Finite Group Databasebeta

← #14418075

Subgroups — #14418075

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
1D3×#4053C212yesmaximal, complemented
2#11753969C211yesmaximal, characteristic
3#11750996C211yesmaximal, characteristic, complemented
4C5×#4893C211yesmaximal, characteristic, complemented
5C3×#65183C211yesmaximal, characteristic, complemented
6#11748233C212yesmaximal, complemented
7#11748206C212yesmaximal, complemented
8#11748174C212yesmaximal, complemented
9#11748070C211yesmaximal, characteristic, complemented
10#11748065C211yesmaximal, characteristic, complemented
11#11748055C211yesmaximal, characteristic, complemented
12#10610988—31nomaximal, Hall
13D3×#709C2212yes—
14#91796C2212yescomplemented
15#91793C2211yescharacteristic
16C5×D3×M16C2212yes—
17C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
18C3×#4053C2212yescomplemented
19C3×#4050C2211yescharacteristic
20#91371C2211yescharacteristic
21#91311C2212yes—
22#91290C2212yescomplemented
23C2×D3×#168C2211yescharacteristic
24#91284C2212yescomplemented
25#91274C412yescomplemented
26#91268—22no—
27#91266—22no—
28#91263C412yescomplemented
29#91254C412yescomplemented
30#91253C412yescomplemented
31D3×#676—22no—
32D3×C8×D5—22no—
33C3×C5×#108C2211yescharacteristic, complemented
34#91109C2212yescomplemented
35C8×Dic15C2211yescharacteristic, complemented
36C5×#822C2212yescomplemented
37C5×#819C2211yescharacteristic, complemented
38C3×#3957C2212yescomplemented
39C3×#3947C2211yescharacteristic, complemented
40#90981C2212yescomplemented
41#90976C2212yescomplemented
42#90954C2211yescharacteristic, complemented
43Dic5×C3⋊C8C2211yescharacteristic, complemented
44#79897—51nomaximal, Hall
45#66082—31no—
46C2×#4053—32no—
47C5×#430—31no—
48#65428—32no—
49#65411—31no—
50#65184—31no—
51#65184—31no—
52#65184—32no—
53#65183—32no—
54#65183—31no—
55#65183D311yescharacteristic, complemented
56#6817C2312yes—
57C2×C4×C5×D3C2311yescharacteristic
58C3×#709C2312yes—
59D3×C22⋊D5—22no—
60#6779—22no—
61D3×D20C2×C412yes—
62C4×D3×D5—22no—
63#6771—22no—
64#6769C2×C412yes—
65D3×Dic10C2×C412yes—
66#6765C2×C412yes—
67C3×C5×M16C2312yes—
68C2×C3×C5×C8C2311yescharacteristic
69C4×Dic15C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71Dic60C2×C411yescharacteristic
72D120C2×C411yescharacteristic
73#6706C2×C412yes—
74#6705—22no—
75C8×D15—22no—
76C5×#208C2312yes—
77C2×C5×C3⋊C8C2311yescharacteristic
78C5×ΓL(1,𝔽25)—22no—
79C5×ΓL(1,𝔽25)C2×C412yes—
80C5×ΓL(1,𝔽25)C2×C412yes—
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—
89Dic3⋊Dic5—21no—
90(C2×D3)⋊Dic5—21no—
91#6662C2×C412yes—
92#6658C2×C412yes—
93#6657C2×C412yes—
94#6653C2×C412yes—
95#6651—22no—
96#6649—22no—
97#6648—22no—
98D3×#168D412yes—
99D3×#168D412yes—
100D5×C3⋊C8—22no—
101#5768—51no—
102D3×#131—52no—
103C3×#444—51no—
104#5196—51no—
105#5145—52no—
106#4895—51no—
107#4893D511yescharacteristic, complemented
108#4824—52no—
