Finite Group Databasebeta

← #14323701

Subgroups — #14323701

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×#91767C211yesmaximal, characteristic
2C2×#91766C211yesmaximal, characteristic
3C2×C4×Dic30C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic
5#11751077C211yesmaximal, characteristic, complemented
6#11751073C211yesmaximal, characteristic, complemented
7#11751052C211yesmaximal, characteristic
8#11751045C211yesmaximal, characteristic
9#11751045C211yesmaximal, characteristic
10#11751043C211yesmaximal, characteristic
11#11751034C211yesmaximal, characteristic, complemented
12#11750754C211yesmaximal, characteristic, complemented
13#11750750C211yesmaximal, characteristic, complemented
14#11750748C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10607191—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91767C418yescomplemented
43#91766—24no—
44C4×Dic30—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#75460—51nomaximal, Hall
56C2×#4024—31no—
57C2×#4023—31no—
58C2×C4×Dic10—31no—
59C5×#388D311yescharacteristic
60#65262—31no—
61#65261—31no—
62#65240—31no—
63#65233—31no—
64#65233—31no—
65#65231—31no—
66#65222—31no—
67#64942—31no—
68#64938—31no—
69#64936—31no—
70#64935—31no—
71C24×C3×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—22no—
79C22×Dic15—22no—
80C22×Dic15C2×C414yes—
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C2×Dic30—22no—
90C2×Dic30—22no—
91C2×Dic30C2×C414yes—
92C3×C5×C4⋊C4—41no—
93C3×C5×C22⋊C4—22no—
94C3×C5×C22⋊C4—41no—
95C3×C5×C22⋊C4C2×C414yes—
96C3×C42×C5—22no—
97#6719—22no—
98#6719—41no—
99#6719C2×C414yes—
100C4⋊Dic15—22no—
101C4⋊Dic15C2×C414yes—
102#6712—22no—
103#6712—22no—
104#6712—22no—
105#6712—22no—
106#6712—22no—
107#6712—41no—
108#6712C2×C414yes—
109#6712C2×C414yes—
110C4×Dic15—22no—
111C4×Dic15—22no—
112C4×Dic15—41no—
113C4×Dic15—41no—
114C4×Dic15D414yes—
115C2×#878—51no—
116C2×#877—51no—
117C2×C4×Dic6—51no—
118C3×#388D511yescharacteristic
119#4976—51no—
120#4972—51no—
121#4951—51no—
122#4944—51no—
123#4944—51no—
124#4942—51no—
125#4933—51no—
126#4653—51no—
127#4649—51no—
128#4647—51no—
129#4646—51no—
130C23×Dic5—31no—
131C22×Dic10—31no—
132C2×C5×C4⋊C4C2×D311yescharacteristic
133C2×C5×C22⋊C4C2×D311yescharacteristic
134C2×C5×C22⋊C4C2×D311yescharacteristic
135C2×C5×C22⋊C4C2×D311yescharacteristic
136C2×C42×C5C2×D311yescharacteristic
137C2×C22⋊Dic5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5—31no—
142C2×#683—31no—
143C2×#683—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×Dic5—31no—
155#4024—38no—
156#4023—64no—
157C4×Dic10—64no—
158C5×#95C2×D311yescharacteristic
159C5×#95C2×D311yescharacteristic
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#2323—151noSylow
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5C22×C412yes—
176C23×C3×C5C2411yescharacteristic
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×C5—21no—
185C2×C3×C4×C5—21no—
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×C5C22×C412yes—
193C2×C3×C4×C5C22×C412yes—
194C2×C3×C4×C5C2×D412yes—
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×Dic15—28no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15C22×C412yes—
214C2×Dic15C22×C412yes—
215C2×Dic15C22×C412yes—
216C2×Dic15C22×C412yes—
217C2×Dic15C2×D412yes—
218C2×Dic15C2×D412yes—
219C2×Dic15#4112yes—
220Dic30—28no—
221C23×Dic3—51no—
222C22×Dic6—51no—
223C2×C3×C4⋊C4C2×D511yescharacteristic
224C2×C3×C22⋊C4C2×D511yescharacteristic
225C2×C3×C22⋊C4C2×D511yescharacteristic
226C2×C3×C22⋊C4C2×D511yescharacteristic
227C2×C3×C42C2×D511yescharacteristic
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⋊C4—51no—
239C2×Dic3⋊C4—51no—
240C2×Dic3⋊C4—51no—
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246#878—58no—
247#877—104no—
248C4×Dic6—104no—
249C3×#95C2×D511yescharacteristic
250C3×#95C2×D511yescharacteristic
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C24×C5C22×D311yescharacteristic
260C22×C4×C5C22×D311yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C22×C4×C5C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×Dic5—31no—
267C22×Dic5—34no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—62no—
276C22×Dic5—62no—
