Finite Group Databasebeta

← #13089371

Subgroups — #13089371

Order 1440.

710 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C3⋊D15C211yesmaximal, characteristic, complemented
2C3×#6819C211yesmaximal, characteristic, complemented
3C3×C5×#237C211yesmaximal, characteristic, complemented
4#10624218C212yesmaximal, complemented
5C2×#67149C212yesmaximal, complemented
6#10624210C212yesmaximal, complemented
7#10624207C212yesmaximal, complemented
8C4×D3×D15C211yesmaximal, characteristic, complemented
9#10624201C211yesmaximal, characteristic, complemented
10#10624198C211yesmaximal, characteristic, complemented
11#10624197C211yesmaximal, characteristic, complemented
12#41×D15—31nomaximal
13#92024—31nomaximal
14C22×C3⋊D15C2212yes—
15C2×D3×D15C2211yescharacteristic
16C32×C5×D4C2211yescharacteristic, complemented
17#67184C2212yescomplemented
18C4⋊(C3⋊D15)C2211yescharacteristic, complemented
19C4×C3⋊D15C2211yescharacteristic
20C3×#1220C2212yescomplemented
21C2×C3×Dic15C2212yescomplemented
22C3×C4×D15C2211yescharacteristic, complemented
23C3×Dic30C2211yescharacteristic, complemented
24C3×C5×#67C2212yescomplemented
25C2×C3×C5×Dic3C2212yescomplemented
26C3×C4×C5×D3C2211yescharacteristic, complemented
27C3×C5×Dic6C2211yescharacteristic, complemented
28#67153C2212yescomplemented
29#67152C2212yescomplemented
30#67151C2212yescomplemented
31#67149C2212yes—
32#67149C2211yescharacteristic
33#67149C2212yescomplemented
34#67149C2212yescomplemented
35D3×Dic15C2211yescharacteristic, complemented
36Dic3×D15C2211yescharacteristic, complemented
37#64312—51nomaximal, Hall
38C3×C5×#41—31no—
39#6821—31no—
40Q8×D15—31no—
41#6819—32no—
42#6819D311yescharacteristic, complemented
43D4×D15—31no—
44D4×D15—31no—
45D4×D15—32no—
46D4×D15—61no—
47#6817—32no—
48#6817—31no—
49C2×C4×D15—32no—
50C2×C4×D15—31no—
51C5×#237D311yescharacteristic, complemented
52C3×#711—31no—
53#6790—32no—
54C2×#1200—32no—
55#6782—32no—
56#6779—32no—
57C4×D3×D5—31no—
58#6773—31no—
59D15⋊Q8—31no—
60#6769—31no—
61C22×C32×C5C2312yes—
62C2×C3⋊D15—24no—
63C2×C3⋊D15C2312yes—
64C2×C3⋊D15C2311yescharacteristic
65C2×C3×D15C2311yescharacteristic
66C2×C3×C5×D3C2311yescharacteristic
67D3×D15—22no—
68C32×C4×C5C2311yescharacteristic
69C3⋊Dic15C2311yescharacteristic
70C3×Dic15C2311yescharacteristic
71C3×Dic15C2312yes—
72C3×C5×Dic3C2311yescharacteristic
73C3×C5×Dic3C2312yes—
74D5×#41—91noHall
75D4×C3⋊D3—51no—
76C3×#237—51no—
77C3×#237D511yescharacteristic, complemented
78#3811—52no—
79C2×#624—52no—
80#3804—52no—
81#3804—52no—
82C4×D32—51no—
83#3799—51no—
84#3799—51no—
85#3797—51no—
86C22×D15—32no—
87C22×D15—32no—
88C22×D15—31no—
89C22×D15—62no—
90C2×D3×D5—31no—
91C3×C5×Q8—31no—
92C3×C5×D4—21no—
93C3×C5×D4—32no—
94C3×C5×D4C2×D311yescharacteristic, complemented
95C3×C5×D4C2×D311yescharacteristic, complemented
96C2×C3×C4×C5—32no—
97C2×C3×C4×C5—31no—
98#1220—32no—
99#1220—32no—
100#1220—32no—
101#1220—62no—
102#1220C2×D312yescomplemented
103C2×Dic15—31no—
104C2×Dic15C2×D312yescomplemented
105D60—32no—
106D60—31no—
107D60—31no—
108D60—61no—
