Finite Group Databasebeta

← #13087486

Subgroups — #13087486

Order 1440.

582 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 100 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
2C2×C4×C3⋊D15C211yesmaximal, characteristic, complemented
3C2×#67149C211yesmaximal, characteristic, complemented
4C3×#6714C211yesmaximal, characteristic, complemented
5C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
7#10623811C211yesmaximal, characteristic, complemented
8C22⋊C4×D15—31nomaximal
9#91473—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C22×C3×C5×D3C2211yescharacteristic
13C2×D3×D15—22no—
14C2×D3×D15—22no—
15C2×D3×D15C414yescomplemented
16C2×C32×C4×C5C2211yescharacteristic, complemented
17C2×C3⋊Dic15C2211yescharacteristic, complemented
18C4×C3⋊D15—22no—
19C2×C3×Dic15C2211yescharacteristic, complemented
20C2×C3×C5×Dic3C2211yescharacteristic, complemented
21#67149—22no—
22#63921—51nomaximal, Hall
23C23×D15—31no—
24C22×D3×D5—31no—
25C2×C4×D15—31no—
26C2×C4×D15—31no—
27C2×C4×D15—31no—
28C2×C4×D15—61no—
29C2×#1200—31no—
30C3×C5×C22⋊C4—31no—
31#6719—31no—
32#6714—31no—
33#6714D311yescharacteristic, complemented
34C5×(C2×D3)⋊C4D311yescharacteristic, complemented
35C3×#685—31no—
36(C2×D3)⋊Dic5—31no—
37#6665—31no—
38C22×C32×C5C2311yescharacteristic
39C2×C3⋊D15C2×C412yes—
40C2×C3⋊D15D412yes—
41C2×C3⋊D15D412yes—
42C2×C3×D15—21no—
43C2×C3×D15—21no—
44C2×C3×D15C2×C412yescomplemented
45C2×C3×C5×D3—21no—
46C2×C3×C5×D3—21no—
47C2×C3×C5×D3C2×C412yescomplemented
48D3×D15—28no—
49C32×C4×C5—21no—
50C3⋊Dic15—21no—
51C3×Dic15—21no—
52C3×C5×Dic3—21no—
53D5×C22⋊C4—91noHall
54C22×D32—51no—
55C2×C4×C3⋊D3—51no—
56C2×#624—51no—
57C3×(C2×D3)⋊C4—51no—
58C3×(C2×D3)⋊C4D511yescharacteristic, complemented
59(C2×D3)⋊Dic3—51no—
60(C2×D3)⋊Dic3—51no—
61C23×C3×C5—31no—
62C22×D15—31no—
63C22×D15—31no—
64C22×D15—34no—
65C22×D15—62no—
66C22×D15—62no—
67C22×D15—61no—
68C22×D15C2×D311yescharacteristic
69C22×C5×D3C2×D311yescharacteristic
70C22×C3×D5—31no—
71C2×D3×D5—34no—
72C2×D3×D5—62no—
73C2×D3×D5—62no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—31no—
76C2×C3×C4×C5C2×D311yescharacteristic, complemented
77C2×C3×C4×C5C2×D311yescharacteristic, complemented
78C2×Dic15—31no—
79C2×Dic15—31no—
80C2×Dic15—61no—
81C2×Dic15C2×D311yescharacteristic, complemented
82C4×D15—62no—
83C4×D15—62no—
84C4×D15—62no—
85C4×D15—64no—
86C2×C5×Dic3C2×D311yescharacteristic, complemented
87C2×C3×Dic5—31no—
88#1200—62no—
89D3×C22⋊C4—151no—
90D3×C22⋊C4—151no—
91C2×C32×C5C22×C411yescharacteristic
92C2×C32×C5C2×D411yescharacteristic
93C2×C32×C5C2×D411yescharacteristic
94C3⋊D15C22⋊C414yescomplemented
95C3×D15—22no—
96C3×C5×D3—22no—
97C23×D5—91no—
98C2×C4×D5—91no—
99C2×C4×D5—91no—
100C5×C22⋊C4—31no—
101C22⋊Dic5—91no—
102#685—31no—
103#685—91no—
104C22×C3⋊D3—51no—
105C22×C3×D3—51no—
106C22×C3×D3C2×D511yescharacteristic
107C2×D32—54no—
108C2×D32—102no—
109C2×D32—102no—
110C2×C32×C4C2×D511yescharacteristic, complemented
111C2×C3⋊Dic3—51no—
112C4×C3⋊D3—102no—
113C2×C3×Dic3—51no—
114C2×C3×Dic3C2×D511yescharacteristic, complemented
115#624—102no—
116C22×C3×C5—21no—
117C22×C3×C5—32no—
118C22×C3×C5—61no—
119C22×C3×C5—61no—
120C22×C3×C5C22×D311yescharacteristic
121C22×C3×C5C22×D311yescharacteristic
