Finite Group Databasebeta

← #14322485

Subgroups — #14322485

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic10C211yesmaximal, characteristic
2C2×#91400C211yesmaximal, characteristic
3C2×#91398C211yesmaximal, characteristic
4#11750747C211yesmaximal, characteristic, complemented
5C5×#4664C211yesmaximal, characteristic
6C3×#64935C211yesmaximal, characteristic, complemented
7#11748935C211yesmaximal, characteristic, complemented
8#11748933C211yesmaximal, characteristic, complemented
9#11748880C211yesmaximal, characteristic
10#11748880C211yesmaximal, characteristic
11#11748777C211yesmaximal, characteristic
12#11748694C211yesmaximal, characteristic, complemented
13#11748672C211yesmaximal, characteristic, complemented
14#11748632C211yesmaximal, characteristic, complemented
15#11748628C211yesmaximal, characteristic, complemented
16#10605784—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×D3×Dic10—24no—
25C2×D3×Dic10—24no—
26C2×D3×Dic10C418yescomplemented
27C2×#6712C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39#91400—24no—
40#91398—24no—
41C3×C5×#95C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#76610—51nomaximal, Hall
58C23×Dic10—31no—
59C2×#4023—31no—
60C2×#4023—31no—
61C5×#381—31no—
62#65500—31no—
63#65232—31no—
64#65232—31no—
65#64935—31no—
66#64935—31no—
67#64935—31no—
68#64935—31no—
69#64935—31no—
70#64935—31no—
71#64935—31no—
72#64935D311yescharacteristic, complemented
73C23×C5×D3C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×Dic30—22no—
82C2×Dic30—22no—
83C2×Dic30C2×C414yes—
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3—22no—
89C2×C4×C5×D3C2×C414yes—
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×Dic10—22no—
95C2×C3×Dic10—22no—
96C2×C3×Dic10C2×C414yes—
97C2×#1204—22no—
98C2×#1204—22no—
99C2×#1204—22no—
100C2×#1204—22no—
101C2×#1204C2×C414yes—
102C2×#1204C2×C414yes—
103C2×D3×Dic5—22no—
104C2×D3×Dic5—22no—
105C2×D3×Dic5C2×C414yes—
106C2×D3×Dic5C2×C414yes—
107C2×D3×Dic5D414yes—
108C2×D3×Dic5D414yes—
109D3×Dic10—232no—
110#6712—22no—
111C4×Dic15—22no—
112C5×(C2×D3)⋊C4—22no—
113C5×(C2×D3)⋊C4—22no—
114C3×#683—22no—
115C3×C4×Dic5—22no—
116#6669—22no—
117#6668—22no—
118(C2×D3)⋊Dic5—22no—
119(C2×D3)⋊Dic5—22no—
120Dic3×Dic5—22no—
121Dic3×Dic5—22no—
122C22×D3×Q8—51no—
123C2×#892—51no—
124C2×#872—51no—
125C3×#391—51no—
126#5229—51no—
127#4973—51no—
128#4929—51no—
129#4664—51no—
130#4664—51no—
131#4664—51no—
132#4664D511yescharacteristic
133#4646—51no—
134#4646—51no—
135#4646—51no—
136#4646—51no—
137C23×C4×C5—31no—
138C23×Dic5—31no—
139C23×Dic5—31no—
140C22×Dic10—31no—
141C22×Dic10—31no—
142C22×Dic10—31no—
143C22×Dic10—38no—
144C22×Dic10—64no—
145C22×Dic10—64no—
146C22×Dic10C2×D311yescharacteristic
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C2×#683—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683C2×D311yescharacteristic
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5C2×D311yescharacteristic
159#4023—64no—
160#4023—64no—
161C5×#95—31no—
162C5×#95—31no—
163C5×#95—31no—
164C5×#95C2×D311yescharacteristic
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#3963C2×D311yescharacteristic
175#3963C2×D311yescharacteristic
176#3963C2×D311yescharacteristic
177#2310—151noSylow
178C23×C3×C5C2411yescharacteristic
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3—21no—
182C22×C5×D3—21no—
183C22×C5×D3C22×C412yes—
184C22×C5×D3C2×D412yes—
185C22×C5×D3C2×D412yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15C22×C412yes—
204C2×Dic15C22×C412yes—
205C2×Dic15C2×D412yes—
