Finite Group Databasebeta

← C3×#10604387 #14298689

Subgroups — C3×#10604387 #14298689

Order 1920.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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×#65850C211yesmaximal, characteristic
2C2×C3×#4005C212yesmaximal
3C3×#64867C214yesmaximal
4#10604387C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×Dic10C2211yescharacteristic
6C2×C3×#704C2214yes—
7C3×C5×#117C411yescharacteristic
8C3×#4072C411yescharacteristic
9C3×#4033—22no—
10C3×#4023C412yes—
11C3×#4023C2212yes—
12C3×C4×Dic10—22no—
13C3×#4005—22no—
14C3×#4005—22no—
15C3×#1830—51nomaximal, Hall
16#65850C2×C311yescharacteristic
17C2×#4005C2×C312yes—
18#64867C2×C314yes—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×Dic5C2×C411yescharacteristic
21C22×C3×Dic5C2311yescharacteristic
22C2×C3×Dic10—24no—
23C2×C3×Dic10D412yes—
24C2×C3×Dic10D412yes—
25C3×#704—24no—
26C3×#704—24no—
27C2×C3×#170—24no—
28C3×C5×C4⋊C4—21no—
29C3×C5×C22⋊C4C2×C412yes—
30C3×C42×C5—21no—
31C3×C22⋊Dic5C2×C412yes—
32C3×C4⋊Dic5—21no—
33C3×#683—22no—
34C3×#683—22no—
35C3×C4×Dic5—21no—
36C3×C4×Dic5—22no—
37C3×C4×Dic5—22no—
38C3×#519—51no—
39C2×C3×#101—52no—
40C3×#344—54no—
41C22×Dic10C22×C311yescharacteristic
42C2×#704C22×C314yes—
43C5×#117C3×C411yescharacteristic
44#4072C3×C411yescharacteristic
45#4033—22no—
46#4023C3×C412yes—
47#4023C22×C312yes—
48C4×Dic10—22no—
49#4005—22no—
50#4005—22no—
51#1830—51noSylow
52C23×C3×C5C22×C411yescharacteristic
53C2×C3×C4×C5—22no—
54C2×C3×C4×C5—22no—
55C2×C3×C4×C5C22⋊C411yescharacteristic
56C2×C3×C4×C5C22⋊C411yescharacteristic
57C2×C3×Dic5—22no—
58C2×C3×Dic5—22no—
59C2×C3×Dic5C22⋊C412yes—
60C2×C3×Dic5C2×D412yes—
61C2×C3×Dic5#4114yes—
62C3×Dic10—24no—
63C3×Dic10—24no—
64C3×#170—44no—
65C22×C3×Q8—51no—
66C2×C3×M16—54no—
67C3×C4×Q8—102no—
68C3×C4×Q8—102no—
69C3×#117—51no—
70C3×#117—52no—
71C3×#117—52no—
72C3×#117AGL(1,𝔽5)11yescharacteristic
73C3×#101—102no—
74C3×#101—102no—
75C22×C4×C5C2×C3×C411yescharacteristic
76C22×Dic5C2×C3×C411yescharacteristic
77C22×Dic5C23×C311yescharacteristic
78C2×Dic10—24no—
79C2×Dic10C3×D412yes—
80C2×Dic10C3×D412yes—
81#704—24no—
82#704—24no—
83C2×#170—24no—
84C5×C4⋊C4—21no—
85C5×C22⋊C4C2×C3×C412yes—
86C42×C5—21no—
87C22⋊Dic5C2×C3×C412yes—
88C4⋊Dic5—21no—
89#683—22no—
90#683—22no—
91C4×Dic5—21no—
92C4×Dic5—22no—
93C4×Dic5—22no—
94#519—51no—
95C2×#101—52no—
96#344—54no—
97C22×C3×C5—41no—
98C22×C3×C5C2×C22⋊C411yescharacteristic
99C22×C3×C5#11712yes—
100C3×C4×C5—21no—
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×Dic5—22no—
104C3×Dic5—42no—
105C3×Dic5#12314yes—
106C2×C3×Q8—52no—
107C2×C3×Q8—52no—
108C2×C3×Q8—104no—
109C22×C3×C4—51no—
110C22×C3×C4—51no—
111C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
112C3×M16—104no—
113C3×M16—104no—
114C2×C3×C8—104no—
115C3×C4⋊C4—21no—
116C3×C4⋊C4—102no—
117C3×C4⋊C4—102no—
118C3×C4⋊C4—101no—
119C3×C22⋊C4—52no—
120C3×C22⋊C4C2×AGL(1,𝔽5)12yes—
121C3×C42—21no—
122C3×C42—102no—
