Finite Group Databasebeta

← #72260156

Subgroups — #72260156

Order 2880.

788 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13089409C211yesmaximal, characteristic
2C42×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3#13087648C211yesmaximal, characteristic, complemented
4C3×#91089C212yesmaximal, complemented
5#13084902C212yesmaximal, complemented
6D3×#3937—32nomaximal
7C2×C4×C5×C3⋊D3—21no—
8C2×C4×C5×C3⋊D3C2211yescharacteristic
9C3×#6817C2212yes—
10#10624236—21no—
11#10624229—21no—
12#10624227C411yescharacteristic, complemented
13C4×(C3⋊D3)⋊D5—21no—
14#10624223—21no—
15#10624222C411yescharacteristic, complemented
16#10624220C412yescomplemented
17C32×C42×C5C2211yescharacteristic, complemented
18C4×C5×C3⋊Dic3—21no—
19C4×C5×C3⋊Dic3C2211yescharacteristic, complemented
20C3×#6710C2212yescomplemented
21#10623820—21no—
22#10623818—21no—
23#10590393—51nomaximal, Hall
24D3×#709—32no—
25C42×C5×D3—32no—
26C42×C5×D3—61no—
27D3×#681—32no—
28#91089D312yescomplemented
29C3×#3937—32no—
30#90980—32no—
31#90977—32no—
32C22×C5×C3⋊D3D411yescharacteristic
33C2×(C3⋊D3)⋊D5—21no—
34C2×C32×C4×C5—21no—
35C2×C32×C4×C5C2311yescharacteristic
36C2×C5×C3⋊Dic3—21no—
37C2×C5×C3⋊Dic3D411yescharacteristic
38C4×C5×C3⋊D3—24no—
39C4×C5×C3⋊D3C2×C411yescharacteristic
40C4×C5×C3⋊D3C2×C411yescharacteristic
41C4×C5×C3⋊D3D411yescharacteristic
42C4×C5×C3⋊D3D411yescharacteristic
43C3×#1220—22no—
44C3×D60C2×C412yescomplemented
45C3×C4×D15—22no—
46C3×Dic30C2×C412yescomplemented
47#67158—21no—
48#67157—21no—
49#67156—22no—
50#67155—21no—
51#67154—22no—
52C3×C3⋊#168—22no—
53C2×#3937—91noHall
54#64306—51no—
55C42×C3⋊D3D511yescharacteristic, complemented
56#63818—51no—
57C3×#805—52no—
58#63568—52no—
59#6817C2×D312yes—
60C2×C4×C5×D3—32no—
61C2×C4×C5×D3—61no—
62C2×C4×C5×D3—62no—
63C2×C4×C5×D3—62no—
64C3×#709—32no—
65D3×C22⋊D5—62no—
66#6779—62no—
67D3×D20—32no—
68C4×D3×D5—62no—
69#6771—62no—
70#6769—32no—
71D3×Dic10—32no—
72#6765—32no—
73C3×C42×C5—21no—
74C3×C42×C5C2×D312yescomplemented
75#6710C2×D312yescomplemented
76C4×C5×Dic3—32no—
77C4×C5×Dic3—61no—
78C4×C5×Dic3—62no—
79C4×C5×Dic3—62no—
80C3×#681—32no—
81#6650—62no—
82D3×#168—62no—
83D3×#104—152no—
84C22×C32×C5C2×D411yescharacteristic
85C2×C5×C3⋊D3—22no—
86C2×C5×C3⋊D3C22⋊C411yescharacteristic
87C2×C5×C3⋊D3C22⋊C411yescharacteristic
88C2×C3×D15—22no—
89(C3⋊D3)⋊D5—42no—
90C32×C4×C5—22no—
91C32×C4×C5C22×C411yescharacteristic
92C32×C4×C5C2×D411yescharacteristic
93C5×C3⋊Dic3—22no—
94C5×C3⋊Dic3C22⋊C411yescharacteristic
95C5×C3⋊Dic3C22⋊C411yescharacteristic
96C3×Dic15—22no—
97C2×#709—91no—
98C2×C42×C5—91no—
99C2×#681—91no—
100#3937—32no—
101#3937—92no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2×D511yescharacteristic
