Finite Group Databasebeta

← #14431351

Subgroups — #14431351

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#11754620C211yesmaximal, characteristic, complemented
2#11754506C211yesmaximal, characteristic
3#11751234C211yesmaximal, characteristic
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65408C211yesmaximal, characteristic, complemented
6C2×#90985C211yesmaximal, characteristic, complemented
7#11748393C211yesmaximal, characteristic
8#11747858C212yesmaximal, complemented
9#11747844C212yesmaximal, complemented
10#11747780C212yesmaximal, complemented
11#11747762C212yesmaximal, complemented
12#10610975—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C5×#926C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20#91576—22no—
21#91556—22no—
22#91469—21no—
23#91468C2212yes—
24#91437—21no—
25#91418C2212yes—
26#91388C2212yes—
27#91381—21no—
28#91347—21no—
29#91333C2212yes—
30#91105C2212yes—
31#91100C2212yes—
32C5×#818C2212yes—
33C5×#817C2212yes—
34C3×#3946C2212yes—
35C3×#3946C2212yes—
36#90985C2212yes—
37#90985C2212yes—
38#90975C2211yescharacteristic
39#90975C2211yescharacteristic
40#90969C2211yescharacteristic
41#90969C2211yescharacteristic
42#79092—51nomaximal, Hall
43#65853—31no—
44#65838—31no—
45C5×#428—31no—
46#65422—31no—
47#65408D311yescharacteristic, complemented
48#65291—31no—
49C2×#3940—31no—
50#65180—32no—
51#65166—32no—
52#65159—32no—
53#65143—32no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—21no—
56C22×Dic15—21no—
57#6817—22no—
58#6817Q814yescomplemented
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C22×C5×Dic3—21no—
63C2×#1204—22no—
64C2×#1200—22no—
65C3×C5×M16—22no—
66C2×C3×C5×C8C2312yes—
67C4⋊Dic15—21no—
68C4⋊Dic15C2312yes—
69C5×#217—21no—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3C2312yes—
72C5×C4⋊Dic3C2311yescharacteristic
73C5×C4⋊Dic3C2311yescharacteristic
74C4×C5×Dic3—21no—
75C3×C22⋊Dic5D412yes—
76C3×C4⋊Dic5D411yescharacteristic
77C3×C4⋊Dic5D411yescharacteristic
78C3×C4×Dic5C2312yes—
79C2×C3×#168—22no—
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6669—22no—
85#6668—22no—
86#6667—22no—
87Dic3×Dic5—22no—
88#5523—51no—
89#5519—51no—
90C3×#424—51no—
91#5133—51no—
92#5121D511yescharacteristic, complemented
93#5113—51no—
94C2×#817—51no—
95#4851—52no—
96#4847—52no—
97#4842—52no—
98#4829—52no—
99C2×#709—31no—
100C2×C5×M16C2×D311yescharacteristic
101C5×#117—31no—
102C2×C5×C4⋊C4—31no—
103C4×C22⋊D5—62no—
104#4072C2×D311yescharacteristic
105C2×C4⋊Dic5—31no—
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#3946C2×D312yes—
121#3946C2×D312yes—
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×D15—21no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×Q812yes—
133C2×C3×C4×C5#4112yes—
134C2×C3×C4×C5C2411yescharacteristic
135#1220—24no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—81no—
139D60—21no—
140D60C2×Q812yes—
141C4×D15—24no—
142Dic30—21no—
143Dic30C2×Q812yes—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—81no—
148C2×C3×Dic5C2×D412yes—
149C2×C3×Dic5C2×D412yes—
150#1204—82no—
151#1200—82no—
152C3×C5×C8—22no—
153C3×#168—21no—
154C3×#168—21no—
155C2×#235—51no—
156C2×C3×M16C2×D511yescharacteristic
157C22×C3×C8—51no—
158C3×#117—51no—
159#926C2×D511yescharacteristic
160C2×C4⋊Dic3—51no—
161C2×C4⋊Dic3C2×D511yescharacteristic
162#892—101no—
163D3×C4⋊C4—101no—
164#890—101no—
165#888—101no—
166#67⋊C4—102no—
167#878—102no—
168C4×D12—52no—
169#870—52no—
170#869—52no—
171C4×Dic6—52no—
172C3×C4⋊C8—52no—
173C3×C4⋊C8—52no—
174#821—52no—
175#821—51no—
176#821—51no—
177#818C2×D512yes—
178#817—52no—
179#817—52no—
180#817C2×D512yes—
181#816—52no—
182#816—51no—
183#816—51no—
184C22×C4×C5—61no—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—61no—
187C22×Dic5—61no—
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—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⋊Dic5D1212yes—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5—61no—
207C4⋊Dic5—62no—
208C4⋊Dic5D1211yescharacteristic
209C4⋊Dic5D1211yescharacteristic
210#683—62no—
211#683—62no—
212#683—62no—
213C4×Dic5—62no—
214C4×Dic5C22×D312yes—
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—151no—
226#424—51no—
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×C5C22⋊Q812yes—
237C3×C4×C5C22×Q811yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—22no—
240Dic15—42no—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C5×Dic3—42no—
244C5×Dic3—41no—
245C5×Dic3—41no—
246C22×C3×C4C22×D511yescharacteristic
247C2×#67—101no—
248C22×Dic3—21no—
249C22×Dic3—101no—
250#235—54no—
251#235—102no—
252C2×D12—51no—
253C2×C4×D3—101no—
254C2×C4×D3—102no—
255C2×Dic6—51no—
256C2×Dic6—102no—
257C3×M16—22no—
258C2×C3×C8—51no—
259C2×C3×C8—51no—
260C2×C3×C8—102no—
