Finite Group Databasebeta

← #14484688

Subgroups — #14484688

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
1C4×#6821C211yesmaximal, characteristic
2C5×#5570C211yesmaximal, characteristic, complemented
3C3×Q8×Dic10C211yesmaximal, characteristic, complemented
4#11755267C212yesmaximal, complemented
5#11755200C212yesmaximal
6#11753557C216yesmaximal, complemented
7#11753522C216yesmaximal, complemented
8#11752645C213yesmaximal, complemented
9#11752539C213yesmaximal, complemented
10C4×D15⋊Q8C213yesmaximal, complemented
11#11752484C213yesmaximal, complemented
12#10618916—31nomaximal, Hall
13C2×#6821C2211yescharacteristic
14C2×D15⋊Q8C2213yes—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2211yescharacteristic
17#91782C2213yes—
18#91781C2213yes—
19C4×D60C2213yes—
20C42×D15C2213yes—
21C5×Q8×Dic3C2212yes—
22C5×#890C2216yes—
23C5×#869C2213yes—
24C4×C5×Dic6C2213yes—
25C3×Q8×Dic5C2212yes—
26C3×#4034C2216yes—
27C3×#4015C2213yes—
28C3×C4×Dic10C2213yes—
29#91468C2216yes—
30C4×#1204C2216yes—
31#91437C2213yes—
32#91428C2216yes—
33#91419C22112yes—
34#91418C2216yes—
35#91411C22112yes—
36#91404C2216yes—
37C4×#1200C2216yes—
38#91390C2216yes—
39#91384C2216yes—
40#91383C2216yes—
41#91381C2216yes—
42#91347C2216yes—
43#91344C2213yes—
44#91331C2216yes—
45#91331C2211yescharacteristic
46#91325C2216yes—
47Q8×#239—51nomaximal, Hall
48C5×#557—31no—
49#66062—33no—
50#66061—33no—
51#66024—36no—
52#66022—36no—
53#65913—33no—
54C4×#713—32no—
55C4×#713—31no—
56C4×Q8×D5—33no—
57#65903—32no—
58Q8×Dic10D311yescharacteristic, complemented
59C2×C3×C5×Q8C2311yescharacteristic
60#6821Q818yescomplemented
61C2×D60C2313yes—
62C2×C4×D15C2313yes—
63C2×C4×D15C2313yes—
64C2×C4×D15C2313yes—
65C2×C5×Dic6C2313yes—
66C2×C3×Dic10C2316yes—
67C2×C3×Dic10C2311yescharacteristic
68C2×#1204C2316yes—
69C2×#1200C2316yes—
70C2×#1200C2316yes—
71D15⋊Q8—212no—
72C3×C5×C4⋊C4C2313yes—
73C3×C42×C5C2313yes—
74#6714C2316yes—
75C4⋊Dic15C2313yes—
76C4×Dic15C2313yes—
77C4×Dic15C2311yescharacteristic
78C4×Dic15C2313yes—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2316yes—
81C5×C4⋊Dic3C2316yes—
82C5×Dic3⋊C4C2316yes—
83C4×C5×Dic3C2316yes—
84C3×C4⋊Dic5C2316yes—
85C3×C4⋊Dic5C2313yes—
86C3×#683C2316yes—
87C3×C4×Dic5C2316yes—
88Dic3⋊Dic5C2316yes—
89#6669C2316yes—
90#6668C2312yes—
91#6668C23112yes—
92#6667C23112yes—
93Dic3×Dic5C2312yes—
94Dic3×Dic5C2316yes—
95C3×Q82—51no—
96#5730—56no—
97#5730—53no—
98#5728—56no—
99#5728—53no—
100Q8×D12—53no—
101C4×#239—51no—
102C4×#239—52no—
103C4×D3×Q8—53no—
104#5570—52no—
105#5570D511yescharacteristic, complemented
106C2×#713—31no—
107C2×Q8×D5—33no—
108C5×C4⋊Q8—33no—
109C5×#125—36no—
110C4×C5×Q8—32no—
111C4×C5×Q8—33no—
112C4×C5×Q8C2×D311yescharacteristic
113#4092—36no—
