Finite Group Databasebeta

← #14301332

Subgroups — #14301332

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×#91838C211yesmaximal, characteristic
2C5×#5827C211yesmaximal, characteristic, complemented
3C2×C3×#3969C211yesmaximal, characteristic, complemented
4#11748768C211yesmaximal, characteristic, complemented
5#11748396C211yesmaximal, characteristic, complemented
6#11745986C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10602460—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×D60C2211yescharacteristic
11#91838—22no—
12#91838C414yescomplemented
13C2×#6717—21no—
14C2×#6715—21no—
15C2×#6710C2211yescharacteristic
16C5×Q8×Dic3—21no—
17C5×D4×Dic3—21no—
18C5×D4×Dic3—22no—
19C5×#926—21no—
20C5×#926C2211yescharacteristic
21C2×C5×C4⋊Dic3—21no—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25C2×#6667—22no—
26C3×#3969—22no—
27#90969—21no—
28#90969—21no—
29#70366—51nomaximal, Hall
30C5×#520—31no—
31C2×#4095—31no—
32C2×#3969D311yescharacteristic, complemented
33#65290—31no—
34#65277—31no—
35#64752—31no—
36#64750—31no—
37C23×D15—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41C2×C412yes—
41C3×C5×#41D412yes—
42C2×C3×C5×Q8D411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4D411yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×D60—21no—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60C2×C412yescomplemented
53C22×C5×Dic3—22no—
54C22×C5×Dic3D412yes—
55C22×C3×Dic5—21no—
56#6717—24no—
57#6715—24no—
58#6710—21no—
59#6710C2×C412yescomplemented
60C2×C3⋊#168—21no—
61C5×#217—22no—
62C5×#217—21no—
63C5×C4⋊Dic3—22no—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3D411yescharacteristic
67C5×C4⋊Dic3D411yescharacteristic
68C4×C5×Dic3—22no—
69C4×C5×Dic3—21no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5—21no—
72C3×#681—21no—
73C3×#681—21no—
74C2×C3×#168—21no—
75#6667—44no—
76#5827D511yescharacteristic, complemented
77C2×#949—51no—
78C2×C3×#104—51no—
79#5131—51no—
80#4939—51no—
81#4554—51no—
82#4523—51no—
83C2×C5×#41C2×D311yescharacteristic
84C22×D20—31no—
85C4×C5×Q8—61no—
86C4×C5×D4—62no—
87C4×C5×D4—61no—
88C5×#117—31no—
89C5×#117—61no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4—61no—
92#4095—34no—
93#4095—62no—
94C2×#688—61no—
95C2×#686—61no—
96C2×#685—62no—
97C2×C4×Dic5C2×D311yescharacteristic
98C2×#681—31no—
99C2×#681C2×D311yescharacteristic
100#3969—22no—
101#3941—61no—
102#3941—61no—
103#1883—151noSylow
104C23×C3×C5—21no—
105C23×C3×C5C2×D411yescharacteristic
106C22×D15—22no—
107C22×D15—42no—
108C22×D15—42no—
109C22×D15—41no—
110C22×D15—41no—
111C3×C5×Q8—21no—
112C3×C5×Q8C22⋊C412yescomplemented
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—21no—
116C3×C5×D4C22⋊C412yescomplemented
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5#4111yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126D60—22no—
127D60—22no—
128D60—41no—
129D60—41no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—21no—
133C2×C5×Dic3—42no—
134C2×C5×Dic3—82no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—41no—
137C2×C3×Dic5—41no—
138C3⋊#168—22no—
139C3×#168—41no—
140C2×C3×#41C2×D511yescharacteristic
141C22×D12—51no—
142C2×C3×M16—51no—
143C2×C3×C42—51no—
144#949—54no—
145#949—102no—
146Q8×Dic3—21no—
147C2×#215—101no—
148D4×Dic3—21no—
149D4×Dic3—22no—
150C2×#213—101no—
151C2×(C2×D3)⋊C4—102no—
152#926—21no—
153#926C2×D511yescharacteristic
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3C2×D511yescharacteristic
156C2×#208—51no—
157C3×#104—102no—
158#821—101no—
159#821—101no—
160C23×D5—61no—
161C5×#41—21no—
162C5×#41—21no—
163C5×#41C4×D312yes—
164C5×#41#6712yes—
165C2×C5×Q8D1211yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4D1211yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—32no—
170C22×C4×C5—62no—
171C22×C4×C5C22×D311yescharacteristic
172C22×Dic5—21no—
173C2×D20—32no—
174C2×D20—61no—
