Finite Group Databasebeta

← #14297754

Subgroups — #14297754

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#893C211yesmaximal, characteristic
2#11748619C211yesmaximal, characteristic, complemented
3C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
4C2×#90967C211yesmaximal, characteristic
5C2×#90966C211yesmaximal, characteristic
6#11746350C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10602398—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C4×C5×D3—21no—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C4×C5×Dic3C2211yescharacteristic
16C5×#893—22no—
17C5×#893C414yescomplemented
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20#90994—21no—
21#90994—21no—
22Dic3⋊#168—22no—
23#90967—22no—
24#90966—22no—
25#68893—51nomaximal, Hall
26C2×C4×C5×D4—31no—
27C2×#3964—31no—
28C2×#3964—31no—
29#65225—31no—
30C2×C4⋊#168—31no—
31#64749—31no—
32#64749D311yescharacteristic, complemented
33C23×C5×D3—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3D411yescharacteristic
38C22×C5×Dic3D411yescharacteristic
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12C2×C412yes—
43C2×C5×D12D412yes—
44C2×C5×D12Q812yes—
45C2×C4×C5×D3—24no—
46C2×C4×C5×D3—42no—
47C2×C4×C5×D3—42no—
48C22×C3×Dic5—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C412yes—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C5×(C2×D3)⋊C4—24no—
57C4×C5×Dic3C2×C412yes—
58C4×C5×Dic3D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×#893D511yescharacteristic
65C2×#821—51no—
66C2×Dic3⋊C8—51no—
67#4977—51no—
68C2×#809—51no—
69C3×#340—51no—
70#4529—51no—
71C22×C5×D4—31no—
72C23×C4×C5—61no—
73C4×C5×D4—34no—
74C4×C5×D4—62no—
75C2×C5×C4⋊C4C2×D311yescharacteristic
76C2×C5×C22⋊C4—61no—
77C2×C42×C5—31no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C22×#168—31no—
81C22×#168C2×D311yescharacteristic
82#3964—62no—
83#3964—62no—
84#3963—61no—
85#3963—61no—
86C4⋊#168—62no—
87#1804—151noSylow
88C23×C3×C5C2×D411yescharacteristic
89C22×C5×D3—22no—
90C22×C5×D3—22no—
91C22×C5×D3—22no—
92C22×C5×D3—41no—
93C22×C5×D3—41no—
94C22×C5×D3—41no—
95C22×C5×D3—41no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×Q811yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3C22⋊C412yes—
113C2×C5×Dic3C22⋊C412yes—
114C5×D12—22no—
115C5×D12—22no—
116C5×D12—22no—
117C5×D12C4⋊C414yes—
118C4×C5×D3—48no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C3⋊#168—41no—
123C3×#168—41no—
124C22×D12C2×D511yescharacteristic
125C22×C4×D3—21no—
126C22×C3×C8—51no—
127C2×C3×C4⋊C4—51no—
128C2×C3×C4⋊C4C2×D511yescharacteristic
129C2×(C2×D3)⋊C4—21no—
130C2×C4⋊Dic3—51no—
131C2×C4×Dic3C2×D511yescharacteristic
132C22×C3⋊C8—51no—
133#893—22no—
134#893Dic514yescomplemented
135C3⋊#95—101no—
136C3⋊#95—101no—
137#821—102no—
138Dic3⋊C8—102no—
139#809—102no—
140C24×C5—61no—
141C2×C5×D4—32no—
142C2×C5×D4—32no—
143C2×C5×D4—32no—
144C2×C5×D4—61no—
145C2×C5×D4—61no—
146C2×C5×D4—61no—
147C22×C4×C5—21no—
148C22×C4×C5—31no—
149C22×C4×C5—31no—
150C22×C4×C5—64no—
151C22×C4×C5—122no—
152C22×C4×C5—122no—
153C22×C4×C5C22×D311yescharacteristic
154C22×Dic5—21no—
155C22×Dic5—61no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4C4×D312yes—
158C5×C22⋊C4—64no—
159C42×C5—32no—
160C42×C5—32no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5—61no—
164C4⋊Dic5—61no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168—21no—
168C2×#168—61no—
169C2×#168—61no—
170C2×#168—61no—
171C2×C4×D4—31no—
172C2×C4⋊C8—151no—
173C2×#102—151no—
174C2×#102—151no—
175#382—151no—
176#340—51no—
177#340—151no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5#12111yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#13511yescharacteristic
