Finite Group Databasebeta

← #11755207

Subgroups — #11755207

Order 960.

472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 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
1#91836C211yesmaximal, characteristic, complemented
2C5×#944C211yesmaximal, characteristic, complemented
3C3×#4093C211yesmaximal, characteristic, complemented
4#91459C212yesmaximal, complemented
5#91455C212yesmaximal, complemented
6#91409C212yesmaximal, complemented
7#91402C212yesmaximal, complemented
8#91395C212yesmaximal, complemented
9#91394C212yesmaximal, complemented
10#66068—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×D60C2211yescharacteristic
13C2×C5×Dic6C2211yescharacteristic
14C2×C3×D20C2211yescharacteristic
15C2×#1202C2212yes—
16C2×#1202C2212yes—
17C2×#1200C2212yes—
18C2×D5×Dic3C2212yes—
19#6714C2212yes—
20#6714C2212yes—
21C4×Dic15C2211yescharacteristic
22C5×Dic3⋊C4C2212yes—
23C5×Dic3⋊C4C2212yes—
24C4×C5×Dic3C2211yescharacteristic
25C3×#685C2212yes—
26C3×#685C2212yes—
27C3×C4×Dic5C2211yescharacteristic
28Dic3⋊Dic5C2212yes—
29#6667C2212yes—
30#6665C2212yes—
31Dic3×Dic5C2212yes—
32#5670—51nomaximal, Hall
33C5×C4⋊Q8—31no—
34#4093—31no—
35#4093—32no—
36#4093D311yescharacteristic, complemented
37#4041—32no—
38#4041—32no—
39#4038—32no—
40#4038—32no—
41C4×D20—32no—
42C22×D15C2312yes—
43C22×C3×D5C2312yes—
44C3×C5×Q8—41no—
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×C3×C4×C5C2311yescharacteristic
48C2×Dic15C2312yes—
49D60—41no—
50C2×C5×Dic3C2312yes—
51C2×C5×Dic3C2312yes—
52C5×Dic6—41no—
53C2×C3×Dic5C2312yes—
54C3×D20—41no—
55#1202—24no—
56#1202—42no—
57#1200—24no—
58D5×Dic3—24no—
59C3×#124—51no—
60#947—51no—
61#944D511yescharacteristic, complemented
62#939—52no—
63#885—52no—
64#884—52no—
65#67⋊C4—52no—
66#877—52no—
67#872—52no—
68C2×C5×Q8—31no—
69C2×C5×Q8C2×D311yescharacteristic
70C2×D20—32no—
71C2×D20—32no—
72C2×D20—31no—
73C2×D20C2×D311yescharacteristic
74C2×C4×D5—32no—
75C2×C4×D5—32no—
76C5×C4⋊C4—32no—
77C5×C4⋊C4—32no—
78C42×C5—31no—
79#685—32no—
80#685—32no—
81#685—32no—
82#685—32no—
83#685C2×D312yes—
84#685C2×D312yes—
85C4⋊Dic5—32no—
86C4×Dic5—31no—
87C4×Dic5—32no—
88C4×Dic5C2×D311yescharacteristic
89#555—151noSylow
90C22×C3×C5C2411yescharacteristic
91C2×D15—22no—
92C2×D15—22no—
93C2×D15—22no—
94C2×C3×D5—22no—
95C2×C3×D5—22no—
96C2×C3×D5—22no—
97C3×C4×C5—21no—
98C3×C4×C5—21no—
99C3×C4×C5—21no—
100Dic15—22no—
101C3×Dic5—22no—
102C5×Dic3—22no—
103C5×Dic3#4114yes—
104C2×C3×Q8C2×D511yescharacteristic
105C2×C3×D4—51no—
106C2×#67—52no—
107C2×#67—52no—
108C22×Dic3—52no—
109C2×D12—51no—
110C2×C4×D3—52no—
111C2×Dic6C2×D511yescharacteristic
112C3×C22⋊C4—52no—
113C3×C22⋊C4—52no—
114C3×C42—51no—
115#217—52no—
116(C2×D3)⋊C4—52no—
117(C2×D3)⋊C4—52no—
118(C2×D3)⋊C4—52no—
119Dic3⋊C4—52no—
120Dic3⋊C4C2×D512yes—
121Dic3⋊C4C2×D512yes—
122C4×Dic3—51no—
123C4×Dic3—52no—
124C4×Dic3C2×D511yescharacteristic
125C22×D5—32no—
126C22×D5C22×D312yes—
127C5×Q8—41no—
128C5×Q8—121no—
129C2×C4×C5—32no—
130C2×C4×C5—32no—
131C2×C4×C5C22×D311yescharacteristic
