Finite Group Databasebeta

← C3×#10604909 #14279867

Subgroups — C3×#10604909 #14279867

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C22×C3×C22⋊AGL(1,𝔽5)C212yesmaximal
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C214yesmaximal, complemented
4#10604909C311yesmaximal, characteristic, direct product factor, Hall
5C24×C3×D5C2211yescharacteristic
6C23×C3×AGL(1,𝔽5)C2214yes—
7C23×C3×C4×C5C411yescharacteristic, complemented
8C23×C3×Dic5C411yescharacteristic, complemented
9C22×C3×C4×D5—24no—
10C22×C3×C4×D5—28no—
11C22×C3×C4×D5C412yescomplemented
12C22×C3×C4×D5C2212yes—
13C2×C3×C22⋊AGL(1,𝔽5)—24no—
14C2×C3×C22⋊AGL(1,𝔽5)—24no—
15C2×C3×C22⋊AGL(1,𝔽5)C418yescomplemented
16C3×(C2×AGL(1,𝔽5))⋊C4—28no—
17C3×C22⋊#95—51nomaximal, Hall
18C23×C4×D5C2×C311yescharacteristic
19C22×C22⋊AGL(1,𝔽5)C2×C312yes—
20C2×(C2×AGL(1,𝔽5))⋊C4C2×C314yescomplemented
21C24×C3×C5C2×C411yescharacteristic
22C23×C3×D5—24no—
23C23×C3×D5—24no—
24C23×C3×D5C2×C411yescharacteristic
25C23×C3×D5C2×C414yes—
26C23×C3×D5D412yes—
27C23×C3×D5D414yes—
28C23×C3×D5Q812yes—
29C23×C3×D5C2311yescharacteristic
30C22×C3×AGL(1,𝔽5)—28no—
31C22×C3×AGL(1,𝔽5)—24no—
32C22×C3×AGL(1,𝔽5)—24no—
33C22×C3×AGL(1,𝔽5)—28no—
34C22×C3×AGL(1,𝔽5)C2×C418yescomplemented
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5—24no—
37C22×C3×C4×C5C2×C412yes—
38C22×C3×Dic5—22no—
39C22×C3×Dic5—24no—
40C22×C3×Dic5C2×C412yes—
41C2×C3×C4×D5—232no—
42C2×C3×C4×D5—24no—
43C2×C3×C4×D5—24no—
44C2×C3×C4×D5—24no—
45C2×C3×C4×D5—24no—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5D418yes—
48C3×C22⋊AGL(1,𝔽5)—216no—
49C24×C3×C4—51no—
50C22×C3×C22⋊C4—52no—
51C2×C3×#95—54no—
52C24×D5C22×C311yescharacteristic
53C23×AGL(1,𝔽5)C22×C314yes—
54C23×C4×C5C3×C411yescharacteristic, complemented
55C23×Dic5C3×C411yescharacteristic, complemented
56C22×C4×D5—24no—
57C22×C4×D5—28no—
58C22×C4×D5C3×C412yescomplemented
59C22×C4×D5C22×C312yes—
60C2×C22⋊AGL(1,𝔽5)—24no—
61C2×C22⋊AGL(1,𝔽5)—24no—
62C2×C22⋊AGL(1,𝔽5)C3×C418yescomplemented
63(C2×AGL(1,𝔽5))⋊C4—28no—
64C22⋊#95—51noSylow
65C23×C3×C5—22no—
66C23×C3×C5—22no—
67C23×C3×C5C4212yes—
68C23×C3×C5C22⋊C412yes—
69C23×C3×C5C4⋊C412yes—
70C23×C3×C5C22×C411yescharacteristic
71C22×C3×D5—22no—
72C22×C3×D5—22no—
73C22×C3×D5—216no—
74C22×C3×D5—28no—
75C22×C3×D5—28no—
76C22×C3×D5—28no—
77C22×C3×D5—28no—
78C22×C3×D5C4212yes—
79C22×C3×D5C22⋊C412yes—
80C22×C3×D5C22⋊C418yes—
81C22×C3×D5C4⋊C412yes—
82C22×C3×D5C4⋊C418yes—
83C22×C3×D5C22×C412yes—
84C22×C3×D5C2×D411yescharacteristic
