Finite Group Databasebeta

← C3×#10604562 #14301444

Subgroups — C3×#10604562 #14301444

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66258C211yesmaximal, characteristic
2C3×D5×#124C211yesmaximal, characteristic
3C3×#65782C212yesmaximal, complemented
4C3×D5⋊#100C211yesmaximal, characteristic
5C3×#64862C212yesmaximal, complemented
6#10604562C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C3×D4×D5C2211yescharacteristic
9C2×C3×C22⋊AGL(1,𝔽5)—22no—
10C3×D4×AGL(1,𝔽5)—24no—
11C3×#4130C2212yes—
12C3×D5⋊M16C2212yes—
13C3×C5×#124C411yescharacteristic, complemented
14C3×#4093C411yescharacteristic, complemented
15C3×#4082C411yescharacteristic, complemented
16C3×#4031—22no—
17C3×D5×C22⋊C4—22no—
18C3×#4021C411yescharacteristic, complemented
19C3×C42×D5C2211yescharacteristic
20C3×#4013—22no—
21C3×#4009—24no—
22C3×#1885—51nomaximal, Hall
23#66258C2×C311yescharacteristic
24D5×#124C2×C311yescharacteristic
25#65782C2×C312yescomplemented
26D5⋊#100C2×C311yescharacteristic
27#64862C2×C312yescomplemented
28C23×C3×D5D412yes—
29C22×C3×AGL(1,𝔽5)—24no—
30C2×C3×C5×Q8C2×C411yescharacteristic, complemented
31C2×C3×C5×D4C2×C411yescharacteristic
32C2×C3×C22⋊D5D412yes—
33C3×Q8×D5—22no—
34C3×Q8×D5—22no—
35C3×D4×D5—22no—
36C3×D4×D5—22no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5C2311yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10C2×C411yescharacteristic, complemented
43C3×C22⋊AGL(1,𝔽5)—24no—
44C3×C22⋊AGL(1,𝔽5)—22no—
45C3×#704—22no—
46C3×C4⋊AGL(1,𝔽5)D414yes—
47C3×C4×AGL(1,𝔽5)—22no—
48C3×#700—22no—
49C3×D5⋊C8—22no—
50C3×C5×C22⋊C4—22no—
51C3×C42×C5C2×C411yescharacteristic, complemented
52C3×C22⋊Dic5—22no—
53C3×#685—22no—
54C3×#685—22no—
55C3×C4×Dic5—21no—
56C3×C4×Dic5C2×C411yescharacteristic, complemented
57C2×C3×#124—51no—
58C3×#518—51no—
59C3×#419—52no—
60C2×C3×#100—51no—
61C3×#339—52no—
62C2×Q8×D5C22×C311yescharacteristic
63C2×D4×D5C22×C311yescharacteristic
64C2×C22⋊AGL(1,𝔽5)—22no—
65D4×AGL(1,𝔽5)—24no—
66#4130C22×C312yes—
67D5⋊M16C22×C312yes—
68C5×#124C3×C411yescharacteristic, complemented
69#4093C3×C411yescharacteristic, complemented
70#4082C3×C411yescharacteristic, complemented
71#4031—22no—
72D5×C22⋊C4—22no—
73#4021C3×C411yescharacteristic, complemented
74C42×D5C22×C311yescharacteristic
75#4013—22no—
76#4009—24no—
77#1885—51noSylow
78C23×C3×C5C22⋊C412yes—
79C22×C3×D5—22no—
80C22×C3×D5—22no—
81C22×C3×D5—44no—
82C22×C3×D5C22⋊C412yes—
83C22×C3×D5C2×D411yescharacteristic
84C2×C3×AGL(1,𝔽5)—24no—
85C2×C3×AGL(1,𝔽5)—84no—
86C3×C5×Q8—22no—
87C3×C5×D4—22no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C3×C22⋊D5—24no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5C2×D411yescharacteristic
95C3×D20—22no—
96C3×C4×D5—42no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×C4×D5C2×D412yes—
100C3×C4×D5#4112yes—
101C3×Dic10—22no—
102C3×Dic10—42no—
103C3×#170—42no—
104C22×C3×Q8—51no—
105C22×C3×D4—51no—
106C2×C3×M16—52no—
107C3×#124—51no—
108C3×#124—51no—
109C3×#124—51no—
110C3×#124—102no—
111C3×#124AGL(1,𝔽5)11yescharacteristic, complemented
112C3×C4×D4—104no—
113C3×#117—52no—
114C2×C3×C22⋊C4—102no—
115C2×C3×C22⋊C4—102no—
116C2×C3×C42—51no—
117C3×#103—104no—
118C3×#100—102no—
119C23×D5C3×D412yes—
120C22×AGL(1,𝔽5)—24no—
121C2×C5×Q8C2×C3×C411yescharacteristic, complemented
122C2×C5×D4C2×C3×C411yescharacteristic
123C2×C22⋊D5C3×D412yes—
124Q8×D5—22no—
125Q8×D5—22no—
126D4×D5—22no—
127D4×D5—22no—
128C2×D20C2×C3×C411yescharacteristic
129C2×C4×D5—21no—
130C2×C4×D5—21no—
131C2×C4×D5C23×C311yescharacteristic
132C2×Dic10—21no—
133C2×Dic10C2×C3×C411yescharacteristic, complemented
134C22⋊AGL(1,𝔽5)—24no—
135C22⋊AGL(1,𝔽5)—22no—
136#704—22no—
137C4⋊AGL(1,𝔽5)C3×D414yes—
138C4×AGL(1,𝔽5)—22no—
139#700—22no—
140D5⋊C8—22no—
141C5×C22⋊C4—22no—
142C42×C5C2×C3×C411yescharacteristic, complemented
143C22⋊Dic5—22no—
144#685—22no—
145#685—22no—
146C4×Dic5—21no—
147C4×Dic5C2×C3×C411yescharacteristic, complemented
148C2×#124—51no—
149#518—51no—
150#419—52no—
151C2×#100—51no—
152#339—52no—
153C22×C3×C5—22no—
154C22×C3×C5—42no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×C3×D5—22no—
157C2×C3×D5—22no—
158C2×C3×D5—44no—
159C2×C3×D5—42no—
160C2×C3×D5—82no—
161C2×C3×D5#12011yescharacteristic
162C2×C3×D5#12311yescharacteristic
163C3×AGL(1,𝔽5)—44no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5C4×D412yes—
167C3×Dic5—41no—
168C3×Dic5—41no—
169C3×Dic5#12112yes—
170C24×C3—52no—
171C2×C3×Q8—51no—
172C2×C3×Q8—101no—
173C2×C3×Q8—102no—
174C2×C3×Q8—102no—
175C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
176C2×C3×D4—52no—
177C2×C3×D4—51no—
178C2×C3×D4—102no—
179C2×C3×D4—102no—
