Finite Group Databasebeta

← #14418058

Subgroups — #14418058

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
2C5×#5822C211yesmaximal, characteristic
3C2×#91288C211yesmaximal, characteristic, complemented
4C3×#65525C211yesmaximal, characteristic, complemented
5#11749443C214yesmaximal, complemented
6#11749442C214yesmaximal, complemented
7#11748480C211yesmaximal, characteristic, complemented
8#11748425C211yesmaximal, characteristic, complemented
9#11748320C211yesmaximal, characteristic, complemented
10#10615730—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13#91837—21no—
14#91837—21no—
15#91837C2212yescomplemented
16#91837C2212yescomplemented
17C2×#6710—21no—
18C2×#6710C2211yescharacteristic
19C22×C3⋊#168—21no—
20C22×C3⋊#168C2211yescharacteristic
21C5×#951C412yescomplemented
22C5×#950C2214yes—
23C5×#949C412yescomplemented
24C5×#942C412yescomplemented
25C5×#932C412yescomplemented
26C2×C5×#208C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29C2×#6650—21no—
30#91288—21no—
31#91288—21no—
32#91288C2212yescomplemented
33#91288C2212yescomplemented
34C2×D3×#168—21no—
35C3×#3969C2214yescomplemented
36#90993C2214yescomplemented
37#90979C2214yescomplemented
38#90952C2212yescomplemented
39Dic5×C3⋊C8C2212yescomplemented
40#78989—51nomaximal, Hall
41C5×#575—31no—
42C2×#4094—31no—
43C2×#4094—31no—
44#65525—31no—
45#65525D311yescharacteristic, complemented
46#65486—34no—
47#65485—34no—
48#65414—31no—
49#65411—31no—
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×C5×#67—21no—
60C5×#235—21no—
61C5×#235—21no—
62C5×#235C2×C412yes—
63C5×#235C2312yes—
64C2×C5×D12C2×C411yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2×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×#216C2×C414yes—
81C5×#215C2×C414yes—
82C5×#214C2×C414yes—
83C5×#213C2×C414yes—
84C5×#208C2×C412yes—
85C5×#208C2×C412yes—
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5—21no—
89C3×C4×Dic5C2312yes—
90C3×#681—21no—
91C3×#681C2312yes—
92C2×C3×#168—21no—
93#6650—22no—
94#6650—22no—
95D3×#168—22no—
96D3×#168—22no—
97#5822D511yescharacteristic
98C2×#948—51no—
99C2×#907—51no—
100C3×#421—51no—
101#5124—51no—
102#5005—51no—
103#4997—51no—
104#4824—54no—
105#4823—54no—
106C2×C5×#41—31no—
107C2×C5×#41C2×D311yescharacteristic
108C5×#137—32no—
109C5×#137—32no—
110C5×AGL(1,ℤ/8)—32no—
111C5×AGL(1,ℤ/8)—32no—
112C5×#135—34no—
113C2×C5×M16—31no—
114#4094—32no—
115#4094—32no—
116#4094—32no—
117#4094—32no—
118#4094—61no—
119#4094—61no—
120#4094—61no—
121#4094—61no—
122#4072C2×D311yescharacteristic
123C2×#681—31no—
124C2×#681—61no—
125C2×#681—61no—
126C2×#681C2×D311yescharacteristic
127C22×#168—31no—
128C22×#168—61no—
129C22×#168—61no—
130#3969—34no—
131#3969C2×D314yescomplemented
132#3951—34no—
133#3947—32no—
134C8×Dic5—32no—
135#2955—151noSylow
136C23×C3×C5—21no—
137C23×C3×C5#4111yescharacteristic
138C22×C5×D3—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
154C5×#67—22no—
155C5×#67—22no—
156C2×C5×Dic3—21no—
157C5×D12—21no—
158C5×D12C22×C412yes—
159C4×C5×D3—22no—
160C4×C5×D3—22no—
161C5×Dic6—21no—
162C5×Dic6C22×C412yes—
163C2×C3×Dic5—22no—
164C3⋊#168—22no—
165C3⋊#168C2×D411yescharacteristic
166C3⋊#168C2×D411yescharacteristic
167C3⋊#168C2×D411yescharacteristic
168C3⋊#168C2×D411yescharacteristic
169C3×#168—22no—
170C5×C3⋊C8C22×C414yes—
171C2×C3×#41C2×D511yescharacteristic
172C2×#235C2×D511yescharacteristic
173C2×C3×M16—51no—
174C3×#117—51no—
175#951Dic512yescomplemented
176#950C2×D514yes—
177#949Dic512yescomplemented
178#948—52no—
179#948—52no—
180#948—101no—
181#948—101no—
182#942Dic512yescomplemented
183#932Dic512yescomplemented
184C2×#208—51no—
185C2×#208—101no—
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#822—54no—
197#805—54no—
198#803—52no—
199C4×C3⋊C8—52no—
200C5×#41—21no—
201C5×#41—21no—
202C5×#41—32no—
203C5×#41—32no—
204C5×#41—61no—
