Finite Group Databasebeta

← #14322555

Subgroups — #14322555

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6771C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751088C211yesmaximal, characteristic, complemented
5C5×#4987C211yesmaximal, characteristic, complemented
6#11748909C212yesmaximal, complemented
7#11748907C212yesmaximal, complemented
8#11748905C212yesmaximal, complemented
9#11748799C211yesmaximal, characteristic, complemented
10#11748786C211yesmaximal, characteristic, complemented
11#11748628C212yesmaximal, complemented
12#10605734—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×#1204C2211yescharacteristic
18C22×#1203C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1201C2211yescharacteristic
21C2×#6771—24no—
22C2×#6771—24no—
23C2×#6771C418yescomplemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6714C2212yes—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C3×D5×C4⋊C4—24no—
32C2×#6667C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×#6665C2212yes—
35C2×Dic3×Dic5C2212yes—
36#91358—24no—
37#91115C2212yes—
38C5×C3⋊#95C2212yes—
39#90994C2212yes—
40#90994C2212yes—
41#82186—51nomaximal, Hall
42C22×#709—31no—
43C2×#4038—31no—
44C2×D5×C4⋊C4D311yescharacteristic, complemented
45C5×#380—31no—
46#65501—31no—
47#65276—31no—
48#65276—31no—
49#65246—32no—
50#65245—32no—
51#64954—32no—
52#64935—32no—
53C23×D15C2311yescharacteristic
54C23×C5×D3C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2311yescharacteristic
60C2×C4×D15—22no—
61C2×C4×D15—22no—
62C2×C4×D15C2×C414yescomplemented
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3C2×C414yescomplemented
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2311yescharacteristic
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—42no—
72C2×C3×C4×D5—42no—
73C2×C3×C4×D5C2×C414yes—
74C2×C3×C4×D5D414yes—
75C2×C3×C4×D5D414yes—
76C2×#1204—22no—
77C2×#1204—22no—
78C2×#1204C2×C414yescomplemented
79C2×#1203—22no—
80C2×#1203—22no—
81C2×#1203C2×C414yescomplemented
82C2×#1202—22no—
83C2×#1202—22no—
84C2×#1202C2×C414yes—
85C2×#1201—22no—
86C2×#1201—22no—
87C2×#1201C2×C414yes—
88#6771—232no—
89C3×C5×C4⋊C4—22no—
90#6714—42no—
91C4⋊Dic15—22no—
92C5×(C2×D3)⋊C4—42no—
93C5×C4⋊Dic3—22no—
94C3×C4⋊Dic5—22no—
95C3×#683—24no—
96#6667—42no—
97(C2×D3)⋊Dic5—42no—
98#6665—24no—
99Dic3×Dic5—24no—
100C22×#235—51no—
101C22×C3×C4⋊C4—51no—
102C2×#926—51no—
103#5213—52no—
104#5213—52no—
105#4988—52no—
106#4987—51no—
107#4987—51no—
108#4987—51no—
109#4987D511yescharacteristic, complemented
110#4973—52no—
111C23×C4×C5—31no—
112C22×C22⋊D5—31no—
113C22×C22⋊D5—31no—
114C2×#709—38no—
115C2×#709—64no—
116C2×#709—64no—
117C22×D20—31no—
118C22×C4×D5—31no—
119C22×C4×D5C2×D312yes—
120C22×C4×D5C2×D311yescharacteristic
121C22×Dic10—31no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C5×C22⋊C4—32no—
125C2×C22⋊Dic5—32no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×#683C2×D312yes—
132C2×C4×Dic5—32no—
133#4038—64no—
134D5×C4⋊C4—24no—
135C5×#95—32no—
136#3963—32no—
137#3963—32no—
138#3963—32no—
139#2311—151noSylow
140C23×C3×C5C2411yescharacteristic
141C22×D15—21no—
142C22×D15—21no—
143C22×D15—21no—
144C22×D15—21no—
145C22×D15—21no—
