Finite Group Databasebeta

← #14431352

Subgroups — #14431352

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754618C211yesmaximal, characteristic, complemented
2#11754499C211yesmaximal, characteristic
3#11751220C211yesmaximal, characteristic, complemented
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic
6C2×#90986C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic
8#11747880C212yesmaximal, complemented
9#11747878C212yesmaximal, complemented
10#11747804C212yesmaximal, complemented
11#11747802C212yesmaximal, complemented
12#10610975—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91574—22no—
21Dic3×C22⋊D5—22no—
22#91470C2212yes—
23#91469—21no—
24#91434C2212yes—
25D5×C4⋊Dic3—21no—
26#91384C2212yes—
27#91381—21no—
28#91358—21no—
29#91331C2212yes—
30#91098C2212yes—
31#91098C2212yes—
32C5×#818C2212yes—
33C5×#817C2212yes—
34C3×#3953C2212yes—
35C3×#3948C2212yes—
36#90986C2212yes—
37#90986C2212yes—
38#90970C2211yescharacteristic
39#90970C2211yescharacteristic
40#90964C2211yescharacteristic
41#90964C2211yescharacteristic
42#78873—51nomaximal, Hall
43#65853—31no—
44#65838—31no—
45C5×#428—31no—
46#65422D311yescharacteristic
47#65408—31no—
48#65291—31no—
49C2×#3940—31no—
50#65180—32no—
51#65166—32no—
52#65159—32no—
53#65143—32no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C5×Dic3—21no—
56C2×C3×C22⋊D5—21no—
57C22×C3×Dic5—21no—
58C3×#709—22no—
59C3×#709Q814yescomplemented
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×Dic10C2311yescharacteristic
63C2×#1204—22no—
64C2×D5×Dic3—22no—
65C3×C5×M16—22no—
66C2×C3×C5×C8C2312yes—
67#6719D412yes—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15D411yescharacteristic
70C4×Dic15C2312yes—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C5×#217—21no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×C4⋊Dic3C2311yescharacteristic
79C4×C5×Dic3—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6668—22no—
85#6668—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#5827—51no—
89#5500—51no—
90C3×#417—51no—
91#5233—51no—
92#5121D511yescharacteristic, complemented
93#5119—51no—
94C2×#808—51no—
95#4796—52no—
96#4791—52no—
97#4766—52no—
98#4761—52no—
99C2×#709C2×D311yescharacteristic
100C2×C5×M16C2×D311yescharacteristic
101C5×#117—31no—
102C2×C5×C4⋊C4—31no—
103C4×C22⋊D5—62no—
104#4072—31no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106C22×#168—31no—
107#4039—32no—
108#4038—61no—
109D5×C4⋊C4—61no—
110#4036—32no—
111#4034—32no—
112#4033—32no—
113#4024—62no—
114#4016—61no—
115#4015—61no—
116C5×#107—32no—
117C5×#106—32no—
118#3953C2×D312yes—
119#3948C2×D312yes—
120#3946—32no—
121#3946—32no—
122#3942—31no—
123#3942—31no—
124#3941—31no—
125#3941—31no—
126#3940—32no—
127#3940—32no—
128#3084—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C3×D5—21no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×Q812yes—
133C2×C3×C4×C5#4112yes—
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—81no—
141C3×C22⋊D5—24no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—81no—
145C3×D20—21no—
146C3×D20C2×Q812yes—
147C3×C4×D5—24no—
148C3×Dic10—21no—
149C3×Dic10C2×Q812yes—
150#1204—82no—
151D5×Dic3—82no—
152C3×C5×C8—22no—
153C3⋊#168—21no—
154C3⋊#168—21no—
155C2×C3×#41—51no—
156C2×C3×M16C2×D511yescharacteristic
157C2×C3×C4⋊C4—51no—
158Q8×Dic3—52no—
159D4×Dic3—52no—
160D4×Dic3—102no—
161#926—51no—
162#926—101no—
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3—101no—
