Finite Group Databasebeta

← #14302577

Subgroups — #14302577

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#11754444C211yesmaximal, characteristic, complemented
2#11754138C211yesmaximal, characteristic
3C5×#5006C211yesmaximal, characteristic, complemented
4C3×#65294C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic, complemented
6#11746353C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10600848—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91559—22no—
17#91434—21no—
18C4×D5×Dic3—21no—
19#91357—21no—
20#91331—21no—
21#91309—21no—
22#91307C412yescomplemented
23#91299C412yescomplemented
24#91298—21no—
25#91297—22no—
26C5×#806—22no—
27C3×#3937—22no—
28#90978—21no—
29#90978—21no—
30#70395—51nomaximal, Hall
31#66156—31no—
32#65856—31no—
33C5×#410—31no—
34C2×#3969—31no—
35#65294D311yescharacteristic, complemented
36#64753—31no—
37#64752—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C2×C5×D12C2×C411yescharacteristic, complemented
46C2×C4×C5×D3—21no—
47C2×C5×Dic6C2×C411yescharacteristic, complemented
48C2×C3×C22⋊D5—21no—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709C2×C412yes—
52C3×#709D412yes—
53C2×C3×D20D411yescharacteristic
54C2×C3×C4×D5—21no—
55C2×C3×Dic10D411yescharacteristic
56C2×D5×Dic3—22no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60C4×Dic15—21no—
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63#6710—21no—
64#6710C2×C412yescomplemented
65C2×C3⋊#168—21no—
66C5×#217D412yes—
67C5×C4⋊Dic3—21no—
68C4×C5×Dic3—21no—
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168—21no—
72#6668—22no—
73#6665—22no—
74Dic3×Dic5—22no—
75#6661—22no—
76#6656—22no—
77#6655—22no—
78#6652—22no—
79Dic3×#41—51no—
80#5822—51no—
81C3×#421—51no—
82C2×#825—51no—
83#5006D511yescharacteristic, complemented
84#4556—51no—
85#4532—51no—
86C2×C5×#41—31no—
87C2×#709C2×D311yescharacteristic
88C5×#117—31no—
89C5×#117C2×D311yescharacteristic
90#4097—61no—
91#4096—62no—
92#4095—61no—
93#4088—32no—
94#4078—32no—
95C2×C4×Dic5—31no—
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—22no—
107#1906—151noSylow
108C23×C3×C5C2×D411yescharacteristic
109C22×C5×D3—21no—
110C22×C3×D5—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
118C2×Dic15—21no—
119C2×Dic15—21no—
120C2×Dic15—42no—
121C5×#67—41no—
122C5×#67—41no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—22no—
125C5×D12—21no—
126C5×D12—21no—
127C4×C5×D3—41no—
128C4×C5×D3—41no—
129C5×Dic6—21no—
130C5×Dic6—21no—
131C3×C22⋊D5—22no—
132C3×C22⋊D5—22no—
133C2×C3×Dic5—21no—
134C3×D20—21no—
135C3×D20C22⋊C412yes—
136C3×C4×D5—22no—
137C3×C4×D5—22no—
138C3×Dic10—21no—
139C3×Dic10C22⋊C412yes—
140D5×Dic3—44no—
141C3⋊#168—22no—
142C3×#168—41no—
143C2×C3×#41—51no—
144C2×#235C2×D511yescharacteristic
145C2×C3×M16—51no—
146C3×#117C2×D511yescharacteristic
147#951—52no—
148#950—102no—
149#949—52no—
150Q8×Dic3—101no—
151#942—101no—
152D4×Dic3—101no—
153D4×Dic3—102no—
154#932—101no—
155#926—101no—
156#926C2×D511yescharacteristic
157C2×C4×Dic3—51no—
158C2×C4×Dic3—101no—
159C2×#208—51no—
160C3×#104—102no—
161#825—101no—
162#825—101no—
163#806—22no—
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—21no—
174C22×Dic5—61no—
175#709—21no—
176#709—21no—
177#709C4×D312yes—
178#709#6712yes—
179C2×D20D1211yescharacteristic
