Finite Group Databasebeta

← #14308856

Subgroups — #14308856

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91384C211yesmaximal, characteristic, complemented
2C2×C3×#3953C211yesmaximal, characteristic
3#11748796C211yesmaximal, characteristic
4C2×#90964C211yesmaximal, characteristic
5#11746371C211yesmaximal, characteristic, complemented
6C5×#4551C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10599692—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×Dic3⋊Dic5—21no—
17C2×#6668—21no—
18C2×#6665—21no—
19C2×#6665—21no—
20#91384—22no—
21#91384—22no—
22C3×#3953—22no—
23#90964—22no—
24#70164—51nomaximal, Hall
25C2×#4036—31no—
26C2×#3953D311yescharacteristic
27#65277—31no—
28C2×#3941—31no—
29C5×#340—31no—
30#64770—31no—
31#64749—31no—
32C23×C3×D5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15D411yescharacteristic
35C22×Dic15D411yescharacteristic
36C22×C5×Dic3—21no—
37C22×C5×Dic3—21no—
38C22×C3×Dic5—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20Q812yes—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C4×Dic15—21no—
49C4×Dic15—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3D412yes—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D412yes—
59Dic3⋊Dic5—24no—
60#6668—24no—
61#6665—42no—
62#6665—42no—
63C2×#890—51no—
64C2×C3×#102—51no—
65#5221—51no—
66C2×#832—51no—
67#4551D511yescharacteristic, complemented
68#4550—51no—
69#4529—51no—
70C22×D20C2×D311yescharacteristic
71C22×C5×C8C2×D311yescharacteristic
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4—31no—
74C2×#685—61no—
75C2×#685—61no—
76C2×C4⋊Dic5—61no—
77C2×C4⋊Dic5C2×D311yescharacteristic
78C2×#683—61no—
79C2×C4×Dic5—31no—
80C22×#168—31no—
81#4036—62no—
82#4036—62no—
83#3953—22no—
84#3941—62no—
85#2025—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C3×D5—22no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5—41no—
91C22×C3×D5—41no—
92C22×C3×D5—41no—
93C22×C3×D5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×Q811yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C3×D20—22no—
116C3×D20—22no—
117C3×D20—41no—
118C3×D20—41no—
119C3×C5×C8—41no—
120C3⋊#168—41no—
121C22×C3×D4—51no—
122C22×C3×C8C2×D511yescharacteristic
123C2×C3×C4⋊C4—51no—
124C2×#217—101no—
125C2×#217—101no—
126C2×C4⋊Dic3—101no—
127C2×C4⋊Dic3C2×D511yescharacteristic
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—101no—
130C2×C4×Dic3—51no—
131C22×C3⋊C8—51no—
132#890—102no—
133#890—102no—
134C3×#102—102no—
135#832—102no—
136C23×D5—21no—
137C22×C4×C5—61no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—21no—
141C22×Dic5—31no—
142C22×Dic5—31no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20Dic612yes—
149C2×C5×C8—21no—
150C2×C5×C8—21no—
151C2×C5×C8—21no—
152C5×C4⋊C4—32no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155C5×C4⋊C4—61no—
156#685—122no—
157#685—122no—
158C4⋊Dic5—21no—
159C4⋊Dic5—64no—
160C4⋊Dic5#6712yes—
161#683—64no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#125—151no—
168C2×#102—51no—
169C2×#102—151no—
170#390—151no—
171#340—31no—
172#340—151no—
173#336—151no—
174C22×C3×C5#12011yescharacteristic
175C22×C3×C5C22⋊Q811yescharacteristic
176C22×C3×C5#12411yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C2×C3×D5—42no—
182C2×C3×D5—42no—
