Finite Group Databasebeta

← #14430270

Subgroups — #14430270

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
1C4×C5×#237C211yesmaximal, characteristic
2#11752478C211yesmaximal, characteristic, complemented
3#11751108C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749088C212yesmaximal, complemented
6#11748965C212yesmaximal
7#11747437C212yesmaximal, complemented
8#11747396C212yesmaximal, complemented
9D3×C4⋊#168C211yesmaximal, characteristic, complemented
10#11746959C211yesmaximal, characteristic, complemented
11#11746945C211yesmaximal, characteristic, complemented
12#10614238—31nomaximal, Hall
13C2×C5×#237C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15#91758C2211yescharacteristic
16C5×D4×Dic3C2211yescharacteristic
17C4×C5×#67—21no—
18C2×C4×C5×Dic3—21no—
19C5×#892C2211yescharacteristic
20C5×#887C2211yescharacteristic
21C5×#67⋊C4—21no—
22C5×#877—21no—
23C42×C5×D3C2211yescharacteristic
24C4×C5×Dic6C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91381C2212yes—
27#91369—21no—
28#91365—21no—
29#91340—21no—
30#91338C2212yes—
31Dic3×Dic10—21no—
32C2×D3×#168C2212yes—
33#91116C2212yes—
34#91091C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C3×#3964C2212yes—
37C3×#3940C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90989C2212yes—
40#90985C2212yes—
41Dic3⋊#168C2212yes—
42#90973C2212yes—
43#90972C2212yes—
44#81059—51nomaximal, Hall
45C4×C5×#41—31no—
46#65804—31no—
47#65522—32no—
48#65311—32no—
49#65310—31no—
50#65309—31no—
51#65298—32no—
52#65297D311yescharacteristic, complemented
53#65296—31no—
54#65287—32no—
55C2×C4⋊#168—31no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C2×Dic30—21no—
59C2×C5×#67—21no—
60C22×C5×Dic3—21no—
61C22×C5×Dic3—21no—
62C5×#237—22no—
63C5×#237Q814yescomplemented
64C2×C4×C5×D3D411yescharacteristic
65C2×C4×C5×D3D411yescharacteristic
66C2×C4×C5×D3C2311yescharacteristic
67C2×C5×Dic6C2311yescharacteristic
68C2×C3×Dic10—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C2×C3⋊#168C2312yes—
75C5×#217—21no—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×Dic3⋊C4—21no—
79C5×Dic3⋊C4—21no—
80C4×C5×Dic3—21no—
81C4×C5×Dic3—21no—
82C4×C5×Dic3—21no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C2×C3×#168C2312yes—
89#6669—22no—
90#6668—22no—
91(C2×D3)⋊Dic5—22no—
92Dic3×Dic5—22no—
93D3×#168—24no—
94#5728—51no—
95C4×#237D511yescharacteristic
96C3×#476—51no—
97#5091—51no—
98#5007—51no—
99#4860—52no—
100#4857—52no—
101#4851—51no—
102D3×C4⋊C8—51no—
103#4772—52no—
104#4763—52no—
105C2×C5×#41—31no—
106C4×C5×Q8—31no—
107C4×C5×Q8—31no—
108C4×C5×D4—31no—
109C4×C5×D4—61no—
110C4×C5×D4—61no—
111C4×C5×D4C2×D311yescharacteristic
112C5×#117—31no—
113C5×#117—61no—
114C2×C42×C5—31no—
115C2×C42×C5—61no—
116#4072—32no—
117#4070—61no—
118#4070—61no—
119C22×#168—32no—
120#4016—32no—
121#4015—31no—
122#4015C2×D311yescharacteristic
123C4×Dic10—61no—
124C4×Dic10—61no—
125#3967—32no—
126#3967—32no—
127#3964—32no—
128#3964C2×D312yes—
129#3940—32no—
130#3940C2×D312yes—
131#3939—32no—
132#3939—32no—
133C4⋊#168—31no—
134C4⋊#168—32no—
135C4⋊#168C2×D311yescharacteristic
136#3076—151noSylow
137C23×C3×C5—21no—
138C22×C5×D3C2×D411yescharacteristic
139C3×C5×D4—21no—
140C3×C5×D4C2×Q812yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C5×#67—24no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—24no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—42no—
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C4×C5×D3—22no—
157C4×C5×D3—41no—
158C4×C5×D3C2×Q812yes—
159C4×C5×D3#4112yes—
160C5×Dic6—21no—
161C5×Dic6C2×Q812yes—
162C2×C3×Dic5—22no—
163C3×Dic10—42no—
164C3⋊#168—22no—
165C3×#168—22no—
166C2×#237C2×D511yescharacteristic
167C3×C4⋊Q8—51no—
168C3×C4×D4C2×D511yescharacteristic
169#946—101no—
170Q8×Dic3—101no—
171D4×Dic3C2×D511yescharacteristic
172C4×#67—21no—
173C2×C4×Dic3—21no—
