Finite Group Databasebeta

← #14302010

Subgroups — #14302010

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic, complemented
2#11754590C211yesmaximal, characteristic
3C2×C3×#3937C211yesmaximal, characteristic, complemented
4C2×#90976C211yesmaximal, characteristic, complemented
5#11748351C211yesmaximal, characteristic, complemented
6C5×#4523C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10599550—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6714—21no—
13C2×#6712—21no—
14C2×C4×Dic15C2211yescharacteristic
15#91761—22no—
16#91761—22no—
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91572—21no—
21#91537—21no—
22#91465C412yescomplemented
23C4×#1202—22no—
24#91390C412yescomplemented
25C3×#3937—22no—
26#90976—22no—
27#90957—22no—
28#70383—51nomaximal, Hall
29#65858—31no—
30C2×#4018—31no—
31C2×#3957—31no—
32#65415—31no—
33C2×#3937D311yescharacteristic, complemented
34C5×#339—31no—
35#64752—31no—
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15C2×C412yes—
46C2×C4×D15D412yes—
47C2×C3×C22⋊D5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709—21no—
52C2×C3×D20C2×C411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×Dic10C2×C411yescharacteristic
55C2×#1202—22no—
56C3×C42×C5—21no—
57C3×C42×C5D412yescomplemented
58#6714—24no—
59#6712—24no—
60C4×Dic15—21no—
61C4×Dic15D412yescomplemented
62C5×#217—21no—
63C5×C4⋊Dic3C2×C412yes—
64C4×C5×Dic3—21no—
65C5×#208—21no—
66C5×#208—21no—
67C2×C5×C3⋊C8—21no—
68C3×#681—21no—
69C3×#681—21no—
70C2×C3×#168—21no—
71Dic3⋊Dic5—22no—
72#6667—22no—
73#6665—22no—
74#5828—51no—
75C2×#872—51no—
76C2×C3×#104—51no—
77C2×#837—51no—
78#5126—51no—
79#4555—51no—
80#4523D511yescharacteristic, complemented
81C2×#709C2×D311yescharacteristic
82C22×C4×D5—31no—
83C2×C5×M16—31no—
84C5×#117—31no—
85C2×C42×C5C2×D311yescharacteristic
86C2×#685—61no—
87C2×#683—61no—
88C2×C4×Dic5—31no—
89C2×#681C2×D311yescharacteristic
90#4043—32no—
91#4041—32no—
92#4032—61no—
93#4028—61no—
94C4×D20—62no—
95#4018—62no—
96#4018—62no—
97#3957—62no—
98#3952—62no—
99#3937—22no—
100#1897—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×D15—21no—
104C22×D15—42no—
105C22×D15C22⋊C412yes—
106C22×C3×D5—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—22no—
118C2×Dic15—42no—
119C2×Dic15C22⋊C412yes—
120C4×D15—22no—
121C4×D15—22no—
122C4×D15—22no—
123C4×D15—22no—
124C2×C5×Dic3—22no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—41no—
127C2×C3×Dic5—21no—
128C3×D20—21no—
129C3×D20—21no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134#1202—44no—
135C3×#168—41no—
136C5×C3⋊C8—41no—
137C2×C3×#41—51no—
138C22×C4×D3—51no—
139C2×C3×M16—51no—
140C2×C3×C42C2×D511yescharacteristic
141#946—52no—
142#938—52no—
143#937—101no—
144#935—101no—
145C4×#67—102no—
146C2×(C2×D3)⋊C4—101no—
147#926C2×D511yescharacteristic
148C2×Dic3⋊C4—101no—
149C2×C4×Dic3—51no—
150C2×#208C2×D511yescharacteristic
151#872—102no—
152#872—102no—
153C3×#104—102no—
154#837—102no—
155(C2×D3)⋊C8—102no—
156C23×D5—31no—
157C22×C4×C5—21no—
158C22×C4×C5C22×D311yescharacteristic
159C2×C22⋊D5—21no—
160C22×Dic5—31no—
161C22×Dic5—61no—
162#709—21no—
163#709—21no—
164#709—21no—
165#709—21no—
166C2×D20—62no—
167C2×D20C4×D311yescharacteristic
168C2×C4×D5—21no—
169C2×C4×D5—32no—
170C2×C4×D5—32no—
171C2×C4×D5—61no—
172C2×C4×D5—61no—
173C2×C4×D5—61no—
174C2×C4×D5—61no—
175C2×Dic10C4×D311yescharacteristic
176C5×M16—61no—
177C5×M16—61no—
178C2×C5×C8—61no—
179C5×C4⋊C4—32no—
180C5×C22⋊C4—61no—