109#4821—52no—
110#4717—51no—
111#4708—51no—
112C2×#709—32no—
113C2×C5×M16—31no—
114C2×C5×M16—32no—
115#4072—31no—
116C22×#168—31no—
117#4055—32no—
118#4055—32no—
119#4054—32no—
120#4054—32no—
121#4053—32no—
122#4053—32no—
123#4053—32no—
124#4053—62no—
125#4053—62no—
126#4053C2×D312yescomplemented
127#4050—32no—
128#4050—31no—
129#4050C2×D311yescharacteristic
130C2×#676—62no—
131C2×C8×D5—62no—
132C5×#108—32no—
133C5×#108—31no—
134C5×#108C2×D311yescharacteristic, complemented
135#3957—32no—
136#3957—32no—
137#3957—32no—
138#3957C2×D312yescomplemented
139#3947—31no—
140#3947C2×D311yescharacteristic, complemented
141C8×Dic5—31no—
142C8×Dic5—31no—
143#2955—151noSylow
144C22×C5×D3#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—22no—
148C2×Dic15—21no—
149D60C22×C412yes—
150C4×D15—22no—
151Dic30C22×C412yes—
152C2×C5×Dic3#4111yescharacteristic
153C4×C5×D3C22×C412yes—
154C4×C5×D3C2×D412yes—
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⋊#168C2×D411yescharacteristic
171C3⋊#168C2×D411yescharacteristic
172C3×#168C2×D412yes—
173C5×C3⋊C8—22no—
174C5×C3⋊C8C22×C412yes—
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—102no—
187D3×M16C2×D512yes—
188#904—51no—
189#901—52no—
190#901—102no—
191C2×ΓL(1,𝔽25)C2×D511yescharacteristic
192C2×D3×C8—51no—
193C2×D3×C8—102no—
194#872—51no—
195C3×#108C2×D511yescharacteristic, complemented
196C3×#104—52no—
197C3×#97—51no—
198#837—52no—
199#825—52no—
200#822C2×D512yescomplemented
201#819C2×D511yescharacteristic, complemented
202#815—51no—
203C8×Dic3—51no—
204#805—52no—
205C4×C3⋊C8—51no—
206C22×C4×C5—31no—
207C2×C22⋊D5—62no—
208#709—32no—
209#709—32no—
210#709—32no—
211#709—62no—
212#709—62no—
213#709C22×D312yes—
214C2×D20—32no—
215C2×C4×D5—62no—
216C2×Dic10—32no—
217C5×M16—32no—
218C5×M16—32no—
219C5×M16—32no—
220C5×M16—62no—
221C5×M16C22×D312yes—
222C2×C5×C8—31no—
223C2×C5×C8—62no—
224C2×C5×C8C22×D311yescharacteristic
225C22⋊Dic5—61no—
226C4⋊Dic5—61no—
227C4×Dic5—31no—
228C4×Dic5C22×D311yescharacteristic
229C2×#168—31no—
230C2×#168—32no—
231C2×#168—32no—
232C2×#168C22×D311yescharacteristic
233Dic20—32no—
234Dic20—31no—
235Dic20C4×D311yescharacteristic
236D40—32no—
237D40—31no—
238D40C4×D311yescharacteristic
239#677—32no—
240#677—32no—
241#677—32no—
242#677C4×D312yes—
243#676—22no—
244#676—62no—
245#676—62no—
246#676—62no—
247C8×D5—22no—
248C8×D5—62no—
249C8×D5—62no—
250C8×D5—62no—
251#575—151no—
252C2×#131—152no—
253#444—51no—
254#444—151no—
255#444—152no—
256#443—152no—
257#443—151no—
258#443—151no—
259#430—31no—
260#421—152no—
261#405—151no—
262C22×C3×C5C2×#4111yescharacteristic
263C2×D15—22no—
264C2×C5×D3—41no—
265C2×C5×D3C4×D412yes—
266C2×C3×D5—22no—
267D3×D5—44no—
268C3×C4×C5C23×C411yescharacteristic
269C3×C4×C5C22×D411yescharacteristic
270Dic15—22no—
271Dic15—41no—
272C3×Dic5—22no—
273C3×Dic5—41no—
274C5×Dic3C4×D412yes—
275C3×#41—52no—
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—102no—
