Finite Group Databasebeta

← C2×#11748908 #14320795

Subgroups — C2×#11748908 #14320795

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1203C211yesmaximal, characteristic
2C22×#6714C211yesmaximal, characteristic, complemented
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
5C22×#6668C211yesmaximal, characteristic, complemented
6C22×#6667C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
8#11748908C218yesmaximal, direct product factor
9C2×#65246—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1203—24no—
18C22×#1203—24no—
19C22×#1203C418yescomplemented
20C22×#1203C2214yes—
21C2×#6714—24no—
22C2×#6714C2214yescomplemented
23C2×C5×(C2×D3)⋊C4—24no—
24C2×C5×(C2×D3)⋊C4C2214yescomplemented
25C2×C3×C4×Dic5—24no—
26C2×C3×C4×Dic5C2214yescomplemented
27C2×#6668—24no—
28C2×#6668C2214yescomplemented
29C2×#6667—24no—
30C2×#6667C2214yescomplemented
31C2×(C2×D3)⋊Dic5—24no—
32C2×(C2×D3)⋊Dic5C2214yescomplemented
33C2×#4939—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C22×C5×C22⋊C4—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#683—31no—
40C22×C4×Dic5D311yescharacteristic, complemented
41#65246—38no—
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15—22no—
48C23×D15—22no—
49C23×D15C2×C414yes—
50C23×D15C2312yes—
51C23×C5×D3—22no—
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3—22no—
56C23×C5×D3—22no—
57C23×C5×D3C2×C414yes—
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×Dic3—22no—
70C22×C5×Dic3C2312yes—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5C2×C414yes—
74C22×C3×Dic5D414yes—
75C22×C3×Dic5D414yes—
76C22×C3×Dic5D414yescomplemented
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2312yes—
79C2×#1203—232no—
80C2×#1203—28no—
81C2×#1203—28no—
82C2×#1203C2×C4116yescomplemented
83#6714—28no—
84C5×(C2×D3)⋊C4—28no—
85C3×C4×Dic5—28no—
86#6668—28no—
87#6667—28no—
88(C2×D3)⋊Dic5—28no—
89C23×D12—51no—
90C22×C3×C42—51no—
91C22×(C2×D3)⋊C4—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4D511yescharacteristic, complemented
95C22×C4⋊Dic3—51no—
96#4939—58no—
97C25×C5—31no—
98C24×D5—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—38no—
102C22×C22⋊D5—34no—
103C22×C22⋊D5—64no—
104C22×C22⋊D5—64no—
105C23×Dic5—31no—
106C23×Dic5C2×D311yescharacteristic
107C23×Dic5C2×D311yescharacteristic
108C2×C5×C22⋊C4—34no—
109C2×C5×C22⋊C4—64no—
110C2×C22⋊Dic5—34no—
111C2×C22⋊Dic5—64no—
112C2×#685—34no—
113C2×#685—34no—
114C2×#685—64no—
115C2×#685—64no—
116C2×#683—34no—
117C2×#683—64no—
118C2×C4×Dic5—24no—
119C2×C4×Dic5C2×D314yescomplemented
120C2×#390—151noSylow
121C23×C3×C5C22×C412yes—
122C23×C3×C5C2×D412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5#4112yes—
128C23×C3×C5C2411yescharacteristic
129C22×D15—28no—
130C22×D15—28no—
131C22×D15—28no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—44no—
139C22×D15—44no—
140C22×D15—44no—
141C22×D15—44no—
142C22×D15C22×C414yes—
143C22×C5×D3—28no—
144C22×C5×D3—28no—
145C22×C5×D3—28no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—44no—
153C22×C5×D3—44no—
154C22×C5×D3—44no—
155C22×C5×D3—44no—
156C22×C5×D3C22×C414yes—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5C2×D414yescomplemented
