Finite Group Databasebeta

← #14438051

Subgroups — #14438051

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5728C211yesmaximal, characteristic, complemented
2#11752543C211yesmaximal, characteristic
3#11751190C211yesmaximal, characteristic, complemented
4C3×#65378C211yesmaximal, characteristic, complemented
5#11747504C212yesmaximal, complemented
6#11747502C212yesmaximal, complemented
7#11747423C212yesmaximal, complemented
8#11747405C212yesmaximal, complemented
9D3×#3935C211yesmaximal, characteristic, complemented
10#11746914C211yesmaximal, characteristic, complemented
11#11746898C211yesmaximal, characteristic, complemented
12#10615066—31nomaximal, Hall
13C2×#6769C2211yescharacteristic
14C2×#6765C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91764C2211yescharacteristic
17C5×#946—21no—
18C5×Q8×Dic3—21no—
19C5×#897—21no—
20C5×#892C2212yes—
21C5×#890C2212yes—
22C5×#887—21no—
23C42×C5×D3C2211yescharacteristic
24C5×#869C2211yescharacteristic
25C3×#4021C2211yescharacteristic
26#91458C2211yescharacteristic
27#91454—21no—
28#91454—21no—
29#91395—21no—
30#91395—21no—
31#91389C2211yescharacteristic
32C2×D3×#168C2212yes—
33#91094C2212yes—
34#91093C2212yes—
35#91087C2211yescharacteristic
36C3×#3942C2212yes—
37C3×#3941C2212yes—
38C3×#3935C2211yescharacteristic
39#90975C2212yes—
40#90970C2212yes—
41#90969C2212yes—
42#90964C2212yes—
43#90953C2212yes—
44#81679—51nomaximal, Hall
45C5×#533—31no—
46#65811—31no—
47#65378—31no—
48#65378—31no—
49#65378—31no—
50#65378D311yescharacteristic, complemented
51#65358—32no—
52#65356—32no—
53#65291—32no—
54#65291—32no—
55C2×#3935—31no—
56C2×C3×C5×Q8—21no—
57C2×D60C2311yescharacteristic
58C2×Dic30C2311yescharacteristic
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3D411yescharacteristic
61C2×C4×C5×D3C2311yescharacteristic
62C2×C5×Dic6—21no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×Dic10C2311yescharacteristic
65C2×#1203—21no—
66C2×#1202—21no—
67C2×#1202—21no—
68C2×#1201—21no—
69C2×#1200—21no—
70C2×D5×Dic3—21no—
71#6769—24no—
72#6765—24no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—21no—
78C2×C3⋊#168C2312yes—
79C5×(C2×D3)⋊C4—22no—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3—22no—
82C5×C4⋊Dic3C2312yes—
83C5×Dic3⋊C4—22no—
84C4×C5×Dic3—22no—
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3D411yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C3×#685—21no—
89C3×#685—21no—
90C2×C3×#168C2312yes—
91Dic3⋊Dic5—21no—
92Dic3⋊Dic5—21no—
93D3×#168—24no—
94#5728D511yescharacteristic, complemented
95#5668—51no—
96C3×#489—51no—
97#5089—51no—
98#5055—51no—
99#4804—52no—
100#4797—52no—
101#4772—52no—
102#4764—52no—
103#4714—51no—
104D3×#97—51no—
105C2×#709—31no—
106C2×#709—31no—
107C5×C4⋊Q8—31no—
108C5×C4⋊Q8C2×D311yescharacteristic
109C5×#125—32no—
110C5×C22⋊Q8—61no—
111C5×C22⋊Q8—61no—
112C4×C5×Q8—61no—
113C4×C5×Q8—61no—
114C5×#117—32no—
115C2×C42×C5—31no—
116#4076—61no—
117#4076—61no—
118C22×#168—32no—
