Finite Group Databasebeta

← C2×#11751057 #14320277

Subgroups — C2×#11751057 #14320277

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×#1220C211yesmaximal, characteristic
2C23×C4×D15C211yesmaximal, characteristic, complemented
3C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C22×#6719C211yesmaximal, characteristic, complemented
5C22×#6714C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#91115C211yesmaximal, characteristic, complemented
8#11751057C218yesmaximal, direct product factor
9C2×#65245—31nomaximal, Hall
10C25×C3×C5C2211yescharacteristic
11C24×D15C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220—24no—
15C22×#1220—24no—
16C22×#1220C418yescomplemented
17C22×#1220C2214yes—
18C23×Dic15C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C4×D15—24no—
22C22×C4×D15—24no—
23C22×C4×D15—24no—
24C22×C4×D15C2214yescomplemented
25C2×C3×C5×C22⋊C4—24no—
26C2×C3×C5×C22⋊C4C2214yescomplemented
27C2×#6719—24no—
28C2×#6719C2214yescomplemented
29C2×#6714—24no—
30C2×#6714C2214yescomplemented
31#91115C2214yescomplemented
32#91115C2214yescomplemented
33C2×#4956—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C23×C4×D5—31no—
36C22×C5×C22⋊C4D311yescharacteristic, complemented
37C22×C22⋊Dic5—31no—
38C22×#685—31no—
39C2×#3963—31no—
40C2×#3963—31no—
41#65245—38no—
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×D15—22no—
52C23×D15—22no—
53C23×D15—22no—
54C23×D15—22no—
55C23×D15C2×C414yes—
56C23×D15D414yes—
57C23×D15D414yes—
58C23×D15C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D414yescomplemented
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C2×#1220—232no—
68C2×#1220—28no—
69C2×#1220—28no—
70C2×#1220C2×C4116yescomplemented
71C22×Dic15—22no—
72C22×Dic15—22no—
73C22×Dic15—22no—
74C22×Dic15—22no—
75C22×Dic15—22no—
76C22×Dic15—22no—
77C22×Dic15—22no—
78C22×Dic15C2×C414yescomplemented
79C22×Dic15D414yescomplemented
80C22×Dic15C2312yes—
81C22×Dic15C2312yes—
82C22×Dic15C2312yes—
83C2×C4×D15—232no—
84C2×C4×D15—28no—
85C2×C4×D15—28no—
86C2×C4×D15—28no—
87C3×C5×C22⋊C4—28no—
88#6719—28no—
89#6714—28no—
90C23×#67—51no—
91C23×C4×D3—51no—
92C22×C3×C22⋊C4D511yescharacteristic, complemented
93C22×#217—51no—
94C22×(C2×D3)⋊C4—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95—51no—
97#4956—58no—
98C25×C5C2×D311yescharacteristic
99C24×D5—31no—
100C23×C4×C5C2×D311yescharacteristic
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×Dic5—31no—
109C22×C4×D5—34no—
110C22×C4×D5—64no—
111C22×C4×D5—64no—
112C22×C4×D5—64no—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4C2×D314yescomplemented
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×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×D15—28no—
145C22×D15—28no—
146C22×D15—28no—
147C22×D15—28no—
148C22×D15—28no—
149C22×D15—28no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—22no—
153C22×D15—22no—
154C22×D15C22⋊C4116yescomplemented
155C22×D15C22×C414yes—
156C22×D15C2×D414yes—
157C22×D15C2×D414yes—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—44no—
165C2×C3×C4×C5C2×D414yescomplemented
166#1220—232no—
167C2×Dic15—28no—
168C2×Dic15—28no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×Dic15—22no—
176C2×Dic15—44no—
177C2×Dic15C22×C414yescomplemented
178C2×Dic15C2×D414yescomplemented
179C4×D15—232no—
180C25×C3C2×D511yescharacteristic
181C24×D3—51no—