146C22×D15—21no—
147C22×D15C22×C412yes—
148C22×C5×D3—21no—
149C22×C5×D3—21no—
150C22×C5×D3—21no—
151C22×C5×D3—21no—
152C22×C5×D3—21no—
153C22×C5×D3—21no—
154C22×C5×D3C22×C412yes—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—21no—
158C22×C3×D5—21no—
159C22×C3×D5C22×C412yes—
160C22×C3×D5C2×D412yes—
161C22×C3×D5C2×D412yes—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2×D412yes—
168C2×Dic15—21no—
169C2×Dic15—21no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—22no—
173C2×Dic15C22×C412yes—
174C4×D15—28no—
175C2×C5×Dic3—21no—
176C2×C5×Dic3—21no—
177C2×C5×Dic3—22no—
178C2×C5×Dic3—22no—
179C2×C5×Dic3—22no—
180C2×C5×Dic3C22×C412yes—
181C4×C5×D3—28no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5—22no—
184C2×C3×Dic5—22no—
185C2×C3×Dic5C22×C412yes—
186C2×C3×Dic5C2×D412yes—
187C2×C3×Dic5C2×D412yes—
188C3×C4×D5—48no—
189C3×C4×D5C22⋊C4116yescomplemented
190#1204—28no—
191#1203—28no—
192#1202—28no—
193#1201—28no—
194C23×C3×C4—51no—
195C23×C3×C4—52no—
196C22×#67—51no—
197C22×#67—51no—
198C2×#235—58no—
199C2×#235—104no—
200C2×#235—104no—
201C22×D12—51no—
202C22×C4×D3—51no—
203C22×C4×D3C2×D511yescharacteristic
204C22×Dic6—51no—
205C2×C3×C4⋊C4—52no—
206C2×C3×C4⋊C4—51no—
207C2×C3×C4⋊C4—104no—
208C2×C3×C4⋊C4C2×D511yescharacteristic
209C2×#217—52no—
210C2×(C2×D3)⋊C4—52no—
211C2×(C2×D3)⋊C4—52no—
212C2×(C2×D3)⋊C4—52no—
213C2×(C2×D3)⋊C4C2×D512yes—
214#926—104no—
215C2×C4⋊Dic3—51no—
216C2×C4⋊Dic3C2×D511yescharacteristic
217C2×C4×Dic3—52no—
218C3⋊#95—52no—
219C3⋊#95—52no—
220C3⋊#95—52no—
221C3⋊#95C2×D512yes—
222C24×C5—31no—
223C23×D5—31no—
224C23×D5C22×D311yescharacteristic
225C22×C4×C5—31no—
226C22×C4×C5—34no—
227C22×C4×C5—32no—
228C22×C4×C5—62no—
229C22×C4×C5—62no—
230C22×C4×C5C22×D312yes—
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—34no—
233C2×C22⋊D5—34no—
234C2×C22⋊D5—62no—
235C2×C22⋊D5—62no—
236C2×C22⋊D5—62no—
237C2×C22⋊D5—62no—
238C22×Dic5—31no—
239C22×Dic5—32no—
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D311yescharacteristic
242#709—632no—
243C2×D20—34no—
244C2×D20—62no—
245C2×D20—62no—
246C2×C4×D5—24no—
247C2×C4×D5—34no—
248C2×C4×D5—42no—
249C2×C4×D5—42no—
250C2×C4×D5—62no—
251C2×C4×D5—62no—
252C2×C4×D5C4×D314yes—
253C2×C4×D5D1214yes—
254C2×C4×D5#6714yes—
255C2×Dic10—34no—
256C2×Dic10—62no—
257C2×Dic10—62no—
258C5×C4⋊C4—22no—
259C5×C4⋊C4—62no—
260C5×C22⋊C4—122no—
261C22⋊Dic5—122no—
262#685—64no—
263#685—122no—
264#685—122no—
265C4⋊Dic5—22no—
266C4⋊Dic5—62no—
267#683—24no—
268C4×Dic5—64no—
269C22×#41—151no—
270C2×#117—151no—
271C22×C4⋊C4—51no—
272#391—152no—
273#390—152no—
274#386—152no—
275#386—152no—
276#380—31no—
277#380—151no—
278#380—151no—
279#380—151no—
280C22×C3×C5C23×C411yescharacteristic
281C22×C3×C5C22×D411yescharacteristic
282C22×C3×C5C22×D411yescharacteristic
283C22×C3×C5H(5,𝔽2)11yescharacteristic
284C22×C3×C5H(5,𝔽2)11yescharacteristic
285C22×C3×C52−1+411yescharacteristic
286C22×C3×C52−1+411yescharacteristic
287C2×D15—22no—
288C2×D15—22no—
289C2×D15—22no—
290C2×D15—41no—
291C2×D15—41no—
292C2×D15—41no—
293C2×D15—41no—
294C2×C5×D3—22no—
295C2×C5×D3—22no—
296C2×C5×D3—22no—
297C2×C5×D3—41no—
298C2×C5×D3—41no—
299C2×C5×D3—41no—