104C3×#235—52no—
105#3811—101no—
106#3805—101no—
107#3802—51no—
108C4×D32—101no—
109#3798—101no—
110#3797—51no—
111#3796—52no—
112C32×C42C2×D511yescharacteristic, complemented
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3C2×D511yescharacteristic, complemented
115C3×#208—52no—
116#3712—101no—
117#3710—101no—
118C22×C5×D3—32no—
119C22×C5×D3—61no—
120C2×D3×D5—62no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C22×D312yes—
125#1220—22no—
126D60C4×D312yescomplemented
127C4×D15—22no—
128Dic30C4×D312yescomplemented
129C2×C5×Dic3—32no—
130C2×C5×Dic3—61no—
131C2×C5×Dic3—62no—
132C2×C5×Dic3—62no—
133C4×C5×D3—32no—
134C4×C5×D3—32no—
135C4×C5×D3—32no—
136C4×C5×D3—32no—
137C4×C5×D3—61no—
138C4×C5×D3—61no—
139C4×C5×D3—61no—
140C4×C5×D3—61no—
141C4×C5×D3—68no—
142C4×C5×D3—68no—
143C3×C22⋊D5—62no—
144C3×D20—32no—
145C3×C4×D5—62no—
146C3×Dic10—32no—
147#1204—62no—
148#1203—62no—
149#1202—62no—
150#1201—62no—
151#1200—62no—
152D3×Dic5—62no—
153D5×Dic3—62no—
154C3⋊#168—22no—
155C3×#168—62no—
156D3×#41—152no—
157D3×M16—152no—
158C42×D3—32no—
159C42×D3—61no—
160C3×#104—152no—
161#837—152no—
162#825—152no—
163#805—52no—
164C2×C32×C5—21no—
165C2×C32×C5C2×C22⋊C411yescharacteristic
166C5×C3⋊D3—21no—
167C5×C3⋊D3#10412yescomplemented
168C3×D15—42no—
169C22×C4×C5—91no—
170C22×C4×C5—181no—
171C2×C22⋊D5—181no—
172#709—32no—
173#709—92no—
174#709—181no—
175#709—181no—
176C2×D20—91no—
177C2×C4×D5—181no—
178C2×Dic10—91no—
179C42×C5—91no—
180C42×C5—181no—
181C42×C5D3211yescharacteristic, complemented
182#681—32no—
183#681—181no—
184C2×#168—181no—
185C22×C3⋊D3C22⋊D511yescharacteristic
186C2×D32—101no—
187C2×C32×C4—21no—
188C2×C32×C4C22×D511yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C22⋊D511yescharacteristic
191C4×C3⋊D3—24no—
192C4×C3⋊D3C4×D511yescharacteristic
193C4×C3⋊D3C4×D511yescharacteristic
194C4×C3⋊D3D2011yescharacteristic
195C4×C3⋊D3D2011yescharacteristic
196C3×#67—102no—
197C3×D12—52no—
198C3×C4×D3—102no—
199C3×Dic6—52no—
200#627—101no—
201#626—102no—
202#625—101no—
203#624—101no—
204D3×Dic3—102no—
205C3×C3⋊C8—102no—
206C2×#104—451noSylow
207C22×C3×C5—21no—
208C22×C3×C5D3×D412yes—
209C2×D15—22no—
210C2×C5×D3—32no—
211C2×C5×D3—32no—
212C2×C5×D3—61no—
213C2×C5×D3—61no—
214C2×C5×D3—64no—
215C2×C5×D3—64no—
216C2×C3×D5—62no—
217D3×D5—124no—
218C3×C4×C5—24no—
219C3×C4×C5—24no—
220C3×C4×C5—21no—
221C3×C4×C5—21no—
222C3×C4×C5C2×C4×D312yes—
223C3×C4×C5D3×D412yes—
224Dic15—22no—
225C3×Dic5—62no—
226C5×Dic3—32no—
227C5×Dic3—32no—
228C5×Dic3—61no—
229C5×Dic3—61no—
230C5×Dic3—64no—
231C5×Dic3—64no—
232C3×#41—152no—
233#239—152no—
234D3×Q8—152no—
235#237—152no—
236#237—302no—
237D3×D4—152no—
