Finite Group Databasebeta

← #14305980

Subgroups — #14305980

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#940C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic, complemented
3C2×C3×#3964C211yesmaximal, characteristic, complemented
4#11748619C211yesmaximal, characteristic, complemented
5C2×#90967C211yesmaximal, characteristic, complemented
6C2×#90966C211yesmaximal, characteristic, complemented
7C2×#90953C211yesmaximal, characteristic, complemented
8#10602558—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×#67—22no—
11C22×C5×D12C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C5×#940—22no—
15C5×#940C414yescomplemented
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19#91116—22no—
20C3×#3964—22no—
21#90994—22no—
22#90967—22no—
23#90966—22no—
24#90953—22no—
25#70160—51nomaximal, Hall
26C2×C5×#127—31no—
27C2×#3964—31no—
28C2×#3964—31no—
29C2×#3964—31no—
30C2×#3964D311yescharacteristic, complemented
31#65225—31no—
32C2×#3935—31no—
33C24×C3×C5—21no—
34C23×C5×D3—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×C5×#67—28no—
44C2×C5×#67—44no—
45C2×C5×#67—44no—
46C22×C5×Dic3D412yes—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12C2×C412yes—
53C22×C3×Dic5—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168D412yescomplemented
59C4×C5×Dic3C2×C412yes—
60C4×C5×Dic3D412yes—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C2×C3×#168D412yescomplemented
66C2×#940D511yescharacteristic
67C2×C3×#102—51no—
68C2×#832—51no—
69C2×#821—51no—
70C2×#815—51no—
71#4977—51no—
72C2×#809—51no—
73C22×C5×D4—31no—
74C22×C5×D4—62no—
75C22×C5×D4C2×D311yescharacteristic
76C5×#127—34no—
77C5×#127—62no—
78C2×C42×C5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5C2×D311yescharacteristic
81C22×#168—31no—
82C22×#168C2×D311yescharacteristic
83#3964—22no—
84#3964—62no—
85#3964—62no—
86#3964—62no—
87#3963—62no—
88#3935—62no—
89#1961—151noSylow
90C23×C3×C5—22no—
91C23×C3×C5—41no—
92C23×C3×C5—41no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—22no—
97C22×C5×D3—41no—
98C22×C5×D3—41no—
99C22×C5×D3—42no—
100C22×C5×D3—42no—
101C3×C5×D4—22no—
102C3×C5×D4—22no—
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—41no—
112C2×Dic15—42no—
113C5×#67—416no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3C22⋊C414yes—
117C5×D12—22no—
118C5×D12—22no—
119C5×D12—41no—
120C5×D12—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—42no—
123C3⋊#168—22no—
124C3×#168—22no—
125C22×C3×D4C2×D511yescharacteristic
126C22×#67—22no—
127C22×D12C2×D511yescharacteristic
128C22×C3×C8—51no—
129C2×C3×C4⋊C4—51no—
130#940—22no—
131#940Dic514yescomplemented
132C2×C4⋊Dic3—51no—
133C2×C4×Dic3C2×D511yescharacteristic
134C22×C3⋊C8—51no—
135C3×#102—102no—
136#832—102no—
137C3⋊#95—102no—
138#821—102no—
139#815—102no—
140#809—102no—
141C24×C5—21no—
142C24×C5—61no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—32no—
149C2×C5×D4—68no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—124no—
156C2×C5×D4—124no—
157C2×C5×D4C4×D312yes—
158C22×C4×C5—32no—
159C22×C4×C5C22×D311yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—61no—
162C42×C5—32no—
163C42×C5—32no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—32no—
171C2×#168—61no—
172C2×#168—61no—
173C2×#168#6712yescomplemented
174C2×#127—31no—
175C2×#102—51no—
176C2×#102—151no—
177C2×#102—151no—
178C2×#102—151no—
179C2×#97—151no—
180#382—151no—
181C22×C3×C5—42no—
