Finite Group Databasebeta

← #13087489

Subgroups — #13087489

Order 1440.

574 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×D3×D15C211yesmaximal, characteristic, complemented
2C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
3C2×#67152C211yesmaximal, characteristic, complemented
4C2×#67151C211yesmaximal, characteristic, complemented
5C3×#6714C211yesmaximal, characteristic, complemented
6C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10623813C211yesmaximal, characteristic, complemented
8#91771—31nomaximal
9#91476—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3⋊D15C2211yescharacteristic, complemented
12C22×C3×D15C2211yescharacteristic
13C22×C3×C5×D3C2211yescharacteristic
14C2×D3×D15—22no—
15C2×D3×D15—22no—
16C2×D3×D15—22no—
17C2×C32×C4×C5C2211yescharacteristic, complemented
18C4⋊(C3⋊D15)—22no—
19C2×C3×Dic15C2211yescharacteristic, complemented
20C2×C3×C5×Dic3C2211yescharacteristic, complemented
21#67152—22no—
22#67151—22no—
23#63923—51nomaximal, Hall
24C23×D15—31no—
25C22×D3×D5—31no—
26C2×#1220—31no—
27C2×D60—31no—
28C2×D60—31no—
29C2×D60—31no—
30C2×D60—61no—
31C2×#1203—31no—
32C2×#1202—31no—
33C3×C5×C22⋊C4—31no—
34#6714—31no—
35#6714D311yescharacteristic, complemented
36C5×(C2×D3)⋊C4D311yescharacteristic, complemented
37C3×#685—31no—
38#6667—31no—
39C22×C32×C5C2311yescharacteristic
40C2×C3⋊D15—21no—
41C2×C3⋊D15—21no—
42C2×C3⋊D15—21no—
43C2×C3⋊D15—21no—
44C2×C3⋊D15—21no—
45C2×C3⋊D15D412yescomplemented
46C2×C3×D15—21no—
47C2×C3×D15—21no—
48C2×C3×D15D412yescomplemented
49C2×C3×C5×D3—21no—
50C2×C3×C5×D3—21no—
51C2×C3×C5×D3D412yescomplemented
52D3×D15—28no—
53C32×C4×C5—21no—
54C3×Dic15—21no—
55C3×C5×Dic3—21no—
56#4028—91noHall
57C22×D32—51no—
58C2×C4⋊(C3⋊D3)—51no—
59C2×#626—51no—
60C2×#626—51no—
61C3×(C2×D3)⋊C4—51no—
62C3×(C2×D3)⋊C4D511yescharacteristic, complemented
63#3722—51no—
64C23×C3×C5—31no—
65C22×D15—31no—
66C22×D15—31no—
67C22×D15—31no—
68C22×D15—31no—
69C22×D15—62no—
70C22×D15—62no—
71C22×D15—62no—
72C22×D15—61no—
73C22×D15—61no—
74C22×D15C2×D311yescharacteristic
75C22×C5×D3C2×D311yescharacteristic
76C22×C3×D5—31no—
77C2×D3×D5—62no—
78C2×D3×D5—62no—
79C2×D3×D5—62no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—31no—
82C2×C3×C4×C5C2×D311yescharacteristic, complemented
83C2×C3×C4×C5C2×D311yescharacteristic, complemented
84#1220—62no—
85C2×Dic15C2×D311yescharacteristic, complemented
86D60—62no—
87D60—62no—
88D60—64no—
89D60—62no—
90C2×C5×Dic3C2×D311yescharacteristic, complemented
91C2×C3×Dic5—31no—
92#1203—62no—
93#1202—62no—
94#882—151no—
95#882—151no—
96C2×C32×C5C2×D411yescharacteristic
97C2×C32×C5C2×D411yescharacteristic
98C2×C32×C5C2×D411yescharacteristic
99C3⋊D15—22no—
100C3⋊D15—41no—
101C3×D15—22no—
102C3×C5×D3—22no—
103C23×D5—91no—
104C2×C22⋊D5—91no—
105C2×D20—91no—
106C2×D20—91no—
107C5×C22⋊C4—31no—
108#685—31no—
109#685—91no—
110C22×C3⋊D3—51no—
111C22×C3⋊D3—51no—
112C22×C3×D3—51no—
113C22×C3×D3C2×D511yescharacteristic
114C2×D32—102no—
115C2×D32—102no—
116C2×D32—102no—
117C2×C32×C4C2×D511yescharacteristic, complemented
118C4⋊(C3⋊D3)—102no—
119C2×C3×Dic3—51no—
120C2×C3×Dic3C2×D511yescharacteristic, complemented
121#626—102no—
122#626—102no—
123C22×C3×C5—21no—
124C22×C3×C5—32no—
125C22×C3×C5—61no—
126C22×C3×C5—61no—
127C22×C3×C5C22×D311yescharacteristic
128C22×C3×C5C22×D311yescharacteristic
129C2×D15—21no—
130C2×D15—21no—
