Finite Group Databasebeta

← #14280906

Subgroups — #14280906

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91442C211yesmaximal, characteristic
2#11750819C211yesmaximal, characteristic, complemented
3#11748331C211yesmaximal, characteristic, complemented
4C5×#4468C211yesmaximal, characteristic, complemented
5C3×#64688C211yesmaximal, characteristic, complemented
6#11745949C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic, complemented
8#10598894—31nomaximal, Hall
9C22×#1201C411yescharacteristic
10C22×D3×Dic5C411yescharacteristic
11C22×D5×Dic3C411yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×#685C2211yescharacteristic
15C2×#6669C411yescharacteristic
16#91442—21no—
17#91442—21no—
18#91442—21no—
19#91442—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21#91114C2211yescharacteristic
22#91098—21no—
23C8×Dic15—21no—
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90951—21no—
28#68101—51nomaximal, Hall
29C2×#4027—31no—
30#65007—31no—
31#65007—31no—
32C5×#323—31no—
33#64745—31no—
34#64688—31no—
35#64688D311yescharacteristic, complemented
36C23×C5×D3C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×#1201—21no—
44C2×#1201—21no—
45C2×#1201—22no—
46C2×#1201C814yescomplemented
47C2×D3×Dic5—21no—
48C2×D3×Dic5—21no—
49C2×D3×Dic5—42no—
50C2×D5×Dic3—21no—
51C2×D5×Dic3—21no—
52C2×D5×Dic3—42no—
53C2×C3×C5×C8—21no—
54C4×Dic15D411yescharacteristic
55C4×Dic15D411yescharacteristic
56C4×Dic15D411yescharacteristic
57C4×Dic15D411yescharacteristic
58C2×C3⋊#168—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C2×C5×C3⋊C8—21no—
62C3×#685—21no—
63C3×#685—21no—
64C2×C3×#168—21no—
65#6669—21no—
66#6669—21no—
67C2×#67⋊C4—51no—
68#4718—51no—
69#4718—51no—
70C3×#323—51no—
71#4525—51no—
72#4468—51no—
73#4468D511yescharacteristic, complemented
74C22×C22⋊D5—31no—
75C23×Dic5—31no—
76C22×C4×D5—31no—
77C2×C5×C22⋊C4—31no—
78C2×#685C2×D311yescharacteristic
79C2×#683—31no—
80C2×C4×Dic5—31no—
81#4027—61no—
82#4027—61no—
83#4027—61no—
84#4027—61no—
85C5×C22⋊C8—31no—
86C5×C22⋊C8C2×D311yescharacteristic
87C22⋊#168—31no—
88C22⋊#168C2×D311yescharacteristic
89#3946—61no—
90#3946—61no—
91C8×Dic5—61no—
92C8×Dic5—61no—
93#1460—151noSylow
94C23×C3×C5C22×C411yescharacteristic
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—41no—
98C22×C5×D3—41no—
99C22×C5×D3C2×C812yes—
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—41no—
103C22×C3×D5—41no—
104C22×C3×D5C2×C812yes—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—22no—
109C2×Dic15C22⋊C411yescharacteristic
110C2×Dic15C22⋊C411yescharacteristic
111C2×Dic15C22⋊C411yescharacteristic
112C2×Dic15C22⋊C411yescharacteristic
113C2×Dic15C2×C812yes—
114C2×Dic15M1612yes—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—41no—
119#1201—24no—
120#1201—24no—
121D3×Dic5—42no—
122D3×Dic5—42no—
123D5×Dic3—42no—
124D5×Dic3—42no—
125C3×C5×C8—41no—
126C3⋊#168—41no—
127C3×#168—41no—
128C5×C3⋊C8—41no—
129C22×#67—51no—
130C23×Dic3—51no—
131C22×C4×D3—51no—
132C2×C3×C22⋊C4—51no—
133C2×(C2×D3)⋊C4C2×D511yescharacteristic
134C2×Dic3⋊C4—51no—
135C2×C4×Dic3—51no—
136#67⋊C4—101no—
137#67⋊C4—101no—
138#67⋊C4—101no—
139#67⋊C4—101no—
140C3×C22⋊C8—51no—
141C3×C22⋊C8C2×D511yescharacteristic
142#830—51no—
143#830C2×D511yescharacteristic
144Dic3⋊C8—101no—
145Dic3⋊C8—101no—
146C8×Dic3—101no—
147C8×Dic3—101no—
148C24×C5—31no—
149C23×D5C4×D311yescharacteristic
150C22×C4×C5—31no—
151C22×C4×C5C22×D311yescharacteristic
152C2×C22⋊D5—34no—
153C2×C22⋊D5—62no—
154C2×C22⋊D5—61no—
155C2×C22⋊D5—61no—
156C22×Dic5—31no—
