Finite Group Databasebeta

← C2×#11748700 #14320311

Subgroups — C2×#11748700 #14320311

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1202C211yesmaximal, characteristic
2C23×#1200C211yesmaximal, characteristic, complemented
3C22×#6714C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×#6665C211yesmaximal, characteristic, complemented
6C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748700C218yesmaximal, direct product factor
9C2×#64954—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1202—24no—
18C22×#1202—24no—
19C22×#1202C418yescomplemented
20C22×#1202C2214yes—
21C22×#1200—24no—
22C22×#1200—24no—
23C22×#1200—24no—
24C22×#1200C2214yescomplemented
25C2×#6714—24no—
26C2×#6714C2214yescomplemented
27C2×C3×#685—24no—
28C2×C3×#685C2214yescomplemented
29C2×#6665—24no—
30C2×#6665C2214yescomplemented
31C5×C3⋊#95C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4956—51nomaximal, Hall
34C23×D20—31no—
35C23×C4×D5—31no—
36C22×#685—31no—
37C22×#685—31no—
38C22×#685D311yescharacteristic, complemented
39C2×C5×#95—31no—
40C2×#3963—31no—
41#64954—38no—
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15C2×C414yes—
48C23×D15D414yes—
49C23×D15D414yes—
50C23×D15C2312yes—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—22no—
56C23×C3×D5—22no—
57C23×C3×D5C2×C414yescomplemented
58C23×C3×D5C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5C2312yes—
63C22×Dic15—22no—
64C22×Dic15—22no—
65C22×Dic15—22no—
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—22no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3C2×C414yescomplemented
72C22×C5×Dic3D414yescomplemented
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5D414yescomplemented
78C22×C3×Dic5C2312yes—
79C2×#1202—232no—
80C2×#1202—28no—
81C2×#1202—28no—
82C2×#1202C2×C4116yescomplemented
83C2×#1200—232no—
84C2×#1200—28no—
85C2×#1200—28no—
86C2×#1200—28no—
87#6714—28no—
88C3×#685—28no—
89#6665—28no—
90C23×#67—51no—
91C23×C4×D3—51no—
92C22×C3×C22⋊C4—51no—
93C22×#217—51no—
94C22×(C2×D3)⋊C4—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95D511yescharacteristic, complemented
97#4956—58no—
98C24×D5—31no—
99C24×D5C2×D311yescharacteristic
100C23×C4×C5—31no—
101C23×C4×C5—31no—
102C23×C4×C5C2×D311yescharacteristic
103C23×Dic5—31no—
104C23×Dic5C2×D311yescharacteristic
105C22×D20—38no—
106C22×D20—34no—
107C22×D20—64no—
108C22×D20—64no—
109C22×C4×D5—34no—
110C22×C4×D5—64no—
111C22×C4×D5—64no—
112C22×C4×D5—64no—
113C2×#685—24no—
114C2×#685—34no—
115C2×#685—34no—
116C2×#685—64no—
117C2×#685—64no—
118C2×#685C2×D314yescomplemented
119C5×#95—34no—
120#3963—34no—
121C2×#386—151noSylow
122C23×C3×C5C22×C412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5#4112yes—
128C23×C3×C5#4112yes—
129C23×C3×C5C2411yescharacteristic
130C22×D15—28no—
131C22×D15—28no—
132C22×D15—28no—
133C22×D15—28no—
134C22×D15—28no—
135C22×D15—28no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15—22no—
140C22×D15C22⋊C4116yescomplemented
141C22×D15C22×C414yes—
142C22×D15C2×D414yes—
143C22×D15C2×D414yes—
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—28no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5—44no—
