Finite Group Databasebeta

← #14430239

Subgroups — #14430239

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5728C211yesmaximal, characteristic, complemented
2C4×#6765C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4C3×#65376C211yesmaximal, characteristic, complemented
5#11747502C212yesmaximal
6#11747435C212yesmaximal, complemented
7#11747290C212yesmaximal, complemented
8#11747251C212yesmaximal, complemented
9D3×C4⋊#168C211yesmaximal, characteristic, complemented
10#11746963C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10615080—31nomaximal, Hall
13C2×#6765C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#946—21no—
17C5×Q8×Dic3—21no—
18C5×#897—21no—
19C5×#892C2212yes—
20C5×#890C2212yes—
21C5×#887—21no—
22C42×C5×D3C2211yescharacteristic
23C5×#869C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91441—21no—
26C4×#1201—21no—
27Dic3×D20C2211yescharacteristic
28#91393—21no—
29C4×D5×Dic3—21no—
30#91340C2211yescharacteristic
31#91338C2211yescharacteristic
32C2×D3×#168C2212yes—
33#91094C2212yes—
34#91092C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C3×#3941C2212yes—
37C3×#3939C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90986C2212yes—
41Dic3⋊#168C2212yes—
42#90975C2212yes—
43#90964C2212yes—
44#80964—51nomaximal, Hall
45C5×#533—31no—
46C4×#709—31no—
47#65383—31no—
48#65380—31no—
49#65376D311yescharacteristic, complemented
50#65373—31no—
51#65355—32no—
52#65352—32no—
53#65291—32no—
54#65287—32no—
55C2×C4⋊#168—31no—
56C2×C3×C5×Q8—21no—
57C2×Dic30C2311yescharacteristic
58C2×C4×C5×D3D411yescharacteristic
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3C2311yescharacteristic
61C2×C5×Dic6—21no—
62C2×C3×D20C2311yescharacteristic
63C2×C3×C4×D5—21no—
64C2×#1201—21no—
65C2×D5×Dic3—21no—
66C2×D5×Dic3—21no—
67#6765—22no—
68#6765Q814yescomplemented
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15C2311yescharacteristic
73#6712—21no—
74C4×Dic15—21no—
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—22no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3—22no—
79C5×C4⋊Dic3C2312yes—
80C5×Dic3⋊C4—22no—
81C4×C5×Dic3—22no—
82C4×C5×Dic3D411yescharacteristic
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3C2311yescharacteristic
85C3×#685—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C2×C3×#168C2312yes—
88#6669—21no—
89(C2×D3)⋊Dic5—21no—
90#6665—21no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93D3×#168—24no—
94#5728D511yescharacteristic, complemented
95C4×#237—51no—
96C3×#474—51no—
97#5094—51no—
98#5008—51no—
99#4880—52no—
100#4877—52no—
101#4850—51no—
102D3×C4⋊C8—51no—
103#4772—52no—
104#4766—52no—
105C2×#709—31no—
106C5×C4⋊Q8—31no—
107C5×C4⋊Q8C2×D311yescharacteristic
108C5×#125—32no—
109C5×C22⋊Q8—61no—
110C5×C22⋊Q8—61no—
111C4×C5×Q8—61no—
112C4×C5×Q8—61no—
113C5×#117—32no—
114C2×C42×C5—31no—
115C4×C22⋊D5—61no—
116C4×C22⋊D5—61no—
117#4072—31no—
118C22×#168—32no—
119C4×D20—31no—
120C4×D20C2×D311yescharacteristic
121#4018—61no—
122C42×D5—61no—
123C4×Dic10—31no—
124C4×Dic10—31no—
125#3942—32no—
126#3942—32no—
127#3941—32no—
128#3941C2×D312yes—
129#3940—32no—
130#3940—32no—
131#3939—32no—
132#3939C2×D312yes—
133C4⋊#168—31no—
134C4⋊#168—32no—
135C4⋊#168C2×D311yescharacteristic
136#3076—151noSylow
137C22×C5×D3C2×D411yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—42no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146Dic30—21no—
147Dic30C2×Q812yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C2×D411yescharacteristic
150C2×C5×Dic3C2×D411yescharacteristic
151C2×C5×Dic3C2×D411yescharacteristic
152C4×C5×D3—22no—
153C4×C5×D3—41no—
154C4×C5×D3C2×Q812yes—
155C4×C5×D3#4112yes—
156C5×Dic6—42no—
157C2×C3×Dic5—21no—
158C3×D20—21no—
159C3×D20C2×Q812yes—
160C3×C4×D5—42no—
161#1201—24no—
162D5×Dic3—24no—
163D5×Dic3—42no—
