Finite Group Databasebeta

← #14471694

Subgroups — #14471694

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#11752645C211yesmaximal, characteristic, complemented
2#11752507C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65131C211yesmaximal, characteristic, complemented
6#11747970C212yesmaximal, complemented
7#11747967C212yesmaximal
8#11747871C212yesmaximal, complemented
9#11747789C212yesmaximal, complemented
10C4×#6653C211yesmaximal, characteristic
11#11746921C211yesmaximal, characteristic, complemented
12#10611657—31nomaximal, Hall
13C2×#6706C2212yes—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91437—21no—
20#91428C2212yes—
21#91411—22no—
22#91383—21no—
23#91381C2212yes—
24#91364C2212yes—
25#91362—22no—
26#91359—21no—
27#91358—21no—
28#91340C2212yes—
29C2×#6653C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91100C2212yes—
32C5×Dic3⋊C8C2212yes—
33C5×C8×Dic3C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3953C2212yes—
36C3×#3949C2212yes—
37#90990C2211yescharacteristic
38#90974C2212yes—
39#90974C2212yes—
40#90968C2211yescharacteristic
41#90965C2211yescharacteristic
42#81087—51nomaximal, Hall
43#65918—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65133—32no—
47#65131D311yescharacteristic, complemented
48#65130—31no—
49#65118—32no—
50#64986—32no—
51C4×D40—31no—
52C4×#677—32no—
53#64970—31no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2312yes—
57C2×C5×Dic6D411yescharacteristic
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×Dic10—21no—
61C2×#1200—22no—
62C2×C3×C5×C8C2312yes—
63C3×C42×C5C2311yescharacteristic
64#6714—21no—
65C4⋊Dic15—21no—
66C4⋊Dic15—21no—
67C4⋊Dic15C2311yescharacteristic
68#6706—24no—
69C5×C4⋊Dic3D411yescharacteristic
70C5×Dic3⋊C4D412yes—
71C4×C5×Dic3C2312yes—
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×#685—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2312yes—
77C3×C4⋊Dic5C2311yescharacteristic
78#6669—22no—
79#6669—22no—
80#6668—22no—
81#6667—22no—
82#6665—22no—
83#6665—22no—
84Dic3×Dic5—22no—
85#6653—22no—
86#5730—51no—
87#5542—51no—
88C3×#476—51no—
89#5093—51no—
90C4×#213—51no—
91#4857—52no—
92#4852—52no—
93#4841—51no—
94#4830D511yescharacteristic, complemented
95#4787—52no—
96#4768—52no—
97C4×C5×Q8—31no—
98#4092—61no—
99#4092—61no—
100C2×D40—31no—
101C2×#677—32no—
102#4044—62no—
103#4042—62no—
104#4038—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107C4×D20—31no—
108C4×D20—32no—
109C4×D20C2×D311yescharacteristic
110#4016—32no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C4×C5×C8—32no—
117C4×C5×C8—31no—
118#3953—31no—
119#3953—31no—
120#3953C2×D312yes—
121#3950—31no—
122#3949C2×D312yes—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3360—151noSylow
127C22×D15—21no—
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—21no—
134D60—21no—
135D60#4112yes—
136C4×D15—42no—
137Dic30—22no—
138Dic30—22no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C3×D20—21no—
145C3×D20—21no—
146C3×C4×D5—42no—
147C3×Dic10—81no—
148#1200—82no—
149C3×C5×C8—22no—
150C5×C3⋊C8—21no—
151C5×C3⋊C8—21no—
152C3×C4⋊Q8—51no—
153C3×C4×D4—51no—
154#946—102no—
155#936—52no—
156C2×#213—51no—
157#926—101no—
158#924—101no—
159C2×#204—52no—
160#897—101no—
161#893—52no—
162D3×C4⋊C4—101no—
163#890—52no—
164#887—52no—
165#879—102no—
166C4×D12—51no—
167#869—51no—
168C4×Dic6C2×D511yescharacteristic
169C3×#106—52no—
170C3×C4⋊C8C2×D511yescharacteristic
171C3×#102—52no—
172#832—51no—
173#816—52no—
174Dic3⋊C8C2×D512yes—
175C8×Dic3C2×D512yes—
176#810—52no—
177#810—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8C2×D511yescharacteristic
181C2×C5×Q8—31no—
182C2×D20—31no—
183C2×D20C22×D311yescharacteristic
184C2×C4×D5—21no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10—21no—
188C2×Dic10—32no—
189C2×C5×C8—31no—
190C2×C5×C8—31no—
191C2×C5×C8C22×D312yes—
192C5×C4⋊C4—32no—
193C5×C4⋊C4—31no—
194C42×C5—32no—
195C42×C5C22×D311yescharacteristic
196#685—21no—
197#685—62no—
198#685—62no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—21no—
202C4⋊Dic5—31no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205C4⋊Dic5C22×D312yes—
206C4⋊Dic5C22×D311yescharacteristic
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—62no—
211D40—62no—
212#677—64no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—51no—
219#463—152no—
220#461—151no—
221C8×Q8—31no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—22no—
226C2×D15—41no—
227C2×D15—41no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—21no—
232C3×C4×C5#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—42no—
236Dic15—41no—
237C3×Dic5—41no—
238C3×Dic5—42no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C2×C3×Q8—101no—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C2×D12—51no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—52no—
