Finite Group Databasebeta

← #14300613

Subgroups — #14300613

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C2×#91390C211yesmaximal, characteristic
3C2×C3×#3942C211yesmaximal, characteristic, complemented
4C2×#90971C211yesmaximal, characteristic, complemented
5C2×#90957C211yesmaximal, characteristic
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10599671—31nomaximal, Hall
9C22×C4×D15—21no—
10C22×C4×D15C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×#6712—21no—
15C4⋊C4×D15—22no—
16C4⋊C4×D15—22no—
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C2×Dic3⋊Dic5—21no—
21C2×#6667—21no—
22#91390—22no—
23#91390C414yescomplemented
24C3×#3942—22no—
25#90971—22no—
26#90957—22no—
27#70268—51nomaximal, Hall
28C2×#4043—31no—
29C2×D5×C4⋊C4—31no—
30C2×#3952—31no—
31C2×#3948—31no—
32C2×#3942D311yescharacteristic, complemented
33C5×#340—31no—
34#64749—31no—
35C23×D15D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—24no—
45C2×C4×D15—42no—
46C2×C4×D15—42no—
47C2×C4×D15C2×C412yes—
48C2×C4×D15D412yes—
49C22×C5×Dic3—21no—
50C22×C3×Dic5—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10—21no—
54C2×C3×Dic10—21no—
55C2×C3×Dic10—21no—
56C2×C3×Dic10C2×C412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yes—
59C4⋊Dic15—21no—
60C4⋊Dic15D412yes—
61#6712—24no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2×C412yescomplemented
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C2×C3×#168—21no—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70Dic3⋊Dic5—24no—
71#6667—24no—
72C2×#946—51no—
73C2×D3×C4⋊C4—51no—
74C2×C3×#103—51no—
75C2×#835—51no—
76C2×(C2×D3)⋊C8—51no—
77#4551—51no—
78#4529D511yescharacteristic, complemented
79C22×C4×D5—31no—
80C22×C4×D5—61no—
81C22×Dic10C2×D311yescharacteristic
82C22×C5×C8—31no—
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#685—61no—
86C2×C4⋊Dic5—31no—
87C2×C4⋊Dic5—61no—
88C2×#683—61no—
89C22×#168C2×D311yescharacteristic
90#4043—34no—
91#4043—62no—
92D5×C4⋊C4—62no—
93D5×C4⋊C4—62no—
94#3952—62no—
95#3948—62no—
96#3942—22no—
97#1872—151noSylow
98C23×C3×C5C2×D411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—21no—
102C22×D15—21no—
103C22×D15C22⋊C412yes—
104C22×D15SD1612yes—
105C22×D15Q1612yes—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
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—41no—
119C2×Dic15—41no—
120C2×Dic15C22⋊C412yes—
121C4×D15—22no—
122C4×D15—22no—
123C4×D15—22no—
124C4×D15—22no—
125C4×D15—48no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C3×Dic10—22no—
133C3×Dic10—22no—
134C3×Dic10—41no—
135C3×Dic10—41no—
136C3×#168—41no—
137C5×C3⋊C8—41no—
138C22×C3×Q8—51no—
139C22×C4×D3—51no—
140C22×C4×D3—101no—
141C22×C3×C8—51no—
142C2×C3×C4⋊C4C2×D511yescharacteristic
143#946—54no—
144#946—102no—
145C2×(C2×D3)⋊C4—101no—
146C2×C4⋊Dic3—51no—
147C2×C4⋊Dic3C2×D511yescharacteristic
148C2×Dic3⋊C4—101no—
149C2×Dic3⋊C4—101no—
150C22×C3⋊C8C2×D511yescharacteristic
151D3×C4⋊C4—102no—
152D3×C4⋊C4—102no—
153C3×#103—102no—
154#835—102no—
155(C2×D3)⋊C8—102no—
156C23×D5—31no—
157C22×C4×C5—21no—
158C22×C4×C5—61no—
159C22×C4×C5C22×D311yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—31no—
162C22×Dic5—61no—
163C2×C4×D5—32no—
164C2×C4×D5—32no—
165C2×C4×D5—61no—
166C2×C4×D5—61no—
167C2×C4×D5—61no—
168C2×C4×D5—61no—
169C2×C4×D5—64no—
170C2×C4×D5—122no—
171C2×C4×D5—122no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10—21no—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10C4×D312yescomplemented
178C2×C5×C8—61no—
179C2×C5×C8—61no—
180C2×C5×C8—61no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—32no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4#6712yes—
185#685—64no—
186C4⋊Dic5—32no—
187C4⋊Dic5—64no—
188C4⋊Dic5—61no—
189#683—64no—
190C2×#168—21no—
191C2×#168—21no—
192C2×#168—21no—
193C2×C22⋊Q8—151no—
194C22×C4⋊C4—151no—
195C2×#103—51no—
196C2×#103—151no—
197C2×C22⋊C8—151no—
198#340—31no—
199#340—151no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C22×C3×C5#12011yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C22×C3×C5C2×SD1611yescharacteristic
