Finite Group Databasebeta

← #13087590

Subgroups — #13087590

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×#67184C211yesmaximal, characteristic, complemented
3C2×C3×#1220C211yesmaximal, characteristic, complemented
4C2×C3×C5×#67C211yesmaximal, characteristic, complemented
5#10623813C211yesmaximal, characteristic, complemented
6(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
7#10623811C211yesmaximal, characteristic, complemented
8#91826—31nomaximal
9#91577—31nomaximal
10C23×C32×C5C2211yescharacteristic, complemented
11C22×C3⋊D15C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic
13C22×C3×C5×D3C2211yescharacteristic
14C2×D3×D15—22no—
15C2×D3×D15—22no—
16C2×D3×D15—22no—
17#67184—22no—
18C2×C3⋊Dic15C2211yescharacteristic, complemented
19C3×#1220—22no—
20C2×C3×Dic15C2211yescharacteristic, complemented
21C3×C5×#67—22no—
22C2×C3×C5×Dic3C2211yescharacteristic, complemented
23#63983—51nomaximal, Hall
24C23×D15—31no—
25C22×D3×D5—31no—
26C2×C3×C5×D4—31no—
27C2×#1220—31no—
28C2×#1220—31no—
29C2×#1220—61no—
30C2×#1220D311yescharacteristic, complemented
31C2×C5×#67D311yescharacteristic, complemented
32C2×C3×C22⋊D5—31no—
33#6719—31no—
34#6714—31no—
35#6714—31no—
36#6667—31no—
37(C2×D3)⋊Dic5—31no—
38#6665—31no—
39C22×C32×C5—21no—
40C22×C32×C5—21no—
41C22×C32×C5—21no—
42C22×C32×C5C2311yescharacteristic
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—
53C3⋊Dic15—21no—
54C3×Dic15—21no—
55C3×C5×Dic3—21no—
56#4083—91noHall
57C22×D32—51no—
58C2×#638—51no—
59C2×C3×#67—51no—
60C2×C3×#67D511yescharacteristic, complemented
61#3722—51no—
62(C2×D3)⋊Dic3—51no—
63(C2×D3)⋊Dic3—51no—
64C23×C3×C5—21no—
65C23×C3×C5—31no—
66C23×C3×C5C2×D311yescharacteristic, complemented
67C23×C3×C5C2×D311yescharacteristic, complemented
68C22×D15—31no—
69C22×D15—31no—
70C22×D15—62no—
71C22×D15—62no—
72C22×D15—62no—
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—
80C3×C5×D4—62no—
81C2×C3×C4×C5—31no—
82#1220—22no—
83#1220—62no—
84#1220—62no—
85#1220—64no—
86C2×Dic15—31no—
87C2×Dic15—31no—
88C2×Dic15—61no—
89C2×Dic15C2×D311yescharacteristic, complemented
90C5×#67—22no—
91C2×C5×Dic3C2×D311yescharacteristic, complemented
92C3×C22⋊D5—62no—
93C2×C3×Dic5—31no—
94#937—151no—
95#937—151no—
96C2×C32×C5—41no—
97C2×C32×C5C2×D411yescharacteristic
98C2×C32×C5C2×D411yescharacteristic
99C2×C32×C5C2×D411yescharacteristic
100C3⋊D15—22no—
101C3×D15—22no—
102C3×C5×D3—22no—
103C23×D5—91no—
104C2×C5×D4—31no—
105C2×C22⋊D5—31no—
106C2×C22⋊D5—91no—
107C22⋊Dic5—91no—
108#685—91no—
109#685—91no—
110C23×C32C2×D511yescharacteristic, complemented
111C22×C3⋊D3—51no—
112C22×C3×D3—51no—
113C22×C3×D3C2×D511yescharacteristic
114C2×D32—102no—
115C2×D32—102no—
116C2×D32—102no—
117#638—102no—
118C2×C3⋊Dic3—51no—
119C3×#67—22no—
120C3×#67—102no—
121C2×C3×Dic3—51no—
122C2×C3×Dic3C2×D511yescharacteristic, complemented
123C22×C3×C5—22no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5—32no—
132C22×C3×C5—41no—
133C22×C3×C5—41no—
134C22×C3×C5—61no—
135C22×C3×C5—61no—
136C22×C3×C5C22×D311yescharacteristic
137C22×C3×C5C22×D311yescharacteristic
138C2×D15—21no—
139C2×D15—21no—
140C2×D15—32no—
141C2×D15—32no—
142C2×D15—62no—
