Finite Group Databasebeta

← C2×#11748914 #14320316

Subgroups — C2×#11748914 #14320316

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×C4×C5×D3C211yesmaximal, characteristic, complemented
2C23×#1203C211yesmaximal, characteristic
3C22×#6714C211yesmaximal, characteristic, complemented
4C22×#6667C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748914C218yesmaximal, direct product factor
9C2×#65502—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C22×C4×C5×D3—24no—
16C22×C4×C5×D3—24no—
17C22×C4×C5×D3—24no—
18C22×C4×C5×D3C2214yescomplemented
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×#1203—24no—
22C22×#1203—24no—
23C22×#1203C418yescomplemented
24C22×#1203C2214yes—
25C2×#6714—24no—
26C2×#6714C2214yescomplemented
27C2×#6667—24no—
28C2×#6667C2214yescomplemented
29C2×(C2×D3)⋊Dic5—24no—
30C2×(C2×D3)⋊Dic5C2214yescomplemented
31C3×#3963C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4665—51nomaximal, Hall
34C24×C4×C5—31no—
35C23×C22⋊D5—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685—31no—
39#65502—38no—
40C2×#3963—31no—
41C2×#3963D311yescharacteristic, complemented
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15—22no—
48C23×D15—22no—
49C23×D15C2×C414yescomplemented
50C23×D15C2312yes—
51C23×C5×D3—22no—
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3C2×C414yes—
56C23×C5×D3D414yes—
57C23×C5×D3D414yes—
58C23×C5×D3C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5D414yescomplemented
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×Dic3D414yescomplemented
70C22×C5×Dic3C2312yes—
71C2×C4×C5×D3—232no—
72C2×C4×C5×D3—28no—
73C2×C4×C5×D3—28no—
74C2×C4×C5×D3—28no—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5—22no—
78C22×C3×Dic5—22no—
79C22×C3×Dic5—22no—
80C22×C3×Dic5C2×C414yescomplemented
81C22×C3×Dic5C2312yes—
82C22×C3×Dic5C2312yes—
83C2×#1203—232no—
84C2×#1203—28no—
85C2×#1203—28no—
86C2×#1203C2×C4116yescomplemented
87#6714—28no—
88#6667—28no—
89(C2×D3)⋊Dic5—28no—
90C23×D12—51no—
91C23×C4×D3D511yescharacteristic, complemented
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4—51no—
95C2×C3×#95—51no—
96C2×C3⋊#95—51no—
97#4665—58no—
98C25×C5—31no—
99C24×D5—31no—
100C23×C4×C5—31no—
101C23×C4×C5—34no—
102C23×C4×C5—64no—
103C23×C4×C5—64no—
104C23×C4×C5—64no—
105C23×C4×C5C2×D311yescharacteristic
106C22×C22⋊D5—38no—
107C22×C22⋊D5—34no—
108C22×C22⋊D5—64no—
109C22×C22⋊D5—64no—
110C23×Dic5—31no—
111C23×Dic5C2×D311yescharacteristic
112C23×Dic5C2×D311yescharacteristic
113C2×C22⋊Dic5—34no—
114C2×C22⋊Dic5—64no—
115C2×#685—34no—
116C2×#685—34no—
117C2×#685—64no—
118C2×#685—64no—
119#3963—34no—
120#3963C2×D314yescomplemented
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—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15—44no—
140C22×D15—44no—
141C22×D15—44no—
142C22×D15—44no—
143C22×D15C22×C414yescomplemented
144C22×C5×D3—28no—
145C22×C5×D3—28no—
146C22×C5×D3—28no—
147C22×C5×D3—28no—
148C22×C5×D3—28no—
149C22×C5×D3—28no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3C22⋊C4116yescomplemented