182C22×C3×C5—44no—
183C22×C3×C5—82no—
184C22×C3×C5—81no—
185C22×C3×C5—81no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12411yescharacteristic
188C22×C3×C5#12711yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)12yes—
190C22×C3×C5AGL(1,ℤ/8)12yes—
191C2×C5×D3—42no—
192C2×C5×D3—44no—
193C2×C5×D3—82no—
194C2×C5×D3—81no—
195C2×C5×D3—81no—
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200Dic15—81no—
201C3×Dic5—81no—
202C5×Dic3—24no—
203C24×C3—21no—
204C23×D3—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4C2×Dic512yes—
211C22×C3×C4—101no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—28no—
214C2×#67—44no—
215C2×#67—44no—
216C22×Dic3—101no—
217C22×Dic3C22⋊D512yes—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C2×Dic512yes—
224C2×C3×C8—52no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C4⋊Dic3—101no—
230C4⋊Dic3—101no—
231C4×Dic3C2×Dic512yes—
232C4×Dic3C22⋊D512yes—
233C2×C3⋊C8—52no—
234C2×C3⋊C8—101no—
235C2×C3⋊C8—101no—
236C23×C5—22no—
237C23×C5—41no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—41no—
241C23×C5—62no—
242C23×C5—121no—
243C23×C5—122no—
244C23×C5—122no—
245C23×C5—121no—
246C23×C5D3×D411yescharacteristic
247C5×D4—22no—
248C5×D4—22no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—62no—
252C5×D4—62no—
253C5×D4—1216no—
254C5×D4—121no—
255C5×D4—121no—
256C2×C4×C5—34no—
257C2×C4×C5—62no—
258C2×C4×C5—62no—
259C2×C4×C5C2×C4×D311yescharacteristic
260C2×C4×C5#23511yescharacteristic
261C2×C4×C5D3×D411yescharacteristic
262C2×C4×C5D3×D411yescharacteristic
263C2×C4×C5#23711yescharacteristic
264C2×C4×C5C2×#6711yescharacteristic
265C2×Dic5—42no—
266C2×Dic5—41no—
267C2×Dic5—122no—
268C2×Dic5—121no—
269#168—22no—
270#168—62no—
271C22×D4—31no—
272C22×D4—62no—
273C22×D4D3×D511yescharacteristic
274C22×C8—51no—
275C22×C8—151no—
276#127—34no—
277#127—62no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4—151no—
280C2×C42—31no—
281#102—102no—
282#102—302no—
283#102—302no—
284#102—302no—
285#97—302no—
286#95—302no—
287C2×C3×C5—82no—
288C2×C3×C5#39011yescharacteristic
289C2×C3×C5#41812yes—
290C2×C3×C5#49012yes—
291C2×C3×C5#49611yescharacteristic
292C2×C3×C5#49611yescharacteristic
293C5×D3—82no—
294C23×C3—22no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3C2×C22⋊D511yescharacteristic
300C22×D3—22no—
301C22×D3—42no—
302C22×D3—42no—
303C22×D3—41no—
304C22×D3—41no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—41no—
308C3×D4—41no—
309C2×C3×C4—202no—
310C2×C3×C4—201no—
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71111yescharacteristic
314C2×C3×C4#71111yescharacteristic
315C2×C3×C4C22×Dic511yescharacteristic
316C2×C3×C4C2×C22⋊D511yescharacteristic
317#67—416no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—202no—
321C2×Dic3—201no—
322C2×Dic3C22⋊Dic514yes—
323D12—22no—
324D12—22no—
325D12—41no—
326D12—41no—
327C3×C8—102no—
328C3⋊C8—102no—
329C22×C5—42no—
330C22×C5—44no—
331C22×C5—81no—
332C22×C5—81no—
333C22×C5—82no—
334C22×C5—122no—
335C22×C5—124no—
336C22×C5—241no—
337C22×C5—241no—
338C22×C5—242no—
339C22×C5D3×C22⋊C411yescharacteristic
340C22×C5#88511yescharacteristic
341C22×C5#91112yes—
342C22×C5#91412yes—
343C22×C5#94011yescharacteristic
344C4×C5—64no—
345C4×C5#67⋊C411yescharacteristic
346C4×C5#88411yescharacteristic
347C4×C5C4×#6711yescharacteristic
348C4×C5#93911yescharacteristic
349Dic5—81no—
350Dic5—241no—
351C24—21no—
