Finite Group Databasebeta

← D3×#65800 #14319817

Subgroups — D3×#65800 #14319817

Order 1920.

6928 conjugacy classes of subgroups; only the 434 normal subgroups are shown.

normal subgroups only

This group has 6928 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D3×D5C211yesmaximal, characteristic
2C2×D3×C22⋊AGL(1,𝔽5)C216yesmaximal, complemented
3#11752459C211yesmaximal, characteristic, complemented
4C3×#65800C211yesmaximal, characteristic, complemented
5#11752025C216yesmaximal, complemented
6C2×#65800—31nomaximal, Hall
7C24×D15C411yescharacteristic, complemented
8C24×C5×D3C411yescharacteristic, complemented
9C24×C3×D5C2211yescharacteristic
10C23×D3×D5—224no—
11C23×D3×D5C413yescomplemented
12C23×D3×D5C413yescomplemented
13C23×D3×D5C2213yes—
14C23×D3×D5C2213yes—
15C22×D3×AGL(1,𝔽5)C2214yescomplemented
16C2×#6763C2216yescomplemented
17C2×C3×C22⋊AGL(1,𝔽5)C2216yescomplemented
18D3×C22⋊AGL(1,𝔽5)—224no—
19C2×(C2×D3)⋊AGL(1,𝔽5)C22112yescomplemented
20D3×#379—51nomaximal, Hall
21C25×D5—31no—
22C22×C22⋊AGL(1,𝔽5)—36no—
23#65800—31no—
24#65800—36no—
25#65800D311yescharacteristic, direct product factor
26C24×C3×C5C2×C411yescharacteristic, complemented
27C23×D15—212no—
28C23×D15C2×C413yes—
29C23×D15C2×C413yescomplemented
30C23×C5×D3—212no—
31C23×C5×D3C2×C413yes—
32C23×C5×D3C2×C413yescomplemented
33C23×C3×D5—212no—
34C23×C3×D5C2×C413yescomplemented
35C23×C3×D5C2313yes—
36C22×D3×D5—2128no—
37C22×D3×D5—212no—
38C22×D3×D5—212no—
39C22×D3×D5—212no—
40C22×D3×D5—224no—
41C22×D3×D5—224no—
42C22×D3×D5—224no—
43C22×D3×D5—224no—
44C22×D3×D5C2×C413yes—
45C22×D3×D5C2×C413yes—
46C22×D3×D5C2×C416yescomplemented
47C22×D3×D5D4124yes—
48C22×D3×D5C2313yes—
49C22×D3×D5C2311yescharacteristic
50C22×ΓL(1,𝔽16)C2314yescomplemented
51C22×C3×AGL(1,𝔽5)C2314yescomplemented
52C2×D3×AGL(1,𝔽5)—224no—
53#6763—212no—
54C3×C22⋊AGL(1,𝔽5)—212no—
55(C2×D3)⋊AGL(1,𝔽5)—224no—
56C25×D3—51no—
57C2×D3×C22⋊C4—56no—
58C3×#379—51no—
59#5247—51no—
60#4955—56no—
61C25×C5—31no—
62C24×D5—33no—
63C24×D5—31no—
64C24×D5—33no—
65C24×D5—33no—
66C24×D5—33no—
67C24×D5—624no—
68C24×D5C2×D311yescharacteristic
69C23×AGL(1,𝔽5)—34no—
70C2×C22⋊AGL(1,𝔽5)—36no—
71C2×C22⋊AGL(1,𝔽5)—312no—
72C2×C22⋊AGL(1,𝔽5)—624no—
73C2×C22⋊AGL(1,𝔽5)C2×D316yescomplemented
74C2×#379—151noSylow
75C23×C3×C5—26no—
76C23×C3×C5C22×C413yes—
77C22×D15—232no—
78C22×D15—26no—
79C22×D15—212no—
80C22×D15—212no—
81C22×D15C22⋊C4112yescomplemented
82C22×D15C22×C413yes—
