Finite Group Databasebeta

← #13085910

Subgroups — #13085910

Order 1440.

430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#67154C211yesmaximal, characteristic, complemented
2C2×D5×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#1202C211yesmaximal, characteristic
4Dic3⋊Dic15C211yesmaximal, characteristic, complemented
5#10623811C211yesmaximal, characteristic, complemented
6C5×Dic32C211yesmaximal, characteristic, complemented
7C3×#6665C211yesmaximal, characteristic, complemented
8Dic3×D20—31nomaximal
9#91395—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C22×C32×D5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#67154—22no—
18D5×C3⋊Dic3—22no—
19C3×#1202C414yescomplemented
20#67⋊Dic3—51nomaximal, Hall
21C2×C3×D20—31no—
22C2×#1202D311yescharacteristic
23C2×#1200—31no—
24C2×D5×Dic3—31no—
25C2×D5×Dic3—31no—
26C2×D5×Dic3—31no—
27C2×D5×Dic3—61no—
28#6714—31no—
29C4⋊Dic15—31no—
30C4×C5×Dic3—31no—
31C4×C5×Dic3—31no—
32C3×#685—31no—
33Dic3⋊Dic5—31no—
34#6665—31no—
35#6665D311yescharacteristic, complemented
36C22×C32×C5C2311yescharacteristic
37C2×C3×D15—21no—
38C2×C3×D15—21no—
39C2×C3×D15C2×C412yescomplemented
40C2×C32×D5—21no—
41C2×C32×D5—21no—
42C2×C32×D5C2×C412yescomplemented
43C3⋊Dic15—21no—
44C5×C3⋊Dic3D412yescomplemented
45C3×Dic15—21no—
46C3×C5×Dic3—21no—
47C3×C5×Dic3C2×C412yescomplemented
48C4×D20—91noHall
49C22×C3⋊Dic3—51no—
50C2×C3×#67—51no—
51C2×D3×Dic3—51no—
52C3×#217—51no—
53Dic3⋊Dic3—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32D511yescharacteristic, complemented
56C22×D15C2×D311yescharacteristic
57C22×C3×D5—21no—
58C22×C3×D5—31no—
59C22×C3×D5C2×D311yescharacteristic
60C22×C3×D5C2×D311yescharacteristic
61C2×C3×C4×C5—31no—
62C2×C3×C4×C5—31no—
63C2×Dic15—31no—
64C2×Dic15—31no—
65C2×Dic15—61no—
66C2×Dic15C2×D311yescharacteristic
67C2×C5×Dic3—31no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—61no—
70C2×C5×Dic3C2×D311yescharacteristic
71C2×C5×Dic3C2×D311yescharacteristic
72C2×C3×Dic5—31no—
73C3×D20—34no—
74#1202Dic314yescomplemented
75#1200—62no—
76D5×Dic3—62no—
77D5×Dic3—62no—
78D5×Dic3—62no—
79D5×Dic3—64no—
80D4×Dic3—151no—
81#67⋊C4—151no—
82C2×C32×C5C22×C411yescharacteristic
83C2×C32×C5C2×D411yescharacteristic
84C2×C32×C5#4111yescharacteristic
85C3×D15—22no—
86C32×D5—22no—
87C2×D20—31no—
88C2×C4×D5—91no—
89C2×C4×D5—91no—
90C42×C5—91no—
91#685—31no—
92#685—91no—
93C4⋊Dic5—91no—
94C23×C32—51no—
95C22×C3×D3—51no—
96C2×C3⋊Dic3—51no—
97C2×C3⋊Dic3—102no—
98C2×C3⋊Dic3C2×D511yescharacteristic
99C3×#67—54no—
100C2×C3×Dic3—51no—
101C2×C3×Dic3C2×D511yescharacteristic
102C2×C3×Dic3C2×D511yescharacteristic
103D3×Dic3—102no—
104C22×C3×C5—21no—
105C22×C3×C5C22×D311yescharacteristic
106C22×C3×C5C22×D311yescharacteristic