85C22×C3×D5C2×D412yes—
86C22×C3×D5C2×D414yes—
87C22×C3×D5C2×Q811yescharacteristic
88C22×C3×D5#4114yes—
89C2×C3×AGL(1,𝔽5)—28no—
90C2×C3×AGL(1,𝔽5)—216no—
91C2×C3×AGL(1,𝔽5)—44no—
92C2×C3×AGL(1,𝔽5)—48no—
93C2×C3×AGL(1,𝔽5)—44no—
94C2×C3×C4×C5—28no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22⋊C414yescomplemented
98C2×C3×Dic5—28no—
99C2×C3×Dic5—22no—
100C2×C3×Dic5—22no—
101C2×C3×Dic5C22⋊C414yescomplemented
102C3×C4×D5—216no—
103C3×C4×D5—216no—
104C25×C3—51no—
105C23×C3×C4—52no—
106C23×C3×C4—54no—
107C23×C3×C4—51no—
108C23×C3×C4—52no—
109C23×C3×C4—108no—
110C23×C3×C4—104no—
111C23×C3×C4AGL(1,𝔽5)11yescharacteristic, complemented
112C2×C3×C22⋊C4—58no—
113C2×C3×C22⋊C4—104no—
114C2×C3×C22⋊C4—104no—
115C3×#95—108no—
116C24×C5C2×C3×C411yescharacteristic
117C23×D5—24no—
118C23×D5—24no—
119C23×D5C2×C3×C411yescharacteristic
120C23×D5C2×C3×C414yes—
121C23×D5C3×D412yes—
122C23×D5C3×D414yes—
123C23×D5C3×Q812yes—
124C23×D5C23×C311yescharacteristic
125C22×AGL(1,𝔽5)—24no—
126C22×AGL(1,𝔽5)—24no—
127C22×AGL(1,𝔽5)—28no—
128C22×AGL(1,𝔽5)—28no—
129C22×AGL(1,𝔽5)C2×C3×C418yescomplemented
130C22×C4×C5—22no—
131C22×C4×C5—24no—
132C22×C4×C5C2×C3×C412yes—
133C22×Dic5—22no—
134C22×Dic5—24no—
135C22×Dic5C2×C3×C412yes—
136C2×C4×D5—232no—
137C2×C4×D5—24no—
138C2×C4×D5—24no—
139C2×C4×D5—24no—
140C2×C4×D5—24no—
141C2×C4×D5—24no—
142C2×C4×D5C3×D418yes—
143C22⋊AGL(1,𝔽5)—216no—
144C24×C4—51no—
145C22×C22⋊C4—52no—
146C2×#95—54no—
147C22×C3×C5—24no—
148C22×C3×C5—22no—
149C22×C3×C5—24no—
150C22×C3×C5—22no—
151C22×C3×C5#9514yescomplemented
152C22×C3×C5C2×C4211yescharacteristic
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C22×C3×C5C2×C22⋊C412yes—
155C22×C3×C5C2×C4⋊C411yescharacteristic
156C22×C3×C5#11712yes—
157C2×C3×D5—24no—
158C2×C3×D5—22no—
159C2×C3×D5—24no—
160C2×C3×D5—22no—
161C2×C3×D5—216no—
162C2×C3×D5—216no—
163C2×C3×D5#9514yescomplemented
164C2×C3×D5C2×C22⋊C412yes—
165C2×C3×D5C2×C4⋊C412yes—
166C2×C3×D5C4×D418yes—
167C2×C3×D5#12014yes—
168C2×C3×D5#12114yes—
169C2×C3×D5C22⋊Q814yes—
170C2×C3×D5#12314yes—
171C3×AGL(1,𝔽5)—48no—
172C3×C4×C5—24no—
173C3×Dic5—24no—
174C24×C3—51no—
175C24×C3—54no—
176C24×C3—52no—
177C24×C3—52no—
178C24×C3—54no—
179C24×C3—51no—
180C24×C3—104no—
181C24×C3—104no—
182C24×C3C2×AGL(1,𝔽5)11yescharacteristic
183C22×C3×C4—22no—
184C22×C3×C4—24no—
185C22×C3×C4—52no—
186C22×C3×C4—58no—
187C22×C3×C4—58no—
188C22×C3×C4—104no—
189C22×C3×C4—104no—
190C22×C3×C4—104no—
191C22×C3×C4—104no—
192C22×C3×C4—1032no—
193C22×C3×C4—104no—
