Finite Group Databasebeta

← #14326201

Subgroups — #14326201

Order 1920.

1744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6771C211yesmaximal, characteristic
2C2×C4×#1204C212yesmaximal, complemented
3#11750767C211yesmaximal, characteristic, complemented
4C5×#4666C211yesmaximal, characteristic, complemented
5C3×#64955C211yesmaximal, characteristic, complemented
6#11748915C212yesmaximal, complemented
7#11748912C212yesmaximal, complemented
8#11748908C212yesmaximal, complemented
9#11748863C211yesmaximal, characteristic, complemented
10#11748782C211yesmaximal, characteristic, complemented
11#11748738C211yesmaximal, characteristic, complemented
12#10605185—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1204C2211yescharacteristic
17C22×#1203C2211yescharacteristic
18C22×#1202C2211yescharacteristic
19C22×#1201C2211yescharacteristic
20C2×#6771—28no—
21C2×#6771C418yescomplemented
22C2×#6714C2212yes—
23C2×C4×Dic15C2212yes—
24C2×C5×(C2×D3)⋊C4C2212yes—
25C2×C4×C5×Dic3C2212yes—
26C2×C3×#685C2212yes—
27C2×C3×C4×Dic5C2212yes—
28C2×Dic3⋊Dic5C2212yes—
29C2×#6669C2212yes—
30C2×#6668C2212yes—
31C2×#6667C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×#6665C2212yes—
34C4×#1204—28no—
35C3×C5×#95C2211yescharacteristic
36#91115C2211yescharacteristic
37C5×C3⋊#95C2211yescharacteristic
38C3×#3963C2211yescharacteristic
39#73454—51nomaximal, Hall
40C22×#709—31no—
41C2×C4×Dic10—32no—
42C4×C5×C22⋊C4—31no—
43#65501—31no—
44#65246—32no—
45#65246—32no—
46#65228—32no—
47#64956—31no—
48#64956—31no—
49#64955—31no—
50#64955D311yescharacteristic, complemented
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×D15C2×C414yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C2×C4×C5×D3—24no—
63C2×C4×C5×D3C2×C414yes—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2311yescharacteristic
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5C2×C414yes—
68C2×#1204C2×C414yes—
69C2×#1204D418yes—
70C2×#1203—24no—
71C2×#1203C2×C414yes—
72C2×#1202—24no—
73C2×#1202C2×C414yes—
74C2×#1201—24no—
75C2×#1201C2×C414yes—
76#6771—232no—
77#6714—24no—
78C4×Dic15—24no—
79C5×(C2×D3)⋊C4—24no—
80C4×C5×Dic3—24no—
81C3×#685—24no—
82C3×C4×Dic5—24no—
83Dic3⋊Dic5—24no—
84#6669—24no—
85#6668—24no—
86#6667—42no—
87(C2×D3)⋊Dic5—42no—
88#6665—42no—
89C22×#235—51no—
90C2×C4×Dic6—52no—
91C3×C4×C22⋊C4—51no—
92#5212—51no—
93#4957—52no—
94#4957—52no—
95#4939—52no—
96#4667—51no—
97#4667—51no—
98#4666—51no—
99#4666D511yescharacteristic, complemented
100C23×C4×C5—31no—
101C22×C22⋊D5—31no—
102C22×C22⋊D5—31no—
103C2×#709—38no—
104C2×#709—68no—
105C22×D20—31no—
106C22×C4×D5—31no—
107C22×C4×D5C2×D311yescharacteristic
108C22×Dic10—31no—
109C2×C5×C22⋊C4—32no—
110C2×C42×C5—32no—
111C2×C22⋊Dic5—32no—
112C2×#685—32no—
113C2×#685—32no—
114C2×#685—32no—
115C2×#685C2×D312yes—
116C2×C4⋊Dic5—32no—
117C2×#683—32no—
118C2×#683—32no—
119C2×C4×Dic5—32no—
120C2×C4×Dic5C2×D312yes—
121C4×Dic10—68no—
122C5×#95—31no—
123C5×#95C2×D311yescharacteristic
124#3963—31no—
125#3963C2×D311yescharacteristic
126#2341—151noSylow
127C23×C3×C5C2411yescharacteristic
128C22×D15—22no—
129C22×D15—22no—
130C22×D15—21no—
131C22×D15—21no—
132C22×D15C22×C412yes—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3—21no—
136C22×C5×D3—21no—
137C22×C5×D3C22×C412yes—
