Finite Group Databasebeta

← C2×#11749519 #14320327

Subgroups — C2×#11749519 #14320327

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×C5×#67C211yesmaximal, characteristic
2C23×D3×Dic5C211yesmaximal, characteristic, complemented
3C22×#6719C211yesmaximal, characteristic, complemented
4C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
6#11749519C218yesmaximal, direct product factor
7C2×#90994C211yesmaximal, characteristic, complemented
8C2×#90994C211yesmaximal, characteristic, complemented
9C2×#65509—31nomaximal, Hall
10C25×C3×C5C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C22×C5×#67—24no—
15C22×C5×#67—24no—
16C22×C5×#67C418yescomplemented
17C22×C5×#67C2214yes—
18C23×C5×Dic3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×D3×Dic5—24no—
22C22×D3×Dic5—24no—
23C22×D3×Dic5—24no—
24C22×D3×Dic5C2214yescomplemented
25C2×#6719—24no—
26C2×#6719C2214yescomplemented
27C2×C3×C22⋊Dic5—24no—
28C2×C3×C22⋊Dic5C2214yescomplemented
29C2×(C2×D3)⋊Dic5—24no—
30C2×(C2×D3)⋊Dic5C2214yescomplemented
31#90994C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4956—51nomaximal, Hall
34C23×C5×D4—31no—
35C24×Dic5—31no—
36C22×C22⋊Dic5—31no—
37C22×C22⋊Dic5—31no—
38C22×C22⋊Dic5D311yescharacteristic, complemented
39#65509—38no—
40C2×#3963—31no—
41C2×#3963—31no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5—22no—
48C24×C3×C5C2×C414yescomplemented
49C24×C3×C5C2312yes—
50C24×C3×C5C2311yescharacteristic
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×Dic15—22no—
60C22×Dic15—22no—
61C22×Dic15—22no—
62C22×Dic15—22no—
63C22×Dic15—22no—
64C22×Dic15D414yescomplemented
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C2×C5×#67—232no—
68C2×C5×#67—28no—
69C2×C5×#67—28no—
70C2×C5×#67C2×C4116yescomplemented
71C22×C5×Dic3—22no—
72C22×C5×Dic3—22no—
73C22×C5×Dic3C2×C414yescomplemented
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5—22no—
78C22×C3×Dic5—22no—
79C22×C3×Dic5—22no—
80C22×C3×Dic5D414yescomplemented
81C22×C3×Dic5C2312yes—
82C22×C3×Dic5C2312yes—
83C2×D3×Dic5—232no—
84C2×D3×Dic5—28no—
85C2×D3×Dic5—28no—
86C2×D3×Dic5—28no—
87#6719—28no—
88C3×C22⋊Dic5—28no—
89(C2×D3)⋊Dic5—28no—
90C23×#67D511yescharacteristic
91C23×C4×D3—51no—
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—
99C25×C5C2×D311yescharacteristic
100C22×C5×D4—38no—
101C22×C5×D4—34no—
102C22×C5×D4—64no—
103C22×C5×D4—64no—
104C23×C4×C5—31no—
105C23×Dic5—31no—
106C23×Dic5—31no—
107C23×Dic5—34no—
108C23×Dic5—64no—
109C23×Dic5—64no—
110C23×Dic5—64no—
111C23×Dic5C2×D311yescharacteristic
112C23×Dic5C2×D311yescharacteristic
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—34no—
115C2×C22⋊Dic5—34no—
116C2×C22⋊Dic5—64no—
117C2×C22⋊Dic5—64no—
118C2×C22⋊Dic5C2×D314yescomplemented
119#3963—34no—
120#3963—34no—
121C2×#386—151noSylow
122C23×C3×C5—28no—
123C23×C3×C5—28no—
124C23×C3×C5—28no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—44no—
132C23×C3×C5—44no—
133C23×C3×C5—44no—
134C23×C3×C5—44no—
135C23×C3×C5C22×C412yes—
