Finite Group Databasebeta

← #14416262

Subgroups — #14416262

Order 1920.

1000 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×#5522C211yesmaximal, characteristic, complemented
2#11754436C211yesmaximal, characteristic, complemented
3C2×#91303C211yesmaximal, characteristic
4#11751103C211yesmaximal, characteristic, complemented
5C3×#65287C211yesmaximal, characteristic, complemented
6#11748382C211yesmaximal, characteristic, complemented
7C2×Dic3×#168C211yesmaximal, characteristic, complemented
8#11747277C212yesmaximal, complemented
9#11747275C212yesmaximal, complemented
10#11747232C212yesmaximal, complemented
11#11747230C212yesmaximal, complemented
12C4×#4096—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C5×#893C2212yes—
19C5×#887C2212yes—
20C5×#67⋊C4—22no—
21C5×#872—21no—
22C42×C5×D3—21no—
23C3×#4072C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91556—22no—
26#91428C2212yes—
27C4×#1200—21no—
28#91386—21no—
29#91340C2212yes—
30C2×#6663C2211yescharacteristic
31C2×#6660C2211yescharacteristic
32C2×#6659C2211yescharacteristic
33#91303C418yescomplemented
34C2×#6654C2211yescharacteristic
35#91094C2212yes—
36#91093C2212yes—
37C3×#3940C2212yes—
38C3×#3939C2212yes—
39#90972C2212yes—
40#90966C2212yes—
41Dic3×#168C2212yes—
42Dic3×#168C2212yes—
43#79165—51nomaximal, Hall
44C4×C5×#41—31no—
45C2×#4096—31no—
46C4×#709—31no—
47#65522—31no—
48C4×#689—32no—
49C4×#688—32no—
50C4×#687—32no—
51C4×#686—32no—
52#65291—31no—
53#65287D311yescharacteristic, complemented
54C2×C4×#168—31no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817C2×C414yescomplemented
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C2×C5×#67—21no—
63C22×C5×Dic3D412yes—
64C5×#235—22no—
65C5×#235C2×C414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C4×C5×D3—22no—
69C2×C5×Dic6C2311yescharacteristic
70C2×#1200—22no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C22⋊C4—21no—
73C3×C42×C5—21no—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—22no—
77C5×Dic3⋊C4—22no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3D411yescharacteristic
81C4×C5×Dic3C2312yes—
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4×Dic5—21no—
85C2×C3×#168C2×C414yescomplemented
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88#6669—22no—
89#6667—22no—
90Dic3×Dic5—22no—
91#6663C2×C414yescomplemented
92#6660C2×C414yescomplemented
93#6659C2×C414yescomplemented
94#6654C2×C414yescomplemented
95C2×#904—51no—
96#5522—51no—
97#5522D511yescharacteristic, complemented
98C3×#427—51no—
99C2×C8×Dic3—51no—
100#5002—51no—
101#5002—51no—
102#4873—52no—
103#4872—52no—
104#4852—52no—
105#4852—52no—
106C2×C5×#41—31no—
107C2×#709—31no—
108C4×C5×Q8—32no—
109C4×C5×D4—32no—
110C4×C5×D4—62no—
111C5×#117—61no—
112C5×#117C2×D311yescharacteristic
113C2×C42×C5—31no—
114C2×C42×C5—61no—
115#4096—38no—
116C2×#689—31no—
117C2×#688—31no—
118C2×#687—31no—
119C2×#686—31no—
120C4×C22⋊D5—62no—
121#4072C2×D311yescharacteristic
122C22×#168—31no—
123C22×#168C2×D311yescharacteristic
124C4×D20—32no—
125#4018—61no—
126C42×D5—61no—
127C4×Dic10—32no—
128#3967—32no—
129#3964—32no—
130#3942—32no—
131#3941—32no—
132#3940C2×D312yes—
133#3939C2×D312yes—
134C4×#168—32no—
135C4×#168—32no—
136C4×#135—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×C5×D3—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—24no—
146C2×Dic15—21no—
147D60—21no—
148D60C22×C412yes—
149C4×D15—24no—
150Dic30—21no—
151Dic30C22×C412yes—
152C5×#67—24no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—24no—
155C2×C5×Dic3C2×D412yes—
156C2×C5×Dic3C2×D412yes—
157C5×D12—21no—
158C5×D12C22×C412yes—
159C4×C5×D3—24no—
160C4×C5×D3—44no—
161C5×Dic6—21no—
162C5×Dic6C22×C412yes—
163C2×C3×Dic5—22no—
164#1200—44no—
165C3⋊#168—22no—
166C3×#168C22×C412yes—
