Finite Group Databasebeta

← #14325936

Subgroups — #14325936

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic
2C22×#6719C211yesmaximal, characteristic, complemented
3C2×#91559C212yesmaximal, complemented
4C2×D5×#217C211yesmaximal, characteristic, complemented
5C5×#5247C211yesmaximal, characteristic, complemented
6#11749518C212yesmaximal, complemented
7#11749506C211yesmaximal, characteristic, complemented
8#11749500C212yesmaximal, complemented
9#11749489C212yesmaximal, complemented
10#11749488C211yesmaximal, characteristic, complemented
11Dic5×#217C211yesmaximal, characteristic, complemented
12#10605581—31nomaximal, Hall
13C25×C3×C5C2211yescharacteristic
14C24×C3×D5C2211yescharacteristic
15C23×Dic15C2212yescomplemented
16C22×C3×C22⋊D5—28no—
17C22×C3×C22⋊D5C418yescomplemented
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×D5×Dic3C2212yescomplemented
24C2×#6719—24no—
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2212yescomplemented
28C2×C5×#217C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C2×C5×#217C2212yescomplemented
31C2×C5×#217C2212yescomplemented
32#91559—28no—
33D5×#217—24no—
34C2×#6668C2212yescomplemented
35C2×#6665C2212yescomplemented
36C2×#6665C2212yescomplemented
37C2×#6665C2212yescomplemented
38C2×Dic3×Dic5C2212yescomplemented
39#90994C2212yescomplemented
40#90994C2212yescomplemented
41D4×#217—51nomaximal, Hall
42C23×C22⋊D5D311yescharacteristic
43C22×C22⋊Dic5—31no—
44C2×#4027—32no—
45C2×D5×C22⋊C4—31no—
46C5×#379—31no—
47#65247—32no—
48#65246—32no—
49#65245—32no—
50#65244—31no—
51#65231—31no—
52C22⋊C4×Dic5—31no—
53C24×C3×C5—24no—
54C24×C3×C5—22no—
55C24×C3×C5—22no—
56C24×C3×C5—42no—
57C24×C3×C5C2×C414yescomplemented
58C24×C3×C5C2311yescharacteristic
59C24×C3×C5C2311yescharacteristic
60C24×C3×C5C2311yescharacteristic
61C23×C3×D5—22no—
62C23×C3×D5—22no—
63C23×C3×D5—24no—
64C23×C3×D5—42no—
65C23×C3×D5C2×C414yescomplemented
66C23×C3×D5C2311yescharacteristic
67C23×C3×D5C2311yescharacteristic
68C22×Dic15—24no—
69C22×Dic15—24no—
70C22×Dic15—42no—
71C22×Dic15C2312yes—
72C22×Dic15C2312yes—
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5—24no—
77C2×C3×C22⋊D5—232no—
78C2×C3×C22⋊D5—24no—
79C2×C3×C22⋊D5C2×C414yes—
80C2×C3×C22⋊D5C2×C414yescomplemented
81C2×C3×C22⋊D5C2×C414yescomplemented
82C2×C3×C22⋊D5C2×C414yescomplemented
83C2×C3×C22⋊D5D418yes—
84C22×C3×Dic5—24no—
85C22×C3×Dic5C2×C414yescomplemented
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C2×D5×Dic3—24no—
89C2×D5×Dic3—24no—
90C2×D5×Dic3—42no—
91#6719—22no—
92#6719—24no—
93#6719D414yescomplemented
94C5×#217—22no—
95C5×#217—24no—
96C5×#217—22no—
97C5×#217—42no—
98#6668—24no—
99#6665—24no—
100#6665—24no—
101#6665—42no—
102Dic3×Dic5—24no—
103C23×C3×D4—51no—
104C22×#217—51no—
105C22×#217—51no—
106C2×D4×Dic3—52no—
107#5247—51no—
108#5247D511yescharacteristic, complemented
109#5221—52no—
110#5220—52no—
111#5220—52no—
112#5212—51no—
113C4×#217—51no—
114C25×C5C2×D311yescharacteristic
