Finite Group Databasebeta

← #14297355

Subgroups — #14297355

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic
2#11751337C211yesmaximal, characteristic, complemented
3C5×#5236C211yesmaximal, characteristic, complemented
4#11748624C211yesmaximal, characteristic, complemented
5#11748367C211yesmaximal, characteristic, complemented
6#11748366C211yesmaximal, characteristic, complemented
7#11748353C211yesmaximal, characteristic, complemented
8#10601207—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4149—22no—
11C3×#4149—22no—
12C3×#4149—22no—
13C3×#4149—22no—
14C2×C3×#713C412yescomplemented
15C2×C3×D4×D5—22no—
16C2×C3×D4×D5C412yescomplemented
17C2×C3×#709—21no—
18C2×C3×#709C2211yescharacteristic
19C22×C3×D20—21no—
20C22×C3×D20C2211yescharacteristic
21#91815C2211yescharacteristic, complemented
22C2×#6710C2211yescharacteristic, complemented
23C5×#926C2211yescharacteristic, complemented
24C2×C5×#208C2211yescharacteristic, complemented
25#91121—22no—
26C5×#837—22no—
27#90995—22no—
28#90965—22no—
29#90964—22no—
30#90961—21no—
31#90958—21no—
32#72141—51nomaximal, Hall
33C2×#4149D311yescharacteristic
34C5×#421—31no—
35#65525—31no—
36#65421—31no—
37#65420—31no—
38#65295—31no—
39#65290—31no—
40C23×C3×D5—21no—
41C23×C3×D5—22no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41D412yes—
45C3×C5×#41D412yes—
46C2×C3×C5×Q8C2×C411yescharacteristic
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4C2×C411yescharacteristic
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C3×C22⋊D5—22no—
52C2×C3×C22⋊D5D412yes—
53C3×#713—24no—
54C3×#713—24no—
55C3×D4×D5—28no—
56C3×D4×D5—28no—
57C3×D4×D5—24no—
58C3×D4×D5—24no—
59C3×#709—24no—
60C3×#709—24no—
61C3×#709—21no—
62C3×#709—21no—
63C3×#709—21no—
64C3×#709—21no—
65C2×C3×D20—24no—
66C2×C3×D20—24no—
67C2×C3×D20—22no—
68C2×C3×D20—21no—
69C2×C3×D20—21no—
70C2×C3×D20—21no—
71C2×C3×D20C2×C412yes—
72C2×C3×D20D411yescharacteristic
73C2×C3×D20D412yes—
74C2×C3×D20D412yes—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5C2×C412yes—
77C2×C3×Dic10D411yescharacteristic
78#6719—21no—
79C4⋊Dic15—21no—
80C4×Dic15—21no—
81#6710—21no—
82#6710—21no—
83C2×C3⋊#168—21no—
84C5×#217—21no—
85C5×C4⋊Dic3—21no—
86C4×C5×Dic3—21no—
87C5×#208—21no—
88C5×#208—21no—
89C2×C5×C3⋊C8—21no—
90C2×C3×H(5,𝔽2)—51no—
91#5240—51no—
92#5237—51no—
93#5236—51no—
94#5236D511yescharacteristic, complemented
95#5215—51no—
96#5215—51no—
97C2×C5×#41C2×D311yescharacteristic
98#4149—22no—
99#4149—22no—
100#4149—22no—
101#4149—22no—
102C2×#713Dic312yescomplemented
103C2×D4×D5—22no—
104C2×D4×D5Dic312yescomplemented
105C2×#709—21no—
106C2×#709C2×D311yescharacteristic
107C22×D20—21no—
108C22×D20C2×D311yescharacteristic
109C2×C5×M16—31no—
110C5×#117—31no—
111#4072—31no—
112C2×#681—31no—
113C5×#104—62no—
114#3969—62no—
115#3956—61no—
116#3955—61no—
117#3953—62no—
118#3941—62no—
119#3938—62no—
120#1795—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×C3×D5—22no—
124C22×C3×D5—28no—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—82no—
128C22×C3×D5—84no—
129C22×C3×D5C22⋊C412yes—
130C3×C5×Q8—21no—
131C3×C5×Q8C22⋊C412yes—
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—21no—
135C3×C5×D4C22⋊C412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×Dic15—41no—
146C2×C5×Dic3—41no—
147C3×C22⋊D5—28no—
148C3×C22⋊D5—22no—
149C3×C22⋊D5—22no—
