Finite Group Databasebeta

← #14418055

Subgroups — #14418055

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×#91837C211yesmaximal, characteristic, complemented
2C3×#66156C211yesmaximal, characteristic
3C2×#91284C211yesmaximal, characteristic, complemented
4C5×#5236C211yesmaximal, characteristic, complemented
5#11749441C214yesmaximal, complemented
6#11749440C214yesmaximal, complemented
7#11748476C211yesmaximal, characteristic, complemented
8#11748421C211yesmaximal, characteristic, complemented
9#11748327C211yesmaximal, characteristic, complemented
10#10610720—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13#91837—21no—
14#91837—21no—
15#91837C2212yescomplemented
16#91837C2212yescomplemented
17C2×#6710—21no—
18C2×#6710C2211yescharacteristic
19C22×C3⋊#168—21no—
20C22×C3⋊#168C2211yescharacteristic
21C5×#926C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C3×#4097C412yescomplemented
24C3×#4096C2214yes—
25C3×#4095C412yescomplemented
26C3×#4088C412yescomplemented
27C3×#4078C412yescomplemented
28C2×C3×#681C2211yescharacteristic
29C2×#6649—21no—
30#91284—21no—
31#91284—21no—
32#91284C2212yescomplemented
33#91284C2212yescomplemented
34C2×D5×C3⋊C8—21no—
35C5×#837C2214yescomplemented
36#90991C2214yescomplemented
37#90977C2214yescomplemented
38#90953C2212yescomplemented
39Dic3×#168C2212yescomplemented
40#83999—51nomaximal, Hall
41#66156D311yescharacteristic
42C2×#4094—31no—
43C2×#4053—31no—
44C5×#421—31no—
45#65413—31no—
46#65294—31no—
47#65286—31no—
48#65113—34no—
49#65112—34no—
50C3×C5×#41—21no—
51C3×C5×#41—21no—
52C3×C5×#41C2×C412yes—
53C3×C5×#41C2312yes—
54C2×C3×C5×Q8C2×C411yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2×C411yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
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
67#6710—21no—
68#6710—22no—
69#6710—22no—
70#6710C2312yes—
71C2×C3⋊#168—21no—
72C2×C3⋊#168—22no—
73C2×C3⋊#168—22no—
74C2×C3⋊#168D411yescharacteristic
75C2×C3⋊#168D411yescharacteristic
76C2×C3⋊#168D411yescharacteristic
77C2×C3⋊#168D411yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C2×C3⋊#168C2311yescharacteristic
80C5×#217—21no—
81C5×C4⋊Dic3—21no—
82C4×C5×Dic3C2312yes—
83C5×#208—21no—
84C5×#208C2312yes—
85C2×C5×C3⋊C8—21no—
86C3×#689C2×C414yes—
87C3×#688C2×C414yes—
88C3×#687C2×C414yes—
89C3×#686C2×C414yes—
90C3×#681C2×C412yes—
91C3×#681C2×C412yes—
92C2×C3×#168C2312yes—
93#6649—22no—
94#6649—22no—
95D5×C3⋊C8—22no—
96D5×C3⋊C8—22no—
97C3×#575—51no—
98C2×#948—51no—
99C2×#948—51no—
100#5236—51no—
101#5236D511yescharacteristic, complemented
102#5197—54no—
103#5196—54no—
104#5125—51no—
105#5122—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709C2×D311yescharacteristic
108C2×C5×M16—31no—
109C5×#117—31no—
110#4097Dic312yescomplemented
111#4096C2×D314yes—
112#4095Dic312yescomplemented
113#4094—32no—
114#4094—32no—
115#4094—61no—
116#4094—61no—
117#4088Dic312yescomplemented
118#4078Dic312yescomplemented
119C2×#681—31no—
120C2×#681—61no—
121C2×#681C2×D311yescharacteristic
122C22×#168—31no—
123C22×#168—61no—
124#4053—32no—
125#4053—32no—
126#4053—61no—
127#4053—61no—
128C2×#676—61no—
129C2×C8×D5—61no—
130C5×#104—34no—
131#3954—34no—
132#3937—34no—
133#3935—32no—
