Finite Group Databasebeta

← C3×#10604633 #14283986

Subgroups — C3×#10604633 #14283986

Order 1920.

540 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4×#700C212yesmaximal, complemented
3C3×#64927C214yesmaximal, complemented
4#10604633C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#713C412yes—
6C2×C3×#700—22no—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×#4093C2212yes—
9C3×#4041—22no—
10C3×#4039—22no—
11C3×#4020C411yescharacteristic
12C3×C42×D5C2211yescharacteristic
13C3×#4002C2214yes—
14C3×C4×#170—22no—
15C3×#1525—51nomaximal, Hall
16#66059C2×C311yescharacteristic
17C4×#700C2×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×#700—28no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2×C411yescharacteristic
31C3×#685—24no—
32C3×C4×Dic5D412yes—
33C3×C4×Dic5C2311yescharacteristic
34C3×#532—51no—
35C3×C4×M16—52no—
36C3×#329—54no—
37C2×#713C3×C412yes—
38C2×#700—22no—
39C5×C4⋊Q8C3×C411yescharacteristic
40#4093C22×C312yes—
41#4041—22no—
42#4039—22no—
43#4020C3×C411yescharacteristic
44C42×D5C22×C311yescharacteristic
45#4002C22×C314yes—
46C4×#170—22no—
47#1525—51noSylow
48C22×C3×D5—22no—
49C22×C3×D5C22⋊C411yescharacteristic
50C3×C5×Q8—42no—
51C2×C3×C4×C5—22no—
52C2×C3×C4×C5C22⋊C412yes—
53C2×C3×C4×C5C22×C411yescharacteristic
54C2×C3×Dic5C22⋊C411yescharacteristic
55C2×C3×Dic5C2×D412yes—
56C3×D20—42no—
57C3×D20—44no—
58C3×D20—44no—
59C3×C4×D5—24no—
60C3×C4×D5—22no—
61C3×C4×D5—44no—
62C3×#170—28no—
63C2×C3×#41—52no—
64C2×C3×M16—102no—
65C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
66C3×#127—51no—
67C3×#124—52no—
68C3×#121—102no—
69C3×C4×D4—102no—
70C2×C3×C42—51no—
71C3×#97—54no—
72C3×C4×C8—102no—
73C2×C5×Q8C2×C3×C412yes—
74#713—44no—
75C2×D20—22no—
76C2×D20—22no—
77C2×D20C2×C3×C412yes—
78C2×C4×D5—22no—
79C2×C4×D5C2×C3×C411yescharacteristic
80C2×C4×D5C3×D412yes—
81C2×#170—24no—
82#700—28no—
83C5×C4⋊C4—22no—
84C42×C5C2×C3×C411yescharacteristic
85#685—24no—
86C4×Dic5C3×D412yes—
87C4×Dic5C23×C311yescharacteristic
88#532—51no—
89C4×M16—52no—
90#329—54no—
91C22×C3×C5C2×C22⋊C411yescharacteristic
92C2×C3×D5—21no—
93C2×C3×D5—22no—
94C2×C3×D5—42no—
95C2×C3×D5—44no—
96C3×C4×C5—21no—
97C3×C4×C5—42no—
98C3×C4×C5#10414yes—
99C3×Dic5—22no—
100C3×Dic5#10012yes—
101C3×#41—204no—
102C2×C3×Q8C2×AGL(1,𝔽5)12yes—
103C2×C3×D4—52no—
104C2×C3×D4—102no—
105C2×C3×D4—102no—
106C22×C3×C4—52no—
107C22×C3×C4—51no—
108C22×C3×C4—102no—
109C3×M16—108no—
110C2×C3×C8—104no—
111C3×C4⋊C4—22no—
112C3×C22⋊C4—104no—
113C3×C42—52no—
114C3×C42—51no—
115C3×C42C2×AGL(1,𝔽5)11yescharacteristic
116C22×D5—22no—
117C22×D5C3×C22⋊C411yescharacteristic
118C5×Q8—42no—
119C2×C4×C5—22no—
120C2×C4×C5C3×C22⋊C412yes—
121C2×C4×C5C22×C3×C411yescharacteristic
122C2×Dic5C3×C22⋊C411yescharacteristic
123C2×Dic5C2×C3×D412yes—
