Finite Group Databasebeta

← #14302578

Subgroups — #14302578

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754414C211yesmaximal, characteristic, complemented
2#11754145C211yesmaximal, characteristic
3#11751106C211yesmaximal, characteristic, complemented
4C5×#5006C211yesmaximal, characteristic, complemented
5C2×#90979C211yesmaximal, characteristic, complemented
6C3×#64752C211yesmaximal, characteristic, complemented
7#11745989C211yesmaximal, characteristic, complemented
8#10600848—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91552—22no—
17#91418—21no—
18C4×#1200—21no—
19#91386—21no—
20#91333—21no—
21#91322—21no—
22#91321C412yescomplemented
23#91305—21no—
24#91304C412yescomplemented
25#91303—22no—
26#91089—22no—
27C5×#806—22no—
28#90979—21no—
29#90979—21no—
30#68778—51nomaximal, Hall
31#66156—31no—
32#65856—31no—
33C5×#410—31no—
34C2×#3969—31no—
35#65294—31no—
36#64753—31no—
37#64752D311yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40#6817—21no—
41#6817—21no—
42#6817C2×C412yes—
43#6817D412yes—
44C2×D60D411yescharacteristic
45C2×C4×D15—21no—
46C2×Dic30D411yescharacteristic
47C2×C5×#67—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C2×C5×D12C2×C411yescharacteristic, complemented
53C2×C4×C5×D3—21no—
54C2×C5×Dic6C2×C411yescharacteristic, complemented
55C22×C3×Dic5—21no—
56C2×#1200—22no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60#6710—21no—
61#6710—21no—
62C2×C3⋊#168—21no—
63C5×#217D412yes—
64C5×C4⋊Dic3—21no—
65C4×C5×Dic3—21no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5D411yescharacteristic
68C3×C4×Dic5D411yescharacteristic
69C3×#681—21no—
70C3×#681C2×C412yescomplemented
71C2×C3×#168—21no—
72#6669—22no—
73#6667—22no—
74Dic3×Dic5—22no—
75#6663—22no—
76#6660—22no—
77#6659—22no—
78#6654—22no—
79#5748—51no—
80C4×#235—51no—
81#5006D511yescharacteristic, complemented
82#5005—51no—
83C2×#805—51no—
84C3×#339—51no—
85#4559—51no—
86C2×C5×#41—31no—
87C2×#709—31no—
88C5×#117—31no—
89C5×#117C2×D311yescharacteristic
90#4097—61no—
91#4096—62no—
92#4095—61no—
93#4088—32no—
94#4078—32no—
95C2×C4×Dic5C2×D311yescharacteristic
96C2×#681—31no—
97C2×#681C2×D311yescharacteristic
98#4039—61no—
99#4033—61no—
100#4027—62no—
101#4018—61no—
102C42×D5—61no—
103C5×#99—62no—
104#3969—61no—
105#3969—61no—
106#3937—62no—
107#1906—151noSylow
108C23×C3×C5C2×D411yescharacteristic
109C22×D15—21no—
110C22×C5×D3—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118#1220—22no—
119#1220—22no—
120C2×Dic15—21no—
121D60—21no—
122D60C22⋊C412yes—
123C4×D15—22no—
124C4×D15—22no—
125Dic30—21no—
126Dic30C22⋊C412yes—
127C5×#67—41no—
128C5×#67—41no—
129C2×C5×Dic3—21no—
130C2×C5×Dic3—22no—
131C5×D12—21no—
132C5×D12—21no—
133C4×C5×D3—41no—
134C4×C5×D3—41no—
135C5×Dic6—21no—
136C5×Dic6—21no—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—42no—
140#1200—44no—
141C3⋊#168—41no—
142C3×#168—22no—
143C2×#235—51no—
144C2×#235C2×D511yescharacteristic
145C2×C3×M16—51no—
146C3×#117C2×D511yescharacteristic
147C2×C3×C42—51no—
148C4×#67—102no—
149#926C2×D511yescharacteristic
150C2×#208—51no—
151#909—52no—
152#909—101no—
153#908—52no—
154#908—101no—
155#904—102no—
156C4×D12—101no—
157#872—101no—
158C42×D3—101no—
159C4×Dic6—101no—
160#806—22no—
161#805—102no—
162#805—101no—
163#805—101no—
164C5×#41—61no—
165C5×#41—61no—
166C5×#41—61no—
167C5×#41—61no—
168C2×C5×Q8—31no—
169C2×C5×D4—31no—
170C2×C5×D4—61no—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—61no—
174C22×Dic5—21no—
175#709—32no—
176#709—32no—
177#709—61no—
178#709—61no—
179C2×D20—31no—
180C2×C4×D5—61no—