155C22×C5×D3C22×C414yes—
156C22×C5×D3C2×D414yes—
157C22×C5×D3C2×D414yes—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5C2×D414yescomplemented
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—44no—
166C2×C5×Dic3—28no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3C2×D414yescomplemented
170C4×C5×D3—232no—
171C2×C3×Dic5—28no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—44no—
178C2×C3×Dic5C22×C414yescomplemented
179#1203—232no—
180C24×D3—51no—
181C24×D3C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C23×Dic3—51no—
186C23×Dic3C2×D511yescharacteristic
187C22×D12—58no—
188C22×D12—54no—
189C22×D12—104no—
190C22×D12—104no—
191C22×C4×D3—24no—
192C22×C4×D3—24no—
193C22×C4×D3—24no—
194C22×C4×D3C2×D514yescomplemented
195C2×(C2×D3)⋊C4—54no—
196C2×(C2×D3)⋊C4—54no—
197C2×(C2×D3)⋊C4—54no—
198C2×(C2×D3)⋊C4—104no—
199C2×(C2×D3)⋊C4—104no—
200C2×(C2×D3)⋊C4—104no—
201C3×#95—54no—
202C3⋊#95—54no—
203C24×C5—34no—
204C24×C5—34no—
205C24×C5—34no—
206C24×C5—32no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5—62no—
211C24×C5C22×D311yescharacteristic
212C23×D5—34no—
213C23×D5—32no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C23×D5—62no—
219C23×D5—62no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—34no—
223C22×C4×C5—32no—
224C22×C4×C5—68no—
225C22×C4×C5—68no—
226C22×C4×C5—632no—
227C22×C4×C5—62no—
228C22×C4×C5—62no—
229C22×C4×C5—68no—
230C22×C4×C5D1214yescomplemented
231C22×C4×C5C22×D312yes—
232C2×C22⋊D5—316no—
233C2×C22⋊D5—632no—
234C2×C22⋊D5—68no—
235C2×C22⋊D5—68no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—32no—
242C22×Dic5—62no—
243C22×Dic5—62no—
244C22×Dic5—62no—
245C22×Dic5C4×D314yescomplemented
246C22×Dic5C22×D312yes—
247C22×Dic5C22×D312yes—
248C22⋊Dic5—68no—
249#685—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—31no—
253C22×C22⋊C4—151no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—51no—
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—42no—
277C2×D15—42no—
278C2×D15—42no—
279C2×D15—42no—
280C2×D15—416no—
281C2×C5×D3—24no—
282C2×C5×D3—24no—
283C2×C5×D3—24no—
284C2×C5×D3—24no—
285C2×C5×D3—24no—
286C2×C5×D3—24no—
287C2×C5×D3—232no—
288C2×C5×D3C2×C22⋊C418yescomplemented
289C3×C4×C5—24no—
290Dic15—42no—
291C3×Dic5—24no—
292C3×Dic5—42no—
293C5×Dic3—24no—
294C24×C3C22×D511yescharacteristic
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—22no—
299C23×D3—54no—
300C23×D3—52no—
301C23×D3—102no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3—102no—
307C23×D3C4×D514yes—
308C23×D3D2014yes—
309C23×D3C22⋊D514yes—
310C23×D3C22×D512yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—54no—
314C22×C3×C4—52no—
315C22×C3×C4—52no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4—102no—
319C22×C3×C4—102no—
320C22×C3×C4—102no—
321C22×C3×C4C22⋊D514yescomplemented
322C22×C3×C4C22×D512yes—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—52no—
326C22×Dic3—102no—
327C22×Dic3—102no—
328C22×Dic3—102no—
329C22×Dic3C22⋊D514yescomplemented
330C22×Dic3C22×D512yes—
331C2×D12—516no—
332C2×D12—1032no—
333C2×D12—108no—
