Finite Group Databasebeta

← #14302617

Subgroups — #14302617

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756507C211yesmaximal, characteristic
2#11754436C211yesmaximal, characteristic, complemented
3#11748626C211yesmaximal, characteristic, complemented
4#11748428C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic, complemented
6C5×#4555C211yesmaximal, characteristic, complemented
7C3×#64779C211yesmaximal, characteristic, complemented
8#10599571—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91798—21no—
13#91798C412yescomplemented
14#91797—21no—
15#91797C412yescomplemented
16#91793—22no—
17C5×#926C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91556—22no—
22#91428—21no—
23C4×#1200—21no—
24#91386—21no—
25#91340—21no—
26#90997—22no—
27#90980—22no—
28#90980—21no—
29#90980—21no—
30#69039—51nomaximal, Hall
31#66082—31no—
32C4×#709—31no—
33#65295—31no—
34#65294—31no—
35C2×#3937—31no—
36C5×#339—31no—
37#64779D311yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817—21no—
44#6817—21no—
45#6817—21no—
46#6817—21no—
47#6817C2×C412yes—
48#6817D412yes—
49C2×D60C2×C411yescharacteristic, complemented
50C2×D60D411yescharacteristic
51C2×C4×D15—21no—
52C2×C4×D15—21no—
53C2×Dic30C2×C411yescharacteristic, complemented
54C2×Dic30D411yescharacteristic
55C22×C5×Dic3—21no—
56C2×#1200—22no—
57C3×C5×M16—21no—
58C3×C5×M16C2×C412yescomplemented
59C2×C3×C5×C8—21no—
60Dic60—22no—
61D120—22no—
62#6706—22no—
63#6706—22no—
64C5×#217—21no—
65C5×C4⋊Dic3—21no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3D411yescharacteristic
69C4×C5×Dic3D411yescharacteristic
70C3×C22⋊Dic5D412yes—
71C3×C4⋊Dic5—21no—
72C3×C4×Dic5—21no—
73C3×#681—21no—
74C3×#681—21no—
75C2×C3×#168—21no—
76#6669—22no—
77#6667—22no—
78Dic3×Dic5—22no—
79#5748—51no—
80#5522—51no—
81#5139—51no—
82C2×#825—51no—
83#5006—51no—
84C3×#344—51no—
85#4555D511yescharacteristic, complemented
86C2×#709—31no—
87C2×#709—31no—
88C2×C5×M16C2×D311yescharacteristic
89C5×#117—31no—
90C2×C42×C5—31no—
91C4×C22⋊D5—62no—
92#4072C2×D311yescharacteristic
93C2×#681C2×D311yescharacteristic
94#4055—32no—
95#4055—61no—
96#4054—32no—
97#4054—61no—
98#4050—62no—
99C4×D20—61no—
100#4018—61no—
101C42×D5—61no—
102C4×Dic10—61no—
103#3938—62no—
104#3937—61no—
105#3937—61no—
106#3937—62no—
107#1906—151noSylow
108C23×C3×C5C2×D411yescharacteristic
109C22×D15—21no—
110C22×D15—21no—
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—
119#1220—41no—
120#1220—41no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123D60—21no—
124D60—21no—
125D60—21no—
126D60C22⋊C412yes—
127C4×D15—22no—
128C4×D15—22no—
129C4×D15—41no—
130C4×D15—41no—
131Dic30—21no—
132Dic30—21no—
133Dic30—21no—
134Dic30C22⋊C412yes—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—42no—
138C2×C5×Dic3—41no—
139C2×C3×Dic5—22no—
140#1200—44no—
141C3×C5×C8—22no—
142C3×#168—41no—
143C2×#235—51no—
144C2×#235—51no—
145C2×C3×M16—51no—
146C2×C3×M16C2×D511yescharacteristic
147C3×#117—51no—
148#926C2×D511yescharacteristic
149C2×C4×Dic3C2×D511yescharacteristic
150#909—52no—
151#909—101no—
152#908—52no—
153#908—101no—
154#904—102no—
155#893—101no—
156#887—101no—
157#67⋊C4—102no—
158#872—101no—
159C42×D3—101no—
160#825—102no—
161#825—101no—
162#825—101no—
163#806—102no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—61no—
167C2×C22⋊D5—61no—
168#709—32no—
169#709—32no—
170#709—61no—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175#709—61no—
176C2×D20—31no—
177C2×D20—31no—
178C2×C4×D5—61no—
179C2×C4×D5—62no—
180C2×C4×D5—61no—
