Finite Group Databasebeta

← #14302618

Subgroups — #14302618

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
1C3×#66082C211yesmaximal, characteristic
2Dic3×#709C211yesmaximal, characteristic, complemented
3#11748624C211yesmaximal, characteristic, complemented
4#11748421C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic, complemented
6#11746380C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8#10599571—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C3×#4055—21no—
17C3×#4055C412yescomplemented
18C3×#4054—21no—
19C3×#4054C412yescomplemented
20C3×#4050—22no—
21Dic3×C22⋊D5—22no—
22Dic3×D20—21no—
23C4×D5×Dic3—21no—
24#91357—21no—
25Dic3×Dic10—21no—
26#90995—22no—
27#90977—22no—
28#90977—21no—
29#90977—21no—
30#72114—51nomaximal, Hall
31#66082D311yescharacteristic
32C4×#709—31no—
33#65295—31no—
34#65294—31no—
35C2×#3937—31no—
36C5×#339—31no—
37#64779—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C5×Dic3—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709C2×C412yes—
49C3×#709D412yes—
50C2×C3×D20C2×C411yescharacteristic, complemented
51C2×C3×D20D411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×Dic10C2×C411yescharacteristic, complemented
55C2×C3×Dic10D411yescharacteristic
56C2×D5×Dic3—22no—
57C3×C5×M16—21no—
58C3×C5×M16C2×C412yescomplemented
59C2×C3×C5×C8—21no—
60#6719D412yes—
61C4⋊Dic15—21no—
62C4×Dic15—21no—
63#6710—21no—
64#6710—21no—
65C2×C3⋊#168—21no—
66C5×#217—21no—
67C5×C4⋊Dic3—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3—21no—
70C4×C5×Dic3D411yescharacteristic
71C4×C5×Dic3D411yescharacteristic
72C3×Dic20—22no—
73C3×D40—22no—
74C3×#677—22no—
75C3×#677—22no—
76#6668—22no—
77#6665—22no—
78Dic3×Dic5—22no—
79C3×#575—51no—
80Dic3×#41—51no—
81#5240—51no—
82#5236—51no—
83C2×#837—51no—
84#4559—51no—
85#4555D511yescharacteristic, complemented
86C2×#709C2×D311yescharacteristic
87C2×#709C2×D311yescharacteristic
88C2×C5×M16C2×D311yescharacteristic
89C5×#117—31no—
90C2×C42×C5—31no—
91C4×C22⋊D5—62no—
92#4072—31no—
93C2×#681—31no—
94#4055—21no—
95#4055Dic312yescomplemented
96#4054—21no—
97#4054Dic312yescomplemented
98#4050—22no—
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×C3×D5—21no—
110C22×C3×D5—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
117C2×Dic15—22no—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—42no—
121C2×C5×Dic3—41no—
122C3×C22⋊D5—22no—
123C3×C22⋊D5—22no—
124C3×C22⋊D5—41no—
125C3×C22⋊D5—41no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C3×D20—21no—
129C3×D20—21no—
130C3×D20—21no—
131C3×D20C22⋊C412yes—
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134C3×C4×D5—41no—
135C3×C4×D5—41no—
136C3×Dic10—21no—
137C3×Dic10—21no—
138C3×Dic10—21no—
139C3×Dic10C22⋊C412yes—
140D5×Dic3—44no—
141C3×C5×C8—22no—
142C3⋊#168—41no—
143C2×C3×#41—51no—
144C2×C3×#41—51no—
145C3×#137—52no—
146C3×#137—101no—
147C3×AGL(1,ℤ/8)—52no—
148C3×AGL(1,ℤ/8)—101no—
149C3×#135—102no—
150C2×C3×M16C2×D511yescharacteristic
151Q8×Dic3—101no—
152D4×Dic3—101no—
153D4×Dic3—102no—
154#926—51no—
155#926—101no—
156#926C2×D511yescharacteristic
157C2×C4×Dic3—101no—
158C2×C4×Dic3C2×D511yescharacteristic
159C2×#208—51no—
160#837—102no—
161#837—101no—
162#837—101no—
163#834—102no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—21no—
167C2×C22⋊D5—21no—
168#709—21no—
169#709—21no—
170#709—21no—
171#709—21no—
172#709—21no—
173#709—21no—
174#709C2×Dic312yes—
175#709#6712yes—
176C2×D20C2×Dic311yescharacteristic, complemented
177C2×D20#6711yescharacteristic
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—62no—
181C2×Dic10C2×Dic311yescharacteristic, complemented