334C2×D12—108no—
335C2×C4×D3—232no—
336C2×C4×D3—28no—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339(C2×D3)⋊C4—108no—
340(C2×D3)⋊C4—108no—
341(C2×D3)⋊C4—108no—
342C23×C5—316no—
343C23×C5—34no—
344C23×C5—34no—
345C23×C5—34no—
346C23×C5—68no—
347C23×C5—68no—
348C23×C5—68no—
349C23×C5—68no—
350C23×C5—68no—
351C23×C5—68no—
352C23×C5—62no—
353C23×C5—62no—
354C23×C5—62no—
355C23×C5—62no—
356C23×C5C2×C4×D312yes—
357C23×C5C2×D1212yes—
358C23×C5#23512yes—
359C23×C5D3×D412yes—
360C23×C5D3×D412yes—
361C23×C5D3×D412yes—
362C23×C5#23912yes—
363C23×C5C23×D311yescharacteristic
364C22×D5—34no—
365C22×D5—68no—
366C22×D5—68no—
367C22×D5—68no—
368C22×D5—62no—
369C22×D5—62no—
370C22×D5—62no—
371C22×D5—62no—
372C22×D5—62no—
373C22×D5—62no—
374C22×D5—124no—
375C22×D5—124no—
376C22×D5—124no—
377C22×D5—124no—
378C2×C4×C5—28no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—34no—
382C2×C4×C5—632no—
383C2×C4×C5—68no—
384C2×C4×C5—62no—
385C2×C4×C5—62no—
386C2×C4×C5C2×D1214yescomplemented
387C22⋊D5—632no—
388C2×Dic5—28no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—44no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5—124no—
399C2×Dic5C2×C4×D314yescomplemented
400C25—31no—
401C25—151no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—34no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—64no—
411C23×C4—64no—
412C23×C4—64no—
413C23×C4—151no—
414C23×C4D3×D511yescharacteristic
415C2×C22⋊C4—154no—
416C2×C22⋊C4—154no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—304no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4—304no—
421#95—54no—
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—44no—
432C5×D3—28no—
433C23×C3C2×C4×D512yes—
434C23×C3C2×D2012yes—
435C23×C3#70912yes—
436C23×C3#70912yes—
437C23×C3C2×C22⋊D512yes—
438C23×C3C2×C22⋊D512yes—
439C23×C3C2×C22⋊D512yes—
440C23×C3C23×D511yescharacteristic
441C22×D3—28no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—28no—
447C22×D3—28no—
448C22×D3—28no—
449C22×D3—28no—
450C22×D3—28no—
451C22×D3—54no—
452C22×D3—102no—
453C22×D3—102no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—102no—
457C22×D3—102no—
458C22×D3—108no—
459C22×D3—108no—
460C22×D3—108no—
461C22×D3—204no—
462C22×D3—204no—
463C22×D3—204no—
464C22×D3—204no—
465C22×D3#685116yescomplemented
466C22×D3C2×C4×D514yes—
467C22×D3C2×D2014yes—
468C22×D3C2×C22⋊D514yes—
469C2×C3×C4—28no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—54no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—108no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—204no—
480C2×C3×C4C2×C22⋊D514yescomplemented
481C2×Dic3—28no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—102no—
485C2×Dic3—102no—
486C2×Dic3—102no—
487C2×Dic3—204no—
488C2×Dic3C2×C22⋊D514yescomplemented
489D12—1032no—
490C4×D3—232no—
491C22×C5—38no—
492C22×C5—632no—
493C22×C5—64no—
494C22×C5—64no—
495C22×C5—64no—
496C22×C5—64no—
497C22×C5—64no—
498C22×C5—64no—
499C22×C5C4×D1214yes—
500C22×C5D3×C22⋊C414yes—
501C22×C5#88214yes—
502C22×C5#88414yes—
503C22×C5#89314yes—
504C22×C5#89414yes—