119#4021—31no—
120#4021C2×D311yescharacteristic
121#4020—31no—
122C4×D20—61no—
123C4×D20—61no—
124#4015—31no—
125#3942—32no—
126#3942—32no—
127#3942—32no—
128#3942C2×D312yes—
129#3941—32no—
130#3941—32no—
131#3941—32no—
132#3941C2×D312yes—
133#3935—31no—
134#3935—32no—
135#3935C2×D311yescharacteristic
136#3135—151noSylow
137C22×D15—21no—
138C22×C5×D3C2×D411yescharacteristic
139C22×C3×D5—21no—
140C3×C5×Q8—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—21no—
146D60—22no—
147Dic30—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C2×D411yescharacteristic
150C2×C5×Dic3C2×D411yescharacteristic
151C2×C5×Dic3C2×D411yescharacteristic
152C4×C5×D3—41no—
153C4×C5×D3—41no—
154C4×C5×D3#4114yes—
155C5×Dic6—42no—
156C2×C3×Dic5—21no—
157C3×D20—22no—
158C3×Dic10—22no—
159#1203—42no—
160#1202—42no—
161#1202—42no—
162#1201—42no—
163#1200—42no—
164D5×Dic3—42no—
165C3⋊#168—22no—
166C3×#168—22no—
167C2×#239—51no—
168C2×#237—51no—
169C3×C4⋊Q8C2×D511yescharacteristic
170C3×#124—51no—
171#946—21no—
172Q8×Dic3—21no—
173#944—51no—
174#940—51no—
175C2×D3×C8—52no—
176#897—21no—
177#892C2×D512yes—
178#890C2×D512yes—
179#887—21no—
180#884—101no—
181#884—101no—
182#67⋊C4—101no—
183#67⋊C4—101no—
184#875—51no—
185C42×D3C2×D511yescharacteristic
186#869C2×D511yescharacteristic
187C3×#103—52no—
188C3×#102—52no—
189C3×#97—51no—
190#835—52no—
191#832—52no—
192#821—52no—
193#816—52no—
194#815—52no—
195#810—52no—
196#809—52no—
197#803—51no—
198C2×C5×Q8—21no—
199C2×C5×Q8—61no—
200C22×C4×C5—31no—
201C22×C4×C5—31no—
202C22×C4×C5—31no—
203C2×C22⋊D5—61no—
204C2×C22⋊D5—61no—
205#709—64no—
206#709—64no—
207C2×D20—31no—
208C2×D20—61no—
209C2×D20—61no—
210C2×D20C22×D311yescharacteristic
211C2×C4×D5—61no—
212C2×C4×D5—61no—
213C2×Dic10—31no—
214C2×Dic10C22×D311yescharacteristic
215C5×C4⋊C4—21no—
216C5×C4⋊C4—32no—
217C5×C4⋊C4—62no—
218C5×C4⋊C4—62no—
219C5×C4⋊C4—61no—
220C5×C4⋊C4C22×D312yes—
221C5×C22⋊C4—62no—
222C42×C5—31no—
223C42×C5—31no—
224C42×C5—31no—
225C42×C5—62no—
226C42×C5C22×D311yescharacteristic
227#685—21no—
228#685—21no—
229#685—61no—
230#685—61no—
231C4⋊Dic5—61no—
232C4⋊Dic5—61no—
233C2×#168—32no—
234C2×#168—64no—
235C2×#168C22×D312yes—
236#533—31no—
237#532—151no—
238#491—152no—
239#490—152no—
240#489—51no—
241#489—151no—
242#489—151no—
243#489—151no—
244#416—152no—
245#416—152no—
246C2×#97—151no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C2×C5×D3—21no—
252C2×C5×D3—21no—
253C2×C5×D3#12412yes—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
256C2×C3×D5—41no—
257C3×C4×C5—21no—
258C3×C4×C5—21no—
259C3×C4×C5—42no—
260C3×C4×C5C2×#4112yes—
261Dic15—41no—
262C3×Dic5—41no—
263C5×Dic3—21no—
264C5×Dic3—21no—
265C5×Dic3—42no—
266C5×Dic3#12412yes—
267C2×C3×Q8—21no—
268C2×C3×Q8—51no—
269C2×C3×D4—51no—
270C2×#67—101no—
271C2×#67—101no—
272C2×#67—101no—
273C22×Dic3—101no—
274#239—104no—
275#237—104no—
276C2×D12—51no—
277C2×D12—101no—
278C2×C4×D3—101no—
279C2×C4×D3C22⋊D511yescharacteristic
