Finite Group Databasebeta

← C3×#10599906 #14316209

Subgroups — C3×#10599906 #14316209

Order 1920.

432 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C22×C3×Dic20C211yesmaximal, characteristic
2C3×#65405C211yesmaximal, characteristic
3C2×C3×Dic40C212yesmaximal, complemented
4C3×C5×C22⋊C16C211yesmaximal, characteristic
5C3×#64723C212yesmaximal, complemented
6#10599906C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×Dic10—21no—
8C22×C3×C5×C8C2211yescharacteristic
9C3×#4070—21no—
10C2×C3×Dic20—21no—
11C2×C3×Dic20—24no—
12C2×C3×Dic20C2211yescharacteristic
13C2×C3×Dic20C2212yes—
14C2×C3×C5×C16C2212yes—
15C3×#3950C2211yescharacteristic
16C3×#3948—21no—
17C3×Dic40—24no—
18C3×#2188—51nomaximal, Hall
19C22×Dic20C2×C311yescharacteristic
20#65405C2×C311yescharacteristic
21C2×Dic40C2×C312yescomplemented
22C5×C22⋊C16C2×C311yescharacteristic
23#64723C2×C312yescomplemented
24C22×C3×C4×C5D411yescharacteristic
25C22×C3×Dic5—41no—
26C2×C3×Dic10—24no—
27C2×C3×Dic10—22no—
28C2×C3×Dic10—21no—
29C2×C3×Dic10—42no—
30C2×C3×Dic10—41no—
31C2×C3×C5×C8—22no—
32C2×C3×C5×C8D411yescharacteristic
33C2×C3×C5×C8C2311yescharacteristic
34C3×C22⋊Dic5—41no—
35C3×C4⋊Dic5—21no—
36C3×#683—41no—
37C3×Dic20—24no—
38C3×Dic20—22no—
39C3×Dic20—22no—
40C3×Dic20D414yes—
41C3×C5×C16—22no—
42C22×C3×Q16—51no—
43C2×C3×Q32—52no—
44C3×#467—51no—
45C3×#358—52no—
46C3×C22⋊C16D511yescharacteristic
47C22×Dic10—21no—
48C22×C5×C8C22×C311yescharacteristic
49#4070—21no—
50C2×Dic20—21no—
51C2×Dic20—24no—
52C2×Dic20C22×C311yescharacteristic
53C2×Dic20C22×C312yes—
54C2×C5×C16C22×C312yes—
55#3950C22×C311yescharacteristic
56#3948—21no—
57Dic40—24no—
58#2188—51noSylow
59C23×C3×C5D811yescharacteristic
60C2×C3×C4×C5—21no—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5D811yescharacteristic
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×Dic5—44no—
65C2×C3×Dic5—42no—
66C2×C3×Dic5—41no—
67C2×C3×Dic5—41no—
68C3×Dic10—24no—
69C3×Dic10—44no—
70C3×Dic10—42no—
71C3×Dic10—41no—
72C3×Dic10—41no—
73C3×C5×C8—21no—
74C3×C5×C8C2×D412yes—
75C22×C3×Q8—101no—
76C2×C3×Q16—52no—
77C2×C3×Q16—51no—
78C2×C3×Q16—104no—
79C2×C3×Q16—101no—
80C22×C3×C8C2×D511yescharacteristic
81C3×C22⋊Q8—101no—
82C3×Q32—104no—
83C2×C3×C16C2×D512yes—
84C3×#107—51no—
85C3×#103—101no—
86C22×C4×C5C3×D411yescharacteristic
87C22×Dic5—41no—
88C2×Dic10—24no—
89C2×Dic10—22no—
90C2×Dic10—21no—
91C2×Dic10—42no—
92C2×Dic10—41no—
93C2×C5×C8—22no—
94C2×C5×C8C3×D411yescharacteristic
95C2×C5×C8C23×C311yescharacteristic
96C22⋊Dic5—41no—
97C4⋊Dic5—21no—
98#683—41no—
99Dic20—24no—
100Dic20—22no—
101Dic20—22no—
102Dic20C3×D414yes—
103C5×C16—22no—
104C22×Q16—51no—
105C2×Q32—52no—
106#467—51no—
107#358—52no—
108C22⋊C16C3×D511yescharacteristic
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5Q3212yescomplemented
112C22×C3×C5C2×D811yescharacteristic
113C3×C4×C5—21no—
114C3×C4×C5#12011yescharacteristic
115C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
116C3×Dic5—44no—
117C3×Dic5—81no—
118C3×Dic5—81no—
119C2×C3×Q8—104no—
120C2×C3×Q8—102no—
121C2×C3×Q8—101no—
122C2×C3×Q8—202no—
123C2×C3×Q8—201no—
124C22×C3×C4—201no—
125C22×C3×C4D2011yescharacteristic
126C3×Q16—54no—
127C3×Q16—104no—
128C3×Q16—102no—
129C3×Q16—102no—
130C2×C3×C8—22no—
131C2×C3×C8D2011yescharacteristic
132C2×C3×C8C22×D511yescharacteristic
133C3×C4⋊C4—101no—
134C3×C4⋊C4—201no—
135C3×C22⋊C4—201no—
136C3×C16—22no—
137C23×C5C3×D811yescharacteristic
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5C3×D811yescharacteristic
141C2×C4×C5C2×C3×D411yescharacteristic
