Finite Group Databasebeta

← C3×#10604469 #14283272

Subgroups — C3×#10604469 #14283272

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#121C211yesmaximal, characteristic
2C3×#65764C211yesmaximal, characteristic, complemented
3C3×#65756C211yesmaximal, characteristic, complemented
4C3×#64920C212yesmaximal, complemented
5C3×#64868C212yesmaximal, complemented
6#10604469C311yesmaximal, 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×#700—21no—
12C3×C5×#121C411yescharacteristic, complemented
13C3×#4085—21no—
14C3×#4084C2211yescharacteristic
15C3×#4076C411yescharacteristic, complemented
16C3×#4041C2211yescharacteristic
17C3×D5×C4⋊C4C411yescharacteristic, complemented
18C3×#4030—21no—
19C3×D5×C22⋊C4—21no—
20C3×C22⋊#170—21no—
21C3×(C2×AGL(1,𝔽5))⋊C4—21no—
22C3×(C2×AGL(1,𝔽5))⋊C4C2212yescomplemented
23C3×#4003C2212yescomplemented
24C3×#1510—51nomaximal, Hall
25D5×#121C2×C311yescharacteristic
26#65764C2×C311yescharacteristic, complemented
27#65756C2×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)—42no—
51C2×C3×#170—22no—
52C3×#700—42no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×#683—21no—
60C2×C3×#121—51no—
61C3×#407—51no—
62C3×#381—51no—
63C3×#327—52no—
64C3×#327—52no—
65C2×D4×D5—21no—
66C2×D4×D5C3×C411yescharacteristic, complemented
67C22×C4×D5C22×C311yescharacteristic
68C2×C22⋊AGL(1,𝔽5)—21no—
69C2×#700—21no—
70C5×#121C3×C411yescharacteristic, complemented
71#4085—21no—
72#4084C22×C311yescharacteristic
73#4076C3×C411yescharacteristic, complemented
74#4041C22×C311yescharacteristic
75D5×C4⋊C4C3×C411yescharacteristic, complemented
76#4030—21no—
77D5×C22⋊C4—21no—
78C22⋊#170—21no—
79(C2×AGL(1,𝔽5))⋊C4—21no—
80(C2×AGL(1,𝔽5))⋊C4C22×C312yescomplemented
81#4003C22×C312yescomplemented
82#1510—51noSylow
83C23×C3×C5—21no—
84C23×C3×C5C22⋊C411yescharacteristic
85C22×C3×D5—22no—
86C22×C3×D5—22no—
87C22×C3×D5—21no—
88C22×C3×D5—41no—
89C22×C3×D5—42no—
90C22×C3×D5—42no—
91C22×C3×D5—42no—
92C22×C3×D5C22⋊C411yescharacteristic
93C22×C3×D5C2×D411yescharacteristic
94C2×C3×AGL(1,𝔽5)—42no—
95C2×C3×AGL(1,𝔽5)—42no—
96C2×C3×AGL(1,𝔽5)—42no—
97C3×C5×D4—41no—
98C3×C5×D4—42no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C3×C22⋊D5—42no—
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C2×D411yescharacteristic
110C3×D20—41no—
111C3×D20—42no—
112C3×C4×D5—22no—
113C3×C4×D5—22no—
114C3×C4×D5—41no—
115C3×C4×D5—41no—
116C3×C4×D5—42no—
117C3×#170—42no—
118C22×C3×D4—51no—
119C22×C3×D4—101no—
120C23×C3×C4—51no—
121C2×C3×M16—101no—
122C3×#121—51no—
123C3×#121—51no—
124C3×#121—51no—
125C3×#121—101no—
126C3×#121—101no—
127C3×#121AGL(1,𝔽5)11yescharacteristic, complemented
128C2×C3×C4⋊C4—51no—
129C2×C3×C22⋊C4—101no—
130C2×C3×C22⋊C4—101no—
131C3×C22⋊C8—52no—
132C3×C22⋊C8—101no—
133C3×#95—52no—
134C3×#95—101no—
135C23×D5—21no—
136C23×D5C3×D411yescharacteristic
137C22×AGL(1,𝔽5)—22no—
138C2×C5×D4—21no—
139C2×C5×D4C2×C3×C411yescharacteristic
140C22×C4×C5C2×C3×C411yescharacteristic
141C2×C22⋊D5—21no—
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C22×Dic5C3×D411yescharacteristic
145D4×D5—42no—
146D4×D5—44no—
147C2×D20—21no—
148C2×D20C2×C3×C411yescharacteristic
149C2×C4×D5—21no—
150C2×C4×D5—42no—
151C2×C4×D5C2×C3×C411yescharacteristic
152C2×C4×D5C3×D411yescharacteristic
153C2×C4×D5C3×D411yescharacteristic
154C2×C4×D5C23×C311yescharacteristic
155C22⋊AGL(1,𝔽5)—42no—
156C2×#170—22no—
157#700—42no—
158C5×C4⋊C4C2×C3×C411yescharacteristic
159C5×C22⋊C4—21no—