238D3×D4—302no—
239#235—52no—
240#235—302no—
241C2×C4×D3—32no—
242C2×C4×D3—61no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—302no—
246C3×M16—152no—
247C3×C42—21no—
248C3×C42D3×D512yescomplemented
249C4×Dic3—32no—
250C4×Dic3—61no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253#208—52no—
254ΓL(1,𝔽25)—302no—
255D3×C8—302no—
256C32×C5C2×#10411yescharacteristic, complemented, Hall
257C23×C5—91no—
258C22×D5—181no—
259C2×C4×C5—21no—
260C2×C4×C5—91no—
261C2×C4×C5—91no—
262C2×C4×C5—91no—
263C2×C4×C5—91no—
264C2×C4×C5—91no—
265C2×C4×C5—184no—
266C2×C4×C5—181no—
267C2×C4×C5C2×D3211yescharacteristic
268C22⋊D5—62no—
269C22⋊D5—182no—
270C2×Dic5—181no—
271D20—32no—
272D20—181no—
273C4×D5—62no—
274C4×D5—182no—
275Dic10—32no—
276Dic10—181no—
277#168—62no—
278C22×C32C2×C22⋊D511yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3#68511yescharacteristic
281C2×C3⋊D3#68511yescharacteristic
282C2×C3×D3—102no—
283D32—202no—
284C32×C4—22no—
285C32×C4C2×C4×D511yescharacteristic
286C32×C4C2×D2011yescharacteristic
287C3⋊Dic3—22no—
288C3⋊Dic3#68511yescharacteristic
289C3⋊Dic3#68511yescharacteristic
290C3×Dic3—102no—
291C2×#41—451no—
292C2×M16—451no—
293C2×C42—91no—
294#104—152no—
295#104—452no—
296C2×C3×C5—22no—
297C2×C3×C5—22no—
298C2×C3×C5—21no—
299C2×C3×C5D3×C22⋊C412yes—
300D15—42no—
301C3×D5—122no—
302C5×D3—34no—
303C5×D3—62no—
304C5×D3—62no—
305C5×D3—62no—
306C22×D3—32no—
307C22×D3—61no—
308C22×D3—302no—
309C3×Q8—152no—
310C3×D4—152no—
311C3×D4—302no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—302no—
316C2×C3×C4C2×D3×D512yes—
317#67—102no—
318#67—302no—
319#67—302no—
320C2×Dic3—32no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—302no—
325D12—52no—
326D12—302no—
327C4×D3—32no—
328C4×D3—32no—
329C4×D3—32no—
330C4×D3—32no—
331C4×D3—61no—
332C4×D3—61no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—68no—
336C4×D3—68no—
337C4×D3—102no—
338C4×D3—302no—
339C4×D3—302no—
340Dic6—52no—
341Dic6—302no—
342C3×C8—302no—
343C3⋊C8—102no—
344C22×C5—91no—
345C22×C5—91no—
346C22×C5—182no—
347C22×C5#381111yescharacteristic
348C2×D5—62no—
349C2×D5—362no—
350C4×C5—22no—
351C4×C5—91no—
352C4×C5—91no—
353C4×C5—182no—
354C4×C5C4×D3211yescharacteristic
355C4×C5#380211yescharacteristic
356Dic5—62no—
357C2×C32—21no—
358C2×C32C2×#68511yescharacteristic
359C3⋊D3—21no—
360C3⋊D3#393712yescomplemented
361C3×D3—202no—
362#41—152no—
363#41—452no—
364#41—901no—
365#41—901no—
366C2×Q8—451no—
367C2×D4—451no—
368C2×D4—901no—
369C22×C4—91no—
370C22×C4—181no—
371C22×C4—901no—
372M16—152no—
373M16—901no—
374C2×C8—901no—
375C42—91no—
376C42—181no—
377C42(C3⋊D3)⋊D511yescharacteristic, complemented
378C3×C5—21no—
379C3×C5D3×#10412yescomplemented
