Finite Group Databasebeta

← C3×#10604638 #14284463

Subgroups — C3×#10604638 #14284463

Order 1920.

476 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 112 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×#66059C211yesmaximal, characteristic
2C3×#65684C212yesmaximal, complemented
3C3×#64927C214yesmaximal, complemented
4#10604638C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#713C412yes—
6C3×C5×C4⋊Q8C411yescharacteristic
7C3×#4093C2212yes—
8C3×#4041—22no—
9C3×#4039—22no—
10C3×#4020C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12C3×#4004—22no—
13C3×#4003—22no—
14C3×#4002C2214yes—
15C3×#1536—51nomaximal, Hall
16#66059C2×C311yescharacteristic
17#65684C2×C312yescomplemented
18#64927C2×C314yescomplemented
19C2×C3×C5×Q8C2×C412yes—
20C3×#713—44no—
21C2×C3×D20—22no—
22C2×C3×D20—22no—
23C2×C3×D20C2×C412yes—
24C2×C3×C4×D5—22no—
25C2×C3×C4×D5C2×C411yescharacteristic
26C2×C3×C4×D5D412yes—
27C2×C3×#170—24no—
28C3×C5×C4⋊C4—22no—
29C3×C42×C5C2×C411yescharacteristic
30C3×#685—24no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5C2311yescharacteristic
33C3×#532—51no—
34C3×#432—52no—
35C3×#329—54no—
36C2×#713C3×C412yes—
37C5×C4⋊Q8C3×C411yescharacteristic
38#4093C22×C312yes—
39#4041—22no—
40#4039—22no—
41#4020C3×C411yescharacteristic
42C42×D5C22×C311yescharacteristic
43#4004—22no—
44#4003—22no—
45#4002C22×C314yes—
46#1536—51noSylow
47C22×C3×D5—22no—
48C22×C3×D5C22⋊C411yescharacteristic
49C3×C5×Q8—42no—
50C2×C3×C4×C5—22no—
51C2×C3×C4×C5C22⋊C412yes—
52C2×C3×C4×C5C22×C411yescharacteristic
53C2×C3×Dic5C22⋊C411yescharacteristic
54C2×C3×Dic5C2×D412yes—
55C3×D20—44no—
56C3×D20—42no—
57C3×D20—44no—
58C3×C4×D5—22no—
59C3×C4×D5—42no—
60C3×C4×D5—44no—
61C3×#170—44no—
62C2×C3×#41—52no—
63C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
64C3×#127—51no—
65C3×#124—52no—
66C3×#121—102no—
67C3×C4×D4—102no—
68C2×C3×C42—51no—
69C3×C4⋊C8—102no—
70C3×C22⋊C8—102no—
71C3×#97—54no—
72C2×C5×Q8C2×C3×C412yes—
73#713—44no—
74C2×D20—22no—
75C2×D20—22no—
76C2×D20C2×C3×C412yes—
77C2×C4×D5—22no—
78C2×C4×D5C2×C3×C411yescharacteristic
79C2×C4×D5C3×D412yes—
80C2×#170—24no—
81C5×C4⋊C4—22no—
82C42×C5C2×C3×C411yescharacteristic
83#685—24no—
84C4×Dic5C3×D412yes—
85C4×Dic5C23×C311yescharacteristic
86#532—51no—
87#432—52no—
88#329—54no—
89C22×C3×C5C2×C22⋊C411yescharacteristic
90C2×C3×D5—21no—
91C2×C3×D5—22no—
92C2×C3×D5—42no—
93C2×C3×D5—44no—
94C3×C4×C5—21no—
95C3×C4×C5—22no—
96C3×C4×C5—42no—
97C3×Dic5—22no—
98C3×Dic5#10012yes—
99C3×#41—204no—
100C2×C3×Q8C2×AGL(1,𝔽5)12yes—
101C2×C3×D4—52no—
102C2×C3×D4—102no—
103C2×C3×D4—102no—
104C22×C3×C4—51no—
105C22×C3×C4—52no—
106C22×C3×C4—102no—
107C2×C3×C8—104no—
108C3×C4⋊C4—22no—
109C3×C22⋊C4—104no—
110C3×C42—52no—
111C3×C42—51no—
112C3×C42C2×AGL(1,𝔽5)11yescharacteristic
113C22×D5—22no—
114C22×D5C3×C22⋊C411yescharacteristic
115C5×Q8—42no—
116C2×C4×C5—22no—
117C2×C4×C5C3×C22⋊C412yes—
