Finite Group Databasebeta

← C3×#10602736 #14288849

Subgroups — C3×#10602736 #14288849

Order 1920.

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

normal subgroups only

This group has 480 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, complemented
2C3×#65362C211yesmaximal, characteristic
3C3×#65316C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C212yesmaximal, complemented
6#10602736C311yesmaximal, 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×#688—22no—
13C2×C3×#686—22no—
14C3×#4020C2211yescharacteristic
15C3×#3941—22no—
16C3×C4⋊#168C2212yes—
17C3×C4×#168C2211yescharacteristic
18C3×#1620—51nomaximal, Hall
19C5×#559C2×C311yescharacteristic, complemented
20#65362C2×C311yescharacteristic
21#65316C2×C312yescomplemented
22#64764C2×C311yescharacteristic, complemented
23Q8⋊#168C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×C3×D20—21no—
29C2×C3×D20—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C5×C22⋊C4—24no—
33C3×C5×C22⋊C4—22no—
34C3×C42×C5—22no—
35C3×C42×C5C2311yescharacteristic
36C3×#688—44no—
37C3×#686—44no—
38C2×C3×#168—21no—
39C2×C3×#168—22no—
40C3×#559D511yescharacteristic, complemented
41C3×#493—51no—
42C3×#460—52no—
43C3×#331—51no—
44C3×Q8⋊C8—52no—
45C5×#127C22×C311yescharacteristic
46C5×#124—22no—
47C5×#123—22no—
48C4×C5×Q8C22×C312yes—
49C4×C5×D4—22no—
50C2×#688—22no—
51C2×#686—22no—
52#4020C22×C311yescharacteristic
53#3941—22no—
54C4⋊#168C22×C312yes—
55C4×#168C22×C311yescharacteristic
56#1620—51noSylow
57C23×C3×C5—22no—
58C22×C3×D5—41no—
59C3×C5×Q8—22no—
60C3×C5×Q8—22no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C3×C5×D4—42no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5—82no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69C3×D20—42no—
70C3×D20—42no—
71C3×D20—42no—
72C3×#168—22no—
73C3×#168—42no—
74C2×C3×SD16—102no—
75C2×C3×D8—102no—
76C3×#127—51no—
77C3×#127C2×D511yescharacteristic
78C3×#124—22no—
79C3×#123—22no—
80C3×C4×Q8C2×D512yes—
81C3×C4×D4—22no—
82C3×C4⋊C8—52no—
83C3×#102—102no—
84C3×C4×C8—51no—
85C2×C5×Q8C3×D412yes—
86C2×C5×D4—22no—
87C2×C5×D4C3×D412yes—
88C22×C4×C5—22no—
89C2×D20—22no—
90C2×D20—21no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4C3×D412yes—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—22no—
95C42×C5—22no—
96C42×C5C23×C311yescharacteristic
97#688—44no—
98#686—44no—
99C2×#168—21no—
100C2×#168—22no—
101#559C3×D511yescharacteristic, complemented
102#493—51no—
103#460—52no—
104#331—51no—
105Q8⋊C8—52no—
106C22×C3×C5—44no—
107C22×C3×C5—42no—
108C22×C3×C5#12011yescharacteristic
109C2×C3×D5—82no—
110C2×C3×D5—81no—
111C3×C4×C5—21no—
112C3×C4×C5—42no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116C2×C3×Q8C22⋊D512yes—
117C2×C3×D4—22no—
118C2×C3×D4—102no—
119C2×C3×D4—101no—
120C2×C3×D4C22⋊D512yes—
121C22×C3×C4—22no—
122C3×SD16—204no—
123C3×D8—204no—
124C2×C3×C8—101no—
125C2×C3×C8—102no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4C22⋊D512yes—
128C3×C22⋊C4—24no—
129C3×C22⋊C4—22no—
130C3×C42—22no—
131C3×C42C22×D511yescharacteristic
132C23×C5—22no—
133C22×D5—41no—
