Finite Group Databasebeta

← #14418076

Subgroups — #14418076

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754017C212yesmaximal, complemented
2#11753979C211yesmaximal, characteristic
3#11750994C211yesmaximal, characteristic, complemented
4C5×#4894C211yesmaximal, characteristic, complemented
5C3×#65184C211yesmaximal, characteristic, complemented
6#11748237C212yesmaximal, complemented
7#11748205C212yesmaximal, complemented
8#11748203C212yesmaximal, complemented
9#11748067C211yesmaximal, characteristic, complemented
10#11748062C211yesmaximal, characteristic, complemented
11#11748053C211yesmaximal, characteristic, complemented
12#10611628—31nomaximal, Hall
13#92016C2212yes—
14M16×D15C2212yes—
15C2×#6705C2211yescharacteristic
16C5×#907C2212yescomplemented
17C5×#904C2211yescharacteristic
18C3×#4053C2212yescomplemented
19C3×#4050C2211yescharacteristic
20#91386C2211yescharacteristic
21#91297C2212yes—
22C2×#6648C2211yescharacteristic
23#91286C2212yescomplemented
24#91283C2212yescomplemented
25#91280C412yescomplemented
26#91278C412yescomplemented
27#91267—22no—
28#91266—22no—
29#91258C412yescomplemented
30#91257C412yescomplemented
31#91246—22no—
32D3×C8×D5—22no—
33C3×C5×#108C2211yescharacteristic, complemented
34#91106C2212yescomplemented
35#91103C2211yescharacteristic, complemented
36C5×#825C2212yescomplemented
37C5×#815C2211yescharacteristic, complemented
38C3×#3957C2212yescomplemented
39C3×C8×Dic5C2211yescharacteristic, complemented
40#90979C2212yescomplemented
41#90977C2212yescomplemented
42#90952C2211yescharacteristic, complemented
43Dic3×#168C2211yescharacteristic, complemented
44#79888—51nomaximal, Hall
45#66102—31no—
46D5×#131—32no—
47C5×#444—31no—
48#65485—31no—
49#65434—32no—
50#65184D311yescharacteristic, complemented
51#65182—31no—
52#65113—32no—
53#65110—32no—
54#65006—31no—
55#64997—31no—
56C2×C4×D15C2311yescharacteristic
57C5×#235C2312yes—
58C3×#709C2312yes—
59#6790—22no—
60#6780—22no—
61#6777C2×C412yes—
62C4×D3×D5—22no—
63#6771—22no—
64D15⋊Q8C2×C412yes—
65#6768C2×C412yes—
66#6766C2×C412yes—
67C3×C5×M16C2312yes—
68C2×C3×C5×C8C2311yescharacteristic
69#6710C2312yes—
70C2×C3⋊#168C2311yescharacteristic
71#6705—22no—
72#6705C2×C412yes—
73#6705C2×C412yes—
74C8×D15—22no—
75C4×C5×Dic3C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C5×Dic12C2×C411yescharacteristic
78C5×D24C2×C411yescharacteristic
79C5×#204C2×C412yes—
80C5×ΓL(1,𝔽25)—22no—
81C5×D3×C8—22no—
82C3×C4×Dic5C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84C3×Dic20C2×C411yescharacteristic
85C3×D40C2×C411yescharacteristic
86C3×#677C2×C412yes—
87C3×#676—22no—
88C3×C8×D5—22no—
89#6669—21no—
90#6667—21no—
91#6661C2×C412yes—
92#6656C2×C412yes—
93#6655C2×C412yes—
94#6652C2×C412yes—
95#6650—22no—
96#6649—22no—
97#6648D412yes—
98#6648D412yes—
99D3×#168—22no—
100D5×C3⋊C8—22no—
101#5768—51no—
102D3×#131—52no—
103C3×#443—51no—
104#5197—51no—
105#5144—52no—
106#4894D511yescharacteristic, complemented
107#4893—51no—
108#4823—52no—
109#4821—52no—
110#4700—51no—
111#4689—51no—
112D5×#41—32no—
113C5×#135—31no—
114C5×#131—32no—
115#4096—32no—
116#4094—32no—
117#4064—32no—
118#4061—32no—
119#4060—32no—
120#4057—32no—
121#4053—62no—
