Finite Group Databasebeta

← C3×#10604350 #14284013

Subgroups — C3×#10604350 #14284013

Order 1920.

452 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 124 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×#65851C211yesmaximal, characteristic
2C3×C4×#704C212yesmaximal
3C3×#64870C214yesmaximal, complemented
4#10604350C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#704—22no—
6C3×C5×#117C411yescharacteristic
7C3×#4072C411yescharacteristic
8C2×C3×C4×Dic5C2211yescharacteristic
9C3×#4036C2212yes—
10C3×#4034C412yes—
11C3×#4024—22no—
12C3×C4×Dic10—22no—
13C3×#4002C2214yes—
14C3×C4×#170—22no—
15C3×#1526—51nomaximal, Hall
16#65851C2×C311yescharacteristic
17C4×#704C2×C312yes—
18#64870C2×C314yescomplemented
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×Dic5D412yes—
21C2×C3×Dic10—22no—
22C3×#704—28no—
23C2×C3×#170—24no—
24C3×C5×C4⋊C4C2×C412yes—
25C3×C5×C22⋊C4—21no—
26C3×C42×C5—21no—
27C3×C22⋊Dic5—21no—
28C3×C4⋊Dic5—22no—
29C3×C4⋊Dic5C2×C412yes—
30C3×#683—22no—
31C3×#683—22no—
32C3×C4×Dic5—21no—
33C3×C4×Dic5C2×C411yescharacteristic
34C3×C4×Dic5D412yes—
35C3×C4×Dic5C2311yescharacteristic
36C3×#533—51no—
37C3×C4×M16—52no—
38C3×#330—54no—
39C2×#704—22no—
40C5×#117C3×C411yescharacteristic
41#4072C3×C411yescharacteristic
42C2×C4×Dic5C22×C311yescharacteristic
43#4036C22×C312yes—
44#4034C3×C412yes—
45#4024—22no—
46C4×Dic10—22no—
47#4002C22×C314yes—
48C4×#170—22no—
49#1526—51noSylow
50C23×C3×C5C22⋊C411yescharacteristic
51C2×C3×C4×C5—22no—
52C2×C3×C4×C5—22no—
53C2×C3×C4×C5C22⋊C411yescharacteristic
54C2×C3×C4×C5C22×C411yescharacteristic
55C2×C3×Dic5—24no—
56C2×C3×Dic5—22no—
57C2×C3×Dic5C22⋊C412yes—
58C2×C3×Dic5C2×D412yes—
59C3×Dic10—44no—
60C3×#170—28no—
61C2×C3×M16—102no—
62C3×C4⋊Q8—52no—
63C3×#125—52no—
64C3×C22⋊Q8—102no—
65C3×C4×Q8—102no—
66C3×#117—51no—
67C3×#117AGL(1,𝔽5)11yescharacteristic
68C2×C3×C42—51no—
69C3×#97—54no—
70C3×C4×C8—102no—
71C22×C4×C5C2×C3×C411yescharacteristic
72C22×Dic5C3×D412yes—
73C2×Dic10—22no—
74#704—28no—
75C2×#170—24no—
76C5×C4⋊C4C2×C3×C412yes—
77C5×C22⋊C4—21no—
78C42×C5—21no—
79C22⋊Dic5—21no—
80C4⋊Dic5—22no—
81C4⋊Dic5C2×C3×C412yes—
82#683—22no—
83#683—22no—
84C4×Dic5—21no—
85C4×Dic5C2×C3×C411yescharacteristic
86C4×Dic5C3×D412yes—
87C4×Dic5C23×C311yescharacteristic
88#533—51no—
89C4×M16—52no—
90#330—54no—
91C22×C3×C5—21no—
92C22×C3×C5—22no—
93C22×C3×C5C2×C22⋊C411yescharacteristic
94C3×C4×C5—21no—
95C3×C4×C5—42no—
96C3×C4×C5#10112yes—
97C3×Dic5—22no—
98C3×Dic5—42no—
99C3×Dic5#10414yes—
100C2×C3×Q8—102no—
101C22×C3×C4—52no—
102C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
103C3×M16—108no—
104C2×C3×C8—104no—
105C3×C4⋊C4—52no—
106C3×C4⋊C4—102no—
107C3×C4⋊C4—102no—
108C3×C4⋊C4—102no—
109C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
110C3×C22⋊C4—21no—
111C3×C22⋊C4—101no—
112C3×C42—21no—
113C3×C42—52no—
114C3×C42—51no—
115C3×C42—51no—
116C3×C42—101no—
117C23×C5C3×C22⋊C411yescharacteristic
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5C3×C22⋊C411yescharacteristic
121C2×C4×C5C22×C3×C411yescharacteristic
122C2×Dic5—24no—
123C2×Dic5—22no—
124C2×Dic5C3×C22⋊C412yes—
125C2×Dic5C2×C3×D412yes—
126Dic10—44no—
127#170—28no—
128C2×M16—102no—
129C4⋊Q8—52no—
130#125—52no—
131C22⋊Q8—102no—
132C4×Q8—102no—
133#117—51no—
134#117C3×AGL(1,𝔽5)11yescharacteristic
135C2×C42—51no—
136#97—54no—
137C4×C8—102no—
138C2×C3×C5—41no—
139C2×C3×C5C2×#10111yescharacteristic
140C2×C3×C5C2×#10412yes—
141C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
142C3×Q8—204no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—52no—
146C2×C3×C4—52no—
147C2×C3×C4—104no—
148C2×C3×C4—102no—
149C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
150C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
151C3×C8—108no—
152C22×C5—21no—
153C22×C5—22no—
154C22×C5C2×C3×C22⋊C411yescharacteristic
155C4×C5—21no—
156C4×C5—42no—
157C4×C5C3×#10112yes—
158Dic5—22no—
159Dic5—42no—
160Dic5C3×#10414yes—
161C2×Q8—102no—
162C22×C4—52no—
163C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
164M16—108no—
165C2×C8—104no—
166C4⋊C4—52no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
171C22⋊C4—21no—
172C22⋊C4—101no—
173C42—21no—
174C42—52no—
175C42—51no—
176C42—51no—
177C42—101no—
178C3×C5#152611yescharacteristic, complemented, Hall
179C22×C3—22no—
180C22×C3—21no—
181C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
182C3×C4—21no—
183C3×C4—42no—
184C3×C4—54no—
185C3×C4—102no—
186C3×C4—202no—
187C3×C4#400512yes—
188C2×C5—41no—
189C2×C5C2×C3×#10111yescharacteristic
190C2×C5C2×C3×#10412yes—
191C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
192Q8—204no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—52no—
196C2×C4—52no—
197C2×C4—104no—
198C2×C4—102no—
199C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
200C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
201C8—108no—
202C2×C3—41no—
203C2×C3C2×#400511yescharacteristic
204C2×C3D5⋊#10412yes—
205C5C3×#152611yescharacteristic, complemented, Sylow
206C22—21no—
207C22—22no—
208C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
209C4—21no—
210C4—42no—
211C4—54no—
212C4—102no—
213C4—202no—
214C4C3×#400512yes—
215C3#1060435011yescharacteristic, direct product factor, Sylow
216C2—41no—
217C2C2×C3×#400511yescharacteristic
218C2C3×D5⋊#10412yes—
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C3×#1526
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
3. C3×#64870C2semidirect
4. #10604350C3direct (N × H)
18. #64870C2×C3semidirect
178. C3×C5#1526semidirect
205. C5C3×#1526semidirect
215. C3#10604350direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658512
C3×C4×#7042
C3×#648702
#106043503
C3×#15265