Finite Group Databasebeta

← #14295973

Subgroups — #14295973

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#948C211yesmaximal, characteristic
2#11752453C211yesmaximal, characteristic
3C3×D5⋊#104C211yesmaximal, characteristic
4#11751696C211yesmaximal, characteristic, complemented
5C2×AGL(1,𝔽5)×C3⋊C8C211yesmaximal, characteristic, complemented
6#11746531C211yesmaximal, characteristic, complemented
7#11746527C211yesmaximal, characteristic, complemented
8#10604777—31nomaximal, Hall
9C3×D5×#41C2211yescharacteristic
10#91989C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
13C3×D5⋊M16C2211yescharacteristic
14#91837C411yescharacteristic, complemented
15C5×#948C411yescharacteristic, complemented
16#91284—21no—
17#91284C411yescharacteristic, complemented
18#91283—21no—
19#91283C411yescharacteristic, complemented
20D5×#208—21no—
21D5×#208C2211yescharacteristic
22C2×D5×C3⋊C8—21no—
23C2×D5×C3⋊C8C2211yescharacteristic
24#91238C412yescomplemented
25#91236C412yescomplemented
26C3×#4010C412yescomplemented
27C3×#4008C412yescomplemented
28#91150—21no—
29ΓL(1,𝔽16)⋊C8—21no—
30AGL(1,𝔽5)×C3⋊C8—21no—
31AGL(1,𝔽5)×C3⋊C8—21no—
32#70369—51nomaximal, Hall
33D5×#131—31no—
34#65794—31no—
35D5⋊#104D311yescharacteristic
36#65718—31no—
37C2×C8×AGL(1,𝔽5)—31no—
38#64901—31no—
39#64900—31no—
40C22×C3×AGL(1,𝔽5)—21no—
41C3×C5×#41C2×C411yescharacteristic
42C3×#713C2×C411yescharacteristic
43C3×Q8×D5C2×C411yescharacteristic
44C3×#711—21no—
45C3×#711C2×C411yescharacteristic
46C3×D4×D5—21no—
47C3×D4×D5C2×C411yescharacteristic
48C3×#709—21no—
49C3×#709C2×C411yescharacteristic
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5C2311yescharacteristic
52#6763—21no—
53C2×C3⋊#170—21no—
54C4⋊ΓL(1,𝔽16)C2×C412yes—
55C4×ΓL(1,𝔽16)—21no—
56D5⋊(C3⋊C8)—21no—
57D5⋊(C3⋊C8)C2×C412yes—
58C3×#704—21no—
59C3×C4×AGL(1,𝔽5)—21no—
60C3×C4×AGL(1,𝔽5)C2×C412yes—
61C3×#700C2×C412yes—
62C3×D5⋊C8—21no—
63#6710—21no—
64#6710C2×C411yescharacteristic
65C2×C3⋊#168—21no—
66C2×C3⋊#168C2×C411yescharacteristic
67C5×#208—21no—
68C5×#208C2×C411yescharacteristic
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8C2×C411yescharacteristic
71#6649—21no—
72#6649—21no—
73#6649—21no—
74D5×C3⋊C8—21no—
75D5×C3⋊C8—21no—
76D5×C3⋊C8—21no—
77D5×C3⋊C8D411yescharacteristic
78D5×C3⋊C8D411yescharacteristic
79D5×C3⋊C8D411yescharacteristic
80D5×C3⋊C8D411yescharacteristic
81C2×#948—51no—
82C2×C3×#104—51no—
83#5233—51no—
84#5122—51no—
85C2×C4×C3⋊C8—51no—
86#4558—51no—
87#4523—51no—
88D5×#41C2×D311yescharacteristic
89#4130—31no—
90C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
91D5⋊M16C2×D311yescharacteristic
92C2×D5⋊C8—31no—
93C5×#131—31no—
94#4094—31no—
95#4053—31no—
96#4053—61no—
97D5×M16—31no—
98D5×M16—61no—
99#4047—31no—
100#4047—61no—
101C2×C8×D5—31no—
102C2×C8×D5—61no—
103#4010Dic312yescomplemented
104#4009—32no—
105#4008Dic312yescomplemented
106#4007—32no—
107#3992—61no—
108C8×AGL(1,𝔽5)—61no—
109C8×AGL(1,𝔽5)—61no—
110C8×AGL(1,𝔽5)—61no—
111#1764—151noSylow
112C22×C3×D5—21no—
113C22×C3×D5#4111yescharacteristic
