Finite Group Databasebeta

← #14471668

Subgroups — #14471668

Order 1920.

700 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
1#11756343C211yesmaximal, characteristic, complemented
2C3×#65913C211yesmaximal, characteristic, complemented
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#11747063C212yesmaximal
5#11747062C211yesmaximal, characteristic, complemented
6C4×#6657C212yesmaximal, complemented
7C4×#6653C211yesmaximal, characteristic
8#11746942C211yesmaximal, characteristic, complemented
9#11746934C212yesmaximal, complemented
10#11746933C212yesmaximal, complemented
11#11746921C211yesmaximal, characteristic, complemented
12#10611657—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91835—21no—
15#91787—22no—
16#91781—21no—
17#91764C2212yes—
18C4×D60C2211yescharacteristic
19#91758C2211yescharacteristic
20C4×Dic30C2212yes—
21C3×#4092—21no—
22C3×#4042—22no—
23C3×D5×C4⋊C4—21no—
24C3×C4×D20C2211yescharacteristic
25C3×C4×D20C2212yes—
26C3×#4016C2212yes—
27C3×#4015C2211yescharacteristic
28C2×#6657C2212yes—
29C2×#6653C2211yescharacteristic
30C5×C4⋊(C3⋊C8)C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C4×C5×C3⋊C8C2211yescharacteristic
33C4×C5×C3⋊C8C2212yes—
34#90990C2211yescharacteristic
35#90987C2212yes—
36#90974C2212yes—
37#90974C2212yes—
38#90974C2212yes—
39#90968C2211yescharacteristic
40#90968C2212yes—
41#90965C2211yescharacteristic
42#83637—51nomaximal, Hall
43#65918—31no—
44#65913D311yescharacteristic, complemented
45C5×C8×Q8—31no—
46#65133—32no—
47#65131—31no—
48#65130—31no—
49#65118—32no—
50#64986—32no—
51C4×D40—31no—
52C4×#677—32no—
53#64970—31no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5—22no—
61C2×C3×Dic10—21no—
62C3×C5×C4⋊C4D411yescharacteristic
63C3×C5×C4⋊C4D412yes—
64C3×C42×C5C2312yes—
65C3×C42×C5C2311yescharacteristic
66#6714—21no—
67#6714—22no—
68#6714—22no—
69C4⋊Dic15—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72#6712—22no—
73C4×Dic15—22no—
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C3×#685—22no—
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—22no—
83C3×#683—22no—
84#6657—24no—
85#6653—22no—
86C3×#554—51no—
87#5584—51no—
88#5093—51no—
89#5084—51no—
90#5068—52no—
91#5063—52no—
92Q8×C3⋊C8D511yescharacteristic, complemented
93#5019—51no—
94C4×#214—52no—
95#5016—52no—
96C4×#213—51no—
97C4×C5×Q8C2×D311yescharacteristic
98#4092—21no—
99#4092—61no—
100C2×D40—31no—
101C2×#677—32no—
102#4044—62no—
103#4042—22no—
104#4038—61no—
105D5×C4⋊C4—21no—
106#4021—32no—
107C4×D20—31no—
108C4×D20C2×D311yescharacteristic
109C4×D20C2×D312yes—
110#4016C2×D312yes—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—31no—
117C4×C5×C8—32no—
118#3953—31no—
119#3953—32no—
120#3953—31no—
121#3950—31no—
122#3949—32no—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3360—151noSylow
127C22×D15—21no—
128C22×C3×D5—21no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—22no—
137D60—21no—
138D60—21no—
139C4×D15—42no—
140Dic30—22no—
141Dic30—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C3×D20—21no—
145C3×D20#4112yes—
146C3×C4×D5—42no—
147C3×C4×D5—82no—
148C3×Dic10—81no—
149C5×C3⋊C8—22no—
150C5×C3⋊C8—21no—
151C5×C3⋊C8—21no—
152C3×C4⋊Q8—51no—
153C3×#125—52no—
154C3×C22⋊Q8—101no—
155C3×C22⋊Q8—102no—
156C3×C4×Q8C2×D511yescharacteristic
157C3×C4×D4—51no—
158C3×C4×D4—52no—
159C2×C3×C4⋊C4—101no—
160#946—101no—
