Finite Group Databasebeta

← #14301729

Subgroups — #14301729

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66079C211yesmaximal, characteristic, complemented
2#11754590C211yesmaximal, characteristic
3#11751227C211yesmaximal, characteristic, complemented
4#11748353C211yesmaximal, characteristic, complemented
5#11748351C211yesmaximal, characteristic, complemented
6C5×#4556C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10599829—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19#91572C412yes—
20#91537C412yes—
21#91465—21no—
22C4×#1202—22no—
23#91390—21no—
24#91104—22no—
25#90961—21no—
26#90958—21no—
27#90957—22no—
28#72029—51nomaximal, Hall
29#66079D311yescharacteristic, complemented
30#65858—31no—
31#65421—31no—
32#65415—31no—
33#65415—31no—
34C5×#344—31no—
35#64753—31no—
36C23×D15C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C3×C22⋊D5C2×C412yes—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709—21no—
49C3×#709—21no—
50C2×C3×D20D411yescharacteristic
51C2×C3×C4×D5D412yes—
52C2×C3×Dic10D411yescharacteristic
53C2×#1202—22no—
54C3×C5×M16—21no—
55C3×C5×M16—21no—
56C2×C3×C5×C8D412yescomplemented
57#6710—21no—
58#6710—21no—
59C2×C3⋊#168—21no—
60C5×#217C2×C412yes—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3—21no—
63C5×#208—21no—
64C5×#208—21no—
65C2×C5×C3⋊C8—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168D412yescomplemented
69C3×#676—24no—
70C3×C8×D5—24no—
71Dic3⋊Dic5—22no—
72#6667—22no—
73#6665—22no—
74C3×#568—51no—
75#5828—51no—
76#5237—51no—
77#5126—51no—
78#5126—51no—
79#4556—51no—
80#4556D511yescharacteristic, complemented
81C2×#709C2×D311yescharacteristic
82C22×C4×D5—31no—
83C2×C5×M16—31no—
84C2×C5×M16C2×D311yescharacteristic
85C5×#117—31no—
86C2×#681—31no—
87C2×#681C2×D311yescharacteristic
88#4053—22no—
89D5×M16—22no—
90#4047—22no—
91#4043—61no—
92#4041—61no—
93#4032—32no—
94#4028—32no—
95C4×D20—62no—
96#3956—61no—
97#3955—61no—
98#3952—62no—
99#3952—62no—
100#1891—151noSylow
101C23×C3×C5C22×C411yescharacteristic
102C22×D15—21no—
103C22×D15—21no—
104C22×D15—21no—
105C22×D15—42no—
106C22×C3×D5C22⋊C412yes—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C4×D15—41no—
117C4×D15—41no—
118C4×D15—41no—
119C4×D15—41no—
120C2×C5×Dic3—22no—
121C3×C22⋊D5—22no—
122C3×C22⋊D5—22no—
123C2×C3×Dic5C22⋊C412yes—
124C3×D20—21no—
125C3×D20—21no—
126C3×C4×D5—22no—
127C3×C4×D5—22no—
128C3×Dic10—21no—
129C3×Dic10—21no—
130#1202—44no—
131C3×C5×C8—22no—
132C3⋊#168—41no—
133C3×#168—22no—
134C5×C3⋊C8—41no—
135C2×C3×#41—51no—
136C22×C4×D3—51no—
137C3×#131—102no—
138C3×#131—102no—
139C2×C3×M16—51no—
140C2×C3×M16—102no—
141C2×C3×M16C2×D511yescharacteristic
142#946—101no—
143#938—101no—
144#937—52no—
145#935—52no—
146C4×#67—102no—
147#926C2×D511yescharacteristic
148C2×#208—51no—
149C2×#208C2×D511yescharacteristic
150#836—101no—
151#833—101no—
152(C2×D3)⋊C8—102no—
153(C2×D3)⋊C8—102no—
154C23×D5—31no—
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5C4×D312yes—
157C22×Dic5—31no—
158#709—21no—
159#709—21no—
160#709—21no—
161#709—21no—
162C2×D20—62no—
163C2×D20D1211yescharacteristic
164C2×C4×D5—61no—
165C2×C4×D5—61no—
166C2×C4×D5—61no—
167C2×C4×D5—61no—
168C2×C4×D5—61no—
169C2×C4×D5—61no—
170C2×C4×D5#6712yes—
171C2×Dic10D1211yescharacteristic
172C5×M16—21no—
173C5×M16—21no—
174C5×M16—61no—
175C5×M16—61no—
176C2×C5×C8—61no—
177C2×C5×C8#6712yescomplemented
178C5×C4⋊C4—61no—
179C5×C22⋊C4—32no—
180C42×C5—61no—