143C2×D15—68no—
144C2×D15—61no—
145C2×D15—61no—
146C2×D15—61no—
147C2×D15—61no—
148C2×D15—121no—
149C2×D15—121no—
150C2×D15#6712yescomplemented
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3#6712yescomplemented
154C2×C3×D5—32no—
155C2×C3×D5—61no—
156C2×C3×D5—61no—
157D3×D5—68no—
158C3×C4×C5—61no—
159Dic15—21no—
160Dic15—62no—
161Dic15—61no—
162Dic15—61no—
163C3×Dic5—61no—
164C5×Dic3—21no—
165C23×D3—151no—
166C23×D3—151no—
167C2×C3×D4—31no—
168C2×C3×D4—151no—
169C2×#67—51no—
170C2×#67—151no—
171C2×#67—151no—
172C2×#67—301no—
173C2×#67D1511yescharacteristic, complemented
174#217—151no—
175#217—151no—
176(C2×D3)⋊C4—151no—
177(C2×D3)⋊C4—151no—
178(C2×D3)⋊C4—151no—
179(C2×D3)⋊C4—151no—
180C32×C5#12011yescharacteristic, complemented, Hall
181C23×C5—31no—
182C23×C5D3211yescharacteristic, complemented
183C22×D5—31no—
184C22×D5—91no—
185C22×D5—182no—
186C22×D5—182no—
187C22×D5—182no—
188C5×D4—62no—
189C2×C4×C5—31no—
190C22⋊D5—62no—
191C22⋊D5—182no—
192C2×Dic5—31no—
193C2×Dic5—91no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32C22×D511yescharacteristic
198C2×C3⋊D3—52no—
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×D3C22⋊D512yescomplemented
207D32—108no—
208C3⋊Dic3—101no—
209C3×Dic3—21no—
210C3×Dic3—101no—
211#120—451noSylow
212C2×C3×C5—21no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—42no—
216C2×C3×C5—41no—
217C2×C3×C5—41no—
218C2×C3×C5—62no—
219C2×C3×C5D3×D411yescharacteristic
220C2×C3×C5D3×D411yescharacteristic
221C2×C3×C5D3×D411yescharacteristic
222C2×C3×C5D3×D411yescharacteristic
223C2×C3×C5C2×#6711yescharacteristic
224C2×C3×C5C2×#6711yescharacteristic
225D15—22no—
226D15—62no—
227D15—62no—
228D15—122no—
229C3×D5—62no—
230C5×D3—22no—
231C23×C3—21no—
232C23×C3—31no—
233C23×C3—151no—
234C23×C3D3×D511yescharacteristic, complemented
235C23×C3C2×D1511yescharacteristic, complemented
236C22×D3—51no—
237C22×D3—151no—
238C22×D3—151no—
239C22×D3—301no—
240C22×D3—302no—
241C22×D3—302no—
242C22×D3—302no—
243C22×D3—302no—
244C22×D3—302no—
245C22×D3—302no—
246C22×D3C2×D1511yescharacteristic
247C3×D4—62no—
248C3×D4—302no—
249C2×C3×C4—31no—
250C2×C3×C4—151no—
251#67—22no—
252#67—102no—
253#67—302no—
254#67—302no—
255#67—304no—
256C2×Dic3—51no—
257C2×Dic3—151no—
258C2×Dic3—151no—
259C2×Dic3—301no—
260C2×Dic3C2×D1511yescharacteristic, complemented
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—32no—
265C22×C5—61no—
266C22×C5—61no—
267C22×C5C2×D3211yescharacteristic
268C2×D5—32no—
269C2×D5—61no—
270C2×D5—61no—
271C2×D5—92no—
272C2×D5—188no—
273C2×D5—181no—
274C2×D5—181no—
275C4×C5—61no—
276Dic5—61no—
277Dic5—181no—
278C2×C32—41no—
279C2×C32D4×D511yescharacteristic
280C2×C32D4×D511yescharacteristic
281C2×C32C2×C22⋊D511yescharacteristic
282C3⋊D3—102no—
283C3×D3—22no—
284C3×D3—102no—
285C24—451no—
286C2×D4—31no—
287C2×D4—151no—
288C2×D4—451no—
289C22⋊C4—451no—
290C22⋊C4—451no—
291C22⋊C4—451no—
292C3×C5—21no—
293C3×C5#93711yescharacteristic, complemented
294C3×C5#93711yescharacteristic, complemented
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—32no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—152no—
309C22×C3—301no—
