Finite Group Databasebeta

← #14417788

Subgroups — #14417788

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756586C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic
3#11754492C211yesmaximal, characteristic, complemented
4C3×#65521C211yesmaximal, characteristic, complemented
5#11749266C212yesmaximal, complemented
6#11749240C212yesmaximal, complemented
7#11749019C212yesmaximal, complemented
8#11748996C212yesmaximal, complemented
9C2×#90987C211yesmaximal, characteristic, complemented
10#11748390C211yesmaximal, characteristic, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10615630—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15Q8×Dic15C2212yes—
16D4×Dic15—22no—
17D4×Dic15C2212yes—
18#91815—21no—
19#91815C2211yescharacteristic
20C2×C4⋊Dic15—21no—
21C2×C4⋊Dic15C2211yescharacteristic
22C5×#950C418yescomplemented
23C2×C5×#216C2211yescharacteristic
24C2×C5×#215C2211yescharacteristic
25C2×C5×#214C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#681C2211yescharacteristic
30Dic5×#67—22no—
31#91435C2212yes—
32D3×C4⋊Dic5—21no—
33#91344C2212yes—
34#91338—21no—
35C3×#3967C2212yes—
36C3×#3964C2212yes—
37#90987C2212yes—
38#90987C2212yes—
39#90973C2212yes—
40#90967C2212yes—
41#90954C2212yes—
42#90951C2212yes—
43#78869—51nomaximal, Hall
44C2×C5×#135—31no—
45#66161—31no—
46#66161—31no—
47#65521—31no—
48#65521D311yescharacteristic, complemented
49#65473—32no—
50SD16×Dic5—32no—
51SD16×Dic5—32no—
52#65441—32no—
53C2×#3949—31no—
54#65390—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—21no—
63C22×Dic15—22no—
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235C2×C414yescomplemented
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C2×D3×Dic5—22no—
72#6719—22no—
73#6719D412yes—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15C2312yes—
79C4×Dic15—22no—
80C4×Dic15C2312yes—
81C5×#216C2×C414yescomplemented
82C5×#215C2×C414yescomplemented
83C5×#214C2×C414yescomplemented
84C5×#213C2×C414yescomplemented
85C2×C5×C3⋊C8C2×C414yescomplemented
86C2×C5×C3⋊C8C2311yescharacteristic
87C2×C5×C3⋊C8C2311yescharacteristic
88C3×C4⋊Dic5—21no—
89C3×C4⋊Dic5C2312yes—
90C3×#681—22no—
91C2×C3×#168C2312yes—
92Dic3⋊Dic5—22no—
93(C2×D3)⋊Dic5—22no—
94Dic3×Dic5—22no—
95#5827—51no—
96C2×#950D511yescharacteristic
97#5504—51no—
98C3×#417—51no—
99#5133—51no—
100#5122—51no—
101C2×#808—51no—
102#4789—52no—
103#4788—52no—
104#4785—52no—
105#4758—52no—
106C2×C5×#41—31no—
107C2×C5×#41C2×D311yescharacteristic
108C5×#135—38no—
109C2×C5×Q16—31no—
110C2×C5×SD16—31no—
111C2×C5×SD16—31no—
112C2×C5×D8—31no—
113C22×C5×C8—31no—
114Q8×Dic5—32no—
115Q8×Dic5—32no—
116D4×Dic5—32no—
117D4×Dic5—32no—
118D4×Dic5—62no—
119D4×Dic5—62no—
120#4072—31no—
121#4072—61no—
122#4072—61no—
123C2×C4⋊Dic5—31no—
124C2×C4⋊Dic5—61no—
125C2×C4⋊Dic5—61no—
126C2×C4⋊Dic5C2×D311yescharacteristic
127C2×#681C2×D311yescharacteristic
128#3967—32no—
129#3967C2×D312yes—
130#3964—32no—
131#3964C2×D312yes—
132#3949—32no—
133#3949—32no—
134#3947—32no—
135C8×Dic5—32no—