205C5×#41—61no—
206C5×#41C4×D312yes—
207C5×#41C22×D312yes—
208C2×C5×Q8—31no—
209C2×C5×Q8C4×D311yescharacteristic
210C2×C5×D4—21no—
211C2×C5×D4—31no—
212C2×C5×D4—61no—
213C2×C5×D4C4×D311yescharacteristic
214C22×C4×C5—21no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C5×Q16—34no—
218C5×SD16—34no—
219C5×SD16—34no—
220C5×D8—34no—
221C5×M16—32no—
222C5×M16—32no—
223C2×C5×C8—32no—
224C22⋊Dic5—21no—
225C4⋊Dic5—21no—
226C4×Dic5C22×D312yes—
227#681—21no—
228#681—32no—
229#681—62no—
230#681—62no—
231#681—62no—
232#681—62no—
233#681—61no—
234#681C22×D312yes—
235C2×#168—21no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#168—31no—
239C2×#168—31no—
240C2×#168—31no—
241C2×#168—31no—
242C2×#168—62no—
243C2×#168—62no—
244C2×#168—62no—
245C2×#168—62no—
246C2×#168—61no—
247#575—31no—
248C2×#131—151no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—151no—
253#421—51no—
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×C5×D3—22no—
263C2×C5×D3—42no—
264C3×C4×C5—22no—
265C3×C4×C5C4×D411yescharacteristic
266C3×C4×C5C4×D411yescharacteristic
267C3×C4×C5C23×C411yescharacteristic
268C3×C4×C5C22×D411yescharacteristic
269C3×Dic5—42no—
270C5×Dic3—22no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41C2×Dic512yes—
274C3×#41C22×D512yes—
275C2×C3×Q8C2×Dic511yescharacteristic
276C2×C3×D4—21no—
277C2×C3×D4C2×Dic511yescharacteristic
278C22×C3×C4—21no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281#235—21no—
282#235—21no—
283#235C2×Dic512yes—
284#235C22×D512yes—
285C2×D12C2×Dic511yescharacteristic
286C2×C4×D3—21no—
287C2×Dic6C2×Dic511yescharacteristic
288C3×M16—52no—
289C3×M16—101no—
290C2×C3×C8—101no—
291C3×C4⋊C4—101no—
292C3×C22⋊C4—101no—
293C3×C42—52no—
294#216C2×Dic514yes—
295#215C2×Dic514yes—
296#214C2×Dic514yes—
297#213C2×Dic514yes—
298#208—52no—
299#208—102no—
300#208—102no—
301#208—101no—
302#208C2×Dic512yes—
303#208C2×Dic512yes—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8—51no—
309C2×C3⋊C8—51no—
310C2×C3⋊C8—102no—
311C2×C3⋊C8—102no—
312C2×C3⋊C8—101no—
313C2×C3⋊C8C22×D512yes—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316D3×C8—102no—
317D3×C8—102no—
318C23×C5—21no—
319C23×C5—61no—
320C23×C5#23711yescharacteristic
321C5×Q8—21no—
322C5×Q8—32no—
323C5×Q8—61no—
324C5×Q8C2×C4×D312yes—
325C5×D4—22no—
326C5×D4—22no—
327C5×D4—21no—
328C5×D4—32no—
329C5×D4—62no—
330C5×D4—62no—
331C5×D4—61no—
332C5×D4C2×C4×D312yes—
333C2×C4×C5—21no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—61no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5C2×C4×D311yescharacteristic
340C2×C4×C5C2×C4×D311yescharacteristic
341C2×C4×C5D3×D411yescharacteristic
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5#23711yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C2×Dic5—22no—
346C5×C8—34no—
347#168—22no—
348#168—31no—
349#168—31no—
350#168—31no—
351#168—31no—
352#168—62no—
353C2×#41—31no—
354C2×#41D3×D511yescharacteristic
355#137—32no—
356#137—32no—
357AGL(1,ℤ/8)—32no—
358AGL(1,ℤ/8)—32no—
359#135—34no—
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—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×C5—42no—
386C2×C3×C5C2×C4×D411yescharacteristic
387C5×D3—42no—
388C23×C3—21no—
389C23×C3#71111yescharacteristic
390C22×D3—21no—
391C3×Q8—21no—
392C3×Q8C22×Dic512yes—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—21no—
396C3×D4C22×Dic512yes—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—102no—
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4#71111yescharacteristic
404C2×C3×C4C22×Dic511yescharacteristic
405C2×C3×C4C22×Dic511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—22no—
408#67—22no—
409C2×Dic3—21no—
410D12—21no—
411D12C22×Dic512yes—
412C4×D3—22no—
413C4×D3—22no—
414Dic6—21no—
415Dic6C22×Dic512yes—
416C3×C8—102no—
417C3⋊C8—51no—
418C3⋊C8—51no—
419C3⋊C8—51no—
420C3⋊C8—51no—
