Finite Group Databasebeta

← C3×#10604662 #14285344

Subgroups — C3×#10604662 #14285344

Order 1920.

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

normal subgroups only

This group has 456 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×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×#65684C212yesmaximal
3C3×#64931C214yesmaximal, complemented
4#10604662C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×Q8×D5C412yes—
6C3×C5×C4⋊Q8C411yescharacteristic
7C3×#4090C2212yes—
8C3×D5×C4⋊C4—22no—
9C3×#4034—22no—
10C3×C42×D5C2211yescharacteristic
11C3×#4015C411yescharacteristic
12C3×#4004C2214yes—
13C3×#4003—22no—
14C3×#4002—22no—
15C3×#1558—51nomaximal, Hall
16D5×C4⋊Q8C2×C311yescharacteristic
17#65684C2×C312yes—
18#64931C2×C314yescomplemented
19C2×C3×C5×Q8C2×C412yes—
20C3×Q8×D5—44no—
21C2×C3×C4×D5—22no—
22C2×C3×C4×D5C2×C411yescharacteristic
23C2×C3×C4×D5D412yes—
24C2×C3×Dic10—22no—
25C2×C3×Dic10C2×C412yes—
26C2×C3×#170—24no—
27C3×C5×C4⋊C4—22no—
28C3×C42×C5C2×C411yescharacteristic
29C3×C4⋊Dic5—22no—
30C3×#683—24no—
31C3×C4×Dic5D412yes—
32C3×C4×Dic5C2311yescharacteristic
33C2×C3×C4⋊Q8—51no—
34C3×#432—52no—
35C3×#333—54no—
36C2×Q8×D5C3×C412yes—
37C5×C4⋊Q8C3×C411yescharacteristic
38#4090C22×C312yes—
39D5×C4⋊C4—22no—
40#4034—22no—
41C42×D5C22×C311yescharacteristic
42#4015C3×C411yescharacteristic
43#4004C22×C314yes—
44#4003—22no—
45#4002—22no—
46#1558—51noSylow
47C22×C3×D5C22⋊C411yescharacteristic
48C3×C5×Q8—42no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5C22⋊C412yes—
51C2×C3×C4×C5C22×C411yescharacteristic
52C2×C3×Dic5—22no—
53C2×C3×Dic5C22⋊C411yescharacteristic
54C2×C3×Dic5C2×D412yes—
55C3×C4×D5—22no—
56C3×C4×D5—24no—
57C3×C4×D5—44no—
58C3×Dic10—44no—
59C3×Dic10—42no—
60C3×#170—44no—
61C22×C3×Q8—52no—
62C3×C4⋊Q8—52no—
63C3×C4⋊Q8—51no—
64C3×C4⋊Q8—102no—
65C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
66C2×C3×C4⋊C4—102no—
67C2×C3×C42—51no—
68C3×C4⋊C8—54no—
69C3×C22⋊C8—102no—
70C3×#97—102no—
71C2×C5×Q8C2×C3×C412yes—
72Q8×D5—44no—
73C2×C4×D5—22no—
74C2×C4×D5C2×C3×C411yescharacteristic
75C2×C4×D5C3×D412yes—
76C2×Dic10—22no—
77C2×Dic10C2×C3×C412yes—
78C2×#170—24no—
79C5×C4⋊C4—22no—
80C42×C5C2×C3×C411yescharacteristic
81C4⋊Dic5—22no—
82#683—24no—
83C4×Dic5C3×D412yes—
84C4×Dic5C23×C311yescharacteristic
85C2×C4⋊Q8—51no—
86#432—52no—
87#333—54no—
88C22×C3×C5C2×C22⋊C411yescharacteristic
89C2×C3×D5—22no—
90C2×C3×D5#10012yes—
91C3×C4×C5—21no—
92C3×C4×C5—22no—
93C3×C4×C5—42no—
94C3×Dic5—21no—
95C3×Dic5—42no—
96C3×Dic5#13714yes—
97C2×C3×Q8—52no—
98C2×C3×Q8—102no—
99C2×C3×Q8—204no—
100C2×C3×Q8C2×AGL(1,𝔽5)12yes—
101C22×C3×C4—52no—
102C22×C3×C4—51no—
103C22×C3×C4—102no—
104C2×C3×C8—104no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—104no—
107C3×C4⋊C4—102no—
108C3×C42—52no—
109C3×C42—51no—
110C3×C42C2×AGL(1,𝔽5)11yescharacteristic
