Finite Group Databasebeta

← #14417258

Subgroups — #14417258

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756571C211yesmaximal, characteristic, complemented
2C2×C5×#942C211yesmaximal, characteristic
3#11754492C211yesmaximal, characteristic
4C2×C3×#3967C211yesmaximal, characteristic, complemented
5#11749266C212yesmaximal, complemented
6#11749265C212yesmaximal, complemented
7#11749242C212yesmaximal, complemented
8#11749240C212yesmaximal, complemented
9#11748453C211yesmaximal, characteristic, complemented
10#11748388C211yesmaximal, characteristic
11#11748324C211yesmaximal, characteristic, complemented
12#10615696—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15Q8×Dic15—21no—
16Q8×Dic15—21no—
17Q8×Dic15C2212yes—
18Q8×Dic15C2212yes—
19#91815—22no—
20#91815C2211yescharacteristic
21#91815C2211yescharacteristic
22C2×C5×#216C2212yes—
23C5×#942C418yescomplemented
24C2×C5×#215C2212yes—
25C2×C5×#208C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28Dic5×#67—22no—
29#91435C2212yes—
30D3×C4⋊Dic5—21no—
31#91344C2212yes—
32#91338—21no—
33C3×#3967C2212yes—
34C3×#3967C2212yes—
35#90990C2212yes—
36#90987C2212yes—
37#90973C2211yescharacteristic
38#90973C2211yescharacteristic
39#90967C2211yescharacteristic
40#90967C2211yescharacteristic
41#90954C2212yes—
42#90951C2212yes—
43#78774—51nomaximal, Hall
44C2×C5×#137—31no—
45#66161—31no—
46#66146—31no—
47#65522—31no—
48C2×#3967D311yescharacteristic, complemented
49#65473—32no—
50Q16×Dic5—32no—
51#65453—32no—
52SD16×Dic5—32no—
53#65411—31no—
54#65410—31no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×Q8C2×C414yescomplemented
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235C2×C414yes—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×D3×Dic5—22no—
69#6719—21no—
70#6719D412yes—
71C4⋊Dic15—22no—
72C4⋊Dic15—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77C4×Dic15—21no—
78C4×Dic15—22no—
79C4×Dic15—22no—
80C4×Dic15C2312yes—
81C5×#216C2×C418yescomplemented
82C5×#215C2×C418yescomplemented
83C5×#208C2×C414yescomplemented
84C2×C5×C3⋊C8C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87C2×C3×#168—22no—
88C2×C3×#168C2311yescharacteristic
89C2×C3×#168C2311yescharacteristic
90Dic3⋊Dic5—22no—
91(C2×D3)⋊Dic5—22no—
92Dic3×Dic5—22no—
93#5812—51no—
94C2×#942D511yescharacteristic
95#5504—51no—
96C2×C3×#103—51no—
97#5113—51no—
98#5101—51no—
99#4964—51no—
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C2×C5×#41—31no—
105C22×C5×Q8C2×D311yescharacteristic
106C5×#137—38no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C2×C5×M16—31no—
110Q8×Dic5—32no—
111Q8×Dic5—32no—
112Q8×Dic5—32no—
113Q8×Dic5—61no—
114Q8×Dic5—61no—
115D4×Dic5—32no—
116D4×Dic5—62no—
117#4072—31no—
118#4072—31no—
119#4072—61no—
120#4072—62no—
121C2×C4⋊Dic5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168C2×D311yescharacteristic
124#3967—31no—
125#3967—31no—
126#3967C2×D312yes—
127#3967C2×D312yes—
128#3964—31no—
129#3964—31no—
130#3950—32no—
131#3949—32no—
132#3947—32no—
133C8×Dic5—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C22×C414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15C2×D412yes—
149C2×Dic15C2×D412yes—
150C5×#67—24no—
151C2×C5×Dic3—21no—
152C5×D12—21no—
153C5×D12C22×C412yes—
154C4×C5×D3—24no—
155C5×Dic6—21no—
156C5×Dic6C22×C412yes—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—81no—
159D3×Dic5—82no—
160C3×#168—21no—
161C3×#168—21no—
162C5×C3⋊C8C22×C414yes—
163C22×C3×Q8C2×D511yescharacteristic
164C2×#235C2×D511yescharacteristic
165C22×C3×C8—51no—
166C2×C3×C4⋊C4—51no—
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216C2×D512yes—
172#942Dic518yescomplemented
173C2×#215C2×D512yes—
174C4×#67—102no—
175#926—51no—
176#926—51no—
177#926—102no—
178C2×#208C2×D511yescharacteristic
179#893—52no—
180#892—101no—
181D3×C4⋊C4—101no—
182#887—52no—
183C3×#103—52no—
184C3×#103—52no—
185#821—51no—
186#821—51no—
187#816—51no—
188#816—51no—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—21no—
196C2×C5×Q8—22no—
197C2×C5×Q8—31no—
198C2×C5×Q8C4×D314yescomplemented
199C2×C5×Q8C22×D312yes—
200C2×C5×D4—31no—
201C2×C5×D4—61no—
202C22×C4×C5—21no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—62no—
207C5×Q16—38no—
208C5×SD16—38no—
209C5×M16—34no—
210C2×C5×C8—32no—
211C22⋊Dic5—32no—
212C22⋊Dic5—62no—
213C22⋊Dic5—61no—
214C4⋊Dic5—21no—
215C4⋊Dic5—31no—
216C4⋊Dic5—31no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219C4⋊Dic5—62no—
220C4⋊Dic5—62no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D312yes—
223C4×Dic5—32no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5—61no—
228C2×#168—22no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231C2×#137—31no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—51no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C3×C4×C5—24no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—22no—
254Dic15—22no—
255Dic15—41no—
256Dic15—41no—
257C3×Dic5—42no—
258C5×Dic3—22no—
259C2×C3×Q8—21no—
260C2×C3×Q8—22no—
261C2×C3×Q8C2×Dic514yescomplemented
262C2×C3×Q8C22×D512yes—
263C22×C3×C4—21no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—21no—