115C24×D5C2×D311yescharacteristic
116C22×C22⋊D5—28no—
117C22×C22⋊D5Dic318yescomplemented
118C22×C22⋊D5C2×D311yescharacteristic
119C22×C22⋊D5C2×D311yescharacteristic
120C22×C22⋊D5C2×D311yescharacteristic
121C22×C22⋊D5C2×D311yescharacteristic
122C23×Dic5—32no—
123C23×Dic5C2×D311yescharacteristic
124C22×C4×D5—32no—
125C2×C5×C22⋊C4—31no—
126C2×C5×C22⋊C4—32no—
127C2×C5×C22⋊C4—31no—
128C2×C5×C22⋊C4—32no—
129C2×C22⋊Dic5—31no—
130C2×C22⋊Dic5—31no—
131C2×C22⋊Dic5—32no—
132C2×C22⋊Dic5—64no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136C2×#683—32no—
137C2×C4×Dic5—32no—
138#4027—68no—
139D5×C22⋊C4—64no—
140#3963—32no—
141#3963—32no—
142D4×C22⋊C4—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—28no—
149C23×C3×C5—28no—
150C23×C3×C5—21no—
151C23×C3×C5—22no—
152C23×C3×C5—21no—
153C23×C3×C5—22no—
154C23×C3×C5—44no—
155C23×C3×C5—48no—
156C23×C3×C5—48no—
157C23×C3×C5C22×C412yes—
158C23×C3×C5C22×C412yes—
159C23×C3×C5C22×C412yes—
160C23×C3×C5C2×D414yes—
161C23×C3×C5C2×D412yes—
162C23×C3×C5#4112yes—
163C23×C3×C5C2411yescharacteristic
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—22no—
167C22×C3×D5—28no—
168C22×C3×D5—21no—
169C22×C3×D5—22no—
170C22×C3×D5—21no—
171C22×C3×D5—22no—
172C22×C3×D5—28no—
173C22×C3×D5—44no—
174C22×C3×D5—48no—
175C22×C3×D5—48no—
176C22×C3×D5C22×C412yes—
177C22×C3×D5C22×C412yes—
178C22×C3×D5C2×D414yes—
179C2×Dic15—22no—
180C2×Dic15—22no—
181C2×Dic15—22no—
182C2×Dic15—22no—
183C2×Dic15—22no—
184C2×Dic15—48no—
185C2×Dic15C2×D414yescomplemented
186C2×C5×Dic3—22no—
187C2×C5×Dic3—22no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3—22no—
190C2×C5×Dic3—22no—
191C2×C5×Dic3—22no—
192C3×C22⋊D5—28no—
193C3×C22⋊D5—28no—
194C3×C22⋊D5—28no—
195C3×C22⋊D5C22⋊C4116yescomplemented
196C2×C3×Dic5—22no—
197C2×C3×Dic5—28no—
198C2×C3×Dic5C22×C412yes—
199C2×C3×Dic5C22×C412yes—
200C2×C3×Dic5C2×D414yes—
201D5×Dic3—48no—
202C25×C3—51no—
203C25×C3C2×D511yescharacteristic
204C22×C3×D4—51no—
205C22×C3×D4—58no—
206C22×C3×D4—51no—
207C22×C3×D4—51no—
208C22×C3×D4—51no—
209C22×C3×D4—108no—
210C23×C3×C4—51no—
211C23×Dic3—52no—
212C23×Dic3—52no—
213C2×#217—51no—
214C2×#217—51no—
215C2×#217—52no—
216C2×#217—52no—
217C2×#217—52no—
218C2×#217—52no—
219C2×#217—104no—
220C2×#217—104no—
221C2×#217C2×D511yescharacteristic
222C2×#217C2×D511yescharacteristic
223C2×#217C2×D512yescomplemented
224C2×#217C2×D512yescomplemented
225D4×Dic3—108no—
226C2×C4⋊Dic3—52no—
227C2×C4×Dic3—52no—
228C3⋊#95—52no—
229C3⋊#95—52no—
230C24×C5—22no—
231C24×C5—22no—
232C24×C5—24no—
233C24×C5—42no—
234C24×C5C2×Dic314yescomplemented
235C24×C5C22×D311yescharacteristic
236C24×C5C22×D311yescharacteristic
237C24×C5C22×D311yescharacteristic
238C23×D5—22no—
239C23×D5—22no—
240C23×D5—24no—
241C23×D5—42no—
242C23×D5C2×Dic314yescomplemented
243C23×D5C22×D311yescharacteristic
244C23×D5C22×D311yescharacteristic
245C22×C4×C5—32no—
246C22×C4×C5—32no—
247C2×C22⋊D5—24no—
248C2×C22⋊D5—24no—
249C2×C22⋊D5—232no—
250C2×C22⋊D5—24no—
251C2×C22⋊D5C2×Dic314yes—
