Finite Group Databasebeta

← #11752715

Subgroups — #11752715

Order 960.

472 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C4×D60C211yesmaximal, characteristic, complemented
2C5×#869C211yesmaximal, characteristic, complemented
3C3×C4×D20C211yesmaximal, characteristic, complemented
4#91465C212yesmaximal, complemented
5#91455C214yesmaximal, complemented
6#91450C212yesmaximal, complemented
7#91358C212yesmaximal, complemented
8#91347C212yesmaximal, complemented
9#66068—31nomaximal, Hall
10C2×D60C2211yescharacteristic
11C2×C4×D15C2212yes—
12C2×C5×Dic6C2212yes—
13C2×C3×D20C2211yescharacteristic
14C2×C3×C4×D5C2212yes—
15C2×#1202C2214yes—
16C3×C42×C5C2211yescharacteristic
17#6714C2212yes—
18C4⋊Dic15C2211yescharacteristic
19C5×C4⋊Dic3C2212yes—
20C5×C4⋊Dic3C2212yes—
21C3×#685C2212yes—
22C3×C4⋊Dic5C2211yescharacteristic
23#6667C2214yes—
24#6665C2214yes—
25Dic3×Dic5C2214yes—
26#5563—51nomaximal, Hall
27C5×C4⋊Q8—31no—
28#4093—34no—
29#4041—32no—
30#4041—32no—
31#4038—32no—
32#4038—32no—
33C4×D20—31no—
34C4×D20D311yescharacteristic, complemented
35C22×D15C2312yes—
36C22×C3×D5C2312yes—
37C2×C3×C4×C5C2311yescharacteristic
38C2×C3×C4×C5C2311yescharacteristic
39C2×C3×C4×C5C2311yescharacteristic
40C2×Dic15C2312yes—
41D60—22no—
42C4×D15—24no—
43C2×C5×Dic3C2314yes—
44C5×Dic6—42no—
45C2×C3×Dic5C2312yes—
46C3×D20—22no—
47C3×C4×D5—24no—
48#1202—44no—
49C3×C4×D4—51no—
50#938—52no—
51#930—52no—
52#926—52no—
53#892—52no—
54#885—54no—
55C4×D12—51no—
56#869D511yescharacteristic, complemented
57C2×C5×Q8—32no—
58C2×D20—31no—
59C2×D20—34no—
60C2×D20C2×D311yescharacteristic
61C2×C4×D5—32no—
62C2×C4×D5C2×D312yes—
63C5×C4⋊C4—32no—
64C5×C4⋊C4—32no—
65C42×C5C2×D311yescharacteristic
66#685—34no—
67#685—32no—
68#685—34no—
69#685C2×D312yes—
70C4⋊Dic5—31no—
71C4⋊Dic5C2×D311yescharacteristic
72C4×Dic5—34no—
73#555—151noSylow
74C22×C3×C5C2411yescharacteristic
75C2×D15—22no—
76C2×D15—22no—
77C2×D15—22no—
78C2×C3×D5—22no—
79C2×C3×D5—22no—
80C2×C3×D5—22no—
81C3×C4×C5—21no—
82C3×C4×C5#4112yes—
83C3×C4×C5#4112yes—
84Dic15—22no—
85C3×Dic5—22no—
86C5×Dic3—24no—
87C2×C3×D4—51no—
88C22×C3×C4—52no—
89C2×#67—54no—
90C2×D12—51no—
91C2×C4×D3—52no—
92C2×Dic6C2×D512yes—
93C3×C4⋊C4—51no—
94C3×C22⋊C4—52no—
95C3×C42C2×D511yescharacteristic
96#217—54no—
97(C2×D3)⋊C4—52no—
98(C2×D3)⋊C4—54no—
99C4⋊Dic3—51no—
100C4⋊Dic3C2×D512yes—
101C4⋊Dic3C2×D512yes—
102C4×Dic3—54no—
103C22×D5—32no—
104C22×D5C22×D312yes—
105C5×Q8—122no—
106C2×C4×C5—34no—
107C2×C4×C5C22×D311yescharacteristic
108C2×C4×C5C22×D311yescharacteristic
109C2×C4×C5C22×D311yescharacteristic
110C2×Dic5—32no—
111C2×Dic5C22×D312yes—
112D20—22no—
113D20—62no—
114D20—124no—
115C4×D5—24no—
116C4×D5—64no—
117C4⋊Q8—31no—
118#124—154no—
119#121—152no—
