Finite Group Databasebeta

← C3×#10604274 #14282290

Subgroups — C3×#10604274 #14282290

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2C3×#65759C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4C3×#64871C214yesmaximal, complemented
5#10604274C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×D20C411yescharacteristic
7C22×C3×C4×D5—21no—
8C2×C3×#704—21no—
9C2×C3×C5×C4⋊C4C411yescharacteristic
10C2×C3×#685—21no—
11C2×C3×C4×Dic5C2211yescharacteristic
12C3×#4039—21no—
13C3×#4039—21no—
14C3×#4039C412yes—
15C3×#4039C2212yes—
16C3×C22⋊#170—21no—
17C3×#4002—21no—
18C3×#4002—21no—
19C3×C4⋊#170C2212yescomplemented
20C3×C4×#170C2212yescomplemented
21C3×#1490—51nomaximal, Hall
22C2×#4039C2×C311yescharacteristic
23#65759C2×C311yescharacteristic, complemented
24C4×#704C2×C311yescharacteristic, complemented
25#64871C2×C314yescomplemented
26C23×C3×D5—21no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×C3×D20—21no—
32C2×C3×D20—24no—
33C2×C3×D20C2×C412yes—
34C2×C3×C4×D5—22no—
35C2×C3×C4×D5—22no—
36C2×C3×C4×D5—44no—
37C3×#704—24no—
38C2×C3×#170—22no—
39C2×C3×#170—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4C2×C412yes—
42C3×#685—22no—
43C3×#685—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48C2×C3×C4×D4—51no—
49C3×#432—51no—
50C3×C4×M16—51no—
51C3×D4⋊C8—54no—
52C22×D20C3×C411yescharacteristic
53C22×C4×D5—21no—
54C2×#704—21no—
55C2×C5×C4⋊C4C3×C411yescharacteristic
56C2×#685—21no—
57C2×C4×Dic5C22×C311yescharacteristic
58#4039—21no—
59#4039—21no—
60#4039C3×C412yes—
61#4039C22×C312yes—
62C22⋊#170—21no—
63#4002—21no—
64#4002—21no—
65C4⋊#170C22×C312yescomplemented
66C4×#170C22×C312yescomplemented
67#1490—51noSylow
68C23×C3×C5C22⋊C411yescharacteristic
69C22×C3×D5—24no—
70C22×C3×D5—22no—
71C22×C3×D5—42no—
72C22×C3×D5—42no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×Dic5—22no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5C22⋊C411yescharacteristic
81C2×C3×Dic5C22⋊C411yescharacteristic
82C2×C3×Dic5C2×D411yescharacteristic
83C2×C3×Dic5C2×D411yescharacteristic
84C3×D20—24no—
85C3×D20—22no—
86C3×D20M1614yescomplemented
87C3×C4×D5—44no—
88C3×C4×D5—44no—
89C3×#170—24no—
90C3×#170—42no—
91C22×C3×D4—51no—
92C23×C3×C4—101no—
93C2×C3×M16—101no—
94C3×C4×D4—52no—
95C3×C4×D4—52no—
96C3×C4×D4—101no—
97C3×C4×D4—101no—
98C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
99C2×C3×C22⋊C4—101no—
100C2×C3×C42—51no—
101C3×C4⋊C8—52no—
102C3×C22⋊C8—101no—
103C3×#97—101no—
104C3×#97—101no—
105C3×C4×C8—52no—
106C23×D5—21no—
107C22×C4×C5—21no—
108C22×C4×C5C2×C3×C411yescharacteristic
109C22×Dic5C3×D411yescharacteristic
110C22×Dic5C3×D411yescharacteristic
111C2×D20—21no—
112C2×D20—24no—
113C2×D20C2×C3×C412yes—
114C2×C4×D5—22no—
115C2×C4×D5—22no—
116C2×C4×D5—44no—
117#704—24no—
118C2×#170—22no—
119C2×#170—22no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4C2×C3×C412yes—
122#685—22no—
123#685—22no—
124C4×Dic5C2×C3×C411yescharacteristic
125C4×Dic5C3×D411yescharacteristic
126C4×Dic5C3×D411yescharacteristic
127C4×Dic5C23×C311yescharacteristic
128C2×C4×D4—51no—
129#432—51no—
130C4×M16—51no—
131D4⋊C8—54no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5#10412yes—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×C3×D5—24no—
137C2×C3×D5—48no—
138C2×C3×D5—42no—
139C2×C3×D5—42no—
140C3×C4×C5—21no—
141C3×C4×C5—42no—
142C3×C4×C5C2×M1612yes—
143C3×Dic5—21no—
144C3×Dic5—21no—
145C3×Dic5—21no—
146C3×Dic5AGL(1,ℤ/8)12yes—
147C24×C3—101no—
148C2×C3×D4—52no—
149C2×C3×D4—104no—
150C2×C3×D4—101no—
151C22×C3×C4—21no—
152C22×C3×C4—51no—
153C22×C3×C4—51no—
154C22×C3×C4—102no—
155C22×C3×C4—102no—
156C22×C3×C4—204no—
157C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
158C3×M16—104no—
159C2×C3×C8—102no—
160C2×C3×C8—102no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
163C3×C22⋊C4—102no—
164C3×C22⋊C4—102no—
165C3×C42—51no—
166C3×C42—51no—
167C3×C42—51no—
168C3×C42—51no—
169C23×C5C3×C22⋊C411yescharacteristic
170C22×D5—24no—
171C22×D5—22no—
172C22×D5—42no—
173C22×D5—42no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—42no—
177C2×C4×C5C3×C22⋊C411yescharacteristic
178C2×C4×C5C22×C3×C411yescharacteristic
179C2×Dic5—22no—
