Finite Group Databasebeta

← #14302019

Subgroups — #14302019

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
1#11756587C211yesmaximal, characteristic
2C2×#91386C211yesmaximal, characteristic, complemented
3C2×C5×#837C211yesmaximal, characteristic, complemented
4C2×C3×#3969C211yesmaximal, characteristic, complemented
5#11748351C211yesmaximal, characteristic, complemented
6#11745978C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601176—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C4×D15C2211yescharacteristic
11#91835C412yescomplemented
12#91827C412yescomplemented
13#91826—21no—
14#91824—21no—
15C4×#1220—22no—
16#91815C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×#6669—21no—
22C2×#6667—21no—
23#91386—22no—
24#91386—22no—
25C5×#837—22no—
26C3×#3969—22no—
27#90957—22no—
28#70383—51nomaximal, Hall
29#66162—31no—
30C2×#4018—31no—
31C2×C5×#104—31no—
32C2×#3969D311yescharacteristic, complemented
33#65415—31no—
34#64775—31no—
35#64743—31no—
36C23×D15D411yescharacteristic
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C2×C3×C5×Q8C2×C411yescharacteristic
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4C2×C411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220—22no—
47C22×Dic15D411yescharacteristic
48C2×C4×D15—21no—
49C2×C4×D15—21no—
50C2×C4×D15—21no—
51C2×C4×D15—21no—
52C2×C4×D15C2×C412yes—
53C2×C4×D15D412yes—
54C22×C5×Dic3—21no—
55C22×C3×Dic5—21no—
56#6719—21no—
57#6719—22no—
58#6714—22no—
59C4⋊Dic15C2×C412yes—
60#6712—22no—
61C4×Dic15—21no—
62C4×C5×Dic3—21no—
63C4×C5×Dic3D412yescomplemented
64C5×#208—21no—
65C5×#208—21no—
66C2×C5×C3⋊C8—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5D412yescomplemented
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168—21no—
72#6669—24no—
73#6667—24no—
74#5828—51no—
75C2×#872—51no—
76C2×C3×#104—51no—
77C2×#837D511yescharacteristic, complemented
78#5126—51no—
79#4555—51no—
80#4523—51no—
81C2×C5×#41C2×D311yescharacteristic
82C22×C4×D5—31no—
83C2×C5×M16—31no—
84C2×C42×C5—31no—
85#4092—32no—
86#4084—32no—
87#4083—61no—
88#4081—61no—
89C4×C22⋊D5—62no—
90C2×#685—61no—
91#4072—31no—
92C2×#683—61no—
93C2×C4×Dic5C2×D311yescharacteristic
94C2×#681C2×D311yescharacteristic
95#4018—62no—
96#4018—62no—
97C5×#104—62no—
98#3969—22no—
99#3952—62no—
100#1897—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5C2×D411yescharacteristic
103C22×D15—21no—
104C22×D15—21no—
105C22×D15—42no—
106C22×D15C22⋊C412yes—
107C3×C5×Q8—21no—
108C3×C5×Q8—21no—
109C3×C5×D4—21no—
110C3×C5×D4—21no—
111C3×C5×D4—41no—
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122#1220—44no—
123C2×Dic15—21no—
124C2×Dic15—21no—
125C2×Dic15—22no—
126C2×Dic15C22⋊C412yes—
127C4×D15—22no—
128C4×D15—22no—
129C4×D15—22no—
130C4×D15—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—42no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—42no—
135C3×#168—41no—
136C5×C3⋊C8—41no—
137C2×C3×#41C2×D511yescharacteristic
138C22×C4×D3—51no—
139C2×C3×M16—51no—
140C2×C3×C42—51no—
141#946—52no—
142#938—52no—
143#937—101no—
144#935—101no—
145C4×#67—102no—
146C2×(C2×D3)⋊C4—101no—
147#926—51no—
148C2×Dic3⋊C4—101no—
149C2×C4×Dic3C2×D511yescharacteristic
150C2×#208C2×D511yescharacteristic
151#872—102no—
152#872—102no—
153C3×#104—102no—
154#837—22no—
155(C2×D3)⋊C8—102no—
156C23×D5—31no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—21no—
161C2×C5×Q8C4×D311yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4C4×D311yescharacteristic
164C22×C4×C5—21no—
