Finite Group Databasebeta

← C3×#10598686 #14277584

Subgroups — C3×#10598686 #14277584

Order 1920.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#65228C211yesmaximal, characteristic
2C3×#64913C212yesmaximal, complemented
3#10598686C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×D20C411yescharacteristic
5C2×C3×C42×C5C411yescharacteristic
6C2×C3×#685—22no—
7C2×C3×C4⋊Dic5C2211yescharacteristic
8C3×C22⋊#170—22no—
9C3×#1318—51nomaximal, Hall
10#65228C2×C311yescharacteristic
11#64913C2×C312yescomplemented
12C23×C3×D5—21no—
13C22×C3×C4×C5—21no—
14C22×C3×C4×C5C2×C411yescharacteristic
15C22×C3×Dic5D412yes—
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×D20—41no—
19C2×C3×D20C812yescomplemented
20C2×C3×#170—42no—
21C3×C42×C5—41no—
22C3×#685—44no—
23C3×C4⋊Dic5—41no—
24C3×#390—51no—
25C3×#324—52no—
26C22×D20C3×C411yescharacteristic
27C2×C42×C5C3×C411yescharacteristic
28C2×#685—22no—
29C2×C4⋊Dic5C22×C311yescharacteristic
30C22⋊#170—22no—
31#1318—51noSylow
32C23×C3×C5C22⋊C411yescharacteristic
33C22×C3×D5—22no—
34C22×C3×D5—42no—
35C22×C3×D5—42no—
36C22×C3×D5—41no—
37C22×C3×D5—41no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—22no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C2×C811yescharacteristic
44C2×C3×C4×C5M1611yescharacteristic
45C2×C3×Dic5—22no—
46C2×C3×Dic5—42no—
47C3×D20—42no—
48C3×D20—42no—
49C3×#170—82no—
50C22×C3×D4—51no—
51C2×C3×C4⋊C4—51no—
52C2×C3×C22⋊C4—102no—
53C2×C3×C42AGL(1,𝔽5)11yescharacteristic
54C3×C22⋊C8—102no—
55C23×D5—21no—
56C22×C4×C5—21no—
57C22×C4×C5C2×C3×C411yescharacteristic
58C22×Dic5C3×D412yes—
59C2×D20—21no—
60C2×D20—41no—
61C2×D20—41no—
62C2×D20C3×C812yescomplemented
63C2×#170—42no—
64C42×C5—41no—
65#685—44no—
66C4⋊Dic5—41no—
67#390—51no—
68#324—52no—
69C22×C3×C5—21no—
70C22×C3×C5—21no—
71C22×C3×C5C22⋊C811yescharacteristic
72C22×C3×C5#9911yescharacteristic
73C22×C3×C5#10011yescharacteristic
74C2×C3×D5—44no—
75C2×C3×D5—42no—
76C2×C3×D5—82no—
77C2×C3×D5—81no—
78C2×C3×D5—81no—
79C3×C4×C5—21no—
80C3×C4×C5—21no—
81C3×C4×C5—42no—
82C3×Dic5—42no—
83C24×C3—101no—
84C2×C3×D4—52no—
85C2×C3×D4—101no—
86C2×C3×D4—201no—
87C2×C3×D4—201no—
88C22×C3×C4—21no—
89C22×C3×C4—52no—
90C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
91C2×C3×C8—202no—
92C3×C4⋊C4—201no—
93C3×C22⋊C4—204no—
94C3×C42—41no—
95C23×C5C3×C22⋊C411yescharacteristic
96C22×D5—22no—
97C22×D5—42no—
98C22×D5—42no—
99C22×D5—41no—
100C22×D5—41no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5C2×C3×C811yescharacteristic
107C2×C4×C5C3×M1611yescharacteristic
108C2×Dic5—22no—
109C2×Dic5—42no—
110D20—42no—
111D20—42no—
112#170—82no—
113C22×D4—51no—
114C2×C4⋊C4—51no—
115C2×C22⋊C4—102no—
116C2×C42C3×AGL(1,𝔽5)11yescharacteristic
117C22⋊C8—102no—
118C2×C3×C5—21no—
119C2×C3×C5—21no—
120C2×C3×C5#32311yescharacteristic
121C2×C3×C5#35311yescharacteristic
122C2×C3×C5#35511yescharacteristic
123C3×D5—82no—
124C23×C3—102no—
125C23×C3—202no—
126C23×C3—202no—
127C23×C3—201no—
128C23×C3—201no—
129C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
130C3×D4—202no—
131C3×D4—202no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—22no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—102no—
138C2×C3×C4—202no—
139C2×C3×C4D5⋊C811yescharacteristic
140C2×C3×C4#70011yescharacteristic
141C3×C8—402no—
142C22×C5—21no—
143C22×C5—21no—
144C22×C5C3×C22⋊C811yescharacteristic
145C22×C5C3×#9911yescharacteristic
146C22×C5C3×#10011yescharacteristic
147C2×D5—44no—
148C2×D5—42no—
149C2×D5—82no—
150C2×D5—81no—
151C2×D5—81no—
152C4×C5—21no—
153C4×C5—21no—
154C4×C5—42no—
155Dic5—42no—
156C24—101no—
157C2×D4—52no—
158C2×D4—101no—
159C2×D4—201no—
160C2×D4—201no—
161C22×C4—21no—
162C22×C4—52no—
163C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
164C2×C8—202no—
165C4⋊C4—201no—
166C22⋊C4—204no—
167C42—41no—
168C3×C5#131811yescharacteristic, complemented, Hall
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—204no—
172C22×C3—202no—
173C22×C3—402no—
174C22×C3—401no—
175C22×C3—401no—
176C22×C3#399911yescharacteristic
177C22×C3#400311yescharacteristic
178C22×C3#401311yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—42no—
182C3×C4—202no—
183C2×C5—21no—
184C2×C5—21no—
185C2×C5C3×#32311yescharacteristic
186C2×C5C3×#35311yescharacteristic
187C2×C5C3×#35511yescharacteristic
188D5—82no—
189C23—102no—
190C23—202no—
191C23—202no—
192C23—201no—
193C23—201no—
194C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
195D4—202no—
196D4—202no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—102no—
203C2×C4—202no—
204C2×C4C3×D5⋊C811yescharacteristic
205C2×C4C3×#70011yescharacteristic
206C8—402no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—402no—
210C2×C3#6485311yescharacteristic
211C2×C3#6485611yescharacteristic
212C2×C3#6491511yescharacteristic
213C5C3×#131811yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22—204no—
217C22—202no—
218C22—402no—
219C22—401no—
220C22—401no—
221C22C3×#399911yescharacteristic
222C22C3×#400311yescharacteristic
223C22C3×#401311yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—202no—
228C3#1059868611yescharacteristic, direct product factor, Sylow
229C2—21no—
230C2—21no—
231C2—402no—
232C2C3×#6485311yescharacteristic
233C2C3×#6485611yescharacteristic
234C2C3×#6491511yescharacteristic
subgroupG/H
centerC22×C3#3999
commutatorC2×C4×C5C2×C3×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socleC22×C3×C5#99
prime radicalC22×C3×D20C4
cosocleC2×C4⋊Dic5C22×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1318
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×C42

Complements

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

NH ≅ G/Ntype
2. C3×#64913C2semidirect
3. #10598686C3direct (N × H)
11. #64913C2×C3semidirect
19. C2×C3×D20C8semidirect
62. C2×D20C3×C8semidirect
168. C3×C5#1318semidirect
213. C5C3×#1318semidirect
228. C3#10598686direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#652282
C3×#649132
#105986863
C3×#13185