Finite Group Databasebeta

← C2×#11748910 #14320315

Subgroups — C2×#11748910 #14320315

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×#1201C211yesmaximal, characteristic
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
5C22×#6665C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748910C218yesmaximal, direct product factor
9C2×#65502—31nomaximal, Hall
10C24×C5×D3C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C4×C5×D3—24no—
17C22×C4×C5×D3—24no—
18C22×C4×C5×D3—24no—
19C22×C4×C5×D3C2214yescomplemented
20C23×C3×Dic5C2211yescharacteristic
21C22×#1201—24no—
22C22×#1201—24no—
23C22×#1201C418yescomplemented
24C22×#1201C2214yes—
25C2×C3×#685—24no—
26C2×C3×#685C2214yescomplemented
27C2×(C2×D3)⋊Dic5—24no—
28C2×(C2×D3)⋊Dic5C2214yescomplemented
29C2×#6665—24no—
30C2×#6665C2214yescomplemented
31#91115C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4956—51nomaximal, Hall
34C24×C4×C5—31no—
35C23×C22⋊D5—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685D311yescharacteristic, complemented
39#65502—38no—
40C2×#3963—31no—
41C2×#3963—31no—
42C24×C3×C5C2311yescharacteristic
43C23×C5×D3—22no—
44C23×C5×D3—22no—
45C23×C5×D3—22no—
46C23×C5×D3—22no—
47C23×C5×D3C2×C414yes—
48C23×C5×D3D414yes—
49C23×C5×D3D414yes—
50C23×C5×D3C2312yes—
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×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×Dic3D414yescomplemented
74C22×C5×Dic3C2312yes—
75C2×C4×C5×D3—232no—
76C2×C4×C5×D3—28no—
77C2×C4×C5×D3—28no—
78C2×C4×C5×D3—28no—
79C22×C3×Dic5—22no—
80C22×C3×Dic5—22no—
81C22×C3×Dic5—22no—
82C22×C3×Dic5C2312yes—
83C2×#1201—232no—
84C2×#1201—28no—
85C2×#1201—28no—
86C2×#1201C2×C4116yescomplemented
87C3×#685—28no—
88(C2×D3)⋊Dic5—28no—
89#6665—28no—
90C23×#67—51no—
91C23×C4×D3D511yescharacteristic, complemented
92C22×C3×C22⋊C4—51no—
93C22×#217—51no—
94C22×(C2×D3)⋊C4—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95—51no—
97#4956—58no—
98C25×C5—31no—
99C24×D5C2×D311yescharacteristic
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×Dic5—31no—
112C23×Dic5C2×D311yescharacteristic
113C2×C22⋊Dic5—34no—
114C2×C22⋊Dic5—64no—
115C2×#685—24no—
116C2×#685—34no—
117C2×#685—64no—
118C2×#685C2×D314yescomplemented
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—28no—
134C22×C5×D3—28no—
135C22×C5×D3—28no—
136C22×C5×D3—22no—
137C22×C5×D3—22no—
138C22×C5×D3—22no—
139C22×C5×D3—22no—
140C22×C5×D3C22⋊C4116yescomplemented
141C22×C5×D3C22×C414yes—
142C22×C5×D3C2×D414yes—
143C22×C5×D3C2×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—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—28no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3C2×D414yescomplemented
174C4×C5×D3—232no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—44no—
179#1201—232no—
180C25×C3—51no—
181C24×D3C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C22×#67—58no—
185C22×#67—54no—
186C22×#67—104no—
187C22×#67—104no—
188C23×Dic3—51no—
189C23×Dic3—51no—
190C23×Dic3C2×D511yescharacteristic
191C22×C4×D3—24no—
192C22×C4×D3—24no—
193C22×C4×D3—24no—
194C22×C4×D3C2×D514yescomplemented
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⋊#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—22no—
213C23×D5—22no—
214C23×D5—22no—
215C23×D5—22no—
216C23×D5—22no—
217C23×D5—22no—
218C23×D5C4×D314yescomplemented
219C23×D5C22×D312yes—
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×C5#6714yescomplemented
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—34no—
240C22×Dic5—32no—
241C22×Dic5—32no—
242C22×Dic5—62no—
243C22×Dic5—62no—
244C22×Dic5—62no—
245C22×Dic5—62no—
246C22×Dic5—62no—
247C22×Dic5C22×D312yes—
248C22⋊Dic5—68no—
249#685—28no—
250#685—68no—
251C23×D4—151no—
252C24×C4—31no—
253C22×C22⋊C4—51no—
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—24no—
277C2×C5×D3—24no—
278C2×C5×D3—24no—
279C2×C5×D3—232no—
280C2×C5×D3C2×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—24no—
290Dic15—24no—
291Dic15—42no—
292C3×Dic5—42no—
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—22no—
304C23×D3—22no—
