Finite Group Databasebeta

← #13087438

Subgroups — #13087438

Order 1440.

410 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 96 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×#67152C211yesmaximal, characteristic
2C2×#67149C211yesmaximal, characteristic, complemented
3C2×D3×Dic15C211yesmaximal, characteristic, complemented
4#10623908C211yesmaximal, characteristic, complemented
5C3×C4×Dic15C211yesmaximal, characteristic, complemented
6C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10623814C211yesmaximal, characteristic, complemented
8#91770—31nomaximal
9#91405—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C32×C4×C5C2211yescharacteristic
13C2×C3⋊Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#67152C414yescomplemented
18#67149—22no—
19D3×Dic15—22no—
20#63880—51nomaximal, Hall
21C2×#1220—31no—
22C22×Dic15—31no—
23C2×C4×D15—31no—
24C2×#1203—31no—
25C2×#1200—31no—
26C2×D3×Dic5—31no—
27C3×C5×C22⋊C4—31no—
28#6714—31no—
29#6714—31no—
30#6714—61no—
31#6712—31no—
32C4×Dic15D311yescharacteristic, complemented
33C5×(C2×D3)⋊C4D311yescharacteristic, complemented
34C3×C4×Dic5—31no—
35#6668—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3⋊D15—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15C2×C412yescomplemented
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—21no—
42C2×C3×C5×D3C2×C412yescomplemented
43C32×C4×C5—21no—
44C3⋊Dic15—21no—
45C3×Dic15C2×C412yescomplemented
46C3×Dic15D412yescomplemented
47C3×C5×Dic3—21no—
48#4027—91noHall
49C2×#626—51no—
50C2×#624—51no—
51C2×D3×Dic3—51no—
52#3752—51no—
53C3×(C2×D3)⋊C4D511yescharacteristic, complemented
54C3×C4×Dic3—51no—
55Dic3⋊Dic3—51no—
56C23×C3×C5—31no—
57C22×D15—31no—
58C22×D15—31no—
59C22×D15—61no—
60C22×C5×D3C2×D311yescharacteristic
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5—31no—
63C2×C3×C4×C5C2×D311yescharacteristic
64C2×C3×C4×C5C2×D311yescharacteristic
65#1220—34no—
66C2×Dic15—31no—
67C2×Dic15—31no—
68C2×Dic15—62no—
69C2×Dic15—61no—
70C2×Dic15C2×D311yescharacteristic
71C2×Dic15C2×D311yescharacteristic
72C4×D15—62no—
73C2×C5×Dic3C2×D311yescharacteristic
74C2×C3×Dic5—31no—
75C2×C3×Dic5—31no—
76#1203—34no—
77#1200—62no—
78D3×Dic5—62no—
79#67⋊C4—151no—
80C4×D12—151no—
81C2×C32×C5C22×C411yescharacteristic
82C2×C32×C5C2×D411yescharacteristic
83C2×C32×C5#4111yescharacteristic
84C3⋊D15—22no—
85C3×C5×D3—22no—
86C2×C22⋊D5—91no—
87C22×Dic5—91no—
88C2×C4×D5—91no—
89C5×C22⋊C4—31no—
90#685—91no—
91#683—91no—
92C4×Dic5—31no—
93C22×C3⋊D3—51no—
94C22×C3×D3C2×D511yescharacteristic
95C2×C32×C4C2×D511yescharacteristic
96C2×C3⋊Dic3—51no—
97C2×C3×Dic3—51no—
98C2×C3×Dic3—51no—
99C2×C3×Dic3C2×D511yescharacteristic
100#626—54no—
101#624—102no—
102D3×Dic3—102no—
103C22×C3×C5—21no—
104C22×C3×C5—32no—