136#2952—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×C5×D3—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—22no—
152C2×Dic15—82no—
153C2×Dic15—81no—
154C2×Dic15C2×D412yes—
155C2×Dic15C2×D412yes—
156C5×#67—24no—
157C2×C5×Dic3—21no—
158C5×D12—21no—
159C5×D12C22×C412yes—
160C4×C5×D3—24no—
161C5×Dic6—21no—
162C5×Dic6C22×C412yes—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—81no—
165D3×Dic5—82no—
166C3×#168—22no—
167C5×C3⋊C8C22×C412yes—
168C5×C3⋊C8C22×C412yes—
169C2×C3×#41C2×D511yescharacteristic
170C2×#235C2×D511yescharacteristic
171C2×C3×M16—51no—
172C2×C3×C4⋊C4—51no—
173#950Dic518yescomplemented
174Q8×Dic3—52no—
175C2×#216C2×D511yescharacteristic
176C2×#215C2×D511yescharacteristic
177D4×Dic3—52no—
178D4×Dic3—102no—
179C2×#214C2×D511yescharacteristic
180C2×#213C2×D511yescharacteristic
181C4×#67—102no—
182#926—51no—
183#926—101no—
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3—101no—
186C22×C3⋊C8C2×D511yescharacteristic
187#893—52no—
188#892—101no—
189D3×C4⋊C4—101no—
190#887—52no—
191C3×#103—52no—
192C3×#102—52no—
193#821—52no—
194#816—52no—
195#815—52no—
196C8×Dic3—52no—
197#808—52no—
198#808—52no—
199C5×#41—22no—
200C5×#41—34no—
201C5×#41—62no—
202C5×#41C4×D314yescomplemented
203C2×C5×Q8—31no—
204C2×C5×Q8C22×D311yescharacteristic
205C2×C5×D4—21no—
206C2×C5×D4—31no—
207C2×C5×D4—61no—
208C2×C5×D4C22×D311yescharacteristic
209C22×C4×C5—21no—
210C22×C4×C5—61no—
211C22×C4×C5C22×D311yescharacteristic
212C22×Dic5—21no—
213C22×Dic5—62no—
214C22×Dic5—62no—
215C22×Dic5—61no—
216C5×Q16—34no—
217C5×SD16—34no—
218C5×SD16—34no—
219C5×D8—34no—
220C2×C5×C8—34no—
221C2×C5×C8—31no—
222C2×C5×C8—31no—
223C22⋊Dic5—32no—
224C22⋊Dic5—62no—
225C22⋊Dic5—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5—31no—
228C4⋊Dic5—31no—
229C4⋊Dic5—32no—
230C4⋊Dic5—62no—
231C4⋊Dic5—62no—
232C4⋊Dic5—61no—
233C4⋊Dic5C22×D312yes—
234C4×Dic5—32no—
235C4×Dic5—62no—
236C4×Dic5—62no—
237#681—22no—
238C2×#168C22×D312yes—
239C2×#135—31no—
240#520—151no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—51no—
248#417—151no—
249#405—151no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5C4×D412yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×C5×D3—22no—
258C2×C5×D3—41no—
259C2×C5×D3—41no—
260C3×C4×C5—22no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—22no—
265Dic15—22no—
266Dic15—42no—
267C3×Dic5—42no—
268C5×Dic3—22no—
269C3×#41—22no—
270C3×#41C2×Dic514yescomplemented
271C2×C3×Q8C22×D511yescharacteristic
272C2×C3×D4—21no—
273C2×C3×D4C22×D511yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—101no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—21no—
278C22×Dic3—102no—
279C22×Dic3—101no—
280#235—22no—
281#235C2×Dic514yescomplemented
282C2×D12C22×D511yescharacteristic
283C2×C4×D3—21no—
284C2×C4×D3—102no—
285C2×Dic6C22×D511yescharacteristic
286C3×M16—102no—
287C2×C3×C8—52no—
288C3×C4⋊C4—52no—
289C3×C4⋊C4—101no—
290#217—52no—
291#217—102no—
292#216C2×Dic514yescomplemented
293#215C2×Dic514yescomplemented
294#214C2×Dic514yescomplemented
295#213C2×Dic514yescomplemented
296(C2×D3)⋊C4—102no—
297C4⋊Dic3—51no—
