Finite Group Databasebeta

← C3×#10598687 #14277599

Subgroups — C3×#10598687 #14277599

Order 1920.

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

normal subgroups only

This group has 268 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×#65218C211yesmaximal, characteristic
2C3×#64913C212yesmaximal
3#10598687C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×Dic10C411yescharacteristic
5C2×C3×C42×C5C411yescharacteristic
6C2×C3×C4⋊Dic5C2211yescharacteristic
7C3×C22⋊#170—22no—
8C3×#3963—22no—
9C3×#1319—51nomaximal, Hall
10#65218C2×C311yescharacteristic
11#64913C2×C312yes—
12C22×C3×C4×C5—21no—
13C22×C3×C4×C5C2×C411yescharacteristic
14C22×C3×Dic5—21no—
15C22×C3×Dic5D412yes—
16C2×C3×Dic10—21no—
17C2×C3×Dic10—41no—
18C2×C3×Dic10—41no—
19C2×C3×Dic10C812yescomplemented
20C2×C3×#170—42no—
21C3×C42×C5—41no—
22C3×C4⋊Dic5—41no—
23C3×#391—51no—
24C3×#324—52no—
25C22×Dic10C3×C411yescharacteristic
26C2×C42×C5C3×C411yescharacteristic
27C2×C4⋊Dic5C22×C311yescharacteristic
28C22⋊#170—22no—
29#3963—22no—
30#1319—51noSylow
31C23×C3×C5C22⋊C411yescharacteristic
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5—22no—
35C2×C3×C4×C5—41no—
36C2×C3×C4×C5—41no—
37C2×C3×C4×C5C2×C811yescharacteristic
38C2×C3×C4×C5M1611yescharacteristic
39C2×C3×Dic5—22no—
40C2×C3×Dic5—22no—
41C2×C3×Dic5—41no—
42C2×C3×Dic5—41no—
43C2×C3×Dic5—42no—
44C3×Dic10—42no—
45C3×Dic10—42no—
46C3×#170—82no—
47C22×C3×Q8—51no—
48C2×C3×C4⋊C4—51no—
49C2×C3×C42AGL(1,𝔽5)11yescharacteristic
50C3×C22⋊C8—102no—
51C3×#95—102no—
52C22×C4×C5—21no—
53C22×C4×C5C2×C3×C411yescharacteristic
54C22×Dic5—21no—
55C22×Dic5C3×D412yes—
56C2×Dic10—21no—
57C2×Dic10—41no—
58C2×Dic10—41no—
59C2×Dic10C3×C812yescomplemented
60C2×#170—42no—
61C42×C5—41no—
62C4⋊Dic5—41no—
63#391—51no—
64#324—52no—
65C22×C3×C5—21no—
66C22×C3×C5—21no—
67C22×C3×C5C22⋊C811yescharacteristic
68C22×C3×C5#9911yescharacteristic
69C22×C3×C5#10011yescharacteristic
70C3×C4×C5—21no—
71C3×C4×C5—21no—
72C3×C4×C5—42no—
73C3×Dic5—42no—
74C3×Dic5—42no—
75C2×C3×Q8—52no—
76C2×C3×Q8—101no—
77C2×C3×Q8—201no—
78C2×C3×Q8—201no—
79C22×C3×C4—21no—
80C22×C3×C4—52no—
81C22×C3×C4—101no—
82C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
83C2×C3×C8—202no—
84C3×C4⋊C4—201no—
85C3×C42—41no—
86C23×C5C3×C22⋊C411yescharacteristic
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—41no—
91C2×C4×C5—41no—
92C2×C4×C5C2×C3×C811yescharacteristic
93C2×C4×C5C3×M1611yescharacteristic
94C2×Dic5—22no—
95C2×Dic5—22no—
96C2×Dic5—41no—
97C2×Dic5—41no—
98C2×Dic5—42no—
99Dic10—42no—
100Dic10—42no—
101#170—82no—
102C22×Q8—51no—
103C2×C4⋊C4—51no—
104C2×C42C3×AGL(1,𝔽5)11yescharacteristic
105C22⋊C8—102no—
106#95—102no—
107C2×C3×C5—21no—
108C2×C3×C5—21no—
109C2×C3×C5#32311yescharacteristic
110C2×C3×C5#35411yescharacteristic
111C2×C3×C5#35611yescharacteristic
112C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
113C3×Q8—202no—
114C3×Q8—202no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—22no—
118C2×C3×C4—41no—
119C2×C3×C4—41no—
120C2×C3×C4—102no—
121C2×C3×C4—102no—
122C2×C3×C4—201no—
123C2×C3×C4—201no—
124C2×C3×C4—202no—
125C2×C3×C4D5⋊C811yescharacteristic
126C2×C3×C4#70011yescharacteristic
127C3×C8—402no—
128C22×C5—21no—
129C22×C5—21no—
130C22×C5C3×C22⋊C811yescharacteristic
131C22×C5C3×#9911yescharacteristic
132C22×C5C3×#10011yescharacteristic
133C4×C5—21no—
134C4×C5—21no—
135C4×C5—42no—
136Dic5—42no—
137Dic5—42no—
138C2×Q8—52no—
139C2×Q8—101no—
140C2×Q8—201no—
141C2×Q8—201no—
142C22×C4—21no—
143C22×C4—52no—
144C22×C4—101no—
145C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
146C2×C8—202no—
147C4⋊C4—201no—
148C42—41no—
149C3×C5#131911yescharacteristic, complemented, Hall
150C22×C3—21no—
151C22×C3—21no—
152C22×C3#399911yescharacteristic
153C22×C3#400311yescharacteristic
154C22×C3#401311yescharacteristic
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—42no—
158C3×C4—202no—
159C3×C4—202no—
160C2×C5—21no—
161C2×C5—21no—
162C2×C5C3×#32311yescharacteristic
163C2×C5C3×#35411yescharacteristic
164C2×C5C3×#35611yescharacteristic
165C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
166Q8—202no—
167Q8—202no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—102no—
174C2×C4—102no—
175C2×C4—201no—
176C2×C4—201no—
177C2×C4—202no—
178C2×C4C3×D5⋊C811yescharacteristic
179C2×C4C3×#70011yescharacteristic
180C8—402no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3#6485411yescharacteristic
184C2×C3#6485511yescharacteristic
185C2×C3#6491511yescharacteristic
186C5C3×#131911yescharacteristic, complemented, Sylow
187C22—21no—
188C22—21no—
189C22C3×#399911yescharacteristic
190C22C3×#400311yescharacteristic
191C22C3×#401311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—202no—
196C4—202no—
197C3#1059868711yescharacteristic, direct product factor, Sylow
198C2—21no—
199C2—21no—
200C2C3×#6485411yescharacteristic
201C2C3×#6485511yescharacteristic
202C2C3×#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 radicalC23×C3×C5C22⋊C4
cosocleC2×C4⋊Dic5C22×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1319
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
3. #10598687C3direct (N × H)
19. C2×C3×Dic10C8semidirect
59. C2×Dic10C3×C8semidirect
149. C3×C5#1319semidirect
186. C5C3×#1319semidirect
197. C3#10598687direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#652182
C3×#649132
#105986873
C3×#13195