Finite Group Databasebeta

← C3×#10602062 #14289008

Subgroups — C3×#10602062 #14289008

Order 1920.

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

normal subgroups only

This group has 456 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×#66056C211yesmaximal, characteristic, complemented
2C3×C5×#492C211yesmaximal, characteristic
3C3×#65364C212yesmaximal
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×#64676C212yesmaximal, complemented
6#10602062C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×SD16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10C3×#4090—22no—
11C2×C3×#687—22no—
12C3×#4034—22no—
13C3×#4033—22no—
14C3×C4×Dic10C2212yes—
15C3×C4×C5×C8C2211yescharacteristic
16C3×#3964—22no—
17C3×C4⋊#168C2212yes—
18C3×#1623—51nomaximal, Hall
19#66056C2×C311yescharacteristic, complemented
20C5×#492C2×C311yescharacteristic
21#65364C2×C312yes—
22#64766C2×C311yescharacteristic, complemented
23#64676C2×C312yescomplemented
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—21no—
27C2×C3×Dic10—22no—
28C2×C3×Dic10D412yes—
29C3×C5×SD16—44no—
30C2×C3×C5×C8—21no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C3×#687—44no—
34C3×C4⋊Dic5D412yes—
35C3×#683—24no—
36C3×#683—22no—
37C3×C4×Dic5—22no—
38C3×C4×Dic5—22no—
39C2×C3×#168—22no—
40C3×Q82—51no—
41C3×#492D511yescharacteristic
42C3×#460—52no—
43C3×#333—51no—
44C3×Q8⋊C8—52no—
45C2×C5×SD16—22no—
46C5×C4⋊Q8C22×C311yescharacteristic
47C5×#127C22×C311yescharacteristic
48#4090—22no—
49C2×#687—22no—
50#4034—22no—
51#4033—22no—
52C4×Dic10C22×C312yes—
53C4×C5×C8C22×C311yescharacteristic
54#3964—22no—
55C4⋊#168C22×C312yes—
56#1623—51noSylow
57C23×C3×C5—41no—
58C3×C5×Q8—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×C4×C5C2×D412yes—
65C2×C3×Dic5—22no—
66C2×C3×Dic5—22no—
67C3×Dic10—22no—
68C3×Dic10—82no—
69C3×Dic10SD1614yescomplemented
70C3×C5×C8—22no—
71C3×#168—42no—
72C2×C3×SD16—22no—
73C2×C3×SD16—102no—
74C3×C4⋊Q8—102no—
75C3×C4⋊Q8—102no—
76C3×C4⋊Q8C2×D511yescharacteristic
77C3×#127C2×D511yescharacteristic
78C3×C4×Q8—52no—
79C3×C4×Q8—102no—
80C3×C4⋊C8—52no—
81C3×#102—102no—
82C3×C4×C8C2×D511yescharacteristic
83C2×C5×Q8C3×D412yes—
84C2×C5×D4—21no—
85C2×C5×D4—22no—
86C2×Dic10—22no—
87C2×Dic10C3×D412yes—
88C5×SD16—44no—
89C2×C5×C8—21no—
90C5×C4⋊C4—22no—
91C42×C5C23×C311yescharacteristic
92#687—44no—
93C4⋊Dic5C3×D412yes—
94#683—24no—
95#683—22no—
96C4×Dic5—22no—
97C4×Dic5—22no—
98C2×#168—22no—
99Q82—51no—
100#492C3×D511yescharacteristic
101#460—52no—
102#333—51no—
103Q8⋊C8—52no—
104C22×C3×C5—82no—
105C22×C3×C5—81no—
106C22×C3×C5#12011yescharacteristic
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111C3×Dic5—24no—
112C3×Dic5—42no—
113C2×C3×Q8—52no—
114C2×C3×Q8—102no—
115C2×C3×Q8C22⋊D512yes—
116C2×C3×D4—22no—
117C2×C3×D4—21no—
118C3×SD16—44no—
119C3×SD16—204no—
120C2×C3×C8—21no—
121C2×C3×C8—102no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—52no—
124C3×C4⋊C4—104no—
