Finite Group Databasebeta

← #14431342

Subgroups — #14431342

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#11756263C211yesmaximal, characteristic
2#11754618C211yesmaximal, characteristic, complemented
3C5×#4964C211yesmaximal, characteristic, complemented
4C2×C3×#3940C211yesmaximal, characteristic, complemented
5#11748435C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic
7#11748393C211yesmaximal, characteristic
8#11747187C212yesmaximal, complemented
9#11747185C212yesmaximal, complemented
10#11747183C212yesmaximal, complemented
11#11747181C212yesmaximal, complemented
12#10610975—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C4×#1220—22no—
16#91815C2211yescharacteristic
17#91782C2212yes—
18#91781—21no—
19C4⋊C4×D15—21no—
20#91776C2212yes—
21C5×#926C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91574—22no—
26#91470C2212yes—
27#91469—21no—
28#91384C2212yes—
29#91381—21no—
30C5×#808C2212yes—
31C5×#807C2212yes—
32C3×#3940C2212yes—
33C3×#3940C2212yes—
34#90983C2212yes—
35#90983C2212yes—
36#90975C2211yescharacteristic
37#90975C2211yescharacteristic
38#90974C2212yes—
39#90969C2211yescharacteristic
40#90969C2211yescharacteristic
41#90968C2212yes—
42#79130—51nomaximal, Hall
43#65853—31no—
44#65838—31no—
45C5×#428—31no—
46#65422—31no—
47#65408—31no—
48#65291—31no—
49C2×#3940D311yescharacteristic, complemented
50#65180—32no—
51#65166—32no—
52#65159—32no—
53#65143—32no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817Q814yescomplemented
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30C2311yescharacteristic
63C22×C3×Dic5—21no—
64C2×#1204—22no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2312yes—
67#6719D412yes—
68#6714—22no—
69C4⋊Dic15D411yescharacteristic
70C4⋊Dic15D411yescharacteristic
71#6712—22no—
72C4×Dic15—22no—
73C4×Dic15C2312yes—
74C5×#217—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C4×C5×Dic3—21no—
78C5×#208—22no—
79C2×C5×C3⋊C8C2312yes—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C2×C3×#168—22no—
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6668—22no—
88#5504—51no—
89#5500—51no—
90C2×C3×#106—51no—
91#5113—51no—
92#5102—51no—
93#4966—51no—
94#4964D511yescharacteristic, complemented
95#4871—52no—
96#4870—52no—
97#4857—52no—
98#4854—52no—
99C2×#709—31no—
100C2×C5×M16—31no—
101C5×#117—31no—
102C2×C5×C4⋊C4C2×D311yescharacteristic
103C4×C22⋊D5—62no—
104#4072—31no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106C22×#168C2×D311yescharacteristic
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#3953—32no—
119#3948—32no—
120#3946—32no—
121#3946—32no—
122#3942—31no—
123#3942—31no—
124#3941—31no—
125#3941—31no—
126#3940C2×D312yes—
127#3940C2×D312yes—
128#3084—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×D15—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
137#1220—24no—
138C2×Dic15—21no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141D60—21no—
142D60C2×Q812yes—
143C4×D15—24no—
144C4×D15—82no—
145Dic30—21no—
146Dic30C2×Q812yes—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—81no—
151#1204—82no—
152C3×#168—21no—
153C3×#168—21no—
154C5×C3⋊C8—22no—
155C2×#235—51no—
156C22×C3×C8—51no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4C2×D511yescharacteristic
159C4×#67—102no—
160#926—51no—
161#926C2×D511yescharacteristic
162#924—102no—
163C2×#208C2×D511yescharacteristic
164#893—52no—
165#892—101no—
166D3×C4⋊C4—101no—
167#890—52no—
168#890—101no—
169#888—52no—
170#888—101no—
171#887—52no—
172C3×#106—52no—
173C3×#106—52no—
174#821—51no—
175#821—51no—
176#816—51no—
177#816—51no—
178Dic3⋊C8—52no—
179Dic3⋊C8—52no—
180#810—52no—
181#809—52no—
182#808C2×D512yes—
183#807C2×D512yes—
184C22×C4×C5—21no—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—61no—
187C22×Dic5—21no—
188#709—34no—
189#709—62no—
190C2×D20—31no—
191C2×C4×D5—61no—
192C2×C4×D5—62no—
193C2×Dic10—31no—
194C2×Dic10—62no—
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—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—22no—
216C2×#168C22×D311yescharacteristic
217C2×#168C22×D311yescharacteristic
218#544—151no—
219#520—151no—
220#479—152no—
221#478—152no—
222#476—152no—
223#475—152no—
224#428—31no—
225C2×#106—51no—
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×D15—22no—
234C2×D15—41no—
235C2×D15—41no—
236C3×C4×C5—42no—
237C3×C4×C5C22⋊Q812yes—
238C3×C4×C5C22×Q811yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—22no—
243C3×Dic5—42no—
244C5×Dic3—41no—
245C5×Dic3—41no—
246C22×C3×C4—21no—
247C22×C3×C4—101no—
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—101no—
250#235—54no—
251#235—102no—
252C2×D12—51no—
253C2×C4×D3—101no—
254C2×C4×D3—102no—
255C2×Dic6—51no—
256C2×Dic6—102no—
257C2×C3×C8—51no—
258C2×C3×C8—51no—
