Finite Group Databasebeta

← #14418010

Subgroups — #14418010

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
1#11756581C211yesmaximal, characteristic
2C2×#91837C211yesmaximal, characteristic, complemented
3C2×#91796C211yesmaximal, characteristic, complemented
4C3×C5×#421C211yesmaximal, characteristic, complemented
5#11751225C211yesmaximal, characteristic, complemented
6#11751106C211yesmaximal, characteristic, complemented
7#11751098C211yesmaximal, characteristic, complemented
8#11750925C214yesmaximal, complemented
9#11750924C214yesmaximal, complemented
10#10610720—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×#6817C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91840C412yescomplemented
16#91839C2214yes—
17#91838C412yescomplemented
18#91837—21no—
19#91837—21no—
20#91837C2212yescomplemented
21#91837C2212yescomplemented
22#91831C412yescomplemented
23#91821C412yescomplemented
24C2×#6710—21no—
25C2×#6710C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168—21no—
28C22×C3⋊#168C2211yescharacteristic
29#91796—21no—
30#91796—21no—
31#91796C2212yescomplemented
32#91796C2212yescomplemented
33C2×#6705—21no—
34C2×C8×D15—21no—
35C3×C5×#104C2214yescomplemented
36#91106C2214yescomplemented
37#91089C2214yescomplemented
38#91087C2212yescomplemented
39C4×C3⋊#168C2212yescomplemented
40#78989—51nomaximal, Hall
41#66156—31no—
42C2×#4094—31no—
43C2×#4053—31no—
44C5×#421D311yescharacteristic, complemented
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×#1220—21no—
60#6817—21no—
61#6817—21no—
62#6817C2×C412yes—
63#6817C2312yes—
64C2×D60C2×C411yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2×C411yescharacteristic
67C3×C5×M16—21no—
68C3×C5×M16C2312yes—
69C2×C3×C5×C8—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2312yes—
73#6718C2×C414yes—
74#6717C2×C414yes—
75#6716C2×C414yes—
76#6715C2×C414yes—
77#6710—21no—
78#6710—22no—
79#6710—22no—
80#6710C2×C412yes—
81#6710C2×C412yes—
82#6710C2312yes—
83C2×C3⋊#168—21no—
84C2×C3⋊#168—22no—
85C2×C3⋊#168—22no—
86C2×C3⋊#168D411yescharacteristic
87C2×C3⋊#168D411yescharacteristic
88C2×C3⋊#168D411yescharacteristic
89C2×C3⋊#168D411yescharacteristic
90C2×C3⋊#168C2312yes—
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93#6705—22no—
94#6705—22no—
95C8×D15—22no—
96C8×D15—22no—
97#5822—51no—
98C2×#948—51no—
99C2×#907—51no—
100C3×#421D511yescharacteristic, complemented
101#5124—51no—
102#5005—51no—
103#4997—51no—
104#4824—54no—
105#4823—54no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C2×C5×M16C2×D311yescharacteristic
109C5×#117C2×D311yescharacteristic
110#4097—32no—
111#4096—34no—
112#4095—32no—
113#4094—32no—
114#4094—32no—
115#4094—61no—
116#4094—61no—
117#4088—32no—
118#4078—32no—
119C2×#681—31no—
120C2×#681—31no—
121C2×#681—61no—
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×#104C2×D314yescomplemented
131#3954—34no—
132#3937—34no—
133#3935—32no—
134C4×#168—32no—
135#2955—151noSylow
136C23×C3×C5—21no—
137C23×C3×C5#4111yescharacteristic
138C22×D15—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×C5—22no—
149C2×C3×C4×C5C22×C411yescharacteristic
150C2×C3×C4×C5C22×C411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5#4111yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155#1220—22no—
156#1220—22no—
157C2×Dic15—21no—
158D60—21no—
159D60C22×C412yes—
160C4×D15—22no—
161C4×D15—22no—
162Dic30—21no—
163Dic30C22×C412yes—
164C3×C5×C8—22no—
165C3⋊#168—22no—
166C3⋊#168C22×C414yes—
167C3⋊#168C2×D411yescharacteristic
168C3⋊#168C2×D411yescharacteristic
169C3⋊#168C2×D411yescharacteristic
170C3⋊#168C2×D411yescharacteristic
171C2×C3×#41C2×D511yescharacteristic
172C2×#235—51no—
173C2×C3×M16C2×D511yescharacteristic
174C3×#117C2×D511yescharacteristic
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—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×#104C2×D514yescomplemented
196#822—54no—
197#805—54no—
