Finite Group Databasebeta

← #13087770

Subgroups — #13087770

Order 1440.

430 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 107 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×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#1220C211yesmaximal, characteristic
3C2×#67154C211yesmaximal, characteristic, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5#10623831C211yesmaximal, characteristic, complemented
6#10623829C211yesmaximal, characteristic, complemented
7#10623828C211yesmaximal, characteristic, complemented
8#91556—31nomaximal
9Dic3×C22⋊D5—31nomaximal
10C23×C32×C5C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C2×C5×C3⋊Dic3—22no—
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C3×#1220C414yescomplemented
16C2×C3×Dic15C2211yescharacteristic
17C2×C3×Dic15C2211yescharacteristic
18C2×C3×Dic15C2211yescharacteristic
19#67154—22no—
20#67⋊Dic3—51nomaximal, Hall
21C2×#1220D311yescharacteristic
22C22×C5×Dic3—31no—
23C22×C5×Dic3—31no—
24C22×C5×Dic3—61no—
25C2×C3×C22⋊D5—31no—
26C2×#1200—31no—
27C2×D5×Dic3—31no—
28#6719D311yescharacteristic, complemented
29C3×C22⋊Dic5—31no—
30#6669—31no—
31#6668—31no—
32#6667—31no—
33#6665—31no—
34Dic3×Dic5—31no—
35Dic3×Dic5—31no—
36C22×C32×C5—21no—
37C22×C32×C5—21no—
38C22×C32×C5C2×C412yescomplemented
39C22×C32×C5C2311yescharacteristic
40C2×C3×D15—21no—
41C2×C3×D15—21no—
42C2×C3×D15C2×C412yescomplemented
43C5×C3⋊Dic3—21no—
44C5×C3⋊Dic3D412yescomplemented
45C3×Dic15—21no—
46C3×Dic15—21no—
47C3×Dic15C2×C412yescomplemented
48C4×C22⋊D5—91noHall
49C22×C3⋊Dic3D511yescharacteristic, complemented
50C2×C3×#67—51no—
51C2×D3×Dic3—51no—
52C3×#217—51no—
53Dic3⋊Dic3—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32—51no—
56C23×C3×C5—21no—
57C23×C3×C5C2×D311yescharacteristic
58C23×C3×C5C2×D311yescharacteristic
59C22×D15C2×D311yescharacteristic
60C22×C3×D5—31no—
61#1220Dic314yescomplemented
62C2×Dic15C2×D311yescharacteristic
63C2×Dic15C2×D311yescharacteristic
64C2×Dic15C2×D311yescharacteristic
65C2×C5×Dic3—31no—
66C2×C5×Dic3—31no—
67C2×C5×Dic3—31no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—62no—
70C2×C5×Dic3—62no—
71C2×C5×Dic3—61no—
72C2×C5×Dic3—61no—
73C2×C5×Dic3—64no—
74C3×C22⋊D5—34no—
75C2×C3×Dic5—31no—
76C2×C3×Dic5—31no—
77C2×C3×Dic5—31no—
78#1200—62no—
79D5×Dic3—62no—
80D4×Dic3—151no—
81#67⋊C4—151no—
82C2×C32×C5—22no—
83C2×C32×C5C22×C411yescharacteristic
84C2×C32×C5C2×D411yescharacteristic
85C2×C32×C5#4111yescharacteristic
86C3×D15—22no—
87C22×C4×C5—91no—
88C2×C22⋊D5—31no—
89C2×C4×D5—91no—
90C22⋊Dic5—31no—
91#685—91no—
92#683—91no—
93C4×Dic5—91no—
94C23×C32C2×D511yescharacteristic
95C22×C3×D3—51no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3C2×D511yescharacteristic
98C2×C3⋊Dic3C2×D511yescharacteristic
99C3×#67—54no—