181C2×Dic10—31no—
182C2×Dic10—31no—
183C5×M16—21no—
184C5×M16C4×D312yescomplemented
185C2×C5×C8—21no—
186C5×C4⋊C4—61no—
187C5×C22⋊C4—61no—
188C42×C5—31no—
189C42×C5—31no—
190C42×C5—61no—
191C42×C5—61no—
192C22⋊Dic5D1212yes—
193#685—62no—
194C4⋊Dic5—21no—
195#683—62no—
196C4×Dic5—21no—
197C4×Dic5—62no—
198#681—21no—
199#681—21no—
200C2×#168—21no—
201Dic20—62no—
202D40—62no—
203#677—62no—
204#677—62no—
205#575—151no—
206C4×#41—151no—
207#421—151no—
208C2×#104—151no—
209#410—151no—
210#344—51no—
211#339—31no—
212C22×C3×C5—41no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×D15—22no—
217C2×D15—42no—
218C2×D15—41no—
219C2×D15—81no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—22no—
225Dic15—41no—
226C3×Dic5—42no—
227C5×Dic3—22no—
228C5×Dic3—41no—
229C5×Dic3—81no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C2×#67—101no—
233C22×Dic3—21no—
234#235—52no—
235#235—52no—
236#235—101no—
237#235—101no—
238#235—101no—
239#235—101no—
240#235—101no—
241#235—101no—
242C2×D12—51no—
243C2×D12—51no—
244C2×C4×D3—101no—
245C2×C4×D3—102no—
246C2×C4×D3—101no—
247C2×Dic6—51no—
248C2×Dic6—51no—
249C3×M16—21no—
250C3×M16—101no—
251C3×M16—101no—
252C3×M16C4×D512yescomplemented
253C2×C3×C8—21no—
254C2×C3×C8—101no—
255C3×C4⋊C4—101no—
256C3×C22⋊C4—52no—
257C3×C42—101no—
258#217—21no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—21no—
261Dic3⋊C4—102no—
262C4×Dic3—21no—
263C4×Dic3—21no—
264C4×Dic3—102no—
265C4×Dic3D2011yescharacteristic
266C4×Dic3D2011yescharacteristic
267Dic12—102no—
268D24—102no—
269#204—102no—
270#204—102no—
271C23×C5C2×D1211yescharacteristic
272C22×D5—61no—
273C22×D5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—122no—
277C2×C4×C5—121no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5#23911yescharacteristic
284C22⋊D5—62no—
285C22⋊D5—62no—
286C22⋊D5—121no—
287C22⋊D5—121no—
288C2×Dic5—22no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291D20—32no—
292D20—61no—
293D20—61no—
294D20—61no—
295C4×D5—62no—
296C4×D5—62no—
297C4×D5—124no—
298C4×D5—121no—
299C4×D5—121no—
300Dic10—32no—
301Dic10—61no—
302Dic10—61no—
303Dic10—61no—
304C5×C8—22no—
305#168—41no—
306C2×#41—151no—
307C2×#41—151no—
308#137—152no—
309#137—301no—
310AGL(1,ℤ/8)—152no—
311AGL(1,ℤ/8)—301no—
312#135—302no—
313C2×M16—51no—
314C2×M16D3×D511yescharacteristic
315C4×Q8—301no—
316C4×D4—301no—
317C4×D4—302no—
318#117—31no—
319#117—51no—
320#117—301no—
321C2×C42—31no—
322C2×C42—301no—
323#104—301no—
324#104—301no—
325#104—302no—
326#99—302no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5—21no—
330C2×C3×C5#38611yescharacteristic
331D15—42no—
332D15—81no—
333C23×C3D4×D511yescharacteristic
334C22×D3—101no—
335C22×D3—101no—
336C2×C3×C4—102no—
337C2×C3×C4C2×C4×D511yescharacteristic
338C2×C3×C4C2×D2011yescharacteristic
339C2×C3×C4#70911yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4#71311yescharacteristic
343#67—102no—
344#67—102no—
345#67—201no—
346#67—201no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—42no—
350C2×Dic3—41no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353D12—52no—
354D12—101no—
355D12—101no—
356D12—101no—
357C4×D3—102no—
358C4×D3—102no—
359C4×D3—204no—
360C4×D3—201no—
361C4×D3—201no—
362Dic6—52no—
363Dic6—101no—
364Dic6—101no—
365Dic6—101no—
366C3×C8—22no—
367C3×C8—201no—
368C22×C5—41no—
369C22×C5C4×D1211yescharacteristic
370C22×C5#88211yescharacteristic
371C22×C5#89511yescharacteristic
372C2×D5—62no—
373C2×D5—122no—
374C2×D5—121no—
375C2×D5—241no—
376C4×C5—62no—
377C4×C5—121no—