206C2×Dic15C2×D412yes—
207Dic30—28no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3C22×C412yes—
217C4×C5×D3—28no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5C2×D412yes—
230C3×Dic10—28no—
231#1204—28no—
232#1204—28no—
233D3×Dic5—28no—
234D3×Dic5C22⋊C4116yes—
235C22×C3×Q8—51no—
236C2×D3×Q8—58no—
237C2×D3×Q8—104no—
238C2×D3×Q8—104no—
239C22×C4×D3—51no—
240C22×C4×D3—51no—
241C22×C4×D3C2×D511yescharacteristic
242C22×Dic6—51no—
243C22×Dic6—51no—
244C22×Dic6—51no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C42—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×(C2×D3)⋊C4C2×D511yescharacteristic
251C2×C4⋊Dic3—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257#892—104no—
258#872—104no—
259C3×#95—51no—
260C3×#95—51no—
261C3×#95—51no—
262C3×#95C2×D511yescharacteristic
263C3⋊#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95C2×D511yescharacteristic
273C3⋊#95C2×D511yescharacteristic
274C3⋊#95C2×D511yescharacteristic
275C24×C5—31no—
276C22×C4×C5—31no—
277C22×C4×C5—34no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5—62no—
281C22×C4×C5—62no—
282C22×C4×C5C22×D311yescharacteristic
283C22×C4×C5C22×D311yescharacteristic
284C22×C4×C5C22×D311yescharacteristic
285C22×Dic5—31no—
286C22×Dic5—34no—
287C22×Dic5—34no—
288C22×Dic5—34no—
289C22×Dic5—31no—
290C22×Dic5—34no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—62no—
294C22×Dic5—62no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C22×Dic5C22×D311yescharacteristic
299C2×Dic10—22no—
300C2×Dic10—22no—
301C2×Dic10—34no—
302C2×Dic10—34no—
303C2×Dic10—34no—
304C2×Dic10—632no—
305C2×Dic10—62no—
306C2×Dic10—62no—
307C2×Dic10—62no—
308C2×Dic10—62no—
309C2×Dic10—62no—
310C2×Dic10—62no—
311C2×Dic10C4×D314yes—
312C5×C22⋊C4—62no—
313C5×C22⋊C4—62no—
314C22⋊Dic5—62no—
315C22⋊Dic5—62no—
316#683—22no—
317#683—62no—
318#683—62no—
319#683—62no—
320C4×Dic5—22no—
321C4×Dic5—62no—
322C4×Dic5—62no—
323C4×Dic5—62no—
324C23×Q8—151no—
325C2×#117—151no—
326C2×#117—151no—
327#391—51no—
328#391—151no—
329#391—151no—
330#391—151no—
331#391—151no—
332#391—151no—
333#391—151no—
334#391—151no—
335#381—31no—
336#381—151no—
337#381—151no—
338#381—151no—
339C22×C3×C5C23×C411yescharacteristic
340C22×C3×C5C22×D411yescharacteristic
341C22×C3×C5C22×D411yescharacteristic
342C22×C3×C52−1+411yescharacteristic
343C22×C3×C52−1+411yescharacteristic
344C22×C3×C52−1+411yescharacteristic
345C22×C3×C52−1+411yescharacteristic
346C2×C5×D3—22no—
347C2×C5×D3—22no—
348C2×C5×D3—22no—
349C2×C5×D3—22no—
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3C2×C22⋊C414yes—
353C3×C4×C5—22no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356Dic15—22no—
357Dic15—41no—
358Dic15—41no—
359Dic15C2×C22⋊C414yes—
360C3×Dic5—22no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5C2×C22⋊C414yes—
364C5×Dic3—22no—
365C5×Dic3—41no—
366C5×Dic3—41no—
367C23×D3C22×D511yescharacteristic
368C2×C3×Q8—54no—
369C2×C3×Q8—102no—
370C2×C3×Q8—102no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C22×Dic3—51no—
379C22×Dic3—51no—
380C22×Dic3—51no—
381C22×Dic3—51no—
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C22×Dic3C22×D511yescharacteristic
385D3×Q8—1032no—
386C2×C4×D3—22no—
387C2×C4×D3—22no—
388C2×C4×D3—54no—
389C2×C4×D3—54no—
390C2×C4×D3—54no—
391C2×C4×D3—54no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×C4×D3C4×D514yes—
395C2×Dic6—54no—
396C2×Dic6—54no—
397C2×Dic6—54no—
398C2×Dic6—102no—
399C2×Dic6—102no—
400C2×Dic6—102no—
401C2×Dic6—102no—
402C2×Dic6—102no—
403C2×Dic6—102no—
