Finite Group Databasebeta

← #14438046

Subgroups — #14438046

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66002C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic, complemented
3#11751156C211yesmaximal, characteristic, complemented
4C5×#5055C211yesmaximal, characteristic, complemented
5#11749330C212yesmaximal, complemented
6#11749207C212yesmaximal, complemented
7#11749084C212yesmaximal, complemented
8#11748961C212yesmaximal, complemented
9D5×#803C211yesmaximal, characteristic, complemented
10#11746898C211yesmaximal, characteristic, complemented
11#11746893C211yesmaximal, characteristic, complemented
12#10613410—31nomaximal, Hall
13C2×C3×#713C2211yescharacteristic
14C2×C3×#711C2211yescharacteristic
15C3×C5×#124C2211yescharacteristic
16#91758C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4090C2211yescharacteristic
19C3×#4086C2211yescharacteristic
20C3×#4030—21no—
21C3×#4030—21no—
22C3×#4027—21no—
23C3×#4027—21no—
24C3×#4021C2211yescharacteristic
25C3×C42×D5C2211yescharacteristic
26#91388C2212yes—
27#91360—21no—
28#91359—21no—
29#91358C2212yes—
30#91333—21no—
31Dic5×Dic6—21no—
32C2×D5×C3⋊C8C2212yes—
33#91119C2212yes—
34#91116C2212yes—
35#91087C2211yescharacteristic
36C5×#835C2212yes—
37C5×#832C2212yes—
38C5×#803C2211yescharacteristic
39#90971C2212yes—
40#90970C2212yes—
41#90965C2212yes—
42#90964C2212yes—
43#90952C2212yes—
44#83282—51nomaximal, Hall
45#66062—31no—
46#66002D311yescharacteristic
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50#65093—32no—
51#65086—32no—
52#65061—32no—
53#65053—32no—
54#65003—31no—
55D5×#97—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C2×Dic30—21no—
59C2×C5×Dic6—21no—
60C2×C3×C22⋊D5—21no—
61C2×C3×C22⋊D5—21no—
62C2×C3×C22⋊D5—21no—
63C22×C3×Dic5—21no—
64C3×#713—24no—
65C3×#711—24no—
66C2×C3×D20—21no—
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×C4×D5D411yescharacteristic
70C2×C3×C4×D5D411yescharacteristic
71C2×C3×C4×D5C2311yescharacteristic
72C2×C3×Dic10C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×C5×C22⋊C4—21no—
75C3×C42×C5C2311yescharacteristic
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C2×C3⋊#168C2312yes—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C2×C5×C3⋊C8C2312yes—
82C3×#685—21no—
83C3×#685—21no—
84C3×#683—21no—
85C3×#683—21no—
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5C2311yescharacteristic
89Dic3⋊Dic5—22no—
90#6669—22no—
91#6665—22no—
92Dic3×Dic5—22no—
93D5×C3⋊C8—24no—
94C3×#532—51no—
95#5470—51no—
96#5233—52no—
97#5233—52no—
98#5082—52no—
99#5071—52no—
100#5055—51no—
101#5055—51no—
102#5055—51no—
103#5055D511yescharacteristic, complemented
104C2×#803—51no—
105C2×#713C2×D311yescharacteristic
106C2×#711C2×D311yescharacteristic
107C5×C4⋊Q8—31no—
108C5×#124C2×D311yescharacteristic
109#4092—61no—
110Q8×Dic5—61no—
111#4090C2×D311yescharacteristic
112#4086C2×D311yescharacteristic
113C2×C8×D5—32no—
114#4043—61no—