248C2×Dic6D2011yescharacteristic
249C2×C3×C8C22×D512yes—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—52no—
252C3×C4⋊C4—101no—
253C3×C22⋊C4—101no—
254C3×C42C22×D511yescharacteristic
255#217—102no—
256#217—102no—
257#213—102no—
258(C2×D3)⋊C4—101no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—51no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4⋊Dic3—102no—
264C4⋊Dic3D2011yescharacteristic
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4D2012yes—
268C4×Dic3—102no—
269C4×Dic3C22×D512yes—
270C2×C3⋊C8C22×D511yescharacteristic
271C2×C3⋊C8C22×D511yescharacteristic
272#204—104no—
273C22×D5—21no—
274C22×D5—61no—
275C5×Q8—62no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—62no—
284C2×Dic5—61no—
285D20—21no—
286D20—21no—
287D20—32no—
288D20—61no—
289C4×D5—42no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—62no—
293Dic10—62no—
294Dic10—81no—
295C5×C8—22no—
296C5×C8—61no—
297C5×C8—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—51no—
301C4⋊Q8—151no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—31no—
309C4×Q8—152no—
310C4×D4—51no—
311C4×D4—152no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—52no—
317C4⋊C8—32no—
318C4⋊C8D3×D511yescharacteristic
319#103—152no—
320#103—152no—
321#103—152no—
322#102—52no—
323#102—151no—
324#102—151no—
325C4×C8—32no—
326C4×C8—31no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331C3×D5—81no—
332C23×C3—101no—
333C22×D3—101no—
334C3×Q8—401no—
335C3×D4—101no—
336C3×D4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—102no—
339C2×C3×C4—202no—
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—102no—
344C2×Dic3—101no—
345C2×Dic3C2×D2012yes—
346C2×Dic3C2×D2012yes—
347D12—52no—
348D12—101no—
349C4×D3—202no—
350C4×D3—402no—
351Dic6—22no—
352Dic6—102no—
353Dic6—102no—
354C3×C8—22no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—41no—
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—62no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—62no—
366C4×C5—62no—
367C4×C5#91612yes—
368C4×C5#100711yescharacteristic
369C4×C5D3×#4111yescharacteristic
370Dic5—41no—
371Dic5—42no—
372Dic5—122no—
373Dic5—121no—
374C2×Q8—31no—
375C2×Q8—101no—
376C2×Q8—152no—
377C2×D4—51no—
378C2×D4—151no—
379C22×C4—101no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—31no—
385C2×C8—31no—
386C2×C8C2×D3×D512yes—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—52no—
390C4⋊C4—51no—
391C4⋊C4—101no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C22⋊C4—101no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—32no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—201no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3C22×D2011yescharacteristic
411C2×D3—102no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—201no—
416C3×C4—202no—
417C3×C4#405012yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—201no—
423Dic3—202no—
424C2×C5#563311yescharacteristic
425C2×C5C2×#91611yescharacteristic
426C2×C5#577511yescharacteristic
427D5—81no—
428D5—122no—
429C23—101no—
430C23—301no—
431Q8—62no—
432Q8—302no—
433Q8—302no—
434Q8—401no—
435D4—101no—
436D4—101no—
437D4—152no—
438D4—301no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—101no—
442C2×C4—102no—
443C2×C4—202no—
444C2×C4—302no—
445C2×C4—301no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D3×D2011yescharacteristic
449C2×C4D3×D2011yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—22no—
452C8—61no—
453C8—61no—
454C2×C3—401no—
455C2×C3#6591011yescharacteristic
456C2×C3C2×#405011yescharacteristic
457C2×C3#6608511yescharacteristic
458D3—202no—
459C5#8108711yescharacteristic, complemented, Sylow
460C22—201no—
461C22—201no—
462C22—201no—
463C22—302no—
464C22—601no—
465C22—601no—
466C22C2×D3×D2011yescharacteristic
467C4—21no—
468C4—62no—
469C4—62no—
470C4—201no—
471C4—202no—
472C4—601no—
473C4—602no—
474C4#9127212yes—
475C4#9202411yescharacteristic
476C4#9202911yescharacteristic
477C3#1061165711yescharacteristic, complemented, Sylow
478C2—401no—
479C2—602no—
480C2#1175334211yescharacteristic
481C2C2×#9127211yescharacteristic
482C2#1175403011yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6653C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752645C2semidirect
2. #11752507C2semidirect
3. #11750942C2semidirect
4. C5×#4830C2semidirect
5. C3×#65131C2semidirect
6. #11747970C2semidirect
8. #11747871C2semidirect
9. #11747789C2semidirect
11. #11746921C2semidirect
47. #65131D3semidirect
94. #4830D5semidirect
406. C3×C5#3360semidirect
459. C5#81087semidirect
477. C3#10611657semidirect

Maximal subgroups

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

subgroupindex
#117526452
#117525072
#117509422
C5×#48302
C3×#651312
#117479702
#117479672
#117478712
#117477892
C4×#66532
#117469212
#106116573
#810875