120#121—152no—
121C4×D4—51no—
122C4×D4—151no—
123#117—152no—
124#117—152no—
125C2×C3×C5C2×#4111yescharacteristic
126C2×C3×C5C2×#4111yescharacteristic
127C2×C3×C5H(5,𝔽2)11yescharacteristic
128D15—42no—
129C3×D5—42no—
130C23×C3—52no—
131C22×D3—52no—
132C3×D4—102no—
133C2×C3×C4—52no—
134C2×C3×C4—104no—
135C2×C3×C4C22×D511yescharacteristic
136C2×C3×C4C22×D511yescharacteristic
137C2×C3×C4C22×D511yescharacteristic
138#67—204no—
139C2×Dic3—52no—
140C2×Dic3C22×D514yes—
141D12—102no—
142C4×D3—104no—
143Dic6—42no—
144C22×C5C23×D311yescharacteristic
145C2×D5—22no—
146C2×D5—22no—
147C2×D5—22no—
148C2×D5—62no—
149C2×D5—62no—
150C2×D5—62no—
151C4×C5—21no—
152C4×C5—64no—
153C4×C5#23512yes—
154C4×C5#23712yes—
155Dic5—22no—
156Dic5—62no—
157C2×Q8—32no—
158C2×D4—51no—
159C2×D4—154no—
160C2×D4—151no—
161C22×C4—52no—
162C22×C4—152no—
163C4⋊C4—32no—
164C4⋊C4—32no—
165C4⋊C4—51no—
166C4⋊C4—151no—
167C22⋊C4—52no—
168C22⋊C4—154no—
169C22⋊C4—154no—
170C22⋊C4—152no—
171C42—154no—
172C42D3×D511yescharacteristic
173C3×C5#55511yescharacteristic, complemented, Hall
174C22×C3—102no—
175C22×C3—102no—
176C22×C3—102no—
177C22×C3C23×D511yescharacteristic
178C2×D3—102no—
179C2×D3—102no—
180C2×D3—102no—
181C3×C4—21no—
182C3×C4—102no—
183C3×C4#71312yes—
184C3×C4#71312yes—
185Dic3—24no—
186Dic3—102no—
187C2×C5C2×#23511yescharacteristic
188C2×C5C2×#23711yescharacteristic
189C2×C5#100911yescharacteristic
190D5—42no—
191D5—122no—
192C23—52no—
193C23—152no—
194Q8—122no—
195D4—102no—
196D4—302no—
197D4—604no—
198C2×C4—34no—
199C2×C4—52no—
200C2×C4—104no—
201C2×C4—152no—
202C2×C4—304no—
203C2×C4C2×D3×D511yescharacteristic
204C2×C4C2×D3×D511yescharacteristic
205C2×C4C2×D3×D511yescharacteristic
206C2×C3—202no—
207C2×C3#414411yescharacteristic
208C2×C3C2×#71311yescharacteristic
209C2×C3C2×#71311yescharacteristic
210D3—202no—
211C5#556311yescharacteristic, complemented, Sylow
212C22—102no—
213C22—102no—
214C22—102no—
215C22—302no—
216C22—302no—
217C22—302no—
218C22C22×D3×D511yescharacteristic
219C4—21no—
220C4—64no—
221C4—102no—
222C4—302no—
223C4#676612yes—
224C4#677312yes—
225C3#6606811yescharacteristic, complemented, Sylow
226C2—202no—
227C2—602no—
228C2C2×#676611yescharacteristic
229C2C2×#677311yescharacteristic
230C2#9201811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×D60C2semidirect
2. C5×#869C2semidirect
3. C3×C4×D20C2semidirect
4. #91465C2semidirect
5. #91455C2semidirect
6. #91450C2semidirect
7. #91358C2semidirect
8. #91347C2semidirect
34. C4×D20D3semidirect
56. #869D5semidirect
173. C3×C5#555semidirect
211. C5#5563semidirect
225. C3#66068semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C5×#8692
C3×C4×D202
#914652
#914552
#914502
#913582
#913472
#660683
#55635