Finite Group Databasebeta

← C3×#10604299 #14281292

Subgroups — C3×#10604299 #14281292

Order 1920.

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

normal subgroups only

This group has 408 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
1C2×C3×#4036C211yesmaximal, characteristic
2C3×#65759C211yesmaximal, characteristic
3C3×#65754C211yesmaximal, characteristic
4C3×#64914C214yesmaximal
5#10604299C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×C4⋊Dic5C411yescharacteristic
8C2×C3×C4⋊Dic5C412yes—
9C2×C3×#683C2212yes—
10C2×C3×C4×Dic5C2211yescharacteristic
11C3×#4036—21no—
12C3×#4036—21no—
13C3×#4036—21no—
14C3×#4036—21no—
15C3×C22⋊#170C2212yes—
16C3×C22⋊#170C2212yes—
17C3×#4004—21no—
18C3×#4002—21no—
19C3×C4⋊#170—21no—
20C3×C4×#170—21no—
21C3×#1470—51nomaximal, Hall
22C2×#4036C2×C311yescharacteristic
23#65759C2×C311yescharacteristic
24#65754C2×C311yescharacteristic
25#64914C2×C314yes—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C412yes—
28C22×C3×Dic5C2×C412yes—
29C22×C3×Dic5C2×C411yescharacteristic
30C22×C3×Dic5C2311yescharacteristic
31C2×C3×#170—22no—
32C2×C3×#170—22no—
33C3×C5×C4⋊C4—21no—
34C3×C5×C4⋊C4—21no—
35C3×C4⋊Dic5—21no—
36C3×C4⋊Dic5—21no—
37C3×C4⋊Dic5—22no—
38C3×C4⋊Dic5—22no—
39C3×#683—22no—
40C3×#683—22no—
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5D411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C2×C3×#125—51no—
46C3×#432—51no—
47C3×#431—51no—
48C3×#324—54no—
49C2×C5×C4⋊C4C3×C411yescharacteristic
50C2×C4⋊Dic5C3×C411yescharacteristic
51C2×C4⋊Dic5C3×C412yes—
52C2×#683C22×C312yes—
53C2×C4×Dic5C22×C311yescharacteristic
54#4036—21no—
55#4036—21no—
56#4036—21no—
57#4036—21no—
58C22⋊#170C22×C312yes—
59C22⋊#170C22×C312yes—
60#4004—21no—
61#4002—21no—
62C4⋊#170—21no—
63C4×#170—21no—
64#1470—51noSylow
65C23×C3×C5C22×C411yescharacteristic
66C2×C3×C4×C5—22no—
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5—42no—
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×Dic5—22no—
72C2×C3×Dic5—22no—
73C2×C3×Dic5—24no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5C22⋊C411yescharacteristic
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C3×#170—42no—
80C3×#170—42no—
81C3×#125—101no—
82C3×#125—101no—
83C3×#125—101no—
84C3×#125—101no—
85C2×C3×C4⋊C4—52no—
86C2×C3×C4⋊C4—52no—
87C2×C3×C4⋊C4—51no—
88C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
89C2×C3×C42—51no—
90C3×C4⋊C8—101no—
91C3×C4⋊C8—101no—
92C3×C22⋊C8—52no—
93C3×C22⋊C8—52no—
94C3×#97—101no—
95C3×C4×C8—101no—
96C22×C4×C5C2×C3×C411yescharacteristic
97C22×C4×C5C2×C3×C412yes—
98C22×Dic5C2×C3×C412yes—
99C22×Dic5C2×C3×C411yescharacteristic
100C22×Dic5C23×C311yescharacteristic
101C2×#170—22no—
102C2×#170—22no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—21no—
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—22no—
108C4⋊Dic5—22no—
109#683—22no—
110#683—22no—
111C4×Dic5C3×D411yescharacteristic
112C4×Dic5C3×D411yescharacteristic
113C4×Dic5C3×D411yescharacteristic
114C4×Dic5C3×D411yescharacteristic
115C2×#125—51no—
116#432—51no—
117#431—51no—
118#324—54no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5C2×C22⋊C411yescharacteristic
122C22×C3×C5#13112yes—
123C3×C4×C5—21no—
124C3×C4×C5—42no—
125C3×C4×C5#10112yes—
126C3×Dic5—21no—
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—21no—
130C3×Dic5—42no—
131C22×C3×C4—51no—
132C22×C3×C4—51no—
133C22×C3×C4—52no—
134C22×C3×C4C2×AGL(1,𝔽5)12yes—
135C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
136C2×C3×C8—102no—
137C2×C3×C8—102no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—102no—
141C3×C4⋊C4—102no—
142C3×C4⋊C4—102no—
143C3×C4⋊C4—102no—