114C2×ΓL(1,𝔽16)—22no—
115C2×C3×AGL(1,𝔽5)—24no—
116C2×C3×AGL(1,𝔽5)—22no—
117C3×C5×Q8C4211yescharacteristic
118C3×C5×D4—21no—
119C3×C5×D4C4211yescharacteristic
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5C22×C411yescharacteristic
122C3×C22⋊D5—21no—
123C3×C22⋊D5—21no—
124C3×C22⋊D5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5#4111yescharacteristic
127C3×D20—21no—
128C3×D20C4211yescharacteristic
129C3×C4×D5—21no—
130C3×C4×D5—21no—
131C3×C4×D5—21no—
132C3×C4×D5C22×C411yescharacteristic
133C3×C4×D5C22×C411yescharacteristic
134C3×C4×D5C2×D411yescharacteristic
135C3×C4×D5C2×D411yescharacteristic
136C3×Dic10—21no—
137C3×Dic10C4211yescharacteristic
138C3⋊#170—22no—
139C3×#170—22no—
140C3⋊#168—21no—
141C3⋊#168C22⋊C411yescharacteristic
142C3⋊#168C22⋊C411yescharacteristic
143C5×C3⋊C8—21no—
144C5×C3⋊C8C22⋊C411yescharacteristic
145C5×C3⋊C8C22⋊C411yescharacteristic
146C2×C3×#41—51no—
147C2×C3×M16—51no—
148C2×C3×C42—51no—
149#948—51no—
150#948—51no—
151#948—51no—
152#948—101no—
153#948—101no—
154#948AGL(1,𝔽5)11yescharacteristic, complemented
155#926—51no—
156C2×#208—51no—
157C2×#208—101no—
158C22×C3⋊C8—51no—
159C22×C3⋊C8—51no—
160C22×C3⋊C8—101no—
161C3×#104—52no—
162C3×#104—52no—
163#835—52no—
164#832—52no—
165#815—101no—
166C8×Dic3—101no—
167C4×C3⋊C8—101no—
168C4×C3⋊C8—101no—
169C22×AGL(1,𝔽5)—21no—
170C5×#41C4×D311yescharacteristic
171#713C2×Dic311yescharacteristic
172Q8×D5C4×D311yescharacteristic
173#711—21no—
174#711C2×Dic311yescharacteristic
175D4×D5—21no—
176D4×D5C4×D311yescharacteristic
177#709—21no—
178#709C4×D311yescharacteristic
179C2×C4×D5—21no—
180C2×C4×D5C22×D311yescharacteristic
181C22⋊AGL(1,𝔽5)—61no—
182#704—21no—
183C2×#170—61no—
184C4⋊AGL(1,𝔽5)—32no—
185C4×AGL(1,𝔽5)—21no—
186C4×AGL(1,𝔽5)—61no—
187C4×AGL(1,𝔽5)C2×Dic312yes—
188#700C2×Dic312yes—
189D5⋊C8—21no—
190D5⋊C8—32no—
191D5⋊C8—61no—
192C5×M16—31no—
193C5×M16—61no—
194C2×C5×C8—31no—
195C2×C5×C8—61no—
196#681—31no—
197#681—61no—
198C2×#168—31no—
199C2×#168—61no—
200#676—61no—
201#676—61no—
202#676—61no—
203C8×D5—31no—
204C8×D5—31no—
205C8×D5—31no—
206C8×D5—31no—
207C8×D5—61no—
208C8×D5—61no—
209C8×D5—61no—
210C2×#131—151no—
211C2×#104—51no—
212#416—151no—
213#405—151no—
214C2×C4×C8—151no—
215#341—151no—
216#339—151no—
217C22×C3×C5—21no—
218C22×C3×C5#11711yescharacteristic
219C2×C3×D5—22no—
220C2×C3×D5—21no—
221C2×C3×D5—42no—
222C2×C3×D5C4×D411yescharacteristic
223C2×C3×D5C4×D411yescharacteristic
224ΓL(1,𝔽16)—42no—
225C3×AGL(1,𝔽5)—24no—
226C3×C4×C5—21no—
227C3×C4×C5C2×C4211yescharacteristic
228C3×C4×C5C2×C22⋊C411yescharacteristic
229C3×Dic5—21no—
230C3×Dic5C4×D411yescharacteristic
231C3×Dic5C4×D411yescharacteristic
232C3×#41—51no—
233C3×#41—51no—
234C3×#41—51no—
235C3×#41—101no—
236C3×#41—101no—
237C3×#41C2×AGL(1,𝔽5)11yescharacteristic
238C2×C3×Q8—51no—
239C2×C3×D4—51no—
240C2×C3×D4—101no—
241C22×C3×C4—51no—
242C22×C3×C4—101no—
243C22×C3×C4—101no—
244C3×M16—52no—
245C3×M16—101no—
246C2×C3×C8—101no—
247C3×C42—52no—
248C3×C42—101no—
249#217—101no—
250C4⋊Dic3—52no—
251C4×Dic3—101no—
