Finite Group Databasebeta

← #14418050

Subgroups — #14418050

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#907C211yesmaximal, characteristic, complemented
2#11754138C211yesmaximal, characteristic
3C2×#91283C211yesmaximal, characteristic, complemented
4#11751225C211yesmaximal, characteristic, complemented
5C3×#65428C211yesmaximal, characteristic, complemented
6#11748425C211yesmaximal, characteristic, complemented
7#11748318C211yesmaximal, characteristic, complemented
8#11748205C214yesmaximal, complemented
9#11748204C214yesmaximal, complemented
10#10615523—31nomaximal, Hall
11C2×C5×#235C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C5×#907—21no—
18C5×#907—21no—
19C5×#907C2212yescomplemented
20C5×#907C2212yescomplemented
21C2×C5×ΓL(1,𝔽25)—21no—
22C2×C5×D3×C8—21no—
23C3×#4072C2211yescharacteristic
24#91309C412yescomplemented
25#91307C412yescomplemented
26#91299C412yescomplemented
27#91298C412yescomplemented
28#91297C2214yes—
29C2×#6649—21no—
30#91283—21no—
31#91283—21no—
32#91283C2212yescomplemented
33#91283C2212yescomplemented
34C2×D5×C3⋊C8—21no—
35#91106C2214yescomplemented
36C3×#3957C2214yescomplemented
37#90979C2214yescomplemented
38#90952C2212yescomplemented
39Dic5×C3⋊C8C2212yescomplemented
40#78989—51nomaximal, Hall
41C2×C5×#131—31no—
42#66156—31no—
43C2×#4047—31no—
44#65525—31no—
45#65434—34no—
46#65433—34no—
47#65428D311yescharacteristic, complemented
48#65413—31no—
49#65390—31no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C5×#67—21no—
52C5×#235—21no—
53C5×#235—21no—
54C5×#235C2×C412yes—
55C5×#235C2312yes—
56C2×C5×D12C2×C411yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6C2×C411yescharacteristic
59C2×C3×C22⋊D5—21no—
60C3×#709—21no—
61C3×#709—21no—
62C3×#709C2×C412yes—
63C3×#709C2312yes—
64C2×C3×D20C2×C411yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2×C411yescharacteristic
67C3×C5×M16—21no—
68C3×C5×M16C2312yes—
69C2×C3×C5×C8—21no—
70#6710—21no—
71#6710C2×C412yes—
72#6710C2×C412yes—
73#6710C2312yes—
74C2×C3⋊#168—21no—
75C2×C3⋊#168C2312yes—
76C2×C5×C3⋊C8D411yescharacteristic
77C2×C5×C3⋊C8D411yescharacteristic
78C2×C5×C3⋊C8D411yescharacteristic
79C2×C5×C3⋊C8D411yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C5×ΓL(1,𝔽25)—22no—
83C5×ΓL(1,𝔽25)—22no—
84C5×D3×C8—22no—
85C5×D3×C8—22no—
86C3×C22⋊Dic5—21no—
87C3×C4⋊Dic5—21no—
88C3×C4×Dic5C2312yes—
89#6661C2×C414yes—
90#6656C2×C414yes—
91#6655C2×C414yes—
92#6652C2×C414yes—
93#6649—22no—
94#6649—22no—
95D5×C3⋊C8—22no—
96D5×C3⋊C8—22no—
97#5822—51no—
98C2×#948—51no—
99C2×#907D511yescharacteristic, complemented
100C3×#421—51no—
101#5124—51no—
102#5005—51no—
103#4997—51no—
104#4824—54no—
105#4823—54no—
106C2×C5×#41—31no—
107C2×#709C2×D311yescharacteristic
108C5×#131—32no—
109C5×#131—32no—
110C5×#131—61no—
111C5×#131—61no—
112C2×C5×M16—61no—
113C2×C5×M16C2×D311yescharacteristic
114C22×C5×C8—31no—
115C22×C5×C8—61no—
116#4097—32no—
117#4096—34no—
118#4095—32no—
119#4088—32no—
120#4078—32no—
121#4072C2×D311yescharacteristic
122C2×#681—31no—
123C2×#681—31no—
124#4047—32no—
125#4047—32no—
126#4047—61no—
127#4047—61no—
128C2×#676—61no—
129C2×C8×D5—61no—
130#3969—34no—
131#3957C2×D314yescomplemented
132#3954—34no—
