Finite Group Databasebeta

← #14326054

Subgroups — #14326054

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6771C211yesmaximal, characteristic
2C2×C4×#1203C212yesmaximal, complemented
3D15×#95C211yesmaximal, characteristic, complemented
4C5×D3×#95C211yesmaximal, characteristic, complemented
5C3×#64955C211yesmaximal, characteristic, complemented
6#11748933C212yesmaximal, complemented
7#11748917C212yesmaximal, complemented
8#11748910C212yesmaximal, complemented
9#11748777C211yesmaximal, characteristic, complemented
10#11748738C211yesmaximal, characteristic, complemented
11#11748606C211yesmaximal, characteristic, complemented
12#10605099—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×#1204C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C2×#6771—28no—
23C2×#6771C418yescomplemented
24C2×C3×#685C2212yes—
25C2×C3×C4×Dic5C2212yes—
26C2×#6668C2212yes—
27C2×#6667C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×#6665C2212yes—
30C4×#1203—28no—
31C3×C5×#95C2211yescharacteristic
32#91115C2212yes—
33#91115C2211yescharacteristic
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2211yescharacteristic
36C3×#3963C2211yescharacteristic
37#90994C2212yes—
38#90994C2212yes—
39#73573—51nomaximal, Hall
40C22×#709—31no—
41C2×C4×C22⋊D5—32no—
42C2×C5×#95—31no—
43#65502—32no—
44#65500—31no—
45#64956—31no—
46#64955D311yescharacteristic, complemented
47#64954—32no—
48#64953—31no—
49D5×#95—31no—
50#64935—32no—
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C23×C3×D5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2312yes—
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C2×C4×D15—24no—
59C2×C4×D15—24no—
60C2×C4×D15—24no—
61C2×C4×D15—42no—
62C2×C4×D15C2×C414yescomplemented
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—24no—
66C2×C4×C5×D3—24no—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—42no—
69C2×C4×C5×D3C2×C414yescomplemented
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5—24no—
73C2×C3×C4×D5C2×C414yescomplemented
74C2×#1204—24no—
75C2×#1204C2×C414yescomplemented
76C2×#1203C2×C414yes—
77C2×#1203D418yes—
78C2×#1202—24no—
79C2×#1202C2×C414yescomplemented
80C2×#1201—24no—
81C2×#1201C2×C414yescomplemented
82#6771—232no—
83C3×#685—24no—
84C3×C4×Dic5—24no—
85#6668—24no—
86#6667—24no—
87(C2×D3)⋊Dic5—24no—
88#6665—42no—
89C22×#235—51no—
90C2×C4×D12—52no—
91C3×C4×C22⋊C4—51no—
92#5212—51no—
93#4956—52no—
94#4956—52no—
95#4929—52no—
96#4664—51no—
97#4664—51no—
98D3×#95—51no—
99D3×#95D511yescharacteristic, complemented
100C23×C4×C5—31no—
101C23×C4×C5—32no—
102C22×C22⋊D5—31no—
103C22×C22⋊D5—31no—
104C2×#709—38no—
105C2×#709—68no—
106C22×D20—31no—
107C22×C4×D5—31no—
108C22×C4×D5—32no—
109C22×C4×D5C2×D311yescharacteristic
110C22×Dic10—31no—
111C2×C22⋊Dic5—32no—
112C4×C22⋊D5—68no—
113C2×#685—32no—
114C2×#685—32no—
115C2×#685C2×D312yes—
116C2×#683—32no—
117C2×C4×Dic5C2×D312yes—
118C5×#95—32no—
119C5×#95—31no—
120C5×#95C2×D311yescharacteristic
121#3963—32no—
122#3963—31no—
123#3963—32no—
124#3963—32no—
125#3963C2×D311yescharacteristic
126#2339—151noSylow
127C23×C3×C5C2411yescharacteristic
128C22×D15—22no—
129C22×D15—21no—
130C22×D15—21no—
131C22×D15C22×C412yes—
132C22×D15C2×D414yes—
133C22×C5×D3—22no—
134C22×C5×D3—21no—
135C22×C5×D3—21no—
136C22×C5×D3C22×C412yes—
137C22×C5×D3C2×D414yes—
138C22×C3×D5—22no—
139C22×C3×D5—22no—
140C22×C3×D5—21no—
141C22×C3×D5—21no—