505C22×C5#89514yes—
506C22×C5C22×C4×D311yescharacteristic
507C22×C5C22×D1211yescharacteristic
508C22×C5C2×#23511yescharacteristic
509C22×C5C2×D3×D411yescharacteristic
510C22×C5C2×D3×D411yescharacteristic
511C22×C5C2×D3×D411yescharacteristic
512C22×C5C2×#23911yescharacteristic
513C2×D5—64no—
514C2×D5—64no—
515C2×D5—64no—
516C2×D5—1216no—
517C2×D5—122no—
518C2×D5—122no—
519C2×D5—122no—
520C2×D5—122no—
521C4×C5—24no—
522C4×C5—64no—
523Dic5—24no—
524Dic5—42no—
525Dic5—122no—
526C24—34no—
527C24—34no—
528C24—34no—
529C24—32no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—154no—
535C24—152no—
536C24—302no—
537C24—302no—
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—34no—
550C22×C4—32no—
551C22×C4—54no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—68no—
555C22×C4—68no—
556C22×C4—632no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—68no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—152no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4#120314yescomplemented
570C22×C4C2×D3×D512yes—
571C22⋊C4—308no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3C2×#68514yes—
576C22×C3C4×C22⋊D514yes—
577C22×C3C4×C22⋊D514yes—
578C22×C3#407514yes—
579C22×C3#407614yes—
580C22×C3#407614yes—
581C22×C3#409914yes—
582C22×C3C22×C4×D511yescharacteristic
583C22×C3C22×D2011yescharacteristic
584C22×C3C2×#70911yescharacteristic
585C22×C3C2×#70911yescharacteristic
586C22×C3C22×C22⋊D511yescharacteristic
587C22×C3C22×C22⋊D511yescharacteristic
588C22×C3C22×C22⋊D511yescharacteristic
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—232no—
596C2×D3—104no—
597C2×D3—104no—
598C2×D3—104no—
599C2×D3—202no—
600C2×D3—202no—
601C2×D3—202no—
602C2×D3—202no—
603C2×D3—2016no—
604C2×D3C2×#68518yescomplemented
605C3×C4—24no—
606C3×C4—104no—
607C3×C4—202no—
608Dic3—24no—
609Dic3—202no—
610C2×C5—68no—
611C2×C5#466518yescomplemented
612C2×C5C2×C4×D1211yescharacteristic
613C2×C5C2×D3×C22⋊C411yescharacteristic
614C2×C5C2×#88211yescharacteristic
615C2×C5C2×#88411yescharacteristic
616C2×C5C2×#89311yescharacteristic
617C2×C5C2×#89411yescharacteristic
618C2×C5C2×#89511yescharacteristic
619D5—124no—
620C23—316no—
621C23—34no—
622C23—34no—
623C23—34no—
624C23—68no—
625C23—68no—
626C23—68no—
627C23—68no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—68no—
633C23—68no—
634C23—154no—
635C23—308no—
636C23—308no—
637C23—308no—
638C23—302no—
639C23—302no—
640C23—302no—
641C23—302no—
642C23—302no—
643C23—302no—
644C23—604no—
645C23—604no—
646C23—604no—
647C23—604no—
648C23#676912yes—
649C23#677112yes—
650C23C4×D3×D512yes—
651C23D3×D2012yes—
652C23C2×#120312yes—
653C23D3×C22⋊D512yes—
654C23D3×C22⋊D512yes—
655C23C22×D3×D511yescharacteristic
656D4—3032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—28no—
660C2×C4—34no—
661C2×C4—54no—
662C2×C4—632no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—68no—
666C2×C4—108no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—204no—
673C2×C4—302no—
674C2×C4—302no—
675C2×C4—302no—
676C2×C4—604no—
677C2×C4C2×#120314yescomplemented