115#4038—32no—
116#4036—32no—
117#4033—61no—
118#4030—21no—
119#4030—21no—
120#4027—21no—
121#4027—21no—
122#4021C2×D311yescharacteristic
123C42×D5C2×D311yescharacteristic
124#4015—31no—
125C5×#103—32no—
126C5×#102—32no—
127C5×#97—31no—
128#3967—32no—
129#3964—32no—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133#3942—32no—
134#3941—32no—
135#3935—31no—
136#3135—151noSylow
137C23×C3×C5—21no—
138C22×C3×D5—21no—
139C22×C3×D5C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×D4—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C2×C5×Dic3—22no—
149C5×Dic6—42no—
150C3×C22⋊D5—42no—
151C3×C22⋊D5—42no—
152C3×C22⋊D5—42no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—42no—
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C3×D20—22no—
159C3×D20—42no—
160C3×C4×D5—41no—
161C3×C4×D5—41no—
162C3×C4×D5—42no—
163C3×C4×D5#4114yes—
164C3×Dic10—22no—
165C3⋊#168—22no—
166C5×C3⋊C8—22no—
167C2×C3×#41—51no—
168C2×C3×#41—51no—
169C3×C4⋊Q8—51no—
170C3×#127—51no—
171C3×#124—51no—
172C3×#124C2×D511yescharacteristic
173C3×#121—101no—
174C3×#121—101no—
175C3×C4×D4—101no—
176C3×C4×D4—101no—
177C2×C3×C42—51no—
178#926—52no—
179#924—101no—
180#924—101no—
181C22×C3⋊C8—52no—
182#870—52no—
183#869—51no—
184#869C2×D511yescharacteristic
185C4×Dic6—101no—
186C4×Dic6—101no—
187#835—52no—
188#835—52no—
189#835—52no—
190#835C2×D512yes—
191#832—52no—
192#832—52no—
193#832—52no—
194#832C2×D512yes—
195#803—51no—
196#803—52no—
197#803C2×D511yescharacteristic
198C2×C5×Q8—61no—
199C2×C5×Q8C22×D311yescharacteristic
200C2×C5×D4C22×D311yescharacteristic
201C2×C22⋊D5—21no—
202C2×C22⋊D5—21no—
203C2×C22⋊D5—21no—
204C22×Dic5—21no—
205#713—24no—
206#711—24no—
207C2×D20—21no—
208C2×D20C22×D311yescharacteristic
209C2×C4×D5—21no—
210C2×C4×D5#6711yescharacteristic
211C2×C4×D5#6711yescharacteristic
212C2×C4×D5C22×D311yescharacteristic
213C2×Dic10—61no—
214C2×Dic10C22×D311yescharacteristic
215C2×C5×C8—32no—
216C5×C4⋊C4—32no—
217C5×C4⋊C4—61no—
218C5×C22⋊C4—21no—
219C5×C22⋊C4—21no—
220C42×C5C22×D311yescharacteristic
221#685—21no—
222#685—21no—
223#685—62no—
224C4⋊Dic5—32no—
225C4⋊Dic5—61no—
226C4⋊Dic5—62no—
227#683—21no—
228#683—21no—
229#683—62no—
230C4×Dic5—62no—
231C4×Dic5#6711yescharacteristic
232C4×Dic5#6711yescharacteristic
233C4×Dic5C22×D311yescharacteristic
234C2×#168—32no—
235C8×D5—64no—
236#533—151no—
237#532—51no—
238#491—152no—
239#490—152no—
240#489—31no—
241#489—151no—
242#489—151no—
243#489—151no—
244#416—152no—
245#416—152no—
246C2×#97—151no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5C22×D411yescharacteristic
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
256C2×C3×D5#12412yes—
257C3×C4×C5—21no—
258C3×C4×C5—21no—
259C3×C4×C5—41no—
260C3×C4×C5C2×#4112yes—
261Dic15—42no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—41no—
265C3×Dic5#12412yes—
266C5×Dic3—42no—
267C3×#41—104no—
268C3×#41—104no—
269C2×C3×Q8—51no—