404C3×C4⋊C4—102no—
405C3×C42—102no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—102no—
409(C2×D3)⋊C4—102no—
410C4⋊Dic3—102no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413C4×Dic3—102no—
414C4×Dic3—102no—
415C4×Dic3—102no—
416C23×C5—32no—
417C23×C5—32no—
418C23×C5—32no—
419C23×C5—61no—
420C23×C5—61no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5C23×D311yescharacteristic
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—32no—
433C2×C4×C5—68no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5C2×C4×D312yes—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—21no—
451C2×Dic5—32no—
452C2×Dic5—32no—
453C2×Dic5—32no—
454C2×Dic5—316no—
455C2×Dic5—32no—
456C2×Dic5—68no—
457C2×Dic5—61no—
458C2×Dic5—61no—
459C2×Dic5—61no—
460C2×Dic5—61no—
461C2×Dic5—61no—
462C2×Dic5—61no—
463C2×Dic5—61no—
464C2×Dic5—61no—
465C2×Dic5C2×C4×D312yes—
466C2×Dic5C2×C4×D312yes—
467C2×Dic5D3×D412yes—
468C2×Dic5D3×D412yes—
469Dic10—28no—
470Dic10—68no—
471Dic10—68no—
472Dic10—68no—
473C22×Q8—51no—
474C22×Q8—151no—
475C22×Q8—151no—
476C22×Q8—158no—
477C22×Q8—151no—
478C22×Q8—304no—
479C22×Q8—304no—
480C23×C4—31no—
481C23×C4—151no—
482C23×C4—151no—
483#117—304no—
484#117—304no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—151no—
492C2×C22⋊C4—151no—
493C2×C42—51no—
494C2×C42—151no—
495C2×C42—151no—
496C2×C42—151no—
497#95—31no—
498#95—31no—
499#95—31no—
500#95—51no—
501#95—51no—
502#95—51no—
503#95—151no—
504#95—151no—
505#95—151no—
506#95—151no—
507#95—151no—
508#95—151no—
509#95—151no—
510#95—151no—
511#95—151no—
512#95D3×D511yescharacteristic
513C2×C3×C5C22×C22⋊C411yescharacteristic
514C2×C3×C5#51911yescharacteristic
515C2×C3×C5#51911yescharacteristic
516C2×C3×C5#53611yescharacteristic
517C2×C3×C5#53611yescharacteristic
518C2×C3×C5#53611yescharacteristic
519C2×C3×C5#53611yescharacteristic
520C5×D3—24no—
521C23×C3C23×D511yescharacteristic
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3C2×C4×D512yes—
527C22×D3D4×D512yes—
528C22×D3D4×D512yes—
529C3×Q8—108no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—52no—
539C2×C3×C4—52no—
540C2×C3×C4—52no—
541C2×C3×C4—52no—
542C2×C3×C4—101no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4C2×C4×D512yes—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—52no—
560C2×Dic3—52no—
561C2×Dic3—52no—
562C2×Dic3—52no—
563C2×Dic3—101no—
564C2×Dic3—101no—
565C2×Dic3—101no—
566C2×Dic3—101no—
567C2×Dic3—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3C2×C4×D512yes—
572C4×D3—28no—
573C4×D3—516no—
574C4×D3—108no—
575Dic6—108no—
576Dic6—108no—
577Dic6—108no—
578C22×C5—34no—
579C22×C5—62no—
580C22×C5—62no—
581C22×C5—62no—
582C22×C5—62no—
583C22×C5—62no—
584C22×C5—62no—
585C22×C5C22×C4×D311yescharacteristic
586C22×C5C2×D3×D411yescharacteristic
587C22×C5C2×D3×D411yescharacteristic
588C22×C5#100711yescharacteristic
589C22×C5#100711yescharacteristic
590C22×C5#101011yescharacteristic
591C22×C5#101011yescharacteristic
592C4×C5—22no—
593C4×C5—41no—
594C4×C5—41no—
595C4×C5—62no—
596C4×C5—121no—
597C4×C5—121no—
598Dic5—22no—
599Dic5—34no—
600Dic5—41no—
601Dic5—41no—
602Dic5—62no—
603Dic5—121no—
604Dic5—121no—
605Dic5D3×C22⋊C414yes—
606C24—31no—
607C2×Q8—54no—
608C2×Q8—102no—
609C2×Q8—102no—
610C2×Q8—154no—
611C2×Q8—154no—
612C2×Q8—154no—
613C2×Q8—302no—
614C2×Q8—302no—
615C2×Q8—302no—
616C2×Q8—302no—
617C2×Q8—302no—
618C2×Q8—302no—
619C2×Q8—3032no—
620C22×C4—31no—
621C22×C4—34no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—154no—
631C22×C4—154no—
632C22×C4—154no—
633C22×C4—154no—
