Finite Group Databasebeta

← #14300569

Subgroups — #14300569

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5524C211yesmaximal, characteristic
2C2×D3×#681C211yesmaximal, characteristic, complemented
3C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
4C2×#90979C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic, complemented
6#11746353C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10602506—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#897C411yescharacteristic, complemented
15C5×#897C411yescharacteristic, complemented
16C5×#895C411yescharacteristic, complemented
17C5×#895C411yescharacteristic, complemented
18C5×#886—21no—
19C5×#882—21no—
20C4×C5×D12—21no—
21C4×C5×D12—21no—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×(C2×D3)⋊Dic5—21no—
25C2×#6650—21no—
26D3×#681—22no—
27D3×#681—22no—
28C2×D3×#168—21no—
29#90994—21no—
30#90979—22no—
31#90978—22no—
32#68755—51nomaximal, Hall
33C5×#525—31no—
34C22×#681—31no—
35C2×#3969—31no—
36C2×#3969—31no—
37C4×C22⋊Dic5—31no—
38#64752—31no—
39#64752D311yescharacteristic, complemented
40C23×C5×D3D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×C5×#67—21no—
44C22×C5×Dic3D411yescharacteristic
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C5×#235—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12C2×C411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3—21no—
55C2×C4×C5×D3—21no—
56C2×C4×C5×D3—21no—
57C2×C4×C5×D3C2×C411yescharacteristic
58C2×C4×C5×D3C2×C411yescharacteristic
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3D411yescharacteristic
61C2×C5×Dic6C2×C411yescharacteristic
62C22×C3×Dic5—21no—
63C3×C5×C4⋊C4C2×C411yescharacteristic
64C3×C5×C4⋊C4C2×C411yescharacteristic
65C3×C5×C22⋊C4—21no—
66C3×C42×C5—21no—
67C4×Dic15—21no—
68C4×Dic15—21no—
69#6710—21no—
70#6710D412yescomplemented
71C2×C3⋊#168—21no—
72C5×(C2×D3)⋊C4—21no—
73C5×(C2×D3)⋊C4—21no—
74C5×(C2×D3)⋊C4—21no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3—21no—
78C3×C4×Dic5—21no—
79C3×C4×Dic5—21no—
80C3×#681—21no—
81C3×#681D412yescomplemented
82C2×C3×#168—21no—
83(C2×D3)⋊Dic5—24no—
84#6650—24no—
85D3×#168—24no—
86C2×D3×M16—51no—
87#5524D511yescharacteristic
88C2×#825—51no—
89C4×(C2×D3)⋊C4—51no—
90C2×#805—51no—
91C3×#339—51no—
92#4532—51no—
93C2×C5×#41—31no—
94C23×C4×C5—31no—
95C5×#123—61no—
96C5×C22⋊Q8—31no—
97C5×C22⋊Q8—31no—
98C5×#121—31no—
99C5×#121—31no—
100C5×#120—61no—
101C4×C5×D4—61no—
102C4×C5×D4—61no—
103C5×#117C2×D311yescharacteristic
104C2×C22⋊Dic5—61no—
105C2×C4×Dic5—31no—
106C2×C4×Dic5C2×D311yescharacteristic
107C2×#681—31no—
108C2×#681—61no—
109C2×#681—62no—
110C2×#681—62no—
111C2×#681C2×D311yescharacteristic
112C22×#168—61no—
113#3969—62no—
114#3969—62no—
115#3963—61no—
116#1871—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C5×D3—21no—
119C22×C5×D3—21no—
120C22×C5×D3—22no—
121C22×C5×D3—21no—
122C22×C5×D3—41no—
123C22×C5×D3C22⋊C411yescharacteristic
124C22×C5×D3C22⋊C411yescharacteristic
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5#4111yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×Dic15—22no—
134C2×Dic15—41no—
135C2×Dic15—41no—
136C5×#67—41no—
137C5×#67—41no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3C22⋊C411yescharacteristic
142C2×C5×Dic3C22⋊C411yescharacteristic
143C5×D12—21no—
144C5×D12—21no—
145C5×D12—42no—
146C5×D12—42no—
147C4×C5×D3—21no—
148C4×C5×D3—21no—
149C4×C5×D3—21no—
150C4×C5×D3—21no—
151C4×C5×D3—21no—
