Finite Group Databasebeta

← #14301342

Subgroups — #14301342

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
1#11754509C211yesmaximal, characteristic, complemented
2C2×#91301C211yesmaximal, characteristic
3#11751040C211yesmaximal, characteristic, complemented
4C2×C3×#3937C211yesmaximal, characteristic, complemented
5#11748396C211yesmaximal, characteristic, complemented
6C5×#4523C211yesmaximal, characteristic, complemented
7#11745987C211yesmaximal, characteristic, complemented
8#10599569—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6714—22no—
13C2×C4⋊Dic15C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91559—22no—
18Dic3×D20—21no—
19D5×C4⋊Dic3—21no—
20#91358—21no—
21Dic3×Dic10—21no—
22C2×#6658—21no—
23#91301—22no—
24#91301C414yescomplemented
25C2×#6653—21no—
26C3×#3937—22no—
27#90969—21no—
28#90969—21no—
29#70366—51nomaximal, Hall
30C2×#4054—31no—
31#65857—31no—
32#65290—31no—
33#65228—31no—
34C2×#3937D311yescharacteristic, complemented
35C5×#339—31no—
36#64774—31no—
37C23×D15—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15D412yes—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60C2×C412yescomplemented
47C2×C3×C22⋊D5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709C2×C412yes—
51C3×#709D412yes—
52C2×C3×D20D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×Dic10D411yescharacteristic
55C2×D5×Dic3—22no—
56C3×C42×C5—21no—
57C3×C42×C5—21no—
58#6714—44no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61C5×#217—21no—
62C5×C4⋊Dic3D411yescharacteristic
63C5×C4⋊Dic3D411yescharacteristic
64C4×C5×Dic3—21no—
65C5×#208—21no—
66C5×#208C2×C412yescomplemented
67C2×C5×C3⋊C8—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71#6668—22no—
72#6665—22no—
73Dic3×Dic5—22no—
74#6658—24no—
75#6653—24no—
76#5827—51no—
77C2×#949—51no—
78C2×C3×#104—51no—
79#5131—51no—
80#4939—51no—
81#4554—51no—
82#4523D511yescharacteristic, complemented
83C2×#709C2×D311yescharacteristic
84C22×D20—31no—
85C2×C5×M16—31no—
86C5×#117—31no—
87C2×C42×C5C2×D311yescharacteristic
88C2×#685—62no—
89C2×C4⋊Dic5—31no—
90C2×#681C2×D311yescharacteristic
91#4054—34no—
92#4054—62no—
93C2×D40—61no—
94C2×#677—61no—
95#4038—61no—
96D5×C4⋊C4—61no—
97#4027—62no—
98C4×D20—61no—
99C4×Dic10—61no—
100#3941—61no—
101#3941—61no—
102#3937—22no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×D15—22no—
106C22×D15—42no—
107C22×D15—42no—
108C22×D15—41no—
109C22×D15—41no—
110C22×C3×D5—21no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×Dic15—22no—
121C2×Dic15—42no—
122D60—22no—
123D60—22no—
124D60—41no—
125D60—41no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C3×C22⋊D5—22no—
129C3×C22⋊D5—22no—
130C2×C3×Dic5—21no—
131C3×D20—21no—
132C3×D20C22⋊C412yescomplemented
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×Dic10—21no—
136C3×Dic10C22⋊C412yescomplemented
137D5×Dic3—82no—
138C3×#168—41no—
139C5×C3⋊C8—22no—
140C2×C3×#41—51no—
141C22×D12—51no—
142C2×C3×M16—51no—
143C2×C3×C42C2×D511yescharacteristic
144#949—54no—
145#949—102no—
146Q8×Dic3—101no—
147C2×#215—101no—
148D4×Dic3—101no—
149D4×Dic3—102no—
150C2×#213—101no—
151C2×(C2×D3)⋊C4—102no—
152#926—101no—
153#926C2×D511yescharacteristic
154C2×C4⋊Dic3—51no—
155C2×C4⋊Dic3—101no—
156C2×#208C2×D511yescharacteristic
157C3×#104—102no—
158#821—101no—
159#821—101no—
160C23×D5—61no—
161C22×C4×C5—21no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—21no—
164C22×Dic5—32no—
165#709—21no—
166#709—21no—
167#709C4×D312yes—
168#709#6712yes—
169C2×D20—32no—
170C2×D20—61no—
171C2×D20—61no—
172C2×D20—61no—
173C2×D20—61no—
174C2×D20—61no—
175C2×D20D1211yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—62no—