111C22×D5C3×C22⋊C411yescharacteristic
112C5×Q8—42no—
113C2×C4×C5—22no—
114C2×C4×C5C3×C22⋊C412yes—
115C2×C4×C5C22×C3×C411yescharacteristic
116C2×Dic5—22no—
117C2×Dic5C3×C22⋊C411yescharacteristic
118C2×Dic5C2×C3×D412yes—
119C4×D5—22no—
120C4×D5—24no—
121C4×D5—44no—
122Dic10—44no—
123Dic10—42no—
124#170—44no—
125C22×Q8—52no—
126C4⋊Q8—52no—
127C4⋊Q8—51no—
128C4⋊Q8—102no—
129C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic
130C2×C4⋊C4—102no—
131C2×C42—51no—
132C4⋊C8—54no—
133C22⋊C8—102no—
134#97—102no—
135C2×C3×C5C2×#10011yescharacteristic
136C2×C3×C5#41912yes—
137C3×D5—22no—
138C23×C3—51no—
139C3×Q8—42no—
140C3×Q8—202no—
141C3×Q8—204no—
142C2×C3×C4—22no—
143C2×C3×C4—52no—
144C2×C3×C4—51no—
145C2×C3×C4—104no—
146C2×C3×C4—102no—
147C2×C3×C4—102no—
148C2×C3×C4—204no—
149C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
150C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
151C3×C8—204no—
152C22×C5C2×C3×C22⋊C411yescharacteristic
153C2×D5—22no—
154C2×D5C3×#10012yes—
155C4×C5—21no—
156C4×C5—22no—
157C4×C5—42no—
158Dic5—21no—
159Dic5—42no—
160Dic5C3×#13714yes—
161C2×Q8—52no—
162C2×Q8—102no—
163C2×Q8—204no—
164C2×Q8C2×C3×AGL(1,𝔽5)12yes—
165C22×C4—52no—
166C22×C4—51no—
167C22×C4—102no—
168C2×C8—104no—
169C4⋊C4—22no—
170C4⋊C4—104no—
171C4⋊C4—102no—
172C42—52no—
173C42—51no—
174C42C2×C3×AGL(1,𝔽5)11yescharacteristic
175C3×C5#155811yescharacteristic, complemented, Hall
176C22×C3—52no—
177C22×C3—102no—
178C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
179C3×C4—21no—
180C3×C4—22no—
181C3×C4—42no—
182C3×C4—54no—
183C3×C4—101no—
184C3×C4—202no—
185C2×C5C2×C3×#10011yescharacteristic
186C2×C5C3×#41912yes—
187D5—22no—
188C23—51no—
189Q8—42no—
190Q8—202no—
191Q8—204no—
192C2×C4—22no—
193C2×C4—52no—
194C2×C4—51no—
195C2×C4—104no—
196C2×C4—102no—
197C2×C4—102no—
198C2×C4—204no—
199C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
200C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
201C8—204no—
202C2×C3—102no—
203C2×C3D5⋊#10011yescharacteristic
204C2×C3#6578212yes—
205C5C3×#155811yescharacteristic, complemented, Sylow
206C22—52no—
207C22—102no—
208C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
209C4—21no—
210C4—22no—
211C4—42no—
212C4—54no—
213C4—101no—
214C4—202no—
215C3#1060466211yescharacteristic, direct product factor, Sylow
216C2—102no—
217C2C3×D5⋊#10011yescharacteristic
218C2C3×#6578212yes—
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 radicalC22×C3×D5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#1558
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
3. C3×#64931C2semidirect
4. #10604662C3direct (N × H)
18. #64931C2×C3semidirect
175. C3×C5#1558semidirect
205. C5C3×#1558semidirect
215. C3#10604662direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×#656842
C3×#649312
#106046623
C3×#15585