Finite Group Databasebeta

← #14416274

Subgroups — #14416274

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#11754414C211yesmaximal, characteristic, complemented
2Dic5×#235C211yesmaximal, characteristic, complemented
3C2×#91303C211yesmaximal, characteristic
4#11751214C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6C2×C3×C8×Dic5C211yesmaximal, characteristic, complemented
7#11748458C211yesmaximal, characteristic, complemented
8#11747834C212yesmaximal, complemented
9#11747833C212yesmaximal, complemented
10#11747745C212yesmaximal, complemented
11#11747744C212yesmaximal, complemented
12#10610549—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20#91552—22no—
21Dic5×#67—22no—
22#91418C2212yes—
23Dic5×D12C2212yes—
24C4×#1200—21no—
25C4×D3×Dic5—21no—
26#91386—21no—
27#91371—21no—
28#91333C2212yes—
29Dic5×Dic6C2212yes—
30C2×#6663C2211yescharacteristic
31C2×#6660C2211yescharacteristic
32C2×#6659C2211yescharacteristic
33#91303C418yescomplemented
34C2×#6654C2211yescharacteristic
35#91105C2212yes—
36#91100C2212yes—
37C5×#821C2212yes—
38C5×#816C2212yes—
39C3×C8×Dic5C2212yes—
40C3×C8×Dic5C2212yes—
41#90988C2212yes—
42#90985C2212yes—
43C4×#904—51nomaximal, Hall
44#41×Dic5—31no—
45C2×#4096—31no—
46#65856—31no—
47C5×#416—31no—
48#65402—31no—
49C2×C8×Dic5D311yescharacteristic, complemented
50#65287—31no—
51#65079—32no—
52#65077—32no—
53#65047—32no—
54#65045—32no—
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—
63C5×#235—22no—
64C5×#235C2×C414yescomplemented
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C22×C3×Dic5D412yes—
69C2×#1200—22no—
70C2×D3×Dic5—22no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2312yes—
73#6719—21no—
74C4⋊Dic15C2312yes—
75C4×Dic15—21no—
76C5×#217—21no—
77C5×C4⋊Dic3C2312yes—
78C4×C5×Dic3—21no—
79C3×C4×Dic5D411yescharacteristic
80C3×C4×Dic5D411yescharacteristic
81C3×C4×Dic5C2312yes—
82C2×C3×#168C2×C414yescomplemented
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6667—22no—
88(C2×D3)⋊Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6663C2×C414yescomplemented
92#6660C2×C414yescomplemented
93#6659C2×C414yescomplemented
94#6654C2×C414yescomplemented
95C2×#904—51no—
96C4×#235—51no—
97C4×#235—51no—
98C2×C3×C4×C8—51no—
99#5113—51no—
100#5113D511yescharacteristic, complemented
101#5106—51no—
102C4×Dic12—52no—
103C4×D24—52no—
104C4×#204—52no—
105C4×#204—52no—
106C2×C5×#41—31no—
107C2×#709—31no—
108C22×C5×C8C2×D311yescharacteristic
109C5×#117—31no—
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—31no—
119#4072—61no—
120C2×C4×Dic5—61no—
121C2×C4×Dic5C2×D311yescharacteristic
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×Dic5C2×D312yes—
133C8×Dic5C2×D312yes—
134#3940—32no—
135#3939—32no—
136C4×#135—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×C5×D3—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—24no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147D60—21no—
148D60C22×C412yes—
149C4×D15—24no—
150Dic30—21no—
151Dic30C22×C412yes—
152C5×#67—24no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—22no—
155C5×D12—21no—
156C5×D12C22×C412yes—
157C4×C5×D3—24no—
158C5×Dic6—21no—
159C5×Dic6C22×C412yes—
160C2×C3×Dic5—24no—
161C2×C3×Dic5C2×D412yes—
162C2×C3×Dic5C2×D412yes—
163#1200—44no—
164D3×Dic5—44no—
