Finite Group Databasebeta

← #72260160

Subgroups — #72260160

Order 2880.

788 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 114 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
2C5×#63818C211yesmaximal, characteristic, complemented
3C4×C3⋊D3×Dic5C211yesmaximal, characteristic, complemented
4#13084852C212yesmaximal, complemented
5C3×#90981C212yesmaximal, complemented
6D3×#3957—32nomaximal
7C2×C4×C5×C3⋊D3C2211yescharacteristic
8C3×#6817C2212yes—
9#10624236—21no—
10#10624229—21no—
11#10624227C411yescharacteristic, complemented
12C4×(C3⋊D3)⋊D5—21no—
13#10624223—21no—
14#10624222C411yescharacteristic, complemented
15#10624220C412yescomplemented
16C2×C3⋊D3×Dic5—21no—
17C4×C3⋊Dic15C2211yescharacteristic, complemented
18C3×C5×#208C2212yescomplemented
19C32×C4×Dic5C2211yescharacteristic, complemented
20C5×#3712—21no—
21C5×#3710—21no—
22Dic5×C3⋊Dic3—21no—
23#10590393—51nomaximal, Hall
24D3×#709—32no—
25C5×D3×M16—32no—
26C4×D3×Dic5—32no—
27C4×D3×Dic5—61no—
28#91109—32no—
29C3×#3957—32no—
30#90981D312yescomplemented
31#90976—32no—
32C22×C5×C3⋊D3D411yescharacteristic
33C2×(C3⋊D3)⋊D5—21no—
34C2×C32×C4×C5C2311yescharacteristic
35C2×C3⋊Dic15—21no—
36C2×C5×C3⋊Dic3D411yescharacteristic
37C4×C5×C3⋊D3C2×C411yescharacteristic
38C4×C5×C3⋊D3C2×C411yescharacteristic
39C4×C5×C3⋊D3D411yescharacteristic
40C4×C5×C3⋊D3D411yescharacteristic
41C3×#1220—22no—
42C3×D60C2×C412yescomplemented
43C3×C4×D15—22no—
44C3×Dic30C2×C412yescomplemented
45C2×C32×Dic5—21no—
46#67158—21no—
47#67157—21no—
48#67156—22no—
49#67155—21no—
50#67154—22no—
51C3⋊D3×Dic5—24no—
52C3×C5×C3⋊C8—22no—
53C2×#3957—91noHall
54#64306—51no—
55C42×C3⋊D3—51no—
56#63818D511yescharacteristic, complemented
57C3×#805—52no—
58#63568—52no—
59#6817C2×D312yes—
60C2×C4×C5×D3—32no—
61C2×C4×C5×D3—61no—
62C3×#709—32no—
63D3×C22⋊D5—62no—
64C2×D3×Dic5—62no—
65C2×D3×Dic5—62no—
66#6779—62no—
67D3×D20—32no—
68C4×D3×D5—62no—
69#6771—62no—
70#6769—32no—
71D3×Dic10—32no—
72#6765—32no—
73C3×C5×M16—32no—
74C4×Dic15—32no—
75C4×Dic15—61no—
76C5×#208C2×D312yescomplemented
77C5×ΓL(1,𝔽25)—62no—
78C5×D3×C8—62no—
79C3×C4×Dic5—21no—
80C3×C4×Dic5C2×D312yescomplemented
81Dic3×Dic5—62no—
82Dic3×Dic5—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×C5C22×C411yescharacteristic
91C32×C4×C5C2×D411yescharacteristic
92C3⋊Dic15—22no—
93C5×C3⋊Dic3C22⋊C411yescharacteristic
94C5×C3⋊Dic3C22⋊C411yescharacteristic
95C3×Dic15—22no—
96C32×Dic5—22no—
97C2×#709—91no—
98C2×C5×M16—91no—
99C2×C4×Dic5—91no—
100#3957—32no—
101#3957—92no—
102C2×C4×C3⋊D3—101no—
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×C42—51no—
113C4×C3⋊Dic3—51no—
114C4×C3⋊Dic3—101no—
115C3×#208C2×D512yescomplemented
116#3712—21no—
117#3710—21no—
118C22×C5×D3—32no—
119C22×C5×D3—61no—
120C2×D3×D5—62no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5C22×D312yes—
123#1220—22no—
124C2×Dic15—62no—
125C2×Dic15—62no—
126D60C4×D312yescomplemented
127C4×D15—22no—
128Dic30C4×D312yescomplemented
129C2×C5×Dic3—32no—
