Finite Group Databasebeta

← #14327709

Subgroups — #14327709

Order 1920.

1264 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
1C2×#91781C211yesmaximal, characteristic, complemented
2C2×C4×#1202C211yesmaximal, characteristic
3C2×#91358C211yesmaximal, characteristic, complemented
4C5×#4975C211yesmaximal, characteristic, complemented
5C3×#65276C211yesmaximal, characteristic, complemented
6#11748913C212yesmaximal
7#11748799C211yesmaximal, characteristic, complemented
8#11748709C212yesmaximal, complemented
9Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
10#11748669C212yesmaximal, complemented
11#11748651C212yesmaximal, complemented
12#10606055—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1202C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6714C2212yes—
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2212yes—
20#91781—24no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yes—
23C2×C5×Dic3⋊C4C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×#685C2212yes—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2211yescharacteristic
28C2×#6667C2212yes—
29C2×#6667C2211yescharacteristic
30C2×#6665C2212yes—
31C2×#6665C2211yescharacteristic
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2212yes—
34C4×#1202C418yescomplemented
35#91358—24no—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73885—51nomaximal, Hall
40C2×#4038—31no—
41C2×#4038—31no—
42C2×C4×D20—31no—
43C5×#384—31no—
44#65279—32no—
45#65279—32no—
46#65277—32no—
47#65276—31no—
48#65276D311yescharacteristic, complemented
49C4⋊C4×Dic5—32no—
50C4×C4⋊Dic5—31no—
51C23×D15C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15C2×C414yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yes—
68C2×#1202—22no—
69C2×#1202—22no—
70C2×#1202C2×C414yes—
71C3×C5×C4⋊C4—22no—
72#6714—24no—
73C4⋊Dic15D414yescomplemented
74C4×Dic15—24no—
75C5×C4⋊Dic3—22no—
76C5×Dic3⋊C4—24no—
77C5×Dic3⋊C4—42no—
78C4×C5×Dic3C2×C414yes—
79C3×#685—42no—
80C3×C4⋊Dic5—22no—
81Dic3⋊Dic5C2×C414yes—
82#6667—42no—
83#6667C2×C414yes—
84#6665—24no—
85#6665C2×C414yes—
86Dic3×Dic5—24no—
87Dic3×Dic5—24no—
88C2×C4×#67—51no—
89C2×#926—51no—
90C2×#892—51no—
91C3×#380—51no—
92#4987—51no—
93#4975D511yescharacteristic, complemented
94Dic3×C4⋊C4—51no—
95#4957—52no—
96#4945—52no—
97#4669—52no—
98#4649—52no—
99C22×D20—31no—
100C22×C4×D5—31no—
101C22×C4×D5C2×D311yescharacteristic
102C2×C5×C4⋊C4—31no—
103C2×C5×C4⋊C4—32no—
104C2×C5×C4⋊C4—32no—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C2×C42×C5—31no—
107C2×#685—31no—
108C2×#685—31no—
109C2×#685—32no—
110C2×#685—32no—
111C2×#685—32no—
112C2×#685C2×D312yes—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5—31no—
115C2×C4⋊Dic5C2×D311yescharacteristic
116C2×C4×Dic5—32no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5—32no—
119#4038—64no—
120#4038—64no—
121C4×D20—38no—
122#3963—32no—
123#3963—32no—
124#3963C2×D312yes—
125#2354—151noSylow
126C23×C3×C5C2411yescharacteristic
127C22×D15—21no—
128C22×D15—21no—
129C22×D15—21no—
130C22×D15—21no—
131C22×D15—21no—
132C22×D15—21no—
133C22×D15C22×C412yes—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5C22×C412yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15—21no—
150C2×Dic15—22no—
151C2×Dic15C22×C412yes—
152C2×Dic15C2×D414yes—
153C4×D15—28no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3C22×C412yes—