161C2×#214—52no—
162C2×#213—51no—
163#898—102no—
164#892—101no—
165#875—52no—
166C4×D12—51no—
167#869—51no—
168C4×Dic6—52no—
169#832—51no—
170#810—52no—
171#810—52no—
172#810—52no—
173#809—51no—
174#809—52no—
175#808—52no—
176#807—51no—
177C4⋊(C3⋊C8)C2×D512yes—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C4×C3⋊C8C2×D511yescharacteristic
180C4×C3⋊C8C2×D512yes—
181C2×C5×Q8#6711yescharacteristic
182C2×D20—31no—
183C2×D20C22×D311yescharacteristic
184C2×C4×D5—21no—
185C2×C4×D5—22no—
186C2×C4×D5—61no—
187C2×Dic10—21no—
188C2×Dic10—32no—
189C2×C5×C8—31no—
190C2×C5×C8—31no—
191C2×C5×C8—32no—
192C5×C4⋊C4#6711yescharacteristic
193C5×C4⋊C4#6712yes—
194C42×C5C22×D312yes—
195C42×C5C22×D311yescharacteristic
196#685—21no—
197#685—22no—
198#685—61no—
199#685—62no—
200#685—62no—
201C4⋊Dic5—21no—
202C4⋊Dic5—31no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205C4⋊Dic5C22×D312yes—
206C4⋊Dic5C22×D311yescharacteristic
207#683—22no—
208#683—22no—
209#683—62no—
210C4×Dic5—62no—
211D40—62no—
212#677—64no—
213#556—151no—
214#554—51no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—31no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—41no—
226C2×D15—41no—
227C2×D15—41no—
228C2×C3×D5—22no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—22no—
232C3×C4×C5—21no—
233C3×C4×C5—22no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—42no—
238Dic15—41no—
239C3×Dic5—41no—
240C3×Dic5—42no—
241C2×C3×Q8—101no—
242C2×C3×Q8D2011yescharacteristic
243C2×C3×D4—51no—
244C22×C3×C4—101no—
245C22×C3×C4—102no—
246C2×D12—51no—
247C2×C4×D3—101no—
248C2×Dic6—52no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—52no—
251C3×C4⋊C4—102no—
252C3×C4⋊C4—102no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4D2011yescharacteristic
255C3×C4⋊C4D2012yes—
256C3×C22⋊C4—101no—
257C3×C22⋊C4—102no—
258C3×C42C22×D512yes—
259C3×C42C22×D511yescharacteristic
260#214—104no—
261#213—102no—
262(C2×D3)⋊C4—101no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—51no—
266C4⋊Dic3—101no—
267C4⋊Dic3—101no—
268Dic3⋊C4—102no—
269C4×Dic3—102no—
270C2×C3⋊C8C22×D511yescharacteristic
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D512yes—
273C22×D5—21no—
274C22×D5—61no—
275C5×Q8—22no—
276C2×C4×C5C2×#6712yes—
277C2×C4×C5C2×#6712yes—
278C2×C4×C5C2×#6711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—61no—
284C2×Dic5—62no—
285D20—21no—
286D20—61no—
287D20—61no—
288D20#23912yes—
289C4×D5—42no—
290C4×D5—82no—
291C4×D5—122no—
292Dic10—62no—
293Dic10—62no—
294Dic10—81no—
295C5×C8—62no—
296C5×C8—61no—
297C5×C8—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—51no—
301C4⋊Q8—151no—
302#126—302no—
303#125—52no—
304#124—152no—
305C22⋊Q8—101no—
306C22⋊Q8—102no—
307C22⋊Q8—301no—
308C4×Q8—152no—
309C4×Q8D3×D511yescharacteristic
310C4×D4—51no—
311C4×D4—52no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—101no—
315#107—151no—
316#106—152no—
317C4⋊C8—31no—
318C4⋊C8—32no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—151no—
323#102—152no—
324#102—151no—
325C4×C8—31no—
326C4×C8—32no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—81no—
331C3×D5—42no—
332C23×C3—101no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—401no—
336C3×D4—52no—
337C3×D4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—102no—
340C2×C3×C4—202no—
341C2×C3×C4—402no—
342C2×C3×C4C2×D2012yes—
