Finite Group Databasebeta

← #14299366

Subgroups — #14299366

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×C5×#807C211yesmaximal, characteristic, complemented
3#11748759C211yesmaximal, characteristic
4C2×#90989C211yesmaximal, characteristic, complemented
5C2×#90955C211yesmaximal, characteristic
6#11746350C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10601425—31nomaximal, Hall
9C22×C3×C4×D5—21no—
10C22×C3×C4×D5C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
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×#6665—21no—
21C5×#807—22no—
22#90994—21no—
23#90989—22no—
24#90955C414yescomplemented
25#71555—51nomaximal, Hall
26C2×D5×C4⋊C4D311yescharacteristic
27C2×C5×#107—31no—
28C2×#3952—31no—
29#65276—31no—
30C2×#3939—31no—
31#64771—31no—
32#64749—31no—
33C23×C3×D5D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—24no—
45C2×C3×C4×D5—42no—
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C412yes—
48C2×C3×C4×D5Q812yes—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4D412yes—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168C2×C412yescomplemented
56C5×C4⋊Dic3—21no—
57C5×C4⋊Dic3—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8C2×C412yescomplemented
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5D412yes—
63C3×#683—24no—
64#6665—42no—
65C22×C3×C4⋊C4—51no—
66#5212—51no—
67C2×#830—51no—
68C2×#807—51no—
69C2×#807D511yescharacteristic, complemented
70#4529—51no—
71#4529—51no—
72C22×C4×D5—21no—
73C22×C4×D5C2×D311yescharacteristic
74C22×C5×C8—31no—
75C2×C5×C4⋊C4—31no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×#685—61no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C2×#683—21no—
81C22×#168—31no—
82D5×C4⋊C4—22no—
83D5×C4⋊C4—22no—
84C5×#107—62no—
85#3963—61no—
86#3952—34no—
87#3939—62no—
88#1852—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—21no—
91C22×C3×D5—21no—
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5C4⋊C412yes—
95C22×C3×D5D812yes—
96C22×C3×D5Q1612yes—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×Q811yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C4⋊C412yes—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×C4×D5—22no—
122C3×C4×D5—48no—
123C3⋊#168—22no—
124C5×C3⋊C8—22no—
125C23×C3×C4—51no—
126C23×C3×C4—101no—
127C2×C3×C4⋊C4—51no—
128C2×C3×C4⋊C4—102no—
129C2×C3×C4⋊C4—101no—
130C2×C3×C4⋊C4—102no—
131C2×C3×C4⋊C4C2×D511yescharacteristic
132C2×#217—101no—
133C2×C4⋊Dic3—51no—
134C2×C4⋊Dic3C2×D511yescharacteristic
135C22×C3⋊C8—51no—
136C22×C3⋊C8C2×D511yescharacteristic
137C3⋊#95—101no—
138#830—54no—
139#807—22no—
140#807—102no—
141C23×D5#6711yescharacteristic
142C22×C4×C5—21no—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—61no—
147C22×Dic5#6711yescharacteristic
148C2×C4×D5—21no—
149C2×C4×D5—21no—
150C2×C4×D5—21no—
151C2×C4×D5—21no—
152C2×C4×D5—24no—
153C2×C4×D5—42no—
154C2×C4×D5—42no—
155C2×C4×D5Dic612yes—
156C2×C4×D5C4×D312yes—
157C2×C5×C8—32no—
158C2×C5×C8—61no—
159C2×C5×C8—61no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—61no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4#6712yes—
164#685—122no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5#6712yes—
169#683—24no—
170C2×#168—32no—
171C2×#168—61no—
172C2×#168—61no—
173C22×C4⋊C4—51no—
174C2×#107—31no—
175C2×#107—151no—
176C2×C22⋊C8—151no—
177#380—151no—
178#340—151no—
179#340—151no—
180C22×C3×C5C2×C4⋊C411yescharacteristic
181C22×C3×C5#12011yescharacteristic
182C22×C3×C5#12311yescharacteristic
183C22×C3×C5C2×D811yescharacteristic
184C22×C3×C5C2×Q1611yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C22×C3×C5#13711yescharacteristic
187C2×C3×D5—22no—
188C2×C3×D5—22no—
189C2×C3×D5—22no—
190C2×C3×D5—22no—
191C2×C3×D5—22no—
192C2×C3×D5—22no—
