Finite Group Databasebeta

← C3×#10604468 #14283119

Subgroups — C3×#10604468 #14283119

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#121C211yesmaximal, characteristic
2C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C3×#65755C211yesmaximal, characteristic, complemented
4C3×#64920C212yesmaximal, complemented
5C3×#64868C212yesmaximal, complemented
6#10604468C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×D4×D5—21no—
8C2×C3×D4×D5C411yescharacteristic, complemented
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C22⋊AGL(1,𝔽5)—21no—
11C2×C3×#704—21no—
12C2×C3×C4×AGL(1,𝔽5)—21no—
13C3×C5×#121C411yescharacteristic, complemented
14C3×#4085—21no—
15C3×#4084C2211yescharacteristic
16C3×#4076C411yescharacteristic, complemented
17C3×#4041C2211yescharacteristic
18C3×D5×C4⋊C4C411yescharacteristic, complemented
19C3×#4030—21no—
20C3×D5×C22⋊C4—21no—
21C3×(C2×AGL(1,𝔽5))⋊C4C2212yescomplemented
22C3×#4003—21no—
23C3×#4003C2212yescomplemented
24C3×#1507—51nomaximal, Hall
25D5×#121C2×C311yescharacteristic
26C4×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
27#65755C2×C311yescharacteristic, complemented
28#64920C2×C312yescomplemented
29#64868C2×C312yescomplemented
30C23×C3×D5—21no—
31C23×C3×D5D411yescharacteristic
32C22×C3×AGL(1,𝔽5)—22no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C2×C3×C22⋊D5—21no—
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5D411yescharacteristic
40C3×D4×D5—42no—
41C3×D4×D5—44no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—42no—
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5C2311yescharacteristic
50C3×C22⋊AGL(1,𝔽5)—24no—
51C3×#704—42no—
52C2×C3×#170—22no—
53C3×C4×AGL(1,𝔽5)—42no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C22⋊Dic5—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×#683—21no—
61C2×C3×#121—51no—
62C3×#407—51no—
63C3×C4×C22⋊C4—51no—
64C3×#327—52no—
65C3×#327—52no—
66C2×D4×D5—21no—
67C2×D4×D5C3×C411yescharacteristic, complemented
68C22×C4×D5C22×C311yescharacteristic
69C2×C22⋊AGL(1,𝔽5)—21no—
70C2×#704—21no—
71C2×C4×AGL(1,𝔽5)—21no—
72C5×#121C3×C411yescharacteristic, complemented
73#4085—21no—
74#4084C22×C311yescharacteristic
75#4076C3×C411yescharacteristic, complemented
76#4041C22×C311yescharacteristic
77D5×C4⋊C4C3×C411yescharacteristic, complemented
78#4030—21no—
79D5×C22⋊C4—21no—
80(C2×AGL(1,𝔽5))⋊C4C22×C312yescomplemented
81#4003—21no—
82#4003C22×C312yescomplemented
83#1507—51noSylow
84C23×C3×C5—21no—
85C23×C3×C5C22⋊C411yescharacteristic
86C22×C3×D5—22no—
87C22×C3×D5—22no—
88C22×C3×D5—21no—
89C22×C3×D5—41no—
90C22×C3×D5—42no—
91C22×C3×D5—42no—
92C22×C3×D5—42no—
93C22×C3×D5C22⋊C411yescharacteristic
94C22×C3×D5C2×D411yescharacteristic
95C2×C3×AGL(1,𝔽5)—24no—
96C2×C3×AGL(1,𝔽5)—42no—
97C2×C3×AGL(1,𝔽5)—42no—
98C3×C5×D4—41no—
99C3×C5×D4—42no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22⋊C411yescharacteristic
103C2×C3×C4×C5C22×C411yescharacteristic
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C3×C22⋊D5—42no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C2×D411yescharacteristic
111C3×D20—41no—
112C3×D20—42no—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×C4×D5—41no—
116C3×C4×D5—41no—
117C3×C4×D5—42no—
118C3×#170—42no—
119C22×C3×D4—51no—
120C22×C3×D4—101no—
121C23×C3×C4—51no—
122C2×C3×M16—101no—
123C3×#121—51no—
124C3×#121—51no—
125C3×#121—51no—
126C3×#121—101no—
127C3×#121—101no—
128C3×#121AGL(1,𝔽5)11yescharacteristic, complemented
129C2×C3×C4⋊C4—51no—
130C2×C3×C22⋊C4—101no—
131C2×C3×C22⋊C4—101no—
132C2×C3×C42—101no—
133C3×C22⋊C8—52no—
134C3×C22⋊C8—101no—
135C3×#95—52no—
136C23×D5—21no—
137C23×D5C3×D411yescharacteristic
138C22×AGL(1,𝔽5)—22no—
139C2×C5×D4—21no—
140C2×C5×D4C2×C3×C411yescharacteristic
141C22×C4×C5C2×C3×C411yescharacteristic
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C22×Dic5C3×D411yescharacteristic
