Finite Group Databasebeta

← #14323710

Subgroups — #14323710

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic
2C2×#91813C211yesmaximal, characteristic
3C2×C4×Dic30C211yesmaximal, characteristic, complemented
4#11751313C211yesmaximal, characteristic
5#11751079C212yesmaximal, complemented
6#11751077C212yesmaximal, complemented
7#11751046C212yesmaximal
8#11751045C212yesmaximal
9C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
10#11751030C211yesmaximal, characteristic, complemented
11#11751029C211yesmaximal, characteristic, complemented
12#10613966—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C3×C5×#117—24no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6719C2212yes—
23C2×#6719C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27#91813C418yescomplemented
28C2×#6712C2212yes—
29C2×#6712C2212yes—
30C2×#6712C2212yes—
31C2×C4×Dic15C2212yes—
32C2×C4×Dic15C2212yes—
33C4×Dic30—24no—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#82235—51nomaximal, Hall
40C2×C5×#117D311yescharacteristic
41C2×#4070—31no—
42C2×C4×Dic10—31no—
43#65501—31no—
44#65267—32no—
45#65261—32no—
46#65234—32no—
47#65233—32no—
48C4×C4⋊Dic5—31no—
49#65218—31no—
50#65217—31no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15C2312yes—
62C22×Dic15C2312yes—
63C22×Dic15C2312yes—
64C22×Dic15C2312yes—
65C2×Dic30—22no—
66C2×Dic30—22no—
67C2×Dic30C2×C414yes—
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—22no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4—22no—
72C3×C42×C5—22no—
73C3×C42×C5D414yes—
74#6719—42no—
75#6719C2×C418yes—
76C4⋊Dic15—22no—
77C4⋊Dic15—22no—
78C4⋊Dic15C2×C414yes—
79#6712—24no—
80#6712—42no—
81#6712C2×C418yes—
82C4×Dic15—24no—
83C4×Dic15—42no—
84C2×C3×#117D511yescharacteristic
85C2×#924—51no—
86C2×C4×Dic6—51no—
87#5212—51no—
88#4978—52no—
89#4976—52no—
90#4945—52no—
91#4944—52no—
92C4×C4⋊Dic3—51no—
93#4929—51no—
94#4928—51no—
95C23×C4×C5C2×D311yescharacteristic
96C22×Dic10—31no—
97C5×#117—24no—
98C2×C5×C4⋊C4C2×D311yescharacteristic
99C2×C5×C4⋊C4C2×D311yescharacteristic
100C2×C5×C22⋊C4C2×D311yescharacteristic
101C2×C5×C22⋊C4C2×D311yescharacteristic
102C2×C42×C5C2×D311yescharacteristic
103C2×C42×C5C2×D311yescharacteristic
104C2×C22⋊Dic5—32no—
105C2×C22⋊Dic5—32no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5—31no—
108C2×C4⋊Dic5—31no—
109#4070—38no—
110C2×#683—32no—
111C2×#683—32no—
112C2×#683—32no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115C4×Dic10—64no—
116#3963—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#2323—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5C22×C412yes—
129C23×C3×C5C2411yescharacteristic
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—28no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15C22×C414yes—
160C2×Dic15C22×C414yes—
161Dic30—28no—
162C23×C3×C4C2×D511yescharacteristic
163C22×Dic6—51no—
164C3×#117—24no—
165C2×C3×C4⋊C4C2×D511yescharacteristic
166C2×C3×C4⋊C4C2×D511yescharacteristic
167C2×C3×C22⋊C4C2×D511yescharacteristic
168C2×C3×C22⋊C4C2×D511yescharacteristic
169C2×C3×C42C2×D511yescharacteristic
170C2×C3×C42C2×D511yescharacteristic
171C2×#217—52no—
172C2×#217—52no—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3—51no—
176#924—58no—
177C2×Dic3⋊C4—52no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—52no—
181C2×C4×Dic3—52no—
182C4×Dic6—104no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C24×C5C22×D311yescharacteristic
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5C4×D314yes—
192C22×C4×C5C22×D311yescharacteristic
193C22×C4×C5C22×D311yescharacteristic
194C22×C4×C5C22×D311yescharacteristic
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—32no—
199C22×Dic5—32no—
200C22×Dic5—32no—
201C22×Dic5—32no—
