Finite Group Databasebeta

← #14430736

Subgroups — #14430736

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756281C211yesmaximal, characteristic
2C2×#91384C211yesmaximal, characteristic, complemented
3C5×#4995C211yesmaximal, characteristic, complemented
4C3×#65284C211yesmaximal, characteristic, complemented
5#11748437C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic
7#11748394C211yesmaximal, characteristic
8#11747187C212yesmaximal, complemented
9#11747186C212yesmaximal, complemented
10#11747185C212yesmaximal, complemented
11#11747184C212yesmaximal, complemented
12#10610972—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16#91782C2211yescharacteristic
17#91782C2211yescharacteristic
18#91776C2211yescharacteristic
19#91776C2211yescharacteristic
20#91770—21no—
21#91770—21no—
22#91761—21no—
23C42×D15—21no—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×#208C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#681C2211yescharacteristic
28C2×Dic3⋊Dic5—21no—
29C2×#6668—21no—
30#91384—21no—
31#91384—21no—
32#91384C2212yes—
33#91384C2212yes—
34C5×#808C2212yes—
35C5×#807C2212yes—
36C3×#3940C2212yes—
37C3×#3939C2212yes—
38#90983C2212yes—
39#90983C2212yes—
40#90975C2212yes—
41#90974C2212yes—
42#90969C2212yes—
43#90968C2212yes—
44#79241—51nomaximal, Hall
45#65856—31no—
46C2×#4036—31no—
47C5×#428—31no—
48#65422—31no—
49#65407—31no—
50#65284D311yescharacteristic, complemented
51#65255—31no—
52#65180—32no—
53#65166—32no—
54#65160—32no—
55#65146—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15D411yescharacteristic
59C22×Dic15D411yescharacteristic
60#6817—22no—
61#6817Q814yes—
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×C4×D15—21no—
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C22×C5×Dic3—21no—
68C22×C3×Dic5—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73#6714—21no—
74#6714—21no—
75#6712—21no—
76#6712—21no—
77C4×Dic15—21no—
78C4×Dic15—21no—
79C4×Dic15D411yescharacteristic
80C4×Dic15D411yescharacteristic
81C4×Dic15C2311yescharacteristic
82C4×Dic15C2311yescharacteristic
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3C2312yes—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91Dic3⋊Dic5—22no—
92Dic3⋊Dic5—22no—
93#6668—22no—
94#6668—22no—
95#5522—51no—
96C2×#890—51no—
97C3×#428—51no—
98#5133—51no—
99#5118—51no—
100#4995D511yescharacteristic, complemented
101#4966—51no—
102#4891—52no—
103#4877—52no—
104#4871—52no—
105#4857—52no—
106C2×#709—31no—
107C2×C5×M16—31no—
108C5×#117C2×D311yescharacteristic
109C2×C5×C4⋊C4—31no—
110C2×C4⋊Dic5—61no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—61no—
113C2×C4×Dic5—31no—
114C2×#681C2×D311yescharacteristic
115#4039—31no—
116#4039—31no—
117#4036—32no—
118#4036—32no—
119#4036—61no—
120#4036—61no—
121#4033—31no—
122#4033—31no—
123#4027—61no—
124#4027—61no—
125#4018—61no—
126C42×D5—61no—
127C5×#107—32no—
128C5×#106—32no—
129#3953—32no—
130#3948—32no—
131#3946—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940C2×D312yes—
136#3939C2×D312yes—
137#3080—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×Q812yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148C2×Dic15—41no—
149C2×Dic15—41no—
150C2×Dic15C2×D411yescharacteristic
151C2×Dic15C2×D411yescharacteristic
152C2×Dic15C2×D411yescharacteristic
153C2×Dic15C2×D411yescharacteristic
154D60—21no—
155D60C2×Q812yes—
156C4×D15—24no—
157C4×D15—42no—
158C4×D15—42no—
159Dic30—21no—
160Dic30C2×Q812yes—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—42no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—42no—
165C3×#168—22no—
166C5×C3⋊C8—22no—
167C2×#235—51no—