252#208—21no—
253#208—51no—
254#208—101no—
255#208—101no—
256#208—101no—
257#208—101no—
258#208C2×AGL(1,𝔽5)11yescharacteristic
259C2×C3⋊C8—21no—
260C2×C3⋊C8—51no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8—51no—
263C2×C3⋊C8—51no—
264C2×C3⋊C8—51no—
265C2×C3⋊C8—52no—
266C2×C3⋊C8—101no—
267C2×C3⋊C8—101no—
268C2×C3⋊C8—101no—
269C2×C3⋊C8—101no—
270C2×C3⋊C8—101no—
271C2×C3⋊C8—101no—
272C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
273C22×D5—21no—
274C22×D5#23711yescharacteristic
275C2×AGL(1,𝔽5)—24no—
276C2×AGL(1,𝔽5)—22no—
277C2×AGL(1,𝔽5)—62no—
278C5×Q8C4×Dic311yescharacteristic
279C5×D4—21no—
280C5×D4C4×Dic311yescharacteristic
281C2×C4×C5—21no—
282C2×C4×C5C2×C4×D311yescharacteristic
283C22⋊D5—21no—
284C22⋊D5—21no—
285C22⋊D5—21no—
286C2×Dic5—21no—
287C2×Dic5#23711yescharacteristic
288D20—21no—
289D20C4×Dic311yescharacteristic
290C4×D5—21no—
291C4×D5—21no—
292C4×D5—21no—
293C4×D5C2×C4×D311yescharacteristic
294C4×D5D3×D411yescharacteristic
295C4×D5D3×D411yescharacteristic
296C4×D5C22×Dic311yescharacteristic
297Dic10—21no—
298Dic10C4×Dic311yescharacteristic
299#170—22no—
300#170—62no—
301C5×C8—31no—
302C5×C8—31no—
303C5×C8—61no—
304#168—31no—
305#168—31no—
306#168—61no—
307C2×#41—51no—
308#131—31no—
309#131—151no—
310#131—151no—
311#131—151no—
312#131—301no—
313#131—301no—
314C2×M16—51no—
315C2×M16—151no—
316C2×M16—301no—
317C22×C8—151no—
318C22×C8—151no—
319C22×C8—301no—
320#117—151no—
321C2×C42—51no—
322#104—52no—
323#104—52no—
324#103—152no—
325#102—152no—
326#97—301no—
327C4×C8—301no—
328C4×C8—301no—
329C4×C8—301no—
330C2×C3×C5—21no—
331C2×C3×C5—41no—
332C2×C3×C5C4×C22⋊C411yescharacteristic
333C3×D5—21no—
334C3×D5—41no—
335C3×D5#44312yes—
336C23×C3—51no—
337C23×C3—101no—
338C3×Q8—51no—
339C3×Q8—101no—
340C3×Q8C4×AGL(1,𝔽5)11yescharacteristic
341C3×D4—21no—
342C3×D4—51no—
343C3×D4—101no—
344C3×D4—101no—
345C3×D4—101no—
346C3×D4—101no—
347C3×D4C4×AGL(1,𝔽5)11yescharacteristic
348C2×C3×C4—21no—
349C2×C3×C4—51no—
350C2×C3×C4—51no—
351C2×C3×C4—51no—
352C2×C3×C4—51no—
353C2×C3×C4—51no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—101no—
357C2×C3×C4—102no—
358C2×C3×C4—104no—
359C2×C3×C4—101no—
360C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
361C2×Dic3—102no—
362C3×C8—102no—
363C3⋊C8—21no—
364C3⋊C8—51no—
365C3⋊C8—51no—
366C3⋊C8—102no—
367C3⋊C8—101no—
368C3⋊C8C22⋊AGL(1,𝔽5)11yescharacteristic
369C3⋊C8C22⋊AGL(1,𝔽5)11yescharacteristic
370C22×C5—21no—
371C22×C5#87711yescharacteristic
372C2×D5—22no—
373C2×D5—21no—
374C2×D5—42no—
375C2×D5#67⋊C411yescharacteristic
376C2×D5D4×Dic311yescharacteristic
377AGL(1,𝔽5)—24no—
378AGL(1,𝔽5)—122no—
379C4×C5—21no—
380C4×C5D3×C22⋊C411yescharacteristic
381C4×C5C2×C4×Dic311yescharacteristic
382Dic5—21no—
383Dic5#67⋊C411yescharacteristic
384Dic5D4×Dic311yescharacteristic
385#41—51no—
386#41—51no—
387#41—51no—
388#41—101no—
389#41—101no—
390#41D3×AGL(1,𝔽5)11yescharacteristic
391C2×Q8—51no—
392C2×D4—51no—
393C2×D4—101no—
394C22×C4—51no—
395C22×C4—101no—
396C22×C4—101no—
397M16—31no—
398M16—52no—
399M16—61no—