131C2×D15—32no—
132C2×D15—32no—
133C2×D15—62no—
134C2×D15—68no—
135C2×D15—61no—
136C2×D15—61no—
137C2×D15—61no—
138C2×D15—61no—
139C2×D15—62no—
140C2×D15—61no—
141C2×D15—61no—
142C2×D15—61no—
143C2×D15—61no—
144C2×D15—61no—
145C2×D15—61no—
146C2×D15—121no—
147C2×D15—121no—
148C2×D15—121no—
149C2×D15—121no—
150C2×D15D1212yescomplemented
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3D1212yescomplemented
154C2×C3×D5—32no—
155C2×C3×D5—61no—
156C2×C3×D5—61no—
157D3×D5—68no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—61no—
162Dic15—21no—
163C3×Dic5—61no—
164C5×Dic3—21no—
165C23×D3—151no—
166C23×D3—151no—
167C2×#67—151no—
168C2×#67—151no—
169C2×D12—151no—
170C2×D12—151no—
171C2×D12—151no—
172C2×D12—151no—
173C2×D12—301no—
174C3×C22⋊C4—31no—
175C3×C22⋊C4—151no—
176(C2×D3)⋊C4—51no—
177(C2×D3)⋊C4—151no—
178(C2×D3)⋊C4—151no—
179(C2×D3)⋊C4D1511yescharacteristic, complemented
180C32×C5#12011yescharacteristic, complemented, Hall
181C23×C5—31no—
182C22×D5—31no—
183C22×D5—91no—
184C22×D5—91no—
185C22×D5—182no—
186C22×D5—182no—
187C22×D5—182no—
188C2×C4×C5—31no—
189C2×C4×C5D3211yescharacteristic, complemented
190C22⋊D5—182no—
191C2×Dic5—31no—
192D20—182no—
193D20—182no—
194C22×C32C22×D511yescharacteristic
195C2×C3⋊D3—52no—
196C2×C3⋊D3—101no—
197C2×C3⋊D3—101no—
198C2×C3⋊D3—101no—
199C2×C3⋊D3—101no—
200C2×C3⋊D3—101no—
201C2×C3×D3—21no—
202C2×C3×D3—21no—
203C2×C3×D3—52no—
204C2×C3×D3—101no—
205C2×C3×D3—101no—
206C2×C3×D3D2012yescomplemented
207D32—108no—
208C32×C4—21no—
209C3×Dic3—21no—
210C3×Dic3—101no—
211#120—451noSylow
212C2×C3×C5—21no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—62no—
216C2×C3×C5C2×D1211yescharacteristic
217C2×C3×C5C2×D1211yescharacteristic
218C2×C3×C5D3×D411yescharacteristic
219C2×C3×C5D3×D411yescharacteristic
220C2×C3×C5D3×D411yescharacteristic
221C2×C3×C5D3×D411yescharacteristic
222D15—22no—
223D15—62no—
224D15—62no—
225D15—122no—
226D15—122no—
227D15—121no—
228D15—121no—
229C3×D5—62no—
230C5×D3—22no—
231C23×C3—31no—
232C23×C3—151no—
233C22×D3—51no—
234C22×D3—151no—
235C22×D3—151no—
236C22×D3—151no—
237C22×D3—151no—
238C22×D3—301no—
239C22×D3—301no—
240C22×D3—302no—
241C22×D3—302no—
242C22×D3—302no—
243C22×D3—302no—
244C22×D3—302no—
245C22×D3—302no—
246C22×D3C2×D1511yescharacteristic
247C2×C3×C4—21no—
248C2×C3×C4—31no—
249C2×C3×C4—151no—
250C2×C3×C4D3×D511yescharacteristic, complemented
251C2×C3×C4C2×D1511yescharacteristic, complemented
252#67—302no—
253#67—302no—
254C2×Dic3—51no—
255C2×Dic3C2×D1511yescharacteristic, complemented
256D12—302no—
257D12—302no—
258D12—304no—
259D12—302no—
260D12—302no—
261C22×C5—32no—
262C22×C5—61no—
263C22×C5—61no—
264C22×C5C2×D3211yescharacteristic
265C2×D5—32no—
266C2×D5—61no—
267C2×D5—61no—
268C2×D5—92no—
269C2×D5—188no—
270C2×D5—181no—
271C2×D5—181no—
272C2×D5—181no—
273C2×D5—181no—
274C2×D5—181no—
275C4×C5—21no—
276C4×C5—61no—
277Dic5—61no—
278C2×C32C2×D2011yescharacteristic
279C2×C32D4×D511yescharacteristic
280C2×C32D4×D511yescharacteristic
281C3⋊D3—102no—
282C3⋊D3—201no—
283C3×D3—22no—
284C3×D3—102no—
285C24—451no—
286C2×D4—451no—
287C2×D4—451no—
288C2×D4—451no—
289C22⋊C4—31no—
290C22⋊C4—151no—
291C22⋊C4—451no—
292C3×C5—21no—
293C3×C5#88211yescharacteristic, complemented
294C3×C5#88211yescharacteristic, complemented
295C22×C3—21no—
296C22×C3—32no—
297C22×C3—61no—
298C22×C3—61no—
299C22×C3—152no—