181#685—62no—
182#685—62no—
183C4⋊Dic5—62no—
184#681—21no—
185#681—21no—
186#681—61no—
187#681—61no—
188C2×#168—61no—
189C2×#168#6712yescomplemented
190#676—24no—
191C8×D5—24no—
192#568—51no—
193#525—151no—
194#413—151no—
195#407—151no—
196#407—151no—
197#344—31no—
198#344—151no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C22×C3×C5C4×D411yescharacteristic
202C22×C3×C5C4×D411yescharacteristic
203C2×D15—22no—
204C2×D15—22no—
205C2×D15—22no—
206C2×D15—41no—
207C2×D15—41no—
208C2×D15—41no—
209C2×D15—41no—
210C2×C3×D5—22no—
211C2×C3×D5—42no—
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—41no—
217C3×Dic5—22no—
218C5×Dic3—42no—
219C23×D3—51no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—51no—
225C2×C3×D4—52no—
226C2×C3×D4—51no—
227C22×C3×C4—52no—
228C22×C3×C4C22×D511yescharacteristic
229C2×#67—102no—
230C22×Dic3—51no—
231C2×C4×D3—101no—
232C2×C4×D3—101no—
233C2×C4×D3—101no—
234C2×C4×D3—101no—
235C2×C4×D3—101no—
236C2×C4×D3—101no—
237C3×M16—21no—
238C3×M16—21no—
239C3×M16—104no—
240C3×M16—101no—
241C3×M16—101no—
242C2×C3×C8—52no—
243C2×C3×C8—104no—
244C2×C3×C8D2012yescomplemented
245#217—102no—
246#217C4×D512yes—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—21no—
249Dic3⋊C4—102no—
250C4×Dic3—21no—
251#208—21no—
252#208—21no—
253#208—101no—
254#208—101no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—101no—
257C23×C5C2×C4×D311yescharacteristic
258C22×D5—61no—
259C22×D5—61no—
260C22×D5—61no—
261C22×D5—122no—
262C22×D5(C2×D3)⋊C412yes—
263C2×C4×C5—62no—
264C2×C4×C5C2×D1211yescharacteristic
265C2×C4×C5#23511yescharacteristic
266C2×C4×C5#23511yescharacteristic
267C2×C4×C5C2×#6711yescharacteristic
268C2×C4×C5C2×#6711yescharacteristic
269C2×C4×C5C2×#6711yescharacteristic
270C22⋊D5—22no—
271C22⋊D5—22no—
272C2×Dic5—61no—
273C2×Dic5—61no—
274C2×Dic5—61no—
275C2×Dic5(C2×D3)⋊C412yes—
276D20—21no—
277D20—21no—
278D20—124no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—121no—
282C4×D5—121no—
283C4×D5—121no—
284C4×D5—121no—
285Dic10—21no—
286Dic10—21no—
287C5×C8—22no—
288C5×C8—121no—
289#168—22no—
290#168—121no—
291C2×#41—51no—
292C23×C4—151no—
293#131—102no—
294#131—102no—
295C2×M16—31no—
296C2×M16—51no—
297C2×M16—102no—
298C2×M16—151no—
299C2×M16D3×D511yescharacteristic
300#123—152no—
301C22⋊Q8—301no—
302#121—301no—
303#120—152no—
304C4×D4—302no—
305#117—31no—
306#101—301no—
307#100—301no—
308C22⋊C8—302no—
309C22⋊C8—302no—
310C2×C3×C5—21no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5#38611yescharacteristic
314D15—42no—
315C3×D5—42no—
316C23×C3—52no—
317C23×C3C2×C4×D511yescharacteristic
318C22×D3—101no—
319C22×D3—101no—
320C22×D3—101no—
321C22×D3—202no—
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—102no—
325C3×D4—102no—
326C3×D4—101no—
327C3×D4—101no—
328C2×C3×C4—52no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4C2×D2011yescharacteristic
332C2×C3×C4#70911yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71311yescharacteristic
337#67—204no—
338C2×Dic3—22no—
339C2×Dic3—101no—
340C2×Dic3—101no—
341C2×Dic3—101no—
342C4×D3—201no—
343C4×D3—201no—
344C4×D3—201no—
345C4×D3—201no—
346C3×C8—22no—
347C3×C8—102no—
348C3⋊C8—41no—
349C3⋊C8—201no—
350C22×C5—41no—
351C22×C5C2×(C2×D3)⋊C411yescharacteristic
352C22×C5C4×#6711yescharacteristic
353C22×C5C4×#6711yescharacteristic
354C2×D5—22no—
355C2×D5—42no—
356C2×D5—62no—
357C2×D5—62no—
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C2×D5—121no—