122#4053C2×D312yescomplemented
123D5×M16—32no—
124D5×M16—62no—
125#4050C2×D311yescharacteristic
126#4047—32no—
127#4047—62no—
128C2×#676—31no—
129C2×C8×D5—31no—
130C2×C8×D5—62no—
131#4018—31no—
132C5×#108C2×D311yescharacteristic, complemented
133C5×#104—32no—
134C5×#97—31no—
135#3969—32no—
136#3957C2×D312yescomplemented
137#3954—32no—
138#3951—31no—
139#3947—31no—
140C8×Dic5C2×D311yescharacteristic, complemented
141#3937—32no—
142C4×#168—31no—
143#2955—151noSylow
144C22×D15#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15#4111yescharacteristic
148C4×D15C22×C412yes—
149C4×D15C2×D412yes—
150C5×#67—22no—
151C2×C5×Dic3—21no—
152C5×D12C22×C412yes—
153C4×C5×D3—22no—
154C5×Dic6C22×C412yes—
155C3×C22⋊D5—22no—
156C2×C3×Dic5—21no—
157C3×D20C22×C412yes—
158C3×C4×D5—22no—
159C3×Dic10C22×C412yes—
160#1204—22no—
161#1203—22no—
162#1202—22no—
163#1201—22no—
164#1200—22no—
165D3×Dic5—22no—
166D5×Dic3—22no—
167C3×C5×C8—22no—
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C22×C411yescharacteristic
170C3⋊#168—22no—
171C3⋊#168C22×C412yes—
172C3×#168C2×D411yescharacteristic
173C3×#168C2×D411yescharacteristic
174C5×C3⋊C8C2×D412yes—
175D3×#41—52no—
176C3×#135—51no—
177C3×#131—52no—
178#950—52no—
179#948—52no—
180#918—52no—
181#915—52no—
182#914—52no—
183#911—52no—
184#907—102no—
185#907C2×D512yescomplemented
186D3×M16—52no—
187D3×M16—102no—
188#904C2×D511yescharacteristic
189#901—52no—
190#901—102no—
191C2×ΓL(1,𝔽25)—51no—
192C2×D3×C8—51no—
193C2×D3×C8—102no—
194#872—51no—
195C3×#108C2×D511yescharacteristic, complemented
196C3×#104—52no—
197C3×C4×C8—51no—
198#837—52no—
199#825C2×D512yescomplemented
200#822—52no—
201#819—51no—
202#815C2×D511yescharacteristic, complemented
203C8×Dic3—51no—
204#805—52no—
205#803—51no—
206C5×#41—32no—
207#713—32no—
208Q8×D5—32no—
209#711—32no—
210#711—62no—
211D4×D5—32no—
212D4×D5—62no—
213#709—62no—
214#709C22×D312yes—
215C2×C4×D5—31no—
216C2×C4×D5—62no—
217C5×Q16—31no—
218C5×SD16—32no—
219C5×D8—31no—
220C5×M16—62no—
221C5×M16C22×D312yes—
222C2×C5×C8—31no—
223C2×C5×C8—62no—
224C2×C5×C8C22×D311yescharacteristic
225C42×C5—31no—
226#689—32no—
227#688—32no—
228#687—32no—
229#686—32no—
230#685—61no—
231#683—61no—
232C4×Dic5C22×D311yescharacteristic
233#681—32no—
234#681—62no—
235C2×#168—31no—
236C2×#168—62no—
237C2×#168C22×D311yescharacteristic
238Dic20C4×D311yescharacteristic
239D40C4×D311yescharacteristic
240#677C4×D312yes—
241#676—22no—
242#676—32no—
243#676—32no—
244#676—62no—
245#676—62no—
246C8×D5—22no—
247C8×D5—32no—
248C8×D5—32no—
249C8×D5—62no—
250C8×D5—62no—
251#575—151no—
252C2×#131—152no—
253#444—31no—
254#444—151no—
255#444—152no—
256#443—51no—
257#443—151no—
258#443—152no—
259#430—151no—
260#421—152no—
261#405—151no—
262C22×C3×C5C2×#4111yescharacteristic
263C2×D15—41no—
264C2×D15C4×D412yes—
265C2×C5×D3—22no—
266C2×C3×D5—22no—
267D3×D5—44no—
268C3×C4×C5C23×C411yescharacteristic
269C3×C4×C5C22×D411yescharacteristic
270Dic15C4×D412yes—
271C3×Dic5—22no—
272C3×Dic5—41no—
273C5×Dic3—22no—
274C5×Dic3—41no—
275C3×#41—52no—
276#239—52no—
277D3×Q8—52no—
278#237—52no—
279#237—102no—
280D3×D4—52no—
281D3×D4—102no—
282#235—102no—
283#235C22×D512yes—
284C2×C4×D3—51no—