152C4×C5×D3—21no—
153C4×C5×D3—21no—
154C4×C5×D3—21no—
155C4×C5×D3—41no—
156C4×C5×D3—41no—
157C5×Dic6—21no—
158C5×Dic6—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—41no—
161C2×C3×Dic5—41no—
162C3⋊#168—22no—
163C3×#168—22no—
164C2×#235C2×D511yescharacteristic
165C22×C4×D3C2×D511yescharacteristic
166C2×C3×M16—51no—
167C3×#117C2×D511yescharacteristic
168C2×C3×C42—51no—
169C2×(C2×D3)⋊C4—101no—
170C2×C4×Dic3—51no—
171C2×#208—51no—
172D3×M16—102no—
173D3×M16—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176#897Dic511yescharacteristic, complemented
177#897Dic511yescharacteristic, complemented
178#895Dic511yescharacteristic, complemented
179#895Dic511yescharacteristic, complemented
180#886—21no—
181#882—21no—
182C4×D12—21no—
183C4×D12—21no—
184C3⋊#95—101no—
185#825—102no—
186#805—102no—
187C24×C5—31no—
188C5×#41—61no—
189C5×#41—61no—
190C5×#41—61no—
191C5×#41—61no—
192C2×C5×Q8—31no—
193C2×C5×D4—31no—
194C2×C5×D4—61no—
195C2×C5×D4—61no—
196C2×C5×D4—61no—
197C22×C4×C5—31no—
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—31no—
202C22×C4×C5—61no—
203C22×C4×C5—61no—
204C22×C4×C5—61no—
205C22×C4×C5—61no—
206C22×C4×C5—61no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—21no—
209C22×Dic5—61no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4C4×D311yescharacteristic
213C5×C4⋊C4C4×D311yescharacteristic
214C5×C22⋊C4—21no—
215C5×C22⋊C4—61no—
216C5×C22⋊C4—61no—
217C5×C22⋊C4—61no—
218C5×C22⋊C4—61no—
219C42×C5—21no—
220C22⋊Dic5—64no—
221C4×Dic5—21no—
222C4×Dic5—21no—
223C4×Dic5—61no—
224C4×Dic5—61no—
225#681—21no—
226#681—32no—
227#681—64no—
228#681—61no—
229#681D1212yescomplemented
230C2×#168—21no—
231C2×#168—64no—
232C2×#168—61no—
233C22×M16—151no—
234#525—31no—
235C2×#104—151no—
236C2×#104—151no—
237C4×C22⋊C4—151no—
238#339—51no—
239#339—151no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5C2×C22⋊C411yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5#12111yescharacteristic
245C2×C5×D3—21no—
246C2×C5×D3—21no—
247C2×C5×D3—21no—
248C2×C5×D3—21no—
249C2×C5×D3—21no—
250C2×C5×D3—42no—
251C2×C5×D3—42no—
252C2×C5×D3—41no—
253C2×C5×D3—41no—
254C2×C5×D3—41no—
255C2×C5×D3#10412yescomplemented
256C3×C4×C5—41no—
257C3×C4×C5—41no—
258C3×C4×C5C4×D411yescharacteristic
259C3×C4×C5C4×D411yescharacteristic
260C3×C4×C5#12011yescharacteristic
261C3×C4×C5#12311yescharacteristic
262Dic15—42no—
263C3×Dic5—42no—
264C5×Dic3—21no—
265C5×Dic3—21no—
266C5×Dic3—41no—
267C23×D3C22⋊D511yescharacteristic
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271C22×Dic3—101no—
272C22×Dic3C22⋊D511yescharacteristic
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12C2×Dic511yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3C2×Dic511yescharacteristic
286C2×C4×D3C2×Dic511yescharacteristic
287C2×C4×D3C22⋊D511yescharacteristic
288C2×C4×D3C22⋊D511yescharacteristic
289C2×Dic6C2×Dic511yescharacteristic
290C3×M16—52no—
291C3×M16—101no—
292C2×C3×C8—101no—
293C3×C4⋊C4C2×Dic511yescharacteristic
294C3×C4⋊C4C2×Dic511yescharacteristic
295C3×C22⋊C4—21no—
296C3×C42—21no—
297C3×C42—101no—
298C3×C42—101no—
299(C2×D3)⋊C4—21no—
300(C2×D3)⋊C4—21no—
301(C2×D3)⋊C4—21no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—104no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4×Dic3—101no—
307C4×Dic3—101no—
308#208—52no—
309#208—101no—
310C2×C3⋊C8—101no—
311ΓL(1,𝔽25)—104no—
312D3×C8—104no—
313C23×C5—31no—
314C23×C5—31no—