114Q8×Dic5—31no—
115Q8×Dic5—33no—
116Q8×Dic5C2×D312yes—
117#4043—36no—
118#4042—312no—
119#4042—312no—
120#4039—33no—
121#4039—36no—
122#4038—33no—
123#4038—36no—
124D5×C4⋊C4—33no—
125D5×C4⋊C4—36no—
126#4036—36no—
127#4034—36no—
128#4034C2×D316yes—
129#4033—36no—
130#4033—31no—
131#4033—36no—
132C4×D20—33no—
133C4×D20—36no—
134C42×D5—33no—
135C42×D5—36no—
136#4016—36no—
137#4015C2×D313yes—
138C4×Dic10—36no—
139C4×Dic10C2×D313yes—
140Q8×#41—151noSylow
141C22×D15C2413yes—
142C3×C5×Q8C2×Q814yescomplemented
143C2×C3×C4×C5C2413yes—
144C2×C3×C4×C5C2413yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C2413yes—
147C2×Dic15C2411yescharacteristic
148C2×Dic15C2411yescharacteristic
149D60C2×Q8112yescomplemented
150C4×D15—26no—
151C4×D15—43no—
152C4×D15C2×Q8112yescomplemented
153C2×C5×Dic3C2416yes—
154C2×C5×Dic3C2412yes—
155C5×Dic6—26no—
156C2×C3×Dic5C2416yes—
157C2×C3×Dic5C2412yes—
158C3×Dic10—46no—
159C3×Dic10#4114yescomplemented
160#1204—212no—
161#1200—212no—
162#1200—46no—
163C2×#239—51no—
164C2×D3×Q8—53no—
165C3×C4⋊Q8—56no—
166C3×C4⋊Q8—53no—
167C3×C4×Q8—52no—
168C3×C4×Q8—53no—
169C3×C4×Q8C2×D511yescharacteristic
170#946—56no—
171#946—512no—
172Q8×Dic3—51no—
173Q8×Dic3—56no—
174Q8×Dic3—51no—
175Q8×Dic3C2×D512yes—
176#897—56no—
177#897—512no—
178#893—53no—
179#893—56no—
180#892—53no—
181#892—56no—
182D3×C4⋊C4—53no—
183D3×C4⋊C4—56no—
184#890—56no—
185#890—56no—
186#890C2×D516yes—
187#887—53no—
188#887—56no—
189C4×D12—53no—
190C4×D12—56no—
191C42×D3—53no—
192C42×D3—56no—
193#869—56no—
194#869C2×D513yes—
195C4×Dic6—56no—
196C4×Dic6C2×D513yes—
197C2×C5×Q8—33no—
198C2×C5×Q8C22×D311yescharacteristic
199#713—38no—
200Q8×D5—612no—
201C2×D20—33no—
202C2×C4×D5—33no—
203C2×C4×D5—33no—
204C2×C4×D5—36no—
205C2×C4×D5—33no—
206C2×C4×D5—36no—
207C2×Dic10—36no—
208C2×Dic10C22×D316yes—
209C2×Dic10C22×D311yescharacteristic
210C5×C4⋊C4—31no—
211C5×C4⋊C4—36no—
212C5×C4⋊C4—36no—
213C5×C4⋊C4—36no—
214C5×C4⋊C4C22×D313yes—
215C42×C5—36no—
216C42×C5C22×D313yes—
217#685—36no—
218#685—312no—
219C4⋊Dic5—33no—
220C4⋊Dic5—36no—
221C4⋊Dic5C22×D313yes—
222C4⋊Dic5C22×D316yes—
223#683—32no—
224#683—312no—
225#683—36no—
226#683C22×D316yes—
227C4×Dic5—33no—
228C4×Dic5—31no—
229C4×Dic5—33no—
230C4×Dic5—32no—
231C4×Dic5—36no—
232C4×Dic5C22×D316yes—
233Q82—51no—
234#557—31no—
235#557—152no—
236#554—153no—
237#554—156no—
238D4×Q8—153no—
239#533—156no—
240#533—153no—
241C4×#41—152no—
242C4×#41—151no—
243C2×C4×Q8—153no—
244C22×C3×C5C2511yescharacteristic
245C2×D15—23no—
246C2×D15—23no—
247C2×D15C22×Q816yes—
248C3×C4×C5—23no—
249C3×C4×C5C22×Q816yes—
250C3×C4×C5C2×#4112yes—
251Dic15—23no—
252Dic15—21no—
253Dic15C22×Q812yes—
254C3×Dic5—26no—
255C3×Dic5C2×#4114yes—
256C5×Dic3—26no—
