Finite Group Databasebeta

← C3×#10602123 #14291035

Subgroups — C3×#10602123 #14291035

Order 1920.

392 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 90 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×#66006C211yesmaximal, characteristic
2C3×C5×#497C211yesmaximal, characteristic
3C3×#65369C212yesmaximal, complemented
4C3×#64760C211yesmaximal, characteristic
5C3×#64685C212yesmaximal, complemented
6#10602123C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×SD16—21no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11C3×#4090—21no—
12C3×#4081—21no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016C2212yes—
16C3×C5×#97C2211yescharacteristic
17C3×#3940—22no—
18C3×#3939—22no—
19C3×#3935C2212yes—
20C3×#1660—51nomaximal, Hall
21#66006C2×C311yescharacteristic
22C5×#497C2×C311yescharacteristic
23#65369C2×C312yescomplemented
24#64760C2×C311yescharacteristic
25#64685C2×C312yescomplemented
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×Dic5—21no—
30C2×C3×Dic10—21no—
31C3×C5×Q16—42no—
32C3×C5×SD16—42no—
33C2×C3×C5×C8—21no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37C3×C22⋊Dic5—22no—
38C3×C22⋊Dic5—21no—
39C3×C4⋊Dic5D412yes—
40C3×C4⋊Dic5D412yes—
41C3×#683—22no—
42C3×#683—22no—
43C3×#683—22no—
44C3×C4×Dic5—21no—
45C2×C3×#168—22no—
46C3×#563—51no—
47C3×#501—52no—
48C3×#497D511yescharacteristic
49C3×#330—52no—
50C3×#329—51no—
51C2×C5×Q16—21no—
52C2×C5×SD16—21no—
53C5×C4⋊Q8C22×C311yescharacteristic
54C5×#124C22×C311yescharacteristic
55#4090—21no—
56#4081—21no—
57#4025—22no—
58#4024—22no—
59#4016C22×C312yes—
60C5×#97C22×C311yescharacteristic
61#3940—22no—
62#3939—22no—
63#3935C22×C312yes—
64#1660—51noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×Q8—41no—
68C3×C5×Q8—41no—
69C3×C5×D4—41no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—81no—
77C3×Dic10—81no—
78C3×C5×C8—22no—
79C3×#168—24no—
80C2×C3×Q16—21no—
81C2×C3×SD16—21no—
82C3×C4⋊Q8—101no—
83C3×C4⋊Q8C2×D511yescharacteristic
84C3×#126—102no—
85C3×#125—52no—
86C3×#124C2×D511yescharacteristic
87C3×#123—101no—
88C3×C22⋊Q8—102no—
89C3×#107—102no—
90C3×#106—102no—
91C3×#97—52no—
92C3×#97C2×D511yescharacteristic
93C2×C5×Q8—21no—
94C2×C5×Q8C3×D411yescharacteristic
95C2×C5×D4C3×D411yescharacteristic
96C22×Dic5—21no—
97C2×Dic10—21no—
98C5×Q16—42no—
99C5×SD16—42no—
100C2×C5×C8—21no—
101C5×C4⋊C4—22no—
102C5×C22⋊C4—22no—
103C42×C5C23×C311yescharacteristic
104C22⋊Dic5—22no—
105C22⋊Dic5—21no—
106C4⋊Dic5C3×D412yes—
107C4⋊Dic5C3×D412yes—
108#683—22no—
109#683—22no—
110#683—22no—
111C4×Dic5—21no—
112C2×#168—22no—
113#563—51no—
114#501—52no—
115#497C3×D511yescharacteristic
116#330—52no—
117#329—51no—
118C22×C3×C5—41no—
119C22×C3×C5—42no—
120C22×C3×C5#12011yescharacteristic
121C3×C4×C5—21no—
122C3×C4×C5—22no—
123C3×C4×C5—41no—
124C3×C4×C5—81no—
125C3×Dic5—42no—
126C3×Dic5—42no—
127C2×C3×Q8—21no—
128C2×C3×Q8—101no—
129C2×C3×Q8C22⋊D511yescharacteristic
130C2×C3×D4C22⋊D511yescharacteristic
131C22×C3×C4—101no—
132C3×Q16—42no—
133C3×SD16—42no—
134C2×C3×C8—21no—
135C2×C3×C8—102no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—52no—