198#803—52no—
199C4×C3⋊C8—52no—
200C5×#41—21no—
201C5×#41—21no—
202C5×#41C4×D312yes—
203C5×#41C22×D312yes—
204C2×C5×Q8C4×D311yescharacteristic
205C2×C5×D4—21no—
206C2×C5×D4C4×D311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—61no—
210#709—32no—
211#709—32no—
212#709—61no—
213#709—61no—
214C2×D20—31no—
215C2×C4×D5—61no—
216C2×Dic10—31no—
217C5×M16—21no—
218C5×M16C22×D312yes—
219C2×C5×C8—21no—
220C5×C4⋊C4—21no—
221C5×C22⋊C4—21no—
222C42×C5C22×D312yes—
223#689—34no—
224#688—34no—
225#687—34no—
226#686—34no—
227#681—32no—
228#681—32no—
229#681—32no—
230#681—62no—
231#681—62no—
232#681—61no—
233C2×#168—31no—
234C2×#168—31no—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168—32no—
238C2×#168—31no—
239C2×#168—31no—
240C2×#168—62no—
241C2×#168—62no—
242C2×#168—61no—
243#676—62no—
244#676—62no—
245C8×D5—62no—
246C8×D5—62no—
247#575—151no—
248C2×#131—151no—
249C2×#131—151no—
250#444—154no—
251#443—154no—
252#430—151no—
253#421—151no—
254#421D1511yescharacteristic, complemented
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×D15—22no—
263C2×D15—42no—
264C3×C4×C5—22no—
265C3×C4×C5—42no—
266C3×C4×C5C4×D411yescharacteristic
267C3×C4×C5C4×D411yescharacteristic
268C3×C4×C5C23×C411yescharacteristic
269C3×C4×C5C22×D411yescharacteristic
270Dic15—22no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41C4×D512yes—
274C3×#41C22×D512yes—
275C2×C3×Q8C4×D511yescharacteristic
276C2×C3×D4—21no—
277C2×C3×D4C4×D511yescharacteristic
278C22×C3×C4—21no—
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—21no—
292C3×C22⋊C4—21no—
293C3×C42C22×D512yes—
294#216—54no—
295#215—54no—
296#214—54no—
297#213—54no—
298#208—52no—
299#208—52no—
300#208—52no—
301#208—102no—
302#208—102no—
303#208—101no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8—51no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—51no—
311C2×C3⋊C8—102no—
312C2×C3⋊C8—102no—
313C2×C3⋊C8—101no—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316D3×C8—102no—
317D3×C8—102no—
318C23×C5—21no—
319C23×C5#23711yescharacteristic
320C22×D5—61no—
321C5×Q8—21no—
322C5×Q8C2×C4×D312yes—
323C5×D4—22no—
324C5×D4—22no—
325C5×D4—21no—
326C5×D4C2×C4×D312yes—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5C2×C4×D311yescharacteristic
332C2×C4×C5C2×C4×D311yescharacteristic
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5D3×D411yescharacteristic
335C2×C4×C5#23711yescharacteristic
336C2×C4×C5C23×D311yescharacteristic
337C22⋊D5—62no—
338C22⋊D5—62no—
339C2×Dic5—61no—
340D20—32no—
341D20—61no—
342C4×D5—62no—
343C4×D5—62no—
344Dic10—32no—
345Dic10—61no—
346C5×C8—22no—
347#168—34no—
348#168—31no—
349#168—31no—
350#168—31no—
351#168—31no—
352#168—62no—
353C2×#41—151no—
354C2×#41C2×D1511yescharacteristic
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—151no—
369C2×M16—151no—
370C2×M16—301no—
371C2×M16—301no—
372C2×M16C2×D1511yescharacteristic
373C22×C8—151no—
374C22×C8—301no—
375C22×C8—301no—
376#117C2×D1511yescharacteristic
377#108—154no—
378#104—154no—
379#104C2×D1514yescomplemented
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
387D15—42no—
388C23×C3—21no—
389C23×C3#71111yescharacteristic
390C22×D3—101no—
391C3×Q8—21no—
392C3×Q8C2×C4×D512yes—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—21no—
396C3×D4C2×C4×D512yes—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4C2×C4×D511yescharacteristic
402C2×C3×C4C2×C4×D511yescharacteristic
403C2×C3×C4D4×D511yescharacteristic
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4#71111yescharacteristic
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—54no—
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×C5#67⋊C411yescharacteristic
427C22×C5#67⋊C411yescharacteristic
428C22×C5C2×#23711yescharacteristic
429C2×D5—62no—
430C2×D5—122no—
431C4×C5—22no—
432C4×C5—42no—
433C4×C5#67⋊C411yescharacteristic
434C4×C5#67⋊C411yescharacteristic
