Finite Group Databasebeta

← #14417288

Subgroups — #14417288

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×C3×#4055C211yesmaximal, characteristic
2#11754499C211yesmaximal, characteristic
3#11754188C211yesmaximal, characteristic, complemented
4#11751223C211yesmaximal, characteristic, complemented
5C5×#5121C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic
8#11747884C212yesmaximal, complemented
9#11747883C212yesmaximal, complemented
10#11747812C212yesmaximal, complemented
11#11747806C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C3×#4055C418yescomplemented
21C2×C3×Dic20C2212yes—
22C2×C3×#677C2212yes—
23Dic3×C22⋊D5—22no—
24#91528—22no—
25#91434C2212yes—
26D5×C4⋊Dic3—21no—
27#91358—21no—
28#91331C2212yes—
29#91331C2212yes—
30#91331C2212yes—
31Dic3×Dic10—21no—
32Dic3×Dic10—21no—
33#91099C2212yes—
34C8×Dic15C2212yes—
35C5×#818C2212yes—
36C5×#817C2212yes—
37#90970C2211yescharacteristic
38#90970C2211yescharacteristic
39#90970C2212yes—
40#90970C2212yes—
41#90964C2211yescharacteristic
42#90964C2211yescharacteristic
43#83965—51nomaximal, Hall
44C2×#4055D311yescharacteristic
45#65850—31no—
46#65838—31no—
47C5×#428—31no—
48#65411—31no—
49#65291—31no—
50C2×#3942—31no—
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C5×Dic3—21no—
57C2×C3×C22⋊D5—21no—
58C22×C3×Dic5—21no—
59C3×#709—22no—
60C3×#709C2×C414yes—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—22no—
65C2×C3×Dic10C2×C414yescomplemented
66C2×C3×Dic10C2312yes—
67C2×C3×Dic10C2311yescharacteristic
68C2×D5×Dic3—22no—
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71#6719D412yes—
72C4⋊Dic15D411yescharacteristic
73C4⋊Dic15D411yescharacteristic
74C4×Dic15C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×#217—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C5×C4⋊Dic3C2311yescharacteristic
82C5×C4⋊Dic3C2311yescharacteristic
83C4×C5×Dic3—21no—
84C3×Dic20C2×C418yescomplemented
85C3×#677C2×C418yescomplemented
86#6668—22no—
87#6668—22no—
88#6668—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C2×C3×#137—51no—
94#5827—51no—
95#5812—51no—
96#5233—51no—
97C2×#835—51no—
98#5184—52no—
99Dic3×Q16—52no—
100#5164—52no—
101Dic3×SD16—52no—
102#5122—51no—
103#5121D511yescharacteristic, complemented
104C2×#709C2×D311yescharacteristic
105C22×Dic10C2×D311yescharacteristic
106C2×C5×M16C2×D311yescharacteristic
107C5×#117—31no—
108C2×C5×C4⋊C4—31no—
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168—31no—
112#4055Dic318yescomplemented
113C2×Dic20C2×D312yes—
114C2×#677C2×D312yes—
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#3947—32no—
127C8×Dic5—32no—
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×C3×D5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—81no—
147C3×C22⋊D5—24no—
148C2×C3×Dic5—24no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—21no—
151C3×D20—21no—
152C3×D20C22×C412yes—
153C3×C4×D5—24no—
154C3×Dic10—24no—
155C3×Dic10—22no—
156C3×Dic10—21no—
157C3×Dic10C22×C414yes—
158C3×Dic10C22×C412yes—
159D5×Dic3—82no—
160C3×C5×C8C22×C414yes—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C2×C3×#41—51no—
164C22×C3×Q8—51no—
165C3×#137—58no—
166C2×C3×Q16—52no—
167C2×C3×SD16—52no—
168C2×C3×M16C2×D511yescharacteristic
169Q8×Dic3—52no—
170Q8×Dic3—52no—
171Q8×Dic3—52no—
172Q8×Dic3—101no—
173Q8×Dic3—101no—
174D4×Dic3—52no—
175D4×Dic3—102no—
176#926—51no—
177#926—101no—
178#926—102no—
179#926C2×D511yescharacteristic
