C22×D512yes—
300C4×Dic3—22no—
301C4×Dic3C22×D512yes—
302#208—54no—
303C2×C3⋊C8—52no—
304C23×C5—21no—
305C23×C5D3×D411yescharacteristic
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C5×Q8—21no—
311C5×Q8C2×C4×D312yes—
312C5×D4—24no—
313C5×D4—21no—
314C5×D4C2×C4×D312yes—
315C2×C4×C5—21no—
316C2×C4×C5—24no—
317C2×C4×C5—32no—
318C2×C4×C5—32no—
319C2×C4×C5—62no—
320C2×C4×C5—242no—
321C2×C4×C5—241no—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5#23712yes—
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—21no—
327C2×Dic5—21no—
328D20—34no—
329D20—64no—
330D20—62no—
331C4×D5—242no—
332C4×D5—242no—
333#168—21no—
334#168—21no—
335#168—34no—
336C2×#41D3×D511yescharacteristic
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—51no—
343C4×Q8—32no—
344C4×D4—32no—
345C4×D4—62no—
346C4×D4—152no—
347C4×D4—152no—
348C4×D4—301no—
349C4×D4—301no—
350#117—31no—
351#117—51no—
352#117—61no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—61no—
355C2×C22⋊C4—302no—
356#107—152no—
357#106—152no—
358#103—51no—
359#103—51no—
360#102—51no—
361#102—51no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—44no—
372C23×C3—21no—
373C23×C3C2×C22⋊D511yescharacteristic
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C3×Q8—21no—
379C3×Q8C2×C4×D512yes—
380C3×D4—24no—
381C3×D4—21no—
382C3×D4C2×C4×D512yes—
383C2×C3×C4—21no—
384C2×C3×C4—24no—
385C2×C3×C4—101no—
386C2×C3×C4—101no—
387C2×C3×C4C2×C4×D512yes—
388C2×C3×C4#70912yes—
389C2×C3×C4C2×C22⋊D511yescharacteristic
390C2×C3×C4C23×D511yescharacteristic
391C2×Dic3—22no—
392C2×Dic3—82no—
393C2×Dic3—81no—
394C2×Dic3C2×C22⋊D512yes—
395C2×Dic3C2×C22⋊D512yes—
396D12—54no—
397D12—102no—
398D12—104no—
399C4×D3—402no—
400C4×D3—402no—
401C3×C8—101no—
402C3×C8—101no—
403C3⋊C8—54no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—22no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5#67⋊C412yes—
410C22×C5C2×D3×D411yescharacteristic
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—22no—
416C4×C5—62no—
417C4×C5—62no—
418C4×C5—122no—
419C4×C5#67⋊C412yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23711yescharacteristic
422Dic5—41no—
423Dic5—41no—
424C24—301no—
425#41—22no—
426#41#120014yescomplemented
427C2×Q8C2×D3×D511yescharacteristic
428C2×D4—21no—
429C2×D4—154no—
430C2×D4—152no—
431C2×D4—302no—
432C2×D4—301no—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—21no—
435C22×C4—62no—
436C22×C4—61no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—102no—
446C2×C8—152no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—32no—
450C4⋊C4—51no—
451C4⋊C4—51no—
452C4⋊C4—62no—
453C4⋊C4—61no—
454C22⋊C4—32no—
455C22⋊C4—62no—
456C22⋊C4—101no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—32no—
460C42—62no—
461C42—101no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3C4×C22⋊D512yes—
469C22×C3C22×C22⋊D511yescharacteristic
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—404no—
474C3×C4—22no—
475C3×C4—201no—
476C3×C4—201no—
477C3×C4C4×C22⋊D512yes—
478C3×C4C22×C4×D511yescharacteristic
479C3×C4C2×#70911yescharacteristic
480Dic3—22no—
481Dic3—22no—
482Dic3—42no—
483C2×C5—22no—
484C2×C5—42no—
485C2×C5C2×#67⋊C411yescharacteristic
486C2×C5#576911yescharacteristic
487C2×C5#577011yescharacteristic
488D5—124no—
489C23—21no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23D3×C22⋊D511yescharacteristic
495Q8—21no—
496Q8C2×#120012yes—
497D4—24no—
498D4—21no—
499D4—154no—
500D4—302no—
501D4—304no—
502D4C2×#120012yes—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—62no—
508C2×C4—101no—
509C2×C4—101no—
510C2×C4—242no—
511C2×C4—241no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#677912yes—
515C2×C4C2×#120012yes—
516C2×C4D3×C22⋊D511yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—101no—
519C8—101no—
520C8—154no—
521C2×C3—22no—
522C2×C3—42no—
523C2×C3C2×C4×C22⋊D511yescharacteristic
524C2×C3#6616911yescharacteristic
525C2×C3#6617111yescharacteristic
526D3—204no—
527C5#7882011yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—304no—
534C22—602no—
535C22—602no—
536C22—1204no—
537C22#9155612yes—
538C22C2×D3×C22⋊D511yescharacteristic
539C4—22no—
540C4—62no—
541C4—62no—
542C4—122no—
543C4—201no—
544C4—201no—
545C4#9155612yes—
546C4C2×#677911yescharacteristic
547C4C22×#120011yescharacteristic
548C3#1061429511yescharacteristic, complemented, Sylow
549C2—22no—
550C2—42no—
551C2—604no—
552C2#1175532511yescharacteristic
553C2#1175532611yescharacteristic
554C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91838C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×#5827C2semidirect
3. #11754515C2semidirect
4. C3×#65522C2semidirect
5. #11749235C2semidirect
6. #11749232C2semidirect
7. #11748989C2semidirect
8. #11748986C2semidirect
9. #11748472C2semidirect
10. C2×#90969C2semidirect
11. #11748323C2semidirect
15. #91838C4semidirect
19. C5×Q8×Dic3C22semidirect
21. C5×D4×Dic3C22semidirect
33. C3×#3967C22semidirect
34. C3×#3967C22semidirect
35. C3×#3964C22semidirect
36. C3×#3964C22semidirect
37. #90989C22semidirect
38. #90986C22semidirect
41. #90953C22semidirect
42. Dic3×#168C22semidirect
47. #65522D3semidirect
57. C3×C5×#41C2×C4semidirect
65. C2×D60C2×C4semidirect
71. #6717C2×C4semidirect
72. #6715C2×C4semidirect
73. #6710C2×C4semidirect
93. #5827D5semidirect
124. #3967C2×D3semidirect
125. #3967C2×D3semidirect
126. #3964C2×D3semidirect
127. #3964C2×D3semidirect
172. Q8×Dic3C2×D5semidirect
175. D4×Dic3C2×D5semidirect
199. C5×#41C4×D3semidirect
268. C3×#41C4×D5semidirect
426. #41#1200semidirect
462. C3×C5#2946semidirect
527. C5#78820semidirect
548. C3#10614295semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C5×#58272
#117545152
C3×#655222
#117492352
#117492322
#117489892
#117489862
#117484722
C2×#909692
#117483232
#106142953
#788205