Finite Group Databasebeta

← #14416269

Subgroups — #14416269

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#41×Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic
3#11754455C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5#11749265C212yesmaximal, complemented
6#11749240C212yesmaximal, complemented
7#11749019C212yesmaximal, complemented
8#11748994C212yesmaximal, complemented
9#11748451C211yesmaximal, characteristic, complemented
10#11748388C211yesmaximal, characteristic, complemented
11C2×#90951C211yesmaximal, characteristic, complemented
12Dic5×#135—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15Q8×Dic15C2212yes—
16D4×Dic15—22no—
17D4×Dic15C2212yes—
18#91815—21no—
19#91815C2211yescharacteristic
20C2×C4×Dic15—21no—
21C2×C4×Dic15C2211yescharacteristic
22C5×#950C418yescomplemented
23C2×C5×#216C2211yescharacteristic
24C2×C5×#215C2211yescharacteristic
25C2×C5×#214C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30#67⋊Dic5—22no—
31#91435C2212yes—
32C4×D3×Dic5—21no—
33#91371—21no—
34#91344C2212yes—
35C3×#3967C2212yes—
36C3×#3964C2212yes—
37#90990C2212yes—
38#90987C2212yes—
39#90973C2212yes—
40#90967C2212yes—
41#90951C2212yes—
42#90951C2212yes—
43#78818—51nomaximal, Hall
44C2×C5×#135—31no—
45#41×Dic5—31no—
46#41×Dic5—31no—
47#65522—31no—
48#65522D311yescharacteristic, complemented
49Q16×Dic5—32no—
50SD16×Dic5—32no—
51SD16×Dic5—32no—
52D8×Dic5—32no—
53#65395—31no—
54C2×C8×Dic5—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—22no—
63C22×Dic15D412yes—
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—
71#6719—21no—
72#6719—22no—
73C4⋊Dic15—22no—
74C4⋊Dic15C2312yes—
75C4×Dic15—21no—
76C4×Dic15—22no—
77C4×Dic15D411yescharacteristic
78C4×Dic15D411yescharacteristic
79C4×Dic15C2312yes—
80C5×#216C2×C414yescomplemented
81C5×#215C2×C414yescomplemented
82C5×#214C2×C414yescomplemented
83C5×#213C2×C414yescomplemented
84C2×C5×C3⋊C8C2×C414yescomplemented
85C2×C5×C3⋊C8C2311yescharacteristic
86C2×C5×C3⋊C8C2311yescharacteristic
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90C2×C3×#168—22no—
91C2×C3×#168C2312yes—
92Dic3⋊Dic5—22no—
93(C2×D3)⋊Dic5—22no—
94Dic3×Dic5—22no—
95Dic3×#41—51no—
96C2×#950D511yescharacteristic
97#5522—51no—
98C3×#416—51no—
99#5113—51no—
100C2×C8×Dic3—51no—
101#4998—51no—
102#4790—52no—
103#4788—52no—
104#4758—52no—
105#4756—52no—
106C2×C5×#41—31no—
107C2×C5×#41C2×D311yescharacteristic
108C5×#135—38no—
109C2×C5×Q16—31no—
110C2×C5×SD16—31no—
111C2×C5×SD16—31no—
112C2×C5×D8—31no—
113C22×C5×C8—31no—
114Q8×Dic5—32no—
115Q8×Dic5—32no—
116D4×Dic5—32no—
117D4×Dic5—32no—
118D4×Dic5—62no—
119D4×Dic5—62no—
120#4072—31no—
121#4072—61no—
122#4072—61no—
123#4072C2×D311yescharacteristic
124C2×C4×Dic5—31no—
125C2×C4×Dic5—61no—
126C2×C4×Dic5—61no—
127C22×#168C2×D311yescharacteristic
128#3967—32no—
129#3967C2×D312yes—
130#3964—32no—
131#3964C2×D312yes—
132#3950—32no—
133#3949—32no—
134C8×Dic5—32no—
135C8×Dic5—32no—
136C4×#135—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×C5×D3—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15—44no—
154C2×Dic15C2×D412yes—
155C2×Dic15C2×D412yes—
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×#168—22no—
166C5×C3⋊C8C22×C412yes—
167C5×C3⋊C8C22×C412yes—
168C2×C3×#41C2×D511yescharacteristic
169C2×#235C2×D511yescharacteristic
170C22×C3×C8—51no—
171C3×#117—51no—
172#950Dic518yescomplemented
173Q8×Dic3—52no—
174C2×#216C2×D511yescharacteristic
175C2×#215C2×D511yescharacteristic
176D4×Dic3—52no—
177D4×Dic3—102no—
178C2×#214C2×D511yescharacteristic
179C2×#213C2×D511yescharacteristic
180#926—51no—
181#926—101no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—101no—
184C22×C3⋊C8C2×D511yescharacteristic
185#893—52no—
186#887—52no—
187#67⋊C4—102no—
188#872—101no—
189C42×D3—101no—
190C3×#103—52no—
191C3×#102—52no—
192#821—52no—
193#816—52no—