182C23×C3×C4C2×D511yescharacteristic
183C23×C3×C4C2×D511yescharacteristic
184C22×#67—58no—
185C22×#67—54no—
186C22×#67—104no—
187C22×#67—104no—
188C23×Dic3—51no—
189C23×Dic3—51no—
190C23×Dic3—51no—
191C22×C4×D3—54no—
192C22×C4×D3—104no—
193C22×C4×D3—104no—
194C22×C4×D3—104no—
195C2×C3×C22⋊C4—24no—
196C2×C3×C22⋊C4C2×D514yescomplemented
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×C5C4×D314yescomplemented
210C24×C5C22×D312yes—
211C24×C5C22×D311yescharacteristic
212C23×D5—34no—
213C23×D5—34no—
214C23×D5—34no—
215C23×D5—32no—
216C23×D5—62no—
217C23×D5—62no—
218C23×D5—62no—
219C23×D5—62no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5#6714yescomplemented
226C22×C4×C5C22×D312yes—
227C22×C4×C5C22×D312yes—
228C2×C22⋊D5—316no—
229C2×C22⋊D5—632no—
230C2×C22⋊D5—68no—
231C2×C22⋊D5—68no—
232C22×Dic5—34no—
233C22×Dic5—34no—
234C22×Dic5—32no—
235C22×Dic5—32no—
236C22×Dic5—32no—
237C22×Dic5—62no—
238C22×Dic5—62no—
239C22×Dic5—62no—
240C22×Dic5—62no—
241C22×Dic5—62no—
242C22×Dic5—62no—
243C22×Dic5—62no—
244C2×C4×D5—68no—
245C2×C4×D5—68no—
246C2×C4×D5—632no—
247C2×C4×D5—68no—
248C5×C22⋊C4—28no—
249C22⋊Dic5—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—151no—
253C22×C22⋊C4—151no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4D1511yescharacteristic, complemented
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×D15—24no—
282C2×D15—24no—
283C2×D15—24no—
284C2×D15—24no—
285C2×D15—24no—
286C2×D15—24no—
287C2×D15—232no—
288C2×D15C2×C22⋊C418yescomplemented
289C3×C4×C5—24no—
290C3×C4×C5—42no—
291Dic15—24no—
292Dic15—24no—
293Dic15—42no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—22no—
297C24×C3—22no—
298C24×C3—22no—
299C24×C3—22no—
300C24×C3C4×D514yescomplemented
301C24×C3C22×D512yes—
302C24×C3C22×D511yescharacteristic
303C23×D3—54no—
304C23×D3—54no—
305C23×D3—54no—
306C23×D3—52no—
307C23×D3—102no—
308C23×D3—102no—
309C23×D3—102no—
310C23×D3—102no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4C22⋊D514yescomplemented
317C22×C3×C4C22×D512yes—
318C22×C3×C4C22×D512yes—
319C2×#67—516no—
320C2×#67—108no—
321C2×#67—108no—
322C2×#67—1032no—
323C22×Dic3—54no—
324C22×Dic3—54no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3—102no—
332C22×Dic3—102no—
333C22×Dic3—102no—
334C22×Dic3—102no—
335C2×C4×D3—108no—
336C2×C4×D3—108no—
337C2×C4×D3—1032no—
338C2×C4×D3—108no—
339C3×C22⋊C4—28no—
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—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5C2×C4×D312yes—
356C23×C5C2×C4×D314yescomplemented
357C23×C5#23512yes—
358C23×C5D3×D412yes—
359C23×C5D3×D412yes—
360C23×C5D3×D412yes—
361C23×C5#23712yes—
362C23×C5C2×#6712yes—
363C23×C5C23×D311yescharacteristic
364C22×D5—316no—
365C22×D5—34no—
366C22×D5—34no—
367C22×D5—34no—
368C22×D5—68no—
369C22×D5—68no—
370C22×D5—68no—
371C22×D5—68no—
372C22×D5—68no—
373C22×D5—68no—
374C22×D5—62no—
375C22×D5—62no—
376C22×D5—62no—
377C22×D5—62no—
378C2×C4×C5—28no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—44no—
385C2×C4×C5C2×#6714yescomplemented
386C22⋊D5—632no—
387C2×Dic5—34no—
388C2×Dic5—34no—
389C2×Dic5—68no—
390C2×Dic5—68no—
391C2×Dic5—62no—
392C2×Dic5—62no—
393C2×Dic5—62no—
394C2×Dic5—62no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5—124no—
399C4×D5—632no—
400C25—151no—
401C25C2×D1511yescharacteristic
402C22×D4—158no—