124D20—42no—
125D20—44no—
126D20—44no—
127C4×D5—24no—
128C4×D5—22no—
129C4×D5—44no—
130#170—28no—
131C2×#41—52no—
132C2×M16—102no—
133C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic
134#127—51no—
135#124—52no—
136#121—102no—
137C4×D4—102no—
138C2×C42—51no—
139#97—54no—
140C4×C8—102no—
141C2×C3×C5C2×#10011yescharacteristic
142C2×C3×C5C2×#10412yes—
143C3×D5—41no—
144C3×D5—82no—
145C23×C3—51no—
146C23×C3—102no—
147C3×Q8—42no—
148C3×D4—202no—
149C3×D4—204no—
150C3×D4—204no—
151C2×C3×C4—22no—
152C2×C3×C4—51no—
153C2×C3×C4—52no—
154C2×C3×C4—102no—
155C2×C3×C4—104no—
156C2×C3×C4—204no—
157C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
158C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
159C3×C8—108no—
160C22×C5C2×C3×C22⋊C411yescharacteristic
161C2×D5—21no—
162C2×D5—22no—
163C2×D5—42no—
164C2×D5—44no—
165C4×C5—21no—
166C4×C5—42no—
167C4×C5C3×#10414yes—
168Dic5—22no—
169Dic5C3×#10012yes—
170#41—204no—
171C2×Q8C2×C3×AGL(1,𝔽5)12yes—
172C2×D4—52no—
173C2×D4—102no—
174C2×D4—102no—
175C22×C4—52no—
176C22×C4—51no—
177C22×C4—102no—
178M16—108no—
179C2×C8—104no—
180C4⋊C4—22no—
181C22⋊C4—104no—
182C42—52no—
183C42—51no—
184C42C2×C3×AGL(1,𝔽5)11yescharacteristic
185C3×C5#152511yescharacteristic, complemented, Hall
186C22×C3—101no—
187C22×C3—102no—
188C22×C3—202no—
189C22×C3—204no—
190C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
191C3×C4—21no—
192C3×C4—42no—
193C3×C4—52no—
194C3×C4—102no—
195C3×C4#401014yes—
196C2×C5C2×C3×#10011yescharacteristic
197C2×C5C2×C3×#10412yes—
198D5—41no—
199D5—82no—
200C23—51no—
201C23—102no—
202Q8—42no—
203D4—202no—
204D4—204no—
205D4—204no—
206C2×C4—22no—
207C2×C4—51no—
208C2×C4—52no—
209C2×C4—102no—
210C2×C4—104no—
211C2×C4—204no—
212C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
213C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
214C8—108no—
215C2×C3—201no—
216C2×C3—402no—
217C2×C3D5⋊#10011yescharacteristic
218C2×C3C2×#401012yes—
219C5C3×#152511yescharacteristic, complemented, Sylow
220C22—101no—
221C22—102no—
222C22—202no—
223C22—204no—
224C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
225C4—21no—
226C4—42no—
227C4—52no—
228C4—102no—
229C4C3×#401014yes—
230C3#1060463311yescharacteristic, direct product factor, Sylow
231C2—201no—
232C2—402no—
233C2C3×D5⋊#10011yescharacteristic
234C2C2×C3×#401012yes—
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×#1525
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×C4×#700C2semidirect
3. C3×#64927C2semidirect
4. #10604633C3direct (N × H)
17. C4×#700C2×C3semidirect
18. #64927C2×C3semidirect
185. C3×C5#1525semidirect
219. C5C3×#1525semidirect
230. C3#10604633direct (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×C4×#7002
C3×#649272
#106046333
C3×#15255