277C2×Dic10—34no—
278C2×Dic10—62no—
279C2×Dic10—62no—
280C5×C4⋊C4—41no—
281C5×C22⋊C4—22no—
282C5×C22⋊C4—41no—
283C5×C22⋊C4C4×D314yes—
284C42×C5—22no—
285C22⋊Dic5—34no—
286C22⋊Dic5—62no—
287C22⋊Dic5—121no—
288C4⋊Dic5—34no—
289C4⋊Dic5—62no—
290#683—34no—
291#683—34no—
292#683—62no—
293#683—62no—
294#683—62no—
295#683—62no—
296#683—62no—
297#683—121no—
298C4×Dic5—34no—
299C4×Dic5—62no—
300C4×Dic5—62no—
301C4×Dic5—121no—
302C4×Dic5—121no—
303C2×C22⋊Q8—151no—
304C2×C4×Q8—151no—
305C2×#117—151no—
306#391—151no—
307#389—151no—
308#389—151no—
309#389—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388D1511yescharacteristic
314#387—151no—
315#387—151no—
316#380—151no—
317C4×C4⋊C4—151no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5—41no—
325C22×C3×C5C23×C411yescharacteristic
326C22×C3×C5C22×D411yescharacteristic
327C22×C3×C5C2×#4111yescharacteristic
328C22×C3×C5H(5,𝔽2)11yescharacteristic
329C22×C3×C52−1+411yescharacteristic
330C22×C3×C52−1+411yescharacteristic
331C22×C3×C52−1+411yescharacteristic
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—41no—
336C3×C4×C5—41no—
337C3×C4×C5—41no—
338Dic15—22no—
339Dic15—22no—
340Dic15—22no—
341Dic15—22no—
342Dic15—41no—
343Dic15—41no—
344Dic15—41no—
345Dic15C4×D414yes—
346C24×C3C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C22×Dic3—51no—
354C22×Dic3—54no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3—51no—
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3—102no—
363C22×Dic3—102no—
364C2×Dic6—54no—
365C2×Dic6—102no—
366C2×Dic6—102no—
367C3×C4⋊C4—41no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4C4×D514yes—
371C3×C42—22no—
372#217—54no—
373#217—102no—
374#217—201no—
375C4⋊Dic3—54no—
376C4⋊Dic3—102no—
377Dic3⋊C4—54no—
378Dic3⋊C4—54no—
379Dic3⋊C4—102no—
380Dic3⋊C4—102no—
381Dic3⋊C4—102no—
382Dic3⋊C4—102no—
383Dic3⋊C4—102no—
384Dic3⋊C4—201no—
385C4×Dic3—54no—
386C4×Dic3—102no—
387C4×Dic3—102no—
388C4×Dic3—201no—
389C4×Dic3—201no—
390C23×C5—21no—
391C23×C5—21no—
392C23×C5—21no—
393C23×C5—21no—
394C23×C5—21no—
395C23×C5—21no—
396C23×C5C2×C4×D312yes—
397C23×C5C23×D311yescharacteristic
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—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5C2×C4×D312yes—
414C2×C4×C5C2×C4×D312yes—
415C2×C4×C5D3×D412yes—
416C2×Dic5—32no—
417C2×Dic5—32no—
418C2×Dic5—32no—
419C2×Dic5—32no—
420C2×Dic5—32no—
421C2×Dic5—32no—
422C2×Dic5—32no—
423C2×Dic5—68no—
424C2×Dic5—61no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441Dic10—68no—
442C22×Q8—151no—
443C23×C4—151no—
444C22⋊Q8—158no—
445C4×Q8—304no—
446#117—304no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
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⋊C4C2×D1511yescharacteristic
458C2×C22⋊C4—151no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—151no—
461C2×C22⋊C4C2×D1511yescharacteristic
462C2×C22⋊C4C2×D1511yescharacteristic
463C2×C22⋊C4C2×D1511yescharacteristic
464C2×C42—151no—
465C2×C42—151no—
466C2×C42—151no—
467C2×C42—151no—
468C2×C42—151no—
469C2×C42C2×D1511yescharacteristic
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95C2×D1511yescharacteristic
479#95C2×D1511yescharacteristic
480C2×C3×C5—42no—
481C2×C3×C5C2×C4×D411yescharacteristic
482C2×C3×C5#51911yescharacteristic
483C2×C3×C5#52011yescharacteristic
484C2×C3×C5#53611yescharacteristic
485C2×C3×C5#53711yescharacteristic
486C2×C3×C5#54111yescharacteristic
487C2×C3×C5#54211yescharacteristic
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3C2×C4×D512yes—
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—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4C2×C4×D512yes—
512C2×C3×C4C2×C4×D512yes—
513C2×C3×C4D4×D512yes—
514C2×Dic3—52no—
515C2×Dic3—52no—
516C2×Dic3—52no—
517C2×Dic3—52no—
518C2×Dic3—52no—
519C2×Dic3—52no—
520C2×Dic3—52no—
521C2×Dic3—108no—
522C2×Dic3—101no—
523C2×Dic3—101no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—101no—
538C2×Dic3—101no—
539Dic6—108no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5C22×C4×D311yescharacteristic
548C22×C5C2×D3×D411yescharacteristic
549C22×C5#100411yescharacteristic
550C22×C5D3×#4111yescharacteristic