403C22×D4—154no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—151no—
407C23×C4—151no—
408C23×C4—151no—
409C23×C4—154no—
410C23×C4—304no—
411C23×C4—304no—
412C23×C4—304no—
413C23×C4C2×D1511yescharacteristic
414C23×C4C2×D1511yescharacteristic
415C2×C22⋊C4—24no—
416C2×C22⋊C4—154no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—304no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4C2×D1514yescomplemented
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
432D15—28no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—28no—
440C23×C3—28no—
441C23×C3—28no—
442C23×C3—44no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3C2×C4×D512yes—
447C23×C3C2×C4×D514yescomplemented
448C23×C3#70912yes—
449C23×C3D4×D512yes—
450C23×C3D4×D512yes—
451C23×C3D4×D512yes—
452C23×C3#71112yes—
453C23×C3C2×C22⋊D512yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—54no—
456C22×D3—54no—
457C22×D3—54no—
458C22×D3—516no—
459C22×D3—102no—
460C22×D3—102no—
461C22×D3—102no—
462C22×D3—102no—
463C22×D3—108no—
464C22×D3—108no—
465C22×D3—108no—
466C22×D3—108no—
467C22×D3—108no—
468C22×D3—108no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—28no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—44no—
476C2×C3×C4C2×C22⋊D514yescomplemented
477#67—1032no—
478C2×Dic3—54no—
479C2×Dic3—54no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—102no—
484C2×Dic3—108no—
485C2×Dic3—108no—
486C2×Dic3—102no—
487C2×Dic3—102no—
488C2×Dic3—102no—
489C2×Dic3—204no—
490C4×D3—1032no—
491C22×C5—24no—
492C22×C5—24no—
493C22×C5—24no—
494C22×C5—416no—
495C22×C5—42no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
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—38no—
514C2×D5—632no—
515C2×D5—64no—
516C2×D5—64no—
517C2×D5—64no—
518C2×D5—64no—
519C2×D5—64no—
520C2×D5—64no—
521C4×C5—24no—
522C4×C5—42no—
523Dic5—64no—
524Dic5—64no—
525Dic5—122no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—154no—
533C24—154no—
534C24—154no—
535C24—152no—
536C24—302no—
537C24—302no—
538C24—302no—
539C24—302no—
540C24C4×D1514yescomplemented
541C24C22×D1512yes—
542C24C22×D1511yescharacteristic
543C2×D4—1516no—
544C2×D4—3032no—
545C2×D4—308no—
546C2×D4—308no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—154no—
553C22×C4—154no—
554C22×C4—152no—
555C22×C4—152no—
556C22×C4—152no—
557C22×C4—308no—
558C22×C4—308no—
559C22×C4—3032no—
560C22×C4—302no—
561C22×C4—302no—
562C22×C4—302no—
563C22×C4—302no—
564C22×C4—308no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4#122014yescomplemented
569C22×C4C22×D1512yes—
570C22×C4C22×D1512yes—
571C22⋊C4—28no—
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×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—58no—
598C2×D3—104no—
599C2×D3—104no—
600C2×D3—104no—
601C2×D3—104no—
602C2×D3—104no—
603C2×D3—104no—
604C2×D3—1032no—
605C3×C4—24no—
606C3×C4—42no—
607Dic3—104no—
608Dic3—104no—
609Dic3—202no—
610C2×C5—44no—
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—68no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—1516no—
634C23—154no—
635C23—154no—
636C23—154no—
637C23—308no—
638C23—308no—
639C23—308no—
640C23—308no—
641C23—308no—
642C23—308no—
643C23—302no—
644C23—302no—
645C23—302no—
646C23—302no—
647C23C2×C4×D1512yes—
648C23C2×C4×D1514yescomplemented
649C23#681712yes—
650C23D4×D1512yes—
651C23D4×D1512yes—
652C23D4×D1512yes—
