Finite Group Databasebeta

← #14285457

Subgroups — #14285457

Order 1920.

420 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 113 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×#65851C211yesmaximal, characteristic
2#11752417C212yesmaximal
3#11746744C214yesmaximal, complemented
4#10604365—31nomaximal, Hall
5C2×#6762—22no—
6C3×C5×#117C411yescharacteristic
7C3×#4072C411yescharacteristic
8C2×C3×C4×Dic5C2211yescharacteristic
9C3×#4036C412yes—
10C3×#4034C2212yes—
11C3×#4024—22no—
12C3×C4×Dic10—22no—
13#91233C2214yes—
14C4⋊(C3⋊#170)—22no—
15#71834—51nomaximal, Hall
16#65851D311yescharacteristic
17#65758—32no—
18#64873—34no—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×Dic5D412yes—
21C2×C3×Dic10—22no—
22#6762—44no—
23C2×C3⋊#170—24no—
24C3×C5×C4⋊C4C2×C412yes—
25C3×C5×C22⋊C4—21no—
26C3×C42×C5—21no—
27C3×C22⋊Dic5—21no—
28C3×C4⋊Dic5—22no—
29C3×C4⋊Dic5C2×C412yes—
30C3×#683—22no—
31C3×#683—22no—
32C3×C4×Dic5—21no—
33C3×C4×Dic5C2×C411yescharacteristic
34C3×C4×Dic5D412yes—
35C3×C4×Dic5C2311yescharacteristic
36C3×#533—51no—
37#4924—52no—
38#4547—54no—
39C2×#704—62no—
40C5×#117Dic311yescharacteristic
41#4072Dic311yescharacteristic
42C2×C4×Dic5C2×D311yescharacteristic
43#4036Dic312yes—
44#4034C2×D312yes—
45#4024—22no—
46C4×Dic10—22no—
47#4004—34no—
48C4⋊#170—62no—
49#1561—151noSylow
50C23×C3×C5C22⋊C411yescharacteristic
51C2×C3×C4×C5—22no—
52C2×C3×C4×C5—22no—
53C2×C3×C4×C5C22⋊C411yescharacteristic
54C2×C3×C4×C5C22×C411yescharacteristic
55C2×C3×Dic5—22no—
56C2×C3×Dic5—22no—
57C2×C3×Dic5—22no—
58C2×C3×Dic5C22⋊C412yes—
59C2×C3×Dic5C2×D412yes—
60C3×Dic10—42no—
61C3×Dic10—42no—
62C3⋊#170—44no—
63C3×C4⋊Q8—52no—
64C3×#125—52no—
65C3×C22⋊Q8—102no—
66C3×C4×Q8—102no—
67C3×#117—51no—
68C3×#117AGL(1,𝔽5)11yescharacteristic
69C2×C3×C42—51no—
70C2×#208—102no—
71C4⋊(C3⋊C8)—54no—
72C4⋊(C3⋊C8)—102no—
73C22×C4×C5C2×Dic311yescharacteristic
74C22×Dic5#6712yes—
75C2×Dic10—22no—
76#704—124no—
77C2×#170—64no—
78C5×C4⋊C4C2×Dic312yes—
79C5×C22⋊C4—21no—
80C42×C5—21no—
81C22⋊Dic5—21no—
82C4⋊Dic5—22no—
83C4⋊Dic5C2×Dic312yes—
84#683—22no—
85#683—22no—
86C4×Dic5—21no—
87C4×Dic5C2×Dic311yescharacteristic
88C4×Dic5#6712yes—
89C4×Dic5C22×D311yescharacteristic
90#533—51no—
91#423—152no—
92#332—154no—
93C22×C3×C5—21no—
94C22×C3×C5—22no—
95C22×C3×C5C2×C22⋊C411yescharacteristic
96C3×C4×C5—21no—
97C3×C4×C5—42no—
98C3×C4×C5#10112yes—
99C3×Dic5—22no—
100C3×Dic5—42no—
101C3×Dic5AGL(1,ℤ/8)12yes—
102C3×Dic5#13712yes—
103C2×C3×Q8—102no—
104C22×C3×C4—52no—
105C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
106C3×C4⋊C4—52no—
107C3×C4⋊C4—102no—
108C3×C4⋊C4—102no—
109C3×C4⋊C4—102no—
110C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
111C3×C22⋊C4—21no—
112C3×C22⋊C4—101no—
113C3×C42—21no—
114C3×C42—52no—
115C3×C42—51no—
116C3×C42—51no—
117C3×C42—101no—
118#208—204no—
119C2×C3⋊C8—104no—
120C23×C5#21711yescharacteristic
