Finite Group Databasebeta

← C3×#10604295 #14281152

Subgroups — C3×#10604295 #14281152

Order 1920.

472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C2×C3×#4033C211yesmaximal, characteristic
2C3×#65757C212yesmaximal
3C3×#64914C214yesmaximal
4#10604295C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×Dic10C411yescharacteristic
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×#683C2212yes—
8C2×C3×C4×Dic5C412yes—
9C2×C3×C4×Dic5C2211yescharacteristic
10C3×#4033—22no—
11C3×#4033—22no—
12C3×C22⋊#170C2214yes—
13C3×#4004—22no—
14C3×#4002—22no—
15C3×#1467—51nomaximal, Hall
16C2×#4033C2×C311yescharacteristic
17#65757C2×C312yes—
18#64914C2×C314yes—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×C4×C5C2×C412yes—
21C22×C3×Dic5C2×C411yescharacteristic
22C22×C3×Dic5C2×C412yes—
23C22×C3×Dic5C2311yescharacteristic
24C2×C3×Dic10—22no—
25C2×C3×Dic10—24no—
26C2×C3×#170—24no—
27C3×C5×C4⋊C4—22no—
28C3×#683—24no—
29C3×C4×Dic5—22no—
30C3×C4×Dic5—22no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5D412yes—
33C2×C3×C4×Q8—51no—
34C3×#432—52no—
35C3×#324—54no—
36C22×Dic10C3×C411yescharacteristic
37C2×C5×C4⋊C4C3×C411yescharacteristic
38C2×#683C22×C312yes—
39C2×C4×Dic5C3×C412yes—
40C2×C4×Dic5C22×C311yescharacteristic
41#4033—22no—
42#4033—22no—
43C22⋊#170C22×C314yes—
44#4004—22no—
45#4002—22no—
46#1467—51noSylow
47C23×C3×C5C22×C411yescharacteristic
48C2×C3×C4×C5—22no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5—42no—
51C2×C3×C4×C5C22⋊C412yes—
52C2×C3×Dic5—22no—
53C2×C3×Dic5—22no—
54C2×C3×Dic5—22no—
55C2×C3×Dic5—41no—
56C2×C3×Dic5C22⋊C411yescharacteristic
57C2×C3×Dic5C22⋊C411yescharacteristic
58C2×C3×Dic5M1614yes—
59C2×C3×Dic5C2×D412yes—
60C3×Dic10—28no—
61C3×#170—44no—
62C22×C3×Q8—51no—
63C3×C4×Q8—102no—
64C3×C4×Q8—102no—
65C2×C3×C4⋊C4—52no—
66C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
67C2×C3×C42—51no—
68C2×C3×C42—52no—
69C3×C4⋊C8—102no—
70C3×C22⋊C8—54no—
71C3×#97—102no—
72C22×C4×C5C2×C3×C411yescharacteristic
73C22×C4×C5C2×C3×C412yes—
74C22×Dic5C2×C3×C411yescharacteristic
75C22×Dic5C2×C3×C412yes—
76C22×Dic5C23×C311yescharacteristic
77C2×Dic10—22no—
78C2×Dic10—24no—
79C2×#170—24no—
80C5×C4⋊C4—22no—
81#683—24no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5C3×D412yes—
85C4×Dic5C3×D412yes—
86C2×C4×Q8—51no—
87#432—52no—
88#324—54no—
89C22×C3×C5—21no—
90C22×C3×C5—21no—
91C22×C3×C5C2×C22⋊C411yescharacteristic
92C22×C3×C5C2×M1612yes—
93C3×C4×C5—22no—
94C3×C4×C5—42no—
95C3×Dic5—24no—
96C3×Dic5—22no—
97C3×Dic5—21no—
98C3×Dic5#10112yes—
99C2×C3×Q8—104no—
100C2×C3×Q8—102no—
101C22×C3×C4—51no—
102C22×C3×C4—52no—
103C22×C3×C4—51no—
104C22×C3×C4C2×AGL(1,𝔽5)12yes—
105C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
106C2×C3×C8—104no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—104no—
109C3×C42—52no—
110C3×C42—52no—
111C3×C42—102no—
112C3×C42—102no—
113C23×C5C22×C3×C411yescharacteristic
