Finite Group Databasebeta

← #14416260

Subgroups — #14416260

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
1#11756281C211yesmaximal, characteristic, complemented
2#11754455C211yesmaximal, characteristic, complemented
3C2×#91303C211yesmaximal, characteristic
4C5×#5002C211yesmaximal, characteristic, complemented
5C3×#65287C211yesmaximal, characteristic, complemented
6#11748411C211yesmaximal, characteristic, complemented
7C2×#90951C211yesmaximal, characteristic, complemented
8#11747279C212yesmaximal, complemented
9#11747278C212yesmaximal, complemented
10#11747234C212yesmaximal, complemented
11#11747233C212yesmaximal, complemented
12#10610549—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C4×Dic15C2211yescharacteristic
17#91782C2212yes—
18#91776C2212yes—
19#91770—22no—
20#91761—21no—
21C42×D15—21no—
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#67⋊Dic5—22no—
26#91435C2212yes—
27C4×D3×Dic5—21no—
28#91371—21no—
29#91344C2212yes—
30C2×#6663C2211yescharacteristic
31C2×#6660C2211yescharacteristic
32C2×#6659C2211yescharacteristic
33#91303C418yescomplemented
34C2×#6654C2211yescharacteristic
35C5×#810C2212yes—
36C5×#809C2212yes—
37C3×#3940C2212yes—
38C3×#3939C2212yes—
39#90974C2212yes—
40#90968C2212yes—
41#90951C2212yes—
42#90951C2212yes—
43#79165—51nomaximal, Hall
44#41×Dic5—31no—
45C2×#4096—31no—
46#65856—31no—
47C5×#416—31no—
48#65402—31no—
49C2×C8×Dic5—31no—
50#65287D311yescharacteristic, complemented
51#65079—32no—
52#65077—32no—
53#65047—32no—
54#65045—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57C22×Dic15D412yes—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15—22no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235C2×C414yescomplemented
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C2×D3×Dic5—22no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C22⋊C4—21no—
73C3×C42×C5—21no—
74#6714—22no—
75#6712—22no—
76C4×Dic15—22no—
77C4×Dic15D411yescharacteristic
78C4×Dic15D411yescharacteristic
79C4×Dic15C2312yes—
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yes—
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4×Dic5—21no—
85C2×C3×#168C2×C414yescomplemented
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6663C2×C414yescomplemented
92#6660C2×C414yescomplemented
93#6659C2×C414yescomplemented
94#6654C2×C414yescomplemented
95C2×#904—51no—
96#5522—51no—
97#5522—51no—
98C3×#427—51no—
99C2×C8×Dic3—51no—
100#5002—51no—
101#5002D511yescharacteristic, complemented
102#4873—52no—
103#4872—52no—
104#4852—52no—
105#4852—52no—
106C2×C5×#41—31no—
107C2×#709—31no—
108C22×C5×C8—31no—
109C5×#117C2×D311yescharacteristic
110#4096—38no—
111Q8×Dic5—32no—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—32no—
115D4×Dic5—62no—
116C2×#687—31no—
117C2×#686—31no—
118#4072—61no—
119#4072C2×D311yescharacteristic
120C2×C4×Dic5—31no—
121C2×C4×Dic5—61no—
122C22×#168C2×D311yescharacteristic
123#4039—32no—
124#4033—32no—
125#4027—62no—
126#4018—61no—
127C42×D5—61no—
128C5×#103—32no—
129C5×#102—32no—
130#3953—32no—
131#3948—32no—
132C8×Dic5—32no—
133C8×Dic5—32no—
134#3940C2×D312yes—
135#3939C2×D312yes—
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—
147C2×Dic15—24no—
148C2×Dic15C2×D412yes—
149C2×Dic15C2×D412yes—
150D60—21no—
151D60C22×C412yes—
152C4×D15—24no—
153C4×D15—44no—
154Dic30—21no—
155Dic30C22×C412yes—
156C5×#67—24no—
157C2×C5×Dic3—21no—
158C5×D12—21no—
159C5×D12C22×C412yes—
160C4×C5×D3—24no—
161C5×Dic6—21no—
162C5×Dic6C22×C412yes—
163C2×C3×Dic5—22no—
164D3×Dic5—44no—
165C3×#168C22×C412yes—
166C3×#168C22×C412yes—
167C5×C3⋊C8—22no—
168C2×#235—51no—
169C2×#235C2×D511yescharacteristic
170C22×C3×C8—51no—
171C3×#117—51no—
172C3×#117C2×D511yescharacteristic
173C2×C4×Dic3—51no—
174C22×C3⋊C8C2×D511yescharacteristic
175C2×Dic12—51no—
176#904—58no—
177C2×D24—51no—
178C2×#204—51no—
179C2×#204—51no—
180#893—52no—
181#893—52no—
182#887—52no—
183#887—52no—
184#67⋊C4—102no—
185#67⋊C4—102no—
186#872—101no—
187#872—101no—
188C42×D3—101no—
189C42×D3—101no—
190C3×#107—52no—
191C3×#106—52no—
192C8×Dic3—52no—
193C8×Dic3—52no—
194#810—52no—
195#810C2×D512yes—
196#809—52no—
197#809C2×D512yes—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—32no—
207C22×Dic5—62no—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C5×C4⋊C4C22×D312yes—
217C5×C22⋊C4—21no—
218C42×C5—21no—
219C22⋊Dic5—21no—
220C22⋊Dic5—62no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—62no—
226C4⋊Dic5—62no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229C4×Dic5—21no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—32no—
233C4×Dic5—62no—
234C4×Dic5—62no—
235C2×#168C4×D314yescomplemented
236C2×#168C22×D311yescharacteristic
237C2×#168C22×D311yescharacteristic
238C2×#135—151no—
239C4×#41—151no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—51no—
246#416—31no—
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—
261Dic15—22no—
262Dic15#13514yescomplemented
263C3×Dic5—42no—
