Finite Group Databasebeta

← C3×#10604293 #14281032

Subgroups — C3×#10604293 #14281032

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C3×#65759C212yesmaximal, complemented
3C3×#64915C212yesmaximal
4C3×#64913C212yesmaximal, complemented
5#10604293C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C4×D5C411yescharacteristic
7C2×C3×C5×C4⋊C4C411yescharacteristic
8C2×C3×#685C411yescharacteristic
9C2×C3×#685C2211yescharacteristic
10C2×C3×C4⋊Dic5C2211yescharacteristic
11C2×C3×C4×Dic5C411yescharacteristic
12C2×C3×C4×Dic5C2211yescharacteristic
13C3×#4038—22no—
14C3×#4038—22no—
15C3×C22⋊#170C2214yes—
16C3×#4002—22no—
17C3×C4⋊#170—22no—
18C3×#1464—51nomaximal, Hall
19C2×#4038C2×C311yescharacteristic
20#65759C2×C312yescomplemented
21#64915C2×C312yes—
22#64913C2×C312yescomplemented
23C23×C3×D5C2×C411yescharacteristic
24C22×C3×C4×C5C2×C411yescharacteristic
25C22×C3×C4×C5C2×C411yescharacteristic
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×Dic5C2×C411yescharacteristic
28C22×C3×Dic5C2×C411yescharacteristic
29C22×C3×Dic5C2311yescharacteristic
30C2×C3×C4×D5—22no—
31C2×C3×C4×D5—22no—
32C2×C3×C4×D5—21no—
33C2×C3×C4×D5—21no—
34C2×C3×#170—24no—
35C3×C5×C4⋊C4—22no—
36C3×#685—22no—
37C3×#685—22no—
38C3×C4⋊Dic5—22no—
39C3×C4×Dic5—21no—
40C3×C4×Dic5—21no—
41C3×C4×Dic5D412yes—
42C3×C4×Dic5D412yes—
43C2×C3×#117—51no—
44C3×#432—52no—
45C3×#324—52no—
46C3×#323—52no—
47C22×C4×D5C3×C411yescharacteristic
48C2×C5×C4⋊C4C3×C411yescharacteristic
49C2×#685C3×C411yescharacteristic
50C2×#685C22×C311yescharacteristic
51C2×C4⋊Dic5C22×C311yescharacteristic
52C2×C4×Dic5C3×C411yescharacteristic
53C2×C4×Dic5C22×C311yescharacteristic
54#4038—22no—
55#4038—22no—
56C22⋊#170C22×C314yes—
57#4002—22no—
58C4⋊#170—22no—
59#1464—51noSylow
60C23×C3×C5C22×C411yescharacteristic
61C22×C3×D5—21no—
62C22×C3×D5—21no—
63C22×C3×D5—41no—
64C22×C3×D5—41no—
65C22×C3×D5M1612yes—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5C22⋊C412yes—
72C2×C3×C4×C5M1612yes—
73C2×C3×Dic5—21no—
74C2×C3×Dic5—21no—
75C2×C3×Dic5—21no—
76C2×C3×Dic5—41no—
77C2×C3×Dic5—41no—
78C2×C3×Dic5C22⋊C411yescharacteristic
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C2×D412yes—
81C3×C4×D5—24no—
82C3×C4×D5—24no—
83C3×#170—44no—
84C23×C3×C4—51no—
85C3×#117—102no—
86C3×#117—102no—
87C2×C3×C4⋊C4—51no—
88C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
89C2×C3×C22⋊C4—51no—
90C2×C3×C22⋊C4—51no—
91C2×C3×C42—51no—
92C2×C3×C42—51no—
93C3×C4⋊C8—102no—
94C3×C22⋊C8—54no—
95C3×#97—102no—
96C23×D5C2×C3×C411yescharacteristic
97C22×C4×C5C2×C3×C411yescharacteristic
98C22×C4×C5C2×C3×C411yescharacteristic
99C22×C4×C5C2×C3×C411yescharacteristic
100C22×Dic5C2×C3×C411yescharacteristic
101C22×Dic5C2×C3×C411yescharacteristic
102C22×Dic5C23×C311yescharacteristic
103C2×C4×D5—22no—
104C2×C4×D5—22no—
105C2×C4×D5—21no—
106C2×C4×D5—21no—
107C2×#170—24no—
108C5×C4⋊C4—22no—
109#685—22no—
110#685—22no—
111C4⋊Dic5—22no—
112C4×Dic5—21no—
113C4×Dic5—21no—
114C4×Dic5C3×D412yes—
115C4×Dic5C3×D412yes—
116C2×#117—51no—
117#432—52no—
118#324—52no—
119#323—52no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5C2×C22⋊C411yescharacteristic
123C22×C3×C5C2×M1611yescharacteristic
124C22×C3×C5C2×M1611yescharacteristic
125C2×C3×D5—22no—
126C2×C3×D5—42no—
127C2×C3×D5—41no—
128C2×C3×D5—41no—
129C2×C3×D5—42no—
130C3×C4×C5—22no—
131C3×C4×C5—22no—
132C3×C4×C5—41no—
133C3×Dic5—21no—
134C3×Dic5—21no—
135C3×Dic5—22no—
136C3×Dic5—41no—
137C24×C3—51no—
138C22×C3×C4—51no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—101no—
142C22×C3×C4—101no—
143C22×C3×C4—102no—
144C22×C3×C4—102no—
145C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
146C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
147C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3×C8—104no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—102no—
151C3×C22⋊C4—102no—
152C3×C22⋊C4—102no—
153C3×C42—52no—
154C3×C42—52no—
155C3×C42—101no—
156C3×C42—101no—
157C23×C5C22×C3×C411yescharacteristic
158C22×D5—21no—
159C22×D5—21no—