136C23×C3×C5C22×C414yescomplemented
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×D412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5C2×D412yes—
141C23×C3×C5#4112yes—
142C23×C3×C5#4112yes—
143C23×C3×C5C2411yescharacteristic
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×Dic15—28no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—44no—
165C2×Dic15C2×D414yescomplemented
166C5×#67—232no—
167C2×C5×Dic3—28no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C22×C414yescomplemented
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×Dic5C2×D414yescomplemented
179D3×Dic5—232no—
180C25×C3C2×D511yescharacteristic
181C24×D3C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C22×#67—24no—
185C22×#67—24no—
186C22×#67Dic518yescomplemented
187C22×#67C2×D514yes—
188C23×Dic3—51no—
189C23×Dic3—51no—
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⋊#95—54no—
203C24×C5—22no—
204C24×C5—22no—
205C24×C5—22no—
206C24×C5—22no—
207C24×C5—22no—
208C24×C5—22no—
209C24×C5—34no—
210C24×C5—34no—
211C24×C5—34no—
212C24×C5—32no—
213C24×C5—62no—
214C24×C5—62no—
215C24×C5—62no—
216C24×C5—62no—
217C24×C5C4×D314yescomplemented
218C24×C5C22×D312yes—
219C24×C5C22×D311yescharacteristic
220C2×C5×D4—316no—
221C2×C5×D4—632no—
222C2×C5×D4—68no—
223C2×C5×D4—68no—
224C22×C4×C5—34no—
225C22×C4×C5—32no—
226C22×C4×C5—62no—
227C22×C4×C5—62no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—34no—
234C22×Dic5—32no—
235C22×Dic5—32no—
236C22×Dic5—68no—
237C22×Dic5—68no—
238C22×Dic5—632no—
239C22×Dic5—62no—
240C22×Dic5—62no—
241C22×Dic5—68no—
242C22×Dic5—62no—
243C22×Dic5—62no—
244C22×Dic5—62no—
245C22×Dic5#6714yescomplemented
246C22×Dic5C22×D312yes—
247C22×Dic5C22×D312yes—
248C22⋊Dic5—28no—
249C22⋊Dic5—68no—
250C22⋊Dic5—68no—
251C23×D4—31no—
252C24×C4—151no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—151no—
258C2×#95—151no—
259C22×C3×C5—24no—
260C22×C3×C5—24no—
261C22×C3×C5—24no—
262C22×C3×C5—42no—
263C22×C3×C5—42no—
264C22×C3×C5—42no—
265C22×C3×C5—42no—
266C22×C3×C5—416no—
267C22×C3×C5C2×C22⋊C414yes—
268C22×C3×C5C4×D414yes—
269C22×C3×C5C4×D414yes—
270C22×C3×C5#12014yes—
271C22×C3×C5#12114yes—
272C22×C3×C5#12114yes—
273C22×C3×C5#12314yes—
274C22×C3×C5C23×C411yescharacteristic
275C22×C3×C5C22×D411yescharacteristic
276C22×C3×C5C22×D411yescharacteristic
277C22×C3×C5C22×D411yescharacteristic
278C22×C3×C5C22×D411yescharacteristic
279C22×C3×C5C2×#4111yescharacteristic
280C22×C3×C5C2×#4111yescharacteristic
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
289Dic15—24no—
290Dic15—42no—
291C3×Dic5—24no—
292C3×Dic5—42no—
293C5×Dic3—24no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—22no—
297C24×C3—22no—
298C24×C3—22no—
299C24×C3—22no—
300C24×C3C2×Dic514yescomplemented
301C24×C3C22×D512yes—
302C24×C3C22×D511yescharacteristic
303C23×D3—22no—
304C23×D3—22no—
305C23×D3—22no—
306C23×D3—22no—
307C23×D3C2×Dic514yes—
308C23×D3C22⋊D514yes—
309C23×D3C22⋊D514yes—
310C23×D3C22×D512yes—