264C5×Dic3—22no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—21no—
267C2×#67—101no—
268C22×Dic3—52no—
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—101no—
277C2×C4×D3—102no—
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—102no—
291(C2×D3)⋊C4—102no—
292Dic3⋊C4—102no—
293Dic3⋊C4—102no—
294C4×Dic3—51no—
295C4×Dic3—51no—
296C4×Dic3—52no—
297C4×Dic3—102no—
298C4×Dic3—102no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8C22×D512yes—
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—61no—
315C2×C4×C5—64no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5#23912yes—
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—64no—
321C2×Dic5—22no—
322C2×Dic5—32no—
323C2×Dic5—32no—
324C2×Dic5—64no—
325C2×Dic5—61no—
326C2×Dic5—124no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—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—31no—
344C22×C8—51no—
345C4×Q8—152no—
346C4×Q8—152no—
347C4×D4—152no—
348C4×D4—152no—
349C4×D4—302no—
350C4×D4—302no—
351#117—51no—
352#117—301no—
353#117—301no—
354#117D3×D511yescharacteristic
355C2×C42—151no—
356C2×C42—301no—
357C2×C42—301no—
358#107—52no—
359#106—52no—
360#103—32no—
361#103—152no—
362#102—32no—
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×C3D4×D511yescharacteristic
372C22×D3—21no—
373C22×D3—101no—
374C2×C3×C4—22no—
375C2×C3×C4—102no—
376C2×C3×C4C2×C4×D512yes—
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4#71112yes—
379C2×C3×C4C23×D511yescharacteristic
380#67—24no—
381#67—104no—
382C2×Dic3—21no—
383C2×Dic3—52no—
384C2×Dic3—52no—
385C2×Dic3—104no—
386C2×Dic3—101no—
387D12—21no—
388D12—52no—
389D12—101no—
390D12C2×C4×D512yes—
391C4×D3—24no—
392C4×D3—104no—
393C4×D3—204no—
394C4×D3—204no—
395Dic6—21no—
396Dic6—52no—
397Dic6—101no—
398Dic6C2×C4×D512yes—
399C3×C8—52no—
400C3×C8—52no—
401C3⋊C8—22no—
402C22×C5—22no—
403C22×C5—62no—
404C22×C5—122no—
405C22×C5#89312yes—
406C22×C5C2×D3×D411yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—42no—
410C4×C5—62no—
411C4×C5#89312yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23911yescharacteristic
414Dic5—34no—
415Dic5—42no—
416Dic5—62no—
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—61no—
429C22×C4—152no—
430C22×C4—302no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—32no—
439C2×C8—54no—
440C2×C8—51no—
441C2×C8—51no—
442C2×C8—62no—
443C4⋊C4—52no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—21no—
448C22⋊C4—101no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—21no—
452C42—101no—
453C42—151no—
454C42—151no—
455C42—152no—
456C42—302no—
457C42—302no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3#402712yes—
461C22×C3C2×D4×D511yescharacteristic
462C2×D3—22no—
463C2×D3—42no—
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—42no—
467C3×C4—202no—
468C3×C4#402712yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#71111yescharacteristic
471Dic3—22no—
472Dic3—54no—
473Dic3—102no—
474Dic3—102no—
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×#89311yescharacteristic
478C2×C5D3×#13512yes—
479D5—122no—
480C23—61no—
481C23—301no—
482C23#679011yescharacteristic
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—61no—
495C2×C4—64no—
496C2×C4—102no—
497C2×C4—152no—
498C2×C4—152no—
499C2×C4—304no—
500C2×C4—301no—
501C2×C4—304no—
502C2×C4—604no—
503C2×C4—604no—
504C2×C4#676812yes—
505C2×C4C4×D3×D512yes—
506C2×C4#679011yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—52no—
509C8—52no—
510C8—62no—
511C2×C3—22no—
512C2×C3C2×#402711yescharacteristic
513C2×C3D5×#13512yes—
514D3—42no—
515D3—202no—
516C5#7916511yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—122no—
520C22—302no—
521C22—602no—
522C22#9140612yes—
523C22C2×#679011yescharacteristic
524C4—42no—
525C4—62no—
526C4—154no—
527C4—202no—
528C4—302no—
529C4—302no—
530C4#9140612yes—
531C4C2×#676811yescharacteristic
532C4C2×C4×D3×D511yescharacteristic
533C3#1061054911yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—602no—
537C2C2×#9140611yescharacteristic
538C2#1175532812yes—
subgroupG/H
centerC2×C4#6790
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. #11756281C2semidirect
2. #11754455C2semidirect
4. C5×#5002C2semidirect
5. C3×#65287C2semidirect
6. #11748411C2semidirect
7. C2×#90951C2semidirect
8. #11747279C2semidirect
9. #11747278C2semidirect
10. #11747234C2semidirect
11. #11747233C2semidirect
33. #91303C4semidirect
50. #65287D3semidirect
59. #6817C2×C4semidirect
66. C5×#235C2×C4semidirect
85. C2×C3×#168C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
101. #5002D5semidirect
235. C2×#168C4×D3semidirect
262. Dic15#135semidirect
272. #235C4×D5semidirect
458. C3×C5C4×#135semidirect
516. C5#79165semidirect
533. C3#10610549semidirect

Maximal subgroups

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

subgroupindex
#117562812
#117544552
C2×#913032
C5×#50022
C3×#652872
#117484112
C2×#909512
#117472792
#117472782
#117472342
#117472332
#106105493
#791655