142C2×Dic5—44no—
143C2×Dic5—42no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146Dic10—24no—
147Dic10—44no—
148Dic10—42no—
149Dic10—41no—
150Dic10—41no—
151C5×C8—21no—
152C5×C8C2×C3×D412yes—
153C22×Q8—101no—
154C2×Q16—52no—
155C2×Q16—51no—
156C2×Q16—104no—
157C2×Q16—101no—
158C22×C8C2×C3×D511yescharacteristic
159C22⋊Q8—101no—
160Q32—104no—
161C2×C16C2×C3×D512yes—
162#107—51no—
163#103—101no—
164C2×C3×C5—22no—
165C2×C3×C5#44711yescharacteristic
166C2×C3×C5C2×Q3211yescharacteristic
167C2×C3×C5#51011yescharacteristic
168C23×C3D4011yescharacteristic
169C3×Q8—104no—
170C3×Q8—204no—
171C3×Q8—202no—
172C3×Q8—201no—
173C3×Q8—201no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—204no—
177C2×C3×C4—202no—
178C2×C3×C4—201no—
179C2×C3×C4—201no—
180C2×C3×C4D4011yescharacteristic
181C2×C3×C4C2×D2011yescharacteristic
182C3×C8—21no—
183C3×C8D4×D512yes—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5C3×Q3212yescomplemented
187C22×C5C2×C3×D811yescharacteristic
188C4×C5—21no—
189C4×C5C3×#12011yescharacteristic
190C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
191Dic5—44no—
192Dic5—81no—
193Dic5—81no—
194C2×Q8—104no—
195C2×Q8—102no—
196C2×Q8—101no—
197C2×Q8—202no—
198C2×Q8—201no—
199C22×C4—201no—
200C22×C4C3×D2011yescharacteristic
201Q16—54no—
202Q16—104no—
203Q16—102no—
204Q16—102no—
205C2×C8—22no—
206C2×C8C3×D2011yescharacteristic
207C2×C8C22×C3×D511yescharacteristic
208C4⋊C4—101no—
209C4⋊C4—201no—
210C22⋊C4—201no—
211C16—22no—
212C3×C5#218811yescharacteristic, complemented, Hall
213C22×C3—21no—
214C22×C3—21no—
215C22×C3Dic4012yescomplemented
216C22×C3C2×D4011yescharacteristic
217C3×C4—21no—
218C3×C4—204no—
219C3×C4—401no—
220C3×C4—401no—
221C3×C4#402811yescharacteristic
222C3×C4#405411yescharacteristic
223C2×C5—22no—
224C2×C5C3×#44711yescharacteristic
225C2×C5C2×C3×Q3211yescharacteristic
226C2×C5C3×#51011yescharacteristic
227C23C3×D4011yescharacteristic
228Q8—104no—
229Q8—204no—
230Q8—202no—
231Q8—201no—
232Q8—201no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—204no—
236C2×C4—202no—
237C2×C4—201no—
238C2×C4—201no—
239C2×C4C3×D4011yescharacteristic
240C2×C4C2×C3×D2011yescharacteristic
241C8—21no—
242C8C3×D4×D512yes—
243C2×C3—22no—
244C2×C3#6502111yescharacteristic
245C2×C3C2×Dic4011yescharacteristic
246C2×C3#6519811yescharacteristic
247C5C3×#218811yescharacteristic, complemented, Sylow
248C22—21no—
249C22—21no—
250C22C3×Dic4012yescomplemented
251C22C2×C3×D4011yescharacteristic
252C4—21no—
253C4—204no—
254C4—401no—
255C4—401no—
256C4C3×#402811yescharacteristic
257C4C3×#405411yescharacteristic
258C3#1059990611yescharacteristic, direct product factor, Sylow
259C2—22no—
260C2C3×#6502111yescharacteristic
261C2C2×C3×Dic4011yescharacteristic
262C2C3×#6519811yescharacteristic
subgroupG/H
centerC22×C3C2×D40
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5C2×D8
prime radicalC23×C3×C5D8
hypercenterC3×C22⋊C16D5
hypocenterC5C3×#2188
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×C22⋊C16

Complements

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

NH ≅ G/Ntype
3. C2×C3×Dic40C2semidirect
5. C3×#64723C2semidirect
6. #10599906C3direct (N × H)
21. C2×Dic40C2×C3semidirect
23. #64723C2×C3semidirect
111. C22×C3×C5Q32semidirect
186. C22×C5C3×Q32semidirect
212. C3×C5#2188semidirect
215. C22×C3Dic40semidirect
247. C5C3×#2188semidirect
250. C22C3×Dic40semidirect
258. C3#10599906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic202
C3×#654052
C2×C3×Dic402
C3×C5×C22⋊C162
C3×#647232
#105999063
C3×#21885