83C22×D15C22×C411yescharacteristic
84C22×C5×D3—232no—
85C22×C5×D3—26no—
86C22×C5×D3—212no—
87C22×C5×D3—212no—
88C22×C5×D3C22⋊C4112yescomplemented
89C22×C5×D3C22×C413yes—
90C22×C5×D3C22×C411yescharacteristic
91C22×C3×D5—232no—
92C22×C3×D5—26no—
93C22×C3×D5—212no—
94C22×C3×D5—212no—
95C22×C3×D5C22×C413yes—
96C22×C3×D5C2×D4112yes—
97C22×C3×D5C2411yescharacteristic
98C2×D3×D5—296no—
99C2×D3×D5—296no—
100C2×D3×D5—296no—
101C2×D3×D5—212no—
102C2×D3×D5—212no—
103C2×D3×D5—212no—
104C2×D3×D5—212no—
105C2×D3×D5—212no—
106C2×D3×D5—212no—
107C2×D3×D5—296no—
108C2×D3×D5C22⋊C4112yescomplemented
109C2×D3×D5C22⋊C4112yescomplemented
110C2×D3×D5C2×D4112yes—
111C2×D3×D5C2×D4112yes—
112C2×ΓL(1,𝔽16)—212no—
113C2×C3×AGL(1,𝔽5)—212no—
114D3×AGL(1,𝔽5)—416no—
115C25×C3—51no—
116C24×D3—53no—
117C24×D3—51no—
118C24×D3—53no—
119C24×D3—53no—
120C24×D3—53no—
121C24×D3—1024no—
122C24×D3AGL(1,𝔽5)11yescharacteristic, complemented
123C22×C4×D3—54no—
124C2×C3×C22⋊C4—56no—
125C2×#217—56no—
126C2×(C2×D3)⋊C4—512no—
127D3×C22⋊C4—1024no—
128C24×C5—33no—
129C24×C5—33no—
130C24×C5—612no—
131C24×C5C4×D311yescharacteristic, complemented
132C23×D5—212no—
133C23×D5—31no—
134C23×D5—33no—
135C23×D5—33no—
136C23×D5—33no—
137C23×D5—324no—
138C23×D5—33no—
139C23×D5—33no—
140C23×D5—36no—
141C23×D5—612no—
142C23×D5—624no—
143C23×D5—624no—
144C23×D5—624no—
145C23×D5—624no—
146C23×D5—612no—
147C23×D5—6128no—
148C23×D5—612no—
149C23×D5—612no—
150C23×D5C4×D313yescomplemented
151C23×D5C22×D313yes—
152C22×AGL(1,𝔽5)—34no—
153C22×AGL(1,𝔽5)—624no—
154C22×AGL(1,𝔽5)C22×D314yescomplemented
155C22⋊AGL(1,𝔽5)—212no—
156C22⋊AGL(1,𝔽5)—624no—
157C22⋊AGL(1,𝔽5)—612no—
158C26—151no—
159C22×C22⋊C4—156no—
160#379—51no—
161#379—156no—
162#379—151no—
163C22×C3×C5—28no—
164C22×C3×C5—26no—
165C22×C3×C5C2×C22⋊C416yescomplemented
166C22×C3×C5C23×C411yescharacteristic
167C2×D15—224no—
168C2×D15—26no—
169C2×D15—224no—
170C2×D15C2×C22⋊C416yes—
171C2×D15C2×C22⋊C416yescomplemented
172C2×C5×D3—224no—
173C2×C5×D3—26no—
174C2×C5×D3—224no—
175C2×C5×D3C2×C22⋊C416yes—
176C2×C5×D3C2×C22⋊C416yescomplemented
177C2×C3×D5—224no—
178C2×C3×D5—26no—
179C2×C3×D5—224no—
180C2×C3×D5C2×C22⋊C416yescomplemented
181C2×C3×D5C22×D416yes—
182D3×D5—248no—
183D3×D5—224no—
184D3×D5—224no—
185D3×D5—224no—
186D3×D5#120116yes—
187ΓL(1,𝔽16)—44no—
188C3×AGL(1,𝔽5)—44no—
189C24×C3—53no—
190C24×C3—53no—
191C24×C3—1012no—
192C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
193C23×D3—212no—
194C23×D3—51no—
