Finite Group Databasebeta

← #14484689

Subgroups — #14484689

Order 1920.

2136 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
1Q8×Dic30C211yesmaximal, characteristic, complemented
2C4×C5×#239C211yesmaximal, characteristic
3C3×#65904C211yesmaximal, characteristic, complemented
4Dic5×#239C212yesmaximal
5#11755147C212yesmaximal, complemented
6#11753634C216yesmaximal, complemented
7#11753618C216yesmaximal, complemented
8#11752660C213yesmaximal, complemented
9#11752558C213yesmaximal, complemented
10C4×D3×Dic10C213yesmaximal, complemented
11#11752478C213yesmaximal, complemented
12#41×Dic10—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×D3×Dic10C2213yes—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2212yes—
17#91777C2216yes—
18#91758C2213yes—
19C4×Dic30C2213yes—
20C5×Q8×Dic3C2211yescharacteristic
21C5×#893C2213yes—
22C5×#892C2213yes—
23C4×C5×D12C2213yes—
24C42×C5×D3C2213yes—
25C3×Q8×Dic5C2212yes—
26C3×#4036C2216yes—
27C3×#4015C2213yes—
28C3×C4×Dic10C2213yes—
29#91470C2216yes—
30C4×#1204C2216yes—
31#91436C22112yes—
32#91435C2216yes—
33#91432C22112yes—
34D3×C4⋊Dic5C2213yes—
35Dic5×D12C2216yes—
36D3×#683C2216yes—
37C4×D3×Dic5C2216yes—
38#91388C2216yes—
39#91381C2216yes—
40#91369C2216yes—
41#91365C2216yes—
42#91340C2216yes—
43#91340C2211yescharacteristic
44#91338C2216yes—
45Dic3×Dic10C2213yes—
46#91324C2216yes—
47#87015—51nomaximal, Hall
48C4×C5×#41—31no—
49#41×Dic5—32no—
50#65904D311yescharacteristic, complemented
51#65903—32no—
52Q8×Dic10—31no—
53#65877—33no—
54#65873—36no—
55D4×Dic10—33no—
56#65851—36no—
57#65804—33no—
58C2×C4×Dic10—33no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×Dic30C2316yes—
61C2×Dic30C2311yescharacteristic
62C5×#239Q818yescomplemented
63C2×C5×D12C2313yes—
64C2×C4×C5×D3C2313yes—
65C2×C4×C5×D3C2313yes—
66C2×C4×C5×D3C2313yes—
67C2×C3×Dic10C2313yes—
68C2×#1204C2316yes—
69C2×D3×Dic5C2316yes—
70C2×D3×Dic5C2316yes—
71D3×Dic10—212no—
72C3×C5×C4⋊C4C2313yes—
73C3×C42×C5C2313yes—
74C4⋊Dic15C2316yes—
75C4⋊Dic15C2313yes—
76#6712C2316yes—
77C4×Dic15C2316yes—
78C5×(C2×D3)⋊C4C2316yes—
79C5×C4⋊Dic3C2313yes—
80C4×C5×Dic3C2311yescharacteristic
81C4×C5×Dic3C2313yes—
82C4×C5×Dic3C2313yes—
83C3×C4⋊Dic5C2316yes—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2316yes—
86C3×#683C2316yes—
87C3×C4×Dic5C2316yes—
88Dic3⋊Dic5C2316yes—
89#6669C2312yes—
90#6669C23112yes—
91#6668C2316yes—
92(C2×D3)⋊Dic5C23112yes—
93Dic3×Dic5C2312yes—
94Dic3×Dic5C2316yes—
95C3×#557—51no—
96#5728—53no—
97#5727—53no—
98#5690—56no—
99#5688—56no—
100#5579—53no—
101C4×#239—52no—
102C4×#239D511yescharacteristic
103C4×D3×Q8—53no—
104#5569—52no—
105Q8×Dic6—51no—
106C2×C5×#41—31no—
107C22×Dic10—33no—
108C4×C5×Q8—31no—
109C4×C5×Q8C2×D311yescharacteristic
110C4×C5×D4—33no—
111C4×C5×D4—33no—
112C5×#117—33no—
113C2×C42×C5—33no—