380C22×C3—21no—
381C22×C3—302no—
382C22×C3D3×C22⋊D512yes—
383C2×D3—32no—
384C2×D3—32no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—64no—
388C2×D3—64no—
389C2×D3—102no—
390C2×D3—604no—
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—302no—
396C3×C4C4×D3×D512yes—
397C3×C4D3×D2012yes—
398Dic3—32no—
399Dic3—32no—
400Dic3—61no—
401Dic3—61no—
402Dic3—64no—
403Dic3—64no—
404Dic3—102no—
405C2×C5—21no—
406C2×C5—92no—
407C2×C5—181no—
408C2×C5#6392111yescharacteristic
409D5—122no—
410C32C2×#393711yescharacteristic, complemented, Sylow
411C23—91no—
412C23—901no—
413Q8—152no—
414Q8—901no—
415D4—152no—
416D4—302no—
417D4—901no—
418D4—902no—
419C2×C4—21no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—184no—
426C2×C4—181no—
427C2×C4—302no—
428C2×C4—902no—
429C2×C4—901no—
430C2×C4C2×(C3⋊D3)⋊D511yescharacteristic
431C8—302no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—602no—
436C2×C3D3×#68512yes—
437D3—34no—
438D3—62no—
439D3—62no—
440D3—62no—
441D3—202no—
442C5#1059039311yescharacteristic, complemented, Sylow
443C22—91no—
444C22—91no—
445C22—182no—
446C22—302no—
447C22—1802no—
448C22#1062423611yescharacteristic
449C4—22no—
450C4—91no—
451C4—91no—
452C4—182no—
453C4—302no—
454C4C4×(C3⋊D3)⋊D511yescharacteristic
455C4#1062422711yescharacteristic
456C3—21no—
457C3D3×#393712yescomplemented
458C2—21no—
459C2—92no—
460C2—181no—
461C2—602no—
462C2#1308772311yescharacteristic
subgroupG/H
centerC4#10624227
commutatorC32×C4×C5C22×C4
FrattiniC2×C4C2×(C3⋊D3)⋊D5
FittingC32×C42×C5C22
socleC2×C32×C5C2×C22⋊C4
prime radical#13089409C2
cosocleC2×C32×C4×C5C23
hypercenterC42(C3⋊D3)⋊D5
hypocenterC32×C5C2×#104
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C42×C5×C3⋊D3C2semidirect
3. #13087648C2semidirect
4. C3×#91089C2semidirect
5. #13084902C2semidirect
12. #10624227C4semidirect
15. #10624222C4semidirect
16. #10624220C4semidirect
17. C32×C42×C5C22semidirect
19. C4×C5×C3⋊Dic3C22semidirect
20. C3×#6710C22semidirect
28. #91089D3semidirect
44. C3×D60C2×C4semidirect
46. C3×Dic30C2×C4semidirect
55. C42×C3⋊D3D5semidirect
74. C3×C42×C5C2×D3semidirect
75. #6710C2×D3semidirect
112. C32×C42C2×D5semidirect
114. C4×C3⋊Dic3C2×D5semidirect
126. D60C4×D3semidirect
128. Dic30C4×D3semidirect
167. C5×C3⋊D3#104semidirect
181. C42×C5D32semidirect
248. C3×C42D3×D5semidirect
256. C32×C5C2×#104semidirect
360. C3⋊D3#3937semidirect
377. C42(C3⋊D3)⋊D5semidirect
379. C3×C5D3×#104semidirect
410. C32C2×#3937semidirect
442. C5#10590393semidirect
457. C3D3×#3937semidirect

Maximal subgroups

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

subgroupindex
#130894092
C42×C5×C3⋊D32
#130876482
C3×#910892
#130849022
D3×#39373
#105903935