Finite Group Databasebeta

← #11756443

Subgroups — #11756443

Order 960.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C3×C5×#124C211yesmaximal, characteristic, complemented
2#91835C212yesmaximal, complemented
3#91828C212yesmaximal, complemented
4#91775C212yesmaximal, complemented
5#91773C212yesmaximal, complemented
6#91772C212yesmaximal, complemented
7#91767C212yesmaximal, complemented
8#91764C211yesmaximal, characteristic, complemented
9#91759C211yesmaximal, characteristic, complemented
10#66018—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C2×#1220C2212yes—
14C2×#1220C2212yes—
15C22×Dic15C2212yes—
16C2×D60C2211yescharacteristic
17C2×C4×D15C2212yes—
18C2×Dic30C2211yescharacteristic
19C3×C5×C22⋊C4C2212yes—
20C3×C5×C22⋊C4C2212yes—
21C3×C42×C5C2211yescharacteristic
22#6719C2212yes—
23#6714C2212yes—
24#6714C2212yes—
25#6714C2212yes—
26C4⋊Dic15C2211yescharacteristic
27C4⋊Dic15C2211yescharacteristic
28C4⋊Dic15C2212yes—
29#6712C2212yes—
30#6712C2212yes—
31#6712C2212yes—
32#5684—51nomaximal, Hall
33C5×#124D311yescharacteristic, complemented
34#4092—32no—
35#4085—32no—
36#4032—32no—
37#4030—32no—
38#4029—32no—
39#4024—32no—
40#4021—31no—
41#4016—31no—
42C23×C3×C5C2312yes—
43C22×D15C2312yes—
44C3×C5×Q8—41no—
45C3×C5×D4—41no—
46C2×C3×C4×C5C2311yescharacteristic
47C2×C3×C4×C5C2311yescharacteristic
48C2×C3×C4×C5C2312yes—
49C2×C3×C4×C5C2311yescharacteristic
50#1220—42no—
51#1220—42no—
52C2×Dic15—42no—
53C2×Dic15C2312yes—
54C2×Dic15C2312yes—
55C2×Dic15C2312yes—
56D60—41no—
57C4×D15—42no—
58Dic30—41no—
59C3×#124D511yescharacteristic, complemented
60#946—52no—
61#939—52no—
62#886—52no—
63#884—52no—
64#883—52no—
65#878—52no—
66#875—51no—
67#870—51no—
68C2×C5×Q8C2×D311yescharacteristic
69C2×C5×D4C2×D311yescharacteristic
70C2×C22⋊D5—32no—
71C2×C22⋊D5—32no—
72C22×Dic5—32no—
73C2×D20—31no—
74C2×C4×D5—32no—
75C2×Dic10—31no—
76C5×C22⋊C4C2×D312yes—
77C5×C22⋊C4C2×D312yes—
78C42×C5C2×D311yescharacteristic
79C22⋊Dic5—32no—
80#685—32no—
81#685—32no—
82#685—32no—
83C4⋊Dic5—31no—
84C4⋊Dic5—31no—
85C4⋊Dic5—32no—
86#683—32no—
87#683—32no—
88#683—32no—
89#562—151noSylow
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—22no—
93C22×C3×C5C2411yescharacteristic
94C2×D15—22no—
95C2×D15—22no—
96C2×D15—22no—
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—21no—
100C3×C4×C5—21no—
101Dic15—22no—
102Dic15—22no—
103Dic15—22no—
104C2×C3×Q8C2×D511yescharacteristic
105C2×C3×D4C2×D511yescharacteristic
106C2×#67—52no—
107C2×#67—52no—
108C22×Dic3—52no—
109C2×D12—51no—
110C2×C4×D3—52no—
111C2×Dic6—51no—
112C3×C22⋊C4C2×D512yes—
113C3×C22⋊C4C2×D512yes—
114C3×C42C2×D511yescharacteristic
115#217—52no—
116(C2×D3)⋊C4—52no—
117(C2×D3)⋊C4—52no—
118(C2×D3)⋊C4—52no—
119C4⋊Dic3—51no—
120C4⋊Dic3—51no—
121C4⋊Dic3—52no—
122Dic3⋊C4—52no—
123Dic3⋊C4—52no—
124Dic3⋊C4—52no—
125C23×C5C22×D312yes—
126C22×D5—32no—
127C5×Q8—41no—
128C5×D4—41no—
129C2×C4×C5C22×D311yescharacteristic
130C2×C4×C5C22×D311yescharacteristic
131C2×C4×C5C22×D312yes—
132C2×C4×C5C22×D311yescharacteristic
133C22⋊D5—122no—
134C22⋊D5—122no—
135C2×Dic5—32no—
136C2×Dic5—32no—
137C2×Dic5—32no—
138C2×Dic5—122no—
139D20—121no—
140C4×D5—122no—
141Dic10—121no—
142#125—151no—
143#124—151no—
