Finite Group Databasebeta

← #14319949

Subgroups — #14319949

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic
2C2×C3×#4038C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751088C211yesmaximal, characteristic, complemented
5C5×#4987C211yesmaximal, characteristic, complemented
6#11748940C212yesmaximal
7#11748875C212yesmaximal, complemented
8Dic5×(C2×D3)⋊C4C212yesmaximal, complemented
9#11748871C212yesmaximal, complemented
10#11748799C211yesmaximal, characteristic, complemented
11#11748786C211yesmaximal, characteristic, complemented
12#10605593—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×#1200C2211yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C4×D3×D5—24no—
21C2×C4×D3×D5—24no—
22C2×C4×D3×D5C418yescomplemented
23C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
24C2×#6714C2212yes—
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
28C2×C3×#685C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
30C2×C3×C4×Dic5C2212yescomplemented
31C3×#4038—24no—
32C2×#6667C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×#6665C2212yes—
35C2×Dic3×Dic5C2212yescomplemented
36#91358—24no—
37#91115C2212yescomplemented
38C5×C3⋊#95C2212yescomplemented
39#90994C2212yescomplemented
40#90994C2212yescomplemented
41#82267—51nomaximal, Hall
42C23×C4×D5—31no—
43C2×#4038—31no—
44C2×#4038D311yescharacteristic, complemented
45C5×#380—31no—
46#65501—31no—
47#65276—31no—
48#65276—31no—
49#65244—32no—
50C22⋊C4×Dic5—32no—
51#64955—32no—
52#64953—32no—
53C23×D15C2311yescharacteristic
54C23×C5×D3C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C22×D3×D5—22no—
57C22×D3×D5—22no—
58C22×D3×D5—22no—
59C22×D3×D5—22no—
60C22×D3×D5—22no—
61C22×D3×D5—22no—
62C22×D3×D5C2×C414yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C2×C4×D15—22no—
68C2×C4×D15—22no—
69C2×C4×D15C2×C414yes—
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2311yescharacteristic
72C2×C4×C5×D3—22no—
73C2×C4×C5×D3—22no—
74C2×C4×C5×D3C2×C414yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2311yescharacteristic
77C2×C3×C4×D5C2×C414yes—
78C2×C3×C4×D5D414yes—
79C2×C3×C4×D5D414yes—
80C2×#1200—22no—
81C2×#1200—22no—
82C2×#1200C2×C414yes—
83C2×D3×Dic5—22no—
84C2×D3×Dic5—22no—
85C2×D3×Dic5C2×C414yes—
86C2×D5×Dic3—22no—
87C2×D5×Dic3—22no—
88C2×D5×Dic3C2×C414yes—
89C4×D3×D5—232no—
90C3×C5×C4⋊C4—22no—
91#6714—24no—
92C4⋊Dic15—22no—
93C5×(C2×D3)⋊C4—24no—
94C5×C4⋊Dic3—22no—
95C3×#685—24no—
96C3×C4⋊Dic5—22no—
97C3×C4×Dic5—24no—
98#6667—24no—
99(C2×D3)⋊Dic5—24no—
100#6665—24no—
101Dic3×Dic5—24no—
102C23×C4×D3—51no—
103C2×C3×#117—51no—
104C2×#926—51no—
105#4987—51no—
106#4987—51no—
107#4987—51no—
108#4987D511yescharacteristic, complemented
109#4955—52no—
110#4943—52no—
111C4×(C2×D3)⋊C4—52no—
112C4×(C2×D3)⋊C4—52no—
113C24×D5—31no—
114C23×C4×C5—31no—
115C23×Dic5—31no—
116C22×C4×D5—31no—
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—38no—