285C2×C4×D3—102no—
286C3×Q16—51no—
287C3×SD16—52no—
288C3×D8—51no—
289C3×M16—102no—
290C3×M16C22×D512yes—
291C2×C3×C8—51no—
292C2×C3×C8—102no—
293C2×C3×C8C22×D511yescharacteristic
294C3×C42—51no—
295#216—52no—
296#215—52no—
297#214—52no—
298#213—52no—
299(C2×D3)⋊C4—101no—
300Dic3⋊C4—101no—
301C4×Dic3C22×D511yescharacteristic
302#208—52no—
303#208—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12C4×D511yescharacteristic
308D24C4×D511yescharacteristic
309#204C4×D512yes—
310ΓL(1,𝔽25)—22no—
311ΓL(1,𝔽25)—52no—
312ΓL(1,𝔽25)—52no—
313ΓL(1,𝔽25)—102no—
314ΓL(1,𝔽25)—102no—
315D3×C8—22no—
316D3×C8—52no—
317D3×C8—52no—
318D3×C8—102no—
319D3×C8—102no—
320C22×D5—31no—
321C22×D5—62no—
322C5×Q8—32no—
323C5×D4—32no—
324C5×D4—62no—
325C2×C4×C5—62no—
326C2×C4×C5—61no—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—22no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C2×Dic5—21no—
332C2×Dic5—31no—
333C2×Dic5—62no—
334D20—62no—
335D20C2×C4×D312yes—
336C4×D5—22no—
337C4×D5—32no—
338C4×D5—32no—
339C4×D5—62no—
340C4×D5—62no—
341Dic10—62no—
342Dic10C2×C4×D312yes—
343C5×C8—22no—
344C5×C8—32no—
345C5×C8C2×C4×D311yescharacteristic
346C5×C8C2×C4×D311yescharacteristic
347#168—32no—
348#168—62no—
349#168D3×D411yescharacteristic
350#168D3×D411yescharacteristic
351C2×#41—152no—
352#137—152no—
353#137—152no—
354AGL(1,ℤ/8)—152no—
355AGL(1,ℤ/8)—152no—
356#135—31no—
357#135—51no—
358#135—152no—
359#131—32no—
360#131—52no—
361#131—152no—
362#131—152no—
363#131—302no—
364#131—302no—
365C2×M16—151no—
366C2×M16—152no—
367C2×M16—302no—
368C22×C8—151no—
369C22×C8—302no—
370#117—151no—
371#108—152no—
372#108—151no—
373#108D3×D511yescharacteristic, complemented
374#104—32no—
375#104—52no—
376#104—152no—
377#104—152no—
378#97—31no—
379#97—151no—
380C4×C8—51no—
381C4×C8—151no—
382C2×C3×C5—21no—
383C2×C3×C5C2×C4×D411yescharacteristic
384D15—22no—
385C3×D5—42no—
386C5×D3—42no—
387C22×D3—51no—
388C22×D3—102no—
389C3×Q8—52no—
390C3×D4—52no—
391C3×D4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—101no—
394C2×C3×C4C23×D511yescharacteristic
395#67—22no—
396#67—102no—
397#67—102no—
398C2×Dic3—21no—
399C2×Dic3—51no—
400C2×Dic3—102no—
401D12—102no—
402D12C2×C4×D512yes—
403C4×D3—22no—
404C4×D3—52no—
405C4×D3—52no—
406C4×D3—102no—
407C4×D3—102no—
408Dic6—102no—
409Dic6C2×C4×D512yes—
410C3×C8—22no—
411C3×C8—51no—
412C3×C8—51no—
413C3×C8C2×C4×D511yescharacteristic
414C3×C8C2×C4×D511yescharacteristic
415C3⋊C8—52no—
416C3⋊C8—102no—
417C3⋊C8D4×D512yes—
418C22×C5—62no—
419C22×C5D3×#4111yescharacteristic
420C2×D5—22no—
421C2×D5—32no—
422C2×D5—124no—
423C2×D5—121no—
424C4×C5—62no—
425C4×C5—121no—
426C4×C5C22×C4×D311yescharacteristic
427C4×C5C2×D3×D411yescharacteristic
428Dic5—22no—
429Dic5—32no—
430Dic5—41no—
431#41—32no—
432#41—52no—
433#41—152no—
434#41—152no—
435#41—302no—
436#41—302no—
437C2×Q8—152no—
438C2×D4—152no—
439C2×D4—302no—
440C22×C4—151no—
441C22×C4—302no—
442Q16—31no—
443Q16—51no—
444Q16—152no—
445SD16—32no—
446SD16—52no—
447SD16—152no—
448SD16—152no—
449D8—31no—
450D8—51no—
451D8—152no—
452M16—62no—
453M16—102no—
454M16—152no—
455M16—152no—
456M16—152no—
457M16—302no—
458M16—302no—
459M16—302no—
460M16C2×D3×D512yes—