180C2×C4⋊Dic3—101no—
181C2×C4⋊Dic3C2×D511yescharacteristic
182C22×C3⋊C8—51no—
183#835—52no—
184#835—52no—
185#835—51no—
186#835—51no—
187#832—51no—
188#832—51no—
189#818C2×D512yes—
190#817C2×D512yes—
191#815—52no—
192C8×Dic3—52no—
193C22×C4×C5—61no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—21no—
196C22×Dic5—21no—
197#709—22no—
198#709C2×Dic314yes—
199C2×D20C22×D311yescharacteristic
200C2×C4×D5—21no—
201C2×C4×D5—62no—
202C2×Dic10—21no—
203C2×Dic10—22no—
204C2×Dic10C2×Dic314yescomplemented
205C2×Dic10C22×D312yes—
206C2×Dic10C22×D311yescharacteristic
207C5×M16C2×Dic314yescomplemented
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⋊Dic5—32no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219#683—62no—
220#683—62no—
221#683—62no—
222C4×Dic5—32no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C2×#168—31no—
227C2×#168—31no—
228C2×#168—62no—
229Dic20C2×Dic318yescomplemented
230#677C2×Dic318yescomplemented
231C2×#137—51no—
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—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C3×D5—22no—
247C2×C3×D5—41no—
248C2×C3×D5—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—22no—
253Dic15—22no—
254C3×Dic5—24no—
255C3×Dic5—22no—
256C5×Dic3—42no—
257C5×Dic3—41no—
258C5×Dic3—41no—
259C3×#41—54no—
260C3×#41—102no—
261C2×C3×Q8—54no—
262C2×C3×Q8—52no—
263C2×C3×Q8—51no—
264C2×C3×Q8—101no—
265C2×C3×Q8—102no—
266C2×C3×D4—51no—
267C2×C3×D4—101no—
268C22×C3×C4—101no—
269C22×C3×C4—101no—
270C22×C3×C4C22×D511yescharacteristic
271C22×Dic3—21no—
272C22×Dic3—102no—
273C3×Q16—58no—
274C3×SD16—58no—
275C3×M16C4×D514yescomplemented
276C2×C3×C8C22×D512yes—
277#217—21no—
278#217—52no—
279#217—102no—
280C4⋊Dic3—21no—
281C4⋊Dic3—51no—
282C4⋊Dic3—51no—
283C4⋊Dic3—102no—
284C4⋊Dic3—102no—
285C4⋊Dic3—102no—
286C4⋊Dic3C22×D511yescharacteristic
287C4⋊Dic3C22×D512yes—
288C4⋊Dic3C22×D511yescharacteristic
289C4×Dic3—21no—
290C4×Dic3—52no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—51no—
296C2×C3⋊C8—102no—
297C23×C5D3×D411yescharacteristic
298C22×D5—21no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—62no—
302C2×C4×C5—241no—
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5#23712yes—
305C2×C4×C5C22×Dic312yes—
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—24no—
308C2×Dic5—24no—
309C2×Dic5—22no—
310C2×Dic5—21no—
311C2×Dic5—32no—
312C2×Dic5—32no—
313D20—21no—
314D20C22×Dic312yes—
315C4×D5—24no—
316C4×D5—242no—
317Dic10—24no—
318Dic10—22no—
319Dic10—21no—
320Dic10C22×Dic314yes—
321Dic10C22×Dic312yes—
322C5×C8C22×Dic314yes—
323#168—61no—
324#168—61no—
325C2×#41—51no—
326C22×Q8—51no—
327#137—58no—
328C2×Q16—52no—
329C2×SD16—52no—
330C2×M16D3×D511yescharacteristic
331C22×C8—151no—
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—151no—
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—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C3×D5—42no—
360C23×C3—101no—
361C23×C3D4×D511yescharacteristic
362C3×Q8—54no—
363C3×Q8—52no—
364C3×Q8—102no—
365C3×Q8—101no—
366C3×Q8—104no—
367C3×D4—52no—
368C3×D4—104no—
369C3×D4—101no—
370C2×C3×C4—101no—
371C2×C3×C4—102no—
372C2×C3×C4—104no—
373C2×C3×C4—104no—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4D4×D511yescharacteristic
376C2×C3×C4#71312yes—
377C2×C3×C4C23×D511yescharacteristic
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—52no—
382C2×Dic3—52no—
383C2×Dic3—81no—