180C2×C4×D5—21no—
181C2×C4×D5—62no—
182C2×Dic10D1211yescharacteristic
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—31no—
196C4×Dic5—31no—
197C4×Dic5—62no—
198C4×Dic5—61no—
199#681—21no—
200#681—21no—
201#681—32no—
202#681—61no—
203C2×#168—21no—
204C2×#168—61no—
205#575—151no—
206C4×#41—151no—
207#421—51no—
208C2×#104—151no—
209#410—31no—
210#344—151no—
211#339—151no—
212C22×C3×C5—41no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×C5×D3—41no—
217C2×C5×D3—81no—
218C2×C3×D5—22no—
219C2×C3×D5—42no—
220C3×C4×C5—81no—
221C3×C4×C5C2×C22⋊C411yescharacteristic
222C3×C4×C5C4×D411yescharacteristic
223C3×C4×C5#12111yescharacteristic
224C3×C4×C5#12311yescharacteristic
225Dic15—22no—
226Dic15—41no—
227C3×Dic5—22no—
228C5×Dic3—42no—
229C5×Dic3—41no—
230C3×#41—52no—
231C3×#41—52no—
232C3×#41—101no—
233C3×#41—101no—
234C2×C3×Q8—51no—
235C2×C3×D4—51no—
236C2×C3×D4—101no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C2×#67—21no—
240C22×Dic3—102no—
241C22×Dic3—101no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246C2×D12C4×D511yescharacteristic, complemented
247C2×C4×D3—21no—
248C2×Dic6C4×D511yescharacteristic, complemented
249C3×M16—101no—
250C3×M16—101no—
251C2×C3×C8—101no—
252C3×C4⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C42—21no—
255#217—102no—
256#217C22⋊D512yes—
257#216—102no—
258#215—102no—
259#214—102no—
260#213—102no—
261C4⋊Dic3—21no—
262C4⋊Dic3—102no—
263C4×Dic3—21no—
264C4×Dic3—51no—
265C4×Dic3—51no—
266C4×Dic3—102no—
267C4×Dic3—101no—
268#208—52no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5—61no—
272C23×C5D3×D411yescharacteristic
273C22×D5—21no—
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—61no—
282C2×C4×C5—62no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5C2×D1211yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5#23711yescharacteristic
289C2×C4×C5#23711yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C22⋊D5—22no—
292C22⋊D5—22no—
293C2×Dic5—21no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—122no—
297D20—21no—
298D20(C2×D3)⋊C412yes—
299C4×D5—22no—
300C4×D5—22no—
301C4×D5—124no—
302Dic10—21no—
303Dic10(C2×D3)⋊C412yes—
304#168—41no—
305#168—62no—
306C2×#41—31no—
307C2×#41—51no—
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—302no—
317C4×D4—301no—
318#117—31no—
319#117—301no—
320#117D3×D511yescharacteristic
321C2×C42—151no—
322C2×C42—301no—
323#104—102no—
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
331C3×D5—42no—
332C5×D3—81no—
333C23×C3—101no—
334C23×C3C2×C22⋊D511yescharacteristic
335C22×D3—21no—
336C3×Q8—52no—
337C3×Q8—101no—
338C3×D4—52no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—101no—
342C2×C3×C4—41no—
343C2×C3×C4—101no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4#70911yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4#71111yescharacteristic
352#67—41no—
353#67—41no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C2×Dic3—204no—
359C2×Dic3—202no—
360D12—21no—
361D12—21no—
362C4×D3—41no—
363C4×D3—41no—
364Dic6—21no—
365Dic6—21no—
366C3×C8—201no—
367C3⋊C8—102no—
368C22×C5—41no—
369C22×C5—121no—
370C22×C5—241no—
371C22×C5#67⋊C411yescharacteristic
372C22×C5#88211yescharacteristic
373C22×C5#93911yescharacteristic
374C2×D5—22no—
375C2×D5—42no—
376C4×C5—81no—
