Finite Group Databasebeta

← #14297719

Subgroups — #14297719

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×D4×Dic15C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic
3C2×#91116C211yesmaximal, characteristic
4C2×#91098C211yesmaximal, characteristic, complemented
5#11751078C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10600947—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C23×Dic15—21no—
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×#6719—21no—
14D4×Dic15—22no—
15D4×Dic15C414yescomplemented
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C3×C5×#102—22no—
21#91116—22no—
22#91115—21no—
23#91115—21no—
24#91098—22no—
25#70154—51nomaximal, Hall
26C2×D4×Dic5—31no—
27C2×C5×#102D311yescharacteristic
28C2×#3964—31no—
29C2×#3946—31no—
30#65266—31no—
31#64771—31no—
32#64749—31no—
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C2×C3×C5×D4Q812yes—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C22×Dic15—24no—
44C22×Dic15—21no—
45C22×Dic15—42no—
46C22×Dic15—42no—
47C22×Dic15D411yescharacteristic
48C22×Dic15D411yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54#6719—24no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15C2×C412yes—
59C4×Dic15C2×C412yes—
60C4×Dic15D412yes—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C2×D4×Dic3—51no—
65C2×C3×#102D511yescharacteristic
66C2×#832—51no—
67C2×Dic3⋊C8—51no—
68#4977—51no—
69#4551—51no—
70#4529—51no—
71C22×C5×D4C2×D311yescharacteristic
72C23×Dic5—61no—
73C22×C5×C8C2×D311yescharacteristic
74C2×C5×C4⋊C4C2×D311yescharacteristic
75C2×C22⋊Dic5—61no—
76D4×Dic5—34no—
77D4×Dic5—62no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4×Dic5—31no—
81C22×#168—31no—
82C5×#102—22no—
83#3964—62no—
84#3963—61no—
85#3963—61no—
86#3946—62no—
87#1804—151noSylow
88C23×C3×C5—22no—
89C23×C3×C5—22no—
90C23×C3×C5—22no—
91C23×C3×C5—41no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—41no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×D4—22no—
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4C4⋊C414yes—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—21no—
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—22no—
114C2×Dic15—48no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×Dic15C22⋊C412yes—
121C2×Dic15C22⋊C412yes—
122C3×C5×C8—41no—
123C3⋊#168—41no—
124C22×C3×D4C2×D511yescharacteristic
125C23×Dic3—101no—
126C22×C3×C8C2×D511yescharacteristic
127C2×C3×C4⋊C4C2×D511yescharacteristic
128C2×#217—101no—
129D4×Dic3—54no—
130D4×Dic3—102no—
131C2×C4⋊Dic3—51no—
132C2×C4⋊Dic3—51no—
133C2×C4×Dic3—51no—
134C22×C3⋊C8—51no—
135C3×#102—22no—
136#832—102no—
137C3⋊#95—101no—
138C3⋊#95—101no—
139Dic3⋊C8—102no—
140C24×C5—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4Dic612yes—
145C2×C5×D4C4×D312yes—
146C2×C5×D4#6712yes—
147C22×C4×C5—21no—
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—31no—
150C22×Dic5—31no—
151C22×Dic5—64no—
152C22×Dic5—61no—
153C22×Dic5—61no—
154C22×Dic5—122no—
155C22×Dic5—122no—
156C2×C5×C8—21no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C22⋊Dic5—64no—
162C4⋊Dic5—32no—
163C4⋊Dic5—61no—
164C4⋊Dic5—61no—
165C4⋊Dic5—61no—
166C4×Dic5—32no—
167C4×Dic5—32no—
168C2×#168—61no—
169C2×#168—61no—
170C2×#168—61no—
171C2×C4×D4—151no—
172C2×C4⋊C8—151no—
173C2×#102—151no—
174C2×#102D1511yescharacteristic
175#382—151no—
176#340—151no—
177#340—151no—
178C22×C3×C5—24no—
179C22×C3×C5—42no—
180C22×C3×C5—42no—