133#3947—32no—
134C8×Dic5—32no—
135#2955—151noSylow
136C23×C3×C5#4111yescharacteristic
137C22×C5×D3—21no—
138C22×C3×D5—21no—
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×C3×C4×C5C22×C411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4111yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C5×#67—22no—
146C5×#67—22no—
147C2×C5×Dic3—21no—
148C5×D12—21no—
149C5×D12C22×C412yes—
150C4×C5×D3—22no—
151C4×C5×D3—22no—
152C5×Dic6—21no—
153C5×Dic6C22×C412yes—
154C3×C22⋊D5—22no—
155C3×C22⋊D5—22no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164C3×C5×C8—22no—
165C3⋊#168—22no—
166C3⋊#168C22×C414yes—
167C5×C3⋊C8C2×D411yescharacteristic
168C5×C3⋊C8C2×D411yescharacteristic
169C5×C3⋊C8C2×D411yescharacteristic
170C5×C3⋊C8C2×D411yescharacteristic
171C2×C3×#41—51no—
172C2×#235C2×D511yescharacteristic
173C2×C3×M16C2×D511yescharacteristic
174C3×#117—51no—
175#951—52no—
176#950—54no—
177#949—52no—
178#948—52no—
179#948—52no—
180#948—101no—
181#948—101no—
182#942—52no—
183#932—52no—
184C2×#208—51no—
185C2×#208—51no—
186C2×#208—101no—
187C22×C3⋊C8—101no—
188C22×C3⋊C8C2×D511yescharacteristic
189#907—21no—
190#907—21no—
191#907C2×D512yescomplemented
192#907C2×D512yescomplemented
193C2×ΓL(1,𝔽25)—21no—
194C2×D3×C8—21no—
195C3×#104—54no—
196#822—54no—
197#805—54no—
198#803—52no—
199C4×C3⋊C8—52no—
200C5×#41—32no—
201C5×#41—32no—
202C5×#41—61no—
203C5×#41—61no—
204C2×C5×Q8—31no—
205C2×C5×D4—31no—
206C2×C5×D4—61no—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—21no—
210#709—21no—
211#709—21no—
212#709C4×D312yes—
213#709C22×D312yes—
214C2×D20C4×D311yescharacteristic
215C2×C4×D5—21no—
216C2×Dic10C4×D311yescharacteristic
217C5×M16—21no—
218C5×M16—62no—
219C5×M16—62no—
220C5×M16C22×D312yes—
221C2×C5×C8—21no—
222C2×C5×C8—31no—
223C2×C5×C8—31no—
224C2×C5×C8—31no—
225C2×C5×C8—31no—
226C2×C5×C8—31no—
227C2×C5×C8—31no—
228C2×C5×C8—62no—
229C2×C5×C8—62no—
230C22⋊Dic5—21no—
231#689—34no—
232#688—34no—
233#687—34no—
234#686—34no—
235C4⋊Dic5—21no—
236C4×Dic5C22×D312yes—
237#681—32no—
238#681—32no—
239#681—32no—
240#681—61no—
241C2×#168—32no—
242C2×#168—61no—
243#676—62no—
244#676—62no—
245C8×D5—62no—
246C8×D5—62no—
247#575—151no—
248C2×#131—31no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—151no—
253#421—51no—
254#421—151no—
255#405—151no—
256C22×C3×C5—41no—
257C22×C3×C5C4×D411yescharacteristic
258C22×C3×C5C4×D411yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C2×C5×D3—22no—
261C2×C5×D3—42no—
262C2×C3×D5—22no—
263C2×C3×D5—42no—
264C3×C4×C5C4×D411yescharacteristic
265C3×C4×C5C4×D411yescharacteristic
266C3×C4×C5C23×C411yescharacteristic
267C3×C4×C5C22×D411yescharacteristic
268C3×Dic5—22no—
269C3×Dic5—42no—
270C5×Dic3—22no—
271C3×#41—52no—
272C3×#41—52no—
273C3×#41—101no—
274C3×#41—101no—
275C2×C3×Q8—51no—
276C2×C3×D4—51no—
277C2×C3×D4—101no—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281#235—21no—
282#235—21no—
283#235C4×D512yes—
284#235C22×D512yes—
285C2×D12C4×D511yescharacteristic
286C2×C4×D3—21no—
287C2×Dic6C4×D511yescharacteristic
288C3×M16—21no—
289C3×M16C22×D512yes—
290C2×C3×C8—21no—
291C3×C4⋊C4—101no—
292C3×C22⋊C4—101no—
293C3×C42—52no—
294#216—54no—
295#215—54no—
296#214—54no—