168C2×C3×M16—51no—
169C3×#117C2×D511yescharacteristic
170C2×C3×C4⋊C4—51no—
171C2×C4⋊Dic3—101no—
172C2×C4⋊Dic3C2×D511yescharacteristic
173C2×Dic3⋊C4—101no—
174C2×C4×Dic3—51no—
175C2×#208C2×D511yescharacteristic
176#893—51no—
177#893—51no—
178#890—52no—
179#890—52no—
180#890—101no—
181#890—101no—
182#887—51no—
183#887—51no—
184#67⋊C4—101no—
185#67⋊C4—101no—
186#872—101no—
187C42×D3—101no—
188C3×#107—52no—
189C3×#106—52no—
190#821—52no—
191#816—52no—
192Dic3⋊C8—52no—
193Dic3⋊C8—52no—
194#810—52no—
195#809—52no—
196#808C2×D512yes—
197#807C2×D512yes—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201C22×Dic5—21no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204#709—34no—
205#709—62no—
206C2×D20—31no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C2×Dic10—31no—
211C5×M16—62no—
212C2×C5×C8—32no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C42×C5—21no—
219#685—61no—
220#685—61no—
221C4⋊Dic5—21no—
222C4⋊Dic5—62no—
223C4⋊Dic5—62no—
224C4⋊Dic5C22×D312yes—
225#683—62no—
226#683—62no—
227#683—61no—
228#683—61no—
229C4×Dic5—31no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—31no—
233C4×Dic5—61no—
234C4×Dic5—61no—
235#681—22no—
236C2×#168C22×D312yes—
237C2×#125—151no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—31no—
244#428—51no—
245#423—151no—
246#417—151no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—22no—
253C2×D15—41no—
254C2×D15—41no—
255C3×C4×C5—41no—
256C3×C4×C5—41no—
257C3×C4×C5C22⋊Q812yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261Dic15—21no—
262Dic15—21no—
263Dic15—21no—
264Dic15—21no—
265C3×Dic5—42no—
266C5×Dic3—42no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—101no—
270C22×Dic3—21no—
271C22×Dic3—51no—
272C22×Dic3—51no—
273#235—54no—
274#235—102no—
275C2×D12—51no—
276C2×C4×D3—101no—
277C2×C4×D3—101no—
278C2×C4×D3—101no—
279C2×Dic6—51no—
280C3×M16—102no—
281C2×C3×C8—52no—
282C3×C4⋊C4—52no—
283C3×C4⋊C4—101no—
284C3×C4⋊C4C22×D511yescharacteristic
285C3×C4⋊C4C22×D511yescharacteristic
286C3×C22⋊C4—21no—
287C3×C42—21no—
288(C2×D3)⋊C4—101no—
289(C2×D3)⋊C4—101no—
290C4⋊Dic3—21no—
291C4⋊Dic3—102no—
292C4⋊Dic3—102no—
293C4⋊Dic3C22×D512yes—
294Dic3⋊C4—102no—
295Dic3⋊C4—102no—
296Dic3⋊C4—101no—
297Dic3⋊C4—101no—
298C4×Dic3—51no—
299C4×Dic3—51no—
300C4×Dic3—51no—
301C4×Dic3—51no—
302C4×Dic3—101no—
303C4×Dic3—101no—
304#208—22no—
305C2×C3⋊C8C22×D512yes—
306C23×C5D3×D411yescharacteristic
307C22×D5—61no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—62no—
311C2×C4×C5—122no—
312C2×C4×C5#23512yes—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×Q812yes—
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—64no—
317C2×Dic5—22no—
318C2×Dic5—31no—
319C2×Dic5—31no—
320C2×Dic5—31no—
321C2×Dic5—31no—
322C2×Dic5—42no—
323C2×Dic5—61no—
324C2×Dic5—121no—
325C2×Dic5—121no—
326D20—32no—
327D20—61no—
328C4×D5—64no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—62no—
334#168—22no—
335C2×#41—151no—
336C2×M16—31no—
337C2×M16—51no—
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—151no—
345C4×D4—151no—
346C4×D4—301no—
347C4×D4—301no—
348#117—301no—
349#117D3×D511yescharacteristic
350C2×C4⋊C4—31no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—151no—
355C2×C42—301no—
356#107—32no—
357#107—52no—
358#106—32no—
359#106—52no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—152no—
363#103—152no—
364#102—152no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370D15—42no—
371C23×C3D4×D511yescharacteristic
372C22×D3—101no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—102no—
376C2×C3×C4—202no—
377C2×C3×C4#70912yes—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4Q8×D512yes—