204C22×C3×C5C2×Q1611yescharacteristic
205C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
206C22×C3×C5#13711yescharacteristic
207C2×D15—22no—
208C2×D15—22no—
209C2×D15—22no—
210C2×D15—22no—
211C2×D15—22no—
212C2×D15—22no—
213C2×D15#10314yescomplemented
214C3×C4×C5—42no—
215C3×C4×C5C4×D411yescharacteristic
216C3×C4×C5C4×D411yescharacteristic
217C3×C4×C5#12111yescharacteristic
218C3×C4×C5#12111yescharacteristic
219Dic15—22no—
220Dic15—42no—
221C3×Dic5—42no—
222C5×Dic3—42no—
223C23×D3—51no—
224C2×C3×Q8—52no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C2×C3×Q8—101no—
228C2×C3×Q8—101no—
229C2×C3×Q8—101no—
230C22×C3×C4—21no—
231C22×C3×C4—101no—
232C22×C3×C4C22×D511yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—51no—
235C22×Dic3—101no—
236C2×C4×D3—52no—
237C2×C4×D3—52no—
238C2×C4×D3—101no—
239C2×C4×D3—101no—
240C2×C4×D3—101no—
241C2×C4×D3—101no—
242C2×C4×D3—104no—
243C2×C4×D3—202no—
244C2×C4×D3—202no—
245C2×C3×C8—101no—
246C2×C3×C8—101no—
247C2×C3×C8—101no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4D2012yes—
250(C2×D3)⋊C4—104no—
251C4⋊Dic3—21no—
252C4⋊Dic3—52no—
253C4⋊Dic3—101no—
254C4⋊Dic3C4×D512yescomplemented
255Dic3⋊C4—104no—
256Dic3⋊C4—104no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C23×C5D3×D411yescharacteristic
261C22×D5—32no—
262C22×D5—32no—
263C22×D5—32no—
264C22×D5—61no—
265C22×D5—61no—
266C22×D5—61no—
267C22×D5—61no—
268C2×C4×C5—22no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—62no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5C2×C4×D311yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5#23711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—32no—
282C2×Dic5—41no—
283C2×Dic5—41no—
284C2×Dic5—61no—
285C2×Dic5—61no—
286C2×Dic5—62no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C4×D5—62no—
290C4×D5—62no—
291C4×D5—62no—
292C4×D5—62no—
293C4×D5—128no—
294Dic10—22no—
295Dic10—22no—
296Dic10—41no—
297Dic10—41no—
298C5×C8—121no—
299#168—41no—
300C22×Q8—51no—
301C23×C4—151no—
302C23×C4—301no—
303C22×C8—31no—
304C22×C8—51no—
305C22⋊Q8—154no—
306C22⋊Q8—302no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—151no—
309C2×C4⋊C4—302no—
310C2×C4⋊C4—301no—
311C2×C4⋊C4—301no—
312C2×C4⋊C4—302no—
313C2×C4⋊C4D3×D511yescharacteristic
314C2×C22⋊C4—301no—
315#103—102no—
316#103—302no—
317C22⋊C8—302no—
318C2×C3×C5#38611yescharacteristic
319C2×C3×C5C2×#10311yescharacteristic
320C2×C3×C5#41711yescharacteristic
321C2×C3×C5#45011yescharacteristic
322C2×C3×C5#45111yescharacteristic
323C2×C3×C5#48311yescharacteristic
324C2×C3×C5#48411yescharacteristic
325D15—24no—
326C23×C3D4×D511yescharacteristic
327C22×D3—52no—
328C22×D3—52no—
329C22×D3—52no—
330C22×D3—101no—
331C22×D3—101no—
332C22×D3—101no—
333C22×D3—101no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×Q8—201no—
337C3×Q8—201no—
338C2×C3×C4—22no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—102no—
342C2×C3×C4—201no—
343C2×C3×C4—201no—
344C2×C3×C4C2×C4×D511yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4#70911yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4#71311yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—52no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—102no—
357C2×Dic3—201no—
358C2×Dic3—201no—
359C4×D3—102no—
360C4×D3—102no—
361C4×D3—102no—
362C4×D3—102no—
363C4×D3—208no—
364C3×C8—201no—
365C3⋊C8—41no—
366C22×C5D3×C22⋊C411yescharacteristic
367C22×C5#88311yescharacteristic
368C22×C5D3×SD1611yescharacteristic
369C22×C5#91411yescharacteristic
370C22×C5D3×Q1611yescharacteristic
371C22×C5#91811yescharacteristic
372C22×C5#93711yescharacteristic
373C2×D5—34no—
374C2×D5—62no—
375C2×D5—62no—
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C2×D5—62no—
380C4×C5—42no—
381C4×C5—122no—
382C4×C5#67⋊C411yescharacteristic
383C4×C5#88411yescharacteristic
384C4×C5C4×#6711yescharacteristic
385C4×C5#93811yescharacteristic
386Dic5—42no—
387Dic5—62no—