252C2×C22⋊D5C2×Dic314yescomplemented
253C2×C22⋊D5C2×Dic314yescomplemented
254C2×C22⋊D5C2×Dic314yescomplemented
255C2×C22⋊D5#6718yes—
256C22×Dic5—24no—
257C22×Dic5—32no—
258C22×Dic5—32no—
259C22×Dic5—64no—
260C22×Dic5—64no—
261C22×Dic5—122no—
262C22×Dic5C2×Dic314yescomplemented
263C22×Dic5C22×D311yescharacteristic
264C22×Dic5C22×D311yescharacteristic
265C2×C4×D5—64no—
266C2×C4×D5—64no—
267C2×C4×D5—122no—
268C5×C22⋊C4—62no—
269C5×C22⋊C4—62no—
270C5×C22⋊C4—64no—
271C5×C22⋊C4—122no—
272C22⋊Dic5—34no—
273C22⋊Dic5—64no—
274C22⋊Dic5—62no—
275#685—64no—
276#685—64no—
277#685—122no—
278#683—64no—
279C4×Dic5—64no—
280C23×D4—51no—
281C2×C4×D4—152no—
282C22×C22⋊C4—151no—
283C22×C22⋊C4—151no—
284#390—152no—
285#386—152no—
286#386—152no—
287#380—151no—
288#379—31no—
289#379—151no—
290C4×C22⋊C4—151no—
291C22×C3×C5—22no—
292C22×C3×C5—22no—
293C22×C3×C5—22no—
294C22×C3×C5—22no—
295C22×C3×C5—24no—
296C22×C3×C5—24no—
297C22×C3×C5—24no—
298C22×C3×C5—24no—
299C22×C3×C5—22no—
300C22×C3×C5—22no—
301C22×C3×C5—22no—
302C22×C3×C5—416no—
303C22×C3×C5—42no—
304C22×C3×C5—42no—
305C22×C3×C5C2×C22⋊C414yescomplemented
306C22×C3×C5C4×D414yescomplemented
307C22×C3×C5C23×C411yescharacteristic
308C22×C3×C5C22×D411yescharacteristic
309C22×C3×C5C22×D412yes—
310C22×C3×C5C2×#4111yescharacteristic
311C22×C3×C5H(5,𝔽2)12yes—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—22no—
317C2×C3×D5—22no—
318C2×C3×D5—22no—
319C2×C3×D5—416no—
320C2×C3×D5—42no—
321C2×C3×D5—42no—
322C2×C3×D5C2×C22⋊C414yescomplemented
323Dic15—24no—
324Dic15—42no—
325C3×Dic5—22no—
326C3×Dic5C2×C22⋊C414yescomplemented
327C5×Dic3—42no—
328C5×Dic3—42no—
329C24×C3—22no—
330C24×C3—24no—
331C24×C3—22no—
332C24×C3—42no—
333C24×C3—51no—
334C24×C3—51no—
335C24×C3—54no—
336C24×C3—104no—
337C24×C3—102no—
338C24×C3—102no—
339C24×C3—202no—
340C24×C3C4×D514yescomplemented
341C24×C3C22×D511yescharacteristic
342C24×C3C22×D511yescharacteristic
343C24×C3C22×D511yescharacteristic
344C2×C3×D4—54no—
345C2×C3×D4—58no—
346C2×C3×D4—54no—
347C2×C3×D4—54no—
348C2×C3×D4—54no—
349C2×C3×D4—104no—
350C2×C3×D4—1032no—
351C2×C3×D4—104no—
352C2×C3×D4—104no—
353C22×C3×C4—51no—
354C22×C3×C4—54no—
355C22×C3×C4—51no—
356C22×C3×C4—104no—
357C22×Dic3—52no—
358C22×Dic3—52no—
359C22×Dic3—104no—
360C22×Dic3—104no—
361C22×Dic3—104no—
362C22×Dic3—104no—
363C22×Dic3—202no—
364C22×Dic3—202no—
365C22×Dic3C22×D512yes—
366C22×Dic3C22×D512yes—
367#217—24no—
368#217—22no—
369#217—22no—
370#217—42no—
371#217—54no—
372#217—104no—
373#217—104no—
374#217—104no—
375#217—102no—
376#217—202no—
377C4⋊Dic3—104no—
378C4×Dic3—104no—
379C23×C5—21no—
380C23×C5—21no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—28no—
385C23×C5—28no—
386C23×C5—21no—
387C23×C5—21no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—44no—
391C23×C5—48no—
392C23×C5—48no—
393C23×C5D3×D412yes—
394C23×C5#23712yes—
395C23×C5C22×Dic312yes—
396C23×C5C22×Dic312yes—
397C23×C5C22×Dic312yes—
398C23×C5C2×#6714yes—