144#124D1511yescharacteristic, complemented
145#123—152no—
146#123—152no—
147C22⋊Q8—152no—
148C22⋊Q8—152no—
149#121—152no—
150#121—152no—
151C2×C3×C5—42no—
152C2×C3×C5H(5,𝔽2)11yescharacteristic
153C2×C3×C5H(5,𝔽2)11yescharacteristic
154C2×C3×C52−1+411yescharacteristic
155D15—42no—
156C23×C3C22×D512yes—
157C22×D3—52no—
158C3×Q8—41no—
159C3×D4—41no—
160C2×C3×C4C22×D511yescharacteristic
161C2×C3×C4C22×D511yescharacteristic
162C2×C3×C4C22×D512yes—
163C2×C3×C4C22×D511yescharacteristic
164#67—202no—
165#67—202no—
166C2×Dic3—52no—
167C2×Dic3—52no—
168C2×Dic3—52no—
169C2×Dic3—202no—
170D12—201no—
171C4×D3—202no—
172Dic6—201no—
173C22×C5—22no—
174C22×C5—22no—
175C22×C5—22no—
176C22×C5C23×D311yescharacteristic
177C2×D5—62no—
178C2×D5—62no—
179C2×D5—62no—
180C4×C5—22no—
181C4×C5—21no—
182C4×C5—21no—
183C4×C5—21no—
184Dic5—62no—
185Dic5—62no—
186Dic5—62no—
187C2×Q8—151no—
188C2×Q8C2×D1511yescharacteristic
189C2×D4—152no—
190C2×D4—152no—
191C2×D4—151no—
192C2×D4C2×D1511yescharacteristic
193C22×C4—152no—
194C22×C4—152no—
195C4⋊C4—152no—
196C4⋊C4—152no—
197C4⋊C4—152no—
198C4⋊C4—152no—
199C4⋊C4—151no—
200C4⋊C4—151no—
201C22⋊C4—152no—
202C22⋊C4—152no—
203C22⋊C4—152no—
204C22⋊C4—152no—
205C22⋊C4C2×D1512yes—
206C22⋊C4C2×D1512yes—
207C42C2×D1511yescharacteristic
208C3×C5#56211yescharacteristic, complemented, Hall
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3C23×D511yescharacteristic
213C2×D3—102no—
214C2×D3—102no—
215C2×D3—102no—
216C3×C4—22no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220Dic3—102no—
221Dic3—102no—
222Dic3—102no—
223C2×C5—42no—
224C2×C5#100411yescharacteristic
225C2×C5#100911yescharacteristic
226C2×C5#101011yescharacteristic
227D5—122no—
228C23—152no—
229C23C22×D1512yes—
230Q8—41no—
231Q8—601no—
232D4—41no—
233D4—601no—
234D4—602no—
235D4—602no—
236C2×C4—152no—
237C2×C4—152no—
238C2×C4—152no—
239C2×C4—602no—
240C2×C4—602no—
241C2×C4C22×D1511yescharacteristic
242C2×C4C22×D1511yescharacteristic
243C2×C4C22×D1511yescharacteristic
244C2×C4C22×D1512yes—
245C2×C3—42no—
246C2×C3#414411yescharacteristic
247C2×C3#414911yescharacteristic
248C2×C3#415011yescharacteristic
249D3—202no—
250C5#568411yescharacteristic, complemented, Sylow
251C22—22no—
252C22—22no—
253C22—22no—
254C22—302no—
255C22—302no—
256C22—302no—
257C22C23×D1511yescharacteristic
258C4—22no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—302no—
263C4—302no—
264C4—302no—
265C3#6601811yescharacteristic, complemented, Sylow
266C2—42no—
267C2—602no—
268C2#9209511yescharacteristic
269C2#9210011yescharacteristic
270C2#9210111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#124C2
hypercenter#124D15
hypocenterC3×C5#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×C5×#124C2semidirect
2. #91835C2semidirect
3. #91828C2semidirect
4. #91775C2semidirect
5. #91773C2semidirect
6. #91772C2semidirect
7. #91767C2semidirect
8. #91764C2semidirect
9. #91759C2semidirect
33. C5×#124D3semidirect
59. C3×#124D5semidirect
144. #124D15semidirect
208. C3×C5#562semidirect
250. C5#5684semidirect
265. C3#66018semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1242
#918352
#918282
#917752
#917732
#917722
#917672
#917642
#917592
#660183
#56845