Finite Group Databasebeta

← C3×#10598785 #14277191

Subgroups — C3×#10598785 #14277191

Order 1920.

492 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 96 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×C4×C22⋊AGL(1,𝔽5)C212yesmaximal
2C3×#65415C211yesmaximal, characteristic
3#10598785C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C4×D5C2211yescharacteristic
5C2×C3×C22⋊AGL(1,𝔽5)—22no—
6C2×C3×C4×AGL(1,𝔽5)—22no—
7C2×C3×C5×M16C411yescharacteristic, complemented
8C2×C3×#681C411yescharacteristic, complemented
9C3×(C2×AGL(1,𝔽5))⋊C4C414yescomplemented
10C3×#3952—22no—
11C3×#1297—51nomaximal, Hall
12C4×C22⋊AGL(1,𝔽5)C2×C312yes—
13#65415C2×C311yescharacteristic
14C23×C3×D5D411yescharacteristic
15C22×C3×AGL(1,𝔽5)—24no—
16C22×C3×C4×C5C2×C411yescharacteristic
17C22×C3×Dic5Q811yescharacteristic
18C2×C3×C4×D5—41no—
19C2×C3×C4×D5—41no—
20C2×C3×C4×D5C2×C412yes—
21C2×C3×C4×D5D412yes—
22C3×C22⋊AGL(1,𝔽5)—28no—
23C3×C4×AGL(1,𝔽5)—42no—
24C3×C4×AGL(1,𝔽5)—42no—
25C3×C5×M16—41no—
26C2×C3×C5×C8—21no—
27C3×#681—41no—
28C2×C3×#168—21no—
29C3×#407—51no—
30C3×C4×C22⋊C4—52no—
31C22×C4×D5C22×C311yescharacteristic
32C2×C22⋊AGL(1,𝔽5)—22no—
33C2×C4×AGL(1,𝔽5)—22no—
34C2×C5×M16C3×C411yescharacteristic, complemented
35C2×#681C3×C411yescharacteristic, complemented
36(C2×AGL(1,𝔽5))⋊C4C3×C414yescomplemented
37#3952—22no—
38#1297—51noSylow
39C23×C3×C5C4⋊C411yescharacteristic
40C22×C3×D5—24no—
41C22×C3×D5—41no—
42C22×C3×D5C22⋊C412yes—
43C2×C3×AGL(1,𝔽5)—28no—
44C2×C3×AGL(1,𝔽5)—44no—
45C2×C3×AGL(1,𝔽5)—44no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5C4211yescharacteristic
49C2×C3×C4×C5C22⋊C411yescharacteristic
50C2×C3×Dic5—41no—
51C2×C3×Dic5C4⋊C412yes—
52C3×C4×D5—22no—
53C3×C4×D5—22no—
54C3×C4×D5—42no—
55C3×C5×C8—41no—
56C3×#168—41no—
57C23×C3×C4—51no—
58C2×C3×M16—51no—
59C2×C3×M16AGL(1,𝔽5)11yescharacteristic, complemented
60C2×C3×C22⋊C4—102no—
61C2×C3×C42—102no—
62C3×C22⋊C8—102no—
63C3×#95—54no—
64C23×D5C3×D411yescharacteristic
65C22×AGL(1,𝔽5)—24no—
66C22×C4×C5C2×C3×C411yescharacteristic
67C22×Dic5C3×Q811yescharacteristic
68C2×C4×D5—41no—
69C2×C4×D5—41no—
70C2×C4×D5C2×C3×C412yes—
71C2×C4×D5C3×D412yes—
72C22⋊AGL(1,𝔽5)—28no—
73C4×AGL(1,𝔽5)—42no—
74C4×AGL(1,𝔽5)—42no—
75C5×M16—41no—
76C2×C5×C8—21no—
77#681—41no—
78C2×#168—21no—
79#407—51no—
80C4×C22⋊C4—52no—
81C22×C3×C5—22no—
82C22×C3×C5—21no—
83C22×C3×C5#9511yescharacteristic
84C2×C3×D5—22no—
85C2×C3×D5—22no—
86C2×C3×D5—44no—
87C2×C3×D5#10414yes—
88C3×AGL(1,𝔽5)—48no—
89C3×C4×C5—21no—
90C3×C4×C5#9911yescharacteristic
91C3×C4×C5#9911yescharacteristic
92C3×Dic5—22no—
93C24×C3—51no—
94C22×C3×C4—51no—
95C22×C3×C4—52no—
96C22×C3×C4—52no—
97C22×C3×C4—104no—
98C22×C3×C4—201no—
99C22×C3×C4—201no—
100C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
101C3×M16—41no—
102C3×M16—201no—
103C2×C3×C8—21no—
104C2×C3×C8—101no—
105C3×C22⋊C4—108no—
106C3×C42—202no—
107C3×C42—202no—
108C23×C5C3×C4⋊C411yescharacteristic
109C22×D5—24no—
110C22×D5—41no—
111C22×D5C3×C22⋊C412yes—
112C2×AGL(1,𝔽5)—28no—
113C2×AGL(1,𝔽5)—44no—
114C2×AGL(1,𝔽5)—44no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5C3×C4211yescharacteristic
118C2×C4×C5C3×C22⋊C411yescharacteristic
119C2×Dic5—41no—
120C2×Dic5C3×C4⋊C412yes—
121C4×D5—22no—
122C4×D5—22no—
