Finite Group Databasebeta

← #14308857

Subgroups — #14308857

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×#91388C211yesmaximal, characteristic, complemented
2C3×#65277C211yesmaximal, characteristic
3C2×#90965C211yesmaximal, characteristic
4C2×#90964C211yesmaximal, characteristic
5#11746350C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745966C211yesmaximal, characteristic, complemented
8#10599692—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×#685—21no—
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×Dic3⋊Dic5—21no—
19C2×#6669—21no—
20#91388—22no—
21#91388—22no—
22#90965—22no—
23#90964—22no—
24#69639—51nomaximal, Hall
25C2×#4036—31no—
26C2×#3953—31no—
27#65277D311yescharacteristic
28C2×#3941—31no—
29C5×#340—31no—
30#64770—31no—
31#64749—31no—
32C23×C3×D5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C22×C5×Dic3—21no—
37C22×C3×Dic5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20Q812yes—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C2×C3⋊#168—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3D412yes—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C3×#685—42no—
58C3×#685—42no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5—21no—
61Dic3⋊Dic5—24no—
62#6669—24no—
63C2×#870—51no—
64C3×#390—51no—
65C2×#832—51no—
66C2×#832—51no—
67#4529—51no—
68#4529D511yescharacteristic, complemented
69#4524—51no—
70C22×D20C2×D311yescharacteristic
71C22×C5×C8—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—61no—
78C2×#683—61no—
79C2×C4×Dic5C2×D311yescharacteristic
80C22×#168—31no—
81#4036—62no—
82#4036—62no—
83#3953—62no—
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×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×Q811yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C3×D20—22no—
116C3×D20—22no—
117C3×D20—41no—
118C3×D20—41no—
119C3⋊#168—41no—
120C5×C3⋊C8—41no—
121C22×C3×D4—51no—
122C2×C3×C4⋊C4C2×D511yescharacteristic
123C2×C3×C22⋊C4—101no—
124C2×C3×C22⋊C4—101no—
125C2×C3×C42—51no—
126C2×C4⋊Dic3—51no—
127C2×C4⋊Dic3C2×D511yescharacteristic
128C2×Dic3⋊C4—101no—
129C2×Dic3⋊C4—101no—
130C22×C3⋊C8—51no—
131C22×C3⋊C8C2×D511yescharacteristic
132#870—102no—
133#870—102no—
134#832—102no—
135#832—102no—
136C23×D5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—61no—
141C22×Dic5#6711yescharacteristic
142C22×Dic5#6711yescharacteristic
143C2×D20—21no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20Dic612yes—
149C2×C5×C8—61no—
150C2×C5×C8—61no—
151C2×C5×C8—61no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—32no—
155C5×C4⋊C4—61no—
156#685—42no—
157#685—42no—
158C4⋊Dic5—32no—
159C4⋊Dic5—64no—
160C4⋊Dic5—61no—
161#683—64no—
162C4×Dic5—21no—
163C4×Dic5—21no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#125—151no—
168C2×#102—151no—
169C2×#102—151no—
170#390—51no—
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×C5—81no—
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12411yescharacteristic
192C3×C4×C5#12411yescharacteristic
193Dic15—42no—
194C3×Dic5—41no—
195C3×Dic5—41no—
196C5×Dic3—42no—
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—21no—
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4C22×D511yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—101no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C22⋊C4—202no—
213C3×C22⋊C4—202no—
214C3×C42—101no—
215C3×C42—101no—
216C4⋊Dic3—21no—
217C4⋊Dic3—52no—
218C4⋊Dic3—101no—
219C4⋊Dic3D2012yes—
220Dic3⋊C4—104no—
221Dic3⋊C4—104no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5C2×#6711yescharacteristic
229C22×D5—22no—
230C22×D5—41no—
231C22×D5—41no—
232C22×D5—41no—
233C22×D5—41no—
234C22×D5—41no—
235C22×D5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—62no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—21no—
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—21no—
254C2×Dic5—62no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257D20—22no—
258D20—22no—
259D20—41no—
260D20—41no—
261C5×C8—121no—
262#168—121no—
263C22×D4—51no—
264C22×C8—31no—
265C22×C8—151no—
266#125—302no—
267#125—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—151no—