257C5×Dic3—22no—
258C2×C3×Q8—51no—
259C2×C3×Q8—56no—
260C2×C3×Q8C22×D511yescharacteristic
261#239—58no—
262D3×Q8—1012no—
263C2×D12—53no—
264C2×C4×D3—53no—
265C2×C4×D3—53no—
266C2×C4×D3—56no—
267C2×C4×D3—53no—
268C2×C4×D3—56no—
269C2×Dic6—56no—
270C2×Dic6C22×D513yes—
271C3×C4⋊C4—56no—
272C3×C4⋊C4—53no—
273C3×C4⋊C4—56no—
274C3×C4⋊C4C22×D513yes—
275C3×C42—56no—
276C3×C42C22×D513yes—
277(C2×D3)⋊C4—56no—
278(C2×D3)⋊C4—512no—
279C4⋊Dic3—53no—
280C4⋊Dic3—52no—
281C4⋊Dic3—512no—
282C4⋊Dic3C22×D511yescharacteristic
283C4⋊Dic3C22×D516yes—
284C4⋊Dic3C22×D516yes—
285Dic3⋊C4—56no—
286Dic3⋊C4—56no—
287Dic3⋊C4C22×D516yes—
288C4×Dic3—53no—
289C4×Dic3—51no—
290C4×Dic3—53no—
291C4×Dic3—52no—
292C4×Dic3—56no—
293C4×Dic3C22×D516yes—
294C22×D5—33no—
295C5×Q8—66no—
296C5×Q8D3×Q814yescomplemented
297C2×C4×C5—32no—
298C2×C4×C5—36no—
299C2×C4×C5C23×D313yes—
300C2×C4×C5C23×D313yes—
301C2×C4×C5C23×D311yescharacteristic
302C2×Dic5—31no—
303C2×Dic5—31no—
304C2×Dic5—33no—
305C2×Dic5C23×D316yes—
306C2×Dic5C23×D312yes—
307D20—312no—
308C4×D5—312no—
309C4×D5—66no—
310C4×D5—612no—
311C4×D5—126no—
312C4×D5—123no—
313Dic10—46no—
314Dic10—612no—
315Dic10#23914yescomplemented
316C2×#41—151no—
317C22×Q8—153no—
318C4⋊Q8—33no—
319C4⋊Q8—56no—
320C4⋊Q8—53no—
321C4⋊Q8—156no—
322#125—36no—
323#125—156no—
324#125—156no—
325C22⋊Q8—1512no—
326C22⋊Q8—1512no—
327C22⋊Q8—156no—
328C22⋊Q8—156no—
329C4×Q8—32no—
330C4×Q8—33no—
331C4×Q8—52no—
332C4×Q8—53no—
333C4×Q8—156no—
334C4×Q8—156no—
335C4×Q8—151no—
336C4×Q8—156no—
337C4×Q8—153no—
338C4×Q8—151no—
339C4×Q8D3×D511yescharacteristic
340C4×D4—156no—
341C4×D4—156no—
342C4×D4—153no—
343C4×D4—153no—
344#117—156no—
345#117—153no—
346C2×C4⋊C4—153no—
347C2×C4⋊C4—156no—
348C2×C42—156no—
349C2×C42—153no—
350C2×C3×C5C23×Q811yescharacteristic
351C2×C3×C5C22×#4111yescharacteristic
352C2×C3×C5#58511yescharacteristic
353D15—26no—
354C22×D3—53no—
355C3×Q8—54no—
356C3×Q8—206no—
357C3×Q8Q8×D514yescomplemented
358C2×C3×C4—52no—
359C2×C3×C4—56no—
360C2×C3×C4C23×D513yes—
361C2×C3×C4C23×D513yes—
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—51no—
364C2×Dic3—51no—
365C2×Dic3—53no—
366C2×Dic3C23×D512yes—
367C2×Dic3C23×D516yes—
368D12—512no—
369C4×D3—512no—
370C4×D3—1012no—
371C4×D3—106no—
372C4×D3—206no—
373C4×D3—203no—
374Dic6—26no—
375Dic6—1012no—
376C22×C5C24×D311yescharacteristic
377C2×D5—36no—
378C2×D5—63no—
379C2×D5—63no—
380C4×C5—23no—
381C4×C5—66no—
382C4×C5—62no—
383C4×C5C2×D3×Q816yes—
384C4×C5C2×#23912yes—
385Dic5—26no—
386Dic5—32no—
387Dic5—63no—
388Dic5—61no—
389Dic5C2×#23914yes—
390#41—158no—
391C2×Q8—33no—
392C2×Q8—51no—
393C2×Q8—56no—
394C2×Q8—156no—
395C2×Q8—3012no—
396C2×Q8C2×D3×D511yescharacteristic
397C2×D4—153no—
398C22×C4—156no—
399C22×C4—156no—