164C3⋊#168—22no—
165C3×#168—22no—
166C2×#237—51no—
167C3×C4⋊Q8C2×D511yescharacteristic
168C3×C4×D4—51no—
169#946—21no—
170Q8×Dic3—21no—
171D4×Dic3—51no—
172C4×#67—101no—
173C2×C4×Dic3—101no—
174C2×D3×C8—52no—
175#897—21no—
176#892—51no—
177#892C2×D512yes—
178#890C2×D512yes—
179#887—21no—
180#887—51no—
181#67⋊C4—101no—
182#877—101no—
183C42×D3C2×D511yescharacteristic
184#869C2×D511yescharacteristic
185C4×Dic6—51no—
186C3×#107—52no—
187C3×C4⋊C8—51no—
188C3×#102—52no—
189#832—52no—
190#818—52no—
191#816—52no—
192Dic3⋊C8—52no—
193#810—52no—
194#808—52no—
195#808—52no—
196C4⋊(C3⋊C8)—51no—
197C2×C5×Q8—21no—
198C2×C5×Q8—61no—
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—31no—
202C2×C22⋊D5—61no—
203#709—34no—
204#709—62no—
205C2×D20C22×D311yescharacteristic
206C2×C4×D5—21no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—62no—
213C5×C4⋊C4—62no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—62no—
217C42×C5—31no—
218C42×C5—31no—
219C42×C5—31no—
220C42×C5—62no—
221C42×C5C22×D311yescharacteristic
222C22⋊Dic5—61no—
223#685—21no—
224#685—61no—
225C4⋊Dic5—31no—
226C4⋊Dic5C22×D311yescharacteristic
227#683—61no—
228#683—61no—
229C4×Dic5—61no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C2×#168—32no—
233C2×#168—64no—
234C2×#168C22×D312yes—
235#533—31no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475—151no—
242#474—51no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×C5×D3—21no—
248C2×C5×D3—21no—
249C2×C5×D3C22⋊Q812yes—
250C2×C3×D5—22no—
251C2×C3×D5—41no—
252C2×C3×D5—41no—
253C3×C4×C5—21no—
254C3×C4×C5—42no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—22no—
259Dic15—41no—
260C3×Dic5—41no—
261C5×Dic3—21no—
262C5×Dic3—21no—
263C5×Dic3—42no—
264C5×Dic3C22⋊Q812yes—
265C2×C3×Q8—21no—
266C2×C3×D4—51no—
267C22×C3×C4—101no—
268C2×#67—101no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271#237—54no—
272#237—102no—
273C2×C4×D3C22⋊D511yescharacteristic
274C2×C4×D3C22⋊D511yescharacteristic
275C2×C4×D3C22×D511yescharacteristic
276C2×Dic6—21no—
277C2×Dic6—51no—
278C2×C3×C8—52no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4C22×D512yes—
282C3×C22⋊C4—101no—
283C3×C42C22×D511yescharacteristic
284#217—101no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—101no—
287C4⋊Dic3—21no—
288C4⋊Dic3—22no—
289C4⋊Dic3—51no—
290C4⋊Dic3C22×D512yes—
291Dic3⋊C4—22no—
292Dic3⋊C4—101no—
293Dic3⋊C4—101no—
294C4×Dic3—22no—
295C4×Dic3—101no—
296C4×Dic3—101no—
297C4×Dic3—101no—
298C4×Dic3C22⋊D511yescharacteristic
299C4×Dic3C22⋊D511yescharacteristic
300C4×Dic3C22×D511yescharacteristic
301C2×C3⋊C8—52no—
302D3×C8—104no—
303C23×C5—31no—
304C22×D5—21no—
305C5×Q8—42no—
306C5×Q8—122no—
307C2×C4×C5—22no—
308C2×C4×C5—31no—
309C2×C4×C5—32no—
310C2×C4×C5—32no—
311C2×C4×C5—31no—
312C2×C4×C5—31no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—121no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C22⋊D5—64no—
320C2×Dic5—21no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323D20—21no—
324D20D3×Q812yes—
325C4×D5—42no—
326C4×D5—64no—
327C4×D5—122no—
328Dic10—32no—
329Dic10—61no—
330#168—22no—
331#168—62no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—31no—
335C4⋊Q8D3×D511yescharacteristic
336#125—32no—
337C22⋊Q8—61no—
338C22⋊Q8—61no—
339C4×Q8—61no—
340C4×Q8—61no—
341C4×Q8—151no—
342C4×Q8—151no—
343C4×D4—51no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—32no—
348#117—151no—
349#117—301no—
350C2×C42—31no—
351C2×C42—301no—
352#107—52no—
353#107—152no—
354#106—152no—
355#106—152no—
356C4⋊C8—51no—
357C4⋊C8—152no—
358C4⋊C8—151no—
359#103—152no—
360#103—152no—
361#102—52no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366C3×D5—42no—
367C5×D3—22no—
368C23×C3—101no—
369C22×D3C2×C22⋊D511yescharacteristic
370C3×Q8—42no—
371C3×D4—52no—
372C3×D4—101no—