178C2×Dic10D1211yescharacteristic
179C5×M16—32no—
180C5×M16—61no—
181C2×C5×C8—61no—
182C5×C4⋊C4—31no—
183C5×C4⋊C4—31no—
184C5×C22⋊C4—61no—
185C42×C5—21no—
186C42×C5—21no—
187C42×C5—61no—
188#685—62no—
189#685—124no—
190C4⋊Dic5—61no—
191C4⋊Dic5—61no—
192#683—62no—
193C4×Dic5—62no—
194#681—21no—
195#681—21no—
196C2×#168—21no—
197D40—64no—
198#677—64no—
199C2×AGL(1,ℤ/8)—151no—
200#520—151no—
201C2×#104—51no—
202#418—151no—
203#390—151no—
204#343—151no—
205#339—31no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×D15—44no—
212C2×D15—42no—
213C2×D15—82no—
214C2×D15—81no—
215C2×D15—81no—
216C2×C3×D5—22no—
217C2×C3×D5—41no—
218C2×C3×D5—41no—
219C3×C4×C5—42no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—42no—
225C3×Dic5—22no—
226C5×Dic3—41no—
227C5×Dic3—41no—
228C23×D3—101no—
229C3×#41—52no—
230C3×#41—52no—
231C3×#41—101no—
232C3×#41—101no—
233C2×C3×Q8—51no—
234C2×C3×D4—51no—
235C2×C3×D4—101no—
236C22×C3×C4—21no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C22×Dic3—52no—
240C22×Dic3—102no—
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—21no—
251C3×C42—21no—
252#217—21no—
253#217—102no—
254#215—104no—
255#213—104no—
256(C2×D3)⋊C4—204no—
257C4⋊Dic3—102no—
258C4⋊Dic3—101no—
259C4⋊Dic3—101no—
260C4⋊Dic3D2011yescharacteristic
261C4⋊Dic3D2011yescharacteristic
262C4×Dic3—21no—
263C4×Dic3—102no—
264#208—21no—
265#208C4×D512yescomplemented
266C2×C3⋊C8—21no—
267C23×C5D3×D411yescharacteristic
268C22×D5—21no—
269C22×D5—62no—
270C22×D5—122no—
271C22×D5—122no—
272C22×D5—121no—
273C22×D5—121no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5C2×C4×D311yescharacteristic
280C2×C4×C5C2×D1211yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5#23711yescharacteristic
283C2×C4×C5#23711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C22⋊D5—22no—
286C22⋊D5—22no—
287C2×Dic5—21no—
288C2×Dic5—62no—
289C2×Dic5—122no—
290D20—21no—
291D20—62no—
292D20—62no—
293D20—121no—
294D20—121no—
295D20(C2×D3)⋊C412yescomplemented
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—242no—
299Dic10—21no—
300Dic10(C2×D3)⋊C412yescomplemented
301C5×C8—62no—
302#168—41no—
303C2×#41—51no—
304C22×D4—151no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—31no—
310C2×M16—51no—
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—31no—
315#117—301no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42D3×D511yescharacteristic
320#104—102no—
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—82no—
329C3×D5—42no—
330C23×C3—101no—
331C23×C3D4×D511yescharacteristic
332C22×D3—102no—
333C22×D3—202no—
334C22×D3—202no—
335C22×D3—201no—
336C22×D3—201no—
337C3×Q8—52no—
338C3×Q8—101no—
339C3×D4—52no—
340C3×D4—102no—
341C3×D4—102no—
342C3×D4—101no—
343C2×C3×C4—22no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—101no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4C2×C4×D511yescharacteristic
350C2×C3×C4C2×D2011yescharacteristic
351C2×C3×C4#70911yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4#71311yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—102no—
358C2×Dic3—202no—
359C2×Dic3—402no—
360D12—102no—
361D12—102no—
362D12—201no—
363D12—201no—
364C3×C8—201no—
365C3⋊C8—22no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5#67⋊C411yescharacteristic
369C22×C5#88211yescharacteristic
370C22×C5#93911yescharacteristic
371C2×D5—22no—
372C2×D5—41no—
373C2×D5—41no—
374C2×D5—124no—
375C2×D5—122no—
376C2×D5—242no—
377C2×D5—241no—
378C2×D5—241no—
379C4×C5—42no—
380C4×C5—121no—
381C4×C5—121no—
382C4×C5#67⋊C411yescharacteristic
383C4×C5#88611yescharacteristic
384C4×C5C2×(C2×D3)⋊C411yescharacteristic