194C8×Dic3—52no—
195C8×Dic3—52no—
196#808—52no—
197#807—52no—
198C5×#41—22no—
199C5×#41—34no—
200C5×#41—62no—
201C5×#41C4×D314yescomplemented
202C2×C5×Q8—31no—
203C2×C5×Q8C22×D311yescharacteristic
204C2×C5×D4—21no—
205C2×C5×D4—31no—
206C2×C5×D4—61no—
207C2×C5×D4C22×D311yescharacteristic
208C22×C4×C5—21no—
209C22×C4×C5—61no—
210C22×C4×C5C22×D311yescharacteristic
211C22×Dic5—32no—
212C22×Dic5—62no—
213C22×Dic5—62no—
214C5×Q16—34no—
215C5×SD16—34no—
216C5×SD16—34no—
217C5×D8—34no—
218C2×C5×C8—34no—
219C2×C5×C8—31no—
220C2×C5×C8—31no—
221C22⋊Dic5—21no—
222C22⋊Dic5—62no—
223C22⋊Dic5—62no—
224C22⋊Dic5—61no—
225C4⋊Dic5—32no—
226C4⋊Dic5—62no—
227C4⋊Dic5—62no—
228C4⋊Dic5C22×D312yes—
229C4×Dic5—21no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—32no—
233C4×Dic5—62no—
234C4×Dic5—62no—
235C4×Dic5—61no—
236C2×#168—22no—
237C2×#168C22×D312yes—
238C2×#135—31no—
239C4×#41—151no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—151no—
246#416—51no—
247#416—151no—
248C2×C4×C8—151no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—42no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×C5×D3—22no—
255C2×C5×D3—42no—
256C3×C4×C5—22no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261Dic15—42no—
262Dic15#13514yescomplemented
263C3×Dic5—42no—
264C5×Dic3—22no—
265C3×#41—22no—
266C3×#41C2×Dic514yescomplemented
267C2×C3×Q8C22×D511yescharacteristic
268C2×C3×D4—21no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—21no—
273C22×Dic3—52no—
274C22×Dic3—102no—
275#235—22no—
276#235C2×Dic514yescomplemented
277C2×D12C22×D511yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—102no—
280C2×Dic6C22×D511yescharacteristic
281C2×C3×C8—52no—
282C2×C3×C8—102no—
283C3×C4⋊C4—52no—
284C3×C22⋊C4—101no—
285C3×C42—101no—
286#217—102no—
287#217—101no—
288#216C2×Dic514yescomplemented
289#215C2×Dic514yescomplemented
290#214C2×Dic514yescomplemented
291#213C2×Dic514yescomplemented
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—52no—
294C4⋊Dic3—102no—
295Dic3⋊C4—102no—
296C4×Dic3—51no—
297C4×Dic3—51no—
298C4×Dic3—52no—
299C4×Dic3—102no—
300C4×Dic3—102no—
301C4×Dic3—101no—
302C2×C3⋊C8C2×Dic514yescomplemented
303C2×C3⋊C8C22×D511yescharacteristic
304C2×C3⋊C8C22×D511yescharacteristic
305C23×C5—21no—
306C23×C5—61no—
307C23×C5D3×D411yescharacteristic
308C5×Q8—21no—
309C5×Q8—32no—
310C5×Q8—61no—
311C5×Q8C2×C4×D312yes—
312C5×D4—24no—
313C5×D4—21no—
314C5×D4—32no—
315C5×D4—64no—
316C5×D4—61no—
317C5×D4C2×C4×D312yes—
318C2×C4×C5—21no—
319C2×C4×C5—24no—
320C2×C4×C5—61no—
321C2×C4×C5—64no—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5#23712yes—
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—32no—
329C2×Dic5—64no—
330C2×Dic5—62no—
331C2×Dic5—124no—
332C2×Dic5—124no—
333C5×C8—32no—
334C5×C8—32no—
335#168—22no—
336C2×#41—31no—
337C2×#41D3×D511yescharacteristic
338#135—38no—
339C2×Q16—31no—
340C2×SD16—31no—
341C2×SD16—31no—
342C2×D8—31no—
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—151no—
353#117—301no—
354#117—301no—
355C2×C42—151no—
356C2×C42—301no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—52no—
361#103—152no—
362#102—52no—
363#102—152no—
364C4×C8—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5C2×#13512yes—
370C5×D3—42no—
371C23×C3—21no—
372C23×C3D4×D511yescharacteristic
373C22×D3—21no—
374C3×Q8—21no—
375C3×Q8C22×Dic512yes—
376C3×D4—24no—
377C3×D4—21no—
378C3×D4C22×Dic512yes—
379C2×C3×C4—21no—
380C2×C3×C4—24no—
381C2×C3×C4—102no—
382C2×C3×C4D4×D511yescharacteristic
383C2×C3×C4#71112yes—
384C2×C3×C4C22×Dic512yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—24no—
387C2×Dic3—21no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390C2×Dic3—104no—
391C2×Dic3—102no—
392C2×Dic3—204no—
393D12—21no—
394D12C22×Dic512yes—
395C4×D3—24no—
396C4×D3—204no—
397Dic6—21no—
398Dic6C22×Dic512yes—
399C3×C8—102no—