181C2×C4×D5—62no—
182C2×Dic10—31no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—61no—
185C5×C22⋊C4—21no—
186C5×C22⋊C4—32no—
187C42×C5—21no—
188C42×C5—61no—
189#689—62no—
190#688—62no—
191#687—62no—
192#686—62no—
193#685—62no—
194#683—62no—
195C4×Dic5—21no—
196C4×Dic5—62no—
197C4×Dic5D1211yescharacteristic
198C4×Dic5D1211yescharacteristic
199#681—21no—
200#681—61no—
201#681—61no—
202#681C4×D312yescomplemented
203C2×#168—21no—
204C2×#168—61no—
205#575—151no—
206C4×#41—151no—
207#421—151no—
208C2×#104—151no—
209#410—31no—
210#344—151no—
211#339—51no—
212C22×C3×C5—41no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×D15—22no—
217C2×D15—42no—
218C2×C5×D3—41no—
219C2×C5×D3—81no—
220C3×C4×C5—81no—
221C3×C4×C5C2×C22⋊C411yescharacteristic
222C3×C4×C5C4×D411yescharacteristic
223C3×C4×C5#12111yescharacteristic
224C3×C4×C5#12311yescharacteristic
225Dic15—22no—
226C3×Dic5—22no—
227C3×Dic5—41no—
228C5×Dic3—42no—
229C5×Dic3—41no—
230C22×C3×C4—101no—
231C22×C3×C4C22×D511yescharacteristic
232C2×#67—21no—
233C2×#67—101no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238#235—52no—
239#235—52no—
240#235—101no—
241#235—101no—
242C2×D12—51no—
243C2×D12C4×D511yescharacteristic, complemented
244C2×C4×D3—21no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—51no—
248C2×Dic6C4×D511yescharacteristic, complemented
249C3×M16—52no—
250C3×M16—101no—
251C2×C3×C8—101no—
252C3×C4⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C42—21no—
255C3×C42—51no—
256C3×C42—51no—
257C3×C42—101no—
258#217C22⋊D512yes—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—21no—
261Dic3⋊C4—102no—
262C4×Dic3—21no—
263C4×Dic3—102no—
264#208—101no—
265#208—101no—
266C2×C3⋊C8—101no—
267Dic12—102no—
268D24—102no—
269#204—102no—
270#204—102no—
271C23×C5—61no—
272C23×C5D3×D411yescharacteristic
273C22×D5—61no—
274C5×Q8—61no—
275C5×Q8—61no—
276C5×D4—61no—
277C5×D4—61no—
278C5×D4—121no—
279C5×D4—121no—
280C2×C4×C5—41no—
281C2×C4×C5—62no—
282C2×C4×C5—61no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5C2×D1211yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5#23911yescharacteristic
291C22⋊D5—62no—
292C22⋊D5—62no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—42no—
296C2×Dic5—61no—
297D20—32no—
298D20—61no—
299C4×D5—62no—
300C4×D5—62no—
301C4×D5—124no—
302Dic10—32no—
303Dic10—61no—
304#168—22no—
305#168—121no—
306C2×#41—31no—
307C2×#41—151no—
308#137—152no—
309#137—301no—
310AGL(1,ℤ/8)—152no—
311AGL(1,ℤ/8)—301no—
312#135—302no—
313C2×M16—51no—
314C2×M16—151no—
315C4×Q8—301no—
316C4×D4—301no—
317C4×D4—302no—
318#117—31no—
319#117—301no—
320#117D3×D511yescharacteristic
321C2×C42—51no—
322C2×C42—301no—
323#104—302no—
324#104—301no—
325#104—301no—
326#99—62no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5—21no—
330C2×C3×C5#38611yescharacteristic
331D15—42no—
332C5×D3—81no—
333C23×C3C2×C22⋊D511yescharacteristic
334C22×D3—21no—
335C22×D3—101no—
336C2×C3×C4—41no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—202no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71111yescharacteristic
346#67—41no—
347#67—41no—
348#67—102no—
349#67—102no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—101no—
353D12—21no—
354D12—21no—
355D12—52no—
356D12—101no—
357C4×D3—41no—
358C4×D3—41no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—204no—
362Dic6—21no—
363Dic6—21no—
364Dic6—52no—
365Dic6—101no—
366C3×C8—102no—
367C3⋊C8—201no—
368C22×C5—41no—
369C22×C5—121no—
370C22×C5—241no—
371C22×C5#88211yescharacteristic
372C22×C5#88411yescharacteristic
373C22×C5#89311yescharacteristic