138C3×C4⋊C4—52no—
139C3×C4⋊C4—102no—
140C3×C4⋊C4—102no—
141C3×C4⋊C4—102no—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—102no—
144C3×C22⋊C4—101no—
145C3×C42—101no—
146C3×C42C22×D511yescharacteristic
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—41no—
150C5×Q8—41no—
151C5×D4—41no—
152C2×C4×C5—21no—
153C2×C4×C5—41no—
154C2×C4×C5C2×C3×D412yes—
155C2×C4×C5C2×C3×D411yescharacteristic
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—81no—
159Dic10—81no—
160C5×C8—22no—
161#168—24no—
162C2×Q16—21no—
163C2×SD16—21no—
164C4⋊Q8—101no—
165C4⋊Q8C2×C3×D511yescharacteristic
166#126—102no—
167#125—52no—
168#124C2×C3×D511yescharacteristic
169#123—101no—
170C22⋊Q8—102no—
171#107—102no—
172#106—102no—
173#97—52no—
174#97C2×C3×D511yescharacteristic
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—41no—
182C3×Q8—401no—
183C3×D4—41no—
184C2×C3×C4—21no—
185C2×C3×C4—41no—
186C2×C3×C4—102no—
187C2×C3×C4—102no—
188C2×C3×C4—401no—
189C2×C3×C4D4×D512yes—
190C2×C3×C4C2×C22⋊D511yescharacteristic
191C3×C8—22no—
192C3×C8—104no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5C3×#12011yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—41no—
199C4×C5—81no—
200Dic5—42no—
201Dic5—42no—
202C2×Q8—21no—
203C2×Q8—101no—
204C2×Q8C3×C22⋊D511yescharacteristic
205C2×D4C3×C22⋊D511yescharacteristic
206C22×C4—101no—
207Q16—42no—
208SD16—42no—
209C2×C8—21no—
210C2×C8—102no—
211C4⋊C4—22no—
212C4⋊C4—52no—
213C4⋊C4—52no—
214C4⋊C4—102no—
215C4⋊C4—102no—
216C4⋊C4—102no—
217C22⋊C4—22no—
218C22⋊C4—102no—
219C22⋊C4—101no—
220C42—101no—
221C42C22×C3×D511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#408311yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—81no—
230C3×C4—202no—
231C3×C4—202no—
232C2×C5—81no—
233C2×C5C3×#45311yescharacteristic
234C2×C5C3×#45612yes—
235C23—21no—
236Q8—41no—
237Q8—41no—
238Q8—41no—
239Q8—401no—
240D4—41no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—102no—
244C2×C4—102no—
245C2×C4—401no—
246C2×C4C3×D4×D512yes—
247C2×C4C2×C3×C22⋊D511yescharacteristic
248C8—22no—
249C8—104no—
250C2×C3—81no—
251C2×C3#6536611yescharacteristic
252C2×C3#6549412yes—
253C5C3×#166011yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22C3×#408311yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—81no—
261C4—202no—
262C4—202no—
263C3#1060212311yescharacteristic, direct product factor, Sylow
264C2—81no—
265C2C3×#6536611yescharacteristic
266C2C3×#6549412yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#497C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#497D5
hypocenterC5C3×#1660
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#497

Complements

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

NH ≅ G/Ntype
3. C3×#65369C2semidirect
5. C3×#64685C2semidirect
6. #10602123C3direct (N × H)
23. #65369C2×C3semidirect
25. #64685C2×C3semidirect
222. C3×C5#1660semidirect
253. C5C3×#1660semidirect
263. C3#10602123direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660062
C3×C5×#4972
C3×#653692
C3×#647602
C3×#646852
#106021233
C3×#16605