105C22×C3×C5—61no—
106C22×C3×C5—61no—
107C22×C3×C5C22×D311yescharacteristic
108C22×C3×C5C22×D311yescharacteristic
109C2×D15—32no—
110C2×D15—32no—
111C2×D15—62no—
112C2×D15—61no—
113C2×D15—61no—
114C2×D15—61no—
115C2×D15—61no—
116C2×D15—121no—
117C2×D15—121no—
118C2×C5×D3—21no—
119C2×C5×D3—21no—
120C2×C5×D3C4×D312yescomplemented
121C3×C4×C5—21no—
122C3×C4×C5—21no—
123C3×C4×C5—41no—
124C3×C4×C5—61no—
125Dic15—61no—
126Dic15—61no—
127Dic15—121no—
128Dic15C4×D312yescomplemented
129Dic15D1212yescomplemented
130C3×Dic5—32no—
131C3×Dic5—32no—
132C5×Dic3—21no—
133C2×#67—151no—
134C22×Dic3—151no—
135C2×D12—151no—
136C2×C4×D3—151no—
137C2×C4×D3—151no—
138C2×C4×D3—151no—
139C3×C22⋊C4—31no—
140C3×C42—151no—
141(C2×D3)⋊C4—151no—
142(C2×D3)⋊C4—151no—
143(C2×D3)⋊C4—301no—
144(C2×D3)⋊C4D1511yescharacteristic, complemented
145C4⋊Dic3—151no—
146Dic3⋊C4—151no—
147C4×Dic3—51no—
148C32×C5C4×D411yescharacteristic, complemented, Hall
149C23×C5—31no—
150C22×D5—91no—
151C2×C4×C5—31no—
152C2×C4×C5D3211yescharacteristic
153C22⋊D5—94no—
154C2×Dic5—31no—
155C2×Dic5—31no—
156C2×Dic5—91no—
157C2×Dic5—182no—
158C4×D5—182no—
159C22×C32C22×D511yescharacteristic
160C2×C3⋊D3—52no—
161C2×C3⋊D3—101no—
162C2×C3⋊D3—101no—
163C2×C3×D3—21no—
164C2×C3×D3—21no—
165C2×C3×D3C4×D512yescomplemented
166C32×C4—21no—
167C3⋊Dic3—101no—
168C3×Dic3—21no—
169C3×Dic3—52no—
170C3×Dic3—52no—
171C4×D4—451noSylow
172C2×C3×C5—21no—
173C2×C3×C5—21no—
174C2×C3×C5—21no—
175C2×C3×C5—62no—
176C2×C3×C5C2×C4×D311yescharacteristic
177C2×C3×C5C2×C4×D311yescharacteristic
178C2×C3×C5C2×D1211yescharacteristic
179C2×C3×C5#23511yescharacteristic
180C2×C3×C5D3×D411yescharacteristic
181C2×C3×C5#23711yescharacteristic
182D15—62no—
183D15—62no—
184D15—122no—
185C5×D3—22no—
186C23×C3—31no—
187C22×D3—151no—
188C22×D3—151no—
189C22×D3—301no—
190C22×D3C2×D1511yescharacteristic
191C2×C3×C4—21no—
192C2×C3×C4—31no—
193C2×C3×C4—151no—
194C2×C3×C4—151no—
195C2×C3×C4D3×D511yescharacteristic
196C2×C3×C4C2×D1511yescharacteristic
197#67—154no—
198C2×Dic3—51no—
199C2×Dic3—51no—
200C2×Dic3—151no—
201C2×Dic3—151no—
202C2×Dic3—301no—
203C2×Dic3—302no—
204C2×Dic3C2×D1511yescharacteristic
205D12—154no—
206C4×D3—302no—
207C4×D3—302no—
208C4×D3—302no—
209C22×C5—32no—
210C22×C5—61no—
211C22×C5—61no—
212C22×C5C2×D3211yescharacteristic
213C2×D5—92no—
214C2×D5—181no—
215C2×D5—181no—
216C4×C5—21no—
217C4×C5—61no—
218Dic5—32no—
219Dic5—32no—
220Dic5—181no—
221C2×C32C2×C4×D511yescharacteristic
222C2×C32D4×D511yescharacteristic
223C2×C32#71111yescharacteristic
224C3⋊D3—102no—
225C3×D3—22no—
226C2×D4—451no—
227C22×C4—451no—
228C22×C4—451no—
229C4⋊C4—451no—
230C22⋊C4—31no—
231C22⋊C4—451no—
232C42—151no—
233C3×C5—21no—
234C3×C5C4×D1211yescharacteristic, complemented
235C3×C5#67⋊C411yescharacteristic, complemented