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—44no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—44no—
169C2×C3×Dic5—28no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5C22⋊C4116yescomplemented
173C2×C3×Dic5C22×C414yes—
174C2×C3×Dic5C2×D414yes—
175C2×C3×Dic5C2×D414yes—
176C2×C3×Dic5C2×D414yescomplemented
177#1203—232no—
178C24×D3—51no—
179C24×D3C2×D511yescharacteristic
180C23×C3×C4—51no—
181C23×C3×C4—51no—
182C23×C3×C4C2×D511yescharacteristic
183C23×Dic3—51no—
184C23×Dic3C2×D511yescharacteristic
185C22×D12—58no—
186C22×D12—54no—
187C22×D12—104no—
188C22×D12—104no—
189C2×C3×C42—54no—
190C2×C3×C42—104no—
191C2×(C2×D3)⋊C4—24no—
192C2×(C2×D3)⋊C4—54no—
193C2×(C2×D3)⋊C4—54no—
194C2×(C2×D3)⋊C4—54no—
195C2×(C2×D3)⋊C4—104no—
196C2×(C2×D3)⋊C4—104no—
197C2×(C2×D3)⋊C4—104no—
198C2×(C2×D3)⋊C4C2×D514yescomplemented
199C2×C4⋊Dic3—54no—
200C2×C4⋊Dic3—104no—
201C24×C5—34no—
202C24×C5—32no—
203C24×C5—62no—
204C24×C5—62no—
205C24×C5—62no—
206C24×C5—62no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5C22×D311yescharacteristic
210C23×D5—34no—
211C23×D5—32no—
212C23×D5—62no—
213C23×D5—62no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—32no—
221C22×C4×C5—62no—
222C22×C4×C5—62no—
223C22×C4×C5—62no—
224C22×C4×C5D1214yescomplemented
225C22×C4×C5C22×D312yes—
226C2×C22⋊D5—316no—
227C2×C22⋊D5—632no—
228C2×C22⋊D5—68no—
229C2×C22⋊D5—68no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—32no—
233C22×Dic5—62no—
234C22×Dic5—62no—
235C22×Dic5—62no—
236C22×Dic5C4×D314yes—
237C22×Dic5D1214yes—
238C22×Dic5D1214yescomplemented
239C22×Dic5#6714yes—
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D312yes—
242C5×C22⋊C4—68no—
243C22⋊Dic5—68no—
244#685—68no—
245#685—68no—
246#683—68no—
247C4×Dic5—28no—
248C23×D4—151no—
249C22×C4⋊C4—151no—
250C22×C22⋊C4—31no—
251C22×C22⋊C4—151no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C42—51no—
255#390—158no—
256C22×C3×C5C2×C22⋊C414yes—
257C22×C3×C5C4×D414yes—
258C22×C3×C5C4×D414yes—
259C22×C3×C5#12114yes—
260C22×C3×C5#12114yes—
261C22×C3×C5#12414yes—
262C22×C3×C5#12714yes—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×D15—24no—
271C2×D15—24no—
272C2×D15—24no—
273C2×D15—42no—
274C2×D15—42no—
275C2×D15—42no—
276C2×D15—42no—
277C2×D15—416no—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—24no—
281C2×C5×D3—42no—
282C2×C5×D3—42no—
283C2×C5×D3—42no—
284C2×C5×D3—42no—
285C2×C5×D3—416no—
286C3×C4×C5—24no—
287Dic15—42no—
288C3×Dic5—24no—
289C3×Dic5C2×C22⋊C418yescomplemented
290C5×Dic3—42no—
291C24×C3C22×D511yescharacteristic
292C23×D3—22no—
293C23×D3—22no—
294C23×D3—22no—
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—54no—
299C23×D3—52no—
300C23×D3—102no—
301C23×D3—102no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3C4×D514yes—
307C23×D3C22×D512yes—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—54no—
311C22×C3×C4—54no—
312C22×C3×C4—54no—
313C22×C3×C4—52no—
314C22×C3×C4—54no—
315C22×C3×C4—52no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4C22⋊D514yescomplemented
319C22×C3×C4C22×D512yes—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—52no—
324C22×Dic3—102no—