165C22×C4×C5—61no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—62no—
168C22×Dic5—21no—
169C22×Dic5—31no—
170C2×C4×D5—32no—
171C2×C4×D5—32no—
172C2×C4×D5—61no—
173C2×C4×D5—61no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C5×M16—61no—
177C5×M16—61no—
178C2×C5×C8—61no—
179C42×C5—32no—
180C42×C5—61no—
181C22⋊Dic5—62no—
182C22⋊Dic5—61no—
183#685—64no—
184#685—62no—
185C4⋊Dic5—32no—
186#683—64no—
187#683—62no—
188C4×Dic5—21no—
189C4×Dic5—61no—
190C4×Dic5#6712yescomplemented
191#681—21no—
192#681—21no—
193C2×#168—21no—
194#525—151no—
195C2×#117—151no—
196C2×#104—31no—
197C2×#104—51no—
198#407—151no—
199#339—151no—
200#339—151no—
201C22×C3×C5—22no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12311yescharacteristic
207C2×D15—22no—
208C2×D15—22no—
209C2×D15—22no—
210C2×D15—42no—
211C2×D15—42no—
212C3×C4×C5—41no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12111yescharacteristic
217Dic15—22no—
218Dic15—42no—
219C3×Dic5—42no—
220C5×Dic3—42no—
221C23×D3—51no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—21no—
226C2×C3×Q8C4×D511yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4C4×D511yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—101no—
231C22×C3×C4C22×D511yescharacteristic
232C2×#67—102no—
233C22×Dic3—21no—
234C22×Dic3—51no—
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—52no—
245C3×C42—101no—
246#217—102no—
247#217—101no—
248(C2×D3)⋊C4—104no—
249(C2×D3)⋊C4—102no—
250C4⋊Dic3—52no—
251Dic3⋊C4—104no—
252Dic3⋊C4—102no—
253C4×Dic3—21no—
254C4×Dic3—101no—
255C4×Dic3C22⋊D512yescomplemented
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C23×C5—21no—
260C23×C5D3×D411yescharacteristic
261C22×D5—32no—
262C22×D5—61no—
263C22×D5—61no—
264C22×D5—122no—
265C5×Q8—21no—
266C5×Q8—21no—
267C5×D4—21no—
268C5×D4—21no—
269C5×D4—41no—
270C5×D4—41no—
271C2×C4×C5—21no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—62no—
275C2×C4×C5—122no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5#23511yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5#23711yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C22⋊D5—124no—
283C2×Dic5—22no—
284C2×Dic5—32no—
285C2×Dic5—42no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288C2×Dic5—62no—
289C4×D5—62no—
290C4×D5—62no—
291C4×D5—62no—
292C4×D5—62no—
293C5×C8—121no—
294#168—41no—
295C2×#41D3×D511yescharacteristic
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—151no—
305#117—302no—
306#117—302no—
307C2×C4⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—31no—
310C2×C42—51no—
311#104—62no—
312#104—102no—
313C22⋊C8—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318C2×C3×C5#42112yes—
319D15—42no—
320C23×C3—21no—
321C23×C3D4×D511yescharacteristic
322C22×D3—52no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—202no—
326C3×Q8—21no—
327C3×Q8—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—41no—
331C3×D4—41no—
332C2×C3×C4—21no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—102no—
336C2×C3×C4—202no—
337C2×C3×C4C2×C4×D511yescharacteristic
338C2×C3×C4#70911yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4#71111yescharacteristic
342C2×C3×C4C2×C22⋊D511yescharacteristic
343#67—204no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—52no—
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—102no—
350C4×D3—102no—
351C4×D3—102no—
352C4×D3—102no—
353C4×D3—102no—
354C3×C8—201no—
355C3⋊C8—41no—
356C22×C5—22no—
357C22×C5—41no—
358C22×C5—42no—
359C22×C5D3×C22⋊C411yescharacteristic
