Finite Group Databasebeta

← C3×#10604423 #14282763

Subgroups — C3×#10604423 #14282763

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65914C211yesmaximal, characteristic
2C3×#65686C211yesmaximal, characteristic, complemented
3C3×#65680C211yesmaximal, characteristic, complemented
4C3×#64926C212yesmaximal, complemented
5C3×#64868C212yesmaximal
6#10604423C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C4×AGL(1,𝔽5)—21no—
8C3×C4×C5×Q8C411yescharacteristic, complemented
9C3×#4093C411yescharacteristic, complemented
10C3×#4092C2211yescharacteristic
11C3×#4044—21no—
12C3×#4041C2211yescharacteristic
13C3×#4040—21no—
14C3×#4036C411yescharacteristic, complemented
15C3×C4×D20—21no—
16C3×C4×D20C411yescharacteristic, complemented
17C3×#4018—21no—
18C3×C42×D5C2211yescharacteristic
19C3×(C2×AGL(1,𝔽5))⋊C4—21no—
20C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
21C3×#4003C2212yes—
22C3×C4⋊#170—21no—
23C3×C4×#170—21no—
24C3×#1500—51nomaximal, Hall
25#65914C2×C311yescharacteristic
26#65686C2×C311yescharacteristic, complemented
27#65680C2×C311yescharacteristic, complemented
28#64926C2×C312yescomplemented
29#64868C2×C312yes—
30C22×C3×AGL(1,𝔽5)—22no—
31C2×C3×C5×Q8C2×C411yescharacteristic
32C2×C3×D20—21no—
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×C3×C4×D5C2311yescharacteristic
38C2×C3×#170—22no—
39C3×C4×AGL(1,𝔽5)—24no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2×C411yescharacteristic
44C3×#685—21no—
45C3×#685—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×#685—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×#529—51no—
57C3×#431—51no—
58C3×#376—51no—
59C3×#328—52no—
60C3×#327—52no—
61C2×C4×AGL(1,𝔽5)—21no—
62C4×C5×Q8C3×C411yescharacteristic, complemented
63#4093C3×C411yescharacteristic, complemented
64#4092C22×C311yescharacteristic
65#4044—21no—
66#4041C22×C311yescharacteristic
67#4040—21no—
68#4036C3×C411yescharacteristic, complemented
69C4×D20—21no—
70C4×D20C3×C411yescharacteristic, complemented
71#4018—21no—
72C42×D5C22×C311yescharacteristic
73(C2×AGL(1,𝔽5))⋊C4—21no—
74(C2×AGL(1,𝔽5))⋊C4C22×C312yes—
75#4003C22×C312yes—
76C4⋊#170—21no—
77C4×#170—21no—
78#1500—51noSylow
79C22×C3×D5—21no—
80C22×C3×D5C2×D411yescharacteristic
81C2×C3×AGL(1,𝔽5)—24no—
82C2×C3×AGL(1,𝔽5)—42no—
83C2×C3×AGL(1,𝔽5)—42no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C3×D20—41no—
95C3×D20—42no—
96C3×C4×D5—22no—
97C3×C4×D5—22no—
98C3×C4×D5—41no—
99C3×C4×D5—42no—
100C3×#170—42no—
101C3×#126—101no—
102C3×#125—51no—
103C3×#124—51no—
104C3×#123—101no—
105C3×C22⋊Q8—51no—
106C3×#121—51no—
107C3×C4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
108C3×C4×D4—51no—
109C3×C4×D4—101no—
110C3×#117—101no—
111C2×C3×C42—51no—
112C2×C3×C42—101no—
113C3×C4⋊C8—101no—
114C3×C22⋊C8—52no—
115C3×C4×C8—101no—
116C3×#95—52no—
117C3×#95—101no—
118C22×AGL(1,𝔽5)—22no—
119C2×C5×Q8C2×C3×C411yescharacteristic
120C2×D20—21no—
121C2×D20C2×C3×C411yescharacteristic
122C2×C4×D5—21no—
123C2×C4×D5C3×D411yescharacteristic
124C2×C4×D5C3×D411yescharacteristic
125C2×C4×D5C23×C311yescharacteristic
126C2×#170—22no—
127C4×AGL(1,𝔽5)—24no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4C2×C3×C411yescharacteristic
130C42×C5—21no—
131C42×C5C2×C3×C411yescharacteristic
132#685—21no—
133#685—21no—
134#685—21no—
135#685—21no—
136#685—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5C2×C3×C411yescharacteristic
139#683—21no—
140#683—21no—
141C4×Dic5C2×C3×C411yescharacteristic
142C4×Dic5C3×D411yescharacteristic
143C4×Dic5C3×D411yescharacteristic
144#529—51no—
145#431—51no—
146#376—51no—
147#328—52no—
148#327—52no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C2×C3×D5#13512yes—
156C3×AGL(1,𝔽5)—44no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5—41no—
161C3×C4×C5#10412yes—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—41no—
166C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
167C2×C3×D4—51no—
168C2×C3×D4—101no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—102no—
173C22×C3×C4—101no—
174C2×C3×C8—102no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
181C3×C22⋊C4—101no—
182C3×C22⋊C4—101no—
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C22⋊C4—101no—
186C3×C42—21no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42—104no—
191C3×C42C2×AGL(1,𝔽5)11yescharacteristic
192C22×D5—21no—
193C22×D5C2×C3×D411yescharacteristic
194C2×AGL(1,𝔽5)—24no—