160C22⋊Dic5—21no—
161#685—21no—
162#685—21no—
163C4⋊Dic5C2×C3×C411yescharacteristic
164#683—21no—
165C2×#121—51no—
166#407—51no—
167#381—51no—
168#327—52no—
169#327—52no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181C2×C3×D5—44no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—84no—
186C2×C3×D5#9912yes—
187C2×C3×D5AGL(1,ℤ/8)12yes—
188C3×AGL(1,𝔽5)—82no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×Dic5—21no—
193C3×Dic5—21no—
194C3×Dic5—41no—
195C24×C3—51no—
196C24×C3—101no—
197C2×C3×D4—21no—
198C2×C3×D4—51no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—202no—
204C2×C3×D4—204no—
205C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—101no—
212C22×C3×C4—102no—
213C22×C3×C4—202no—
214C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
215C3×M16—202no—
216C2×C3×C8—102no—
217C3×C4⋊C4—51no—
218C3×C4⋊C4—101no—
219C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
220C3×C22⋊C4—21no—
221C3×C22⋊C4—101no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4—101no—
224C3×C22⋊C4—202no—
225C23×C5—21no—
226C23×C5C3×C22⋊C411yescharacteristic
227C22×D5—22no—
228C22×D5—22no—
229C22×D5—21no—
230C22×D5—41no—
231C22×D5—42no—
232C22×D5—42no—
233C22×D5—42no—
234C22×D5C3×C22⋊C411yescharacteristic
235C22×D5C2×C3×D411yescharacteristic
236C2×AGL(1,𝔽5)—42no—
237C2×AGL(1,𝔽5)—42no—
238C2×AGL(1,𝔽5)—42no—
239C5×D4—41no—
240C5×D4—42no—
241C2×C4×C5—21no—
242C2×C4×C5—41no—
243C2×C4×C5C3×C22⋊C411yescharacteristic
244C2×C4×C5C22×C3×C411yescharacteristic
245C22⋊D5—42no—
246C22⋊D5—42no—
247C22⋊D5—42no—
248C2×Dic5—21no—
249C2×Dic5—41no—
250C2×Dic5C3×C22⋊C411yescharacteristic
251C2×Dic5C2×C3×D411yescharacteristic
252D20—41no—
253D20—42no—
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—41no—
257C4×D5—41no—
258C4×D5—42no—
259#170—42no—
260C22×D4—51no—
261C22×D4—101no—
262C23×C4—51no—
263C2×M16—101no—
264#121—51no—
265#121—51no—
266#121—51no—
267#121—101no—
268#121—101no—
269#121C3×AGL(1,𝔽5)11yescharacteristic, complemented
270C2×C4⋊C4—51no—
271C2×C22⋊C4—101no—
272C2×C22⋊C4—101no—
273C22⋊C8—52no—
274C22⋊C8—101no—
275#95—52no—
276#95—101no—
277C2×C3×C5—41no—
278C2×C3×C5—81no—
279C2×C3×C5C2×#9911yescharacteristic
280C2×C3×C5#41811yescharacteristic
281C2×C3×C5#42111yescharacteristic
282C3×D5—22no—
283C3×D5—22no—
284C3×D5—81no—
285C23×C3—21no—
286C23×C3—51no—
287C23×C3—51no—
288C23×C3—102no—
289C23×C3—102no—
290C23×C3—101no—
291C23×C3—201no—
292C23×C3—202no—
293C23×C3—202no—
294C23×C3—202no—
295C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
296C3×D4—41no—
297C3×D4—42no—
298C3×D4—201no—
299C3×D4—202no—
300C3×D4—202no—
301C3×D4—202no—
302C3×D4—202no—
303C2×C3×C4—21no—
304C2×C3×C4—41no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—102no—
308C2×C3×C4—102no—
309C2×C3×C4—101no—
310C2×C3×C4—201no—
311C2×C3×C4—201no—
312C2×C3×C4—202no—
313C2×C3×C4—201no—
314C2×C3×C4—202no—
315C2×C3×C4—202no—
316C2×C3×C4—202no—
317C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
318C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
319C3×C8—202no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5C2×C3×C22⋊C411yescharacteristic
327C2×D5—21no—
328C2×D5—21no—
329C2×D5—21no—
330C2×D5—21no—
331C2×D5—44no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5—84no—
336C2×D5C3×#9912yes—
337C2×D5C3×AGL(1,ℤ/8)12yes—
338AGL(1,𝔽5)—82no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342Dic5—21no—
343Dic5—21no—
344Dic5—41no—
345C24—51no—
346C24—101no—
