Finite Group Databasebeta

← #14323726

Subgroups — #14323726

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×#91431C211yesmaximal, characteristic
3C2×#91394C211yesmaximal, characteristic
4C5×#4976C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic
6#11748885C211yesmaximal, characteristic
7C4×#6669C211yesmaximal, characteristic, complemented
8#11748810C211yesmaximal, characteristic, complemented
9#11748801C211yesmaximal, characteristic, complemented
10#11748791C211yesmaximal, characteristic
11#11748709C211yesmaximal, characteristic
12#11748706C211yesmaximal, characteristic
13#11748694C211yesmaximal, characteristic, complemented
14#11748633C211yesmaximal, characteristic, complemented
15#11748605C211yesmaximal, characteristic, complemented
16#10607702—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25#91776—24no—
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91431C418yescomplemented
44#91394—24no—
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#75459—51nomaximal, Hall
56C2×#4042—31no—
57C2×#4038—31no—
58C2×#4033—31no—
59C5×#389—31no—
60#65279—31no—
61#65279D311yescharacteristic
62#65270—31no—
63#65261—31no—
64#65261—31no—
65#65229—31no—
66C4×#683—31no—
67#64958—31no—
68#64956—31no—
69#64944—31no—
70#64935—31no—
71C23×C3×D5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×Dic30—22no—
80C2×Dic30—22no—
81C2×Dic30C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×D5×Dic3—22no—
90C2×D5×Dic3—22no—
91C2×D5×Dic3C2×C414yes—
92C3×C5×C4⋊C4—22no—
93#6712—22no—
94#6712—22no—
95C4×Dic15—22no—
96C4×Dic15—22no—
97C4×Dic15D414yes—
98C5×Dic3⋊C4—22no—
99C5×Dic3⋊C4—41no—
100C5×Dic3⋊C4C2×C414yes—
101C4×C5×Dic3—41no—
102C3×#685—22no—
103C3×#685—41no—
104C3×#685C2×C414yes—
105C3×C4×Dic5—41no—
106Dic3⋊Dic5—22no—
107#6669—22no—
108#6669C2×C414yes—
109#6668—41no—
110#6668C2×C414yes—
111#6665—22no—
112#6665—41no—
113#6665C2×C414yes—
114Dic3×Dic5—22no—
115C2×#887—51no—
116C2×#878—51no—
117C2×#877—51no—
118C3×#388—51no—
119#4976D511yescharacteristic, complemented
120#4951—51no—
121#4945—51no—
122#4945—51no—
123#4942—51no—
124C4×Dic3⋊C4—51no—
125#4928—51no—
126#4654—51no—
127#4652—51no—
128#4647—51no—
129#4646—51no—
130C22×C4×D5—31no—
131C22×Dic10—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4C2×D311yescharacteristic
136C2×C42×C5—31no—
137C2×#685—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685C2×D311yescharacteristic
141C2×#685C2×D311yescharacteristic
142C2×#685C2×D311yescharacteristic
143C2×C4⋊Dic5—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5C2×D311yescharacteristic
155#4042—38no—
156#4038—64no—
157#4033—64no—
158C5×#95—31no—
159C5×#95—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963C2×D311yescharacteristic
167#3963C2×D311yescharacteristic
168#2323—151noSylow
169C23×C3×C5C2411yescharacteristic
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—21no—
173C22×C3×D5—21no—
174C22×C3×D5—21no—
175C22×C3×D5—21no—
176C22×C3×D5C22×C412yes—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5C22×C412yes—
185C2×C3×C4×C5C2×D412yes—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15C22×C412yes—
194C2×Dic15C22×C412yes—
195C2×Dic15C2×D412yes—
196C2×Dic15C2×D412yes—
197C2×Dic15#4112yes—