123C3×C42—102no—
124C3×C42—101no—
125C23×C5C22×C3×C411yescharacteristic
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5C3×C22⋊C411yescharacteristic
129C2×C4×C5C3×C22⋊C411yescharacteristic
130C2×Dic5—22no—
131C2×Dic5—22no—
132C2×Dic5C3×C22⋊C412yes—
133C2×Dic5C2×C3×D412yes—
134C2×Dic5C3×#4114yes—
135Dic10—24no—
136Dic10—24no—
137#170—44no—
138C22×Q8—51no—
139C2×M16—54no—
140C4×Q8—102no—
141C4×Q8—102no—
142#117—51no—
143#117—52no—
144#117—52no—
145#117C3×AGL(1,𝔽5)11yescharacteristic
146#101—102no—
147#101—102no—
148C2×C3×C5—21no—
149C2×C3×C5—22no—
150C2×C3×C5#38111yescharacteristic
151C23×C3C22×AGL(1,𝔽5)11yescharacteristic
152C3×Q8—104no—
153C3×Q8—104no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—54no—
157C2×C3×C4—52no—
158C2×C3×C4—52no—
159C2×C3×C4—102no—
160C2×C3×C4—102no—
161C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
162C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
163C3×C8—204no—
164C22×C5—41no—
165C22×C5C2×C3×C22⋊C411yescharacteristic
166C22×C5C3×#11712yes—
167C4×C5—21no—
168C4×C5—21no—
169C4×C5—42no—
170Dic5—22no—
171Dic5—42no—
172Dic5C3×#12314yes—
173C2×Q8—52no—
174C2×Q8—52no—
175C2×Q8—104no—
176C22×C4—51no—
177C22×C4—51no—
178C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
179M16—104no—
180M16—104no—
181C2×C8—104no—
182C4⋊C4—21no—
183C4⋊C4—102no—
184C4⋊C4—102no—
185C4⋊C4—101no—
186C22⋊C4—52no—
187C22⋊C4C2×C3×AGL(1,𝔽5)12yes—
188C42—21no—
189C42—102no—
190C42—102no—
191C42—101no—
192C3×C5#183011yescharacteristic, complemented, Hall
193C22×C3—41no—
194C22×C3#413012yes—
195C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—42no—
199C3×C4—54no—
200C3×C4—102no—
201C3×C4—202no—
202C2×C5—21no—
203C2×C5—22no—
204C2×C5C3×#38111yescharacteristic
205C23C22×C3×AGL(1,𝔽5)11yescharacteristic
206Q8—104no—
207Q8—104no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—54no—
211C2×C4—52no—
212C2×C4—52no—
213C2×C4—102no—
214C2×C4—102no—
215C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
216C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
217C8—204no—
218C2×C3—21no—
219C2×C3—22no—
220C2×C3#6576411yescharacteristic
221C5C3×#183011yescharacteristic, complemented, Sylow
222C22—41no—
223C22C3×#413012yes—
224C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
225C4—21no—
226C4—21no—
227C4—42no—
228C4—54no—
229C4—102no—
230C4—202no—
231C3#1060438711yescharacteristic, direct product factor, Sylow
232C2—21no—
233C2—22no—
234C2C3×#6576411yescharacteristic
subgroupG/H
centerC2×C3#65764
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC2×C3×C5#381
prime radicalC23×C3×C5C22×C4
cosocleC22×Dic5C23×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C3×#1830
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
4. #10604387C3direct (N × H)
192. C3×C5#1830semidirect
221. C5C3×#1830semidirect
231. C3#10604387direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658502
C2×C3×#40052
C3×#648672
#106043873
C3×#18305