120C22×C4×D5—64no—
121C22×C4×D5—64no—
122C22×C4×D5C2×D311yescharacteristic
123C2×C5×C4⋊C4—31no—
124C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
125C2×C5×C22⋊C4—32no—
126C2×C22⋊Dic5—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685C2×D312yes—
131C2×C4⋊Dic5—31no—
132C2×C4⋊Dic5C2×D311yescharacteristic, complemented
133C2×C4×Dic5—32no—
134C2×C4×Dic5C2×D312yescomplemented
135#4038—24no—
136#4038—64no—
137C5×#95—32no—
138#3963—32no—
139#3963—32no—
140#3963—32no—
141#2280—151noSylow
142C23×C3×C5C2411yescharacteristic
143C22×D15—21no—
144C22×D15—21no—
145C22×D15—21no—
146C22×D15—21no—
147C22×D15C22×C412yes—
148C22×D15#4112yes—
149C22×D15#4112yes—
150C22×C5×D3—21no—
151C22×C5×D3—21no—
152C22×C5×D3—21no—
153C22×C5×D3—21no—
154C22×C5×D3C22×C412yes—
155C22×C5×D3#4112yes—
156C22×C5×D3#4112yes—
157C22×C3×D5—21no—
158C22×C3×D5—21no—
159C22×C3×D5—21no—
160C22×C3×D5—21no—
161C22×C3×D5C22×C412yes—
162C22×C3×D5C2×D412yes—
163C22×C3×D5C2×D412yes—
164C2×D3×D5—28no—
165C2×D3×D5—28no—
166C2×D3×D5—28no—
167C2×D3×D5—28no—
168C2×D3×D5—28no—
169C2×D3×D5—28no—
170C2×D3×D5—28no—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5—22no—
173C2×C3×C4×C5—22no—
174C2×C3×C4×C5C22×C412yes—
175C2×C3×C4×C5C2×D412yes—
176C2×C3×C4×C5C2×D412yes—
177C2×Dic15—21no—
178C2×Dic15—21no—
179C2×Dic15—22no—
180C2×Dic15—22no—
181C2×Dic15—22no—
182C2×Dic15C22×C412yes—
183C4×D15—28no—
184C2×C5×Dic3—21no—
185C2×C5×Dic3—21no—
186C2×C5×Dic3—22no—
187C2×C5×Dic3—22no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3C22×C412yes—
190C4×C5×D3—28no—
191C2×C3×Dic5—22no—
192C2×C3×Dic5—22no—
193C2×C3×Dic5—22no—
194C2×C3×Dic5C22×C412yes—
195C2×C3×Dic5C2×D412yes—
196C2×C3×Dic5C2×D412yes—
197C3×C4×D5C22⋊C4116yescomplemented
198#1200—28no—
199D3×Dic5—28no—
200D5×Dic3—28no—
201C24×D3—51no—
202C23×C3×C4—51no—
203C23×Dic3—51no—
204C22×C4×D3—51no—
205C22×C4×D3—51no—
206C22×C4×D3—51no—
207C22×C4×D3—58no—
208C22×C4×D3—104no—
209C22×C4×D3—104no—
210C22×C4×D3C2×D511yescharacteristic
211C3×#117—104no—
212C2×C3×C4⋊C4—51no—
213C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
214C2×C3×C22⋊C4—52no—
215C2×C3×C42—52no—
216C2×#217—52no—
217C2×(C2×D3)⋊C4—52no—
218C2×(C2×D3)⋊C4—52no—
219C2×(C2×D3)⋊C4—52no—
220C2×(C2×D3)⋊C4C2×D512yes—
221#926—104no—
222C2×C4⋊Dic3—51no—
223C2×C4⋊Dic3C2×D511yescharacteristic, complemented
224C2×C4×Dic3—52no—
225C3⋊#95—52no—
226C3⋊#95—52no—
227C3⋊#95—52no—
228C3⋊#95C2×D512yescomplemented
229C24×C5—31no—
230C23×D5—31no—
231C23×D5—34no—
232C23×D5—62no—
233C23×D5—62no—
234C23×D5—62no—
235C23×D5—62no—
236C23×D5—62no—
237C23×D5—62no—
238C23×D5C22×D311yescharacteristic
239C22×C4×C5—31no—
240C22×C4×C5—34no—
241C22×C4×C5—32no—
242C22×C4×C5—62no—
243C22×C4×C5—62no—
244C22×C4×C5C22×D312yes—
245C22×C4×C5C22×D311yescharacteristic
246C22×Dic5—31no—
247C22×Dic5—34no—
248C22×Dic5—32no—
249C22×Dic5—62no—
250C22×Dic5—62no—
251C22×Dic5C22×D312yes—
