Finite Group Databasebeta

← #14438048

Subgroups — #14438048

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×#5668C211yesmaximal, characteristic
2#11752478C211yesmaximal, characteristic, complemented
3#11751156C211yesmaximal, characteristic, complemented
4C3×#65344C211yesmaximal, characteristic, complemented
5#11749211C212yesmaximal, complemented
6#11749192C212yesmaximal, complemented
7#11748965C212yesmaximal, complemented
8#11748946C212yesmaximal, complemented
9D3×#3935C211yesmaximal, characteristic, complemented
10#11746909C211yesmaximal, characteristic, complemented
11#11746904C211yesmaximal, characteristic, complemented
12#10615013—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×C5×#237C2211yescharacteristic
15C3×C5×#124C2211yescharacteristic
16#91758C2211yescharacteristic
17C5×#944C2211yescharacteristic
18C5×#940C2211yescharacteristic
19C5×#884—21no—
20C5×#884—21no—
21C5×#67⋊C4—21no—
22C5×#67⋊C4—21no—
23C5×#875C2211yescharacteristic
24C42×C5×D3C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91381C2212yes—
27#91369—21no—
28#91365—21no—
29#91340—21no—
30#91338C2212yes—
31Dic3×Dic10—21no—
32C2×D3×#168C2212yes—
33#91119C2212yes—
34#91116C2212yes—
35#91087C2211yescharacteristic
36C3×#3967C2212yes—
37C3×#3964C2212yes—
38C3×#3935C2211yescharacteristic
39#90973C2212yes—
40#90972C2212yes—
41#90967C2212yes—
42#90966C2212yes—
43#90953C2212yes—
44#81679—51nomaximal, Hall
45C5×#532—31no—
46#65804—31no—
47#65522—32no—
48#65522—32no—
49#65371—32no—
50#65360—32no—
51#65344—31no—
52#65344—31no—
53#65344—31no—
54#65344D311yescharacteristic, complemented
55C2×#3935—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C2×Dic30—21no—
59C2×C5×#67—21no—
60C2×C5×#67—21no—
61C2×C5×#67—21no—
62C22×C5×Dic3—21no—
63C5×#239—24no—
64C5×#237—24no—
65C2×C5×D12—21no—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C4×C5×D3D411yescharacteristic
69C2×C4×C5×D3D411yescharacteristic
70C2×C4×C5×D3C2311yescharacteristic
71C2×C5×Dic6C2311yescharacteristic
72C2×C3×Dic10—21no—
73C3×C5×C22⋊C4—21no—
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C2×C3⋊#168C2312yes—
79C5×(C2×D3)⋊C4—21no—
80C5×(C2×D3)⋊C4—21no—
81C5×Dic3⋊C4—21no—
82C5×Dic3⋊C4—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—
95#5668D511yescharacteristic
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×C5×#41—31no—
106C2×C5×#41—31no—
107C5×C4⋊Q8—31no—
108C5×#127—31no—
109C5×#124—31no—
110C5×#124C2×D311yescharacteristic
111C5×#121—61no—
112C5×#121—61no—
113C4×C5×D4—61no—
114C4×C5×D4—61no—
115C2×C42×C5—31no—
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#3967—32no—
128#3967C2×D312yes—
129#3964—32no—
130#3964—32no—
131#3964—32no—
132#3964C2×D312yes—
133#3935—31no—
134#3935—32no—
135#3935C2×D311yescharacteristic
136#3135—151noSylow
137C23×C3×C5—21no—
138C22×C5×D3—21no—
139C22×C5×D3C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×D4—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C5×#67—42no—
149C5×#67—42no—
150C5×#67—42no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—42no—
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C5×D12—22no—
157C5×D12—42no—
158C4×C5×D3—41no—
159C4×C5×D3—41no—
160C4×C5×D3—42no—
161C4×C5×D3#4114yes—
162C5×Dic6—22no—
163C2×C3×Dic5—22no—
164C3×Dic10—42no—
165C3⋊#168—22no—
166C3×#168—22no—
167C2×#239C2×D511yescharacteristic
168C2×#237C2×D511yescharacteristic
169C3×C4⋊Q8—51no—
170C3×#124C2×D511yescharacteristic
171#946—101no—
172Q8×Dic3—101no—
173#944C2×D511yescharacteristic
174#940C2×D511yescharacteristic
175C2×D3×C8—52no—
176#897—101no—
177#892—52no—
178#890—52no—
179#887—101no—
180#884—21no—
181#884—21no—
182#67⋊C4—21no—
183#67⋊C4—21no—