551C22×C5#101011yescharacteristic
552C22×C5#101011yescharacteristic
553C22×C5#101011yescharacteristic
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—22no—
557C4×C5—41no—
558C4×C5—41no—
559C4×C5—41no—
560Dic5—34no—
561Dic5—62no—
562Dic5—62no—
563Dic5—62no—
564Dic5—62no—
565Dic5—121no—
566Dic5—121no—
567Dic5—121no—
568C24C22×D1511yescharacteristic
569C2×Q8—154no—
570C2×Q8—302no—
571C2×Q8—302no—
572C22×C4—151no—
573C22×C4—154no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—151no—
577C22×C4—151no—
578C22×C4—151no—
579C22×C4—151no—
580C22×C4—151no—
581C22×C4—302no—
582C22×C4—302no—
583C22×C4C22×D1511yescharacteristic
584C22×C4C22×D1511yescharacteristic
585C22×C4C22×D1511yescharacteristic
586C22×C4C22×D1511yescharacteristic
587C22×C4C22×D1511yescharacteristic
588C22×C4C22×D1511yescharacteristic
589C4⋊C4—41no—
590C4⋊C4—154no—
591C4⋊C4—154no—
592C4⋊C4—154no—
593C4⋊C4—302no—
594C4⋊C4—302no—
595C4⋊C4—302no—
596C4⋊C4—302no—
597C4⋊C4—302no—
598C4⋊C4—302no—
599C4⋊C4—601no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—154no—
603C22⋊C4—302no—
604C22⋊C4—601no—
605C22⋊C4C4×D1514yes—
606C42—22no—
607C42—154no—
608C42—302no—
609C42—302no—
610C42—601no—
611C42—601no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3C22×C4×D511yescharacteristic
621C22×C3C2×D4×D511yescharacteristic
622C22×C3#414411yescharacteristic
623C22×C3D5×#4111yescharacteristic
624C22×C3#415011yescharacteristic
625C22×C3#415011yescharacteristic
626C22×C3#415011yescharacteristic
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633Dic3—54no—
634Dic3—102no—
635Dic3—102no—
636Dic3—102no—
637Dic3—102no—
638Dic3—201no—
639Dic3—201no—
640Dic3—201no—
641C2×C5—42no—
642C2×C5#551611yescharacteristic
643C2×C5C4×D3×D411yescharacteristic
644C2×C5#554611yescharacteristic
645C2×C5#560811yescharacteristic
646C2×C5#564811yescharacteristic
647C2×C5#566911yescharacteristic
648C2×C5#570111yescharacteristic
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23C2×C4×D1512yes—
656C23C23×D1511yescharacteristic
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—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—152no—
674C2×C4—152no—
675C2×C4—152no—
676C2×C4—152no—
677C2×C4—152no—
678C2×C4—152no—
679C2×C4—152no—
680C2×C4—308no—
681C2×C4—301no—
682C2×C4—301no—
683C2×C4—301no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4—301no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4C2×C4×D1512yes—
699C2×C4C2×C4×D1512yes—
700C2×C4D4×D1512yes—
701C2×C3—42no—
702C2×C3#6585011yescharacteristic
703C2×C3C4×D4×D511yescharacteristic
704C2×C3#6588011yescharacteristic
705C2×C3#6594211yescharacteristic
706C2×C3#6598211yescharacteristic
707C2×C3#6600311yescharacteristic
708C2×C3#6603511yescharacteristic
709C5#7546011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C22×C4×D1511yescharacteristic
718C22C2×D4×D1511yescharacteristic
719C22#9209511yescharacteristic
720C22#41×D1511yescharacteristic
721C22#9210111yescharacteristic
722C22#9210111yescharacteristic
723C22#9210111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—154no—
731C4—302no—
732C4—302no—
733C4—302no—
734C4—302no—
735C4—601no—
736C4—601no—
737C4—601no—
738C3#1060719111yescharacteristic, complemented, Sylow
739C2—42no—
740C2#1175627511yescharacteristic
741C2C4×D4×D1511yescharacteristic
742C2#1175630511yescharacteristic
743C2#1175636711yescharacteristic
744C2#1175640711yescharacteristic
745C2#1175642811yescharacteristic
746C2#1175646011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenter#388D15
hypocenterC3×C5#2323
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic30C2semidirect
5. #11751077C2semidirect
6. #11751073C2semidirect
11. #11751034C2semidirect
12. #11750754C2semidirect
13. #11750750C2semidirect
14. #11750748C2semidirect
15. #11750747C2semidirect
42. #91767C4semidirect
612. C3×C5#2323semidirect
709. C5#75460semidirect
738. C3#10607191semidirect

Maximal subgroups

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

subgroupindex
C2×#917672
C2×#917662
C2×C4×Dic302
C3×C5×#3882
#117510772
#117510732
#117510522
#117510452
#117510432
#117510342
#117507542
#117507502
#117507482
#117507472
#106071913
#754605