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C2×D3×D411yescharacteristic
437Dic5—62no—
438#41—21no—
439#41—21no—
440#41—152no—
441#41—152no—
442#41—301no—
443#41—301no—
444#41C4×D1512yes—
445#41C22×D1512yes—
446C2×Q8—151no—
447C2×Q8C4×D1511yescharacteristic
448C2×D4—21no—
449C2×D4—151no—
450C2×D4—301no—
451C2×D4C4×D1511yescharacteristic
452C22×C4—21no—
453C22×C4—301no—
454C22×C4C22×D1511yescharacteristic
455Q16—154no—
456SD16—154no—
457SD16—154no—
458D8—154no—
459M16—21no—
460M16—152no—
461M16—152no—
462M16—152no—
463M16—302no—
464M16—302no—
465M16—302no—
466M16—302no—
467M16—301no—
468M16C22×D1512yes—
469C2×C8—21no—
470C2×C8—151no—
471C2×C8—151no—
472C2×C8—151no—
473C2×C8—151no—
474C2×C8—151no—
475C2×C8—152no—
476C2×C8—151no—
477C2×C8—302no—
478C2×C8—302no—
479C2×C8—302no—
480C2×C8—302no—
481C2×C8—301no—
482C4⋊C4—21no—
483C22⋊C4—21no—
484C42C22×D1512yes—
485C3×C5#295511yescharacteristic, complemented, Hall
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—42no—
489C22×C3#402711yescharacteristic
490C22×C3#402711yescharacteristic
491C22×C3C2×#71111yescharacteristic
492C2×D3—102no—
493C2×D3—202no—
494C3×C4—22no—
495C3×C4—42no—
496C3×C4#402711yescharacteristic
497C3×C4#402711yescharacteristic
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C2×D4×D511yescharacteristic
500Dic3—102no—
501C2×C5—21no—
502C2×C5—21no—
503C2×C5—21no—
504C2×C5—42no—
505C2×C5C2×#67⋊C411yescharacteristic
506D5—122no—
507C23—21no—
508C23—301no—
509C23#681911yescharacteristic
510Q8—21no—
511Q8—152no—
512Q8—301no—
513Q8C2×C4×D1512yes—
514D4—22no—
515D4—22no—
516D4—21no—
517D4—152no—
518D4—302no—
519D4—302no—
520D4—301no—
521D4C2×C4×D1512yes—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—301no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4C2×C4×D1511yescharacteristic
530C2×C4C2×C4×D1511yescharacteristic
531C2×C4D4×D1511yescharacteristic
532C2×C4D4×D1511yescharacteristic
533C2×C4#681911yescharacteristic
534C2×C4C23×D1511yescharacteristic
535C8—22no—
536C8—154no—
537C8—151no—
538C8—151no—
539C8—151no—
540C8—151no—
541C8—302no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3C2×#402711yescharacteristic
547D3—202no—
548C5#7898911yescharacteristic, complemented, Sylow
549C22—22no—
550C22—41no—
551C22—42no—
552C22—302no—
553C22—602no—
554C22#9177011yescharacteristic
555C22#9177011yescharacteristic
556C22C2×#681911yescharacteristic
557C4—22no—
558C4—42no—
559C4—302no—
560C4#9177011yescharacteristic
561C4#9177011yescharacteristic
562C4C22×C4×D1511yescharacteristic
563C4C2×D4×D1511yescharacteristic
564C3#1061072011yescharacteristic, complemented, Sylow
565C2—21no—
566C2—21no—
567C2—21no—
568C2—42no—
569C2—602no—
570C2C2×#9177011yescharacteristic
subgroupG/H
centerC4C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#421C2
socleC2×C3×C5C2×C4×D4
prime radical#11756581C2
cosocleC2×C3×C4×C5C24
hypercenter#421D15
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C2×#91837C2semidirect
3. C2×#91796C2semidirect
4. C3×C5×#421C2semidirect
5. #11751225C2semidirect
6. #11751106C2semidirect
7. #11751098C2semidirect
8. #11750925C2semidirect
9. #11750924C2semidirect
15. #91840C4semidirect
17. #91838C4semidirect
20. #91837C22semidirect
21. #91837C22semidirect
22. #91831C4semidirect
23. #91821C4semidirect
31. #91796C22semidirect
32. #91796C22semidirect
35. C3×C5×#104C22semidirect
36. #91106C22semidirect
37. #91089C22semidirect
38. #91087C22semidirect
39. C4×C3⋊#168C22semidirect
44. C5×#421D3semidirect
100. C3×#421D5semidirect
130. C5×#104C2×D3semidirect
195. C3×#104C2×D5semidirect
254. #421D15semidirect
379. #104C2×D15semidirect
485. C3×C5#2955semidirect
548. C5#78989semidirect
564. C3#10610720semidirect

Maximal subgroups

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

subgroupindex
#117565812
C2×#918372
C2×#917962
C3×C5×#4212
#117512252
#117511062
#117510982
#117509252
#117509242
#106107203
#789895