100C2×C3×Dic3—51no—
101C2×C3×Dic3—51no—
102C2×C3×Dic3—51no—
103D3×Dic3—102no—
104C22×C3×C5—22no—
105C22×C3×C5—22no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—22no—
111C22×C3×C5—21no—
112C22×C3×C5C4×D312yescomplemented
113C22×C3×C5C2×Dic312yescomplemented
114C22×C3×C5C22×D311yescharacteristic
115C22×C3×C5C22×D311yescharacteristic
116C2×D15—21no—
117C2×D15—21no—
118C2×D15C2×Dic312yescomplemented
119C2×C3×D5—32no—
120C2×C3×D5—61no—
121C2×C3×D5—61no—
122Dic15—21no—
123Dic15—21no—
124Dic15C2×Dic312yescomplemented
125C3×Dic5—32no—
126C3×Dic5—61no—
127C3×Dic5—61no—
128C5×Dic3—32no—
129C5×Dic3—32no—
130C5×Dic3—62no—
131C5×Dic3—62no—
132C5×Dic3—61no—
133C5×Dic3—61no—
134C2×C3×D4—151no—
135C2×#67—51no—
136C22×Dic3—31no—
137C22×Dic3—31no—
138C22×Dic3—61no—
139C22×Dic3—151no—
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—151no—
148C4×Dic3—151no—
149C32×C5C4×D411yescharacteristic, complemented, Hall
150C23×C5D3211yescharacteristic
151C22×D5—31no—
152C2×C4×C5—91no—
153C2×C4×C5—91no—
154C2×C4×C5—182no—
155C22⋊D5—34no—
156C2×Dic5—31no—
157C2×Dic5—31no—
158C2×Dic5—31no—
159C4×D5—182no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32C4×D512yescomplemented
163C22×C32C22×D511yescharacteristic
164C2×C3×D3—52no—
165C2×C3×D3—101no—
166C2×C3×D3—101no—
167C3⋊Dic3—21no—
168C3⋊Dic3C22⋊D512yescomplemented
169C3×Dic3—52no—
170C3×Dic3—101no—
171C3×Dic3—101no—
172C4×D4—451noSylow
173C2×C3×C5—24no—
174C2×C3×C5—22no—
175C2×C3×C5—22no—
176C2×C3×C5—21no—
177C2×C3×C5—21no—
178C2×C3×C5—21no—
179C2×C3×C5C2×C4×D311yescharacteristic
180C2×C3×C5D3×D411yescharacteristic
181C2×C3×C5D3×D411yescharacteristic
182C2×C3×C5#23711yescharacteristic
183C2×C3×C5#23711yescharacteristic
184C2×C3×C5C22×Dic311yescharacteristic
185D15—22no—
186C3×D5—62no—
187C23×C3—21no—
188C23×C3—151no—
189C23×C3D3×D511yescharacteristic
190C23×C3D3×D511yescharacteristic
191C22×D3—51no—
192C3×D4—154no—
193C2×C3×C4—151no—
194C2×C3×C4—151no—
195C2×C3×C4—151no—
196#67—54no—
197C2×Dic3—31no—
198C2×Dic3—31no—
199C2×Dic3—31no—
200C2×Dic3—31no—
201C2×Dic3—51no—
202C2×Dic3—51no—
203C2×Dic3—51no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—64no—
209C2×Dic3—302no—
210C4×D3—302no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5D3×Dic312yescomplemented
214C22×C5C2×D3211yescharacteristic
215C2×D5—32no—
216C2×D5—61no—
217C2×D5—61no—
218C4×C5—92no—
219C4×C5—181no—
220Dic5—32no—
221Dic5—61no—
222Dic5—61no—
223C2×C32—22no—
224C2×C32C2×C4×D511yescharacteristic
225C2×C32#70911yescharacteristic
226C2×C32C2×C22⋊D511yescharacteristic
227C3×D3—102no—
228C2×D4—151no—
229C22×C4—91no—
230C22×C4—451no—
231C4⋊C4—451no—
232C22⋊C4—151no—
233C22⋊C4—451no—
234C42—451no—
235C3×C5—21no—
236C3×C5#67⋊C411yescharacteristic, complemented
237C3×C5D4×Dic311yescharacteristic, complemented
