Finite Group Databasebeta

← #14301348

Subgroups — #14301348

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
1C3×#65838C211yesmaximal, characteristic, complemented
2C2×#91301C211yesmaximal, characteristic
3#11751089C211yesmaximal, characteristic, complemented
4C2×#90976C211yesmaximal, characteristic, complemented
5#11748392C211yesmaximal, characteristic, complemented
6C5×#4530C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10599798—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6714—22no—
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×C4×C22⋊D5—22no—
17C3×#4072C2211yescharacteristic
18C3×#4039—21no—
19C3×#4038—21no—
20C3×D5×C4⋊C4—21no—
21C3×#4033—21no—
22C2×#6658—21no—
23#91301—22no—
24#91301C414yescomplemented
25C2×#6653—21no—
26#90976—22no—
27#90968—21no—
28#90968—21no—
29#71667—51nomaximal, Hall
30C2×#4054—31no—
31#65838D311yescharacteristic, complemented
32C2×#3957—31no—
33#65420—31no—
34#65277—31no—
35C5×#343—31no—
36#64775—31no—
37C23×D15—21no—
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
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×C4×D5—22no—
55C2×C3×Dic10D411yescharacteristic
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6714—44no—
59C4×Dic15—21no—
60C4×Dic15—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208—21no—
64C5×#208C2×C412yescomplemented
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C3×C22⋊Dic5—21no—
68C3×#685—22no—
69C3×C4⋊Dic5D411yescharacteristic
70C3×C4⋊Dic5D411yescharacteristic
71C3×#683—22no—
72C3×C4×Dic5—22no—
73C3×C4×Dic5—21no—
74#6658—24no—
75#6653—24no—
76C3×#520—51no—
77C2×#949—51no—
78C2×#837—51no—
79#5001—51no—
80#4988—51no—
81#4532—51no—
82#4530D511yescharacteristic, complemented
83C2×#709C2×D311yescharacteristic
84C22×D20—31no—
85C2×C5×M16—31no—
86C2×C5×M16—31no—
87C2×C5×C4⋊C4C2×D311yescharacteristic
88C4×C22⋊D5—22no—
89C2×#685—62no—
90#4072C2×D311yescharacteristic
91C2×C4×Dic5—31no—
92#4054—34no—
93#4054—62no—
94C2×D40—61no—
95C2×#677—61no—
96#4039—21no—
97#4038—21no—
98D5×C4⋊C4—21no—
99#4033—21no—
100#3957—62no—
101#3953—61no—
102#3953—61no—
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—42no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×Dic15—22no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122D60—22no—
123D60—22no—
124D60—41no—
125D60—41no—
126C3×C22⋊D5—22no—
127C3×C22⋊D5—22no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—21no—
131C3×D20—21no—
132C3×D20C22⋊C412yescomplemented
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×C4×D5—82no—
136C3×Dic10—21no—
137C3×Dic10C22⋊C412yescomplemented
138C5×C3⋊C8—22no—
139C5×C3⋊C8—41no—
140C2×C3×#41—51no—
141C22×D12—51no—
142C3×C4×Q8—101no—
143C3×C4×D4—101no—
144C3×C4×D4—102no—
145C3×#117—51no—
146C3×#117—101no—
147C2×C3×C4⋊C4—101no—
148C2×C3×C4⋊C4C2×D511yescharacteristic
149#949—54no—
150#949—102no—
151C2×#215—101no—
152C2×#213—101no—
153C2×(C2×D3)⋊C4—102no—
154C2×C4×Dic3—51no—
155C2×#208C2×D511yescharacteristic
156C2×#208C2×D511yescharacteristic
157#837—102no—
158#809—101no—
159#809—101no—
160C23×D5—61no—
161C22×C4×C5#6712yes—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—21no—
164C22×Dic5—61no—
165#709—21no—
166#709—21no—
167#709C4×D312yes—
168#709D1212yes—
169C2×D20—32no—
170C2×D20—61no—
171C2×D20—61no—
172C2×D20—61no—
173C2×D20—61no—
174C2×D20—61no—
175C2×D20#6711yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—22no—
178C2×Dic10#6711yescharacteristic
179C5×M16—32no—
180C5×M16—61no—
181C5×M16—61no—
182C5×M16—61no—
183C2×C5×C8—61no—
184C2×C5×C8—61no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C22⋊Dic5—21no—
188#685—22no—
189#685—124no—
190C4⋊Dic5#6711yescharacteristic
191C4⋊Dic5#6711yescharacteristic
192#683—22no—
193C4×Dic5—22no—
194C4×Dic5—21no—
195C4×Dic5—61no—
196C4×Dic5—61no—
197D40—64no—
198#677—64no—
199C2×AGL(1,ℤ/8)—151no—
200#520—51no—
201C2×#104—151no—
202#418—151no—
203#390—151no—
204#343—31no—
205#339—151no—
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—
226C3×Dic5—41no—
227C3×Dic5—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—102no—
237C22×C3×C4—101no—
238C22×C3×C4D2012yes—
239C22×C3×C4C22×D511yescharacteristic
240C22×Dic3—101no—
241C2×D12—52no—
242C2×D12—101no—
243C2×D12—101no—
244C2×D12—101no—
245C2×D12—101no—
246C2×D12—101no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—102no—
252C3×C22⋊C4—102no—
253C3×C22⋊C4—101no—
254C3×C42—102no—
255C3×C42—101no—
256#215—104no—
257#213—104no—
258(C2×D3)⋊C4—204no—
259C4×Dic3—101no—
260C4×Dic3—101no—
261#208—21no—
262#208—21no—
263#208—21no—
264#208C4×D512yescomplemented
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C23×C5C2×#6711yescharacteristic
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—42no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5C2×D1211yescharacteristic