181C22×C3×C5—42no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—42no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5#12111yescharacteristic
187C22×C3×C5C22⋊Q811yescharacteristic
188C22×C3×C5#13511yescharacteristic
189C22×C3×C5#13511yescharacteristic
190C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
191C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
192C3×C4×C5—81no—
193C3×C4×C5C2×C4⋊C411yescharacteristic
194C3×C4×C5#11711yescharacteristic
195C3×C4×C5#12111yescharacteristic
196C3×C4×C5C22⋊Q811yescharacteristic
197Dic15—22no—
198Dic15—22no—
199Dic15—42no—
200Dic15—81no—
201C24×C3—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4Dic1012yes—
206C2×C3×D4C4×D512yes—
207C2×C3×D4C22⋊D512yes—
208C22×C3×C4—21no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—51no—
211C22×Dic3—51no—
212C22×Dic3—104no—
213C22×Dic3—101no—
214C22×Dic3—101no—
215C22×Dic3—202no—
216C22×Dic3—202no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222#217—104no—
223C4⋊Dic3—52no—
224C4⋊Dic3—101no—
225C4⋊Dic3—101no—
226C4⋊Dic3—101no—
227C4×Dic3—52no—
228C4×Dic3—52no—
229C2×C3⋊C8—101no—
230C2×C3⋊C8—101no—
231C2×C3⋊C8—101no—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5—41no—
239C23×C5D3×D411yescharacteristic
240C5×D4—22no—
241C5×D4—22no—
242C5×D4—22no—
243C5×D4Dic3⋊C414yes—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5C2×Dic611yescharacteristic
248C2×C4×C5C2×C4×D311yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5#23711yescharacteristic
252C2×C4×C5C2×#6711yescharacteristic
253C2×Dic5—32no—
254C2×Dic5—32no—
255C2×Dic5—61no—
256C2×Dic5—61no—
257C2×Dic5—61no—
258C2×Dic5—61no—
259C2×Dic5—62no—
260C2×Dic5—128no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C2×Dic5—121no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266C5×C8—41no—
267#168—121no—
268C22×D4C2×D1511yescharacteristic
269C23×C4—301no—
270C22×C8—151no—
271C22×C8C2×D1511yescharacteristic
272C4×D4—154no—
273C4×D4—302no—
274C2×C4⋊C4—151no—
275C2×C4⋊C4—151no—
276C2×C4⋊C4C2×D1511yescharacteristic
277C2×C22⋊C4—301no—
278C2×C42—151no—
279C4⋊C8—302no—
280#102—22no—
281#102—302no—
282#95—301no—
283#95—301no—
284C2×C3×C5—44no—
285C2×C3×C5#38011yescharacteristic
286C2×C3×C5#41611yescharacteristic
287C2×C3×C5#41811yescharacteristic
288C2×C3×C5#46311yescharacteristic
289C2×C3×C5#46311yescharacteristic
290C2×C3×C5#47811yescharacteristic
291C2×C3×C5#47811yescharacteristic
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3D4×D511yescharacteristic
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4#68314yes—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4C2×Dic1011yescharacteristic
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313C2×Dic3—52no—
314C2×Dic3—52no—
315C2×Dic3—101no—
316C2×Dic3—101no—
317C2×Dic3—101no—
318C2×Dic3—101no—
319C2×Dic3—102no—
320C2×Dic3—208no—
321C2×Dic3—201no—
322C2×Dic3—201no—
323C2×Dic3—201no—
324C2×Dic3—201no—
325C2×Dic3—201no—
326C3×C8—41no—
327C3⋊C8—201no—
328C22×C5—24no—
329C22×C5—42no—
330C22×C5—42no—
331C22×C5—42no—
332C22×C5—42no—
333C22×C5—42no—
334C22×C5—42no—
335C22×C5#87811yescharacteristic
336C22×C5D3×C22⋊C411yescharacteristic
337C22×C5#91111yescharacteristic
338C22×C5#91211yescharacteristic
339C22×C5#91411yescharacteristic
340C22×C5#91611yescharacteristic
341C22×C5#93911yescharacteristic
342C4×C5—81no—
343C4×C5#87711yescharacteristic
344C4×C5#87811yescharacteristic
345C4×C5C2×Dic3⋊C411yescharacteristic
346C4×C5#93911yescharacteristic
347Dic5—62no—
348Dic5—62no—
349Dic5—122no—
350Dic5—241no—
351C24—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4Dic3012yes—
