Finite Group Databasebeta

← #14300614

Subgroups — #14300614

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×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#91360C211yesmaximal, characteristic
3C2×#91094C211yesmaximal, characteristic, complemented
4C2×#90974C211yesmaximal, characteristic, complemented
5C2×#90955C211yesmaximal, characteristic
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10599671—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×#683—21no—
18C3×D5×C4⋊C4—22no—
19C3×D5×C4⋊C4—22no—
20C2×Dic3⋊Dic5—21no—
21C2×#6665—21no—
22#91360—22no—
23#91360C414yescomplemented
24#91094—22no—
25#90974—22no—
26#90955—22no—
27#71559—51nomaximal, Hall
28C2×#4043—31no—
29C2×D5×C4⋊C4D311yescharacteristic
30C2×#3952—31no—
31C2×#3948—31no—
32C2×#3942—31no—
33C5×#340—31no—
34#64749—31no—
35C23×C3×D5D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30C2×C412yescomplemented
45C22×C5×Dic3—21no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5D411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5—24no—
53C2×C3×C4×D5—42no—
54C2×C3×C4×D5—42no—
55C2×C3×C4×D5C2×C412yes—
56C2×C3×C4×D5D412yes—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yes—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2×C412yescomplemented
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5D412yes—
69C3×#683—24no—
70Dic3⋊Dic5—24no—
71#6665—24no—
72C22×C3×C4⋊C4—51no—
73C2×#924—51no—
74C2×#830—51no—
75C2×#810—51no—
76C2×#810—51no—
77#4529—51no—
78#4529D511yescharacteristic, complemented
79C22×C4×D5—21no—
80C22×C4×D5C2×D311yescharacteristic
81C22×Dic10—31no—
82C22×C5×C8—31no—
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#685—61no—
86C2×C4⋊Dic5—61no—
87C2×C4⋊Dic5C2×D311yescharacteristic
88C2×#683—21no—
89C22×#168—31no—
90#4043—34no—
91#4043—62no—
92D5×C4⋊C4—22no—
93D5×C4⋊C4—22no—
94#3952—62no—
95#3948—62no—
96#3942—62no—
97#1872—151noSylow
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—21no—
103C22×C3×D5C22⋊C412yes—
104C22×C3×D5SD1612yes—
105C22×C3×D5Q1612yes—
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—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118Dic30—22no—
119Dic30—22no—
120Dic30—41no—
121Dic30—41no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5C22⋊C412yes—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×C4×D5—48no—
136C3⋊#168—41no—
137C5×C3⋊C8—41no—
138C23×C3×C4—51no—
139C23×C3×C4—101no—
140C22×Dic6—51no—
141C2×C3×C4⋊C4—51no—
142C2×C3×C4⋊C4—102no—
143C2×C3×C4⋊C4—101no—
144C2×C3×C4⋊C4—102no—
145C2×C3×C4⋊C4C2×D511yescharacteristic
146C2×#217—101no—
147C2×C4⋊Dic3C2×D511yescharacteristic
148#924—54no—
149#924—102no—
150C2×Dic3⋊C4—101no—
151C22×C3⋊C8—51no—
152C22×C3⋊C8C2×D511yescharacteristic
153#830—102no—
154#810—102no—
155#810—102no—
156C23×D5#6711yescharacteristic
157C22×C4×C5—21no—
158C22×C4×C5—61no—
159C22×C4×C5C22×D311yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—61no—
162C22×Dic5#6711yescharacteristic
163C2×C4×D5—21no—
164C2×C4×D5—21no—
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×C4×D5—24no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C2×C4×D5C4×D312yes—
171C2×C4×D5D1212yes—
172C2×Dic10—32no—
173C2×Dic10—61no—
174C2×Dic10—61no—
175C2×Dic10—61no—
176C2×Dic10—61no—
177C2×Dic10—61no—
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—21no—
187C4⋊Dic5—64no—
188C4⋊Dic5#6712yes—
189#683—24no—
190C2×#168—61no—
191C2×#168—61no—
192C2×#168—61no—
193C2×C22⋊Q8—151no—
194C22×C4⋊C4—51no—
195C2×#103—151no—
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×C3×D5—22no—
208C2×C3×D5—22no—
209C2×C3×D5—22no—
210C2×C3×D5—22no—
211C2×C3×D5—22no—
