Finite Group Databasebeta

← #14418013

Subgroups — #14418013

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#11756527C211yesmaximal, characteristic
2D15×#131C212yesmaximal, complemented
3C3×C5×#444C211yesmaximal, characteristic, complemented
4#11751297C211yesmaximal, characteristic, complemented
5#11751246C212yesmaximal, complemented
6#11750996C211yesmaximal, characteristic, complemented
7#11750994C211yesmaximal, characteristic, complemented
8#11750925C212yesmaximal, complemented
9#11750922C212yesmaximal, complemented
10#11750818C211yesmaximal, characteristic, complemented
11#11750809C211yesmaximal, characteristic, complemented
12#10611628—31nomaximal, Hall
13#41×D15C2212yes—
14C3×C5×#135C2211yescharacteristic
15C3×C5×#131C2212yescomplemented
16#91839C2212yes—
17#91837C2212yescomplemented
18#91807C412yescomplemented
19#91804C412yescomplemented
20#91803C412yescomplemented
21#91800C412yescomplemented
22#91796—22no—
23#91796C2212yescomplemented
24M16×D15—22no—
25M16×D15C2212yes—
26#91793C2211yescharacteristic
27#91790—22no—
28#91790C2212yescomplemented
29C2×#6705C2211yescharacteristic
30C2×C8×D15—22no—
31C2×C8×D15C2211yescharacteristic
32#91761C2211yescharacteristic
33C3×C5×#108C2211yescharacteristic, complemented
34C3×C5×#104C2212yescomplemented
35C3×C5×#97C2211yescharacteristic, complemented
36#91121C2212yescomplemented
37#91109C2212yescomplemented
38#91106C2212yescomplemented
39#91103C2211yescharacteristic, complemented
40#91099C2211yescharacteristic, complemented
41C8×Dic15C2211yescharacteristic, complemented
42#91089C2212yescomplemented
43C4×C3⋊#168C2211yescharacteristic, complemented
44#79897—51nomaximal, Hall
45#66102—31no—
46D5×#131—32no—
47C5×#444D311yescharacteristic, complemented
48#65485—31no—
49#65434—32no—
50#65184—31no—
51#65182—31no—
52#65113—32no—
53#65110—32no—
54#65006—31no—
55#64997—31no—
56C3×C5×#41C2312yes—
57#6821C2×C412yes—
58Q8×D15C2×C412yes—
59#6819—22no—
60#6819C2×C412yes—
61D4×D15—22no—
62D4×D15C2×C412yes—
63#6817—22no—
64#6817C2312yes—
65C2×C4×D15—22no—
66C2×C4×D15C2311yescharacteristic
67C3×C5×Q16C2×C411yescharacteristic
68C3×C5×SD16C2×C412yes—
69C3×C5×D8C2×C411yescharacteristic
70C3×C5×M16—22no—
71C3×C5×M16C2312yes—
72C2×C3×C5×C8—22no—
73C2×C3×C5×C8C2311yescharacteristic
74C2×C3×C5×C8C2311yescharacteristic
75C3×C42×C5C2311yescharacteristic
76#6718C2×C412yes—
77#6717C2×C412yes—
78#6716C2×C412yes—
79#6715C2×C412yes—
80#6714—21no—
81#6712—21no—
82C4×Dic15C2311yescharacteristic
83#6710—22no—
84#6710C2312yes—
85C2×C3⋊#168—22no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88Dic60C2×C411yescharacteristic
89D120C2×C411yescharacteristic
90#6706C2×C412yes—
91#6705—22no—
92#6705—22no—
93#6705—22no—
94#6705C2×C412yes—
95#6705C2×C412yes—
96C8×D15—22no—
97C8×D15—22no—
98C8×D15—22no—
99C8×D15D412yes—
100C8×D15D412yes—
101#5768—51no—
102D3×#131—52no—
103C3×#444D511yescharacteristic, complemented
104#5196—51no—
105#5145—52no—
106#4895—51no—
107#4893—51no—
108#4824—52no—
109#4821—52no—
110#4717—51no—
111#4708—51no—
112D5×#41—32no—
113C5×#135C2×D311yescharacteristic
114C5×#131C2×D312yescomplemented
115#4096—32no—
116#4094—32no—
117#4064—32no—
118#4061—32no—
119#4060—32no—
120#4057—32no—
121#4053—32no—
122#4053—62no—
123D5×M16—32no—
124D5×M16—62no—
125#4050—31no—
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×#104C2×D312yescomplemented
134C5×#97C2×D311yescharacteristic, complemented
135#3969—32no—
136#3957—32no—
137#3954—32no—
138#3951—31no—
139#3947—31no—
140C8×Dic5—31no—
141#3937—32no—
142C4×#168—31no—
143#2955—151noSylow
144C22×D15—22no—
145C22×D15#4111yescharacteristic
146C3×C5×Q8C22×C412yes—
147C3×C5×D4—22no—
148C3×C5×D4C22×C412yes—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5C2411yescharacteristic
152#1220—22no—
153#1220—22no—
154#1220—22no—
155C2×Dic15—22no—