194C22×C3×C4—102no—
195C22×C3×C4—104no—
196C22×C3×C4—108no—
197C22×C3×C4—104no—
198C22×C3×C4—104no—
199C22×C3×C4—108no—
200C22×C3×C4C2×AGL(1,𝔽5)12yes—
201C3×C22⋊C4—1016no—
202C23×C5—22no—
203C23×C5—22no—
204C23×C5C3×C4212yes—
205C23×C5C3×C22⋊C412yes—
206C23×C5C3×C4⋊C412yes—
207C23×C5C22×C3×C411yescharacteristic
208C22×D5—22no—
209C22×D5—22no—
210C22×D5—216no—
211C22×D5—28no—
212C22×D5—28no—
213C22×D5—28no—
214C22×D5—28no—
215C22×D5C3×C4212yes—
216C22×D5C3×C22⋊C412yes—
217C22×D5C3×C22⋊C418yes—
218C22×D5C3×C4⋊C412yes—
219C22×D5C3×C4⋊C418yes—
220C22×D5C22×C3×C412yes—
221C22×D5C2×C3×D411yescharacteristic
222C22×D5C2×C3×D412yes—
223C22×D5C2×C3×D414yes—
224C22×D5C2×C3×Q811yescharacteristic
225C22×D5C3×#4114yes—
226C2×AGL(1,𝔽5)—28no—
227C2×AGL(1,𝔽5)—216no—
228C2×AGL(1,𝔽5)—44no—
229C2×AGL(1,𝔽5)—48no—
230C2×AGL(1,𝔽5)—44no—
231C2×C4×C5—28no—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5C3×C22⋊C414yescomplemented
235C2×Dic5—28no—
236C2×Dic5—22no—
237C2×Dic5—22no—
238C2×Dic5C3×C22⋊C414yescomplemented
239C4×D5—216no—
240C4×D5—216no—
241C25—51no—
242C23×C4—52no—
243C23×C4—54no—
244C23×C4—51no—
245C23×C4—52no—
246C23×C4—108no—
247C23×C4—104no—
248C23×C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
249C2×C22⋊C4—58no—
250C2×C22⋊C4—104no—
251C2×C22⋊C4—104no—
252#95—108no—
253C2×C3×C5—24no—
254C2×C3×C5C2×#9511yescharacteristic
255C2×C3×C5C4×C22⋊C412yes—
256C2×C3×C5#37911yescharacteristic
257C2×C3×C5#38012yes—
258C2×C3×C5#38111yescharacteristic
259C3×D5—24no—
260C3×D5#38514yes—
261C3×D5#38614yes—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—52no—
265C23×C3—51no—
266C23×C3—51no—
267C23×C3—54no—
268C23×C3—54no—
269C23×C3—52no—
270C23×C3—52no—
271C23×C3—52no—
272C23×C3—52no—
273C23×C3—58no—
274C23×C3—58no—
275C23×C3—108no—
276C23×C3—1016no—
277C23×C3—108no—
278C23×C3—108no—
279C23×C3—108no—
280C23×C3—102no—
281C23×C3—102no—
282C23×C3C4×AGL(1,𝔽5)12yes—
283C23×C3C4⋊AGL(1,𝔽5)12yes—
284C23×C3C22⋊AGL(1,𝔽5)12yes—
285C23×C3C22×AGL(1,𝔽5)11yescharacteristic
286C2×C3×C4—28no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—54no—
290C2×C3×C4—1016no—
291C2×C3×C4—1016no—
292C2×C3×C4—108no—
293C2×C3×C4—102no—
294C2×C3×C4—102no—
295C2×C3×C4—108no—
296C2×C3×C4—1016no—
297C2×C3×C4—204no—
298C2×C3×C4—204no—
299C2×C3×C4—208no—
300C2×C3×C4C22⋊AGL(1,𝔽5)14yescomplemented
301C22×C5—24no—
302C22×C5—22no—
303C22×C5—24no—
304C22×C5—22no—
305C22×C5C3×#9514yescomplemented
306C22×C5C2×C3×C4211yescharacteristic
307C22×C5C2×C3×C22⋊C411yescharacteristic