252C22×Dic5C22×D311yescharacteristic
253C2×C4×D5—34no—
254C2×C4×D5—34no—
255C2×C4×D5—34no—
256C2×C4×D5—62no—
257C2×C4×D5—62no—
258C2×C4×D5—62no—
259C2×C4×D5—62no—
260C2×C4×D5—62no—
261C2×C4×D5—62no—
262C2×C4×D5—632no—
263C2×C4×D5C4×D314yes—
264C2×C4×D5D1214yes—
265C2×C4×D5#6714yes—
266C5×C4⋊C4—22no—
267C5×C4⋊C4—62no—
268C5×C22⋊C4—64no—
269C22⋊Dic5—64no—
270#685—24no—
271#685—64no—
272#685—64no—
273#685—64no—
274C4⋊Dic5—22no—
275C4⋊Dic5—62no—
276C4×Dic5—24no—
277C4×Dic5—64no—
278C24×C4—151no—
279C2×#117—51no—
280C2×#117—151no—
281#381—152no—
282#380—31no—
283#380—151no—
284#380—151no—
285#380—151no—
286#379—152no—
287C4×C22⋊C4—152no—
288C4×C22⋊C4—152no—
289C22×C3×C5C23×C411yescharacteristic
290C22×C3×C5C22×D411yescharacteristic
291C22×C3×C5C22×D411yescharacteristic
292C22×C3×C5C2×#4111yescharacteristic
293C22×C3×C5C2×#4111yescharacteristic
294C22×C3×C5C2×#4111yescharacteristic
295C22×C3×C5C2×#4111yescharacteristic
296C2×D15—22no—
297C2×D15—22no—
298C2×D15—22no—
299C2×D15—22no—
300C2×D15—22no—
301C2×D15—22no—
302C2×D15#11714yescomplemented
303C2×C5×D3—22no—
304C2×C5×D3—22no—
305C2×C5×D3—22no—
306C2×C5×D3—22no—
307C2×C5×D3—22no—
308C2×C5×D3—22no—
309C2×C5×D3#11714yescomplemented
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—22no—
315C2×C3×D5—22no—
316C2×C3×D5C2×C22⋊C414yes—
317D3×D5—232no—
318C3×C4×C5—42no—
319C3×C4×C5C2×C22⋊C414yes—
320Dic15—22no—
321Dic15—42no—
322C3×Dic5—42no—
323C3×Dic5C2×C22⋊C414yes—
324C5×Dic3—22no—
325C5×Dic3—42no—
326C24×C3—51no—
327C23×D3—51no—
328C23×D3—54no—
329C23×D3—102no—
330C23×D3—102no—
331C23×D3—102no—
332C23×D3—102no—
333C23×D3—102no—
334C23×D3—102no—
335C23×D3C22×D511yescharacteristic
336C22×C3×C4—51no—
337C22×C3×C4—54no—
338C22×C3×C4—54no—
339C22×C3×C4—54no—
340C22×C3×C4—52no—
341C22×C3×C4C22×D512yes—
342C22×C3×C4C22×D511yescharacteristic
343C22×Dic3—51no—
344C22×Dic3—54no—
345C22×Dic3—52no—
346C22×Dic3—102no—
347C22×Dic3—102no—
348C22×Dic3C22×D512yes—
349C22×Dic3C22×D511yescharacteristic
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—54no—
353C2×C4×D3—54no—
354C2×C4×D3—54no—
355C2×C4×D3—1032no—
356C2×C4×D3—102no—
357C2×C4×D3—102no—
358C2×C4×D3—102no—
359C2×C4×D3—102no—
360C2×C4×D3—102no—
361C2×C4×D3—102no—
362C2×C4×D3C4×D514yes—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—102no—
365C3×C22⋊C4—104no—
366C3×C42—104no—
367#217—104no—
368(C2×D3)⋊C4—24no—
369(C2×D3)⋊C4—104no—
370(C2×D3)⋊C4—104no—
371(C2×D3)⋊C4—104no—
372C4⋊Dic3—22no—
373C4⋊Dic3—102no—
374C4×Dic3—104no—
375C23×C5—32no—
376C23×C5—32no—
377C23×C5—32no—
378C23×C5—61no—
379C23×C5—61no—
380C23×C5—61no—
381C23×C5—61no—
382C23×C5C23×D311yescharacteristic
383C22×D5—21no—
384C22×D5—21no—
385C22×D5—21no—
386C22×D5—21no—
387C22×D5—32no—
388C22×D5—32no—
389C22×D5—32no—
390C22×D5—68no—
391C22×D5—68no—
392C22×D5—68no—
393C22×D5—68no—
394C22×D5—68no—
395C22×D5—68no—
396C22×D5—61no—
397C22×D5—61no—
398C22×D5—61no—