202C2×Dic10—34no—
203C2×Dic10—62no—
204C2×Dic10—62no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C22⋊C4—22no—
208C5×C22⋊C4—22no—
209C42×C5—22no—
210C42×C5#6714yes—
211C22⋊Dic5—38no—
212C22⋊Dic5—122no—
213C4⋊Dic5—34no—
214C4⋊Dic5—62no—
215C4⋊Dic5—62no—
216#683—38no—
217#683—64no—
218#683—122no—
219C4×Dic5—64no—
220C4×Dic5—122no—
221C2×C22⋊Q8—151no—
222C2×C4×Q8—151no—
223C2×#117D1511yescharacteristic
224#391—151no—
225#389—152no—
226#389—151no—
227#388—152no—
228#388—152no—
229#387—152no—
230#380—151no—
231C4×C4⋊C4—151no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5C23×C411yescharacteristic
240C22×C3×C5C22×D411yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5H(5,𝔽2)11yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C22×C3×C52−1+411yescharacteristic
245C22×C3×C52−1+411yescharacteristic
246C3×C4×C5—22no—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249C3×C4×C5—41no—
250C3×C4×C5—41no—
251C3×C4×C5C4×D414yes—
252Dic15—24no—
253Dic15—24no—
254Dic15—42no—
255Dic15—42no—
256C24×C3C22×D511yescharacteristic
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4C4×D514yes—
260C22×C3×C4C22×D511yescharacteristic
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—52no—
267C22×Dic3—52no—
268C22×Dic3—52no—
269C22×Dic3—52no—
270C2×Dic6—54no—
271C2×Dic6—102no—
272C2×Dic6—102no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C42—22no—
278C3×C42C22⋊D514yes—
279#217—58no—
280#217—202no—
281C4⋊Dic3—54no—
282C4⋊Dic3—102no—
283C4⋊Dic3—102no—
284Dic3⋊C4—58no—
285Dic3⋊C4—104no—
286Dic3⋊C4—202no—
287C4×Dic3—104no—
288C4×Dic3—202no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5C2×C4×D312yes—
296C23×C5C23×D311yescharacteristic
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—28no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5C2×C4×D312yes—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5#23512yes—
313C2×C4×C5C2×#6712yes—
314C2×C4×C5C2×#6712yes—
315C2×C4×C5C2×#6712yes—
316C2×Dic5—34no—
317C2×Dic5—34no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328Dic10—68no—
329C22×Q8—151no—
330C23×C4C2×D1511yescharacteristic
331C22⋊Q8—158no—
332C4×Q8—304no—
333#117—24no—
334C2×C4⋊C4—151no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—151no—
337C2×C4⋊C4—152no—
338C2×C4⋊C4—151no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4C2×D1511yescharacteristic
341C2×C4⋊C4C2×D1511yescharacteristic
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4C2×D1511yescharacteristic
345C2×C22⋊C4C2×D1511yescharacteristic
346C2×C42—152no—
347C2×C42—152no—
348C2×C42C2×D1511yescharacteristic
349C2×C42C2×D1511yescharacteristic
350#95—152no—
351#95—152no—
352#95—152no—
353#95—152no—
354#95—152no—
355C2×C3×C5—42no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#51911yescharacteristic
358C2×C3×C5#52011yescharacteristic
359C2×C3×C5#53611yescharacteristic
360C2×C3×C5#53711yescharacteristic
361C2×C3×C5#54111yescharacteristic
362C2×C3×C5#54211yescharacteristic
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3C2×C4×D512yes—
370C23×C3C23×D511yescharacteristic
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—28no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4C2×C4×D512yes—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4#70912yes—
387C2×C3×C4C2×C22⋊D512yes—
388C2×C3×C4C2×C22⋊D512yes—
389C2×C3×C4C2×C22⋊D512yes—
390C2×Dic3—54no—
391C2×Dic3—54no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402Dic6—108no—
403C22×C5—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5C22×C4×D311yescharacteristic
411C22×C5C2×#23511yescharacteristic
412C22×C5#100911yescharacteristic
413C22×C5#101011yescharacteristic
414C22×C5#101011yescharacteristic
415C22×C5#101011yescharacteristic
416C22×C5C22×#6711yescharacteristic
