Finite Group Databasebeta

← #13087779

Subgroups — #13087779

Order 1440.

654 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C23×C5×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#1220C211yesmaximal, characteristic, complemented
3C2×#67156C212yesmaximal, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5#10623830C212yesmaximal, complemented
6#91570—31nomaximal
7#91568—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C5×C3⋊D3—22no—
10C22×C5×C3⋊D3—24no—
11C22×C5×C3⋊D3C2212yes—
12C22×C3×D15C2211yescharacteristic, complemented
13C3×#1220—22no—
14C2×C3×Dic15C2211yescharacteristic, complemented
15C2×C3×Dic15C2212yescomplemented
16#67156—24no—
17#63981—51nomaximal, Hall
18C23×C5×D3—31no—
19C23×C5×D3—31no—
20C23×C5×D3—61no—
21C2×#1220D311yescharacteristic, complemented
22C2×C3×C22⋊D5—31no—
23C2×#1203—32no—
24C2×#1201—32no—
25#6719D311yescharacteristic, complemented
26C3×C22⋊Dic5—31no—
27(C2×D3)⋊Dic5—32no—
28(C2×D3)⋊Dic5—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C5×C3⋊D3—28no—
33C2×C5×C3⋊D3—22no—
34C2×C5×C3⋊D3—22no—
35C2×C5×C3⋊D3D414yescomplemented
36C2×C3×D15—22no—
37C2×C3×D15—21no—
38C3×Dic15—22no—
39C3×Dic15—21no—
40#4099—91noHall
41C23×C3⋊D3D511yescharacteristic, complemented
42C2×C3×#67—51no—
43C2×#626—52no—
44C3×#217—51no—
45#3722—52no—
46C23×C3×C5—21no—
47C23×C3×C5C2×D311yescharacteristic
48C23×C3×C5C2×D311yescharacteristic
49C22×D15C2×D311yescharacteristic, complemented
50C22×C5×D3—32no—
51C22×C5×D3—32no—
52C22×C5×D3—64no—
53C22×C5×D3—64no—
54C22×C5×D3—62no—
55C22×C5×D3—68no—
56C22×C5×D3—64no—
57C22×C5×D3—62no—
58C22×C5×D3—62no—
59C22×C3×D5—31no—
60#1220—22no—
61C2×Dic15C2×D311yescharacteristic, complemented
62C2×Dic15C2×D312yescomplemented
63C3×C22⋊D5—62no—
64C2×C3×Dic5—31no—
65C2×C3×Dic5—32no—
66#1203—64no—
67#1201—64no—
68#937—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D411yescharacteristic
72C2×C32×C5C2×D412yes—
73C5×C3⋊D3—24no—
74C3×D15—41no—
75C24×C5—91no—
76C2×C22⋊D5—31no—
77C2×C22⋊D5—92no—
78C22⋊Dic5—31no—
79C22⋊Dic5—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3—22no—
82C22×C3⋊D3—24no—
83C22×C3⋊D3C2×D512yes—
84C22×C3×D3—51no—
85C3×#67—102no—
86C2×C3×Dic3—51no—
87C2×C3×Dic3—52no—
88#626—104no—
89C22×C3×C5—24no—
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—22no—
93C22×C3×C5—21no—
94C22×C3×C5D1212yescomplemented
95C22×C3×C5#6712yescomplemented
96C22×C3×C5C22×D311yescharacteristic
97C22×C3×C5C22×D311yescharacteristic
98C2×D15—22no—
99C2×D15—21no—
100C2×C5×D3—34no—
101C2×C5×D3—34no—
102C2×C5×D3—64no—
103C2×C5×D3—616no—
104C2×C5×D3—68no—
105C2×C5×D3—68no—
106C2×C5×D3—64no—
107C2×C5×D3—64no—
108C2×C5×D3—62no—
109C2×C5×D3—62no—
110C2×C5×D3—62no—
111C2×C5×D3—62no—
112C2×C3×D5—61no—
113C2×C3×D5—62no—
114Dic15—22no—
115Dic15—21no—
116C3×Dic5—61no—
117C3×Dic5—62no—
118C23×D3—31no—
119C23×D3—31no—
120C23×D3—61no—
121C2×C3×D4—151no—
122C2×#67—51no—
123C2×#67—152no—
124C2×D12—152no—
125C3×C22⋊C4—151no—
126#217—51no—
127(C2×D3)⋊C4—152no—
128(C2×D3)⋊C4—152no—
129C32×C5#12011yescharacteristic, complemented, Hall
130C23×C5—92no—
131C23×C5—184no—
132C23×C5—182no—
133C23×C5D3211yescharacteristic
134C22×D5—31no—
135C22⋊D5—62no—
136C22⋊D5—184no—
137C2×Dic5—32no—
138C2×Dic5—31no—
139C22×C32—22no—
140C22×C32C22⋊D512yescomplemented
141C22×C32C22×D511yescharacteristic
142C2×C3⋊D3—28no—
143C2×C3⋊D3—22no—
144C2×C3⋊D3—22no—
145C2×C3⋊D3C22⋊D514yescomplemented
146C2×C3×D3—102no—
147C2×C3×D3—101no—
148C3×Dic3—102no—
149C3×Dic3—101no—
150#120—451noSylow
151C2×C3×C5—24no—
152C2×C3×C5—22no—
153C2×C3×C5—22no—
154C2×C3×C5—21no—
155C2×C3×C5—22no—
156C2×C3×C5C2×D1211yescharacteristic
157C2×C3×C5D3×D412yes—