142C22×C3×D5C22×C412yes—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5#4114yescomplemented
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15C22×C412yes—
153C4×D15—28no—
154C4×D15—48no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3C22×C412yes—
160C4×C5×D3—28no—
161C4×C5×D3—48no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5C22×C412yes—
166C2×C3×Dic5C2×D414yes—
167C3×C4×D5—28no—
168#1204—28no—
169#1203C22⋊C4116yescomplemented
170#1202—28no—
171#1201—28no—
172C23×C3×C4—51no—
173C22×#67—51no—
174C22×#67—51no—
175C2×#235—58no—
176C2×#235—108no—
177C22×D12—51no—
178C22×C4×D3—51no—
179C22×C4×D3—52no—
180C22×C4×D3C2×D512yes—
181C22×C4×D3C2×D511yescharacteristic
182C22×Dic6—51no—
183C2×C3×C22⋊C4—52no—
184C2×C3×C42—52no—
185C2×#217—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×(C2×D3)⋊C4—52no—
188C2×C4⋊Dic3—52no—
189C4×D12—108no—
190C3×#95—51no—
191C3×#95C2×D511yescharacteristic
192C3⋊#95—51no—
193C3⋊#95—52no—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95C2×D511yescharacteristic
197C3⋊#95C2×D512yes—
198C24×C5—31no—
199C23×D5—31no—
200C23×D5C22×D311yescharacteristic
201C22×C4×C5—31no—
202C22×C4×C5—34no—
203C22×C4×C5—32no—
204C22×C4×C5—64no—
205C22×C4×C5—64no—
206C22×C4×C5—64no—
207C22×C4×C5—122no—
208C22×C4×C5C22×D311yescharacteristic
209C22×C4×C5C22×D312yes—
210C2×C22⋊D5—34no—
211C2×C22⋊D5—34no—
212C2×C22⋊D5—38no—
213C2×C22⋊D5—64no—
214C22×Dic5—31no—
215C22×Dic5—32no—
216C22×Dic5C22×D312yes—
217C22×Dic5C22×D311yescharacteristic
218#709—632no—
219C2×D20—34no—
220C2×D20—64no—
221C2×C4×D5—24no—
222C2×C4×D5—34no—
223C2×C4×D5—64no—
224C2×C4×D5—64no—
225C2×C4×D5—64no—
226C2×C4×D5—122no—
227C2×C4×D5C4×D314yescomplemented
228C2×Dic10—34no—
229C2×Dic10—64no—
230C22⋊Dic5—64no—
231#685—24no—
232#685—64no—
233#685—122no—
234#683—64no—
235C4×Dic5—24no—
236C22×#41—151no—
237C2×C4×D4—152no—
238#391—152no—
239#386—152no—
240#386—152no—
241#381—151no—
242#381—151no—
243#380—151no—
244C4×C22⋊C4—51no—
245C2×#95—31no—
246C2×#95—151no—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D412yes—
249C22×C3×C5C2×#4112yes—
250C22×C3×C5H(5,𝔽2)11yescharacteristic
251C22×C3×C52−1+411yescharacteristic
252C2×D15—22no—
253C2×D15—22no—
254C2×D15—24no—
255C2×D15—24no—
256C2×D15C2×C22⋊C414yes—
257C2×C5×D3—22no—
258C2×C5×D3—22no—
259C2×C5×D3—24no—
260C2×C5×D3—24no—
261C2×C5×D3C2×C22⋊C414yes—
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—42no—
266C2×C3×D5—42no—
267C3×C4×C5—22no—
268C3×C4×C5—24no—
269Dic15—22no—
270Dic15—42no—
271C3×Dic5—42no—
272C3×Dic5C2×C22⋊C414yes—
273C5×Dic3—22no—
274C5×Dic3—42no—
275C24×C3—51no—
276C23×D3—51no—
277C23×D3C22×D511yescharacteristic
278C22×C3×C4—51no—
279C22×C3×C4—54no—
280C22×C3×C4—52no—
281C22×C3×C4—104no—
282C22×C3×C4C22×D511yescharacteristic
283C22×C3×C4C22×D512yes—
284C2×#67—54no—
285C2×#67—54no—
286C2×#67—104no—
287C2×#67—104no—
288C22×Dic3—51no—
289C22×Dic3—52no—
290C22×Dic3C22×D512yes—
291C22×Dic3C22×D511yescharacteristic
292#235—1032no—
293C2×D12—54no—
294C2×D12—58no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3—42no—
299C2×C4×D3—54no—
300C2×C4×D3—104no—
301C2×C4×D3—104no—
302C2×C4×D3—104no—
303C2×C4×D3—202no—
304C2×C4×D3C4×D514yescomplemented
305C2×Dic6—54no—
306C2×Dic6—104no—
307C3×C22⋊C4—104no—
308C3×C42—104no—
309#217—202no—
310(C2×D3)⋊C4—104no—
311(C2×D3)⋊C4—104no—
312C4⋊Dic3—104no—
313C23×C5—32no—
314C23×C5—34no—