347C2×D4—21no—
348C2×D4—51no—
349C2×D4—101no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—202no—
354C2×D4—204no—
355C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—101no—
362C22×C4—102no—
363C22×C4—202no—
364C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
365M16—202no—
366C2×C8—102no—
367C4⋊C4—51no—
368C4⋊C4—101no—
369C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—101no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C22⋊C4—202no—
375C3×C5#151011yescharacteristic, complemented, Hall
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—52no—
383C22×C3—52no—
384C22×C3—101no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3—101no—
388C22×C3—204no—
389C22×C3—201no—
390C22×C3—201no—
391C22×C3—201no—
392C22×C3—404no—
393C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—101no—
398C3×C4—101no—
399C3×C4—201no—
400C3×C4—402no—
401C2×C5—41no—
402C2×C5—81no—
403C2×C5C2×C3×#9911yescharacteristic
404C2×C5C3×#41811yescharacteristic
405C2×C5C3×#42111yescharacteristic
406D5—22no—
407D5—22no—
408D5—81no—
409C23—21no—
410C23—51no—
411C23—51no—
412C23—102no—
413C23—102no—
414C23—101no—
415C23—201no—
416C23—202no—
417C23—202no—
418C23—202no—
419C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
420D4—41no—
421D4—42no—
422D4—201no—
423D4—202no—
424D4—202no—
425D4—202no—
426D4—202no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—101no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—202no—
437C2×C4—201no—
438C2×C4—202no—
439C2×C4—202no—
440C2×C4—202no—
441C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
442C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
443C8—202no—
444C2×C3—41no—
445C2×C3—81no—
446C2×C3—102no—
447C2×C3—102no—
448C2×C3—401no—
449C2×C3#6576711yescharacteristic
450C2×C3D5⋊#9911yescharacteristic
451C2×C3#6579511yescharacteristic
452C5C3×#151011yescharacteristic, complemented, Sylow
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—52no—
460C22—52no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—101no—
465C22—204no—
466C22—201no—
467C22—201no—
468C22—201no—
469C22—404no—
470C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
471C4—21no—
472C4—21no—
473C4—41no—
474C4—101no—
475C4—101no—
476C4—201no—
477C4—402no—
478C3#1060446911yescharacteristic, direct product factor, Sylow
479C2—41no—
480C2—81no—
481C2—102no—
482C2—102no—
483C2—401no—
484C2C3×#6576711yescharacteristic
485C2C3×D5⋊#9911yescharacteristic
486C2C3×#6579511yescharacteristic
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×#1510
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×#65764C2semidirect
3. C3×#65756C2semidirect
4. C3×#64920C2semidirect
5. C3×#64868C2semidirect
6. #10604469C3direct (N × H)
8. C2×C3×D4×D5C4semidirect
12. C3×C5×#121C4semidirect
15. C3×#4076C4semidirect
17. C3×D5×C4⋊C4C4semidirect
22. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
23. C3×#4003C22semidirect
26. #65764C2×C3semidirect
27. #65756C2×C3semidirect
28. #64920C2×C3semidirect
29. #64868C2×C3semidirect
66. C2×D4×D5C3×C4semidirect
70. C5×#121C3×C4semidirect
73. #4076C3×C4semidirect
75. D5×C4⋊C4C3×C4semidirect
80. (C2×AGL(1,𝔽5))⋊C4C22×C3semidirect
81. #4003C22×C3semidirect
127. C3×#121AGL(1,𝔽5)semidirect
269. #121C3×AGL(1,𝔽5)semidirect
375. C3×C5#1510semidirect
452. C5C3×#1510semidirect
478. C3#10604469direct (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×#657642
C3×#657562
C3×#649202
C3×#648682
#106044693
C3×#15105