Finite Group Databasebeta

← C3×#10604451 #14297684

Subgroups — C3×#10604451 #14297684

Order 1920.

616 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
1C3×C4×Q8×D5C211yesmaximal, characteristic
2C2×C3×#4009C212yesmaximal
3C3×#65688C211yesmaximal, characteristic
4C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic
5C3×#64874C212yesmaximal
6#10604451C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C3×C4⋊AGL(1,𝔽5)—21no—
9C2×C3×C4⋊AGL(1,𝔽5)—21no—
10C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
11C2×C3×D5⋊C8C2212yes—
12C3×C4×C5×Q8C411yescharacteristic, complemented
13C3×Q8×Dic5C411yescharacteristic, complemented
14C3×D5×C4⋊C4—21no—
15C3×D5×C4⋊C4C2211yescharacteristic
16C3×#4033—21no—
17C3×#4033C411yescharacteristic, complemented
18C3×C42×D5—21no—
19C3×C42×D5C2211yescharacteristic
20C3×C4×Dic10—21no—
21C3×C4×Dic10C411yescharacteristic, complemented
22C3×#4009—24no—
23C3×#4004—21no—
24C3×C4⋊#170—21no—
25C3×#1803—51nomaximal, Hall
26C4×Q8×D5C2×C311yescharacteristic
27C2×#4009C2×C312yes—
28#65688C2×C311yescharacteristic
29D5⋊(C4⋊C8)C2×C311yescharacteristic
30#64874C2×C312yes—
31C22×C3×AGL(1,𝔽5)—22no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C3×Q8×D5—21no—
34C3×Q8×D5—21no—
35C3×Q8×D5D412yes—
36C3×Q8×D5Q812yes—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5C2311yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C2×C3×#170—22no—
45C3×C4⋊AGL(1,𝔽5)—22no—
46C3×C4⋊AGL(1,𝔽5)—22no—
47C3×C4⋊AGL(1,𝔽5)—42no—
48C3×C4⋊AGL(1,𝔽5)—42no—
49C3×D5⋊C8—22no—
50C3×D5⋊C8—22no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C42×C5—21no—
54C3×C42×C5C2×C411yescharacteristic
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65C3×C4×Dic5D411yescharacteristic
66C2×C3×C4×Q8—51no—
67C2×C3×C4⋊C8—51no—
68C2×C3×#103—52no—
69C3×#384—51no—
70C3×#340—52no—
71C2×Q8×D5C22×C311yescharacteristic
72C2×C4⋊AGL(1,𝔽5)—21no—
73C2×C4⋊AGL(1,𝔽5)—21no—
74C2×C4⋊AGL(1,𝔽5)C22×C312yes—
75C2×D5⋊C8C22×C312yes—
76C4×C5×Q8C3×C411yescharacteristic, complemented
77Q8×Dic5C3×C411yescharacteristic, complemented
78D5×C4⋊C4—21no—
79D5×C4⋊C4C22×C311yescharacteristic
80#4033—21no—
81#4033C3×C411yescharacteristic, complemented
82C42×D5—21no—
83C42×D5C22×C311yescharacteristic
84C4×Dic10—21no—
85C4×Dic10C3×C411yescharacteristic, complemented
86#4009—24no—
87#4004—21no—
88C4⋊#170—21no—
89#1803—51noSylow
90C22×C3×D5C2×D411yescharacteristic
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×AGL(1,𝔽5)—42no—
93C2×C3×AGL(1,𝔽5)—42no—
94C3×C5×Q8—21no—
95C3×C5×Q8C4⋊C412yescomplemented
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112C3×C4×D5SD1612yes—
113C3×C4×D5Q1612yes—
114C3×C4×D5C2×D411yescharacteristic
115C3×C4×D5C2×Q811yescharacteristic
116C3×C4×D5#4111yescharacteristic
117C3×C4×D5#4111yescharacteristic
118C3×Dic10—21no—
119C3×Dic10—22no—
120C3×Dic10—22no—
121C3×Dic10C4⋊C412yescomplemented
122C3×#170—42no—
123C22×C3×Q8—51no—
124C22×C3×C8—52no—
125C3×C4×Q8—51no—
126C3×C4×Q8—51no—
127C3×C4×Q8—51no—