380C2×C3×C4C23×D511yescharacteristic
381#67—104no—
382C2×Dic3—22no—
383C2×Dic3—42no—
384C2×Dic3—51no—
385C2×Dic3—51no—
386C2×Dic3—51no—
387C2×Dic3—51no—
388C2×Dic3—101no—
389C2×Dic3—201no—
390C2×Dic3—201no—
391D12—52no—
392D12—101no—
393C4×D3—104no—
394C4×D3—202no—
395C4×D3—202no—
396Dic6—52no—
397Dic6—101no—
398C3×C8—102no—
399C3⋊C8—22no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5#89612yes—
403C22×C5C2×D3×D411yescharacteristic
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—122no—
410C4×C5#89612yes—
411C4×C5C2×#23511yescharacteristic
412C4×C5C2×D3×Q811yescharacteristic
413Dic5—42no—
414Dic5—62no—
415Dic5—61no—
416Dic5—61no—
417Dic5—61no—
418Dic5—61no—
419#41—154no—
420#41—302no—
421C2×Q8—151no—
422C2×D4—151no—
423C2×D4—301no—
424C22×C4—61no—
425C22×C4—101no—
426C22×C4—151no—
427C22×C4—151no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—62no—
433M16—102no—
434C2×C8—32no—
435C2×C8—52no—
436C4⋊C4—32no—
437C4⋊C4—52no—
438C4⋊C4—61no—
439C4⋊C4—101no—
440C4⋊C4—301no—
441C4⋊C4—301no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D511yescharacteristic
447C4⋊C4C2×D3×D511yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—21no—
452C42—151no—
453C42—151no—
454C42—151no—
455C42—151no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3#404212yes—
462C22×C3C2×D4×D511yescharacteristic
463C2×D3—102no—
464C2×D3—201no—
465C2×D3—201no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—202no—
469C3×C4#404212yes—
470C3×C4C2×#70911yescharacteristic
471C3×C4C2×Q8×D511yescharacteristic
472Dic3—42no—
473Dic3—102no—
474Dic3—101no—
475Dic3—101no—
476Dic3—101no—
477Dic3—101no—
478C2×C5—22no—
479C2×C5C2×#89611yescharacteristic
480C2×C5#577311yescharacteristic
481C2×C5#577711yescharacteristic
482D5—122no—
483C23—301no—
484C23#679011yescharacteristic
485Q8—152no—
486Q8—301no—
487D4—152no—
488D4—304no—
489D4—301no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—62no—
493C2×C4—102no—
494C2×C4—122no—
495C2×C4—151no—
496C2×C4—151no—
497C2×C4—151no—
498C2×C4—151no—
499C2×C4—202no—
500C2×C4—301no—
501C2×C4—304no—
502C2×C4—602no—
503C2×C4—602no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4D15⋊Q812yes—
507C2×C4#677112yes—
508C2×C4#679011yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—102no—
512C2×C3—22no—
513C2×C3C2×#404211yescharacteristic
514C2×C3#6610711yescharacteristic
515C2×C3#6611111yescharacteristic
516D3—202no—
517C5#7924111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—302no—
521C22—601no—
522C22—601no—
523C22#9137712yes—
524C22C2×#679011yescharacteristic
525C4—41no—
526C4—41no—
527C4—122no—
528C4—202no—
529C4—302no—
530C4—301no—
531C4—301no—
532C4—301no—
533C4—301no—
534C4#9137712yes—
535C4C2×D15⋊Q811yescharacteristic
536C4C2×#677111yescharacteristic
537C3#1061097211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—602no—
540C2C2×#9137711yescharacteristic
541C2#1175534911yescharacteristic
542C2#1175535211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#117D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#91384C2semidirect
3. C5×#4995C2semidirect
4. C3×#65284C2semidirect
5. #11748437C2semidirect
8. #11747187C2semidirect
9. #11747186C2semidirect
10. #11747185C2semidirect
11. #11747184C2semidirect
50. #65284D3semidirect
100. #4995D5semidirect
458. C3×C5#3080semidirect
517. C5#79241semidirect
537. C3#10610972semidirect

Maximal subgroups

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

subgroupindex
#117562812
C2×#913842
C5×#49952
C3×#652842
#117484372
#117484132
#117483942
#117471872
#117471862
#117471852
#117471842
#106109723
#792415