400C22×C4—153no—
401C22×C4—153no—
402C22×C4—153no—
403C4⋊C4—31no—
404C4⋊C4—36no—
405C4⋊C4—36no—
406C4⋊C4—36no—
407C4⋊C4—56no—
408C4⋊C4—53no—
409C4⋊C4—56no—
410C4⋊C4—152no—
411C4⋊C4—156no—
412C4⋊C4—156no—
413C4⋊C4—1512no—
414C4⋊C4—153no—
415C4⋊C4C2×D3×D513yes—
416C22⋊C4—1512no—
417C22⋊C4—156no—
418C42—36no—
419C42—56no—
420C42—152no—
421C42—156no—
422C42—151no—
423C42—153no—
424C42—153no—
425C42C2×D3×D513yes—
426C3×C5Q8×#4111yescharacteristic, complemented, Hall
427C22×C3C24×D511yescharacteristic
428C2×D3—56no—
429C2×D3—103no—
430C2×D3—103no—
431C3×C4—23no—
432C3×C4—54no—
433C3×C4—106no—
434C3×C4C2×Q8×D516yes—
435C3×C4D5×#4112yes—
436Dic3—26no—
437Dic3—22no—
438Dic3—52no—
439Dic3—103no—
440Dic3—101no—
441C2×C5C22×D3×Q811yescharacteristic
442C2×C5C22×#23911yescharacteristic
443C2×C5#596611yescharacteristic
444D5—66no—
445C23—153no—
446Q8—54no—
447Q8—66no—
448Q8—206no—
449Q8—3012no—
450Q8D15⋊Q814yescomplemented
451D4—1512no—
452C2×C4—32no—
453C2×C4—36no—
454C2×C4—52no—
455C2×C4—56no—
456C2×C4—151no—
457C2×C4—1512no—
458C2×C4—151no—
459C2×C4—153no—
460C2×C4—3012no—
461C2×C4—306no—
462C2×C4—603no—
463C2×C4—606no—
464C2×C4C22×D3×D513yes—
465C2×C4C22×D3×D513yes—
466C2×C4C22×D3×D511yescharacteristic
467C2×C3C22×Q8×D511yescharacteristic
468C2×C3C2×D5×#4111yescharacteristic
469C2×C3#6628711yescharacteristic
470D3—106no—
471C5Q8×#23911yescharacteristic, complemented, Sylow
472C22—156no—
473C22—303no—
474C22—303no—
475C22C23×D3×D511yescharacteristic
476C4—23no—
477C4—54no—
478C4—62no—
479C4—66no—
480C4—106no—
481C4—152no—
482C4—301no—
483C4—303no—
484C4C2×D15⋊Q816yes—
485C4D5×#23912yes—
486C3#1061891611yescharacteristic, complemented, Sylow
487C2—306no—
488C2C22×D15⋊Q811yescharacteristic
489C2C2×D5×#23911yescharacteristic
490C2#1175706211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×#6821C22
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
2. C5×#5570C2semidirect
3. C3×Q8×Dic10C2semidirect
4. #11755267C2semidirect
6. #11753557C2semidirect
7. #11753522C2semidirect
8. #11752645C2semidirect
9. #11752539C2semidirect
10. C4×D15⋊Q8C2semidirect
11. #11752484C2semidirect
58. Q8×Dic10D3semidirect
60. #6821Q8semidirect
105. #5570D5semidirect
142. C3×C5×Q8C2×Q8semidirect
149. D60C2×Q8semidirect
152. C4×D15C2×Q8semidirect
159. C3×Dic10#41semidirect
296. C5×Q8D3×Q8semidirect
315. Dic10#239semidirect
357. C3×Q8Q8×D5semidirect
426. C3×C5Q8×#41semidirect
450. Q8D15⋊Q8semidirect
471. C5Q8×#239semidirect
486. C3#10618916semidirect

Maximal subgroups

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

subgroupindex
C4×#68212
C5×#55702
C3×Q8×Dic102
#117552672
#117552002
#117535572
#117535222
#117526452
#117525392
C4×D15⋊Q82
#117524842
#106189163
Q8×#2395