Finite Group Databasebeta

← #14297342

Subgroups — #14297342

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×C5×#1004C211yesmaximal, characteristic
2#11751316C211yesmaximal, characteristic, complemented
3C3×#65504C211yesmaximal, characteristic, complemented
4#11748625C211yesmaximal, characteristic, complemented
5#11748425C211yesmaximal, characteristic, complemented
6#11748424C211yesmaximal, characteristic, complemented
7#11748355C211yesmaximal, characteristic, complemented
8#10602934—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×#67—22no—
11C5×#1004—22no—
12C5×#1004—22no—
13C5×#1004—22no—
14C5×#1004—22no—
15C2×C5×#237—21no—
16C2×C5×#237C412yescomplemented
17C2×C5×D3×D4—21no—
18C2×C5×D3×D4C412yescomplemented
19C2×C5×#235C2211yescharacteristic
20C2×C5×#235C2211yescharacteristic
21#91815C2211yescharacteristic, complemented
22C2×#6710C2211yescharacteristic, complemented
23C3×#4072C2211yescharacteristic, complemented
24C2×C3×#681C2211yescharacteristic, complemented
25#91116—22no—
26C3×#3964—22no—
27#90996—22no—
28#90979—22no—
29#90978—22no—
30#90962—21no—
31#90959—21no—
32#70327—51nomaximal, Hall
33C2×C5×H(5,𝔽2)—31no—
34#65529—31no—
35#65526—31no—
36#65525—31no—
37#65525—31no—
38#65504—31no—
39#65504D311yescharacteristic, complemented
40C24×C3×C5—21no—
41C23×C5×D3—22no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4C2×C412yes—
46C2×C3×C5×D4D412yes—
47C2×C3×C5×D4D412yes—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C5×#67—28no—
50C2×C5×#67—28no—
51C2×C5×#67—21no—
52C2×C5×#67—22no—
53C2×C5×#67—22no—
54C2×C5×#67D412yes—
55C22×C5×Dic3—22no—
56C5×#237—24no—
57C5×#237—24no—
58C5×#237—24no—
59C5×#237—24no—
60C5×D3×D4—24no—
61C5×D3×D4—24no—
62C5×D3×D4—24no—
63C5×D3×D4—24no—
64C5×#235—21no—
65C5×#235—21no—
66C5×#235—21no—
67C5×#235—21no—
68C5×#235—21no—
69C5×#235—21no—
70C5×#235D412yes—
71C5×#235D412yes—
72C2×C5×D12C2×C411yescharacteristic
73C2×C5×D12D411yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C4×C5×D3C2×C412yes—
76C2×C5×Dic6C2×C411yescharacteristic
77C2×C5×Dic6D411yescharacteristic
78#6719—21no—
79C4⋊Dic15—21no—
80C4×Dic15—21no—
81#6710—21no—
82#6710—21no—
83C2×C3⋊#168—21no—
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5—21no—
86C3×C4×Dic5—21no—
87C3×#681—21no—
88C3×#681—21no—
89C2×C3×#168—21no—
90C2×#1004D511yescharacteristic
91C3×#418—51no—
92#5215—51no—
93#5139—51no—
94#5132—51no—
95#5006—51no—
96#5005—51no—
97C5×H(5,𝔽2)—62no—
98C5×H(5,𝔽2)—62no—
99C5×H(5,𝔽2)—62no—
100C5×H(5,𝔽2)—62no—
101C2×C5×#41—31no—
102C2×C5×#41—32no—
103C2×C5×#41—31no—
104C2×C5×#41—61no—
105C22×C5×D4—32no—
106C22×C5×D4—61no—
107C22×C5×D4—62no—
108C22×C5×D4C2×D311yescharacteristic
109#4072—31no—
110#4072C2×D311yescharacteristic, complemented
111C2×#681—31no—
112C2×#681C2×D311yescharacteristic, complemented
113#3969—62no—
114#3969—62no—
115#3968—61no—
116#3966—62no—
117#3965—61no—
118#3964—22no—
119#3964—62no—
120#1795—151noSylow
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—82no—
125C23×C3×C5C2×D411yescharacteristic
126C22×C5×D3—21no—
127C22×C5×D3—28no—
128C22×C5×D3—84no—
129C22×C5×D3C22⋊C412yes—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—22no—
133C3×C5×D4C22⋊C414yes—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×Dic15—41no—
141C5×#67—28no—