308C22×C5C2×C3×C22⋊C412yes—
309C22×C5C2×C3×C4⋊C411yescharacteristic
310C22×C5C3×#11712yes—
311C2×D5—24no—
312C2×D5—22no—
313C2×D5—24no—
314C2×D5—22no—
315C2×D5—216no—
316C2×D5—216no—
317C2×D5C3×#9514yescomplemented
318C2×D5C2×C3×C22⋊C412yes—
319C2×D5C2×C3×C4⋊C412yes—
320C2×D5C3×C4×D418yes—
321C2×D5C3×#12014yes—
322C2×D5C3×#12114yes—
323C2×D5C3×C22⋊Q814yes—
324C2×D5C3×#12314yes—
325AGL(1,𝔽5)—48no—
326C4×C5—24no—
327Dic5—24no—
328C24—51no—
329C24—54no—
330C24—52no—
331C24—52no—
332C24—54no—
333C24—51no—
334C24—104no—
335C24—104no—
336C24C2×C3×AGL(1,𝔽5)11yescharacteristic
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—52no—
340C22×C4—58no—
341C22×C4—58no—
342C22×C4—104no—
343C22×C4—104no—
344C22×C4—104no—
345C22×C4—104no—
346C22×C4—1032no—
347C22×C4—104no—
348C22×C4—102no—
349C22×C4—104no—
350C22×C4—108no—
351C22×C4—104no—
352C22×C4—104no—
353C22×C4—108no—
354C22×C4C2×C3×AGL(1,𝔽5)12yes—
355C22⋊C4—1016no—
356C3×C5C22⋊#9511yescharacteristic, complemented, Hall
357C22×C3—22no—
358C22×C3—24no—
359C22×C3—22no—
360C22×C3—24no—
361C22×C3—54no—
362C22×C3—52no—
363C22×C3—52no—
364C22×C3—58no—
365C22×C3—54no—
366C22×C3—54no—
367C22×C3—54no—
368C22×C3—54no—
369C22×C3—1016no—
370C22×C3—1016no—
371C22×C3—102no—
372C22×C3—104no—
373C22×C3—102no—
374C22×C3—104no—
375C22×C3(C2×AGL(1,𝔽5))⋊C414yescomplemented
376C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
377C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
378C22×C3#413012yes—
379C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
380C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
381C3×C4—24no—
382C3×C4—104no—
383C3×C4—208no—
384C2×C5—24no—
385C2×C5C2×C3×#9511yescharacteristic
386C2×C5C3×C4×C22⋊C412yes—
387C2×C5C3×#37911yescharacteristic
388C2×C5C3×#38012yes—
389C2×C5C3×#38111yescharacteristic
390D5—24no—
391D5C3×#38514yes—
392D5C3×#38614yes—
393C23—22no—
394C23—22no—
395C23—52no—
396C23—51no—
397C23—51no—
398C23—54no—
399C23—54no—
400C23—52no—
401C23—52no—
402C23—52no—
403C23—58no—
404C23—58no—
405C23—52no—
406C23—108no—
407C23—1016no—
408C23—108no—
409C23—108no—
410C23—108no—
411C23—102no—
412C23—102no—
413C23C3×C4×AGL(1,𝔽5)12yes—
414C23C3×C4⋊AGL(1,𝔽5)12yes—
415C23C3×C22⋊AGL(1,𝔽5)12yes—
416C23C22×C3×AGL(1,𝔽5)11yescharacteristic
417C2×C4—28no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—54no—
421C2×C4—1016no—
422C2×C4—1016no—
423C2×C4—108no—
424C2×C4—102no—
425C2×C4—102no—
426C2×C4—108no—
427C2×C4—1016no—
428C2×C4—204no—
429C2×C4—208no—