156C2×Dic15—21no—
157C2×Dic15#4111yescharacteristic
158D60—22no—
159D60C22×C412yes—
160C4×D15—22no—
161C4×D15—22no—
162C4×D15—22no—
163C4×D15C22×C412yes—
164C4×D15C2×D412yes—
165Dic30—22no—
166Dic30C22×C412yes—
167C3×C5×C8—22no—
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C22×C411yescharacteristic
170C3×C5×C8C2×D412yes—
171C3⋊#168—22no—
172C3⋊#168C22×C412yes—
173C3⋊#168C2×D411yescharacteristic
174C3⋊#168C2×D411yescharacteristic
175D3×#41—52no—
176C3×#135C2×D511yescharacteristic
177C3×#131C2×D512yescomplemented
178#950—52no—
179#948—52no—
180#918—52no—
181#915—52no—
182#914—52no—
183#911—52no—
184#907—52no—
185#907—102no—
186D3×M16—52no—
187D3×M16—102no—
188#904—51no—
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×#104C2×D512yescomplemented
197C3×#97C2×D511yescharacteristic, complemented
198#837—52no—
199#825—52no—
200#822—52no—
201#819—51no—
202#815—51no—
203C8×Dic3—51no—
204#805—52no—
205C4×C3⋊C8—51no—
206C5×#41C22×D312yes—
207#713—32no—
208Q8×D5—32no—
209#711—32no—
210#711—62no—
211D4×D5—32no—
212D4×D5—62no—
213#709—32no—
214#709—62no—
215C2×C4×D5—31no—
216C2×C4×D5—62no—
217C5×Q16C4×D311yescharacteristic
218C5×SD16C4×D312yes—
219C5×D8C4×D311yescharacteristic
220C5×M16—22no—
221C5×M16C22×D312yes—
222C2×C5×C8—22no—
223C2×C5×C8C22×D311yescharacteristic
224C2×C5×C8C22×D311yescharacteristic
225C42×C5C22×D311yescharacteristic
226#689—32no—
227#688—32no—
228#687—32no—
229#686—32no—
230#685—61no—
231#683—61no—
232C4×Dic5—31no—
233#681—32no—
234#681—62no—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168—62no—
238Dic20—31no—
239D40—31no—
240#677—32no—
241#676—32no—
242#676—32no—
243#676—62no—
244#676—62no—
245#676—62no—
246C8×D5—32no—
247C8×D5—32no—
248C8×D5—62no—
249C8×D5—62no—
250C8×D5—62no—
251#575—151no—
252C2×#131—152no—
253#444—152no—
254#444—151no—
255#444D1511yescharacteristic, complemented
256#443—151no—
257#443—151no—
258#443—152no—
259#430—151no—
260#421—152no—
261#405—151no—
262C22×C3×C5—22no—
263C22×C3×C5C2×#4111yescharacteristic
264C2×D15—22no—
265C2×D15—41no—
266C2×D15—44no—
267C2×D15C4×D412yes—
268C3×C4×C5—22no—
269C3×C4×C5—41no—
270C3×C4×C5C23×C411yescharacteristic
271C3×C4×C5C22×D411yescharacteristic
272Dic15—22no—
273Dic15—41no—
274Dic15C4×D412yes—
275C3×#41C22×D512yes—
276#239—52no—
277D3×Q8—52no—
278#237—52no—
279#237—102no—
280D3×D4—52no—
281D3×D4—102no—
282#235—52no—
283#235—102no—
284C2×C4×D3—51no—
285C2×C4×D3—102no—
286C3×Q16C4×D511yescharacteristic
287C3×SD16C4×D512yes—
288C3×D8C4×D511yescharacteristic
289C3×M16—22no—
290C3×M16C22×D512yes—
291C2×C3×C8—22no—
292C2×C3×C8C22×D511yescharacteristic
293C2×C3×C8C22×D511yescharacteristic
294C3×C42C22×D511yescharacteristic
295#216—52no—
296#215—52no—
297#214—52no—
298#213—52no—
299(C2×D3)⋊C4—101no—
300Dic3⋊C4—101no—
301C4×Dic3—51no—
302#208—52no—
303#208—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—102no—
307Dic12—51no—
308D24—51no—
309#204—52no—
310ΓL(1,𝔽25)—52no—
311ΓL(1,𝔽25)—52no—
312ΓL(1,𝔽25)—102no—
313ΓL(1,𝔽25)—102no—
314ΓL(1,𝔽25)—102no—
315D3×C8—52no—
316D3×C8—52no—
317D3×C8—102no—
318D3×C8—102no—
319D3×C8—102no—
320C22×D5—31no—
321C22×D5—62no—
322C5×Q8C2×C4×D312yes—
323C5×D4—22no—
324C5×D4C2×C4×D312yes—
325C2×C4×C5—22no—
326C2×C4×C5—21no—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—62no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C2×Dic5—31no—
332C2×Dic5—62no—
333C2×Dic5—61no—
334D20—32no—
335D20—62no—
336C4×D5—32no—
337C4×D5—32no—
338C4×D5—62no—
339C4×D5—62no—
340C4×D5—62no—
341Dic10—32no—
342Dic10—62no—
343C5×C8—22no—
344C5×C8C2×C4×D311yescharacteristic
345C5×C8C2×C4×D311yescharacteristic
346C5×C8D3×D412yes—
347#168—32no—
348#168—31no—
349#168—31no—
350#168—62no—
351C2×#41—152no—
352#137—152no—
353#137—152no—
354AGL(1,ℤ/8)—152no—
355AGL(1,ℤ/8)—152no—
356#135—152no—
357#135—151no—