128C3×C4×Q8—101no—
129C3×C4×Q8—101no—
130C3×C4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—52no—
133C2×C3×C4⋊C4—101no—
134C2×C3×C4⋊C4—101no—
135C2×C3×C4⋊C4—101no—
136C2×C3×C42—51no—
137C2×C3×C42—101no—
138C3×C4⋊C8—101no—
139C3×C4⋊C8—101no—
140C3×#103—104no—
141C22×AGL(1,𝔽5)—22no—
142C2×C5×Q8C2×C3×C411yescharacteristic
143Q8×D5—21no—
144Q8×D5—21no—
145Q8×D5C3×D412yes—
146Q8×D5C3×Q812yes—
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5C3×D411yescharacteristic
150C2×C4×D5C3×D411yescharacteristic
151C2×C4×D5C23×C311yescharacteristic
152C2×Dic10—21no—
153C2×Dic10C2×C3×C411yescharacteristic
154C2×#170—22no—
155C4⋊AGL(1,𝔽5)—22no—
156C4⋊AGL(1,𝔽5)—22no—
157C4⋊AGL(1,𝔽5)—42no—
158C4⋊AGL(1,𝔽5)—42no—
159D5⋊C8—22no—
160D5⋊C8—22no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4C2×C3×C411yescharacteristic
163C42×C5—21no—
164C42×C5C2×C3×C411yescharacteristic
165C4⋊Dic5—21no—
166C4⋊Dic5C2×C3×C411yescharacteristic
167#683—21no—
168#683—21no—
169#683—21no—
170C4×Dic5—21no—
171C4×Dic5—21no—
172C4×Dic5—21no—
173C4×Dic5C2×C3×C411yescharacteristic
174C4×Dic5C3×D411yescharacteristic
175C4×Dic5C3×D411yescharacteristic
176C2×C4×Q8—51no—
177C2×C4⋊C8—51no—
178C2×#103—52no—
179#384—51no—
180#340—52no—
181C22×C3×C5C2×C22⋊C411yescharacteristic
182C2×C3×D5#12111yescharacteristic
183C2×C3×D5C22⋊Q811yescharacteristic
184C2×C3×D5C2×SD1611yescharacteristic
185C2×C3×D5C2×Q1611yescharacteristic
186C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
187C2×C3×D5#13711yescharacteristic
188C3×AGL(1,𝔽5)—82no—
189C3×C4×C5—22no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×C4×C5#10312yescomplemented
193C3×C4×C5C2×C4⋊C411yescharacteristic
194C3×C4×C5#11711yescharacteristic
195C3×Dic5—22no—
196C3×Dic5—21no—
197C3×Dic5—41no—
198C3×Dic5#10312yescomplemented
199C3×Dic5#12111yescharacteristic
200C3×Dic5C22⋊Q811yescharacteristic
201C2×C3×Q8—52no—
202C2×C3×Q8—52no—
203C2×C3×Q8—51no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8—101no—
207C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—101no—
212C22×C3×C4—101no—
213C22×C3×C4—102no—
214C2×C3×C8—102no—
215C2×C3×C8—102no—
216C2×C3×C8—102no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—102no—
223C3×C4⋊C4—102no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—202no—
226C3×C4⋊C4—202no—
227C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
228C3×C42—21no—
229C3×C42—51no—
230C3×C42—51no—
231C3×C42—51no—
232C3×C42—101no—
233C3×C42—101no—
234C3×C42—101no—
235C3×C42C2×AGL(1,𝔽5)11yescharacteristic
236C22×D5C2×C3×D411yescharacteristic
237C2×AGL(1,𝔽5)—42no—
238C2×AGL(1,𝔽5)—42no—
239C2×AGL(1,𝔽5)—42no—
240C5×Q8—21no—
241C5×Q8C3×C4⋊C412yescomplemented
242C2×C4×C5—21no—
243C2×C4×C5—21no—
244C2×C4×C5C3×C22⋊C411yescharacteristic
245C2×C4×C5C3×C22⋊C411yescharacteristic
246C2×C4×C5C22×C3×C411yescharacteristic
247C2×Dic5—21no—
248C2×Dic5—21no—
249C2×Dic5C3×C22⋊C411yescharacteristic
250C2×Dic5C3×C22⋊C411yescharacteristic
251C2×Dic5C2×C3×D411yescharacteristic
