Finite Group Databasebeta

← #13088983

Subgroups — #13088983

Order 1440.

710 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 144 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#10624236C211yesmaximal, characteristic, complemented
2#10624208C212yesmaximal, complemented
3C5×#3811C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×Dic5C211yesmaximal, characteristic, complemented
5C3×#6782C212yesmaximal, complemented
6#10624056C212yesmaximal, complemented
7#10624049C212yesmaximal, complemented
8#10624039C211yesmaximal, characteristic, complemented
9#10624034C211yesmaximal, characteristic, complemented
10#10624022C211yesmaximal, characteristic, complemented
11D32×Dic5C211yesmaximal, characteristic, complemented
12D3×#711—32nomaximal
13C22×C5×C3⋊D3C2211yescharacteristic
14C2×(C3⋊D3)⋊D5C2211yescharacteristic
15C2×C5×D32C2211yescharacteristic
16C2×C3⋊Dic15C2211yescharacteristic, complemented
17C3×#1220C2212yescomplemented
18C3×C5×#67C2212yescomplemented
19C2×C32×Dic5C2211yescharacteristic, complemented
20#67156C2212yescomplemented
21#67155C2211yescharacteristic
22#67153C2212yescomplemented
23#67150C2212yescomplemented
24D3×Dic15C2212yescomplemented
25Dic3×D15C2212yescomplemented
26C5×#626C2212yescomplemented
27C5×#624C2211yescharacteristic
28C3⋊D3×Dic5C2211yescharacteristic
29C3⋊D3×Dic5C2211yescharacteristic
30C3⋊D3×Dic5C2211yescharacteristic, complemented
31C3⋊D3×Dic5C2211yescharacteristic, complemented
32C3×#1204C2212yescomplemented
33C3×#1203C2212yescomplemented
34C3×#1200C2212yescomplemented
35C3×D3×Dic5C2212yescomplemented
36#64306—51nomaximal, Hall
37#6819—32no—
38C5×D3×D4—32no—
39C3×#711—32no—
40D3×C22⋊D5—32no—
41D3×C22⋊D5—32no—
42#6782—32no—
43#6782D312yescomplemented
44C2×D3×Dic5—32no—
45C2×D3×Dic5—32no—
46C2×D3×Dic5—61no—
47#6780—32no—
48#6780—32no—
49C4×D3×D5—32no—
50#6772—32no—
51#6768—32no—
52D3×Dic10—32no—
53C22×C32×C5C2311yescharacteristic
54C2×C5×C3⋊D3—22no—
55C2×C5×C3⋊D3C2311yescharacteristic
56C2×C5×C3⋊D3C2311yescharacteristic
57C2×C3×D15C2312yes—
58C2×C3×C5×D3C2312yes—
59(C3⋊D3)⋊D5—22no—
60C5×D32—22no—
61C3⋊Dic15C2311yescharacteristic
62C3⋊Dic15C2311yescharacteristic
63C3×Dic15C2312yes—
64C3×C5×Dic3C2312yes—
65C32×Dic5C2311yescharacteristic
66C32×Dic5C2311yescharacteristic
67C2×#711—91noHall
68C2×C4×C3⋊D3—51no—
69C3×#235—52no—
70#3811—51no—
71#3811D511yescharacteristic, complemented
72#3805—52no—
73#3802—51no—
74C4×D32—51no—
75C4×D32—51no—
76#3798—52no—
77#3797—51no—
78#3796—52no—
79C22×C5×D3—32no—
80C22×C5×D3—32no—
81C22×C5×D3—61no—
82C2×D3×D5—32no—
83C3×C5×D4—32no—
84#1220—32no—
