Finite Group Databasebeta

← #14417289

Subgroups — #14417289

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic
2#11754506C211yesmaximal, characteristic
3#11754213C211yesmaximal, characteristic, complemented
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65411C211yesmaximal, characteristic, complemented
6C2×#90975C211yesmaximal, characteristic, complemented
7#11748393C211yesmaximal, characteristic
8#11747854C212yesmaximal, complemented
9#11747851C212yesmaximal, complemented
10#11747778C212yesmaximal, complemented
11#11747760C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91798C418yescomplemented
17C2×Dic60C2212yes—
18C2×#6706C2212yes—
19C5×#926C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C3×#4072C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23#91556—22no—
24#91532—22no—
25#91437—21no—
26#91418C2212yes—
27#91347—21no—
28#91340—21no—
29#91340—21no—
30#91333C2212yes—
31#91333C2212yes—
32#91333C2212yes—
33C5×#818C2212yes—
34C5×#817C2212yes—
35C3×#3947C2212yes—
36C3×C8×Dic5C2212yes—
37#90975C2211yescharacteristic
38#90975C2212yes—
39#90975C2211yescharacteristic
40#90975C2212yes—
41#90969C2211yescharacteristic
42#90969C2211yescharacteristic
43#78571—51nomaximal, Hall
44C2×#4055—31no—
45#65850—31no—
46#65838—31no—
47C5×#428—31no—
48#65411D311yescharacteristic, complemented
49#65291—31no—
50C2×#3942—31no—
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57C22×Dic15—21no—
58#6817—22no—
59#6817C2×C414yes—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30—21no—
63C2×Dic30—22no—
64C2×Dic30C2×C414yescomplemented
65C2×Dic30C2312yes—
66C2×Dic30C2311yescharacteristic
67C22×C5×Dic3—21no—
68C2×#1200—22no—
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71Dic60C2×C418yescomplemented
72#6706C2×C418yescomplemented
73C5×#217—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
79C3×C22⋊Dic5D412yes—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5D411yescharacteristic
82C3×C4×Dic5C2312yes—
83C2×C3×#168—22no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86#6669—22no—
87#6669—22no—
88#6669—22no—
89#6667—22no—
90Dic3×Dic5—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C2×#909—51no—
94#5523—51no—
95#5516—51no—
96C3×#405—51no—
97#5121D511yescharacteristic, complemented
98#5113—51no—
99C2×#816—51no—
100#4716—52no—
101#4710—52no—
102C4×Dic12—52no—
103C4×#204—52no—
104C2×#709—31no—
105C22×Dic10—31no—
106C2×C5×M16C2×D311yescharacteristic
107C5×#117—31no—
108C2×C5×C4⋊C4—31no—
109C4×C22⋊D5—62no—
110#4072C2×D311yescharacteristic
111C22×#168C2×D311yescharacteristic
112#4055—38no—
113C2×Dic20—32no—
114C2×#677—32no—
115#4039—32no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4033—32no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#107—32no—
125C5×#106—32no—
126#3947C2×D312yes—
127C8×Dic5C2×D312yes—
128#3942—31no—
129#3942—31no—
130#3942—32no—
131#3942—32no—
132#3941—31no—
133#3941—31no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220—24no—
142C2×Dic15—24no—
143C2×Dic15—22no—
144C2×Dic15—21no—
145D60—21no—
146D60C22×C412yes—
147C4×D15—24no—
148Dic30—24no—
149Dic30—22no—
150Dic30—21no—
151Dic30C22×C414yes—
152Dic30C22×C412yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—81no—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159#1200—82no—
160C3×C5×C8C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C2×#235—51no—
164C22×Dic6—51no—
165C2×C3×M16C2×D511yescharacteristic
166C22×C3×C8—51no—
167C3×#117—51no—
168#926C2×D511yescharacteristic
169C2×C4⋊Dic3C2×D511yescharacteristic
170#909—58no—
171C2×Dic12—52no—
172C2×#204—52no—
173#892—101no—
174D3×C4⋊C4—101no—
175#887—101no—
176#887—101no—
177#67⋊C4—102no—
178#877—102no—
179C4×D12—52no—
180C4×Dic6—52no—
181C4×Dic6—52no—
182C4×Dic6—52no—
183C3×#97—52no—
184C3×C4×C8—52no—
185#821—51no—
186#821—51no—
187#818C2×D512yes—
188#817C2×D512yes—
189#816—52no—
190#816—51no—
191#816—52no—
192#816—51no—
193C22×C4×C5—61no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—61no—
196C22×Dic5—61no—
197#709—34no—
198#709—62no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×Dic10—34no—
203C2×Dic10—32no—
204C2×Dic10—31no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C5×M16C4×D314yescomplemented
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—61no—
213C5×C22⋊C4—61no—
214C42×C5—61no—
215C22⋊Dic5D1212yes—
216#685—62no—
217C4⋊Dic5D1211yescharacteristic
218C4⋊Dic5D1211yescharacteristic
219#683—62no—
220#683—62no—
221#683—62no—
222C4×Dic5—62no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5C22×D312yes—
226C2×#168—22no—
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D311yescharacteristic
229Dic20—38no—
230#677—38no—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—31no—
239#416—151no—
240C2×#103—151no—
241#405—51no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—24no—
253Dic15—22no—
254C3×Dic5—22no—
255C3×Dic5—22no—
256C5×Dic3—42no—
257C5×Dic3—41no—
258C5×Dic3—41no—
259C22×C3×C4C22×D511yescharacteristic
260C2×#67—101no—
261C22×Dic3—21no—
262C22×Dic3—101no—
263#235—54no—
264#235—102no—
265C2×D12—51no—