193C2×C3×D5#10714yescomplemented
194C3×C4×C5—42no—
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198C3×C4×C5C22⋊Q811yescharacteristic
199Dic15—81no—
200C3×Dic5—22no—
201C3×Dic5—42no—
202C5×Dic3—81no—
203C24×C3—51no—
204C22×C3×C4—21no—
205C22×C3×C4—51no—
206C22×C3×C4—52no—
207C22×C3×C4—52no—
208C22×C3×C4—104no—
209C22×C3×C4—101no—
210C22×C3×C4—101no—
211C22×C3×C4—101no—
212C22×C3×C4—101no—
213C22×C3×C4—101no—
214C22×C3×C4—202no—
215C22×C3×C4—202no—
216C22×C3×C4C22×D511yescharacteristic
217C22×Dic3—21no—
218C22×Dic3—101no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—52no—
221C3×C4⋊C4—104no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4C22⋊D512yes—
224#217—202no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—101no—
228C4⋊Dic3—101no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—52no—
232C2×C3⋊C8—101no—
233C2×C3⋊C8—101no—
234C2×C3⋊C8C4×D512yescomplemented
235C23×C5C2×#6711yescharacteristic
236C22×D5—21no—
237C22×D5—21no—
238C22×D5—21no—
239C22×D5—21no—
240C22×D5Dic3⋊C412yes—
241C22×D5#21312yes—
242C22×D5#21612yes—
243C2×C4×C5—22no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—121no—
247C2×C4×C5—121no—
248C2×C4×C5—121no—
249C2×C4×C5C2×Dic611yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5#23511yescharacteristic
253C2×C4×C5C2×#6711yescharacteristic
254C2×C4×C5C2×#6711yescharacteristic
255C2×Dic5—21no—
256C2×Dic5—21no—
257C2×Dic5—22no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—121no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C2×Dic5Dic3⋊C412yes—
264C4×D5—22no—
265C4×D5—22no—
266C4×D5—22no—
267C4×D5—22no—
268C4×D5—48no—
269C5×C8—62no—
270#168—62no—
271C23×C4—51no—
272C23×C4—101no—
273C22×C8—31no—
274C22×C8—151no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—51no—
277C2×C4⋊C4—102no—
278C2×C4⋊C4—101no—
279C2×C4⋊C4—102no—
280C2×C4⋊C4—151no—
281C2×C4⋊C4D3×D511yescharacteristic
282C2×C22⋊C4—301no—
283#107—62no—
284#107—302no—
285C22⋊C8—154no—
286#95—301no—
287C2×C3×C5#38511yescharacteristic
288C2×C3×C5C2×#10711yescharacteristic
289C2×C3×C5#42811yescharacteristic
290C2×C3×C5#44711yescharacteristic
291C2×C3×C5#45111yescharacteristic
292C2×C3×C5#48011yescharacteristic
293C2×C3×C5#48411yescharacteristic
294C3×D5—24no—
295C23×C3—52no—
296C23×C3—52no—
297C23×C3—52no—
298C23×C3—101no—
299C23×C3—101no—
300C23×C3—101no—
301C23×C3—101no—
302C23×C3D4×D511yescharacteristic
303C2×C3×C4—22no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—52no—
307C2×C3×C4—101no—
308C2×C3×C4—101no—
309C2×C3×C4—102no—
310C2×C3×C4—102no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—208no—
315C2×C3×C4—201no—
316C2×C3×C4—201no—
317C2×C3×C4C2×C4×D511yescharacteristic
318C2×C3×C4#70911yescharacteristic
319C2×C3×C4D4×D511yescharacteristic
320C2×C3×C4Q8×D511yescharacteristic
321C2×C3×C4#71311yescharacteristic
322C2×C3×C4C2×C22⋊D511yescharacteristic
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—201no—
327C2×Dic3—201no—
328C2×Dic3—201no—
329C3⋊C8—22no—
330C3⋊C8—102no—
331C22×C5C2×Dic3⋊C411yescharacteristic
332C22×C5#92911yescharacteristic
333C22×C5C2×#21311yescharacteristic
334C22×C5#93211yescharacteristic
335C22×C5#94211yescharacteristic
336C22×C5C2×#21611yescharacteristic
337C22×C5#95311yescharacteristic
338C2×D5—22no—
339C2×D5—22no—
340C2×D5—22no—
341C2×D5—22no—
342C2×D5—22no—
343C2×D5—22no—
344C2×D5#80714yescomplemented
345C4×C5—42no—
346C4×C5—241no—
347C4×C5#92411yescharacteristic
348C4×C5#92411yescharacteristic
349C4×C5C4×#6711yescharacteristic
350C4×C5C4×#6711yescharacteristic
351Dic5—22no—
352Dic5—42no—
353Dic5—241no—
354C24—51no—
355C22×C4—21no—
356C22×C4—51no—
357C22×C4—52no—
358C22×C4—52no—
359C22×C4—61no—
360C22×C4—104no—
361C22×C4—101no—