634C22×C4—151no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4C2×D3×D511yescharacteristic
641C22×C4C2×D3×D511yescharacteristic
642C22×C4C2×D3×D511yescharacteristic
643C4⋊C4—102no—
644C4⋊C4—302no—
645C4⋊C4—302no—
646C4⋊C4—302no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—302no—
650C22⋊C4—302no—
651C42—102no—
652C42—302no—
653C42—302no—
654C42—302no—
655C3×C5#231011yescharacteristic, complemented, Hall
656C22×C3C22×C4×D511yescharacteristic
657C22×C3C2×D4×D511yescharacteristic
658C22×C3C2×D4×D511yescharacteristic
659C22×C3#415011yescharacteristic
660C22×C3#415011yescharacteristic
661C22×C3#415011yescharacteristic
662C22×C3#415011yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—22no—
669C2×D3D5×C22⋊C414yes—
670C3×C4—22no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—54no—
674C3×C4—102no—
675C3×C4—201no—
676C3×C4—201no—
677Dic3—22no—
678Dic3—41no—
679Dic3—41no—
680Dic3—54no—
681Dic3—102no—
682Dic3—201no—
683Dic3—201no—
684C2×C5—64no—
685C2×C5C2×D3×C22⋊C411yescharacteristic
686C2×C5#557211yescharacteristic
687C2×C5#557211yescharacteristic
688C2×C5#562811yescharacteristic
689C2×C5#562811yescharacteristic
690C2×C5#567511yescharacteristic
691C2×C5#572411yescharacteristic
692C23—32no—
693C23—32no—
694C23—32no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23C22×D3×D511yescharacteristic
700Q8—108no—
701Q8—308no—
702Q8—308no—
703Q8—308no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—52no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—52no—
717C2×C4—68no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—1516no—
735C2×C4—152no—
736C2×C4—152no—
737C2×C4—152no—
738C2×C4—152no—
739C2×C4—308no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—301no—
746C2×C4—301no—
747C2×C4—301no—
748C2×C4C4×D3×D512yes—
749C2×C3C2×D5×C22⋊C411yescharacteristic
750C2×C3#6585011yescharacteristic
751C2×C3#6585011yescharacteristic
752C2×C3#6598211yescharacteristic
753C2×C3#6598211yescharacteristic
754C2×C3#6598211yescharacteristic
755C2×C3#6598211yescharacteristic
756D3—24no—
757C5#7661011yescharacteristic, complemented, Sylow
758C22—34no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22#9200111yescharacteristic
766C22#9200411yescharacteristic
767C22C2×C4×D3×D511yescharacteristic
768C22#9202011yescharacteristic
769C22D3×D4×D511yescharacteristic
770C22D3×D4×D511yescharacteristic
771C22#9203011yescharacteristic
772C4—22no—
773C4—41no—
774C4—41no—
775C4—54no—
776C4—62no—
777C4—102no—
778C4—121no—
779C4—121no—
780C4—154no—
781C4—201no—
782C4—201no—
783C4—302no—
784C4—601no—
785C4—601no—
786C3#1060578411yescharacteristic, complemented, Sylow
787C2—64no—
788C2#1175252311yescharacteristic
789C2#1175284411yescharacteristic
790C2#1175284711yescharacteristic
791C2D3×D5×C22⋊C411yescharacteristic
792C2#1175340511yescharacteristic
793C2#1175342011yescharacteristic
794C2#1175342211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5#2310
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #11750747C2semidirect
6. C3×#64935C2semidirect
7. #11748935C2semidirect
8. #11748933C2semidirect
12. #11748694C2semidirect
13. #11748672C2semidirect
14. #11748632C2semidirect
15. #11748628C2semidirect
26. C2×D3×Dic10C4semidirect
72. #64935D3semidirect
655. C3×C5#2310semidirect
757. C5#76610semidirect
786. C3#10605784semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C2×#914002
C2×#913982
#117507472
C5×#46642
C3×#649352
#117489352
#117489332
#117488802
#117487772
#117486942
#117486722
#117486322
#117486282
#106057843
#766105