134C4×#168—32no—
135#2955—151noSylow
136C23×C3×C5—21no—
137C23×C3×C5#4111yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—21no—
140C3×C5×Q8C22×C412yes—
141C3×C5×D4—22no—
142C3×C5×D4—22no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22×C411yescharacteristic
149C2×C3×C4×C5C22×C411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5#4111yescharacteristic
153C2×C3×C4×C5C2411yescharacteristic
154C2×C5×Dic3—22no—
155C3×C22⋊D5—22no—
156C3×C22⋊D5—22no—
157C2×C3×Dic5—21no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164C3⋊#168—22no—
165C3⋊#168C2×D411yescharacteristic
166C3⋊#168C2×D411yescharacteristic
167C3⋊#168C2×D411yescharacteristic
168C3⋊#168C2×D411yescharacteristic
169C3×#168C22×C414yes—
170C5×C3⋊C8—22no—
171C2×C3×#41—51no—
172C2×C3×#41C2×D511yescharacteristic
173C3×#137—52no—
174C3×#137—52no—
175C3×AGL(1,ℤ/8)—52no—
176C3×AGL(1,ℤ/8)—52no—
177C3×#135—54no—
178C2×C3×M16—51no—
179#948—52no—
180#948—52no—
181#948—52no—
182#948—52no—
183#948—101no—
184#948—101no—
185#948—101no—
186#948—101no—
187#926C2×D511yescharacteristic
188C2×#208—51no—
189C2×#208—101no—
190C2×#208—101no—
191C2×#208C2×D511yescharacteristic
192C22×C3⋊C8—51no—
193C22×C3⋊C8—101no—
194C22×C3⋊C8—101no—
195#837—54no—
196#837C2×D514yescomplemented
197#819—54no—
198#815—52no—
199C8×Dic3—52no—
200C5×#41—21no—
201C5×#41—21no—
202C5×#41C2×Dic312yes—
203C5×#41C22×D312yes—
204C2×C5×Q8C2×Dic311yescharacteristic
205C2×C5×D4—21no—
206C2×C5×D4C2×Dic311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—21no—
210#709—21no—
211#709—21no—
212#709C2×Dic312yes—
213#709C22×D312yes—
214C2×D20C2×Dic311yescharacteristic
215C2×C4×D5—21no—
216C2×Dic10C2×Dic311yescharacteristic
217C5×M16—32no—
218C5×M16—61no—
219C2×C5×C8—61no—
220C5×C4⋊C4—61no—
221C5×C22⋊C4—61no—
222C42×C5—32no—
223#689C2×Dic314yes—
224#688C2×Dic314yes—
225#687C2×Dic314yes—
226#686C2×Dic314yes—
227#681—32no—
228#681—62no—
229#681—62no—
230#681—61no—
231#681C2×Dic312yes—
232#681C2×Dic312yes—
233C2×#168—31no—
234C2×#168—31no—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#168—31no—
239C2×#168—62no—
240C2×#168—62no—
241C2×#168—61no—
242C2×#168C22×D312yes—
243#676—62no—
244#676—62no—
245C8×D5—62no—
246C8×D5—62no—
247#575—51no—
248C2×#131—151no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—151no—
253#421—31no—
254#421—151no—
255#405—151no—
256C22×C3×C5—22no—
257C22×C3×C5—41no—
258C22×C3×C5—42no—
259C22×C3×C5C4×D411yescharacteristic
260C22×C3×C5C4×D411yescharacteristic
261C22×C3×C5C2×#4111yescharacteristic
262C2×C3×D5—22no—
263C2×C3×D5—42no—
264C3×C4×C5—22no—
265C3×C4×C5C4×D411yescharacteristic
266C3×C4×C5C4×D411yescharacteristic
267C3×C4×C5C23×C411yescharacteristic
268C3×C4×C5C22×D411yescharacteristic
269C3×Dic5—22no—
270C5×Dic3—42no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—52no—
274C3×#41—52no—
275C3×#41—101no—
276C3×#41—101no—
277C3×#41C4×D512yes—
278C3×#41C22×D512yes—
279C2×C3×Q8—51no—
280C2×C3×Q8C4×D511yescharacteristic
281C2×C3×D4—21no—
282C2×C3×D4—51no—
283C2×C3×D4—101no—
284C2×C3×D4C4×D511yescharacteristic
285C22×C3×C4—21no—
286C22×C3×C4—101no—
287C22×C3×C4C22×D511yescharacteristic
288C3×Q16—54no—
289C3×SD16—54no—
290C3×SD16—54no—
291C3×D8—54no—
292C3×M16—52no—