352C24—61no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—32no—
359C2×D4—68no—
360C2×D4—61no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—124no—
366C2×D4—124no—
367C2×D4D3×Dic512yes—
368C22×C4—32no—
369C22×C4—101no—
370C22×C4—301no—
371C22×C4C2×D3×D511yescharacteristic
372C2×C8—52no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—152no—
376C2×C8—301no—
377C2×C8—301no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—301no—
381C4⋊C4—301no—
382C42—32no—
383C42—32no—
384C3×C5#196111yescharacteristic, complemented, Hall
385C22×C3—44no—
386C22×C3—42no—
387C22×C3—82no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3#407812yes—
391C22×C3#407812yes—
392C22×C3#408211yescharacteristic
393C22×C3#408611yescharacteristic
394C22×C3C2×C22⋊Dic511yescharacteristic
395C2×D3—44no—
396C2×D3—42no—
397C2×D3—82no—
398C2×D3—81no—
399C2×D3—81no—
400C3×C4—401no—
401C3×C4D4×Dic511yescharacteristic
402C3×C4D4×Dic511yescharacteristic
403C3×C4#408411yescharacteristic
404C3×C4#408411yescharacteristic
405Dic3—24no—
406Dic3—401no—
407C2×C5—82no—
408C2×C5—242no—
409C2×C5#476412yes—
410C2×C5#477012yes—
411C2×C5#495711yescharacteristic
412C2×C5#515411yescharacteristic
413C2×C5#517611yescharacteristic
414C23—22no—
415C23—42no—
416C23—42no—
417C23—41no—
418C23—41no—
419C23—62no—
420C23—122no—
421C23—122no—
422C23—121no—
423C23—121no—
424C23D3×C22⋊D511yescharacteristic
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429D4—62no—
430D4—62no—
431D4—1216no—
432D4—121no—
433D4—121no—
434C2×C4—34no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—202no—
438C2×C4—201no—
439C2×C4—602no—
440C2×C4—601no—
441C2×C4#678011yescharacteristic
442C2×C4C2×D3×Dic511yescharacteristic
443C2×C4#678211yescharacteristic
444C2×C4D5×#6711yescharacteristic
445C2×C4D3×C22⋊D511yescharacteristic
446C2×C4#679011yescharacteristic
447C8—102no—
448C8—302no—
449C2×C3—82no—
450C2×C3#6536012yes—
451C2×C3#6536311yescharacteristic
452C2×C3#6536311yescharacteristic
453C2×C3#6550412yes—
454C2×C3#6551011yescharacteristic
455D3—82no—
456C5#7016011yescharacteristic, complemented, Sylow
457C22—44no—
458C22—42no—
459C22—82no—
460C22—81no—
461C22—81no—
462C22—124no—
463C22—122no—
464C22—242no—
465C22—241no—
466C22—241no—
467C22#9149412yes—
468C22#9149612yes—
469C22#9152511yescharacteristic
470C22D3×C22⋊Dic511yescharacteristic
471C22#9156711yescharacteristic
472C4—64no—
473C4—401no—
474C4—1201no—
475C4#9154911yescharacteristic
476C4Dic5×#6711yescharacteristic
477C4#9155711yescharacteristic
478C4#67⋊Dic511yescharacteristic
479C3#1060255811yescharacteristic, complemented, Sylow
480C2—82no—
481C2—242no—
482C2#1174894612yes—
483C2#1174896712yes—
484C2#1174907111yescharacteristic
485C2#1174907611yescharacteristic
486C2#1174948211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC2×C5×#940C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1961
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91116C2semidirect
3. C2×C3×#3964C2semidirect
4. #11748619C2semidirect
5. C2×#90967C2semidirect
6. C2×#90966C2semidirect
7. C2×#90953C2semidirect
15. C5×#940C4semidirect
30. C2×#3964D3semidirect
58. C2×C3⋊#168D4semidirect
65. C2×C3×#168D4semidirect
131. #940Dic5semidirect
173. C2×#168#67semidirect
384. C3×C5#1961semidirect
456. C5#70160semidirect
479. C3#10602558semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9402
C2×#911162
C2×C3×#39642
#117486192
C2×#909672
C2×#909662
C2×#909532
#106025583
#701605