261C2×C3×C8C22×D512yes—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—51no—
264C3×C22⋊C4—52no—
265C3×C42—52no—
266#217—21no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—21no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271C4⋊Dic3—101no—
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D511yescharacteristic
274C4⋊Dic3C22×D512yes—
275Dic3⋊C4—102no—
276Dic3⋊C4—102no—
277Dic3⋊C4—102no—
278C4×Dic3—21no—
279C4×Dic3—102no—
280C23×C5C2×D1211yescharacteristic
281C22×D5—61no—
282C2×C4×C5—62no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—241no—
286C2×C4×C5C2×D1211yescharacteristic
287C2×C4×C5#23712yes—
288C2×C4×C5D3×Q812yes—
289C2×C4×C5C23×D311yescharacteristic
290C22⋊D5—64no—
291C2×Dic5—61no—
292C2×Dic5—62no—
293C2×Dic5—241no—
294C2×Dic5C2×D1212yes—
295C2×Dic5C2×D1212yes—
296D20—32no—
297D20—61no—
298C4×D5—64no—
299C4×D5—242no—
300Dic10—32no—
301Dic10—61no—
302Dic10—242no—
303C5×C8—22no—
304#168—21no—
305#168—21no—
306C2×#41—151no—
307C2×M16D3×D511yescharacteristic
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—51no—
319#117—301no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4—301no—
323#107—32no—
324#106—32no—
325#106—152no—
326#106—152no—
327C4⋊C8—52no—
328C4⋊C8—52no—
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—52no—
343C2×C3×C4—52no—
344C2×C3×C4#70912yes—
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4Q8×D512yes—
347C2×C3×C4C23×D511yescharacteristic
348#67—104no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—81no—
353C2×Dic3—101no—
354C2×Dic3—102no—
355C2×Dic3—401no—
356D12—52no—
357D12—101no—
358C4×D3—104no—
359C4×D3—402no—
360Dic6—52no—
361Dic6—101no—
362Dic6—402no—
363C3×C8—22no—
364C3×C8—101no—
365C3×C8—101no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#89712yes—
369C22×C5C22×D1211yescharacteristic
370C2×D5—62no—
371C2×D5—121no—
372C2×D5—121no—
373C4×C5—121no—
374C4×C5—122no—
375C4×C5—121no—
376C4×C5#89712yes—
377C4×C5C2×#23711yescharacteristic
378C4×C5C2×D3×Q811yescharacteristic
379Dic5—22no—
380Dic5—22no—
381Dic5—62no—
382Dic5—122no—
383#41—154no—
384#41—302no—
385C2×Q8—151no—
386C2×Q8—302no—
387C2×D4—151no—
388C2×D4—301no—
389C22×C4—61no—
390C22×C4—302no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4C2×D3×D511yescharacteristic
394M16—22no—
395C2×C8—51no—
396C2×C8—51no—
397C2×C8—102no—
398C2×C8C2×D3×D512yes—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—51no—
403C4⋊C4—51no—
404C4⋊C4—61no—
405C4⋊C4—152no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—301no—
411C22⋊C4—52no—
412C22⋊C4—61no—
413C22⋊C4—302no—
414C42—52no—
415C42—61no—
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—102no—
426C3×C4—102no—
427C3×C4#404212yes—
428C3×C4C2×#70911yescharacteristic
429C3×C4C2×Q8×D511yescharacteristic
430Dic3—42no—
431Dic3—41no—
432Dic3—41no—
433Dic3—102no—
434Dic3—202no—
435C2×C5—22no—
436C2×C5C2×#89711yescharacteristic
437C2×C5#575111yescharacteristic
438C2×C5#575111yescharacteristic
439D5—122no—
440C23—301no—
441C23D5×D1211yescharacteristic
442Q8—152no—
443Q8—301no—
444Q8—1202no—
445D4—152no—
446D4—304no—
447D4—301no—
448C2×C4—52no—
449C2×C4—52no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—62no—
453C2×C4—241no—
454C2×C4—301no—
455C2×C4—304no—
456C2×C4—302no—
457C2×C4—1202no—
458C2×C4—1201no—
459C2×C4D15⋊Q812yes—
460C2×C4D5×D1211yescharacteristic
461C2×C4#677912yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—22no—
464C8—101no—
465C8—101no—
466C2×C3—22no—
467C2×C3C2×#404211yescharacteristic
468C2×C3#6610911yescharacteristic
469C2×C3#6611211yescharacteristic
470D3—202no—
471C5#7909211yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—302no—
475C22—601no—
476C22—601no—
477C22#9141912yes—
478C22C2×D5×D1211yescharacteristic
479C4—102no—
480C4—102no—
481C4—122no—
482C4—121no—
483C4—121no—
484C4—302no—
485C4—602no—
486C4#9141912yes—
487C4C2×D15⋊Q811yescharacteristic
488C4C2×#677911yescharacteristic
489C3#1061097511yescharacteristic, complemented, Sylow
490C2—22no—
491C2—602no—
492C2#1175402311yescharacteristic
493C2#1175402511yescharacteristic
494C2C2×#9141911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
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. #11754620C2semidirect
4. C5×#5121C2semidirect
5. C3×#65408C2semidirect
6. C2×#90985C2semidirect
8. #11747858C2semidirect
9. #11747844C2semidirect
10. #11747780C2semidirect
11. #11747762C2semidirect
47. #65408D3semidirect
58. #6817Q8semidirect
92. #5121D5semidirect
417. C3×C5#3084semidirect
471. C5#79092semidirect
489. C3#10610975semidirect

Maximal subgroups

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

subgroupindex
#117546202
#117545062
#117512342
C5×#51212
C3×#654082
C2×#909852
#117483932
#117478582
#117478442
#117477802
#117477622
#106109753
#790925