Finite Group Databasebeta

← #14301358

Subgroups — #14301358

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic
2#11754506C211yesmaximal, characteristic, complemented
3#11748768C211yesmaximal, characteristic, complemented
4C2×#90981C211yesmaximal, characteristic, complemented
5#11748392C211yesmaximal, characteristic, complemented
6C5×#4554C211yesmaximal, characteristic, complemented
7C3×#64775C211yesmaximal, characteristic, complemented
8#10599798—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91797—22no—
13#91797C414yescomplemented
14C2×D120—21no—
15C2×#6706—21no—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20#91556—22no—
21C2×#6667—22no—
22#91437—21no—
23#91418—21no—
24#91347—21no—
25#91333—21no—
26#90981—22no—
27#90968—21no—
28#90968—21no—
29#68776—51nomaximal, Hall
30C2×#4054—31no—
31#65838—31no—
32C2×#3957—31no—
33#65420—31no—
34#65277—31no—
35C5×#343—31no—
36#64775D311yescharacteristic, complemented
37C23×D15—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40#6817—21no—
41#6817—21no—
42#6817C2×C412yes—
43#6817D412yes—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60—21no—
49C2×D60C2×C412yescomplemented
50C2×D60D411yescharacteristic
51C2×C4×D15—21no—
52C2×Dic30D411yescharacteristic
53C22×C5×Dic3D412yes—
54C22×C3×Dic5—21no—
55C2×#1200—22no—
56C3×C5×M16—21no—
57C3×C5×M16C2×C412yescomplemented
58C2×C3×C5×C8—21no—
59D120—24no—
60#6706—24no—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3—21no—
63C5×#208—21no—
64C5×#208—21no—
65C2×C5×C3⋊C8—21no—
66C3×C22⋊Dic5—21no—
67C3×C4⋊Dic5D411yescharacteristic
68C3×C4⋊Dic5D411yescharacteristic
69C3×C4×Dic5—21no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5—21no—
72#6669—22no—
73#6667—22no—
74#6667—44no—
75Dic3×Dic5—22no—
76C2×#908—51no—
77#5523—51no—
78#5001—51no—
79#4939—51no—
80C2×#805—51no—
81C3×#339—51no—
82#4554D511yescharacteristic, complemented
83C2×#709—31no—
84C22×D20—31no—
85C2×C5×M16—31no—
86C2×C5×M16C2×D311yescharacteristic
87C2×C5×C4⋊C4—31no—
88C4×C22⋊D5—62no—
89C2×#685—62no—
90#4072C2×D311yescharacteristic
91C2×C4×Dic5C2×D311yescharacteristic
92#4054—34no—
93#4054—62no—
94C2×D40—61no—
95C2×#677—61no—
96#4039—61no—
97#4038—61no—
98D5×C4⋊C4—61no—
99#4033—61no—
100#3957—62no—
101#3953—61no—
102#3953—61no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×D15—21no—
106C22×D15—22no—
107C22×D15—42no—
108C22×D15—42no—
109C22×D15—41no—
110C22×D15—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117#1220—22no—
118#1220—22no—
119C2×Dic15—21no—
120D60—22no—
121D60—22no—
122D60—21no—
123D60—41no—
124D60—41no—
125D60C22⋊C412yescomplemented
126C4×D15—22no—
127C4×D15—22no—
128Dic30—21no—
129Dic30C22⋊C412yescomplemented
130C2×C5×Dic3—22no—
131C2×C5×Dic3—42no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137#1200—82no—
138C3×C5×C8—22no—
139C5×C3⋊C8—41no—
140C2×#235—51no—
141C22×D12—51no—
142C2×C3×M16C2×D511yescharacteristic
143C3×#117—51no—
144C2×C3×C42—51no—
145C2×(C2×D3)⋊C4—102no—
146C2×C4⋊Dic3C2×D511yescharacteristic
147C2×#208C2×D511yescharacteristic
148#908—54no—
149#908—102no—
150C2×D24—101no—
151C2×#204—101no—
152#892—101no—
153D3×C4⋊C4—101no—
154#67⋊C4—102no—
155C4×D12—101no—
156C4×Dic6—101no—
157#809—101no—
158#809—101no—
159#805—102no—
160C23×D5—61no—
161C22×C4×C5—32no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C22×Dic5—21no—
165#709—32no—
166#709—32no—
167#709—61no—
168#709—61no—
169C2×D20—31no—
170C2×D20—32no—
171C2×D20—61no—
172C2×D20—61no—
173C2×D20—61no—
174C2×D20—61no—
175C2×D20—61no—
176C2×C4×D5—61no—
177C2×C4×D5—62no—
178C2×Dic10—31no—
179C5×M16—21no—
180C5×M16—61no—
181C5×M16—61no—
182C5×M16C4×D312yescomplemented
183C2×C5×C8—21no—