297#213—54no—
298#208—52no—
299#208—52no—
300#208—52no—
301#208—101no—
302#208—102no—
303#208—102no—
304C2×C3⋊C8—52no—
305C2×C3⋊C8—101no—
306C2×C3⋊C8—102no—
307C2×C3⋊C8—102no—
308C2×C3⋊C8C22⋊D511yescharacteristic
309C2×C3⋊C8C22⋊D511yescharacteristic
310C2×C3⋊C8C22⋊D511yescharacteristic
311C2×C3⋊C8C22⋊D511yescharacteristic
312C2×C3⋊C8C22×D511yescharacteristic
313C2×C3⋊C8C22×D511yescharacteristic
314ΓL(1,𝔽25)—22no—
315ΓL(1,𝔽25)—22no—
316D3×C8—22no—
317D3×C8—22no—
318C23×C5—61no—
319C23×C5#23711yescharacteristic
320C22×D5—21no—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—32no—
324C5×D4—62no—
325C5×D4—62no—
326C5×D4—61no—
327C2×C4×C5—61no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5C2×C4×D311yescharacteristic
331C2×C4×C5C2×C4×D311yescharacteristic
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5#23711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—22no—
337C22⋊D5—22no—
338C2×Dic5—21no—
339C2×Dic5—22no—
340D20—21no—
341D20C2×C4×D312yes—
342C4×D5—22no—
343C4×D5—22no—
344Dic10—21no—
345Dic10C2×C4×D312yes—
346C5×C8—22no—
347C5×C8—31no—
348C5×C8—31no—
349C5×C8—31no—
350C5×C8—31no—
351#168—34no—
352#168—62no—
353C2×#41—31no—
354C2×#41—51no—
355#137—152no—
356#137—152no—
357AGL(1,ℤ/8)—152no—
358AGL(1,ℤ/8)—152no—
359#135—154no—
360#131—32no—
361#131—32no—
362#131—61no—
363#131—61no—
364#131—152no—
365#131—152no—
366#131—301no—
367#131—301no—
368C2×M16—61no—
369C2×M16—151no—
370C2×M16—151no—
371C2×M16—301no—
372C2×M16D3×D511yescharacteristic
373C22×C8—31no—
374C22×C8—61no—
375C22×C8—301no—
376#117—51no—
377#108—154no—
378#104—54no—
379#104—154no—
380#97—152no—
381C4×C8—152no—
382C2×C3×C5—21no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5C2×C4×D411yescharacteristic
386C3×D5—42no—
387C5×D3—42no—
388C23×C3—101no—
389C23×C3#70911yescharacteristic
390C22×D3—21no—
391C3×Q8—52no—
392C3×Q8—101no—
393C3×D4—52no—
394C3×D4—102no—
395C3×D4—102no—
396C3×D4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4C2×C4×D511yescharacteristic
402C2×C3×C4C2×C4×D511yescharacteristic
403C2×C3×C4#70911yescharacteristic
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—22no—
408#67—22no—
409C2×Dic3—21no—
410D12—21no—
411D12C2×C4×D512yes—
412C4×D3—22no—
413C4×D3—22no—
414Dic6—21no—
415Dic6C2×C4×D512yes—
416C3×C8—22no—
417C3⋊C8—54no—
418C3⋊C8—102no—
419C3⋊C8C2×C22⋊D511yescharacteristic
420C3⋊C8C2×C22⋊D511yescharacteristic
421C3⋊C8C2×C22⋊D511yescharacteristic
422C3⋊C8C2×C22⋊D511yescharacteristic
423C22×C5—41no—
424C22×C5—62no—
425C22×C5—122no—
426C22×C5#67⋊C411yescharacteristic
427C22×C5#67⋊C411yescharacteristic
428C22×C5C2×#23711yescharacteristic
429C2×D5—22no—
430C2×D5—42no—
431C4×C5—62no—
432C4×C5#67⋊C411yescharacteristic
433C4×C5#67⋊C411yescharacteristic
434C4×C5C22×C4×D311yescharacteristic
435C4×C5C2×D3×D411yescharacteristic
436Dic5—22no—
437Dic5—42no—
438#41—32no—
439#41—32no—
440#41—52no—
441#41—52no—
442#41—61no—
443#41—61no—
444#41—101no—
445#41—101no—
446C2×Q8—31no—
447C2×Q8—51no—
448C2×D4—31no—
449C2×D4—51no—
450C2×D4—61no—
451C2×D4—101no—
452C22×C4—61no—
453C22×C4—101no—
454C22×C4C2×D3×D511yescharacteristic
455Q16—154no—
456SD16—154no—
457SD16—154no—
458D8—154no—
459M16—21no—