278C2×C4×C5#23511yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5C2×#6711yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C22⋊D5—22no—
283C22⋊D5—22no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—62no—
288C2×Dic5—121no—
289C2×Dic5—121no—
290D20—21no—
291D20—62no—
292D20—62no—
293D20—121no—
294D20—121no—
295D20(C2×D3)⋊C412yescomplemented
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—82no—
299Dic10—21no—
300Dic10(C2×D3)⋊C412yescomplemented
301C5×C8—62no—
302C5×C8—121no—
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—31no—
311C4×Q8—101no—
312C4×D4—101no—
313C4×D4—102no—
314#117—51no—
315#117—101no—
316C2×C4⋊C4—101no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—302no—
319C2×C42—151no—
320#104—302no—
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×C3C2×D2011yescharacteristic
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—42no—
345C2×C3×C4—101no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—402no—
351C2×C3×C4C2×C4×D511yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4#71311yescharacteristic
357C2×Dic3—102no—
358C2×Dic3—201no—
359C2×Dic3—201no—
360D12—102no—
361D12—102no—
362D12—201no—
363D12—201no—
364C3⋊C8—22no—
365C3⋊C8—41no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5C4×#6711yescharacteristic
369C22×C5#93011yescharacteristic
370C22×C5#95311yescharacteristic
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×C5C2×(C2×D3)⋊C411yescharacteristic
381C4×C5C4×#6711yescharacteristic
382C4×C5#92911yescharacteristic
383C4×C5#93011yescharacteristic
384Dic5—22no—
385Dic5—41no—
386Dic5—41no—
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—102no—
403C22×C4—101no—
404C22×C4—301no—
405C22×C4#120212yes—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—32no—
410M16—61no—
411M16—61no—
412M16—61no—
413C2×C8—61no—
414C2×C8—61no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—51no—
418C4⋊C4—51no—
419C4⋊C4—102no—
420C22⋊C4—102no—
421C22⋊C4—101no—
422C22⋊C4—604no—
423C42—102no—
424C42—101no—
425C42—301no—
426C42—301no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—102no—
431C22×C3—201no—
432C22×C3—201no—
433C22×C3C4×D2011yescharacteristic
434C22×C3#402811yescharacteristic
435C22×C3#404111yescharacteristic
436C2×D3—204no—
437C2×D3—202no—
438C2×D3—402no—
439C2×D3—401no—
440C2×D3—401no—
441C3×C4—42no—
442C3×C4—102no—
443C3×C4—201no—
444C3×C4—201no—
445C3×C4D5×C22⋊C411yescharacteristic
446C3×C4#403011yescharacteristic
447C3×C4#403911yescharacteristic
448C3×C4#404011yescharacteristic
449Dic3—202no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5#521311yescharacteristic
453C2×C5#524111yescharacteristic
454C2×C5#524511yescharacteristic
455D5—42no—
456D5—242no—
457C23—101no—
458C23—302no—
459C23—602no—
460C23—602no—
461C23—601no—
462C23—601no—
463C23C2×#120211yescharacteristic
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—42no—
476C2×C4—101no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—101no—
480C2×C4—101no—
481C2×C4—302no—
482C2×C4—402no—
483C2×C4—601no—
484C2×C4—601no—
485C2×C4#677111yescharacteristic
486C2×C4#677311yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4D5×D1211yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4D5×#6711yescharacteristic
491C8—62no—
492C8—121no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—202no—
496C2×C3#6495411yescharacteristic
497C2×C3#6503611yescharacteristic
498C2×C3#6504211yescharacteristic
499D3—402no—
500C5#7166711yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—102no—
504C22—201no—
505C22—201no—
506C22—604no—
507C22—602no—
508C22—1202no—
509C22—1201no—
510C22—1201no—
511C22C4×#120211yescharacteristic
512C22#9145011yescharacteristic
513C22#9156411yescharacteristic
514C4—42no—
515C4—102no—
516C4—201no—
517C4—201no—
518C4—602no—
519C4#9134811yescharacteristic
520C4#9144411yescharacteristic
521C4#9144811yescharacteristic
522C4D5×(C2×D3)⋊C411yescharacteristic
523C3#1059979811yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—202no—
527C2—1202no—
528C2#1174890711yescharacteristic
529C2#1174913811yescharacteristic
530C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91301C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65838C2semidirect
3. #11751089C2semidirect
4. C2×#90976C2semidirect
5. #11748392C2semidirect
6. C5×#4530C2semidirect
7. #11745973C2semidirect
24. #91301C4semidirect
31. #65838D3semidirect
46. C2×D60C2×C4semidirect
64. C5×#208C2×C4semidirect
82. #4530D5semidirect
132. C3×D20C22⋊C4semidirect
137. C3×Dic10C22⋊C4semidirect
264. #208C4×D5semidirect
295. D20(C2×D3)⋊C4semidirect
300. Dic10(C2×D3)⋊C4semidirect
427. C3×C5#1883semidirect
500. C5#71667semidirect
523. C3#10599798semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
C2×#913012
#117510892
C2×#909762
#117483922
C5×#45302
#117459732
#105997983
#716675