212C2×C3×D5—22no—
213C2×C3×D5#10314yescomplemented
214C3×C4×C5—42no—
215C3×C4×C5C4×D411yescharacteristic
216C3×C4×C5C4×D411yescharacteristic
217C3×C4×C5#12111yescharacteristic
218C3×C4×C5#12111yescharacteristic
219Dic15—42no—
220C3×Dic5—22no—
221C3×Dic5—42no—
222C5×Dic3—42no—
223C24×C3—51no—
224C22×C3×C4—21no—
225C22×C3×C4—51no—
226C22×C3×C4—52no—
227C22×C3×C4—52no—
228C22×C3×C4—104no—
229C22×C3×C4—101no—
230C22×C3×C4—101no—
231C22×C3×C4—101no—
232C22×C3×C4—101no—
233C22×C3×C4—101no—
234C22×C3×C4—202no—
235C22×C3×C4—202no—
236C22×C3×C4C22×D511yescharacteristic
237C22×Dic3—21no—
238C22×Dic3—101no—
239C2×Dic6—52no—
240C2×Dic6—101no—
241C2×Dic6—101no—
242C2×Dic6—101no—
243C2×Dic6—101no—
244C2×Dic6—101no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—52no—
247C3×C4⋊C4—104no—
248C3×C4⋊C4—101no—
249C3×C4⋊C4D2012yes—
250#217—104no—
251C4⋊Dic3—21no—
252C4⋊Dic3C4×D512yescomplemented
253Dic3⋊C4—104no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—101no—
258C2×C3⋊C8—101no—
259C2×C3⋊C8—101no—
260C23×C5C2×#6711yescharacteristic
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5(C2×D3)⋊C412yes—
266C22×D5#21412yes—
267C22×D5#21612yes—
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×C5C2×D1211yescharacteristic
276C2×C4×C5#23511yescharacteristic
277C2×C4×C5#23511yescharacteristic
278C2×C4×C5C2×#6711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—62no—
286C2×Dic5—121no—
287C2×Dic5—121no—
288C2×Dic5(C2×D3)⋊C412yes—
289C4×D5—22no—
290C4×D5—22no—
291C4×D5—22no—
292C4×D5—22no—
293C4×D5—48no—
294Dic10—62no—
295Dic10—62no—
296Dic10—121no—
297Dic10—121no—
298C5×C8—121no—
299#168—121no—
300C22×Q8—151no—
301C23×C4—51no—
302C23×C4—101no—
303C22×C8—31no—
304C22×C8—151no—
305C22⋊Q8—154no—
306C22⋊Q8—302no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—51no—
309C2×C4⋊C4—102no—
310C2×C4⋊C4—101no—
311C2×C4⋊C4—102no—
312C2×C4⋊C4—301no—
313C2×C4⋊C4D3×D511yescharacteristic
314C2×C22⋊C4—301no—
315#103—302no—
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
325C3×D5—24no—
326C23×C3—52no—
327C23×C3—52no—
328C23×C3—52no—
329C23×C3—101no—
330C23×C3—101no—
331C23×C3—101no—
332C23×C3—101no—
333C23×C3D4×D511yescharacteristic
334C2×C3×C4—22no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—52no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—208no—
346C2×C3×C4—201no—
347C2×C3×C4—201no—
348C2×C3×C4C2×C4×D511yescharacteristic
349C2×C3×C4C2×D2011yescharacteristic
350C2×C3×C4#70911yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4#71311yescharacteristic
354C2×Dic3—22no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—102no—
358C2×Dic3—201no—
359C2×Dic3—201no—
360Dic6—102no—
361Dic6—102no—
362Dic6—201no—
363Dic6—201no—
364C3⋊C8—41no—
365C3⋊C8—201no—
366C22×C5C2×(C2×D3)⋊C411yescharacteristic
367C22×C5#92911yescharacteristic
368C22×C5#93211yescharacteristic
369C22×C5C2×#21411yescharacteristic
370C22×C5#94211yescharacteristic
371C22×C5C2×#21611yescharacteristic
372C22×C5#95311yescharacteristic
373C2×D5—22no—
374C2×D5—22no—
375C2×D5—22no—
376C2×D5—22no—
377C2×D5—22no—
378C2×D5—22no—
379C2×D5#81014yescomplemented
380C4×C5—42no—
381C4×C5—122no—
382C4×C5C4×#6711yescharacteristic
383C4×C5C4×#6711yescharacteristic
384C4×C5#93011yescharacteristic
385C4×C5#93011yescharacteristic
386Dic5—22no—
387Dic5—42no—
388Dic5—122no—
389C24—51no—
390C2×Q8—152no—
391C2×Q8—301no—
392C2×Q8—301no—
393C2×Q8—301no—
394C2×Q8—301no—
395C2×Q8—301no—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—52no—
399C22×C4—52no—
400C22×C4—61no—
401C22×C4—104no—
402C22×C4—101no—
403C22×C4—101no—
404C22×C4—101no—
405C22×C4—101no—
406C22×C4—101no—