678C2×C3#6550218yescomplemented
679C2×C3C22×#68511yescharacteristic
680C2×C3C2×C4×C22⋊D511yescharacteristic
681C2×C3C2×C4×C22⋊D511yescharacteristic
682C2×C3C2×#407511yescharacteristic
683C2×C3C2×#407611yescharacteristic
684C2×C3C2×#407611yescharacteristic
685C2×C3C2×#409911yescharacteristic
686D3—28no—
687D3—204no—
688C5C2×#466511yescharacteristic, complemented, Sylow
689C22—38no—
690C22—64no—
691C22—64no—
692C22—64no—
693C22—632no—
694C22—64no—
695C22—64no—
696C22—64no—
697C22—304no—
698C22—304no—
699C22—304no—
700C22—602no—
701C22—6016no—
702C22—602no—
703C22—602no—
704C22—602no—
705C22#9135114yes—
706C22C4×#120314yes—
707C22#9144614yes—
708C22#9145414yes—
709C22#9146014yes—
710C22D3×#68514yes—
711C22#9157014yes—
712C22C2×#676911yescharacteristic
713C22C2×#677111yescharacteristic
714C22C2×C4×D3×D511yescharacteristic
715C22C2×D3×D2011yescharacteristic
716C22C22×#120311yescharacteristic
717C22C2×D3×C22⋊D511yescharacteristic
718C22C2×D3×C22⋊D511yescharacteristic
719C4—24no—
720C4—64no—
721C4—104no—
722C4—202no—
723C4—602no—
724C3C2×#6550211yescharacteristic, complemented, Sylow
725C2—68no—
726C2—604no—
727C2#1174891418yesdirect product factor
728C2C2×#9135111yescharacteristic
729C2C2×C4×#120311yescharacteristic
730C2C2×#9144611yescharacteristic
731C2C2×#9145411yescharacteristic
732C2C2×#9146011yescharacteristic
733C2C2×D3×#68511yescharacteristic
734C2C2×#9157011yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1203C2
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
1. C23×C4×C5×D3C2semidirect
3. C22×#6714C2semidirect
4. C22×#6667C2semidirect
5. C22×(C2×D3)⋊Dic5C2semidirect
6. C2×C3×#3963C2semidirect
7. C2×#90994C2semidirect
8. #11748914C2direct (N × H)
18. C22×C4×C5×D3C22semidirect
23. C22×#1203C4semidirect
26. C2×#6714C22semidirect
28. C2×#6667C22semidirect
30. C2×(C2×D3)⋊Dic5C22semidirect
31. C3×#3963C22semidirect
32. #90994C22semidirect
41. C2×#3963D3semidirect
49. C23×D15C2×C4semidirect
61. C22×C3×C4×C5D4semidirect
69. C22×C5×Dic3D4semidirect
80. C22×C3×Dic5C2×C4semidirect
86. C2×#1203C2×C4semidirect
91. C23×C4×D3D5semidirect
120. #3963C2×D3semidirect
143. C22×D15C22×C4semidirect
154. C22×C5×D3C22⋊C4semidirect
161. C2×C3×C4×C5C2×D4semidirect
169. C2×C5×Dic3C2×D4semidirect
178. C2×C3×Dic5C22×C4semidirect
194. C22×C4×D3C2×D5semidirect
230. C22×C4×C5D12semidirect
245. C22×Dic5C4×D3semidirect
288. C2×C5×D3C2×C22⋊C4semidirect
321. C22×C3×C4C22⋊D5semidirect
329. C22×Dic3C22⋊D5semidirect
386. C2×C4×C5C2×D12semidirect
399. C2×Dic5C2×C4×D3semidirect
423. C2×C3×C5#386semidirect
465. C22×D3#685semidirect
480. C2×C3×C4C2×C22⋊D5semidirect
488. C2×Dic3C2×C22⋊D5semidirect
569. C22×C4#1203semidirect
574. C3×C5C2×#386semidirect
604. C2×D3C2×#685semidirect
611. C2×C5#4665semidirect
677. C2×C4C2×#1203semidirect
678. C2×C3#65502semidirect
688. C5C2×#4665semidirect
724. C3C2×#65502semidirect
727. C2#11748914direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C5×D32
C23×#12032
C22×#67142
C22×#66672
C22×(C2×D3)⋊Dic52
C2×C3×#39632
C2×#909942
#117489142
C2×#655023
C2×#46655