175C2×D20—61no—
176C2×D20—61no—
177C2×D20—61no—
178C2×D20—61no—
179C5×C4⋊C4—31no—
180C5×C4⋊C4—31no—
181C5×C4⋊C4—62no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4—61no—
184C5×C22⋊C4—62no—
185C5×C22⋊C4—61no—
186C42×C5—62no—
187C42×C5—61no—
188#688—64no—
189#686—64no—
190#685—124no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193#681—21no—
194#681—21no—
195#681—32no—
196#681—61no—
197C2×#168—21no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—151no—
200#520—31no—
201C2×#104—51no—
202#418—151no—
203#390—151no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5—22no—
209C22×C3×C5—41no—
210C22×C3×C5—41no—
211C22×C3×C5C4×D411yescharacteristic
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C2×D15—44no—
215C2×D15—42no—
216C2×D15—82no—
217C2×D15—81no—
218C2×D15—81no—
219C3×C4×C5—22no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224C3×Dic5—42no—
225C5×Dic3—42no—
226C5×Dic3—41no—
227C5×Dic3—41no—
228C23×D3—101no—
229C3×#41—21no—
230C3×#41—21no—
231C3×#41C4×D512yes—
232C3×#41D2012yes—
233C2×C3×Q8C22⋊D511yescharacteristic
234C2×C3×D4—21no—
235C2×C3×D4C22⋊D511yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C22×Dic3—22no—
240C22×Dic3C22⋊D512yes—
241C2×D12—52no—
242C2×D12—101no—
243C2×D12—101no—
244C2×D12—101no—
245C2×D12—101no—
246C2×D12—101no—
247C3×M16—101no—
248C3×M16—101no—
249C2×C3×C8—101no—
250C3×C42—101no—
251C3×C42—101no—
252#217—22no—
253#217—21no—
254#215—104no—
255#213—104no—
256(C2×D3)⋊C4—204no—
257C4⋊Dic3—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3C22⋊D511yescharacteristic
261C4⋊Dic3C22⋊D511yescharacteristic
262C4×Dic3—22no—
263C4×Dic3—21no—
264#208—52no—
265#208—101no—
266C2×C3⋊C8—101no—
267C23×C5—21no—
268C23×C5D3×D411yescharacteristic
269C22×D5—62no—
270C22×D5—122no—
271C22×D5—122no—
272C22×D5—121no—
273C22×D5—121no—
274C5×Q8—21no—
275C5×Q8(C2×D3)⋊C412yescomplemented
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—21no—
279C5×D4(C2×D3)⋊C412yescomplemented
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—62no—
286C2×C4×C5—122no—
287C2×C4×C5—242no—
288C2×C4×C5C2×C4×D311yescharacteristic
289C2×C4×C5C2×D1211yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5#23711yescharacteristic
292C2×C4×C5#23711yescharacteristic
293C2×C4×C5C2×#6711yescharacteristic
294C2×Dic5—22no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297D20—62no—
298D20—62no—
299D20—121no—
300D20—121no—
301#168—41no—
302#168—62no—
303C2×#41D3×D511yescharacteristic
304C22×D4—151no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—51no—
310C2×M16—151no—
311C4×Q8—61no—
312C4×D4—62no—
313C4×D4—61no—
314#117—31no—
315#117—61no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—61no—
318C2×C22⋊C4—302no—
319C2×C42—51no—
320#104—102no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5—42no—
326C2×C3×C5#38611yescharacteristic
327C2×C3×C5#45311yescharacteristic
328C2×C3×C5#45411yescharacteristic
329D15—82no—
330C23×C3—21no—
331C23×C3C2×C22⋊D511yescharacteristic
332C22×D3—102no—
333C22×D3—202no—
334C22×D3—202no—
335C22×D3—201no—
336C22×D3—201no—
337C3×Q8—21no—
338C3×Q8#68512yescomplemented
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—21no—
342C3×D4#68512yescomplemented
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—102no—
347C2×C3×C4—201no—
348C2×C3×C4—201no—
349C2×C3×C4C2×C4×D511yescharacteristic
350C2×C3×C4C2×D2011yescharacteristic
351C2×C3×C4#70911yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4C2×C22⋊D511yescharacteristic
354C2×C3×C4C2×C22⋊D511yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—42no—
359C2×Dic3—82no—
360D12—102no—
361D12—102no—
362D12—201no—
363D12—201no—
364C3×C8—201no—
365C3⋊C8—102no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—22no—
369C22×C5—41no—
370C22×C5—41no—
371C22×C5#67⋊C411yescharacteristic
372C22×C5#88211yescharacteristic
373C22×C5#93911yescharacteristic