400M16—101no—
401M16—151no—
402M16—301no—
403M16—301no—
404M16—301no—
405M16—301no—
406C2×C8—31no—
407C2×C8—61no—
408C2×C8—101no—
409C2×C8—151no—
410C2×C8—151no—
411C2×C8—151no—
412C2×C8—151no—
413C2×C8—151no—
414C2×C8—152no—
415C2×C8—301no—
416C2×C8—301no—
417C2×C8—301no—
418C2×C8—301no—
419C2×C8—301no—
420C2×C8—301no—
421C4⋊C4—152no—
422C22⋊C4—301no—
423C42—52no—
424C42—101no—
425C42—301no—
426C3×C5#176411yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—51no—
429C22×C3—51no—
430C22×C3—102no—
431C22×C3—101no—
432C22×C3—202no—
433C22×C3#413011yescharacteristic
434C3×C4—21no—
435C3×C4—51no—
436C3×C4—51no—
437C3×C4—104no—
438C3×C4—101no—
439C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
440C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
441Dic3—202no—
442C2×C5—21no—
443C2×C5—41no—
444C2×C5Dic3×C22⋊C411yescharacteristic
445D5—21no—
446D5—41no—
447D5#482412yes—
448C23—51no—
449C23—101no—
450Q8—51no—
451Q8—101no—
452Q8Dic3×AGL(1,𝔽5)11yescharacteristic
453D4—21no—
454D4—51no—
455D4—101no—
456D4—101no—
457D4—101no—
458D4—101no—
459D4Dic3×AGL(1,𝔽5)11yescharacteristic
460C2×C4—21no—
461C2×C4—51no—
462C2×C4—51no—
463C2×C4—51no—
464C2×C4—51no—
465C2×C4—51no—
466C2×C4—101no—
467C2×C4—101no—
468C2×C4—101no—
469C2×C4—102no—
470C2×C4—104no—
471C2×C4—101no—
472C2×C4—302no—
473C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
474C8—31no—
475C8—31no—
476C8—61no—
477C8—102no—
478C8—151no—
479C8—151no—
480C8—302no—
481C8—301no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—52no—
485C2×C3—101no—
486C2×C3—201no—
487C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
488C5#7036911yescharacteristic, complemented, Sylow
489C22—21no—
490C22—51no—
491C22—51no—
492C22—102no—
493C22—101no—
494C22—202no—
495C22#9192311yescharacteristic
496C4—21no—
497C4—51no—
498C4—51no—
499C4—104no—
500C4—101no—
501C4—602no—
502C4C2×Dic3×AGL(1,𝔽5)11yescharacteristic
503C4D3×C22⋊AGL(1,𝔽5)11yescharacteristic
504C3#1060477711yescharacteristic, complemented, Sylow
505C2—21no—
506C2—41no—
507C2—52no—
508C2—101no—
509C2—201no—
510C2Dic3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC4D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×#41C2×C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C3×C4×D5C23
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5#1764
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
4. #11751696C2semidirect
5. C2×AGL(1,𝔽5)×C3⋊C8C2semidirect
6. #11746531C2semidirect
7. #11746527C2semidirect
14. #91837C4semidirect
15. C5×#948C4semidirect
17. #91284C4semidirect
19. #91283C4semidirect
24. #91238C4semidirect
25. #91236C4semidirect
26. C3×#4010C4semidirect
27. C3×#4008C4semidirect
103. #4010Dic3semidirect
105. #4008Dic3semidirect
154. #948AGL(1,𝔽5)semidirect
426. C3×C5#1764semidirect
488. C5#70369semidirect
504. C3#10604777semidirect

Maximal subgroups

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

subgroupindex
D5×#9482
#117524532
C3×D5⋊#1042
#117516962
C2×AGL(1,𝔽5)×C3⋊C82
#117465312
#117465272
#106047773
#703695