280C2×C4×D3C22⋊D511yescharacteristic
281C2×C4×D3C22×D511yescharacteristic
282C2×Dic6—21no—
283C2×Dic6—51no—
284C2×C3×C8—52no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C22×D512yes—
287C3×C22⋊C4—101no—
288C3×C22⋊C4—101no—
289C3×C42C22×D511yescharacteristic
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—101no—
292(C2×D3)⋊C4—101no—
293C4⋊Dic3—21no—
294C4⋊Dic3—22no—
295C4⋊Dic3C22×D512yes—
296Dic3⋊C4—22no—
297Dic3⋊C4—101no—
298Dic3⋊C4—101no—
299C4×Dic3—22no—
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22⋊D511yescharacteristic
302C4×Dic3C22×D511yescharacteristic
303C2×C3⋊C8—52no—
304D3×C8—104no—
305C23×C5—31no—
306C22×D5—21no—
307C22×D5—61no—
308C5×Q8—42no—
309C5×Q8—122no—
310C2×C4×C5—22no—
311C2×C4×C5—31no—
312C2×C4×C5—34no—
313C2×C4×C5—31no—
314C2×C4×C5—31no—
315C2×C4×C5—62no—
316C2×C4×C5—121no—
317C2×C4×C5—121no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—122no—
322C22⋊D5—122no—
323C2×Dic5—21no—
324C2×Dic5—61no—
325D20—22no—
326D20—62no—
327D20—122no—
328D20—122no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—22no—
332Dic10—62no—
333#168—22no—
334#168—62no—
335C2×#41—151no—
336C2×#41—151no—
337C22×C8—152no—
338C4⋊Q8—31no—
339C4⋊Q8—151no—
340C4⋊Q8D3×D511yescharacteristic
341#127—151no—
342#125—32no—
343#124—51no—
344#124—151no—
345C22⋊Q8—61no—
346C22⋊Q8—61no—
347#121—301no—
348#121—301no—
349C4×Q8—61no—
350C4×Q8—61no—
351C4×D4—301no—
352C4×D4—301no—
353#117—32no—
354C2×C42—31no—
355#103—52no—
356#103—152no—
357#103—152no—
358#103—152no—
359#102—52no—
360#102—152no—
361#102—152no—
362#102—152no—
363#97—51no—
364#97—152no—
365#97—151no—
366C2×C3×C5C2×#12411yescharacteristic
367C2×C3×C5#57511yescharacteristic
368C2×C3×C5#57511yescharacteristic
369D15—81no—
370C3×D5—81no—
371C5×D3—22no—
372C23×C3—101no—
373C22×D3—101no—
374C22×D3C2×C22⋊D511yescharacteristic
375C3×Q8—42no—
376C3×Q8—102no—
377C3×D4—102no—
378C2×C3×C4—22no—
379C2×C3×C4—101no—
380C2×C3×C4C2×C22⋊D511yescharacteristic
381C2×C3×C4C2×C22⋊D511yescharacteristic
382C2×C3×C4C23×D511yescharacteristic
383#67—202no—
384#67—202no—
385#67—202no—
386C2×Dic3—22no—
387C2×Dic3—101no—
388C2×Dic3—202no—
389C2×Dic3C2×C22⋊D511yescharacteristic
390C2×Dic3C2×C22⋊D511yescharacteristic
391C2×Dic3C2×C22⋊D511yescharacteristic
392D12—102no—
393D12—202no—
394C4×D3—41no—
395C4×D3—41no—
396C4×D3—202no—
397C4×D3#71314yes—
398Dic6—42no—
399Dic6—102no—
400C3×C8—102no—
401C3⋊C8—102no—
402C22×C5—32no—
403C22×C5—61no—
404C22×C5—61no—
405C22×C5C2×D3×D411yescharacteristic
406C2×D5—41no—
407C2×D5—41no—
408C2×D5—41no—
409C2×D5—121no—
410C2×D5—121no—
411C2×D5—121no—
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—32no—
415C4×C5—42no—
416C4×C5—61no—
417C4×C5—61no—
418C4×C5—122no—
419C4×C5D3×#4112yes—
420Dic5—41no—
421Dic5—121no—
422#41—304no—
423#41—304no—
424C2×Q8—21no—
425C2×Q8—51no—
426C2×Q8—61no—
427C2×Q8—151no—
428C2×D4—51no—
429C2×D4—151no—
430C2×D4—301no—
431C2×D4—301no—
432C2×D4—301no—
433C2×D4—301no—