311C22×C3×C4—54no—
312C22×C3×C4—52no—
313C22×C3×C4—52no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4—102no—
319C2×#67—232no—
320C2×#67—28no—
321C2×#67—28no—
322C2×#67C2×Dic5116yescomplemented
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×Dic3C2×Dic514yescomplemented
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×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—316no—
352C23×C5—34no—
353C23×C5—34no—
354C23×C5—34no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—68no—
360C23×C5—68no—
361C23×C5—68no—
362C23×C5—68no—
363C23×C5—68no—
364C23×C5—68no—
365C23×C5—62no—
366C23×C5—62no—
367C23×C5—62no—
368C23×C5—62no—
369C23×C5C2×C4×D312yes—
370C23×C5C2×C4×D314yescomplemented
371C23×C5#23512yes—
372C23×C5D3×D412yes—
373C23×C5D3×D412yes—
374C23×C5D3×D412yes—
375C23×C5#23712yes—
376C23×C5C2×#6712yes—
377C23×C5C23×D311yescharacteristic
378C5×D4—632no—
379C2×C4×C5—34no—
380C2×C4×C5—68no—
381C2×C4×C5—62no—
382C2×C4×C5—62no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—34no—
390C2×Dic5—44no—
391C2×Dic5—632no—
392C2×Dic5—68no—
393C2×Dic5—62no—
394C2×Dic5—62no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5—124no—
399C2×Dic5C2×#6714yescomplemented
400C25—31no—
401C25D3×D511yescharacteristic
402C22×D4—38no—
403C22×D4—34no—
404C22×D4—64no—
405C22×D4—64no—
406C23×C4—31no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—154no—
410C23×C4—151no—
411C23×C4—151no—
412C23×C4—304no—
413C23×C4—304no—
414C23×C4—304no—
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—44no—
424C2×C3×C5#38618yescomplemented
425C2×C3×C5C22×C22⋊C411yescharacteristic
426C2×C3×C5C2×C4×D411yescharacteristic
427C2×C3×C5C2×C4×D411yescharacteristic
428C2×C3×C5C2×#12011yescharacteristic
429C2×C3×C5C2×#12111yescharacteristic
430C2×C3×C5C2×#12111yescharacteristic
431C2×C3×C5C2×#12311yescharacteristic
432C5×D3—28no—
433C23×C3—28no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—28no—
441C23×C3—28no—
442C23×C3—44no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3D4×D512yes—
447C23×C3D4×D512yes—
448C23×C3#71112yes—
449C23×C3#71112yes—
450C23×C3C22×Dic512yes—
451C23×C3C22×Dic514yescomplemented
452C23×C3C2×C22⋊D512yes—
453C23×C3C2×C22⋊D512yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—28no—
460C22×D3—28no—
461C22×D3—28no—
462C22×D3—28no—
463C22×D3—28no—
464C22×D3—28no—
465C22×D3C22⋊Dic5116yescomplemented
466C22×D3C22×Dic514yes—
467C22×D3C2×C22⋊D514yes—
468C22×D3C2×C22⋊D514yes—
469C2×C3×C4—54no—
470C2×C3×C4—102no—
471C2×C3×C4—102no—
472C2×C3×C4—108no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—204no—
477#67—232no—
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×Dic3C22×Dic514yescomplemented
490C4×D3—1032no—
491C22×C5—24no—
492C22×C5—24no—
493C22×C5—24no—
494C22×C5—38no—
495C22×C5—416no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—632no—
501C22×C5—64no—
502C22×C5—64no—
503C22×C5—64no—
504C22×C5—64no—
505C22×C5—64no—
506C22×C5—64no—
507C22×C5D3×C22⋊C414yes—
