Finite Group Databasebeta

← #14417266

Subgroups — #14417266

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
1#11754506C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3C2×#91321C211yesmaximal, characteristic
4#11751214C211yesmaximal, characteristic
5C2×C5×#816C211yesmaximal, characteristic, complemented
6C3×#65390C211yesmaximal, characteristic, complemented
7#11748459C211yesmaximal, characteristic, complemented
8#11747835C212yesmaximal, complemented
9#11747834C212yesmaximal, complemented
10#11747833C212yesmaximal, complemented
11#11747748C212yesmaximal, complemented
12#10610505—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91556—22no—
21#91529—22no—
22#91437—21no—
23#91418C2212yes—
24#91347—21no—
25#91344—21no—
26#91344—21no—
27#91333C2212yes—
28Dic5×Dic6C2212yes—
29Dic5×Dic6C2212yes—
30#91321C418yescomplemented
31C2×#6663C2212yes—
32C2×#6660C2212yes—
33#91105C2211yescharacteristic
34#91105C2211yescharacteristic
35#91100C2211yescharacteristic
36#91100C2211yescharacteristic
37C5×#816C2212yes—
38C5×#816C2212yes—
39C3×#3947C2212yes—
40C3×C8×Dic5C2212yes—
41#90988C2212yes—
42#90985C2212yes—
43#78571—51nomaximal, Hall
44#66146—31no—
45C2×#4088—31no—
46#65838—31no—
47C2×C5×#103—31no—
48#65402—31no—
49#65390D311yescharacteristic, complemented
50#65253—31no—
51#65106—32no—
52#65079—32no—
53#65078—32no—
54#65077—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817C2×C414yes—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C22×C5×Dic3—21no—
63C22×C5×Dic3—21no—
64C2×C5×Dic6—21no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6C2×C414yescomplemented
67C2×C5×Dic6C2312yes—
68C2×#1200—22no—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72#6719—21no—
73C4⋊Dic15C2311yescharacteristic
74C4⋊Dic15C2311yescharacteristic
75C4×Dic15—21no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C3×C22⋊Dic5D412yes—
79C3×C4⋊Dic5D411yescharacteristic
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4×Dic5C2312yes—
82C3×#681C2×C414yescomplemented
83C2×C3×#168C2312yes—
84Dic3⋊Dic5—22no—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6667—22no—
88Dic3×Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6663C2×C418yescomplemented
92#6660C2×C418yescomplemented
93C2×#909—51no—
94#5523—51no—
95#5516—51no—
96C3×#405—51no—
97#5121—51no—
98#5113—51no—
99C2×#816D511yescharacteristic, complemented
100#4716—52no—
101#4710—52no—
102C4×Dic12—52no—
103C4×#204—52no—
104C22×C5×Q8—31no—
105C2×#709—31no—
106C22×C5×C8C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108Q8×Dic5—32no—
109Q8×Dic5—32no—
110Q8×Dic5—61no—
111Q8×Dic5—61no—
112C2×#689—32no—
113#4088—38no—
114C2×#688—32no—
115C4×C22⋊D5—62no—
116#4072—31no—
117#4072—62no—
118#4072C2×D311yescharacteristic
119C2×#681C2×D311yescharacteristic
120#4039—32no—
121#4038—61no—
122D5×C4⋊C4—61no—
123#4033—32no—
124C5×#103—32no—
125C5×#103—32no—
126#3953—31no—
127#3953—31no—
128#3948—31no—
129#3948—31no—
130#3947C2×D312yes—
131C8×Dic5C2×D312yes—
132#3940—32no—
133#3939—32no—
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—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145D60—21no—
146D60C22×C412yes—
147C4×D15—24no—
148Dic30—21no—
149Dic30C22×C412yes—
150C2×C5×Dic3—24no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—81no—
154C5×Dic6—24no—
155C5×Dic6—22no—
156C5×Dic6C22×C414yes—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159#1200—82no—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C3×#168C22×C414yes—
163C2×#235—51no—
164C22×Dic6C2×D511yescharacteristic
165C2×C3×M16—51no—
166C22×C3×C8C2×D511yescharacteristic
167C3×#117—51no—
168#926—51no—
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#818—52no—
188#817—52no—
189#816—51no—
190#816—51no—
191#816C2×D512yes—
192#816C2×D512yes—
193C2×C5×Q8—34no—
194C2×C5×Q8—32no—
195C2×C5×Q8—61no—
196C2×C5×Q8—62no—
197C22×C4×C5—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201#709—34no—
202#709—62no—
203C2×D20—31no—
204C2×C4×D5—61no—
205C2×C4×D5—62no—
206C2×Dic10—31no—
207C2×C5×C8—22no—
208C2×C5×C8C22×D311yescharacteristic
209C2×C5×C8C22×D311yescharacteristic
210C5×C4⋊C4—32no—
211C5×C4⋊C4—61no—
212C22⋊Dic5—61no—
213C22⋊Dic5D1212yes—
214#689—38no—
215#688—38no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219C4⋊Dic5—62no—
220C4⋊Dic5—62no—
221C4⋊Dic5D1211yescharacteristic
222C4⋊Dic5D1211yescharacteristic
223#683—62no—
224C4×Dic5—61no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5C22×D312yes—
229#681C4×D314yescomplemented
230C2×#168C22×D312yes—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—31no—
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—22no—
253Dic15—41no—
254Dic15—41no—
255C3×Dic5—22no—
256C3×Dic5—22no—
257C5×Dic3—24no—
258C5×Dic3—42no—
259C22×C3×C4C22×D511yescharacteristic
260C2×#67—101no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263#235—54no—