198Dic30—28no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C22×C412yes—
220D5×Dic3—28no—
221C23×Dic3—51no—
222C22×Dic6—51no—
223C2×C3×C4⋊C4C2×D511yescharacteristic
224C2×C3×C22⋊C4—51no—
225C2×C3×C22⋊C4—51no—
226C2×C3×C22⋊C4—51no—
227C2×C3×C42—51no—
228C2×#217—51no—
229C2×#217—51no—
230C2×#217—51no—
231C2×C4⋊Dic3—51no—
232C2×C4⋊Dic3—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4—51no—
237C2×Dic3⋊C4—51no—
238C2×Dic3⋊C4C2×D511yescharacteristic
239C2×Dic3⋊C4C2×D511yescharacteristic
240C2×Dic3⋊C4C2×D511yescharacteristic
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3C2×D511yescharacteristic
246#887—104no—
247#878—58no—
248#877—104no—
249C3×#95—51no—
250C3×#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95C2×D511yescharacteristic
258C3⋊#95C2×D511yescharacteristic
259C23×D5C22×D311yescharacteristic
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×C4×C5C22×D311yescharacteristic
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5C22×D311yescharacteristic
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C2×C4×D5—34no—
275C2×C4×D5—62no—
276C2×C4×D5—62no—
277C2×Dic10—34no—
278C2×Dic10—62no—
279C2×Dic10—62no—
280C5×C4⋊C4—22no—
281C5×C4⋊C4—34no—
282C5×C4⋊C4—62no—
283C5×C4⋊C4—121no—
284C42×C5—121no—
285#685—22no—
286#685—34no—
287#685—41no—
288#685—62no—
289#685—121no—
290#685C4×D314yes—
291C4⋊Dic5—62no—
292#683—34no—
293#683—34no—
294#683—62no—
295#683—62no—
296#683—62no—
297#683—121no—
298C4×Dic5—34no—
299C4×Dic5—41no—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5—62no—
303C2×C22⋊Q8—151no—
304C2×C4×Q8—151no—
305C2×#117—151no—
306#391—151no—
307#389—31no—
308#389—151no—
309#389—151no—
310#388—51no—
311#388—151no—
312#388—151no—
313#388—151no—
314#387—151no—
315#387—151no—
316#380—151no—
317C4×C4⋊C4—151no—
318C22×C3×C5C23×C411yescharacteristic
319C22×C3×C5C22×D411yescharacteristic
320C22×C3×C5C2×#4111yescharacteristic
321C22×C3×C5H(5,𝔽2)11yescharacteristic
322C22×C3×C52−1+411yescharacteristic
323C22×C3×C52−1+411yescharacteristic
324C22×C3×C52−1+411yescharacteristic
325C2×C3×D5—22no—
326C2×C3×D5—22no—
327C2×C3×D5—22no—
328C2×C3×D5—41no—
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—41no—
335Dic15—22no—
336Dic15—22no—
337Dic15—41no—
338Dic15C4×D414yes—
339C3×Dic5—22no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C5×Dic3—22no—
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C24×C3—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C22×Dic3—51no—
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—54no—
357C22×Dic3—51no—
358C22×Dic3—102no—
359C22×Dic3—102no—
360C22×Dic3C22×D511yescharacteristic
361C22×Dic3C22×D511yescharacteristic
362C22×Dic3C22×D511yescharacteristic
363C22×Dic3C22×D511yescharacteristic
364C2×Dic6—54no—
365C2×Dic6—102no—
366C2×Dic6—102no—
367C3×C4⋊C4—22no—
368C3×C22⋊C4—54no—
369C3×C22⋊C4—102no—
370C3×C22⋊C4—201no—
371C3×C42—201no—
372#217—54no—
373#217—102no—
374#217—201no—
375C4⋊Dic3—54no—
376C4⋊Dic3—201no—
377Dic3⋊C4—22no—
378Dic3⋊C4—41no—
379Dic3⋊C4—54no—
380Dic3⋊C4—102no—
381Dic3⋊C4—102no—
382Dic3⋊C4—102no—
383Dic3⋊C4—102no—
384Dic3⋊C4C4×D514yes—
385C4×Dic3—41no—
386C4×Dic3—54no—
387C4×Dic3—102no—
388C4×Dic3—102no—
389C4×Dic3—102no—