461C2×C8—31no—
462C2×C8—51no—
463C2×C8—62no—
464C2×C8—102no—
465C2×C8—152no—
466C2×C8—152no—
467C2×C8—151no—
468C2×C8—302no—
469C2×C8—302no—
470C2×C8—302no—
471C2×C8C2×D3×D511yescharacteristic
472C4⋊C4—301no—
473C22⋊C4—301no—
474C42—31no—
475C42—51no—
476C3×C5#295511yescharacteristic, complemented, Hall
477C22×C3—102no—
478C22×C3D5×#4111yescharacteristic
479C2×D3—22no—
480C2×D3—52no—
481C2×D3—204no—
482C2×D3—201no—
483C3×C4—102no—
484C3×C4—201no—
485C3×C4C22×C4×D511yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—22no—
488Dic3—41no—
489Dic3—52no—
490C2×C5—21no—
491C2×C5—122no—
492C2×C5C4×D3×D411yescharacteristic
493D5—42no—
494D5—62no—
495C23—151no—
496C23—302no—
497Q8—32no—
498Q8—52no—
499Q8—302no—
500D4—32no—
501D4—52no—
502D4—62no—
503D4—102no—
504D4—302no—
505D4—302no—
506D4—302no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—102no—
510C2×C4—101no—
511C2×C4—151no—
512C2×C4—152no—
513C2×C4—152no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4C22×D3×D511yescharacteristic
518C8—22no—
519C8—32no—
520C8—51no—
521C8—51no—
522C8—152no—
523C8—302no—
524C8C4×D3×D511yescharacteristic
525C8C4×D3×D511yescharacteristic
526C2×C3—21no—
527C2×C3—202no—
528C2×C3C4×D4×D511yescharacteristic
529D3—42no—
530D3—102no—
531C5#7988811yescharacteristic, complemented, Sylow
532C22—62no—
533C22—102no—
534C22—152no—
535C22—601no—
536C22—604no—
537C22#9203411yescharacteristic
538C4—62no—
539C4—102no—
540C4—121no—
541C4—152no—
542C4—201no—
543C4C2×C4×D3×D511yescharacteristic
544C4D3×D4×D511yescharacteristic
545C3#1061162811yescharacteristic, complemented, Sylow
546C2—21no—
547C2—122no—
548C2—202no—
549C2—302no—
550C2#1175384011yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5C2×C4×D4
prime radical#11753979C2
cosocleC2×C3×C4×C5C24
hypercenter#108D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #11754017C2semidirect
3. #11750994C2semidirect
4. C5×#4894C2semidirect
5. C3×#65184C2semidirect
6. #11748237C2semidirect
7. #11748205C2semidirect
8. #11748203C2semidirect
9. #11748067C2semidirect
10. #11748062C2semidirect
11. #11748053C2semidirect
16. C5×#907C22semidirect
18. C3×#4053C22semidirect
23. #91286C22semidirect
24. #91283C22semidirect
25. #91280C4semidirect
26. #91278C4semidirect
29. #91258C4semidirect
30. #91257C4semidirect
33. C3×C5×#108C22semidirect
34. #91106C22semidirect
35. #91103C22semidirect
36. C5×#825C22semidirect
37. C5×#815C22semidirect
38. C3×#3957C22semidirect
39. C3×C8×Dic5C22semidirect
40. #90979C22semidirect
41. #90977C22semidirect
42. #90952C22semidirect
43. Dic3×#168C22semidirect
50. #65184D3semidirect
106. #4894D5semidirect
122. #4053C2×D3semidirect
132. C5×#108C2×D3semidirect
136. #3957C2×D3semidirect
140. C8×Dic5C2×D3semidirect
185. #907C2×D5semidirect
195. C3×#108C2×D5semidirect
199. #825C2×D5semidirect
202. #815C2×D5semidirect
373. #108D3×D5semidirect
476. C3×C5#2955semidirect
531. C5#79888semidirect
545. C3#10611628semidirect

Maximal subgroups

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

subgroupindex
#117540172
#117539792
#117509942
C5×#48942
C3×#651842
#117482372
#117482052
#117482032
#117480672
#117480622
#117480532
#106116283
#798885