184#875C2×D511yescharacteristic
185C42×D3C2×D511yescharacteristic
186#869—51no—
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—
198C5×#41—64no—
199C5×#41—64no—
200C2×C5×Q8—31no—
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4—31no—
203C2×C5×D4—61no—
204C2×C5×D4—61no—
205C2×C5×D4—61no—
206C2×C5×D4—61no—
207C2×C5×D4C22×D311yescharacteristic
208C22×C4×C5—31no—
209C22×C4×C5—31no—
210C22×C4×C5—31no—
211C22×C4×C5—61no—
212C22×C4×C5—61no—
213C2×Dic10—21no—
214C2×Dic10—61no—
215C5×C4⋊C4—61no—
216C5×C4⋊C4—61no—
217C5×C22⋊C4—21no—
218C5×C22⋊C4—21no—
219C5×C22⋊C4—61no—
220C5×C22⋊C4—61no—
221C42×C5—31no—
222C42×C5—31no—
223C42×C5—31no—
224C42×C5C22×D311yescharacteristic
225C22⋊Dic5—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5—32no—
228C4⋊Dic5—61no—
229C4⋊Dic5C22×D312yes—
230#683—62no—
231#683—62no—
232C4×Dic5—62no—
233C2×#168—32no—
234C2×#168—64no—
235C2×#168C22×D312yes—
236#533—151no—
237#532—31no—
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×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5C22×D411yescharacteristic
251C2×C5×D3—21no—
252C2×C5×D3—21no—
253C2×C5×D3—41no—
254C2×C5×D3—41no—
255C2×C5×D3—41no—
256C2×C5×D3#12412yes—
257C3×C4×C5—21no—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×#4112yes—
261Dic15—42no—
262C3×Dic5—42no—
263C5×Dic3—21no—
264C5×Dic3—21no—
265C5×Dic3—41no—
266C5×Dic3#12412yes—
267C2×C3×Q8—101no—
268C2×C3×Q8C22×D511yescharacteristic
269C2×C3×D4C22×D511yescharacteristic
270C2×#67—21no—
271C2×#67—21no—
272C2×#67—21no—
273C22×Dic3—21no—
274#239—24no—
275#237—24no—
276C2×D12—21no—
277C2×D12C22×D511yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3C22⋊D511yescharacteristic
280C2×C4×D3C22⋊D511yescharacteristic
281C2×C4×D3C22×D511yescharacteristic
282C2×Dic6—101no—
283C2×Dic6C22×D511yescharacteristic
284C2×C3×C8—52no—
285C3×C4⋊C4—52no—
286C3×C4⋊C4—101no—
287C3×C22⋊C4—21no—
288C3×C22⋊C4—21no—
289C3×C42C22×D511yescharacteristic
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—52no—
294C4⋊Dic3—101no—
295C4⋊Dic3—102no—
296Dic3⋊C4—21no—
297Dic3⋊C4—21no—
298Dic3⋊C4—102no—
299C4×Dic3—102no—
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22⋊D511yescharacteristic
302C4×Dic3C22×D511yescharacteristic
303C2×C3⋊C8—52no—
304D3×C8—104no—
305C23×C5—21no—
306C23×C5—31no—
307C23×C5—61no—
308C5×Q8—22no—
309C5×Q8—62no—
310C5×D4—22no—
311C5×D4—62no—
312C5×D4—122no—
313C5×D4—122no—
314C5×D4—122no—
315C5×D4—122no—
316C2×C4×C5—21no—
317C2×C4×C5—31no—
318C2×C4×C5—34no—
319C2×C4×C5—31no—
320C2×C4×C5—31no—
321C2×C4×C5—61no—
322C2×C4×C5—121no—
323C2×C4×C5—121no—
324C2×C4×C5—122no—
325C2×C4×C5—122no—
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5C23×D311yescharacteristic
329C2×Dic5—22no—
330C2×Dic5—62no—
331Dic10—42no—
332Dic10—122no—
333#168—22no—
334#168—62no—
335C2×#41—31no—
336C2×#41—31no—
337C22×C8—152no—
338C4⋊Q8—31no—
339C4⋊Q8—51no—
340C4⋊Q8—151no—
341#127—31no—
342#125—152no—
343#124—31no—
344#124D3×D511yescharacteristic
345C22⋊Q8—301no—
346C22⋊Q8—301no—
347#121—61no—
348#121—61no—
349C4×Q8—301no—
350C4×Q8—301no—
351C4×D4—61no—
352C4×D4—61no—
353#117—152no—
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×C5—81no—
367C2×C3×C5C2×#12411yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C5×D3—22no—
371C5×D3—81no—
372C23×C3—21no—
373C22×D3—21no—
374C22×D3C2×C22⋊D511yescharacteristic
375C3×Q8—22no—
376C3×Q8—202no—
377C3×D4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—102no—
380C2×C3×C4C2×C22⋊D511yescharacteristic
381C2×C3×C4C2×C22⋊D511yescharacteristic
382C2×C3×C4C23×D511yescharacteristic
383#67—42no—
384#67—42no—
385#67—42no—
386C2×Dic3—21no—
387C2×Dic3—42no—
388C2×Dic3—102no—