421C3⋊C8—102no—
422C3⋊C8C22×Dic514yes—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5—62no—
427C22×C5—122no—
428C22×C5#67⋊C411yescharacteristic
429C22×C5#67⋊C411yescharacteristic
430C22×C5C2×#23711yescharacteristic
431C4×C5—22no—
432C4×C5—62no—
433C4×C5#67⋊C411yescharacteristic
434C4×C5#67⋊C411yescharacteristic
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C2×D3×D411yescharacteristic
437Dic5—42no—
438#41—21no—
439#41—21no—
440#41—32no—
441#41—32no—
442#41—61no—
443#41—61no—
444#41D3×Dic512yes—
445#41C2×D3×D512yes—
446C2×Q8—31no—
447C2×Q8D3×Dic511yescharacteristic
448C2×D4—21no—
449C2×D4—31no—
450C2×D4—61no—
451C2×D4D3×Dic511yescharacteristic
452C22×C4—21no—
453C22×C4—61no—
454C22×C4C2×D3×D511yescharacteristic
455Q16—34no—
456SD16—34no—
457SD16—34no—
458D8—34no—
459M16—32no—
460M16—32no—
461M16—52no—
462M16—101no—
463M16—152no—
464M16—302no—
465M16—302no—
466M16—302no—
467M16—302no—
468M16—301no—
469C2×C8—32no—
470C2×C8—101no—
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—101no—
483C22⋊C4—101no—
484C42—52no—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—42no—
489C22×C3D4×Dic511yescharacteristic
490C22×C3D4×Dic511yescharacteristic
491C22×C3C2×#71111yescharacteristic
492C2×D3—22no—
493C2×D3—42no—
494C3×C4—22no—
495C3×C4—202no—
496C3×C4D4×Dic511yescharacteristic
497C3×C4D4×Dic511yescharacteristic
498C3×C4C2×D4×D511yescharacteristic
499C3×C4C23×Dic511yescharacteristic
500Dic3—22no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5—42no—
505C2×C5—122no—
506C2×C5C2×#67⋊C411yescharacteristic
507C23—21no—
508C23—61no—
509C23#678011yescharacteristic
510Q8—21no—
511Q8—32no—
512Q8—61no—
513Q8C2×D3×Dic512yes—
514D4—22no—
515D4—22no—
516D4—21no—
517D4—32no—
518D4—62no—
519D4—62no—
520D4—61no—
521D4C2×D3×Dic512yes—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—102no—
529C2×C4#678011yescharacteristic
530C2×C4C2×D3×Dic511yescharacteristic
531C2×C4C2×D3×Dic511yescharacteristic
532C2×C4#679011yescharacteristic
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—34no—
536C8—102no—
537C8—151no—
538C8—151no—
539C8—151no—
540C8—151no—
541C8—302no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3C2×D4×Dic511yescharacteristic
547D3—42no—
548C5#7898911yescharacteristic, complemented, Sylow
549C22—22no—
550C22—41no—
551C22—42no—
552C22—62no—
553C22—122no—
554C22#67⋊Dic511yescharacteristic
555C22#67⋊Dic511yescharacteristic
556C22C2×#678011yescharacteristic
557C4—22no—
558C4—62no—
559C4—202no—
560C4#67⋊Dic511yescharacteristic
561C4#67⋊Dic511yescharacteristic
562C4C22×D3×Dic511yescharacteristic
563C4C2×#679011yescharacteristic
564C3#1061573011yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—42no—
569C2—122no—
570C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC4C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×C4×D4
prime radicalC5×#5822C2
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×#91288C2semidirect
4. C3×#65525C2semidirect
5. #11749443C2semidirect
6. #11749442C2semidirect
7. #11748480C2semidirect
8. #11748425C2semidirect
9. #11748320C2semidirect
15. #91837C22semidirect
16. #91837C22semidirect
21. C5×#951C4semidirect
23. C5×#949C4semidirect
24. C5×#942C4semidirect
25. C5×#932C4semidirect
32. #91288C22semidirect
33. #91288C22semidirect
35. C3×#3969C22semidirect
36. #90993C22semidirect
37. #90979C22semidirect
38. #90952C22semidirect
39. Dic5×C3⋊C8C22semidirect
45. #65525D3semidirect
131. #3969C2×D3semidirect
175. #951Dic5semidirect
177. #949Dic5semidirect
182. #942Dic5semidirect
183. #932Dic5semidirect
485. C3×C5#2955semidirect
548. C5#78989semidirect
564. C3#10615730semidirect

Maximal subgroups

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

subgroupindex
C2×#918372
C5×#58222
C2×#912882
C3×#655252
#117494432
#117494422
#117484802
#117484252
#117483202
#106157303
#789895