Finite Group Databasebeta

← #14431341

Subgroups — #14431341

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
1C3×#65838C211yesmaximal, characteristic
2#11754620C211yesmaximal, characteristic, complemented
3C2×#91092C211yesmaximal, characteristic, complemented
4C5×#4964C211yesmaximal, characteristic, complemented
5#11748433C211yesmaximal, characteristic, complemented
6#11748369C211yesmaximal, characteristic
7#11748364C211yesmaximal, characteristic
8#11747415C212yesmaximal, complemented
9#11747411C212yesmaximal, complemented
10#11747391C212yesmaximal, complemented
11#11747389C212yesmaximal, complemented
12#10610975—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×C4×C22⋊D5—22no—
20C3×#4072C2211yescharacteristic
21C3×#4039C2212yes—
22C3×#4038—21no—
23C3×D5×C4⋊C4—21no—
24C3×#4033C2212yes—
25#91576—22no—
26#91469—21no—
27#91468C2212yes—
28#91388C2212yes—
29#91381—21no—
30#91092C2212yes—
31#91092C2212yes—
32C5×#808C2212yes—
33C5×#807C2212yes—
34#90982C2212yes—
35#90982C2212yes—
36#90971C2212yes—
37#90970C2211yescharacteristic
38#90970C2211yescharacteristic
39#90965C2212yes—
40#90964C2211yescharacteristic
41#90964C2211yescharacteristic
42#82560—51nomaximal, Hall
43#65853—31no—
44#65838D311yescharacteristic
45C5×#428—31no—
46#65422—31no—
47#65408—31no—
48#65291—31no—
49C2×#3940—31no—
50#65180—32no—
51#65166—32no—
52#65159—32no—
53#65143—32no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×C3×C22⋊D5—21no—
58C3×#709—22no—
59C3×#709Q814yescomplemented
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—22no—
63C2×C3×Dic10C2311yescharacteristic
64C2×#1204—22no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2312yes—
67C4⋊Dic15—21no—
68C4⋊Dic15C2312yes—
69C2×C3⋊#168—22no—
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×#217—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C4×C5×Dic3—21no—
76C5×#208—22no—
77C2×C5×C3⋊C8C2312yes—
78C3×C22⋊Dic5D412yes—
79C3×#685—22no—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5D411yescharacteristic
82C3×#683—22no—
83C3×C4×Dic5—22no—
84C3×C4×Dic5C2312yes—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6668—22no—
88C3×#520—51no—
89#5519—51no—
90#5233—51no—
91#5232—51no—
92#5022—52no—
93#5020—52no—
94#5009—52no—
95#5008—52no—
96#4999—51no—
97#4964D511yescharacteristic, complemented
98C2×#808—51no—
99C2×#709C2×D311yescharacteristic
100C2×C5×M16—31no—
101C5×#117—31no—
102C2×C5×C4⋊C4C2×D311yescharacteristic
103C4×C22⋊D5—22no—
104#4072C2×D311yescharacteristic
105C2×C4⋊Dic5—31no—
106C22×#168—31no—
107#4039C2×D312yes—
108#4038—21no—
109D5×C4⋊C4—21no—
110#4036—32no—
111#4034—32no—
112#4033C2×D312yes—
113#4024—62no—
114#4016—61no—
115#4015—61no—
116C5×#107—32no—
117C5×#106—32no—
118#3953—32no—
119#3948—32no—
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×C5—22no—
132C2×C3×C4×C5—81no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×Q812yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138C2×Dic15—81no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C3×C22⋊D5—24no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×D20—21no—
146C3×D20C2×Q812yes—
147C3×C4×D5—24no—
148C3×C4×D5—82no—
149C3×Dic10—21no—
150C3×Dic10C2×Q812yes—
151#1204—82no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C5×C3⋊C8—22no—
155C2×C3×#41—51no—
156C3×C4×Q8—52no—
157C3×C4×D4—52no—