142C5×#67—28no—
143C5×#67—22no—
144C5×#67—22no—
145C5×#67—22no—
146C5×#67—22no—
147C2×C5×Dic3—28no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3C22⋊C412yes—
150C5×D12—21no—
151C5×D12—21no—
152C5×D12—21no—
153C5×D12C22⋊C412yes—
154C4×C5×D3—22no—
155C4×C5×D3—22no—
156C4×C5×D3—22no—
157C4×C5×D3—22no—
158C5×Dic6—21no—
159C5×Dic6—21no—
160C5×Dic6—21no—
161C5×Dic6C22⋊C412yes—
162C2×C3×Dic5—41no—
163C3⋊#168—41no—
164C3×#168—41no—
165C22×C3×D4C2×D511yescharacteristic
166C22×#67—22no—
167#1004—22no—
168#1004—22no—
169#1004—22no—
170#1004—22no—
171C2×#237—21no—
172C2×#237Dic512yescomplemented
173C2×D3×D4—21no—
174C2×D3×D4Dic512yescomplemented
175C2×#235C2×D511yescharacteristic
176C2×#235C2×D511yescharacteristic
177C2×C3×M16—51no—
178C3×#117—51no—
179#926—51no—
180C2×#208—51no—
181C3×#102—102no—
182#832—102no—
183#825—102no—
184#824—101no—
185#823—101no—
186#806—102no—
187#805—102no—
188C24×C5—21no—
189C24×C5—62no—
190C5×#41—32no—
191C5×#41—32no—
192C5×#41—64no—
193C5×#41—64no—
194C5×#41—64no—
195C5×#41—64no—
196C5×#41—61no—
197C5×#41—61no—
198C5×#41—61no—
199C5×#41—61no—
200C5×#41—61no—
201C5×#41—61no—
202C2×C5×Q8—31no—
203C2×C5×Q8—31no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—32no—
208C2×C5×D4—31no—
209C2×C5×D4—31no—
210C2×C5×D4—62no—
211C2×C5×D4—64no—
212C2×C5×D4—64no—
213C2×C5×D4—64no—
214C2×C5×D4—62no—
215C2×C5×D4—68no—
216C2×C5×D4—68no—
217C2×C5×D4—61no—
218C2×C5×D4—64no—
219C2×C5×D4C4×D312yes—
220C2×C5×D4D1212yes—
221C2×C5×D4#6712yes—
222C22×C4×C5—32no—
223C22×C4×C5—62no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C22⋊Dic5—21no—
227C22⋊Dic5—61no—
228C4⋊Dic5—21no—
229C4⋊Dic5—61no—
230C4×Dic5—21no—
231C4×Dic5—61no—
232#681—21no—
233#681—21no—
234#681—61no—
235#681—61no—
236C2×#168—21no—
237C2×#168—61no—
238C2×H(5,𝔽2)—31no—
239#421—151no—
240#421—151no—
241#418—51no—
242#418—151no—
243#413—151no—
244#410—151no—
245C22×C3×C5—24no—
246C22×C3×C5—41no—
247C22×C3×C5—44no—
248C22×C3×C5—82no—
249C22×C3×C5—82no—
250C22×C3×C5C2×C22⋊C411yescharacteristic
251C22×C3×C5#12011yescharacteristic
252C22×C3×C5#12011yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—22no—
255C2×C5×D3—42no—
256C2×C5×D3—42no—
257C2×C5×D3—88no—
258C3×C4×C5C2×C22⋊C411yescharacteristic
259C3×C4×C5C2×C22⋊C411yescharacteristic
260C3×C4×C5#12011yescharacteristic
261C3×C4×C5#12011yescharacteristic
262Dic15—81no—
263C3×Dic5—81no—
264C5×Dic3—22no—
265C5×Dic3—22no—
266C24×C3—21no—
267C23×D3—22no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4C2×Dic512yes—
272C2×C3×D4C22⋊D512yes—
273C2×C3×D4C22⋊D512yes—
274C22×C3×C4C22×D511yescharacteristic
275C2×#67—28no—
276C2×#67—28no—
277C2×#67—21no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67C22⋊D512yes—
281C22×Dic3—22no—
282#237—24no—
283#237—24no—
284#237—24no—
285#237—24no—
286D3×D4—24no—
287D3×D4—24no—
288D3×D4—24no—
289D3×D4—24no—
290#235—21no—
291#235—21no—
292#235—21no—
293#235—21no—
294#235—21no—
295#235—21no—
296#235C22⋊D512yes—
297#235C22⋊D512yes—
298C2×D12C2×Dic511yescharacteristic
299C2×D12C22⋊D511yescharacteristic
300C2×C4×D3—21no—
301C2×C4×D3C2×Dic512yes—
302C2×Dic6C2×Dic511yescharacteristic
303C2×Dic6C22⋊D511yescharacteristic
304C3×M16—101no—
305C3×M16—101no—
306C2×C3×C8—101no—
307C3×C4⋊C4—101no—
308C3×C22⋊C4—101no—
309C3×C42—101no—