180C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
181C22×C3×C4—51no—
182C22×C3×C4—101no—
183C22×C3×C4—101no—
184C22×C3×C4—104no—
185C3×M16—102no—
186C3×M16—102no—
187C2×C3×C8—102no—
188C3×C4⋊C4—54no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C22⋊C4—102no—
193C3×C22⋊C4—104no—
194C3×C22⋊C4—102no—
195C3×C42—51no—
196C3×C42—101no—
197C3×C42—102no—
198C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
199C23×C5C3×C22⋊C412yes—
200C22×D5—22no—
201C22×D5—22no—
202C22×D5—44no—
203C22×D5C3×C22⋊C412yes—
204C22×D5C2×C3×D411yescharacteristic
205C2×AGL(1,𝔽5)—24no—
206C2×AGL(1,𝔽5)—84no—
207C5×Q8—22no—
208C5×D4—22no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5C22×C3×C411yescharacteristic
212C22⋊D5—24no—
213C2×Dic5—21no—
214C2×Dic5—21no—
215C2×Dic5C2×C3×D411yescharacteristic
216D20—22no—
217C4×D5—42no—
218C4×D5—41no—
219C4×D5—41no—
220C4×D5C2×C3×D412yes—
221C4×D5C3×#4112yes—
222Dic10—22no—
223Dic10—42no—
224#170—42no—
225C22×Q8—51no—
226C22×D4—51no—
227C2×M16—52no—
228#124—51no—
229#124—51no—
230#124—51no—
231#124—102no—
232#124C3×AGL(1,𝔽5)11yescharacteristic, complemented
233C4×D4—104no—
234#117—52no—
235C2×C22⋊C4—102no—
236C2×C22⋊C4—102no—
237C2×C42—51no—
238#103—104no—
239#100—102no—
240C2×C3×C5—21no—
241C2×C3×C5—42no—
242C2×C3×C5#38611yescharacteristic
243C3×D5—21no—
244C3×D5—42no—
245C3×D5#45512yes—
246C23×C3—51no—
247C23×C3—52no—
248C23×C3—102no—
249C23×C3—102no—
250C23×C3—204no—
251C23×C3C22⋊AGL(1,𝔽5)12yes—
252C3×Q8—22no—
253C3×Q8—102no—
254C3×Q8—202no—
255C3×D4—22no—
256C3×D4—104no—
257C3×D4—102no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—51no—
261C2×C3×C4—52no—
262C2×C3×C4—52no—
263C2×C3×C4—104no—
264C2×C3×C4—101no—
265C2×C3×C4—101no—
266C2×C3×C4—201no—
267C2×C3×C4—201no—
268C2×C3×C4—202no—
269C2×C3×C4—404no—
270C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
271C3×C8—202no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5C2×C3×C22⋊C411yescharacteristic
275C2×D5—22no—
276C2×D5—22no—
277C2×D5—44no—
278C2×D5—42no—
279C2×D5—82no—
280C2×D5C3×#12011yescharacteristic
281C2×D5C3×#12311yescharacteristic
282AGL(1,𝔽5)—44no—
283C4×C5—41no—
284C4×C5—41no—
285C4×C5C3×C4×D412yes—
286Dic5—41no—
287Dic5—41no—
288Dic5C3×#12112yes—
289C24—52no—
290C2×Q8—51no—
291C2×Q8—101no—
292C2×Q8—102no—
293C2×Q8—102no—
294C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
295C2×D4—52no—
296C2×D4—51no—
297C2×D4—102no—
298C2×D4—102no—
299C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
300C22×C4—51no—
301C22×C4—101no—
302C22×C4—101no—
303C22×C4—104no—
304M16—102no—
305M16—102no—
306C2×C8—102no—
307C4⋊C4—54no—
308C22⋊C4—22no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C22⋊C4—104no—
313C22⋊C4—102no—
314C42—51no—
315C42—101no—
316C42—102no—
317C42C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
318C3×C5#188511yescharacteristic, complemented, Hall
319C22×C3—22no—
320C22×C3—42no—
321C22×C3—51no—
322C22×C3—51no—
323C22×C3—102no—
324C22×C3—102no—
325C22×C3—202no—
326C22×C3—204no—
327C22×C3—402no—
328C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—52no—
332C3×C4—201no—
333C3×C4—204no—
334C3×C4—201no—
335C3×C4D4×AGL(1,𝔽5)12yes—
336C2×C5—21no—
337C2×C5—42no—
338C2×C5C3×#38611yescharacteristic
339D5—21no—
340D5—42no—
341D5C3×#45512yes—
342C23—51no—
343C23—52no—
344C23—102no—
345C23—102no—
346C23—204no—
347C23C3×C22⋊AGL(1,𝔽5)12yes—
348Q8—22no—
349Q8—102no—
350Q8—202no—
351D4—22no—
352D4—104no—
353D4—102no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—51no—
357C2×C4—52no—
358C2×C4—52no—
359C2×C4—104no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—202no—
365C2×C4—404no—
366C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
367C8—202no—
368C2×C3—21no—
369C2×C3—42no—
370C2×C3—52no—
371C2×C3—101no—
372C2×C3—202no—
373C2×C3#6577911yescharacteristic
374C5C3×#188511yescharacteristic, complemented, Sylow
375C22—22no—
376C22—42no—
377C22—51no—
378C22—51no—
379C22—102no—
380C22—102no—
381C22—202no—
382C22—204no—
383C22—402no—
384C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
385C4—41no—
386C4—41no—
387C4—52no—
388C4—201no—
389C4—204no—
390C4—201no—
391C4C3×D4×AGL(1,𝔽5)12yes—
392C3#1060456211yescharacteristic, direct product factor, Sylow
393C2—21no—
394C2—42no—
395C2—52no—
396C2—101no—
397C2—202no—
398C2C3×#6577911yescharacteristic
subgroupG/H
centerC2×C3#65779
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#124C4
socleC2×C3×C5#386
prime radicalC2×C3×D4×D5C22
cosocleC2×C4×D5C23×C3
hypercenterC3×#124AGL(1,𝔽5)
hypocenterC5C3×#1885
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#124