165C3×C5×C8—22no—
166C3×#168C22×C412yes—
167C3×#168C22×C412yes—
168C2×#235—51no—
169C2×#235C2×D511yescharacteristic
170C22×C3×C8—51no—
171C22×C3×C8C2×D511yescharacteristic
172C2×C3×C42—51no—
173C4×#67—102no—
174C4×#67—102no—
175#926—51no—
176#926C2×D511yescharacteristic
177C2×Dic12—51no—
178#904—58no—
179C2×D24—51no—
180C2×#204—51no—
181C2×#204—51no—
182C4×D12—52no—
183C4×D12—52no—
184#872—101no—
185#872—101no—
186C42×D3—101no—
187C42×D3—101no—
188C4×Dic6—52no—
189C4×Dic6—52no—
190C3×C4×C8—52no—
191C3×C4×C8—52no—
192#821—52no—
193#821C2×D512yes—
194#818—52no—
195#817—52no—
196#816—52no—
197#816C2×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—62no—
207C22×Dic5D1212yes—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C2×C5×C8—22no—
215C2×C5×C8C22×D312yes—
216C5×C4⋊C4—32no—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219C22⋊Dic5—61no—
220C22⋊Dic5—62no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—62no—
228#683—62no—
229C4×Dic5—61no—
230C4×Dic5—62no—
231C4×Dic5—62no—
232C4×Dic5D1211yescharacteristic
233C4×Dic5D1211yescharacteristic
234C4×Dic5C22×D312yes—
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—151no—
246#416—31no—
247#416—151no—
248C2×C4×C8—51no—
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×C5C4×D412yes—
257C3×C4×C5C23×C411yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260Dic15—42no—
261C3×Dic5—22no—
262C3×Dic5#13514yescomplemented
263C5×Dic3—22no—
264C5×Dic3—42no—
265C22×C3×C4—52no—
266C22×C3×C4C22×D511yescharacteristic
267C2×#67—21no—
268C2×#67—101no—
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—22no—
282C2×C3×C8—54no—
283C2×C3×C8—51no—
284C2×C3×C8—51no—
285C2×C3×C8C22×D512yes—
286C3×C42—51no—
287C3×C42—51no—
288C3×C42—52no—
289#217—21no—
290#217—101no—
291(C2×D3)⋊C4—102no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—52no—
294C4⋊Dic3C22×D512yes—
295Dic3⋊C4—102no—
296Dic3⋊C4—102no—
297C4×Dic3—21no—
298C4×Dic3—102no—
299C4×Dic3—102no—
300C4×Dic3—101no—
301Dic12—54no—
302D24—54no—
303#204—54no—
304#204—54no—
305C23×C5—61no—
306C23×C5C2×D1211yescharacteristic
307C22×D5—61no—
308C5×Q8—32no—
309C5×Q8—61no—
310C5×D4—32no—
311C5×D4—64no—
312C5×D4—61no—
313C2×C4×C5—61no—
314C2×C4×C5—64no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5C2×D1211yescharacteristic
318C2×C4×C5#23512yes—
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—64no—
321C2×Dic5—24no—
322C2×Dic5—61no—
323C2×Dic5—62no—
324C2×Dic5—124no—
325C2×Dic5C2×D1212yes—
326C2×Dic5C2×D1212yes—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—22no—
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×C8D3×D511yescharacteristic
345C4×Q8—152no—
346C4×Q8—152no—
347C4×D4—152no—
348C4×D4—152no—
349C4×D4—302no—
350C4×D4—302no—
351#117—31no—
352#117—151no—
353#117—301no—
354#117—301no—
355C2×C42—51no—
356C2×C42—301no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—32no—
361#103—152no—
362#102—32no—
363#102—152no—
364C4×C8—52no—
365C4×C8—52no—
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—52no—
375C2×C3×C4—52no—
376C2×C3×C4—104no—
377C2×C3×C4C2×C4×D512yes—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4#71112yes—
380C2×C3×C4C23×D511yescharacteristic
381#67—24no—
382#67—104no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—101no—
386C2×Dic3—102no—