399C22×D5—61no—
400C22×D5—68no—
401C22×D5C2×C4×D312yes—
402C22×D5C2×D1212yes—
403C22×D5C2×#6712yes—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—32no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—68no—
411C2×C4×C5—62no—
412C2×C4×C5—62no—
413C2×C4×C5—62no—
414C2×C4×C5C2×C4×D312yes—
415C2×C4×C5C2×D1212yes—
416C2×C4×C5C2×#6712yes—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—32no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423C2×Dic5—68no—
424C2×Dic5—62no—
425C2×Dic5—62no—
426C2×Dic5—62no—
427C2×Dic5C2×C4×D312yes—
428C2×Dic5C2×D1212yes—
429C2×Dic5C2×#6712yes—
430C4×D5—68no—
431C4×D5—68no—
432C4×D5—68no—
433C4×D5(C2×D3)⋊C4116yescomplemented
434C25—151no—
435C23×C4—31no—
436C23×C4—51no—
437C23×C4—151no—
438C23×C4—158no—
439C23×C4—151no—
440C23×C4—151no—
441C23×C4—151no—
442C23×C4—304no—
443C23×C4—304no—
444#117—104no—
445#117—304no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—51no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4D3×D511yescharacteristic, complemented
450C2×C22⋊C4—32no—
451C2×C22⋊C4—52no—
452C2×C22⋊C4—152no—
453C2×C22⋊C4—152no—
454C2×C22⋊C4—152no—
455C2×C22⋊C4—152no—
456C2×C42—52no—
457C2×C42—152no—
458#95—32no—
459#95—152no—
460#95—152no—
461#95—152no—
462C2×C3×C5C22×C22⋊C411yescharacteristic
463C2×C3×C5C2×#11711yescharacteristic
464C2×C3×C5C2×#11711yescharacteristic
465C2×C3×C5#52511yescharacteristic
466C2×C3×C5#52511yescharacteristic
467C2×C3×C5#52511yescharacteristic
468C2×C3×C5#52511yescharacteristic
469D15—24no—
470C3×D5—24no—
471C5×D3—24no—
472C23×C3—52no—
473C23×C3—52no—
474C23×C3—52no—
475C23×C3—101no—
476C23×C3—101no—
477C23×C3—101no—
478C23×C3—101no—
479C23×C3C23×D511yescharacteristic
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—52no—
485C22×D3—52no—
486C22×D3—52no—
487C22×D3—108no—
488C22×D3—108no—
489C22×D3—108no—
490C22×D3—108no—
491C22×D3—108no—
492C22×D3—108no—
493C22×D3—101no—
494C22×D3—101no—
495C22×D3—101no—
496C22×D3—101no—
497C22×D3—108no—
498C22×D3C2×C4×D512yes—
499C22×D3#71112yes—
500C22×D3#71312yes—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—52no—
505C2×C3×C4—52no—
506C2×C3×C4—52no—
507C2×C3×C4—516no—
508C2×C3×C4—102no—
509C2×C3×C4—102no—
510C2×C3×C4—102no—
511C2×C3×C4C2×C4×D512yes—
512C2×C3×C4D4×D512yes—
513C2×C3×C4D4×D512yes—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—52no—
520C2×Dic3—108no—
521C2×Dic3—101no—
522C2×Dic3—101no—
523C2×Dic3—102no—
524C2×Dic3—102no—
525C2×Dic3—102no—
526C2×Dic3C2×C4×D512yes—
527C4×D3—28no—
528C4×D3—108no—
529C4×D3—108no—
530C4×D3—108no—
531C22×C5—34no—
532C22×C5—62no—
533C22×C5—62no—
534C22×C5—62no—
535C22×C5—62no—
536C22×C5—62no—
537C22×C5—62no—
538C22×C5C22×C4×D311yescharacteristic
539C22×C5C22×D1211yescharacteristic
540C22×C5D3×#4111yescharacteristic
541C22×C5D3×#4111yescharacteristic
542C22×C5D3×#4111yescharacteristic
543C22×C5D3×#4111yescharacteristic