315C23×C5—62no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5—61no—
319C23×C5—121no—
320C23×C5D3×D411yescharacteristic
321C5×Q8—61no—
322C5×Q8—61no—
323C5×D4—61no—
324C5×D4—61no—
325C5×D4—122no—
326C5×D4—122no—
327C5×D4—121no—
328C5×D4—121no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—31no—
332C2×C4×C5—31no—
333C2×C4×C5—61no—
334C2×C4×C5—61no—
335C2×C4×C5—61no—
336C2×C4×C5—61no—
337C2×C4×C5—61no—
338C2×C4×C5—61no—
339C2×C4×C5—61no—
340C2×C4×C5—61no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5—61no—
344C2×C4×C5—121no—
345C2×C4×C5—121no—
346C2×C4×C5C2×C4×D311yescharacteristic
347C2×C4×C5C2×D1211yescharacteristic
348C2×C4×C5#23511yescharacteristic
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5#23911yescharacteristic
352C2×Dic5—22no—
353C2×Dic5—41no—
354C2×Dic5—41no—
355C2×Dic5—62no—
356C2×Dic5—121no—
357C2×Dic5—121no—
358#168—22no—
359#168—62no—
360C2×#41—31no—
361C23×C4—31no—
362C2×M16—51no—
363C2×M16—151no—
364C2×M16—301no—
365C2×M16—302no—
366C2×M16—302no—
367C22×C8—301no—
368#123—61no—
369C22⋊Q8—31no—
370C22⋊Q8—31no—
371#121—31no—
372#121—31no—
373#120—61no—
374C4×D4—61no—
375C4×D4—61no—
376#117D3×D511yescharacteristic
377C2×C22⋊C4—301no—
378C2×C42—51no—
379C2×C42—151no—
380#104—302no—
381#104—302no—
382#95—301no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5#38611yescharacteristic
386C2×C3×C5C2×#10411yescharacteristic
387C2×C3×C5#42111yescharacteristic
388C5×D3—22no—
389C5×D3—41no—
390C5×D3—81no—
391C23×C3C2×C22⋊D511yescharacteristic
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—22no—
395C22×D3—21no—
396C22×D3—41no—
397C22×D3C22⋊Dic511yescharacteristic
398C22×D3C22⋊Dic511yescharacteristic
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—102no—
402C2×C3×C4—201no—
403C2×C3×C4—201no—
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4#71111yescharacteristic
407C2×C3×C4#71111yescharacteristic
408C2×C3×C4C22×Dic511yescharacteristic
409C2×C3×C4C2×C22⋊D511yescharacteristic
410#67—41no—
411#67—41no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—102no—
416C2×Dic3—201no—
417C2×Dic3—201no—
418C2×Dic3C22⋊Dic511yescharacteristic
419C2×Dic3C22⋊Dic511yescharacteristic
420D12—21no—
421D12—21no—
422D12—42no—
423D12—42no—
424C4×D3—21no—
425C4×D3—21no—
426C4×D3—21no—
427C4×D3—21no—
428C4×D3—21no—
429C4×D3—21no—
430C4×D3—21no—
431C4×D3—21no—
432C4×D3—41no—
433C4×D3—41no—
434Dic6—21no—
435Dic6—21no—
436C3×C8—102no—
437C3⋊C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—32no—
441C22×C5—61no—
442C22×C5—61no—
443C22×C5—61no—
444C22×C5—61no—
445C22×C5—61no—
446C22×C5—122no—
447C22×C5—122no—
448C22×C5—121no—
449C22×C5—121no—
450C22×C5—121no—
451C22×C5D3×C22⋊C411yescharacteristic
452C22×C5#88411yescharacteristic
453C22×C5#89511yescharacteristic
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—61no—
457C4×C5—61no—
458C4×C5—121no—
459C4×C5C4×D1211yescharacteristic
460C4×C5#88211yescharacteristic
461C4×C5#89311yescharacteristic
462C4×C5#89411yescharacteristic
463Dic5—42no—
464Dic5—122no—
465C24—31no—
466#41—61no—
467#41—61no—
468#41—61no—
469#41—61no—
470C2×Q8—31no—
471C2×D4—31no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—101no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488M16—52no—
489M16—101no—
490M16—152no—
491M16—304no—
492M16—301no—
493C2×C8—101no—
494C2×C8—304no—
495C2×C8—301no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C4⋊C4D3×Dic511yescharacteristic
