Finite Group Databasebeta

← C3×#10604584 #14284747

Subgroups — C3×#10604584 #14284747

Order 1920.

404 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 120 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×#66022C211yesmaximal, characteristic
2C3×#65678C212yesmaximal
3C3×#64873C214yesmaximal, complemented
4#10604584C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#125C411yescharacteristic
6C3×#4042—22no—
7C3×#4038C412yes—
8C3×#4034C2212yes—
9C3×#4033—22no—
10C3×C42×D5C2211yescharacteristic
11C3×#4016C411yescharacteristic
12C3×#4004C2214yes—
13C3×#4003—22no—
14C3×C4×#170—22no—
15C3×#1544—51nomaximal, Hall
16#66022C2×C311yescharacteristic
17#65678C2×C312yes—
18#64873C2×C314yescomplemented
19C2×C3×C4×D5C2×C411yescharacteristic
20C2×C3×C4×D5D412yes—
21C2×C3×Dic10—22no—
22C2×C3×#170—24no—
23C3×C5×C4⋊C4—22no—
24C3×C5×C4⋊C4C2×C412yes—
25C3×C42×C5C2×C411yescharacteristic
26C3×#685—22no—
27C3×C4⋊Dic5C2×C412yes—
28C3×#683—22no—
29C3×#683—22no—
30C3×C4×Dic5—22no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5C2311yescharacteristic
33C3×#533—51no—
34C3×#431—52no—
35C3×#332—54no—
36C5×#125C3×C411yescharacteristic
37#4042—22no—
38#4038C3×C412yes—
39#4034C22×C312yes—
40#4033—22no—
41C42×D5C22×C311yescharacteristic
42#4016C3×C411yescharacteristic
43#4004C22×C314yes—
44#4003—22no—
45C4×#170—22no—
46#1544—51noSylow
47C22×C3×D5C22⋊C411yescharacteristic
48C2×C3×C4×C5—22no—
49C2×C3×C4×C5C22⋊C412yes—
50C2×C3×C4×C5C22×C411yescharacteristic
51C2×C3×Dic5—22no—
52C2×C3×Dic5C22⋊C411yescharacteristic
53C2×C3×Dic5C2×D412yes—
54C3×C4×D5—22no—
55C3×C4×D5—24no—
56C3×Dic10—44no—
57C3×#170—44no—
58C3×C4⋊Q8—52no—
59C3×#125—51no—
60C3×#125AGL(1,𝔽5)11yescharacteristic
61C3×C22⋊Q8—102no—
62C3×C4×Q8—102no—
63C3×#117—52no—
64C2×C3×C42—51no—
65C3×C4⋊C8—54no—
66C3×C22⋊C8—102no—
67C3×C4×C8—102no—
68C2×C4×D5C2×C3×C411yescharacteristic
69C2×C4×D5C3×D412yes—
70C2×Dic10—22no—
71C2×#170—24no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4C2×C3×C412yes—
74C42×C5C2×C3×C411yescharacteristic
75#685—22no—
76C4⋊Dic5C2×C3×C412yes—
77#683—22no—
78#683—22no—
79C4×Dic5—22no—
80C4×Dic5C3×D412yes—
81C4×Dic5C23×C311yescharacteristic
82#533—51no—
83#431—52no—
84#332—54no—
85C22×C3×C5C2×C22⋊C411yescharacteristic
86C2×C3×D5—21no—
87C2×C3×D5—22no—
88C3×C4×C5—21no—
89C3×C4×C5—22no—
90C3×C4×C5—42no—
91C3×Dic5—42no—
92C3×Dic5#10112yes—
93C3×Dic5#13514yes—
94C2×C3×Q8—102no—
95C22×C3×C4—52no—
96C22×C3×C4—51no—
97C2×C3×C8—104no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—52no—
100C3×C4⋊C4—102no—
101C3×C4⋊C4—102no—
102C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
103C3×C22⋊C4—102no—
104C3×C42—52no—
105C3×C42—51no—
106C3×C42—102no—
107C3×C42C2×AGL(1,𝔽5)11yescharacteristic
108C22×D5C3×C22⋊C411yescharacteristic
109C2×C4×C5—22no—
110C2×C4×C5C3×C22⋊C412yes—
111C2×C4×C5C22×C3×C411yescharacteristic
112C2×Dic5—22no—
113C2×Dic5C3×C22⋊C411yescharacteristic
114C2×Dic5C2×C3×D412yes—
115C4×D5—22no—
116C4×D5—24no—
117Dic10—44no—
118#170—44no—
119C4⋊Q8—52no—
120#125—51no—
121#125C3×AGL(1,𝔽5)11yescharacteristic
122C22⋊Q8—102no—
123C4×Q8—102no—
124#117—52no—
125C2×C42—51no—
126C4⋊C8—54no—
127C22⋊C8—102no—
128C4×C8—102no—
129C2×C3×C5C2×#10111yescharacteristic
130C2×C3×C5#41612yes—
131C3×D5—41no—
132C23×C3—51no—
133C3×Q8—204no—
134C2×C3×C4—22no—
135C2×C3×C4—51no—
136C2×C3×C4—52no—
137C2×C3×C4—104no—
138C2×C3×C4—102no—
139C2×C3×C4—102no—
140C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
141C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
142C3×C8—204no—
143C22×C5C2×C3×C22⋊C411yescharacteristic
144C2×D5—21no—
145C2×D5—22no—
146C4×C5—21no—
147C4×C5—22no—
148C4×C5—42no—
149Dic5—42no—
150Dic5C3×#10112yes—
151Dic5C3×#13514yes—
152C2×Q8—102no—
153C22×C4—52no—
154C22×C4—51no—
155C2×C8—104no—
156C4⋊C4—22no—
157C4⋊C4—52no—
158C4⋊C4—102no—
159C4⋊C4—102no—
160C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
161C22⋊C4—102no—
162C42—52no—
163C42—51no—
164C42—102no—
165C42C2×C3×AGL(1,𝔽5)11yescharacteristic
166C3×C5#154411yescharacteristic, complemented, Hall
167C22×C3—102no—
168C22×C3—101no—
169C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
170C3×C4—22no—
171C3×C4—21no—
172C3×C4—42no—
173C3×C4—54no—
174C3×C4—52no—
175C3×C4—202no—
176C2×C5C2×C3×#10111yescharacteristic
177C2×C5C3×#41612yes—
178D5—41no—
179C23—51no—
180Q8—204no—
181C2×C4—22no—
182C2×C4—51no—
183C2×C4—52no—
184C2×C4—102no—
185C2×C4—104no—
186C2×C4—102no—
187C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
188C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
189C8—204no—
190C2×C3—201no—
191C2×C3D5⋊#10111yescharacteristic
192C2×C3#6579412yes—
193C5C3×#154411yescharacteristic, complemented, Sylow
194C22—101no—
195C22—102no—
196C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
197C4—21no—
198C4—22no—
199C4—42no—
200C4—52no—
201C4—54no—
202C4—202no—
203C3#1060458411yescharacteristic, direct product factor, Sylow
204C2—201no—
205C2C3×D5⋊#10111yescharacteristic
206C2C3×#6579412yes—
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#125C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×#125AGL(1,𝔽5)
hypocenterC5C3×#1544
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
3. C3×#64873C2semidirect
4. #10604584C3direct (N × H)
18. #64873C2×C3semidirect
166. C3×C5#1544semidirect
193. C5C3×#1544semidirect
203. C3#10604584direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660222
C3×#656782
C3×#648732
#106045843
C3×#15445