182C22×C3×C5#13511yescharacteristic
183C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
185C2×C5×D3—24no—
186C2×C5×D3—42no—
187C2×C5×D3—42no—
188C2×C5×D3—42no—
189C2×C5×D3—42no—
190C2×C5×D3—42no—
191C2×C5×D3—42no—
192C3×C4×C5—42no—
193C3×C4×C5C2×C4⋊C411yescharacteristic
194C3×C4×C5#11711yescharacteristic
195C3×C4×C5#12111yescharacteristic
196C3×C4×C5C22⋊Q811yescharacteristic
197Dic15—81no—
198C3×Dic5—81no—
199C5×Dic3—22no—
200C5×Dic3—22no—
201C23×D3—21no—
202C22×C3×C4—21no—
203C22×C3×C4—101no—
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—101no—
206C22×Dic3C22⋊D511yescharacteristic
207C22×Dic3C22⋊D511yescharacteristic
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12Dic1012yes—
212C2×D12D2012yes—
213C2×D12C2×Dic512yes—
214C2×C4×D3—24no—
215C2×C4×D3—42no—
216C2×C4×D3—42no—
217C2×C3×C8—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4C2×Dic512yes—
224(C2×D3)⋊C4—24no—
225C4⋊Dic3—101no—
226C4⋊Dic3—101no—
227C4×Dic3C2×Dic512yes—
228C4×Dic3C22⋊D512yes—
229C2×C3⋊C8—101no—
230C2×C3⋊C8—101no—
231C2×C3⋊C8—101no—
232C23×C5—62no—
233C23×C5—62no—
234C23×C5—62no—
235C23×C5—121no—
236C23×C5—121no—
237C23×C5—121no—
238C23×C5—121no—
239C23×C5D3×D411yescharacteristic
240C5×D4—34no—
241C5×D4—62no—
242C5×D4—62no—
243C5×D4—62no—
244C2×C4×C5—22no—
245C2×C4×C5—32no—
246C2×C4×C5—32no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—61no—
250C2×C4×C5—61no—
251C2×C4×C5—61no—
252C2×C4×C5—61no—
253C2×C4×C5—128no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5#23511yescharacteristic
256C2×C4×C5#23511yescharacteristic
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5D3×D411yescharacteristic
259C2×C4×C5D3×Q811yescharacteristic
260C2×Dic5—41no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—121no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266#168—41no—
267#168—121no—
268C22×D4—31no—
269C23×C4—61no—
270C22×C8—51no—
271C22×C8—151no—
272C4×D4—34no—
273C4×D4—62no—
274C2×C4⋊C4—51no—
275C2×C4⋊C4—151no—
276C2×C4⋊C4D3×D511yescharacteristic
277C2×C22⋊C4—61no—
278C2×C42—31no—
279C4⋊C8—302no—
280#102—302no—
281#102—302no—
282#95—301no—
283#95—301no—
284C2×C3×C5#38011yescharacteristic
285C2×C3×C5#41611yescharacteristic
286C2×C3×C5#41811yescharacteristic
287C2×C3×C5#46311yescharacteristic
288C2×C3×C5#46311yescharacteristic
289C2×C3×C5#47811yescharacteristic
290C2×C3×C5#47811yescharacteristic
291C5×D3—44no—
292C23×C3C2×C22⋊D511yescharacteristic
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C2×C3×C4—22no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4C2×Dic1011yescharacteristic
307C2×C3×C4C2×D2011yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4C22×Dic511yescharacteristic
311C2×C3×C4C2×C22⋊D511yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—201no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319C2×Dic3C22⋊Dic512yes—
320C2×Dic3C22⋊Dic512yes—
321D12—22no—
322D12—22no—
323D12—22no—
324D12C4⋊Dic514yes—
325C4×D3—48no—
326C3×C8—201no—
327C3⋊C8—201no—
328C22×C5—64no—
329C22×C5—122no—
330C22×C5—122no—
331C22×C5—122no—
332C22×C5—122no—
333C22×C5—122no—
334C22×C5—122no—
335C22×C5D3×C22⋊C411yescharacteristic
336C22×C5#88411yescharacteristic
337C22×C5#89611yescharacteristic
338C22×C5#91111yescharacteristic
339C22×C5#91411yescharacteristic
340C22×C5#91611yescharacteristic
341C22×C5#91911yescharacteristic
342C4×C5—42no—
343C4×C5—62no—
344C4×C5—62no—
345C4×C5#87211yescharacteristic
346C4×C5#88411yescharacteristic
347C4×C5D3×C4⋊C411yescharacteristic
348C4×C5#89611yescharacteristic
349Dic5—81no—
350Dic5—241no—
351C24—61no—
352C2×D4—32no—