Complements

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

NH ≅ G/Ntype
3. C3×#65782C2semidirect
5. C3×#64862C2semidirect
6. #10604562C3direct (N × H)
13. C3×C5×#124C4semidirect
14. C3×#4093C4semidirect
15. C3×#4082C4semidirect
18. C3×#4021C4semidirect
25. #65782C2×C3semidirect
27. #64862C2×C3semidirect
30. C2×C3×C5×Q8C2×C4semidirect
42. C2×C3×Dic10C2×C4semidirect
51. C3×C42×C5C2×C4semidirect
56. C3×C4×Dic5C2×C4semidirect
68. C5×#124C3×C4semidirect
69. #4093C3×C4semidirect
70. #4082C3×C4semidirect
73. #4021C3×C4semidirect
111. C3×#124AGL(1,𝔽5)semidirect
121. C2×C5×Q8C2×C3×C4semidirect
133. C2×Dic10C2×C3×C4semidirect
142. C42×C5C2×C3×C4semidirect
147. C4×Dic5C2×C3×C4semidirect
175. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
198. C3×C42C2×AGL(1,𝔽5)semidirect
232. #124C3×AGL(1,𝔽5)semidirect
294. C2×Q8C2×C3×AGL(1,𝔽5)semidirect
317. C42C2×C3×AGL(1,𝔽5)semidirect
318. C3×C5#1885semidirect
374. C5C3×#1885semidirect
392. C3#10604562direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662582
C3×D5×#1242
C3×#657822
C3×D5⋊#1002
C3×#648622
#106045623
C3×#18855