180C2×Dic5—22no—
181C2×Dic5C3×C22⋊C411yescharacteristic
182C2×Dic5C3×C22⋊C411yescharacteristic
183C2×Dic5C2×C3×D411yescharacteristic
184C2×Dic5C2×C3×D411yescharacteristic
185D20—24no—
186D20—22no—
187D20C3×M1614yescomplemented
188C4×D5—44no—
189C4×D5—44no—
190#170—24no—
191#170—42no—
192C22×D4—51no—
193C23×C4—101no—
194C2×M16—101no—
195C4×D4—52no—
196C4×D4—52no—
197C4×D4—101no—
198C4×D4—101no—
199C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
200C2×C22⋊C4—101no—
201C2×C42—51no—
202C4⋊C8—52no—
203C22⋊C8—101no—
204#97—101no—
205#97—101no—
206C4×C8—52no—
207C2×C3×C5—22no—
208C2×C3×C5#40711yescharacteristic
209C2×C3×C5#41811yescharacteristic
210C2×C3×C5C2×#10411yescharacteristic
211C3×D5—44no—
212C23×C3—104no—
213C23×C3—102no—
214C23×C3—202no—
215C23×C3—202no—
216C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
217C3×D4—54no—
218C3×D4—104no—
219C3×D4—102no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—42no—
223C2×C3×C4—51no—
224C2×C3×C4—51no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—102no—
228C2×C3×C4—102no—
229C2×C3×C4—204no—
230C2×C3×C4—204no—
231C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
233C3×C8—104no—
234C3×C8—202no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5C3×#10412yes—
238C22×C5C2×C3×C22⋊C411yescharacteristic
239C2×D5—24no—
240C2×D5—48no—
241C2×D5—42no—
242C2×D5—42no—
243C4×C5—21no—
244C4×C5—42no—
245C4×C5C2×C3×M1612yes—
246Dic5—21no—
247Dic5—21no—
248Dic5—21no—
249Dic5C3×AGL(1,ℤ/8)12yes—
250C24—101no—
251C2×D4—52no—
252C2×D4—104no—
253C2×D4—101no—
254C22×C4—21no—
255C22×C4—51no—
256C22×C4—51no—
257C22×C4—102no—
258C22×C4—102no—
259C22×C4—204no—
260C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
261M16—104no—
262C2×C8—102no—
263C2×C8—102no—
264C4⋊C4—21no—
265C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
266C22⋊C4—102no—
267C22⋊C4—102no—
268C42—51no—
269C42—51no—
270C42—51no—
271C42—51no—
272C3×C5#149011yescharacteristic, complemented, Hall
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—104no—
276C22×C3—208no—
277C22×C3—202no—
278C22×C3—202no—
279C22×C3#401012yes—
280C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
281C3×C4—21no—
282C3×C4—42no—
283C3×C4—52no—
284C3×C4—101no—
285C3×C4—101no—
286C3×C4—101no—
287C3×C4D5⋊M1612yes—
288C2×C5—22no—
289C2×C5C3×#40711yescharacteristic
290C2×C5C3×#41811yescharacteristic
291C2×C5C2×C3×#10411yescharacteristic
292D5—44no—
293C23—104no—
294C23—102no—
295C23—202no—
296C23—202no—
297C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
298D4—54no—
299D4—104no—
300D4—102no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—51no—
307C2×C4—51no—
308C2×C4—102no—
309C2×C4—102no—
310C2×C4—204no—
311C2×C4—204no—
312C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
313C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
314C8—104no—
315C8—202no—
316C2×C3—22no—
317C2×C3—204no—
318C2×C3#6575511yescharacteristic
319C2×C3#6576711yescharacteristic
320C2×C3C2×#401011yescharacteristic
321C5C3×#149011yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—104no—
325C22—208no—
326C22—202no—
327C22—202no—
328C22C3×#401012yes—
329C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
330C4—21no—
331C4—42no—
332C4—52no—
333C4—101no—
334C4—101no—
335C4—101no—
336C4C3×D5⋊M1612yes—
337C3#1060427411yescharacteristic, direct product factor, Sylow
338C2—22no—
339C2—204no—
340C2C3×#6575511yescharacteristic
341C2C3×#6576711yescharacteristic
342C2C2×C3×#401011yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C4
cosocleC4×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1490
LCSG ▷ C2×C4×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
3. C3×C4×#704C2semidirect
4. C3×#64871C2semidirect
5. #10604274C3direct (N × H)
19. C3×C4⋊#170C22semidirect
20. C3×C4×#170C22semidirect
23. #65759C2×C3semidirect
24. C4×#704C2×C3semidirect
25. #64871C2×C3semidirect
65. C4⋊#170C22×C3semidirect
66. C4×#170C22×C3semidirect
86. C3×D20M16semidirect
187. D20C3×M16semidirect
272. C3×C5#1490semidirect
321. C5C3×#1490semidirect
337. C3#10604274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C3×#657592
C3×C4×#7042
C3×#648712
#106042743
C3×#14905