114Q8×Dic5—32no—
115Q8×Dic5C2×D312yes—
116D4×Dic5—36no—
117D4×Dic5—36no—
118#4072—36no—
119C2×C4⋊Dic5—33no—
120#4070—36no—
121#4070—36no—
122C2×#683—36no—
123C2×C4×Dic5—36no—
124#4036—36no—
125#4036C2×D316yes—
126#4034—36no—
127#4034—36no—
128#4024—312no—
129#4024—312no—
130#4016—36no—
131#4015—33no—
132#4015C2×D313yes—
133C4×Dic10—33no—
134C4×Dic10—33no—
135C4×Dic10—31no—
136C4×Dic10—36no—
137C4×Dic10—36no—
138C4×Dic10—36no—
139C4×Dic10C2×D313yes—
140Q8×#41—151noSylow
141C22×C5×D3C2413yes—
142C3×C5×Q8C2×Q814yescomplemented
143C2×C3×C4×C5C2413yes—
144C2×C3×C4×C5C2413yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C2416yes—
147C2×Dic15C2412yes—
148Dic30—46no—
149Dic30#4114yescomplemented
150C2×C5×Dic3C2411yescharacteristic
151C2×C5×Dic3C2413yes—
152C2×C5×Dic3C2411yescharacteristic
153C5×D12C2×Q8112yescomplemented
154C4×C5×D3—26no—
155C4×C5×D3—43no—
156C4×C5×D3C2×Q8112yescomplemented
157C2×C3×Dic5C2416yes—
158C2×C3×Dic5C2412yes—
159C3×Dic10—26no—
160#1204—212no—
161D3×Dic5—212no—
162D3×Dic5—46no—
163C2×#239C2×D511yescharacteristic
164C2×D3×Q8—53no—
165C3×C4⋊Q8—53no—
166C3×#125—56no—
167C3×C4×Q8—52no—
168C3×C4×Q8—53no—
169C3×C4×Q8C2×D511yescharacteristic
170#946—56no—
171Q8×Dic3—52no—
172Q8×Dic3—53no—
173Q8×Dic3C2×D511yescharacteristic
174#897—56no—
175#896—512no—
176#896—512no—
177#893—56no—
178#893C2×D513yes—
179#892—56no—
180#892C2×D513yes—
181D3×C4⋊C4—56no—
182D3×C4⋊C4—53no—
183#890—56no—
184#888—56no—
185#888—56no—
186#887—56no—
187#887—56no—
188#887—51no—
189C4×D12—56no—
190C4×D12C2×D513yes—
191C42×D3—56no—
192C42×D3C2×D513yes—
193#870—56no—
194#869—53no—
195C4×Dic6—53no—
196C4×Dic6—56no—
197C5×#41—38no—
198C2×C5×Q8C22×D311yescharacteristic
199C2×C5×D4—33no—
200C22×C4×C5—33no—
201C22×C4×C5—33no—
202C22×C4×C5—33no—
203C22×Dic5—36no—
204C22×Dic5—36no—
205C2×Dic10—31no—
206C2×Dic10—36no—
207C2×Dic10—36no—
208C2×Dic10—612no—
209C2×Dic10C22×D313yes—
210C5×C4⋊C4—33no—
211C5×C4⋊C4C22×D313yes—
212C5×C22⋊C4—36no—
213C42×C5—31no—
214C42×C5—33no—
215C42×C5—33no—
216C42×C5C22×D313yes—
217C22⋊Dic5—312no—
218C4⋊Dic5—33no—
219C4⋊Dic5—36no—
220C4⋊Dic5—36no—
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D316yes—
223C4⋊Dic5C22×D316yes—
224#683—36no—
225#683—36no—
226#683—32no—
227#683—312no—
228#683C22×D316yes—
229C4×Dic5—36no—
230C4×Dic5—32no—
231C4×Dic5—36no—
232C4×Dic5C22×D316yes—
233Q82—151no—
234#557—51no—
235#557—152no—
236#554—153no—
237#554—156no—
238D4×Q8—153no—
239#533—153no—
240#533—156no—
241C4×#41—31no—
242C4×#41—152no—
243C2×C4×Q8—153no—
244C22×C3×C5C2511yescharacteristic
245C2×C5×D3—23no—
246C2×C5×D3—23no—
247C2×C5×D3C22×Q816yes—
248C3×C4×C5—23no—
249C3×C4×C5C22×Q816yes—
250C3×C4×C5C2×#4112yes—
251Dic15—26no—
252Dic15C2×#4114yes—
253C3×Dic5—26no—
254C3×Dic5—22no—
255C5×Dic3—23no—
256C5×Dic3—21no—
257C5×Dic3C22×Q812yes—
