Finite Group Databasebeta

← #14471911

Subgroups — #14471911

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic30C211yesmaximal, characteristic, complemented
2#11756312C211yesmaximal, characteristic
3C3×C4×C5×SD16C211yesmaximal, characteristic, complemented
4#11751264C212yesmaximal, complemented
5#11751128C211yesmaximal, characteristic, complemented
6#11751109C211yesmaximal, characteristic, complemented
7#11750971C212yesmaximal, complemented
8#11750889C212yesmaximal, complemented
9#11750861C212yesmaximal, complemented
10#11750795C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10611353—31nomaximal, Hall
13C2×#6817—21no—
14C2×C3×C5×SD16C2211yescharacteristic
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×D4C2211yescharacteristic
17Q8×Dic15C2212yes—
18C2×#6717C2212yes—
19#91829C2212yes—
20#91819—21no—
21#91782C2212yes—
22#91777—22no—
23#91777C2212yes—
24#91773—22no—
25#91763C2211yescharacteristic
26#91758—21no—
27#91758C2211yescharacteristic
28C4×Dic30—21no—
29C4×Dic30C2211yescharacteristic
30C3×C5×#106C2211yescharacteristic
31C3×C5×#103C2211yescharacteristic
32C3×C5×#102C2211yescharacteristic
33C3×C4×C5×C8C2211yescharacteristic
34#91116C2212yes—
35#91105C2212yes—
36#91105C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79622—51nomaximal, Hall
43Q8×Dic10—31no—
44#65887—31no—
45C4×C5×SD16D311yescharacteristic, complemented
46#65452—32no—
47#65316—31no—
48#65297—31no—
49#65159—32no—
50#65077—32no—
51#65049—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58C2×#1220—22no—
59#6817—44no—
60C2×D60—21no—
61C2×D60—21no—
62C2×D60C2312yes—
63C2×C4×D15—22no—
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×Dic30D411yescharacteristic
67C3×C5×SD16—22no—
68C2×C3×C5×C8C2311yescharacteristic
69C2×C3×C5×C8C2311yescharacteristic
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×C42×C5—21no—
75C3×C42×C5C2311yescharacteristic
76#6717—24no—
77#6714—22no—
78C4⋊Dic15—21no—
79C4⋊Dic15—22no—
80C4⋊Dic15D411yescharacteristic
81C4⋊Dic15C2312yes—
82#6712—22no—
83#6712D412yes—
84C4×Dic15—22no—
85C4×Dic15C2312yes—
86C2×C3⋊#168C2312yes—
87Q8×Dic6—51no—
88#5553—51no—
89C3×C4×SD16D511yescharacteristic, complemented
90#5163—52no—
91#5027—51no—
92#5008—51no—
93#4870—52no—
94#4788—52no—
95#4760—52no—
96#4694—51no—
97C8×Dic6—51no—
98C2×#709—61no—
99C2×C5×SD16C2×D311yescharacteristic
100C4×C5×Q8C2×D311yescharacteristic
101C4×C5×D4C2×D311yescharacteristic
102Q8×Dic5—32no—
103C2×#688—32no—
104#4086—32no—
105#4076—61no—
106#4039—32no—
107#4034—32no—
108#4034—62no—
109#4030—62no—
110#4020—31no—
111#4015—31no—
112#4015—61no—
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106C2×D311yescharacteristic
116C5×#103C2×D311yescharacteristic
117C5×#102C2×D311yescharacteristic
118C4×C5×C8C2×D311yescharacteristic
119#3964—32no—
120#3953—32no—
121#3953—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C23×C3×C5—21no—
129C22×D15—22no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—42no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141#1220—44no—
142#1220—82no—
143C2×Dic15—22no—
144C2×Dic15C2×D412yes—
145C2×Dic15C2×D412yes—
146D60—22no—
147D60—22no—
148D60—42no—
149D60—81no—
150C4×D15—44no—
151Dic30—82no—
152Dic30—81no—
153Dic30SD1614yescomplemented
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#235—101no—
158C2×C3×SD16C2×D511yescharacteristic
159C3×C4×Q8C2×D511yescharacteristic
160C3×C4×D4C2×D511yescharacteristic
161Q8×Dic3—52no—
162C2×#215—52no—
163#940—52no—
164#930—101no—
165#893—52no—
166#888—52no—
167#888—102no—
168#884—102no—
169#874—51no—
170#869—51no—
171#869—101no—
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×#106C2×D511yescharacteristic
175C3×#103C2×D511yescharacteristic
176C3×#102C2×D511yescharacteristic
177C3×C4×C8C2×D511yescharacteristic
178#832—52no—
179#821—52no—
180#821—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8C22×D311yescharacteristic
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10—61no—
199C5×SD16—22no—
200C2×C5×C8C22×D311yescharacteristic
201C2×C5×C8C22×D311yescharacteristic
202C5×C4⋊C4—21no—
203C5×C4⋊C4C22×D311yescharacteristic
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—21no—
206C42×C5—21no—
207C42×C5C22×D311yescharacteristic
208#688—64no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—32no—
212C4⋊Dic5—62no—
213C4⋊Dic5—61no—
214#683—32no—
215#683—62no—
216C4×Dic5—32no—
217C4×Dic5—62no—
218C2×#168—32no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—151no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16D1511yescharacteristic, complemented
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—42no—
237C3×C4×C5—22no—
238C3×C4×C5—21no—
239C3×C4×C5—41no—
240C3×C4×C5—41no—
241C3×C4×C5C2×SD1612yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C52−1+411yescharacteristic
