Finite Group Databasebeta

← #14323707

Subgroups — #14323707

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×#91785C211yesmaximal, characteristic
2C2×#91781C211yesmaximal, characteristic
3C2×C4×Dic30C211yesmaximal, characteristic, complemented
4C3×C5×#387C211yesmaximal, characteristic, complemented
5#11751085C211yesmaximal, characteristic, complemented
6#11751079C211yesmaximal, characteristic, complemented
7#11751041C211yesmaximal, characteristic
8#11750771C211yesmaximal, characteristic
9#11750771C211yesmaximal, characteristic
10#11750770C211yesmaximal, characteristic
11#11750768C211yesmaximal, characteristic
12#11750750C211yesmaximal, characteristic, complemented
13#11750748C211yesmaximal, characteristic, complemented
14#11750748C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10606678—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
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#91785C418yescomplemented
43#91781—24no—
44C4×Dic30—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#74947—51nomaximal, Hall
56C2×#4042—31no—
57C2×#4038—31no—
58C2×C4×Dic10—31no—
59C5×#387D311yescharacteristic, complemented
60#65274—31no—
61#65267—31no—
62#65229—31no—
63#64959—31no—
64#64959—31no—
65#64958—31no—
66#64956—31no—
67#64938—31no—
68#64936—31no—
69#64936—31no—
70#64935—31no—
71C23×D15C2311yescharacteristic
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×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C4×D15—22no—
87C2×C4×D15—22no—
88C2×C4×D15C2×C414yes—
89C2×Dic30—22no—
90C2×Dic30—22no—
91C2×Dic30C2×C414yes—
92C3×C5×C4⋊C4—22no—
93C3×C5×C4⋊C4C2×C414yes—
94C3×C42×C5—22no—
95#6714—22no—
96#6714—22no—
97#6714—41no—
98#6714—41no—
99#6714C2×C414yes—
100#6714C2×C414yes—
101C4⋊Dic15—22no—
102C4⋊Dic15—22no—
103C4⋊Dic15—41no—
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×#896—51no—
116C2×#892—51no—
117C2×C4×Dic6—51no—
118C3×#387D511yescharacteristic, complemented
119#4984—51no—
120#4978—51no—
121#4940—51no—
122#4670—51no—
123#4670—51no—
124#4669—51no—
125#4667—51no—
126#4649—51no—
127#4647—51no—
128#4647—51no—
129#4646—51no—
130C22×C4×D5—31no—
131C22×Dic10—31no—
132C2×C5×C4⋊C4C2×D311yescharacteristic
133C2×C5×C4⋊C4C2×D311yescharacteristic
134C2×C42×C5C2×D311yescharacteristic
135C2×#685—31no—
136C2×#685—31no—
137C2×#685—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685—31no—
141C2×C4⋊Dic5—31no—
142C2×C4⋊Dic5—31no—
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×Dic5—31no—
155#4042—38no—
156#4038—64no—
157C4×Dic10—64no—
158C5×#95C2×D311yescharacteristic
159C5×#95C2×D311yescharacteristic
160C5×#95C2×D311yescharacteristic
161C5×#95C2×D311yescharacteristic
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#2323—151noSylow
169C23×C3×C5C2411yescharacteristic
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15—21no—
175C22×D15—21no—
176C22×D15C22×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×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×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×C3×C4×C5C22×C412yes—
196C2×C3×C4×C5C22×C412yes—
197C2×C3×C4×C5C2×D412yes—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
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×Dic15C2×D412yes—
217C2×Dic15C2×D412yes—
218C2×Dic15#4112yes—
219C4×D15—28no—
220Dic30—28no—
221C22×C4×D3—51no—
222C22×Dic6—51no—
223C2×C3×C4⋊C4C2×D511yescharacteristic
224C2×C3×C4⋊C4C2×D511yescharacteristic
225C2×C3×C42C2×D511yescharacteristic
226C2×(C2×D3)⋊C4—51no—
227C2×(C2×D3)⋊C4—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×(C2×D3)⋊C4—51no—
230C2×(C2×D3)⋊C4—51no—
231C2×(C2×D3)⋊C4—51no—
232C2×C4⋊Dic3—51no—
233C2×C4⋊Dic3—51no—
234C2×C4⋊Dic3—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#896—58no—
247#892—104no—
248C4×Dic6—104no—
249C3×#95C2×D511yescharacteristic
250C3×#95C2×D511yescharacteristic
251C3×#95C2×D511yescharacteristic
