Finite Group Databasebeta

← C2×#11748905 #14320313

Subgroups — C2×#11748905 #14320313

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×C3×C4×D5C211yesmaximal, characteristic, complemented
2C23×#1201C211yesmaximal, characteristic
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
5C22×#6665C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748905C218yesmaximal, direct product factor
9C2×#65245—31nomaximal, Hall
10C24×C5×D3C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×C3×C4×D5—24no—
18C22×C3×C4×D5—24no—
19C22×C3×C4×D5—24no—
20C22×C3×C4×D5C2214yescomplemented
21C22×#1201—24no—
22C22×#1201—24no—
23C22×#1201C418yescomplemented
24C22×#1201C2214yes—
25C2×C5×(C2×D3)⋊C4—24no—
26C2×C5×(C2×D3)⋊C4C2214yescomplemented
27C2×(C2×D3)⋊Dic5—24no—
28C2×(C2×D3)⋊Dic5C2214yescomplemented
29C2×#6665—24no—
30C2×#6665C2214yescomplemented
31#91115C2214yescomplemented
32#90994C2214yescomplemented
33C2×#5213—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C23×C4×D5D311yescharacteristic, complemented
36C22×C5×C22⋊C4—31no—
37C22×C22⋊Dic5—31no—
38C22×#685—31no—
39C2×#3963—31no—
40C2×#3963—31no—
41#65245—38no—
42C24×C3×C5C2311yescharacteristic
43C23×C5×D3—22no—
44C23×C5×D3—22no—
45C23×C5×D3—22no—
46C23×C5×D3—22no—
47C23×C5×D3—22no—
48C23×C5×D3—22no—
49C23×C5×D3C2×C414yescomplemented
50C23×C5×D3C2312yes—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5C2×C414yes—
56C23×C3×D5D414yes—
57C23×C3×D5D414yes—
58C23×C3×D5C2312yes—
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×Dic15—22no—
67C22×Dic15—22no—
68C22×Dic15C2×C414yescomplemented
69C22×Dic15C2312yes—
70C22×Dic15C2312yes—
71C22×C5×Dic3—22no—
72C22×C5×Dic3—22no—
73C22×C5×Dic3—22no—
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5D414yescomplemented
78C22×C3×Dic5C2312yes—
79C2×C3×C4×D5—232no—
80C2×C3×C4×D5—28no—
81C2×C3×C4×D5—28no—
82C2×C3×C4×D5—28no—
83C2×#1201—232no—
84C2×#1201—28no—
85C2×#1201—28no—
86C2×#1201C2×C4116yescomplemented
87C5×(C2×D3)⋊C4—28no—
88(C2×D3)⋊Dic5—28no—
89#6665—28no—
90C24×C3×C4—51no—
91C23×#67—51no—
92C22×#217—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4D511yescharacteristic, complemented
95#5213—58no—
96C2×C3⋊#95—51no—
97C2×C3⋊#95—51no—
98C25×C5—31no—
99C24×D5C2×D311yescharacteristic
100C23×C4×C5—31no—
101C23×C4×C5C2×D311yescharacteristic
102C22×C22⋊D5—38no—
103C22×C22⋊D5—34no—
104C22×C22⋊D5—64no—
105C22×C22⋊D5—64no—
106C23×Dic5—31no—
107C23×Dic5—31no—
108C23×Dic5C2×D311yescharacteristic
109C22×C4×D5—24no—
110C22×C4×D5—24no—
111C22×C4×D5—24no—
112C22×C4×D5C2×D314yescomplemented
113C2×C5×C22⋊C4—34no—
114C2×C5×C22⋊C4—64no—
115C2×C22⋊Dic5—34no—
116C2×C22⋊Dic5—64no—
117C2×#685—34no—
118C2×#685—64no—
119#3963—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×C5×D3—28no—
131C22×C5×D3—28no—
132C22×C5×D3—28no—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3—22no—
136C22×C5×D3—22no—
137C22×C5×D3—22no—
138C22×C5×D3—22no—
139C22×C5×D3—44no—
140C22×C5×D3—44no—
141C22×C5×D3—44no—
142C22×C5×D3—44no—
143C22×C5×D3C22×C414yescomplemented
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—28no—
147C22×C3×D5—28no—
148C22×C3×D5—28no—
