Finite Group Databasebeta

← C3×#91826 #13088036

Subgroups — C3×#91826 #13088036

Order 1440.

574 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 118 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×C3×D15C211yesmaximal, characteristic, complemented
2C2×C32×C5×D4C211yesmaximal, characteristic, complemented
3C2×C3×#1220C212yesmaximal, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5C3×#6714C212yesmaximal, complemented
6#91826C311yesmaximal, characteristic, direct product factor
7C3×#4083—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C23×C32×C5C2211yescharacteristic, complemented
10C22×C3×D15—22no—
11C22×C3×D15—24no—
12C22×C3×D15C2212yes—
13C32×C5×D4—22no—
14C2×C32×C4×C5C2211yescharacteristic, complemented
15C3×#1220—24no—
16C2×C3×Dic15C2212yescomplemented
17C3×#937—51nomaximal, Hall
18C23×D15C2×C311yescharacteristic, complemented
19C23×C3×D5—31no—
20C2×C3×C5×D4—21no—
21C2×C3×C5×D4D311yescharacteristic, complemented
22C2×C3×C5×D4C2×C311yescharacteristic, complemented
23C2×#1220C2×C312yescomplemented
24C2×C3×C22⋊D5—32no—
25#6719C2×C311yescharacteristic, complemented
26#6714C2×C312yescomplemented
27C3×C22⋊Dic5—31no—
28C3×#685—32no—
29C22×C32×C5—22no—
30C22×C32×C5—21no—
31C22×C32×C5—22no—
32C22×C32×C5D412yescomplemented
33C22×C32×C5C2311yescharacteristic
34C2×C3×D15—28no—
35C2×C3×D15—22no—
36C2×C3×D15—22no—
37C2×C3×D15D414yescomplemented
38C32×C4×C5—21no—
39C3×Dic15—22no—
40#4083—31noHall
41C23×C3×D3—51no—
42C2×C32×D4D511yescharacteristic, complemented
43C2×C3×#67—52no—
44C3×#217—51no—
45C3×(C2×D3)⋊C4—52no—
46C23×C3×C5—21no—
47C23×C3×C5—21no—
48C23×C3×C5C2×D311yescharacteristic
49C23×C3×C5C2×D311yescharacteristic, complemented
50C23×C3×C5C22×C311yescharacteristic
51C23×C3×C5C22×C311yescharacteristic, complemented
52C22×D15—22no—
53C22×D15—24no—
54C22×D15C22×C312yes—
55C22×C3×D5—32no—
56C22×C3×D5—64no—
57C22×C3×D5—62no—
58C3×C5×D4—24no—
59C3×C5×D4—22no—
60C3×C5×D4—22no—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5C2×D311yescharacteristic, complemented
63C2×C3×C4×C5C22×C311yescharacteristic, complemented
64#1220—24no—
65C2×Dic15C22×C312yescomplemented
66C3×C22⋊D5—64no—
67C2×C3×Dic5—32no—
68C3×#120—151no—
69#937—51no—
70C2×C32×C5—22no—
71C2×C32×C5—41no—
72C2×C32×C5C2×D412yes—
73C2×C32×C5C2×D411yescharacteristic
74C3×D15—24no—
75C23×D5—31no—
76C2×C5×D4C3×D311yescharacteristic, complemented
77C2×C22⋊D5—32no—
78C22⋊Dic5—31no—
79#685—32no—
80C23×C32C2×D511yescharacteristic
81C23×C32C2×D511yescharacteristic, complemented
82C22×C3×D3—52no—
83C22×C3×D3—104no—
84C22×C3×D3—102no—
85C32×D4—22no—
86C2×C32×C4C2×D511yescharacteristic, complemented
87C3×#67—104no—
88C2×C3×Dic3—52no—
89C22×C3×C5—22no—
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—22no—
93C22×C3×C5—21no—
94C22×C3×C5—22no—
95C22×C3×C5—21no—
96C22×C3×C5—22no—
97C22×C3×C5—21no—
98C22×C3×C5—42no—
99C22×C3×C5—42no—
100C22×C3×C5#6712yescomplemented
101C22×C3×C5C3×D412yescomplemented