508C22×C5#67⋊C414yes—
509C22×C5#88314yes—
510C22×C5#88414yes—
511C22×C5C4×#6714yes—
512C22×C5#93714yes—
513C22×C5#93814yes—
514C22×C5C22×C4×D311yescharacteristic
515C22×C5C2×#23511yescharacteristic
516C22×C5C2×D3×D411yescharacteristic
517C22×C5C2×D3×D411yescharacteristic
518C22×C5C2×D3×D411yescharacteristic
519C22×C5C2×#23711yescharacteristic
520C22×C5C22×#6711yescharacteristic
521C4×C5—64no—
522Dic5—24no—
523Dic5—42no—
524Dic5—64no—
525Dic5—122no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—34no—
533C24—34no—
534C24—34no—
535C24—32no—
536C24—62no—
537C24—62no—
538C24—62no—
539C24—62no—
540C24D3×Dic514yescomplemented
541C24C2×D3×D512yes—
542C24C2×D3×D511yescharacteristic
543C2×D4—316no—
544C2×D4—68no—
545C2×D4—68no—
546C2×D4—632no—
547C22×C4—34no—
548C22×C4—32no—
549C22×C4—54no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—154no—
560C22×C4—152no—
561C22×C4—152no—
562C22×C4—308no—
563C22×C4—308no—
564C22×C4—308no—
565C22×C4—3032no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22⋊C4—108no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3—24no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—416no—
583C22×C3D4×Dic514yes—
584C22×C3D4×Dic514yes—
585C22×C3#408114yes—
586C22×C3#408314yes—
587C22×C3#408514yes—
588C22×C3#408514yes—
589C22×C3C2×C22⋊Dic514yes—
590C22×C3C2×D4×D511yescharacteristic
591C22×C3C2×D4×D511yescharacteristic
592C22×C3C2×#71111yescharacteristic
593C22×C3C2×#71111yescharacteristic
594C22×C3C23×Dic511yescharacteristic
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×C22⋊Dic518yescomplemented
605C3×C4—104no—
606C3×C4—202no—
607Dic3—24no—
608Dic3—104no—
609Dic3—202no—
610C2×C5—44no—
611C2×C5—68no—
612C2×C5#495618yescomplemented
613C2×C5C2×D3×C22⋊C411yescharacteristic
614C2×C5C2×#67⋊C411yescharacteristic
615C2×C5C2×#88311yescharacteristic
616C2×C5C2×#88411yescharacteristic
617C2×C5C2×C4×#6711yescharacteristic
618C2×C5C2×#93711yescharacteristic
619C2×C5C2×#93811yescharacteristic
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—34no—
630C23—34no—
631C23—34no—
632C23—316no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—68no—
642C23—68no—
643C23—68no—
644C23—68no—
645C23—68no—
646C23—68no—
647C23#678012yes—
648C23C2×D3×Dic512yes—
649C23C2×D3×Dic514yescomplemented
650C23#678212yes—
651C23D5×#6712yes—
652C23D3×C22⋊D512yes—
653C23D3×C22⋊D512yes—
654C23#679012yes—
655C23C22×D3×D511yescharacteristic
656D4—632no—
657C2×C4—34no—
658C2×C4—54no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—68no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—108no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—154no—
669C2×C4—204no—
670C2×C4—3032no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—308no—
674C2×C4—302no—
675C2×C4—302no—
676C2×C4—302no—
677C2×C4—604no—
678C2×C3—44no—
679C2×C3#6550918yescomplemented
680C2×C3C2×D4×Dic511yescharacteristic
681C2×C3C2×D4×Dic511yescharacteristic
682C2×C3C2×#408111yescharacteristic
683C2×C3C2×#408311yescharacteristic