399C23×C5C23×D311yescharacteristic
400C22×D5—21no—
401C22×D5—21no—
402C22×D5—22no—
403C22×D5—28no—
404C22×D5—21no—
405C22×D5—21no—
406C22×D5—22no—
407C22×D5—22no—
408C22×D5—28no—
409C22×D5—44no—
410C22×D5—48no—
411C22×D5—48no—
412C22×D5C22×Dic312yes—
413C22×D5C22×Dic312yes—
414C22×D5C2×#6714yes—
415C2×C4×C5—62no—
416C2×C4×C5—62no—
417C2×C4×C5—62no—
418C2×C4×C5—62no—
419C2×C4×C5—62no—
420C2×C4×C5—62no—
421C22⋊D5—28no—
422C22⋊D5—28no—
423C22⋊D5—28no—
424C22⋊D5#217116yescomplemented
425C2×Dic5—22no—
426C2×Dic5—28no—
427C2×Dic5—34no—
428C2×Dic5—62no—
429C2×Dic5—62no—
430C2×Dic5—62no—
431C2×Dic5—62no—
432C2×Dic5—62no—
433C2×Dic5—128no—
434C2×Dic5C22×Dic312yes—
435C2×Dic5C22×Dic312yes—
436C2×Dic5C2×#6714yes—
437C4×D5—128no—
438C25—51no—
439C25D3×D511yescharacteristic
440C22×D4—51no—
441C22×D4—58no—
442C22×D4—51no—
443C22×D4—51no—
444C22×D4—51no—
445C22×D4—108no—
446C23×C4—51no—
447C23×C4—152no—
448C23×C4—152no—
449C4×D4—308no—
450C2×C4⋊C4—152no—
451C2×C22⋊C4—31no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—151no—
456C2×C22⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—151no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—304no—
462C2×C22⋊C4—304no—
463C2×C42—152no—
464#95—152no—
465#95—152no—
466C2×C3×C5—24no—
467C2×C3×C5—24no—
468C2×C3×C5—42no—
469C2×C3×C5C22×C22⋊C411yescharacteristic
470C2×C3×C5C2×C4×D411yescharacteristic
471C2×C3×C5#51811yescharacteristic
472C2×C3×C5D4212yes—
473C2×C3×C5#54612yes—
474C3×D5—24no—
475C3×D5—42no—
476C23×C3—21no—
477C23×C3—22no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—22no—
483C23×C3—21no—
484C23×C3—22no—
485C23×C3—28no—
486C23×C3—28no—
487C23×C3—44no—
488C23×C3—48no—
489C23×C3—48no—
490C23×C3—52no—
491C23×C3—54no—
492C23×C3—52no—
493C23×C3—108no—
494C23×C3—101no—
495C23×C3—101no—
496C23×C3—102no—
497C23×C3—101no—
498C23×C3—102no—
499C23×C3—101no—
500C23×C3—102no—
501C23×C3—108no—
502C23×C3—204no—
503C23×C3—208no—
504C23×C3—208no—
505C23×C3C2×C4×D512yes—
506C23×C3C2×C4×D512yes—
507C23×C3C2×C4×D512yes—
508C23×C3D4×D514yes—
509C23×C3D4×D512yes—
510C23×C3#71112yes—
511C23×C3C23×D511yescharacteristic
512C3×D4—516no—
513C3×D4—108no—
514C3×D4—108no—
515C3×D4—108no—
516C2×C3×C4—52no—
517C2×C3×C4—54no—
518C2×C3×C4—52no—
519C2×C3×C4—108no—
520C2×C3×C4—102no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—54no—
528C2×Dic3—102no—
529C2×Dic3—102no—
530C2×Dic3—102no—
531C2×Dic3—102no—
532C2×Dic3—102no—
533C2×Dic3—208no—
534C2×Dic3—208no—
535C22×C5—22no—
536C22×C5—22no—
537C22×C5—22no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5—22no—
545C22×C5—22no—
546C22×C5—416no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5D4×Dic314yescomplemented
550C22×C5C2×#21714yescomplemented
551C22×C5C2×D3×D411yescharacteristic
552C22×C5C2×#23711yescharacteristic
553C22×C5#100412yes—
554C22×C5C23×Dic311yescharacteristic
555C22×C5C22×#6712yes—
556C2×D5—22no—
557C2×D5—22no—
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—22no—
561C2×D5—22no—