293C3×M16—52no—
294C2×C3×C8—52no—
295#217—21no—
296C4⋊Dic3—21no—
297C4×Dic3C22×D512yes—
298#208—21no—
299#208—52no—
300#208—102no—
301#208—102no—
302#208—102no—
303#208—102no—
304#208—101no—
305#208C22×D512yes—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8—51no—
309C2×C3⋊C8—51no—
310C2×C3⋊C8—51no—
311C2×C3⋊C8—51no—
312C2×C3⋊C8—51no—
313C2×C3⋊C8—102no—
314C2×C3⋊C8—102no—
315C2×C3⋊C8—102no—
316C2×C3⋊C8—102no—
317C2×C3⋊C8—101no—
318C23×C5—21no—
319C23×C5#23711yescharacteristic
320C22×D5—21no—
321C5×Q8—21no—
322C5×Q8C22×Dic312yes—
323C5×D4—22no—
324C5×D4—22no—
325C5×D4—21no—
326C5×D4C22×Dic312yes—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—62no—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5#23711yescharacteristic
334C2×C4×C5C22×Dic311yescharacteristic
335C2×C4×C5C22×Dic311yescharacteristic
336C2×C4×C5C23×D311yescharacteristic
337C22⋊D5—22no—
338C22⋊D5—22no—
339C2×Dic5—21no—
340D20—21no—
341D20C22×Dic312yes—
342C4×D5—22no—
343C4×D5—22no—
344Dic10—21no—
345Dic10C22×Dic312yes—
346C5×C8—62no—
347#168—31no—
348#168—31no—
349#168—31no—
350#168—31no—
351#168—62no—
352#168C22×Dic314yes—
353C2×#41—51no—
354C2×#41D3×D511yescharacteristic
355#137—52no—
356#137—52no—
357AGL(1,ℤ/8)—52no—
358AGL(1,ℤ/8)—52no—
359#135—54no—
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—51no—
370C2×M16—151no—
371C2×M16—301no—
372C2×M16—301no—
373C22×C8—151no—
374C22×C8—301no—
375C22×C8—301no—
376#117—31no—
377#108—154no—
378#104—34no—
379#104—154no—
380#97—152no—
381C4×C8—152no—
382C2×C3×C5—21no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5—42no—
386C2×C3×C5C2×C4×D411yescharacteristic
387C3×D5—42no—
388C23×C3—21no—
389C23×C3—101no—
390C23×C3#71111yescharacteristic
391C3×Q8—21no—
392C3×Q8—52no—
393C3×Q8—101no—
394C3×Q8C2×C4×D512yes—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—21no—
398C3×D4—52no—
399C3×D4—102no—
400C3×D4—102no—
401C3×D4—101no—
402C3×D4C2×C4×D512yes—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—101no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4C2×C4×D511yescharacteristic
410C2×C3×C4C2×C4×D511yescharacteristic
411C2×C3×C4D4×D511yescharacteristic
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4#71111yescharacteristic
414C2×C3×C4C23×D511yescharacteristic
415C2×Dic3—22no—
416C3×C8—54no—
417C3⋊C8—22no—
418C3⋊C8—51no—
419C3⋊C8—51no—
420C3⋊C8—51no—
421C3⋊C8—51no—
422C3⋊C8—102no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5D4×Dic311yescharacteristic
427C22×C5D4×Dic311yescharacteristic
428C22×C5C2×#23711yescharacteristic
429C2×D5—22no—
430C2×D5—42no—
431C4×C5—22no—
432C4×C5—122no—
433C4×C5D4×Dic311yescharacteristic
434C4×C5D4×Dic311yescharacteristic
435C4×C5C2×D3×D411yescharacteristic
436C4×C5C23×Dic311yescharacteristic
437Dic5—22no—
438#41—21no—
439#41—21no—
440#41—52no—
441#41—52no—
442#41—101no—
443#41—101no—
444#41D5×Dic312yes—
445#41C2×D3×D512yes—
446C2×Q8—51no—
447C2×Q8D5×Dic311yescharacteristic
448C2×D4—21no—
449C2×D4—51no—
450C2×D4—101no—
451C2×D4D5×Dic311yescharacteristic
452C22×C4—21no—
453C22×C4—101no—
454C22×C4C2×D3×D511yescharacteristic
455Q16—54no—
456SD16—54no—
457SD16—54no—
458D8—54no—
459M16—32no—
460M16—52no—
461M16—52no—
462M16—61no—