181C42×C5—21no—
182C42×C5—61no—
183C42×C5#6712yescomplemented
184#685—62no—
185#685—62no—
186#685—64no—
187C4⋊Dic5—62no—
188#683—64no—
189C4×Dic5—32no—
190C4×Dic5—61no—
191#681—21no—
192#681—21no—
193C2×#168—21no—
194#525—151no—
195C2×#117—151no—
196C2×#104—51no—
197C2×#104—151no—
198#407—151no—
199#339—31no—
200#339—151no—
201C22×C3×C5—22no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5#12011yescharacteristic
204C22×C3×C5#12311yescharacteristic
205C2×D15—22no—
206C2×D15—22no—
207C2×D15—22no—
208C2×D15—42no—
209C2×D15—42no—
210C2×C3×D5—41no—
211C2×C3×D5—42no—
212C3×C4×C5—42no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12111yescharacteristic
217Dic15—22no—
218Dic15—42no—
219C3×Dic5—41no—
220C5×Dic3—42no—
221C23×D3—51no—
222C3×#41—101no—
223C3×#41—101no—
224C3×#41—101no—
225C3×#41—101no—
226C2×C3×Q8—51no—
227C2×C3×D4—51no—
228C2×C3×D4—101no—
229C22×C3×C4—21no—
230C22×C3×C4—101no—
231C22×C3×C4C22×D511yescharacteristic
232C2×#67—102no—
233C22×Dic3—51no—
234C22×Dic3—101no—
235C2×C4×D3—52no—
236C2×C4×D3—52no—
237C2×C4×D3—101no—
238C2×C4×D3—101no—
239C2×C4×D3—101no—
240C2×C4×D3—101no—
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C3×C42—21no—
245C3×C42D2012yescomplemented
246#217—21no—
247#217—102no—
248(C2×D3)⋊C4—102no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3C4×D512yes—
251Dic3⋊C4—102no—
252Dic3⋊C4—104no—
253C4×Dic3—21no—
254C4×Dic3—52no—
255C4×Dic3—101no—
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C23×C5D3×D411yescharacteristic
260C22×D5—21no—
261C22×D5—32no—
262C22×D5—61no—
263C22×D5—61no—
264C22×D5—122no—
265C2×C4×C5—22no—
266C2×C4×C5—42no—
267C2×C4×C5—62no—
268C2×C4×C5C2×C4×D311yescharacteristic
269C2×C4×C5#23511yescharacteristic
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5#23711yescharacteristic
273C2×C4×C5C2×#6711yescharacteristic
274C22⋊D5—41no—
275C22⋊D5—41no—
276C2×Dic5—21no—
277C2×Dic5—32no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281C2×Dic5—122no—
282D20—21no—
283D20—21no—
284D20—124no—
285C4×D5—41no—
286C4×D5—41no—
287C4×D5—62no—
288C4×D5—62no—
289C4×D5—62no—
290C4×D5—62no—
291Dic10—21no—
292Dic10—21no—
293C5×C8—121no—
294#168—41no—
295C2×#41—51no—
296C23×C4—151no—
297C2×M16—31no—
298C2×M16—51no—
299#123—301no—
300C22⋊Q8—152no—
301#121—152no—
302#120—301no—
303C4×D4—302no—
304#117—31no—
305#117—302no—
306#117—302no—
307C2×C4⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42D3×D511yescharacteristic
311#104—102no—
312#104—302no—
313C22⋊C8—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C2×C3×C5#42112yes—
318D15—42no—
319C3×D5—81no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C22×D3—52no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—202no—
326C3×Q8—101no—
327C3×Q8—101no—
328C3×D4—101no—
329C3×D4—101no—
330C3×D4—201no—
331C3×D4—201no—
332C2×C3×C4—22no—
333C2×C3×C4—42no—
334C2×C3×C4—101no—
335C2×C3×C4—201no—
336C2×C3×C4—201no—
337C2×C3×C4C2×C4×D511yescharacteristic
338C2×C3×C4C2×D2011yescharacteristic
339C2×C3×C4#70911yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4#71311yescharacteristic
343#67—204no—
344C2×Dic3—22no—
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—102no—
349C2×Dic3—202no—
350C4×D3—102no—
351C4×D3—102no—
352C4×D3—102no—
353C4×D3—102no—
354C3×C8—201no—
355C3⋊C8—41no—
356C22×C5—22no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88311yescharacteristic
359C22×C5#93711yescharacteristic
360C2×D5—41no—
361C2×D5—42no—
362C2×D5—62no—
