Finite Group Databasebeta

← C3×#10602020 #14294138

Subgroups — C3×#10602020 #14294138

Order 1920.

352 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 122 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×C5×#487C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic
3C3×#65381C211yesmaximal, characteristic
4C3×#65368C211yesmaximal, characteristic
5C3×#65367C211yesmaximal, characteristic
6C3×#64971C211yesmaximal, characteristic
7C3×#64674C211yesmaximal, characteristic
8#10602020C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C2×C3×#689—22no—
12C3×#4015C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C3×C5×#103—22no—
15C3×C4×C5×C8C2211yescharacteristic
16C3×#3950—22no—
17C3×#3942—22no—
18C3×#3940—22no—
19C3×#3939—22no—
20C3×C4×#168C2211yescharacteristic
21C3×C4×#168C2211yescharacteristic
22C3×#1723—51nomaximal, Hall
23C5×#487C2×C311yescharacteristic
24#65382C2×C311yescharacteristic
25#65381C2×C311yescharacteristic
26#65368C2×C311yescharacteristic
27#65367C2×C311yescharacteristic
28#64971C2×C311yescharacteristic
29#64674C2×C311yescharacteristic
30C2×C3×C5×Q8—21no—
31C2×C3×C5×Q8—21no—
32C2×C3×Dic10—21no—
33C2×C3×Dic10—21no—
34C2×C3×C5×C8D412yes—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40C3×#689—44no—
41C3×C4⋊Dic5—21no—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C2×C3×#168D412yes—
46C2×C3×#168D412yes—
47C3×#500—51no—
48C3×#500—51no—
49C3×#498—51no—
50C3×#494—51no—
51C3×#487—51no—
52C3×#487D511yescharacteristic
53C3×#322—51no—
54C5×C4⋊Q8C22×C311yescharacteristic
55C5×C4⋊Q8C22×C311yescharacteristic
56C2×#689—22no—
57#4015C22×C311yescharacteristic
58#4015C22×C311yescharacteristic
59C5×#103—22no—
60C4×C5×C8C22×C311yescharacteristic
61#3950—22no—
62#3942—22no—
63#3940—22no—
64#3939—22no—
65C4×#168C22×C311yescharacteristic
66C4×#168C22×C311yescharacteristic
67#1723—51noSylow
68C3×C5×Q8—42no—
69C3×C5×Q8—42no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×Dic5—41no—
76C2×C3×Dic5—41no—
77C3×Dic10—42no—
78C3×Dic10—42no—
79C3×C5×C8—22no—
80C3×#168—22no—
81C3×#168Q1614yescomplemented
82C2×C3×Q16—102no—
83C3×C4⋊Q8—51no—
84C3×C4⋊Q8—51no—
85C3×C4⋊Q8C2×D511yescharacteristic
86C3×C4⋊Q8C2×D511yescharacteristic
87C3×#107—102no—
88C3×#107—102no—
89C3×#106—102no—
90C3×#103—22no—
91C3×#103—102no—
92C3×C4×C8—51no—
93C3×C4×C8—51no—
94C3×C4×C8C2×D511yescharacteristic
95C2×C5×Q8—21no—
96C2×C5×Q8—21no—
97C2×Dic10—21no—
98C2×Dic10—21no—
99C2×C5×C8C3×D412yes—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C42×C5C23×C311yescharacteristic
105#689—44no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109C4⋊Dic5—21no—
110C2×#168C3×D412yes—
111C2×#168C3×D412yes—
112#500—51no—
113#500—51no—
114#498—51no—
115#494—51no—
116#487—51no—
117#487C3×D511yescharacteristic
118#322—51no—
119C22×C3×C5#12711yescharacteristic
120C3×C4×C5—81no—
121C3×C4×C5—81no—
122C3×C4×C5C2×Q1612yes—
123C3×C4×C5AGL(1,ℤ/8)12yes—
124C3×C4×C5#13712yes—
125C3×Dic5—81no—
126C3×Dic5—81no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×Q8—101no—
130C2×C3×Q8—101no—
131C3×Q16—204no—
132C2×C3×C8—52no—
133C2×C3×C8—52no—
134C2×C3×C8C22⋊D512yes—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—101no—