315C23×C5—62no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5C23×D311yescharacteristic
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—32no—
324C22×D5—34no—
325C22×D5—62no—
326C22×D5—61no—
327C22×D5—61no—
328C22×D5C2×C4×D312yes—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—32no—
333C2×C4×C5—68no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5—128no—
339C2×C4×C5C2×C4×D312yes—
340C2×C4×C5#23514yescomplemented
341C22⋊D5—316no—
342C22⋊D5—68no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—32no—
347C2×Dic5—62no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5—62no—
351C2×Dic5C2×C4×D312yes—
352C2×Dic5D3×D414yes—
353D20—68no—
354C4×D5—28no—
355C4×D5—68no—
356C4×D5—128no—
357Dic10—68no—
358C2×#41—158no—
359C2×#41—308no—
360C22×Q8—151no—
361C22×D4—151no—
362C22×D4—151no—
363C22×D4—151no—
364C23×C4—31no—
365C23×C4—32no—
366C23×C4—51no—
367C23×C4—151no—
368C23×C4—152no—
369C4×D4—308no—
370C2×C4⋊C4—152no—
371C2×C22⋊C4—52no—
372C2×C22⋊C4—152no—
373C2×C22⋊C4—152no—
374C2×C22⋊C4—152no—
375C2×C42—52no—
376#95—31no—
377#95—32no—
378#95—51no—
379#95—152no—
380#95—152no—
381#95—151no—
382#95—152no—
383#95D3×D511yescharacteristic
384C2×C3×C5C22×C22⋊C411yescharacteristic
385C2×C3×C5C4×#4111yescharacteristic
386C2×C3×C5#52011yescharacteristic
387C2×C3×C5#54612yes—
388C2×C3×C5#54712yes—
389D15—24no—
390C3×D5—42no—
391C5×D3—24no—
392C23×C3—52no—
393C23×C3—102no—
394C23×C3—102no—
395C23×C3—101no—
396C23×C3—101no—
397C23×C3C23×D511yescharacteristic
398C22×D3—22no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—52no—
402C22×D3—54no—
403C22×D3—102no—
404C22×D3—101no—
405C22×D3—101no—
406C22×D3C2×C4×D512yes—
407C22×D3D4×D514yes—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—52no—
412C2×C3×C4—54no—
413C2×C3×C4—108no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4C2×C4×D512yes—
418C2×C3×C4#70914yescomplemented
419#67—108no—
420#67—108no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—52no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3—102no—
430C2×Dic3C2×C4×D512yes—
431D12—516no—
432C4×D3—28no—
433C4×D3—48no—
434C4×D3—108no—
435C4×D3—208no—
436Dic6—108no—
437C22×C5—34no—
438C22×C5—62no—
439C22×C5—62no—
440C22×C5—64no—
441C22×C5—64no—
442C22×C5C22×C4×D311yescharacteristic
443C22×C5C2×#23512yes—
444C22×C5C2×D3×D412yes—
445C22×C5#100911yescharacteristic
446C22×C5#101011yescharacteristic
447C2×D5—22no—
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—34no—
451C2×D5—42no—
452C2×D5—42no—
453C2×D5—62no—
454C2×D5—62no—
455C2×D5—64no—
456C2×D5—64no—
457C4×C5—22no—
458C4×C5—24no—
459C4×C5—62no—
460C4×C5—122no—
461Dic5—42no—
462Dic5—62no—
463Dic5—122no—
464Dic5D3×C22⋊C414yes—
465C24—31no—
466C24—51no—
467C24—151no—
468#41—3032no—
469C2×Q8—154no—
470C2×Q8—304no—
471C2×D4—154no—
472C2×D4—158no—
473C2×D4—154no—
474C2×D4—154no—
475C2×D4—304no—
476C2×D4—304no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—32no—
480C22×C4—51no—
481C22×C4—54no—
482C22×C4—52no—
483C22×C4—64no—
484C22×C4—64no—
485C22×C4—64no—
486C22×C4—104no—
487C22×C4—122no—
488C22×C4—151no—
489C22×C4—154no—
490C22×C4—152no—
491C22×C4—304no—
492C22×C4—304no—
493C22×C4—304no—
494C22×C4—602no—
495C22×C4C2×D3×D512yes—
496C22×C4C2×D3×D511yescharacteristic
497C4⋊C4—304no—
498C22⋊C4—104no—
499C22⋊C4—304no—
500C22⋊C4—304no—
501C22⋊C4—602no—
502C42—104no—
503C3×C5#233911yescharacteristic, complemented, Hall
504C22×C3—102no—
505C22×C3—102no—
506C22×C3—102no—