195C23×D3—53no—
196C23×D3—524no—
197C23×D3—53no—
198C23×D3—53no—
199C23×D3—53no—
200C23×D3—53no—
201C23×D3—56no—
202C23×D3—1012no—
203C23×D3—1024no—
204C23×D3—1024no—
205C23×D3—1024no—
206C23×D3—1024no—
207C23×D3—1012no—
208C23×D3—10128no—
209C23×D3—1012no—
210C23×D3—1012no—
211C23×D3C2×AGL(1,𝔽5)13yes—
212C23×D3C2×AGL(1,𝔽5)13yescomplemented
213C22×C3×C4—54no—
214C22×Dic3—54no—
215C2×C4×D3—1024no—
216C3×C22⋊C4—1012no—
217#217—1012no—
218(C2×D3)⋊C4—1024no—
219C23×C5—26no—
220C23×C5—31no—
221C23×C5—312no—
222C23×C5—33no—
223C23×C5—612no—
224C23×C5—612no—
225C23×C5—632no—
226C23×C5—66no—
227C23×C5C2×C4×D313yes—
228C22×D5—232no—
229C22×D5—26no—
230C22×D5—212no—
231C22×D5—212no—
232C22×D5—31no—
233C22×D5—312no—
234C22×D5—312no—
235C22×D5—33no—
236C22×D5—312no—
237C22×D5—312no—
238C22×D5—312no—
239C22×D5—612no—
240C22×D5—612no—
241C22×D5—696no—
242C22×D5—612no—
243C22×D5—612no—
244C22×D5—696no—
245C22×D5—696no—
246C22×D5—696no—
247C22×D5—612no—
248C22×D5—612no—
249C22×D5—632no—
250C22×D5—66no—
251C22×D5—612no—
252C22×D5—612no—
253C22×D5C2×C4×D313yes—
254C22×D5D3×D4112yes—
255C22×D5C23×D311yescharacteristic
256C2×AGL(1,𝔽5)—212no—
257C2×AGL(1,𝔽5)—612no—
258C2×AGL(1,𝔽5)—1216no—
259C25—31no—
260C25—51no—
261C25—153no—
262C25—153no—
263C25—153no—
264C25—153no—
265C25—151no—
266C25—3024no—
267C23×C4—154no—
268C2×C22⋊C4—56no—
269C2×C22⋊C4—1512no—
270C2×C22⋊C4—156no—
271C2×C22⋊C4—3024no—
272C2×C3×C5—26no—
273C2×C3×C5C22×C22⋊C413yes—
274D15—26no—
275D15#37914yescomplemented
276C3×D5—26no—
277C3×D5C2×#12014yes—
278C5×D3—26no—
279C5×D3#37914yescomplemented
280C23×C3—26no—
281C23×C3—51no—
282C23×C3—512no—
283C23×C3—53no—
284C23×C3—1012no—
285C23×C3—1012no—
286C23×C3—1032no—
287C23×C3—106no—
288C23×C3C22×AGL(1,𝔽5)13yes—
289C22×D3—232no—
290C22×D3—26no—
291C22×D3—212no—
292C22×D3—212no—
293C22×D3—51no—
294C22×D3—512no—
295C22×D3—512no—
296C22×D3—53no—
297C22×D3—512no—
298C22×D3—512no—
299C22×D3—512no—
300C22×D3—1012no—
301C22×D3—1012no—
302C22×D3—1096no—
303C22×D3—1012no—
304C22×D3—1012no—
305C22×D3—1096no—
306C22×D3—1096no—
307C22×D3—1096no—
308C22×D3—1012no—
309C22×D3—1012no—
310C22×D3—1032no—
311C22×D3—106no—
312C22×D3—1012no—
313C22×D3—1012no—
314C22×D3C22⋊AGL(1,𝔽5)112yescomplemented
315C22×D3C22×AGL(1,𝔽5)13yes—
316C22×D3C22×AGL(1,𝔽5)11yescharacteristic
317C2×C3×C4—1012no—
318C2×Dic3—1012no—
319C4×D3—2016no—
320C22×C5—28no—
321C22×C5—26no—
322C22×C5—36no—
323C22×C5—36no—
324C22×C5—624no—