174C2×D3×C8—52no—
175#897—101no—
176#892—52no—
177#892C2×D511yescharacteristic
178#890—52no—
179#887—101no—
180#887C2×D511yescharacteristic
181#67⋊C4—21no—
182#877—21no—
183C42×D3C2×D511yescharacteristic
184#869—51no—
185C4×Dic6C2×D511yescharacteristic
186C3×#106—52no—
187C3×C4⋊C8—51no—
188C3×#102—52no—
189#832—52no—
190#817—52no—
191#816—52no—
192Dic3⋊C8—52no—
193#810—52no—
194#807—52no—
195#807—52no—
196C4⋊(C3⋊C8)—51no—
197C5×#41—34no—
198C5×#41—62no—
199C2×C5×Q8—31no—
200C2×C5×D4—61no—
201C2×C5×D4C22×D311yescharacteristic
202C22×C4×C5—21no—
203C22×C4×C5—31no—
204C22×C4×C5—31no—
205C22×C4×C5—31no—
206C22×C4×C5—61no—
207C22×C4×C5—61no—
208C2×Dic10—21no—
209C2×Dic10—61no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C22⋊C4—21no—
215C5×C22⋊C4—61no—
216C5×C22⋊C4—61no—
217C42×C5—31no—
218C42×C5—31no—
219C42×C5—31no—
220C42×C5—61no—
221C42×C5—61no—
222C42×C5—61no—
223C42×C5C22×D311yescharacteristic
224C22⋊Dic5—62no—
225C4⋊Dic5—21no—
226C4⋊Dic5—32no—
227C4⋊Dic5—61no—
228C4⋊Dic5C22×D312yes—
229#683—62no—
230#683—62no—
231C4×Dic5—62no—
232C2×#168—32no—
233C2×#168—64no—
234C2×#168C22×D312yes—
235#533—151no—
236C4×#41—31no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—51no—
241#475—151no—
242#474—151no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5—22no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5C22×D411yescharacteristic
250C2×C5×D3—21no—
251C2×C5×D3—21no—
252C2×C5×D3C22⋊Q812yes—
253C3×C4×C5—21no—
254C3×C4×C5—41no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—42no—
259C3×Dic5—42no—
260C5×Dic3—22no—
261C5×Dic3—21no—
262C5×Dic3—21no—
263C5×Dic3—41no—
264C5×Dic3C22⋊Q812yes—
265C2×C3×Q8—101no—
266C2×C3×D4C22×D511yescharacteristic
267C22×C3×C4—21no—
268C2×#67—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271#237—22no—
272#237Dic1014yescomplemented
273C2×C4×D3C22⋊D511yescharacteristic
274C2×C4×D3C22⋊D511yescharacteristic
275C2×C4×D3C22×D511yescharacteristic
276C2×Dic6—101no—
277C2×Dic6C22×D511yescharacteristic
278C2×C3×C8—52no—
279C3×C4⋊C4—52no—
280C3×C4⋊C4—101no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C22⋊C4—21no—
283C3×C42C22×D511yescharacteristic
284#217—21no—
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—102no—
287C4⋊Dic3—52no—
288C4⋊Dic3—101no—
289C4⋊Dic3—102no—
290C4⋊Dic3C22×D511yescharacteristic
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—102no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—102no—
298C4×Dic3C22⋊D511yescharacteristic
299C4×Dic3C22⋊D511yescharacteristic
300C4×Dic3C22×D511yescharacteristic
301C2×C3⋊C8—52no—
302D3×C8—104no—
303C23×C5—21no—
304C23×C5—31no—
305C5×Q8—32no—
306C5×Q8—61no—
307C5×D4—21no—
308C5×D4—64no—
309C5×D4D3×Q812yes—
310C2×C4×C5—21no—
311C2×C4×C5—31no—
312C2×C4×C5—32no—
313C2×C4×C5—32no—
314C2×C4×C5—31no—
315C2×C4×C5—31no—
316C2×C4×C5—42no—
317C2×C4×C5—64no—
318C2×C4×C5—61no—
319C2×C4×C5—62no—
320C2×C4×C5—61no—
321C2×C4×C5—121no—
322C2×C4×C5—122no—
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—22no—
327C2×Dic5—62no—
328Dic10—42no—
329Dic10—122no—
330#168—22no—
331#168—62no—
332C2×#41—31no—
333C22×C8—152no—
334C4⋊Q8—51no—
335C4⋊Q8—151no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—31no—
340C4×Q8—31no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—31no—
344C4×D4—61no—
345C4×D4—61no—
346C4×D4D3×D511yescharacteristic
347#117—31no—
348#117—61no—
349#117—152no—
350C2×C42—31no—
351C2×C42—61no—
352#107—152no—
353#107—152no—
354#106—52no—
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×C5—42no—
364C2×C3×C5C2×C22⋊Q811yescharacteristic
365C2×C3×C5C2×#13511yescharacteristic
366C2×C3×C5#57511yescharacteristic
367C5×D3—22no—
368C23×C3—21no—
369C22×D3C2×C22⋊D511yescharacteristic
370C3×Q8—202no—
371C3×D4—21no—
372C3×D4C2×Dic1012yes—
373C2×C3×C4—21no—
374C2×C3×C4—42no—
375C2×C3×C4—102no—