107C2×D15—21no—
108C2×D15—21no—
109C2×D15C2×Dic312yescomplemented
110C2×C3×D5—22no—
111C2×C3×D5—22no—
112C2×C3×D5—21no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—21no—
116C2×C3×D5—22no—
117C2×C3×D5—32no—
118C2×C3×D5—61no—
119C2×C3×D5—61no—
120C2×C3×D5C4×D312yescomplemented
121C2×C3×D5C2×Dic312yescomplemented
122C3×C4×C5—32no—
123C3×C4×C5—61no—
124Dic15—21no—
125Dic15—62no—
126Dic15—61no—
127Dic15—61no—
128C3×Dic5—61no—
129C5×Dic3—21no—
130C5×Dic3—32no—
131C5×Dic3—32no—
132C5×Dic3—62no—
133C5×Dic3C2×Dic312yescomplemented
134C2×C3×D4—151no—
135C2×#67—51no—
136C22×Dic3—151no—
137C22×Dic3—151no—
138C22×Dic3—151no—
139C22×Dic3—301no—
140C2×C4×D3—151no—
141C3×C22⋊C4—151no—
142#217—51no—
143#217—151no—
144(C2×D3)⋊C4—151no—
145C4⋊Dic3—151no—
146Dic3⋊C4—151no—
147C4×Dic3—31no—
148C4×Dic3—31no—
149C32×C5C4×D411yescharacteristic, complemented, Hall
150C22×D5—31no—
151C22×D5D3211yescharacteristic
152C2×C4×C5—31no—
153C2×C4×C5—31no—
154C2×C4×C5—91no—
155C2×Dic5—31no—
156C2×Dic5—91no—
157D20—34no—
158C4×D5—182no—
159C4×D5—182no—
160C22×C32—52no—
161C22×C32—101no—
162C22×C32—101no—
163C22×C32C22×D511yescharacteristic
164C2×C3×D3—52no—
165C2×C3×D3—101no—
166C2×C3×D3—101no—
167C3⋊Dic3—101no—
168C3⋊Dic3D2012yescomplemented
169C3×Dic3—21no—
170C3×Dic3—101no—
171C3×Dic3C4×D512yescomplemented
172C4×D4—451noSylow
173C2×C3×C5—21no—
174C2×C3×C5—21no—
175C2×C3×C5—21no—
176C2×C3×C5C2×C4×D311yescharacteristic
177C2×C3×C5D3×D411yescharacteristic
178C2×C3×C5D3×D411yescharacteristic
179C2×C3×C5#23711yescharacteristic
180C2×C3×C5#23711yescharacteristic
181C2×C3×C5C22×Dic311yescharacteristic
182D15—22no—
183C3×D5—24no—
184C3×D5—22no—
185C3×D5—22no—
186C3×D5—62no—
187C23×C3—51no—
188C23×C3—51no—
189C23×C3—101no—
190C23×C3—151no—
191C22×D3—51no—
192C3×D4—154no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—151no—
196#67—54no—
197C2×Dic3—31no—
198C2×Dic3—31no—
199C2×Dic3—51no—
200C2×Dic3—61no—
201C2×Dic3—151no—
202C2×Dic3—151no—
203C2×Dic3—301no—
204C2×Dic3—302no—
205C2×Dic3—302no—
206C2×Dic3—302no—
207C2×Dic3—304no—
208C2×Dic3D3×D511yescharacteristic
209C2×Dic3D3×D511yescharacteristic
210C4×D3—302no—
211C22×C5C2×D3211yescharacteristic
212C2×D5—21no—
213C2×D5—21no—
214C2×D5—32no—
215C2×D5—61no—
216C2×D5—61no—
217C2×D5D3×Dic312yescomplemented
218C4×C5—32no—
219C4×C5—61no—
220C4×C5—92no—
221Dic5—61no—
222Dic5—181no—
223C2×C32—102no—
224C2×C32C2×C4×D511yescharacteristic
225C2×C32C2×D2011yescharacteristic
226C2×C32#70911yescharacteristic
227C3×D3—102no—
228C2×D4—151no—
229C22×C4—451no—
230C22×C4—451no—
231C4⋊C4—451no—
232C22⋊C4—151no—
233C22⋊C4—451no—
234C42—91no—
235C3×C5—21no—
236C3×C5#67⋊C411yescharacteristic, complemented
237C3×C5D4×Dic311yescharacteristic, complemented
238C22×C3—21no—