118C2×C4×C5C22×C3×C411yescharacteristic
119C2×Dic5C3×C22⋊C411yescharacteristic
120C2×Dic5C2×C3×D412yes—
121D20—42no—
122D20—44no—
123D20—44no—
124C4×D5—22no—
125C4×D5—42no—
126C4×D5—44no—
127#170—44no—
128C2×#41—52no—
129C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic
130#127—51no—
131#124—52no—
132#121—102no—
133C4×D4—102no—
134C2×C42—51no—
135C4⋊C8—102no—
136C22⋊C8—102no—
137#97—54no—
138C2×C3×C5C2×#10011yescharacteristic
139C2×C3×C5#42112yes—
140C3×D5—41no—
141C3×D5—82no—
142C23×C3—51no—
143C23×C3—102no—
144C3×Q8—42no—
145C3×D4—202no—
146C3×D4—204no—
147C3×D4—204no—
148C2×C3×C4—22no—
149C2×C3×C4—51no—
150C2×C3×C4—52no—
151C2×C3×C4—102no—
152C2×C3×C4—202no—
153C2×C3×C4—204no—
154C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
155C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
156C3×C8—204no—
157C22×C5C2×C3×C22⋊C411yescharacteristic
158C2×D5—21no—
159C2×D5—22no—
160C2×D5—42no—
161C2×D5—44no—
162C4×C5—21no—
163C4×C5—22no—
164C4×C5—42no—
165Dic5—22no—
166Dic5C3×#10012yes—
167#41—204no—
168C2×Q8C2×C3×AGL(1,𝔽5)12yes—
169C2×D4—52no—
170C2×D4—102no—
171C2×D4—102no—
172C22×C4—51no—
173C22×C4—52no—
174C22×C4—102no—
175C2×C8—104no—
176C4⋊C4—22no—
177C22⋊C4—104no—
178C42—52no—
179C42—51no—
180C42C2×C3×AGL(1,𝔽5)11yescharacteristic
181C3×C5#153611yescharacteristic, complemented, Hall
182C22×C3—101no—
183C22×C3—102no—
184C22×C3—202no—
185C22×C3—204no—
186C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
187C3×C4—21no—
188C3×C4—22no—
189C3×C4—42no—
190C3×C4—52no—
191C3×C4—102no—
192C2×C5C2×C3×#10011yescharacteristic
193C2×C5C3×#42112yes—
194D5—41no—
195D5—82no—
196C23—51no—
197C23—102no—
198Q8—42no—
199D4—202no—
200D4—204no—
201D4—204no—
202C2×C4—22no—
203C2×C4—51no—
204C2×C4—52no—
205C2×C4—102no—
206C2×C4—202no—
207C2×C4—204no—
208C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
209C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
210C8—204no—
211C2×C3—201no—
212C2×C3—402no—
213C2×C3D5⋊#10011yescharacteristic
214C2×C3#6578412yes—
215C5C3×#153611yescharacteristic, complemented, Sylow
216C22—101no—
217C22—102no—
218C22—202no—
219C22—204no—
220C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
221C4—21no—
222C4—22no—
223C4—42no—
224C4—52no—
225C4—102no—
226C3#1060463811yescharacteristic, direct product factor, Sylow
227C2—201no—
228C2—402no—
229C2C3×D5⋊#10011yescharacteristic
230C2C3×#6578412yes—
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC4×Dic5C23×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#1536
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65684C2semidirect
3. C3×#64927C2semidirect
4. #10604638C3direct (N × H)
17. #65684C2×C3semidirect
18. #64927C2×C3semidirect
181. C3×C5#1536semidirect
215. C5C3×#1536semidirect
226. C3#10604638direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660592
C3×#656842
C3×#649272
#106046383
C3×#15365