Finite Group Databasebeta

← #14430729

Subgroups — #14430729

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#709C211yesmaximal, characteristic
2C2×#91381C211yesmaximal, characteristic, complemented
3#11751222C211yesmaximal, characteristic, complemented
4C5×#5118C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic
6#11748453C211yesmaximal, characteristic, complemented
7#11748369C211yesmaximal, characteristic
8#11747864C212yesmaximal, complemented
9#11747863C212yesmaximal, complemented
10#11747784C212yesmaximal, complemented
11#11747783C212yesmaximal, complemented
12#10610792—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20Dic3×C22⋊D5—21no—
21Dic3×C22⋊D5—21no—
22C2×#6669—21no—
23C2×#6668—21no—
24Dic3×D20C2211yescharacteristic
25Dic3×D20C2211yescharacteristic
26C4×D5×Dic3—21no—
27#91381—21no—
28#91381—21no—
29#91381C2212yes—
30#91381C2212yes—
31#91357—21no—
32Dic3×Dic10C2211yescharacteristic
33Dic3×Dic10C2211yescharacteristic
34#91102C2212yes—
35#91101C2212yes—
36C5×Dic3⋊C8C2212yes—
37C5×Dic3⋊C8C2212yes—
38C3×#3953C2212yes—
39C3×#3948C2212yes—
40#90990C2212yes—
41#90987C2212yes—
42#90971C2212yes—
43#90965C2212yes—
44#78871—51nomaximal, Hall
45C4×#709—31no—
46C2×#4016—31no—
47C5×#423—31no—
48#65422—31no—
49#65422D311yescharacteristic
50#65410—31no—
51#65410—31no—
52#65136—32no—
53#65136—32no—
54#65118—32no—
55#65118—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C22×C5×Dic3D411yescharacteristic
59C22×C5×Dic3D411yescharacteristic
60C2×C3×C22⋊D5—21no—
61C22×C3×Dic5—21no—
62C3×#709—22no—
63C3×#709Q814yes—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×D5×Dic3—21no—
68C2×D5×Dic3—21no—
69C3×C5×M16—22no—
70C2×C3×C5×C8C2312yes—
71#6719—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15C2311yescharacteristic
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2312yes—
76C4×Dic15—21no—
77C4×C5×Dic3D411yescharacteristic
78C4×C5×Dic3D411yescharacteristic
79C4×C5×Dic3C2311yescharacteristic
80C4×C5×Dic3C2311yescharacteristic
81C5×#208—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85#6669—22no—
86#6669—22no—
87#6668—22no—
88#6668—22no—
89#6668—21no—
90#6668—21no—
91#6665—21no—
92#6665—21no—
93Dic3×Dic5—21no—
94Dic3×Dic5—21no—
95Dic3×#41—51no—
96C2×#890—51no—
97C3×#417—51no—
98#5232—51no—
99#5121—51no—
100#5118D511yescharacteristic, complemented
101#4964—51no—
102#4799—52no—
103#4796—52no—
104#4766—52no—
105#4763—52no—
106C2×#709C2×D311yescharacteristic
107C2×C5×M16—31no—
108C2×C5×M16C2×D311yescharacteristic
109C2×C42×C5—31no—
110C4×C22⋊D5—61no—
111C4×C22⋊D5—61no—
112#4072—31no—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5C2×D311yescharacteristic
115C2×#683—61no—
116C2×#683—61no—
117C4×D20—31no—
118C4×D20—31no—
119#4018—61no—
120C42×D5—61no—
121#4016—32no—
122#4016—32no—
123#4016—61no—
124#4016—61no—
125C4×Dic10—31no—
126C4×Dic10—31no—
127C5×C4⋊C8—32no—
128C5×C4⋊C8—32no—
129#3953—32no—
130#3953C2×D312yes—
131#3950—32no—
132#3950—32no—
133#3949—32no—
134#3949—32no—
135#3948—32no—
136#3948C2×D312yes—
137#3080—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×C3×D5—21no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×Q812yes—
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—42no—
148C2×C5×Dic3—41no—
149C2×C5×Dic3—41no—
150C2×C5×Dic3C2×D411yescharacteristic
151C2×C5×Dic3C2×D411yescharacteristic
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C3×C22⋊D5—24no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—42no—
158C3×D20—21no—
159C3×D20C2×Q812yes—
160C3×C4×D5—24no—
161C3×Dic10—21no—
162C3×Dic10C2×Q812yes—
163D5×Dic3—42no—
164D5×Dic3—42no—
165C3×C5×C8—22no—
166C5×C3⋊C8—22no—
167C2×C3×#41—51no—
168C2×C3×M16C2×D511yescharacteristic
169C2×C3×C4⋊C4—51no—
170Q8×Dic3—51no—