377C4×C5—122no—
378C4×C5—121no—
379C4×C5#67⋊C411yescharacteristic
380C4×C5#88611yescharacteristic
381C4×C5C2×(C2×D3)⋊C411yescharacteristic
382C4×C5#93911yescharacteristic
383Dic5—22no—
384Dic5—62no—
385Dic5—121no—
386#41—52no—
387#41—52no—
388#41—61no—
389#41—61no—
390#41—61no—
391#41—61no—
392#41—101no—
393#41—101no—
394C2×Q8—31no—
395C2×Q8—51no—
396C2×D4—31no—
397C2×D4—51no—
398C2×D4—61no—
399C2×D4—101no—
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—101no—
410M16—101no—
411M16—152no—
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—61no—
423C42—151no—
424C42—151no—
425C42—302no—
426C42—301no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3—102no—
430C22×C3—202no—
431C22×C3C4×C22⋊D511yescharacteristic
432C22×C3#408311yescharacteristic
433C22×C3#408411yescharacteristic
434C2×D3—41no—
435C2×D3—81no—
436C3×C4—81no—
437C3×C4—102no—
438C3×C4D5×C22⋊C411yescharacteristic
439C3×C4#402711yescharacteristic
440C3×C4#402911yescharacteristic
441C3×C4#403011yescharacteristic
442Dic3—42no—
443Dic3—41no—
444Dic3—102no—
445Dic3—201no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—241no—
450C2×C5#495811yescharacteristic
451D5—42no—
452C23—61no—
453C23—101no—
454C23D3×C22⋊D511yescharacteristic
455Q8—52no—
456Q8—61no—
457Q8—61no—
458Q8—101no—
459D4—52no—
460D4—61no—
461D4—61no—
462D4—102no—
463D4—102no—
464D4—101no—
465D4—121no—
466D4—121no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—101no—
471C2×C4—102no—
472C2×C4—102no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—301no—
476C2×C4—301no—
477C2×C4—604no—
478C2×C4—602no—
479C2×C4#676511yescharacteristic
480C2×C4C4×D3×D511yescharacteristic
481C2×C4D5×D1211yescharacteristic
482C2×C4#677711yescharacteristic
483C2×C4#678011yescharacteristic
484C2×C4D5×#6711yescharacteristic
485C8—201no—
486C8—302no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—202no—
491C2×C3#6524511yescharacteristic
492D3—81no—
493C5#7039511yescharacteristic, complemented, Sylow
494C22—41no—
495C22—102no—
496C22—121no—
497C22—202no—
498C22—241no—
499C22#9144111yescharacteristic
500C22#9147511yescharacteristic
501C22#9154911yescharacteristic
502C4—81no—
503C4—102no—
504C4—122no—
505C4—121no—
506C4—302no—
507C4—601no—
508C4#9140811yescharacteristic
509C4#9141411yescharacteristic
510C4#9144211yescharacteristic
511C4D5×(C2×D3)⋊C411yescharacteristic
512C3#1060084811yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—202no—
517C2—241no—
518C2#1174890611yescharacteristic
subgroupG/H
centerC4#91408
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754138C2
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. #11754444C2semidirect
3. C5×#5006C2semidirect
4. C3×#65294C2semidirect
5. C2×#90978C2semidirect
6. #11746353C2semidirect
7. #11745988C2semidirect
22. #91307C4semidirect
23. #91299C4semidirect
35. #65294D3semidirect
45. C2×C5×D12C2×C4semidirect
47. C2×C5×Dic6C2×C4semidirect
64. #6710C2×C4semidirect
83. #5006D5semidirect
246. C2×D12C4×D5semidirect
248. C2×Dic6C4×D5semidirect
427. C3×C5#1906semidirect
493. C5#70395semidirect
512. C3#10600848semidirect

Maximal subgroups

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

subgroupindex
#117544442
#117541382
C5×#50062
C3×#652942
C2×#909782
#117463532
#117459882
#106008483
#703955