Finite Group Databasebeta

← #14323869

Subgroups — #14323869

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic
2C2×#91815C211yesmaximal, characteristic, complemented
3C2×#91782C211yesmaximal, characteristic, complemented
4C3×C5×#380C211yesmaximal, characteristic, complemented
5#11751089C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
7#11751073C211yesmaximal, characteristic, complemented
8#11751058C212yesmaximal, complemented
9#11751057C212yesmaximal, complemented
10#11750771C212yesmaximal, complemented
11#11750769C212yesmaximal, complemented
12#10605603—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2212yes—
15C22×D60C2211yescharacteristic
16C22×C4×D15C2212yes—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×#6719C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22#91819C418yescomplemented
23C2×#6714C2212yes—
24C2×#6714C2212yes—
25C2×#6714C2212yes—
26C2×#6714C2212yes—
27#91815—24no—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31C2×#6712C2212yes—
32C2×C4×Dic15C2211yescharacteristic
33C2×C4×Dic15C2212yes—
34C2×C4×Dic15C2211yescharacteristic
35#91782—24no—
36C3×C5×#95C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#73872—51nomaximal, Hall
40C2×#4076—31no—
41C2×#4072—31no—
42C2×#4039—31no—
43C5×#380D311yescharacteristic, complemented
44#65277—31no—
45C4⋊C4×Dic5—31no—
46#65262—31no—
47#65246—32no—
48#65245—32no—
49#64959—32no—
50#64957—32no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2312yes—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—42no—
61C2×#1220—42no—
62C2×#1220C2×C418yescomplemented
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C2×D60—22no—
69C2×D60—22no—
70C2×D60C2×C414yes—
71C2×C4×D15—24no—
72C2×C4×D15—42no—
73C2×C4×D15—42no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C22⋊C4—42no—
77#6719—22no—
78#6719—22no—
79#6714—24no—
80#6714—42no—
81#6714—42no—
82#6714C2×C418yescomplemented
83C4⋊Dic15—22no—
84C4⋊Dic15—22no—
85C4⋊Dic15C2×C414yescomplemented
86#6712—42no—
87C4×Dic15—22no—
88C4×Dic15—42no—
89C4×Dic15D414yescomplemented
90C2×#930—51no—
91C2×#926—51no—
92C2×#893—51no—
93C3×#380D511yescharacteristic, complemented
94#4988—51no—
95Dic3×C4⋊C4—51no—
96#4972—51no—
97#4957—52no—
98#4956—52no—
99#4670—52no—
100#4668—52no—
101C23×C4×C5C2×D311yescharacteristic
102C22×C22⋊D5—32no—
103C22×D20—31no—
104C22×C4×D5—32no—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C2×C5×C4⋊C4C2×D311yescharacteristic
107C2×C5×C22⋊C4C2×D312yes—
108C2×C22⋊Dic5—31no—
109C2×C22⋊Dic5—31no—
110#4076—38no—
111C2×#685—32no—
112C2×#685—32no—
113C2×#685—32no—
114C2×#685—32no—
115#4072—64no—
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—31no—
118C2×C4⋊Dic5—31no—
119C2×#683—32no—
120C2×C4×Dic5—31no—
121C2×C4×Dic5—31no—
122C2×C4×Dic5—32no—
123#4039—64no—
124C5×#95C2×D312yes—
125#3963—32no—
126#3963—32no—
127#2324—151noSylow
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5C22×C412yes—
135C23×C3×C5C2411yescharacteristic
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15—22no—
140C22×D15—22no—
141C22×D15—22no—
142C22×D15C22×C414yes—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—28no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5#4112yes—
156#1220—48no—
157C2×Dic15—21no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—21no—
161C2×Dic15—21no—
162C2×Dic15—21no—
163C2×Dic15—21no—
164C2×Dic15—21no—
165C2×Dic15—21no—
166C2×Dic15—21no—