183C2×C3×D5—42no—
184C2×C3×D5—81no—
185C2×C3×D5—81no—
186C2×C3×D5—81no—
187C2×C3×D5—81no—
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5#12411yescharacteristic
191C3×C4×C5#12411yescharacteristic
192Dic15—41no—
193Dic15—41no—
194C3×Dic5—42no—
195C5×Dic3—42no—
196C5×Dic3—81no—
197C24×C3—101no—
198C2×C3×D4—52no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—51no—
209C22×Dic3—51no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C3×C4⋊C4—52no—
214C3×C4⋊C4—101no—
215#217—202no—
216#217—202no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—104no—
221C4⋊Dic3D2012yes—
222Dic3⋊C4—104no—
223C4×Dic3—101no—
224C4×Dic3—101no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5D3×D411yescharacteristic
229C22×D5—22no—
230C22×D5—41no—
231C22×D5—41no—
232C22×D5—41no—
233C22×D5—41no—
234C22×D5—41no—
235C22×D5—41no—
236C2×C4×C5—62no—
237C2×C4×C5—121no—
238C2×C4×C5—121no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C2×Dic5—22no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251C2×Dic5—61no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254C2×Dic5—61no—
255C2×Dic5—61no—
256C2×Dic5—61no—
257D20—22no—
258D20—22no—
259D20—41no—
260D20—41no—
261C5×C8—41no—
262#168—121no—
263C22×D4—51no—
264C22×C8—151no—
265C22×C8D3×D511yescharacteristic
266#125—302no—
267#125—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—301no—
273C2×C22⋊C4—301no—
274C2×C22⋊C4—301no—
275C2×C42—151no—
276#102—102no—
277#102—302no—
278C2×C3×C5#39311yescharacteristic
279C2×C3×C5#44911yescharacteristic
280C2×C3×C5#44911yescharacteristic
281C2×C3×C5#47811yescharacteristic
282C2×C3×C5#47811yescharacteristic
283C2×C3×C5#48811yescharacteristic
284C2×C3×C5#49011yescharacteristic
285C3×D5—82no—
286C23×C3—102no—
287C23×C3—201no—
288C23×C3—201no—
289C23×C3—201no—
290C23×C3—201no—
291C23×C3—201no—
292C23×C3—201no—
293C23×C3D4×D511yescharacteristic
294C3×D4—102no—
295C3×D4—102no—
296C3×D4—201no—
297C3×D4—201no—
298C2×C3×C4—102no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4C2×D2011yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4#70911yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4Q8×D511yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—101no—
314C2×Dic3—101no—
315C2×Dic3—101no—
316C2×Dic3—101no—
317C2×Dic3—101no—
318C2×Dic3—101no—
319C3×C8—41no—
320C3⋊C8—201no—
321C22×C5#87811yescharacteristic
322C22×C5#88511yescharacteristic
323C22×C5#91111yescharacteristic
324C22×C5#91211yescharacteristic
325C22×C5#91411yescharacteristic
326C22×C5#91611yescharacteristic
327C22×C5#93711yescharacteristic
328C2×D5—42no—
329C2×D5—42no—
330C2×D5—42no—
331C2×D5—81no—
332C2×D5—81no—
333C2×D5—81no—
334C2×D5—81no—
335C4×C5—122no—
336C4×C5—241no—
337C4×C5#87811yescharacteristic
338C4×C5#88511yescharacteristic
339C4×C5#92411yescharacteristic
340C4×C5#93611yescharacteristic
341Dic5—42no—
342Dic5—121no—
343Dic5—121no—
344C24—101no—
345C2×D4—52no—
346C2×D4—101no—
347C2×D4—101no—
348C2×D4—101no—
349C2×D4—101no—
350C2×D4—101no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—101no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—301no—
361C2×C8—301no—
362C2×C8—301no—
363C4⋊C4—32no—
364C4⋊C4—52no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—101no—
369C4⋊C4—304no—
