Finite Group Databasebeta

← #14471697

Subgroups — #14471697

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#11752654C211yesmaximal, characteristic, complemented
2#11752491C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic, complemented
4C5×#4842C211yesmaximal, characteristic, complemented
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747963C212yesmaximal, complemented
7#11747852C212yesmaximal, complemented
8#11747779C212yesmaximal
9#11747760C212yesmaximal, complemented
10C4×#6654C211yesmaximal, characteristic
11#11746930C211yesmaximal, characteristic, complemented
12#10612818—31nomaximal, Hall
13C2×#6706C2212yes—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91437—21no—
20#91424—22no—
21#91418C2212yes—
22#91390—21no—
23#91388C2212yes—
24#91373C2212yes—
25#91369—21no—
26#91342—22no—
27#91338—21no—
28#91333C2212yes—
29C2×#6654C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91100C2212yes—
32C5×#821C2212yes—
33C5×#817C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90988C2211yescharacteristic
38#90975C2212yes—
39#90975C2212yes—
40#90969C2211yescharacteristic
41#90967C2211yescharacteristic
42#79926—51nomaximal, Hall
43#66064—31no—
44#65876—31no—
45C5×#476—31no—
46#65382—31no—
47C4×#686—31no—
48#65146—32no—
49#65141—32no—
50#65130—31no—
51#65119D311yescharacteristic, complemented
52#65076—32no—
53#65057—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2312yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C5×Dic6—21no—
60C2×C3×Dic10D411yescharacteristic
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×(C2×D3)⋊C4—21no—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3C2312yes—
72C5×C4⋊Dic3C2311yescharacteristic
73C3×C4⋊Dic5D411yescharacteristic
74C3×#683D412yes—
75C3×C4×Dic5C2312yes—
76C2×C3×#168C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78Dic3⋊Dic5—22no—
79#6669—22no—
80#6669—22no—
81#6667—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84Dic3×Dic5—22no—
85#6654—22no—
86#5584—51no—
87#5579—51no—
88C3×C8×Q8—51no—
89#4844—52no—
90#4842D511yescharacteristic, complemented
91#4841—51no—
92#4829—52no—
93#4697—52no—
94C4×D24—51no—
95C4×#204—52no—
96#4681—51no—
97C5×C4⋊Q8—31no—
98C4×C5×D4—31no—
99#4092—62no—
100#4082—32no—
101C2×#686—31no—
102#4072—61no—
103#4070—61no—
104C2×#677—32no—
105#4043—61no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4033—32no—
110#4025—62no—
111C4×D20—31no—
112#4015—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#106—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102—32no—
117#3964—31no—
118#3948—32no—
119#3946C2×D312yes—
120C8×Dic5C2×D312yes—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3939—31no—
125C4×#168C2×D311yescharacteristic
126#3360—151noSylow
127C22×D15—21no—
128C22×C5×D3—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×Dic3—21no—
140C2×C5×Dic3—22no—
141C5×D12—21no—
142C5×D12—21no—
143C4×C5×D3—42no—
144C5×Dic6—81no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—22no—
148#1200—82no—
149C3×C5×C8—22no—
150C3×#168—21no—
151C3×#168—21no—
152C3×C4×Q8—51no—
153#946—101no—
154#946—101no—
155C2×D24—51no—
156C2×#204—52no—
157#898—102no—
158#896—102no—
159#892—101no—
160D3×C4⋊C4—101no—
161#875—52no—
162C4×D12—51no—
163C4×D12—52no—
164C4×D12C2×D511yescharacteristic
165#870—52no—
166#869—51no—
167#869C2×D511yescharacteristic
168C4×Dic6—52no—
169C3×C4⋊C8—52no—
170C3×C4⋊C8C2×D511yescharacteristic
171C3×C4×C8—52no—
172C3×C4×C8—51no—
173#821—51no—
174#821—51no—
175#821C2×D512yes—
176#818—51no—
177#817C2×D512yes—
178#816—52no—
179#816—52no—
180#816—52no—
181C2×C5×Q8—61no—
182C2×C5×D4—31no—
183C22×C4×C5—61no—
184C2×D20—31no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10—32no—
188C2×Dic10D1211yescharacteristic
189C2×C5×C8C22×D312yes—
190C5×C4⋊C4—31no—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—61no—
193C5×C22⋊C4—61no—
194C42×C5C22×D311yescharacteristic
195C22⋊Dic5—62no—
196C22⋊Dic5—62no—
197#686—62no—
198#685—61no—
199#685—62no—
200C4⋊Dic5—31no—
201C4⋊Dic5—61no—
202C4⋊Dic5—61no—
203C4⋊Dic5—62no—
204C4⋊Dic5D1211yescharacteristic
205#683—62no—
206#683—62no—
207#683D1212yes—
208C4×Dic5—62no—
209C4×Dic5C22×D312yes—
210C2×#168C22×D311yescharacteristic
211C2×#168C22×D311yescharacteristic
212#677—64no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—31no—
219#463—152no—
220#461—151no—
221C8×Q8—51no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—22no—
226C2×D15—41no—
227C2×D15—41no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C5×D3—41no—
231C3×C4×C5—21no—
232C3×C4×C5#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—42no—
236Dic15—41no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C5×Dic3—41no—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×D12—51no—
243C2×D12C22×D511yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—21no—
248C2×Dic6—52no—