85#1220C2×D312yescomplemented
86C2×Dic15—32no—
87C2×Dic15—32no—
88C2×Dic15—61no—
89C4×D15—32no—
90Dic30—32no—
91C5×#67—32no—
92C5×#67C2×D312yescomplemented
93C5×D12—32no—
94C4×C5×D3—32no—
95C3×C22⋊D5—32no—
96C3×C22⋊D5—32no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—32no—
99C2×C3×Dic5C2×D312yescomplemented
100C3×C4×D5—32no—
101C3×Dic10—32no—
102#1204—32no—
103#1204C2×D312yescomplemented
104#1203—32no—
105#1203C2×D312yescomplemented
106#1201—32no—
107#1201—32no—
108#1200C2×D312yescomplemented
109D3×Dic5—32no—
110D3×Dic5—32no—
111D3×Dic5—32no—
112D3×Dic5—32no—
113D3×Dic5—32no—
114D3×Dic5—32no—
115D3×Dic5—61no—
116D3×Dic5—61no—
117D3×Dic5—61no—
118D3×Dic5—61no—
119D3×Dic5C2×D312yescomplemented
120D5×Dic3—32no—
121D3×#41—152no—
122C2×C32×C5—21no—
123C2×C32×C5C2411yescharacteristic
124C5×C3⋊D3—21no—
125C5×C3⋊D3#4112yescomplemented
126C3×D15—22no—
127C3×C5×D3—22no—
128C2×C5×D4—91no—
129C2×C22⋊D5—91no—
130C2×C22⋊D5—91no—
131C22×Dic5—91no—
132C22×Dic5—91no—
133#711—32no—
134#711—92no—
135#711—92no—
136#711—92no—
137C2×C4×D5—91no—
138C2×Dic10—91no—
139C22×C3⋊D3C2×D511yescharacteristic
140C2×D32—51no—
141C2×D32C2×D511yescharacteristic
142C2×C32×C4—51no—
143C2×C3⋊Dic3—51no—
144C4×C3⋊D3—51no—
145C4×C3⋊D3—51no—
146C4×C3⋊D3—51no—
147C4×C3⋊D3—51no—
148C3×#67—52no—
149C3×#67C2×D512yescomplemented
150C3×D12—52no—
151C3×C4×D3—52no—
152C3×C4×D3—52no—
153C3×Dic6—52no—
154#627—52no—
155#626—52no—
156#626C2×D512yescomplemented
157#625—52no—
158#624—51no—
159#624C2×D511yescharacteristic
160D3×Dic3—52no—
161D3×Dic3—52no—
162C22×C3×C5—21no—
163C22×C3×C5—32no—
164C22×C3×C5C22×D312yes—
165C2×D15C22×D312yes—
166C2×C5×D3—32no—
167C2×C5×D3—32no—
168C2×C5×D3—61no—
169C2×C5×D3—61no—
170C2×C5×D3—64no—
171C2×C5×D3—64no—
172C2×C5×D3—64no—
173C2×C5×D3C22×D312yes—
174C2×C3×D5—32no—
175D3×D5—64no—
176C3×C4×C5—32no—
177Dic15—32no—
178Dic15—32no—
179Dic15—61no—
180Dic15—61no—
181Dic15C22×D312yes—
182C3×Dic5—21no—
183C3×Dic5—21no—
184C3×Dic5—32no—
185C3×Dic5C22×D312yes—
186C3×Dic5C22×D312yes—
187C5×Dic3C22×D312yes—
188C3×#41—152no—
189#239—152no—
190D3×Q8—152no—
191#237—152no—
192#237—152no—
193#237—152no—
194D3×D4—32no—
195D3×D4—152no—
196D3×D4—152no—
197#235—52no—
198#235—152no—
199#235—152no—
200C2×C4×D3—152no—
201C2×C4×D3—152no—
202C2×C4×D3—152no—
203C2×C4×D3—301no—
204C32×C5C2×#4111yescharacteristic, complemented, Hall
205C23×C5—91no—
206C23×C5—91no—
207C22×D5—91no—
208C5×D4—32no—
209C5×D4—92no—
210C2×C4×C5—91no—
211C22⋊D5—32no—
212C22⋊D5—32no—
213C22⋊D5—92no—
214C22⋊D5—92no—
215C2×Dic5—32no—
216C2×Dic5—91no—
217C2×Dic5—92no—