165C2×C4⋊Dic3C2×D511yescharacteristic
166#924—102no—
167C22×C3⋊C8—51no—
168#890—52no—
169#890—101no—
170#888—52no—
171#888—101no—
172C3×#103—52no—
173C3×#102—52no—
174#835—51no—
175#835—51no—
176#832—51no—
177#832—51no—
178#818C2×D512yes—
179#817C2×D512yes—
180Dic3⋊C8—52no—
181Dic3⋊C8—52no—
182#808—52no—
183#808—52no—
184C22×C4×C5—61no—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—21no—
187C22×Dic5—21no—
188#709—22no—
189#709Dic614yescomplemented
190C2×D20C22×D311yescharacteristic
191C2×C4×D5—21no—
192C2×C4×D5—62no—
193C2×Dic10—62no—
194C2×Dic10C22×D311yescharacteristic
195C5×M16—22no—
196C2×C5×C8C22×D312yes—
197C5×C4⋊C4—32no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—31no—
200C5×C4⋊C4—61no—
201C5×C22⋊C4—61no—
202C42×C5—61no—
203C22⋊Dic5—32no—
204#685—62no—
205C4⋊Dic5—21no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5C22×D312yes—
210#683—62no—
211#683—62no—
212#683—62no—
213C4×Dic5—32no—
214C4×Dic5—62no—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#520—151no—
220#479—152no—
221#478—152no—
222#476—152no—
223#475—152no—
224#428—31no—
225C2×#106—151no—
226#424—151no—
227#417—51no—
228#416—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—22no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C3×C4×C5C22⋊Q812yes—
237C3×C4×C5C22×Q811yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—22no—
240Dic15—22no—
241C3×Dic5—22no—
242C3×Dic5—42no—
243C5×Dic3—42no—
244C5×Dic3—41no—
245C5×Dic3—41no—
246C3×#41—54no—
247C3×#41—102no—
248C2×C3×Q8—51no—
249C2×C3×D4—51no—
250C2×C3×D4—101no—
251C22×C3×C4—101no—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—21no—
255C22×Dic3—102no—
256C2×Dic6—102no—
257C3×M16—22no—
258C2×C3×C8C22×D512yes—
259C3×C4⋊C4—52no—
260C3×C4⋊C4—101no—
261#217—21no—
262#217—52no—
263#217—102no—
264C4⋊Dic3—21no—
265C4⋊Dic3—51no—
266C4⋊Dic3—51no—
267C4⋊Dic3—102no—
268C4⋊Dic3—102no—
269C4⋊Dic3C22×D512yes—
270C4⋊Dic3C22×D511yescharacteristic
271C4⋊Dic3C22×D511yescharacteristic
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—102no—
280C23×C5D3×D411yescharacteristic
281C22×D5—21no—
282C2×C4×C5—62no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—241no—
286C2×C4×C5C2×Dic612yes—
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5#23712yes—
289C2×C4×C5C23×D311yescharacteristic
290C22⋊D5—24no—
291C2×Dic5—21no—
292C2×Dic5—22no—
293C2×Dic5—32no—
294C2×Dic5—32no—
295C2×Dic5—81no—
296D20—21no—
297D20C2×Dic612yes—
298C4×D5—24no—
299C4×D5—242no—
300Dic10—21no—
301Dic10—242no—
302Dic10C2×Dic612yes—
303C5×C8—22no—
304#168—61no—
305#168—61no—
306C2×#41—51no—
307C2×M16D3×D511yescharacteristic
308C22×C8—151no—
309C4⋊Q8—152no—
310C4⋊Q8—301no—
311#125—152no—
312#125—301no—
313C22⋊Q8—302no—
314C4×Q8—152no—
315C4×D4—152no—
316C4×D4—302no—
317#117—31no—
318#117—151no—
319#117—301no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—51no—
322C2×C4⋊C4—301no—
323#107—32no—
324#106—32no—
325#106—152no—
326#106—152no—
327C4⋊C8—152no—
328C4⋊C8—152no—
329#103—52no—
330#103—151no—
331#103—151no—
332#102—52no—
333#102—151no—
334#102—151no—
335C2×C3×C5—22no—
336C2×C3×C5C2×C22⋊Q811yescharacteristic
337C2×C3×C5#57711yescharacteristic
338C2×C3×C5#57711yescharacteristic
339C3×D5—42no—
340C23×C3—101no—
341C23×C3D4×D511yescharacteristic
342C3×Q8—52no—
343C3×Q8—101no—
344C3×D4—52no—
345C3×D4—104no—
346C3×D4—101no—
347C2×C3×C4—101no—
348C2×C3×C4—104no—
349C2×C3×C4—102no—
350C2×C3×C4—401no—
