Finite Group Databasebeta

← C3×#10602737 #14289383

Subgroups — C3×#10602737 #14289383

Order 1920.

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

normal subgroups only

This group has 436 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
1C3×C5×#559C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic
3C3×#65310C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic
5C3×Q8⋊#168C212yesmaximal, complemented
6#10602737C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#127C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#123—22no—
10C3×C4×C5×Q8C2212yes—
11C3×C4×C5×D4—22no—
12C2×C3×#687—22no—
13C3×#4015C2211yescharacteristic
14C3×#3967—22no—
15C3×#3939—22no—
16C3×C4⋊#168C2212yes—
17C3×C4×#168C2211yescharacteristic
18C3×#1630—51nomaximal, Hall
19C5×#559C2×C311yescharacteristic
20#65365C2×C311yescharacteristic
21#65310C2×C312yescomplemented
22#64764C2×C311yescharacteristic
23Q8⋊#168C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×C3×Dic10—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C5×C22⋊C4—24no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35C3×#687—44no—
36C3×C4⋊Dic5—22no—
37C2×C3×#168—21no—
38C2×C3×#168—22no—
39C3×#559D511yescharacteristic
40C3×#492—51no—
41C3×#477—52no—
42C3×#331—51no—
43C3×Q8⋊C8—52no—
44C5×#127C22×C311yescharacteristic
45C5×#124—22no—
46C5×#123—22no—
47C4×C5×Q8C22×C312yes—
48C4×C5×D4—22no—
49C2×#687—22no—
50#4015C22×C311yescharacteristic
51#3967—22no—
52#3939—22no—
53C4⋊#168C22×C312yes—
54C4×#168C22×C311yescharacteristic
55#1630—51noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—22no—
58C3×C5×Q8—22no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—82no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×C3×Dic5—41no—
68C3×Dic10—42no—
69C3×#168—22no—
70C3×#168—42no—
71C2×C3×SD16—102no—
72C3×C4⋊Q8—51no—
73C3×#127C2×D511yescharacteristic
74C3×#124—22no—
75C3×#123—22no—
76C3×C4×Q8C2×D512yes—
77C3×C4×D4—22no—
78C3×#107—102no—
79C3×C4⋊C8—52no—
80C3×#103—102no—
81C3×C4×C8—51no—
82C2×C5×Q8C3×D412yes—
83C2×C5×D4—22no—
84C2×C5×D4C3×D412yes—
85C22×C4×C5—22no—
86C2×Dic10—21no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4C3×D412yes—
89C5×C22⋊C4—24no—
90C5×C22⋊C4—22no—
91C42×C5—22no—
92C42×C5C23×C311yescharacteristic
93#687—44no—
94C4⋊Dic5—22no—
95C2×#168—21no—
96C2×#168—22no—
97#559C3×D511yescharacteristic
98#492—51no—
99#477—52no—
100#331—51no—
101Q8⋊C8—52no—
102C22×C3×C5—44no—
103C22×C3×C5—42no—
104C22×C3×C5#12011yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110C3×Dic5—81no—
111C2×C3×Q8—101no—
112C2×C3×Q8C22⋊D512yes—
113C2×C3×D4—22no—
114C2×C3×D4C22⋊D512yes—
115C22×C3×C4—22no—
116C3×SD16—204no—
117C2×C3×C8—101no—
118C2×C3×C8—102no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—102no—
121C3×C4⋊C4C22⋊D512yes—
122C3×C22⋊C4—24no—
123C3×C22⋊C4—22no—
124C3×C42—22no—
125C3×C42C22×D511yescharacteristic
126C23×C5—22no—
127C5×Q8—22no—
128C5×Q8—22no—
129C5×D4—42no—
130C5×D4—42no—
131C5×D4—42no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—82no—
135C2×C4×C5C2×C3×D411yescharacteristic
136C2×C4×C5C2×C3×D412yes—
137C2×Dic5—41no—
138Dic10—42no—
139#168—22no—
140#168—42no—
141C2×SD16—102no—
142C4⋊Q8—51no—
143#127C2×C3×D511yescharacteristic
144#124—22no—
145#123—22no—
146C4×Q8C2×C3×D512yes—
147C4×D4—22no—
148#107—102no—
149C4⋊C8—52no—
150#103—102no—
151C4×C8—51no—
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×Q8—22no—
157C3×Q8—22no—
158C3×Q8—202no—
159C3×D4—42no—
160C3×D4—42no—
161C3×D4—42no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—82no—
165C2×C3×C4—201no—
166C2×C3×C4C2×C22⋊D511yescharacteristic
167C2×C3×C4C2×C22⋊D512yes—
168C3×C8—102no—
169C3×C8—202no—
170C22×C5—44no—
171C22×C5—42no—
172C22×C5C3×#12011yescharacteristic
173C4×C5—21no—
174C4×C5—42no—
175C4×C5—42no—
176C4×C5C3×#13512yes—
177C4×C5C3×#13712yes—
178Dic5—81no—
179C2×Q8—101no—
180C2×Q8C3×C22⋊D512yes—
181C2×D4—22no—
182C2×D4C3×C22⋊D512yes—
183C22×C4—22no—
184SD16—204no—
185C2×C8—101no—
186C2×C8—102no—
187C4⋊C4—22no—
188C4⋊C4—102no—
189C4⋊C4C3×C22⋊D512yes—
190C22⋊C4—24no—
191C22⋊C4—22no—
192C42—22no—
193C42C22×C3×D511yescharacteristic
194C3×C5#163011yescharacteristic, complemented, Hall
195C22×C3—44no—
196C22×C3—42no—
197C22×C3#409911yescharacteristic
198C3×C4—21no—
199C3×C4—42no—
200C3×C4—42no—
201C3×C4—401no—
202C3×C4#409612yes—
203C3×C4#409712yes—
204C2×C5—82no—
205C2×C5C3×#45212yes—
206C2×C5C3×#45311yescharacteristic
207C23—22no—
208Q8—22no—
209Q8—22no—
210Q8—202no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—82no—
217C2×C4—201no—
218C2×C4C2×C3×C22⋊D511yescharacteristic
219C2×C4C2×C3×C22⋊D512yes—
220C8—102no—
221C8—202no—
222C2×C3—82no—
223C2×C3#6552812yes—
224C2×C3#6553011yescharacteristic
225C5C3×#163011yescharacteristic, complemented, Sylow
226C22—44no—
227C22—42no—
228C22C3×#409911yescharacteristic
229C4—21no—
230C4—42no—
231C4—42no—
232C4—401no—
233C4C3×#409612yes—
234C4C3×#409712yes—
235C3#1060273711yescharacteristic, direct product factor, Sylow
236C2—82no—
237C2C3×#6552812yes—
238C2C3×#6553011yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#559C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC3×#559D5
hypocenterC5C3×#1630
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#559

Complements

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

NH ≅ G/Ntype
3. C3×#65310C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #10602737C3direct (N × H)
21. #65310C2×C3semidirect
23. Q8⋊#168C2×C3semidirect
194. C3×C5#1630semidirect
225. C5C3×#1630semidirect
235. C3#10602737direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5592
C3×#653652
C3×#653102
C3×#647642
C3×Q8⋊#1682
#106027373
C3×#16305