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—24no—
380C2×Dic3—21no—
381C2×Dic3—24no—
382C2×Dic3—21no—
383C2×Dic3—42no—
384C2×Dic3—102no—
385C2×Dic3C2×C22⋊D511yescharacteristic
386C2×Dic3C2×C22⋊D511yescharacteristic
387C2×Dic3C2×C22⋊D511yescharacteristic
388C4×D3—22no—
389C4×D3—41no—
390C4×D3C2×Dic1012yes—
391C4×D3#70912yes—
392Dic6—21no—
393Dic6—202no—
394Dic6C2×Dic1012yes—
395C3×C8—102no—
396C3⋊C8—102no—
397C22×C5—22no—
398C22×C5—32no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—61no—
402C22×C5—61no—
403C22×C5C2×D3×D411yescharacteristic
404C4×C5—21no—
405C4×C5—32no—
406C4×C5—41no—
407C4×C5—61no—
408C4×C5—61no—
409C4×C5—62no—
410C4×C5—121no—
411C4×C5#91612yes—
412C4×C5C2×D3×Q811yescharacteristic
413C4×C5D3×#4111yescharacteristic
414Dic5—42no—
415Dic5—122no—
416#41—34no—
417#41—62no—
418C2×Q8—31no—
419C2×Q8—101no—
420C2×Q8—301no—
421C2×D4—61no—
422C2×D4C2×D3×D511yescharacteristic
423C22×C4—21no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—61no—
428C22×C4—61no—
429C2×C8—52no—
430C2×C8—152no—
431C2×C8—304no—
432C4⋊C4—31no—
433C4⋊C4—52no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—101no—
437C4⋊C4—152no—
438C4⋊C4—302no—
439C4⋊C4—302no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D511yescharacteristic
442C22⋊C4—21no—
443C22⋊C4—61no—
444C22⋊C4—61no—
445C22⋊C4—302no—
446C42—31no—
447C42—31no—
448C42—31no—
449C42—61no—
450C42—61no—
451C42—61no—
452C42—302no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—22no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3C22×C22⋊D511yescharacteristic
459C2×D3—21no—
460C2×D3—21no—
461C2×D3#407012yes—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—202no—
465C3×C4#409612yes—
466C3×C4C22×Dic1011yescharacteristic
467C3×C4C2×#70911yescharacteristic
468Dic3—22no—
469Dic3—21no—
470Dic3—21no—
471Dic3—41no—
472Dic3—202no—
473Dic3#407012yes—
474C2×C5—42no—
475C2×C5—62no—
476C2×C5D3×C22⋊Q811yescharacteristic
477C2×C5C2×#91611yescharacteristic
478C2×C5#577311yescharacteristic
479C23—21no—
480C23—31no—
481Q8—32no—
482Q8—61no—
483Q8—202no—
484Q8—602no—
485D4—21no—
486D4—64no—
487D4D3×Dic1012yes—
488C2×C4—21no—
489C2×C4—31no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—31no—
493C2×C4—31no—
494C2×C4—42no—
495C2×C4—64no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—102no—
500C2×C4—121no—
501C2×C4—122no—
502C2×C4—302no—
503C2×C4D3×C22⋊D511yescharacteristic
504C2×C4D3×C22⋊D511yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—102no—
507C8—302no—
508C2×C3—42no—
509C2×C3C2×#407011yescharacteristic
510C2×C3C2×#409611yescharacteristic
511C2×C3#6615611yescharacteristic
512D3—22no—
513C5#8105911yescharacteristic, complemented, Sylow
514C22—22no—
515C22—32no—
516C22—41no—
517C22—41no—
518C22—61no—
519C22—61no—
520C22C2×D3×C22⋊D511yescharacteristic
521C4—21no—
522C4—32no—
523C4—41no—
524C4—61no—
525C4—62no—
526C4—61no—
527C4—121no—
528C4—202no—
529C4—602no—
530C4#9149512yes—
531C4C2×D3×Dic1011yescharacteristic
532C4D3×#70911yescharacteristic
533C3#1061423811yescharacteristic, complemented, Sylow
534C2—42no—
535C2—62no—
536C2D3×#407011yescharacteristic
537C2C2×#9149511yescharacteristic
538C2#1175534511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#237C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752478C2semidirect
3. #11751108C2semidirect
4. C3×#65297C2semidirect
5. #11749088C2semidirect
7. #11747437C2semidirect
8. #11747396C2semidirect
9. D3×C4⋊#168C2semidirect
10. #11746959C2semidirect
11. #11746945C2semidirect
52. #65297D3semidirect
63. C5×#237Q8semidirect
272. #237Dic10semidirect
454. C3×C5#3076semidirect
513. C5#81059semidirect
533. C3#10614238semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#2372
#117524782
#117511082
C3×#652972
#117490882
#117489652
#117474372
#117473962
D3×C4⋊#1682
#117469592
#117469452
#106142383
#810595