160C2×C5×Dic3C22×C412yes—
161C2×C5×Dic3#4112yes—
162C2×C5×Dic3#4112yes—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5C22×C412yes—
169C3×C4×D5—28no—
170#1202—28no—
171C23×C3×C4—51no—
172C22×#67—51no—
173C22×C4×D3—51no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176C2×C3×C22⋊C4—52no—
177C2×#217—51no—
178C2×#217—52no—
179C4×#67—58no—
180C2×(C2×D3)⋊C4—51no—
181C2×(C2×D3)⋊C4—52no—
182C2×(C2×D3)⋊C4—52no—
183#926—104no—
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3C2×D511yescharacteristic
186C2×Dic3⋊C4—51no—
187C2×Dic3⋊C4C2×D512yes—
188C2×Dic3⋊C4C2×D512yes—
189C2×C4×Dic3—52no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3C2×D511yescharacteristic
193#892—104no—
194C3×#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C23×D5—31no—
198C23×D5C22×D311yescharacteristic
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—32no—
202C22×C4×C5C22×D312yes—
203C22×C4×C5C22×D311yescharacteristic
204C22×Dic5—31no—
205C22×Dic5—32no—
206C22×Dic5C22×D312yes—
207C22×Dic5C22×D311yescharacteristic
208C2×D20—34no—
209C2×D20—62no—
210C2×D20—62no—
211C2×C4×D5—22no—
212C2×C4×D5—22no—
213C2×C4×D5—34no—
214C2×C4×D5—62no—
215C2×C4×D5—62no—
216C2×C4×D5C4×D314yes—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—64no—
219C5×C4⋊C4—62no—
220C5×C4⋊C4—122no—
221C42×C5—34no—
222#685—34no—
223#685—34no—
224#685—42no—
225#685—64no—
226#685—64no—
227#685—122no—
228C4⋊Dic5—22no—
229C4⋊Dic5—34no—
230C4⋊Dic5—34no—
231C4×Dic5—64no—
232C4×Dic5—64no—
233C4×Dic5—64no—
234C2×C4×D4—151no—
235C2×#117—151no—
236C2×#117—151no—
237#390—152no—
238#388—152no—
239#388—152no—
240#384—31no—
241#380—51no—
242#380—151no—
243C4×C4⋊C4—152no—
244C4×C4⋊C4—151no—
245C22×C3×C5C23×C411yescharacteristic
246C22×C3×C5C22×D411yescharacteristic
247C22×C3×C5C2×#4111yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5H(5,𝔽2)11yescharacteristic
251C22×C3×C52−1+411yescharacteristic
252C2×D15—22no—
253C2×D15—22no—
254C2×D15—22no—
255C2×D15—41no—
256C2×D15—41no—
257C2×D15—41no—
258C2×D15—41no—
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—41no—
263C2×C3×D5—41no—
264C2×C3×D5—41no—
265C2×C3×D5—41no—
266C3×C4×C5—42no—
267C3×C4×C5C4×D414yes—
268Dic15—22no—
269Dic15—24no—
270C3×Dic5—22no—
271C3×Dic5—42no—
272C5×Dic3—22no—
273C5×Dic3—42no—
274C5×Dic3#11714yescomplemented
275C24×C3—51no—
276C23×D3—51no—
277C22×C3×C4—51no—
278C22×C3×C4—54no—
279C22×C3×C4—52no—
280C22×C3×C4—102no—
281C22×C3×C4—102no—
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—54no—
285C2×#67—102no—
286C2×#67—102no—
287C22×Dic3—51no—
288C22×Dic3—52no—
289C22×Dic3C22×D512yes—
290C22×Dic3C22×D511yescharacteristic
291C22×Dic3C22×D511yescharacteristic
292C2×C4×D3—54no—
293C2×C4×D3—102no—
294C2×C4×D3—102no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—102no—
297C3×C22⋊C4—202no—
298#217—54no—
299#217—104no—
300(C2×D3)⋊C4—54no—
301(C2×D3)⋊C4—104no—
302(C2×D3)⋊C4—202no—
303C4⋊Dic3—22no—
304C4⋊Dic3—54no—
305Dic3⋊C4—24no—
306Dic3⋊C4—42no—
307Dic3⋊C4—54no—
308C4×Dic3—104no—
309C4×Dic3—104no—
310C4×Dic3—104no—
311C4×Dic3C4×D514yes—
312C23×C5C23×D311yescharacteristic
313C22×D5—21no—
314C22×D5—21no—
315C22×D5—21no—
316C22×D5—21no—
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—32no—
320C22×D5—61no—
321C22×D5—61no—
322C22×D5—61no—
323C22×D5—61no—
