Finite Group Databasebeta

← #14301349

Subgroups — #14301349

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#11756263C211yesmaximal, characteristic, complemented
2C2×#91312C211yesmaximal, characteristic
3C3×#65277C211yesmaximal, characteristic, complemented
4C2×#90981C211yesmaximal, characteristic, complemented
5#11748367C211yesmaximal, characteristic, complemented
6C5×#4530C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10599798—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91782—21no—
15#91781—21no—
16C4⋊C4×D15—21no—
17#91776—21no—
18C2×C5×#208C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×#685—22no—
21C2×C3×C4×Dic5C2211yescharacteristic
22#91312—22no—
23#91312C414yescomplemented
24C2×#6657—21no—
25C2×#6653—21no—
26#90981—22no—
27#90965—21no—
28#90965—21no—
29#69663—51nomaximal, Hall
30C2×#4054—31no—
31#65838—31no—
32C2×#3957—31no—
33#65420—31no—
34#65277D311yescharacteristic, complemented
35C5×#343—31no—
36#64775—31no—
37C23×C3×D5—21no—
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41#6817—21no—
42#6817—21no—
43#6817C2×C412yes—
44#6817D412yes—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×C4×D15—22no—
48C2×Dic30D411yescharacteristic
49C22×C3×Dic5—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20—21no—
54C2×C3×D20—21no—
55C2×C3×D20C2×C412yescomplemented
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6719—21no—
59#6714—22no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15—21no—
65C5×#208—21no—
66C5×#208—21no—
67C5×#208—21no—
68C5×#208C2×C412yescomplemented
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8—21no—
71C3×#685—44no—
72C3×C4×Dic5—21no—
73C3×C4×Dic5—21no—
74#6657—24no—
75#6653—24no—
76C2×#932—51no—
77#5504—51no—
78C3×#390—51no—
79#5215—51no—
80C2×#805—51no—
81#4530D511yescharacteristic, complemented
82#4523—51no—
83C2×#709—31no—
84C22×D20C2×D311yescharacteristic
85C2×C5×M16—31no—
86C2×C5×M16—31no—
87C2×C5×C4⋊C4C2×D311yescharacteristic
88C4×C22⋊D5—62no—
89C2×#685—22no—
90#4072—31no—
91C2×C4×Dic5C2×D311yescharacteristic
92#4054—34no—
93#4054—62no—
94C2×D40—61no—
95C2×#677—61no—
96#4039—61no—
97#4038—61no—
98D5×C4⋊C4—61no—
99#4033—61no—
100#3957—62no—
101#3953—61no—
102#3953—61no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×D15—21no—
106C22×C3×D5—22no—
107C22×C3×D5—42no—
108C22×C3×D5—42no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
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
119#1220—22no—
120#1220—22no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123C2×Dic15—21no—
124D60—21no—
125D60C22⋊C412yescomplemented
126C4×D15—22no—
127C4×D15—22no—
128C4×D15—82no—
129Dic30—21no—
130Dic30C22⋊C412yescomplemented
131C2×C3×Dic5—22no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C3×D20—22no—
135C3×D20—22no—
136C3×D20—41no—
137C3×D20—41no—
138C5×C3⋊C8—22no—
139C5×C3⋊C8—41no—
140C22×C3×D4—51no—
141C2×#235—51no—
142C2×C3×C4⋊C4C2×D511yescharacteristic
143C2×C3×C22⋊C4—102no—
144C2×C3×C42—51no—
145C2×#214—101no—
146#932—54no—
147#932—102no—
148C2×#213—101no—
149C4×#67—102no—
150#926—51no—
151C2×#208C2×D511yescharacteristic
152C2×#208C2×D511yescharacteristic
153#893—101no—
154#892—101no—
155D3×C4⋊C4—101no—
156#887—101no—
157#832—101no—
158#832—101no—
159#805—102no—
160C23×D5—21no—
161C22×C4×C5#6712yes—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C22×Dic5—21no—
165#709—32no—
166#709—32no—
167#709—61no—
168#709—61no—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20—21no—
173C2×D20—21no—
174C2×D20—31no—
175C2×D20C4×D312yescomplemented
176C2×C4×D5—61no—
177C2×C4×D5—62no—
178C2×Dic10—31no—
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—61no—
188#685—44no—
189#685—62no—
190C4⋊Dic5—31no—
191C4⋊Dic5—31no—
192#683—62no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—62no—
196C4×Dic5—61no—
197D40—64no—
198#677—64no—
199C2×AGL(1,ℤ/8)—151no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—51no—
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—22no—
212C2×D15—41no—
213C2×D15—41no—
214C2×C3×D5—44no—
215C2×C3×D5—42no—
216C2×C3×D5—82no—
217C2×C3×D5—81no—
218C2×C3×D5—81no—
219C3×C4×C5—42no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—22no—
225Dic15—41no—
226Dic15—41no—
227C3×Dic5—42no—
228C24×C3—101no—
229C2×C3×D4—52no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—101no—
234C2×C3×D4—101no—
235C22×C3×C4—101no—
236C22×C3×C4D2012yes—
237C22×C3×C4C22×D511yescharacteristic
238C2×#67—101no—
239#235—52no—
240#235—52no—
241#235—101no—
242#235—101no—
243C2×D12—51no—
244C2×C4×D3—101no—
245C2×C4×D3—102no—
246C2×Dic6—51no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C22⋊C4—204no—
250C3×C42—101no—
251C3×C42—101no—
252#217—101no—
253#214—104no—
254#213—104no—
255(C2×D3)⋊C4—102no—
256C4⋊Dic3—51no—
257C4⋊Dic3—51no—
258Dic3⋊C4—102no—
259C4×Dic3—102no—
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—22no—
269C22×D5—42no—
270C22×D5—42no—
271C22×D5—41no—
272C22×D5—41no—
273C22×D5—61no—
274C2×C4×C5—22no—
275C2×C4×C5—42no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5#23511yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23711yescharacteristic