130C2×C5×Dic3—61no—
131C4×C5×D3—32no—
132C4×C5×D3—32no—
133C4×C5×D3—32no—
134C4×C5×D3—32no—
135C4×C5×D3—61no—
136C4×C5×D3—61no—
137C4×C5×D3—61no—
138C4×C5×D3—61no—
139C3×C22⋊D5—62no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C3×D20—32no—
143C3×C4×D5—62no—
144C3×Dic10—32no—
145#1204—62no—
146#1203—62no—
147#1202—62no—
148#1201—62no—
149#1200—62no—
150D3×Dic5—68no—
151D3×Dic5—68no—
152D3×Dic5—62no—
153D5×Dic3—62no—
154C3×C5×C8—62no—
155C5×C3⋊C8—22no—
156D3×#41—152no—
157D3×M16—32no—
158C42×D3—152no—
159C42×D3—301no—
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—
170C2×C22⋊D5—181no—
171C22×Dic5—181no—
172#709—32no—
173#709—92no—
174#709—181no—
175#709—181no—
176C2×D20—91no—
177C2×C4×D5—181no—
178C2×Dic10—91no—
179C5×M16—32no—
180C5×M16—181no—
181C2×C5×C8—181no—
182C4×Dic5—91no—
183C4×Dic5—181no—
184C4×Dic5D3211yescharacteristic, complemented
185C22×C3⋊D3D2011yescharacteristic
186C2×D32—101no—
187C2×C32×C4—101no—
188C2×C32×C4C22×D511yescharacteristic
189C2×C3⋊Dic3—101no—
190C2×C3⋊Dic3D2011yescharacteristic
191C4×C3⋊D3—104no—
192C4×C3⋊D3C4×D511yescharacteristic
193C4×C3⋊D3C4×D511yescharacteristic
194C4×C3⋊D3C22⋊D511yescharacteristic
195C4×C3⋊D3C22⋊D511yescharacteristic
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—22no—
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—21no—
219C3×C4×C5—21no—
220C3×C4×C5C2×C4×D312yes—
221C3×C4×C5D3×D412yes—
222Dic15—22no—
223Dic15—64no—
224Dic15—64no—
225C3×Dic5—24no—
226C3×Dic5—24no—
227C3×Dic5—62no—
228C5×Dic3—32no—
229C5×Dic3—32no—
230C5×Dic3—61no—
231C5×Dic3—61no—
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—302no—
244C2×C4×D3—302no—
245C2×C4×D3—302no—
246C3×M16—32no—
247C3×C42—52no—
248C3×C42—101no—
249C4×Dic3—152no—
250C4×Dic3—301no—
251C4×Dic3—302no—
252C4×Dic3—302no—
253#208D3×D512yescomplemented
254ΓL(1,𝔽25)—62no—
255D3×C8—62no—
256C32×C5C2×#10411yescharacteristic, complemented, Hall
257C23×C5—91no—
258C22×D5—181no—
259C2×C4×C5—91no—
260C2×C4×C5—91no—
261C2×C4×C5—91no—
262C2×C4×C5—91no—
263C2×C4×C5—91no—
264C2×C4×C5C2×D3211yescharacteristic
265C22⋊D5—62no—
266C22⋊D5—182no—
267C2×Dic5—21no—
268C2×Dic5—184no—
269C2×Dic5—181no—
270C2×Dic5—181no—
271D20—32no—
272D20—181no—
273C4×D5—62no—
274C4×D5—182no—
275Dic10—32no—
276Dic10—181no—
277C5×C8—62no—
278C22×C32C2×D2011yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3#68511yescharacteristic
281C2×C3⋊D3#68511yescharacteristic
282C2×C3×D3—102no—
283D32—202no—
284C32×C4—102no—
285C32×C4C2×C4×D511yescharacteristic
286C32×C4C2×C22⋊D511yescharacteristic
287C3⋊Dic3—102no—
288C3⋊Dic3#68511yescharacteristic
289C3⋊Dic3#68511yescharacteristic
290C3×Dic3—102no—
291C2×#41—451no—
292C2×M16—91no—
293C2×C42—451no—
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—21no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
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—302no—
323C2×Dic3—302no—
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—102no—
336C4×D3—302no—
