Finite Group Databasebeta

← #14418082

Subgroups — #14418082

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#11753979C211yesmaximal, characteristic
2#11753952C212yesmaximal, complemented
3#11750809C211yesmaximal, characteristic, complemented
4C5×#4717C211yesmaximal, characteristic, complemented
5C3×#65006C211yesmaximal, characteristic, complemented
6#11748075C212yesmaximal, complemented
7#11748072C211yesmaximal, characteristic, complemented
8#11748070C211yesmaximal, characteristic, complemented
9#11748061C211yesmaximal, characteristic, complemented
10#11747113C212yesmaximal, complemented
11#11747106C212yesmaximal, complemented
12#10611628—31nomaximal, Hall
13#92016C2212yes—
14C2×#6705C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16#91761C2211yescharacteristic
17C5×#904C2211yescharacteristic
18C5×#901C2212yescomplemented
19C3×#4050C2211yescharacteristic
20C3×#4047C2212yescomplemented
21#91297C2212yes—
22#91292C2212yes—
23#91288C2212yescomplemented
24#91284C2212yescomplemented
25#91280C412yescomplemented
26#91278C412yescomplemented
27#91268—22no—
28#91265—22no—
29#91258C412yescomplemented
30#91257C412yescomplemented
31#91246—22no—
32D3×C8×D5—22no—
33C3×C5×#97C2211yescharacteristic, complemented
34#91099C2211yescharacteristic, complemented
35C8×Dic15C2211yescharacteristic, complemented
36C4×C3⋊#168C2211yescharacteristic, complemented
37C5×#819C2211yescharacteristic, complemented
38C5×#805C2212yescomplemented
39C3×#3951C2211yescharacteristic, complemented
40C3×#3937C2212yescomplemented
41#90992C2212yescomplemented
42#90978C2212yescomplemented
43#90976C2212yescomplemented
44#79897—51nomaximal, Hall
45#66102—31no—
46D5×#131—32no—
47C5×#444—31no—
48#65485—31no—
49#65434—32no—
50#65184—31no—
51#65182—31no—
52#65113—32no—
53#65110—32no—
54#65006D311yescharacteristic, complemented
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—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70#6714—21no—
71#6712—21no—
72C4×Dic15C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75#6705C2×C412yes—
76#6705C2×C412yes—
77C8×D15D412yes—
78C8×D15D412yes—
79C5×#208C2312yes—
80C5×Dic12C2×C411yescharacteristic
81C5×D24C2×C411yescharacteristic
82C5×#204C2×C412yes—
83C5×ΓL(1,𝔽25)—22no—
84C5×D3×C8—22no—
85C3×#681C2312yes—
86C3×Dic20C2×C411yescharacteristic
87C3×D40C2×C411yescharacteristic
88C3×#677C2×C412yes—
89C3×#676—22no—
90C3×C8×D5—22no—
91#6661C2×C412yes—
92#6656C2×C412yes—
93#6655C2×C412yes—
94#6652C2×C412yes—
95#6651—22no—
96#6650—22no—
97#6649—22no—
98#6648—22no—
99D3×#168—22no—
100D5×C3⋊C8—22no—
101#5768—51no—
102D3×#131—52no—
103C3×#444—51no—
104#5196—51no—
105#5145—52no—
106#4895—51no—
107#4893—51no—
108#4824—52no—
109#4821—52no—
110#4717D511yescharacteristic, complemented
111#4708—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—32no—
122#4053—62no—
123D5×M16—32no—
124D5×M16—62no—
125#4050C2×D311yescharacteristic
126#4047—62no—
127#4047C2×D312yescomplemented
128C2×#676—31no—
129C2×C8×D5—31no—
130C2×C8×D5—62no—
131#4018—31no—
132C5×#108—31no—
133C5×#104—32no—
134C5×#97C2×D311yescharacteristic, complemented
135#3969—32no—
136#3957—32no—
137#3954—32no—
138#3951C2×D311yescharacteristic, complemented
139#3947—31no—
140C8×Dic5—31no—
141#3937C2×D312yescomplemented
142C4×#168—31no—
143#2955—151noSylow
144C22×D15#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15#4111yescharacteristic
150C4×D15C22×C412yes—
151C4×D15C2×D412yes—
152C5×#67—22no—
153C5×D12C22×C412yes—
154C4×C5×D3—22no—
155C5×Dic6C22×C412yes—
156C3×C22⋊D5—22no—
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×C8C22×C411yescharacteristic
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C2×D412yes—
170C3⋊#168C22×C412yes—
171C3⋊#168C2×D411yescharacteristic
172C3⋊#168C2×D411yescharacteristic
173C3×#168—22no—
174C5×C3⋊C8—22no—
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—52no—
185#907—102no—
186D3×M16—52no—
187D3×M16—102no—
188#904C2×D511yescharacteristic
189#901—102no—
190#901C2×D512yescomplemented
191C2×ΓL(1,𝔽25)—51no—
192C2×D3×C8—51no—
193C2×D3×C8—102no—
194#872—51no—
195C3×#108—51no—
196C3×#104—52no—
197C3×#97C2×D511yescharacteristic, complemented
198#837—52no—
199#825—52no—
200#822—52no—
201#819C2×D511yescharacteristic, complemented
202#815—51no—
203C8×Dic3—51no—
204#805C2×D512yescomplemented
205C4×C3⋊C8—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—32no—
221C5×M16—62no—
222C2×C5×C8—62no—
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—62no—
234#681C22×D312yes—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168—62no—
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—51no—
255#444—152no—
256#443—152no—
257#443—151no—
258#443—151no—
