Finite Group Databasebeta

← C3×#10598823 #14277582

Subgroups — C3×#10598823 #14277582

Order 1920.

340 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 72 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×#65510C211yesmaximal, characteristic
2C3×#64913C212yesmaximal, complemented
3#10598823C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C5×D4C411yescharacteristic
5C2×C3×C22⋊Dic5—22no—
6C2×C3×C4⋊Dic5C2211yescharacteristic
7C2×C3×C4×Dic5C411yescharacteristic
8C3×C22⋊#170—22no—
9C3×#1318—51nomaximal, Hall
10#65510C2×C311yescharacteristic
11#64913C2×C312yescomplemented
12C24×C3×C5—21no—
13C2×C3×C5×D4—21no—
14C2×C3×C5×D4—41no—
15C2×C3×C5×D4—41no—
16C2×C3×C5×D4C812yescomplemented
17C22×C3×C4×C5C2×C411yescharacteristic
18C22×C3×Dic5—21no—
19C22×C3×Dic5D412yes—
20C2×C3×#170—42no—
21C3×C22⋊Dic5—44no—
22C3×C4⋊Dic5—41no—
23C3×C4×Dic5—41no—
24C3×#390—51no—
25C3×#324—52no—
26C22×C5×D4C3×C411yescharacteristic
27C2×C22⋊Dic5—22no—
28C2×C4⋊Dic5C22×C311yescharacteristic
29C2×C4×Dic5C3×C411yescharacteristic
30C22⋊#170—22no—
31#1318—51noSylow
32C23×C3×C5—22no—
33C23×C3×C5—42no—
34C23×C3×C5—42no—
35C23×C3×C5—41no—
36C23×C3×C5—41no—
37C23×C3×C5C22⋊C411yescharacteristic
38C3×C5×D4—42no—
39C3×C5×D4—42no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C2×C811yescharacteristic
43C2×C3×C4×C5M1611yescharacteristic
44C2×C3×Dic5—22no—
45C2×C3×Dic5—22no—
46C2×C3×Dic5—41no—
47C2×C3×Dic5—41no—
48C2×C3×Dic5—42no—
49C3×#170—82no—
50C22×C3×D4AGL(1,𝔽5)11yescharacteristic
51C2×C3×C4⋊C4—51no—
52C2×C3×C22⋊C4—102no—
53C2×C3×C42—51no—
54C3×C22⋊C8—102no—
55C24×C5—21no—
56C2×C5×D4—21no—
57C2×C5×D4—41no—
58C2×C5×D4—41no—
59C2×C5×D4C3×C812yescomplemented
60C22×C4×C5C2×C3×C411yescharacteristic
61C22×Dic5—21no—
62C22×Dic5C3×D412yes—
63C2×#170—42no—
64C22⋊Dic5—44no—
65C4⋊Dic5—41no—
66C4×Dic5—41no—
67#390—51no—
68#324—52no—
69C22×C3×C5—21no—
70C22×C3×C5—21no—
71C22×C3×C5—44no—
72C22×C3×C5—42no—
73C22×C3×C5—82no—
74C22×C3×C5—81no—
75C22×C3×C5—81no—
76C22×C3×C5C22⋊C811yescharacteristic
77C22×C3×C5#9911yescharacteristic
78C22×C3×C5#10011yescharacteristic
79C3×C4×C5—21no—
80C3×C4×C5—21no—
81C3×Dic5—42no—
82C3×Dic5—42no—
83C24×C3—21no—
84C2×C3×D4—21no—
85C2×C3×D4—41no—
86C2×C3×D4—41no—
87C2×C3×D4#17012yescomplemented
88C22×C3×C4—52no—
89C22×C3×C4—101no—
90C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
91C2×C3×C8—202no—
92C3×C4⋊C4—201no—
93C3×C22⋊C4—204no—
94C3×C42—201no—
95C23×C5—22no—
96C23×C5—42no—
97C23×C5—42no—
98C23×C5—41no—
99C23×C5—41no—
100C23×C5C3×C22⋊C411yescharacteristic
101C5×D4—42no—
102C5×D4—42no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5C2×C3×C811yescharacteristic
106C2×C4×C5C3×M1611yescharacteristic
107C2×Dic5—22no—
108C2×Dic5—22no—
109C2×Dic5—41no—
110C2×Dic5—41no—
111C2×Dic5—42no—
112#170—82no—
113C22×D4C3×AGL(1,𝔽5)11yescharacteristic
114C2×C4⋊C4—51no—
115C2×C22⋊C4—102no—
116C2×C42—51no—
117C22⋊C8—102no—
118C2×C3×C5—21no—
119C2×C3×C5—21no—
120C2×C3×C5—82no—
121C2×C3×C5#32311yescharacteristic
122C2×C3×C5#35311yescharacteristic
123C2×C3×C5#35511yescharacteristic
124C23×C3—22no—