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—152no—
247C22×C3—301no—
248C22×C3—301no—
249C22×C3D5×Dic312yescomplemented
250C22×C3#120012yescomplemented
251C22×C3C2×D3×D511yescharacteristic
252C22×C3C2×D3×D511yescharacteristic
253C2×D3—52no—
254C2×D3—101no—
255C2×D3—101no—
256C3×C4—152no—
257C3×C4—301no—
258C3×C4—301no—
259Dic3—32no—
260Dic3—32no—
261Dic3—52no—
262Dic3—62no—
263Dic3—62no—
264Dic3—61no—
265Dic3—61no—
266Dic3—101no—
267Dic3—101no—
268C2×C5—22no—
269C2×C5C2×D3×Dic311yescharacteristic
270C2×C5#380511yescharacteristic
271C2×C5#381111yescharacteristic
272D5—62no—
273C32C4×C22⋊D511yescharacteristic, complemented, Sylow
274C23—151no—
275C23(C3⋊D3)⋊D511yescharacteristic
276D4—154no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—151no—
280C2×C4—151no—
281C2×C4—151no—
282C2×C4—182no—
283C2×C4—902no—
284C2×C3—24no—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—302no—
291C2×C3C2×D5×Dic311yescharacteristic
292C2×C3#677911yescharacteristic
293C2×C3#677911yescharacteristic
294C2×C3C2×#120011yescharacteristic
295C2×C3D3×C22⋊D511yescharacteristic
296C2×C3D3×C22⋊D511yescharacteristic
297D3—102no—
298C5#67⋊Dic311yescharacteristic, complemented, Sylow
299C22—21no—
300C22—21no—
301C22—152no—
302C22—301no—
303C22—301no—
304C22#6715412yescomplemented
305C22C2×(C3⋊D3)⋊D511yescharacteristic
306C4—92no—
307C4—152no—
308C4—181no—
309C4—301no—
310C4—301no—
311C3—21no—
312C3Dic3×C22⋊D511yescharacteristic, complemented
313C3#9155611yescharacteristic, complemented
314C2—22no—
315C2—302no—
316C2C2×#6715411yescharacteristic
317C2#1062422911yescharacteristic
318C2#1062423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC2×C3×#1220C2
hypercenterC23(C3⋊D3)⋊D5
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C5×C3⋊Dic3C2semidirect
3. C2×#67154C2semidirect
4. C3×#6719C2semidirect
5. #10623831C2semidirect
6. #10623829C2semidirect
7. #10623828C2semidirect
15. C3×#1220C4semidirect
28. #6719D3semidirect
38. C22×C32×C5C2×C4semidirect
42. C2×C3×D15C2×C4semidirect
44. C5×C3⋊Dic3D4semidirect
47. C3×Dic15C2×C4semidirect
49. C22×C3⋊Dic3D5semidirect
61. #1220Dic3semidirect
112. C22×C3×C5C4×D3semidirect
113. C22×C3×C5C2×Dic3semidirect
118. C2×D15C2×Dic3semidirect
124. Dic15C2×Dic3semidirect
149. C32×C5C4×D4semidirect
162. C22×C32C4×D5semidirect
168. C3⋊Dic3C22⋊D5semidirect
213. C22×C5D3×Dic3semidirect
236. C3×C5#67⋊C4semidirect
237. C3×C5D4×Dic3semidirect
249. C22×C3D5×Dic3semidirect
250. C22×C3#1200semidirect
273. C32C4×C22⋊D5semidirect
298. C5#67⋊Dic3semidirect
304. C22#67154semidirect
312. C3Dic3×C22⋊D5semidirect
313. C3#91556semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C3⋊Dic32
C2×C3×#12202
C2×#671542
C3×#67192
#106238312
#106238292
#106238282
#915563
Dic3×C22⋊D53
#67⋊Dic35