388Dic5—122no—
389C24—151no—
390C2×Q8—52no—
391C2×Q8—101no—
392C2×Q8—101no—
393C2×Q8—101no—
394C2×Q8—101no—
395C2×Q8—101no—
396C22×C4—21no—
397C22×C4—61no—
398C22×C4—101no—
399C22×C4—151no—
400C22×C4—152no—
401C22×C4—152no—
402C22×C4—304no—
403C22×C4—301no—
404C22×C4—301no—
405C22×C4—301no—
406C22×C4—301no—
407C22×C4—301no—
408C22×C4—602no—
409C22×C4—602no—
410C22×C4C2×D3×D511yescharacteristic
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—101no—
415C2×C8—101no—
416C2×C8—101no—
417C4⋊C4—21no—
418C4⋊C4—32no—
419C4⋊C4—61no—
420C4⋊C4—152no—
421C4⋊C4—304no—
422C4⋊C4—304no—
423C4⋊C4—301no—
424C4⋊C4#120212yes—
425C22⋊C4—304no—
426C3×C5#187211yescharacteristic, complemented, Hall
427C22×C3D5×C22⋊C411yescharacteristic
428C22×C3#402811yescharacteristic
429C22×C3#404011yescharacteristic
430C22×C3#405711yescharacteristic
431C22×C3D5×SD1611yescharacteristic
432C22×C3#406111yescharacteristic
433C22×C3D5×Q1611yescharacteristic
434C2×D3—54no—
435C2×D3—102no—
436C2×D3—102no—
437C2×D3—102no—
438C2×D3—102no—
439C2×D3—102no—
440C2×D3—102no—
441C3×C4—42no—
442C3×C4—202no—
443C3×C4C4×D2011yescharacteristic
444C3×C4#403011yescharacteristic
445C3×C4#403911yescharacteristic
446C3×C4#404111yescharacteristic
447Dic3—42no—
448Dic3—102no—
449Dic3—202no—
450C2×C5D3×#10311yescharacteristic
451C2×C5#480311yescharacteristic
452C2×C5#480511yescharacteristic
453C2×C5#481111yescharacteristic
454C2×C5#495611yescharacteristic
455C2×C5#516911yescharacteristic
456C2×C5#518611yescharacteristic
457D5—64no—
458C23—152no—
459C23—152no—
460C23—152no—
461C23—301no—
462C23—301no—
463C23—301no—
464C23—301no—
465C23#679011yescharacteristic
466Q8—102no—
467Q8—102no—
468Q8—201no—
469Q8—201no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—62no—
474C2×C4—102no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—152no—
478C2×C4—201no—
479C2×C4—201no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—302no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4—608no—
488C2×C4—601no—
489C2×C4—601no—
490C2×C4#676611yescharacteristic
491C2×C4#677111yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4#677711yescharacteristic
494C2×C4C2×#120211yescharacteristic
495C2×C4#679011yescharacteristic
496C8—121no—
497C8—201no—
498C2×C3#6495411yescharacteristic
499C2×C3#6506011yescharacteristic
500C2×C3#6506511yescharacteristic
501C2×C3D5×#10311yescharacteristic
502C2×C3#6509711yescharacteristic
503C2×C3#6515111yescharacteristic
504C2×C3#6517311yescharacteristic
505D3—104no—
506C5#7026811yescharacteristic, complemented, Sylow
507C22—154no—
508C22—302no—
509C22—302no—
510C22—302no—
511C22—302no—
512C22—302no—
513C22—302no—
514C22#9135411yescharacteristic
515C22#9147311yescharacteristic
516C22#9148711yescharacteristic
517C22#9150011yescharacteristic
518C22#9151111yescharacteristic
519C22#9152411yescharacteristic
520C22#9157211yescharacteristic
521C4—42no—
522C4—122no—
523C4—202no—
524C4—302no—
525C4—602no—
526C4#9139611yescharacteristic
527C4C4×#120211yescharacteristic
528C4#9146111yescharacteristic
529C4#9146511yescharacteristic
530C3#1059967111yescharacteristic, complemented, Sylow
531C2—304no—
532C2#1174736511yescharacteristic
533C2#1174736711yescharacteristic
534C2#1174749011yescharacteristic
535C2#1174750911yescharacteristic
536C2#1174891711yescharacteristic
537C2#1174906411yescharacteristic
538C2#1174931011yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1872
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3942C2semidirect
4. C2×#90971C2semidirect
6. C5×#4529C2semidirect
7. #11745981C2semidirect
23. #91390C4semidirect
32. C2×#3942D3semidirect
56. C2×C3×Dic10C2×C4semidirect
63. C5×C4⋊Dic3C2×C4semidirect
78. #4529D5semidirect
177. C2×Dic10C4×D3semidirect
213. C2×D15#103semidirect
254. C4⋊Dic3C4×D5semidirect
426. C3×C5#1872semidirect
506. C5#70268semidirect
530. C3#10599671semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×#913902
C2×C3×#39422
C2×#909712
C2×#909572
C5×#45292
#117459812
#105996713
#702685