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—32no—
332C2×C4×C5—32no—
333C2×C4×C5—32no—
334C2×C4×C5—61no—
335C2×C4×C5—61no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5C2×C4×D312yes—
340C2×C4×C5D3×D412yes—
341C2×C4×C5#23712yes—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—32no—
348C2×Dic5—34no—
349C2×Dic5—61no—
350C2×Dic5—61no—
351C2×Dic5—62no—
352C2×Dic5—62no—
353C2×Dic5C2×C4×D312yes—
354D20—68no—
355C4×D5—28no—
356C4×D5—68no—
357C22×D4—151no—
358C23×C4—51no—
359C23×C4—151no—
360C4×D4—158no—
361#117—304no—
362#117—304no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4D3×D511yescharacteristic
370C2×C22⋊C4—52no—
371C2×C22⋊C4—151no—
372C2×C22⋊C4—151no—
373C2×C22⋊C4—152no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C42—31no—
377C2×C42—152no—
378C2×C42—152no—
379C2×C42—152no—
380#95—52no—
381#95—152no—
382#95—152no—
383C2×C3×C5C2×#11711yescharacteristic
384C2×C3×C5C2×C4×D411yescharacteristic
385C2×C3×C5#52011yescharacteristic
386C2×C3×C5#54711yescharacteristic
387C2×C3×C5#55011yescharacteristic
388C2×C3×C5#55511yescharacteristic
389C2×C3×C5#55611yescharacteristic
390D15—42no—
391C3×D5—42no—
392C23×C3—52no—
393C23×C3—101no—
394C23×C3—101no—
395C23×C3—101no—
396C23×C3—101no—
397C23×C3—101no—
398C23×C3—101no—
399C23×C3C23×D511yescharacteristic
400C22×D3—52no—
401C22×D3—101no—
402C22×D3—101no—
403C22×D3—101no—
404C22×D3—101no—
405C22×D3—101no—
406C22×D3—101no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—52no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4—108no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4C2×C4×D512yes—
418C2×C3×C4D4×D512yes—
419C2×C3×C4#71312yes—
420#67—108no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—52no—
427C2×Dic3—54no—
428C2×Dic3—101no—
429C2×Dic3—102no—
430C2×Dic3—101no—
431C2×Dic3—102no—
432C2×Dic3C2×C4×D512yes—
433C2×Dic3C2×C4×D512yes—
434C2×Dic3#71112yes—
435C2×Dic3#71312yes—
436C4×D3—108no—
437C22×C5C22×C4×D311yescharacteristic
438C22×C5C2×D3×D411yescharacteristic
439C22×C5C2×#23711yescharacteristic
440C22×C5#100411yescharacteristic
441C22×C5#100711yescharacteristic
442C22×C5D3×#4111yescharacteristic
443C22×C5D3×#4111yescharacteristic
444C2×D5—22no—
445C2×D5—22no—
446C2×D5—22no—
447C2×D5—41no—
448C2×D5—41no—
449C2×D5—41no—
450C2×D5—41no—
451C2×D5—62no—
452C2×D5—62no—
453C2×D5—62no—
454C2×D5—121no—
455C2×D5—121no—
456C2×D5—121no—
457C2×D5—121no—
458C4×C5—34no—
459C4×C5—42no—
460C4×C5—62no—
461C4×C5—122no—
462C4×C5#67⋊C414yes—
463Dic5—22no—
464Dic5—42no—
465Dic5—62no—
466Dic5—64no—
467C24—51no—
468C24—151no—
469C2×D4—154no—
470C2×D4—302no—
471C2×D4—302no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—32no—
475C22×C4—51no—
476C22×C4—54no—
477C22×C4—52no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—151no—
481C22×C4—152no—
482C22×C4—154no—
483C22×C4—302no—
484C22×C4—302no—
485C22×C4C2×D3×D512yes—
486C22×C4C2×D3×D511yescharacteristic
487C4⋊C4—22no—
488C4⋊C4—64no—
489C4⋊C4—62no—
490C4⋊C4—102no—
491C4⋊C4—122no—
492C4⋊C4—154no—
493C4⋊C4—154no—
494C22⋊C4—154no—
495C22⋊C4—154no—
496C22⋊C4—202no—
497C22⋊C4—304no—
498C22⋊C4—304no—
499C22⋊C4—602no—
500C42—34no—
501C42—304no—
502C42—304no—
503C42—304no—
504C3×C5#235411yescharacteristic, complemented, Hall
505C22×C3—102no—
506C22×C3—102no—
507C22×C3—102no—
508C22×C3—201no—
509C22×C3—201no—
510C22×C3—201no—
511C22×C3—201no—