134C5×Q8—22no—
135C5×Q8—22no—
136C5×D4—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—82no—
142C2×C4×C5C2×C3×D411yescharacteristic
143C2×C4×C5C2×C3×D412yes—
144D20—42no—
145D20—42no—
146D20—42no—
147#168—22no—
148#168—42no—
149C2×SD16—102no—
150C2×D8—102no—
151#127—51no—
152#127C2×C3×D511yescharacteristic
153#124—22no—
154#123—22no—
155C4×Q8C2×C3×D512yes—
156C4×D4—22no—
157C4⋊C8—52no—
158#102—102no—
159C4×C8—51no—
160C2×C3×C5—82no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163C3×D5—161no—
164C23×C3—22no—
165C23×C3—201no—
166C3×Q8—22no—
167C3×Q8—22no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—42no—
171C3×D4—202no—
172C3×D4—202no—
173C3×D4—202no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—82no—
177C2×C3×C4C2×C22⋊D511yescharacteristic
178C2×C3×C4C2×C22⋊D512yes—
179C3×C8—102no—
180C3×C8—202no—
181C22×C5—44no—
182C22×C5—42no—
183C22×C5C3×#12011yescharacteristic
184C2×D5—82no—
185C2×D5—81no—
186C4×C5—21no—
187C4×C5—42no—
188C4×C5—42no—
189C4×C5C3×#13512yes—
190C4×C5C3×AGL(1,ℤ/8)12yes—
191C2×Q8C3×C22⋊D512yes—
192C2×D4—22no—
193C2×D4—102no—
194C2×D4—101no—
195C2×D4C3×C22⋊D512yes—
196C22×C4—22no—
197SD16—204no—
198D8—204no—
199C2×C8—101no—
200C2×C8—102no—
201C4⋊C4—22no—
202C4⋊C4C3×C22⋊D512yes—
203C22⋊C4—24no—
204C22⋊C4—22no—
205C42—22no—
206C42C22×C3×D511yescharacteristic
207C3×C5#162011yescharacteristic, complemented, Hall
208C22×C3—44no—
209C22×C3—42no—
210C22×C3—402no—
211C22×C3—401no—
212C22×C3#409911yescharacteristic
213C3×C4—21no—
214C3×C4—42no—
215C3×C4—42no—
216C3×C4#409512yes—
217C3×C4#409612yes—
218C2×C5—82no—
219C2×C5C3×#44912yes—
220C2×C5C3×#45311yescharacteristic
221D5—161no—
222C23—22no—
223C23—201no—
224Q8—22no—
225Q8—22no—
226D4—42no—
227D4—42no—
228D4—42no—
229D4—202no—
230D4—202no—
231D4—202no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—82no—
235C2×C4C2×C3×C22⋊D511yescharacteristic
236C2×C4C2×C3×C22⋊D512yes—
237C8—102no—
238C8—202no—
239C2×C3—82no—
240C2×C3—801no—
241C2×C3#6552712yes—
242C2×C3#6553011yescharacteristic
243C5C3×#162011yescharacteristic, complemented, Sylow
244C22—44no—
245C22—42no—
246C22—402no—
247C22—401no—
248C22C3×#409911yescharacteristic
249C4—21no—
250C4—42no—
251C4—42no—
252C4C3×#409512yes—
253C4C3×#409612yes—
254C3#1060273611yescharacteristic, direct product factor, Sylow
255C2—82no—
256C2—801no—
257C2C3×#6552712yes—
258C2C3×#6553011yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#559C2
socleC22×C3×C5#120
prime radicalC3×#65362C2
hypercenterC3×#559D5
hypocenterC5C3×#1620
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
1. C3×C5×#559C2semidirect
3. C3×#65316C2semidirect
4. C3×#64764C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #10602736C3direct (N × H)
19. C5×#559C2×C3semidirect
21. #65316C2×C3semidirect
22. #64764C2×C3semidirect
23. Q8⋊#168C2×C3semidirect
40. C3×#559D5semidirect
101. #559C3×D5semidirect
207. C3×C5#1620semidirect
243. C5C3×#1620semidirect
254. C3#10602736direct (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×#653622
C3×#653162
C3×#647642
C3×Q8⋊#1682
#106027363
C3×#16205