285C2×C4×D3C22×D511yescharacteristic
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×Dic3—51no—
302#208—102no—
303#208C22×D512yes—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—51no—
308D24—51no—
309#204—52no—
310ΓL(1,𝔽25)—22no—
311ΓL(1,𝔽25)—102no—
312ΓL(1,𝔽25)—102no—
313ΓL(1,𝔽25)C4×D512yes—
314ΓL(1,𝔽25)C4×D512yes—
315D3×C8—22no—
316D3×C8—52no—
317D3×C8—52no—
318D3×C8—102no—
319D3×C8—102no—
320C23×C5—31no—
321C22×D5—62no—
322C2×C4×C5—31no—
323C2×C4×C5—32no—
324C2×C4×C5—32no—
325C2×C4×C5C23×D311yescharacteristic
326C22⋊D5—22no—
327C22⋊D5—62no—
328C22⋊D5—62no—
329C22⋊D5—62no—
330C2×Dic5—21no—
331C2×Dic5—62no—
332C2×Dic5—61no—
333D20—32no—
334D20—62no—
335D20C2×C4×D312yes—
336C4×D5—22no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5—62no—
340Dic10—32no—
341Dic10—62no—
342Dic10C2×C4×D312yes—
343C5×C8—22no—
344C5×C8—32no—
345C5×C8—62no—
346C5×C8C2×C4×D311yescharacteristic
347C5×C8C2×C4×D311yescharacteristic
348#168—31no—
349#168—31no—
350#168D3×D412yes—
351C2×#41—152no—
352#137—152no—
353#137—152no—
354AGL(1,ℤ/8)—152no—
355AGL(1,ℤ/8)—152no—
356#135—51no—
357#135—152no—
358#135—151no—
359#131—52no—
360#131—152no—
361#131—152no—
362#131—152no—
363#131—302no—
364#131—302no—
365C2×M16—31no—
366C2×M16—32no—
367C2×M16—302no—
368C22×C8—151no—
369C22×C8—302no—
370#117—151no—
371#108—32no—
372#108—31no—
373#108D3×D511yescharacteristic, complemented
374#104—52no—
375#104—152no—
376#104—152no—
377#104—152no—
378#97—51no—
379#97—151no—
380C4×C8—151no—
381C4×C8—151no—
382C2×C3×C5—21no—
383C2×C3×C5C2×C4×D411yescharacteristic
384D15—42no—
385C3×D5—42no—
386C5×D3—22no—
387C22×D3—102no—
388C22×D3#71311yescharacteristic
389C3×Q8—52no—
390C3×D4—52no—
391C3×D4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—101no—
394C2×C3×C4C23×D511yescharacteristic
395#67—102no—
396#67—102no—
397#67—102no—
398C2×Dic3—102no—
399C2×Dic3—101no—
400C2×Dic3#71311yescharacteristic
401D12—52no—
402D12—102no—
403C4×D3—102no—
404C4×D3—102no—
405C4×D3—102no—
406C4×D3C2×C4×D512yes—
407C4×D3D4×D512yes—
408Dic6—52no—
409Dic6—102no—
410C3×C8—22no—
411C3×C8—52no—
412C3×C8C2×C4×D511yescharacteristic
413C3×C8C2×C4×D511yescharacteristic
414C3⋊C8—22no—
415C3⋊C8—51no—
416C3⋊C8—51no—
417C3⋊C8C2×C4×D512yes—
418C22×C5—32no—
419C22×C5—121no—
420C22×C5D3×#4111yescharacteristic
421C2×D5—22no—
422C2×D5—62no—
423C2×D5—124no—
424C4×C5—32no—
425C4×C5C22×C4×D311yescharacteristic
426C4×C5C2×D3×D411yescharacteristic
427Dic5—22no—
428Dic5—41no—
429Dic5—62no—
430Dic5—121no—
431#41—52no—
432#41—152no—
433#41—152no—
434#41—152no—
435#41—302no—
436#41—302no—
437C2×Q8—152no—
438C2×D4—152no—
439C2×D4—302no—
440C22×C4—31no—
441C22×C4—302no—
442Q16—51no—
443Q16—152no—
444Q16—151no—
445SD16—52no—
446SD16—152no—
447SD16—152no—
448SD16—152no—
449D8—51no—
450D8—152no—
451D8—151no—
452M16—32no—
453M16—32no—
454M16—32no—
455M16—62no—
456M16—102no—