132C2×C4×C5C22×D311yescharacteristic
133C2×C4×C5C22×D311yescharacteristic
134C2×Dic5—32no—
135C2×Dic5C22×D312yes—
136D20—41no—
137D20—64no—
138D20—121no—
139D20—122no—
140C4×D5—64no—
141C4×D5—64no—
142C4⋊Q8—31no—
143#124—51no—
144#124—152no—
145#124—151no—
146#121—152no—
147#121—152no—
148C4×D4—152no—
149#117—152no—
150#117—152no—
151C2×C3×C5C2×#4112yes—
152C2×C3×C5H(5,𝔽2)11yescharacteristic
153D15—42no—
154C3×D5—42no—
155C23×C3—52no—
156C22×D3—52no—
157C3×Q8—41no—
158C3×D4—201no—
159C2×C3×C4—52no—
160C2×C3×C4C22×D511yescharacteristic
161C2×C3×C4C22×D511yescharacteristic
162C2×C3×C4C22×D511yescharacteristic
163#67—104no—
164#67—202no—
165C2×Dic3—52no—
166C2×Dic3—104no—
167C2×Dic3C22×D512yes—
168C2×Dic3C22×D512yes—
169D12—201no—
170C4×D3—104no—
171Dic6—41no—
172C22×C5C23×D311yescharacteristic
173C2×D5—22no—
174C2×D5—22no—
175C2×D5—22no—
176C2×D5—62no—
177C2×D5—62no—
178C2×D5—62no—
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—34no—
183C4×C5—62no—
184Dic5—22no—
185Dic5—62no—
186C2×Q8—31no—
187C2×Q8D3×D511yescharacteristic
188C2×D4—51no—
189C2×D4—152no—
190C2×D4—152no—
191C2×D4—151no—
192C22×C4—152no—
193C22×C4—152no—
194C4⋊C4—32no—
195C4⋊C4—32no—
196C4⋊C4—152no—
197C22⋊C4—52no—
198C22⋊C4—52no—
199C22⋊C4—152no—
200C22⋊C4—152no—
201C22⋊C4—152no—
202C22⋊C4—152no—
203C42—31no—
204C42—51no—
205C42—152no—
206C42—151no—
207C3×C5#55511yescharacteristic, complemented, Hall
208C22×C3—102no—
209C22×C3—102no—
210C22×C3—102no—
211C22×C3C23×D511yescharacteristic
212C2×D3—102no—
213C2×D3—102no—
214C2×D3—102no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—102no—
219Dic3—22no—
220Dic3—102no—
221Dic3#71314yes—
222C2×C5#100411yescharacteristic
223C2×C5D3×#4112yes—
224D5—42no—
225D5—122no—
226C23—52no—
227C23—152no—
228Q8—41no—
229Q8—121no—
230D4—201no—
231D4—304no—
232D4—601no—
233D4—602no—
234C2×C4—32no—
235C2×C4—32no—
236C2×C4—52no—
237C2×C4—152no—
238C2×C4—304no—
239C2×C4—304no—
240C2×C4C2×D3×D511yescharacteristic
241C2×C4C2×D3×D511yescharacteristic
242C2×C4C2×D3×D511yescharacteristic
243C2×C3—202no—
244C2×C3#414411yescharacteristic
245C2×C3C2×#71312yes—
246D3—202no—
247C5#567011yescharacteristic, complemented, Sylow
248C22—102no—
249C22—102no—
250C22—102no—
251C22—302no—
252C22—302no—
253C22—302no—
254C22C22×D3×D511yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—34no—
259C4—62no—
260C4—102no—
261C4—302no—
262C3#6606811yescharacteristic, complemented, Sylow
263C2—202no—
264C2—602no—
265C2D3×#71312yes—
266C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #91836C2semidirect
2. C5×#944C2semidirect
3. C3×#4093C2semidirect
4. #91459C2semidirect
5. #91455C2semidirect
6. #91409C2semidirect
7. #91402C2semidirect
8. #91395C2semidirect
9. #91394C2semidirect
36. #4093D3semidirect
61. #944D5semidirect
207. C3×C5#555semidirect
247. C5#5670semidirect
262. C3#66068semidirect

Maximal subgroups

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

subgroupindex
#918362
C5×#9442
C3×#40932
#914592
#914552
#914092
#914022
#913952
#913942
#660683
#56705