146D4×D5—42no—
147D4×D5—44no—
148C2×D20—21no—
149C2×D20C2×C3×C411yescharacteristic
150C2×C4×D5—21no—
151C2×C4×D5—42no—
152C2×C4×D5C2×C3×C411yescharacteristic
153C2×C4×D5C3×D411yescharacteristic
154C2×C4×D5C3×D411yescharacteristic
155C2×C4×D5C23×C311yescharacteristic
156C22⋊AGL(1,𝔽5)—24no—
157#704—42no—
158C2×#170—22no—
159C4×AGL(1,𝔽5)—42no—
160C5×C4⋊C4C2×C3×C411yescharacteristic
161C5×C22⋊C4—21no—
162C22⋊Dic5—21no—
163#685—21no—
164#685—21no—
165C4⋊Dic5C2×C3×C411yescharacteristic
166#683—21no—
167C2×#121—51no—
168#407—51no—
169C4×C22⋊C4—51no—
170#327—52no—
171#327—52no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—44no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187C2×C3×D5—84no—
188C2×C3×D5#10412yes—
189C2×C3×D5AGL(1,ℤ/8)12yes—
190C3×AGL(1,𝔽5)—44no—
191C3×C4×C5—21no—
192C3×C4×C5—21no—
193C3×C4×C5—41no—
194C3×Dic5—21no—
195C3×Dic5—41no—
196C3×Dic5#9912yes—
197C24×C3—51no—
198C24×C3—101no—
199C2×C3×D4—21no—
200C2×C3×D4—51no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C2×C3×D4—101no—
205C2×C3×D4—202no—
206C2×C3×D4—204no—
207C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—101no—
214C22×C3×C4—102no—
215C22×C3×C4—202no—
216C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
217C3×M16—202no—
218C2×C3×C8—102no—
219C3×C4⋊C4—51no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
222C3×C22⋊C4—21no—
223C3×C22⋊C4—101no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—104no—
226C3×C22⋊C4—101no—
227C3×C42—202no—
228C23×C5—21no—
229C23×C5C3×C22⋊C411yescharacteristic
230C22×D5—22no—
231C22×D5—22no—
232C22×D5—21no—
233C22×D5—41no—
234C22×D5—42no—
235C22×D5—42no—
236C22×D5—42no—
237C22×D5C3×C22⋊C411yescharacteristic
238C22×D5C2×C3×D411yescharacteristic
239C2×AGL(1,𝔽5)—24no—
240C2×AGL(1,𝔽5)—42no—
241C2×AGL(1,𝔽5)—42no—
242C5×D4—41no—
243C5×D4—42no—
244C2×C4×C5—21no—
245C2×C4×C5—41no—
246C2×C4×C5C3×C22⋊C411yescharacteristic
247C2×C4×C5C22×C3×C411yescharacteristic
248C22⋊D5—42no—
249C22⋊D5—42no—
250C22⋊D5—42no—
251C2×Dic5—22no—
252C2×Dic5—21no—
253C2×Dic5C3×C22⋊C411yescharacteristic
254C2×Dic5C2×C3×D411yescharacteristic
255D20—41no—
256D20—42no—
257C4×D5—22no—
258C4×D5—22no—
259C4×D5—41no—
260C4×D5—41no—
261C4×D5—42no—
262#170—42no—
263C22×D4—51no—
264C22×D4—101no—
265C23×C4—51no—
266C2×M16—101no—
267#121—51no—
268#121—51no—
269#121—51no—
270#121—101no—
271#121—101no—
272#121C3×AGL(1,𝔽5)11yescharacteristic, complemented
273C2×C4⋊C4—51no—
274C2×C22⋊C4—101no—
275C2×C22⋊C4—101no—
276C2×C42—101no—
277C22⋊C8—52no—
278C22⋊C8—101no—
279#95—52no—
280C2×C3×C5—41no—
281C2×C3×C5—81no—
282C2×C3×C5C2×#9911yescharacteristic
283C2×C3×C5#41811yescharacteristic
284C2×C3×C5C2×#10411yescharacteristic
285C3×D5—22no—
286C3×D5—22no—
287C3×D5—81no—
288C23×C3—21no—
289C23×C3—51no—
290C23×C3—51no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—101no—
294C23×C3—201no—
295C23×C3—202no—
296C23×C3—202no—
297C23×C3—202no—
298C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
299C3×D4—41no—
300C3×D4—42no—
301C3×D4—201no—
302C3×D4—202no—
303C3×D4—202no—
304C3×D4—202no—
305C3×D4—202no—
306C2×C3×C4—21no—
307C2×C3×C4—41no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—102no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—104no—
314C2×C3×C4—101no—
315C2×C3×C4—201no—
316C2×C3×C4—201no—
317C2×C3×C4—202no—
318C2×C3×C4—202no—
319C2×C3×C4—202no—
320C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
321C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
322C3×C8—202no—
323C22×C5—21no—
324C22×C5—21no—
325C22×C5—21no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5C2×C3×C22⋊C411yescharacteristic
330C2×D5—21no—
331C2×D5—21no—
332C2×D5—21no—
333C2×D5—21no—
334C2×D5—44no—
335C2×D5—41no—
336C2×D5—41no—
337C2×D5—41no—
338C2×D5—84no—
339C2×D5C3×#10412yes—
340C2×D5C3×AGL(1,ℤ/8)12yes—