544C22×C5C22×#6711yescharacteristic
545C2×D5—22no—
546C2×D5—22no—
547C2×D5—22no—
548C2×D5—22no—
549C2×D5—22no—
550C2×D5—22no—
551C2×D5—34no—
552C2×D5—632no—
553C2×D5—62no—
554C2×D5—62no—
555C2×D5—62no—
556C2×D5—62no—
557C2×D5—62no—
558C2×D5—62no—
559C2×D5C2×(C2×D3)⋊C414yes—
560C4×C5—42no—
561C4×C5—62no—
562C4×C5—122no—
563C4×C5C2×(C2×D3)⋊C414yes—
564Dic5—42no—
565Dic5—62no—
566Dic5—122no—
567Dic5C2×(C2×D3)⋊C414yes—
568C24—31no—
569C24—51no—
570C24—154no—
571C24—151no—
572C24—302no—
573C24—302no—
574C24—302no—
575C24—302no—
576C24—302no—
577C24—302no—
578C22×C4—31no—
579C22×C4—34no—
580C22×C4—32no—
581C22×C4—51no—
582C22×C4—54no—
583C22×C4—54no—
584C22×C4—54no—
585C22×C4—52no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—154no—
589C22×C4—154no—
590C22×C4—154no—
591C22×C4—151no—
592C22×C4—154no—
593C22×C4—152no—
594C22×C4—302no—
595C22×C4—302no—
596C22×C4—3032no—
597C22×C4—302no—
598C22×C4—302no—
599C22×C4—302no—
600C22×C4—302no—
601C22×C4—302no—
602C22×C4—302no—
603C22×C4C2×D3×D512yes—
604C22×C4C2×D3×D511yescharacteristic
605C4⋊C4—22no—
606C4⋊C4—62no—
607C4⋊C4—102no—
608C4⋊C4—302no—
609C22⋊C4—64no—
610C22⋊C4—104no—
611C22⋊C4—304no—
612C22⋊C4—304no—
613C22⋊C4—304no—
614C22⋊C4—304no—
615C42—104no—
616C42—304no—
617C3×C5#228011yescharacteristic, complemented, Hall
618C22×C3—54no—
619C22×C3—102no—
620C22×C3—102no—
621C22×C3—102no—
622C22×C3—102no—
623C22×C3—102no—
624C22×C3—102no—
625C22×C3C22×C4×D511yescharacteristic
626C22×C3C2×D4×D511yescharacteristic
627C22×C3C2×D4×D511yescharacteristic
628C22×C3C2×#71111yescharacteristic
629C22×C3C2×#71311yescharacteristic
630C22×C3D5×#4111yescharacteristic
631C22×C3D5×#4111yescharacteristic
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—54no—
639C2×D3—1032no—
640C2×D3—102no—
641C2×D3—102no—
642C2×D3—102no—
643C2×D3—102no—
644C2×D3—102no—
645C2×D3—102no—
646C2×D3#403814yescomplemented
647C3×C4—42no—
648C3×C4—54no—
649C3×C4—202no—
650C3×C4D5×C22⋊C414yes—
651Dic3—22no—
652Dic3—42no—
653Dic3—102no—
654Dic3—202no—
655C2×C5—64no—
656C2×C5D3×#11711yescharacteristic
657C2×C5D3×#11711yescharacteristic
658C2×C5#552411yescharacteristic
659C2×C5#552411yescharacteristic
660C2×C5C22×(C2×D3)⋊C411yescharacteristic
661C2×C5#582811yescharacteristic
662C2×C5#582811yescharacteristic
663D5—24no—
664D5—64no—
665C23—32no—
666C23—32no—
667C23—32no—
668C23—52no—
669C23—52no—
670C23—52no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—101no—
676C23—101no—
677C23—101no—
678C23—101no—
679C23—152no—
680C23—152no—
681C23—152no—
682C23—308no—
683C23—308no—
684C23—308no—
685C23—308no—
686C23—308no—
687C23—308no—
688C23—308no—
689C23—301no—
690C23—301no—
691C23—301no—
692C23—301no—
693C23C22×D3×D511yescharacteristic
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—32no—
698C2×C4—52no—
699C2×C4—52no—
700C2×C4—52no—
701C2×C4—516no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—68no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—152no—