325C22×C5—624no—
326C22×C5—66no—
327C22×C5D3×C22⋊C416yescomplemented
328C22×C5C22×C4×D311yescharacteristic
329C2×D5—224no—
330C2×D5—26no—
331C2×D5—224no—
332C2×D5—36no—
333C2×D5—316no—
334C2×D5—36no—
335C2×D5—624no—
336C2×D5—624no—
337C2×D5—648no—
338C2×D5—624no—
339C2×D5—624no—
340C2×D5—66no—
341C2×D5—624no—
342C2×D5D3×C22⋊C416yescomplemented
343C2×D5C2×D3×D416yes—
344AGL(1,𝔽5)—44no—
345AGL(1,𝔽5)—124no—
346C24—33no—
347C24—33no—
348C24—53no—
349C24—53no—
350C24—612no—
351C24—1012no—
352C24—151no—
353C24—153no—
354C24—1524no—
355C24—153no—
356C24—153no—
357C24—156no—
358C24—153no—
359C24—153no—
360C24—3012no—
361C24—3012no—
362C24—3012no—
363C24—3024no—
364C24—3024no—
365C24—3024no—
366C24—3024no—
367C24—3012no—
368C24—30128no—
369C24D3×AGL(1,𝔽5)11yescharacteristic, complemented
370C22×C4—54no—
371C22×C4—154no—
372C22×C4—3024no—
373C22⋊C4—1012no—
374C22⋊C4—3024no—
375C22⋊C4—3012no—
376C3×C5C2×#37911yescharacteristic, complemented, Hall
377C22×C3—28no—
378C22×C3—26no—
379C22×C3—56no—
380C22×C3—56no—
381C22×C3—1024no—
382C22×C3—1024no—
383C22×C3—106no—
384C22×C3C2×C22⋊AGL(1,𝔽5)16yescomplemented
385C22×C3C23×AGL(1,𝔽5)11yescharacteristic
386C2×D3—224no—
387C2×D3—26no—
388C2×D3—224no—
389C2×D3—56no—
390C2×D3—516no—
391C2×D3—56no—
392C2×D3—1024no—
393C2×D3—1024no—
394C2×D3—1048no—
395C2×D3—1024no—
396C2×D3—1024no—
397C2×D3—106no—
398C2×D3—1024no—
399C2×D3C2×C22⋊AGL(1,𝔽5)16yes—
400C2×D3C2×C22⋊AGL(1,𝔽5)16yescomplemented
401C3×C4—204no—
402Dic3—204no—
403C2×C5—26no—
404C2×C5—34no—
405C2×C5—66no—
406C2×C5C2×D3×C22⋊C413yes—
407D5—26no—
408D5—34no—
409D5—66no—
410D5D3×#12014yes—
411C23—26no—
412C23—31no—
413C23—312no—
414C23—33no—
415C23—51no—
416C23—512no—
417C23—53no—
418C23—612no—
419C23—612no—
420C23—632no—
421C23—66no—
422C23—1012no—
423C23—1012no—
424C23—1032no—
425C23—106no—
426C23—1512no—
427C23—1512no—
428C23—1512no—
429C23—1512no—
430C23—151no—
431C23—1512no—
432C23—153no—
433C23—3012no—
434C23—3012no—
435C23—3032no—
436C23—3012no—
437C23—3012no—
438C23—3012no—
439C23—3012no—
440C23—3096no—
441C23—3012no—
442C23—3012no—
443C23—3096no—
444C23—3096no—
445C23—3096no—
446C23—306no—
447C23C2×D3×AGL(1,𝔽5)13yes—
448C2×C4—1012no—
449C2×C4—3012no—
450C2×C4—6016no—
451C2×C3—26no—
452C2×C3—54no—
453C2×C3—106no—
454C2×C3C22×C22⋊AGL(1,𝔽5)13yes—
455D3—26no—
456D3—54no—
457D3—106no—
458D3#6580014yesdirect product factor
459C5D3×#37911yescharacteristic, complemented, Sylow
460C22—28no—
461C22—26no—