123C4×D5—42no—
124C5×C8—41no—
125#168—41no—
126C23×C4—51no—
127C2×M16—51no—
128C2×M16C3×AGL(1,𝔽5)11yescharacteristic, complemented
129C2×C22⋊C4—102no—
130C2×C42—102no—
131C22⋊C8—102no—
132#95—54no—
133C2×C3×C5—41no—
134C2×C3×C5#33912yes—
135C2×C3×C5#34211yescharacteristic
136C3×D5—24no—
137C23×C3—52no—
138C23×C3—104no—
139C23×C3—201no—
140C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—52no—
144C2×C3×C4—102no—
145C2×C3×C4—102no—
146C2×C3×C4—108no—
147C2×C3×C4—202no—
148C2×C3×C4—201no—
149C2×C3×C4—204no—
150C2×C3×C4—204no—
151C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
152C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
153C3×C8—41no—
154C3×C8—201no—
155C22×C5—22no—
156C22×C5—21no—
157C22×C5C3×#9511yescharacteristic
158C2×D5—22no—
159C2×D5—22no—
160C2×D5—44no—
161C2×D5C3×#10414yes—
162AGL(1,𝔽5)—48no—
163C4×C5—21no—
164C4×C5C3×#9911yescharacteristic
165C4×C5C3×#9911yescharacteristic
166Dic5—22no—
167C24—51no—
168C22×C4—51no—
169C22×C4—52no—
170C22×C4—52no—
171C22×C4—104no—
172C22×C4—201no—
173C22×C4—201no—
174C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
175M16—41no—
176M16—201no—
177C2×C8—21no—
178C2×C8—101no—
179C22⋊C4—108no—
180C42—202no—
181C42—202no—
182C3×C5#129711yescharacteristic, complemented, Hall
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—54no—
186C22×C3—102no—
187C22×C3—102no—
188C22×C3—204no—
189C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
190C3×C4—21no—
191C3×C4—102no—
192C3×C4—208no—
193C3×C4#399911yescharacteristic
194C3×C4#401111yescharacteristic
195C2×C5—41no—
196C2×C5C3×#33912yes—
197C2×C5C3×#34211yescharacteristic
198D5—24no—
199C23—52no—
200C23—104no—
201C23—201no—
202C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—52no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—108no—
209C2×C4—202no—
210C2×C4—201no—
211C2×C4—204no—
212C2×C4—204no—
213C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
214C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
215C8—41no—
216C8—201no—
217C2×C3—41no—
218C2×C3—104no—
219C2×C3#6490012yes—
220C2×C3#6491711yescharacteristic
221C5C3×#129711yescharacteristic, complemented, Sylow
222C22—22no—
223C22—21no—
224C22—54no—
225C22—102no—
226C22—102no—
227C22—204no—
228C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
229C4—21no—
230C4—102no—
231C4—208no—
232C4C3×#399911yescharacteristic
233C4C3×#401111yescharacteristic
234C3#1059878511yescharacteristic, direct product factor, Sylow
235C2—41no—
236C2—104no—
237C2C3×#6490012yes—
238C2C3×#6491711yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C4×D5C22×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#1297
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×M16

Complements

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

NH ≅ G/Ntype
3. #10598785C3direct (N × H)
7. C2×C3×C5×M16C4semidirect
8. C2×C3×#681C4semidirect
9. C3×(C2×AGL(1,𝔽5))⋊C4C4semidirect
34. C2×C5×M16C3×C4semidirect
35. C2×#681C3×C4semidirect
36. (C2×AGL(1,𝔽5))⋊C4C3×C4semidirect
59. C2×C3×M16AGL(1,𝔽5)semidirect
128. C2×M16C3×AGL(1,𝔽5)semidirect
182. C3×C5#1297semidirect
221. C5C3×#1297semidirect
234. C3#10598785direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊AGL(1,𝔽5)2
C3×#654152
#105987853
C3×#12975