400C3⋊C8C22×Dic512yes—
401C3⋊C8C22×Dic512yes—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—42no—
405C22×C5—62no—
406C22×C5—122no—
407C22×C5#67⋊C412yes—
408C22×C5C2×D3×D411yescharacteristic
409C4×C5—22no—
410C4×C5—62no—
411C4×C5#67⋊C412yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23711yescharacteristic
414Dic5—34no—
415Dic5—42no—
416Dic5—62no—
417Dic5—122no—
418#41—22no—
419#41—34no—
420#41—62no—
421#41D3×Dic514yescomplemented
422C2×Q8—31no—
423C2×Q8C2×D3×D511yescharacteristic
424C2×D4—21no—
425C2×D4—31no—
426C2×D4—61no—
427C2×D4C2×D3×D511yescharacteristic
428C22×C4—21no—
429C22×C4—61no—
430C22×C4—152no—
431C22×C4—302no—
432C22×C4—302no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—34no—
435SD16—34no—
436SD16—34no—
437D8—34no—
438C2×C8—34no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—52no—
442C2×C8—102no—
443C4⋊C4—52no—
444C4⋊C4—152no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—101no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—101no—
452C42—151no—
453C42—151no—
454C42—152no—
455C42—302no—
456C42—302no—
457C42—301no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—42no—
462C22×C3D4×Dic512yes—
463C22×C3C2×D4×D511yescharacteristic
464C2×D3—22no—
465C2×D3—42no—
466C3×C4—22no—
467C3×C4—202no—
468C3×C4D4×Dic512yes—
469C3×C4C2×#71111yescharacteristic
470C3×C4C23×Dic511yescharacteristic
471Dic3—22no—
472Dic3—54no—
473Dic3—102no—
474Dic3—202no—
475C2×C5—22no—
476C2×C5—42no—
477C2×C5—122no—
478C2×C5C2×#67⋊C411yescharacteristic
479C2×C5D3×#13512yes—
480C23—21no—
481C23—61no—
482C23#679011yescharacteristic
483Q8—21no—
484Q8—32no—
485Q8—61no—
486Q8C2×D3×Dic512yes—
487D4—24no—
488D4—21no—
489D4—32no—
490D4—64no—
491D4—61no—
492D4C2×D3×Dic512yes—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—61no—
496C2×C4—64no—
497C2×C4—102no—
498C2×C4—152no—
499C2×C4—152no—
500C2×C4—304no—
501C2×C4—302no—
502C2×C4—604no—
503C2×C4—604no—
504C2×C4#678012yes—
505C2×C4C2×D3×Dic512yes—
506C2×C4#679011yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—32no—
509C8—32no—
510C8—102no—
511C2×C3—22no—
512C2×C3—42no—
513C2×C3D5×#13512yes—
514C2×C3C2×D4×Dic511yescharacteristic
515D3—42no—
516C5#7881811yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—42no—
520C22—62no—
521C22—122no—
522C22#67⋊Dic512yes—
523C22C2×#679011yescharacteristic
524C4—22no—
525C4—62no—
526C4—154no—
527C4—202no—
528C4—302no—
529C4—602no—
530C4#67⋊Dic512yes—
531C4C2×#678011yescharacteristic
532C4C22×D3×Dic511yescharacteristic
533C3Dic5×#13511yescharacteristic, complemented, Sylow
534C2—22no—
535C2—42no—
536C2—122no—
537C2#1175532812yes—
538C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#950C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×Dic15C2semidirect
3. #11754455C2semidirect
4. C3×#65522C2semidirect
5. #11749265C2semidirect
6. #11749240C2semidirect
7. #11749019C2semidirect
8. #11748994C2semidirect
9. #11748451C2semidirect
10. #11748388C2semidirect
11. C2×#90951C2semidirect
22. C5×#950C4semidirect
48. #65522D3semidirect
56. C3×C5×#41C2×C4semidirect
66. C5×#235C2×C4semidirect
80. C5×#216C2×C4semidirect
81. C5×#215C2×C4semidirect
82. C5×#214C2×C4semidirect
83. C5×#213C2×C4semidirect
84. C2×C5×C3⋊C8C2×C4semidirect
172. #950Dic5semidirect
201. C5×#41C4×D3semidirect
262. Dic15#135semidirect
266. C3×#41C2×Dic5semidirect
276. #235C2×Dic5semidirect
288. #216C2×Dic5semidirect
289. #215C2×Dic5semidirect
290. #214C2×Dic5semidirect
291. #213C2×Dic5semidirect
302. C2×C3⋊C8C2×Dic5semidirect
421. #41D3×Dic5semidirect
458. C3×C5C4×#135semidirect
516. C5#78818semidirect
533. C3Dic5×#135semidirect

Maximal subgroups

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

subgroupindex
#41×Dic152
C2×C5×#9502
#117544552
C3×#655222
#117492652
#117492402
#117490192
#117489942
#117484512
#117483882
C2×#909512
Dic5×#1353
#788185