150C2×C3×Dic5C22⋊C412yes—
151C3×D20—28no—
152C3×D20—22no—
153C3×D20—21no—
154C3×D20—22no—
155C3×D20—21no—
156C3×D20—22no—
157C3×D20C22⋊C414yes—
158C3×C4×D5—28no—
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161C3×Dic10—21no—
162C3×Dic10—21no—
163C3⋊#168—41no—
164C5×C3⋊C8—41no—
165C3×H(5,𝔽2)—102no—
166C3×H(5,𝔽2)—102no—
167C3×H(5,𝔽2)—102no—
168C3×H(5,𝔽2)—102no—
169C2×C3×#41—51no—
170C2×C3×#41—52no—
171C2×C3×#41—101no—
172C2×C3×#41C2×D511yescharacteristic
173C22×C3×D4—52no—
174C22×C3×D4—51no—
175C22×C3×D4—101no—
176C22×C3×D4—102no—
177#926—51no—
178#926C2×D511yescharacteristic, complemented
179C2×#208—51no—
180C2×#208C2×D511yescharacteristic, complemented
181#837—22no—
182#837—102no—
183#836—101no—
184#834—102no—
185#833—101no—
186#832—102no—
187#832—102no—
188C23×D5—21no—
189C23×D5—22no—
190C5×#41—21no—
191C5×#41—21no—
192C5×#41#6712yes—
193C5×#41#6712yes—
194C2×C5×Q8C2×Dic311yescharacteristic
195C2×C5×D4—21no—
196C2×C5×D4C2×Dic311yescharacteristic
197C22×C4×C5—21no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—22no—
200C2×C22⋊D5#6712yes—
201#713—24no—
202#713—24no—
203D4×D5—28no—
204D4×D5—28no—
205D4×D5—24no—
206D4×D5—24no—
207#709—24no—
208#709—24no—
209#709—21no—
210#709—21no—
211#709—21no—
212#709—21no—
213C2×D20—24no—
214C2×D20—24no—
215C2×D20—22no—
216C2×D20—21no—
217C2×D20—21no—
218C2×D20—21no—
219C2×D20C2×Dic312yes—
220C2×D20#6711yescharacteristic
221C2×D20#6712yes—
222C2×D20#6712yes—
223C2×C4×D5—22no—
224C2×C4×D5C2×Dic312yes—
225C2×Dic10#6711yescharacteristic
226C5×M16—61no—
227C5×M16—61no—
228C2×C5×C8—61no—
229C5×C4⋊C4—61no—
230C5×C22⋊C4—61no—
231C42×C5—61no—
232C22⋊Dic5—61no—
233C4⋊Dic5—61no—
234C4×Dic5—61no—
235#681—61no—
236#681—61no—
237C2×#168—61no—
238C2×H(5,𝔽2)—51no—
239#421—31no—
240#421—151no—
241#418—151no—
242#418—151no—
243#413—151no—
244#410—151no—
245C22×C3×C5—22no—
246C22×C3×C5—41no—
247C22×C3×C5—42no—
248C22×C3×C5C2×C22⋊C411yescharacteristic
249C22×C3×C5#12011yescharacteristic
250C22×C3×C5#12011yescharacteristic
251C2×C3×D5—22no—
252C2×C3×D5—24no—
253C2×C3×D5—44no—
254C2×C3×D5—42no—
255C2×C3×D5—82no—
256C2×C3×D5—82no—
257C2×C3×D5—88no—
258C3×C4×C5—22no—
259C3×C4×C5C2×C22⋊C411yescharacteristic
260C3×C4×C5C2×C22⋊C411yescharacteristic
261C3×C4×C5#12011yescharacteristic
262C3×C4×C5#12011yescharacteristic
263Dic15—81no—
264C3×Dic5—22no—
265C5×Dic3—81no—
266C24×C3—102no—
267C24×C3—101no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—104no—
271C3×#41—104no—
272C3×#41—104no—
273C3×#41—104no—
274C3×#41—101no—
275C3×#41—101no—
276C3×#41—101no—
277C3×#41—101no—
278C3×#41D2012yes—
279C3×#41C22⋊D512yes—
280C2×C3×Q8—51no—
281C2×C3×Q8C4×D511yescharacteristic
282C2×C3×D4—21no—
283C2×C3×D4—52no—
284C2×C3×D4—52no—
285C2×C3×D4—52no—
286C2×C3×D4—52no—
287C2×C3×D4—51no—
288C2×C3×D4—102no—
289C2×C3×D4—104no—
290C2×C3×D4—104no—
291C2×C3×D4—102no—
292C2×C3×D4—104no—
293C2×C3×D4—108no—
294C2×C3×D4—108no—
295C2×C3×D4—104no—
296C2×C3×D4—101no—
297C2×C3×D4—101no—
298C2×C3×D4—101no—
299C2×C3×D4C4×D511yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—52no—
302C22×C3×C4—102no—
303C22×C3×C4C22×D511yescharacteristic
304#217—21no—
305#217—101no—
306C4⋊Dic3—21no—
307C4⋊Dic3—101no—
308C4×Dic3—21no—
309C4×Dic3—101no—
310#208—21no—
311#208—21no—
312#208—101no—
313#208—101no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—101no—