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×C5—41no—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—41no—
272Dic15C4×D412yes—
273C3×Dic5—22no—
274C5×Dic3—22no—
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—52no—
290C3×M16—102no—
291C2×C3×C8—102no—
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—102no—
303#208C22×D512yes—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—102no—
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—21no—
326C2×C4×C5—62no—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—22no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C2×Dic5—31no—
332C2×Dic5—62no—
333C2×Dic5—61no—
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—62no—
344C5×C8C2×C4×D311yescharacteristic
345C5×C8C2×C4×D311yescharacteristic
346C5×C8D3×D412yes—
347#168—22no—
348#168—32no—
349#168—31no—
350#168—31no—
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—31no—
372#108—51no—
373#108—152no—
374#104—32no—
375#104—52no—
376#104—152no—
377#104—152no—
378#97—151no—
379#97D3×D511yescharacteristic, complemented
380C4×C8—151no—
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—21no—
393C2×C3×C4—102no—
394C2×C3×C4C23×D511yescharacteristic
395#67—22no—
396#67—102no—
397#67—102no—
398C2×Dic3—51no—
399C2×Dic3—102no—
400C2×Dic3—101no—
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—102no—
411C3×C8C2×C4×D511yescharacteristic
412C3×C8C2×C4×D511yescharacteristic
413C3×C8D4×D512yes—
414C3⋊C8—22no—
415C3⋊C8—52no—
416C3⋊C8—51no—
417C3⋊C8—51no—
418C22×C5—62no—
419C22×C5D3×#4111yescharacteristic
420C2×D5—22no—
421C2×D5—32no—
422C2×D5—124no—
423C2×D5—121no—
424C4×C5—41no—
425C4×C5—62no—
426C4×C5C22×C4×D311yescharacteristic
427C4×C5C2×D3×D411yescharacteristic
428Dic5—22no—
429Dic5—32no—
430Dic5—121no—
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—32no—
453M16—52no—
454M16—62no—
455M16—102no—
456M16—152no—
457M16—152no—
458M16—302no—
459M16—302no—
460M16—302no—
461C2×C8—62no—
462C2×C8—102no—
463C2×C8—151no—
464C2×C8—151no—
465C2×C8—152no—
466C2×C8—152no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8—302no—
470C2×C8C2×D3×D511yescharacteristic
471C2×C8C2×D3×D511yescharacteristic
472C4⋊C4—301no—
473C22⋊C4—301no—
474C42—151no—
475C42C2×D3×D511yescharacteristic
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—41no—
484C3×C4—102no—
485C3×C4C22×C4×D511yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—22no—
488Dic3—52no—
489Dic3—201no—
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—21no—
508C2×C4—62no—
509C2×C4—102no—
510C2×C4—151no—
511C2×C4—152no—
512C2×C4—152no—
513C2×C4—302no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—301no—
517C2×C4C22×D3×D511yescharacteristic
518C8—62no—
519C8—102no—
520C8—152no—
521C8—151no—
522C8—151no—
523C8C4×D3×D511yescharacteristic
524C8C4×D3×D511yescharacteristic
525C8#677712yes—
526C2×C3—21no—
527C2×C3—202no—
528C2×C3C4×D4×D511yescharacteristic
529D3—42no—
530D3—102no—
531C5#7989711yescharacteristic, complemented, Sylow
532C22—62no—
533C22—102no—
534C22—152no—
535C22—601no—
536C22—604no—
537C22#9201611yescharacteristic
538C4—41no—
539C4—62no—
540C4—102no—
541C4—152no—
542C4—601no—
543C4C2×C4×D3×D511yescharacteristic
544C4C2×#677711yescharacteristic
545C3#1061162811yescharacteristic, complemented, Sylow
546C2—21no—
547C2—122no—
548C2—202no—
549C2—302no—
550C2C4×#677711yescharacteristic
subgroupG/H
centerC4C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC2×C3×C5C2×C4×D4
prime radical#11753979C2
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11753952C2semidirect
3. #11750809C2semidirect
4. C5×#4717C2semidirect
5. C3×#65006C2semidirect
6. #11748075C2semidirect
7. #11748072C2semidirect
8. #11748070C2semidirect
9. #11748061C2semidirect
10. #11747113C2semidirect
11. #11747106C2semidirect
18. C5×#901C22semidirect
20. C3×#4047C22semidirect
23. #91288C22semidirect
24. #91284C22semidirect
25. #91280C4semidirect
26. #91278C4semidirect
29. #91258C4semidirect
30. #91257C4semidirect
33. C3×C5×#97C22semidirect
34. #91099C22semidirect
35. C8×Dic15C22semidirect
36. C4×C3⋊#168C22semidirect
37. C5×#819C22semidirect
38. C5×#805C22semidirect
39. C3×#3951C22semidirect
40. C3×#3937C22semidirect
41. #90992C22semidirect
42. #90978C22semidirect
43. #90976C22semidirect
54. #65006D3semidirect
110. #4717D5semidirect
127. #4047C2×D3semidirect
134. C5×#97C2×D3semidirect
138. #3951C2×D3semidirect
141. #3937C2×D3semidirect
190. #901C2×D5semidirect
197. C3×#97C2×D5semidirect
201. #819C2×D5semidirect
204. #805C2×D5semidirect
379. #97D3×D5semidirect
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
#117539792
#117539522
#117508092
C5×#47172
C3×#650062
#117480752
#117480722
#117480702
#117480612
#117471132
#117471062
#106116283
#798975