305C23×D3—22no—
306C23×D3—22no—
307C23×D3C4×D514yes—
308C23×D3D2014yes—
309C23×D3C22⋊D514yes—
310C23×D3C22×D512yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—52no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4C22⋊D514yescomplemented
318C22×C3×C4C22×D512yes—
319C2×#67—516no—
320C2×#67—1032no—
321C2×#67—108no—
322C2×#67—108no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—54no—
326C22×Dic3—52no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3—102no—
332C22×Dic3—102no—
333C22×Dic3C22⋊D514yescomplemented
334C22×Dic3C22×D512yes—
335C2×C4×D3—232no—
336C2×C4×D3—28no—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339C3×C22⋊C4—108no—
340#217—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×C5#23512yes—
358C23×C5D3×D412yes—
359C23×C5D3×D412yes—
360C23×C5D3×D412yes—
361C23×C5#23712yes—
362C23×C5C2×#6712yes—
363C23×C5C23×D311yescharacteristic
364C22×D5—28no—
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—44no—
374C22×D5—44no—
375C22×D5—44no—
376C22×D5—44no—
377C22×D5C2×C4×D314yescomplemented
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×#6714yescomplemented
387C22⋊D5—632no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—34no—
392C2×Dic5—44no—
393C2×Dic5—68no—
394C2×Dic5—62no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5—62no—
399C2×Dic5—124no—
400C25—31no—
401C25—51no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—34no—
408C23×C4—51no—
409C23×C4—64no—
410C23×C4—64no—
411C23×C4—64no—
412C23×C4—151no—
413C23×C4—151no—
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—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—44no—
432C5×D3—28no—
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×C3#70912yes—
451C23×C3C2×C22⋊D512yes—
452C23×C3C2×C22⋊D512yes—
453C23×C3C2×C22⋊D512yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—28no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—28no—
461C22×D3—28no—
462C22×D3—28no—
463C22×D3—28no—
464C22×D3—28no—
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—102no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—204no—
476C2×C3×C4C2×C22⋊D514yescomplemented
477#67—1032no—
478C2×Dic3—28no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—54no—
482C2×Dic3—102no—
483C2×Dic3—102no—
484C2×Dic3—108no—
485C2×Dic3—102no—
486C2×Dic3—102no—
487C2×Dic3—102no—
488C2×Dic3—204no—
489C2×Dic3C2×C22⋊D514yescomplemented
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×C5D3×C22⋊C414yes—
500C22×C5#67⋊C414yes—
501C22×C5#88314yes—
502C22×C5#88414yes—
503C22×C5C4×#6714yes—
504C22×C5#93714yes—
505C22×C5#93814yes—
506C22×C5C22×C4×D311yescharacteristic
507C22×C5C2×#23511yescharacteristic
508C22×C5C2×D3×D411yescharacteristic
509C22×C5C2×D3×D411yescharacteristic
510C22×C5C2×D3×D411yescharacteristic
511C22×C5C2×#23711yescharacteristic
512C22×C5C22×#6711yescharacteristic
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—24no—
516C2×D5—416no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C4×C5—24no—
522C4×C5—64no—
523Dic5—42no—
524Dic5—64no—
525Dic5—122no—
526C24—34no—
527C24—34no—
528C24—34no—
529C24—32no—
530C24—54no—
531C24—52no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—102no—
537C24—102no—
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—34no—
550C22×C4—32no—
551C22×C4—52no—
552C22×C4—68no—
553C22×C4—68no—
554C22×C4—632no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—68no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
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—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×C3C2×#68514yes—
584C22×C3C4×C22⋊D514yes—
585C22×C3C4×C22⋊D514yes—
586C22×C3#407514yes—
587C22×C3#407614yes—
588C22×C3#407614yes—
589C22×C3#409914yes—
590C22×C3C22×C4×D511yescharacteristic
591C22×C3C22×D2011yescharacteristic
592C22×C3C2×#70911yescharacteristic
593C22×C3C2×#70911yescharacteristic
594C22×C3C22×C22⋊D511yescharacteristic
595C22×C3C22×C22⋊D511yescharacteristic
596C22×C3C22×C22⋊D511yescharacteristic
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—24no—
603C2×D3—232no—