160C22×D5—41no—
161C22×D5—41no—
162C22×D5C3×M1612yes—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5C3×C22⋊C412yes—
169C2×C4×C5C3×M1612yes—
170C2×Dic5—21no—
171C2×Dic5—21no—
172C2×Dic5—21no—
173C2×Dic5—41no—
174C2×Dic5—41no—
175C2×Dic5C3×C22⋊C411yescharacteristic
176C2×Dic5C3×C22⋊C411yescharacteristic
177C2×Dic5C2×C3×D412yes—
178C4×D5—24no—
179C4×D5—24no—
180#170—44no—
181C23×C4—51no—
182#117—102no—
183#117—102no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
186C2×C22⋊C4—51no—
187C2×C22⋊C4—51no—
188C2×C42—51no—
189C2×C42—51no—
190C4⋊C8—102no—
191C22⋊C8—54no—
192#97—102no—
193C2×C3×C5—21no—
194C2×C3×C5—21no—
195C2×C3×C5#40711yescharacteristic
196C2×C3×C5#41011yescharacteristic
197C2×C3×C5#41311yescharacteristic
198C3×D5—42no—
199C23×C3—52no—
200C23×C3—101no—
201C23×C3—101no—
202C23×C3—201no—
203C23×C3—201no—
204C23×C3C22×AGL(1,𝔽5)11yescharacteristic
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—51no—
211C2×C3×C4—51no—
212C2×C3×C4—52no—
213C2×C3×C4—104no—
214C2×C3×C4—104no—
215C2×C3×C4—101no—
216C2×C3×C4—101no—
217C2×C3×C4—101no—
218C2×C3×C4—201no—
219C2×C3×C4—201no—
220C2×C3×C4#70012yes—
221C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
222C3×C8—204no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5C2×C3×C22⋊C411yescharacteristic
226C22×C5C2×C3×M1611yescharacteristic
227C22×C5C2×C3×M1611yescharacteristic
228C2×D5—22no—
229C2×D5—42no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5—42no—
233C4×C5—22no—
234C4×C5—22no—
235C4×C5—41no—
236Dic5—21no—
237Dic5—21no—
238Dic5—22no—
239Dic5—41no—
240C24—51no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4—102no—
247C22×C4—102no—
248C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
249C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
250C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
251C2×C8—104no—
252C4⋊C4—22no—
253C4⋊C4—102no—
254C22⋊C4—102no—
255C22⋊C4—102no—
256C42—52no—
257C42—52no—
258C42—101no—
259C42—101no—
260C3×C5#146411yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—102no—
264C22×C3—202no—
265C22×C3—202no—
266C22×C3—201no—
267C22×C3—201no—
268C22×C3C2×#70011yescharacteristic
269C22×C3D5⋊M1611yescharacteristic
270C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—41no—
274C3×C4—101no—
275C3×C4—101no—
276C3×C4—102no—
277C3×C4—201no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5C3×#40711yescharacteristic
281C2×C5C3×#41011yescharacteristic
282C2×C5C3×#41311yescharacteristic
283D5—42no—
284C23—52no—
285C23—101no—
286C23—101no—
287C23—201no—
288C23—201no—
289C23C22×C3×AGL(1,𝔽5)11yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—52no—
298C2×C4—104no—
299C2×C4—104no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4C3×#70012yes—
306C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
307C8—204no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—202no—
311C2×C3#6575611yescharacteristic
312C2×C3#6577711yescharacteristic
313C2×C3#6578511yescharacteristic
314C5C3×#146411yescharacteristic, complemented, Sylow
315C22—21no—
316C22—21no—
317C22—102no—
318C22—202no—
319C22—202no—
320C22—201no—
321C22—201no—
322C22C2×C3×#70011yescharacteristic
323C22C3×D5⋊M1611yescharacteristic
324C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—101no—
329C4—101no—
330C4—102no—
331C4—201no—
332C3#1060429311yescharacteristic, direct product factor, Sylow
333C2—21no—
334C2—21no—
335C2—202no—
336C2C3×#6575611yescharacteristic
337C2C3×#6577711yescharacteristic
338C2C3×#6578511yescharacteristic
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×D5C2×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1464
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
2. C3×#65759C2semidirect
4. C3×#64913C2semidirect
5. #10604293C3direct (N × H)
20. #65759C2×C3semidirect
22. #64913C2×C3semidirect
260. C3×C5#1464semidirect
314. C5C3×#1464semidirect
332. C3#10604293direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C3×#657592
C3×#649152
C3×#649132
#106042933
C3×#14645