149C22×C3×D5—28no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5C22⋊C4116yescomplemented
155C22×C3×D5C22×C414yes—
156C22×C3×D5C2×D414yes—
157C22×C3×D5C2×D414yes—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5C2×D414yescomplemented
162C2×Dic15—28no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15—22no—
167C2×Dic15—22no—
168C2×Dic15—44no—
169C2×Dic15C22×C414yescomplemented
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—44no—
174C2×C3×Dic5—28no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5C2×D414yescomplemented
178C3×C4×D5—232no—
179#1201—232no—
180C25×C3—51no—
181C24×D3C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4—54no—
184C23×C3×C4—104no—
185C23×C3×C4—104no—
186C23×C3×C4—104no—
187C23×C3×C4C2×D511yescharacteristic
188C22×#67—58no—
189C22×#67—54no—
190C22×#67—104no—
191C22×#67—104no—
192C23×Dic3—51no—
193C23×Dic3—51no—
194C23×Dic3C2×D511yescharacteristic
195C2×#217—54no—
196C2×#217—104no—
197C2×(C2×D3)⋊C4—24no—
198C2×(C2×D3)⋊C4—54no—
199C2×(C2×D3)⋊C4—104no—
200C2×(C2×D3)⋊C4C2×D514yescomplemented
201C3⋊#95—54no—
202C3⋊#95—54no—
203C24×C5—34no—
204C24×C5—32no—
205C24×C5—62no—
206C24×C5—62no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5—62no—
211C24×C5C22×D311yescharacteristic
212C23×D5—22no—
213C23×D5—22no—
214C23×D5—22no—
215C23×D5—22no—
216C23×D5C4×D314yes—
217C23×D5D1214yes—
218C23×D5#6714yes—
219C23×D5C22×D312yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—32no—
223C22×C4×C5—62no—
224C22×C4×C5—62no—
225C22×C4×C5—62no—
226C22×C4×C5#6714yescomplemented
227C22×C4×C5C22×D312yes—
228C2×C22⋊D5—316no—
229C2×C22⋊D5—632no—
230C2×C22⋊D5—68no—
231C2×C22⋊D5—68no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—34no—
235C22×Dic5—32no—
236C22×Dic5—32no—
237C22×Dic5—62no—
238C22×Dic5—62no—
239C22×Dic5—62no—
240C22×Dic5—62no—
241C22×Dic5—62no—
242C22×Dic5#6714yescomplemented
243C22×Dic5C22×D312yes—
244C2×C4×D5—232no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C5×C22⋊C4—68no—
249C22⋊Dic5—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—51no—
253C22×C22⋊C4—31no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—151no—
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×C5×D3—24no—
274C2×C5×D3—24no—
275C2×C5×D3—24no—
276C2×C5×D3—42no—
277C2×C5×D3—42no—
278C2×C5×D3—42no—
279C2×C5×D3—42no—
280C2×C5×D3—416no—
281C2×C3×D5—24no—
282C2×C3×D5—24no—
283C2×C3×D5—24no—
284C2×C3×D5—24no—
285C2×C3×D5—24no—
286C2×C3×D5—24no—
287C2×C3×D5—232no—
288C2×C3×D5C2×C22⋊C418yescomplemented
289C3×C4×C5—24no—
290Dic15—24no—
291Dic15—42no—
292C3×Dic5—24no—
293C5×Dic3—42no—
294C24×C3—54no—
295C24×C3—54no—
296C24×C3—54no—
297C24×C3—52no—
298C24×C3—102no—
299C24×C3—102no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3C22×D511yescharacteristic
303C23×D3—22no—
304C23×D3—22no—
305C23×D3—22no—
306C23×D3—22no—
307C23×D3—22no—
308C23×D3—22no—
309C23×D3C4×D514yescomplemented
310C23×D3C22×D512yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—54no—
314C22×C3×C4—52no—
315C22×C3×C4—108no—
316C22×C3×C4—108no—
317C22×C3×C4—1032no—
318C22×C3×C4—102no—
319C22×C3×C4—102no—
320C22×C3×C4—108no—
321C22×C3×C4C22⋊D514yescomplemented
322C22×C3×C4C22×D512yes—
323C2×#67—516no—