300C2×C5×D3—41no—
301C2×C3×D5—22no—
302C2×C3×D5—22no—
303C2×C3×D5—22no—
304C2×C3×D5—22no—
305C2×C3×D5—22no—
306C2×C3×D5—22no—
307C2×C3×D5C2×C22⋊C414yes—
308C3×C4×C5—42no—
309C3×C4×C5C2×C22⋊C414yes—
310Dic15—22no—
311Dic15—42no—
312C3×Dic5—42no—
313C3×Dic5C2×C22⋊C414yes—
314C5×Dic3—22no—
315C5×Dic3—42no—
316C24×C3—51no—
317C23×D3—51no—
318C23×D3C22×D511yescharacteristic
319C22×C3×C4—51no—
320C22×C3×C4—54no—
321C22×C3×C4—54no—
322C22×C3×C4—54no—
323C22×C3×C4—52no—
324C22×C3×C4—104no—
325C22×C3×C4—202no—
326C22×C3×C4—202no—
327C22×C3×C4C22×D512yes—
328C22×C3×C4C22×D511yescharacteristic
329C2×#67—54no—
330C2×#67—54no—
331C2×#67—102no—
332C2×#67—102no—
333C2×#67—102no—
334C2×#67—102no—
335C22×Dic3—51no—
336C22×Dic3—52no—
337C22×Dic3C22×D512yes—
338C22×Dic3C22×D511yescharacteristic
339#235—1032no—
340C2×D12—54no—
341C2×D12—102no—
342C2×D12—102no—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—54no—
346C2×C4×D3—102no—
347C2×C4×D3—102no—
348C2×C4×D3C4×D514yescomplemented
349C2×Dic6—54no—
350C2×Dic6—102no—
351C2×Dic6—102no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—104no—
354C3×C4⋊C4—102no—
355#217—104no—
356(C2×D3)⋊C4—42no—
357(C2×D3)⋊C4—202no—
358(C2×D3)⋊C4—202no—
359(C2×D3)⋊C4—202no—
360C4⋊Dic3—22no—
361C4⋊Dic3—102no—
362C4×Dic3—104no—
363C23×C5—32no—
364C23×C5—61no—
365C23×C5—61no—
366C23×C5—61no—
367C23×C5—61no—
368C23×C5—61no—
369C23×C5—61no—
370C23×C5C23×D311yescharacteristic
371C22×D5—21no—
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—32no—
376C22×D5—61no—
377C22×D5—61no—
378C22×D5—61no—
379C22×D5—61no—
380C22×D5—61no—
381C22×D5—61no—
382C22×D5C2×C4×D312yes—
383C22×D5C2×D1212yes—
384C22×D5C2×#6712yes—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—32no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
391C2×C4×C5—68no—
392C2×C4×C5—62no—
393C2×C4×C5—62no—
394C2×C4×C5—62no—
395C2×C4×C5C2×C4×D312yes—
396C2×C4×C5C2×D1212yes—
397C2×C4×C5C2×#6712yes—
398C22⋊D5—68no—
399C22⋊D5—68no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—32no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—62no—
407C2×Dic5—62no—
408C2×Dic5—62no—
409C2×Dic5C2×C4×D312yes—
410C2×Dic5C2×D1212yes—
411C2×Dic5C2×#6712yes—
412D20—68no—
413C4×D5—48no—
414C4×D5—68no—
415C4×D5(C2×D3)⋊C4116yescomplemented
416Dic10—68no—
417C2×#41—158no—
418C2×#41—304no—
419C2×#41—304no—
420C22×Q8—151no—
421C22×D4—151no—
422C22×D4—151no—
423C22×D4—151no—
424C23×C4—31no—
425C23×C4—51no—
426C23×C4—52no—
427C23×C4—151no—
428#117—304no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—52no—
432C2×C4⋊C4—104no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4D3×D511yescharacteristic
435C2×C22⋊C4—32no—
436C2×C22⋊C4—152no—
437C2×C22⋊C4—152no—
438C2×C22⋊C4—152no—
439C2×C22⋊C4—152no—
440C2×C42—152no—
441#95—32no—
442#95—152no—
443#95—152no—
444#95—152no—
445C2×C3×C5C22×C22⋊C411yescharacteristic
446C2×C3×C5#52011yescharacteristic
447C2×C3×C5#52011yescharacteristic
448C2×C3×C5#53511yescharacteristic
449C2×C3×C5#53611yescharacteristic
450C2×C3×C5#53711yescharacteristic
451C2×C3×C5#53711yescharacteristic
452D15—42no—
453C3×D5—24no—
454C5×D3—42no—
455C23×C3—52no—
456C23×C3—52no—
457C23×C3—52no—
458C23×C3—101no—