109C4×D15—31no—
110C4×D15—31no—
111C4×D15—31no—
112C4×D15—31no—
113C4×D15—32no—
114C4×D15—32no—
115C4×D15—32no—
116C4×D15—61no—
117C4×D15C2×D311yescharacteristic, complemented
118Dic30—32no—
119Dic30C2×D311yescharacteristic, complemented
120C5×#67C2×D312yescomplemented
121C2×C5×Dic3C2×D312yescomplemented
122C4×C5×D3C2×D311yescharacteristic, complemented
123C5×Dic6C2×D311yescharacteristic, complemented
124C3×C22⋊D5—32no—
125C2×C3×Dic5—32no—
126C3×C4×D5—31no—
127C3×Dic10—31no—
128#1204—32no—
129#1203—32no—
130#1202—32no—
131#1200—32no—
132#1200—31no—
133#1200—32no—
134#1200—32no—
135D3×Dic5—31no—
136D5×Dic3—31no—
137D3×#41—151no—
138D3×#41—151no—
139C2×C32×C5—22no—
140C2×C32×C5C2411yescharacteristic
141C3⋊D15—22no—
142C3⋊D15#4112yescomplemented
143C3×D15—21no—
144C3×C5×D3—21no—
145C5×#41—31no—
146#713—91no—
147Q8×D5—91no—
148#711—31no—
149#711—92no—
150D4×D5—92no—
151D4×D5—91no—
152#709—91no—
153#709—92no—
154C2×C4×D5—91no—
155C2×C4×D5—92no—
156C22×C3⋊D3—52no—
157C2×D32—51no—
158C32×D4C2×D511yescharacteristic, complemented
159#638—52no—
160C4⋊(C3⋊D3)—51no—
161C4×C3⋊D3—51no—
162C3×#67—52no—
163C3×#67C2×D512yescomplemented
164C2×C3×Dic3—52no—
165C2×C3×Dic3C2×D512yescomplemented
166C3×C4×D3—51no—
167C3×C4×D3C2×D511yescharacteristic, complemented
168C3×Dic6—51no—
169C3×Dic6C2×D511yescharacteristic, complemented
170#627—52no—
171#626—52no—
172#626—52no—
173#624—52no—
174#624—51no—
175#624—52no—
176#624—52no—
177D3×Dic3—51no—
178D3×Dic3—51no—
179C22×C3×C5—22no—
180C22×C3×C5—31no—
181C22×C3×C5C22×D312yes—
182C22×C3×C5C22×D312yes—
183C2×D15—31no—
184C2×D15—31no—
185C2×D15—32no—
186C2×D15—32no—
187C2×D15—61no—
188C2×D15—62no—
189C2×D15—62no—
190C2×D15—64no—
191C2×D15—64no—
192C2×D15—124no—
193C2×D15C22×D311yescharacteristic
194C2×C5×D3C22×D311yescharacteristic
195C2×C3×D5—31no—
196D3×D5—62no—
197C3×C4×C5—21no—
198C3×C4×C5—32no—
199C3×C4×C5—31no—
200C3×C4×C5C22×D311yescharacteristic
201C3×C4×C5C22×D311yescharacteristic
202Dic15—31no—
203Dic15—31no—
204Dic15—61no—
205Dic15C22×D312yes—
206Dic15C22×D311yescharacteristic
207C3×Dic5—31no—
208C3×Dic5—32no—
209C5×Dic3C22×D311yescharacteristic
210C5×Dic3C22×D312yes—
211C3×#41—31no—
212C3×#41—151no—
213#239—151no—
214#239—151no—
215D3×Q8—151no—
216D3×Q8—151no—
217#237—51no—
218#237—152no—
219#237—152no—
220#237D1511yescharacteristic, complemented
221D3×D4—152no—
222D3×D4—151no—
223D3×D4—151no—
224D3×D4—152no—
225D3×D4—301no—
226#235—151no—
227#235—152no—
228#235—152no—
229#235—151no—
230C2×C4×D3—151no—
231C2×C4×D3—152no—
232C2×C4×D3—152no—
233C2×C4×D3—151no—
234C32×C5C2×#4111yescharacteristic, complemented, Hall
235C22×D5—91no—
236C22×D5—92no—
237C5×Q8—31no—
238C5×D4—32no—
239C5×D4D3211yescharacteristic, complemented
240C2×C4×C5—32no—
241C2×C4×C5—31no—
242C22⋊D5—32no—
243C22⋊D5—92no—
244C22⋊D5—92no—
245C2×Dic5—32no—
246C2×Dic5—91no—
247D20—92no—
248D20—91no—
249C4×D5—31no—
250C4×D5—91no—
251C4×D5—92no—
252C4×D5—92no—
253C4×D5—92no—
254C4×D5—91no—
255C4×D5—91no—
256Dic10—31no—
257Dic10—92no—
258C22×C32C22×D512yes—