125C3×C4⋊C4—102no—
126C3×C42—102no—
127C3×C42—102no—
128C3×C42C22×D511yescharacteristic
129C23×C5—41no—
130C5×Q8—42no—
131C5×D4—42no—
132C5×D4—42no—
133C5×D4—42no—
134C2×C4×C5—22no—
135C2×C4×C5C2×C3×D412yes—
136C2×C4×C5C2×C3×D411yescharacteristic
137C2×Dic5—22no—
138C2×Dic5—22no—
139Dic10—22no—
140Dic10—82no—
141Dic10C3×SD1614yescomplemented
142C5×C8—22no—
143#168—42no—
144C2×SD16—22no—
145C2×SD16—102no—
146C4⋊Q8—102no—
147C4⋊Q8—102no—
148C4⋊Q8C2×C3×D511yescharacteristic
149#127C2×C3×D511yescharacteristic
150C4×Q8—52no—
151C4×Q8—102no—
152C4⋊C8—52no—
153#102—102no—
154C4×C8C2×C3×D511yescharacteristic
155C2×C3×C5—161no—
156C2×C3×C5#44812yes—
157C2×C3×C5#45311yescharacteristic
158C23×C3—41no—
159C3×Q8—42no—
160C3×Q8—54no—
161C3×Q8—102no—
162C3×Q8—402no—
163C3×D4—42no—
164C3×D4—42no—
165C3×D4—42no—
166C2×C3×C4—22no—
167C2×C3×C4—102no—
168C2×C3×C4—102no—
169C2×C3×C4D4×D512yes—
170C2×C3×C4C2×C22⋊D511yescharacteristic
171C3×C8—22no—
172C3×C8—202no—
173C22×C5—82no—
174C22×C5—81no—
175C22×C5C3×#12011yescharacteristic
176C4×C5—21no—
177C4×C5—42no—
178C4×C5C2×C3×SD1612yes—
179C4×C5C3×#13712yes—
180Dic5—24no—
181Dic5—42no—
182C2×Q8—52no—
183C2×Q8—102no—
184C2×Q8C3×C22⋊D512yes—
185C2×D4—22no—
186C2×D4—21no—
187SD16—44no—
188SD16—204no—
189C2×C8—21no—
190C2×C8—102no—
191C4⋊C4—22no—
192C4⋊C4—52no—
193C4⋊C4—104no—
194C4⋊C4—102no—
195C42—102no—
196C42—102no—
197C42C22×C3×D511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3—81no—
200C22×C3—82no—
201C22×C3#408311yescharacteristic
202C3×C4—21no—
203C3×C4—42no—
204C3×C4—104no—
205C3×C4—202no—
206C3×C4D5×SD1612yes—
207C3×C4#406112yes—
208C2×C5—161no—
209C2×C5C3×#44812yes—
210C2×C5C3×#45311yescharacteristic
211C23—41no—
212Q8—42no—
213Q8—54no—
214Q8—102no—
215Q8—402no—
216D4—42no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4C3×D4×D512yes—
223C2×C4C2×C3×C22⋊D511yescharacteristic
224C8—22no—
225C8—202no—
226C2×C3—161no—
227C2×C3#6536611yescharacteristic
228C2×C3#6545912yes—
229C5C3×#162311yescharacteristic, complemented, Sylow
230C22—81no—
231C22—82no—
232C22C3×#408311yescharacteristic
233C4—21no—
234C4—42no—
235C4—104no—
236C4—202no—
237C4C3×D5×SD1612yes—
238C4C3×#406112yes—
239C3#1060206211yescharacteristic, direct product factor, Sylow
240C2—161no—
241C2C3×#6536611yescharacteristic
242C2C3×#6545912yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#492C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC3×#492D5
hypocenterC5C3×#1623
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×#66056C2semidirect
4. C3×#64766C2semidirect
5. C3×#64676C2semidirect
6. #10602062C3direct (N × H)
19. #66056C2×C3semidirect
22. #64766C2×C3semidirect
23. #64676C2×C3semidirect
69. C3×Dic10SD16semidirect
141. Dic10C3×SD16semidirect
198. C3×C5#1623semidirect
229. C5C3×#1623semidirect
239. C3#10602062direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660562
C3×C5×#4922
C3×#653642
C3×#647662
C3×#646762
#106020623
C3×#16235