Finite Group Databasebeta

← #13087583

Subgroups — #13087583

Order 1440.

654 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3×C5×#67C211yesmaximal, characteristic, complemented
3C2×#67152C212yesmaximal, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5#10623813C212yesmaximal, complemented
6#91826—31nomaximal
7#91573—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3⋊D15—22no—
10C22×C3⋊D15—24no—
11C22×C3⋊D15C2212yes—
12C22×C3×C5×D3C2211yescharacteristic, complemented
13C2×C3×Dic15C2212yescomplemented
14C3×C5×#67—22no—
15C2×C3×C5×Dic3C2211yescharacteristic, complemented
16#67152—24no—
17#63981—51nomaximal, Hall
18C23×D15—31no—
19C23×D15—31no—
20C23×D15—61no—
21C2×C3×C5×D4—31no—
22C2×#1220—32no—
23C2×C5×#67D311yescharacteristic, complemented
24C2×#1203—32no—
25#6719D311yescharacteristic, complemented
26#6714—32no—
27C3×C22⋊Dic5—31no—
28#6667—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3⋊D15—28no—
33C2×C3⋊D15—22no—
34C2×C3⋊D15—22no—
35C2×C3⋊D15D414yescomplemented
36C2×C3×C5×D3—22no—
37C2×C3×C5×D3—21no—
38C3×Dic15—22no—
39C3×C5×Dic3—21no—
40#4083—91noHall
41C23×C3⋊D3—51no—
42C2×C3×#67D511yescharacteristic, complemented
43C2×#626—52no—
44C3×#217—51no—
45#3722—52no—
46C23×C3×C5—21no—
47C23×C3×C5—31no—
48C23×C3×C5C2×D311yescharacteristic
49C23×C3×C5C2×D311yescharacteristic
50C22×D15—32no—
51C22×D15—32no—
52C22×D15—64no—
53C22×D15—64no—
54C22×D15—62no—
55C22×D15—68no—
56C22×D15—64no—
57C22×D15—62no—
58C22×D15—62no—
59C22×C5×D3C2×D311yescharacteristic, complemented
60C3×C5×D4—62no—
61C2×C3×C4×C5—31no—
62#1220—64no—
63C2×Dic15C2×D312yescomplemented
64C5×#67—22no—
65C2×C5×Dic3C2×D311yescharacteristic, complemented
66C2×C3×Dic5—32no—
67#1203—64no—
68#937—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D412yes—
72C2×C32×C5C2×D411yescharacteristic
73C3⋊D15—24no—
74C3×C5×D3—41no—
75C23×D5—91no—
76C2×C5×D4—31no—
77C2×C22⋊D5—92no—
78C22⋊Dic5—31no—
79#685—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3—52no—
82C22×C3⋊D3—104no—
83C22×C3⋊D3—102no—
84C22×C3×D3C2×D511yescharacteristic, complemented
85C3×#67—22no—
86C2×C3×Dic3—52no—
87C2×C3×Dic3C2×D511yescharacteristic, complemented
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×C5—61no—
95C22×C3×C5—62no—
96C22×C3×C5D1212yescomplemented
97C22×C3×C5#6712yescomplemented
98C22×C3×C5C22×D311yescharacteristic
99C22×C3×C5C22×D311yescharacteristic
100C2×D15—34no—
101C2×D15—34no—
102C2×D15—64no—
103C2×D15—616no—
104C2×D15—68no—
105C2×D15—68no—
106C2×D15—64no—
107C2×D15—64no—
108C2×D15—62no—
109C2×D15—62no—
110C2×D15—62no—
111C2×D15—62no—
112C2×C5×D3—22no—
113C2×C5×D3—21no—
114C3×C4×C5—61no—
115Dic15—22no—
116C3×Dic5—62no—
117C5×Dic3—21no—
118C23×D3—151no—
119C23×D3—151no—
120C23×D3—301no—
121C2×C3×D4—31no—
122C2×#67—152no—
123C2×#67D1511yescharacteristic, complemented
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—31no—
131C23×C5D3211yescharacteristic
132C22×D5—92no—
133C22×D5—184no—
134C22×D5—182no—
135C5×D4—62no—
136C2×C4×C5—31no—
137C22⋊D5—184no—
138C2×Dic5—32no—
139C22×C32—22no—
140C22×C32C22⋊D512yescomplemented
141C22×C32C22×D511yescharacteristic
142C2×C3⋊D3—54no—
143C2×C3⋊D3—108no—
144C2×C3⋊D3—102no—
145C2×C3⋊D3—102no—
146C2×C3×D3—22no—
147C2×C3×D3—21no—
148C3×Dic3—21no—
149C3×Dic3—102no—
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×C5—121no—
157C2×C3×C5C2×D1211yescharacteristic
158C2×C3×C5D3×D412yes—
159C2×C3×C5D3×D412yes—
160C2×C3×C5C2×#6711yescharacteristic
161D15—68no—
162D15—64no—
163D15—64no—
164C5×D3—41no—
165C23×C3—21no—