157C22×Dic5—31no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160C22×Dic5—122no—
161C22×Dic5C4×D311yescharacteristic
162C2×C4×D5—61no—
163C2×C4×D5—61no—
164C2×C4×D5—122no—
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C5×C22⋊C4—61no—
168C5×C22⋊C4—61no—
169#685—21no—
170#685—21no—
171#683—61no—
172#683—61no—
173C4×Dic5—31no—
174C4×Dic5—31no—
175C4×Dic5—31no—
176C4×Dic5—31no—
177C2×#168—21no—
178C2×#168—61no—
179C2×C4×D4—151no—
180#431—151no—
181#431—151no—
182#323—31no—
183#323—51no—
184#323—151no—
185#323—151no—
186C22×C3×C5—21no—
187C22×C3×C5—21no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5C22×C811yescharacteristic
190C22×C3×C5C2×M1611yescharacteristic
191C2×C5×D3—22no—
192C2×C5×D3—42no—
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C5×D3—42no—
196C2×C3×D5—22no—
197C2×C3×D5—42no—
198C2×C3×D5—41no—
199C2×C3×D5—41no—
200C2×C3×D5—42no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203Dic15—21no—
204Dic15C22⋊C812yes—
205Dic15C22⋊C812yes—
206Dic15#10012yes—
207C3×Dic5—41no—
208C5×Dic3—41no—
209C24×C3—51no—
210C23×D3C4×D511yescharacteristic
211C22×C3×C4—51no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—54no—
214C2×#67—101no—
215C2×#67—101no—
216C2×#67—102no—
217C22×Dic3—51no—
218C22×Dic3—51no—
219C22×Dic3—101no—
220C22×Dic3—101no—
221C22×Dic3—202no—
222C22×Dic3C4×D511yescharacteristic
223C2×C4×D3—101no—
224C2×C4×D3—101no—
225C2×C4×D3—202no—
226C2×C3×C8—21no—
227C2×C3×C8—101no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—101no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232Dic3⋊C4—101no—
233Dic3⋊C4—101no—
234C4×Dic3—51no—
235C4×Dic3—51no—
236C4×Dic3—51no—
237C4×Dic3—51no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—101no—
240C23×C5—32no—
241C23×C5—61no—
242C23×C5—61no—
243C23×C5—121no—
244C23×C5—121no—
245C23×C5C2×C4×D311yescharacteristic
246C22×D5—21no—
247C22×D5—21no—
248C22×D5—41no—
249C22×D5—41no—
250C22×D5D3×C812yes—
251C2×C4×C5—41no—
252C2×C4×C5—61no—
253C2×C4×C5—121no—
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C22⋊D5—64no—
257C22⋊D5—64no—
258C2×Dic5—21no—
259C2×Dic5—31no—
260C2×Dic5—31no—
261C2×Dic5—31no—
262C2×Dic5—32no—
263C2×Dic5—32no—
264C2×Dic5—31no—
265C2×Dic5—41no—
266C2×Dic5—62no—
267C2×Dic5—122no—
268C2×Dic5—122no—
269C4×D5—122no—
270C4×D5—122no—
271C5×C8—41no—
272C5×C8—121no—
273#168—41no—
274#168—121no—
275C22×D4—151no—
276C23×C4—151no—
277C23×C4—151no—
278C4×D4—301no—
279C4×D4—301no—
280C4×D4—301no—
281C4×D4—301no—
282C2×C4⋊C4—151no—
283C2×C22⋊C4—31no—
284C2×C22⋊C4—51no—
285C2×C42—151no—
286C4⋊C8—301no—
287C4⋊C8—301no—
288C22⋊C8—31no—
289C22⋊C8—51no—
290C22⋊C8—151no—
291C22⋊C8D3×D511yescharacteristic
292C4×C8—301no—
293C4×C8—301no—
294C2×C3×C5—21no—
295C2×C3×C5—21no—
296C2×C3×C5C2×C22⋊C811yescharacteristic
297C2×C3×C5#41011yescharacteristic
298C2×C3×C5C2×#10011yescharacteristic
299C3×D5—42no—
300C5×D3—42no—
301C23×C3—52no—
302C23×C3—101no—
303C23×C3—101no—
304C23×C3—201no—
305C23×C3—201no—
306C23×C3C2×C4×D511yescharacteristic
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—41no—
310C22×D3—41no—
311C22×D3C8×D512yes—
312C2×C3×C4—41no—
313C2×C3×C4—101no—
314C2×C3×C4—201no—
315C2×C3×C4D4×D511yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317#67—104no—
318#67—104no—
319C2×Dic3—21no—
320C2×Dic3—41no—
321C2×Dic3—51no—
322C2×Dic3—51no—
323C2×Dic3—51no—
324C2×Dic3—52no—
325C2×Dic3—52no—
326C2×Dic3—51no—
327C2×Dic3—102no—
328C2×Dic3—202no—
329C2×Dic3—202no—
330C4×D3—202no—
331C4×D3—202no—
332C3×C8—41no—
333C3×C8—201no—
334C3⋊C8—41no—
335C3⋊C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—62no—
