Finite Group Databasebeta

← C3×#10604287 #14298548

Subgroups — C3×#10604287 #14298548

Order 1920.

612 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C3×#65756C211yesmaximal, characteristic
4C3×#64875C214yesmaximal, complemented
5#10604287C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C4×D5C2211yescharacteristic
7C2×C3×C22⋊AGL(1,𝔽5)—21no—
8C2×C3×C4×AGL(1,𝔽5)C2212yes—
9C2×C3×#700C2212yes—
10C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
11C2×C3×#685—21no—
12C2×C3×C4⋊Dic5C411yescharacteristic, complemented
13C2×C3×C4×Dic5—21no—
14C3×#4038—21no—
15C3×#4038—21no—
16C3×#4038C412yescomplemented
17C3×#4038C2212yes—
18C3×C22⋊#170—21no—
19C3×(C2×AGL(1,𝔽5))⋊C4—21no—
20C3×#4003—21no—
21C3×#1826—51nomaximal, Hall
22C2×#4038C2×C311yescharacteristic
23C4×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic
24#65756C2×C311yescharacteristic
25#64875C2×C314yescomplemented
26C23×C3×D5D411yescharacteristic
27C22×C3×AGL(1,𝔽5)—22no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×Dic5—21no—
31C22×C3×Dic5D411yescharacteristic
32C2×C3×C4×D5—24no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5C2311yescharacteristic
37C3×C22⋊AGL(1,𝔽5)—24no—
38C2×C3×#170—22no—
39C3×C4×AGL(1,𝔽5)—24no—
40C3×#700—24no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4C2×C412yes—
43C3×#685—22no—
44C3×#685—22no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5C2×C412yes—
47C3×C4×Dic5—22no—
48C3×C4×Dic5—22no—
49C2×C3×#117—51no—
50C3×#407—51no—
51C3×C4×C22⋊C4—51no—
52C3×#339—54no—
53C22×C4×D5C22×C311yescharacteristic
54C2×C22⋊AGL(1,𝔽5)—21no—
55C2×C4×AGL(1,𝔽5)C22×C312yes—
56C2×#700C22×C312yes—
57C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
58C2×#685—21no—
59C2×C4⋊Dic5C3×C411yescharacteristic, complemented
60C2×C4×Dic5—21no—
61#4038—21no—
62#4038—21no—
63#4038C3×C412yescomplemented
64#4038C22×C312yes—
65C22⋊#170—21no—
66(C2×AGL(1,𝔽5))⋊C4—21no—
67#4003—21no—
68#1826—51noSylow
69C23×C3×C5C22⋊C411yescharacteristic
70C22×C3×D5—22no—
71C22×C3×D5—22no—
72C22×C3×D5—41no—
73C22×C3×D5C22⋊C411yescharacteristic
74C22×C3×D5C2×D411yescharacteristic
75C2×C3×AGL(1,𝔽5)—24no—
76C2×C3×AGL(1,𝔽5)—42no—
77C2×C3×AGL(1,𝔽5)—42no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—42no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×Dic5—22no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—42no—
86C2×C3×Dic5C22⋊C411yescharacteristic
87C2×C3×Dic5C2×D411yescharacteristic
88C3×C4×D5—22no—
89C3×C4×D5—22no—
90C3×C4×D5—22no—
91C3×C4×D5#4114yes—
92C3×#170—42no—
93C23×C3×C4—51no—
94C2×C3×M16—52no—
95C3×#117—52no—
96C3×#117—52no—
97C3×#117—101no—
98C3×#117—101no—
99C2×C3×C4⋊C4—51no—
100C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
101C2×C3×C22⋊C4—101no—
102C2×C3×C22⋊C4—101no—
103C2×C3×C42—52no—
104C2×C3×C42—101no—
105C3×C22⋊C8—101no—
106C3×C22⋊C8—101no—
107C3×#95—101no—
108C23×D5C3×D411yescharacteristic
109C22×AGL(1,𝔽5)—22no—
110C22×C4×C5—21no—
111C22×C4×C5C2×C3×C411yescharacteristic
112C22×Dic5—21no—
113C22×Dic5C3×D411yescharacteristic