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×Dic15C22×C412yes—
152C2×Dic15C2×D414yes—
153C4×D15—28no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3C22×C412yes—
158C2×C5×Dic3C2×D414yes—
159C4×C5×D3—28no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5C22×C412yes—
164C2×C3×Dic5C2×D414yes—
165C3×C4×D5—28no—
166#1204C22⋊C4116yescomplemented
167#1203—28no—
168#1202—28no—
169#1201—28no—
170C23×C3×C4—51no—
171C22×#67—51no—
172C22×#67—51no—
173C2×#235—58no—
174C2×#235—108no—
175C22×D12—51no—
176C22×C4×D3—51no—
177C22×C4×D3C2×D511yescharacteristic
178C22×Dic6—51no—
179C2×C3×C22⋊C4—52no—
180C2×C3×C42—52no—
181C2×#217—52no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4—52no—
184C2×(C2×D3)⋊C4—52no—
185C2×(C2×D3)⋊C4C2×D512yes—
186C2×C4⋊Dic3—52no—
187C2×Dic3⋊C4—52no—
188C2×Dic3⋊C4—52no—
189C2×C4×Dic3—52no—
190C2×C4×Dic3C2×D512yes—
191C4×Dic6—108no—
192C3×#95—51no—
193C3×#95C2×D511yescharacteristic
194C3⋊#95—51no—
195C3⋊#95C2×D511yescharacteristic
196C24×C5—31no—
197C23×D5—31no—
198C23×D5C22×D311yescharacteristic
199C22×C4×C5—31no—
200C22×C4×C5—34no—
201C22×C4×C5—32no—
202C22×C4×C5—64no—
203C22×C4×C5C22×D311yescharacteristic
204C22×C4×C5C22×D312yes—
205C2×C22⋊D5—34no—
206C2×C22⋊D5—34no—
207C2×C22⋊D5—64no—
208C2×C22⋊D5—64no—
209C22×Dic5—31no—
210C22×Dic5—32no—
211C22×Dic5C22×D312yes—
212C22×Dic5C22×D311yescharacteristic
213#709—632no—
214C2×D20—34no—
215C2×D20—64no—
216C2×C4×D5—24no—
217C2×C4×D5—34no—
218C2×C4×D5—64no—
219C2×C4×D5C4×D314yes—
220C2×Dic10—34no—
221C2×Dic10—38no—
222C5×C22⋊C4—64no—
223C42×C5—64no—
224C22⋊Dic5—122no—
225#685—24no—
226#685—64no—
227#685—122no—
228#685—122no—
229C4⋊Dic5—64no—
230#683—64no—
231#683—64no—
232C4×Dic5—24no—
233C4×Dic5—64no—
234C22×#41—151no—
235C2×C4×Q8—152no—
236#390—152no—
237#390—152no—
238#390—152no—
239#380—151no—
240#380—151no—
241#380—151no—
242C4×C22⋊C4—31no—
243C4×C22⋊C4—51no—
244C4×C22⋊C4—151no—
245C22×C3×C5C23×C411yescharacteristic
246C22×C3×C5C22×D412yes—
247C22×C3×C5C2×#4112yes—
248C22×C3×C5H(5,𝔽2)11yescharacteristic
249C22×C3×C52−1+411yescharacteristic
250C2×D15—22no—
251C2×D15—22no—
252C2×D15—22no—
253C2×D15—42no—
254C2×D15—42no—
255C2×C5×D3—22no—
256C2×C5×D3—22no—
257C2×C5×D3—22no—
258C2×C5×D3—42no—
259C2×C5×D3—42no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—42no—
264C2×C3×D5—42no—
265C3×C4×C5—22no—
266C3×C4×C5—24no—
267Dic15—42no—
268Dic15C2×C22⋊C414yes—
269C3×Dic5—42no—
270C3×Dic5C2×C22⋊C414yes—
271C5×Dic3—42no—
272C5×Dic3C2×C22⋊C414yes—
273C24×C3—51no—
274C23×D3—51no—
275C23×D3C22×D511yescharacteristic
276C22×C3×C4—51no—
277C22×C3×C4—54no—
278C22×C3×C4—52no—
279C22×C3×C4—104no—
280C22×C3×C4C22×D511yescharacteristic
281C22×C3×C4C22×D512yes—
282C2×#67—54no—
283C2×#67—54no—
284C2×#67—104no—
285C2×#67—104no—
286C22×Dic3—51no—
287C22×Dic3—52no—
288C22×Dic3C22×D512yes—
289C22×Dic3C22×D511yescharacteristic
290#235—1032no—
291C2×D12—54no—
292C2×D12—104no—
293C2×C4×D3—24no—
294C2×C4×D3—54no—
295C2×C4×D3—104no—
296C2×C4×D3C4×D514yes—
297C2×Dic6—54no—
298C2×Dic6—58no—
299C3×C22⋊C4—104no—
300C3×C42—104no—
301#217—202no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—104no—
304(C2×D3)⋊C4—202no—
305(C2×D3)⋊C4—202no—
306C4⋊Dic3—104no—
307Dic3⋊C4—104no—
308Dic3⋊C4—104no—
309C4×Dic3—24no—
310C4×Dic3—104no—