102C22×C3×C5C22×D311yescharacteristic
103C22×C3×C5C23×C311yescharacteristic
104C2×D15—28no—
105C2×D15—22no—
106C2×D15—22no—
107C2×D15C3×D414yescomplemented
108C2×C3×D5—34no—
109C2×C3×D5—68no—
110C2×C3×D5—62no—
111C2×C3×D5—62no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—21no—
115Dic15—22no—
116C3×Dic5—62no—
117C24×C3—151no—
118C23×D3—51no—
119C2×C3×D4—21no—
120C2×C3×D4—152no—
121C2×C3×D4C3×D511yescharacteristic, complemented
122C2×C3×D4D1511yescharacteristic, complemented
123C2×#67—52no—
124C3×C22⋊C4—151no—
125C3×C22⋊C4—152no—
126#217—51no—
127(C2×D3)⋊C4—52no—
128C32×C5#12011yescharacteristic, complemented, Hall
129C23×C5C2×C3×D311yescharacteristic
130C23×C5C2×C3×D311yescharacteristic, complemented
131C22×D5—32no—
132C22×D5—64no—
133C22×D5—62no—
134C5×D4—22no—
135C2×C4×C5C2×C3×D311yescharacteristic, complemented
136C22⋊D5—64no—
137C2×Dic5—32no—
138C22×C32—21no—
139C22×C32—22no—
140C22×C32—22no—
141C22×C32C22⋊D512yescomplemented
142C22×C32C22×D511yescharacteristic
143C2×C3×D3—54no—
144C2×C3×D3—108no—
145C2×C3×D3—102no—
146C2×C3×D3—102no—
147C32×C4—21no—
148C3×Dic3—102no—
149#120—151noSylow
150C2×C3×C5—22no—
151C2×C3×C5—22no—
152C2×C3×C5—22no—
153C2×C3×C5—21no—
154C2×C3×C5—42no—
155C2×C3×C5—42no—
156C2×C3×C5—41no—
157C2×C3×C5—41no—
158C2×C3×C5D3×D412yes—
159C2×C3×C5C2×#6711yescharacteristic
160C2×C3×C5C2×C3×D412yes—
161C2×C3×C5C2×C3×D411yescharacteristic
162D15—24no—
163C3×D5—64no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—152no—
167C23×C3—304no—
168C23×C3—302no—
169C23×C3C2×C3×D511yescharacteristic
170C23×C3C2×C3×D511yescharacteristic, complemented
171C23×C3C2×D1511yescharacteristic
172C23×C3C2×D1511yescharacteristic, complemented
173C22×D3—52no—
174C22×D3—104no—
175C22×D3—102no—
176C3×D4—24no—
177C3×D4—22no—
178C3×D4—22no—
179C3×D4—304no—
180C2×C3×C4—21no—
181C2×C3×C4—152no—
182C2×C3×C4C2×C3×D511yescharacteristic, complemented
183C2×C3×C4C2×D1511yescharacteristic, complemented
184#67—104no—
185C2×Dic3—52no—
186C22×C5—22no—
187C22×C5—22no—
188C22×C5—21no—
189C22×C5C3×#6712yescomplemented
190C22×C5C22×C3×D311yescharacteristic
191C2×D5—34no—
192C2×D5—68no—
193C2×D5—62no—
194C2×D5—62no—
195C4×C5—21no—
196Dic5—62no—
197C2×C32—22no—
198C2×C32—41no—
199C2×C32D4×D512yes—
200C2×C32C2×C22⋊D511yescharacteristic
201C3×D3—104no—
202C24—151no—
203C2×D4—152no—
204C2×D4C3×D1511yescharacteristic, complemented
205C22⋊C4—151no—
206C22⋊C4—152no—
207C3×C5—21no—
208C3×C5#93711yescharacteristic, complemented
209C3×C5C3×#12011yescharacteristic, complemented
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—21no—
215C22×C3—22no—
216C22×C3—21no—
217C22×C3—22no—
218C22×C3—21no—
219C22×C3—42no—
220C22×C3—42no—
221C22×C3—154no—
222C22×C3—308no—
223C22×C3—302no—
224C22×C3—302no—
225C22×C3C3×C22⋊D512yescomplemented
226C22×C3#122012yescomplemented
227C22×C3C22×C3×D511yescharacteristic
228C22×C3C22×D1511yescharacteristic
229C2×D3—54no—
230C2×D3—108no—