298C4⋊Dic3—51no—
299C4⋊Dic3—52no—
300C4⋊Dic3—102no—
301C4⋊Dic3—101no—
302Dic3⋊C4—102no—
303C4×Dic3—52no—
304C4×Dic3—102no—
305C4×Dic3—102no—
306C2×C3⋊C8C2×Dic514yescomplemented
307C2×C3⋊C8C22×D511yescharacteristic
308C2×C3⋊C8C22×D511yescharacteristic
309C23×C5—21no—
310C23×C5—61no—
311C23×C5D3×D411yescharacteristic
312C5×Q8—21no—
313C5×Q8—32no—
314C5×Q8—61no—
315C5×Q8C2×C4×D312yes—
316C5×D4—24no—
317C5×D4—21no—
318C5×D4—32no—
319C5×D4—64no—
320C5×D4—61no—
321C5×D4C2×C4×D312yes—
322C2×C4×C5—21no—
323C2×C4×C5—24no—
324C2×C4×C5—61no—
325C2×C4×C5—64no—
326C2×C4×C5C2×C4×D312yes—
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5#23712yes—
329C2×C4×C5C23×D311yescharacteristic
330C2×Dic5—22no—
331C2×Dic5—32no—
332C2×Dic5—32no—
333C2×Dic5—62no—
334C2×Dic5—81no—
335C2×Dic5—242no—
336C2×Dic5—242no—
337C2×Dic5—241no—
338C5×C8—32no—
339C5×C8—32no—
340#168—22no—
341C2×#41—31no—
342C2×#41D3×D511yescharacteristic
343#135—38no—
344C2×Q16—31no—
345C2×SD16—31no—
346C2×SD16—31no—
347C2×D8—31no—
348C2×M16—51no—
349C22×C8—31no—
350C4×Q8—152no—
351C4×Q8—152no—
352C4×D4—152no—
353C4×D4—152no—
354C4×D4—302no—
355C4×D4—302no—
356#117—151no—
357#117—301no—
358#117—301no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—151no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4—301no—
363#106—152no—
364#106—152no—
365#103—52no—
366#103—152no—
367#102—52no—
368#102—152no—
369#97—152no—
370C4×C8—152no—
371C2×C3×C5—22no—
372C2×C3×C5—42no—
373C2×C3×C5C2×C4×D411yescharacteristic
374C2×C3×C5#57711yescharacteristic
375C2×C3×C5#57711yescharacteristic
376C5×D3—42no—
377C23×C3—21no—
378C23×C3D4×D511yescharacteristic
379C22×D3—21no—
380C3×Q8—21no—
381C3×Q8C22×Dic512yes—
382C3×D4—24no—
383C3×D4—21no—
384C3×D4C22×Dic512yes—
385C2×C3×C4—21no—
386C2×C3×C4—24no—
387C2×C3×C4—102no—
388C2×C3×C4—401no—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4#71112yes—
391C2×C3×C4C22×Dic512yes—
392C2×C3×C4C23×D511yescharacteristic
393#67—24no—
394C2×Dic3—21no—
395C2×Dic3—52no—
396C2×Dic3—52no—
397C2×Dic3—102no—
398C2×Dic3—402no—
399C2×Dic3—401no—
400D12—21no—
401D12C22×Dic512yes—
402C4×D3—24no—
403C4×D3—402no—
404Dic6—21no—
405Dic6C22×Dic512yes—
406C3×C8—102no—
407C3⋊C8C22×Dic512yes—
408C3⋊C8C22×Dic512yes—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—22no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—62no—
415C22×C5—121no—
416C22×C5—121no—
417C22×C5#67⋊C412yes—
418C22×C5C2×D3×D411yescharacteristic
419C4×C5—22no—
420C4×C5—62no—
421C4×C5#67⋊C412yes—
422C4×C5C22×C4×D311yescharacteristic
423C4×C5C2×#23711yescharacteristic
424Dic5—42no—
425Dic5—62no—
426Dic5—62no—
427Dic5—122no—
428#41—22no—
429#41—34no—
430#41—62no—
431#41D3×Dic514yescomplemented
432C2×Q8—31no—
433C2×Q8C2×D3×D511yescharacteristic
434C2×D4—21no—
435C2×D4—31no—
436C2×D4—61no—
437C2×D4C2×D3×D511yescharacteristic
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—101no—
441C22×C4—302no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—34no—
446SD16—34no—
447SD16—34no—
448D8—34no—
449M16—102no—
450C2×C8—34no—
451C2×C8—31no—