158C3×C4×D4—102no—
159C3×#117—51no—
160C3×#117—101no—
161C2×C3×C4⋊C4—101no—
162C2×C3×C4⋊C4C2×D511yescharacteristic
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3—51no—
165C2×#208C2×D511yescharacteristic
166C22×C3⋊C8—51no—
167#890—101no—
168#888—101no—
169#878—102no—
170#870—52no—
171#869—52no—
172#835—51no—
173#835—51no—
174#835—52no—
175#832—51no—
176#832—51no—
177#832—52no—
178#808—52no—
179#808—52no—
180#808C2×D512yes—
181#807C2×D512yes—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)—52no—
184C22×C4×C5—21no—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—21no—
187C22×Dic5—61no—
188#709—22no—
189#709Dic614yescomplemented
190C2×D20C22×D311yescharacteristic
191C2×C4×D5—21no—
192C2×C4×D5—22no—
193C2×Dic10—62no—
194C2×Dic10C22×D311yescharacteristic
195C5×M16—62no—
196C2×C5×C8—32no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—31no—
200C5×C4⋊C4C22×D312yes—
201C5×C22⋊C4—61no—
202C42×C5—61no—
203C22⋊Dic5#6712yes—
204#685—22no—
205C4⋊Dic5—32no—
206C4⋊Dic5—61no—
207C4⋊Dic5—62no—
208C4⋊Dic5#6711yescharacteristic
209C4⋊Dic5#6711yescharacteristic
210#683—22no—
211#683—62no—
212#683—62no—
213C4×Dic5—22no—
214C4×Dic5C22×D312yes—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#520—51no—
220#479—152no—
221#478—152no—
222#476—152no—
223#475—152no—
224#428—31no—
225C2×#106—151no—
226#424—151no—
227#417—151no—
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×C5—42no—
237C3×C4×C5C22⋊Q812yes—
238C3×C4×C5C22×Q811yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—42no—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—22no—
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—21no—
252C22×C3×C4—102no—
253C22×C3×C4—101no—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—101no—
256C2×Dic6—102no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—51no—
259C3×C4⋊C4—51no—
260C3×C4⋊C4—102no—
261C3×C4⋊C4C22×D512yes—
262C3×C22⋊C4—52no—
263C3×C22⋊C4—102no—
264C3×C42—52no—
265C3×C42—102no—
266#217—21no—
267C4⋊Dic3—52no—
268C4⋊Dic3—102no—
269C4⋊Dic3—101no—
270C4⋊Dic3C22×D511yescharacteristic
271C4⋊Dic3C22×D511yescharacteristic
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275#208—22no—
276C2×C3⋊C8—51no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—102no—
279C2×C3⋊C8C22×D512yes—
280C23×C5C2×#6711yescharacteristic
281C22×D5—21no—
282C2×C4×C5—22no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—81no—
286C2×C4×C5C2×Dic612yes—
287C2×C4×C5#23512yes—
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C23×D311yescharacteristic
290C22⋊D5—24no—
291C2×Dic5—21no—
292C2×Dic5—62no—
293C2×Dic5—241no—
294C2×Dic5C2×#6712yes—
295C2×Dic5C2×#6712yes—
296D20—21no—
297D20C2×Dic612yes—
298C4×D5—24no—
299C4×D5—82no—
300Dic10—21no—
301Dic10—242no—
302Dic10C2×Dic612yes—
303C5×C8—62no—
304#168—61no—
305#168—61no—
306C2×#41—51no—
307C2×M16—31no—
308C22×C8—151no—
309C4⋊Q8—152no—
310C4⋊Q8—301no—
311#125—152no—
312#125—301no—
313C22⋊Q8—302no—
314C4×Q8—52no—
315C4×D4—52no—
316C4×D4—102no—
317#117—31no—
318#117—51no—
319#117—101no—
320C2×C4⋊C4—101no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4D3×D511yescharacteristic
323#107—32no—
324#106—32no—
325#106—152no—
326#106—152no—
327C4⋊C8—152no—
328C4⋊C8—152no—
329#103—151no—
330#103—151no—
331#103—152no—
332#102—151no—
333#102—151no—
334#102—152no—