114C2×C4×D5—24no—
115C2×C4×D5C2×C3×C411yescharacteristic
116C2×C4×D5C3×D411yescharacteristic
117C2×C4×D5C3×D411yescharacteristic
118C2×C4×D5C23×C311yescharacteristic
119C22⋊AGL(1,𝔽5)—24no—
120C2×#170—22no—
121C4×AGL(1,𝔽5)—24no—
122#700—24no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4C2×C3×C412yes—
125#685—22no—
126#685—22no—
127C4⋊Dic5—21no—
128C4⋊Dic5C2×C3×C412yes—
129C4×Dic5—22no—
130C4×Dic5—22no—
131C2×#117—51no—
132#407—51no—
133C4×C22⋊C4—51no—
134#339—54no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5#10412yes—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C2×C3×D5—21no—
140C2×C3×D5—21no—
141C2×C3×D5—21no—
142C2×C3×D5—21no—
143C2×C3×D5—21no—
144C2×C3×D5—44no—
145C2×C3×D5#12312yes—
146C3×AGL(1,𝔽5)—44no—
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5#11712yes—
150C3×Dic5—21no—
151C3×Dic5—42no—
152C3×Dic5#12312yes—
153C24×C3—51no—
154C22×C3×C4—21no—
155C22×C3×C4—51no—
156C22×C3×C4—51no—
157C22×C3×C4—51no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C22×C3×C4—104no—
161C22×C3×C4—102no—
162C22×C3×C4—101no—
163C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
164C3×M16—104no—
165C2×C3×C8—102no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—52no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
170C3×C22⋊C4—102no—
171C3×C22⋊C4—102no—
172C3×C22⋊C4—104no—
173C3×C42—102no—
174C3×C42—102no—
175C3×C42—104no—
176C23×C5C3×C22⋊C411yescharacteristic
177C22×D5—22no—
178C22×D5—22no—
179C22×D5—41no—
180C22×D5C3×C22⋊C411yescharacteristic
181C22×D5C2×C3×D411yescharacteristic
182C2×AGL(1,𝔽5)—24no—
183C2×AGL(1,𝔽5)—42no—
184C2×AGL(1,𝔽5)—42no—
185C2×C4×C5—22no—
186C2×C4×C5—22no—
187C2×C4×C5—42no—
188C2×C4×C5C3×C22⋊C411yescharacteristic
189C2×C4×C5C22×C3×C411yescharacteristic
190C2×Dic5—22no—
191C2×Dic5—22no—
192C2×Dic5—42no—
193C2×Dic5C3×C22⋊C411yescharacteristic
194C2×Dic5C2×C3×D411yescharacteristic
195C4×D5—22no—
196C4×D5—22no—
197C4×D5—22no—
198C4×D5C3×#4114yes—
199#170—42no—
200C23×C4—51no—
201C2×M16—52no—
202#117—52no—
203#117—52no—
204#117—101no—
205#117—101no—
206C2×C4⋊C4—51no—
207C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
208C2×C22⋊C4—101no—
209C2×C22⋊C4—101no—
210C2×C42—52no—
211C2×C42—101no—
212C22⋊C8—101no—
213C22⋊C8—101no—
214#95—101no—
215C2×C3×C5—22no—
216C2×C3×C5#38111yescharacteristic
217C2×C3×C5C2×#10411yescharacteristic
218C2×C3×C5#42111yescharacteristic
219C3×D5—22no—
220C3×D5—41no—
221C23×C3—51no—
222C23×C3—51no—
223C23×C3—102no—
224C23×C3—102no—
225C23×C3—201no—
226C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—42no—
230C2×C3×C4—51no—
231C2×C3×C4—54no—
232C2×C3×C4—51no—
233C2×C3×C4—102no—
234C2×C3×C4—102no—
235C2×C3×C4—102no—
236C2×C3×C4—102no—
237C2×C3×C4—104no—
238C2×C3×C4—102no—
239C2×C3×C4—202no—
240C2×C3×C4—202no—
241C2×C3×C4—202no—
242C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
243C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
244C3×C8—202no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5C3×#10412yes—