270C2×C3×Q8C22×D511yescharacteristic
271C2×C3×D4—51no—
272C2×C3×D4—101no—
273C2×C3×D4—101no—
274C2×C3×D4—101no—
275C2×C3×D4—101no—
276C2×C3×D4C22×D511yescharacteristic
277C22×C3×C4—51no—
278C22×C3×C4—51no—
279C22×C3×C4—51no—
280C22×C3×C4—101no—
281C22×C3×C4—101no—
282C2×Dic6—21no—
283C2×Dic6—101no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4—101no—
286C3×C22⋊C4—21no—
287C3×C22⋊C4—21no—
288C3×C22⋊C4—101no—
289C3×C22⋊C4—101no—
290C3×C42—51no—
291C3×C42—51no—
292C3×C42—51no—
293C3×C42C22×D511yescharacteristic
294#217—102no—
295C4⋊Dic3—21no—
296C4⋊Dic3—52no—
297C4⋊Dic3—101no—
298C4⋊Dic3C22×D512yes—
299Dic3⋊C4—102no—
300Dic3⋊C4—102no—
301C4×Dic3—102no—
302C2×C3⋊C8—52no—
303C2×C3⋊C8—104no—
304C2×C3⋊C8C22×D512yes—
305C23×C5—21no—
306C22×D5—21no—
307C22×D5C2×#6711yescharacteristic
308C5×Q8—22no—
309C5×Q8—122no—
310C5×D4—22no—
311C2×C4×C5—21no—
312C2×C4×C5—62no—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—42no—
317C22⋊D5—42no—
318C22⋊D5—42no—
319C2×Dic5—21no—
320C2×Dic5—42no—
321C2×Dic5—62no—
322C2×Dic5C2×#6711yescharacteristic
323C2×Dic5C2×#6711yescharacteristic
324C2×Dic5C2×#6711yescharacteristic
325D20—22no—
326D20—42no—
327C4×D5—41no—
328C4×D5—41no—
329C4×D5—42no—
330C4×D5#23714yes—
331Dic10—22no—
332Dic10—122no—
333C5×C8—62no—
334#168—62no—
335C2×#41—51no—
336C2×#41—51no—
337C22×C8—152no—
338C4⋊Q8—31no—
339C4⋊Q8—51no—
340C4⋊Q8—151no—
341#127—51no—
342#125—152no—
343#124—51no—
344#124D3×D511yescharacteristic
345C22⋊Q8—301no—
346C22⋊Q8—301no—
347#121—101no—
348#121—101no—
349C4×Q8—301no—
350C4×Q8—301no—
351C4×D4—101no—
352C4×D4—101no—
353#117—152no—
354C2×C42—51no—
355#103—32no—
356#103—152no—
357#103—152no—
358#103—152no—
359#102—32no—
360#102—152no—
361#102—152no—
362#102—152no—
363#97—31no—
364#97—152no—
365#97—151no—
366C2×C3×C5—81no—
367C2×C3×C5C2×#12411yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C3×D5—22no—
371C3×D5—81no—
372C23×C3—21no—
373C23×C3—51no—
374C23×C3—101no—
375C3×Q8—22no—
376C3×Q8—102no—
377C3×D4—22no—
378C3×D4—102no—
379C3×D4—202no—
380C3×D4—202no—
381C3×D4—202no—
382C3×D4—202no—
383C2×C3×C4—21no—
384C2×C3×C4—51no—
385C2×C3×C4—54no—
386C2×C3×C4—51no—
387C2×C3×C4—51no—
388C2×C3×C4—101no—
389C2×C3×C4—201no—
390C2×C3×C4—201no—
391C2×C3×C4—202no—
392C2×C3×C4—202no—
393C2×C3×C4D4×D511yescharacteristic
394C2×C3×C4D4×D511yescharacteristic
395C2×C3×C4C23×D511yescharacteristic
396C2×Dic3—22no—
397C2×Dic3—102no—
398Dic6—42no—
399Dic6—202no—
400C3⋊C8—22no—
401C3⋊C8—102no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5C22×#6711yescharacteristic
406C2×D5—21no—
407C2×D5—21no—
408C2×D5—41no—
409C2×D5—41no—
410C2×D5—41no—
411C2×D5#93612yes—
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—41no—
415C4×C5—122no—
416C4×C5C2×#23712yes—
417Dic5—21no—
418Dic5—21no—
419Dic5—41no—
420Dic5—122no—
421Dic5#93612yes—
422#41—104no—
423#41—104no—
424C2×Q8—51no—
425C2×Q8—61no—
426C2×Q8—301no—
427C2×Q8C2×D3×D511yescharacteristic