337C4×D3—302no—
338C4×D3—308no—
339C4×D3—308no—
340Dic6—52no—
341Dic6—302no—
342C3×C8—62no—
343C3⋊C8—22no—
344C22×C5—91no—
345C22×C5—91no—
346C22×C5—182no—
347C22×C5#381111yescharacteristic
348C2×D5—62no—
349C2×D5—362no—
350C4×C5—91no—
351C4×C5—91no—
352C4×C5C4×D3211yescharacteristic
353C4×C5#380211yescharacteristic
354Dic5—22no—
355Dic5—62no—
356Dic5—182no—
357C2×C32—21no—
358C2×C32C2×#68511yescharacteristic
359C3⋊D3—21no—
360C3⋊D3#395712yescomplemented
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—901no—
371C22×C4—901no—
372M16—32no—
373M16—181no—
374C2×C8—181no—
375C42—51no—
376C42—451no—
377C42—901no—
378C3×C5—21no—
379C3×C5D3×#10412yescomplemented
380C22×C3—21no—
381C22×C3—302no—
382C22×C3D3×D2012yes—
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—21no—
392C3×C4—21no—
393C3×C4—104no—
394C3×C4—104no—
395C3×C4—302no—
396C3×C4C4×D3×D512yes—
397C3×C4D3×C22⋊D512yes—
398Dic3—32no—
399Dic3—32no—
400Dic3—61no—
401Dic3—61no—
402Dic3—102no—
403Dic3—304no—
404Dic3—304no—
405C2×C5—21no—
406C2×C5—92no—
407C2×C5—181no—
408C2×C5#6392111yescharacteristic
409D5—122no—
410C32C2×#395711yescharacteristic, complemented, Sylow
411C23—91no—
412C23—901no—
413Q8—152no—
414Q8—901no—
415D4—152no—
416D4—302no—
417D4—901no—
418D4—902no—
419C2×C4—91no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—101no—
425C2×C4—302no—
426C2×C4—902no—
427C2×C4—904no—
428C2×C4—901no—
429C2×C4—901no—
430C2×C4D32×D511yescharacteristic
431C8—62no—
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#1062403111yescharacteristic
449C4—91no—
450C4—91no—
451C4—102no—
452C4—302no—
453C4—902no—
454C4#1062402211yescharacteristic
455C4#1062403411yescharacteristic
456C3—21no—
457C3D3×#395712yescomplemented
458C2—21no—
459C2—92no—
460C2—181no—
461C2—602no—
462C2#1308586611yescharacteristic
subgroupG/H
centerC4#10624034
commutatorC32×C4×C5C22×C4
Frattini, hypercenterC2×C4D32×D5
Fitting, cosocleC2×C32×C4×C5C23
socleC2×C32×C5C2×C22⋊C4
prime radical#13089409C2
hypocenterC32×C5C2×#104
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C5×#63818C2semidirect
3. C4×C3⋊D3×Dic5C2semidirect
4. #13084852C2semidirect
5. C3×#90981C2semidirect
11. #10624227C4semidirect
14. #10624222C4semidirect
15. #10624220C4semidirect
17. C4×C3⋊Dic15C22semidirect
18. C3×C5×#208C22semidirect
19. C32×C4×Dic5C22semidirect
30. #90981D3semidirect
42. C3×D60C2×C4semidirect
44. C3×Dic30C2×C4semidirect
56. #63818D5semidirect
76. C5×#208C2×D3semidirect
80. C3×C4×Dic5C2×D3semidirect
115. C3×#208C2×D5semidirect
126. D60C4×D3semidirect
128. Dic30C4×D3semidirect
167. C5×C3⋊D3#104semidirect
184. C4×Dic5D32semidirect
253. #208D3×D5semidirect
256. C32×C5C2×#104semidirect
360. C3⋊D3#3957semidirect
379. C3×C5D3×#104semidirect
410. C32C2×#3957semidirect
442. C5#10590393semidirect
457. C3D3×#3957semidirect

Maximal subgroups

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

subgroupindex
#130894092
C5×#638182
C4×C3⋊D3×Dic52
#130848522
C3×#909812
D3×#39573
#105903935