244Dic15—22no—
245Dic15—42no—
246Dic15C2×SD1614yes—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4C22×D511yescharacteristic
249C22×C3×C4—21no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—52no—
254C2×D12—101no—
255C2×D12—101no—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6—101no—
260C3×SD16—22no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—21no—
264C3×C4⋊C4C22×D511yescharacteristic
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—21no—
267C3×C42—21no—
268C3×C42C22×D511yescharacteristic
269#215—104no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—51no—
272C4⋊Dic3—52no—
273C4⋊Dic3—102no—
274C4⋊Dic3—101no—
275Dic3⋊C4—52no—
276Dic3⋊C4—102no—
277C4×Dic3—52no—
278C4×Dic3—102no—
279C2×C3⋊C8—52no—
280C23×C5—21no—
281C22×D5—62no—
282C5×Q8—21no—
283C5×Q8#23512yescomplemented
284C5×D4—21no—
285C5×D4—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—42no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—62no—
298D20—62no—
299D20—62no—
300D20—122no—
301D20—241no—
302C4×D5—124no—
303Dic10—34no—
304Dic10—242no—
305Dic10—241no—
306C5×C8—21no—
307C5×C8—21no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—152no—
311C2×SD16C2×D1511yescharacteristic
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—301no—
323C4×Q8C2×D1511yescharacteristic
324C4×D4—152no—
325C4×D4C2×D1511yescharacteristic
326#106—152no—
327#106C2×D1511yescharacteristic
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103C2×D1511yescharacteristic
331#102—152no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102C2×D1511yescharacteristic
336C4×C8—152no—
337C4×C8C2×D1511yescharacteristic
338C2×C3×C5—81no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—82no—
343C23×C3—21no—
344C22×D3—102no—
345C3×Q8—21no—
346C3×Q8#70912yescomplemented
347C3×D4—21no—
348C3×D4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—42no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—102no—
361D12—102no—
362D12—102no—
363D12—202no—
364D12—401no—
365C4×D3—204no—
366Dic6—54no—
367Dic6—402no—
368Dic6—401no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5D3×SD1612yes—
384C4×C5C2×#23511yescharacteristic
385C4×C5#101011yescharacteristic
386Dic5—34no—
387Dic5—62no—
388Dic5—122no—
389#41—604no—
390C2×Q8—151no—
391C2×Q8—302no—
392C2×Q8—301no—
393C2×Q8C22×D1511yescharacteristic
394C2×D4—152no—
395C2×D4—302no—
396C2×D4—302no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4C22×D1511yescharacteristic
400C22×C4—21no—
401C22×C4—302no—
402SD16—22no—
403SD16—304no—
404C2×C8—152no—
405C2×C8C22×D1511yescharacteristic
406C2×C8C22×D1511yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4—152no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4C22×D1511yescharacteristic
415C4⋊C4C22×D1511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—302no—
418C42—21no—
419C42—152no—
420C42—302no—
421C42C22×D1511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4D5×SD1612yes—
435C3×C4C2×#70911yescharacteristic
436C3×C4#415011yescharacteristic
437Dic3—54no—
438Dic3—102no—
439Dic3—202no—
440C2×C5—81no—
441C2×C5#555211yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#576911yescharacteristic
444D5—242no—
445C23—21no—
446C23—302no—
447Q8—21no—
448Q8—154no—
449Q8—1201no—
450Q8—1202no—
451Q8#681712yescomplemented
452D4—21no—
453D4—21no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3—81no—
475C2×C3#6588611yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610311yescharacteristic
478D3—402no—
479C5#7962211yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D4×D1511yescharacteristic
487C4—22no—
488C4—21no—
489C4—41no—
490C4—41no—
491C4—154no—
492C4—302no—
493C4—602no—
494C4SD16×D1512yes—
495C4C2×#681711yescharacteristic
496C4#9210111yescharacteristic
497C3#1061135311yescharacteristic, complemented, Sylow
498C2—81no—
499C2—1202no—
500C2#1175631111yescharacteristic
501C2C2×SD16×D1511yescharacteristic
502C2#1175652811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radical#11756312C2
hypercenterC4×SD16D15
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic30C2semidirect
3. C3×C4×C5×SD16C2semidirect
4. #11751264C2semidirect
5. #11751128C2semidirect
6. #11751109C2semidirect
7. #11750971C2semidirect
8. #11750889C2semidirect
9. #11750861C2semidirect
10. #11750795C2semidirect
11. C8×Dic30C2semidirect
45. C4×C5×SD16D3semidirect
89. C3×C4×SD16D5semidirect
131. C3×C5×Q8#41semidirect
153. Dic30SD16semidirect
229. C4×SD16D15semidirect
283. C5×Q8#235semidirect
346. C3×Q8#709semidirect
422. C3×C5#3362semidirect
451. Q8#6817semidirect
479. C5#79622semidirect
497. C3#10611353semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic302
#117563122
C3×C4×C5×SD162
#117512642
#117511282
#117511092
#117509712
#117508892
#117508612
#117507952
C8×Dic302
#106113533
#796225