218C2×Dic5—91no—
219C2×Dic5—91no—
220C2×Dic5—91no—
221C2×Dic5—91no—
222C2×Dic5—91no—
223C2×Dic5D3211yescharacteristic, complemented
224C4×D5—32no—
225C4×D5—92no—
226Dic10—32no—
227Dic10—92no—
228C22×C32C22×D511yescharacteristic
229C2×C3⋊D3—22no—
230C2×C3⋊D3C22×D511yescharacteristic
231C2×C3⋊D3C22×D511yescharacteristic
232C2×C3×D3—52no—
233C2×C3×D3C22×D512yes—
234D32—22no—
235D32—102no—
236C32×C4—51no—
237C32×C4—51no—
238C3⋊Dic3—51no—
239C3⋊Dic3—51no—
240C3×Dic3—52no—
241C3×Dic3C22×D512yes—
242C2×#41—451noSylow
243C2×C3×C5—22no—
244C2×C3×C5—22no—
245C2×C3×C5—21no—
246C2×C3×C5—62no—
247C2×C3×C5C23×D312yes—
248D15—22no—
249C3×D5—62no—
250C5×D3—22no—
251C5×D3—34no—
252C5×D3—62no—
253C5×D3—62no—
254C5×D3—62no—
255C22×D3—32no—
256C22×D3—32no—
257C22×D3—61no—
258C22×D3—152no—
259C3×Q8—152no—
260C3×D4—32no—
261C3×D4—152no—
262C3×D4—152no—
263C2×C3×C4—52no—
264C2×C3×C4—101no—
265C2×C3×C4—152no—
266C2×C3×C4—152no—
267#67—32no—
268#67—52no—
269#67—152no—
270#67—152no—
271#67—152no—
272#67D3×D512yescomplemented
273C2×Dic3—152no—
274C2×Dic3—152no—
275C2×Dic3—152no—
276C2×Dic3—301no—
277D12—32no—
278D12—52no—
279D12—152no—
280C4×D3—32no—
281C4×D3—52no—
282C4×D3—52no—
283C4×D3—152no—
284C4×D3—152no—
285C4×D3—152no—
286C4×D3—152no—
287C4×D3—152no—
288C4×D3—152no—
289C4×D3—152no—
290C4×D3—301no—
291C4×D3—301no—
292C4×D3—301no—
293C4×D3—301no—
294Dic6—52no—
295Dic6—152no—
296Dic6—152no—
297C22×C5—32no—
298C22×C5—91no—
299C22×C5—91no—
300C22×C5—182no—
301C22×C5—182no—
302C22×C5C2×D3211yescharacteristic
303C2×D5—32no—
304C2×D5—182no—
305C4×C5—32no—
306Dic5—32no—
307Dic5—91no—
308Dic5—91no—
309Dic5C2×D3211yescharacteristic
310Dic5C2×D3211yescharacteristic
311C2×C32—21no—
312C2×C32C23×D511yescharacteristic
313C3⋊D3—21no—
314C3⋊D3#71112yescomplemented
315C3×D3—22no—
316C3×D3—102no—
317#41—152no—
318#41—452no—
319#41—452no—
320#41—452no—
321C2×Q8—451no—
322C2×D4—91no—
323C2×D4—451no—
324C2×D4—451no—
325C22×C4—451no—
326C22×C4—451no—
327C22×C4—451no—
328C3×C5—21no—
329C3×C5D3×#4112yescomplemented
330C22×C3—21no—
331C22×C3—32no—
332C22×C3—152no—
333C22×C3C2×D3×D512yes—
334C2×D3—32no—
335C2×D3—32no—
336C2×D3—52no—
337C2×D3—61no—
338C2×D3—61no—
339C2×D3—64no—
340C2×D3—64no—
341C2×D3—64no—
342C2×D3—304no—
343C2×D3C2×D3×D512yes—
344C3×C4—32no—
345C3×C4—52no—
346C3×C4—52no—
347C3×C4—101no—
348C3×C4—101no—
349C3×C4—152no—
350Dic3—52no—
351Dic3—152no—
352Dic3—152no—
353Dic3—301no—
354Dic3—301no—
355Dic3C2×D3×D512yes—
356C2×C5—21no—
357C2×C5—62no—
358C2×C5—92no—
359C2×C5—181no—
360C2×C5C22×D3211yescharacteristic
361D5—62no—
