Finite Group Databasebeta

← #14281153

Subgroups — #14281153

Order 1920.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×C3×#4033C211yesmaximal, characteristic
2#11752416C212yesmaximal
3#11746785C214yesmaximal
4#10604295—31nomaximal, Hall
5C22×C3×Dic10C411yescharacteristic
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×#683C2212yes—
8C2×C3×C4×Dic5C412yes—
9C2×C3×C4×Dic5C2211yescharacteristic
10C3×#4033—22no—
11C3×#4033—22no—
12#91241C2214yes—
13#91233—22no—
14#91231—22no—
15#71625—51nomaximal, Hall
16C2×#4033D311yescharacteristic
17#65757—32no—
18#64914—34no—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×C4×C5C2×C412yes—
21C22×C3×Dic5C2×C411yescharacteristic
22C22×C3×Dic5C2×C412yes—
23C22×C3×Dic5C2311yescharacteristic
24C2×C3×Dic10—22no—
25C2×C3×Dic10—24no—
26C2×C3⋊#170—24no—
27C3×C5×C4⋊C4—22no—
28C3×#683—24no—
29C3×C4×Dic5—22no—
30C3×C4×Dic5—22no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5D412yes—
33C2×C3×C4×Q8—51no—
34#4926—52no—
35#4528—54no—
36C22×Dic10Dic311yescharacteristic
37C2×C5×C4⋊C4Dic311yescharacteristic
38C2×#683C2×D312yes—
39C2×C4×Dic5Dic312yes—
40C2×C4×Dic5C2×D311yescharacteristic
41#4033—22no—
42#4033—22no—
43C22⋊#170—34no—
44#4004—62no—
45#4002—62no—
46#1467—151noSylow
47C23×C3×C5C22×C411yescharacteristic
48C2×C3×C4×C5—22no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5—42no—
51C2×C3×C4×C5C22⋊C412yes—
52C2×C3×Dic5—22no—
53C2×C3×Dic5—22no—
54C2×C3×Dic5—22no—
55C2×C3×Dic5—41no—
56C2×C3×Dic5C22⋊C411yescharacteristic
57C2×C3×Dic5C22⋊C411yescharacteristic
58C2×C3×Dic5M1614yes—
59C2×C3×Dic5C2×D412yes—
60C3×Dic10—28no—
61C3⋊#170—44no—
62C22×C3×Q8—51no—
63C3×C4×Q8—102no—
64C3×C4×Q8—102no—
65C2×C3×C4⋊C4—52no—
66C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
67C2×C3×C42—51no—
68C2×C3×C42—52no—
69#830—54no—
70C4⋊(C3⋊C8)—102no—
71#803—102no—
72C22×C4×C5C2×Dic312yes—
73C22×C4×C5C2×Dic311yescharacteristic
74C22×Dic5C2×Dic312yes—
75C22×Dic5C2×Dic311yescharacteristic
76C22×Dic5C22×D311yescharacteristic
77C2×Dic10—22no—
78C2×Dic10—24no—
79C2×#170—64no—
80C5×C4⋊C4—22no—
81#683—24no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5#6712yes—
85C4×Dic5#6712yes—
86C2×C4×Q8—51no—
87#432—152no—
88#324—154no—
89C22×C3×C5—21no—
90C22×C3×C5—21no—
91C22×C3×C5C2×C22⋊C411yescharacteristic
92C22×C3×C5C2×M1612yes—
93C3×C4×C5—22no—
94C3×C4×C5—42no—
95C3×Dic5—24no—
96C3×Dic5—22no—
97C3×Dic5—21no—
98C3×Dic5#10112yes—
99C2×C3×Q8—104no—
100C2×C3×Q8—102no—
101C22×C3×C4—51no—
102C22×C3×C4—52no—
103C22×C3×C4—51no—
104C22×C3×C4C2×AGL(1,𝔽5)12yes—
105C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
106C3×C4⋊C4—22no—
107C3×C4⋊C4—104no—
108C3×C42—52no—
109C3×C42—52no—
110C3×C42—102no—
111C3×C42—102no—
112C2×C3⋊C8—104no—
113C23×C5C22×Dic311yescharacteristic
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—42no—
117C2×C4×C5#21712yes—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—41no—
122C2×Dic5#20814yes—
123C2×Dic5#21711yescharacteristic
124C2×Dic5#21711yescharacteristic
125C2×Dic5C2×#6712yes—
126Dic10—28no—
127#170—124no—
128C22×Q8—51no—
129C4×Q8—102no—
130C4×Q8—102no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
133C2×C42—51no—
134C2×C42—52no—
135C4⋊C8—302no—
136C22⋊C8—154no—
137#97—302no—
138C2×C3×C5—22no—
139C2×C3×C5#40711yescharacteristic
140C2×C3×C5#41011yescharacteristic
141C2×C3×C5C2×#10111yescharacteristic
142C23×C3C22×AGL(1,𝔽5)11yescharacteristic
143C3×Q8—108no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—42no—
147C2×C3×C4—51no—
148C2×C3×C4—54no—
149C2×C3×C4—51no—
150C2×C3×C4—52no—
151C2×C3×C4—102no—
152C2×C3×C4—102no—
153C2×C3×C4—102no—
154C2×C3×C4—201no—
155C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
156C3⋊C8—204no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5C2×#20812yes—
160C22×C5C2×#21711yescharacteristic
161C4×C5—22no—
162C4×C5—42no—
163Dic5—24no—
164Dic5—21no—
165Dic5—22no—
166Dic5#83612yes—
167C2×Q8—104no—
168C2×Q8—102no—
169C22×C4—51no—
170C22×C4—52no—
171C22×C4—51no—
172C22×C4C2×ΓL(1,𝔽16)12yes—
173C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
174C2×C8—304no—
175C4⋊C4—22no—
176C4⋊C4—104no—
177C42—52no—
178C42—52no—
179C42—102no—
180C42—102no—
181C3×C5#146711yescharacteristic, complemented, Hall
182C22×C3—21no—
183C22×C3—21no—
184C22×C3D5⋊M1612yes—
185C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
186C3×C4—22no—
187C3×C4—42no—
188C3×C4—52no—
189C3×C4—104no—
190C3×C4—102no—
191C3×C4—101no—
192C2×C5—22no—
193C2×C5#520711yescharacteristic
194C2×C5C2×#83611yescharacteristic
195C2×C5#524011yescharacteristic
196C23C22×ΓL(1,𝔽16)11yescharacteristic
197Q8—108no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—51no—
202C2×C4—54no—
203C2×C4—51no—
204C2×C4—52no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—201no—
209C2×C4#676312yes—
210C8—604no—
211C2×C3—22no—
212C2×C3#6575511yescharacteristic
213C2×C3#6577111yescharacteristic
214C2×C3D5⋊#10111yescharacteristic
215C5#7162511yescharacteristic, complemented, Sylow
216C22—21no—
217C22—21no—
218C22D5⋊#20812yes—
219C22C2×#676311yescharacteristic
220C4—22no—
221C4—42no—
222C4—52no—
223C4—101no—
224C4—104no—
225C4—102no—
226C3#1060429511yescharacteristic, complemented, Sylow
227C2—22no—
228C2#1175241411yescharacteristic
229C2#1175243011yescharacteristic
230C2D5⋊#83611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1467
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
181. C3×C5#1467semidirect
215. C5#71625semidirect
226. C3#10604295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40332
#117524162
#117467852
#106042953
#716255