239C22×C3—52no—
240C22×C3—52no—
241C22×C3—102no—
242C22×C3—102no—
243C22×C3—102no—
244C22×C3—101no—
245C22×C3—101no—
246C22×C3—101no—
247C22×C3—101no—
248C22×C3—152no—
249C22×C3—301no—
250C22×C3—301no—
251C22×C3C2×D3×D511yescharacteristic
252C22×C3C2×D3×D511yescharacteristic
253C2×D3—52no—
254C2×D3—101no—
255C2×D3—101no—
256C3×C4—32no—
257C3×C4—61no—
258C3×C4—301no—
259Dic3—21no—
260Dic3—32no—
261Dic3—32no—
262Dic3—62no—
263Dic3—101no—
264Dic3—302no—
265Dic3—301no—
266Dic3—301no—
267Dic3D5×Dic312yescomplemented
268C2×C5C2×D3×Dic311yescharacteristic
269C2×C5#380511yescharacteristic
270C2×C5#381111yescharacteristic
271D5—22no—
272D5—62no—
273C32C4×D2011yescharacteristic, complemented, Sylow
274C23—51no—
275C23—151no—
276D4—154no—
277C2×C4—31no—
278C2×C4—31no—
279C2×C4—91no—
280C2×C4—151no—
281C2×C4—451no—
282C2×C4—902no—
283C2×C4—902no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—104no—
288C2×C3—102no—
289C2×C3—102no—
290C2×C3—302no—
291C2×C3#676511yescharacteristic
292C2×C3C4×D3×D511yescharacteristic
293C2×C3D3×D2011yescharacteristic
294C2×C3D3×D2011yescharacteristic
295C2×C3C2×D5×Dic311yescharacteristic
296C2×C3#677911yescharacteristic
297D3—102no—
298C5#67⋊Dic311yescharacteristic, complemented, Sylow
299C22—52no—
300C22—101no—
301C22—101no—
302C22—152no—
303C22—301no—
304C22—301no—
305C22D32×D511yescharacteristic
306C4—32no—
307C4—61no—
308C4—92no—
309C4—301no—
310C4—901no—
311C3—21no—
312C3#9139511yescharacteristic, complemented
313C3Dic3×D2011yescharacteristic, complemented
314C2—102no—
315C2—302no—
316C2D3×D5×Dic311yescharacteristic
317C2#1062403111yescharacteristic
318C2#1062404511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C3×#1202C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67154C2semidirect
2. C2×D5×C3⋊Dic3C2semidirect
4. Dic3⋊Dic15C2semidirect
5. #10623811C2semidirect
6. C5×Dic32C2semidirect
7. C3×#6665C2semidirect
19. C3×#1202C4semidirect
35. #6665D3semidirect
39. C2×C3×D15C2×C4semidirect
42. C2×C32×D5C2×C4semidirect
44. C5×C3⋊Dic3D4semidirect
47. C3×C5×Dic3C2×C4semidirect
55. Dic32D5semidirect
74. #1202Dic3semidirect
109. C2×D15C2×Dic3semidirect
120. C2×C3×D5C4×D3semidirect
121. C2×C3×D5C2×Dic3semidirect
133. C5×Dic3C2×Dic3semidirect
149. C32×C5C4×D4semidirect
168. C3⋊Dic3D20semidirect
171. C3×Dic3C4×D5semidirect
217. C2×D5D3×Dic3semidirect
236. C3×C5#67⋊C4semidirect
237. C3×C5D4×Dic3semidirect
267. Dic3D5×Dic3semidirect
273. C32C4×D20semidirect
298. C5#67⋊Dic3semidirect
312. C3#91395semidirect
313. C3Dic3×D20semidirect

Maximal subgroups

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

subgroupindex
C2×#671542
C2×D5×C3⋊Dic32
C2×C3×#12022
Dic3⋊Dic152
#106238112
C5×Dic322
C3×#66652
Dic3×D203
#913953
#67⋊Dic35