249C2×C3×C8—51no—
250C2×C3×C8—51no—
251C2×C3×C8C22×D512yes—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—51no—
254C3×C42—52no—
255C3×C42C22×D511yescharacteristic
256(C2×D3)⋊C4—21no—
257(C2×D3)⋊C4—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—101no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3—101no—
264C4⋊Dic3—101no—
265C4⋊Dic3C22×D512yes—
266C4⋊Dic3C22×D511yescharacteristic
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C4×Dic3—102no—
271D24—102no—
272#204—104no—
273C23×C5—61no—
274C22×D5—61no—
275C5×Q8—241no—
276C5×D4—61no—
277C5×D4—61no—
278C2×C4×C5—61no—
279C2×C4×C5—62no—
280C2×C4×C5—122no—
281C2×C4×C5C2×D1211yescharacteristic
282C2×C4×C5C2×D1211yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—62no—
285C2×Dic5—61no—
286C2×Dic5C2×D1212yes—
287C2×Dic5C2×D1212yes—
288D20—32no—
289D20—61no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—22no—
293Dic10—62no—
294Dic10—62no—
295C5×C8—22no—
296#168—21no—
297#168—21no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—31no—
301C4⋊Q8—151no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—51no—
309C4×Q8—152no—
310C4×D4—31no—
311C4×D4—152no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—32no—
317C4⋊C8—52no—
318C4⋊C8D3×D511yescharacteristic
319#103—152no—
320#103—152no—
321#103—152no—
322#102—32no—
323#102—151no—
324#102—151no—
325C4×C8—52no—
326C4×C8—51no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331C5×D3—81no—
332C22×D3—21no—
333C22×D3—101no—
334C3×Q8—102no—
335C2×C3×C4—52no—
336C2×C3×C4—52no—
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4C23×D511yescharacteristic
340C2×Dic3—21no—
341C2×Dic3—22no—
342C2×Dic3—102no—
343C2×Dic3—101no—
344D12—21no—
345D12—21no—
346D12—52no—
347D12—101no—
348C4×D3—42no—
349C4×D3—202no—
350C4×D3—402no—
351Dic6—81no—
352Dic6—102no—
353Dic6—102no—
354C3×C8—22no—
355C3×C8—101no—
356C3×C8—101no—
357C22×C5—121no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C22×D1211yescharacteristic
361C2×D5—62no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—121no—
366C4×C5—122no—
367C4×C5#90412yes—
368C4×C5#100711yescharacteristic
369C4×C5D3×#4111yescharacteristic
370Dic5—22no—
371Dic5—22no—
372Dic5—121no—
373Dic5—122no—
374C2×Q8—51no—
375C2×Q8—61no—
376C2×Q8—152no—
377C2×D4—31no—
378C2×D4—151no—
379C22×C4—61no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—51no—
385C2×C8—51no—
386C2×C8C2×D3×D512yes—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—51no—
390C4⋊C4—52no—
391C4⋊C4—61no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C22⋊C4—61no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—52no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—41no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—102no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—102no—
416C3×C4—102no—
417C3×C4#406212yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—41no—
421Dic3—42no—
422Dic3—201no—
423Dic3—202no—
424C2×C5—241no—
425C2×C5#557611yescharacteristic
426C2×C5C2×#90411yescharacteristic
427C2×C5#575111yescharacteristic
428D5—122no—
429C23—61no—
430C23—301no—
431Q8—102no—
432Q8—241no—
433Q8—302no—
434Q8—302no—
435D4—61no—
436D4—61no—
437D4—152no—
438D4—301no—
439C2×C4—52no—
440C2×C4—52no—
441C2×C4—61no—
442C2×C4—62no—
443C2×C4—122no—
444C2×C4—302no—
445C2×C4—301no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D5×D1211yescharacteristic
449C2×C4D5×D1211yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—22no—
452C8—101no—
453C8—101no—
454C2×C3#6596711yescharacteristic
455C2×C3C2×#406211yescharacteristic
456C2×C3#6610911yescharacteristic
457D3—81no—
458D3—202no—
459C5#7992611yescharacteristic, complemented, Sylow
460C22—121no—
461C22—121no—
462C22—121no—
463C22—302no—
464C22—601no—
465C22—601no—
466C22C2×D5×D1211yescharacteristic
467C4—21no—
468C4—102no—
469C4—102no—
470C4—121no—
471C4—122no—
472C4—601no—
473C4—602no—
474C4#9126912yes—
475C4#9202411yescharacteristic
476C4#9202911yescharacteristic
477C3#1061281811yescharacteristic, complemented, Sylow
478C2—241no—
479C2—602no—
480C2#1175334111yescharacteristic
481C2C2×#9126911yescharacteristic
482C2#1175402311yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6654C22
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. #11752654C2semidirect
2. #11752491C2semidirect
3. #11750942C2semidirect
4. C5×#4842C2semidirect
5. C3×#65119C2semidirect
6. #11747963C2semidirect
7. #11747852C2semidirect
9. #11747760C2semidirect
11. #11746930C2semidirect
51. #65119D3semidirect
90. #4842D5semidirect
406. C3×C5#3360semidirect
459. C5#79926semidirect
477. C3#10612818semidirect

Maximal subgroups

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

subgroupindex
#117526542
#117524912
#117509422
C5×#48422
C3×#651192
#117479632
#117478522
#117477792
#117477602
C4×#66542
#117469302
#106128183
#799265