507C22×C3—202no—
508C22×C3—202no—
509C22×C3C22×C4×D511yescharacteristic
510C22×C3C2×#70912yes—
511C22×C3C2×D4×D512yes—
512C22×C3#414411yescharacteristic
513C22×C3#414711yescharacteristic
514C2×D3—22no—
515C2×D3—24no—
516C2×D3—22no—
517C2×D3—24no—
518C2×D3—54no—
519C2×D3—102no—
520C2×D3—104no—
521C2×D3—102no—
522C2×D3—104no—
523C2×D3D5×C22⋊C414yes—
524C3×C4—22no—
525C3×C4—24no—
526C3×C4—54no—
527C3×C4—202no—
528Dic3—22no—
529Dic3—42no—
530Dic3—102no—
531Dic3—202no—
532C2×C5—64no—
533C2×C5C4×#23511yescharacteristic
534C2×C5C2×D3×C22⋊C411yescharacteristic
535C2×C5#552311yescharacteristic
536C2×C5#555012yes—
537C2×C5#555112yes—
538D5—42no—
539D5—64no—
540C23—32no—
541C23—34no—
542C23—52no—
543C23—62no—
544C23—61no—
545C23—61no—
546C23—102no—
547C23—102no—
548C23—101no—
549C23—101no—
550C23—152no—
551C23—154no—
552C23—302no—
553C23—301no—
554C23—301no—
555C23C22×D3×D511yescharacteristic
556Q8—308no—
557D4—1516no—
558D4—308no—
559D4—308no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—32no—
564C2×C4—52no—
565C2×C4—54no—
566C2×C4—68no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—108no—
572C2×C4—102no—
573C2×C4—102no—
574C2×C4—102no—
575C2×C4—128no—
576C2×C4—152no—
577C2×C4—308no—
578C2×C4—302no—
579C2×C4—302no—
580C2×C4—302no—
581C2×C4—302no—
582C2×C4—608no—
583C2×C4#677114yescomplemented
584C2×C4C4×D3×D512yes—
585C2×C3—202no—
586C2×C3C4×#70911yescharacteristic
587C2×C3C2×D5×C22⋊C411yescharacteristic
588C2×C3#6582412yes—
589C2×C3#6583811yescharacteristic
590C2×C3#6584112yes—
591D3—24no—
592D3—104no—
593C5#7357311yescharacteristic, complemented, Sylow
594C22—34no—
595C22—64no—
596C22—62no—
597C22—64no—
598C22—62no—
599C22—102no—
600C22—102no—
601C22—102no—
602C22—154no—
603C22—202no—
604C22—202no—
605C22—304no—
606C22—302no—
607C22—304no—
608C22—302no—
609C22C2×#677112yes—
610C22C2×C4×D3×D511yescharacteristic
611C22D3×D4×D512yes—
612C22#9202711yescharacteristic
613C22#9202811yescharacteristic
614C4—24no—
615C4—22no—
616C4—54no—
617C4—62no—
618C4—122no—
619C4—202no—
620C4—302no—
621C4—602no—
622C3#1060509911yescharacteristic, complemented, Sylow
623C2—64no—
624C2—202no—
625C2—304no—
626C2C4×#677111yescharacteristic
627C2#1175307612yes—
628C2D3×D5×C22⋊C411yescharacteristic
629C2#1175366911yescharacteristic
630C2#1175368412yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6771C2
hypercenter#95D3×D5
hypocenterC3×C5#2339
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1203C2semidirect
3. D15×#95C2semidirect
4. C5×D3×#95C2semidirect
5. C3×#64955C2semidirect
6. #11748933C2semidirect
7. #11748917C2semidirect
8. #11748910C2semidirect
9. #11748777C2semidirect
10. #11748738C2semidirect
11. #11748606C2semidirect
23. C2×#6771C4semidirect
46. #64955D3semidirect
62. C2×C4×D15C2×C4semidirect
69. C2×C4×C5×D3C2×C4semidirect
73. C2×C3×C4×D5C2×C4semidirect
75. C2×#1204C2×C4semidirect
79. C2×#1202C2×C4semidirect
81. C2×#1201C2×C4semidirect
99. D3×#95D5semidirect
147. C2×C3×C4×C5#41semidirect
169. #1203C22⋊C4semidirect
227. C2×C4×D5C4×D3semidirect
304. C2×C4×D3C4×D5semidirect
340. C2×C4×C5#235semidirect
418. C2×C3×C4#709semidirect
503. C3×C5#2339semidirect
583. C2×C4#6771semidirect
593. C5#73573semidirect
622. C3#10605099semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×C4×#12032
D15×#952
C5×D3×#952
C3×#649552
#117489332
#117489172
#117489102
#117487772
#117487382
#117486062
#106050993
#735735