428C2×D4—51no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—101no—
432C2×D4—101no—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—101no—
438C22×C4—101no—
439C2×C8—32no—
440C2×C8—152no—
441C2×C8—304no—
442C4⋊C4—32no—
443C4⋊C4—61no—
444C4⋊C4—101no—
445C4⋊C4—101no—
446C4⋊C4—152no—
447C4⋊C4—302no—
448C4⋊C4—302no—
449C4⋊C4—301no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—101no—
453C22⋊C4—101no—
454C22⋊C4—302no—
455C42—51no—
456C42—51no—
457C42—51no—
458C42—302no—
459C42C2×D3×D511yescharacteristic
460C3×C5#313511yescharacteristic, complemented, Hall
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—52no—
465C22×C3—101no—
466C22×C3—101no—
467C22×C3—201no—
468C22×C3—201no—
469C22×C3—201no—
470C22×C3C2×D4×D511yescharacteristic
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—41no—
474C3×C4—52no—
475C3×C4—101no—
476C3×C4—101no—
477C3×C4—201no—
478C3×C4D5×#4112yes—
479Dic3—42no—
480Dic3—202no—
481C2×C5—81no—
482C2×C5C2×#93611yescharacteristic
483C2×C5#582211yescharacteristic
484C2×C5#582211yescharacteristic
485D5—22no—
486D5—81no—
487C23—21no—
488C23—51no—
489C23—101no—
490Q8—22no—
491Q8—102no—
492Q8—122no—
493Q8—602no—
494D4—22no—
495D4—102no—
496D4—202no—
497D4—202no—
498D4—202no—
499D4—202no—
500C2×C4—21no—
501C2×C4—51no—
502C2×C4—54no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—62no—
506C2×C4—101no—
507C2×C4—201no—
508C2×C4—201no—
509C2×C4—202no—
510C2×C4—202no—
511C2×C4—302no—
512C2×C4D5×#6711yescharacteristic
513C2×C4D5×#6711yescharacteristic
514C2×C4C22×D3×D511yescharacteristic
515C8—62no—
516C8—302no—
517C2×C3—81no—
518C2×C3—102no—
519C2×C3—401no—
520C2×C3D5×#12411yescharacteristic
521C2×C3#6610711yescharacteristic
522C2×C3#6611111yescharacteristic
523C5#8328211yescharacteristic, complemented, Sylow
524C22—41no—
525C22—41no—
526C22—41no—
527C22—52no—
528C22—101no—
529C22—101no—
530C22—201no—
531C22—201no—
532C22—201no—
533C22C2×D5×#6711yescharacteristic
534C4—21no—
535C4—21no—
536C4—41no—
537C4—52no—
538C4—101no—
539C4—101no—
540C4—122no—
541C4—201no—
542C4—602no—
543C4D5×#23712yes—
544C3#1061341011yescharacteristic, complemented, Sylow
545C2—81no—
546C2—102no—
547C2—401no—
548C2D5×#93611yescharacteristic
549C2#1175534311yescharacteristic
550C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC3×#66002C2
hypercenter#124D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752506C2semidirect
3. #11751156C2semidirect
4. C5×#5055C2semidirect
5. #11749330C2semidirect
6. #11749207C2semidirect
7. #11749084C2semidirect
8. #11748961C2semidirect
9. D5×#803C2semidirect
10. #11746898C2semidirect
11. #11746893C2semidirect
103. #5055D5semidirect
460. C3×C5#3135semidirect
523. C5#83282semidirect
544. C3#10613410semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
#117525062
#117511562
C5×#50552
#117493302
#117492072
#117490842
#117489612
D5×#8032
#117468982
#117468932
#106134103
#832825