311C23×C5—32no—
312C23×C5—62no—
313C23×C5—62no—
314C23×C5—61no—
315C23×C5—61no—
316C23×C5C23×D311yescharacteristic
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—21no—
320C22×D5—21no—
321C22×D5—32no—
322C22×D5—62no—
323C22×D5—62no—
324C22×D5—61no—
325C22×D5—61no—
326C22×D5C2×C4×D312yes—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—32no—
331C2×C4×C5—34no—
332C2×C4×C5—68no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5C2×C4×D312yes—
337C2×C4×C5#23514yescomplemented
338C22⋊D5—68no—
339C22⋊D5—68no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—32no—
344C2×Dic5—34no—
345C2×Dic5—62no—
346C2×Dic5—62no—
347C2×Dic5—62no—
348C2×Dic5C2×C4×D312yes—
349C2×Dic5D3×D414yes—
350D20—68no—
351C4×D5—28no—
352C4×D5—68no—
353Dic10—316no—
354C2×#41—158no—
355C2×#41—308no—
356C22×Q8—151no—
357C22×D4—151no—
358C22×D4—151no—
359C22×D4—151no—
360C23×C4—31no—
361C23×C4—51no—
362C23×C4—151no—
363C4×Q8—308no—
364C2×C4⋊C4—152no—
365C2×C4⋊C4—152no—
366C2×C4⋊C4—152no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—52no—
369C2×C22⋊C4—152no—
370C2×C22⋊C4—152no—
371C2×C22⋊C4—152no—
372C2×C22⋊C4—152no—
373C2×C42—32no—
374C2×C42—52no—
375C2×C42—152no—
376#95—31no—
377#95—51no—
378#95—151no—
379#95D3×D511yescharacteristic
380C2×C3×C5C22×C22⋊C411yescharacteristic
381C2×C3×C5C4×#4111yescharacteristic
382C2×C3×C5#52011yescharacteristic
383C2×C3×C5#54812yes—
384C2×C3×C5#55012yes—
385D15—42no—
386C3×D5—42no—
387C5×D3—42no—
388C23×C3—52no—
389C23×C3—102no—
390C23×C3—102no—
391C23×C3—101no—
392C23×C3—101no—
393C23×C3C23×D511yescharacteristic
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—52no—
399C22×D3—102no—
400C22×D3—102no—
401C22×D3—101no—
402C22×D3—101no—
403C22×D3C2×C4×D512yes—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—52no—
408C2×C3×C4—54no—
409C2×C3×C4—108no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4C2×C4×D512yes—
414C2×C3×C4#70914yescomplemented
415#67—108no—
416#67—108no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—52no—
421C2×Dic3—54no—
422C2×Dic3—102no—
423C2×Dic3—102no—
424C2×Dic3—102no—
425C2×Dic3C2×C4×D512yes—
426C2×Dic3D4×D514yes—
427D12—108no—
428C4×D3—28no—
429C4×D3—108no—
430Dic6—516no—
431C22×C5—62no—
432C22×C5—62no—
433C22×C5—62no—
434C22×C5—122no—
435C22×C5—122no—
436C22×C5C22×C4×D311yescharacteristic
437C22×C5C2×#23512yes—
438C22×C5C2×D3×D412yes—
439C22×C5#100911yescharacteristic
440C22×C5#101011yescharacteristic
441C2×D5—22no—
442C2×D5—22no—
443C2×D5—22no—
444C2×D5—42no—
445C2×D5—42no—
446C2×D5—62no—
447C2×D5—62no—
448C2×D5—62no—
449C2×D5—122no—
450C2×D5—122no—
451C4×C5—22no—
452C4×C5—24no—
453C4×C5—34no—
454C4×C5—122no—
455Dic5—34no—
456Dic5—42no—
457Dic5—122no—
458Dic5D3×C22⋊C414yes—
459C24—31no—
460C24—51no—
461C24—151no—
462#41—3032no—
463C2×Q8—158no—
464C2×Q8—154no—
465C2×D4—154no—
466C2×D4—154no—
467C2×D4—154no—
468C2×D4—304no—
469C2×D4—304no—
470C2×D4—304no—
471C22×C4—31no—
472C22×C4—34no—
473C22×C4—32no—
474C22×C4—51no—
475C22×C4—54no—
476C22×C4—52no—
477C22×C4—64no—
478C22×C4—104no—
479C22×C4—151no—
480C22×C4—154no—
481C22×C4—152no—
482C22×C4—304no—
483C22×C4C2×D3×D512yes—
484C22×C4C2×D3×D511yescharacteristic
485C4⋊C4—304no—
486C4⋊C4—304no—
487C4⋊C4—304no—
488C22⋊C4—64no—
489C22⋊C4—104no—
490C22⋊C4—304no—