259C2×C3⋊D3—51no—
260C2×C3⋊D3—52no—
261C2×C3⋊D3—104no—
262C2×C3×D3—51no—
263C2×C3×D3C22×D511yescharacteristic
264D32—102no—
265C32×C4C22×D511yescharacteristic
266C3⋊Dic3—51no—
267C3×Dic3—51no—
268C3×Dic3—52no—
269C3×Dic3C22×D511yescharacteristic
270C3×Dic3C22×D512yes—
271C2×#41—451noSylow
272C2×C3×C5—22no—
273C2×C3×C5—22no—
274C2×C3×C5—21no—
275C2×C3×C5—42no—
276C2×C3×C5—61no—
277C2×C3×C5C23×D311yescharacteristic
278C2×C3×C5C23×D311yescharacteristic
279D15—21no—
280D15—32no—
281D15—32no—
282D15—62no—
283D15—62no—
284D15—62no—
285D15—122no—
286C3×D5—61no—
287C5×D3—21no—
288C22×D3—151no—
289C22×D3—152no—
290C22×D3—152no—
291C22×D3—151no—
292C22×D3—302no—
293C3×Q8—31no—
294C3×Q8—151no—
295C3×D4—21no—
296C3×D4—32no—
297C3×D4—152no—
298C3×D4D3×D511yescharacteristic, complemented
299C3×D4C2×D1511yescharacteristic, complemented
300C2×C3×C4—32no—
301C2×C3×C4—31no—
302C2×C3×C4—152no—
303C2×C3×C4—151no—
304#67—52no—
305#67—152no—
306#67—152no—
307#67—152no—
308#67—152no—
309#67—302no—
310#67C2×D1512yescomplemented
311C2×Dic3—52no—
312C2×Dic3—151no—
313C2×Dic3—151no—
314C2×Dic3C2×D1512yescomplemented
315D12—152no—
316D12—152no—
317D12—151no—
318D12—151no—
319D12—301no—
320C4×D3—51no—
321C4×D3—151no—
322C4×D3—152no—
323C4×D3—152no—
324C4×D3—152no—
325C4×D3—151no—
326C4×D3—151no—
327C4×D3—151no—
328C4×D3—151no—
329C4×D3—151no—
330C4×D3—152no—
331C4×D3—152no—
332C4×D3—152no—
333C4×D3—301no—
334C4×D3C2×D1511yescharacteristic, complemented
335Dic6—51no—
336Dic6—152no—
337Dic6—152no—
338Dic6C2×D1511yescharacteristic, complemented
339C22×C5—31no—
340C22×C5C2×D3212yes—
341C2×D5—31no—
342C2×D5—91no—
343C2×D5—92no—
344C2×D5—182no—
345C2×D5—184no—
346C4×C5—32no—
347C4×C5—31no—
348C4×C5C2×D3211yescharacteristic
349Dic5—32no—
350Dic5—31no—
351Dic5—91no—
352C2×C32—22no—
353C2×C32C23×D511yescharacteristic
354C3⋊D3—52no—
355C3⋊D3—102no—
356C3×D3—21no—
357C3×D3—101no—
358#41—31no—
359#41—151no—
360#41—452no—
361#41—451no—
362#41—452no—
363#41—451no—
364C2×Q8—451no—
365C2×D4—452no—
366C2×D4—451no—
367C22×C4—452no—
368C22×C4—451no—
369C3×C5—21no—
370C3×C5D3×#4111yescharacteristic, complemented
371C3×C5D3×#4111yescharacteristic, complemented
372C22×C3—22no—
373C22×C3—31no—
374C22×C3—151no—
375C22×C3C2×D3×D512yes—
376C22×C3C22×D1512yes—
377C2×D3—51no—
378C2×D3—151no—
379C2×D3—151no—
380C2×D3—152no—
381C2×D3—152no—
382C2×D3—301no—
383C2×D3—302no—
384C2×D3—302no—
385C2×D3—302no—
386C2×D3—304no—
387C2×D3—304no—
388C2×D3—604no—
389C2×D3C22×D1511yescharacteristic
390C3×C4—21no—
391C3×C4—32no—
392C3×C4—31no—
393C3×C4—152no—
394C3×C4—151no—
395C3×C4C2×D3×D511yescharacteristic
396C3×C4C22×D1511yescharacteristic
397Dic3—52no—
398Dic3—51no—
399Dic3—151no—
400Dic3—151no—
401Dic3—301no—
402Dic3C22×D1512yes—
403Dic3C22×D1511yescharacteristic
404C2×C5—22no—
405C2×C5—61no—
406C2×C5C22×D3211yescharacteristic
407D5—61no—
408D5—92no—
409D5—182no—
410C32D5×#4111yescharacteristic, complemented, Sylow
411C23—451no—
412C23—452no—
413Q8—31no—
414Q8—151no—
415Q8—452no—
416D4—32no—
417D4—152no—
418D4—452no—