339C22×C5—122no—
340C22×C5—122no—
341C22×C5—121no—
342C22×C5—121no—
343C22×C5D3×C22⋊C411yescharacteristic
344C22×C5C2×D3×C811yescharacteristic
345C22×C5D3×M1611yescharacteristic
346C2×D5—22no—
347C2×D5—42no—
348C2×D5—41no—
349C2×D5—41no—
350C2×D5—42no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—121no—
354Dic5—32no—
355Dic5—32no—
356Dic5—32no—
357Dic5—41no—
358Dic5—61no—
359C24—31no—
360C24—51no—
361C2×D4—154no—
362C2×D4—301no—
363C2×D4—301no—
364C2×D4—302no—
365C22×C4—31no—
366C22×C4—51no—
367C22×C4—151no—
368C22×C4—151no—
369C22×C4—301no—
370C22×C4—301no—
371C22×C4—301no—
372C22×C4—301no—
373C22×C4—602no—
374C22×C4—602no—
375C22×C4C2×D3×D511yescharacteristic
376C2×C8—21no—
377C2×C8—61no—
378C2×C8—101no—
379C2×C8—301no—
380C4⋊C4—301no—
381C4⋊C4—301no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C42—151no—
387C42—151no—
388C42—151no—
389C42—151no—
390C3×C5#146011yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—102no—
394C22×C3—202no—
395C22×C3—202no—
396C22×C3—201no—
397C22×C3—201no—
398C22×C3D5×C22⋊C411yescharacteristic
399C22×C3C2×C8×D511yescharacteristic
400C22×C3D5×M1611yescharacteristic
401C2×D3—22no—
402C2×D3—42no—
403C2×D3—41no—
404C2×D3—41no—
405C2×D3—42no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—201no—
409Dic3—41no—
410Dic3—52no—
411Dic3—52no—
412Dic3—52no—
413Dic3—101no—
414C2×C5—21no—
415C2×C5—21no—
416C2×C5—122no—
417C2×C5D3×C22⋊C811yescharacteristic
418C2×C5#474011yescharacteristic
419C2×C5D3×#10011yescharacteristic
420D5—42no—
421C23—32no—
422C23—52no—
423C23—61no—
424C23—61no—
425C23—101no—
426C23—101no—
427C23—121no—
428C23—121no—
429C23—201no—
430C23—201no—
431C23C4×D3×D511yescharacteristic
432D4—304no—
433D4—304no—
434C2×C4—41no—
435C2×C4—61no—
436C2×C4—101no—
437C2×C4—121no—
438C2×C4—151no—
439C2×C4—151no—
440C2×C4—151no—
441C2×C4—152no—
442C2×C4—152no—
443C2×C4—151no—
444C2×C4—201no—
445C2×C4—302no—
446C2×C4—602no—
447C2×C4—602no—
448C2×C4—602no—
449C2×C4—602no—
450C2×C4#677711yescharacteristic
451C2×C4#679011yescharacteristic
452C8—41no—
453C8—121no—
454C8—201no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—202no—
459C2×C3D5×C22⋊C811yescharacteristic
460C2×C3#6502911yescharacteristic
461C2×C3D5×#10011yescharacteristic
462D3—42no—
463C5#6810111yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—62no—
467C22—102no—
468C22—122no—
469C22—122no—
470C22—121no—
471C22—121no—
472C22—202no—
473C22—202no—
474C22—201no—
475C22—201no—
476C22D3×C8×D511yescharacteristic
477C22#9124611yescharacteristic
478C22#9147311yescharacteristic
479C4—21no—
480C4—21no—
481C4—121no—
482C4—152no—
483C4—152no—
484C4—152no—
485C4—201no—
486C4—301no—
487C3#1059889411yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—122no—
491C2—202no—
492C2#1174713111yescharacteristic
493C2#1174810011yescharacteristic
494C2#1174822411yescharacteristic
subgroupG/H
centerC22#91473
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1201C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1460
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
3. #11748331C2semidirect
4. C5×#4468C2semidirect
5. C3×#64688C2semidirect
6. #11745949C2semidirect
7. #11745948C2semidirect
35. #64688D3semidirect
46. C2×#1201C8semidirect
73. #4468D5semidirect
390. C3×C5#1460semidirect
463. C5#68101semidirect
487. C3#10598894semidirect

Maximal subgroups

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

subgroupindex
C2×#914422
#117508192
#117483312
C5×#44682
C3×#646882
#117459492
#117459482
#105988943
#681015