270C2×C4⋊C4—301no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4D3×D511yescharacteristic
273C2×C22⋊C4—101no—
274C2×C22⋊C4—101no—
275C2×C42—51no—
276#102—302no—
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—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—101no—
302C2×C3×C4—101no—
303C2×C3×C4—101no—
304C2×C3×C4—101no—
305C2×C3×C4—101no—
306C2×C3×C4—101no—
307C2×C3×C4C2×D2011yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4Q8×D511yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—102no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319C3⋊C8—41no—
320C3⋊C8—201no—
321C22×C5#92411yescharacteristic
322C22×C5#93211yescharacteristic
323C22×C5#93211yescharacteristic
324C22×C5#93611yescharacteristic
325C22×C5#93711yescharacteristic
326C22×C5#95011yescharacteristic
327C22×C5#95011yescharacteristic
328C2×D5—42no—
329C2×D5—42no—
330C2×D5—42no—
331C2×D5—81no—
332C2×D5—81no—
333C2×D5—81no—
334C2×D5—81no—
335C4×C5—81no—
336C4×C5—122no—
337C4×C5#87811yescharacteristic
338C4×C5#87811yescharacteristic
339C4×C5#88511yescharacteristic
340C4×C5#88511yescharacteristic
341Dic5—41no—
342Dic5—41no—
343Dic5—122no—
344C24—101no—
345C2×D4—52no—
346C2×D4—101no—
347C2×D4—101no—
348C2×D4—101no—
349C2×D4—101no—
350C2×D4—101no—
351C22×C4—21no—
352C22×C4—51no—
353C22×C4—51no—
354C22×C4—61no—
355C22×C4—301no—
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—301no—
361C2×C8—301no—
362C2×C8—301no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—32no—
366C4⋊C4—61no—
367C4⋊C4—152no—
368C4⋊C4—304no—
369C4⋊C4—304no—
370C4⋊C4—301no—
371C22⋊C4—202no—
372C22⋊C4—202no—
373C42—101no—
374C42—101no—
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—81no—
391C3×C4—201no—
392C3×C4—201no—
393C3×C4#402111yescharacteristic
394C3×C4#403111yescharacteristic
395C3×C4#404211yescharacteristic
396C3×C4#404311yescharacteristic
397Dic3—42no—
398Dic3—202no—
399C2×C5#494711yescharacteristic
400C2×C5#500911yescharacteristic
401C2×C5#500911yescharacteristic
402C2×C5#503711yescharacteristic
403C2×C5#503711yescharacteristic
404C2×C5#505611yescharacteristic
405C2×C5#507111yescharacteristic
406D5—82no—
407C23—102no—
408C23—201no—
409C23—201no—
410C23—201no—
411C23—201no—
412C23—201no—
413C23—201no—
414C23D5×#6711yescharacteristic
415D4—102no—
416D4—102no—
417D4—201no—
418D4—201no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—62no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—302no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4D5×Dic611yescharacteristic
435C2×C4#677111yescharacteristic
436C2×C4D3×D2011yescharacteristic
437C2×C4#677711yescharacteristic
438C2×C4#677911yescharacteristic
439C2×C4#678011yescharacteristic
440C8—121no—
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#6963911yescharacteristic, complemented, Sylow
451C22—202no—
452C22—202no—
453C22—202no—
454C22—401no—
455C22—401no—
456C22—401no—
457C22—401no—
458C22#9134911yescharacteristic
459C22#9147411yescharacteristic
460C22#9148911yescharacteristic
461C22#9149111yescharacteristic
462C22#9151411yescharacteristic
463C22#9151611yescharacteristic
464C22#9153411yescharacteristic
465C4—81no—
466C4—122no—
467C4—201no—
468C4—201no—
469C4—602no—
470C4#9135311yescharacteristic
471C4#9142211yescharacteristic
472C4#9143011yescharacteristic
473C4#9146411yescharacteristic
474C3#1059969211yescharacteristic, complemented, Sylow
475C2—402no—
476C2#1174738911yescharacteristic
477C2#1174739211yescharacteristic
478C2#1174751011yescharacteristic
479C2#1174751211yescharacteristic
480C2#1174873611yescharacteristic
481C2#1174908411yescharacteristic
482C2#1174933111yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2025
LCSG ▷ C22×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
1. C2×#91388C2semidirect
5. #11746350C2semidirect
6. C5×#4529C2semidirect
7. #11745966C2semidirect
68. #4529D5semidirect
375. C3×C5#2025semidirect
450. C5#69639semidirect
474. C3#10599692semidirect

Maximal subgroups

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

subgroupindex
C2×#913882
C3×#652772
C2×#909652
C2×#909642
#117463502
C5×#45292
#117459662
#105996923
#696395