Finite Group Databasebeta

← C3×#10602733 #14289548

Subgroups — C3×#10602733 #14289548

Order 1920.

412 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 130 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×Q82C211yesmaximal, characteristic
2C3×#65381C211yesmaximal, characteristic
3C3×#65310C212yesmaximal
4C3×#64766C211yesmaximal, characteristic
5C3×Q8⋊#168C212yesmaximal
6#10602733C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8—22no—
8C3×C5×C4⋊Q8—22no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8—22no—
11C3×C4×C5×Q8C2212yes—
12C2×C3×#689—22no—
13C3×#4015C2211yescharacteristic
14C3×#3967—22no—
15C3×#3939—22no—
16C3×C4⋊#168C2212yes—
17C3×C4×#168C2211yescharacteristic
18C3×#1633—51nomaximal, Hall
19C5×Q82C2×C311yescharacteristic
20#65381C2×C311yescharacteristic
21#65310C2×C312yes—
22#64766C2×C311yescharacteristic
23Q8⋊#168C2×C312yes—
24C2×C3×C5×Q8—22no—
25C2×C3×C5×Q8D412yes—
26C2×C3×C5×Q8D412yes—
27C2×C3×Dic10—21no—
28C3×C5×C4⋊C4—24no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35C3×#689—44no—
36C3×C4⋊Dic5—22no—
37C2×C3×#168—21no—
38C2×C3×#168—22no—
39C3×Q82D511yescharacteristic
40C3×#494—51no—
41C3×#477—52no—
42C3×#333—51no—
43C3×Q8⋊C8—52no—
44C5×C4⋊Q8—22no—
45C5×C4⋊Q8—22no—
46C5×C4⋊Q8C22×C311yescharacteristic
47C4×C5×Q8—22no—
48C4×C5×Q8C22×C312yes—
49C2×#689—22no—
50#4015C22×C311yescharacteristic
51#3967—22no—
52#3939—22no—
53C4⋊#168C22×C312yes—
54C4×#168C22×C311yescharacteristic
55#1633—51noSylow
56C3×C5×Q8—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—82no—
59C3×C5×Q8Q1614yescomplemented
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×C4×C5C2×D412yes—
65C2×C3×Dic5—41no—
66C3×Dic10—42no—
67C3×#168—22no—
68C3×#168—42no—
69C2×C3×Q16—102no—
70C3×C4⋊Q8—22no—
71C3×C4⋊Q8—22no—
72C3×C4⋊Q8—51no—
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×C4×Q8—22no—
75C3×C4×Q8C2×D512yes—
76C3×#107—102no—
77C3×C4⋊C8—52no—
78C3×#103—102no—
79C3×C4×C8—51no—
80C2×C5×Q8—22no—
81C2×C5×Q8C3×D412yes—
82C2×C5×Q8C3×D412yes—
83C2×Dic10—21no—
84C5×C4⋊C4—24no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4C3×D412yes—
88C42×C5—22no—
89C42×C5—22no—
90C42×C5C23×C311yescharacteristic
91#689—44no—
92C4⋊Dic5—22no—
93C2×#168—21no—
94C2×#168—22no—
95Q82C3×D511yescharacteristic
96#494—51no—
97#477—52no—
98#333—51no—
99Q8⋊C8—52no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—24no—
102C3×C4×C5—21no—
103C3×C4×C5—42no—
104C3×C4×C5—42no—
105C3×C4×C5C2×Q1612yes—
106C3×C4×C5#13712yes—
107C3×Dic5—81no—
108C2×C3×Q8—22no—
109C2×C3×Q8—101no—
110C2×C3×Q8C22⋊D512yes—
111C2×C3×Q8C22⋊D512yes—
112C3×Q16—204no—
113C2×C3×C8—101no—
114C2×C3×C8—102no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—102no—
119C3×C4⋊C4C22⋊D512yes—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42C22×D511yescharacteristic
123C5×Q8—22no—
124C5×Q8—42no—
125C5×Q8—82no—
126C5×Q8C3×Q1614yescomplemented
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5C2×C3×D411yescharacteristic
131C2×C4×C5C2×C3×D412yes—
132C2×Dic5—41no—
133Dic10—42no—
134#168—22no—
135#168—42no—
136C2×Q16—102no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—51no—
140C4⋊Q8C2×C3×D511yescharacteristic
141C4×Q8—22no—
142C4×Q8C2×C3×D512yes—
143#107—102no—
144C4⋊C8—52no—
145#103—102no—
146C4×C8—51no—
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—22no—
150C3×Q8—42no—
151C3×Q8—82no—
152C3×Q8—202no—
153C3×Q8#68914yescomplemented
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—201no—
158C2×C3×C4C2×C22⋊D511yescharacteristic
159C2×C3×C4C2×C22⋊D512yes—
160C3×C8—102no—
161C3×C8—202no—
162C22×C5C3×#12011yescharacteristic
163C4×C5—24no—
164C4×C5—21no—
165C4×C5—42no—
166C4×C5—42no—
167C4×C5C2×C3×Q1612yes—
168C4×C5C3×#13712yes—
169Dic5—81no—
170C2×Q8—22no—
171C2×Q8—101no—
172C2×Q8C3×C22⋊D512yes—
173C2×Q8C3×C22⋊D512yes—
174Q16—204no—
175C2×C8—101no—
176C2×C8—102no—
177C4⋊C4—24no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—102no—
181C4⋊C4C3×C22⋊D512yes—
182C42—22no—
183C42—22no—
184C42C22×C3×D511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#409911yescharacteristic
187C3×C4—24no—
188C3×C4—21no—
189C3×C4—42no—
190C3×C4—42no—
191C3×C4—401no—
192C3×C4#408812yes—
193C3×C4C2×#68912yes—
194C2×C5C3×#45112yes—
195C2×C5C3×#45311yescharacteristic
196Q8—22no—
197Q8—42no—
198Q8—82no—
199Q8—202no—
200Q8C3×#68914yescomplemented
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—201no—
205C2×C4C2×C3×C22⋊D511yescharacteristic
206C2×C4C2×C3×C22⋊D512yes—
207C8—102no—
208C8—202no—
209C2×C3#6551712yes—
210C2×C3#6553011yescharacteristic
211C5C3×#163311yescharacteristic, complemented, Sylow
212C22C3×#409911yescharacteristic
213C4—24no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—401no—
218C4C3×#408812yes—
219C4C2×C3×#68912yes—
220C3#1060273311yescharacteristic, direct product factor, Sylow
221C2C3×#6551712yes—
222C2C3×#6553011yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q82C2
socle, prime radicalC22×C3×C5#120
hypercenterC3×Q82D5
hypocenterC5C3×#1633
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q82

Complements

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

NH ≅ G/Ntype
6. #10602733C3direct (N × H)
59. C3×C5×Q8Q16semidirect
126. C5×Q8C3×Q16semidirect
153. C3×Q8#689semidirect
185. C3×C5#1633semidirect
200. Q8C3×#689semidirect
211. C5C3×#1633semidirect
220. C3#10602733direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×Q822
C3×#653812
C3×#653102
C3×#647662
C3×Q8⋊#1682
#106027333
C3×#16335