Finite Group Databasebeta

← #14284748

Subgroups — #14284748

Order 1920.

404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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×#66022C211yesmaximal, characteristic
2#11752337C212yesmaximal
3#11746744C214yesmaximal, complemented
4#10604584—31nomaximal, Hall
5C3×C5×#125C411yescharacteristic
6C3×#4042—22no—
7C3×#4038C412yes—
8C3×#4034C2212yes—
9C3×#4033—22no—
10C3×C42×D5C2211yescharacteristic
11C3×#4016C411yescharacteristic
12#91233C2214yes—
13#91232—22no—
14C4×C3⋊#170—22no—
15#71829—51nomaximal, Hall
16#66022D311yescharacteristic
17#65678—32no—
18#64873—34no—
19C2×C3×C4×D5C2×C411yescharacteristic
20C2×C3×C4×D5D412yes—
21C2×C3×Dic10—22no—
22C2×C3⋊#170—24no—
23C3×C5×C4⋊C4—22no—
24C3×C5×C4⋊C4C2×C412yes—
25C3×C42×C5C2×C411yescharacteristic
26C3×#685—22no—
27C3×C4⋊Dic5C2×C412yes—
28C3×#683—22no—
29C3×#683—22no—
30C3×C4×Dic5—22no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5C2311yescharacteristic
33C3×#533—51no—
34#4925—52no—
35#4547—54no—
36C5×#125Dic311yescharacteristic
37#4042—22no—
38#4038Dic312yes—
39#4034C2×D312yes—
40#4033—22no—
41C42×D5C2×D311yescharacteristic
42#4016Dic311yescharacteristic
43#4004—34no—
44#4003—62no—
45C4×#170—62no—
46#1544—151noSylow
47C22×C3×D5C22⋊C411yescharacteristic
48C2×C3×C4×C5—22no—
49C2×C3×C4×C5C22⋊C412yes—
50C2×C3×C4×C5C22×C411yescharacteristic
51C2×C3×Dic5—22no—
52C2×C3×Dic5C22⋊C411yescharacteristic
53C2×C3×Dic5C2×D412yes—
54C3×C4×D5—22no—
55C3×C4×D5—24no—
56C3×Dic10—44no—
57C3⋊#170—44no—
58C3×C4⋊Q8—52no—
59C3×#125—51no—
60C3×#125AGL(1,𝔽5)11yescharacteristic
61C3×C22⋊Q8—102no—
62C3×C4×Q8—102no—
63C3×#117—52no—
64C2×C3×C42—51no—
65#830—102no—
66C4⋊(C3⋊C8)—54no—
67C4×C3⋊C8—102no—
68C2×C4×D5C2×Dic311yescharacteristic
69C2×C4×D5#6712yes—
70C2×Dic10—22no—
71C2×#170—64no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4C2×Dic312yes—
74C42×C5C2×Dic311yescharacteristic
75#685—22no—
76C4⋊Dic5C2×Dic312yes—
77#683—22no—
78#683—22no—
79C4×Dic5—22no—
80C4×Dic5#6712yes—
81C4×Dic5C22×D311yescharacteristic
82#533—51no—
83#431—152no—
84#332—154no—
85C22×C3×C5C2×C22⋊C411yescharacteristic
86C2×C3×D5—21no—
87C2×C3×D5—22no—
88C3×C4×C5—21no—
89C3×C4×C5—22no—
90C3×C4×C5—42no—
91C3×Dic5—42no—
92C3×Dic5#10112yes—
93C3×Dic5#13514yes—
94C2×C3×Q8—102no—
95C22×C3×C4—52no—
96C22×C3×C4—51no—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—52no—
99C3×C4⋊C4—102no—
100C3×C4⋊C4—102no—
101C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
102C3×C22⋊C4—102no—
103C3×C42—52no—
104C3×C42—51no—
105C3×C42—102no—
106C3×C42C2×AGL(1,𝔽5)11yescharacteristic
107C2×C3⋊C8—104no—
108C22×D5#21711yescharacteristic
109C2×C4×C5—22no—
110C2×C4×C5#21712yes—
111C2×C4×C5C22×Dic311yescharacteristic
112C2×Dic5—22no—
113C2×Dic5#21711yescharacteristic
114C2×Dic5C2×#6712yes—
115C4×D5—22no—
116C4×D5—24no—
117Dic10—44no—
118#170—124no—
119C4⋊Q8—52no—
120#125—51no—
121#125ΓL(1,𝔽16)11yescharacteristic
122C22⋊Q8—102no—
123C4×Q8—102no—
124#117—52no—
125C2×C42—51no—
126C4⋊C8—154no—
127C22⋊C8—302no—
128C4×C8—302no—
129C2×C3×C5C2×#10111yescharacteristic
130C2×C3×C5#41612yes—
131C3×D5—41no—
132C23×C3—51no—
133C3×Q8—204no—
134C2×C3×C4—22no—
135C2×C3×C4—51no—
136C2×C3×C4—52no—
137C2×C3×C4—104no—
138C2×C3×C4—102no—
139C2×C3×C4—102no—
140C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
141C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
142C3⋊C8—204no—
143C22×C5C2×#21711yescharacteristic
144C2×D5—21no—
145C2×D5—22no—
146C4×C5—21no—
147C4×C5—22no—
148C4×C5—42no—
149Dic5—42no—
150Dic5#83612yes—
151Dic5#95014yes—
152C2×Q8—102no—
153C22×C4—52no—
154C22×C4—51no—
155C2×C8—304no—
156C4⋊C4—22no—
157C4⋊C4—52no—
158C4⋊C4—102no—
159C4⋊C4—102no—
160C4⋊C4C2×ΓL(1,𝔽16)12yes—
161C22⋊C4—102no—
162C42—52no—
163C42—51no—
164C42—102no—
165C42C2×ΓL(1,𝔽16)11yescharacteristic
166C3×C5#154411yescharacteristic, complemented, Hall
167C22×C3—102no—
168C22×C3—101no—
169C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
170C3×C4—22no—
171C3×C4—21no—
172C3×C4—42no—
173C3×C4—54no—
174C3×C4—52no—
175C3×C4—202no—
176C2×C5C2×#83611yescharacteristic
177C2×C5#523312yes—
178D5—41no—
179C23—51no—
180Q8—204no—
181C2×C4—22no—
182C2×C4—51no—
183C2×C4—52no—
184C2×C4—102no—
185C2×C4—104no—
186C2×C4—102no—
187C2×C4#676312yes—
188C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
189C8—604no—
190C2×C3—201no—
191C2×C3D5⋊#10111yescharacteristic
192C2×C3#6579412yes—
193C5#7182911yescharacteristic, complemented, Sylow
194C22—101no—
195C22—102no—
196C22C2×#676311yescharacteristic
197C4—21no—
198C4—22no—
199C4—42no—
200C4—52no—
201C4—54no—
202C4—202no—
203C3#1060458411yescharacteristic, complemented, Sylow
204C2—201no—
205C2D5⋊#83611yescharacteristic
206C2#1175245312yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#125C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenter#125ΓL(1,𝔽16)
hypocenterC3×C5#1544
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11746744C2semidirect
166. C3×C5#1544semidirect
193. C5#71829semidirect
203. C3#10604584semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
#117523372
#117467442
#106045843
#718295