356C2×D4C4×D1512yes—
357C2×D4#122012yes—
358C22×C4—21no—
359C22×C4—151no—
360C22×C4—151no—
361C22×C4—304no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4—602no—
365C22×C4—602no—
366C22×C4C22×D1511yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—301no—
371C2×C8—301no—
372C2×C8—301no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—152no—
376C4⋊C4—301no—
377C4⋊C4—301no—
378C4⋊C4—301no—
379C22⋊C4—304no—
380C42—152no—
381C42—152no—
382C3×C5#180411yescharacteristic, complemented, Hall
383C22×C3—24no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3#402411yescharacteristic
391C22×C3D5×C22⋊C411yescharacteristic
392C22×C3#405711yescharacteristic
393C22×C3#405811yescharacteristic
394C22×C3#406011yescharacteristic
395C22×C3#406211yescharacteristic
396C22×C3#408511yescharacteristic
397C3×C4—81no—
398C3×C4#402311yescharacteristic
399C3×C4#402411yescharacteristic
400C3×C4C2×#68311yescharacteristic
401C3×C4#408511yescharacteristic
402Dic3—102no—
403Dic3—102no—
404Dic3—202no—
405Dic3—401no—
406C2×C5—44no—
407C2×C5#476311yescharacteristic
408C2×C5#476611yescharacteristic
409C2×C5#477011yescharacteristic
410C2×C5#477211yescharacteristic
411C2×C5#494211yescharacteristic
412C2×C5#515311yescharacteristic
413C2×C5#516511yescharacteristic
414C23—22no—
415C23—22no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23D4×D1511yescharacteristic
422D4—22no—
423D4—22no—
424D4—22no—
425D4#671214yes—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—152no—
430C2×C4—152no—
431C2×C4—301no—
432C2×C4—301no—
433C2×C4—301no—
434C2×C4—301no—
435C2×C4—302no—
436C2×C4—608no—
437C2×C4—601no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4C2×Dic3011yescharacteristic
443C2×C4C2×C4×D1511yescharacteristic
444C2×C4D4×D1511yescharacteristic
445C2×C4#681911yescharacteristic
446C2×C4#681911yescharacteristic
447C2×C4C2×#122011yescharacteristic
448C8—41no—
449C8—601no—
450C2×C3—44no—
451C2×C3#6505211yescharacteristic
452C2×C3#6505511yescharacteristic
453C2×C3#6505911yescharacteristic
454C2×C3#6506111yescharacteristic
455C2×C3#6523111yescharacteristic
456C2×C3#6544211yescharacteristic
457C2×C3#6545411yescharacteristic
458C5#7015411yescharacteristic, complemented, Sylow
459C22—24no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22#9176711yescharacteristic
467C22C22⋊C4×D1511yescharacteristic
468C22#9180011yescharacteristic
469C22#9180111yescharacteristic
470C22#9180311yescharacteristic
471C22#9180511yescharacteristic
472C22#9182811yescharacteristic
473C4—81no—
474C4—302no—
475C4—302no—
476C4—602no—
477C4—1201no—
478C4#9176611yescharacteristic
479C4#9176711yescharacteristic
480C4C2×#671211yescharacteristic
481C4#9182811yescharacteristic
482C3#1060094711yescharacteristic, complemented, Sylow
483C2—44no—
484C2#1175086411yescharacteristic
485C2#1175086711yescharacteristic
486C2#1175087111yescharacteristic
487C2#1175087311yescharacteristic
488C2#1175104311yescharacteristic
489C2#1175125411yescharacteristic
490C2#1175126611yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#102D15
hypocenterC3×C5#1804
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
4. C2×#91098C2semidirect
5. #11751078C2semidirect
6. #11746372C2semidirect
7. #11746350C2semidirect
15. D4×Dic15C4semidirect
382. C3×C5#1804semidirect
458. C5#70154semidirect
482. C3#10600947semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C3×C5×#1022
C2×#911162
C2×#910982
#117510782
#117463722
#117463502
#106009473
#701545