499C4⋊C4D3×Dic511yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—61no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C22⋊C4—61no—
505C22⋊C4—304no—
506C42—21no—
507C42—101no—
508C42—101no—
509C42—301no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3#408511yescharacteristic
515C22×C3#408511yescharacteristic
516C22×C3C2×C22⋊Dic511yescharacteristic
517C2×D3—21no—
518C2×D3—21no—
519C2×D3—21no—
520C2×D3—21no—
521C2×D3—21no—
522C2×D3—42no—
523C2×D3—42no—
524C2×D3—41no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3#396912yescomplemented
528C3×C4—41no—
529C3×C4—41no—
530C3×C4—202no—
531C3×C4D4×Dic511yescharacteristic
532C3×C4D4×Dic511yescharacteristic
533C3×C4#408111yescharacteristic
534C3×C4#408311yescharacteristic
535Dic3—21no—
536Dic3—21no—
537Dic3—41no—
538Dic3—202no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5—62no—
542C2×C5—121no—
543C2×C5—241no—
544C2×C5#466511yescharacteristic
545C2×C5D3×#10411yescharacteristic
546C2×C5#482111yescharacteristic
547C23—31no—
548C23—31no—
549C23—62no—
550C23—61no—
551C23—61no—
552C23—61no—
553C23—121no—
554C23D3×C22⋊D511yescharacteristic
555Q8—61no—
556Q8—61no—
557D4—61no—
558D4—61no—
559D4—122no—
560D4—122no—
561D4—121no—
562D4—121no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—102no—
579C2×C4—121no—
580C2×C4—121no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—302no—
584C2×C4—601no—
585C2×C4—601no—
586C2×C4#676811yescharacteristic
587C2×C4#677211yescharacteristic
588C2×C4D5×D1211yescharacteristic
589C2×C4#677711yescharacteristic
590C2×C4C2×D3×Dic511yescharacteristic
591C2×C4D3×C22⋊D511yescharacteristic
592C8—102no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3#6550911yescharacteristic
597C2×C3C2×#396911yescharacteristic
598C2×C3#6552511yescharacteristic
599D3—22no—
600D3—41no—
601D3—81no—
602C5#6875511yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—32no—
606C22—61no—
607C22—61no—
608C22—61no—
609C22—61no—
610C22—61no—
611C22—122no—
612C22—122no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22#9141611yescharacteristic
617C22#9145311yescharacteristic
618C22D3×C22⋊Dic511yescharacteristic
619C4—41no—
620C4—41no—
621C4—61no—
622C4—61no—
623C4—121no—
624C4—202no—
625C4—602no—
626C4Dic5×D1211yescharacteristic
627C4#9142311yescharacteristic
628C4#9143511yescharacteristic
629C4#9147511yescharacteristic
630C3#1060250611yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—62no—
634C2—121no—
635C2—241no—
636C2#1174890111yescharacteristic
637C2D3×#396911yescharacteristic
638C2#1174942911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5524C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×D3×#681C2semidirect
3. C4×(C2×D3)⋊Dic5C2semidirect
4. C2×#90979C2semidirect
5. C2×#90978C2semidirect
6. #11746353C2semidirect
7. C3×#64752C2semidirect
14. C5×#897C4semidirect
15. C5×#897C4semidirect
16. C5×#895C4semidirect
17. C5×#895C4semidirect
39. #64752D3semidirect
70. #6710D4semidirect
81. C3×#681D4semidirect
176. #897Dic5semidirect
177. #897Dic5semidirect
178. #895Dic5semidirect
179. #895Dic5semidirect
229. #681D12semidirect
255. C2×C5×D3#104semidirect
511. C3×C5#1871semidirect
527. C2×D3#3969semidirect
602. C5#68755semidirect
630. C3#10602506semidirect

Maximal subgroups

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

subgroupindex
C5×#55242
C2×D3×#6812
C4×(C2×D3)⋊Dic52
C2×#909792
C2×#909782
#117463532
C3×#647522
#106025063
#687555