122C2×D15—21no—
123C2×D15—21no—
124C2×D15—32no—
125C2×D15—32no—
126C2×D15—32no—
127C2×D15—32no—
128C2×D15—32no—
129C2×D15—32no—
130C2×D15—62no—
131C2×D15—62no—
132C2×D15—62no—
133C2×D15—68no—
134C2×D15C4×D312yescomplemented
135C2×C5×D3—21no—
136C2×C5×D3—21no—
137C2×C5×D3C4×D312yescomplemented
138C2×C3×D5—32no—
139C2×C3×D5—61no—
140C2×C3×D5—61no—
141D3×D5—68no—
142C3×C4×C5—22no—
143C3×C4×C5—21no—
144C3×C4×C5—21no—
145C3×C4×C5—61no—
146Dic15—21no—
147Dic15—62no—
148Dic15—61no—
149Dic15—61no—
150C3×Dic5—61no—
151C5×Dic3—21no—
152C23×D3—151no—
153C23×D3—151no—
154C2×C4×D3—151no—
155C2×C4×D3—151no—
156C2×C4×D3—151no—
157C2×C4×D3—151no—
158C2×C4×D3—301no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—151no—
161#217—151no—
162#217—151no—
163(C2×D3)⋊C4—51no—
164(C2×D3)⋊C4—151no—
165(C2×D3)⋊C4—151no—
166(C2×D3)⋊C4D1511yescharacteristic, complemented
167C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
168C23×C5—31no—
169C22×D5—31no—
170C22×D5—94no—
171C22×D5—91no—
172C22×D5—182no—
173C22×D5—182no—
174C2×C4×C5—31no—
175C2×C4×C5D3211yescharacteristic, complemented
176C2×Dic5—31no—
177C2×Dic5—91no—
178C4×D5—182no—
179C4×D5—182no—
180C22×C32C22×D511yescharacteristic
181C2×C3⋊D3—52no—
182C2×C3⋊D3—52no—
183C2×C3⋊D3—52no—
184C2×C3×D3—21no—
185C2×C3×D3—21no—
186C2×C3×D3—52no—
187C2×C3×D3—101no—
188C2×C3×D3—101no—
189C2×C3×D3C4×D512yescomplemented
190D32—108no—
191C32×C4—21no—
192C3⋊Dic3—101no—
193C3×Dic3—21no—
194C3×Dic3—101no—
195C2×C22⋊C4—451noSylow
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—21no—
199C2×C3×C5—62no—
200C2×C3×C5C2×C4×D311yescharacteristic
201C2×C3×C5C2×C4×D311yescharacteristic
202C2×C3×C5D3×D411yescharacteristic
203C2×C3×C5D3×D411yescharacteristic
204C2×C3×C5D3×D411yescharacteristic
205C2×C3×C5D3×D411yescharacteristic
206D15—22no—
207D15—34no—
208D15—34no—
209D15—64no—
210C3×D5—62no—
211C5×D3—22no—
212C23×C3—31no—
213C23×C3—151no—
214C22×D3—51no—
215C22×D3—154no—
216C22×D3—151no—
217C22×D3—151no—
218C22×D3—154no—
219C22×D3—301no—
220C22×D3—302no—
221C22×D3—302no—
222C22×D3—302no—
223C22×D3—302no—
224C22×D3C2×D1511yescharacteristic
225C2×C3×C4—21no—
226C2×C3×C4—31no—
227C2×C3×C4—151no—
228C2×C3×C4D3×D511yescharacteristic, complemented
229C2×C3×C4C2×D1511yescharacteristic, complemented
230C2×Dic3—51no—
231C2×Dic3—151no—
232C2×Dic3—151no—
233C2×Dic3—301no—
234C2×Dic3C2×D1511yescharacteristic, complemented
235C4×D3—302no—
236C4×D3—302no—
237C4×D3—302no—
238C4×D3—302no—
239C4×D3—304no—
240C22×C5—32no—
241C22×C5—61no—
242C22×C5—61no—
243C22×C5C2×D3211yescharacteristic
244C2×D5—32no—
245C2×D5—61no—
246C2×D5—61no—
247C2×D5—92no—
248C2×D5—92no—
249C2×D5—92no—
250C2×D5—188no—
251C4×C5—21no—
252C4×C5—61no—
253Dic5—61no—
254Dic5—181no—
255C2×C32C2×C4×D511yescharacteristic
256C2×C32D4×D511yescharacteristic
257C2×C32D4×D511yescharacteristic
258C3⋊D3—54no—
259C3×D3—22no—
260C3×D3—102no—
261C24—451no—
262C22×C4—451no—
263C22×C4—451no—
264C22⋊C4—31no—
265C22⋊C4—151no—
266C22⋊C4—451no—
267C22⋊C4—451no—
268C3×C5—21no—
269C3×C5D3×C22⋊C411yescharacteristic, complemented
270C3×C5D3×C22⋊C411yescharacteristic, complemented
271C22×C3—21no—
272C22×C3—32no—
273C22×C3—61no—
274C22×C3—61no—
275C22×C3—152no—
276C22×C3—301no—