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—42no—
117C2×C4×C5C3×C22⋊C412yes—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—41no—
122C2×Dic5C3×C22⋊C411yescharacteristic
123C2×Dic5C3×C22⋊C411yescharacteristic
124C2×Dic5C3×M1614yes—
125C2×Dic5C2×C3×D412yes—
126Dic10—28no—
127#170—44no—
128C22×Q8—51no—
129C4×Q8—102no—
130C4×Q8—102no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
133C2×C42—51no—
134C2×C42—52no—
135C4⋊C8—102no—
136C22⋊C8—54no—
137#97—102no—
138C2×C3×C5—22no—
139C2×C3×C5#40711yescharacteristic
140C2×C3×C5#41011yescharacteristic
141C2×C3×C5C2×#10111yescharacteristic
142C23×C3C22×AGL(1,𝔽5)11yescharacteristic
143C3×Q8—108no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—42no—
147C2×C3×C4—51no—
148C2×C3×C4—54no—
149C2×C3×C4—51no—
150C2×C3×C4—52no—
151C2×C3×C4—102no—
152C2×C3×C4—102no—
153C2×C3×C4—102no—
154C2×C3×C4—201no—
155C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
156C3×C8—204no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5C2×C3×C22⋊C411yescharacteristic
160C22×C5C2×C3×M1612yes—
161C4×C5—22no—
162C4×C5—42no—
163Dic5—24no—
164Dic5—22no—
165Dic5—21no—
166Dic5C3×#10112yes—
167C2×Q8—104no—
168C2×Q8—102no—
169C22×C4—51no—
170C22×C4—52no—
171C22×C4—51no—
172C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
173C22×C4C2×C3×AGL(1,𝔽5)12yes—
174C2×C8—104no—
175C4⋊C4—22no—
176C4⋊C4—104no—
177C42—52no—
178C42—52no—
179C42—102no—
180C42—102no—
181C3×C5#146711yescharacteristic, complemented, Hall
182C22×C3—21no—
183C22×C3—21no—
184C22×C3D5⋊M1612yes—
185C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
186C3×C4—22no—
187C3×C4—42no—
188C3×C4—52no—
189C3×C4—104no—
190C3×C4—102no—
191C3×C4—101no—
192C2×C5—22no—
193C2×C5C3×#40711yescharacteristic
194C2×C5C3×#41011yescharacteristic
195C2×C5C2×C3×#10111yescharacteristic
196C23C22×C3×AGL(1,𝔽5)11yescharacteristic
197Q8—108no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—51no—
202C2×C4—54no—
203C2×C4—51no—
204C2×C4—52no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—201no—
209C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
210C8—204no—
211C2×C3—22no—
212C2×C3#6575511yescharacteristic
213C2×C3#6577111yescharacteristic
214C2×C3D5⋊#10111yescharacteristic
215C5C3×#146711yescharacteristic, complemented, Sylow
216C22—21no—
217C22—21no—
218C22C3×D5⋊M1612yes—
219C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
220C4—22no—
221C4—42no—
222C4—52no—
223C4—104no—
224C4—102no—
225C4—101no—
226C3#1060429511yescharacteristic, direct product factor, Sylow
227C2—22no—
228C2C3×#6575511yescharacteristic
229C2C3×#6577111yescharacteristic
230C2C3×D5⋊#10111yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1467
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10604295C3direct (N × H)
181. C3×C5#1467semidirect
215. C5C3×#1467semidirect
226. C3#10604295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40332
C3×#657572
C3×#649142
#106042953
C3×#14675