167C2×Dic15—21no—
168C2×Dic15—21no—
169C2×Dic15C22×C414yes—
170C2×Dic15C2×D412yes—
171C2×Dic15C2×D412yes—
172D60—28no—
173C4×D15—48no—
174C23×C3×C4C2×D511yescharacteristic
175C22×#67—52no—
176C22×D12—51no—
177C22×C4×D3—52no—
178C2×C3×C4⋊C4C2×D511yescharacteristic
179C2×C3×C4⋊C4C2×D511yescharacteristic
180C2×C3×C22⋊C4C2×D512yes—
181C2×#217—51no—
182C2×#217—51no—
183#930—58no—
184C2×(C2×D3)⋊C4—52no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×(C2×D3)⋊C4—52no—
188#926—104no—
189C2×C4⋊Dic3—51no—
190C2×C4⋊Dic3—51no—
191C2×C4⋊Dic3—51no—
192C2×Dic3⋊C4—52no—
193C2×C4×Dic3—51no—
194C2×C4×Dic3—51no—
195C2×C4×Dic3—52no—
196#893—104no—
197C3×#95C2×D512yes—
198C3⋊#95—52no—
199C3⋊#95—52no—
200C24×C5C22×D311yescharacteristic
201C23×D5—32no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5C4×D314yescomplemented
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D312yes—
207C22×C4×C5C22×D311yescharacteristic
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—38no—
210C2×C22⋊D5—122no—
211C2×C22⋊D5—122no—
212C22×Dic5—31no—
213C22×Dic5—31no—
214C22×Dic5—32no—
215C22×Dic5—31no—
216C22×Dic5—31no—
217C2×D20—34no—
218C2×D20—62no—
219C2×D20—62no—
220C2×C4×D5—64no—
221C2×C4×D5—122no—
222C2×C4×D5—122no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C22⋊C4—42no—
226C22⋊Dic5—62no—
227C22⋊Dic5—62no—
228#685—38no—
229#685—64no—
230#685—122no—
231#685—122no—
232C4⋊Dic5—34no—
233C4⋊Dic5—62no—
234C4⋊Dic5—62no—
235#683—122no—
236C4×Dic5—34no—
237C4×Dic5—62no—
238C4×Dic5—122no—
239C2×#121—151no—
240C2×C4×D4—151no—
241C2×#117—151no—
242#390—151no—
243#390—152no—
244#389—151no—
245#388—152no—
246#386—152no—
247#385—152no—
248#380D1511yescharacteristic, complemented
249C4×C4⋊C4—151no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5C23×C411yescharacteristic
258C22×C3×C5C22×D411yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C22×C3×C5H(5,𝔽2)11yescharacteristic
263C22×C3×C52−1+411yescharacteristic
264C2×D15—24no—
265C2×D15—24no—
266C2×D15—24no—
267C2×D15—42no—
268C2×D15—42no—
269C2×D15—42no—
270C2×D15—42no—
271C3×C4×C5—22no—
272C3×C4×C5—42no—
273C3×C4×C5—42no—
274C3×C4×C5C4×D414yes—
275Dic15—24no—
276Dic15—22no—
277Dic15—22no—
278Dic15—41no—
279Dic15—41no—
280C24×C3C22×D511yescharacteristic
281C23×D3—52no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4C4×D514yescomplemented
285C22×C3×C4C22×D512yes—
286C22×C3×C4C22×D512yes—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C2×#67—58no—
290C2×#67—202no—
291C2×#67—202no—
292C22×Dic3—52no—
293C22×Dic3—51no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C2×D12—54no—
298C2×D12—102no—
299C2×D12—102no—
300C2×C4×D3—104no—
301C2×C4×D3—202no—
302C2×C4×D3—202no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C22⋊C4—42no—
306#217—102no—
307#217—102no—
308(C2×D3)⋊C4—58no—
309(C2×D3)⋊C4—104no—
310(C2×D3)⋊C4—202no—
311(C2×D3)⋊C4—202no—
312C4⋊Dic3—54no—
313C4⋊Dic3—102no—
314C4⋊Dic3—102no—
315Dic3⋊C4—202no—
316C4×Dic3—54no—
317C4×Dic3—102no—
318C4×Dic3—202no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5C2×C4×D312yes—
326C23×C5C23×D311yescharacteristic
327C22×D5—34no—
328C22×D5—62no—
329C22×D5—62no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C22×D5—62no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—28no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5C2×C4×D312yes—
344C2×C4×C5C2×C4×D312yes—
345C2×C4×C5D3×D412yes—
346C2×C4×C5#23712yes—
