Finite Group Databasebeta

← #14435438

Subgroups — #14435438

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5600C211yesmaximal, characteristic
2C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
3#11751135C211yesmaximal, characteristic
4C3×#65329C211yesmaximal, characteristic
5#11749010C212yesmaximal, complemented
6#11749006C212yesmaximal, complemented
7#11748555C211yesmaximal, characteristic, complemented
8#11748467C211yesmaximal, characteristic, complemented
9#11748337C211yesmaximal, characteristic, complemented
10#11747295C212yesmaximal, complemented
11#11747267C212yesmaximal, complemented
12#10614884—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C3×C5×#121C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C5×#936C2211yescharacteristic
17C5×#935—21no—
18C5×D4×Dic3—21no—
19C5×D4×Dic3C2211yescharacteristic
20C5×#924C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C5×#890C2211yescharacteristic
23C5×#887C2211yescharacteristic
24C5×#879—21no—
25C5×#877—21no—
26C2×C3×#687C2212yes—
27C2×#6668—21no—
28C2×Dic3×Dic5—21no—
29Dic3×Dic10—21no—
30Dic3×Dic10—21no—
31Dic3×Dic10C2212yes—
32Dic3×Dic10C2212yes—
33C2×#6661C2212yes—
34#91116C2212yes—
35#91114C2211yescharacteristic
36#91092C2212yes—
37C3×C22⋊#168C2211yescharacteristic
38C3×#3942C2212yes—
39#90988C2212yes—
40Dic3⋊#168C2212yes—
41#90973C2212yes—
42#90970C2212yes—
43#90953C2212yes—
44#80031—51nomaximal, Hall
45C5×#529—31no—
46C2×C4×Dic10—31no—
47#65352—32no—
48#65343—32no—
49#65339—31no—
50#65333—31no—
51#65329D311yescharacteristic
52#65323—31no—
53#65319—32no—
54#65307—32no—
55#65215—31no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×C5×Dic3—21no—
61C22×C5×Dic3D411yescharacteristic
62C22×C5×Dic3D411yescharacteristic
63C2×C5×Dic6C2311yescharacteristic
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10C2312yes—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C22⋊C4—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2312yes—
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×#217—21no—
75C5×#217—21no—
76C5×#217—21no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×Dic3⋊C4—21no—
80C5×Dic3⋊C4—21no—
81C5×Dic3⋊C4—21no—
82C4×C5×Dic3—21no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C3×#687—24no—
88C2×C3×#168C2312yes—
89#6668—22no—
90#6668—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6661—24no—
94C2×Q8×Dic3—51no—
95#5600D511yescharacteristic
96C3×#448—51no—
97#5228—51no—
98#5166—52no—
99#5164—52no—
100#5034—51no—
101#4796—52no—
102#4789—52no—
103#4722—51no—
104#4719—51no—
105C22×Dic10C2×D311yescharacteristic
106C5×#126—61no—
107C5×#125—31no—
108C5×#124—31no—
109C5×#123—61no—
110C5×C22⋊Q8—31no—
111C5×#121C2×D311yescharacteristic
112C4×C5×Q8—31no—
113C4×C5×D4—31no—
114C4×C5×D4—61no—
115C5×#117—61no—
116C2×C42×C5—31no—
117C2×#689—32no—
118C2×#687C2×D312yes—
119C2×C4⋊Dic5—31no—
120C2×#683—61no—
121C2×C4×Dic5—61no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C4×Dic10—61no—
125C4×Dic10—61no—
126#3967—32no—
127#3964—32no—
128C22⋊#168—31no—
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3942C2×D312yes—
132#3940—32no—
133#3939—32no—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C3×C5×D4—22no—
140C3×C5×D4—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C2×Dic15—42no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—41no—
151C2×C5×Dic3—42no—
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C5×Dic6—22no—
157C2×C3×Dic5—24no—