562C2×D5—22no—
563C2×D5—416no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5C2×#21714yescomplemented
567C4×C5—122no—
568C4×C5—122no—
569Dic5—22no—
570Dic5—64no—
571Dic5—122no—
572Dic5C2×#21714yescomplemented
573C24—22no—
574C24—24no—
575C24—22no—
576C24—42no—
577C24—51no—
578C24—51no—
579C24—54no—
580C24—104no—
581C24—102no—
582C24—102no—
583C24—202no—
584C24D5×Dic314yescomplemented
585C24C2×D3×D511yescharacteristic
586C24C2×D3×D511yescharacteristic
587C24C2×D3×D511yescharacteristic
588C2×D4—54no—
589C2×D4—58no—
590C2×D4—54no—
591C2×D4—54no—
592C2×D4—54no—
593C2×D4—104no—
594C2×D4—1032no—
595C2×D4—104no—
596C2×D4—104no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—51no—
600C22×C4—54no—
601C22×C4—51no—
602C22×C4—104no—
603C22×C4—152no—
604C22×C4—152no—
605C22×C4—304no—
606C22×C4—304no—
607C22×C4—304no—
608C22×C4—304no—
609C22×C4—602no—
610C22×C4—602no—
611C4⋊C4—304no—
612C22⋊C4—62no—
613C22⋊C4—64no—
614C22⋊C4—62no—
615C22⋊C4—122no—
616C22⋊C4—154no—
617C22⋊C4—304no—
618C22⋊C4—304no—
619C22⋊C4—304no—
620C22⋊C4—302no—
621C22⋊C4—602no—
622C42—304no—
623C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—416no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—54no—
639C22×C3—102no—
640C22×C3—102no—
641C22×C3—104no—
642C22×C3—104no—
643C22×C3—102no—
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—2016no—
647C22×C3—202no—
648C22×C3—202no—
649C22×C3D5×C22⋊C414yescomplemented
650C22×C3#402714yescomplemented
651C22×C3C22×C4×D511yescharacteristic
652C22×C3C2×D4×D512yes—
653C22×C3C2×D4×D511yescharacteristic
654C22×C3C2×#71111yescharacteristic
655C22×C3#414412yes—
656C3×C4—54no—
657C3×C4—102no—
658Dic3—42no—
659Dic3—42no—
660Dic3—104no—
661Dic3—202no—
662C2×C5—24no—
663C2×C5—24no—
664C2×C5—42no—
665C2×C5C2×D4×Dic311yescharacteristic
666C2×C5#579811yescharacteristic
667C2×C5D4×#6712yes—
668C2×C5#580612yes—
669C2×C5C22×#21711yescharacteristic
670D5—24no—
671D5—42no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—21no—
680C23—22no—
681C23—28no—
682C23—28no—
683C23—44no—
684C23—48no—
685C23—48no—
686C23—52no—
687C23—54no—
688C23—52no—
689C23—108no—
690C23—101no—
691C23—101no—
692C23—102no—
693C23—101no—
694C23—102no—
695C23—101no—
696C23—102no—
697C23—108no—
698C23—204no—
699C23—208no—
700C23—208no—
701C23C2×D5×Dic312yes—
702C23C2×D5×Dic312yes—
703C23C2×D5×Dic312yes—
704C23#678012yes—
705C23D5×#6714yes—
706C23#679012yes—
707C23C22×D3×D511yescharacteristic
708D4—516no—
709D4—108no—
710D4—108no—
711D4—108no—
712C2×C4—52no—
713C2×C4—54no—
714C2×C4—52no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—108no—
722C2×C4—102no—
723C2×C4—154no—
724C2×C4—302no—
725C2×C4—302no—
726C2×C4—302no—
727C2×C4—302no—
728C2×C4—302no—
729C2×C4—608no—
730C2×C4—608no—
731C2×C3—24no—
732C2×C3—24no—
733C2×C3—42no—
734C2×C3—104no—
735C2×C3—202no—
736C2×C3C2×D5×C22⋊C411yescharacteristic
737C2×C3C2×#402711yescharacteristic
738C2×C3#6582011yescharacteristic
739C2×C3#6592412yes—
740C2×C3#6592512yes—
