Finite Group Databasebeta

← #14330688

Subgroups — #14330688

Order 1920.

1024 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
1C2×#91772C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3#11751088C211yesmaximal, characteristic, complemented
4#11751079C211yesmaximal, characteristic, complemented
5#11751059C211yesmaximal, characteristic
6#11751058C211yesmaximal, characteristic
7#11751051C211yesmaximal, characteristic, complemented
8#11751047C211yesmaximal, characteristic, complemented
9#11751046C211yesmaximal, characteristic, complemented
10#11751041C211yesmaximal, characteristic, complemented
11#11751029C211yesmaximal, characteristic, complemented
12#11750771C211yesmaximal, characteristic, complemented
13#11750768C211yesmaximal, characteristic, complemented
14#11750755C211yesmaximal, characteristic, complemented
15#11750748C211yesmaximal, characteristic, complemented
16#10607572—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×C4⋊Dic15C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic
34C2×C4⋊Dic15C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×#6712C2211yescharacteristic
38C2×#6712C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91772C418yescomplemented
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#75841—51nomaximal, Hall
54C2×#4029—31no—
55C5×#388D311yescharacteristic, complemented
56#65276—31no—
57#65267—31no—
58#65247—31no—
59#65246—31no—
60#65239—31no—
61#65235—31no—
62#65234—31no—
63#65229—31no—
64#65217—31no—
65#64959—31no—
66#64956—31no—
67#64943—31no—
68#64936—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220—41no—
78C2×#1220—41no—
79C2×#1220C2×C414yes—
80C22×Dic15—41no—
81C22×Dic15—41no—
82C22×Dic15—41no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C2×C4×D15—41no—
91C2×C4×D15—41no—
92C2×C4×D15C2×C414yescomplemented
93C3×C5×C4⋊C4—41no—
94C3×C5×C22⋊C4—41no—
95C3×C5×C22⋊C4—41no—
96C3×C5×C22⋊C4C2×C414yes—
97C3×C42×C5—41no—
98#6719—41no—
99#6719C2×C414yes—
100#6714—41no—
101#6714—41no—
102#6714—41no—
103#6714—41no—
104#6714C2×C414yescomplemented
105C4⋊Dic15—41no—
106C4⋊Dic15—41no—
107C4⋊Dic15C2×C414yescomplemented
108#6712—41no—
109#6712—41no—
110#6712—41no—
111#6712—41no—
112#6712C2×C414yescomplemented
113C4×Dic15—41no—
114C4×Dic15—41no—
115C2×#883—51no—
116C3×#388D511yescharacteristic, complemented
117#4987—51no—
118#4978—51no—
119#4958—51no—
120#4957—51no—
121#4950—51no—
122#4946—51no—
123#4945—51no—
124#4940—51no—
125#4928—51no—
126#4670—51no—
127#4667—51no—
128#4654—51no—
129#4647—51no—
130C22×C22⋊D5—31no—
131C23×Dic5—31no—
132C22×C4×D5—31no—
133C2×C5×C4⋊C4C2×D311yescharacteristic
134C2×C5×C22⋊C4C2×D311yescharacteristic
135C2×C5×C22⋊C4C2×D311yescharacteristic
136C2×C5×C22⋊C4C2×D311yescharacteristic
137C2×C42×C5C2×D311yescharacteristic
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×C4⋊Dic5—31no—
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×#683—31no—
151C2×#683—31no—
152C2×#683—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155#4029—38no—
156C5×#95C2×D311yescharacteristic
157C5×#95C2×D311yescharacteristic
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#2376—151noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15C22×C412yes—
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×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C22×C412yes—
199C2×C3×C4×C5C22×C412yes—
200#1220—44no—
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×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—44no—
220C2×Dic15C22×C412yes—
221C2×Dic15C22×C412yes—
222C2×Dic15C22×C412yes—
223C4×D15—44no—