154C22×C3×D5—44no—
155C22×C3×D5—44no—
156C22×C3×D5—44no—
157C22×C3×D5C22×C414yescomplemented
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—44no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—44no—
166C2×C5×Dic3—28no—
167C2×C5×Dic3—28no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3C22×C414yescomplemented
173C2×C5×Dic3C2×D414yescomplemented
174C2×C3×Dic5—28no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5C2×D414yescomplemented
178#1202—232no—
179#1200—232no—
180C25×C3—51no—
181C24×D3—51no—
182C23×C3×C4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C22×#67—58no—
185C22×#67—54no—
186C22×#67—104no—
187C22×#67—104no—
188C23×Dic3—51no—
189C23×Dic3C2×D511yescharacteristic
190C23×Dic3C2×D511yescharacteristic
191C22×C4×D3—54no—
192C22×C4×D3—104no—
193C22×C4×D3—104no—
194C22×C4×D3—104no—
195C2×C3×C22⋊C4—54no—
196C2×C3×C22⋊C4—104no—
197C2×#217—54no—
198C2×#217—104no—
199C2×(C2×D3)⋊C4—54no—
200C2×(C2×D3)⋊C4—104no—
201C3⋊#95—54no—
202C3⋊#95C2×D514yescomplemented
203C24×C5C22×D311yescharacteristic
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—22no—
210C23×D5—34no—
211C23×D5—34no—
212C23×D5—34no—
213C23×D5—32no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C23×D5C4×D314yescomplemented
219C23×D5C22×D312yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—34no—
224C22×C4×C5—34no—
225C22×C4×C5—32no—
226C22×C4×C5—32no—
227C22×C4×C5—62no—
228C22×C4×C5—62no—
229C22×C4×C5—62no—
230C22×C4×C5—62no—
231C22×C4×C5C22×D312yes—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—32no—
235C22×Dic5—62no—
236C22×Dic5—62no—
237C22×Dic5—62no—
238C22×Dic5#6714yescomplemented
239C22×Dic5C22×D312yes—
240C2×D20—316no—
241C2×D20—632no—
242C2×D20—68no—
243C2×D20—68no—
244C2×C4×D5—68no—
245C2×C4×D5—68no—
246C2×C4×D5—632no—
247C2×C4×D5—68no—
248#685—28no—
249#685—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—151no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—31no—
258C2×#95—151no—
259C22×C3×C5C2×C22⋊C414yes—
260C22×C3×C5C4×D414yes—
261C22×C3×C5C4×D414yes—
262C22×C3×C5#12014yes—
263C22×C3×C5#12114yes—
264C22×C3×C5#12114yes—
265C22×C3×C5#12314yes—
266C22×C3×C5C23×C411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C2×D15—24no—
274C2×D15—24no—
275C2×D15—24no—
276C2×D15—24no—
277C2×D15—24no—
278C2×D15—24no—
279C2×D15—232no—
280C2×D15C2×C22⋊C418yescomplemented
281C2×C3×D5—24no—
282C2×C3×D5—24no—
283C2×C3×D5—24no—
284C2×C3×D5—42no—
285C2×C3×D5—42no—
286C2×C3×D5—42no—
287C2×C3×D5—42no—
288C2×C3×D5—416no—
289C3×C4×C5—42no—
290Dic15—42no—
291C3×Dic5—24no—
292C5×Dic3—24no—
293C5×Dic3—24no—
294C24×C3—54no—
295C24×C3—52no—
296C24×C3—102no—
297C24×C3—102no—
298C24×C3—102no—
299C24×C3—102no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3C22×D511yescharacteristic
303C23×D3—54no—
304C23×D3—54no—
305C23×D3—54no—
306C23×D3—52no—
307C23×D3—102no—
308C23×D3—102no—
309C23×D3—102no—
310C23×D3—102no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—54no—
315C22×C3×C4—52no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4C22×D512yes—
319C2×#67—516no—