316C23×C5—21no—
317C23×C5C2×#6711yescharacteristic
318C22×D5—22no—
319C22×D5—28no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—82no—
323C22×D5—84no—
324C22×D5#21712yes—
325C5×Q8—21no—
326C5×Q8#21712yes—
327C5×D4—22no—
328C5×D4—22no—
329C5×D4—21no—
330C5×D4#21712yes—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—121no—
335C2×C4×C5C22×Dic311yescharacteristic
336C2×C4×C5C2×#6711yescharacteristic
337C2×C4×C5C2×#6711yescharacteristic
338C2×C4×C5C2×#6711yescharacteristic
339C2×C4×C5C2×#6711yescharacteristic
340C2×C4×C5C2×#6711yescharacteristic
341C22⋊D5—28no—
342C22⋊D5—22no—
343C22⋊D5—22no—
344C2×Dic5—121no—
345C2×Dic5#21712yes—
346D20—28no—
347D20—22no—
348D20—21no—
349D20—22no—
350D20—21no—
351D20—22no—
352D20#21714yes—
353C4×D5—28no—
354C4×D5—22no—
355C4×D5—22no—
356Dic10—21no—
357Dic10—21no—
358C5×C8—121no—
359#168—121no—
360H(5,𝔽2)—102no—
361H(5,𝔽2)—102no—
362H(5,𝔽2)—102no—
363H(5,𝔽2)—102no—
364C2×#41—51no—
365C2×#41—52no—
366C2×#41—101no—
367C2×#41D3×D511yescharacteristic
368C22×D4—52no—
369C22×D4—51no—
370C22×D4—101no—
371C22×D4—102no—
372C2×M16—31no—
373C2×M16—151no—
374#117—31no—
375#117—151no—
376#104—62no—
377#104—302no—
378#102—302no—
379#102—302no—
380#101—301no—
381#100—301no—
382#99—302no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5—21no—
386C2×C3×C5—42no—
387C2×C3×C5#37911yescharacteristic
388C3×D5—44no—
389C3×D5—42no—
390C23×C3—21no—
391C23×C3—52no—
392C23×C3—108no—
393C23×C3—102no—
394C23×C3—102no—
395C23×C3—102no—
396C23×C3—402no—
397C23×C3—404no—
398C23×C3D4×D511yescharacteristic
399C3×Q8—21no—
400C3×Q8—101no—
401C3×Q8—101no—
402C3×Q8#68512yes—
403C3×D4—22no—
404C3×D4—22no—
405C3×D4—21no—
406C3×D4—54no—
407C3×D4—108no—
408C3×D4—108no—
409C3×D4—102no—
410C3×D4—102no—
411C3×D4—102no—
412C3×D4—101no—
413C3×D4—102no—
414C3×D4—102no—
415C3×D4—101no—
416C3×D4#68512yes—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—52no—
421C2×C3×C4—108no—
422C2×C3×C4—102no—
423C2×C3×C4—102no—
424C2×C3×C4C2×C4×D511yescharacteristic
425C2×C3×C4C2×D2011yescharacteristic
426C2×C3×C4D4×D511yescharacteristic
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4D4×D511yescharacteristic
429C2×C3×C4C2×C22⋊D511yescharacteristic
430C2×Dic3—41no—
431C2×Dic3—201no—
432C3⋊C8—41no—
433C3⋊C8—201no—
434C22×C5—22no—
435C22×C5—41no—
436C22×C5—42no—
437C22×C5C2×#21711yescharacteristic
438C22×C5#95311yescharacteristic
439C22×C5#95311yescharacteristic
440C2×D5—22no—
441C2×D5—24no—
442C2×D5—44no—
443C2×D5—42no—
444C2×D5—82no—
445C2×D5—82no—
446C2×D5—88no—
447C4×C5—22no—
448C4×C5—241no—
449C4×C5C2×#21711yescharacteristic
450C4×C5C2×#21711yescharacteristic
451C4×C5#95311yescharacteristic
452C4×C5#95311yescharacteristic
453Dic5—22no—
454Dic5—241no—
455C24—102no—
456C24—101no—
457#41—21no—
458#41—21no—
459#41—104no—
460#41—104no—
461#41—104no—
462#41—104no—
463#41—101no—
464#41—101no—
465#41—101no—
466#41—101no—
467#41#120112yes—
468#41#120212yes—
469C2×Q8—51no—
470C2×Q8D5×Dic311yescharacteristic
471C2×D4—21no—
472C2×D4—52no—
473C2×D4—52no—
474C2×D4—52no—
475C2×D4—52no—
476C2×D4—51no—
477C2×D4—102no—
478C2×D4—104no—
479C2×D4—104no—
480C2×D4—102no—
481C2×D4—104no—
482C2×D4—108no—
483C2×D4—108no—
484C2×D4—104no—
485C2×D4—101no—
486C2×D4—101no—
487C2×D4—101no—
488C2×D4D5×Dic311yescharacteristic
489C22×C4—21no—