248C22×C5C2×C3×C22⋊C411yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—44no—
255C2×D5C3×#12312yes—
256AGL(1,𝔽5)—44no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5C3×#11712yes—
260Dic5—21no—
261Dic5—42no—
262Dic5C3×#12312yes—
263C24—51no—
264C22×C4—21no—
265C22×C4—51no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—104no—
271C22×C4—102no—
272C22×C4—101no—
273C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
274M16—104no—
275C2×C8—102no—
276C4⋊C4—21no—
277C4⋊C4—52no—
278C4⋊C4—101no—
279C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
280C22⋊C4—102no—
281C22⋊C4—102no—
282C22⋊C4—104no—
283C42—102no—
284C42—102no—
285C42—104no—
286C3×C5#182611yescharacteristic, complemented, Hall
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—52no—
290C22×C3—101no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3—101no—
295C22×C3—204no—
296C22×C3#401012yes—
297C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
298C3×C4—21no—
299C3×C4—42no—
300C3×C4—52no—
301C3×C4—101no—
302C3×C4—204no—
303C3×C4—202no—
304C3×C4#413012yes—
305C2×C5—22no—
306C2×C5C3×#38111yescharacteristic
307C2×C5C2×C3×#10411yescharacteristic
308C2×C5C3×#42111yescharacteristic
309D5—22no—
310D5—41no—
311C23—51no—
312C23—51no—
313C23—102no—
314C23—102no—
315C23—201no—
316C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—51no—
321C2×C4—54no—
322C2×C4—51no—
323C2×C4—102no—
324C2×C4—102no—
325C2×C4—102no—
326C2×C4—102no—
327C2×C4—104no—
328C2×C4—102no—
329C2×C4—202no—
330C2×C4—202no—
331C2×C4—202no—
332C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
333C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
334C8—202no—
335C2×C3—22no—
336C2×C3—102no—
337C2×C3—201no—
338C2×C3#6576411yescharacteristic
339C2×C3#6576911yescharacteristic
340C2×C3C2×#401011yescharacteristic
341C5C3×#182611yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—52no—
345C22—101no—
346C22—101no—
347C22—101no—
348C22—101no—
349C22—101no—
350C22—204no—
351C22C3×#401012yes—
352C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
353C4—21no—
354C4—42no—
355C4—52no—
356C4—101no—
357C4—204no—
358C4—202no—
359C4C3×#413012yes—
360C3#1060428711yescharacteristic, direct product factor, Sylow
361C2—22no—
362C2—102no—
363C2—201no—
364C2C3×#6576411yescharacteristic
365C2C3×#6576911yescharacteristic
366C2C2×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 radicalC23×C3×D5D4
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1826
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
4. C3×#64875C2semidirect
5. #10604287C3direct (N × H)
10. C2×C3×C5×C4⋊C4C4semidirect
12. C2×C3×C4⋊Dic5C4semidirect
16. C3×#4038C4semidirect
25. #64875C2×C3semidirect
57. C2×C5×C4⋊C4C3×C4semidirect
59. C2×C4⋊Dic5C3×C4semidirect
63. #4038C3×C4semidirect
100. C2×C3×C4⋊C4AGL(1,𝔽5)semidirect
207. C2×C4⋊C4C3×AGL(1,𝔽5)semidirect
286. C3×C5#1826semidirect
341. C5C3×#1826semidirect
360. C3#10604287direct (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×C4×C22⋊AGL(1,𝔽5)2
C3×#657562
C3×#648752
#106042873
C3×#18265