252C3×#95C2×D511yescharacteristic
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C23×D5—31no—
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×C4×C5C22×D311yescharacteristic
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
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⋊C4C4×D314yes—
282C42×C5—22no—
283#685—34no—
284#685—34no—
285#685—62no—
286#685—62no—
287#685—121no—
288#685—121no—
289C4⋊Dic5—62no—
290C4⋊Dic5—62no—
291C4⋊Dic5—121no—
292#683—34no—
293#683—34no—
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#388—151no—
314#387—151no—
315#387D1511yescharacteristic, complemented
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×D15—22no—
326C2×D15—22no—
327C2×D15—22no—
328C2×D15—41no—
329C2×D15—41no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—22no—
336C3×C4×C5—41no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339Dic15—22no—
340Dic15—22no—
341Dic15—22no—
342Dic15—41no—
343Dic15—41no—
344Dic15—41no—
345Dic15C4×D414yes—
346C23×D3—51no—
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×C3×C4C22×D511yescharacteristic
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3—51no—
360C22×Dic3—51no—
361C2×C4×D3—54no—
362C2×C4×D3—102no—
363C2×C4×D3—102no—
364C2×Dic6—54no—
365C2×Dic6—102no—
366C2×Dic6—102no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4C4×D514yes—
369C3×C42—22no—
370(C2×D3)⋊C4—54no—
371(C2×D3)⋊C4—54no—
372(C2×D3)⋊C4—102no—
373(C2×D3)⋊C4—102no—
374(C2×D3)⋊C4—201no—
375(C2×D3)⋊C4—201no—
376C4⋊Dic3—102no—
377C4⋊Dic3—102no—
378C4⋊Dic3—201no—
379Dic3⋊C4—54no—
380Dic3⋊C4—54no—
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×C5C23×D311yescharacteristic
391C22×D5—32no—
392C22×D5—61no—
393C22×D5—61no—
394C22×D5—61no—
395C22×D5—61no—
396C22×D5—61no—
397C22×D5—61no—
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×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5C2×C4×D312yes—
416C2×C4×C5C2×C4×D312yes—
417C2×C4×C5C2×C4×D312yes—
418C2×C4×C5D3×D412yes—
419C2×Dic5—32no—
420C2×Dic5—32no—
421C2×Dic5—32no—
422C2×Dic5—32no—
423C2×Dic5—32no—
424C2×Dic5—32no—
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—
440C4×D5—68no—
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⋊C4C2×D1511yescharacteristic
457C2×C4⋊C4C2×D1511yescharacteristic
458C2×C22⋊C4—151no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—151no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—151no—
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#95C2×D1511yescharacteristic
477#95C2×D1511yescharacteristic
478#95C2×D1511yescharacteristic
479#95C2×D1511yescharacteristic
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
487D15—42no—
488C23×C3C23×D511yescharacteristic
489C22×D3—52no—
490C22×D3—101no—
491C22×D3—101no—
492C22×D3—101no—
493C22×D3—101no—
494C22×D3—101no—
495C22×D3—101no—
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×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4C2×C4×D512yes—
514C2×C3×C4C2×C4×D512yes—
515C2×C3×C4C2×C4×D512yes—
516C2×C3×C4D4×D512yes—
517C2×Dic3—52no—
518C2×Dic3—52no—
519C2×Dic3—52no—
520C2×Dic3—52no—
521C2×Dic3—52no—
522C2×Dic3—52no—
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—
538C4×D3—108no—
539Dic6—108no—
540C22×C5C22×C4×D311yescharacteristic
541C22×C5C2×D3×D411yescharacteristic
542C22×C5#100711yescharacteristic
543C22×C5D3×#4111yescharacteristic
544C22×C5#100911yescharacteristic
545C22×C5#101011yescharacteristic
546C22×C5#101011yescharacteristic
547C2×D5—62no—
548C2×D5—62no—
549C2×D5—62no—
550C2×D5—121no—
551C2×D5—121no—
552C2×D5—121no—
553C2×D5—121no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—22no—
557C4×C5—22no—
558C4×C5—41no—
559C4×C5—41no—
560C4×C5—41no—
561Dic5—34no—
562Dic5—62no—
563Dic5—62no—
564Dic5—62no—
565Dic5—121no—
566Dic5—121no—
567Dic5—121no—
568C24—151no—
569C2×Q8—154no—
570C2×Q8—302no—
571C2×Q8—302no—
572C22×C4—151no—
