Finite Group Databasebeta

← C3×#10604247 #14298408

Subgroups — C3×#10604247 #14298408

Order 1920.

544 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 132 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×#4023C211yesmaximal, characteristic
2C3×#65798C212yesmaximal
3C3×#64919C214yesmaximal, complemented
4#10604247C311yesmaximal, characteristic, direct product factor, Hall
5C23×C3×Dic5C2211yescharacteristic
6C2×C3×#704C2214yes—
7C2×C3×C5×C22⋊C4C411yescharacteristic
8C2×C3×C22⋊Dic5C411yescharacteristic
9C2×C3×#683C2212yes—
10C2×C3×C4×Dic5C412yes—
11C3×#4023—24no—
12C3×C22⋊#170—24no—
13C3×#1822—51nomaximal, Hall
14C2×#4023C2×C311yescharacteristic
15#65798C2×C312yes—
16#64919C2×C314yescomplemented
17C24×C3×C5C2×C411yescharacteristic
18C22×C3×C4×C5C2×C412yes—
19C22×C3×Dic5—24no—
20C22×C3×Dic5C2×C411yescharacteristic
21C22×C3×Dic5C2×C412yes—
22C22×C3×Dic5D414yes—
23C22×C3×Dic5C2311yescharacteristic
24C3×#704—28no—
25C2×C3×#170—24no—
26C3×C5×C22⋊C4—22no—
27C3×C22⋊Dic5—22no—
28C3×#683—24no—
29C3×C4×Dic5—24no—
30C2×C3×#117—51no—
31C3×#407—52no—
32C3×#343—54no—
33C23×Dic5C22×C311yescharacteristic
34C2×#704C22×C314yes—
35C2×C5×C22⋊C4C3×C411yescharacteristic
36C2×C22⋊Dic5C3×C411yescharacteristic
37C2×#683C22×C312yes—
38C2×C4×Dic5C3×C412yes—
39#4023—24no—
40C22⋊#170—24no—
41#1822—51noSylow
42C23×C3×C5—22no—
43C23×C3×C5—42no—
44C23×C3×C5C22⋊C412yes—
45C23×C3×C5C22×C411yescharacteristic
46C2×C3×C4×C5—22no—
47C2×C3×C4×C5—42no—
48C2×C3×Dic5—22no—
49C2×C3×Dic5—28no—
50C2×C3×Dic5—22no—
51C2×C3×Dic5—42no—
52C2×C3×Dic5C22⋊C412yes—
53C2×C3×Dic5C2×D412yes—
54C2×C3×Dic5#4114yes—
55C3×#170—44no—
56C23×C3×C4—51no—
57C2×C3×M16—54no—
58C3×#117—104no—
59C2×C3×C4⋊C4—52no—
60C2×C3×C22⋊C4—51no—
61C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
62C2×C3×C42—52no—
63C3×C22⋊C8—104no—
64C24×C5C2×C3×C411yescharacteristic
65C22×C4×C5C2×C3×C412yes—
66C22×Dic5—24no—
67C22×Dic5C2×C3×C411yescharacteristic
68C22×Dic5C2×C3×C412yes—
69C22×Dic5C3×D414yes—
70C22×Dic5C23×C311yescharacteristic
71#704—28no—
72C2×#170—24no—
73C5×C22⋊C4—22no—
74C22⋊Dic5—22no—
75#683—24no—
76C4×Dic5—24no—
77C2×#117—51no—
78#407—52no—
79#343—54no—
80C22×C3×C5—22no—
81C22×C3×C5—22no—
82C22×C3×C5—24no—
83C22×C3×C5—44no—
84C22×C3×C5C2×C22⋊C411yescharacteristic
85C22×C3×C5#11712yes—
86C3×C4×C5—42no—
87C3×Dic5—22no—
88C3×Dic5—42no—
89C3×Dic5#12314yes—
90C24×C3C2×AGL(1,𝔽5)11yescharacteristic
91C22×C3×C4—51no—
92C22×C3×C4—54no—
93C22×C3×C4—51no—
94C22×C3×C4—52no—
95C22×C3×C4—104no—
96C22×C3×C4C2×AGL(1,𝔽5)12yes—
97C3×M16—108no—
98C2×C3×C8—104no—
99C3×C4⋊C4—104no—
100C3×C22⋊C4—22no—
101C3×C22⋊C4—102no—
102C3×C42—104no—
103C23×C5—22no—
104C23×C5—42no—
105C23×C5C3×C22⋊C412yes—