231C2×D3—102no—
232C2×D3—102no—
233C3×C4—22no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—302no—
237Dic3—102no—
238C2×C5—22no—
239C2×C5—41no—
240C2×C5C3×D3×D412yes—
241C2×C5C2×C3×#6711yescharacteristic
242D5—64no—
243C32#408311yescharacteristic, complemented, Sylow
244C23—152no—
245C23—304no—
246C23—302no—
247C23C2×C3×D1511yescharacteristic
248C23C2×C3×D1511yescharacteristic, complemented
249D4—22no—
250D4—304no—
251C2×C4—152no—
252C2×C4C2×C3×D1511yescharacteristic, complemented
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—21no—
257C2×C3—42no—
258C2×C3—42no—
259C2×C3—41no—
260C2×C3—41no—
261C2×C3—304no—
262C2×C3C3×D4×D512yes—
263C2×C3C2×C3×C22⋊D511yescharacteristic
264C2×C3D4×D1512yes—
265C2×C3C2×#122011yescharacteristic
266D3—104no—
267C5C3×#93711yescharacteristic, complemented, Sylow
268C22—22no—
269C22—22no—
270C22—21no—
271C22—154no—
272C22—308no—
273C22—302no—
274C22—302no—
275C22C3×#122012yescomplemented
276C22C22×C3×D1511yescharacteristic
277C4—21no—
278C4—302no—
279C3—21no—
280C3C3×#408311yescharacteristic, complemented
281C3#9182611yescharacteristic, direct product factor
282C2—22no—
283C2—41no—
284C2—304no—
285C2C3×D4×D1512yes—
286C2C2×C3×#122011yescharacteristic
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C3×D4D15
hypocenterC3×C5C3×#120
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D15C2semidirect
2. C2×C32×C5×D4C2semidirect
3. C2×C3×#1220C2semidirect
4. C3×#6719C2semidirect
5. C3×#6714C2semidirect
6. #91826C3direct (N × H)
9. C23×C32×C5C22semidirect
14. C2×C32×C4×C5C22semidirect
16. C2×C3×Dic15C22semidirect
18. C23×D15C2×C3semidirect
21. C2×C3×C5×D4D3semidirect
22. C2×C3×C5×D4C2×C3semidirect
23. C2×#1220C2×C3semidirect
25. #6719C2×C3semidirect
26. #6714C2×C3semidirect
32. C22×C32×C5D4semidirect
37. C2×C3×D15D4semidirect
42. C2×C32×D4D5semidirect
49. C23×C3×C5C2×D3semidirect
51. C23×C3×C5C22×C3semidirect
62. C2×C3×C4×C5C2×D3semidirect
63. C2×C3×C4×C5C22×C3semidirect
65. C2×Dic15C22×C3semidirect
76. C2×C5×D4C3×D3semidirect
81. C23×C32C2×D5semidirect
86. C2×C32×C4C2×D5semidirect
100. C22×C3×C5#67semidirect
101. C22×C3×C5C3×D4semidirect
107. C2×D15C3×D4semidirect
121. C2×C3×D4C3×D5semidirect
122. C2×C3×D4D15semidirect
128. C32×C5#120semidirect
130. C23×C5C2×C3×D3semidirect
135. C2×C4×C5C2×C3×D3semidirect
141. C22×C32C22⋊D5semidirect
170. C23×C3C2×C3×D5semidirect
172. C23×C3C2×D15semidirect
182. C2×C3×C4C2×C3×D5semidirect
183. C2×C3×C4C2×D15semidirect
189. C22×C5C3×#67semidirect
204. C2×D4C3×D15semidirect
208. C3×C5#937semidirect
209. C3×C5C3×#120semidirect
225. C22×C3C3×C22⋊D5semidirect
226. C22×C3#1220semidirect
243. C32#4083semidirect
248. C23C2×C3×D15semidirect
252. C2×C4C2×C3×D15semidirect
267. C5C3×#937semidirect
275. C22C3×#1220semidirect
280. C3C3×#4083semidirect
281. C3#91826direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×C32×C5×D42
C2×C3×#12202
C3×#67192
C3×#67142
#918263
C3×#40833
C3×#9375