712C2×C4—308no—
713C2×C4—308no—
714C2×C4—308no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—308no—
718C2×C4—302no—
719C2×C4—302no—
720C2×C4—302no—
721C2×C4C4×D3×D512yes—
722C2×C4D5×D1212yes—
723C2×C4D5×#6712yes—
724C2×C3—104no—
725C2×C3C2×D5×C22⋊C411yescharacteristic
726C2×C3C2×#403811yescharacteristic
727C2×C3D5×#11711yescharacteristic
728C2×C3#6594011yescharacteristic
729C2×C3#6594011yescharacteristic
730C2×C3#6596111yescharacteristic
731C2×C3#6596111yescharacteristic
732D3—24no—
733D3—104no—
734C5#8226711yescharacteristic, complemented, Sylow
735C22—34no—
736C22—54no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—102no—
744C22—102no—
745C22—102no—
746C22—102no—
747C22—102no—
748C22—102no—
749C22—154no—
750C22—3032no—
751C22—302no—
752C22—302no—
753C22—302no—
754C22—302no—
755C22—302no—
756C22—302no—
757C22C2×C4×D3×D511yescharacteristic
758C22C2×D5×D1211yescharacteristic
759C22D3×#71111yescharacteristic
760C22#9202411yescharacteristic
761C22D3×#71311yescharacteristic
762C22#9203411yescharacteristic
763C22C2×D5×#6711yescharacteristic
764C4—42no—
765C4—54no—
766C4—62no—
767C4—122no—
768C4—202no—
769C4—302no—
770C4—602no—
771C4D5×(C2×D3)⋊C414yes—
772C3#1060559311yescharacteristic, complemented, Sylow
773C2—64no—
774C2—104no—
775C2—304no—
776C2D3×#403811yescharacteristic
777C2#1175383511yescharacteristic
778C2#1175387311yescharacteristic
779C2#1175387411yescharacteristic
780C2C2×D5×(C2×D3)⋊C411yescharacteristic
781C2#1175506011yescharacteristic
782C2#1175527011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2280
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×#4038C2semidirect
3. C2×#91358C2semidirect
4. #11751088C2semidirect
5. C5×#4987C2semidirect
7. #11748875C2semidirect
8. Dic5×(C2×D3)⋊C4C2semidirect
9. #11748871C2semidirect
10. #11748799C2semidirect
11. #11748786C2semidirect
22. C2×C4×D3×D5C4semidirect
23. C2×C3×C5×C4⋊C4C22semidirect
25. C2×C4⋊Dic15C22semidirect
27. C2×C5×C4⋊Dic3C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
30. C2×C3×C4×Dic5C22semidirect
35. C2×Dic3×Dic5C22semidirect
37. #91115C22semidirect
38. C5×C3⋊#95C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
44. C2×#4038D3semidirect
108. #4987D5semidirect
124. C2×C5×C4⋊C4C2×D3semidirect
132. C2×C4⋊Dic5C2×D3semidirect
134. C2×C4×Dic5C2×D3semidirect
197. C3×C4×D5C22⋊C4semidirect
213. C2×C3×C4⋊C4C2×D5semidirect
223. C2×C4⋊Dic3C2×D5semidirect
228. C3⋊#95C2×D5semidirect
302. C2×D15#117semidirect
309. C2×C5×D3#117semidirect
433. C4×D5(C2×D3)⋊C4semidirect
449. C2×C4⋊C4D3×D5semidirect
617. C3×C5#2280semidirect
646. C2×D3#4038semidirect
734. C5#82267semidirect
772. C3#10605593semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×C3×#40382
C2×#913582
#117510882
C5×#49872
#117489402
#117488752
Dic5×(C2×D3)⋊C42
#117488712
#117487992
#117487862
#106055933
#822675