378C4×C5—241no—
379C4×C5D3×C22⋊C411yescharacteristic
380C4×C5#88411yescharacteristic
381C4×C5#89311yescharacteristic
382C4×C5#89411yescharacteristic
383Dic5—42no—
384Dic5—62no—
385Dic5—121no—
386#41—152no—
387#41—152no—
388#41—301no—
389#41—301no—
390#41—301no—
391#41—301no—
392#41—301no—
393#41—301no—
394C2×Q8—151no—
395C2×Q8—151no—
396C2×D4—151no—
397C2×D4—151no—
398C2×D4—301no—
399C2×D4—301no—
400C22×C4—61no—
401C22×C4—302no—
402C22×C4—301no—
403C22×C4—301no—
404C22×C4C2×D3×D511yescharacteristic
405Q16—302no—
406SD16—302no—
407SD16—302no—
408D8—302no—
409M16—21no—
410M16—101no—
411M16—101no—
412M16#120012yescomplemented
413C2×C8—21no—
414C2×C8—101no—
415C4⋊C4—61no—
416C4⋊C4—101no—
417C4⋊C4—302no—
418C22⋊C4—52no—
419C22⋊C4—61no—
420C22⋊C4—302no—
421C42—31no—
422C42—31no—
423C42—61no—
424C42—61no—
425C42—101no—
426C42—302no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3#402811yescharacteristic
430C22×C3#403011yescharacteristic
431C22×C3#403911yescharacteristic
432C2×D3—102no—
433C2×D3—202no—
434C2×D3—201no—
435C2×D3—401no—
436C3×C4—202no—
437C3×C4C4×D2011yescharacteristic
438C3×C4D5×C22⋊C411yescharacteristic
439C3×C4#404011yescharacteristic
440C3×C4#404111yescharacteristic
441Dic3—22no—
442Dic3—41no—
443Dic3—81no—
444Dic3—102no—
445Dic3—201no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5#466511yescharacteristic
450D5—122no—
451D5—241no—
452C23—301no—
453C23—301no—
454C23D5×D1211yescharacteristic
455Q8—152no—
456Q8—301no—
457Q8—301no—
458Q8—301no—
459D4—152no—
460D4—302no—
461D4—302no—
462D4—301no—
463D4—301no—
464D4—301no—
465D4—601no—
466D4—601no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—102no—
470C2×C4—122no—
471C2×C4—121no—
472C2×C4—301no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—301no—
476C2×C4—604no—
477C2×C4—601no—
478C2×C4—601no—
479C2×C4#676911yescharacteristic
480C2×C4#677311yescharacteristic
481C2×C4D3×D2011yescharacteristic
482C2×C4C2×#120011yescharacteristic
483C2×C4#679011yescharacteristic
484C2×C4#679011yescharacteristic
485C8—22no—
486C8—201no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3#6495411yescharacteristic
491D3—202no—
492D3—401no—
493C5#6903911yescharacteristic, complemented, Sylow
494C22—41no—
495C22—302no—
496C22—602no—
497C22—601no—
498C22—1201no—
499C22#9141811yescharacteristic
500C22#9142011yescharacteristic
501C22#9147611yescharacteristic
502C4—62no—
503C4—121no—
504C4—202no—
505C4—241no—
506C4—302no—
507C4—601no—
508C4#9142811yescharacteristic
509C4#9143311yescharacteristic
510C4#9145911yescharacteristic
511C4#9156111yescharacteristic
512C3#1059957111yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—602no—
517C2—1201no—
518C2#1174890411yescharacteristic
subgroupG/H
centerC4#91459
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11756507C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754436C2semidirect
3. #11748626C2semidirect
4. #11748428C2semidirect
5. C2×#90980C2semidirect
6. C5×#4555C2semidirect
7. C3×#64779C2semidirect
13. #91798C4semidirect
15. #91797C4semidirect
37. #64779D3semidirect
49. C2×D60C2×C4semidirect
53. C2×Dic30C2×C4semidirect
58. C3×C5×M16C2×C4semidirect
85. #4555D5semidirect
184. C5×M16C4×D3semidirect
252. C3×M16C4×D5semidirect
412. M16#1200semidirect
427. C3×C5#1906semidirect
493. C5#69039semidirect
512. C3#10599571semidirect

Maximal subgroups

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

subgroupindex
#117565072
#117544362
#117486262
#117484282
C2×#909802
C5×#45552
C3×#647792
#105995713
#690395