167C3×#168C22×C412yes—
168C2×#235—51no—
169C2×#235C2×D511yescharacteristic
170C22×C3×C8—51no—
171C3×#117—51no—
172C3×#117C2×D511yescharacteristic
173C2×C4×Dic3C2×D511yescharacteristic
174C22×C3⋊C8—51no—
175C2×Dic12—51no—
176#904—58no—
177C2×D24—51no—
178C2×#204—51no—
179C2×#204—51no—
180#893—52no—
181#893C2×D512yes—
182#887—52no—
183#887C2×D512yes—
184#67⋊C4—22no—
185#67⋊C4—102no—
186#872—21no—
187#872—101no—
188C42×D3—21no—
189C42×D3—101no—
190C3×#107—52no—
191C3×#106—52no—
192C8×Dic3—52no—
193C8×Dic3—52no—
194#810—52no—
195#810—52no—
196#809—52no—
197#809—52no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—32no—
204C22×C4×C5—62no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—61no—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C5×C4⋊C4—62no—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—21no—
217C5×C22⋊C4—62no—
218C42×C5—21no—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—32no—
222C42×C5—62no—
223C22⋊Dic5—21no—
224#689—34no—
225#688—34no—
226#687—34no—
227#686—34no—
228#685—62no—
229C4⋊Dic5C22×D312yes—
230#683—62no—
231C4×Dic5—21no—
232C4×Dic5—62no—
233C2×#168—32no—
234C2×#168—62no—
235C2×#168C4×D314yescomplemented
236C2×#168C22×D311yescharacteristic
237C2×#168C22×D311yescharacteristic
238C2×#135—151no—
239C4×#41—31no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—51no—
246#416—151no—
247#416—151no—
248C2×C4×C8—151no—
249C22×C3×C5—22no—
250C22×C3×C5C4×D412yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—22no—
253C2×D15—42no—
254C2×C5×D3—22no—
255C2×C5×D3—42no—
256C3×C4×C5—42no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261C3×Dic5—42no—
262C5×Dic3—22no—
263C5×Dic3—22no—
264C5×Dic3#13514yescomplemented
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—21no—
267C2×#67—101no—
268C22×Dic3C22⋊D512yes—
269#235—22no—
270#235—54no—
271#235—102no—
272#235C4×D514yescomplemented
273C2×D12—51no—
274C2×D12C22×D511yescharacteristic
275C2×C4×D3—21no—
276C2×C4×D3—22no—
277C2×C4×D3—101no—
278C2×C4×D3—102no—
279C2×Dic6—51no—
280C2×Dic6C22×D511yescharacteristic
281C2×C3×C8—54no—
282C2×C3×C8—51no—
283C2×C3×C8—51no—
284C3×C4⋊C4—52no—
285C3×C4⋊C4C22×D512yes—
286C3×C22⋊C4—21no—
287C3×C22⋊C4—101no—
288C3×C42—21no—
289C3×C42—101no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—102no—
292Dic3⋊C4—22no—
293Dic3⋊C4—102no—
294C4×Dic3—22no—
295C4×Dic3—102no—
296C4×Dic3C22⋊D511yescharacteristic
297C4×Dic3C22⋊D511yescharacteristic
298C4×Dic3C22×D512yes—
299C2×C3⋊C8—52no—
300C2×C3⋊C8—102no—
301Dic12—54no—
302D24—54no—
303#204—54no—
304#204—54no—
305C23×C5—61no—
306C23×C5D3×D411yescharacteristic
307C22×D5—61no—
308C5×Q8—32no—
309C5×Q8—61no—
310C5×D4—32no—
311C5×D4—64no—
312C5×D4—61no—
313C2×C4×C5—22no—
314C2×C4×C5—32no—
315C2×C4×C5—32no—
316C2×C4×C5—64no—
317C2×C4×C5—61no—
318C2×C4×C5—64no—
319C2×C4×C5—124no—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5#23912yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—64no—
325C2×Dic5—22no—
326C2×Dic5—61no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333#168—62no—
334#168C2×C4×D312yes—
335#168C2×C4×D312yes—
336C2×#41—31no—
337C2×#41—151no—
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—51no—
344C22×C8—151no—
345C4×Q8—32no—
346C4×Q8—152no—
347C4×D4—32no—
348C4×D4—62no—
349C4×D4—152no—
350C4×D4—302no—
351#117—51no—
352#117—61no—
353#117—301no—
354#117D3×D511yescharacteristic
355C2×C42—31no—
356C2×C42—61no—
357C2×C42—301no—
358#107—52no—
359#106—52no—
360#103—152no—
361#103—152no—
362#102—152no—
363#102—152no—
364C4×C8—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5C2×#13512yes—
369D15—42no—
370C5×D3—42no—
371C23×C3C2×C22⋊D511yescharacteristic
372C22×D3—21no—
373C22×D3—101no—
374C2×C3×C4—22no—
375C2×C3×C4—102no—
376C2×C3×C4C2×C4×D512yes—
377C2×C3×C4#70912yes—