140C3×C4⋊C4—101no—
141C3×C4⋊C4—101no—
142C3×C4⋊C4—101no—
143C3×C42C22×D511yescharacteristic
144C5×Q8—42no—
145C5×Q8—42no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5C2×C3×D411yescharacteristic
149C2×C4×C5C2×C3×D411yescharacteristic
150C2×C4×C5C2×C3×D411yescharacteristic
151C2×Dic5—41no—
152C2×Dic5—41no—
153Dic10—42no—
154Dic10—42no—
155C5×C8—22no—
156#168—22no—
157#168C3×Q1614yescomplemented
158C2×Q16—102no—
159C4⋊Q8—51no—
160C4⋊Q8—51no—
161C4⋊Q8C2×C3×D511yescharacteristic
162C4⋊Q8C2×C3×D511yescharacteristic
163#107—102no—
164#107—102no—
165#106—102no—
166#103—22no—
167#103—102no—
168C4×C8—51no—
169C4×C8—51no—
170C4×C8C2×C3×D511yescharacteristic
171C2×C3×C5#49411yescharacteristic
172C2×C3×C5#49611yescharacteristic
173C2×C3×C5#49711yescharacteristic
174C3×Q8—42no—
175C3×Q8—42no—
176C3×Q8—202no—
177C3×Q8—202no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—201no—
181C2×C3×C4—201no—
182C2×C3×C4D4×D511yescharacteristic
183C2×C3×C4D4×D511yescharacteristic
184C2×C3×C4C2×C22⋊D511yescharacteristic
185C3×C8—22no—
186C3×C8—54no—
187C3×C8—102no—
188C22×C5C3×#12711yescharacteristic
189C4×C5—81no—
190C4×C5—81no—
191C4×C5C2×C3×Q1612yes—
192C4×C5C3×AGL(1,ℤ/8)12yes—
193C4×C5C3×#13712yes—
194Dic5—81no—
195Dic5—81no—
196C2×Q8—21no—
197C2×Q8—21no—
198C2×Q8—101no—
199C2×Q8—101no—
200Q16—204no—
201C2×C8—52no—
202C2×C8—52no—
203C2×C8C3×C22⋊D512yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—101no—
209C4⋊C4—101no—
210C4⋊C4—101no—
211C4⋊C4—101no—
212C42C22×C3×D511yescharacteristic
213C3×C5#172311yescharacteristic, complemented, Hall
214C22×C3#408611yescharacteristic
215C3×C4—81no—
216C3×C4—81no—
217C3×C4—401no—
218C3×C4—401no—
219C3×C4#406012yes—
220C3×C4D5×Q1612yes—
221C3×C4#409712yes—
222C2×C5C3×#49411yescharacteristic
223C2×C5C3×#49611yescharacteristic
224C2×C5C3×#49711yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—202no—
228Q8—202no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—201no—
232C2×C4—201no—
233C2×C4C3×D4×D511yescharacteristic
234C2×C4C3×D4×D511yescharacteristic
235C2×C4C2×C3×C22⋊D511yescharacteristic
236C8—22no—
237C8—54no—
238C8—102no—
239C2×C3#6534911yescharacteristic
240C2×C3#6546511yescharacteristic
241C2×C3#6547011yescharacteristic
242C5C3×#172311yescharacteristic, complemented, Sylow
243C22C3×#408611yescharacteristic
244C4—81no—
245C4—81no—
246C4—401no—
247C4—401no—
248C4C3×#406012yes—
249C4C3×D5×Q1612yes—
250C4C3×#409712yes—
251C3#1060202011yescharacteristic, direct product factor, Sylow
252C2C3×#6534911yescharacteristic
253C2C3×#6546511yescharacteristic
254C2C3×#6547011yescharacteristic
subgroupG/H
centerC22×C3#4086
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#487C2
socle, prime radicalC22×C3×C5#127
hypercenterC3×#487D5
hypocenterC5C3×#1723
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
8. #10602020C3direct (N × H)
81. C3×#168Q16semidirect
157. #168C3×Q16semidirect
213. C3×C5#1723semidirect
242. C5C3×#1723semidirect
251. C3#10602020direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4872
C3×#653822
C3×#653812
C3×#653682
C3×#653672
C3×#649712
C3×#646742
#106020203
C3×#17235