158C2×C3×Dic5—22no—
159C3×Dic10—24no—
160C3×Dic10—22no—
161C3×Dic10#4114yes—
162C3⋊#168—22no—
163C3×#168—22no—
164C22×C3×Q8—51no—
165C2×C3×SD16—52no—
166C3×#121C2×D511yescharacteristic
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216—52no—
172#936C2×D511yescharacteristic
173#935—21no—
174D4×Dic3—21no—
175D4×Dic3C2×D511yescharacteristic
176C2×C4⋊Dic3—51no—
177C2×C4⋊Dic3—101no—
178#924C2×D511yescharacteristic
179C2×C4×Dic3—101no—
180C2×C4×Dic3C2×D511yescharacteristic
181#890C2×D511yescharacteristic
182#887C2×D511yescharacteristic
183#879—21no—
184#877—21no—
185C3×#103—52no—
186C3×C22⋊C8—51no—
187#835—52no—
188#832—52no—
189#830—51no—
190#818—52no—
191#816—52no—
192#815—52no—
193Dic3⋊C8—52no—
194#808—52no—
195C2×C5×Q8—31no—
196C2×C5×D4—21no—
197C2×C5×D4C22×D311yescharacteristic
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C22×Dic5—61no—
204C2×Dic10—21no—
205C2×Dic10—24no—
206C2×Dic10C22×D312yes—
207C5×C4⋊C4—31no—
208C5×C4⋊C4—61no—
209C5×C4⋊C4—61no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C5×C22⋊C4—61no—
215C5×C22⋊C4—61no—
216C5×C22⋊C4—61no—
217C5×C22⋊C4—61no—
218C42×C5—31no—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—31no—
222C42×C5—61no—
223#689—64no—
224#687—24no—
225C4⋊Dic5—32no—
226C4⋊Dic5—61no—
227#683—62no—
228#683—62no—
229C4×Dic5—62no—
230C4×Dic5—62no—
231C2×#168—32no—
232C2×#168C22×D312yes—
233#529—31no—
234C2×C4×Q8—151no—
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—51no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5#13712yes—
250C22×C3×C5C22×D411yescharacteristic
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×#4112yes—
254Dic15—42no—
255C3×Dic5—24no—
256C5×Dic3—21no—
257C5×Dic3—21no—
258C5×Dic3—21no—
259C5×Dic3—21no—
260C5×Dic3—41no—
261C5×Dic3—41no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C2×C3×D4—21no—
266C2×C3×D4C22×D511yescharacteristic
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—101no—
271C22×Dic3C22⋊D511yescharacteristic
272C22×Dic3C22⋊D511yescharacteristic
273C2×Dic6C22×D511yescharacteristic
274C3×SD16—104no—
275C2×C3×C8—52no—
276C3×C4⋊C4C22×D511yescharacteristic
277C3×C22⋊C4—21no—
278#217—21no—
279#217—21no—
280#217—21no—
281#217—21no—
282#216—104no—
283C4⋊Dic3—21no—
284C4⋊Dic3—52no—
285C4⋊Dic3—101no—
286C4⋊Dic3—102no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292C4×Dic3—21no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295C4×Dic3C22⋊D511yescharacteristic
296C4×Dic3C22⋊D511yescharacteristic
297C4×Dic3C22×D511yescharacteristic
298C4×Dic3C22×D511yescharacteristic
299C2×C3⋊C8—52no—
300C23×C5—21no—
301C23×C5D3×D411yescharacteristic
302C5×Q8—62no—
303C5×D4—22no—
304C5×D4—42no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—31no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—62no—
312C2×C4×C5—61no—
313C2×C4×C5—61no—
314C2×C4×C5—121no—
315C2×C4×C5—122no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C2×Dic5—24no—
319C2×Dic5—22no—
320C2×Dic5—62no—
321C2×Dic5—122no—
322Dic10—24no—
323Dic10—22no—
324Dic10#23714yes—
325#168—22no—
326#168—62no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—52no—
330#126—61no—
331#125—31no—
332#124—31no—
333#123—61no—
334C22⋊Q8—31no—
335#121D3×D511yescharacteristic
336C4×Q8—31no—
337C4×Q8—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—31no—
342C4×D4—61no—
343#117—61no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—301no—
346C2×C42—31no—
347C2×C42—301no—
348#107—152no—
349#106—152no—