490C22×C4—52no—
491C22×C4—102no—
492C22×C4C2×D3×D511yescharacteristic
493M16—61no—
494M16—61no—
495M16—301no—
496M16—301no—
497C2×C8—61no—
498C2×C8—301no—
499C4⋊C4—61no—
500C4⋊C4—301no—
501C22⋊C4—61no—
502C22⋊C4—301no—
503C42—61no—
504C42—301no—
505C3×C5#179511yescharacteristic, complemented, Hall
506C22×C3—22no—
507C22×C3—41no—
508C22×C3—42no—
509C22×C3—104no—
510C22×C3—102no—
511C22×C3—202no—
512C22×C3—204no—
513C22×C3—402no—
514C22×C3—402no—
515C22×C3—408no—
516C22×C3D5×C22⋊C411yescharacteristic
517C22×C3#402811yescharacteristic
518C22×C3#408311yescharacteristic
519C3×C4—22no—
520C3×C4—102no—
521C3×C4D5×C22⋊C411yescharacteristic
522C3×C4#402811yescharacteristic
523C3×C4C2×#68511yescharacteristic
524C3×C4#408311yescharacteristic
525Dic3—81no—
526Dic3—401no—
527C2×C5—21no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—42no—
531C2×C5#524711yescharacteristic
532D5—44no—
533D5—42no—
534C23—21no—
535C23—52no—
536C23—108no—
537C23—102no—
538C23—102no—
539C23—102no—
540C23—402no—
541C23—404no—
542C23D5×#6711yescharacteristic
543Q8—21no—
544Q8—101no—
545Q8—101no—
546Q8#666512yes—
547D4—22no—
548D4—22no—
549D4—21no—
550D4—54no—
551D4—108no—
552D4—108no—
553D4—102no—
554D4—102no—
555D4—102no—
556D4—102no—
557D4—101no—
558D4—102no—
559D4—101no—
560D4#666512yes—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—52no—
565C2×C4—108no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—121no—
569C2×C4—601no—
570C2×C4C2×D5×Dic311yescharacteristic
571C2×C4C2×#120111yescharacteristic
572C2×C4C2×#120211yescharacteristic
573C2×C4D5×#6711yescharacteristic
574C2×C4D5×#6711yescharacteristic
575C2×C4D5×#6711yescharacteristic
576C8—121no—
577C8—601no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—42no—
582C2×C3—204no—
583C2×C3—202no—
584C2×C3#6524411yescharacteristic
585C5#7214111yescharacteristic, complemented, Sylow
586C22—22no—
587C22—41no—
588C22—42no—
589C22—104no—
590C22—102no—
591C22—202no—
592C22—204no—
593C22—402no—
594C22—402no—
595C22—408no—
596C22D5×#21711yescharacteristic
597C22#9156311yescharacteristic
598C22#9156411yescharacteristic
599C4—22no—
600C4—102no—
601C4—241no—
602C4—1201no—
603C4C2×#666511yescharacteristic
604C4D5×#21711yescharacteristic
605C4#9156311yescharacteristic
606C4#9156411yescharacteristic
607C3#1060120711yescharacteristic, complemented, Sylow
608C2—21no—
609C2—21no—
610C2—21no—
611C2—42no—
612C2—204no—
613C2—202no—
614C2#1174948811yescharacteristic
subgroupG/H
centerC2#11749488
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#379
prime radicalC2×C3×#4149C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1795
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751337C2semidirect
3. C5×#5236C2semidirect
4. #11748624C2semidirect
5. #11748367C2semidirect
6. #11748366C2semidirect
7. #11748353C2semidirect
14. C2×C3×#713C4semidirect
16. C2×C3×D4×D5C4semidirect
21. #91815C22semidirect
22. C2×#6710C22semidirect
23. C5×#926C22semidirect
24. C2×C5×#208C22semidirect
94. #5236D5semidirect
102. C2×#713Dic3semidirect
104. C2×D4×D5Dic3semidirect
178. #926C2×D5semidirect
180. C2×#208C2×D5semidirect
505. C3×C5#1795semidirect
585. C5#72141semidirect
607. C3#10601207semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41492
#117513372
C5×#52362
#117486242
#117483672
#117483662
#117483532
#106012073
#721415