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—51no—
475C42—151no—
476C3×C5#295511yescharacteristic, complemented, Hall
477C22×C3—102no—
478C22×C3C2×#71311yescharacteristic
479C2×D3—41no—
480C2×D3—102no—
481C2×D3—204no—
482C2×D3#403912yes—
483C3×C4—102no—
484C3×C4—201no—
485C3×C4C22×C4×D511yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—102no—
488Dic3—201no—
489Dic3#403912yes—
490C2×C5—21no—
491C2×C5—62no—
492C2×C5C4×D3×D411yescharacteristic
493D5—42no—
494D5—122no—
495C23—31no—
496C23—302no—
497Q8—52no—
498Q8—152no—
499Q8—302no—
500D4—52no—
501D4—102no—
502D4—152no—
503D4—302no—
504D4—302no—
505D4—302no—
506D4—302no—
507C2×C4—31no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—102no—
511C2×C4—101no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—301no—
517C2×C4C22×D3×D511yescharacteristic
518C8—22no—
519C8—32no—
520C8—52no—
521C8—62no—
522C8—151no—
523C8—151no—
524C8C4×D3×D511yescharacteristic
525C8C4×D3×D511yescharacteristic
526C2×C3—21no—
527C2×C3—202no—
528C2×C3C2×#403911yescharacteristic
529D3—22no—
530D3—202no—
531C5#7989711yescharacteristic, complemented, Sylow
532C22—32no—
533C22—102no—
534C22—121no—
535C22—302no—
536C22—604no—
537C22D3×#71311yescharacteristic
538C4—32no—
539C4—102no—
540C4—201no—
541C4—302no—
542C4—601no—
543C4C2×C4×D3×D511yescharacteristic
544C4D3×D4×D511yescharacteristic
545C3#1061098811yescharacteristic, complemented, Sylow
546C2—21no—
547C2—62no—
548C2—202no—
549C2—602no—
550C2D3×#403911yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5C2×C4×D4
prime radical#11753969C2
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. D3×#4053C2semidirect
3. #11750996C2semidirect
4. C5×#4893C2semidirect
5. C3×#65183C2semidirect
6. #11748233C2semidirect
7. #11748206C2semidirect
8. #11748174C2semidirect
9. #11748070C2semidirect
10. #11748065C2semidirect
11. #11748055C2semidirect
14. #91796C22semidirect
18. C3×#4053C22semidirect
22. #91290C22semidirect
24. #91284C22semidirect
25. #91274C4semidirect
28. #91263C4semidirect
29. #91254C4semidirect
30. #91253C4semidirect
33. C3×C5×#108C22semidirect
34. #91109C22semidirect
35. C8×Dic15C22semidirect
36. C5×#822C22semidirect
37. C5×#819C22semidirect
38. C3×#3957C22semidirect
39. C3×#3947C22semidirect
40. #90981C22semidirect
41. #90976C22semidirect
42. #90954C22semidirect
43. Dic5×C3⋊C8C22semidirect
55. #65183D3semidirect
107. #4893D5semidirect
126. #4053C2×D3semidirect
134. C5×#108C2×D3semidirect
138. #3957C2×D3semidirect
140. #3947C2×D3semidirect
195. C3×#108C2×D5semidirect
200. #822C2×D5semidirect
201. #819C2×D5semidirect
373. #108D3×D5semidirect
476. C3×C5#2955semidirect
531. C5#79897semidirect
545. C3#10610988semidirect

Maximal subgroups

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

subgroupindex
D3×#40532
#117539692
#117509962
C5×#48932
C3×#651832
#117482332
#117482062
#117481742
#117480702
#117480652
#117480552
#106109883
#798975