Finite Group Databasebeta

← C3×#10598764 #14277043

Subgroups — C3×#10598764 #14277043

Order 1920.

456 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 112 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×#65765C212yesmaximal
2C2×C3×#3952C211yesmaximal, characteristic
3#10598764C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C4×D5C2211yescharacteristic
5C2×C3×C22⋊AGL(1,𝔽5)—22no—
6C2×C3×C4⋊AGL(1,𝔽5)—22no—
7C22×C3×C5×C8C411yescharacteristic, complemented
8C22×C3×#168C411yescharacteristic, complemented
9C3×(C2×AGL(1,𝔽5))⋊C4C414yescomplemented
10C3×#3952—22no—
11C3×#1289—51nomaximal, Hall
12#65765C2×C312yes—
13C2×#3952C2×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)—42no—
23C3×C22⋊AGL(1,𝔽5)—42no—
24C3×C4⋊AGL(1,𝔽5)—42no—
25C3×C4⋊AGL(1,𝔽5)—42no—
26C2×C3×C5×C8—21no—
27C2×C3×C5×C8—41no—
28C2×C3×#168—21no—
29C2×C3×#168—41no—
30C2×C3×C22⋊C8—51no—
31C3×#380—52no—
32C22×C4×D5C22×C311yescharacteristic
33C2×C22⋊AGL(1,𝔽5)—22no—
34C2×C4⋊AGL(1,𝔽5)—22no—
35C22×C5×C8C3×C411yescharacteristic, complemented
36C22×#168C3×C411yescharacteristic, complemented
37(C2×AGL(1,𝔽5))⋊C4C3×C414yescomplemented
38#3952—22no—
39#1289—51noSylow
40C23×C3×C5C4⋊C411yescharacteristic
41C22×C3×D5—41no—
42C22×C3×D5—41no—
43C22×C3×D5C22⋊C412yes—
44C22×C3×D5D811yescharacteristic
45C22×C3×D5SD1612yes—
46C22×C3×D5Q1611yescharacteristic
47C2×C3×AGL(1,𝔽5)—44no—
48C2×C3×AGL(1,𝔽5)—44no—
49C2×C3×AGL(1,𝔽5)—44no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5C4211yescharacteristic
53C2×C3×C4×C5C22⋊C411yescharacteristic
54C2×C3×Dic5—41no—
55C2×C3×Dic5C4⋊C412yes—
56C3×C4×D5—22no—
57C3×C4×D5—22no—
58C3×C4×D5—42no—
59C3×C5×C8—41no—
60C3×#168—41no—
61C23×C3×C4—51no—
62C22×C3×C8—51no—
63C22×C3×C8AGL(1,𝔽5)11yescharacteristic, complemented
64C2×C3×C4⋊C4—102no—
65C2×C3×C22⋊C4—102no—
66C3×C22⋊C8—102no—
67C3×#95—54no—
68C23×D5C3×D411yescharacteristic
69C22×AGL(1,𝔽5)—24no—
70C22×C4×C5C2×C3×C411yescharacteristic
71C22×Dic5C3×Q811yescharacteristic
72C2×C4×D5—41no—
73C2×C4×D5—41no—
74C2×C4×D5C2×C3×C412yes—
75C2×C4×D5C3×D412yes—
76C22⋊AGL(1,𝔽5)—42no—
77C22⋊AGL(1,𝔽5)—42no—
78C4⋊AGL(1,𝔽5)—42no—
79C4⋊AGL(1,𝔽5)—42no—
80C2×C5×C8—21no—
81C2×C5×C8—41no—
82C2×#168—21no—
83C2×#168—41no—
84C2×C22⋊C8—51no—
85#380—52no—
86C22×C3×C5—21no—
87C22×C3×C5—21no—
88C22×C3×C5#9511yescharacteristic
89C22×C3×C5#10611yescharacteristic
90C22×C3×C5#10711yescharacteristic
91C2×C3×D5—22no—
92C2×C3×D5—22no—
93C2×C3×D5—41no—
94C2×C3×D5—42no—
95C2×C3×D5—41no—
96C2×C3×D5#10212yes—
97C2×C3×D5#10312yes—
98C3×AGL(1,𝔽5)—84no—
99C3×C4×C5—21no—
100C3×C4×C5#9911yescharacteristic
101C3×C4×C5#9911yescharacteristic
102C3×Dic5—22no—
103C24×C3—51no—
104C22×C3×C4—51no—
105C22×C3×C4—52no—
106C22×C3×C4—52no—
107C22×C3×C4—104no—
108C22×C3×C4—201no—
109C22×C3×C4—201no—
110C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
111C2×C3×C8—21no—
112C2×C3×C8—41no—
113C2×C3×C8—101no—
114C2×C3×C8—201no—
115C3×C4⋊C4—202no—
116C3×C4⋊C4—202no—
117C3×C22⋊C4—202no—
118C3×C22⋊C4—202no—
119C23×C5C3×C4⋊C411yescharacteristic
120C22×D5—41no—
121C22×D5—41no—
122C22×D5C3×C22⋊C412yes—
123C22×D5C3×D811yescharacteristic
124C22×D5C3×SD1612yes—
125C22×D5C3×Q1611yescharacteristic
126C2×AGL(1,𝔽5)—44no—
127C2×AGL(1,𝔽5)—44no—
128C2×AGL(1,𝔽5)—44no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5C3×C4211yescharacteristic
132C2×C4×C5C3×C22⋊C411yescharacteristic
133C2×Dic5—41no—
134C2×Dic5C3×C4⋊C412yes—
135C4×D5—22no—
136C4×D5—22no—
137C4×D5—42no—
138C5×C8—41no—
139#168—41no—
140C23×C4—51no—
141C22×C8—51no—
142C22×C8C3×AGL(1,𝔽5)11yescharacteristic, complemented
143C2×C4⋊C4—102no—
144C2×C22⋊C4—102no—
145C22⋊C8—102no—
146#95—54no—
147C2×C3×C5—21no—
148C2×C3×C5—21no—
149C2×C3×C5H(3,ℤ/4)11yescharacteristic