684C2×C3C2×#408511yescharacteristic
685C2×C3C2×#408511yescharacteristic
686C2×C3C22×C22⋊Dic511yescharacteristic
687D3—28no—
688C5C2×#495611yescharacteristic, complemented, Sylow
689C22—24no—
690C22—24no—
691C22—24no—
692C22—38no—
693C22—42no—
694C22—42no—
695C22—416no—
696C22—42no—
697C22—42no—
698C22—64no—
699C22—64no—
700C22—64no—
701C22—64no—
702C22—632no—
703C22—64no—
704C22—64no—
705C22Dic5×#6714yes—
706C22D3×C22⋊Dic514yes—
707C22#9155514yes—
708C22#9155814yes—
709C22#67⋊Dic514yes—
710C22#9156514yes—
711C22#9157714yes—
712C22C2×#678011yescharacteristic
713C22C22×D3×Dic511yescharacteristic
714C22C2×#678211yescharacteristic
715C22C2×D5×#6711yescharacteristic
716C22C2×D3×C22⋊D511yescharacteristic
717C22C2×D3×C22⋊D511yescharacteristic
718C22C2×#679011yescharacteristic
719C4—64no—
720C4—104no—
721C4—202no—
722C4—304no—
723C4—602no—
724C3C2×#6550911yescharacteristic, complemented, Sylow
725C2—44no—
726C2—68no—
727C2#1174951918yesdirect product factor
728C2C2×Dic5×#6711yescharacteristic
729C2C2×D3×C22⋊Dic511yescharacteristic
730C2C2×#9155511yescharacteristic
731C2C2×#9155811yescharacteristic
732C2C2×#67⋊Dic511yescharacteristic
733C2C2×#9156511yescharacteristic
734C2C2×#9157711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC25×C3×C5C22
socleC24×C3×C5C23
prime radicalC23×C5×#67C2
cosocleC23×C3×C5C24
hypercenterC25D3×D5
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C23×D3×Dic5C2semidirect
3. C22×#6719C2semidirect
4. C22×C3×C22⋊Dic5C2semidirect
5. C22×(C2×D3)⋊Dic5C2semidirect
6. #11749519C2direct (N × H)
7. C2×#90994C2semidirect
8. C2×#90994C2semidirect
16. C22×C5×#67C4semidirect
24. C22×D3×Dic5C22semidirect
26. C2×#6719C22semidirect
28. C2×C3×C22⋊Dic5C22semidirect
30. C2×(C2×D3)⋊Dic5C22semidirect
31. #90994C22semidirect
32. #90994C22semidirect
38. C22×C22⋊Dic5D3semidirect
48. C24×C3×C5C2×C4semidirect
64. C22×Dic15D4semidirect
70. C2×C5×#67C2×C4semidirect
73. C22×C5×Dic3C2×C4semidirect
80. C22×C3×Dic5D4semidirect
118. C2×C22⋊Dic5C2×D3semidirect
136. C23×C3×C5C22×C4semidirect
154. C22×C5×D3C22⋊C4semidirect
165. C2×Dic15C2×D4semidirect
170. C2×C5×Dic3C22×C4semidirect
178. C2×C3×Dic5C2×D4semidirect
186. C22×#67Dic5semidirect
217. C24×C5C4×D3semidirect
245. C22×Dic5#67semidirect
288. C2×C5×D3C2×C22⋊C4semidirect
300. C24×C3C2×Dic5semidirect
322. C2×#67C2×Dic5semidirect
333. C22×Dic3C2×Dic5semidirect
370. C23×C5C2×C4×D3semidirect
399. C2×Dic5C2×#67semidirect
424. C2×C3×C5#386semidirect
451. C23×C3C22×Dic5semidirect
465. C22×D3C22⋊Dic5semidirect
489. C2×Dic3C22×Dic5semidirect
540. C24D3×Dic5semidirect
574. C3×C5C2×#386semidirect
604. C2×D3C2×C22⋊Dic5semidirect
612. C2×C5#4956semidirect
649. C23C2×D3×Dic5semidirect
679. C2×C3#65509semidirect
688. C5C2×#4956semidirect
724. C3C2×#65509semidirect
727. C2#11749519direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×#672
C23×D3×Dic52
C22×#67192
C22×C3×C22⋊Dic52
C22×(C2×D3)⋊Dic52
#117495192
C2×#909942
C2×#655093
C2×#49565