390C23×C5C23×D311yescharacteristic
391C22×D5—21no—
392C22×D5—21no—
393C22×D5—21no—
394C22×D5—21no—
395C22×D5—21no—
396C22×D5—21no—
397C22×D5C2×C4×D312yes—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—32no—
406C2×C4×C5—32no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—61no—
417C2×C4×C5C2×C4×D312yes—
418C2×C4×C5D3×D412yes—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—32no—
428C2×Dic5—32no—
429C2×Dic5—32no—
430C2×Dic5—32no—
431C2×Dic5—32no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C2×Dic5C2×C4×D312yes—
440C4×D5—68no—
441Dic10—68no—
442C22×Q8—151no—
443C23×C4—151no—
444C22⋊Q8—158no—
445C4×Q8—304no—
446#117—304no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—151no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C4⋊C4D3×D511yescharacteristic
458C2×C22⋊C4—51no—
459C2×C22⋊C4—51no—
460C2×C22⋊C4—51no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—151no—
464C2×C42—31no—
465C2×C42—51no—
466C2×C42—151no—
467C2×C42—151no—
468C2×C42—151no—
469C2×C42—151no—
470#95—31no—
471#95—31no—
472#95—51no—
473#95—51no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95—151no—
479#95—151no—
480C2×C3×C5C2×C4×D411yescharacteristic
481C2×C3×C5#51911yescharacteristic
482C2×C3×C5#52011yescharacteristic
483C2×C3×C5#53611yescharacteristic
484C2×C3×C5#53711yescharacteristic
485C2×C3×C5#54111yescharacteristic
486C2×C3×C5#54211yescharacteristic
487C3×D5—42no—
488C23×C3—52no—
489C23×C3—101no—
490C23×C3—101no—
491C23×C3—101no—
492C23×C3—101no—
493C23×C3—101no—
494C23×C3—101no—
495C23×C3C23×D511yescharacteristic
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—52no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4C2×C4×D512yes—
513C2×C3×C4D4×D512yes—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—52no—
525C2×Dic3—52no—
526C2×Dic3—52no—
527C2×Dic3—52no—
528C2×Dic3—52no—
529C2×Dic3—108no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3C2×C4×D512yes—
538C2×Dic3C2×C4×D512yes—
539Dic6—108no—
540C22×C5C22×C4×D311yescharacteristic
541C22×C5C2×D3×D411yescharacteristic
542C22×C5#100411yescharacteristic
543C22×C5D3×#4111yescharacteristic
544C22×C5#101011yescharacteristic
545C22×C5#101011yescharacteristic
546C22×C5#101011yescharacteristic
547C2×D5—22no—
548C2×D5—22no—
549C2×D5—22no—
550C2×D5—41no—
551C2×D5—41no—
552C2×D5—41no—
553C2×D5—41no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—41no—
557C4×C5—62no—
558C4×C5—62no—
559C4×C5—121no—
560C4×C5—121no—
561Dic5—22no—
562Dic5—34no—
563Dic5—41no—
564Dic5—41no—
565Dic5—62no—
566Dic5—62no—
567Dic5—121no—
568C24—51no—
569C2×Q8—154no—
570C2×Q8—302no—
571C2×Q8—302no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—154no—
580C22×C4—151no—
581C22×C4—151no—
582C22×C4—151no—
583C22×C4—151no—
584C22×C4—302no—
585C22×C4—302no—
586C22×C4C2×D3×D511yescharacteristic
587C22×C4C2×D3×D511yescharacteristic
588C22×C4C2×D3×D511yescharacteristic
589C4⋊C4—22no—
590C4⋊C4—34no—
591C4⋊C4—62no—
592C4⋊C4—121no—
593C4⋊C4—154no—
594C4⋊C4—154no—
595C4⋊C4—302no—
596C4⋊C4—302no—
597C4⋊C4—302no—
598C4⋊C4—302no—
599C4⋊C4—601no—
600C22⋊C4—54no—
601C22⋊C4—102no—
602C22⋊C4—154no—
603C22⋊C4—201no—
604C22⋊C4—302no—
605C22⋊C4—601no—
606C42—121no—
607C42—154no—