362C22×C4—101no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4—101no—
366C22×C4—202no—
367C22×C4—202no—
368C22×C4—301no—
369C22×C4C2×D3×D511yescharacteristic
370C2×C8—32no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—152no—
374C2×C8—301no—
375C2×C8—301no—
376C4⋊C4—21no—
377C4⋊C4—52no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—104no—
381C4⋊C4—101no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4#120112yes—
385C22⋊C4—602no—
386C3×C5#185211yescharacteristic, complemented, Hall
387C22×C3—54no—
388C22×C3—102no—
389C22×C3—102no—
390C22×C3—102no—
391C22×C3—102no—
392C22×C3—102no—
393C22×C3—102no—
394C22×C3D5×C4⋊C411yescharacteristic
395C22×C3#404011yescharacteristic
396C22×C3D5×D811yescharacteristic
397C22×C3#405711yescharacteristic
398C22×C3D5×Q1611yescharacteristic
399C22×C3#406411yescharacteristic
400C22×C3#408311yescharacteristic
401C3×C4—42no—
402C3×C4—102no—
403C3×C4—202no—
404C3×C4#403911yescharacteristic
405C3×C4#404211yescharacteristic
406C3×C4C4×C22⋊D511yescharacteristic
407C3×C4#409211yescharacteristic
408Dic3—81no—
409Dic3—401no—
410C2×C5C2×#80711yescharacteristic
411C2×C5#496411yescharacteristic
412C2×C5#496711yescharacteristic
413C2×C5#497011yescharacteristic
414C2×C5#521011yescharacteristic
415C2×C5#521711yescharacteristic
416C2×C5#522811yescharacteristic
417D5—24no—
418C23—52no—
419C23—52no—
420C23—52no—
421C23—101no—
422C23—101no—
423C23—101no—
424C23—101no—
425C23D5×#6711yescharacteristic
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—52no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—102no—
433C2×C4—102no—
434C2×C4—102no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—208no—
441C2×C4—201no—
442C2×C4—201no—
443C2×C4—601no—
444C2×C4—601no—
445C2×C4—601no—
446C2×C4D5×Dic611yescharacteristic
447C2×C4#677111yescharacteristic
448C2×C4#677311yescharacteristic
449C2×C4C4×D3×D511yescharacteristic
450C2×C4C2×#120111yescharacteristic
451C2×C4D5×#6711yescharacteristic
452C8—62no—
453C8—302no—
454C2×C3—104no—
455C2×C3D5×#10711yescharacteristic
456C2×C3#6517011yescharacteristic
457C2×C3#6517111yescharacteristic
458C2×C3#6517311yescharacteristic
459C2×C3#6527811yescharacteristic
460C2×C3#6544511yescharacteristic
461C2×C3#6547511yescharacteristic
462C5#7155511yescharacteristic, complemented, Sylow
463C22—54no—
464C22—102no—
465C22—102no—
466C22—102no—
467C22—102no—
468C22—102no—
469C22—102no—
470C22#9134811yescharacteristic
471C22D5×Dic3⋊C411yescharacteristic
472C22D5×#21311yescharacteristic
473C22#9148911yescharacteristic
474C22D5×#21611yescharacteristic
475C22#9151511yescharacteristic
476C22#9156311yescharacteristic
477C4—42no—
478C4—102no—
479C4—202no—
480C4—241no—
481C4—1201no—
482C4#9134911yescharacteristic
483C4#9135911yescharacteristic
484C4C4×#120111yescharacteristic
485C4#9144411yescharacteristic
486C3#1060142511yescharacteristic, complemented, Sylow
487C2—104no—
488C2#1174716411yescharacteristic
489C2#1174716911yescharacteristic
490C2D5×#80711yescharacteristic
491C2#1174745211yescharacteristic
492C2#1174870311yescharacteristic
493C2#1174902111yescharacteristic
494C2#1174929011yescharacteristic
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#1852
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
2. C2×C5×#807C2semidirect
4. C2×#90989C2semidirect
6. #11746350C2semidirect
7. #11745980C2semidirect
24. #90955C4semidirect
55. C2×C3⋊#168C2×C4semidirect
60. C2×C5×C3⋊C8C2×C4semidirect
69. C2×#807D5semidirect
193. C2×C3×D5#107semidirect
234. C2×C3⋊C8C4×D5semidirect
344. C2×D5#807semidirect
386. C3×C5#1852semidirect
462. C5#71555semidirect
486. C3#10601425semidirect

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×C5×#8072
#117487592
C2×#909892
C2×#909552
#117463502
#117459802
#106014253
#715555