236C22×C3—21no—
237C22×C3—32no—
238C22×C3—61no—
239C22×C3—61no—
240C22×C3C2×D3×D511yescharacteristic
241C22×C3C22×D1511yescharacteristic
242C2×D3—21no—
243C2×D3—21no—
244C2×D3—152no—
245C2×D3—152no—
246C2×D3—302no—
247C2×D3—301no—
248C2×D3—301no—
249C2×D3—301no—
250C2×D3—301no—
251C2×D3—601no—
252C2×D3—601no—
253C2×D3C4×D1512yescomplemented
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—61no—
258C3×C4—152no—
259C3×C4—152no—
260Dic3—21no—
261Dic3—52no—
262Dic3—52no—
263Dic3—301no—
264Dic3—301no—
265Dic3—601no—
266C2×C5—62no—
267C2×C5C4×D3211yescharacteristic
268C2×C5D3×D1211yescharacteristic
269C2×C5#380411yescharacteristic
270D5—182no—
271C32#402711yescharacteristic, complemented, Sylow
272C23—31no—
273C23—451no—
274D4—454no—
275C2×C4—31no—
276C2×C4—151no—
277C2×C4—151no—
278C2×C4—451no—
279C2×C4—902no—
280C2×C4—902no—
281C2×C4D3×D1511yescharacteristic
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—62no—
286C2×C3C4×D3×D511yescharacteristic
287C2×C3D5×D1211yescharacteristic
288C2×C3#678211yescharacteristic
289C2×C3C2×C4×D1511yescharacteristic
290C2×C3D4×D1511yescharacteristic
291C2×C3#681911yescharacteristic
292D3—22no—
293D3—302no—
294D3—302no—
295D3—602no—
296C5#6388011yescharacteristic, complemented, Sylow
297C22—32no—
298C22—61no—
299C22—61no—
300C22—452no—
301C22—901no—
302C22—901no—
303C22C2×D3×D1511yescharacteristic
304C4—21no—
305C4—61no—
306C4—152no—
307C4—152no—
308C4—901no—
309C3—21no—
310C3#9140511yescharacteristic, complemented
311C3#9177011yescharacteristic, complemented
312C2—62no—
313C2—902no—
314C2C4×D3×D1511yescharacteristic
315C2D12×D1511yescharacteristic
316C2#1062421011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC2×#67152C2
hypercenterC2×C4D3×D15
hypocenterC32×C5C4×D4
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×#67149C2semidirect
3. C2×D3×Dic15C2semidirect
4. #10623908C2semidirect
5. C3×C4×Dic15C2semidirect
6. C3×C5×(C2×D3)⋊C4C2semidirect
7. #10623814C2semidirect
17. #67152C4semidirect
32. C4×Dic15D3semidirect
33. C5×(C2×D3)⋊C4D3semidirect
39. C2×C3⋊D15C2×C4semidirect
42. C2×C3×C5×D3C2×C4semidirect
45. C3×Dic15C2×C4semidirect
46. C3×Dic15D4semidirect
53. C3×(C2×D3)⋊C4D5semidirect
120. C2×C5×D3C4×D3semidirect
128. Dic15C4×D3semidirect
129. Dic15D12semidirect
144. (C2×D3)⋊C4D15semidirect
148. C32×C5C4×D4semidirect
165. C2×C3×D3C4×D5semidirect
234. C3×C5C4×D12semidirect
235. C3×C5#67⋊C4semidirect
253. C2×D3C4×D15semidirect
271. C32#4027semidirect
296. C5#63880semidirect
310. C3#91405semidirect
311. C3#91770semidirect

Maximal subgroups

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

subgroupindex
C2×#671522
C2×#671492
C2×D3×Dic152
#106239082
C3×C4×Dic152
C3×C5×(C2×D3)⋊C42
#106238142
#917703
#914053
#638805