195C2×AGL(1,𝔽5)—42no—
196C2×AGL(1,𝔽5)—42no—
197C5×Q8—41no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5C3×C22⋊C411yescharacteristic
201C2×C4×C5C3×C22⋊C411yescharacteristic
202C2×C4×C5C22×C3×C411yescharacteristic
203C2×Dic5—21no—
204C2×Dic5C3×C22⋊C411yescharacteristic
205C2×Dic5C3×C22⋊C411yescharacteristic
206C2×Dic5C2×C3×D411yescharacteristic
207D20—41no—
208D20—42no—
209C4×D5—22no—
210C4×D5—22no—
211C4×D5—41no—
212C4×D5—42no—
213#170—42no—
214#126—101no—
215#125—51no—
216#124—51no—
217#123—101no—
218C22⋊Q8—51no—
219#121—51no—
220C4×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
221C4×D4—51no—
222C4×D4—101no—
223#117—101no—
224C2×C42—51no—
225C2×C42—101no—
226C4⋊C8—101no—
227C22⋊C8—52no—
228C4×C8—101no—
229#95—52no—
230#95—101no—
231C2×C3×C5#41011yescharacteristic
232C2×C3×C5#41611yescharacteristic
233C2×C3×C5C2×#10411yescharacteristic
234C3×D5—22no—
235C3×D5—81no—
236C23×C3—51no—
237C23×C3—101no—
238C3×Q8—41no—
239C3×D4—201no—
240C3×D4—202no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—102no—
247C2×C3×C4—102no—
248C2×C3×C4—104no—
249C2×C3×C4—101no—
250C2×C3×C4—201no—
251C2×C3×C4—202no—
252C2×C3×C4—202no—
253C2×C3×C4—202no—
254C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
255C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
256C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
257C3×C8—202no—
258C22×C5C2×C3×C22⋊C411yescharacteristic
259C2×D5—21no—
260C2×D5—21no—
261C2×D5—41no—
262C2×D5—41no—
263C2×D5—41no—
264C2×D5C3×#13512yes—
265AGL(1,𝔽5)—44no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—41no—
269C4×C5—41no—
270C4×C5C3×#10412yes—
271Dic5—21no—
272Dic5—21no—
273Dic5—21no—
274Dic5—41no—
275C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
276C2×D4—51no—
277C2×D4—101no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—102no—
282C22×C4—101no—
283C2×C8—102no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
290C22⋊C4—101no—
291C22⋊C4—101no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C42—21no—
296C42—51no—
297C42—51no—
298C42—51no—
299C42—104no—
300C42C2×C3×AGL(1,𝔽5)11yescharacteristic
301C3×C5#150011yescharacteristic, complemented, Hall
302C22×C3—52no—
303C22×C3—101no—
304C22×C3—101no—
305C22×C3—201no—
306C22×C3—201no—
307C22×C3—201no—
308C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—101no—
314C3×C4—101no—
315C3×C4—101no—
316C3×C4—204no—
317C3×C4—201no—
318C3×C4#401012yes—
319C2×C5C3×#41011yescharacteristic
320C2×C5C3×#41611yescharacteristic
321C2×C5C2×C3×#10411yescharacteristic
322D5—22no—
323D5—81no—
324C23—51no—
325C23—101no—
326Q8—41no—
327D4—201no—
328D4—202no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—51no—
334C2×C4—102no—
335C2×C4—102no—
336C2×C4—104no—
337C2×C4—101no—
338C2×C4—201no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
343C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
344C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
345C8—202no—
346C2×C3—102no—
347C2×C3—401no—
348C2×C3#6574511yescharacteristic
349C2×C3C2×#401011yescharacteristic
350C2×C3#6579411yescharacteristic
351C5C3×#150011yescharacteristic, complemented, Sylow
352C22—52no—
353C22—101no—
354C22—101no—
355C22—201no—
356C22—201no—
357C22—201no—
358C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—101no—
364C4—101no—
365C4—101no—
366C4—204no—
367C4—201no—
368C4C3×#401012yes—
369C3#1060442311yescharacteristic, direct product factor, Sylow
370C2—102no—
371C2—401no—
372C2C3×#6574511yescharacteristic
373C2C2×C3×#401011yescharacteristic
374C2C3×#6579411yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4041C22
cosocleC2×C4×D5C23×C3
hypercenterC3×C4×Q8AGL(1,𝔽5)
hypocenterC5C3×#1500
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65686C2semidirect
3. C3×#65680C2semidirect
4. C3×#64926C2semidirect
6. #10604423C3direct (N × H)
8. C3×C4×C5×Q8C4semidirect
9. C3×#4093C4semidirect
14. C3×#4036C4semidirect
16. C3×C4×D20C4semidirect
26. #65686C2×C3semidirect
27. #65680C2×C3semidirect
28. #64926C2×C3semidirect
62. C4×C5×Q8C3×C4semidirect
63. #4093C3×C4semidirect
68. #4036C3×C4semidirect
70. C4×D20C3×C4semidirect
107. C3×C4×Q8AGL(1,𝔽5)semidirect
220. C4×Q8C3×AGL(1,𝔽5)semidirect
301. C3×C5#1500semidirect
351. C5C3×#1500semidirect
369. C3#10604423direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659142
C3×#656862
C3×#656802
C3×#649262
C3×#648682
#106044233
C3×#15005