171Q8×Dic3—51no—
172D4×Dic3—51no—
173D4×Dic3—51no—
174D4×Dic3—101no—
175D4×Dic3—101no—
176#926—51no—
177#926—101no—
178C2×C4⋊Dic3—51no—
179C2×C4⋊Dic3—101no—
180C2×Dic3⋊C4—101no—
181C2×C4×Dic3—101no—
182C2×C4×Dic3C2×D511yescharacteristic
183C2×#208C2×D511yescharacteristic
184#890—52no—
185#890—52no—
186#890—101no—
187#890—101no—
188C3×#103—52no—
189C3×#102—52no—
190#835—52no—
191#832—52no—
192#818—52no—
193#817—52no—
194Dic3⋊C8C2×D512yes—
195Dic3⋊C8C2×D512yes—
196#808—52no—
197#807—52no—
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—21no—
202C22×Dic5—21no—
203C22×Dic5—61no—
204#709—22no—
205#709Dic614yes—
206C2×D20C22×D311yescharacteristic
207C2×C4×D5—21no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C2×Dic10C22×D311yescharacteristic
211C5×M16—22no—
212C5×M16—62no—
213C2×C5×C8—32no—
214C2×C5×C8C22×D312yes—
215C42×C5—31no—
216C42×C5—31no—
217C42×C5—31no—
218C42×C5—31no—
219C22⋊Dic5—61no—
220#685—61no—
221#685—61no—
222C4⋊Dic5—21no—
223C4⋊Dic5—32no—
224C4⋊Dic5—31no—
225C4⋊Dic5—31no—
226C4⋊Dic5—61no—
227C4⋊Dic5C22×D312yes—
228#683—61no—
229#683—61no—
230#683—62no—
231#683—62no—
232#683—62no—
233#683—62no—
234C4×Dic5—61no—
235C4×Dic5—61no—
236C4×Dic5—61no—
237C2×#125—151no—
238C4×#41—151no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—151no—
244#428—151no—
245#423—31no—
246#417—51no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×C3×D5—22no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C3×C4×C5C22⋊Q812yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—41no—
259Dic15—41no—
260Dic15—42no—
261C3×Dic5—22no—
262C3×Dic5—42no—
263C5×Dic3—21no—
264C5×Dic3—21no—
265C5×Dic3—21no—
266C5×Dic3—21no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C22×C3×C4—101no—
273C22×C3×C4—101no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—101no—
276C22×Dic3—101no—
277C22×Dic3—101no—
278C22×Dic3D2011yescharacteristic
279C22×Dic3D2011yescharacteristic
280C3×M16—22no—
281C2×C3×C8C22×D512yes—
282C3×C4⋊C4—52no—
283C3×C4⋊C4—101no—
284#217—101no—
285#217—101no—
286#217—101no—
287C4⋊Dic3—51no—
288C4⋊Dic3—51no—
289C4⋊Dic3—52no—
290C4⋊Dic3—101no—
291C4⋊Dic3—102no—
292C4⋊Dic3—102no—
293C4⋊Dic3—101no—
294C4⋊Dic3—101no—
295Dic3⋊C4—102no—
296Dic3⋊C4—102no—
297C4×Dic3—101no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3D2011yescharacteristic
301C4×Dic3D2011yescharacteristic
302C4×Dic3C22×D511yescharacteristic
303C4×Dic3C22×D511yescharacteristic
304#208—22no—
305C2×C3⋊C8C22×D512yes—
306C23×C5D3×D411yescharacteristic
307C22×D5—21no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—31no—
312C2×C4×C5—121no—
313C2×C4×C5—121no—
314C2×C4×C5C2×Dic612yes—
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5#23712yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—24no—
319C2×Dic5—21no—
320C2×Dic5—22no—
321C2×Dic5—42no—
322C2×Dic5—61no—
323C2×Dic5—61no—
324C2×Dic5—62no—
325C2×Dic5—122no—
326D20—21no—
327D20C2×Dic612yes—
328C4×D5—24no—
329C4×D5—122no—
330C4×D5—122no—
331Dic10—21no—
332Dic10C2×Dic612yes—
333C5×C8—22no—
334C5×C8—62no—
335C2×#41—51no—
336C2×M16—31no—
337C2×M16D3×D511yescharacteristic
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
342C4×Q8—151no—
343C4×Q8—151no—
344C4×D4—151no—
345C4×D4—151no—
346C4×D4—301no—
347C4×D4—301no—
348#117—151no—
349#117—301no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—31no—
355C2×C42—301no—
356#107—152no—
357#107—152no—
358#106—152no—
359#106—152no—
360C4⋊C8—32no—
361C4⋊C8—32no—
362#103—52no—
363#103—152no—
364#102—52no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C3×D5—42no—
371C23×C3—101no—
372C23×C3C2×D2011yescharacteristic
373C3×Q8—52no—
374C3×Q8—101no—
375C3×D4—52no—
376C3×D4—104no—
377C3×D4—101no—
378C2×C3×C4—101no—
379C2×C3×C4—104no—