417C4×C5—22no—
418C4×C5—22no—
419C4×C5—22no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5C4×#6714yes—
423Dic5—64no—
424Dic5—64no—
425Dic5—122no—
426Dic5—122no—
427C24C22×D1511yescharacteristic
428C2×Q8—154no—
429C2×Q8—302no—
430C2×Q8—302no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—152no—
434C22×C4—152no—
435C22×C4—152no—
436C22×C4—152no—
437C22×C4C4×D1514yes—
438C22×C4C22×D1511yescharacteristic
439C22×C4C22×D1511yescharacteristic
440C22×C4C22×D1511yescharacteristic
441C22×C4C22×D1511yescharacteristic
442C22×C4C22×D1511yescharacteristic
443C22×C4C22×D1511yescharacteristic
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—158no—
447C4⋊C4—154no—
448C4⋊C4—302no—
449C4⋊C4—304no—
450C4⋊C4—302no—
451C4⋊C4—602no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—158no—
455C22⋊C4—602no—
456C42—22no—
457C42—304no—
458C42—602no—
459C42#122014yes—
460C3×C5#232311yescharacteristic, complemented, Hall
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3C22×C4×D511yescharacteristic
469C22×C3C2×#70911yescharacteristic
470C22×C3#414911yescharacteristic
471C22×C3#415011yescharacteristic
472C22×C3#415011yescharacteristic
473C22×C3#415011yescharacteristic
474C22×C3C22×C22⋊D511yescharacteristic
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4C4×C22⋊D514yes—
481Dic3—104no—
482Dic3—104no—
483Dic3—202no—
484Dic3—202no—
485C2×C5—42no—
486C2×C5#551611yescharacteristic
487C2×C5#551811yescharacteristic
488C2×C5#552311yescharacteristic
489C2×C5#553411yescharacteristic
490C2×C5C2×C4×#6711yescharacteristic
491C2×C5#582511yescharacteristic
492C2×C5#583311yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23C2×C4×D1512yes—
500C23C23×D1511yescharacteristic
501Q8—308no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—28no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—154no—
516C2×C4—154no—
517C2×C4—302no—
518C2×C4—302no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4C2×C4×D1512yes—
528C2×C4C2×C4×D1512yes—
529C2×C4#681712yes—
530C2×C4C2×#122012yes—
531C2×C4C2×#122012yes—
532C2×C4C2×#122012yes—
533C2×C3—42no—
534C2×C3#6585011yescharacteristic
535C2×C3#6585211yescharacteristic
536C2×C3#6585711yescharacteristic
537C2×C3#6586811yescharacteristic
538C2×C3C2×C4×C22⋊D511yescharacteristic
539C2×C3#6615911yescharacteristic
540C2×C3#6616711yescharacteristic
541C5#8223511yescharacteristic, complemented, Sylow
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22C22×C4×D1511yescharacteristic
550C22C2×#681711yescharacteristic
551C22#9210011yescharacteristic
552C22#9210111yescharacteristic
553C22#9210111yescharacteristic
554C22#9210111yescharacteristic
555C22C22×#122011yescharacteristic
556C4—22no—
557C4—22no—
558C4—22no—
559C4—41no—
560C4—41no—
561C4—304no—
562C4—304no—
563C4—602no—
564C4—602no—
565C4C4×#122014yes—
566C3#1061396611yescharacteristic, complemented, Sylow
567C2—42no—
568C2#1175627511yescharacteristic
569C2#1175627711yescharacteristic
570C2#1175628211yescharacteristic
571C2#1175629311yescharacteristic
572C2C2×C4×#122011yescharacteristic
573C2#1175658411yescharacteristic
574C2#1175659211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×#117C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×#117D15
hypocenterC3×C5#2323
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic30C2semidirect
5. #11751079C2semidirect
6. #11751077C2semidirect
9. C4×C4⋊Dic15C2semidirect
10. #11751030C2semidirect
11. #11751029C2semidirect
27. #91813C4semidirect
460. C3×C5#2323semidirect
541. C5#82235semidirect
566. C3#10613966semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×#918132
C2×C4×Dic302
#117513132
#117510792
#117510772
#117510462
#117510452
C4×C4⋊Dic152
#117510302
#117510292
#106139663
#822355