463M16—152no—
464M16—302no—
465M16—302no—
466M16—302no—
467M16—302no—
468M16—301no—
469C2×C8—52no—
470C2×C8—61no—
471C2×C8—151no—
472C2×C8—151no—
473C2×C8—151no—
474C2×C8—151no—
475C2×C8—151no—
476C2×C8—151no—
477C2×C8—302no—
478C2×C8—302no—
479C2×C8—302no—
480C2×C8—302no—
481C2×C8—301no—
482C4⋊C4—61no—
483C22⋊C4—61no—
484C42—32no—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—42no—
489C22×C3—102no—
490C22×C3—202no—
491C22×C3#402711yescharacteristic
492C22×C3#402711yescharacteristic
493C22×C3C2×#71111yescharacteristic
494C3×C4—22no—
495C3×C4—102no—
496C3×C4#402711yescharacteristic
497C3×C4#402711yescharacteristic
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C2×D4×D511yescharacteristic
500Dic3—42no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5—42no—
505C2×C5C2×D4×Dic311yescharacteristic
506D5—42no—
507C23—21no—
508C23—101no—
509C23#678011yescharacteristic
510Q8—21no—
511Q8—52no—
512Q8—101no—
513Q8C2×D5×Dic312yes—
514D4—22no—
515D4—22no—
516D4—21no—
517D4—52no—
518D4—102no—
519D4—102no—
520D4—101no—
521D4C2×D5×Dic312yes—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—62no—
526C2×C4—101no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4C2×D5×Dic311yescharacteristic
530C2×C4C2×D5×Dic311yescharacteristic
531C2×C4#678011yescharacteristic
532C2×C4#679011yescharacteristic
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—54no—
536C8—62no—
537C8—151no—
538C8—151no—
539C8—151no—
540C8—151no—
541C8—302no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3—202no—
547C2×C3C2×#402711yescharacteristic
548C5#8399911yescharacteristic, complemented, Sylow
549C22—22no—
550C22—41no—
551C22—42no—
552C22—102no—
553C22—202no—
554C22#9155911yescharacteristic
555C22#9155911yescharacteristic
556C22C2×#678011yescharacteristic
557C4—22no—
558C4—102no—
559C4—122no—
560C4#9155911yescharacteristic
561C4#9155911yescharacteristic
562C4C22×D5×Dic311yescharacteristic
563C4C2×#679011yescharacteristic
564C3#1061072011yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—42no—
569C2—202no—
570C2C2×#9155911yescharacteristic
subgroupG/H
centerC4C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×C4×D4
prime radicalC3×#66156C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91837C2semidirect
3. C2×#91284C2semidirect
4. C5×#5236C2semidirect
5. #11749441C2semidirect
6. #11749440C2semidirect
7. #11748476C2semidirect
8. #11748421C2semidirect
9. #11748327C2semidirect
15. #91837C22semidirect
16. #91837C22semidirect
23. C3×#4097C4semidirect
25. C3×#4095C4semidirect
26. C3×#4088C4semidirect
27. C3×#4078C4semidirect
32. #91284C22semidirect
33. #91284C22semidirect
35. C5×#837C22semidirect
36. #90991C22semidirect
37. #90977C22semidirect
38. #90953C22semidirect
39. Dic3×#168C22semidirect
101. #5236D5semidirect
110. #4097Dic3semidirect
112. #4095Dic3semidirect
117. #4088Dic3semidirect
118. #4078Dic3semidirect
196. #837C2×D5semidirect
485. C3×C5#2955semidirect
548. C5#83999semidirect
564. C3#10610720semidirect

Maximal subgroups

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

subgroupindex
C2×#918372
C3×#661562
C2×#912842
C5×#52362
#117494412
#117494402
#117484762
#117484212
#117483272
#106107203
#839995