363C2×D5—62no—
364C2×D5—62no—
365C2×D5—122no—
366C2×D5—122no—
367C4×C5—42no—
368C4×C5—122no—
369C4×C5#67⋊C411yescharacteristic
370C4×C5#88411yescharacteristic
371C4×C5C4×#6711yescharacteristic
372C4×C5#93811yescharacteristic
373Dic5—41no—
374Dic5—62no—
375Dic5—122no—
376C24—151no—
377#41—101no—
378#41—101no—
379#41—101no—
380#41—101no—
381C2×Q8—51no—
382C2×D4—51no—
383C2×D4—101no—
384C2×D4—302no—
385C22×C4—21no—
386C22×C4—101no—
387C22×C4—151no—
388C22×C4—152no—
389C22×C4—152no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—61no—
397M16—61no—
398M16—101no—
399M16—101no—
400C2×C8—61no—
401C2×C8—101no—
402C4⋊C4—32no—
403C4⋊C4—304no—
404C4⋊C4—302no—
405C22⋊C4—61no—
406C22⋊C4—304no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—21no—
410C42—61no—
411C42—152no—
412C42—301no—
413C42#120212yescomplemented
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3—202no—
417C22×C3—201no—
418C22×C3D5×C22⋊C411yescharacteristic
419C22×C3#402811yescharacteristic
420C22×C3#404011yescharacteristic
421C2×D3—102no—
422C2×D3—102no—
423C2×D3—102no—
424C2×D3—202no—
425C2×D3—202no—
426C3×C4—42no—
427C3×C4—201no—
428C3×C4C4×D2011yescharacteristic
429C3×C4#403011yescharacteristic
430C3×C4#403911yescharacteristic
431C3×C4#404111yescharacteristic
432Dic3—42no—
433Dic3—102no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#482112yes—
438C2×C5#495611yescharacteristic
439D5—81no—
440D5—122no—
441C23—101no—
442C23—152no—
443C23—301no—
444C23—301no—
445C23—602no—
446C23#679011yescharacteristic
447Q8—101no—
448Q8—101no—
449D4—101no—
450D4—101no—
451D4—201no—
452D4—201no—
453D4—604no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—62no—
457C2×C4—101no—
458C2×C4—152no—
459C2×C4—201no—
460C2×C4—201no—
461C2×C4—301no—
462C2×C4—301no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—602no—
469C2×C4#676611yescharacteristic
470C2×C4#677111yescharacteristic
471C2×C4C4×D3×D511yescharacteristic
472C2×C4#677711yescharacteristic
473C2×C4C2×#120211yescharacteristic
474C2×C4#679011yescharacteristic
475C8—121no—
476C8—201no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—401no—
480C2×C3#6495411yescharacteristic
481C2×C3#6511012yes—
482D3—202no—
483C5#7038311yescharacteristic, complemented, Sylow
484C22—22no—
485C22—202no—
486C22—201no—
487C22—302no—
488C22—302no—
489C22—302no—
490C22—602no—
491C22—602no—
492C22#9135411yescharacteristic
493C22#9147311yescharacteristic
494C22#9157211yescharacteristic
495C4—42no—
496C4—122no—
497C4—201no—
498C4—302no—
499C4—602no—
500C4#9139611yescharacteristic
501C4C4×#120211yescharacteristic
502C4#9146111yescharacteristic
503C4#9146511yescharacteristic
504C3#1059955011yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—401no—
508C2—602no—
509C2#1174711312yes—
510C2#1174891711yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754590C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91761C2semidirect
3. C2×C3×#3937C2semidirect
4. C2×#90976C2semidirect
5. #11748351C2semidirect
6. C5×#4523C2semidirect
7. #11745975C2semidirect
22. #91465C4semidirect
24. #91390C4semidirect
33. C2×#3937D3semidirect
57. C3×C42×C5D4semidirect
61. C4×Dic15D4semidirect
80. #4523D5semidirect
183. C42×C5#67semidirect
245. C3×C42D20semidirect
413. C42#1202semidirect
414. C3×C5#1897semidirect
483. C5#70383semidirect
504. C3#10599550semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
#117545902
C2×C3×#39372
C2×#909762
#117483512
C5×#45232
#117459752
#105995503
#703835