374C2×D5—124no—
375C2×D5—122no—
376C2×D5—242no—
377C2×D5—241no—
378C2×D5—241no—
379C4×C5—22no—
380C4×C5—122no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5#67⋊C411yescharacteristic
384C4×C5#88611yescharacteristic
385C4×C5C2×(C2×D3)⋊C411yescharacteristic
386C4×C5#93911yescharacteristic
387Dic5—42no—
388C24—301no—
389#41—21no—
390#41—21no—
391#41#120012yes—
392#41#120212yes—
393C2×Q8#120311yescharacteristic
394C2×D4—21no—
395C2×D4—152no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4—301no—
400C2×D4—301no—
401C2×D4#120311yescharacteristic
402C22×C4—21no—
403C22×C4—32no—
404C22×C4—62no—
405C22×C4—101no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—101no—
410M16—101no—
411M16—152no—
412M16—301no—
413C2×C8—101no—
414C2×C8—301no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—62no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C22⋊C4—604no—
423C42—62no—
424C42—61no—
425C42—101no—
426C42—101no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3C4×C22⋊D511yescharacteristic
434C22×C3#407611yescharacteristic
435C22×C3#409911yescharacteristic
436C2×D3—204no—
437C2×D3—202no—
438C2×D3—402no—
439C2×D3—401no—
440C2×D3—401no—
441C3×C4—22no—
442C3×C4—202no—
443C3×C4C2×#68511yescharacteristic
444C3×C4C4×C22⋊D511yescharacteristic
445C3×C4#407511yescharacteristic
446C3×C4#407611yescharacteristic
447Dic3—42no—
448Dic3—41no—
449Dic3—41no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—42no—
453C2×C5#482211yescharacteristic
454C2×C5#482711yescharacteristic
455C2×C5#495811yescharacteristic
456D5—242no—
457C23—21no—
458C23—302no—
459C23—602no—
460C23—602no—
461C23—601no—
462C23—601no—
463C23D3×C22⋊D511yescharacteristic
464Q8—21no—
465Q8#666712yescomplemented
466D4—22no—
467D4—22no—
468D4—21no—
469D4—302no—
470D4—302no—
471D4—601no—
472D4—601no—
473D4#666712yescomplemented
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—102no—
481C2×C4—122no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—242no—
485C2×C4#677911yescharacteristic
486C2×C4#677911yescharacteristic
487C2×C4C2×#120011yescharacteristic
488C2×C4C2×#120211yescharacteristic
489C2×C4C2×#120311yescharacteristic
490C2×C4D3×C22⋊D511yescharacteristic
491C8—201no—
492C8—302no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—42no—
496C2×C3#6550211yescharacteristic
497C2×C3#6553011yescharacteristic
498C2×C3#6553411yescharacteristic
499D3—402no—
500C5#7036611yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—604no—
507C22—602no—
508C22—1202no—
509C22—1201no—
510C22—1201no—
511C22#9155611yescharacteristic
512C22#9156911yescharacteristic
513C22#9157011yescharacteristic
514C4—22no—
515C4—122no—
516C4—121no—
517C4—121no—
518C4—202no—
519C4C2×#666711yescharacteristic
520C4#9154211yescharacteristic
521C4#9155611yescharacteristic
522C4#9156911yescharacteristic
523C3#1060246011yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—42no—
527C2—1202no—
528C2#1174942011yescharacteristic
529C2#1174945911yescharacteristic
530C2#1174949811yescharacteristic
subgroupG/H
centerC22#91570
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
prime radicalC2×#91838C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×#5827C2semidirect
3. C2×C3×#3969C2semidirect
4. #11748768C2semidirect
5. #11748396C2semidirect
6. #11745986C2semidirect
7. #11745977C2semidirect
12. #91838C4semidirect
32. C2×#3969D3semidirect
52. C2×D60C2×C4semidirect
59. #6710C2×C4semidirect
76. #5827D5semidirect
112. C3×C5×Q8C22⋊C4semidirect
116. C3×C5×D4C22⋊C4semidirect
275. C5×Q8(C2×D3)⋊C4semidirect
279. C5×D4(C2×D3)⋊C4semidirect
338. C3×Q8#685semidirect
342. C3×D4#685semidirect
427. C3×C5#1883semidirect
465. Q8#6667semidirect
473. D4#6667semidirect
500. C5#70366semidirect
523. C3#10602460semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C5×#58272
C2×C3×#39692
#117487682
#117483962
#117459862
#117459772
#106024603
#703665