358#135C2×D1511yescharacteristic
359#131—152no—
360#131—152no—
361#131—152no—
362#131—302no—
363#131—302no—
364#131C2×D1512yescomplemented
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#108C2×D1511yescharacteristic, complemented
374#104—152no—
375#104—152no—
376#104—152no—
377#104C2×D1512yescomplemented
378#97—151no—
379#97C2×D1511yescharacteristic, complemented
380C4×C8—151no—
381C4×C8—151no—
382C2×C3×C5—21no—
383C2×C3×C5—42no—
384C2×C3×C5C2×C4×D411yescharacteristic
385D15—22no—
386D15—42no—
387C22×D3—51no—
388C22×D3—102no—
389C3×Q8C2×C4×D512yes—
390C3×D4—22no—
391C3×D4C2×C4×D512yes—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4C23×D511yescharacteristic
395#67—102no—
396#67—102no—
397#67—102no—
398C2×Dic3—51no—
399C2×Dic3—102no—
400C2×Dic3—101no—
401D12—52no—
402D12—102no—
403C4×D3—52no—
404C4×D3—52no—
405C4×D3—102no—
406C4×D3—102no—
407C4×D3—102no—
408Dic6—52no—
409Dic6—102no—
410C3×C8—22no—
411C3×C8C2×C4×D511yescharacteristic
412C3×C8C2×C4×D511yescharacteristic
413C3×C8D4×D512yes—
414C3⋊C8—52no—
415C3⋊C8—51no—
416C3⋊C8—51no—
417C3⋊C8—102no—
418C22×C5—22no—
419C22×C5D3×#4111yescharacteristic
420C2×D5—32no—
421C2×D5—62no—
422C2×D5—121no—
423C2×D5—124no—
424C4×C5—22no—
425C4×C5—41no—
426C4×C5C22×C4×D311yescharacteristic
427C4×C5C2×D3×D411yescharacteristic
428Dic5—32no—
429Dic5—62no—
430Dic5—121no—
431#41—152no—
432#41—152no—
433#41—152no—
434#41—302no—
435#41—302no—
436#41C22×D1512yes—
437C2×Q8—152no—
438C2×D4—152no—
439C2×D4—302no—
440C22×C4—151no—
441C22×C4—302no—
442Q16—152no—
443Q16—151no—
444Q16C4×D1511yescharacteristic
445SD16—152no—
446SD16—152no—
447SD16—152no—
448SD16C4×D1512yes—
449D8—152no—
450D8—151no—
451D8C4×D1511yescharacteristic
452M16—22no—
453M16—152no—
454M16—152no—
455M16—152no—
456M16—302no—
457M16—302no—
458M16—302no—
459M16—302no—
460M16C22×D1512yes—
461C2×C8—22no—
462C2×C8—151no—
463C2×C8—151no—
464C2×C8—152no—
465C2×C8—152no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8—302no—
470C2×C8C22×D1511yescharacteristic
471C2×C8C22×D1511yescharacteristic
472C4⋊C4—301no—
473C22⋊C4—301no—
474C42—151no—
475C42C22×D1511yescharacteristic
476C3×C5#295511yescharacteristic, complemented, Hall
477C22×C3—22no—
478C22×C3D5×#4111yescharacteristic
479C2×D3—52no—
480C2×D3—102no—
481C2×D3—201no—
482C2×D3—204no—
483C3×C4—22no—
484C3×C4—41no—
485C3×C4C22×C4×D511yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—52no—
488Dic3—102no—
489Dic3—201no—
490C2×C5—21no—
491C2×C5—42no—
492C2×C5C4×D3×D411yescharacteristic
493D5—62no—
494D5—122no—
495C23—151no—
496C23—302no—
497Q8—152no—
498Q8—302no—
499Q8C2×C4×D1512yes—
500D4—22no—
501D4—152no—
502D4—302no—
503D4—302no—
504D4—302no—
505D4—302no—
506D4C2×C4×D1512yes—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—151no—
510C2×C4—152no—
511C2×C4—152no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—301no—
517C2×C4C23×D1511yescharacteristic
518C8—22no—
519C8—152no—
520C8—151no—
521C8—151no—
522C8—302no—
523C8C2×C4×D1511yescharacteristic
524C8C2×C4×D1511yescharacteristic
525C8D4×D1512yes—
526C2×C3—21no—
527C2×C3—42no—
528C2×C3C4×D4×D511yescharacteristic
529D3—102no—
530D3—202no—
531C5#7989711yescharacteristic, complemented, Sylow
532C22—22no—
533C22—152no—
534C22—302no—
535C22—601no—
536C22—604no—
537C22#41×D1511yescharacteristic
538C4—22no—
539C4—41no—
540C4—152no—
541C4—302no—
542C4—601no—
543C4C22×C4×D1511yescharacteristic
544C4C2×D4×D1511yescharacteristic
545C3#1061162811yescharacteristic, complemented, Sylow
546C2—21no—
547C2—42no—
548C2—302no—
549C2—602no—
550C2C4×D4×D1511yescharacteristic
subgroupG/H
centerC4C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#444C2
socleC2×C3×C5C2×C4×D4
prime radical#11756527C2
cosocleC2×C3×C4×C5C24
hypercenter#444D15
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #444