325C22×Dic3—102no—
326C22×Dic3—102no—
327C22×Dic3C22×D512yes—
328C2×D12—516no—
329C2×D12—108no—
330C2×D12—108no—
331C2×D12—1032no—
332C3×C42—108no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—108no—
335(C2×D3)⋊C4—108no—
336(C2×D3)⋊C4—108no—
337C4⋊Dic3—108no—
338C23×C5—34no—
339C23×C5—68no—
340C23×C5—68no—
341C23×C5—68no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—124no—
349C23×C5—124no—
350C23×C5—124no—
351C23×C5—124no—
352C23×C5C2×C4×D312yes—
353C23×C5C2×D1212yes—
354C23×C5C2×D1212yes—
355C23×C5C2×D1212yes—
356C23×C5#23512yes—
357C23×C5#23512yes—
358C23×C5C2×#6712yes—
359C23×C5C23×D311yescharacteristic
360C22×D5—34no—
361C22×D5—68no—
362C22×D5—68no—
363C22×D5—68no—
364C22×D5—62no—
365C22×D5—62no—
366C22×D5—62no—
367C22×D5—62no—
368C22×D5—62no—
369C22×D5—62no—
370C22×D5—124no—
371C22×D5—124no—
372C22×D5—124no—
373C22×D5—124no—
374C2×C4×C5—28no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—62no—
378C2×C4×C5—62no—
379C2×C4×C5—62no—
380C2×C4×C5—124no—
381C2×C4×C5C2×D1214yescomplemented
382C22⋊D5—632no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—62no—
387C2×Dic5—62no—
388C2×Dic5—62no—
389C2×Dic5—124no—
390C2×Dic5(C2×D3)⋊C4116yescomplemented
391C2×Dic5C2×C4×D314yes—
392C2×Dic5C2×D1214yes—
393C2×Dic5C2×D1214yescomplemented
394C2×Dic5C2×#6714yes—
395C25—31no—
396C25—151no—
397C22×D4—154no—
398C22×D4—158no—
399C22×D4—304no—
400C22×D4—304no—
401C23×C4—31no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—151no—
405C23×C4D3×D511yescharacteristic
406C2×C4⋊C4—154no—
407C2×C4⋊C4—304no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—154no—
411C2×C22⋊C4—154no—
412C2×C22⋊C4—154no—
413C2×C22⋊C4—304no—
414C2×C22⋊C4—304no—
415C2×C22⋊C4—304no—
416C2×C42—54no—
417C2×C42—104no—
418C2×C3×C5#39018yescomplemented
419C2×C3×C5C22×C22⋊C411yescharacteristic
420C2×C3×C5C2×C4×D411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×#12111yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12411yescharacteristic
425C2×C3×C5C2×#12711yescharacteristic
426D15—44no—
427C5×D3—44no—
428C23×C3C2×C4×D512yes—
429C23×C3#70912yes—
430C23×C3D4×D512yes—
431C23×C3D4×D512yes—
432C23×C3D4×D512yes—
433C23×C3#71112yes—
434C23×C3C2×C22⋊D512yes—
435C23×C3C23×D511yescharacteristic
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—28no—
443C22×D3—28no—
444C22×D3—28no—
445C22×D3—44no—
446C22×D3—44no—
447C22×D3—44no—
448C22×D3—44no—
449C22×D3—54no—
450C22×D3—102no—
451C22×D3—102no—
452C22×D3—102no—
453C22×D3—102no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—108no—
457C22×D3—108no—
458C22×D3—108no—
459C22×D3—204no—
460C22×D3—204no—
461C22×D3—204no—
462C22×D3—204no—
463C22×D3C2×C4×D514yes—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—28no—
467C2×C3×C4—54no—
468C2×C3×C4—54no—
469C2×C3×C4—54no—
470C2×C3×C4—516no—
471C2×C3×C4—54no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—108no—
475C2×C3×C4C2×C22⋊D514yescomplemented
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—44no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—204no—
484D12—1032no—
485C22×C5—64no—
486C22×C5—64no—
487C22×C5—64no—
488C22×C5—1216no—
489C22×C5—122no—