158C2×C3×C5D3×D412yes—
159C2×C3×C5C2×#6711yescharacteristic
160D15—41no—
161C3×D5—121no—
162C5×D3—68no—
163C5×D3—64no—
164C5×D3—64no—
165C23×C3—21no—
166C23×C3—151no—
167C23×C3D3×D511yescharacteristic
168C23×C3D3×D511yescharacteristic
169C22×D3—32no—
170C22×D3—32no—
171C22×D3—51no—
172C22×D3—62no—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—68no—
176C22×D3—64no—
177C22×D3—62no—
178C22×D3—62no—
179C3×D4—302no—
180C2×C3×C4—151no—
181C2×C3×C4—152no—
182#67—102no—
183#67—304no—
184C2×Dic3—51no—
185C2×Dic3—52no—
186D12—304no—
187C22×C5—22no—
188C22×C5—94no—
189C22×C5—188no—
190C22×C5—182no—
191C22×C5—182no—
192C22×C5#62612yescomplemented
193C22×C5C2×D3211yescharacteristic
194C2×D5—61no—
195C2×D5—62no—
196Dic5—61no—
197Dic5—62no—
198C2×C32—22no—
199C2×C32C2×C22⋊D511yescharacteristic
200C2×C32C2×C22⋊D512yes—
201C3⋊D3—24no—
202C3×D3—201no—
203C24—91no—
204C2×D4—151no—
205C2×D4—452no—
206C22⋊C4—151no—
207C22⋊C4—452no—
208C3×C5—21no—
209C3×C5#88211yescharacteristic, complemented
210C3×C5#93711yescharacteristic, complemented
211C22×C3—24no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—21no—
216C22×C3—301no—
217C22×C3—302no—
218C22×C3#120112yescomplemented
219C22×C3#120312yescomplemented
220C22×C3C2×D3×D511yescharacteristic
221C22×C3C2×D3×D511yescharacteristic
222C2×D3—34no—
223C2×D3—34no—
224C2×D3—64no—
225C2×D3—616no—
226C2×D3—68no—
227C2×D3—68no—
228C2×D3—64no—
229C2×D3—64no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—101no—
235C2×D3—102no—
236C3×C4—301no—
237C3×C4—302no—
238Dic3—101no—
239Dic3—102no—
240C2×C5—22no—
241C2×C5—184no—
242C2×C5C2×#62611yescharacteristic
243C2×C5#381112yes—
244D5—121no—
245C32#409911yescharacteristic, complemented, Sylow
246C23—92no—
247C23—151no—
248C23—184no—
249C23—182no—
250C23(C3⋊D3)⋊D511yescharacteristic
251D4—302no—
252D4—904no—
253C2×C4—152no—
254C2×C4—151no—
255C2×C3—24no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—21no—
259C2×C3—22no—
260C2×C3—601no—
261C2×C3C2×#120111yescharacteristic
262C2×C3C2×#120311yescharacteristic
263C2×C3D3×C22⋊D512yes—
264C2×C3D3×C22⋊D512yes—
265D3—68no—
266D3—64no—
267D3—64no—
268D3—201no—
269C5#6398111yescharacteristic, complemented, Sylow
270C22—22no—
271C22—94no—
272C22—188no—
273C22—182no—
274C22—182no—
275C22—301no—
276C22—302no—
277C22#6715612yescomplemented
278C22C2×(C3⋊D3)⋊D511yescharacteristic
279C4—301no—
280C4—302no—
281C3—21no—
282C3#9156811yescharacteristic, complemented
283C3#9157011yescharacteristic, complemented
284C2—22no—
285C2—184no—
286C2—601no—
287C2C2×#6715611yescharacteristic
288C2#1062423612yes—
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23(C3⋊D3)⋊D5
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. C23×C5×C3⋊D3C2semidirect
2. C2×C3×#1220C2semidirect
3. C2×#67156C2semidirect
4. C3×#6719C2semidirect
5. #10623830C2semidirect
12. C22×C3×D15C22semidirect
14. C2×C3×Dic15C22semidirect
15. C2×C3×Dic15C22semidirect
21. C2×#1220D3semidirect
25. #6719D3semidirect
30. C22×C32×C5D4semidirect
35. C2×C5×C3⋊D3D4semidirect
41. C23×C3⋊D3D5semidirect
49. C22×D15C2×D3semidirect
61. C2×Dic15C2×D3semidirect
62. C2×Dic15C2×D3semidirect
94. C22×C3×C5D12semidirect
95. C22×C3×C5#67semidirect
129. C32×C5#120semidirect
140. C22×C32C22⋊D5semidirect
145. C2×C3⋊D3C22⋊D5semidirect
192. C22×C5#626semidirect
209. C3×C5#882semidirect
210. C3×C5#937semidirect
218. C22×C3#1201semidirect
219. C22×C3#1203semidirect
245. C32#4099semidirect
269. C5#63981semidirect
277. C22#67156semidirect
282. C3#91568semidirect
283. C3#91570semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C2×C3×#12202
C2×#671562
C3×#67192
#106238302
#915703
#915683
#639815