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—301no—
438C22×C4—301no—
439C2×C8—52no—
440C2×C8—152no—
441C2×C8—304no—
442C4⋊C4—21no—
443C4⋊C4—32no—
444C4⋊C4—62no—
445C4⋊C4—62no—
446C4⋊C4—61no—
447C4⋊C4—301no—
448C4⋊C4—301no—
449C4⋊C4C2×D3×D512yes—
450C22⋊C4—62no—
451C22⋊C4—101no—
452C22⋊C4—101no—
453C22⋊C4—301no—
454C22⋊C4—301no—
455C42—31no—
456C42—31no—
457C42—31no—
458C42—62no—
459C42C2×D3×D511yescharacteristic
460C3×C5#313511yescharacteristic, complemented, Hall
461C22×C3—201no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3C22×C22⋊D511yescharacteristic
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—201no—
468C2×D3—201no—
469C2×D3—201no—
470C2×D3#409312yes—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—42no—
474C3×C4—201no—
475C3×C4C2×#71312yes—
476Dic3—21no—
477Dic3—21no—
478Dic3—42no—
479Dic3—201no—
480Dic3#409312yes—
481C2×C5—62no—
482C2×C5D3×#12411yescharacteristic
483C2×C5#577311yescharacteristic
484C2×C5#577711yescharacteristic
485D5—81no—
486D5—241no—
487C23—31no—
488C23—101no—
489C23—301no—
490Q8—42no—
491Q8—102no—
492Q8—122no—
493Q8—302no—
494D4—102no—
495D4—302no—
496D4—602no—
497D4—602no—
498D4—602no—
499D4—602no—
500C2×C4—22no—
501C2×C4—31no—
502C2×C4—34no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—62no—
506C2×C4—101no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—301no—
510C2×C4—602no—
511C2×C4—602no—
512C2×C4D3×C22⋊D511yescharacteristic
513C2×C4D3×C22⋊D511yescharacteristic
514C2×C4C22×D3×D511yescharacteristic
515C8—102no—
516C8—302no—
517C2×C3—401no—
518C2×C3C2×#409311yescharacteristic
519C2×C3#6615611yescharacteristic
520C2×C3#6615611yescharacteristic
521D3—22no—
522D3—401no—
523C5#8167911yescharacteristic, complemented, Sylow
524C22—32no—
525C22—61no—
526C22—61no—
527C22—201no—
528C22—201no—
529C22—201no—
530C22—601no—
531C22—601no—
532C22—601no—
533C22C2×D3×C22⋊D511yescharacteristic
534C4—21no—
535C4—21no—
536C4—32no—
537C4—42no—
538C4—61no—
539C4—61no—
540C4—122no—
541C4—201no—
542C4—601no—
543C4D3×#71312yes—
544C3#1061506611yescharacteristic, complemented, Sylow
545C2—62no—
546C2—401no—
547C2—1201no—
548C2#1175469611yescharacteristic
549C2#1175509011yescharacteristic
550C2D3×#409311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752543C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3135
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. #11751190C2semidirect
4. C3×#65378C2semidirect
5. #11747504C2semidirect
6. #11747502C2semidirect
7. #11747423C2semidirect
8. #11747405C2semidirect
9. D3×#3935C2semidirect
10. #11746914C2semidirect
11. #11746898C2semidirect
50. #65378D3semidirect
94. #5728D5semidirect
460. C3×C5#3135semidirect
523. C5#81679semidirect
544. C3#10615066semidirect

Maximal subgroups

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

subgroupindex
C5×#57282
#117525432
#117511902
C3×#653782
#117475042
#117475022
#117474232
#117474052
D3×#39352
#117469142
#117468982
#106150663
#816795