350C4⋊C8—152no—
351#103—52no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—51no—
356C22⋊C8—151no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5—81no—
360C2×C3×C5#52511yescharacteristic
361C2×C3×C5C2×#13711yescharacteristic
362C2×C3×C5#57511yescharacteristic
363C23×C3—21no—
364C23×C3C2×C22⋊D511yescharacteristic
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C3×D4—22no—
369C3×D4—42no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—104no—
373C2×C3×C4—102no—
374C2×C3×C4C2×C22⋊D511yescharacteristic
375C2×C3×C4C23×D511yescharacteristic
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—41no—
380C2×Dic3—42no—
381C2×Dic3—102no—
382C2×Dic3—202no—
383C2×Dic3C2×C22⋊D511yescharacteristic
384C2×Dic3C2×C22⋊D511yescharacteristic
385C2×Dic3C2×C22⋊D511yescharacteristic
386C2×Dic3C2×C22⋊D511yescharacteristic
387Dic6—22no—
388C3×C8—102no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5#91512yes—
396C22×C5C2×D3×D411yescharacteristic
397C4×C5—21no—
398C4×C5—41no—
399C4×C5—61no—
400C4×C5—61no—
401C4×C5—61no—
402C4×C5—61no—
403C4×C5—121no—
404C4×C5—121no—
405C4×C5C2×#23712yes—
406Dic5—24no—
407Dic5—122no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—104no—
411C2×Q8—101no—
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—101no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—104no—
422C2×C8—52no—
423C2×C8—152no—
424C4⋊C4—31no—
425C4⋊C4—61no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—152no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—61no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—61no—
444C42—302no—
445C42—302no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3#409712yes—
453C22×C3C22×C22⋊D511yescharacteristic
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—104no—
457C3×C4D5×#4112yes—
458Dic3—21no—
459Dic3—21no—
460Dic3—21no—
461Dic3—21no—
462Dic3—41no—
463Dic3—41no—
464Dic3—202no—
465C2×C5—22no—
466C2×C5—81no—
467C2×C5#558611yescharacteristic
468C2×C5C2×#91511yescharacteristic
469C2×C5#577711yescharacteristic
470C23—21no—
471C23D3×C22⋊D511yescharacteristic
472Q8—54no—
473Q8—62no—
474Q8—104no—
475Q8—102no—
476D4—22no—
477D4—42no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—104no—
488C2×C4—102no—
489C2×C4—121no—
490C2×C4—122no—
491C2×C4—302no—
492C2×C4—602no—
493C2×C4D3×C22⋊D511yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—302no—
497C2×C3—22no—
498C2×C3—81no—
499C2×C3#6615611yescharacteristic
500C2×C3C2×#409711yescharacteristic
501C2×C3#6616211yescharacteristic
502C5#8003111yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22#9148612yes—
509C22C2×D3×C22⋊D511yescharacteristic
510C4—21no—
511C4—41no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—104no—
517C4—121no—
518C4—121no—
519C4—602no—
520C4D5×#23712yes—
521C3#1061488411yescharacteristic, complemented, Sylow
522C2—22no—
523C2—81no—
524C2C2×#9148611yescharacteristic
525C2#1175480111yescharacteristic
526C2#1175534811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic10C2semidirect
5. #11749010C2semidirect
6. #11749006C2semidirect
7. #11748555C2semidirect
8. #11748467C2semidirect
9. #11748337C2semidirect
10. #11747295C2semidirect
11. #11747267C2semidirect
446. C3×C5#3117semidirect
502. C5#80031semidirect
521. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C5×#56002
C2×Dic3×Dic102
#117511352
C3×#653292
#117490102
#117490062
#117485552
#117484672
#117483372
#117472952
#117472672
#106148843
#800315