459C23×C3—101no—
460C23×C3—101no—
461C23×C3—101no—
462C23×C3C23×D511yescharacteristic
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—52no—
470C22×D3—101no—
471C22×D3—101no—
472C22×D3—101no—
473C22×D3—101no—
474C22×D3—101no—
475C22×D3—101no—
476C22×D3C2×C4×D512yes—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—52no—
481C2×C3×C4—52no—
482C2×C3×C4—52no—
483C2×C3×C4—516no—
484C2×C3×C4—102no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—208no—
488C2×C3×C4C2×C4×D512yes—
489C2×C3×C4D4×D512yes—
490C2×C3×C4D4×D512yes—
491#67—108no—
492#67—108no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—52no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—102no—
502C2×Dic3—102no—
503C2×Dic3—102no—
504C2×Dic3C2×C4×D512yes—
505D12—108no—
506C4×D3—28no—
507C4×D3—108no—
508Dic6—108no—
509C22×C5—62no—
510C22×C5—62no—
511C22×C5—62no—
512C22×C5—121no—
513C22×C5—121no—
514C22×C5—121no—
515C22×C5—121no—
516C22×C5C22×C4×D311yescharacteristic
517C22×C5C22×D1211yescharacteristic
518C22×C5#100411yescharacteristic
519C22×C5#100411yescharacteristic
520C22×C5#100711yescharacteristic
521C22×C5#100711yescharacteristic
522C22×C5C22×#6711yescharacteristic
523C2×D5—22no—
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—62no—
530C2×D5—62no—
531C2×D5—62no—
532C2×D5—121no—
533C2×D5—121no—
534C2×D5—121no—
535C2×D5—121no—
536C2×D5C2×(C2×D3)⋊C414yes—
537C4×C5—42no—
538C4×C5—62no—
539C4×C5—122no—
540C4×C5C2×(C2×D3)⋊C414yes—
541Dic5—42no—
542Dic5—62no—
543Dic5—122no—
544Dic5C2×(C2×D3)⋊C414yes—
545C24—31no—
546C24—51no—
547C24—151no—
548#41—3032no—
549C2×Q8—154no—
550C2×Q8—302no—
551C2×Q8—302no—
552C2×D4—154no—
553C2×D4—154no—
554C2×D4—154no—
555C2×D4—302no—
556C2×D4—302no—
557C2×D4—302no—
558C2×D4—302no—
559C2×D4—302no—
560C2×D4—302no—
561C22×C4—31no—
562C22×C4—34no—
563C22×C4—32no—
564C22×C4—51no—
565C22×C4—54no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—52no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—104no—
572C22×C4—151no—
573C22×C4—154no—
574C22×C4—152no—
575C22×C4—202no—
576C22×C4—202no—
577C22×C4—302no—
578C22×C4—302no—
579C22×C4C2×D3×D512yes—
580C22×C4C2×D3×D511yescharacteristic
581C4⋊C4—22no—
582C4⋊C4—62no—
583C4⋊C4—104no—
584C4⋊C4—102no—
585C4⋊C4—302no—
586C22⋊C4—122no—
587C22⋊C4—304no—
588C22⋊C4—602no—
589C22⋊C4—602no—
590C22⋊C4—602no—
591C42—304no—
592C3×C5#231111yescharacteristic, complemented, Hall
593C22×C3—54no—
594C22×C3—102no—
595C22×C3—102no—
596C22×C3—102no—
597C22×C3—102no—
598C22×C3—102no—
599C22×C3—102no—
600C22×C3C22×C4×D511yescharacteristic
601C22×C3C2×D4×D511yescharacteristic
602C22×C3C2×D4×D511yescharacteristic
603C22×C3#414411yescharacteristic
604C22×C3#414711yescharacteristic
605C22×C3#414911yescharacteristic
606C22×C3#415011yescharacteristic
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—102no—
615C2×D3—102no—
616C2×D3—102no—
617C2×D3—201no—
618C2×D3—201no—
619C2×D3—201no—
620C2×D3—201no—
621C3×C4—42no—
622C3×C4—54no—
623C3×C4—202no—
624C3×C4D5×C22⋊C414yes—
625Dic3—22no—
626Dic3—42no—
627Dic3—102no—
628Dic3—202no—
629C2×C5—122no—
630C2×C5#550411yescharacteristic
631C2×C5#550411yescharacteristic
632C2×C5#551011yescharacteristic