374C2×D5—62no—
375C2×D5—122no—
376C4×C5—81no—
377C4×C5—122no—
378C4×C5—121no—
379C4×C5C4×D1211yescharacteristic
380C4×C5D3×C22⋊C411yescharacteristic
381C4×C5#89411yescharacteristic
382C4×C5#89511yescharacteristic
383Dic5—22no—
384Dic5—41no—
385Dic5—62no—
386#41—61no—
387#41—61no—
388#41—61no—
389#41—61no—
390#41—152no—
391#41—152no—
392#41—301no—
393#41—301no—
394C2×Q8—31no—
395C2×Q8—151no—
396C2×D4—31no—
397C2×D4—61no—
398C2×D4—151no—
399C2×D4—301no—
400C22×C4—61no—
401C22×C4—101no—
402C22×C4—302no—
403C22×C4—301no—
404C22×C4C2×D3×D511yescharacteristic
405Q16—302no—
406SD16—302no—
407SD16—302no—
408D8—302no—
409M16—52no—
410M16—101no—
411M16—301no—
412M16—301no—
413C2×C8—101no—
414C2×C8—301no—
415C4⋊C4—21no—
416C4⋊C4—61no—
417C4⋊C4—302no—
418C22⋊C4—21no—
419C22⋊C4—32no—
420C22⋊C4—302no—
421C42—21no—
422C42—51no—
423C42—51no—
424C42—61no—
425C42—101no—
426C42—302no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3C4×C22⋊D511yescharacteristic
430C22×C3#408311yescharacteristic
431C22×C3#408411yescharacteristic
432C2×D3—41no—
433C2×D3—81no—
434C2×D3—102no—
435C2×D3—202no—
436C3×C4—81no—
437C3×C4—102no—
438C3×C4—201no—
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#402711yescharacteristic
441C3×C4#402911yescharacteristic
442C3×C4#403011yescharacteristic
443Dic3—42no—
444Dic3—41no—
445Dic3—102no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—241no—
450C2×C5#466511yescharacteristic
451D5—122no—
452C23—61no—
453C23—301no—
454C23D3×C22⋊D511yescharacteristic
455Q8—61no—
456Q8—61no—
457Q8—152no—
458Q8—301no—
459D4—61no—
460D4—61no—
461D4—121no—
462D4—121no—
463D4—152no—
464D4—302no—
465D4—302no—
466D4—301no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—101no—
471C2×C4—101no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—202no—
475C2×C4—301no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—604no—
479C2×C4#676911yescharacteristic
480C2×C4C4×D3×D511yescharacteristic
481C2×C4D5×D1211yescharacteristic
482C2×C4#677711yescharacteristic
483C2×C4#678211yescharacteristic
484C2×C4#679011yescharacteristic
485C8—102no—
486C8—601no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3#6524511yescharacteristic
491D3—81no—
492D3—202no—
493C5#6877811yescharacteristic, complemented, Sylow
494C22—41no—
495C22—121no—
496C22—241no—
497C22—302no—
498C22—602no—
499C22#9144611yescharacteristic
500C22#9147511yescharacteristic
501C22#9155711yescharacteristic
502C4—81no—
503C4—102no—
504C4—122no—
505C4—121no—
506C4—201no—
507C4—302no—
508C4#9140511yescharacteristic
509C4#9142011yescharacteristic
510C4#9143811yescharacteristic
511C4#9147311yescharacteristic
512C3#1060084811yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—241no—
517C2—602no—
518C2#1174891911yescharacteristic
subgroupG/H
centerC4#91420
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754145C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11754414C2semidirect
3. #11751106C2semidirect
4. C5×#5006C2semidirect
5. C2×#90979C2semidirect
6. C3×#64752C2semidirect
7. #11745989C2semidirect
22. #91321C4semidirect
24. #91304C4semidirect
37. #64752D3semidirect
52. C2×C5×D12C2×C4semidirect
54. C2×C5×Dic6C2×C4semidirect
70. C3×#681C2×C4semidirect
81. #5006D5semidirect
202. #681C4×D3semidirect
243. C2×D12C4×D5semidirect
248. C2×Dic6C4×D5semidirect
427. C3×C5#1906semidirect
493. C5#68778semidirect
512. C3#10600848semidirect

Maximal subgroups

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

subgroupindex
#117544142
#117541452
#117511062
C5×#50062
C2×#909792
C3×#647522
#117459892
#106008483
#687785