282C22⋊D5—62no—
283C22⋊D5—62no—
284C2×Dic5—22no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290D20—22no—
291D20—22no—
292D20—32no—
293D20—41no—
294D20—41no—
295D20—61no—
296C4×D5—62no—
297C4×D5—62no—
298C4×D5—242no—
299Dic10—32no—
300Dic10—61no—
301C5×C8—62no—
302C5×C8—121no—
303C2×#41—151no—
304C22×D4—51no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—31no—
310C2×M16—31no—
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—151no—
315#117—301no—
316C2×C4⋊C4—301no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—102no—
319C2×C42—51no—
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—42no—
329C3×D5—82no—
330C23×C3—102no—
331C23×C3—202no—
332C23×C3—202no—
333C23×C3—201no—
334C23×C3—201no—
335C23×C3C2×D2011yescharacteristic
336C22×D3—101no—
337C3×D4—102no—
338C3×D4—102no—
339C3×D4—201no—
340C3×D4—201no—
341C2×C3×C4—22no—
342C2×C3×C4—42no—
343C2×C3×C4—102no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4#70911yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4#71311yescharacteristic
352#67—102no—
353#67—102no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—101no—
357D12—52no—
358D12—101no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—402no—
362Dic6—52no—
363Dic6—101no—
364C3⋊C8—22no—
365C3⋊C8—41no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5C4×#6711yescharacteristic
369C22×C5#93711yescharacteristic
370C22×C5#93811yescharacteristic
371C2×D5—44no—
372C2×D5—42no—
373C2×D5—62no—
374C2×D5—82no—
375C2×D5—81no—
376C2×D5—81no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—42no—
380C4×C5D3×C22⋊C411yescharacteristic
381C4×C5#67⋊C411yescharacteristic
382C4×C5#88311yescharacteristic
383C4×C5#88411yescharacteristic
384Dic5—42no—
385Dic5—62no—
386Dic5—121no—
387Dic5—121no—
388C24—101no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—52no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4—101no—
400C2×D4—151no—
401C2×D4—301no—
402C22×C4—101no—
403C22×C4—302no—
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—151no—
418C4⋊C4—151no—
419C4⋊C4—302no—
420C22⋊C4—204no—
421C22⋊C4—302no—
422C22⋊C4—301no—
423C42—101no—
424C42—101no—
425C42—302no—
426C42—301no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—204no—
431C22×C3—202no—
432C22×C3—402no—
433C22×C3—401no—
434C22×C3—401no—
435C22×C3C4×D2011yescharacteristic
436C22×C3#402811yescharacteristic
437C22×C3#404111yescharacteristic
438C2×D3—102no—
439C2×D3—201no—
440C2×D3—201no—
441C3×C4—42no—
442C3×C4—202no—
443C3×C4D5×C22⋊C411yescharacteristic
444C3×C4#403011yescharacteristic
445C3×C4#403911yescharacteristic
446C3×C4#404011yescharacteristic
447Dic3—102no—
448Dic3—201no—
449Dic3—201no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5#495611yescharacteristic
453C2×C5#506211yescharacteristic
454C2×C5#507711yescharacteristic
455D5—82no—
456D5—122no—
457C23—102no—
458C23—202no—
459C23—202no—
460C23—201no—
461C23—201no—
462C23—301no—
463C23C2×#120211yescharacteristic
464Q8—152no—
465Q8—301no—
466D4—102no—
467D4—102no—
468D4—152no—
469D4—201no—
470D4—201no—
471D4—302no—
472D4—302no—
473D4—301no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—102no—
477C2×C4—201no—
478C2×C4—201no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—301no—
483C2×C4—301no—
484C2×C4—1202no—
485C2×C4#676611yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4#677711yescharacteristic
489C2×C4#679011yescharacteristic
490C2×C4#679011yescharacteristic
491C8—62no—
492C8—121no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—402no—
496C2×C3#6495411yescharacteristic
497C2×C3#6503611yescharacteristic
498C2×C3#6504211yescharacteristic
499D3—202no—
500C5#6966311yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—204no—
504C22—202no—
505C22—302no—
506C22—402no—
507C22—401no—
508C22—401no—
509C22—601no—
510C22—601no—
511C22C4×#120211yescharacteristic
512C22#9146511yescharacteristic
513C22#9157211yescharacteristic
514C4—42no—
515C4—202no—
516C4—302no—
517C4—601no—
518C4—601no—
519C4#9135411yescharacteristic
520C4#9139611yescharacteristic
521C4#9146111yescharacteristic
522C4#9147311yescharacteristic
523C3#1059979811yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—402no—
527C2—602no—
528C2#1174891711yescharacteristic
529C2#1174914211yescharacteristic
530C2#1174938811yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91312C2
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. #11756263C2semidirect
3. C3×#65277C2semidirect
4. C2×#90981C2semidirect
5. #11748367C2semidirect
6. C5×#4530C2semidirect
7. #11745978C2semidirect
23. #91312C4semidirect
34. #65277D3semidirect
55. C2×C3×D20C2×C4semidirect
68. C5×#208C2×C4semidirect
81. #4530D5semidirect
125. D60C22⋊C4semidirect
130. Dic30C22⋊C4semidirect
175. C2×D20C4×D3semidirect
264. #208C4×D5semidirect
427. C3×C5#1883semidirect
500. C5#69663semidirect
523. C3#10599798semidirect

Maximal subgroups

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

subgroupindex
#117562632
C2×#913122
C3×#652772
C2×#909812
#117483672
C5×#45302
#117459782
#105997983
#696635