633C2×C5#551011yescharacteristic
634C2×C5C22×(C2×D3)⋊C411yescharacteristic
635C2×C5#580511yescharacteristic
636C2×C5#581611yescharacteristic
637D5—24no—
638D5—122no—
639C23—32no—
640C23—52no—
641C23—52no—
642C23—52no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—101no—
650C23—101no—
651C23—101no—
652C23—101no—
653C23—152no—
654C23—301no—
655C23—301no—
656C23—301no—
657C23—301no—
658C23—301no—
659C23—301no—
660C23C22×D3×D511yescharacteristic
661Q8—308no—
662D4—308no—
663D4—308no—
664D4—308no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—32no—
669C2×C4—52no—
670C2×C4—52no—
671C2×C4—52no—
672C2×C4—516no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—68no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—152no—
683C2×C4—208no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4—308no—
687C2×C4—302no—
688C2×C4—302no—
689C2×C4—302no—
690C2×C4C4×D3×D512yes—
691C2×C4D5×D1212yes—
692C2×C4D5×#6712yes—
693C2×C3—104no—
694C2×C3C2×D5×C22⋊C411yescharacteristic
695C2×C3#6583811yescharacteristic
696C2×C3#6585711yescharacteristic
697C2×C3#6594111yescharacteristic
698C2×C3#6594211yescharacteristic
699C2×C3#6596211yescharacteristic
700C2×C3#6596311yescharacteristic
701D3—42no—
702D3—202no—
703C5#8218611yescharacteristic, complemented, Sylow
704C22—54no—
705C22—62no—
706C22—62no—
707C22—62no—
708C22—102no—
709C22—102no—
710C22—102no—
711C22—102no—
712C22—102no—
713C22—102no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—302no—
719C22—302no—
720C22—302no—
721C22—601no—
722C22—601no—
723C22—601no—
724C22—601no—
725C22C2×C4×D3×D511yescharacteristic
726C22C2×D5×D1211yescharacteristic
727C22#9202511yescharacteristic
728C22#9202611yescharacteristic
729C22#9202911yescharacteristic
730C22#9203011yescharacteristic
731C22C2×D5×#6711yescharacteristic
732C4—42no—
733C4—54no—
734C4—62no—
735C4—122no—
736C4—202no—
737C4—302no—
738C4—602no—
739C4D5×(C2×D3)⋊C414yes—
740C3#1060573411yescharacteristic, complemented, Sylow
741C2—104no—
742C2—122no—
743C2—602no—
744C2#1175366711yescharacteristic
745C2#1175366811yescharacteristic
746C2#1175369011yescharacteristic
747C2#1175369111yescharacteristic
748C2C2×D5×(C2×D3)⋊C411yescharacteristic
749C2#1175493311yescharacteristic
750C2#1175522211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6771C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2311
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C2×#91358C2semidirect
4. #11751088C2semidirect
5. C5×#4987C2semidirect
6. #11748909C2semidirect
7. #11748907C2semidirect
8. #11748905C2semidirect
9. #11748799C2semidirect
10. #11748786C2semidirect
11. #11748628C2semidirect
23. C2×#6771C4semidirect
44. C2×D5×C4⋊C4D3semidirect
62. C2×C4×D15C2×C4semidirect
67. C2×C4×C5×D3C2×C4semidirect
78. C2×#1204C2×C4semidirect
81. C2×#1203C2×C4semidirect
109. #4987D5semidirect
189. C3×C4×D5C22⋊C4semidirect
348. C2×C4×D3C4×D5semidirect
415. C4×D5(C2×D3)⋊C4semidirect
592. C3×C5#2311semidirect
703. C5#82186semidirect
740. C3#10605734semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×C3×D5×C4⋊C42
C2×#913582
#117510882
C5×#49872
#117489092
#117489072
#117489052
#117487992
#117487862
#117486282
#106057343
#821865