452C2×C8—31no—
453C2×C8—52no—
454C4⋊C4—52no—
455C4⋊C4—101no—
456C4⋊C4—151no—
457C4⋊C4—151no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—152no—
463C22⋊C4—302no—
464C22⋊C4—302no—
465C42—152no—
466C42—302no—
467C42—302no—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3D4×Dic512yes—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—22no—
477C2×D3—41no—
478C2×D3—41no—
479C3×C4—22no—
480C3×C4—202no—
481C3×C4D4×Dic512yes—
482C3×C4C2×#71111yescharacteristic
483C3×C4C23×Dic511yescharacteristic
484Dic3—22no—
485Dic3—102no—
486Dic3—102no—
487Dic3—202no—
488C2×C5—22no—
489C2×C5—42no—
490C2×C5—122no—
491C2×C5C2×#67⋊C411yescharacteristic
492C2×C5#577511yescharacteristic
493C2×C5#577811yescharacteristic
494C23—21no—
495C23—61no—
496C23#679011yescharacteristic
497Q8—21no—
498Q8—32no—
499Q8—61no—
500Q8C2×D3×Dic512yes—
501D4—24no—
502D4—21no—
503D4—32no—
504D4—64no—
505D4—61no—
506D4C2×D3×Dic512yes—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—61no—
510C2×C4—64no—
511C2×C4—102no—
512C2×C4—152no—
513C2×C4—152no—
514C2×C4—302no—
515C2×C4—401no—
516C2×C4—1202no—
517C2×C4—1202no—
518C2×C4—1201no—
519C2×C4#678012yes—
520C2×C4C2×D3×Dic512yes—
521C2×C4#679011yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—32no—
524C8—32no—
525C8—102no—
526C2×C3—22no—
527C2×C3—42no—
528C2×C3#6610411yescharacteristic
529C2×C3#6610411yescharacteristic
530C2×C3C2×D4×Dic511yescharacteristic
531D3—42no—
532C5#7886911yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22—62no—
539C22—121no—
540C22—121no—
541C22#67⋊Dic512yes—
542C22C2×#679011yescharacteristic
543C4—22no—
544C4—62no—
545C4—202no—
546C4—302no—
547C4—302no—
548C4—602no—
549C4#67⋊Dic512yes—
550C4C2×#678011yescharacteristic
551C4C22×D3×Dic511yescharacteristic
552C3#1061563011yescharacteristic, complemented, Sylow
553C2—22no—
554C2—42no—
555C2—122no—
556C2#1175533111yescharacteristic
557C2#1175535411yescharacteristic
558C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#950C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756586C2semidirect
3. #11754492C2semidirect
4. C3×#65521C2semidirect
5. #11749266C2semidirect
6. #11749240C2semidirect
7. #11749019C2semidirect
8. #11748996C2semidirect
9. C2×#90987C2semidirect
10. #11748390C2semidirect
11. #11748326C2semidirect
22. C5×#950C4semidirect
48. #65521D3semidirect
56. C3×C5×#41C2×C4semidirect
66. C5×#235C2×C4semidirect
81. C5×#216C2×C4semidirect
82. C5×#215C2×C4semidirect
83. C5×#214C2×C4semidirect
84. C5×#213C2×C4semidirect
85. C2×C5×C3⋊C8C2×C4semidirect
173. #950Dic5semidirect
202. C5×#41C4×D3semidirect
270. C3×#41C2×Dic5semidirect
281. #235C2×Dic5semidirect
292. #216C2×Dic5semidirect
293. #215C2×Dic5semidirect
294. #214C2×Dic5semidirect
295. #213C2×Dic5semidirect
306. C2×C3⋊C8C2×Dic5semidirect
431. #41D3×Dic5semidirect
468. C3×C5#2952semidirect
532. C5#78869semidirect
552. C3#10615630semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×C5×#9502
#117544922
C3×#655212
#117492662
#117492402
#117490192
#117489962
C2×#909872
#117483902
#117483262
#106156303
#788695