264#235—102no—
265C2×D12—51no—
266C2×C4×D3—101no—
267C2×C4×D3—102no—
268C2×Dic6—21no—
269C2×Dic6—22no—
270C2×Dic6—51no—
271C2×Dic6C4×D514yescomplemented
272C2×Dic6C22×D512yes—
273C3×M16—54no—
274C2×C3×C8—22no—
275C2×C3×C8—52no—
276C2×C3×C8C22×D511yescharacteristic
277C2×C3×C8C22×D511yescharacteristic
278C3×C4⋊C4—51no—
279C3×C4⋊C4—51no—
280C3×C22⋊C4—52no—
281C3×C42—52no—
282#217—101no—
283(C2×D3)⋊C4—102no—
284C4⋊Dic3—21no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287C4⋊Dic3C22×D512yes—
288Dic3⋊C4—102no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—101no—
295Dic12—58no—
296#204—58no—
297C23×C5C2×D1211yescharacteristic
298C22×D5—61no—
299C5×Q8—34no—
300C5×Q8—64no—
301C5×Q8—62no—
302C2×C4×C5—64no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5—241no—
306C2×C4×C5C2×C4×D312yes—
307C2×C4×C5C2×D1211yescharacteristic
308C2×C4×C5#23512yes—
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—64no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5C2×D1212yes—
315C2×Dic5C2×D1212yes—
316D20—32no—
317D20—61no—
318C4×D5—64no—
319C4×D5—242no—
320Dic10—32no—
321Dic10—61no—
322C5×C8—21no—
323C5×C8—21no—
324#168C2×C4×D314yes—
325C2×#41—151no—
326C22×Q8—31no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—51no—
331C22×C8D3×D511yescharacteristic
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—32no—
348#103—32no—
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#71112yes—
367C2×C3×C4C23×D511yescharacteristic
368#67—104no—
369C2×Dic3—22no—
370C2×Dic3—24no—
371C2×Dic3—22no—
372C2×Dic3—81no—
373C2×Dic3—101no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376D12—52no—
377D12—101no—
378C4×D3—104no—
379C4×D3—402no—
380Dic6—22no—
381Dic6—24no—
382Dic6—52no—
383Dic6—101no—
384Dic6C2×C4×D514yes—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5C4×D1212yes—
391C22×C5C22×D1211yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—64no—
396C4×C5—122no—
397C4×C5C4×D1212yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23511yescharacteristic
400Dic5—22no—
401Dic5—22no—
402Dic5—62no—
403Dic5—121no—
404Dic5—121no—
405#41—154no—
406#41—302no—
407C2×Q8—34no—
408C2×Q8—32no—
409C2×Q8—61no—
410C2×Q8—62no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—54no—
422C2×C8—22no—
423C2×C8—52no—
424C2×C8C2×D3×D511yescharacteristic
425C2×C8C2×D3×D511yescharacteristic
426C4⋊C4—32no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—61no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—52no—
436C22⋊C4—302no—
437C22⋊C4—301no—
438C42—52no—
439C42—302no—
440C42—302no—
441C42—302no—
442C42—301no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#402712yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—102no—
452C3×C4—102no—
453C3×C4#402712yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71111yescharacteristic
456Dic3—24no—
457Dic3—42no—
458Dic3—102no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5C2×C4×D1211yescharacteristic
463C2×C5#575111yescharacteristic
464C2×C5#575311yescharacteristic
465D5—122no—
466C23—301no—
467C23D5×D1211yescharacteristic
468Q8—34no—
469Q8—64no—
470Q8—62no—
471Q8—152no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—52no—
477C2×C4—52no—
478C2×C4—64no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—241no—
482C2×C4—301no—
483C2×C4—304no—
484C2×C4—301no—
485C2×C4—301no—
486C2×C4—1202no—
487C2×C4C4×D3×D512yes—
488C2×C4D5×D1211yescharacteristic
489C2×C4#678212yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—54no—
494C2×C3—22no—
495C2×C3C2×#402711yescharacteristic
496C2×C3#6609611yescharacteristic
497C2×C3#6610011yescharacteristic
498D3—202no—
499C5#7857111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9140512yes—
506C22C2×D5×D1211yescharacteristic
507C4—64no—
508C4—102no—
509C4—102no—
510C4—122no—
511C4—302no—
512C4—601no—
513C4—601no—
514C4#9140512yes—
515C4C2×C4×D3×D511yescharacteristic
516C4C2×#678211yescharacteristic
517C3#1061050511yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175396011yescharacteristic
521C2#1175398711yescharacteristic
522C2C2×#9140511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754211C2semidirect
5. C2×C5×#816C2semidirect
6. C3×#65390C2semidirect
7. #11748459C2semidirect
8. #11747835C2semidirect
9. #11747834C2semidirect
10. #11747833C2semidirect
11. #11747748C2semidirect
30. #91321C4semidirect
49. #65390D3semidirect
66. C2×C5×Dic6C2×C4semidirect
82. C3×#681C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
99. C2×#816D5semidirect
229. #681C4×D3semidirect
271. C2×Dic6C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78571semidirect
517. C3#10610505semidirect

Maximal subgroups

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

subgroupindex
#117545062
#117542112
C2×#913212
#117512142
C2×C5×#8162
C3×#653902
#117484592
#117478352
#117478342
#117478332
#117477482
#106105053
#785715