144C3×C4⋊C4—101no—
145C3×C4⋊C4—101no—
146C3×C42—51no—
147C3×C42—51no—
148C3×C42—51no—
149C3×C42—51no—
150C23×C5C22×C3×C411yescharacteristic
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—42no—
154C2×C4×C5C3×C22⋊C411yescharacteristic
155C2×C4×C5C3×C22⋊C411yescharacteristic
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—24no—
159C2×Dic5—41no—
160C2×Dic5C3×C22⋊C411yescharacteristic
161C2×Dic5C3×C22⋊C411yescharacteristic
162C2×Dic5C2×C3×D411yescharacteristic
163C2×Dic5C2×C3×D411yescharacteristic
164#170—42no—
165#170—42no—
166#125—101no—
167#125—101no—
168#125—101no—
169#125—101no—
170C2×C4⋊C4—52no—
171C2×C4⋊C4—52no—
172C2×C4⋊C4—51no—
173C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
174C2×C42—51no—
175C4⋊C8—101no—
176C4⋊C8—101no—
177C22⋊C8—52no—
178C22⋊C8—52no—
179#97—101no—
180C4×C8—101no—
181C2×C3×C5—22no—
182C2×C3×C5#40811yescharacteristic
183C2×C3×C5#41011yescharacteristic
184C2×C3×C5C2×#10111yescharacteristic
185C23×C3C22×AGL(1,𝔽5)11yescharacteristic
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—42no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—51no—
192C2×C3×C4—51no—
193C2×C3×C4—102no—
194C2×C3×C4—104no—
195C2×C3×C4—102no—
196C2×C3×C4—201no—
197C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
198C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
199C3×C8—202no—
200C3×C8—202no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5C2×C3×C22⋊C411yescharacteristic
204C22×C5C3×#13112yes—
205C4×C5—21no—
206C4×C5—42no—
207C4×C5C3×#10112yes—
208Dic5—21no—
209Dic5—21no—
210Dic5—21no—
211Dic5—21no—
212Dic5—42no—
213C22×C4—51no—
214C22×C4—51no—
215C22×C4—52no—
216C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
217C22×C4C2×C3×AGL(1,𝔽5)12yes—
218C2×C8—102no—
219C2×C8—102no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—102no—
223C4⋊C4—102no—
224C4⋊C4—102no—
225C4⋊C4—102no—
226C4⋊C4—101no—
227C4⋊C4—101no—
228C42—51no—
229C42—51no—
230C42—51no—
231C42—51no—
232C3×C5#147011yescharacteristic, complemented, Hall
233C22×C3—21no—
234C22×C3—21no—
235C22×C3#413312yes—
236C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
237C3×C4—21no—
238C3×C4—42no—
239C3×C4—101no—
240C3×C4—101no—
241C3×C4—101no—
242C3×C4—101no—
243C3×C4—202no—
244C3×C4#400512yes—
245C2×C5—22no—
246C2×C5C3×#40811yescharacteristic
247C2×C5C3×#41011yescharacteristic
248C2×C5C2×C3×#10111yescharacteristic
249C23C22×C3×AGL(1,𝔽5)11yescharacteristic
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—51no—
254C2×C4—51no—
255C2×C4—51no—
256C2×C4—51no—
257C2×C4—102no—
258C2×C4—104no—
259C2×C4—102no—
260C2×C4—201no—
261C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
262C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
263C8—202no—
264C8—202no—
265C2×C3—22no—
266C2×C3C2×#400511yescharacteristic
267C2×C3#6577111yescharacteristic
268C2×C3#6578711yescharacteristic
269C5C3×#147011yescharacteristic, complemented, Sylow
270C22—21no—
271C22—21no—
272C22C3×#413312yes—
273C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
274C4—21no—
275C4—42no—
276C4—101no—
277C4—101no—
278C4—101no—
279C4—101no—
280C4—202no—
281C4C3×#400512yes—
282C3#1060429911yescharacteristic, direct product factor, Sylow
283C2—22no—
284C2C2×C3×#400511yescharacteristic
285C2C3×#6577111yescharacteristic
286C2C3×#6578711yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1470
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #10604299C3direct (N × H)
232. C3×C5#1470semidirect
269. C5C3×#1470semidirect
282. C3#10604299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40362
C3×#657592
C3×#657542
C3×#649142
#106042993
C3×#14705