125C23×C3—42no—
126C23×C3—42no—
127C23×C3—41no—
128C23×C3—41no—
129C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
130C3×D4—42no—
131C3×D4—42no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—102no—
135C2×C3×C4—102no—
136C2×C3×C4—201no—
137C2×C3×C4—201no—
138C2×C3×C4—202no—
139C2×C3×C4C2×#17011yescharacteristic
140C2×C3×C4#70411yescharacteristic
141C3×C8—402no—
142C22×C5—21no—
143C22×C5—21no—
144C22×C5—44no—
145C22×C5—42no—
146C22×C5—82no—
147C22×C5—81no—
148C22×C5—81no—
149C22×C5C3×C22⋊C811yescharacteristic
150C22×C5C3×#9911yescharacteristic
151C22×C5C3×#10011yescharacteristic
152C4×C5—21no—
153C4×C5—21no—
154Dic5—42no—
155Dic5—42no—
156C24—21no—
157C2×D4—21no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4C3×#17012yescomplemented
161C22×C4—52no—
162C22×C4—101no—
163C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
164C2×C8—202no—
165C4⋊C4—201no—
166C22⋊C4—204no—
167C42—201no—
168C3×C5#131811yescharacteristic, complemented, Hall
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—44no—
172C22×C3—42no—
173C22×C3—82no—
174C22×C3—81no—
175C22×C3—81no—
176C22×C3#401111yescharacteristic
177C22×C3C22⋊#17011yescharacteristic
178C22×C3#401311yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—202no—
182C3×C4—202no—
183C2×C5—21no—
184C2×C5—21no—
185C2×C5—82no—
186C2×C5C3×#32311yescharacteristic
187C2×C5C3×#35311yescharacteristic
188C2×C5C3×#35511yescharacteristic
189C23—22no—
190C23—42no—
191C23—42no—
192C23—41no—
193C23—41no—
194C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
195D4—42no—
196D4—42no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—201no—
202C2×C4—201no—
203C2×C4—202no—
204C2×C4C2×C3×#17011yescharacteristic
205C2×C4C3×#70411yescharacteristic
206C8—402no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—82no—
210C2×C3#6492211yescharacteristic
211C2×C3#6492311yescharacteristic
212C2×C3#6493311yescharacteristic
213C5C3×#131811yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22—44no—
217C22—42no—
218C22—82no—
219C22—81no—
220C22—81no—
221C22C3×#401111yescharacteristic
222C22C3×C22⋊#17011yescharacteristic
223C22C3×#401311yescharacteristic
224C4—21no—
225C4—21no—
226C4—202no—
227C4—202no—
228C3#1059882311yescharacteristic, direct product factor, Sylow
229C2—21no—
230C2—21no—
231C2—82no—
232C2C3×#6492211yescharacteristic
233C2C3×#6492311yescharacteristic
234C2C3×#6493311yescharacteristic
subgroupG/H
centerC22×C3#4011
commutatorC2×C4×C5C2×C3×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
Fitting, prime radicalC22×C3×C5×D4C4
socleC22×C3×C5#99
cosocleC2×C4⋊Dic5C22×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1318
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64913C2semidirect
3. #10598823C3direct (N × H)
11. #64913C2×C3semidirect
16. C2×C3×C5×D4C8semidirect
59. C2×C5×D4C3×C8semidirect
87. C2×C3×D4#170semidirect
160. C2×D4C3×#170semidirect
168. C3×C5#1318semidirect
213. C5C3×#1318semidirect
228. C3#10598823direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#655102
C3×#649132
#105988233
C3×#13185