389C2×Dic3C2×C22⋊D511yescharacteristic
390C2×Dic3C2×C22⋊D511yescharacteristic
391C2×Dic3C2×C22⋊D511yescharacteristic
392D12—22no—
393D12—42no—
394C4×D3—41no—
395C4×D3—41no—
396C4×D3—42no—
397C4×D3#71114yes—
398Dic6—22no—
399Dic6—202no—
400C3×C8—102no—
401C3⋊C8—102no—
402C22×C5—32no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—61no—
407C22×C5—61no—
408C22×C5—121no—
409C22×C5—121no—
410C22×C5—121no—
411C22×C5C2×D3×D411yescharacteristic
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—32no—
415C4×C5—41no—
416C4×C5—61no—
417C4×C5—61no—
418C4×C5—121no—
419C4×C5D3×#4112yes—
420Dic5—42no—
421Dic5—122no—
422#41—64no—
423#41—64no—
424C2×Q8—31no—
425C2×Q8—101no—
426C2×Q8—301no—
427C2×Q8C2×D3×D511yescharacteristic
428C2×D4—31no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—61no—
438C22×C4—61no—
439C2×C8—52no—
440C2×C8—152no—
441C2×C8—304no—
442C4⋊C4—52no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—101no—
446C4⋊C4—152no—
447C4⋊C4—302no—
448C4⋊C4—302no—
449C4⋊C4—301no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—61no—
453C22⋊C4—61no—
454C22⋊C4—302no—
455C42—31no—
456C42—31no—
457C42—31no—
458C42—302no—
459C42C2×D3×D511yescharacteristic
460C3×C5#313511yescharacteristic, complemented, Hall
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3C22×C22⋊D511yescharacteristic
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—41no—
468C2×D3—41no—
469C2×D3—41no—
470C2×D3#408212yes—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—41no—
474C3×C4—202no—
475C3×C4C2×#71112yes—
476Dic3—21no—
477Dic3—21no—
478Dic3—41no—
479Dic3—202no—
480Dic3#408212yes—
481C2×C5—62no—
482C2×C5—81no—
483C2×C5—241no—
484C2×C5D3×#12411yescharacteristic
485C2×C5#577311yescharacteristic
486C2×C5#577711yescharacteristic
487C23—21no—
488C23—31no—
489C23—61no—
490Q8—22no—
491Q8—62no—
492Q8—202no—
493Q8—602no—
494D4—22no—
495D4—62no—
496D4—122no—
497D4—122no—
498D4—122no—
499D4—122no—
500C2×C4—21no—
501C2×C4—31no—
502C2×C4—34no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—61no—
506C2×C4—102no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—122no—
510C2×C4—122no—
511C2×C4—302no—
512C2×C4D3×C22⋊D511yescharacteristic
513C2×C4D3×C22⋊D511yescharacteristic
514C2×C4C22×D3×D511yescharacteristic
515C8—102no—
516C8—302no—
517C2×C3—81no—
518C2×C3C2×#408211yescharacteristic
519C2×C3#6615611yescharacteristic
520C2×C3#6615611yescharacteristic
521D3—22no—
522D3—81no—
523C5#8167911yescharacteristic, complemented, Sylow
524C22—32no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—61no—
529C22—61no—
530C22—121no—
531C22—121no—
532C22—121no—
533C22C2×D3×C22⋊D511yescharacteristic
534C4—21no—
535C4—21no—
536C4—32no—
537C4—41no—
538C4—61no—
539C4—61no—
540C4—121no—
541C4—202no—
542C4—602no—
543C4D3×#71112yes—
544C3#1061501311yescharacteristic, complemented, Sylow
545C2—62no—
546C2—81no—
547C2—241no—
548C2D3×#408211yescharacteristic
549C2#1175534511yescharacteristic
550C2#1175534811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#5668C2
hypercenter#124D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752478C2semidirect
3. #11751156C2semidirect
4. C3×#65344C2semidirect
5. #11749211C2semidirect
6. #11749192C2semidirect
7. #11748965C2semidirect
8. #11748946C2semidirect
9. D3×#3935C2semidirect
10. #11746909C2semidirect
11. #11746904C2semidirect
54. #65344D3semidirect
460. C3×C5#3135semidirect
523. C5#81679semidirect
544. C3#10615013semidirect

Maximal subgroups

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

subgroupindex
C5×#56682
#117524782
#117511562
C3×#653442
#117492112
#117491922
#117489652
#117489462
D3×#39352
#117469092
#117469042
#106150133
#816795