385C4×C5#93911yescharacteristic
386Dic5—22no—
387Dic5—122no—
388C24—301no—
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—51no—
395C2×D4—101no—
396C2×D4—152no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4—301no—
400C2×D4—301no—
401C2×D4—301no—
402C22×C4—21no—
403C22×C4—101no—
404C22×C4—152no—
405C22×C4—302no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—32no—
410M16—61no—
411M16—101no—
412M16—101no—
413C2×C8—61no—
414C2×C8—101no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—302no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C22⋊C4—61no—
421C22⋊C4—302no—
422C22⋊C4—604no—
423C42—21no—
424C42—21no—
425C42—61no—
426C42—302no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—102no—
431C22×C3—201no—
432C22×C3—201no—
433C22×C3#402811yescharacteristic
434C22×C3#403011yescharacteristic
435C22×C3#403911yescharacteristic
436C2×D3—204no—
437C2×D3—202no—
438C2×D3—402no—
439C2×D3—401no—
440C2×D3—401no—
441C3×C4—42no—
442C3×C4—102no—
443C3×C4C4×D2011yescharacteristic
444C3×C4D5×C22⋊C411yescharacteristic
445C3×C4#404011yescharacteristic
446C3×C4#404111yescharacteristic
447Dic3—41no—
448Dic3—41no—
449Dic3—202no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5#482211yescharacteristic
453C2×C5#482711yescharacteristic
454C2×C5#495811yescharacteristic
455D5—42no—
456D5—242no—
457C23—101no—
458C23—302no—
459C23—602no—
460C23—602no—
461C23—601no—
462C23—601no—
463C23#679011yescharacteristic
464Q8—52no—
465Q8—101no—
466D4—52no—
467D4—102no—
468D4—102no—
469D4—101no—
470D4—302no—
471D4—302no—
472D4—601no—
473D4—601no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—101no—
480C2×C4—102no—
481C2×C4—102no—
482C2×C4—302no—
483C2×C4—602no—
484C2×C4—1202no—
485C2×C4#676611yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4D5×D1211yescharacteristic
488C2×C4D3×D2011yescharacteristic
489C2×C4#677911yescharacteristic
490C2×C4D5×#6711yescharacteristic
491C8—62no—
492C8—201no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—202no—
496C2×C3#6495411yescharacteristic
497C2×C3#6511111yescharacteristic
498C2×C3#6511611yescharacteristic
499D3—402no—
500C5#7036611yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—102no—
504C22—201no—
505C22—201no—
506C22—604no—
507C22—602no—
508C22—1202no—
509C22—1201no—
510C22—1201no—
511C22#9139611yescharacteristic
512C22#9147611yescharacteristic
513C22#9155011yescharacteristic
514C4—42no—
515C4—102no—
516C4—121no—
517C4—121no—
518C4—602no—
519C4#9139511yescharacteristic
520C4#9140911yescharacteristic
521C4#9141311yescharacteristic
522C4D5×(C2×D3)⋊C411yescharacteristic
523C3#1059956911yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—202no—
527C2—1202no—
528C2#1174711811yescharacteristic
529C2#1174712511yescharacteristic
530C2#1174887211yescharacteristic
subgroupG/H
centerC22#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC2×#91301C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #11754509C2semidirect
3. #11751040C2semidirect
4. C2×C3×#3937C2semidirect
5. #11748396C2semidirect
6. C5×#4523C2semidirect
7. #11745987C2semidirect
24. #91301C4semidirect
34. C2×#3937D3semidirect
46. C2×D60C2×C4semidirect
66. C5×#208C2×C4semidirect
82. #4523D5semidirect
132. C3×D20C22⋊C4semidirect
136. C3×Dic10C22⋊C4semidirect
265. #208C4×D5semidirect
295. D20(C2×D3)⋊C4semidirect
300. Dic10(C2×D3)⋊C4semidirect
427. C3×C5#1883semidirect
500. C5#70366semidirect
523. C3#10599569semidirect

Maximal subgroups

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

subgroupindex
#117545092
C2×#913012
#117510402
C2×C3×#39372
#117483962
C5×#45232
#117459872
#105995693
#703665