347C22⋊D5—128no—
348C2×Dic5—34no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—61no—
352C2×Dic5—61no—
353C2×Dic5—61no—
354C2×Dic5—62no—
355C2×Dic5—62no—
356C2×Dic5—61no—
357C2×Dic5—61no—
358C2×Dic5—61no—
359C2×Dic5—61no—
360C2×Dic5—61no—
361C2×Dic5—61no—
362C2×Dic5—61no—
363D20—68no—
364C4×D5—128no—
365C22×D4—152no—
366C22×D4—151no—
367C23×C4—152no—
368C23×C4C2×D1511yescharacteristic
369#121—158no—
370C4×D4—304no—
371#117—304no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—151no—
374C2×C4⋊C4—151no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4C2×D1511yescharacteristic
377C2×C4⋊C4C2×D1511yescharacteristic
378C2×C22⋊C4—152no—
379C2×C22⋊C4—151no—
380C2×C22⋊C4—151no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4C2×D1512yes—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42—152no—
388#95—152no—
389#95—152no—
390#95C2×D1512yes—
391C2×C3×C5—42no—
392C2×C3×C5C2×C4×D411yescharacteristic
393C2×C3×C5#51811yescharacteristic
394C2×C3×C5#52011yescharacteristic
395C2×C3×C5#53511yescharacteristic
396C2×C3×C5#53711yescharacteristic
397C2×C3×C5#54011yescharacteristic
398C2×C3×C5#54211yescharacteristic
399D15—44no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3C2×C4×D512yes—
407C23×C3C23×D511yescharacteristic
408C22×D3—54no—
409C22×D3—102no—
410C22×D3—102no—
411C22×D3—102no—
412C22×D3—102no—
413C22×D3—102no—
414C22×D3—102no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4C2×C4×D512yes—
425C2×C3×C4C2×C4×D512yes—
426C2×C3×C4D4×D512yes—
427C2×C3×C4#71112yes—
428#67—208no—
429C2×Dic3—54no—
430C2×Dic3—52no—
431C2×Dic3—52no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—101no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3—101no—
441C2×Dic3—101no—
442C2×Dic3—101no—
443C2×Dic3—101no—
444D12—108no—
445C4×D3—208no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5C22×C4×D311yescharacteristic
454C22×C5C2×D3×D411yescharacteristic
455C22×C5C2×#23711yescharacteristic
456C22×C5#100411yescharacteristic
457C22×C5#100711yescharacteristic
458C22×C5#100911yescharacteristic
459C22×C5#100911yescharacteristic
460C2×D5—64no—
461C2×D5—64no—
462C2×D5—64no—
463C2×D5—122no—
464C2×D5—122no—
465C2×D5—122no—
466C2×D5—122no—
467C4×C5—22no—
468C4×C5—42no—
469C4×C5—42no—
470C4×C5#67⋊C414yes—
471Dic5—64no—
472Dic5—62no—
473Dic5—62no—
474Dic5—121no—
475Dic5—121no—
476C24—152no—
477C24C22×D1511yescharacteristic
478C2×D4—158no—
479C2×D4—154no—
480C2×D4—302no—
481C2×D4—302no—
482C2×D4—602no—
483C2×D4—602no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—152no—
487C22×C4—151no—
488C22×C4—151no—
489C22×C4—151no—
490C22×C4—151no—
491C22×C4—304no—
492C22×C4—602no—
493C22×C4—602no—
494C22×C4C4×D1514yescomplemented
495C22×C4C22×D1512yes—
496C22×C4C22×D1512yes—
497C22×C4C22×D1511yescharacteristic
498C22×C4C22×D1511yescharacteristic
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—154no—
502C4⋊C4—302no—
503C4⋊C4—302no—
504C4⋊C4—602no—
505C22⋊C4—42no—
506C22⋊C4—158no—
507C22⋊C4—304no—
508C22⋊C4—302no—
509C22⋊C4—302no—
510C22⋊C4—602no—
511C22⋊C4—602no—
512C42—154no—
513C42—302no—
514C42—602no—
515C3×C5#232411yescharacteristic, complemented, Hall
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3C22×C4×D511yescharacteristic
524C22×C3C2×D4×D511yescharacteristic
525C22×C3C2×#71111yescharacteristic
526C22×C3#414411yescharacteristic
527C22×C3#414711yescharacteristic
528C22×C3#414911yescharacteristic
