Finite Group Databasebeta

← #14285459

Subgroups — #14285459

Order 1920.

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

normal subgroups only

This group has 420 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#11752341C212yesmaximal
3#11746744C214yesmaximal, complemented
4#10604586—31nomaximal, Hall
5C2×#6758—22no—
6C3×C5×#125C411yescharacteristic
7C3×#4042—22no—
8C3×#4038C412yes—
9C3×#4034C2212yes—
10C3×#4033—22no—
11C3×C42×D5C2211yescharacteristic
12C3×#4016C411yescharacteristic
13#91233—22no—
14#91233C2214yes—
15#71834—51nomaximal, Hall
16#66022D311yescharacteristic
17#65682—32no—
18#64873—34no—
19C2×C3×C4×D5C2×C411yescharacteristic
20C2×C3×C4×D5D412yes—
21C2×C3×Dic10—22no—
22C2×C3⋊#170—24no—
23#6758—44no—
24C3×C5×C4⋊C4—22no—
25C3×C5×C4⋊C4C2×C412yes—
26C3×C42×C5C2×C411yescharacteristic
27C3×#685—22no—
28C3×C4⋊Dic5C2×C412yes—
29C3×#683—22no—
30C3×#683—22no—
31C3×C4×Dic5—22no—
32C3×C4×Dic5D412yes—
33C3×C4×Dic5C2311yescharacteristic
34C3×#533—51no—
35#4924—52no—
36#4547—54no—
37C2×#700—62no—
38C5×#125Dic311yescharacteristic
39#4042—22no—
40#4038Dic312yes—
41#4034C2×D312yes—
42#4033—22no—
43C42×D5C2×D311yescharacteristic
44#4016Dic311yescharacteristic
45#4004—34no—
46#4004—62no—
47#1561—151noSylow
48C22×C3×D5C22⋊C411yescharacteristic
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5C22⋊C412yes—
51C2×C3×C4×C5C22×C411yescharacteristic
52C2×C3×Dic5—22no—
53C2×C3×Dic5C22⋊C411yescharacteristic
54C2×C3×Dic5C2×D412yes—
55C3×C4×D5—22no—
56C3×C4×D5—22no—
57C3×C4×D5—22no—
58C3×Dic10—42no—
59C3×Dic10—42no—
60C3⋊#170—44no—
61C3×C4⋊Q8—52no—
62C3×#125—51no—
63C3×#125AGL(1,𝔽5)11yescharacteristic
64C3×C22⋊Q8—102no—
65C3×C4×Q8—102no—
66C3×#117—52no—
67C2×C3×C42—51no—
68C2×#208—102no—
69C4⋊(C3⋊C8)—54no—
70C4⋊(C3⋊C8)—102no—
71C2×C4×D5C2×Dic311yescharacteristic
72C2×C4×D5#6712yes—
73C2×Dic10—22no—
74C2×#170—64no—
75#700—124no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4C2×Dic312yes—
78C42×C5C2×Dic311yescharacteristic
79#685—22no—
80C4⋊Dic5C2×Dic312yes—
81#683—22no—
82#683—22no—
83C4×Dic5—22no—
84C4×Dic5#6712yes—
85C4×Dic5C22×D311yescharacteristic
86#533—51no—
87#423—152no—
88#332—154no—
89C22×C3×C5C2×C22⋊C411yescharacteristic
90C2×C3×D5—21no—
91C2×C3×D5—22no—
92C3×C4×C5—21no—
93C3×C4×C5—22no—
94C3×C4×C5—42no—
95C3×Dic5—42no—
96C3×Dic5#10112yes—
97C3×Dic5AGL(1,ℤ/8)12yes—
98C3×Dic5#13712yes—
99C2×C3×Q8—102no—
100C22×C3×C4—52no—
101C22×C3×C4—51no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—52no—
104C3×C4⋊C4—102no—
105C3×C4⋊C4—102no—
106C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
107C3×C22⋊C4—102no—
108C3×C42—52no—
109C3×C42—51no—
110C3×C42—102no—
111C3×C42C2×AGL(1,𝔽5)11yescharacteristic
112#208—204no—
113C2×C3⋊C8—104no—
114C22×D5#21711yescharacteristic
115C2×C4×C5—22no—
116C2×C4×C5#21712yes—
117C2×C4×C5C22×Dic311yescharacteristic
118C2×Dic5—22no—
119C2×Dic5#21711yescharacteristic
120C2×Dic5C2×#6712yes—
121C4×D5—22no—
122C4×D5—22no—
123C4×D5—22no—
124Dic10—42no—
125Dic10—42no—
126#170—124no—
127C2×M16—302no—
128C4⋊Q8—52no—
129#125—51no—
130#125ΓL(1,𝔽16)11yescharacteristic
131C22⋊Q8—102no—
132C4×Q8—102no—
133#117—52no—
134C2×C42—51no—
135C4⋊C8—154no—
136C4⋊C8—302no—
137C2×C3×C5C2×#10111yescharacteristic
138C2×C3×C5#41712yes—
139C3×D5—41no—
140C23×C3—51no—
141C3×Q8—202no—
142C3×Q8—202no—
143C2×C3×C4—22no—
144C2×C3×C4—51no—
145C2×C3×C4—52no—
146C2×C3×C4—102no—
147C2×C3×C4—102no—
148C2×C3×C4—102no—
149C2×C3×C4—102no—
150C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
151C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
152C3⋊C8—204no—
153C22×C5C2×#21711yescharacteristic
154C2×D5—21no—
155C2×D5—22no—
156C4×C5—21no—
157C4×C5—22no—
158C4×C5—42no—
159Dic5—42no—
160Dic5#83612yes—
161Dic5#94912yes—
162Dic5#95112yes—
163C2×Q8—102no—
164C22×C4—52no—
165C22×C4—51no—
166M16—604no—
167C2×C8—304no—
168C4⋊C4—22no—
169C4⋊C4—52no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4C2×ΓL(1,𝔽16)12yes—
173C22⋊C4—102no—
174C42—52no—
175C42—51no—
176C42—102no—
177C42C2×ΓL(1,𝔽16)11yescharacteristic
178C3×C5#156111yescharacteristic, complemented, Hall
179C22×C3—102no—
180C22×C3—101no—
181C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
182C3×C4—22no—
183C3×C4—21no—
184C3×C4—42no—
185C3×C4—52no—
186C3×C4—52no—
187C3×C4—52no—
188C3×C4—202no—
189C2×C5C2×#83611yescharacteristic
190C2×C5#523212yes—
191D5—41no—
192C23—51no—
193Q8—202no—
194Q8—202no—
195C2×C4—22no—
196C2×C4—51no—
197C2×C4—52no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4#676312yes—
203C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
204C8—604no—
205C2×C3—201no—
206C2×C3D5⋊#10111yescharacteristic
207C2×C3#6579312yes—
208C5#7183411yescharacteristic, complemented, Sylow
209C22—101no—
210C22—102no—
211C22C2×#676311yescharacteristic
212C4—21no—
213C4—22no—
214C4—42no—
215C4—52no—
216C4—52no—
217C4—52no—
218C4—202no—
219C3#1060458611yescharacteristic, complemented, Sylow
220C2—201no—
221C2D5⋊#83611yescharacteristic
222C2#1175245212yes—
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#1561
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
178. C3×C5#1561semidirect
208. C5#71834semidirect
219. C3#10604586semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
#117523412
#117467442
#106045863
#718345