490C22×C5—122no—
491C22×C5—122no—
492C22×C5—122no—
493C22×C5C4×D1214yes—
494C22×C5C4×D1214yes—
495C22×C5#87414yes—
496C22×C5#87514yes—
497C22×C5C2×(C2×D3)⋊C414yes—
498C22×C5#93014yes—
499C22×C5#93014yes—
500C22×C5C22×C4×D311yescharacteristic
501C22×C5C22×D1211yescharacteristic
502C22×C5C22×D1211yescharacteristic
503C22×C5C22×D1211yescharacteristic
504C22×C5C2×#23511yescharacteristic
505C22×C5C2×#23511yescharacteristic
506C22×C5C22×#6711yescharacteristic
507C2×D5—64no—
508C2×D5—64no—
509C2×D5—64no—
510C2×D5—1216no—
511C2×D5—122no—
512C2×D5—122no—
513C2×D5—122no—
514C2×D5—122no—
515C4×C5—24no—
516C4×C5—122no—
517Dic5—24no—
518Dic5—122no—
519Dic5C2×(C2×D3)⋊C418yescomplemented
520C24—34no—
521C24—32no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—154no—
529C24—152no—
530C24—302no—
531C24—302no—
532C24—302no—
533C24—302no—
534C24—302no—
535C24—302no—
536C24C2×D3×D511yescharacteristic
537C2×D4—1516no—
538C2×D4—3032no—
539C2×D4—308no—
540C2×D4—308no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—32no—
544C22×C4—54no—
545C22×C4—54no—
546C22×C4—54no—
547C22×C4—52no—
548C22×C4—54no—
549C22×C4—52no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—152no—
556C22×C4—302no—
557C22×C4—302no—
558C22×C4—302no—
559C22×C4#120314yescomplemented
560C22×C4C2×D3×D512yes—
561C4⋊C4—308no—
562C22⋊C4—68no—
563C22⋊C4—308no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—108no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3D5×C22⋊C414yes—
569C22×C3#402714yes—
570C22×C3#403014yes—
571C22×C3#403114yes—
572C22×C3C4×C22⋊D514yes—
573C22×C3#408514yes—
574C22×C3#408614yes—
575C22×C3C22×C4×D511yescharacteristic
576C22×C3C2×#70911yescharacteristic
577C22×C3C2×D4×D511yescharacteristic
578C22×C3C2×D4×D511yescharacteristic
579C22×C3C2×D4×D511yescharacteristic
580C22×C3C2×#71111yescharacteristic
581C22×C3C22×C22⋊D511yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—416no—
590C2×D3—104no—
591C2×D3—104no—
592C2×D3—104no—
593C2×D3—202no—
594C2×D3—202no—
595C2×D3—202no—
596C2×D3—202no—
597C2×D3—2016no—
598C3×C4—24no—
599C3×C4—58no—
600C3×C4—104no—
601Dic3—42no—
602Dic3—202no—
603C2×C5—124no—
604C2×C5#493918yescomplemented
605C2×C5C2×C4×D1211yescharacteristic
606C2×C5C2×C4×D1211yescharacteristic
607C2×C5C2×#87411yescharacteristic
608C2×C5C2×#87511yescharacteristic
609C2×C5C22×(C2×D3)⋊C411yescharacteristic
610C2×C5C2×#93011yescharacteristic
611C2×C5C2×#93011yescharacteristic
612D5—124no—
613C23—34no—
614C23—68no—
615C23—68no—
616C23—68no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—124no—
624C23—124no—
625C23—124no—
626C23—124no—
627C23—154no—
628C23—308no—
629C23—308no—
630C23—308no—
631C23—302no—
632C23—302no—
633C23—302no—
634C23—302no—
635C23—302no—
636C23—302no—
637C23—604no—
638C23—604no—
639C23—604no—
640C23—604no—
641C23#677112yes—
642C23C4×D3×D512yes—
643C23D5×D1212yes—
644C23D5×D1212yes—
645C23#678212yes—
646C23C2×#120312yes—
647C23D5×#6712yes—
648C23C22×D3×D511yescharacteristic
649D4—3032no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—516no—
654C2×C4—54no—
655C2×C4—54no—
656C2×C4—54no—