266C2×C4×D3—101no—
267C2×C4×D3—102no—
268C2×Dic6—54no—
269C2×Dic6—52no—
270C2×Dic6—51no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C3×M16C4×D514yescomplemented
274C2×C3×C8—51no—
275C2×C3×C8—51no—
276C2×C3×C8—102no—
277C2×C3×C8C22×D512yes—
278C3×C4⋊C4—51no—
279C3×C4⋊C4—51no—
280C3×C22⋊C4—52no—
281C3×C42—52no—
282#217—21no—
283(C2×D3)⋊C4—102no—
284C4⋊Dic3—21no—
285C4⋊Dic3C22×D512yes—
286C4⋊Dic3C22×D511yescharacteristic
287C4⋊Dic3C22×D511yescharacteristic
288Dic3⋊C4—102no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—21no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295Dic12—58no—
296#204—58no—
297C23×C5C2×D1211yescharacteristic
298C22×D5—61no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—62no—
302C2×C4×C5—241no—
303C2×C4×C5C2×C4×D312yes—
304C2×C4×C5C2×D1211yescharacteristic
305C2×C4×C5#23512yes—
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—64no—
308C2×Dic5—64no—
309C2×Dic5—62no—
310C2×Dic5—61no—
311C2×Dic5C2×D1212yes—
312C2×Dic5C2×D1212yes—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—34no—
318Dic10—32no—
319Dic10—64no—
320Dic10—62no—
321Dic10—61no—
322C5×C8C2×C4×D314yes—
323#168—21no—
324#168—21no—
325C2×#41—151no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16D3×D511yescharacteristic
331C22×C8—51no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—31no—
340#117—51no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—32no—
346#106—32no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—52no—
354C4×C8—52no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—101no—
362C2×C3×C4—52no—
363C2×C3×C4—52no—
364C2×C3×C4C2×C4×D512yes—
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4#71312yes—
367C2×C3×C4C23×D511yescharacteristic
368#67—104no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—81no—
373C2×Dic3—102no—
374C2×Dic3—101no—
375C2×Dic3—104no—
376D12—52no—
377D12—101no—
378C4×D3—104no—
379C4×D3—402no—
380Dic6—54no—
381Dic6—52no—
382Dic6—102no—
383Dic6—101no—
384Dic6—104no—
385C3×C8—101no—
386C3×C8—101no—
387C3×C8C2×C4×D514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5C4×D1212yes—
391C22×C5C22×D1211yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—122no—
396C4×C5—121no—
397C4×C5—121no—
398C4×C5C4×D1212yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23511yescharacteristic
401Dic5—22no—
402Dic5—22no—
403Dic5—64no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—151no—
410C2×Q8—302no—
411C2×Q8—301no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—61no—
415C22×C4—302no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16#120014yescomplemented
422C2×C8—51no—
423C2×C8—51no—
424C2×C8—102no—
425C2×C8C2×D3×D512yes—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—51no—
430C4⋊C4—51no—
431C4⋊C4—61no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—52no—
436C22⋊C4—61no—
437C22⋊C4—302no—
438C42—52no—
439C42—61no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#403912yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—102no—
452C3×C4—102no—
453C3×C4#403912yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71311yescharacteristic
456Dic3—42no—
457Dic3—41no—
458Dic3—41no—
459Dic3—104no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×C4×D1211yescharacteristic
463C2×C5#575111yescharacteristic
464C2×C5#575311yescharacteristic
465D5—122no—
466C23—301no—
467C23D5×D1211yescharacteristic
468Q8—154no—
469Q8—152no—
470Q8—304no—
471Q8—302no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—52no—
477C2×C4—52no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—241no—
482C2×C4—304no—
483C2×C4—301no—
484C2×C4—302no—
485C2×C4—304no—
486C2×C4—1202no—
487C2×C4#677312yes—
488C2×C4D5×D1211yescharacteristic
489C2×C4C2×#120012yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8C2×#120014yes—
494C2×C3—22no—
495C2×C3C2×#403911yescharacteristic
496C2×C3#6610911yescharacteristic
497C2×C3#6611311yescharacteristic
498D3—202no—
499C5#7857111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9141812yes—
506C22C2×D5×D1211yescharacteristic
507C4—102no—
508C4—102no—
509C4—122no—
510C4—121no—
511C4—121no—
512C4—302no—
513C4—304no—
514C4#9141812yes—
515C4C2×#677311yescharacteristic
516C4C22×#120011yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175402311yescharacteristic
521C2#1175404011yescharacteristic
522C2C2×#9141811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #11754213C2semidirect
4. C5×#5121C2semidirect
5. C3×#65411C2semidirect
6. C2×#90975C2semidirect
8. #11747854C2semidirect
9. #11747851C2semidirect
10. #11747778C2semidirect
11. #11747760C2semidirect
16. #91798C4semidirect
48. #65411D3semidirect
64. C2×Dic30C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
71. Dic60C2×C4semidirect
72. #6706C2×C4semidirect
97. #5121D5semidirect
207. C5×M16C4×D3semidirect
273. C3×M16C4×D5semidirect
421. M16#1200semidirect
443. C3×C5#2947semidirect
499. C5#78571semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
#117545062
#117542132
C5×#51212
C3×#654112
C2×#909752
#117483932
#117478542
#117478512
#117477782
#117477602
#106109333
#785715