430C2×C4—204no—
431C2×C4C3×C22⋊AGL(1,𝔽5)14yescomplemented
432C2×C3—24no—
433C2×C3—54no—
434C2×C3—54no—
435C2×C3—104no—
436C2×C3C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
437C2×C3C4×C22⋊AGL(1,𝔽5)12yes—
438C2×C3#6576411yescharacteristic
439C2×C3#6576512yes—
440C2×C3#6580011yescharacteristic
441C5C3×C22⋊#9511yescharacteristic, complemented, Sylow
442C22—24no—
443C22—22no—
444C22—24no—
445C22—22no—
446C22—52no—
447C22—52no—
448C22—58no—
449C22—54no—
450C22—54no—
451C22—54no—
452C22—54no—
453C22—54no—
454C22—1016no—
455C22—1016no—
456C22—104no—
457C22—102no—
458C22—104no—
459C22—102no—
460C22C3×(C2×AGL(1,𝔽5))⋊C414yescomplemented
461C22C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
462C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
463C22C3×#413012yes—
464C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
465C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
466C4—24no—
467C4—104no—
468C4—208no—
469C3#1060490911yescharacteristic, direct product factor, Sylow
470C2—24no—
471C2—54no—
472C2—54no—
473C2—104no—
474C2C2×C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
475C2C3×C4×C22⋊AGL(1,𝔽5)12yes—
476C2C3×#6576411yescharacteristic
477C2C3×#6576512yes—
478C2C3×#6580011yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC23×D5C23×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C3×C22⋊#95
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
4. #10604909C3direct (N × H)
7. C23×C3×C4×C5C4semidirect
8. C23×C3×Dic5C4semidirect
11. C22×C3×C4×D5C4semidirect
15. C2×C3×C22⋊AGL(1,𝔽5)C4semidirect
20. C2×(C2×AGL(1,𝔽5))⋊C4C2×C3semidirect
34. C22×C3×AGL(1,𝔽5)C2×C4semidirect
54. C23×C4×C5C3×C4semidirect
55. C23×Dic5C3×C4semidirect
58. C22×C4×D5C3×C4semidirect
62. C2×C22⋊AGL(1,𝔽5)C3×C4semidirect
97. C2×C3×C4×C5C22⋊C4semidirect
101. C2×C3×Dic5C22⋊C4semidirect
111. C23×C3×C4AGL(1,𝔽5)semidirect
129. C22×AGL(1,𝔽5)C2×C3×C4semidirect
151. C22×C3×C5#95semidirect
163. C2×C3×D5#95semidirect
234. C2×C4×C5C3×C22⋊C4semidirect
238. C2×Dic5C3×C22⋊C4semidirect
248. C23×C4C3×AGL(1,𝔽5)semidirect
300. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
305. C22×C5C3×#95semidirect
317. C2×D5C3×#95semidirect
356. C3×C5C22⋊#95semidirect
375. C22×C3(C2×AGL(1,𝔽5))⋊C4semidirect
431. C2×C4C3×C22⋊AGL(1,𝔽5)semidirect
441. C5C3×C22⋊#95semidirect
460. C22C3×(C2×AGL(1,𝔽5))⋊C4semidirect
469. C3#10604909direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C22×C3×C22⋊AGL(1,𝔽5)2
C2×C3×(C2×AGL(1,𝔽5))⋊C42
#106049093
C3×C22⋊#955