657C2×C4—54no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—108no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—124no—
665C2×C4—302no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—604no—
669C2×C4C2×#120314yescomplemented
670C2×C3#6524618yescomplemented
671C2×C3C2×D5×C22⋊C411yescharacteristic
672C2×C3C2×#402711yescharacteristic
673C2×C3C2×#403011yescharacteristic
674C2×C3C2×#403111yescharacteristic
675C2×C3C2×C4×C22⋊D511yescharacteristic
676C2×C3C2×#408511yescharacteristic
677C2×C3C2×#408611yescharacteristic
678D3—44no—
679D3—204no—
680C5C2×#493911yescharacteristic, complemented, Sylow
681C22—64no—
682C22—64no—
683C22—64no—
684C22—122no—
685C22—122no—
686C22—1216no—
687C22—122no—
688C22—122no—
689C22—304no—
690C22—304no—
691C22—304no—
692C22—602no—
693C22—602no—
694C22—6016no—
695C22—602no—
696C22—602no—
697C22#9135014yes—
698C22#9140514yes—
699C22C4×#120314yes—
700C22#9144814yes—
701C22#9145114yes—
702C22D5×(C2×D3)⋊C414yes—
703C22#9156614yes—
704C22C2×#677111yescharacteristic
705C22C2×C4×D3×D511yescharacteristic
706C22C2×D5×D1211yescharacteristic
707C22C2×D5×D1211yescharacteristic
708C22C2×#678211yescharacteristic
709C22C22×#120311yescharacteristic
710C22C2×D5×#6711yescharacteristic
711C4—24no—
712C4—58no—
713C4—104no—
714C4—122no—
715C4—602no—
716C3C2×#6524611yescharacteristic, complemented, Sylow
717C2—124no—
718C2—604no—
719C2#1174890818yesdirect product factor
720C2C2×#9135011yescharacteristic
721C2C2×#9140511yescharacteristic
722C2C2×C4×#120311yescharacteristic
723C2C2×#9144811yescharacteristic
724C2C2×#9145111yescharacteristic
725C2C2×D5×(C2×D3)⋊C411yescharacteristic
726C2C2×#9156611yescharacteristic
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×#390
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. C22×#6714C2semidirect
3. C22×C5×(C2×D3)⋊C4C2semidirect
4. C22×C3×C4×Dic5C2semidirect
5. C22×#6668C2semidirect
6. C22×#6667C2semidirect
7. C22×(C2×D3)⋊Dic5C2semidirect
8. #11748908C2direct (N × H)
19. C22×#1203C4semidirect
22. C2×#6714C22semidirect
24. C2×C5×(C2×D3)⋊C4C22semidirect
26. C2×C3×C4×Dic5C22semidirect
28. C2×#6668C22semidirect
30. C2×#6667C22semidirect
32. C2×(C2×D3)⋊Dic5C22semidirect
40. C22×C4×Dic5D3semidirect
61. C22×C3×C4×C5D4semidirect
76. C22×C3×Dic5D4semidirect
82. C2×#1203C2×C4semidirect
94. C22×(C2×D3)⋊C4D5semidirect
119. C2×C4×Dic5C2×D3semidirect
160. C2×C3×C4×C5C2×D4semidirect
172. C2×C3×Dic5C22⋊C4semidirect
176. C2×C3×Dic5C2×D4semidirect
198. C2×(C2×D3)⋊C4C2×D5semidirect
224. C22×C4×C5D12semidirect
238. C22×Dic5D12semidirect
289. C3×Dic5C2×C22⋊C4semidirect
318. C22×C3×C4C22⋊D5semidirect
381. C2×C4×C5C2×D12semidirect
390. C2×Dic5(C2×D3)⋊C4semidirect
393. C2×Dic5C2×D12semidirect
418. C2×C3×C5#390semidirect
475. C2×C3×C4C2×C22⋊D5semidirect
519. Dic5C2×(C2×D3)⋊C4semidirect
559. C22×C4#1203semidirect
567. C3×C5C2×#390semidirect
604. C2×C5#4939semidirect
669. C2×C4C2×#1203semidirect
670. C2×C3#65246semidirect
680. C5C2×#4939semidirect
716. C3C2×#65246semidirect
719. C2#11748908direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12032
C22×#67142
C22×C5×(C2×D3)⋊C42
C22×C3×C4×Dic52
C22×#66682
C22×#66672
C22×(C2×D3)⋊Dic52
#117489082
C2×#652463
C2×#49395