419D4—452no—
420D4—452no—
421D4—451no—
422D4D3×D1511yescharacteristic, complemented
423C2×C4—32no—
424C2×C4—31no—
425C2×C4—152no—
426C2×C4—151no—
427C2×C4—451no—
428C2×C4—452no—
429C2×C4—452no—
430C2×C4—452no—
431C2×C4—451no—
432C2×C4—451no—
433C2×C4—451no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—42no—
438C2×C3—61no—
439C2×C3—301no—
440C2×C3C22×D3×D511yescharacteristic
441C2×C3C23×D1511yescharacteristic
442D3—21no—
443D3—101no—
444D3—152no—
445D3—152no—
446D3—302no—
447D3—302no—
448D3—302no—
449D3—602no—
450C5#6431211yescharacteristic, complemented, Sylow
451C22—31no—
452C22—151no—
453C22—451no—
454C22—452no—
455C22—904no—
456C22—902no—
457C22C2×D3×D1512yes—
458C4—31no—
459C4—32no—
460C4—151no—
461C4—152no—
462C4—451no—
463C4C2×D3×D1511yescharacteristic
464C3—21no—
465C3#9202411yescharacteristic, complemented
466C3#41×D1511yescharacteristic, complemented
467C2—22no—
468C2—61no—
469C2—301no—
470C2—452no—
471C2—902no—
472C2C22×D3×D1511yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D15
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C5×D4C22
hypercenterD4D3×D15
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×C3⋊D15C2semidirect
2. C3×#6819C2semidirect
3. C3×C5×#237C2semidirect
4. #10624218C2semidirect
5. C2×#67149C2semidirect
6. #10624210C2semidirect
7. #10624207C2semidirect
8. C4×D3×D15C2semidirect
9. #10624201C2semidirect
10. #10624198C2semidirect
11. #10624197C2semidirect
16. C32×C5×D4C22semidirect
17. #67184C22semidirect
18. C4⋊(C3⋊D15)C22semidirect
20. C3×#1220C22semidirect
21. C2×C3×Dic15C22semidirect
22. C3×C4×D15C22semidirect
23. C3×Dic30C22semidirect
24. C3×C5×#67C22semidirect
25. C2×C3×C5×Dic3C22semidirect
26. C3×C4×C5×D3C22semidirect
27. C3×C5×Dic6C22semidirect
28. #67153C22semidirect
29. #67152C22semidirect
30. #67151C22semidirect
33. #67149C22semidirect
34. #67149C22semidirect
35. D3×Dic15C22semidirect
36. Dic3×D15C22semidirect
42. #6819D3semidirect
51. C5×#237D3semidirect
77. C3×#237D5semidirect
94. C3×C5×D4C2×D3semidirect
95. C3×C5×D4C2×D3semidirect
102. #1220C2×D3semidirect
104. C2×Dic15C2×D3semidirect
117. C4×D15C2×D3semidirect
119. Dic30C2×D3semidirect
120. C5×#67C2×D3semidirect
121. C2×C5×Dic3C2×D3semidirect
122. C4×C5×D3C2×D3semidirect
123. C5×Dic6C2×D3semidirect
142. C3⋊D15#41semidirect
158. C32×D4C2×D5semidirect
163. C3×#67C2×D5semidirect
165. C2×C3×Dic3C2×D5semidirect
167. C3×C4×D3C2×D5semidirect
169. C3×Dic6C2×D5semidirect
220. #237D15semidirect
234. C32×C5C2×#41semidirect
239. C5×D4D32semidirect
298. C3×D4D3×D5semidirect
299. C3×D4C2×D15semidirect
310. #67C2×D15semidirect
314. C2×Dic3C2×D15semidirect
334. C4×D3C2×D15semidirect
338. Dic6C2×D15semidirect
370. C3×C5D3×#41semidirect
371. C3×C5D3×#41semidirect
410. C32D5×#41semidirect
422. D4D3×D15semidirect
450. C5#64312semidirect
465. C3#92024semidirect
466. C3#41×D15semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊D152
C3×#68192
C3×C5×#2372
#106242182
C2×#671492
#106242102
#106242072
C4×D3×D152
#106242012
#106241982
#106241972
#41×D153
#920243
#643125