373C2×C3×C4—22no—
374C2×C3×C4—101no—
375C2×C3×C4—202no—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—104no—
380C2×Dic3—22no—
381C2×Dic3—101no—
382C2×Dic3—104no—
383C2×Dic3—101no—
384C2×Dic3—202no—
385C2×Dic3C2×C22⋊D511yescharacteristic
386C2×Dic3C2×C22⋊D511yescharacteristic
387C2×Dic3C2×C22⋊D511yescharacteristic
388C4×D3—22no—
389C4×D3—41no—
390C4×D3Q8×D512yes—
391C4×D3#71312yes—
392Dic6—42no—
393Dic6—52no—
394Dic6—101no—
395C3×C8—102no—
396C3⋊C8—102no—
397C22×C5—32no—
398C22×C5—61no—
399C22×C5—61no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C4×C5—21no—
405C4×C5—32no—
406C4×C5—42no—
407C4×C5—61no—
408C4×C5—61no—
409C4×C5—122no—
410C4×C5#91212yes—
411C4×C5C2×D3×Q811yescharacteristic
412C4×C5D3×#4111yescharacteristic
413Dic5—41no—
414Dic5—62no—
415Dic5—121no—
416#41—154no—
417#41—302no—
418C2×Q8—21no—
419C2×Q8—61no—
420C2×Q8—151no—
421C2×D4—51no—
422C2×D4—301no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—101no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—52no—
430C2×C8—152no—
431C2×C8—304no—
432C4⋊C4—21no—
433C4⋊C4—32no—
434C4⋊C4—51no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—151no—
439C4⋊C4—301no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D512yes—
442C22⋊C4—62no—
443C22⋊C4—101no—
444C22⋊C4—301no—
445C22⋊C4—301no—
446C42—31no—
447C42—31no—
448C42—31no—
449C42—62no—
450C42—301no—
451C42—301no—
452C42—301no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—102no—
456C22×C3—201no—
457C22×C3—201no—
458C22×C3C22×C22⋊D511yescharacteristic
459C2×D3—21no—
460C2×D3—21no—
461C2×D3#409212yes—
462C3×C4—21no—
463C3×C4—42no—
464C3×C4—201no—
465C3×C4#409612yes—
466C3×C4C2×Q8×D511yescharacteristic
467C3×C4C2×#71311yescharacteristic
468Dic3—21no—
469Dic3—21no—
470Dic3—42no—
471Dic3—102no—
472Dic3—201no—
473Dic3#409212yes—
474C2×C5—62no—
475C2×C5D3×C22⋊Q811yescharacteristic
476C2×C5C2×#91211yescharacteristic
477C2×C5#577711yescharacteristic
478D5—42no—
479C23—31no—
480C23—101no—
481Q8—42no—
482Q8—122no—
483Q8—152no—
484Q8—301no—
485D4—52no—
486D4—101no—
487D4—304no—
488C2×C4—22no—
489C2×C4—31no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—31no—
493C2×C4—31no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—101no—
497C2×C4—121no—
498C2×C4—202no—
499C2×C4—304no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—602no—
503C2×C4D3×C22⋊D511yescharacteristic
504C2×C4D3×C22⋊D511yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—102no—
507C8—302no—
508C2×C3—202no—
509C2×C3C2×#409211yescharacteristic
510C2×C3C2×#409611yescharacteristic
511C2×C3#6615611yescharacteristic
512D3—22no—
513C5#8096411yescharacteristic, complemented, Sylow
514C22—32no—
515C22—61no—
516C22—61no—
517C22—102no—
518C22—201no—
519C22—201no—
520C22C2×D3×C22⋊D511yescharacteristic
521C4—21no—
522C4—32no—
523C4—42no—
524C4—61no—
525C4—61no—
526C4—122no—
527C4—201no—
528C4—302no—
529C4—601no—
530C4#9149312yes—
531C4D3×Q8×D511yescharacteristic
532C4D3×#71311yescharacteristic
533C3#1061508011yescharacteristic, complemented, Sylow
534C2—62no—
535C2—202no—
536C2C2×#9149311yescharacteristic
537C2#1175509011yescharacteristic
538C2D3×#409211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5728C2semidirect
3. #11751195C2semidirect
4. C3×#65376C2semidirect
6. #11747435C2semidirect
7. #11747290C2semidirect
8. #11747251C2semidirect
9. D3×C4⋊#168C2semidirect
10. #11746963C2semidirect
11. #11746880C2semidirect
49. #65376D3semidirect
68. #6765Q8semidirect
94. #5728D5semidirect
454. C3×C5#3076semidirect
513. C5#80964semidirect
533. C3#10615080semidirect

Maximal subgroups

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

subgroupindex
C5×#57282
C4×#67652
#117511952
C3×#653762
#117475022
#117474352
#117472902
#117472512
D3×C4⋊#1682
#117469632
#117468802
#106150803
#809645