258C2×C3×Q8—53no—
259C2×C3×Q8C22×D511yescharacteristic
260#239Dic1018yescomplemented
261D3×Q8—1012no—
262C2×D12C22×D513yes—
263C2×C4×D3—56no—
264C2×C4×D3—56no—
265C2×C4×D3C22×D513yes—
266C2×C4×D3C22×D513yes—
267C2×C4×D3C22×D513yes—
268C2×Dic6—51no—
269C2×Dic6—56no—
270C2×Dic6—56no—
271C3×C4⋊C4—56no—
272C3×C4⋊C4—51no—
273C3×C4⋊C4—56no—
274C3×C4⋊C4—56no—
275C3×C4⋊C4C22×D513yes—
276C3×C42—56no—
277C3×C42C22×D513yes—
278(C2×D3)⋊C4—512no—
279(C2×D3)⋊C4C22×D516yes—
280C4⋊Dic3—53no—
281C4⋊Dic3—56no—
282C4⋊Dic3—56no—
283C4⋊Dic3C22×D513yes—
284Dic3⋊C4—56no—
285Dic3⋊C4—52no—
286Dic3⋊C4—512no—
287Dic3⋊C4—56no—
288C4×Dic3—56no—
289C4×Dic3—52no—
290C4×Dic3—56no—
291C4×Dic3C22×D513yes—
292C4×Dic3C22×D511yescharacteristic
293C4×Dic3C22×D513yes—
294C23×C5—33no—
295C5×Q8D3×Q814yescomplemented
296C5×D4—312no—
297C2×C4×C5—31no—
298C2×C4×C5—312no—
299C2×C4×C5—31no—
300C2×C4×C5—33no—
301C2×C4×C5—66no—
302C2×C4×C5—123no—
303C2×C4×C5C23×D313yes—
304C2×C4×C5C23×D313yes—
305C2×C4×C5C23×D311yescharacteristic
306C2×Dic5—32no—
307C2×Dic5—36no—
308C2×Dic5—612no—
309C2×Dic5—126no—
310C2×Dic5C23×D312yes—
311C2×Dic5C23×D316yes—
312Dic10—26no—
313Dic10—34no—
314Dic10—612no—
315Dic10—126no—
316C2×#41—31no—
317C22×Q8—153no—
318C4⋊Q8—53no—
319C4⋊Q8—156no—
320C4⋊Q8—156no—
321C4⋊Q8—153no—
322#125—56no—
323#125—156no—
324#125—156no—
325C22⋊Q8—1512no—
326C22⋊Q8—1512no—
327C22⋊Q8—156no—
328C22⋊Q8—156no—
329C4×Q8—31no—
330C4×Q8—52no—
331C4×Q8—53no—
332C4×Q8—156no—
333C4×Q8—151no—
334C4×Q8—156no—
335C4×Q8—156no—
336C4×Q8—153no—
337C4×Q8—152no—
338C4×Q8—153no—
339C4×Q8D3×D511yescharacteristic
340C4×D4—33no—
341C4×D4—33no—
342C4×D4—156no—
343C4×D4—156no—
344#117—33no—
345#117—156no—
346C2×C4⋊C4—156no—
347C2×C4⋊C4—153no—
348C2×C42—33no—
349C2×C42—156no—
350C2×C3×C5C23×Q811yescharacteristic
351C2×C3×C5C22×#4111yescharacteristic
352C2×C3×C5#58511yescharacteristic
353C5×D3—26no—
354C22×D3C23×D513yes—
355C3×Q8—106no—
356C3×Q8C2×Dic1014yescomplemented
357C2×C3×C4—52no—
358C2×C3×C4—56no—
359C2×C3×C4C23×D513yes—
360C2×C3×C4C23×D513yes—
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—52no—
363C2×Dic3—56no—
364C2×Dic3C23×D511yescharacteristic
365C2×Dic3C23×D513yes—
366C2×Dic3C23×D511yescharacteristic
367D12C2×Dic10112yescomplemented
368C4×D3—26no—
369C4×D3—43no—
370C4×D3—1012no—
371C4×D3—206no—
372C4×D3C2×Dic10112yescomplemented
373Dic6—54no—
374Dic6—1012no—
375Dic6—206no—
376C22×C5—36no—
377C22×C5—63no—
378C22×C5—63no—
379C22×C5C24×D311yescharacteristic
380C4×C5—23no—
381C4×C5—32no—
382C4×C5—63no—
383C4×C5—61no—
384C4×C5C2×D3×Q816yes—
385C4×C5D3×#4112yes—
386Dic5—26no—
387Dic5—22no—
388Dic5—34no—
389Dic5—66no—
390#41—38no—
391C2×Q8—53no—
392C2×Q8—156no—
393C2×Q8—151no—
394C2×Q8—156no—
395C2×Q8—3012no—
396C2×Q8C2×D3×D511yescharacteristic
397C2×D4—33no—
