Finite Group Databasebeta

← C3×#10603882 #14298867

Subgroups — C3×#10603882 #14298867

Order 1920.

448 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 148 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×#65689C211yesmaximal, characteristic
2C3×#65688C211yesmaximal, characteristic
3C3×D5×#97C211yesmaximal, characteristic
4C3×#64893C214yesmaximal
5#10603882C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C4⋊AGL(1,𝔽5)—22no—
7C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
8C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
9C2×C3×C8×D5C2212yes—
10C3×C42×D5C2211yescharacteristic
11C3×(C2×AGL(1,𝔽5))⋊C4—22no—
12C3×C5×#97C411yescharacteristic, complemented
13C3×#3947C412yescomplemented
14C3×#3935C411yescharacteristic, complemented
15C3×#1836—51nomaximal, Hall
16#65689C2×C311yescharacteristic
17#65688C2×C311yescharacteristic
18D5×#97C2×C311yescharacteristic
19#64893C2×C314yes—
20C22×C3×AGL(1,𝔽5)—22no—
21C22×C3×AGL(1,𝔽5)—22no—
22C2×C3×C4×D5D412yes—
23C2×C3×C4×D5C2311yescharacteristic
24C3×C4⋊AGL(1,𝔽5)—24no—
25C3×C4⋊AGL(1,𝔽5)—24no—
26C3×C4⋊AGL(1,𝔽5)—44no—
27C2×C3×C5×C8C2×C412yes—
28C3×C42×C5C2×C411yescharacteristic
29C3×C4×Dic5C2×C411yescharacteristic
30C3×C4×Dic5Q812yes—
31C2×C3×#168C2×C412yes—
32C3×C8×D5—22no—
33C3×C8×D5—22no—
34C2×C3×#97—51no—
35C3×#384—51no—
36C3×#382—51no—
37C3×#340—54no—
38C2×C4⋊AGL(1,𝔽5)—22no—
39C2×C4⋊AGL(1,𝔽5)C22×C312yes—
40C2×C4⋊AGL(1,𝔽5)C22×C312yes—
41C2×C8×D5C22×C312yes—
42C42×D5C22×C311yescharacteristic
43(C2×AGL(1,𝔽5))⋊C4—22no—
44C5×#97C3×C411yescharacteristic, complemented
45#3947C3×C412yescomplemented
46#3935C3×C411yescharacteristic, complemented
47#1836—51noSylow
48C22×C3×D5C2×D411yescharacteristic
49C2×C3×AGL(1,𝔽5)—42no—
50C2×C3×AGL(1,𝔽5)—42no—
51C2×C3×AGL(1,𝔽5)—44no—
52C2×C3×AGL(1,𝔽5)—42no—
53C2×C3×AGL(1,𝔽5)—42no—
54C2×C3×C4×C5C4⋊C412yes—
55C2×C3×C4×C5C22×C411yescharacteristic
56C2×C3×Dic5C4⋊C412yes—
57C2×C3×Dic5C2×Q811yescharacteristic
58C3×C4×D5—22no—
59C3×C4×D5—22no—
60C3×C4×D5#4112yes—
61C3×C4×D5#4112yes—
62C3×C5×C8—22no—
63C3×#168—22no—
64C22×C3×C8—52no—
65C2×C3×C4⋊C4—52no—
66C2×C3×C4⋊C4—52no—
67C2×C3×C4⋊C4—102no—
68C2×C3×C42—51no—
69C3×#97—52no—
70C3×#97—51no—
71C3×#97AGL(1,𝔽5)11yescharacteristic, complemented
72C3×#95—102no—
73C22×AGL(1,𝔽5)—22no—
74C22×AGL(1,𝔽5)—22no—
75C2×C4×D5C3×D412yes—
76C2×C4×D5C23×C311yescharacteristic
77C4⋊AGL(1,𝔽5)—24no—
78C4⋊AGL(1,𝔽5)—24no—
79C4⋊AGL(1,𝔽5)—44no—
80C2×C5×C8C2×C3×C412yes—
81C42×C5C2×C3×C411yescharacteristic
82C4×Dic5C2×C3×C411yescharacteristic
83C4×Dic5C3×Q812yes—
84C2×#168C2×C3×C412yes—
85C8×D5—22no—
86C8×D5—22no—
87C2×#97—51no—
88#384—51no—
89#382—51no—
90#340—54no—
91C22×C3×C5C2×C4⋊C411yescharacteristic
92C2×C3×D5#12411yescharacteristic
93C2×C3×D5#12411yescharacteristic
94C2×C3×D5AGL(1,ℤ/8)12yes—
95C2×C3×D5#13712yes—
96C3×AGL(1,𝔽5)—82no—
97C3×AGL(1,𝔽5)—82no—
98C3×C4×C5—22no—
99C3×C4×C5#11712yes—
100C3×Dic5—22no—
101C3×Dic5#12512yes—
102C22×C3×C4—51no—
103C22×C3×C4—52no—
104C22×C3×C4—102no—
105C22×C3×C4—102no—
106C2×C3×C8—52no—
107C2×C3×C8—102no—
108C2×C3×C8—102no—
109C2×C3×C8C2×AGL(1,𝔽5)12yes—
110C3×C4⋊C4—104no—
111C3×C4⋊C4—104no—
112C3×C4⋊C4—204no—
113C3×C42—52no—
114C3×C42—51no—
115C3×C42C2×AGL(1,𝔽5)11yescharacteristic
116C22×D5C2×C3×D411yescharacteristic
117C2×AGL(1,𝔽5)—42no—
118C2×AGL(1,𝔽5)—42no—
119C2×AGL(1,𝔽5)—44no—
120C2×AGL(1,𝔽5)—42no—
121C2×AGL(1,𝔽5)—42no—
122C2×C4×C5C3×C4⋊C412yes—