121C2×C4×C5—22no—
122C2×C4×C5—22no—
123C2×C4×C5#21711yescharacteristic
124C2×C4×C5C22×Dic311yescharacteristic
125C2×Dic5—22no—
126C2×Dic5—22no—
127C2×Dic5—22no—
128C2×Dic5#21712yes—
129C2×Dic5C2×#6712yes—
130Dic10—42no—
131Dic10—42no—
132#170—124no—
133C2×M16—302no—
134C4⋊Q8—52no—
135#125—52no—
136C22⋊Q8—102no—
137C4×Q8—102no—
138#117—51no—
139#117ΓL(1,𝔽16)11yescharacteristic
140C2×C42—51no—
141C4⋊C8—154no—
142C4⋊C8—302no—
143C2×C3×C5—41no—
144C2×C3×C5C2×#10111yescharacteristic
145C2×C3×C5#41712yes—
146C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
147C3×Q8—202no—
148C3×Q8—202no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—52no—
152C2×C3×C4—52no—
153C2×C3×C4—102no—
154C2×C3×C4—102no—
155C2×C3×C4—102no—
156C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
157C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
158C3⋊C8—204no—
159C22×C5—21no—
160C22×C5—22no—
161C22×C5C2×#21711yescharacteristic
162C4×C5—21no—
163C4×C5—42no—
164C4×C5#83612yes—
165Dic5—22no—
166Dic5—42no—
167Dic5#94912yes—
168Dic5#95112yes—
169C2×Q8—102no—
170C22×C4—52no—
171C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
172M16—604no—
173C2×C8—304no—
174C4⋊C4—52no—
175C4⋊C4—102no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C4⋊C4C2×ΓL(1,𝔽16)12yes—
179C22⋊C4—21no—
180C22⋊C4—101no—
181C42—21no—
182C42—52no—
183C42—51no—
184C42—51no—
185C42—101no—
186C3×C5#156111yescharacteristic, complemented, Hall
187C22×C3—22no—
188C22×C3—21no—
189C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
190C3×C4—21no—
191C3×C4—42no—
192C3×C4—52no—
193C3×C4—52no—
194C3×C4—102no—
195C3×C4—202no—
196C3×C4#400512yes—
197C2×C5—41no—
198C2×C5C2×#83611yescharacteristic
199C2×C5#523212yes—
200C23#676311yescharacteristic
201Q8—202no—
202Q8—202no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—52no—
206C2×C4—52no—
207C2×C4—102no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4#676311yescharacteristic
211C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
212C8—604no—
213C2×C3—41no—
214C2×C3C2×#400511yescharacteristic
215C2×C3#6579312yes—
216C5#7183411yescharacteristic, complemented, Sylow
217C22—22no—
218C22—21no—
219C22C2×#676311yescharacteristic
220C4—21no—
221C4—42no—
222C4—52no—
223C4—52no—
224C4—102no—
225C4—202no—
226C4#9123412yes—
227C3#1060436511yescharacteristic, complemented, Sylow
228C2—41no—
229C2C2×#9123411yescharacteristic
230C2#1175245212yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#117C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenter#117ΓL(1,𝔽16)
hypocenterC3×C5#1561
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #11746744C2semidirect
186. C3×C5#1561semidirect
216. C5#71834semidirect
227. C3#10604365semidirect

Maximal subgroups

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

subgroupindex
C3×#658512
#117524172
#117467442
#106043653
#718345