267#235—22no—
268#235C2×Dic514yes—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—102no—
272C2×Dic6C22×D511yescharacteristic
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278#217—52no—
279#217—101no—
280#216C2×Dic518yescomplemented
281#215C2×Dic518yescomplemented
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3—102no—
289Dic3⋊C4—102no—
290C4×Dic3—52no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—101no—
295#208C2×Dic514yescomplemented
296C2×C3⋊C8C22×D512yes—
297C23×C5—61no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—24no—
300C5×Q8—22no—
301C5×Q8—32no—
302C5×Q8—61no—
303C5×Q8C2×C4×D314yes—
304C5×D4—32no—
305C5×D4—64no—
306C5×D4—61no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—61no—
310C2×C4×C5—64no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23712yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—22no—
316C2×Dic5—32no—
317C2×Dic5—32no—
318C2×Dic5—61no—
319C2×Dic5—61no—
320C2×Dic5—81no—
321C2×Dic5—242no—
322C5×C8—34no—
323#168—21no—
324#168—21no—
325C2×#41—31no—
326C22×Q8D3×D511yescharacteristic
327#137—38no—
328C2×Q16—32no—
329C2×SD16—32no—
330C2×M16—31no—
331C22×C8—51no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—151no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—52no—
348#103—52no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
362C3×Q8—22no—
363C3×Q8—24no—
364C3×Q8C22×Dic514yes—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—102no—
368C2×C3×C4—401no—
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4#71112yes—
371C2×C3×C4C22×Dic512yes—
372C2×C3×C4C23×D511yescharacteristic
373#67—24no—
374C2×Dic3—21no—
375C2×Dic3—52no—
376C2×Dic3—52no—
377C2×Dic3—101no—
378C2×Dic3—101no—
379D12—21no—
380D12C22×Dic512yes—
381C4×D3—24no—
382C4×D3—402no—
383Dic6—21no—
384Dic6C22×Dic512yes—
385C3×C8—101no—
386C3×C8—101no—
387C3⋊C8C22×Dic514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5#67⋊C412yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—24no—
396C4×C5—62no—
397C4×C5#67⋊C412yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23711yescharacteristic
400Dic5—42no—
401Dic5—62no—
402Dic5—62no—
403Dic5—121no—
404Dic5—121no—
405#41—34no—
406#41—62no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—31no—
410C2×Q8D3×Dic514yescomplemented
411C2×Q8C2×D3×D512yes—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—21no—
415C22×C4—61no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—38no—
420SD16—38no—
421M16—34no—
422C2×C8—32no—
423C2×C8—51no—
424C2×C8—51no—
425C2×C8—102no—
426C4⋊C4—52no—
427C4⋊C4—101no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—152no—
436C22⋊C4—302no—
437C22⋊C4—301no—
438C42—152no—
439C42—302no—
440C42—302no—
441C42—302no—
442C42—301no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3D4×Dic512yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—24no—
452C3×C4—202no—
453C3×C4D4×Dic512yes—
454C3×C4C2×#71111yescharacteristic
455C3×C4C23×Dic511yescharacteristic
456Dic3—22no—
457Dic3—102no—
458Dic3—102no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#576211yescharacteristic
465C2×C5#576611yescharacteristic
466C23—61no—
467C23#679011yescharacteristic
468Q8—22no—
469Q8—24no—
470Q8—32no—
471Q8—61no—
472Q8C2×D3×Dic514yes—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—61no—
479C2×C4—64no—
480C2×C4—102no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—301no—
484C2×C4—301no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4#678012yes—
488C2×C4C2×D3×Dic512yes—
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—101no—
493C8—101no—
494C2×C3—22no—
495C2×C3#6611211yescharacteristic
496C2×C3#6611311yescharacteristic
497C2×C3C2×D4×Dic511yescharacteristic
498D3—42no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#67⋊Dic512yes—
506C22C2×#679011yescharacteristic
507C4—24no—
508C4—62no—
509C4—202no—
510C4—302no—
511C4—302no—
512C4—601no—
513C4—601no—
514C4#67⋊Dic512yes—
515C4C2×#678011yescharacteristic
516C4C22×D3×Dic511yescharacteristic
517C3#1061569611yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2#1175509711yescharacteristic
521C2#1175512211yescharacteristic
522C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #11756571C2semidirect
4. C2×C3×#3967C2semidirect
5. #11749266C2semidirect
6. #11749265C2semidirect
7. #11749242C2semidirect
8. #11749240C2semidirect
9. #11748453C2semidirect
11. #11748324C2semidirect
23. C5×#942C4semidirect
48. C2×#3967D3semidirect
57. C2×C3×C5×Q8C2×C4semidirect
81. C5×#216C2×C4semidirect
82. C5×#215C2×C4semidirect
83. C5×#208C2×C4semidirect
172. #942Dic5semidirect
198. C2×C5×Q8C4×D3semidirect
261. C2×C3×Q8C2×Dic5semidirect
280. #216C2×Dic5semidirect
281. #215C2×Dic5semidirect
295. #208C2×Dic5semidirect
410. C2×Q8D3×Dic5semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10615696semidirect

Maximal subgroups

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

subgroupindex
#117565712
C2×C5×#9422
#117544922
C2×C3×#39672
#117492662
#117492652
#117492422
#117492402
#117484532
#117483882
#117483242
#106156963
#787745