653C23#681912yes—
654C23C2×#122012yes—
655C23C23×D1511yescharacteristic
656D4—3032no—
657C2×C4—28no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—154no—
665C2×C4—154no—
666C2×C4—3032no—
667C2×C4—308no—
668C2×C4—308no—
669C2×C4—302no—
670C2×C4—302no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—302no—
674C2×C4—302no—
675C2×C4—302no—
676C2×C4—604no—
677C2×C4C2×#122014yescomplemented
678C2×C3—44no—
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—108no—
688C5C2×#495611yescharacteristic, complemented, Sylow
689C22—24no—
690C22—24no—
691C22—24no—
692C22—42no—
693C22—42no—
694C22—416no—
695C22—42no—
696C22—42no—
697C22—158no—
698C22—304no—
699C22—304no—
700C22—304no—
701C22—3032no—
702C22—304no—
703C22—304no—
704C22—304no—
705C22C22⋊C4×D1514yes—
706C22#9177014yes—
707C22#9177214yes—
708C22#9177314yes—
709C22C4×#122014yes—
710C22#9182614yes—
711C22#9182714yes—
712C22C22×C4×D1511yescharacteristic
713C22C2×#681711yescharacteristic
714C22C2×D4×D1511yescharacteristic
715C22C2×D4×D1511yescharacteristic
716C22C2×D4×D1511yescharacteristic
717C22C2×#681911yescharacteristic
718C22C22×#122011yescharacteristic
719C4—24no—
720C4—42no—
721C4—304no—
722C4—304no—
723C4—602no—
724C3C2×#6524511yescharacteristic, complemented, Sylow
725C2—44no—
726C2—308no—
727C2#1175105718yesdirect product factor
728C2C2×C22⋊C4×D1511yescharacteristic
729C2C2×#9177011yescharacteristic
730C2C2×#9177211yescharacteristic
731C2C2×#9177311yescharacteristic
732C2C2×C4×#122011yescharacteristic
733C2C2×#9182611yescharacteristic
734C2C2×#9182711yescharacteristic
subgroupG/H
centerC24C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×#1220C2
cosocleC23×C3×C5C24
hypercenterC22×C22⋊C4D15
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D15C2semidirect
3. C22×C3×C5×C22⋊C4C2semidirect
4. C22×#6719C2semidirect
5. C22×#6714C2semidirect
6. C2×#91115C2semidirect
7. C2×#91115C2semidirect
8. #11751057C2direct (N × H)
16. C22×#1220C4semidirect
24. C22×C4×D15C22semidirect
26. C2×C3×C5×C22⋊C4C22semidirect
28. C2×#6719C22semidirect
30. C2×#6714C22semidirect
31. #91115C22semidirect
32. #91115C22semidirect
36. C22×C5×C22⋊C4D3semidirect
48. C24×C3×C5C2×C4semidirect
64. C22×C3×C4×C5D4semidirect
70. C2×#1220C2×C4semidirect
78. C22×Dic15C2×C4semidirect
79. C22×Dic15D4semidirect
92. C22×C3×C22⋊C4D5semidirect
114. C2×C5×C22⋊C4C2×D3semidirect
136. C23×C3×C5C22×C4semidirect
154. C22×D15C22⋊C4semidirect
165. C2×C3×C4×C5C2×D4semidirect
177. C2×Dic15C22×C4semidirect
178. C2×Dic15C2×D4semidirect
196. C2×C3×C22⋊C4C2×D5semidirect
209. C24×C5C4×D3semidirect
225. C22×C4×C5#67semidirect
255. C22×C22⋊C4D15semidirect
288. C2×D15C2×C22⋊C4semidirect
300. C24×C3C4×D5semidirect
316. C22×C3×C4C22⋊D5semidirect
356. C23×C5C2×C4×D3semidirect
385. C2×C4×C5C2×#67semidirect
420. C2×C22⋊C4C2×D15semidirect
424. C2×C3×C5#386semidirect
447. C23×C3C2×C4×D5semidirect
476. C2×C3×C4C2×C22⋊D5semidirect
540. C24C4×D15semidirect
568. C22×C4#1220semidirect
574. C3×C5C2×#386semidirect
611. C2×C5#4956semidirect
648. C23C2×C4×D15semidirect
677. C2×C4C2×#1220semidirect
679. C2×C3#65245semidirect
688. C5C2×#4956semidirect
724. C3C2×#65245semidirect
727. C2#11751057direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12202
C23×C4×D152
C22×C3×C5×C22⋊C42
C22×#67192
C22×#67142
C2×#911152
#117510572
C2×#652453
C2×#49565