398C22×C4—33no—
399C22×C4—33no—
400C22×C4—33no—
401C22×C4—156no—
402C22×C4—156no—
403C4⋊C4—33no—
404C4⋊C4—51no—
405C4⋊C4—56no—
406C4⋊C4—56no—
407C4⋊C4—56no—
408C4⋊C4—152no—
409C4⋊C4—156no—
410C4⋊C4—156no—
411C4⋊C4—1512no—
412C4⋊C4—156no—
413C4⋊C4—153no—
414C4⋊C4—156no—
415C4⋊C4C2×D3×D513yes—
416C22⋊C4—36no—
417C22⋊C4—1512no—
418C42—31no—
419C42—33no—
420C42—33no—
421C42—56no—
422C42—152no—
423C42—156no—
424C42—156no—
425C42C2×D3×D513yes—
426C3×C5Q8×#4111yescharacteristic, complemented, Hall
427C22×C3C24×D511yescharacteristic
428C2×D3—23no—
429C2×D3—23no—
430C2×D3C22×Dic1016yes—
431C3×C4—23no—
432C3×C4—106no—
433C3×C4—102no—
434C3×C4C22×Dic1016yes—
435C3×C4D5×#4112yes—
436Dic3—23no—
437Dic3—21no—
438Dic3—54no—
439Dic3—106no—
440Dic3C22×Dic1012yes—
441C2×C5—66no—
442C2×C5C22×D3×Q811yescharacteristic
443C2×C5C2×D3×#4111yescharacteristic
444C2×C5#596811yescharacteristic
445C23—33no—
446Q8—106no—
447Q8—154no—
448Q8—3012no—
449Q8—606no—
450Q8D3×Dic1014yescomplemented
451D4—312no—
452C2×C4—31no—
453C2×C4—312no—
454C2×C4—31no—
455C2×C4—33no—
456C2×C4—52no—
457C2×C4—56no—
458C2×C4—66no—
459C2×C4—123no—
460C2×C4—152no—
461C2×C4—156no—
462C2×C4—3012no—
463C2×C4—606no—
464C2×C4C22×D3×D513yes—
465C2×C4C22×D3×D513yes—
466C2×C4C22×D3×D511yescharacteristic
467C2×C3C23×Dic1011yescharacteristic
468C2×C3C2×D5×#4111yescharacteristic
469C2×C3#6628311yescharacteristic
470D3—26no—
471C5#8701511yescharacteristic, complemented, Sylow
472C22—36no—
473C22—63no—
474C22—63no—
475C22C23×D3×D511yescharacteristic
476C4—23no—
477C4—32no—
478C4—61no—
479C4—63no—
480C4—102no—
481C4—106no—
482C4—154no—
483C4—306no—
484C4C2×D3×Dic1016yes—
485C4#9203412yes—
486C3#41×Dic1011yescharacteristic, complemented, Sylow
487C2—66no—
488C2C22×D3×Dic1011yescharacteristic
489C2C2×#9203411yescharacteristic
490C2#1175706311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×C5×#239C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5Q8×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×Dic30C2semidirect
3. C3×#65904C2semidirect
5. #11755147C2semidirect
6. #11753634C2semidirect
7. #11753618C2semidirect
8. #11752660C2semidirect
9. #11752558C2semidirect
10. C4×D3×Dic10C2semidirect
11. #11752478C2semidirect
50. #65904D3semidirect
62. C5×#239Q8semidirect
142. C3×C5×Q8C2×Q8semidirect
149. Dic30#41semidirect
153. C5×D12C2×Q8semidirect
156. C4×C5×D3C2×Q8semidirect
260. #239Dic10semidirect
295. C5×Q8D3×Q8semidirect
356. C3×Q8C2×Dic10semidirect
367. D12C2×Dic10semidirect
372. C4×D3C2×Dic10semidirect
426. C3×C5Q8×#41semidirect
450. Q8D3×Dic10semidirect
471. C5#87015semidirect
486. C3#41×Dic10semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic302
C4×C5×#2392
C3×#659042
Dic5×#2392
#117551472
#117536342
#117536182
#117526602
#117525582
C4×D3×Dic102
#117524782
#41×Dic103
#870155