184C2×C5×C8—61no—
185C5×C4⋊C4—61no—
186C5×C4⋊C4—61no—
187C22⋊Dic5—21no—
188#685—62no—
189#685—124no—
190C4⋊Dic5D1211yescharacteristic
191C4⋊Dic5D1211yescharacteristic
192#683—62no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—62no—
197D40—64no—
198#677—64no—
199C2×AGL(1,ℤ/8)—151no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—151no—
204#343—31no—
205#339—51no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×D15—22no—
212C2×D15—41no—
213C2×D15—41no—
214C2×D15—44no—
215C2×D15—42no—
216C2×D15—82no—
217C2×D15—81no—
218C2×D15—81no—
219C3×C4×C5C2×C22⋊C411yescharacteristic
220C3×C4×C5C4×D411yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5#12311yescharacteristic
223Dic15—22no—
224C3×Dic5—42no—
225C3×Dic5—41no—
226C3×Dic5—41no—
227C5×Dic3—42no—
228C23×D3—101no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C22×Dic3D2012yes—
233#235—52no—
234#235—52no—
235#235—101no—
236#235—101no—
237C2×D12—51no—
238C2×D12—52no—
239C2×D12—101no—
240C2×D12—101no—
241C2×D12—101no—
242C2×D12—101no—
243C2×D12—101no—
244C2×C4×D3—101no—
245C2×C4×D3—102no—
246C2×Dic6—51no—
247C3×M16—21no—
248C3×M16C4×D512yescomplemented
249C2×C3×C8—21no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—51no—
252C3×C22⋊C4—101no—
253C3×C42—101no—
254C3×C42—101no—
255C3×C42—101no—
256(C2×D3)⋊C4—102no—
257(C2×D3)⋊C4—204no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260Dic3⋊C4—102no—
261C4×Dic3—102no—
262#208—21no—
263#208—21no—
264C2×C3⋊C8—21no—
265D24—104no—
266#204—104no—
267C23×C5D3×D411yescharacteristic
268C22×D5—61no—
269C22×D5—62no—
270C22×D5—122no—
271C22×D5—122no—
272C22×D5—121no—
273C22×D5—121no—
274C2×C4×C5—62no—
275C2×C4×C5—122no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5#23511yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23911yescharacteristic
282C22⋊D5—62no—
283C22⋊D5—62no—
284C2×Dic5—22no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—41no—
288C2×Dic5—41no—
289C2×Dic5—61no—
290D20—32no—
291D20—62no—
292D20—62no—
293D20—61no—
294D20—121no—
295D20—121no—
296C4×D5—62no—
297C4×D5—62no—
298C4×D5—242no—
299Dic10—32no—
300Dic10—61no—
301C5×C8—22no—
302C5×C8—121no—
303C2×#41—151no—
304C22×D4—151no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—31no—
310C2×M16D3×D511yescharacteristic
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—51no—
315#117—301no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42—51no—
320#104—302no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#38611yescharacteristic
326C2×C3×C5#45311yescharacteristic
327C2×C3×C5#45411yescharacteristic
328D15—42no—
329D15—82no—
330C23×C3C2×D2011yescharacteristic
331C22×D3—101no—
332C22×D3—102no—
333C22×D3—202no—
334C22×D3—202no—
335C22×D3—201no—
336C22×D3—201no—
337C2×C3×C4—102no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4C2×C4×D511yescharacteristic
343C2×C3×C4#70911yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4#71311yescharacteristic
348#67—102no—
349#67—102no—
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—101no—
353D12—52no—
354D12—102no—
355D12—102no—
356D12—101no—
357D12—201no—
358D12—201no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—402no—
362Dic6—52no—
363Dic6—101no—
364C3×C8—22no—
365C3⋊C8—41no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#88211yescharacteristic
369C22×C5#88411yescharacteristic
370C22×C5#89311yescharacteristic
371C2×D5—62no—
372C2×D5—121no—
373C2×D5—121no—
374C2×D5—124no—
375C2×D5—122no—
376C2×D5—242no—
377C2×D5—241no—
378C2×D5—241no—
379C4×C5—122no—
380C4×C5C4×D1211yescharacteristic
381C4×C5D3×C22⋊C411yescharacteristic
382C4×C5#89411yescharacteristic
383C4×C5#89511yescharacteristic