343C2×C3×C4C2×D2012yes—
344C2×C3×C4C2×D2011yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3—102no—
349D12—101no—
350D12—101no—
351C4×D3—202no—
352Dic6—102no—
353Dic6—102no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—22no—
357C22×C5C22×#6711yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—22no—
365C4×C5—21no—
366C4×C5—22no—
367C4×C5#95012yes—
368C4×C5C2×#23911yescharacteristic
369C4×C5#100711yescharacteristic
370Dic5—41no—
371Dic5—42no—
372Dic5—122no—
373Dic5—121no—
374C2×Q8—101no—
375C2×Q8—152no—
376C2×Q8#120211yescharacteristic
377C2×D4—51no—
378C2×D4—151no—
379C22×C4—101no—
380C22×C4—102no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—31no—
385C2×C8—32no—
386C2×C8—31no—
387C4⋊C4—52no—
388C4⋊C4—51no—
389C4⋊C4—102no—
390C4⋊C4—101no—
391C4⋊C4—102no—
392C4⋊C4—151no—
393C4⋊C4—301no—
394C4⋊C4—302no—
395C4⋊C4—301no—
396C4⋊C4#120211yescharacteristic
397C4⋊C4#120212yes—
398C22⋊C4—101no—
399C22⋊C4—102no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—302no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C42C2×D3×D512yes—
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—102no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3C22×D2011yescharacteristic
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—21no—
417C3×C4—201no—
418C3×C4—202no—
419C3×C4#405012yes—
420C3×C4#414711yescharacteristic
421C3×C4D5×#4111yescharacteristic
422Dic3—201no—
423Dic3—202no—
424C2×C5#581711yescharacteristic
425C2×C5C2×#95011yescharacteristic
426C2×C5#583611yescharacteristic
427D5—42no—
428D5—241no—
429C23—101no—
430C23—301no—
431Q8—22no—
432Q8—302no—
433Q8—302no—
434Q8—401no—
435D4—52no—
436D4—101no—
437D4—301no—
438D4—301no—
439C2×C4—101no—
440C2×C4—102no—
441C2×C4—202no—
442C2×C4—301no—
443C2×C4—302no—
444C2×C4—402no—
445C2×C4—602no—
446C2×C4C2×#120212yes—
447C2×C4C2×#120212yes—
448C2×C4C2×#120211yescharacteristic
449C2×C4C2×#120211yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—61no—
452C8—61no—
453C8—62no—
454C2×C3—202no—
455C2×C3#6591011yescharacteristic
456C2×C3C2×#405011yescharacteristic
457C2×C3#6608511yescharacteristic
458D3—401no—
459C5#8363711yescharacteristic, complemented, Sylow
460C22—102no—
461C22—201no—
462C22—201no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C22×#120211yescharacteristic
467C4—22no—
468C4—21no—
469C4—22no—
470C4—202no—
471C4—201no—
472C4—602no—
473C4—601no—
474C4#9131112yes—
475C4#9202911yescharacteristic
476C4D5×#23911yescharacteristic
477C3#1061165711yescharacteristic, complemented, Sylow
478C2—202no—
479C2—1201no—
480C2C2×#9131111yescharacteristic
481C2#1175512811yescharacteristic
482C2#1175530911yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6653C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756343C2semidirect
2. C3×#65913C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
5. #11747062C2semidirect
6. C4×#6657C2semidirect
8. #11746942C2semidirect
9. #11746934C2semidirect
10. #11746933C2semidirect
11. #11746921C2semidirect
44. #65913D3semidirect
92. Q8×C3⋊C8D5semidirect
406. C3×C5#3360semidirect
459. C5#83637semidirect
477. C3#10611657semidirect

Maximal subgroups

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

subgroupindex
#117563432
C3×#659132
C5×Q8×C3⋊C82
#117470632
#117470622
C4×#66572
C4×#66532
#117469422
#117469342
#117469332
#117469212
#106116573
#836375