320C2×#67—108no—
321C2×#67—108no—
322C2×#67—1032no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3C4×D514yescomplemented
332C22×Dic3D2014yescomplemented
333C22×Dic3C22×D512yes—
334C22×Dic3C22×D512yes—
335C2×C4×D3—108no—
336C2×C4×D3—108no—
337C2×C4×D3—1032no—
338C2×C4×D3—108no—
339C3×C22⋊C4—108no—
340#217—108no—
341(C2×D3)⋊C4—108no—
342C23×C5C2×C4×D312yes—
343C23×C5#23512yes—
344C23×C5D3×D412yes—
345C23×C5D3×D412yes—
346C23×C5D3×D412yes—
347C23×C5#23712yes—
348C23×C5C2×#6712yes—
349C23×C5C23×D311yescharacteristic
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—316no—
360C22×D5—34no—
361C22×D5—34no—
362C22×D5—34no—
363C22×D5—44no—
364C22×D5—44no—
365C22×D5—44no—
366C22×D5—44no—
367C22×D5—68no—
368C22×D5—68no—
369C22×D5—68no—
370C22×D5—68no—
371C22×D5—68no—
372C22×D5—68no—
373C22×D5—62no—
374C22×D5—62no—
375C22×D5—62no—
376C22×D5—62no—
377C22×D5C2×C4×D314yescomplemented
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—34no—
382C2×C4×C5—34no—
383C2×C4×C5—44no—
384C2×C4×C5—68no—
385C2×C4×C5—68no—
386C2×C4×C5—62no—
387C2×C4×C5—62no—
388C2×C4×C5—62no—
389C2×C4×C5—62no—
390C2×Dic5—28no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—62no—
394C2×Dic5—62no—
395C2×Dic5—62no—
396C2×Dic5—124no—
397C2×Dic5C2×#6714yescomplemented
398D20—632no—
399C4×D5—632no—
400C25—51no—
401C25—151no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—51no—
409C23×C4—154no—
410C23×C4—151no—
411C23×C4—304no—
412C23×C4—304no—
413C23×C4—304no—
414C23×C4D3×D511yescharacteristic
415C2×C22⋊C4—54no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—154no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4—304no—
421#95—34no—
422#95—154no—
423C2×C3×C5#38618yescomplemented
424C2×C3×C5C22×C22⋊C411yescharacteristic
425C2×C3×C5C2×C4×D411yescharacteristic
426C2×C3×C5C2×C4×D411yescharacteristic
427C2×C3×C5C2×#12011yescharacteristic
428C2×C3×C5C2×#12111yescharacteristic
429C2×C3×C5C2×#12111yescharacteristic
430C2×C3×C5C2×#12311yescharacteristic
431D15—28no—
432C3×D5—44no—
433C23×C3—54no—
434C23×C3—102no—
435C23×C3—102no—
436C23×C3—102no—
437C23×C3—102no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—108no—
441C23×C3—108no—
442C23×C3—108no—
443C23×C3—204no—
444C23×C3—204no—
445C23×C3—204no—
446C23×C3—204no—
447C23×C3C2×C4×D512yes—
448C23×C3C2×D2012yes—
449C23×C3#70912yes—
450C23×C3D4×D512yes—
451C23×C3D4×D512yes—
452C23×C3D4×D512yes—
453C23×C3#71312yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—54no—
456C22×D3—54no—
457C22×D3—54no—
458C22×D3—516no—
459C22×D3—102no—
460C22×D3—102no—
461C22×D3—102no—
462C22×D3—102no—
463C22×D3—108no—
464C22×D3—108no—
465C22×D3—108no—
466C22×D3—108no—
467C22×D3—108no—
468C22×D3—108no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—44no—
473C2×C3×C4—54no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—108no—
477#67—1032no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—28no—
483C2×Dic3—28no—
484C2×Dic3—102no—
485C2×Dic3—102no—
486C2×Dic3—102no—
487C2×Dic3—204no—
488C2×Dic3C2×C4×D514yescomplemented
489C2×Dic3C2×D2014yescomplemented
490C4×D3—1032no—
491C22×C5D3×C22⋊C414yes—
492C22×C5#67⋊C414yes—