106C23×C5C22×C3×C411yescharacteristic
107C2×C4×C5—22no—
108C2×C4×C5—42no—
109C2×Dic5—22no—
110C2×Dic5—28no—
111C2×Dic5—22no—
112C2×Dic5—42no—
113C2×Dic5C3×C22⋊C412yes—
114C2×Dic5C2×C3×D412yes—
115C2×Dic5C3×#4114yes—
116#170—44no—
117C23×C4—51no—
118C2×M16—54no—
119#117—104no—
120C2×C4⋊C4—52no—
121C2×C22⋊C4—51no—
122C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic
123C2×C42—52no—
124C22⋊C8—104no—
125C2×C3×C5—22no—
126C2×C3×C5—42no—
127C2×C3×C5#38111yescharacteristic
128C2×C3×C5#41312yes—
129C23×C3—22no—
130C23×C3—42no—
131C23×C3C22⋊AGL(1,𝔽5)12yes—
132C23×C3C22×AGL(1,𝔽5)11yescharacteristic
133C2×C3×C4—22no—
134C2×C3×C4—42no—
135C2×C3×C4—54no—
136C2×C3×C4—52no—
137C2×C3×C4—52no—
138C2×C3×C4—108no—
139C2×C3×C4—102no—
140C2×C3×C4—102no—
141C2×C3×C4—202no—
142C3×C8—204no—
143C22×C5—22no—
144C22×C5—22no—
145C22×C5—24no—
146C22×C5—44no—
147C22×C5C2×C3×C22⋊C411yescharacteristic
148C22×C5C3×#11712yes—
149C4×C5—42no—
150Dic5—22no—
151Dic5—42no—
152Dic5C3×#12314yes—
153C24C2×C3×AGL(1,𝔽5)11yescharacteristic
154C22×C4—51no—
155C22×C4—54no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4—104no—
159C22×C4C2×C3×AGL(1,𝔽5)12yes—
160M16—108no—
161C2×C8—104no—
162C4⋊C4—104no—
163C22⋊C4—22no—
164C22⋊C4—102no—
165C42—104no—
166C3×C5#182211yescharacteristic, complemented, Hall
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—24no—
170C22×C3—44no—
171C22×C3#413012yes—
172C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
173C3×C4—42no—
174C3×C4—54no—
175C3×C4—102no—
176C3×C4—202no—
177C2×C5—22no—
178C2×C5—42no—
179C2×C5C3×#38111yescharacteristic
180C2×C5C3×#41312yes—
181C23—22no—
182C23—42no—
183C23C3×C22⋊AGL(1,𝔽5)12yes—
184C23C22×C3×AGL(1,𝔽5)11yescharacteristic
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—54no—
188C2×C4—52no—
189C2×C4—52no—
190C2×C4—108no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—202no—
194C8—204no—
195C2×C3—22no—
196C2×C3—42no—
197C2×C3#6576411yescharacteristic
198C2×C3#6577712yes—
199C5C3×#182211yescharacteristic, complemented, Sylow
200C22—22no—
201C22—22no—
202C22—24no—
203C22—44no—
204C22C3×#413012yes—
205C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
206C4—42no—
207C4—54no—
208C4—102no—
209C4—202no—
210C3#1060424711yescharacteristic, direct product factor, Sylow
211C2—22no—
212C2—42no—
213C2C3×#6576411yescharacteristic
214C2C3×#6577712yes—
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1822
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#64919C2semidirect
4. #10604247C3direct (N × H)
16. #64919C2×C3semidirect
166. C3×C5#1822semidirect
199. C5C3×#1822semidirect
210. C3#10604247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40232
C3×#657982
C3×#649192
#106042473
C3×#18225