512C22×C3C22×C4×D511yescharacteristic
513C22×C3C2×D4×D511yescharacteristic
514C22×C3C2×#71111yescharacteristic
515C22×C3#414411yescharacteristic
516C22×C3C2×#71311yescharacteristic
517C22×C3C2×#71311yescharacteristic
518C22×C3#414711yescharacteristic
519C2×D3—102no—
520C2×D3—102no—
521C2×D3—102no—
522C2×D3—201no—
523C2×D3—201no—
524C2×D3—201no—
525C2×D3—201no—
526C3×C4—42no—
527C3×C4—102no—
528C3×C4—202no—
529C3×C4#403914yes—
530Dic3—22no—
531Dic3—42no—
532Dic3—104no—
533Dic3—102no—
534Dic3#403814yescomplemented
535C2×C5C2×#67⋊C411yescharacteristic
536C2×C5#550411yescharacteristic
537C2×C5D3×#11711yescharacteristic
538C2×C5#559911yescharacteristic
539C2×C5#561611yescharacteristic
540C2×C5#563111yescharacteristic
541C2×C5#564111yescharacteristic
542D5—42no—
543D5—122no—
544C23—52no—
545C23—101no—
546C23—101no—
547C23—101no—
548C23—101no—
549C23—101no—
550C23—101no—
551C23—152no—
552C23—301no—
553C23—301no—
554C23—301no—
555C23—301no—
556C23—301no—
557C23—301no—
558C23C22×D3×D511yescharacteristic
559D4—308no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—32no—
564C2×C4—32no—
565C2×C4—32no—
566C2×C4—32no—
567C2×C4—52no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—108no—
576C2×C4—102no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—152no—
580C2×C4—154no—
581C2×C4—301no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4—301no—
585C2×C4—308no—
586C2×C4#676612yes—
587C2×C4C4×D3×D512yes—
588C2×C4#679012yes—
589C2×C3—202no—
590C2×C3C2×#403811yescharacteristic
591C2×C3C2×#403911yescharacteristic
592C2×C3#6583811yescharacteristic
593C2×C3#6605211yescharacteristic
594C2×C3#6606011yescharacteristic
595C2×C3#6606611yescharacteristic
596C2×C3#6606811yescharacteristic
597D3—202no—
598C5#7388511yescharacteristic, complemented, Sylow
599C22—102no—
600C22—102no—
601C22—102no—
602C22—201no—
603C22—201no—
604C22—201no—
605C22—201no—
606C22—302no—
607C22—302no—
608C22—302no—
609C22—601no—
610C22—601no—
611C22—601no—
612C22—601no—
613C22C2×#676611yescharacteristic
614C22C2×C4×D3×D511yescharacteristic
615C22D3×#71111yescharacteristic
616C22#9202511yescharacteristic
617C22#9202911yescharacteristic
618C22D3×#71311yescharacteristic
619C22C2×#679011yescharacteristic
620C4—34no—
621C4—42no—
622C4—62no—
623C4—102no—
624C4—122no—
625C4—202no—
626C4—302no—
627C4—304no—
628C4#9139614yes—
629C3#1060605511yescharacteristic, complemented, Sylow
630C2—202no—
631C2—602no—
632C2#1175359211yescharacteristic
633C2#1175366711yescharacteristic
634C2#1175376911yescharacteristic
635C2D3×#403811yescharacteristic
636C2C2×#9139611yescharacteristic
637C2#1175495611yescharacteristic
638C2#1175523911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91781C2semidirect
3. C2×#91358C2semidirect
4. C5×#4975C2semidirect
5. C3×#65276C2semidirect
7. #11748799C2semidirect
8. #11748709C2semidirect
9. Dic3×C4⋊Dic5C2semidirect
10. #11748669C2semidirect
11. #11748651C2semidirect
34. C4×#1202C4semidirect
48. #65276D3semidirect
73. C4⋊Dic15D4semidirect
93. #4975D5semidirect
274. C5×Dic3#117semidirect
504. C3×C5#2354semidirect
534. Dic3#4038semidirect
598. C5#73885semidirect
629. C3#10606055semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C4×#12022
C2×#913582
C5×#49752
C3×#652762
#117489132
#117487992
#117487092
Dic3×C4⋊Dic52
#117486692
#117486512
#106060553
#738855