324C2×#67—108no—
325C2×#67—108no—
326C2×#67—1032no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—54no—
331C22×Dic3—52no—
332C22×Dic3—52no—
333C22×Dic3—102no—
334C22×Dic3—102no—
335C22×Dic3—102no—
336C22×Dic3—102no—
337C22×Dic3—102no—
338C22×Dic3C22×D512yes—
339#217—108no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—108no—
342C23×C5—34no—
343C23×C5—68no—
344C23×C5—68no—
345C23×C5—68no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—62no—
349C23×C5—62no—
350C23×C5—62no—
351C23×C5—62no—
352C23×C5—124no—
353C23×C5—124no—
354C23×C5—124no—
355C23×C5—124no—
356C23×C5C2×C4×D312yes—
357C23×C5C2×D1212yes—
358C23×C5#23512yes—
359C23×C5#23512yes—
360C23×C5C2×#6712yes—
361C23×C5C2×#6712yes—
362C23×C5C2×#6712yes—
363C23×C5C23×D311yescharacteristic
364C22×D5—28no—
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5(C2×D3)⋊C4116yescomplemented
375C22×D5C2×C4×D314yes—
376C22×D5C2×D1214yes—
377C22×D5C2×#6714yes—
378C2×C4×C5—28no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—62no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—124no—
385C2×C4×C5C2×#6714yescomplemented
386C22⋊D5—632no—
387C2×Dic5—28no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—34no—
391C2×Dic5—68no—
392C2×Dic5—62no—
393C2×Dic5—62no—
394C2×Dic5—62no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—124no—
398C2×Dic5C2×#6714yescomplemented
399C4×D5—232no—
400C25—31no—
401C25—51no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—51no—
408C23×C4—54no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4—151no—
413C23×C4—151no—
414C23×C4D3×D511yescharacteristic
415C2×C22⋊C4—34no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—154no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4—304no—
421#95—154no—
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
431C3×D5—28no—
432C5×D3—44no—
433C23×C3—54no—
434C23×C3—54no—
435C23×C3—54no—
436C23×C3—516no—
437C23×C3—102no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—102no—
441C23×C3—108no—
442C23×C3—108no—
443C23×C3—108no—
444C23×C3—108no—
445C23×C3—108no—
446C23×C3—108no—
447C23×C3C2×C4×D512yes—
448C23×C3#70912yes—
449C23×C3D4×D512yes—
450C23×C3D4×D512yes—
451C23×C3D4×D512yes—
452C23×C3#71112yes—
453C23×C3C2×C22⋊D512yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—28no—
462C22×D3—28no—
463C22×D3—28no—
464C22×D3—44no—
465C22×D3—44no—
466C22×D3—44no—
467C22×D3—44no—
468C22×D3C2×C4×D514yescomplemented
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—28no—
472C2×C3×C4—54no—
473C2×C3×C4—1032no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—108no—
477C2×C3×C4C2×C22⋊D514yescomplemented
478#67—1032no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—44no—
483C2×Dic3—54no—
484C2×Dic3—102no—
485C2×Dic3—102no—
486C2×Dic3—108no—
487C2×Dic3—102no—
488C2×Dic3—102no—
489C2×Dic3—102no—
490C2×Dic3—204no—
491C22×C5—64no—
492C22×C5—64no—
493C22×C5—64no—
494C22×C5—1216no—
495C22×C5—122no—
496C22×C5—122no—
497C22×C5—122no—
498C22×C5—122no—
499C22×C5C2×(C2×D3)⋊C414yes—
500C22×C5C4×#6714yes—
501C22×C5C4×#6714yes—
502C22×C5#92914yes—
503C22×C5#93014yes—
504C22×C5#93014yes—
505C22×C5#95314yes—
506C22×C5C22×C4×D311yescharacteristic