493C22×C5#88314yes—
494C22×C5#88414yes—
495C22×C5C4×#6714yes—
496C22×C5#93714yes—
497C22×C5#93814yes—
498C22×C5C22×C4×D311yescharacteristic
499C22×C5C2×#23511yescharacteristic
500C22×C5C2×D3×D411yescharacteristic
501C22×C5C2×D3×D411yescharacteristic
502C22×C5C2×D3×D411yescharacteristic
503C22×C5C2×#23711yescharacteristic
504C22×C5C22×#6711yescharacteristic
505C2×D5—24no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—38no—
509C2×D5—416no—
510C2×D5—42no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—632no—
515C2×D5—64no—
516C2×D5—64no—
517C2×D5—64no—
518C2×D5—64no—
519C2×D5—64no—
520C2×D5—64no—
521C4×C5—42no—
522C4×C5—64no—
523C4×C5—64no—
524Dic5—24no—
525Dic5—122no—
526C24—54no—
527C24—52no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—154no—
535C24—154no—
536C24—154no—
537C24—152no—
538C24—302no—
539C24—302no—
540C24—302no—
541C24—302no—
542C24C2×D3×D511yescharacteristic
543C2×D4—1516no—
544C2×D4—3032no—
545C2×D4—308no—
546C2×D4—308no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—34no—
551C22×C4—34no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—54no—
555C22×C4—52no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—152no—
563C22×C4—308no—
564C22×C4—308no—
565C22×C4—308no—
566C22×C4—3032no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4C2×D3×D512yes—
571C22⋊C4—108no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3—104no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—202no—
579C22×C3—202no—
580C22×C3—202no—
581C22×C3—202no—
582C22×C3—2016no—
583C22×C3C4×D2014yes—
584C22×C3D5×C22⋊C414yes—
585C22×C3#402814yes—
586C22×C3#403014yes—
587C22×C3#403914yes—
588C22×C3#404014yes—
589C22×C3#404114yes—
590C22×C3C22×C4×D511yescharacteristic
591C22×C3C22×D2011yescharacteristic
592C22×C3C2×#70911yescharacteristic
593C22×C3C2×D4×D511yescharacteristic
594C22×C3C2×D4×D511yescharacteristic
595C22×C3C2×D4×D511yescharacteristic
596C22×C3C2×#71311yescharacteristic
597C2×D3—58no—
598C2×D3—104no—
599C2×D3—104no—
600C2×D3—104no—
601C2×D3—104no—
602C2×D3—104no—
603C2×D3—104no—
604C2×D3—1032no—
605C3×C4—42no—
606C3×C4—104no—
607Dic3—24no—
608Dic3—24no—
609Dic3—202no—
610C2×C5#495618yescomplemented
611C2×C5C2×D3×C22⋊C411yescharacteristic
612C2×C5C2×#67⋊C411yescharacteristic
613C2×C5C2×#88311yescharacteristic
614C2×C5C2×#88411yescharacteristic
615C2×C5C2×C4×#6711yescharacteristic
616C2×C5C2×#93711yescharacteristic
617C2×C5C2×#93811yescharacteristic
618D5—44no—
619D5—68no—
620C23—54no—
621C23—108no—
622C23—108no—
623C23—108no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—1516no—
631C23—154no—
632C23—154no—
633C23—154no—
634C23—204no—
635C23—204no—
636C23—204no—
637C23—204no—
638C23—308no—
639C23—308no—
640C23—308no—
641C23—308no—
642C23—302no—
643C23—302no—
644C23—302no—
645C23—308no—
646C23—302no—
647C23—308no—
648C23#677312yes—
649C23C4×D3×D512yes—
650C23D3×D2012yes—
651C23#677712yes—
652C23#677912yes—
653C23D5×#6712yes—
654C23#679012yes—
655C23C22×D3×D511yescharacteristic
656D4—3032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—34no—
661C2×C4—34no—
662C2×C4—44no—