351C2×C3×C4#70912yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4Q8×D512yes—
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—81no—
361C2×Dic3—402no—
362Dic6—402no—
363C3×C8—22no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#87812yes—
369C22×C5C2×D3×D411yescharacteristic
370C2×D5—22no—
371C2×D5—41no—
372C2×D5—41no—
373C4×C5—121no—
374C4×C5—122no—
375C4×C5—121no—
376C4×C5#87812yes—
377C4×C5C22×Dic611yescharacteristic
378C4×C5C2×#23711yescharacteristic
379Dic5—22no—
380Dic5—42no—
381Dic5—62no—
382Dic5—62no—
383#41—54no—
384#41—102no—
385C2×Q8—51no—
386C2×Q8—302no—
387C2×D4—51no—
388C2×D4—101no—
389C22×C4—61no—
390C22×C4—101no—
391C22×C4—101no—
392C22×C4—302no—
393C22×C4C2×D3×D511yescharacteristic
394M16—22no—
395C2×C8—151no—
396C2×C8—151no—
397C2×C8—302no—
398C2×C8C2×D3×D512yes—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—52no—
403C4⋊C4—61no—
404C4⋊C4—101no—
405C4⋊C4—151no—
406C4⋊C4—151no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—61no—
412C22⋊C4—152no—
413C22⋊C4—302no—
414C42—61no—
415C42—152no—
416C42—302no—
417C3×C5#308411yescharacteristic, complemented, Hall
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—102no—
421C22×C3—201no—
422C22×C3—201no—
423C22×C3#404212yes—
424C22×C3C2×D4×D511yescharacteristic
425C3×C4—102no—
426C3×C4—202no—
427C3×C4#404212yes—
428C3×C4C2×#70911yescharacteristic
429C3×C4C2×Q8×D511yescharacteristic
430Dic3—41no—
431Dic3—42no—
432Dic3—41no—
433Dic3—102no—
434Dic3—102no—
435C2×C5—22no—
436C2×C5C2×#87811yescharacteristic
437C2×C5#577511yescharacteristic
438C2×C5#577811yescharacteristic
439D5—42no—
440C23—101no—
441C23#677711yescharacteristic
442Q8—52no—
443Q8—101no—
444Q8—1202no—
445D4—52no—
446D4—104no—
447D4—101no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—62no—
451C2×C4—101no—
452C2×C4—104no—
453C2×C4—102no—
454C2×C4—152no—
455C2×C4—152no—
456C2×C4—241no—
457C2×C4—401no—
458C2×C4—1202no—
459C2×C4D5×Dic612yes—
460C2×C4#677711yescharacteristic
461C2×C4#677912yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—22no—
464C8—301no—
465C8—301no—
466C2×C3—22no—
467C2×C3—202no—
468C2×C3C2×#404211yescharacteristic
469C2×C3#6610911yescharacteristic
470C2×C3#6611211yescharacteristic
471C5#7887311yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—102no—
475C22—201no—
476C22—201no—
477C22#9143012yes—
478C22C2×#677711yescharacteristic
479C4—102no—
480C4—121no—
481C4—122no—
482C4—121no—
483C4—202no—
484C4—302no—
485C4—302no—
486C4#9143012yes—
487C4C2×D5×Dic611yescharacteristic
488C4C2×#677911yescharacteristic
489C3#1061097511yescharacteristic, complemented, Sylow
490C2—22no—
491C2—202no—
492C2#1175403711yescharacteristic
493C2#1175403911yescharacteristic
494C2C2×#9143011yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×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
1. #11754618C2semidirect
3. #11751220C2semidirect
4. C5×#5121C2semidirect
6. C2×#90986C2semidirect
8. #11747880C2semidirect
9. #11747878C2semidirect
10. #11747804C2semidirect
11. #11747802C2semidirect
59. C3×#709Q8semidirect
92. #5121D5semidirect
189. #709Dic6semidirect
417. C3×C5#3084semidirect
471. C5#78873semidirect
489. C3#10610975semidirect

Maximal subgroups

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

subgroupindex
#117546182
#117544992
#117512202
C5×#51212
C3×#654222
C2×#909862
#117483642
#117478802
#117478782
#117478042
#117478022
#106109753
#788735