166C23×C3—31no—
167C23×C3D3×D511yescharacteristic
168C23×C3C2×D1511yescharacteristic
169C22×D3—152no—
170C22×D3—152no—
171C22×D3—302no—
172C22×D3—304no—
173C22×D3—304no—
174C22×D3—308no—
175C22×D3—304no—
176C22×D3—302no—
177C22×D3—302no—
178C22×D3C2×D1511yescharacteristic, complemented
179C3×D4—62no—
180C2×C3×C4—31no—
181C2×C3×C4—152no—
182#67—22no—
183#67—304no—
184C2×Dic3—52no—
185C2×Dic3C2×D1511yescharacteristic, complemented
186D12—304no—
187C22×C5—22no—
188C22×C5—61no—
189C22×C5—62no—
190C22×C5#62612yescomplemented
191C22×C5C2×D3211yescharacteristic
192C2×D5—94no—
193C2×D5—188no—
194C2×D5—182no—
195C2×D5—182no—
196C4×C5—61no—
197Dic5—62no—
198C2×C32—22no—
199C2×C32D4×D512yes—
200C2×C32C2×C22⋊D511yescharacteristic
201C3⋊D3—104no—
202C3×D3—41no—
203C24—451no—
204C2×D4—31no—
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—61no—
217C22×C3—62no—
218C22×C3#120312yescomplemented
219C22×C3#122012yescomplemented
220C22×C3C2×D3×D511yescharacteristic
221C22×C3C22×D1511yescharacteristic
222C2×D3—22no—
223C2×D3—21no—
224C2×D3—154no—
225C2×D3—154no—
226C2×D3—304no—
227C2×D3—3016no—
228C2×D3—308no—
229C2×D3—308no—
230C2×D3—304no—
231C2×D3—304no—
232C2×D3—302no—
233C2×D3—302no—
234C2×D3—302no—
235C2×D3—302no—
236C3×C4—61no—
237C3×C4—302no—
238Dic3—21no—
239Dic3—102no—
240C2×C5—22no—
241C2×C5—121no—
242C2×C5C2×#62611yescharacteristic
243C2×C5#381112yes—
244D5—184no—
245C32#408311yescharacteristic, complemented, Sylow
246C23—31no—
247C23—452no—
248C23—904no—
249C23—902no—
250C23D3×D1511yescharacteristic
251D4—62no—
252D4—904no—
253C2×C4—31no—
254C2×C4—152no—
255C2×C3—24no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—21no—
259C2×C3—22no—
260C2×C3—121no—
261C2×C3C2×#120311yescharacteristic
262C2×C3#679012yes—
263C2×C3D4×D1512yes—
264C2×C3C2×#122011yescharacteristic
265D3—41no—
266D3—308no—
267D3—304no—
268D3—304no—
269C5#6398111yescharacteristic, complemented, Sylow
270C22—22no—
271C22—61no—
272C22—62no—
273C22—454no—
274C22—908no—
275C22—902no—
276C22—902no—
277C22#6715212yescomplemented
278C22C2×D3×D1511yescharacteristic
279C4—61no—
280C4—302no—
281C3—21no—
282C3#9157311yescharacteristic, complemented
283C3#9182611yescharacteristic, complemented
284C2—22no—
285C2—121no—
286C2—904no—
287C2C2×#6715211yescharacteristic
288C2#1062421812yes—
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D3×D15
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×C3⋊D15C2semidirect
2. C2×C3×C5×#67C2semidirect
3. C2×#67152C2semidirect
4. C3×#6719C2semidirect
5. #10623813C2semidirect
12. C22×C3×C5×D3C22semidirect
13. C2×C3×Dic15C22semidirect
15. C2×C3×C5×Dic3C22semidirect
23. C2×C5×#67D3semidirect
25. #6719D3semidirect
30. C22×C32×C5D4semidirect
35. C2×C3⋊D15D4semidirect
42. C2×C3×#67D5semidirect
59. C22×C5×D3C2×D3semidirect
63. C2×Dic15C2×D3semidirect
65. C2×C5×Dic3C2×D3semidirect
84. C22×C3×D3C2×D5semidirect
87. C2×C3×Dic3C2×D5semidirect
96. C22×C3×C5D12semidirect
97. C22×C3×C5#67semidirect
123. C2×#67D15semidirect
129. C32×C5#120semidirect
140. C22×C32C22⋊D5semidirect
178. C22×D3C2×D15semidirect
185. C2×Dic3C2×D15semidirect
190. C22×C5#626semidirect
209. C3×C5#882semidirect
210. C3×C5#937semidirect
218. C22×C3#1203semidirect
219. C22×C3#1220semidirect
245. C32#4083semidirect
269. C5#63981semidirect
277. C22#67152semidirect
282. C3#91573semidirect
283. C3#91826semidirect

Maximal subgroups

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

subgroupindex
C23×C3⋊D152
C2×C3×C5×#672
C2×#671522
C3×#67192
#106238132
#918263
#915733
#639815