362C2×D5—121no—
363C4×C5—122no—
364C4×C5#92911yescharacteristic
365C4×C5#93011yescharacteristic
366C4×C5#93011yescharacteristic
367C4×C5#95311yescharacteristic
368Dic5—22no—
369Dic5—121no—
370C24—151no—
371#41—101no—
372#41—101no—
373#41—101no—
374#41—101no—
375C2×Q8—51no—
376C2×D4—52no—
377C2×D4—51no—
378C2×D4—302no—
379C22×C4—52no—
380C22×C4—151no—
381C22×C4—301no—
382C22×C4—301no—
383C22×C4—301no—
384C22×C4—301no—
385C22×C4—301no—
386C22×C4—301no—
387C22×C4C2×D3×D511yescharacteristic
388M16—21no—
389M16—21no—
390M16—61no—
391M16—61no—
392M16—104no—
393M16—101no—
394M16—101no—
395M16—301no—
396M16—301no—
397C2×C8—52no—
398C2×C8—61no—
399C2×C8—104no—
400C2×C8—301no—
401C2×C8#120212yescomplemented
402C4⋊C4—61no—
403C4⋊C4—302no—
404C22⋊C4—32no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C42—61no—
408C3×C5#189111yescharacteristic, complemented, Hall
409C22×C3—41no—
410C22×C3—102no—
411C22×C3—202no—
412C22×C3C4×D2011yescharacteristic
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#403911yescharacteristic
415C2×D3—102no—
416C2×D3—102no—
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C2×D3—201no—
421C2×D3—201no—
422C3×C4—102no—
423C3×C4#402811yescharacteristic
424C3×C4#403011yescharacteristic
425C3×C4#404011yescharacteristic
426C3×C4#404111yescharacteristic
427Dic3—42no—
428Dic3—201no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5#521311yescharacteristic
433D5—42no—
434D5—122no—
435C23—52no—
436C23—301no—
437C23—301no—
438C23—301no—
439C23—602no—
440C23C4×D3×D511yescharacteristic
441Q8—101no—
442Q8—101no—
443D4—102no—
444D4—102no—
445D4—101no—
446D4—101no—
447D4—604no—
448C2×C4—52no—
449C2×C4—62no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4—601no—
458C2×C4—601no—
459C2×C4#677111yescharacteristic
460C2×C4#677311yescharacteristic
461C2×C4D5×D1211yescharacteristic
462C2×C4C2×#120211yescharacteristic
463C2×C4D5×#6711yescharacteristic
464C2×C4D5×#6711yescharacteristic
465C8—22no—
466C8—102no—
467C8—121no—
468C8—601no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—202no—
473C2×C3#6495411yescharacteristic
474D3—202no—
475C5#7202911yescharacteristic, complemented, Sylow
476C22—41no—
477C22—102no—
478C22—202no—
479C22—302no—
480C22—302no—
481C22—302no—
482C22—601no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C4×#120211yescharacteristic
487C22#9144411yescharacteristic
488C22D5×(C2×D3)⋊C411yescharacteristic
489C4—102no—
490C4—122no—
491C4—601no—
492C4#9134811yescharacteristic
493C4#9144811yescharacteristic
494C4#9145011yescharacteristic
495C4#9156411yescharacteristic
496C3#1059982911yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—202no—
501C2—602no—
502C2#1174890711yescharacteristic
subgroupG/H
centerC4#91564
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754590C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#66079C2semidirect
3. #11751227C2semidirect
4. #11748353C2semidirect
5. #11748351C2semidirect
6. C5×#4556C2semidirect
7. #11745988C2semidirect
29. #66079D3semidirect
56. C2×C3×C5×C8D4semidirect
68. C2×C3×#168D4semidirect
80. #4556D5semidirect
177. C2×C5×C8#67semidirect
189. C2×#168#67semidirect
244. C2×C3×C8D20semidirect
401. C2×C8#1202semidirect
408. C3×C5#1891semidirect
475. C5#72029semidirect
496. C3#10599829semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117545902
#117512272
#117483532
#117483512
C5×#45562
#117459882
#105998293
#720295