310#217—101no—
311C4⋊Dic3—101no—
312C4×Dic3—101no—
313#208—101no—
314#208—101no—
315C2×C3⋊C8—101no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—32no—
320C23×C5—68no—
321C23×C5—61no—
322C23×C5—82no—
323C23×C5—244no—
324C23×C5D3×D411yescharacteristic
325C5×Q8—32no—
326C5×Q8—61no—
327C5×Q8—61no—
328C5×Q8—61no—
329C5×D4—22no—
330C5×D4—22no—
331C5×D4—22no—
332C5×D4—32no—
333C5×D4—68no—
334C5×D4—68no—
335C5×D4—62no—
336C5×D4—62no—
337C5×D4—62no—
338C5×D4—62no—
339C5×D4—61no—
340C5×D4—61no—
341C5×D4—61no—
342C5×D4(C2×D3)⋊C414yes—
343C2×C4×C5—32no—
344C2×C4×C5—68no—
345C2×C4×C5—61no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5C2×C4×D311yescharacteristic
351C2×C4×C5C2×D1211yescharacteristic
352C2×C4×C5D3×D411yescharacteristic
353C2×C4×C5D3×D411yescharacteristic
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5C2×#6711yescharacteristic
356C2×Dic5—41no—
357C2×Dic5—121no—
358#168—41no—
359#168—121no—
360H(5,𝔽2)—62no—
361H(5,𝔽2)—62no—
362H(5,𝔽2)—62no—
363H(5,𝔽2)—62no—
364C2×#41—31no—
365C2×#41—32no—
366C2×#41—31no—
367C2×#41—61no—
368C22×D4—32no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4D3×D511yescharacteristic
372C2×M16—51no—
373C2×M16—151no—
374#117—51no—
375#117—151no—
376#104—302no—
377#104—302no—
378#102—102no—
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—44no—
387C2×C3×C5#37911yescharacteristic
388C5×D3—42no—
389C5×D3—42no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—82no—
394C23×C3C2×C22⋊D511yescharacteristic
395C22×D3—21no—
396C22×D3—28no—
397C22×D3—84no—
398C22×D3C22⋊Dic512yes—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4C22⋊Dic514yes—
403C2×C3×C4—201no—
404C2×C3×C4C22×Dic511yescharacteristic
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C2×C22⋊D511yescharacteristic
408C2×C3×C4C2×C22⋊D511yescharacteristic
409C2×C3×C4C2×C22⋊D511yescharacteristic
410#67—28no—
411#67—28no—
412#67—22no—
413#67—22no—
414#67—22no—
415#67—22no—
416C2×Dic3—28no—
417C2×Dic3—21no—
418C2×Dic3—201no—
419C2×Dic3C22⋊Dic512yes—
420D12—21no—
421D12—21no—
422D12—21no—
423D12C22⋊Dic512yes—
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—22no—
428Dic6—21no—
429Dic6—21no—
430Dic6—21no—
431Dic6C22⋊Dic512yes—
432C3×C8—201no—
433C3⋊C8—201no—
434C22×C5—24no—
435C22×C5—41no—
436C22×C5—44no—
437C22×C5—62no—
438C22×C5—62no—
439C22×C5—82no—
440C22×C5—82no—
441C22×C5—122no—
442C22×C5—122no—
443C22×C5—248no—
444C22×C5D3×C22⋊C411yescharacteristic
445C22×C5#88211yescharacteristic
446C22×C5#93711yescharacteristic
447C4×C5—62no—
448C4×C5—62no—
449C4×C5D3×C22⋊C411yescharacteristic
450C4×C5#88211yescharacteristic
451C4×C5C2×(C2×D3)⋊C411yescharacteristic
452C4×C5#93711yescharacteristic
453Dic5—81no—
454Dic5—241no—
455C24—21no—
456C24—62no—
457#41—32no—
458#41—32no—
459#41—64no—
460#41—64no—
461#41—64no—
462#41—64no—
463#41—61no—
464#41—61no—
465#41—61no—
466#41—61no—
467#41—61no—
468#41—61no—
469C2×Q8—31no—
470C2×Q8—31no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—32no—
475C2×D4—31no—
476C2×D4—31no—
477C2×D4—62no—
478C2×D4—64no—
479C2×D4—64no—
480C2×D4—64no—
481C2×D4—62no—
482C2×D4—68no—
483C2×D4—68no—
484C2×D4—61no—
485C2×D4—64no—
486C2×D4D3×Dic512yes—
487C2×D4#120112yes—
488C2×D4#120312yes—
489C22×C4—32no—
490C22×C4—62no—
491C22×C4—61no—