491C22⋊C4—602no—
492C22⋊C4—602no—
493C22⋊C4—602no—
494C42—64no—
495C42—104no—
496C42—304no—
497C3×C5#234111yescharacteristic, complemented, Hall
498C22×C3—102no—
499C22×C3—102no—
500C22×C3—102no—
501C22×C3—202no—
502C22×C3—202no—
503C22×C3C22×C4×D511yescharacteristic
504C22×C3C2×#70912yes—
505C22×C3C2×D4×D512yes—
506C22×C3#414911yescharacteristic
507C22×C3#415011yescharacteristic
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—102no—
514C2×D3—102no—
515C2×D3—102no—
516C2×D3—202no—
517C2×D3—202no—
518C3×C4—22no—
519C3×C4—24no—
520C3×C4—54no—
521C3×C4—202no—
522Dic3—42no—
523Dic3—54no—
524Dic3—202no—
525Dic3D5×C22⋊C414yes—
526C2×C5—122no—
527C2×C5C4×#23511yescharacteristic
528C2×C5C2×D3×C22⋊C411yescharacteristic
529C2×C5#552311yescharacteristic
530C2×C5#555212yes—
531C2×C5#555312yes—
532D5—42no—
533D5—122no—
534C23—32no—
535C23—52no—
536C23—62no—
537C23—61no—
538C23—62no—
539C23—61no—
540C23—102no—
541C23—101no—
542C23—102no—
543C23—101no—
544C23—152no—
545C23—302no—
546C23—301no—
547C23—302no—
548C23—301no—
549C23C22×D3×D511yescharacteristic
550Q8—1516no—
551D4—308no—
552D4—308no—
553D4—308no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—32no—
558C2×C4—34no—
559C2×C4—52no—
560C2×C4—54no—
561C2×C4—68no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—108no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—152no—
570C2×C4—154no—
571C2×C4—308no—
572C2×C4—302no—
573C2×C4—302no—
574C2×C4—302no—
575C2×C4#677114yescomplemented
576C2×C4C4×D3×D512yes—
577C2×C3—202no—
578C2×C3C4×#70911yescharacteristic
579C2×C3C2×D5×C22⋊C411yescharacteristic
580C2×C3#6585711yescharacteristic
581C2×C3#6588612yes—
582C2×C3#6588712yes—
583D3—42no—
584D3—202no—
585C5#7345411yescharacteristic, complemented, Sylow
586C22—62no—
587C22—62no—
588C22—62no—
589C22—102no—
590C22—102no—
591C22—102no—
592C22—122no—
593C22—122no—
594C22—202no—
595C22—202no—
596C22—302no—
597C22—302no—
598C22—302no—
599C22—602no—
600C22—602no—
601C22C2×#677112yes—
602C22C2×C4×D3×D511yescharacteristic
603C22#9202011yescharacteristic
604C22D3×D4×D512yes—
605C22#9203511yescharacteristic
606C4—24no—
607C4—22no—
608C4—34no—
609C4—54no—
610C4—122no—
611C4—154no—
612C4—202no—
613C4—602no—
614C3#1060518511yescharacteristic, complemented, Sylow
615C2—122no—
616C2—202no—
617C2—602no—
618C2C4×#677111yescharacteristic
619C2#1175307912yes—
620C2D3×D5×C22⋊C411yescharacteristic
621C2#1175367011yescharacteristic
622C2#1175368712yes—
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#2341
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×#1204C2semidirect
3. #11750767C2semidirect
4. C5×#4666C2semidirect
5. C3×#64955C2semidirect
6. #11748915C2semidirect
7. #11748912C2semidirect
8. #11748908C2semidirect
9. #11748863C2semidirect
10. #11748782C2semidirect
11. #11748738C2semidirect
21. C2×#6771C4semidirect
50. #64955D3semidirect
99. #4666D5semidirect
147. C2×C3×C4×C5#41semidirect
166. #1204C22⋊C4semidirect
337. C2×C4×C5#235semidirect
414. C2×C3×C4#709semidirect
497. C3×C5#2341semidirect
575. C2×C4#6771semidirect
585. C5#73454semidirect
614. C3#10605185semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×C4×#12042
#117507672
C5×#46662
C3×#649552
#117489152
#117489122
#117489082
#117488632
#117487822
#117487382
#106051853
#734545