741C5D4×#21711yescharacteristic, complemented, Sylow
742C22—22no—
743C22—24no—
744C22—24no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—24no—
749C22—24no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—54no—
757C22—104no—
758C22—102no—
759C22—102no—
760C22—104no—
761C22—102no—
762C22—102no—
763C22—102no—
764C22—2016no—
765C22—202no—
766C22—202no—
767C22D5×#21714yescomplemented
768C22#9155914yescomplemented
769C22C22×D5×Dic311yescharacteristic
770C22C2×#678011yescharacteristic
771C22C2×D5×#6712yes—
772C22C2×#679011yescharacteristic
773C22#9204912yes—
774C4—54no—
775C4—102no—
776C4—122no—
777C4—122no—
778C4—304no—
779C4—602no—
780C3#1060558111yescharacteristic, complemented, Sylow
781C2—24no—
782C2—24no—
783C2—42no—
784C2—104no—
785C2—202no—
786C2C2×D5×#21711yescharacteristic
787C2#1175538112yes—
788C2C2×#9155911yescharacteristic
789C2#1175540611yescharacteristic
790C2#1175543712yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC25×C3×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×C22⋊D5C2
hypercenterC25D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×#6719C2semidirect
3. C2×#91559C2semidirect
4. C2×D5×#217C2semidirect
5. C5×#5247C2semidirect
6. #11749518C2semidirect
7. #11749506C2semidirect
8. #11749500C2semidirect
9. #11749489C2semidirect
10. #11749488C2semidirect
11. Dic5×#217C2semidirect
15. C23×Dic15C22semidirect
17. C22×C3×C22⋊D5C4semidirect
23. C22×D5×Dic3C22semidirect
27. C2×#6719C22semidirect
30. C2×C5×#217C22semidirect
31. C2×C5×#217C22semidirect
34. C2×#6668C22semidirect
35. C2×#6665C22semidirect
36. C2×#6665C22semidirect
37. C2×#6665C22semidirect
38. C2×Dic3×Dic5C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
57. C24×C3×C5C2×C4semidirect
65. C23×C3×D5C2×C4semidirect
80. C2×C3×C22⋊D5C2×C4semidirect
81. C2×C3×C22⋊D5C2×C4semidirect
82. C2×C3×C22⋊D5C2×C4semidirect
85. C22×C3×Dic5C2×C4semidirect
93. #6719D4semidirect
108. #5247D5semidirect
117. C22×C22⋊D5Dic3semidirect
185. C2×Dic15C2×D4semidirect
195. C3×C22⋊D5C22⋊C4semidirect
223. C2×#217C2×D5semidirect
224. C2×#217C2×D5semidirect
234. C24×C5C2×Dic3semidirect
242. C23×D5C2×Dic3semidirect
252. C2×C22⋊D5C2×Dic3semidirect
253. C2×C22⋊D5C2×Dic3semidirect
254. C2×C22⋊D5C2×Dic3semidirect
262. C22×Dic5C2×Dic3semidirect
305. C22×C3×C5C2×C22⋊C4semidirect
306. C22×C3×C5C4×D4semidirect
322. C2×C3×D5C2×C22⋊C4semidirect
326. C3×Dic5C2×C22⋊C4semidirect
340. C24×C3C4×D5semidirect
424. C22⋊D5#217semidirect
549. C22×C5D4×Dic3semidirect
550. C22×C5C2×#217semidirect
566. C2×D5C2×#217semidirect
572. Dic5C2×#217semidirect
584. C24D5×Dic3semidirect
623. C3×C5D4×C22⋊C4semidirect
649. C22×C3D5×C22⋊C4semidirect
650. C22×C3#4027semidirect
741. C5D4×#217semidirect
767. C22D5×#217semidirect
768. C22#91559semidirect
780. C3#10605581semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×#67192
C2×#915592
C2×D5×#2172
C5×#52472
#117495182
#117495062
#117495002
#117494892
#117494882
Dic5×#2172
#106055813
D4×#2175