362C32C2×#71111yescharacteristic, complemented, Sylow
363C23—91no—
364C23—91no—
365C23—451no—
366Q8—152no—
367Q8—452no—
368D4—32no—
369D4—92no—
370D4—152no—
371D4—152no—
372D4—452no—
373D4—452no—
374C2×C4—51no—
375C2×C4—91no—
376C2×C4—152no—
377C2×C4—152no—
378C2×C4—452no—
379C2×C4—451no—
380C2×C4—451no—
381C2×C4—451no—
382C2×C4—451no—
383C2×C4—451no—
384C2×C4—452no—
385C2×C4—451no—
386C2×C3—22no—
387C2×C3—22no—
388C2×C3—21no—
389C2×C3—62no—
390C2×C3—302no—
391C2×C3C22×D3×D512yes—
392D3—22no—
393D3—34no—
394D3—62no—
395D3—62no—
396D3—62no—
397D3—102no—
398C5#6430611yescharacteristic, complemented, Sylow
399C22—32no—
400C22—91no—
401C22—91no—
402C22—152no—
403C22—182no—
404C22—182no—
405C22—902no—
406C22D32×D511yescharacteristic
407C4—32no—
408C4—51no—
409C4—51no—
410C4—152no—
411C4—451no—
412C4—451no—
413C3—21no—
414C3D3×#71112yescomplemented
415C2—21no—
416C2—62no—
417C2—92no—
418C2—181no—
419C2—302no—
420C2C2×D32×D511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×D5
commutator, socle, cosocleC2×C32×C5C24
FittingC22×C32×C5C23
hypercenterC22D32×D5
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #10624236C2semidirect
2. #10624208C2semidirect
3. C5×#3811C2semidirect
4. C2×C3⋊D3×Dic5C2semidirect
5. C3×#6782C2semidirect
6. #10624056C2semidirect
7. #10624049C2semidirect
8. #10624039C2semidirect
9. #10624034C2semidirect
10. #10624022C2semidirect
11. D32×Dic5C2semidirect
16. C2×C3⋊Dic15C22semidirect
17. C3×#1220C22semidirect
18. C3×C5×#67C22semidirect
19. C2×C32×Dic5C22semidirect
20. #67156C22semidirect
22. #67153C22semidirect
23. #67150C22semidirect
24. D3×Dic15C22semidirect
25. Dic3×D15C22semidirect
26. C5×#626C22semidirect
30. C3⋊D3×Dic5C22semidirect
31. C3⋊D3×Dic5C22semidirect
32. C3×#1204C22semidirect
33. C3×#1203C22semidirect
34. C3×#1200C22semidirect
35. C3×D3×Dic5C22semidirect
43. #6782D3semidirect
71. #3811D5semidirect
85. #1220C2×D3semidirect
92. C5×#67C2×D3semidirect
99. C2×C3×Dic5C2×D3semidirect
103. #1204C2×D3semidirect
105. #1203C2×D3semidirect
108. #1200C2×D3semidirect
119. D3×Dic5C2×D3semidirect
125. C5×C3⋊D3#41semidirect
149. C3×#67C2×D5semidirect
156. #626C2×D5semidirect
204. C32×C5C2×#41semidirect
223. C2×Dic5D32semidirect
272. #67D3×D5semidirect
314. C3⋊D3#711semidirect
329. C3×C5D3×#41semidirect
362. C32C2×#711semidirect
398. C5#64306semidirect
414. C3D3×#711semidirect

Maximal subgroups

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

subgroupindex
#106242362
#106242082
C5×#38112
C2×C3⋊D3×Dic52
C3×#67822
#106240562
#106240492
#106240392
#106240342
#106240222
D32×Dic52
D3×#7113
#643065