Finite Group Databasebeta

← #14418052

Subgroups — #14418052

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×#91796C211yesmaximal, characteristic, complemented
2#11754154C211yesmaximal, characteristic
3C2×#91284C211yesmaximal, characteristic, complemented
4C5×#5124C211yesmaximal, characteristic, complemented
5C3×#65428C211yesmaximal, characteristic, complemented
6#11748429C211yesmaximal, characteristic, complemented
7#11748320C211yesmaximal, characteristic, complemented
8#11748175C214yesmaximal, complemented
9#11748174C214yesmaximal, complemented
10#10610988—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15#91796—21no—
16#91796—21no—
17#91796C2212yescomplemented
18#91796C2212yescomplemented
19C2×#6705—21no—
20C2×C8×D15—21no—
21C2×C5×#208C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24#91315C412yescomplemented
25#91313C412yescomplemented
26#91312C412yescomplemented
27#91311C2214yes—
28#91301C412yescomplemented
29C2×#6649—21no—
30#91284—21no—
31#91284—21no—
32#91284C2212yescomplemented
33#91284C2212yescomplemented
34C2×D5×C3⋊C8—21no—
35C5×#822C2214yescomplemented
36C3×#3957C2214yescomplemented
37#90981C2214yescomplemented
38#90952C2212yescomplemented
39Dic5×C3⋊C8C2212yescomplemented
40#78989—51nomaximal, Hall
41#66082—31no—
42C2×#4053—31no—
43C2×#4053—31no—
44C5×#430—31no—
45#65428—31no—
46#65428D311yescharacteristic, complemented
47#65411—31no—
48#65184—34no—
49#65183—34no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—21no—
52#6817—21no—
53#6817—21no—
54#6817C2×C412yes—
55#6817C2312yes—
56C2×D60C2×C411yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30C2×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—
70C2×C3⋊#168D411yescharacteristic
71C2×C3⋊#168D411yescharacteristic
72C2×C3⋊#168D411yescharacteristic
73C2×C3⋊#168D411yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76#6705—22no—
77#6705—22no—
78C8×D15—22no—
79C8×D15—22no—
80C5×#208—21no—
81C5×#208C2×C412yes—
82C5×#208C2×C412yes—
83C5×#208C2312yes—
84C2×C5×C3⋊C8—21no—
85C2×C5×C3⋊C8C2312yes—
86C3×C22⋊Dic5—21no—
87C3×C4⋊Dic5—21no—
88C3×C4×Dic5C2312yes—
89#6662C2×C414yes—
90#6658C2×C414yes—
91#6657C2×C414yes—
92#6653C2×C414yes—
93#6649—22no—
94#6649—22no—
95D5×C3⋊C8—22no—
96D5×C3⋊C8—22no—
97#5822—51no—
98C2×#948—51no—
99C2×#907—51no—
100C3×#421—51no—
101#5124D511yescharacteristic, complemented
102#5005—51no—
103#4997—51no—
104#4824—54no—
105#4823—54no—
106C2×#709—31no—
107C2×#709C2×D311yescharacteristic
108C2×C5×M16—31no—
109C2×C5×M16—31no—
110C2×C5×M16C2×D311yescharacteristic
111#4072C2×D311yescharacteristic
112C22×#168—31no—
113#4055—32no—
114#4055—32no—
115#4054—32no—
116#4054—32no—
117#4053—32no—
118#4053—32no—
119#4053—32no—
120#4053—32no—
121#4053—61no—
122#4053—61no—
123#4053—61no—
124#4053—61no—
125#4050—34no—
126C2×#676—61no—
127C2×#676—61no—
128C2×C8×D5—61no—
129C2×C8×D5—61no—
130C5×#108—34no—
131#3957—34no—
132#3957C2×D314yescomplemented
133#3947—32no—
134C8×Dic5—32no—
135#2955—151noSylow
136C23×C3×C5#4111yescharacteristic
137C22×D15—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
145#1220—22no—
146#1220—22no—
147C2×Dic15—21no—
148D60—21no—
149D60C22×C412yes—
150C4×D15—22no—
151C4×D15—22no—
152Dic30—21no—
153Dic30C22×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⋊#168C2×D411yescharacteristic
166C3⋊#168C2×D411yescharacteristic
167C3⋊#168C2×D411yescharacteristic
168C3⋊#168C2×D411yescharacteristic
169C5×C3⋊C8—22no—
170C5×C3⋊C8C22×C414yes—
171C2×C3×#41—51no—
172C2×#235—51no—
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—101no—
185C2×#208C2×D511yescharacteristic
186C2×#208C2×D511yescharacteristic
187C22×C3⋊C8—51no—
188C22×C3⋊C8—101no—
189#907—52no—
190#907—52no—
191#907—101no—
192#907—101no—