259C2×C3×C8—102no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4C22×D512yes—
264#217—21no—
265#217—52no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—51no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D511yescharacteristic
271C4⋊Dic3C22×D511yescharacteristic
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—21no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278#208—22no—
279C2×C3⋊C8C22×D512yes—
280C23×C5D3×D411yescharacteristic
281C22×D5—61no—
282C2×C4×C5—22no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—81no—
286C2×C4×C5#23512yes—
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×Q812yes—
289C2×C4×C5C23×D311yescharacteristic
290C22⋊D5—64no—
291C2×Dic5—22no—
292C2×Dic5—32no—
293C2×Dic5—32no—
294C2×Dic5—61no—
295C2×Dic5—81no—
296D20—32no—
297D20—61no—
298C4×D5—64no—
299C4×D5—242no—
300Dic10—32no—
301Dic10—61no—
302Dic10—242no—
303C5×C8—62no—
304#168—21no—
305#168—21no—
306C2×#41—151no—
307C2×M16—31no—
308C22×C8—51no—
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—51no—
321C2×C4⋊C4—301no—
322C2×C4⋊C4D3×D511yescharacteristic
323#107—32no—
324#106—32no—
325#106—52no—
326#106—52no—
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
339D15—42no—
340C23×C3D4×D511yescharacteristic
341C22×D3—101no—
342C2×C3×C4—22no—
343C2×C3×C4—81no—
344C2×C3×C4—102no—
345C2×C3×C4—401no—
346C2×C3×C4#70912yes—
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4Q8×D512yes—
349C2×C3×C4C23×D511yescharacteristic
350#67—104no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—52no—
354C2×Dic3—52no—
355C2×Dic3—101no—
356D12—52no—
357D12—101no—
358C4×D3—104no—
359C4×D3—402no—
360Dic6—52no—
361Dic6—101no—
362Dic6—402no—
363C3×C8—101no—
364C3×C8—101no—
365C3⋊C8—22no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#89612yes—
369C22×C5C2×D3×D411yescharacteristic
370C2×D5—62no—
371C2×D5—121no—
372C2×D5—121no—
373C4×C5—42no—
374C4×C5—121no—
375C4×C5—121no—
376C4×C5#89612yes—
377C4×C5C2×#23511yescharacteristic
378C4×C5C2×D3×Q811yescharacteristic
379Dic5—42no—
380Dic5—62no—
381Dic5—62no—
382Dic5—62no—
383#41—154no—
384#41—302no—
385C2×Q8—151no—
386C2×Q8—302no—
387C2×D4—151no—
388C2×D4—301no—
389C22×C4—21no—
390C22×C4—101no—
391C22×C4—302no—
392C22×C4—301no—
393C22×C4C2×D3×D511yescharacteristic
394M16—62no—
395C2×C8—32no—
396C2×C8—51no—
397C2×C8—51no—
398C2×C8—102no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—52no—
403C4⋊C4—101no—
404C4⋊C4—151no—
405C4⋊C4—151no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4C2×D3×D512yes—
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#404212yes—
421C22×C3C2×D4×D511yescharacteristic
422C2×D3—102no—
423C2×D3—201no—
424C2×D3—201no—
425C3×C4—42no—
426C3×C4—202no—
427C3×C4#404212yes—
428C3×C4C2×#70911yescharacteristic
429C3×C4C2×Q8×D511yescharacteristic
430Dic3—41no—
431Dic3—41no—
432Dic3—102no—
433Dic3—102no—
434Dic3—102no—
435C2×C5—22no—
436C2×C5C2×#89611yescharacteristic
437C2×C5#576211yescharacteristic
438C2×C5#576211yescharacteristic
439D5—122no—
440C23—301no—
441C23#679011yescharacteristic
442Q8—152no—
443Q8—301no—
444Q8—1202no—
445D4—152no—
446D4—304no—
447D4—301no—
448C2×C4—22no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—81no—
452C2×C4—102no—
453C2×C4—152no—
454C2×C4—152no—
455C2×C4—301no—
456C2×C4—304no—
457C2×C4—401no—
458C2×C4—1202no—
459C2×C4D15⋊Q812yes—
460C2×C4#677112yes—
461C2×C4#679011yescharacteristic
462C2×C4C22×D3×D511yescharacteristic
463C8—62no—
464C8—101no—
465C8—101no—
466C2×C3—22no—
467C2×C3C2×#404211yescharacteristic
468C2×C3#6610911yescharacteristic
469C2×C3#6611211yescharacteristic
470D3—202no—
471C5#7913011yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—302no—
475C22—601no—
476C22—601no—
477C22#9137712yes—
478C22C2×#679011yescharacteristic
479C4—42no—
480C4—121no—
481C4—121no—
482C4—202no—
483C4—302no—
484C4—302no—
485C4—302no—
486C4#9137712yes—
487C4C2×D15⋊Q811yescharacteristic
488C4C2×#677111yescharacteristic
489C3#1061097511yescharacteristic, complemented, Sylow
490C2—22no—
491C2—602no—
492C2C2×#9137711yescharacteristic
493C2#1175472811yescharacteristic
494C2#1175509711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
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. #11754618C2semidirect
3. C5×#4964C2semidirect
4. C2×C3×#3940C2semidirect
5. #11748435C2semidirect
8. #11747187C2semidirect
9. #11747185C2semidirect
10. #11747183C2semidirect
11. #11747181C2semidirect
49. C2×#3940D3semidirect
58. #6817Q8semidirect
94. #4964D5semidirect
417. C3×C5#3084semidirect
471. C5#79130semidirect
489. C3#10610975semidirect

Maximal subgroups

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

subgroupindex
#117562632
#117546182
C5×#49642
C2×C3×#39402
#117484352
#117484132
#117483932
#117471872
#117471852
#117471832
#117471812
#106109753
#791305