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—22no—
348C2×C3×C4—52no—
349C2×C3×C4—52no—
350C2×C3×C4—81no—
351C2×C3×C4—101no—
352C2×C3×C4—104no—
353C2×C3×C4—402no—
354C2×C3×C4#70912yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4Q8×D512yes—
357C2×C3×C4C23×D511yescharacteristic
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—102no—
361C2×Dic3—401no—
362Dic6—402no—
363C3⋊C8—22no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#92412yes—
369C22×C5C22×#6711yescharacteristic
370C2×D5—22no—
371C2×D5—41no—
372C2×D5—41no—
373C4×C5—42no—
374C4×C5—121no—
375C4×C5—121no—
376C4×C5#92412yes—
377C4×C5C22×Dic611yescharacteristic
378C4×C5C2×#23511yescharacteristic
379Dic5—22no—
380Dic5—22no—
381Dic5—22no—
382Dic5—122no—
383#41—54no—
384#41—102no—
385C2×Q8—51no—
386C2×Q8—302no—
387C2×D4—51no—
388C2×D4—101no—
389C22×C4—21no—
390C22×C4—102no—
391C22×C4—101no—
392C22×C4—301no—
393C22×C4C2×D3×D511yescharacteristic
394M16—62no—
395C2×C8—32no—
396C2×C8—151no—
397C2×C8—151no—
398C2×C8—302no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—51no—
403C4⋊C4—51no—
404C4⋊C4—102no—
405C4⋊C4—152no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—301no—
410C4⋊C4C2×D3×D512yes—
411C22⋊C4—52no—
412C22⋊C4—61no—
413C22⋊C4—102no—
414C42—52no—
415C42—61no—
416C42—102no—
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—42no—
426C3×C4—102no—
427C3×C4—102no—
428C3×C4—102no—
429C3×C4#404212yes—
430C3×C4C2×#70911yescharacteristic
431C3×C4C2×Q8×D511yescharacteristic
432Dic3—41no—
433Dic3—41no—
434Dic3—202no—
435C2×C5—22no—
436C2×C5C2×#92411yescharacteristic
437C2×C5#583611yescharacteristic
438C2×C5#583711yescharacteristic
439D5—42no—
440C23—101no—
441C23D5×#6711yescharacteristic
442Q8—52no—
443Q8—101no—
444Q8—1202no—
445D4—52no—
446D4—104no—
447D4—101no—
448C2×C4—22no—
449C2×C4—52no—
450C2×C4—52no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—81no—
454C2×C4—101no—
455C2×C4—104no—
456C2×C4—302no—
457C2×C4—402no—
458C2×C4—1201no—
459C2×C4D5×Dic612yes—
460C2×C4#677112yes—
461C2×C4D5×#6711yescharacteristic
462C2×C4C22×D3×D511yescharacteristic
463C8—62no—
464C8—301no—
465C8—301no—
466C2×C3—22no—
467C2×C3—202no—
468C2×C3C2×#404211yescharacteristic
469C2×C3#6610911yescharacteristic
470C2×C3#6611211yescharacteristic
471C5#8256011yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—102no—
475C22—201no—
476C22—201no—
477C22#9134912yes—
478C22C2×D5×#6711yescharacteristic
479C4—42no—
480C4—102no—
481C4—102no—
482C4—102no—
483C4—121no—
484C4—121no—
485C4—602no—
486C4#9134912yes—
487C4C2×D5×Dic611yescharacteristic
488C4C2×#677111yescharacteristic
489C3#1061097511yescharacteristic, complemented, Sylow
490C2—22no—
491C2—202no—
492C2C2×#9134911yescharacteristic
493C2#1175470811yescharacteristic
494C2#1175508611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754620C2semidirect
3. C2×#91092C2semidirect
4. C5×#4964C2semidirect
5. #11748433C2semidirect
8. #11747415C2semidirect
9. #11747411C2semidirect
10. #11747391C2semidirect
11. #11747389C2semidirect
59. C3×#709Q8semidirect
97. #4964D5semidirect
189. #709Dic6semidirect
417. C3×C5#3084semidirect
471. C5#82560semidirect
489. C3#10610975semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
#117546202
C2×#910922
C5×#49642
#117484332
#117483692
#117483642
#117474152
#117474112
#117473912
#117473892
#106109753
#825605