380C2×C3×C4—102no—
381C2×C3×C4—202no—
382C2×C3×C4C2×D2011yescharacteristic
383C2×C3×C4#71112yes—
384C2×C3×C4Q8×D512yes—
385C2×C3×C4C23×D511yescharacteristic
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—102no—
391C2×Dic3—202no—
392C2×Dic3—202no—
393C2×Dic3—202no—
394C2×Dic3C2×D2011yescharacteristic
395C2×Dic3C2×D2011yescharacteristic
396C2×Dic3C2×D2011yescharacteristic
397C2×Dic3C2×D2011yescharacteristic
398C3×C8—22no—
399C3⋊C8—22no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5#87812yes—
403C22×C5C2×D3×D411yescharacteristic
404C2×D5—22no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—61no—
408C4×C5—61no—
409C4×C5—61no—
410C4×C5—61no—
411C4×C5#87812yes—
412C4×C5C22×Dic611yescharacteristic
413C4×C5C2×#23711yescharacteristic
414Dic5—22no—
415Dic5—42no—
416Dic5—121no—
417Dic5—121no—
418Dic5—122no—
419#41—54no—
420#41—102no—
421C2×Q8—51no—
422C2×D4—51no—
423C2×D4—101no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—101no—
427C22×C4—101no—
428C22×C4—301no—
429C22×C4—301no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—22no—
433M16—62no—
434C2×C8—32no—
435C2×C8C2×D3×D512yes—
436C4⋊C4—52no—
437C4⋊C4—101no—
438C4⋊C4—152no—
439C4⋊C4—151no—
440C4⋊C4—151no—
441C4⋊C4—302no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4—301no—
447C4⋊C4—301no—
448C22⋊C4—301no—
449C22⋊C4—301no—
450C22⋊C4—301no—
451C42—31no—
452C42—31no—
453C42—31no—
454C42—31no—
455C42—301no—
456C42—301no—
457C42—301no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—102no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3#404312yes—
465C22×C3C22×D2011yescharacteristic
466C3×C4—102no—
467C3×C4—202no—
468C3×C4#404312yes—
469C3×C4C2×#71111yescharacteristic
470C3×C4C2×Q8×D511yescharacteristic
471Dic3—21no—
472Dic3—21no—
473Dic3—21no—
474Dic3—21no—
475Dic3—201no—
476Dic3—202no—
477Dic3—201no—
478C2×C5—22no—
479C2×C5C2×#87811yescharacteristic
480C2×C5#577311yescharacteristic
481C2×C5#577711yescharacteristic
482D5—42no—
483C23—101no—
484C23D3×D2011yescharacteristic
485Q8—52no—
486Q8—101no—
487D4—52no—
488D4—104no—
489D4—101no—
490C2×C4—31no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—31no—
494C2×C4—101no—
495C2×C4—104no—
496C2×C4—102no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—202no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4—602no—
505C2×C4—602no—
506C2×C4D5×Dic612yes—
507C2×C4D3×D2011yescharacteristic
508C2×C4#678012yes—
509C2×C4C22×D3×D511yescharacteristic
510C8—22no—
511C8—62no—
512C2×C3—22no—
513C2×C3—202no—
514C2×C3C2×#404311yescharacteristic
515C2×C3#6608211yescharacteristic
516C2×C3#6608211yescharacteristic
517C5#7887111yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—102no—
521C22—201no—
522C22—201no—
523C22#9142212yes—
524C22C2×D3×D2011yescharacteristic
525C4—61no—
526C4—61no—
527C4—61no—
528C4—61no—
529C4—102no—
530C4—202no—
531C4—601no—
532C4—602no—
533C4—601no—
534C4#9142212yes—
535C4C2×D5×Dic611yescharacteristic
536C4C2×#678011yescharacteristic
537C3#1061079211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—202no—
540C2#1175402811yescharacteristic
541C2#1175402911yescharacteristic
542C2C2×#9142211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91381C2semidirect
3. #11751222C2semidirect
4. C5×#5118C2semidirect
6. #11748453C2semidirect
8. #11747864C2semidirect
9. #11747863C2semidirect
10. #11747784C2semidirect
11. #11747783C2semidirect
100. #5118D5semidirect
458. C3×C5#3080semidirect
517. C5#78871semidirect
537. C3#10610792semidirect

Maximal subgroups

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

subgroupindex
Dic3×#7092
C2×#913812
#117512222
C5×#51182
C3×#654222
#117484532
#117483692
#117478642
#117478632
#117477842
#117477832
#106107923
#788715