608C42—201no—
609C42—302no—
610C42—302no—
611C42—302no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3—102no—
614C22×C3—102no—
615C22×C3—102no—
616C22×C3—201no—
617C22×C3—201no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3C22×C4×D511yescharacteristic
621C22×C3C2×D4×D511yescharacteristic
622C22×C3#414411yescharacteristic
623C22×C3#414711yescharacteristic
624C22×C3#414711yescharacteristic
625C22×C3D5×#4111yescharacteristic
626C22×C3#415011yescharacteristic
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—41no—
630C3×C4—102no—
631C3×C4—201no—
632C3×C4—201no—
633Dic3—22no—
634Dic3—22no—
635Dic3—41no—
636Dic3—41no—
637Dic3—54no—
638Dic3—102no—
639Dic3—102no—
640Dic3—201no—
641C2×C5#551611yescharacteristic
642C2×C5C4×D3×D411yescharacteristic
643C2×C5#554611yescharacteristic
644C2×C5#559711yescharacteristic
645C2×C5#566211yescharacteristic
646C2×C5#567511yescharacteristic
647C2×C5#570111yescharacteristic
648D5—42no—
649C23—52no—
650C23—101no—
651C23—101no—
652C23—101no—
653C23—101no—
654C23—101no—
655C23—101no—
656C23C22×D3×D511yescharacteristic
657Q8—308no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—52no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—152no—
687C2×C4—152no—
688C2×C4—152no—
689C2×C4—152no—
690C2×C4—152no—
691C2×C4—308no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4C4×D3×D512yes—
700C2×C4#679012yes—
701C2×C3—202no—
702C2×C3#6583811yescharacteristic
703C2×C3C4×D4×D511yescharacteristic
704C2×C3#6590611yescharacteristic
705C2×C3#6593111yescharacteristic
706C2×C3#6597411yescharacteristic
707C2×C3#6603011yescharacteristic
708C2×C3#6605811yescharacteristic
709C5#7545911yescharacteristic, complemented, Sylow
710C22—102no—
711C22—102no—
712C22—102no—
713C22—201no—
714C22—201no—
715C22—201no—
716C22—201no—
717C22C2×C4×D3×D511yescharacteristic
718C22#9201611yescharacteristic
719C22#9202011yescharacteristic
720C22#9202511yescharacteristic
721C22#9202811yescharacteristic
722C22#9202811yescharacteristic
723C22C2×#679011yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—62no—
728C4—62no—
729C4—102no—
730C4—121no—
731C4—121no—
732C4—154no—
733C4—201no—
734C4—201no—
735C4—302no—
736C4—302no—
737C4—601no—
738C3#1060770211yescharacteristic, complemented, Sylow
739C2—202no—
740C2#1175339711yescharacteristic
741C2#1175339911yescharacteristic
742C2#1175360511yescharacteristic
743C2#1175378411yescharacteristic
744C2C4×#679011yescharacteristic
745C2#1175482111yescharacteristic
746C2#1175516811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2323
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
1. C2×#91776C2semidirect
4. C5×#4976C2semidirect
7. C4×#6669C2semidirect
8. #11748810C2semidirect
9. #11748801C2semidirect
13. #11748694C2semidirect
14. #11748633C2semidirect
15. #11748605C2semidirect
43. #91431C4semidirect
119. #4976D5semidirect
612. C3×C5#2323semidirect
709. C5#75459semidirect
738. C3#10607702semidirect

Maximal subgroups

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

subgroupindex
C2×#917762
C2×#914312
C2×#913942
C5×#49762
C3×#652792
#117488852
C4×#66692
#117488102
#117488012
#117487912
#117487092
#117487062
#117486942
#117486332
#117486052
#106077023
#754595