529C22×C3#414911yescharacteristic
530C2×D3—104no—
531C2×D3—104no—
532C2×D3—104no—
533C2×D3—202no—
534C2×D3—202no—
535C2×D3—202no—
536C2×D3—202no—
537C3×C4—22no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4#402714yes—
541Dic3—104no—
542Dic3—102no—
543Dic3—102no—
544Dic3—201no—
545Dic3—201no—
546C2×C5—42no—
547C2×C5C2×#67⋊C411yescharacteristic
548C2×C5#550411yescharacteristic
549C2×C5#552111yescharacteristic
550C2×C5#560711yescharacteristic
551C2×C5#561911yescharacteristic
552C2×C5#562911yescharacteristic
553C2×C5#564311yescharacteristic
554D5—124no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—154no—
562C23—302no—
563C23—302no—
564C23—302no—
565C23—302no—
566C23—302no—
567C23—302no—
568C23C2×C4×D1512yes—
569C23C23×D1511yescharacteristic
570D4—308no—
571D4—608no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—28no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—154no—
582C2×C4—152no—
583C2×C4—152no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4—301no—
587C2×C4—302no—
588C2×C4—302no—
589C2×C4—301no—
590C2×C4—301no—
591C2×C4—301no—
592C2×C4—301no—
593C2×C4—301no—
594C2×C4—301no—
595C2×C4—301no—
596C2×C4—608no—
597C2×C4C2×C4×D1512yes—
598C2×C4C2×C4×D1512yes—
599C2×C4D4×D1512yes—
600C2×C4#681912yes—
601C2×C3—42no—
602C2×C3C2×#402711yescharacteristic
603C2×C3#6583811yescharacteristic
604C2×C3#6585511yescharacteristic
605C2×C3#6594111yescharacteristic
606C2×C3#6595311yescharacteristic
607C2×C3#6596311yescharacteristic
608C2×C3#6597711yescharacteristic
609D3—204no—
610C5#7387211yescharacteristic, complemented, Sylow
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—304no—
619C22—304no—
620C22—304no—
621C22—602no—
622C22—602no—
623C22—602no—
624C22—602no—
625C22C22×C4×D1511yescharacteristic
626C22C2×D4×D1511yescharacteristic
627C22C2×#681911yescharacteristic
628C22#9209511yescharacteristic
629C22#9209811yescharacteristic
630C22#9210011yescharacteristic
631C22#9210011yescharacteristic
632C4—22no—
633C4—42no—
634C4—42no—
635C4—302no—
636C4—302no—
637C4—304no—
638C4—601no—
639C4—601no—
640C4#9177014yes—
641C3#1060560311yescharacteristic, complemented, Sylow
642C2—42no—
643C2—604no—
644C2C2×#9177011yescharacteristic
645C2#1175626311yescharacteristic
646C2#1175628011yescharacteristic
647C2#1175636611yescharacteristic
648C2#1175637811yescharacteristic
649C2#1175638811yescharacteristic
650C2#1175640211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenter#380D15
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#91815C2semidirect
3. C2×#91782C2semidirect
4. C3×C5×#380C2semidirect
5. #11751089C2semidirect
6. C4⋊C4×Dic15C2semidirect
7. #11751073C2semidirect
8. #11751058C2semidirect
9. #11751057C2semidirect
10. #11750771C2semidirect
11. #11750769C2semidirect
22. #91819C4semidirect
43. C5×#380D3semidirect
55. C22×C3×C4×C5C2×C4semidirect
62. C2×#1220C2×C4semidirect
82. #6714C2×C4semidirect
85. C4⋊Dic15C2×C4semidirect
89. C4×Dic15D4semidirect
93. C3×#380D5semidirect
204. C22×C4×C5C4×D3semidirect
248. #380D15semidirect
284. C22×C3×C4C4×D5semidirect
494. C22×C4C4×D15semidirect
515. C3×C5#2324semidirect
610. C5#73872semidirect
641. C3#10605603semidirect

Maximal subgroups

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

subgroupindex
C2×#918192
C2×#918152
C2×#917822
C3×C5×#3802
#117510892
C4⋊C4×Dic152
#117510732
#117510582
#117510572
#117507712
#117507692
#106056033
#738725