193C2×ΓL(1,𝔽25)—101no—
194C2×D3×C8—101no—
195C3×#104—54no—
196#822C2×D514yescomplemented
197#805—54no—
198#803—52no—
199C4×C3⋊C8—52no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—21no—
202C2×C22⋊D5—61no—
203#709—21no—
204#709—21no—
205#709—32no—
206#709—32no—
207#709—61no—
208#709—61no—
209#709C4×D312yes—
210#709C22×D312yes—
211C2×D20—31no—
212C2×D20C4×D311yescharacteristic
213C2×C4×D5—21no—
214C2×C4×D5—61no—
215C2×Dic10—31no—
216C2×Dic10C4×D311yescharacteristic
217C5×M16—21no—
218C5×M16—32no—
219C5×M16—32no—
220C5×M16—32no—
221C5×M16—61no—
222C5×M16C22×D312yes—
223C2×C5×C8—21no—
224C2×C5×C8—32no—
225C2×C5×C8—61no—
226C22⋊Dic5—21no—
227C4⋊Dic5—21no—
228C4×Dic5C22×D312yes—
229C2×#168—31no—
230C2×#168—31no—
231C2×#168—31no—
232C2×#168—31no—
233C2×#168—31no—
234C2×#168—31no—
235Dic20—34no—
236D40—34no—
237#677—34no—
238#677—34no—
239#676—62no—
240#676—62no—
241#676—62no—
242#676—62no—
243C8×D5—62no—
244C8×D5—62no—
245C8×D5—62no—
246C8×D5—62no—
247#575—151no—
248C2×#131—151no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—31no—
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×D15—22no—
261C2×D15—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
268Dic15—22no—
269C3×Dic5—22no—
270C3×Dic5—42no—
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—101no—
281#235—52no—
282#235—52no—
283#235—101no—
284#235—101no—
285C2×D12—51no—
286C2×C4×D3—101no—
287C2×Dic6—51no—
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—21no—
299#208—102no—
300#208—102no—
301#208C4×D512yes—
302#208C4×D512yes—
303#208C22×D512yes—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8—51no—
309C2×C3⋊C8—51no—
310C2×C3⋊C8—51no—
311C2×C3⋊C8—102no—
312C2×C3⋊C8—102no—
313C2×C3⋊C8C22×D512yes—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316D3×C8—102no—
317D3×C8—102no—
318C23×C5#23711yescharacteristic
319C22×D5—21no—
320C22×D5—61no—
321C2×C4×C5C2×C4×D311yescharacteristic
322C2×C4×C5C2×C4×D311yescharacteristic
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5#23711yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—22no—
328C22⋊D5—22no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C2×Dic5—21no—
332C2×Dic5—22no—
333C2×Dic5—61no—
334D20—21no—
335D20—32no—
336D20—61no—
337D20C2×C4×D312yes—
338C4×D5—22no—
339C4×D5—22no—
340C4×D5—62no—
341C4×D5—62no—
342Dic10—21no—
343Dic10—32no—
344Dic10—61no—
345Dic10C2×C4×D312yes—
346C5×C8—22no—
347C5×C8—34no—
348C5×C8—62no—
349#168—31no—
350#168—31no—
351#168—31no—
352#168—31no—
353C2×#41—51no—
354C2×#41—151no—
355#137—152no—
356#137—152no—
357AGL(1,ℤ/8)—152no—
358AGL(1,ℤ/8)—152no—
359#135—154no—
360#131—152no—
361#131—152no—
362#131—152no—
363#131—152no—
364#131—301no—
365#131—301no—
366#131—301no—
367#131—301no—
368C2×M16—31no—
369C2×M16—31no—
370C2×M16—301no—
371C2×M16—301no—
372C2×M16D3×D511yescharacteristic
373C22×C8—151no—
374C22×C8—301no—
375C22×C8—301no—
376#117—51no—
377#108—34no—
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
386D15—42no—
387C3×D5—42no—
388C23×C3—101no—
389C23×C3#71311yescharacteristic
390C22×D3—101no—
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×C4D4×D511yescharacteristic
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4#71311yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—102no—
408#67—102no—
409C2×Dic3—101no—
410D12—52no—
411D12—101no—
412C4×D3—102no—
413C4×D3—102no—
414Dic6—52no—
415Dic6—101no—
416C3×C8—22no—
417C3⋊C8—22no—
418C3⋊C8—51no—
419C3⋊C8—51no—
420C3⋊C8—51no—
421C3⋊C8—51no—
422C3⋊C8C2×C4×D514yes—
423C22×C5—41no—
424C22×C5#67⋊C411yescharacteristic
425C22×C5#67⋊C411yescharacteristic
426C22×C5C2×#23711yescharacteristic
427C2×D5—22no—
428C2×D5—42no—
429C2×D5—62no—
430C2×D5—122no—
431C4×C5#67⋊C411yescharacteristic