604C2×D3C2×#68518yescomplemented
605C3×C4—24no—
606C3×C4—202no—
607Dic3—24no—
608Dic3—104no—
609Dic3—202no—
610C2×C5—68no—
611C2×C5#495618yescomplemented
612C2×C5C2×D3×C22⋊C411yescharacteristic
613C2×C5C2×#67⋊C411yescharacteristic
614C2×C5C2×#88311yescharacteristic
615C2×C5C2×#88411yescharacteristic
616C2×C5C2×C4×#6711yescharacteristic
617C2×C5C2×#93711yescharacteristic
618C2×C5C2×#93811yescharacteristic
619D5—44no—
620C23—316no—
621C23—34no—
622C23—34no—
623C23—34no—
624C23—54no—
625C23—68no—
626C23—68no—
627C23—68no—
628C23—68no—
629C23—68no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—68no—
635C23—108no—
636C23—108no—
637C23—108no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23#676512yes—
649C23#677112yes—
650C23C4×D3×D512yes—
651C23D3×D2012yes—
652C23C2×#120112yes—
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—632no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—68no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—154no—
669C2×C4—204no—
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—204no—
679C2×C3#6550218yescomplemented
680C2×C3C22×#68511yescharacteristic
681C2×C3C2×C4×C22⋊D511yescharacteristic
682C2×C3C2×C4×C22⋊D511yescharacteristic
683C2×C3C2×#407511yescharacteristic
684C2×C3C2×#407611yescharacteristic
685C2×C3C2×#407611yescharacteristic
686C2×C3C2×#409911yescharacteristic
687D3—28no—
688C5C2×#495611yescharacteristic, complemented, Sylow
689C22—38no—
690C22—64no—
691C22—64no—
692C22—64no—
693C22—632no—
694C22—64no—
695C22—64no—
696C22—64no—
697C22—104no—
698C22—104no—
699C22—104no—
700C22—202no—
701C22—2016no—
702C22—202no—
703C22—202no—
704C22—202no—
705C22C4×#120114yes—
706C22#9144114yes—
707C22#9145214yes—
708C22#9145414yes—
709C22#9145614yes—
710C22D3×#68514yes—
711C22#9156814yes—
712C22C2×#676511yescharacteristic
713C22C2×#677111yescharacteristic
714C22C2×C4×D3×D511yescharacteristic
715C22C2×D3×D2011yescharacteristic
716C22C22×#120111yescharacteristic
717C22C2×D3×C22⋊D511yescharacteristic
718C22C2×D3×C22⋊D511yescharacteristic
719C4—24no—
720C4—64no—
721C4—202no—
722C4—304no—
723C4—602no—
724C3C2×#6550211yescharacteristic, complemented, Sylow
725C2—68no—
726C2—204no—
727C2#1174891018yesdirect product factor
728C2C2×C4×#120111yescharacteristic
729C2C2×#9144111yescharacteristic
730C2C2×#9145211yescharacteristic
731C2C2×#9145411yescharacteristic
732C2C2×#9145611yescharacteristic
733C2C2×D3×#68511yescharacteristic
734C2C2×#9156811yescharacteristic
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×C4×C5×D3C2semidirect
3. C22×C3×#685C2semidirect
4. C22×(C2×D3)⋊Dic5C2semidirect
5. C22×#6665C2semidirect
6. C2×#91115C2semidirect
7. C2×#90994C2semidirect
8. #11748910C2direct (N × H)
19. C22×C4×C5×D3C22semidirect
23. C22×#1201C4semidirect
26. C2×C3×#685C22semidirect
28. C2×(C2×D3)⋊Dic5C22semidirect
30. C2×#6665C22semidirect
31. #91115C22semidirect
32. #90994C22semidirect
38. C22×#685D3semidirect
57. C23×C3×D5C2×C4semidirect
61. C22×C3×C4×C5D4semidirect
68. C22×Dic15C2×C4semidirect
73. C22×C5×Dic3D4semidirect
86. C2×#1201C2×C4semidirect
91. C23×C4×D3D5semidirect
118. C2×#685C2×D3semidirect
140. C22×C5×D3C22⋊C4semidirect
157. C22×C3×D5C22×C4semidirect
161. C2×C3×C4×C5C2×D4semidirect
169. C2×Dic15C22×C4semidirect
173. C2×C5×Dic3C2×D4semidirect
194. C22×C4×D3C2×D5semidirect
218. C23×D5C4×D3semidirect
230. C22×C4×C5#67semidirect
280. C2×C5×D3C2×C22⋊C4semidirect
317. C22×C3×C4C22⋊D5semidirect
333. C22×Dic3C22⋊D5semidirect
377. C22×D5C2×C4×D3semidirect
386. C2×C4×C5C2×#67semidirect
423. C2×C3×C5#386semidirect
465. C22×D3#685semidirect
476. C2×C3×C4C2×C22⋊D5semidirect
489. C2×Dic3C2×C22⋊D5semidirect
569. C22×C4#1201semidirect
574. C3×C5C2×#386semidirect
604. C2×D3C2×#685semidirect
611. C2×C5#4956semidirect
677. C2×C4C2×#1201semidirect
679. C2×C3#65502semidirect
688. C5C2×#4956semidirect
724. C3C2×#65502semidirect
727. C2#11748910direct (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×#12012
C22×C3×#6852
C22×(C2×D3)⋊Dic52
C22×#66652
C2×#911152
C2×#909942
#117489102
C2×#655023
C2×#49565