663C2×C4—54no—
664C2×C4—68no—
665C2×C4—68no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—108no—
671C2×C4—102no—
672C2×C4—102no—
673C2×C4—3032no—
674C2×C4—302no—
675C2×C4—302no—
676C2×C4—302no—
677C2×C4—604no—
678C2×C3—204no—
679C2×C3#6495418yescomplemented
680C2×C3C2×C4×D2011yescharacteristic
681C2×C3C2×D5×C22⋊C411yescharacteristic
682C2×C3C2×#402811yescharacteristic
683C2×C3C2×#403011yescharacteristic
684C2×C3C2×#403911yescharacteristic
685C2×C3C2×#404011yescharacteristic
686C2×C3C2×#404111yescharacteristic
687D3—108no—
688C5C2×#495611yescharacteristic, complemented, Sylow
689C22—104no—
690C22—104no—
691C22—104no—
692C22—158no—
693C22—202no—
694C22—2016no—
695C22—202no—
696C22—202no—
697C22—202no—
698C22—304no—
699C22—304no—
700C22—304no—
701C22—3032no—
702C22—304no—
703C22—304no—
704C22—304no—
705C22#9135614yes—
706C22#9139514yes—
707C22#9144414yes—
708C22#9145914yes—
709C22#9147314yes—
710C22#9147414yes—
711C22#9153314yes—
712C22C2×#677311yescharacteristic
713C22C2×C4×D3×D511yescharacteristic
714C22C2×D3×D2011yescharacteristic
715C22C2×#677711yescharacteristic
716C22C2×#677911yescharacteristic
717C22C2×D5×#6711yescharacteristic
718C22C2×#679011yescharacteristic
719C4—42no—
720C4—64no—
721C4—64no—
722C4—104no—
723C4—602no—
724C3C2×#6495411yescharacteristic, complemented, Sylow
725C2—204no—
726C2—308no—
727C2#1174870018yesdirect product factor
728C2C2×#9135611yescharacteristic
729C2C2×#9139511yescharacteristic
730C2C2×#9144411yescharacteristic
731C2C2×#9145911yescharacteristic
732C2C2×#9147311yescharacteristic
733C2C2×#9147411yescharacteristic
734C2C2×#9153311yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1202C2
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×#1200C2semidirect
3. C22×#6714C2semidirect
4. C22×C3×#685C2semidirect
5. C22×#6665C2semidirect
6. C2×C5×C3⋊#95C2semidirect
7. C2×#90994C2semidirect
8. #11748700C2direct (N × H)
19. C22×#1202C4semidirect
24. C22×#1200C22semidirect
26. C2×#6714C22semidirect
28. C2×C3×#685C22semidirect
30. C2×#6665C22semidirect
31. C5×C3⋊#95C22semidirect
32. #90994C22semidirect
38. C22×#685D3semidirect
57. C23×C3×D5C2×C4semidirect
71. C22×C5×Dic3C2×C4semidirect
72. C22×C5×Dic3D4semidirect
77. C22×C3×Dic5D4semidirect
82. C2×#1202C2×C4semidirect
96. C2×C3⋊#95D5semidirect
118. C2×#685C2×D3semidirect
140. C22×D15C22⋊C4semidirect
157. C22×C3×D5C22×C4semidirect
172. C2×C5×Dic3C22×C4semidirect
173. C2×C5×Dic3C2×D4semidirect
177. C2×C3×Dic5C2×D4semidirect
202. C3⋊#95C2×D5semidirect
218. C23×D5C4×D3semidirect
238. C22×Dic5#67semidirect
280. C2×D15C2×C22⋊C4semidirect
331. C22×Dic3C4×D5semidirect
332. C22×Dic3D20semidirect
377. C22×D5C2×C4×D3semidirect
397. C2×Dic5C2×#67semidirect
423. C2×C3×C5#386semidirect
488. C2×Dic3C2×C4×D5semidirect
489. C2×Dic3C2×D20semidirect
574. C3×C5C2×#386semidirect
610. C2×C5#4956semidirect
679. C2×C3#64954semidirect
688. C5C2×#4956semidirect
724. C3C2×#64954semidirect
727. C2#11748700direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12022
C23×#12002
C22×#67142
C22×C3×#6852
C22×#66652
C2×C5×C3⋊#952
C2×#909942
#117487002
C2×#649543
C2×#49565