507C22×C5C22×D1211yescharacteristic
508C22×C5C2×#23511yescharacteristic
509C22×C5C2×#23511yescharacteristic
510C22×C5C22×#6711yescharacteristic
511C22×C5C22×#6711yescharacteristic
512C22×C5C22×#6711yescharacteristic
513C2×D5—232no—
514C2×D5—24no—
515C2×D5—24no—
516C2×D5—24no—
517C2×D5—24no—
518C2×D5—24no—
519C2×D5—24no—
520C2×D5C2×(C2×D3)⋊C418yescomplemented
521C4×C5—24no—
522C4×C5—122no—
523Dic5—24no—
524Dic5—64no—
525Dic5—122no—
526C24—34no—
527C24—32no—
528C24—54no—
529C24—54no—
530C24—54no—
531C24—52no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—62no—
537C24—62no—
538C24—102no—
539C24—102no—
540C24—102no—
541C24—102no—
542C24C2×D3×D511yescharacteristic
543C2×D4—1516no—
544C2×D4—3032no—
545C2×D4—308no—
546C2×D4—308no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—32no—
550C22×C4—54no—
551C22×C4—52no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—108no—
556C22×C4—108no—
557C22×C4—1032no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—108no—
561C22×C4—154no—
562C22×C4—152no—
563C22×C4—152no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4#120114yescomplemented
570C22×C4C2×D3×D512yes—
571C22⋊C4—68no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3—58no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—104no—
580C22×C3—104no—
581C22×C3—104no—
582C22×C3—1032no—
583C22×C3D5×C22⋊C414yes—
584C22×C3#402714yes—
585C22×C3#402914yes—
586C22×C3#403014yes—
587C22×C3C4×C22⋊D514yes—
588C22×C3#408314yes—
589C22×C3#408414yes—
590C22×C3C22×C4×D511yescharacteristic
591C22×C3C2×#70911yescharacteristic
592C22×C3C2×D4×D511yescharacteristic
593C22×C3C2×D4×D511yescharacteristic
594C22×C3C2×D4×D511yescharacteristic
595C22×C3C2×#71111yescharacteristic
596C22×C3C22×C22⋊D511yescharacteristic
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—42no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—416no—
605C3×C4—24no—
606C3×C4—104no—
607Dic3—42no—
608Dic3—104no—
609Dic3—202no—
610C2×C5—124no—
611C2×C5#521318yescomplemented
612C2×C5C22×(C2×D3)⋊C411yescharacteristic
613C2×C5C2×C4×#6711yescharacteristic
614C2×C5C2×C4×#6711yescharacteristic
615C2×C5C2×#92911yescharacteristic
616C2×C5C2×#93011yescharacteristic
617C2×C5C2×#93011yescharacteristic
618C2×C5C2×#95311yescharacteristic
619D5—28no—
620C23—34no—
621C23—516no—
622C23—54no—
623C23—54no—
624C23—54no—
625C23—68no—
626C23—68no—
627C23—68no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—108no—
635C23—108no—
636C23—108no—
637C23—108no—
638C23—108no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—108no—
644C23—124no—
645C23—124no—
646C23—124no—
647C23—124no—
648C23#677112yes—
649C23#677212yes—
650C23C4×D3×D512yes—
651C23D5×D1212yes—
652C23C2×#120112yes—
653C23D5×#6712yes—
654C23D5×#6712yes—
655C23C22×D3×D511yescharacteristic
656D4—3032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—28no—
660C2×C4—54no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—1032no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—108no—
668C2×C4—124no—
669C2×C4—154no—
670C2×C4—308no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—302no—
674C2×C4—302no—
675C2×C4—302no—
676C2×C4—604no—