573C22×C4—151no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—154no—
577C22×C4—151no—
578C22×C4—151no—
579C22×C4—151no—
580C22×C4—302no—
581C22×C4—302no—
582C22×C4C22×D1511yescharacteristic
583C22×C4C22×D1511yescharacteristic
584C22×C4C22×D1511yescharacteristic
585C22×C4C22×D1511yescharacteristic
586C22×C4C22×D1511yescharacteristic
587C22×C4C22×D1511yescharacteristic
588C22×C4C22×D1511yescharacteristic
589C4⋊C4—22no—
590C4⋊C4—154no—
591C4⋊C4—154no—
592C4⋊C4—302no—
593C4⋊C4—302no—
594C4⋊C4—302no—
595C4⋊C4—302no—
596C4⋊C4—302no—
597C4⋊C4—601no—
598C4⋊C4—601no—
599C4⋊C4C4×D1514yes—
600C22⋊C4—154no—
601C22⋊C4—154no—
602C22⋊C4—302no—
603C22⋊C4—302no—
604C22⋊C4—601no—
605C22⋊C4—601no—
606C42—22no—
607C42—154no—
608C42—302no—
609C42—302no—
610C42—601no—
611C42—601no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3C22×C4×D511yescharacteristic
614C22×C3C2×D4×D511yescharacteristic
615C22×C3#414711yescharacteristic
616C22×C3D5×#4111yescharacteristic
617C22×C3#414911yescharacteristic
618C22×C3#415011yescharacteristic
619C22×C3#415011yescharacteristic
620C2×D3—102no—
621C2×D3—102no—
622C2×D3—102no—
623C2×D3—201no—
624C2×D3—201no—
625C2×D3—201no—
626C2×D3—201no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634Dic3—54no—
635Dic3—102no—
636Dic3—102no—
637Dic3—102no—
638Dic3—201no—
639Dic3—201no—
640Dic3—201no—
641C2×C5#552311yescharacteristic
642C2×C5C4×D3×D411yescharacteristic
643C2×C5#557211yescharacteristic
644C2×C5#562911yescharacteristic
645C2×C5#564811yescharacteristic
646C2×C5#569611yescharacteristic
647C2×C5#571011yescharacteristic
648D5—122no—
649C23—152no—
650C23—301no—
651C23—301no—
652C23—301no—
653C23—301no—
654C23—301no—
655C23—301no—
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—21no—
674C2×C4—21no—
675C2×C4—152no—
676C2×C4—152no—
677C2×C4—152no—
678C2×C4—152no—
679C2×C4—152no—
680C2×C4—152no—
681C2×C4—308no—
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×C4C2×C4×D1512yes—
698C2×C4C2×C4×D1512yes—
699C2×C4C2×C4×D1512yes—
700C2×C4D4×D1512yes—
701C2×C3#6585711yescharacteristic
702C2×C3C4×D4×D511yescharacteristic
703C2×C3#6590611yescharacteristic
704C2×C3#6596311yescharacteristic
705C2×C3#6598211yescharacteristic
706C2×C3#6603011yescharacteristic
707C2×C3#6604411yescharacteristic
708D3—202no—
709C5#7494711yescharacteristic, complemented, Sylow
710C22—302no—
711C22—302no—
712C22—302no—
713C22—601no—
714C22—601no—
715C22—601no—
716C22—601no—
717C22C22×C4×D1511yescharacteristic
718C22C2×D4×D1511yescharacteristic
719C22#9209811yescharacteristic
720C22#41×D1511yescharacteristic
721C22#9210011yescharacteristic
722C22#9210111yescharacteristic
723C22#9210111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—154no—
732C4—302no—
733C4—302no—
734C4—302no—
735C4—601no—
736C4—601no—
737C4—601no—
738C3#1060667811yescharacteristic, complemented, Sylow
739C2—602no—
740C2#1175628211yescharacteristic
741C2C4×D4×D1511yescharacteristic
742C2#1175633111yescharacteristic
743C2#1175638811yescharacteristic
744C2#1175640711yescharacteristic
745C2#1175645511yescharacteristic
746C2#1175646911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#387C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#387D15
hypocenterC3×C5#2323
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic30C2semidirect
4. C3×C5×#387C2semidirect
5. #11751085C2semidirect
6. #11751079C2semidirect
12. #11750750C2semidirect
13. #11750748C2semidirect
14. #11750748C2semidirect
15. #11750747C2semidirect
42. #91785C4semidirect
59. C5×#387D3semidirect
118. C3×#387D5semidirect
315. #387D15semidirect
612. C3×C5#2323semidirect
709. C5#74947semidirect
738. C3#10606678semidirect

Maximal subgroups

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

subgroupindex
C2×#917852
C2×#917812
C2×C4×Dic302
C3×C5×#3872
#117510852
#117510792
#117510412
#117507712
#117507702
#117507682
#117507502
#117507482
#117507472
#106066783
#749475