Finite Group Databasebeta

← C3×#10598724 #14279140

Subgroups — C3×#10598724 #14279140

Order 1920.

344 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4005C212yesmaximal
2C3×#65263C211yesmaximal, characteristic
3#10598724C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×Dic10C2211yescharacteristic
5C2×C3×#704—22no—
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×C4×Dic5C411yescharacteristic
8C3×#4005—22no—
9C3×#4005C414yescomplemented
10C3×#3963—22no—
11C3×#1394—51nomaximal, Hall
12C2×#4005C2×C312yes—
13#65263C2×C311yescharacteristic
14C22×C3×C4×C5—21no—
15C22×C3×C4×C5C2×C411yescharacteristic
16C22×C3×Dic5—21no—
17C22×C3×Dic5D412yes—
18C2×C3×Dic10—41no—
19C2×C3×Dic10—41no—
20C2×C3×Dic10C2×C412yes—
21C2×C3×Dic10D411yescharacteristic
22C2×C3×Dic10Q811yescharacteristic
23C3×#704—24no—
24C3×#704—42no—
25C2×C3×#170—42no—
26C3×C5×C4⋊C4—41no—
27C3×C4×Dic5—41no—
28C2×C3×#101—52no—
29C3×#391—51no—
30C22×Dic10C22×C311yescharacteristic
31C2×#704—22no—
32C2×C5×C4⋊C4C3×C411yescharacteristic
33C2×C4×Dic5C3×C411yescharacteristic
34#4005—22no—
35#4005C3×C414yescomplemented
36#3963—22no—
37#1394—51noSylow
38C23×C3×C5C22⋊C411yescharacteristic
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—42no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C4211yescharacteristic
44C2×C3×C4×C5C4⋊C411yescharacteristic
45C2×C3×Dic5—22no—
46C2×C3×Dic5—22no—
47C2×C3×Dic5—22no—
48C2×C3×Dic5—41no—
49C2×C3×Dic5—41no—
50C2×C3×Dic5C22⋊C412yes—
51C2×C3×Dic5C4⋊C412yes—
52C3×Dic10—42no—
53C3×Dic10—41no—
54C3×Dic10—41no—
55C3×#170—44no—
56C22×C3×Q8—51no—
57C2×C3×M16—102no—
58C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
59C2×C3×C42—51no—
60C3×#101—54no—
61C3×#101—102no—
62C3×#95—102no—
63C22×C4×C5—21no—
64C22×C4×C5C2×C3×C411yescharacteristic
65C22×Dic5—21no—
66C22×Dic5C3×D412yes—
67C2×Dic10—41no—
68C2×Dic10—41no—
69C2×Dic10C2×C3×C412yes—
70C2×Dic10C3×D411yescharacteristic
71C2×Dic10C3×Q811yescharacteristic
72#704—24no—
73#704—42no—
74C2×#170—42no—
75C5×C4⋊C4—41no—
76C4×Dic5—41no—
77C2×#101—52no—
78#391—51no—
79C22×C3×C5—21no—
80C22×C3×C5—21no—
81C22×C3×C5#9511yescharacteristic
82C22×C3×C5#9911yescharacteristic
83C22×C3×C5#9911yescharacteristic
84C3×C4×C5—21no—
85C3×C4×C5—21no—
86C3×C4×C5—81no—
87C3×Dic5—22no—
88C3×Dic5—22no—
89C3×Dic5—42no—
90C2×C3×Q8—52no—
91C2×C3×Q8—51no—
92C2×C3×Q8—51no—
93C2×C3×Q8—201no—
94C2×C3×Q8—201no—
95C22×C3×C4—21no—
96C22×C3×C4—52no—
97C22×C3×C4—101no—
98C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
99C3×M16—104no—
100C3×M16—202no—
101C2×C3×C8—202no—
102C3×C4⋊C4—41no—
103C3×C42—201no—
104C23×C5C3×C22⋊C411yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—42no—
108C2×C4×C5—41no—
109C2×C4×C5C3×C4211yescharacteristic
110C2×C4×C5C3×C4⋊C411yescharacteristic
111C2×Dic5—22no—
112C2×Dic5—22no—
113C2×Dic5—22no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5C3×C22⋊C412yes—
117C2×Dic5C3×C4⋊C412yes—
118Dic10—42no—
119Dic10—41no—
120Dic10—41no—
121#170—44no—
122C22×Q8—51no—
123C2×M16—102no—
124C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
125C2×C42—51no—
126#101—54no—
127#101—102no—
128#95—102no—
129C2×C3×C5—21no—
130C2×C3×C5—21no—
131C2×C3×C5#34211yescharacteristic
132C2×C3×C5#35511yescharacteristic
133C2×C3×C5#35611yescharacteristic
134C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
135C3×Q8—202no—
136C3×Q8—201no—
137C3×Q8—201no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—42no—
141C2×C3×C4—41no—
142C2×C3×C4—52no—
143C2×C3×C4—52no—
144C2×C3×C4—102no—
145C2×C3×C4—102no—
146C2×C3×C4—102no—
147C2×C3×C4—201no—
148C2×C3×C4—201no—
149C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
150C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
151C3×C8—204no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5C3×#9511yescharacteristic
155C22×C5C3×#9911yescharacteristic
156C22×C5C3×#9911yescharacteristic
157C4×C5—21no—
158C4×C5—21no—
159C4×C5—81no—
160Dic5—22no—
161Dic5—22no—
162Dic5—42no—
163C2×Q8—52no—
164C2×Q8—51no—
165C2×Q8—51no—
166C2×Q8—201no—
167C2×Q8—201no—
168C22×C4—21no—
169C22×C4—52no—
170C22×C4—101no—
171C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
172M16—104no—
173M16—202no—
174C2×C8—202no—
175C4⋊C4—41no—
176C42—201no—
177C3×C5#139411yescharacteristic, complemented, Hall
178C22×C3—21no—
179C22×C3—21no—
180C22×C3#399911yescharacteristic
181C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
182C22×C3#401111yescharacteristic
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—81no—
186C3×C4—102no—
187C3×C4—102no—
188C3×C4—202no—
189C2×C5—21no—
190C2×C5—21no—
191C2×C5C3×#34211yescharacteristic
192C2×C5C3×#35511yescharacteristic
193C2×C5C3×#35611yescharacteristic
194C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
195Q8—202no—
196Q8—201no—
197Q8—201no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—52no—
203C2×C4—52no—
204C2×C4—102no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—201no—
208C2×C4—201no—
209C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
210C2×C4C3×C4⋊AGL(1,𝔽5)11yescharacteristic
211C8—204no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3#6491711yescharacteristic
215C2×C3#6492311yescharacteristic
216C2×C3#6492911yescharacteristic
217C5C3×#139411yescharacteristic, complemented, Sylow
218C22—21no—
219C22—21no—
220C22C3×#399911yescharacteristic
221C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
222C22C3×#401111yescharacteristic
223C4—21no—
224C4—21no—
225C4—81no—
226C4—102no—
227C4—102no—
228C4—202no—
229C3#1059872411yescharacteristic, direct product factor, Sylow
230C2—21no—
231C2—21no—
232C2C3×#6491711yescharacteristic
233C2C3×#6492311yescharacteristic
234C2C3×#6492911yescharacteristic
subgroupG/H
centerC22×C3#4011
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC22×Dic10C22×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1394
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10598724C3direct (N × H)
9. C3×#4005C4semidirect
35. #4005C3×C4semidirect
177. C3×C5#1394semidirect
217. C5C3×#1394semidirect
229. C3#10598724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40052
C3×#652632
#105987243
C3×#13945