341AGL(1,𝔽5)—44no—
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—41no—
345Dic5—21no—
346Dic5—41no—
347Dic5C3×#9912yes—
348C24—51no—
349C24—101no—
350C2×D4—21no—
351C2×D4—51no—
352C2×D4—101no—
353C2×D4—101no—
354C2×D4—101no—
355C2×D4—101no—
356C2×D4—202no—
357C2×D4—204no—
358C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—51no—
363C22×C4—51no—
364C22×C4—101no—
365C22×C4—102no—
366C22×C4—202no—
367C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
368M16—202no—
369C2×C8—102no—
370C4⋊C4—51no—
371C4⋊C4—101no—
372C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
373C22⋊C4—21no—
374C22⋊C4—101no—
375C22⋊C4—101no—
376C22⋊C4—104no—
377C22⋊C4—101no—
378C42—202no—
379C3×C5#150711yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—52no—
387C22×C3—52no—
388C22×C3—101no—
389C22×C3—101no—
390C22×C3—101no—
391C22×C3—101no—
392C22×C3—204no—
393C22×C3—201no—
394C22×C3—201no—
395C22×C3—201no—
396C22×C3—404no—
397C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—52no—
402C3×C4—101no—
403C3×C4—204no—
404C3×C4—201no—
405C2×C5—41no—
406C2×C5—81no—
407C2×C5C2×C3×#9911yescharacteristic
408C2×C5C3×#41811yescharacteristic
409C2×C5C2×C3×#10411yescharacteristic
410D5—22no—
411D5—22no—
412D5—81no—
413C23—21no—
414C23—51no—
415C23—51no—
416C23—102no—
417C23—102no—
418C23—101no—
419C23—201no—
420C23—202no—
421C23—202no—
422C23—202no—
423C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
424D4—41no—
425D4—42no—
426D4—201no—
427D4—202no—
428D4—202no—
429D4—202no—
430D4—202no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—102no—
438C2×C4—104no—
439C2×C4—101no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4—202no—
443C2×C4—202no—
444C2×C4—202no—
445C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
446C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
447C8—202no—
448C2×C3—41no—
449C2×C3—81no—
450C2×C3—102no—
451C2×C3—102no—
452C2×C3—401no—
453C2×C3#6576711yescharacteristic
454C2×C3D5⋊#9911yescharacteristic
455C2×C3D5⋊#10411yescharacteristic
456C5C3×#150711yescharacteristic, complemented, Sylow
457C22—21no—
458C22—21no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—52no—
464C22—52no—
465C22—101no—
466C22—101no—
467C22—101no—
468C22—101no—
469C22—204no—
470C22—201no—
471C22—201no—
472C22—201no—
473C22—404no—
474C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
475C4—21no—
476C4—21no—
477C4—41no—
478C4—52no—
479C4—101no—
480C4—204no—
481C4—201no—
482C3#1060446811yescharacteristic, direct product factor, Sylow
483C2—41no—
484C2—81no—
485C2—102no—
486C2—102no—
487C2—401no—
488C2C3×#6576711yescharacteristic
489C2C3×D5⋊#9911yescharacteristic
490C2C3×D5⋊#10411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#121C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#121C2
cosocleC2×C4×D5C23×C3
hypercenterC3×#121AGL(1,𝔽5)
hypocenterC5C3×#1507
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
2. C3×C4×C22⋊AGL(1,𝔽5)C2semidirect
3. C3×#65755C2semidirect
4. C3×#64920C2semidirect
5. C3×#64868C2semidirect
6. #10604468C3direct (N × H)
8. C2×C3×D4×D5C4semidirect
13. C3×C5×#121C4semidirect
16. C3×#4076C4semidirect
18. C3×D5×C4⋊C4C4semidirect
21. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
23. C3×#4003C22semidirect
26. C4×C22⋊AGL(1,𝔽5)C2×C3semidirect
27. #65755C2×C3semidirect
28. #64920C2×C3semidirect
29. #64868C2×C3semidirect
67. C2×D4×D5C3×C4semidirect
72. C5×#121C3×C4semidirect
75. #4076C3×C4semidirect
77. D5×C4⋊C4C3×C4semidirect
80. (C2×AGL(1,𝔽5))⋊C4C22×C3semidirect
82. #4003C22×C3semidirect
128. C3×#121AGL(1,𝔽5)semidirect
272. #121C3×AGL(1,𝔽5)semidirect
379. C3×C5#1507semidirect
456. C5C3×#1507semidirect
482. C3#10604468direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1212
C3×C4×C22⋊AGL(1,𝔽5)2
C3×#657552
C3×#649202
C3×#648682
#106044683
C3×#15075