277C22×C3—301no—
278C22×C3C2×D3×D511yescharacteristic
279C22×C3C22×D1511yescharacteristic
280C2×D3—21no—
281C2×D3—21no—
282C2×D3—52no—
283C2×D3—101no—
284C2×D3—101no—
285C2×D3—152no—
286C2×D3—152no—
287C2×D3—152no—
288C2×D3—152no—
289C2×D3—152no—
290C2×D3—152no—
291C2×D3—302no—
292C2×D3—302no—
293C2×D3—302no—
294C2×D3—308no—
295C2×D3—308no—
296C2×D3C4×D1512yescomplemented
297C3×C4—22no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—61no—
301C3×C4—301no—
302Dic3—21no—
303Dic3—101no—
304Dic3—302no—
305Dic3—301no—
306Dic3—301no—
307C2×C5—62no—
308C2×C5C4×D3211yescharacteristic
309C2×C5#380211yescharacteristic
310C2×C5#381111yescharacteristic
311D5—62no—
312D5—94no—
313C32D5×C22⋊C411yescharacteristic, complemented, Sylow
314C23—31no—
315C23—151no—
316C23—454no—
317C23—451no—
318C23—902no—
319C23—902no—
320C2×C4—31no—
321C2×C4—151no—
322C2×C4—451no—
323C2×C4—902no—
324C2×C4—902no—
325C2×C4D3×D1511yescharacteristic, complemented
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—62no—
330C2×C3—302no—
331C2×C3C4×D3×D511yescharacteristic
332C2×C3#677711yescharacteristic
333C2×C3#679011yescharacteristic
334C2×C3C2×C4×D1511yescharacteristic
335C2×C3D4×D1511yescharacteristic
336C2×C3D4×D1511yescharacteristic
337D3—22no—
338D3—102no—
339D3—154no—
340D3—154no—
341D3—304no—
342C5#6392111yescharacteristic, complemented, Sylow
343C22—32no—
344C22—61no—
345C22—61no—
346C22—152no—
347C22—301no—
348C22—301no—
349C22—452no—
350C22—452no—
351C22—452no—
352C22—908no—
353C22C2×D3×D1511yescharacteristic
354C4—21no—
355C4—61no—
356C4—301no—
357C4—901no—
358C3—21no—
359C3#9147311yescharacteristic, complemented
360C3C22⋊C4×D1511yescharacteristic, complemented
361C2—62no—
362C2—302no—
363C2—454no—
364C2C4×D3×D1511yescharacteristic
365C2#1062420511yescharacteristic
366C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×D3×D15C2
hypercenterC2×C4D3×D15
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊D15C2semidirect
3. C2×#67149C2semidirect
4. C3×#6714C2semidirect
5. C3×C5×(C2×D3)⋊C4C2semidirect
6. (C2×D3)⋊Dic15C2semidirect
7. #10623811C2semidirect
15. C2×D3×D15C4semidirect
16. C2×C32×C4×C5C22semidirect
17. C2×C3⋊Dic15C22semidirect
19. C2×C3×Dic15C22semidirect
20. C2×C3×C5×Dic3C22semidirect
33. #6714D3semidirect
34. C5×(C2×D3)⋊C4D3semidirect
44. C2×C3×D15C2×C4semidirect
47. C2×C3×C5×D3C2×C4semidirect
58. C3×(C2×D3)⋊C4D5semidirect
76. C2×C3×C4×C5C2×D3semidirect
77. C2×C3×C4×C5C2×D3semidirect
81. C2×Dic15C2×D3semidirect
86. C2×C5×Dic3C2×D3semidirect
94. C3⋊D15C22⋊C4semidirect
110. C2×C32×C4C2×D5semidirect
114. C2×C3×Dic3C2×D5semidirect
134. C2×D15C4×D3semidirect
137. C2×C5×D3C4×D3semidirect
166. (C2×D3)⋊C4D15semidirect
167. C32×C5C2×C22⋊C4semidirect
175. C2×C4×C5D32semidirect
189. C2×C3×D3C4×D5semidirect
228. C2×C3×C4D3×D5semidirect
229. C2×C3×C4C2×D15semidirect
234. C2×Dic3C2×D15semidirect
269. C3×C5D3×C22⋊C4semidirect
270. C3×C5D3×C22⋊C4semidirect
296. C2×D3C4×D15semidirect
313. C32D5×C22⋊C4semidirect
325. C2×C4D3×D15semidirect
342. C5#63921semidirect
359. C3#91473semidirect
360. C3C22⋊C4×D15semidirect

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⋊D152
C2×#671492
C3×#67142
C3×C5×(C2×D3)⋊C42
(C2×D3)⋊Dic152
#106238112
C22⋊C4×D153
#914733
#639215