407C22×C4—202no—
408C22×C4—202no—
409C22×C4—301no—
410C22×C4C2×D3×D511yescharacteristic
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—301no—
415C2×C8—301no—
416C2×C8—301no—
417C4⋊C4—21no—
418C4⋊C4—32no—
419C4⋊C4—52no—
420C4⋊C4—61no—
421C4⋊C4—104no—
422C4⋊C4—101no—
423C4⋊C4—304no—
424C4⋊C4#120212yes—
425C22⋊C4—304no—
426C3×C5#187211yescharacteristic, complemented, Hall
427C22×C3—54no—
428C22×C3—102no—
429C22×C3—102no—
430C22×C3—102no—
431C22×C3—102no—
432C22×C3—102no—
433C22×C3—102no—
434C22×C3D5×C22⋊C411yescharacteristic
435C22×C3#402811yescharacteristic
436C22×C3#404011yescharacteristic
437C22×C3#405711yescharacteristic
438C22×C3D5×SD1611yescharacteristic
439C22×C3#406111yescharacteristic
440C22×C3D5×Q1611yescharacteristic
441C3×C4—42no—
442C3×C4—102no—
443C3×C4—202no—
444C3×C4C4×D2011yescharacteristic
445C3×C4#403011yescharacteristic
446C3×C4#403911yescharacteristic
447C3×C4#404111yescharacteristic
448Dic3—42no—
449Dic3—202no—
450C2×C5#496611yescharacteristic
451C2×C5C2×#81011yescharacteristic
452C2×C5#497011yescharacteristic
453C2×C5#497111yescharacteristic
454C2×C5#521311yescharacteristic
455C2×C5#521811yescharacteristic
456C2×C5#522811yescharacteristic
457D5—24no—
458C23—52no—
459C23—52no—
460C23—52no—
461C23—101no—
462C23—101no—
463C23—101no—
464C23—101no—
465C23D5×#6711yescharacteristic
466Q8—302no—
467Q8—302no—
468Q8—601no—
469Q8—601no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—52no—
474C2×C4—62no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—102no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—208no—
485C2×C4—201no—
486C2×C4—201no—
487C2×C4—302no—
488C2×C4—601no—
489C2×C4—601no—
490C2×C4#677111yescharacteristic
491C2×C4#677311yescharacteristic
492C2×C4C4×D3×D511yescharacteristic
493C2×C4D5×D1211yescharacteristic
494C2×C4C2×#120211yescharacteristic
495C2×C4D5×#6711yescharacteristic
496C8—121no—
497C8—601no—
498C2×C3—104no—
499C2×C3#6495411yescharacteristic
500C2×C3#6506011yescharacteristic
501C2×C3#6506511yescharacteristic
502C2×C3D5×#10311yescharacteristic
503C2×C3#6509711yescharacteristic
504C2×C3#6515111yescharacteristic
505C2×C3#6517311yescharacteristic
506C5#7155911yescharacteristic, complemented, Sylow
507C22—54no—
508C22—102no—
509C22—102no—
510C22—102no—
511C22—102no—
512C22—102no—
513C22—102no—
514C22#9134811yescharacteristic
515C22D5×(C2×D3)⋊C411yescharacteristic
516C22D5×#21411yescharacteristic
517C22#9148911yescharacteristic
518C22D5×#21611yescharacteristic
519C22#9151311yescharacteristic
520C22#9156411yescharacteristic
521C4—42no—
522C4—102no—
523C4—122no—
524C4—202no—
525C4—602no—
526C4C4×#120211yescharacteristic
527C4#9144411yescharacteristic
528C4#9144811yescharacteristic
529C4#9145011yescharacteristic
530C3#1059967111yescharacteristic, complemented, Sylow
531C2—104no—
532C2#1174716811yescharacteristic
533C2#1174716911yescharacteristic
534C2D5×#81011yescharacteristic
535C2#1174749811yescharacteristic
536C2#1174890711yescharacteristic
537C2#1174904511yescharacteristic
538C2#1174929111yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
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×#91094C2semidirect
4. C2×#90974C2semidirect
6. C5×#4529C2semidirect
7. #11745979C2semidirect
23. #91360C4semidirect
44. C2×Dic30C2×C4semidirect
63. C5×C4⋊Dic3C2×C4semidirect
78. #4529D5semidirect
213. C2×C3×D5#103semidirect
252. C4⋊Dic3C4×D5semidirect
379. C2×D5#810semidirect
426. C3×C5#1872semidirect
506. C5#71559semidirect
530. C3#10599671semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#913602
C2×#910942
C2×#909742
C2×#909552
C5×#45292
#117459792
#105996713
#715595