Complements

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

NH ≅ G/Ntype
2. D15×#131C2semidirect
3. C3×C5×#444C2semidirect
4. #11751297C2semidirect
5. #11751246C2semidirect
6. #11750996C2semidirect
7. #11750994C2semidirect
8. #11750925C2semidirect
9. #11750922C2semidirect
10. #11750818C2semidirect
11. #11750809C2semidirect
15. C3×C5×#131C22semidirect
17. #91837C22semidirect
18. #91807C4semidirect
19. #91804C4semidirect
20. #91803C4semidirect
21. #91800C4semidirect
23. #91796C22semidirect
28. #91790C22semidirect
33. C3×C5×#108C22semidirect
34. C3×C5×#104C22semidirect
35. C3×C5×#97C22semidirect
36. #91121C22semidirect
37. #91109C22semidirect
38. #91106C22semidirect
39. #91103C22semidirect
40. #91099C22semidirect
41. C8×Dic15C22semidirect
42. #91089C22semidirect
43. C4×C3⋊#168C22semidirect
47. C5×#444D3semidirect
103. C3×#444D5semidirect
114. C5×#131C2×D3semidirect
132. C5×#108C2×D3semidirect
133. C5×#104C2×D3semidirect
134. C5×#97C2×D3semidirect
177. C3×#131C2×D5semidirect
195. C3×#108C2×D5semidirect
196. C3×#104C2×D5semidirect
197. C3×#97C2×D5semidirect
255. #444D15semidirect
364. #131C2×D15semidirect
373. #108C2×D15semidirect
377. #104C2×D15semidirect
379. #97C2×D15semidirect
476. C3×C5#2955semidirect
531. C5#79897semidirect
545. C3#10611628semidirect

Maximal subgroups

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

subgroupindex
#117565272
D15×#1312
C3×C5×#4442
#117512972
#117512462
#117509962
#117509942
#117509252
#117509222
#117508182
#117508092
#106116283
#798975