310C22×C3—301no—
311C22×C3C2×D3×D511yescharacteristic
312C22×C3C22×D1511yescharacteristic
313C2×D3—21no—
314C2×D3—21no—
315C2×D3—52no—
316C2×D3—101no—
317C2×D3—101no—
318C2×D3—152no—
319C2×D3—152no—
320C2×D3—302no—
321C2×D3—308no—
322C2×D3—308no—
323C2×D3—301no—
324C2×D3—301no—
325C2×D3—301no—
326C2×D3—301no—
327C2×D3—601no—
328C2×D3—601no—
329C2×D3#122012yescomplemented
330C3×C4—61no—
331C3×C4—301no—
332Dic3—21no—
333Dic3—101no—
334Dic3—302no—
335Dic3—301no—
336Dic3—301no—
337C2×C5—41no—
338C2×C5—62no—
339C2×C5D3×#6711yescharacteristic
340C2×C5D3×#6711yescharacteristic
341C2×C5#381111yescharacteristic
342D5—62no—
343D5—182no—
344C32#408311yescharacteristic, complemented, Sylow
345C23—31no—
346C23—151no—
347C23—451no—
348C23—902no—
349C23—902no—
350C23—902no—
351C23D3×D1511yescharacteristic, complemented
352D4—62no—
353D4—302no—
354D4—902no—
355C2×C4—31no—
356C2×C4—151no—
357C2×C4—451no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—42no—
362C2×C3—41no—
363C2×C3—41no—
364C2×C3—62no—
365C2×C3—302no—
366C2×C3D5×#6711yescharacteristic
367C2×C3D3×C22⋊D511yescharacteristic
368C2×C3#679011yescharacteristic
369C2×C3D4×D1511yescharacteristic
370C2×C3D4×D1511yescharacteristic
371C2×C3C2×#122011yescharacteristic
372D3—22no—
373D3—102no—
374D3—302no—
375D3—302no—
376D3—602no—
377C5#6398311yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—21no—
381C22—32no—
382C22—61no—
383C22—61no—
384C22—152no—
385C22—301no—
386C22—301no—
387C22—452no—
388C22—908no—
389C22—901no—
390C22—901no—
391C22C2×D3×D1511yescharacteristic
392C4—61no—
393C4—301no—
394C4—901no—
395C3—21no—
396C3#9157711yescharacteristic, complemented
397C3#9182611yescharacteristic, complemented
398C2—41no—
399C2—62no—
400C2—302no—
401C2—902no—
402C2#67×D1511yescharacteristic
403C2D3×#122011yescharacteristic
404C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D3×D15
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×D3×D15C2semidirect
2. C2×#67184C2semidirect
3. C2×C3×#1220C2semidirect
4. C2×C3×C5×#67C2semidirect
5. #10623813C2semidirect
6. (C2×D3)⋊Dic15C2semidirect
7. #10623811C2semidirect
10. C23×C32×C5C22semidirect
18. C2×C3⋊Dic15C22semidirect
20. C2×C3×Dic15C22semidirect
22. C2×C3×C5×Dic3C22semidirect
30. C2×#1220D3semidirect
31. C2×C5×#67D3semidirect
45. C2×C3⋊D15D4semidirect
48. C2×C3×D15D4semidirect
51. C2×C3×C5×D3D4semidirect
60. C2×C3×#67D5semidirect
66. C23×C3×C5C2×D3semidirect
67. C23×C3×C5C2×D3semidirect
89. C2×Dic15C2×D3semidirect
91. C2×C5×Dic3C2×D3semidirect
110. C23×C32C2×D5semidirect
122. C2×C3×Dic3C2×D5semidirect
150. C2×D15#67semidirect
153. C2×C5×D3#67semidirect
173. C2×#67D15semidirect
180. C32×C5#120semidirect
182. C23×C5D32semidirect
206. C2×C3×D3C22⋊D5semidirect
234. C23×C3D3×D5semidirect
235. C23×C3C2×D15semidirect
260. C2×Dic3C2×D15semidirect
293. C3×C5#937semidirect
294. C3×C5#937semidirect
329. C2×D3#1220semidirect
344. C32#4083semidirect
351. C23D3×D15semidirect
377. C5#63983semidirect
396. C3#91577semidirect
397. C3#91826semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×#671842
C2×C3×#12202
C2×C3×C5×#672
#106238132
(C2×D3)⋊Dic152
#106238112
#918263
#915773
#639835