182C2×Dic10#6711yescharacteristic
183C5×M16—21no—
184C5×M16C2×Dic312yescomplemented
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⋊Dic5—32no—
193#685—62no—
194C4⋊Dic5—61no—
195#683—62no—
196C4×Dic5—62no—
197C4×Dic5—61no—
198#681—61no—
199#681—61no—
200C2×#168—61no—
201Dic20—22no—
202D40—22no—
203#677—22no—
204#677—22no—
205#575—51no—
206C4×#41—151no—
207#421—151no—
208C2×#104—151no—
209#410—151no—
210#344—151no—
211#339—31no—
212C22×C3×C5—41no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×C3×D5—22no—
217C2×C3×D5—42no—
218C2×C3×D5—41no—
219C2×C3×D5—81no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—42no—
225C3×Dic5—22no—
226C3×Dic5—41no—
227C5×Dic3—22no—
228C5×Dic3—41no—
229C5×Dic3—81no—
230C3×#41—52no—
231C3×#41—52no—
232C3×#41—101no—
233C3×#41—101no—
234C3×#41—101no—
235C3×#41—101no—
236C3×#41—101no—
237C3×#41—101no—
238C2×C3×Q8—51no—
239C2×C3×Q8—51no—
240C2×C3×D4—51no—
241C2×C3×D4—51no—
242C2×C3×D4—101no—
243C2×C3×D4—101no—
244C22×C3×C4—101no—
245C22×C3×C4—101no—
246C22×C3×C4C22×D511yescharacteristic
247C22×Dic3—21no—
248C22×Dic3—102no—
249C3×Q16—102no—
250C3×SD16—102no—
251C3×SD16—102no—
252C3×D8—102no—
253C3×M16—21no—
254C3×M16C4×D512yescomplemented
255C2×C3×C8—21no—
256#217—21no—
257#217—52no—
258#217—102no—
259C4⋊Dic3—21no—
260C4⋊Dic3—102no—
261C4⋊Dic3—101no—
262C4×Dic3—21no—
263C4×Dic3—21no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C4×Dic3D2011yescharacteristic
267C4×Dic3D2011yescharacteristic
268#208—101no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5D3×D411yescharacteristic
272C22×D5—21no—
273C22×D5—21no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—122no—
277C2×C4×C5—121no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×C4×C5#23711yescharacteristic
281C2×C4×C5C22×Dic311yescharacteristic
282C2×C4×C5C2×#6711yescharacteristic
283C2×C4×C5C2×#6711yescharacteristic
284C22⋊D5—22no—
285C22⋊D5—22no—
286C22⋊D5—41no—
287C22⋊D5—41no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—62no—
291D20—21no—
292D20—21no—
293D20—21no—
294D20#21712yes—
295C4×D5—22no—
296C4×D5—22no—
297C4×D5—41no—
298C4×D5—41no—
299C4×D5—124no—
300Dic10—21no—
301Dic10—21no—
302Dic10—21no—
303Dic10#21712yes—
304C5×C8—22no—
305#168—121no—
306C2×#41—51no—
307C2×#41—51no—
308#137—52no—
309#137—101no—
310AGL(1,ℤ/8)—52no—
311AGL(1,ℤ/8)—101no—
312#135—102no—
313C2×M16—151no—
314C2×M16D3×D511yescharacteristic
315C4×Q8—301no—
316C4×D4—301no—
317C4×D4—302no—
318#117—31no—
319#117—151no—
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
331C3×D5—42no—
332C3×D5—81no—
333C23×C3—101no—
334C23×C3—101no—
335C23×C3D4×D511yescharacteristic
336C3×Q8—52no—
337C3×Q8—101no—
338C3×Q8—101no—
339C3×Q8—101no—
340C3×D4—52no—
341C3×D4—102no—
342C3×D4—102no—
343C3×D4—101no—
344C3×D4—101no—
345C3×D4—101no—
346C3×D4—201no—
347C3×D4—201no—
348C2×C3×C4—101no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—101no—
352C2×C3×C4—201no—
353C2×C3×C4—201no—
354C2×C3×C4C2×C4×D511yescharacteristic
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4#70911yescharacteristic
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4#71311yescharacteristic
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—42no—
363C2×Dic3—41no—
364C2×Dic3—102no—
365C2×Dic3—204no—
366C3×C8—22no—
367C3⋊C8—201no—
368C22×C5—41no—
369C22×C5D4×Dic311yescharacteristic
370C22×C5#93711yescharacteristic
371C22×C5#93911yescharacteristic
372C2×D5—22no—
373C2×D5—42no—
374C2×D5—41no—
375C2×D5—81no—
376C4×C5—62no—
377C4×C5—121no—
378C4×C5—241no—
379C4×C5D4×Dic311yescharacteristic