252C4×D5—22no—
253C4×D5—22no—
254C4×D5—21no—
255C4×D5—21no—
256C4×D5—41no—
257C4×D5—41no—
258C4×D5C3×SD1612yes—
259C4×D5C3×Q1612yes—
260C4×D5C2×C3×D411yescharacteristic
261C4×D5C2×C3×Q811yescharacteristic
262C4×D5C3×#4111yescharacteristic
263C4×D5C3×#4111yescharacteristic
264Dic10—21no—
265Dic10—22no—
266Dic10—22no—
267Dic10C3×C4⋊C412yescomplemented
268#170—42no—
269C22×Q8—51no—
270C22×C8—52no—
271C4×Q8—51no—
272C4×Q8—51no—
273C4×Q8—51no—
274C4×Q8—101no—
275C4×Q8—101no—
276C4×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
277C2×C4⋊C4—51no—
278C2×C4⋊C4—52no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—101no—
281C2×C4⋊C4—101no—
282C2×C42—51no—
283C2×C42—101no—
284C4⋊C8—101no—
285C4⋊C8—101no—
286#103—104no—
287C2×C3×C5#38011yescharacteristic
288C2×C3×C5C2×#10311yescharacteristic
289C2×C3×C5#41711yescharacteristic
290C3×D5#46011yescharacteristic
291C3×D5#46211yescharacteristic
292C3×D5#47511yescharacteristic
293C3×D5#47711yescharacteristic
294C23×C3—51no—
295C3×Q8—21no—
296C3×Q8—52no—
297C3×Q8—102no—
298C3×Q8—102no—
299C3×Q8—101no—
300C3×Q8C4⋊AGL(1,𝔽5)12yescomplemented
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—51no—
308C2×C3×C4—51no—
309C2×C3×C4—52no—
310C2×C3×C4—52no—
311C2×C3×C4—51no—
312C2×C3×C4—101no—
313C2×C3×C4—101no—
314C2×C3×C4—102no—
315C2×C3×C4—102no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4—202no—
321C2×C3×C4—202no—
322C2×C3×C4—202no—
323C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
324C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
325C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
326C3×C8—202no—
327C22×C5C2×C3×C22⋊C411yescharacteristic
328C2×D5C3×#12111yescharacteristic
329C2×D5C3×C22⋊Q811yescharacteristic
330C2×D5C2×C3×SD1611yescharacteristic
331C2×D5C2×C3×Q1611yescharacteristic
332C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
333C2×D5C3×#13711yescharacteristic
334AGL(1,𝔽5)—82no—
335C4×C5—22no—
336C4×C5—21no—
337C4×C5—41no—
338C4×C5C3×#10312yescomplemented
339C4×C5C2×C3×C4⋊C411yescharacteristic
340C4×C5C3×#11711yescharacteristic
341Dic5—22no—
342Dic5—21no—
343Dic5—41no—
344Dic5C3×#10312yescomplemented
345Dic5C3×#12111yescharacteristic
346Dic5C3×C22⋊Q811yescharacteristic
347C2×Q8—52no—
348C2×Q8—52no—
349C2×Q8—51no—
350C2×Q8—101no—
351C2×Q8—101no—
352C2×Q8—101no—
353C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—101no—
358C22×C4—101no—
359C22×C4—102no—
360C2×C8—102no—
361C2×C8—102no—
362C2×C8—102no—
363C4⋊C4—21no—
364C4⋊C4—51no—
365C4⋊C4—101no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—102no—
369C4⋊C4—102no—
370C4⋊C4—101no—
371C4⋊C4—202no—
372C4⋊C4—202no—
373C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
374C42—21no—
375C42—51no—
376C42—51no—
377C42—51no—
378C42—101no—
379C42—101no—
380C42—101no—
381C42C2×C3×AGL(1,𝔽5)11yescharacteristic
382C3×C5#180311yescharacteristic, complemented, Hall
383C22×C3—51no—
384C22×C3—51no—
385C22×C3—51no—
386C22×C3—51no—
387C22×C3—51no—