150C2×C3×C5#34011yescharacteristic
151C2×C3×C5#34211yescharacteristic
152C3×D5—22no—
153C3×D5—22no—
154C23×C3—52no—
155C23×C3—52no—
156C23×C3—51no—
157C23×C3—51no—
158C23×C3—201no—
159C23×C3—201no—
160C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—52no—
164C2×C3×C4—102no—
165C2×C3×C4—102no—
166C2×C3×C4—202no—
167C2×C3×C4—201no—
168C2×C3×C4—204no—
169C2×C3×C4—204no—
170C2×C3×C4—204no—
171C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
172C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
173C3×C8—41no—
174C3×C8—201no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5C3×#9511yescharacteristic
178C22×C5C3×#10611yescharacteristic
179C22×C5C3×#10711yescharacteristic
180C2×D5—22no—
181C2×D5—22no—
182C2×D5—41no—
183C2×D5—42no—
184C2×D5—41no—
185C2×D5C3×#10212yes—
186C2×D5C3×#10312yes—
187AGL(1,𝔽5)—84no—
188C4×C5—21no—
189C4×C5C3×#9911yescharacteristic
190C4×C5C3×#9911yescharacteristic
191Dic5—22no—
192C24—51no—
193C22×C4—51no—
194C22×C4—52no—
195C22×C4—52no—
196C22×C4—104no—
197C22×C4—201no—
198C22×C4—201no—
199C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
200C2×C8—21no—
201C2×C8—41no—
202C2×C8—101no—
203C2×C8—201no—
204C4⋊C4—202no—
205C4⋊C4—202no—
206C22⋊C4—202no—
207C22⋊C4—202no—
208C3×C5#128911yescharacteristic, complemented, Hall
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—52no—
212C22×C3—52no—
213C22×C3—102no—
214C22×C3—102no—
215C22×C3—202no—
216C22×C3—201no—
217C22×C3—201no—
218C22×C3#399311yescharacteristic
219C22×C3#399411yescharacteristic
220C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
221C3×C4—21no—
222C3×C4—102no—
223C3×C4—404no—
224C3×C4#399911yescharacteristic
225C3×C4#401111yescharacteristic
226C2×C5—21no—
227C2×C5—21no—
228C2×C5C3×H(3,ℤ/4)11yescharacteristic
229C2×C5C3×#34011yescharacteristic
230C2×C5C3×#34211yescharacteristic
231D5—22no—
232D5—22no—
233C23—52no—
234C23—52no—
235C23—51no—
236C23—51no—
237C23—201no—
238C23—201no—
239C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—52no—
243C2×C4—102no—
244C2×C4—102no—
245C2×C4—202no—
246C2×C4—201no—
247C2×C4—204no—
248C2×C4—204no—
249C2×C4—204no—
250C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
251C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
252C8—41no—
253C8—201no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—102no—
257C2×C3—102no—
258C2×C3#6489311yescharacteristic
259C2×C3#6489511yescharacteristic
260C2×C3#6491711yescharacteristic
261C5C3×#128911yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—52no—
265C22—52no—
266C22—102no—
267C22—102no—
268C22—202no—
269C22—201no—
270C22—201no—
271C22C3×#399311yescharacteristic
272C22C3×#399411yescharacteristic
273C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
274C4—21no—
275C4—102no—
276C4—404no—
277C4C3×#399911yescharacteristic
278C4C3×#401111yescharacteristic
279C3#1059876411yescharacteristic, direct product factor, Sylow
280C2—21no—
281C2—21no—
282C2—102no—
283C2—102no—
284C2C3×#6489311yescharacteristic
285C2C3×#6489511yescharacteristic
286C2C3×#6491711yescharacteristic
subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C4×D5C22×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1289
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
3. #10598764C3direct (N × H)
7. C22×C3×C5×C8C4semidirect
8. C22×C3×#168C4semidirect
9. C3×(C2×AGL(1,𝔽5))⋊C4C4semidirect
35. C22×C5×C8C3×C4semidirect
36. C22×#168C3×C4semidirect
37. (C2×AGL(1,𝔽5))⋊C4C3×C4semidirect
63. C22×C3×C8AGL(1,𝔽5)semidirect
142. C22×C8C3×AGL(1,𝔽5)semidirect
208. C3×C5#1289semidirect
261. C5C3×#1289semidirect
279. C3#10598764direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657652
C2×C3×#39522
#105987643
C3×#12895