432C4×C5#67⋊C411yescharacteristic
433C4×C5C22×C4×D311yescharacteristic
434C4×C5C2×D3×D411yescharacteristic
435Dic5—22no—
436Dic5—42no—
437Dic5—62no—
438#41—52no—
439#41—52no—
440#41—101no—
441#41—101no—
442#41—152no—
443#41—152no—
444#41—301no—
445#41—301no—
446C2×Q8—51no—
447C2×Q8—151no—
448C2×D4—51no—
449C2×D4—101no—
450C2×D4—151no—
451C2×D4—301no—
452C22×C4—101no—
453C22×C4—301no—
454C22×C4C2×D3×D511yescharacteristic
455Q16—154no—
456SD16—154no—
457SD16—154no—
458D8—154no—
459M16—21no—
460M16—32no—
461M16—32no—
462M16—32no—
463M16—61no—
464M16—302no—
465M16—302no—
466M16—302no—
467M16—302no—
468M16C2×D3×D512yes—
469C2×C8—21no—
470C2×C8—32no—
471C2×C8—61no—
472C2×C8—151no—
473C2×C8—151no—
474C2×C8—151no—
475C2×C8—151no—
476C2×C8—151no—
477C2×C8—151no—
478C2×C8—302no—
479C2×C8—302no—
480C2×C8—302no—
481C2×C8—302no—
482C4⋊C4—101no—
483C22⋊C4—101no—
484C42—52no—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—41no—
487C22×C3—102no—
488C22×C3—202no—
489C22×C3#403911yescharacteristic
490C22×C3#403911yescharacteristic
491C22×C3C2×#71311yescharacteristic
492C2×D3—102no—
493C2×D3—202no—
494C3×C4—102no—
495C3×C4—202no—
496C3×C4#403911yescharacteristic
497C3×C4#403911yescharacteristic
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C2×D4×D511yescharacteristic
500Dic3—102no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5C2×#67⋊C411yescharacteristic
505D5—42no—
506D5—122no—
507C23—101no—
508C23—301no—
509C23#676611yescharacteristic
510Q8—52no—
511Q8—101no—
512Q8—152no—
513Q8—301no—
514D4—52no—
515D4—102no—
516D4—102no—
517D4—101no—
518D4—152no—
519D4—302no—
520D4—302no—
521D4—301no—
522C2×C4—101no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—301no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4#676611yescharacteristic
530C2×C4C4×D3×D511yescharacteristic
531C2×C4C4×D3×D511yescharacteristic
532C2×C4#679011yescharacteristic
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—22no—
536C8—34no—
537C8—62no—
538C8—151no—
539C8—151no—
540C8—151no—
541C8—151no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—202no—
546C2×C3C2×#403911yescharacteristic
547D3—202no—
548C5#7898911yescharacteristic, complemented, Sylow
549C22—41no—
550C22—102no—
551C22—202no—
552C22—302no—
553C22—602no—
554C22#9139611yescharacteristic
555C22#9139611yescharacteristic
556C22C2×#676611yescharacteristic
557C4—102no—
558C4—202no—
559C4—302no—
560C4#9139611yescharacteristic
561C4#9139611yescharacteristic
562C4C2×C4×D3×D511yescharacteristic
563C4C2×#679011yescharacteristic
564C3#1061098811yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—202no—
569C2—602no—
570C2C2×#9139611yescharacteristic
subgroupG/H
centerC4C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C2×C4×D4
prime radical#11754154C2
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×#91796C2semidirect
3. C2×#91284C2semidirect
4. C5×#5124C2semidirect
5. C3×#65428C2semidirect
6. #11748429C2semidirect
7. #11748320C2semidirect
8. #11748175C2semidirect
9. #11748174C2semidirect
17. #91796C22semidirect
18. #91796C22semidirect
24. #91315C4semidirect
25. #91313C4semidirect
26. #91312C4semidirect
28. #91301C4semidirect
32. #91284C22semidirect
33. #91284C22semidirect
35. C5×#822C22semidirect
36. C3×#3957C22semidirect
37. #90981C22semidirect
38. #90952C22semidirect
39. Dic5×C3⋊C8C22semidirect
46. #65428D3semidirect
101. #5124D5semidirect
132. #3957C2×D3semidirect
196. #822C2×D5semidirect
485. C3×C5#2955semidirect
548. C5#78989semidirect
564. C3#10610988semidirect

Maximal subgroups

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

subgroupindex
C2×#917962
#117541542
C2×#912842
C5×#51242
C3×#654282
#117484292
#117483202
#117481752
#117481742
#106109883
#789895