460M16—62no—
461M16—62no—
462M16—152no—
463M16—152no—
464M16—152no—
465M16—302no—
466M16—302no—
467M16—301no—
468M16C2×D3×D512yes—
469C2×C8—21no—
470C2×C8—31no—
471C2×C8—31no—
472C2×C8—31no—
473C2×C8—31no—
474C2×C8—31no—
475C2×C8—31no—
476C2×C8—62no—
477C2×C8—62no—
478C2×C8—152no—
479C2×C8—302no—
480C2×C8—302no—
481C2×C8—301no—
482C4⋊C4—101no—
483C22⋊C4—101no—
484C42—52no—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—41no—
487C22×C3—102no—
488C22×C3—202no—
489C22×C3C4×C22⋊D511yescharacteristic
490C22×C3C4×C22⋊D511yescharacteristic
491C22×C3C2×#70911yescharacteristic
492C2×D3—22no—
493C2×D3—42no—
494C3×C4—102no—
495C3×C4—202no—
496C3×C4C4×C22⋊D511yescharacteristic
497C3×C4C4×C22⋊D511yescharacteristic
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C22×C22⋊D511yescharacteristic
500Dic3—22no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5—122no—
505C2×C5C2×#67⋊C411yescharacteristic
506D5—42no—
507C23—61no—
508C23—101no—
509C23#676511yescharacteristic
510Q8—32no—
511Q8—52no—
512Q8—61no—
513Q8—101no—
514D4—32no—
515D4—52no—
516D4—62no—
517D4—62no—
518D4—61no—
519D4—102no—
520D4—102no—
521D4—101no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—101no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4#676511yescharacteristic
530C2×C4C4×D3×D511yescharacteristic
531C2×C4C4×D3×D511yescharacteristic
532C2×C4D3×C22⋊D511yescharacteristic
533C2×C4D3×C22⋊D511yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—22no—
536C8—31no—
537C8—31no—
538C8—31no—
539C8—31no—
540C8—154no—
541C8—302no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—202no—
546C2×C3C2×C4×C22⋊D511yescharacteristic
547D3—42no—
548C5#7898911yescharacteristic, complemented, Sylow
549C22—41no—
550C22—62no—
551C22—102no—
552C22—122no—
553C22—202no—
554C22#9144111yescharacteristic
555C22#9144111yescharacteristic
556C22C2×#676511yescharacteristic
557C4—62no—
558C4—102no—
559C4—202no—
560C4#9144111yescharacteristic
561C4#9144111yescharacteristic
562C4C2×C4×D3×D511yescharacteristic
563C4C2×D3×C22⋊D511yescharacteristic
564C3#1061552311yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—122no—
569C2—202no—
570C2C2×#9144111yescharacteristic
subgroupG/H
centerC4C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754138C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#907C2semidirect
3. C2×#91283C2semidirect
4. #11751225C2semidirect
5. C3×#65428C2semidirect
6. #11748425C2semidirect
7. #11748318C2semidirect
8. #11748205C2semidirect
9. #11748204C2semidirect
19. C5×#907C22semidirect
20. C5×#907C22semidirect
24. #91309C4semidirect
25. #91307C4semidirect
26. #91299C4semidirect
27. #91298C4semidirect
32. #91283C22semidirect
33. #91283C22semidirect
35. #91106C22semidirect
36. C3×#3957C22semidirect
37. #90979C22semidirect
38. #90952C22semidirect
39. Dic5×C3⋊C8C22semidirect
47. #65428D3semidirect
99. C2×#907D5semidirect
131. #3957C2×D3semidirect
191. #907C2×D5semidirect
192. #907C2×D5semidirect
485. C3×C5#2955semidirect
548. C5#78989semidirect
564. C3#10615523semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9072
#117541382
C2×#912832
#117512252
C3×#654282
#117484252
#117483182
#117482052
#117482042
#106155233
#789895