123C2×C4×C5C22×C3×C411yescharacteristic
124C2×Dic5C3×C4⋊C412yes—
125C2×Dic5C2×C3×Q811yescharacteristic
126C4×D5—22no—
127C4×D5—22no—
128C4×D5C3×#4112yes—
129C4×D5C3×#4112yes—
130C5×C8—22no—
131#168—22no—
132C22×C8—52no—
133C2×C4⋊C4—52no—
134C2×C4⋊C4—52no—
135C2×C4⋊C4—102no—
136C2×C42—51no—
137#97—52no—
138#97—51no—
139#97C3×AGL(1,𝔽5)11yescharacteristic, complemented
140#95—102no—
141C2×C3×C5#38211yescharacteristic
142C2×C3×C5#42812yes—
143C3×D5#48912yes—
144C3×D5#49011yescharacteristic
145C3×D5#49111yescharacteristic
146C23×C3—51no—
147C2×C3×C4—51no—
148C2×C3×C4—52no—
149C2×C3×C4—52no—
150C2×C3×C4—52no—
151C2×C3×C4—102no—
152C2×C3×C4—102no—
153C2×C3×C4—202no—
154C2×C3×C4—202no—
155C2×C3×C4—204no—
156C2×C3×C4—202no—
157C2×C3×C4—202no—
158C2×C3×C4C4⋊AGL(1,𝔽5)12yes—
159C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
160C3×C8—22no—
161C3×C8—102no—
162C22×C5C2×C3×C4⋊C411yescharacteristic
163C2×D5C3×#12411yescharacteristic
164C2×D5C3×#12411yescharacteristic
165C2×D5C3×AGL(1,ℤ/8)12yes—
166C2×D5C3×#13712yes—
167AGL(1,𝔽5)—82no—
168AGL(1,𝔽5)—82no—
169C4×C5—22no—
170C4×C5C3×#11712yes—
171Dic5—22no—
172Dic5C3×#12512yes—
173C22×C4—51no—
174C22×C4—52no—
175C22×C4—102no—
176C22×C4—102no—
177C2×C8—52no—
178C2×C8—102no—
179C2×C8—102no—
180C2×C8C2×C3×AGL(1,𝔽5)12yes—
181C4⋊C4—104no—
182C4⋊C4—104no—
183C4⋊C4—204no—
184C42—52no—
185C42—51no—
186C42C2×C3×AGL(1,𝔽5)11yescharacteristic
187C3×C5#183611yescharacteristic, complemented, Hall
188C22×C3—51no—
189C22×C3—51no—
190C22×C3—52no—
191C22×C3—52no—
192C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
193C3×C4—22no—
194C3×C4—52no—
195C3×C4—102no—
196C3×C4—402no—
197C3×C4—402no—
198C3×C4#413012yes—
199C2×C5C3×#38211yescharacteristic
200C2×C5C3×#42812yes—
201D5C3×#48912yes—
202D5C3×#49011yescharacteristic
203D5C3×#49111yescharacteristic
204C23—51no—
205C2×C4—51no—
206C2×C4—52no—
207C2×C4—52no—
208C2×C4—52no—
209C2×C4—102no—
210C2×C4—102no—
211C2×C4—202no—
212C2×C4—202no—
213C2×C4—204no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4C3×C4⋊AGL(1,𝔽5)12yes—
217C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
218C8—22no—
219C8—102no—
220C2×C3—51no—
221C2×C3—52no—
222C2×C3—51no—
223C2×C3#6568911yescharacteristic
224C2×C3#6572712yes—
225C5C3×#183611yescharacteristic, complemented, Sylow
226C22—51no—
227C22—51no—
228C22—52no—
229C22—52no—
230C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
231C4—22no—
232C4—52no—
233C4—102no—
234C4—402no—
235C4—402no—
236C4C3×#413012yes—
237C3#1060388211yescharacteristic, direct product factor, Sylow
238C2—51no—
239C2—52no—
240C2—51no—
241C2C3×#6568911yescharacteristic
242C2C3×#6572712yes—
subgroupG/H
centerC22×C3C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#97C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×#97AGL(1,𝔽5)
hypocenterC5C3×#1836
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#97

Complements

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

NH ≅ G/Ntype
5. #10603882C3direct (N × H)
12. C3×C5×#97C4semidirect
13. C3×#3947C4semidirect
14. C3×#3935C4semidirect
44. C5×#97C3×C4semidirect
45. #3947C3×C4semidirect
46. #3935C3×C4semidirect
71. C3×#97AGL(1,𝔽5)semidirect
139. #97C3×AGL(1,𝔽5)semidirect
187. C3×C5#1836semidirect
225. C5C3×#1836semidirect
237. C3#10603882direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#656892
C3×#656882
C3×D5×#972
C3×#648932
#106038823
C3×#18365