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—22no—
400C3×C8—52no—
401C3×C8—52no—
402C22×C5—22no—
403C22×C5—62no—
404C22×C5—122no—
405C22×C5C4×D1212yes—
406C22×C5C22×D1211yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—62no—
410C4×C5—122no—
411C4×C5C4×D1212yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23511yescharacteristic
414Dic5—22no—
415Dic5—62no—
416Dic5—122no—
417Dic5#90414yescomplemented
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—52no—
429C22×C4—61no—
430C22×C4—302no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—22no—
439C2×C8—54no—
440C2×C8—51no—
441C2×C8—51no—
442C2×C8C2×D3×D512yes—
443C4⋊C4—32no—
444C4⋊C4—152no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—61no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—51no—
452C42—51no—
453C42—52no—
454C42—61no—
455C42—302no—
456C42—302no—
457C42—301no—
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—54no—
467C3×C4—102no—
468C3×C4#402712yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#71111yescharacteristic
471Dic3—22no—
472Dic3—42no—
473Dic3—102no—
474Dic3—202no—
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×C4×D1211yescharacteristic
478C2×C5C2×#90412yes—
479D5—122no—
480C23—61no—
481C23—301no—
482C23D5×D1211yescharacteristic
483Q8—32no—
484Q8—61no—
485Q8—152no—
486Q8—301no—
487D4—32no—
488D4—64no—
489D4—61no—
490D4—152no—
491D4—304no—
492D4—301no—
493C2×C4—52no—
494C2×C4—52no—
495C2×C4—61no—
496C2×C4—64no—
497C2×C4—62no—
498C2×C4—104no—
499C2×C4—301no—
500C2×C4—304no—
501C2×C4—302no—
502C2×C4—604no—
503C2×C4—604no—
504C2×C4C4×D3×D512yes—
505C2×C4D5×D1211yescharacteristic
506C2×C4#678212yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—22no—
509C8—52no—
510C8—52no—
511C2×C3—22no—
512C2×C3C2×#402711yescharacteristic
513C2×C3D5×#13512yes—
514D3—42no—
515D3—202no—
516C5C4×#90411yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—122no—
520C22—302no—
521C22—602no—
522C22#9140512yes—
523C22C2×D5×D1211yescharacteristic
524C4—54no—
525C4—62no—
526C4—102no—
527C4—122no—
528C4—302no—
529C4—602no—
530C4#9140512yes—
531C4C2×C4×D3×D511yescharacteristic
532C4C2×#678211yescharacteristic
533C3#1061054911yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—602no—
537C2D5×#90412yes—
538C2C2×#9140511yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754414C2semidirect
2. Dic5×#235C2semidirect
4. #11751214C2semidirect
5. C5×#5113C2semidirect
6. C2×C3×C8×Dic5C2semidirect
7. #11748458C2semidirect
8. #11747834C2semidirect
9. #11747833C2semidirect
10. #11747745C2semidirect
11. #11747744C2semidirect
33. #91303C4semidirect
49. C2×C8×Dic5D3semidirect
58. #6817C2×C4semidirect
64. C5×#235C2×C4semidirect
82. C2×C3×#168C2×C4semidirect
91. #6663C2×C4semidirect
92. #6660C2×C4semidirect
93. #6659C2×C4semidirect
94. #6654C2×C4semidirect
100. #5113D5semidirect
235. C2×#168C4×D3semidirect
262. C3×Dic5#135semidirect
272. #235C4×D5semidirect
417. Dic5#904semidirect
458. C3×C5C4×#135semidirect
516. C5C4×#904semidirect
533. C3#10610549semidirect

Maximal subgroups

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

subgroupindex
#117544142
Dic5×#2352
C2×#913032
#117512142
C5×#51132
C2×C3×C8×Dic52
#117484582
#117478342
#117478332
#117477452
#117477442
#106105493
C4×#9045