380C4×C5#93511yescharacteristic
381C4×C5#93911yescharacteristic
382C4×C5C2×#21711yescharacteristic
383Dic5—22no—
384Dic5—41no—
385Dic5—122no—
386#41—52no—
387#41—52no—
388#41—101no—
389#41—101no—
390#41—101no—
391#41—101no—
392#41—101no—
393#41—101no—
394C2×Q8—51no—
395C2×Q8—51no—
396C2×D4—51no—
397C2×D4—51no—
398C2×D4—101no—
399C2×D4—101no—
400C22×C4—61no—
401C22×C4—101no—
402C22×C4—101no—
403C22×C4—302no—
404C22×C4C2×D3×D511yescharacteristic
405Q16—102no—
406SD16—102no—
407SD16—102no—
408D8—102no—
409M16—21no—
410M16—301no—
411M16—301no—
412M16D5×Dic312yescomplemented
413C2×C8—21no—
414C2×C8—301no—
415C4⋊C4—61no—
416C4⋊C4—302no—
417C4⋊C4—301no—
418C22⋊C4—61no—
419C22⋊C4—152no—
420C22⋊C4—302no—
421C42—31no—
422C42—31no—
423C42—61no—
424C42—61no—
425C42—302no—
426C42—301no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3—102no—
430C22×C3—202no—
431C22×C3—201no—
432C22×C3—401no—
433C22×C3#402811yescharacteristic
434C22×C3#403011yescharacteristic
435C22×C3#403911yescharacteristic
436C3×C4—102no—
437C3×C4—201no—
438C3×C4C4×D2011yescharacteristic
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#404011yescharacteristic
441C3×C4#404111yescharacteristic
442Dic3—22no—
443Dic3—41no—
444Dic3—81no—
445Dic3—202no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5#522011yescharacteristic
450D5—42no—
451D5—81no—
452C23—101no—
453C23—101no—
454C23#677711yescharacteristic
455Q8—52no—
456Q8—101no—
457Q8—101no—
458Q8—101no—
459D4—52no—
460D4—102no—
461D4—102no—
462D4—101no—
463D4—101no—
464D4—101no—
465D4—201no—
466D4—201no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—101no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—101no—
473C2×C4—122no—
474C2×C4—121no—
475C2×C4—201no—
476C2×C4—201no—
477C2×C4—302no—
478C2×C4—604no—
479C2×C4#676511yescharacteristic
480C2×C4#676611yescharacteristic
481C2×C4D3×D2011yescharacteristic
482C2×C4C2×D5×Dic311yescharacteristic
483C2×C4D5×#6711yescharacteristic
484C2×C4D5×#6711yescharacteristic
485C8—22no—
486C8—601no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—202no—
491C2×C3—401no—
492C2×C3#6495411yescharacteristic
493C5#7211411yescharacteristic, complemented, Sylow
494C22—41no—
495C22—102no—
496C22—202no—
497C22—201no—
498C22—401no—
499C22#9140811yescharacteristic
500C22#9143411yescharacteristic
501C22#9147411yescharacteristic
502C4—62no—
503C4—102no—
504C4—121no—
505C4—201no—
506C4—241no—
507C4—602no—
508C4#9140711yescharacteristic
509C4#9140911yescharacteristic
510C4Dic3×D2011yescharacteristic
511C4D5×#21711yescharacteristic
512C3#1059957111yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—202no—
517C2—401no—
518C2#1174889611yescharacteristic
subgroupG/H
centerC4#91409
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC3×#66082C2
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. Dic3×#709C2semidirect
3. #11748624C2semidirect
4. #11748421C2semidirect
5. C2×#90977C2semidirect
6. #11746380C2semidirect
7. C5×#4555C2semidirect
17. C3×#4055C4semidirect
19. C3×#4054C4semidirect
50. C2×C3×D20C2×C4semidirect
54. C2×C3×Dic10C2×C4semidirect
58. C3×C5×M16C2×C4semidirect
85. #4555D5semidirect
95. #4055Dic3semidirect
97. #4054Dic3semidirect
176. C2×D20C2×Dic3semidirect
181. C2×Dic10C2×Dic3semidirect
184. C5×M16C2×Dic3semidirect
254. C3×M16C4×D5semidirect
412. M16D5×Dic3semidirect
427. C3×C5#1906semidirect
493. C5#72114semidirect
512. C3#10599571semidirect

Maximal subgroups

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

subgroupindex
C3×#660822
Dic3×#7092
#117486242
#117484212
C2×#909772
#117463802
C5×#45552
#105995713
#721145