384C2×Dic3—402no—
385C3×C8C2×C4×D514yes—
386C3⋊C8—101no—
387C3⋊C8—101no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5D4×Dic312yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—22no—
393C2×D5—41no—
394C2×D5—41no—
395C4×C5—122no—
396C4×C5—121no—
397C4×C5—121no—
398C4×C5D4×Dic312yes—
399C4×C5C2×#23711yescharacteristic
400C4×C5C23×Dic311yescharacteristic
401Dic5—24no—
402Dic5—22no—
403Dic5—62no—
404Dic5—62no—
405#41—54no—
406#41—102no—
407C2×Q8—54no—
408C2×Q8—52no—
409C2×Q8—51no—
410C2×Q8—102no—
411C2×Q8—101no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—58no—
420SD16—58no—
421M16D5×Dic314yescomplemented
422C2×C8—151no—
423C2×C8—151no—
424C2×C8—302no—
425C2×C8C2×D3×D512yes—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—61no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—61no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—61no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—102no—
447C22×C3—201no—
448C22×C3—201no—
449C22×C3#403912yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—102no—
452C3×C4—104no—
453C3×C4#403912yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71311yescharacteristic
456Dic3—41no—
457Dic3—42no—
458Dic3—41no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5#577811yescharacteristic
463C2×C5#577911yescharacteristic
464C2×C5C2×D4×Dic311yescharacteristic
465D5—42no—
466C23—101no—
467C23#677711yescharacteristic
468Q8—54no—
469Q8—52no—
470Q8—104no—
471Q8—102no—
472Q8—101no—
473D4—52no—
474D4—104no—
475D4—101no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—104no—
480C2×C4—101no—
481C2×C4—102no—
482C2×C4—104no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—241no—
486C2×C4—1202no—
487C2×C4#676612yes—
488C2×C4#677711yescharacteristic
489C2×C4C2×D5×Dic312yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—301no—
492C8—301no—
493C8C2×D5×Dic314yes—
494C2×C3—22no—
495C2×C3—202no—
496C2×C3C2×#403911yescharacteristic
497C2×C3#6610911yescharacteristic
498C2×C3#6611311yescharacteristic
499C5#8396511yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—102no—
503C22—201no—
504C22—201no—
505C22#9143412yes—
506C22C2×#677711yescharacteristic
507C4—102no—
508C4—104no—
509C4—122no—
510C4—121no—
511C4—121no—
512C4—302no—
513C4—302no—
514C4#9143412yes—
515C4C2×#676611yescharacteristic
516C4C22×D5×Dic311yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—202no—
520C2#1175403911yescharacteristic
521C2#1175404311yescharacteristic
522C2C2×#9143411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
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. #11754188C2semidirect
4. #11751223C2semidirect
5. C5×#5121C2semidirect
6. C2×#90970C2semidirect
8. #11747884C2semidirect
9. #11747883C2semidirect
10. #11747812C2semidirect
11. #11747806C2semidirect
20. C3×#4055C4semidirect
65. C2×C3×Dic10C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
84. C3×Dic20C2×C4semidirect
85. C3×#677C2×C4semidirect
103. #5121D5semidirect
112. #4055Dic3semidirect
204. C2×Dic10C2×Dic3semidirect
207. C5×M16C2×Dic3semidirect
229. Dic20C2×Dic3semidirect
230. #677C2×Dic3semidirect
275. C3×M16C4×D5semidirect
421. M16D5×Dic3semidirect
443. C3×C5#2947semidirect
499. C5#83965semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40552
#117544992
#117541882
#117512232
C5×#51212
C2×#909702
#117483642
#117478842
#117478832
#117478122
#117478062
#106109333
#839655