492C22×C4C2×D3×D511yescharacteristic
493M16—101no—
494M16—101no—
495M16—301no—
496M16—301no—
497C2×C8—101no—
498C2×C8—301no—
499C4⋊C4—101no—
500C4⋊C4—301no—
501C22⋊C4—101no—
502C22⋊C4—301no—
503C42—101no—
504C42—301no—
505C3×C5#179511yescharacteristic, complemented, Hall
506C22×C3—24no—
507C22×C3—41no—
508C22×C3—44no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3C2×C22⋊Dic511yescharacteristic
512C22×C3#409911yescharacteristic
513C22×C3#409911yescharacteristic
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—42no—
517C2×D3—42no—
518C2×D3—88no—
519C3×C4—401no—
520C3×C4C2×C22⋊Dic511yescharacteristic
521C3×C4C2×C22⋊Dic511yescharacteristic
522C3×C4#409911yescharacteristic
523C3×C4#409911yescharacteristic
524Dic3—22no—
525Dic3—22no—
526Dic3—401no—
527C2×C5—21no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—44no—
531C2×C5—122no—
532C2×C5—122no—
533C2×C5#495511yescharacteristic
534C23—22no—
535C23—22no—
536C23—22no—
537C23—32no—
538C23—68no—
539C23—61no—
540C23—82no—
541C23—244no—
542C23D3×C22⋊D511yescharacteristic
543Q8—32no—
544Q8—61no—
545Q8—61no—
546Q8—61no—
547D4—22no—
548D4—22no—
549D4—22no—
550D4—32no—
551D4—68no—
552D4—68no—
553D4—62no—
554D4—62no—
555D4—62no—
556D4—62no—
557D4—61no—
558D4—61no—
559D4—61no—
560D4(C2×D3)⋊Dic514yes—
561C2×C4—32no—
562C2×C4—68no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—201no—
569C2×C4—601no—
570C2×C4C2×D3×Dic511yescharacteristic
571C2×C4C2×#120111yescharacteristic
572C2×C4C2×#120311yescharacteristic
573C2×C4D3×C22⋊D511yescharacteristic
574C2×C4D3×C22⋊D511yescharacteristic
575C2×C4D3×C22⋊D511yescharacteristic
576C8—201no—
577C8—601no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—44no—
582C2×C3#6553611yescharacteristic
583D3—42no—
584D3—42no—
585C5#7032711yescharacteristic, complemented, Sylow
586C22—24no—
587C22—41no—
588C22—44no—
589C22—62no—
590C22—62no—
591C22—82no—
592C22—82no—
593C22—122no—
594C22—122no—
595C22—248no—
596C22D3×C22⋊Dic511yescharacteristic
597C22#9156811yescharacteristic
598C22#9157011yescharacteristic
599C4—62no—
600C4—62no—
601C4—401no—
602C4—1201no—
603C4C2×(C2×D3)⋊Dic511yescharacteristic
604C4D3×C22⋊Dic511yescharacteristic
605C4#9156811yescharacteristic
606C4#9157011yescharacteristic
607C3#1060293411yescharacteristic, complemented, Sylow
608C2—21no—
609C2—21no—
610C2—21no—
611C2—44no—
612C2—122no—
613C2—122no—
614C2#1174949611yescharacteristic
subgroupG/H
centerC2#11749496
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#379
prime radicalC2×C5×#1004C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1795
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11751316C2semidirect
3. C3×#65504C2semidirect
4. #11748625C2semidirect
5. #11748425C2semidirect
6. #11748424C2semidirect
7. #11748355C2semidirect
16. C2×C5×#237C4semidirect
18. C2×C5×D3×D4C4semidirect
21. #91815C22semidirect
22. C2×#6710C22semidirect
23. C3×#4072C22semidirect
24. C2×C3×#681C22semidirect
39. #65504D3semidirect
110. #4072C2×D3semidirect
112. C2×#681C2×D3semidirect
172. C2×#237Dic5semidirect
174. C2×D3×D4Dic5semidirect
505. C3×C5#1795semidirect
585. C5#70327semidirect
607. C3#10602934semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10042
#117513162
C3×#655042
#117486252
#117484252
#117484242
#117483552
#106029343
#703275