360C22×C5#88311yescharacteristic
361C22×C5#93711yescharacteristic
362C2×D5—62no—
363C2×D5—62no—
364C2×D5—62no—
365C2×D5—122no—
366C2×D5—122no—
367C4×C5—41no—
368C4×C5—122no—
369C4×C5#67⋊C411yescharacteristic
370C4×C5#88411yescharacteristic
371C4×C5C4×#6711yescharacteristic
372C4×C5#93811yescharacteristic
373Dic5—42no—
374Dic5—62no—
375Dic5—122no—
376C24—151no—
377#41—21no—
378#41—21no—
379#41—21no—
380#41—21no—
381C2×Q8#120011yescharacteristic
382C2×D4—21no—
383C2×D4—302no—
384C2×D4#120011yescharacteristic
385C22×C4—21no—
386C22×C4—61no—
387C22×C4—101no—
388C22×C4—151no—
389C22×C4—152no—
390C22×C4—152no—
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—152no—
403C4⋊C4—302no—
404C4⋊C4—304no—
405C22⋊C4—302no—
406C22⋊C4—304no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—32no—
410C42—52no—
411C42—61no—
412C42—101no—
413C42—301no—
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3D5×C22⋊C411yescharacteristic
419C22×C3#402911yescharacteristic
420C22×C3#408311yescharacteristic
421C2×D3—102no—
422C2×D3—102no—
423C2×D3—102no—
424C2×D3—202no—
425C2×D3—202no—
426C3×C4—41no—
427C3×C4—202no—
428C3×C4#402711yescharacteristic
429C3×C4#403011yescharacteristic
430C3×C4C4×C22⋊D511yescharacteristic
431C3×C4#408411yescharacteristic
432Dic3—42no—
433Dic3—102no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—81no—
438C2×C5#482112yes—
439C2×C5#495611yescharacteristic
440D5—122no—
441C23—21no—
442C23—152no—
443C23—301no—
444C23—301no—
445C23—602no—
446C23#679011yescharacteristic
447Q8—21no—
448Q8—21no—
449D4—21no—
450D4—21no—
451D4—41no—
452D4—41no—
453D4—604no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—62no—
458C2×C4—102no—
459C2×C4—122no—
460C2×C4—152no—
461C2×C4—202no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—302no—
469C2×C4#677911yescharacteristic
470C2×C4#678211yescharacteristic
471C2×C4C2×#120011yescharacteristic
472C2×C4D5×#6711yescharacteristic
473C2×C4D3×C22⋊D511yescharacteristic
474C2×C4#679011yescharacteristic
475C8—121no—
476C8—201no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—81no—
480C2×C3#6511012yes—
481C2×C3#6524511yescharacteristic
482D3—202no—
483C5#7038311yescharacteristic, complemented, Sylow
484C22—22no—
485C22—42no—
486C22—41no—
487C22—302no—
488C22—302no—
489C22—302no—
490C22—602no—
491C22—602no—
492C22#9156111yescharacteristic
493C22#9156211yescharacteristic
494C22#9157711yescharacteristic
495C4—41no—
496C4—122no—
497C4—202no—
498C4—302no—
499C4—602no—
500C4#9153311yescharacteristic
501C4#9155211yescharacteristic
502C4#9155611yescharacteristic
503C4#9155711yescharacteristic
504C3#1060117611yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—81no—
508C2—602no—
509C2#1174943112yes—
510C2#1174952011yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756587C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91386C2semidirect
3. C2×C5×#837C2semidirect
4. C2×C3×#3969C2semidirect
5. #11748351C2semidirect
6. #11745978C2semidirect
7. #11745976C2semidirect
11. #91835C4semidirect
12. #91827C4semidirect
32. C2×#3969D3semidirect
63. C4×C5×Dic3D4semidirect
68. C3×C4×Dic5D4semidirect
77. C2×#837D5semidirect
190. C4×Dic5#67semidirect
255. C4×Dic3C22⋊D5semidirect
414. C3×C5#1897semidirect
483. C5#70383semidirect
504. C3#10601176semidirect

Maximal subgroups

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

subgroupindex
#117565872
C2×#913862
C2×C5×#8372
C2×C3×#39692
#117483512
#117459782
#117459762
#106011763
#703835