388C22×C3—51no—
389C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—41no—
393C3×C4—51no—
394C3×C4—51no—
395C3×C4—52no—
396C3×C4—101no—
397C3×C4—102no—
398C3×C4—201no—
399C3×C4—402no—
400C3×C4#400912yescomplemented
401C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
402C3×C4#413011yescharacteristic
403C2×C5C3×#38011yescharacteristic
404C2×C5C2×C3×#10311yescharacteristic
405C2×C5C3×#41711yescharacteristic
406D5C3×#46011yescharacteristic
407D5C3×#46211yescharacteristic
408D5C3×#47511yescharacteristic
409D5C3×#47711yescharacteristic
410C23—51no—
411Q8—21no—
412Q8—52no—
413Q8—102no—
414Q8—102no—
415Q8—101no—
416Q8C3×C4⋊AGL(1,𝔽5)12yescomplemented
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—51no—
420C2×C4—51no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—51no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—102no—
431C2×C4—102no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—202no—
437C2×C4—202no—
438C2×C4—202no—
439C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
440C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
441C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
442C8—202no—
443C2×C3—51no—
444C2×C3—51no—
445C2×C3—51no—
446C2×C3—51no—
447C2×C3#6576511yescharacteristic
448C2×C3C2×#400911yescharacteristic
449C2×C3#6579311yescharacteristic
450C5C3×#180311yescharacteristic, complemented, Sylow
451C22—51no—
452C22—51no—
453C22—51no—
454C22—51no—
455C22—51no—
456C22—51no—
457C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
458C4—22no—
459C4—21no—
460C4—41no—
461C4—51no—
462C4—51no—
463C4—52no—
464C4—102no—
465C4—101no—
466C4—201no—
467C4—402no—
468C4C3×#400912yescomplemented
469C4C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
470C4C3×#413011yescharacteristic
471C3#1060445111yescharacteristic, direct product factor, Sylow
472C2—51no—
473C2—51no—
474C2—51no—
475C2—51no—
476C2C3×#6576511yescharacteristic
477C2C2×C3×#400911yescharacteristic
478C2C3×#6579311yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×C4×Q8AGL(1,𝔽5)
hypocenterC5C3×#1803
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
6. #10604451C3direct (N × H)
12. C3×C4×C5×Q8C4semidirect
13. C3×Q8×Dic5C4semidirect
17. C3×#4033C4semidirect
21. C3×C4×Dic10C4semidirect
76. C4×C5×Q8C3×C4semidirect
77. Q8×Dic5C3×C4semidirect
81. #4033C3×C4semidirect
85. C4×Dic10C3×C4semidirect
95. C3×C5×Q8C4⋊C4semidirect
121. C3×Dic10C4⋊C4semidirect
130. C3×C4×Q8AGL(1,𝔽5)semidirect
192. C3×C4×C5#103semidirect
198. C3×Dic5#103semidirect
241. C5×Q8C3×C4⋊C4semidirect
267. Dic10C3×C4⋊C4semidirect
276. C4×Q8C3×AGL(1,𝔽5)semidirect
300. C3×Q8C4⋊AGL(1,𝔽5)semidirect
338. C4×C5C3×#103semidirect
344. Dic5C3×#103semidirect
382. C3×C5#1803semidirect
400. C3×C4#4009semidirect
416. Q8C3×C4⋊AGL(1,𝔽5)semidirect
450. C5C3×#1803semidirect
468. C4C3×#4009semidirect
471. C3#10604451direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
C2×C3×#40092
C3×#656882
C3×D5⋊(C4⋊C8)2
C3×#648742
#106044513
C3×#18035