677C2×C4C2×#120114yescomplemented
678C2×C3—108no—
679C2×C3#6524518yescomplemented
680C2×C3C2×D5×C22⋊C411yescharacteristic
681C2×C3C2×#402711yescharacteristic
682C2×C3C2×#402911yescharacteristic
683C2×C3C2×#403011yescharacteristic
684C2×C3C2×C4×C22⋊D511yescharacteristic
685C2×C3C2×#408311yescharacteristic
686C2×C3C2×#408411yescharacteristic
687D3—44no—
688C5C2×#521311yescharacteristic, complemented, Sylow
689C22—58no—
690C22—64no—
691C22—64no—
692C22—64no—
693C22—104no—
694C22—104no—
695C22—104no—
696C22—104no—
697C22—104no—
698C22—1032no—
699C22—104no—
700C22—122no—
701C22—122no—
702C22—122no—
703C22—1216no—
704C22—122no—
705C22C4×#120114yes—
706C22#9144014yes—
707C22#9144714yes—
708C22#9144814yes—
709C22#9144914yes—
710C22D5×(C2×D3)⋊C414yes—
711C22#9156314yes—
712C22C2×#677111yescharacteristic
713C22C2×#677211yescharacteristic
714C22C2×C4×D3×D511yescharacteristic
715C22C2×D5×D1211yescharacteristic
716C22C22×#120111yescharacteristic
717C22C2×D5×#6711yescharacteristic
718C22C2×D5×#6711yescharacteristic
719C4—24no—
720C4—104no—
721C4—122no—
722C4—304no—
723C4—602no—
724C3C2×#6524511yescharacteristic, complemented, Sylow
725C2—108no—
726C2—124no—
727C2#1174890518yesdirect product factor
728C2C2×C4×#120111yescharacteristic
729C2C2×#9144011yescharacteristic
730C2C2×#9144711yescharacteristic
731C2C2×#9144811yescharacteristic
732C2C2×#9144911yescharacteristic
733C2C2×D5×(C2×D3)⋊C411yescharacteristic
734C2C2×#9156311yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1201C2
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×C3×C4×D5C2semidirect
3. C22×C5×(C2×D3)⋊C4C2semidirect
4. C22×(C2×D3)⋊Dic5C2semidirect
5. C22×#6665C2semidirect
6. C2×#91115C2semidirect
7. C2×#90994C2semidirect
8. #11748905C2direct (N × H)
20. C22×C3×C4×D5C22semidirect
23. C22×#1201C4semidirect
26. C2×C5×(C2×D3)⋊C4C22semidirect
28. C2×(C2×D3)⋊Dic5C22semidirect
30. C2×#6665C22semidirect
31. #91115C22semidirect
32. #90994C22semidirect
35. C23×C4×D5D3semidirect
49. C23×C5×D3C2×C4semidirect
61. C22×C3×C4×C5D4semidirect
68. C22×Dic15C2×C4semidirect
77. C22×C3×Dic5D4semidirect
86. C2×#1201C2×C4semidirect
94. C22×(C2×D3)⋊C4D5semidirect
112. C22×C4×D5C2×D3semidirect
143. C22×C5×D3C22×C4semidirect
154. C22×C3×D5C22⋊C4semidirect
161. C2×C3×C4×C5C2×D4semidirect
169. C2×Dic15C22×C4semidirect
177. C2×C3×Dic5C2×D4semidirect
200. C2×(C2×D3)⋊C4C2×D5semidirect
226. C22×C4×C5#67semidirect
242. C22×Dic5#67semidirect
288. C2×C3×D5C2×C22⋊C4semidirect
309. C23×D3C4×D5semidirect
321. C22×C3×C4C22⋊D5semidirect
374. C22×D5(C2×D3)⋊C4semidirect
385. C2×C4×C5C2×#67semidirect
398. C2×Dic5C2×#67semidirect
423. C2×C3×C5#386semidirect
468. C22×D3C2×C4×D5semidirect
477. C2×C3×C4C2×C22⋊D5semidirect
520. C2×D5C2×(C2×D3)⋊C4semidirect
569. C22×C4#1201semidirect
574. C3×C5C2×#386semidirect
611. C2×C5#5213semidirect
677. C2×C4C2×#1201semidirect
679. C2×C3#65245semidirect
688. C5C2×#5213semidirect
724. C3C2×#65245semidirect
727. C2#11748905direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C23×#12012
C22×C5×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic52
C22×#66652
C2×#911152
C2×#909942
#117489052
C2×#652453
C2×#52135