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380#67—24no—
381#67—104no—
382C2×Dic3—21no—
383C2×Dic3—24no—
384C2×Dic3—101no—
385C2×Dic3C2×C22⋊D512yes—
386C2×Dic3C2×C22⋊D512yes—
387D12—21no—
388D12—52no—
389D12—101no—
390D12C2×C4×D512yes—
391C4×D3—24no—
392C4×D3—44no—
393C4×D3—104no—
394C4×D3—204no—
395Dic6—21no—
396Dic6—52no—
397Dic6—101no—
398Dic6C2×C4×D512yes—
399C3×C8—52no—
400C3×C8—52no—
401C3⋊C8—102no—
402C22×C5—22no—
403C22×C5—62no—
404C22×C5—122no—
405C22×C5#89312yes—
406C22×C5C2×D3×D411yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—34no—
410C4×C5—42no—
411C4×C5—62no—
412C4×C5—62no—
413C4×C5#89312yes—
414C4×C5C22×C4×D311yescharacteristic
415C4×C5C2×#23911yescharacteristic
416Dic5—42no—
417Dic5—62no—
418#41—34no—
419#41—62no—
420#41—154no—
421#41—302no—
422C2×Q8—31no—
423C2×Q8—151no—
424C2×D4—31no—
425C2×D4—61no—
426C2×D4—151no—
427C2×D4—301no—
428C22×C4—32no—
429C22×C4—62no—
430C22×C4—61no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—54no—
439C2×C8—51no—
440C2×C8—51no—
441C2×C8—152no—
442C2×C8—302no—
443C4⋊C4—52no—
444C4⋊C4—62no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—21no—
448C22⋊C4—62no—
449C22⋊C4—101no—
450C22⋊C4—302no—
451C42—21no—
452C42—31no—
453C42—31no—
454C42—32no—
455C42—62no—
456C42—101no—
457C42—302no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3C4×C22⋊D512yes—
461C22×C3C22×C22⋊D511yescharacteristic
462C2×D3—22no—
463C2×D3—42no—
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—42no—
467C3×C4—202no—
468C3×C4C4×C22⋊D512yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#70911yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—102no—
474Dic3#409614yescomplemented
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×#89311yescharacteristic
478C2×C5D3×#13512yes—
479D5—122no—
480C23—61no—
481C23—301no—
482C23D3×C22⋊D511yescharacteristic
483Q8—32no—
484Q8—61no—
485Q8—152no—
486Q8—301no—
487D4—32no—
488D4—64no—
489D4—61no—
490D4—152no—
491D4—304no—
492D4—301no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—64no—
497C2×C4—61no—
498C2×C4—64no—
499C2×C4—102no—
500C2×C4—124no—
501C2×C4—301no—
502C2×C4—304no—
503C2×C4—604no—
504C2×C4#676912yes—
505C2×C4C4×D3×D512yes—
506C2×C4D3×C22⋊D511yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—52no—
509C8—52no—
510C8—302no—
511C2×C3—22no—
512C2×C3C2×C4×C22⋊D511yescharacteristic
513C2×C3C2×#409612yes—
514D3—42no—
515D3—202no—
516C5#7916511yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—122no—
520C22—302no—
521C22—602no—
522C22#9144612yes—
523C22C2×D3×C22⋊D511yescharacteristic
524C4—34no—
525C4—42no—
526C4—62no—
527C4—62no—
528C4—202no—
529C4—302no—
530C4#9144612yes—
531C4C2×#676911yescharacteristic
532C4C2×C4×D3×D511yescharacteristic
533C3C4×#409611yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—602no—
537C2C2×#9144611yescharacteristic
538C2D3×#409612yes—
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5522C2semidirect
2. #11754436C2semidirect
4. #11751103C2semidirect
5. C3×#65287C2semidirect
6. #11748382C2semidirect
7. C2×Dic3×#168C2semidirect
8. #11747277C2semidirect
9. #11747275C2semidirect
10. #11747232C2semidirect
11. #11747230C2semidirect
33. #91303C4semidirect
53. #65287D3semidirect
58. #6817C2×C4semidirect
65. C5×#235C2×C4semidirect
85. C2×C3×#168C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
97. #5522D5semidirect
235. C2×#168C4×D3semidirect
264. C5×Dic3#135semidirect
272. #235C4×D5semidirect
458. C3×C5C4×#135semidirect
474. Dic3#4096semidirect
516. C5#79165semidirect
533. C3C4×#4096semidirect

Maximal subgroups

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

subgroupindex
C5×#55222
#117544362
C2×#913032
#117511032
C3×#652872
#117483822
C2×Dic3×#1682
#117472772
#117472752
#117472322
#117472302
C4×#40963
#791655