300C22×C3—301no—
301C22×C3—301no—
302C22×C3C2×D3×D511yescharacteristic
303C22×C3C22×D1511yescharacteristic
304C2×D3—21no—
305C2×D3—21no—
306C2×D3—52no—
307C2×D3—101no—
308C2×D3—101no—
309C2×D3—152no—
310C2×D3—152no—
311C2×D3—302no—
312C2×D3—308no—
313C2×D3—308no—
314C2×D3—301no—
315C2×D3—301no—
316C2×D3—301no—
317C2×D3—301no—
318C2×D3—302no—
319C2×D3—301no—
320C2×D3—301no—
321C2×D3—301no—
322C2×D3—301no—
323C2×D3—301no—
324C2×D3—301no—
325C2×D3—601no—
326C2×D3—601no—
327C2×D3—601no—
328C2×D3—601no—
329C2×D3D6012yescomplemented
330C3×C4—22no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—61no—
334C3×C4—301no—
335Dic3—21no—
336Dic3—101no—
337C2×C5—62no—
338C2×C5D3×D1211yescharacteristic
339C2×C5D3×D1211yescharacteristic
340C2×C5#381111yescharacteristic
341D5—62no—
342D5—182no—
343D5—361no—
344C32#402811yescharacteristic, complemented, Sylow
345C23—31no—
346C23—151no—
347C23—451no—
348C23—451no—
349C23—902no—
350C23—902no—
351C23—902no—
352D4—902no—
353D4—902no—
354D4—902no—
355C2×C4—31no—
356C2×C4—151no—
357C2×C4D3×D1511yescharacteristic, complemented
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—62no—
362C2×C3—302no—
363C2×C3D5×D1211yescharacteristic
364C2×C3D3×D2011yescharacteristic
365C2×C3#679011yescharacteristic
366C2×C3C2×D6011yescharacteristic
367C2×C3D4×D1511yescharacteristic
368C2×C3D4×D1511yescharacteristic
369D3—22no—
370D3—102no—
371D3—302no—
372D3—302no—
373D3—602no—
374D3—602no—
375D3—601no—
376D3—601no—
377C5#6392311yescharacteristic, complemented, Sylow
378C22—32no—
379C22—61no—
380C22—61no—
381C22—152no—
382C22—301no—
383C22—301no—
384C22—452no—
385C22—908no—
386C22—901no—
387C22—901no—
388C22—901no—
389C22—901no—
390C22—901no—
391C22C2×D3×D1511yescharacteristic
392C4—21no—
393C4—61no—
394C4—301no—
395C3—21no—
396C3#9147611yescharacteristic, complemented
397C3#9177111yescharacteristic, complemented
398C2—62no—
399C2—302no—
400C2—902no—
401C2—1801no—
402C2D12×D1511yescharacteristic
403C2D3×D6011yescharacteristic
404C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D3×D15
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D15C2semidirect
2. C2×C4⋊(C3⋊D15)C2semidirect
3. C2×#67152C2semidirect
4. C2×#67151C2semidirect
5. C3×#6714C2semidirect
6. C3×C5×(C2×D3)⋊C4C2semidirect
7. #10623813C2semidirect
11. C22×C3⋊D15C22semidirect
17. C2×C32×C4×C5C22semidirect
19. C2×C3×Dic15C22semidirect
20. C2×C3×C5×Dic3C22semidirect
35. #6714D3semidirect
36. C5×(C2×D3)⋊C4D3semidirect
45. C2×C3⋊D15D4semidirect
48. C2×C3×D15D4semidirect
51. C2×C3×C5×D3D4semidirect
62. C3×(C2×D3)⋊C4D5semidirect
82. C2×C3×C4×C5C2×D3semidirect
83. C2×C3×C4×C5C2×D3semidirect
85. C2×Dic15C2×D3semidirect
90. C2×C5×Dic3C2×D3semidirect
117. C2×C32×C4C2×D5semidirect
120. C2×C3×Dic3C2×D5semidirect
150. C2×D15D12semidirect
153. C2×C5×D3D12semidirect
179. (C2×D3)⋊C4D15semidirect
180. C32×C5#120semidirect
189. C2×C4×C5D32semidirect
206. C2×C3×D3D20semidirect
250. C2×C3×C4D3×D5semidirect
251. C2×C3×C4C2×D15semidirect
255. C2×Dic3C2×D15semidirect
293. C3×C5#882semidirect
294. C3×C5#882semidirect
329. C2×D3D60semidirect
344. C32#4028semidirect
357. C2×C4D3×D15semidirect
377. C5#63923semidirect
396. C3#91476semidirect
397. C3#91771semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×C4⋊(C3⋊D15)2
C2×#671522
C2×#671512
C3×#67142
C3×C5×(C2×D3)⋊C42
#106238132
#917713
#914763
#639235