462C22—36no—
463C22—36no—
464C22—56no—
465C22—56no—
466C22—624no—
467C22—624no—
468C22—66no—
469C22—1024no—
470C22—1024no—
471C22—106no—
472C22—1516no—
473C22—156no—
474C22—156no—
475C22—3024no—
476C22—3024no—
477C22—3024no—
478C22—3024no—
479C22—3024no—
480C22—3048no—
481C22—306no—
482C22D3×C22⋊AGL(1,𝔽5)16yescomplemented
483C22C22×D3×AGL(1,𝔽5)11yescharacteristic
484C4—204no—
485C4—604no—
486C3C2×#6580011yescharacteristic, complemented, Sylow
487C2—26no—
488C2—34no—
489C2—54no—
490C2—66no—
491C2—106no—
492C2—154no—
493C2—306no—
494C2C2×D3×C22⋊AGL(1,𝔽5)13yes—
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC24×C3×C5C2×C4
prime radicalC24×D3×D5C2
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#379
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×D3×C22⋊AGL(1,𝔽5)C2semidirect
3. #11752459C2semidirect
4. C3×#65800C2semidirect
5. #11752025C2semidirect
7. C24×D15C4semidirect
8. C24×C5×D3C4semidirect
11. C23×D3×D5C4semidirect
12. C23×D3×D5C4semidirect
15. C22×D3×AGL(1,𝔽5)C22semidirect
16. C2×#6763C22semidirect
17. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
19. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
25. #65800D3direct (N × H)
26. C24×C3×C5C2×C4semidirect
29. C23×D15C2×C4semidirect
32. C23×C5×D3C2×C4semidirect
34. C23×C3×D5C2×C4semidirect
46. C22×D3×D5C2×C4semidirect
50. C22×ΓL(1,𝔽16)C23semidirect
51. C22×C3×AGL(1,𝔽5)C23semidirect
73. C2×C22⋊AGL(1,𝔽5)C2×D3semidirect
81. C22×D15C22⋊C4semidirect
88. C22×C5×D3C22⋊C4semidirect
108. C2×D3×D5C22⋊C4semidirect
109. C2×D3×D5C22⋊C4semidirect
122. C24×D3AGL(1,𝔽5)semidirect
131. C24×C5C4×D3semidirect
150. C23×D5C4×D3semidirect
154. C22×AGL(1,𝔽5)C22×D3semidirect
165. C22×C3×C5C2×C22⋊C4semidirect
171. C2×D15C2×C22⋊C4semidirect
176. C2×C5×D3C2×C22⋊C4semidirect
180. C2×C3×D5C2×C22⋊C4semidirect
192. C24×C3C2×AGL(1,𝔽5)semidirect
212. C23×D3C2×AGL(1,𝔽5)semidirect
275. D15#379semidirect
279. C5×D3#379semidirect
314. C22×D3C22⋊AGL(1,𝔽5)semidirect
327. C22×C5D3×C22⋊C4semidirect
342. C2×D5D3×C22⋊C4semidirect
369. C24D3×AGL(1,𝔽5)semidirect
376. C3×C5C2×#379semidirect
384. C22×C3C2×C22⋊AGL(1,𝔽5)semidirect
400. C2×D3C2×C22⋊AGL(1,𝔽5)semidirect
458. D3#65800direct (N × H)
459. C5D3×#379semidirect
482. C22D3×C22⋊AGL(1,𝔽5)semidirect
486. C3C2×#65800semidirect

Maximal subgroups

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

subgroupindex
C24×D3×D52
C2×D3×C22⋊AGL(1,𝔽5)2
#117524592
C3×#658002
#117520252
C2×#658003
D3×#3795