353C2×D4—32no—
354C2×D4—32no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C22×C4—21no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—64no—
362C22×C4—101no—
363C22×C4—122no—
364C22×C4—122no—
365C22×C4—301no—
366C22×C4C2×D3×D511yescharacteristic
367C2×C8—101no—
368C2×C8—101no—
369C2×C8—101no—
370C2×C8—301no—
371C2×C8—301no—
372C2×C8—301no—
373C4⋊C4—21no—
374C4⋊C4—101no—
375C4⋊C4—101no—
376C4⋊C4—301no—
377C4⋊C4—301no—
378C4⋊C4D3×Dic512yes—
379C22⋊C4—64no—
380C42—32no—
381C42—32no—
382C3×C5#180411yescharacteristic, complemented, Hall
383C22×C3#407011yescharacteristic
384C22×C3#407611yescharacteristic
385C22×C3#407811yescharacteristic
386C22×C3#407811yescharacteristic
387C22×C3#409611yescharacteristic
388C22×C3#409611yescharacteristic
389C22×C3C2×C22⋊Dic511yescharacteristic
390C2×D3—24no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—42no—
395C2×D3—42no—
396C2×D3—42no—
397C3×C4—42no—
398C3×C4—401no—
399C3×C4#407011yescharacteristic
400C3×C4C2×C4⋊Dic511yescharacteristic
401C3×C4#407211yescharacteristic
402C3×C4#407611yescharacteristic
403Dic3—22no—
404Dic3—22no—
405Dic3—401no—
406C2×C5—124no—
407C2×C5#466711yescharacteristic
408C2×C5#477011yescharacteristic
409C2×C5#478711yescharacteristic
410C2×C5#480411yescharacteristic
411C2×C5#481911yescharacteristic
412C2×C5#487111yescharacteristic
413C2×C5#489111yescharacteristic
414C23—62no—
415C23—62no—
416C23—62no—
417C23—121no—
418C23—121no—
419C23—121no—
420C23—121no—
421C23D3×C22⋊D511yescharacteristic
422D4—34no—
423D4—62no—
424D4—62no—
425D4—62no—
426C2×C4—22no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—128no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4—201no—
439C2×C4—601no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4D3×Dic1011yescharacteristic
443C2×C4#677111yescharacteristic
444C2×C4#677111yescharacteristic
445C2×C4D3×D2011yescharacteristic
446C2×C4C2×D3×Dic511yescharacteristic
447C2×C4D3×C22⋊D511yescharacteristic
448C8—201no—
449C8—601no—
450C2×C3#6529811yescharacteristic
451C2×C3#6529811yescharacteristic
452C2×C3#6530511yescharacteristic
453C2×C3#6530511yescharacteristic
454C2×C3#6550111yescharacteristic
455C2×C3#6550411yescharacteristic
456C2×C3#6552211yescharacteristic
457D3—44no—
458C5#6889311yescharacteristic, complemented, Sylow
459C22—64no—
460C22—122no—
461C22—122no—
462C22—122no—
463C22—122no—
464C22—122no—
465C22—122no—
466C22#9135211yescharacteristic
467C22#9145411yescharacteristic
468C22#9149411yescharacteristic
469C22#9149611yescharacteristic
470C22#9151711yescharacteristic
471C22#9151911yescharacteristic
472C22D3×C22⋊Dic511yescharacteristic
473C4—42no—
474C4—62no—
475C4—62no—
476C4—401no—
477C4—1201no—
478C4#9135211yescharacteristic
479C4#9137111yescharacteristic
480C4D3×C4⋊Dic511yescharacteristic
481C4#9145411yescharacteristic
482C3#1060239811yescharacteristic, complemented, Sylow
483C2—124no—
484C2#1174737511yescharacteristic
485C2#1174737711yescharacteristic
486C2#1174739411yescharacteristic
487C2#1174739511yescharacteristic
488C2#1174878211yescharacteristic
489C2#1174896711yescharacteristic
490C2#1174921111yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1804
LCSG ▷ C2×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
2. #11748619C2semidirect
3. C2×Dic3⋊#168C2semidirect
6. #11746350C2semidirect
7. C3×#64749C2semidirect
17. C5×#893C4semidirect
32. #64749D3semidirect
134. #893Dic5semidirect
382. C3×C5#1804semidirect
458. C5#68893semidirect
482. C3#10602398semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
#117486192
C2×Dic3⋊#1682
C2×#909672
C2×#909662
#117463502
C3×#647492
#106023983
#688935