370C4⋊C4—304no—
371C22⋊C4—602no—
372C22⋊C4—602no—
373C42—301no—
374C42—301no—
375C3×C5#202511yescharacteristic, complemented, Hall
376C22×C3—202no—
377C22×C3—202no—
378C22×C3—202no—
379C22×C3—401no—
380C22×C3—401no—
381C22×C3—401no—
382C22×C3—401no—
383C22×C3#402811yescharacteristic
384C22×C3#403111yescharacteristic
385C22×C3#404211yescharacteristic
386C22×C3#405711yescharacteristic
387C22×C3#406011yescharacteristic
388C22×C3#406211yescharacteristic
389C22×C3#406511yescharacteristic
390C3×C4—202no—
391C3×C4#402111yescharacteristic
392C3×C4#403111yescharacteristic
393C3×C4#404211yescharacteristic
394C3×C4#404311yescharacteristic
395Dic3—42no—
396Dic3—81no—
397Dic3—201no—
398Dic3—201no—
399C2×C5#476311yescharacteristic
400C2×C5#476411yescharacteristic
401C2×C5#476611yescharacteristic
402C2×C5#476811yescharacteristic
403C2×C5#494711yescharacteristic
404C2×C5#515811yescharacteristic
405C2×C5#517211yescharacteristic
406D5—82no—
407C23—102no—
408C23—201no—
409C23—201no—
410C23—201no—
411C23—201no—
412C23—201no—
413C23—201no—
414C23#677711yescharacteristic
415D4—102no—
416D4—102no—
417D4—201no—
418D4—201no—
419C2×C4—62no—
420C2×C4—102no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—201no—
427C2×C4—201no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4—301no—
433C2×C4—301no—
434C2×C4D5×Dic611yescharacteristic
435C2×C4#677111yescharacteristic
436C2×C4D3×D2011yescharacteristic
437C2×C4#677911yescharacteristic
438C2×C4#678011yescharacteristic
439C2×C4D5×#6711yescharacteristic
440C8—41no—
441C8—601no—
442C2×C3—402no—
443C2×C3#6496211yescharacteristic
444C2×C3#6505311yescharacteristic
445C2×C3#6507011yescharacteristic
446C2×C3#6508911yescharacteristic
447C2×C3#6510011yescharacteristic
448C2×C3#6516011yescharacteristic
449C2×C3#6518011yescharacteristic
450C5#7016411yescharacteristic, complemented, Sylow
451C22—202no—
452C22—202no—
453C22—202no—
454C22—401no—
455C22—401no—
456C22—401no—
457C22—401no—
458C22#9125711yescharacteristic
459C22#9125811yescharacteristic
460C22#9127611yescharacteristic
461C22#9127711yescharacteristic
462C22#9143011yescharacteristic
463C22#9146411yescharacteristic
464C22#9147411yescharacteristic
465C4—122no—
466C4—202no—
467C4—241no—
468C4—601no—
469C4—601no—
470C4#9134911yescharacteristic
471C4#9135311yescharacteristic
472C4#9142211yescharacteristic
473C4#9153411yescharacteristic
474C3#1059969211yescharacteristic, complemented, Sylow
475C2—402no—
476C2#1174780411yescharacteristic
477C2#1174780511yescharacteristic
478C2#1174788911yescharacteristic
479C2#1174797811yescharacteristic
480C2#1174801411yescharacteristic
481C2#1174815011yescharacteristic
482C2#1174873611yescharacteristic
subgroupG/H
centerC23#6777
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
hypercenterC22×C8D3×D5
hypocenterC3×C5#2025
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#91384C2semidirect
5. #11746371C2semidirect
6. C5×#4551C2semidirect
7. #11745979C2semidirect
67. #4551D5semidirect
375. C3×C5#2025semidirect
450. C5#70164semidirect
474. C3#10599692semidirect

Maximal subgroups

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

subgroupindex
C2×#913842
C2×C3×#39532
#117487962
C2×#909642
#117463712
C5×#45512
#117459792
#105996923
#701645