384Dic5—42no—
385Dic5—41no—
386Dic5—41no—
387Dic5—62no—
388C24—301no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—152no—
395C2×D4—151no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4—301no—
400C2×D4—301no—
401C2×D4—301no—
402C22×C4—32no—
403C22×C4—101no—
404C22×C4—302no—
405C22×C4—301no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—21no—
410M16—61no—
411M16—61no—
412M16#120012yescomplemented
413C2×C8—21no—
414C2×C8—61no—
415C4⋊C4—51no—
416C4⋊C4—51no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—302no—
420C22⋊C4—101no—
421C22⋊C4—302no—
422C22⋊C4—604no—
423C42—101no—
424C42—101no—
425C42—101no—
426C42—302no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3C4×D2011yescharacteristic
431C22×C3#402811yescharacteristic
432C22×C3#404111yescharacteristic
433C2×D3—102no—
434C2×D3—201no—
435C2×D3—201no—
436C2×D3—204no—
437C2×D3—202no—
438C2×D3—402no—
439C2×D3—401no—
440C2×D3—401no—
441C3×C4—202no—
442C3×C4—201no—
443C3×C4—201no—
444C3×C4D5×C22⋊C411yescharacteristic
445C3×C4#403011yescharacteristic
446C3×C4#403911yescharacteristic
447C3×C4#404011yescharacteristic
448Dic3—42no—
449Dic3—102no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5#466511yescharacteristic
453C2×C5#482211yescharacteristic
454C2×C5#482711yescharacteristic
455D5—122no—
456D5—242no—
457C23—301no—
458C23—302no—
459C23—602no—
460C23—602no—
461C23—601no—
462C23—601no—
463C23D3×D2011yescharacteristic
464Q8—152no—
465Q8—301no—
466D4—152no—
467D4—302no—
468D4—302no—
469D4—302no—
470D4—301no—
471D4—302no—
472D4—601no—
473D4—601no—
474C2×C4—62no—
475C2×C4—102no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—122no—
479C2×C4—201no—
480C2×C4—201no—
481C2×C4—301no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—1202no—
485C2×C4#676911yescharacteristic
486C2×C4#677311yescharacteristic
487C2×C4D5×D1211yescharacteristic
488C2×C4C2×#120011yescharacteristic
489C2×C4#679011yescharacteristic
490C2×C4#679011yescharacteristic
491C8—22no—
492C8—121no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3#6495411yescharacteristic
496C2×C3#6503611yescharacteristic
497C2×C3#6504211yescharacteristic
498D3—202no—
499D3—402no—
500C5#6877611yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—302no—
504C22—604no—
505C22—601no—
506C22—601no—
507C22—602no—
508C22—1202no—
509C22—1201no—
510C22—1201no—
511C22#9142811yescharacteristic
512C22#9145911yescharacteristic
513C22#9147611yescharacteristic
514C4—122no—
515C4—202no—
516C4—201no—
517C4—201no—
518C4—302no—
519C4#9141811yescharacteristic
520C4#9142011yescharacteristic
521C4#9143311yescharacteristic
522C4#9156111yescharacteristic
523C3#1059979811yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—602no—
527C2—1202no—
528C2#1174824911yescharacteristic
529C2#1174826111yescharacteristic
530C2#1174890411yescharacteristic
subgroupG/H
centerC22#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×#91797C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1883
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
2. #11754506C2semidirect
3. #11748768C2semidirect
4. C2×#90981C2semidirect
5. #11748392C2semidirect
6. C5×#4554C2semidirect
7. C3×#64775C2semidirect
13. #91797C4semidirect
36. #64775D3semidirect
49. C2×D60C2×C4semidirect
57. C3×C5×M16C2×C4semidirect
82. #4554D5semidirect
125. D60C22⋊C4semidirect
129. Dic30C22⋊C4semidirect
182. C5×M16C4×D3semidirect
248. C3×M16C4×D5semidirect
412. M16#1200semidirect
427. C3×C5#1883semidirect
500. C5#68776semidirect
523. C3#10599798semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
#117545062
#117487682
C2×#909812
#117483922
C5×#45542
C3×#647752
#105997983
#687765