224C22×#67—51no—
225C23×Dic3—51no—
226C22×C4×D3—51no—
227C2×C3×C4⋊C4C2×D511yescharacteristic
228C2×C3×C22⋊C4C2×D511yescharacteristic
229C2×C3×C22⋊C4C2×D511yescharacteristic
230C2×C3×C22⋊C4C2×D511yescharacteristic
231C2×C3×C42C2×D511yescharacteristic
232C2×#217—51no—
233C2×#217—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×C4⋊Dic3—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249#883—58no—
250C3×#95C2×D511yescharacteristic
251C3×#95C2×D511yescharacteristic
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C24×C5C22×D311yescharacteristic
261C23×D5—31no—
262C22×C4×C5C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C2×C22⋊D5—34no—
269C2×C22⋊D5—121no—
270C2×C22⋊D5—121no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—121no—
279C22×Dic5—121no—
280C22×Dic5—121no—
281C2×C4×D5—34no—
282C2×C4×D5—121no—
283C2×C4×D5—121no—
284C5×C4⋊C4—41no—
285C5×C22⋊C4—41no—
286C5×C22⋊C4—41no—
287C5×C22⋊C4C4×D314yes—
288C42×C5—41no—
289C22⋊Dic5—34no—
290C22⋊Dic5—121no—
291#685—34no—
292#685—121no—
293#685—121no—
294#685—121no—
295#685—121no—
296C4⋊Dic5—34no—
297C4⋊Dic5—121no—
298C4⋊Dic5—121no—
299#683—34no—
300#683—121no—
301#683—121no—
302#683—121no—
303#683—121no—
304C4×Dic5—121no—
305C4×Dic5—121no—
306C2×#123—151no—
307#390—151no—
308#389—151no—
309#389—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388D1511yescharacteristic, complemented
314#387—151no—
315#387—151no—
316#386—151no—
317#385—151no—
318#385—151no—
319#380—151no—
320#380—151no—
321C22×C3×C5—22no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C23×C411yescharacteristic
329C22×C3×C5H(5,𝔽2)11yescharacteristic
330C22×C3×C5H(5,𝔽2)11yescharacteristic
331C22×C3×C5H(5,𝔽2)11yescharacteristic
332C22×C3×C5H(5,𝔽2)11yescharacteristic
333C22×C3×C52−1+411yescharacteristic
334C22×C3×C52−1+411yescharacteristic
335C2×D15—22no—
336C2×D15—22no—
337C2×D15—22no—
338C2×D15—41no—
339C2×D15—41no—
340C2×D15—41no—
341C2×D15—41no—
342C3×C4×C5—22no—
343C3×C4×C5—22no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348Dic15—22no—
349Dic15—22no—
350Dic15—22no—
351Dic15—41no—
352Dic15—41no—
353Dic15—41no—
354Dic15—41no—
355C24×C3C22×D511yescharacteristic
356C23×D3—51no—
357C22×C3×C4C22×D511yescharacteristic
358C22×C3×C4C22×D511yescharacteristic
359C22×C3×C4C22×D511yescharacteristic
360C22×C3×C4C22×D511yescharacteristic
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C2×#67—54no—
364C2×#67—201no—
365C2×#67—201no—
366C22×Dic3—51no—
367C22×Dic3—51no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—201no—
374C22×Dic3—201no—
375C22×Dic3—201no—
376C2×C4×D3—54no—
377C2×C4×D3—201no—
378C2×C4×D3—201no—
379C3×C4⋊C4—41no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4C4×D514yes—
383C3×C42—41no—
384#217—54no—
385#217—201no—
386(C2×D3)⋊C4—54no—
387(C2×D3)⋊C4—201no—
388(C2×D3)⋊C4—201no—
389(C2×D3)⋊C4—201no—
390(C2×D3)⋊C4—201no—
391C4⋊Dic3—54no—
392C4⋊Dic3—201no—
393C4⋊Dic3—201no—
394Dic3⋊C4—54no—
395Dic3⋊C4—201no—
396Dic3⋊C4—201no—
397Dic3⋊C4—201no—
398Dic3⋊C4—201no—
399C4×Dic3—201no—
400C4×Dic3—201no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C2×C4×D312yes—
408C23×C5C23×D311yescharacteristic
409C22×D5—32no—
410C22×D5—61no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—61no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
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×C5C2×C4×D312yes—
433C2×C4×C5C2×C4×D312yes—
434C22⋊D5—124no—
435C2×Dic5—32no—
436C2×Dic5—32no—
437C2×Dic5—32no—
438C2×Dic5—61no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—124no—
457C4×D5—124no—
458C22×D4—151no—
459C23×C4—151no—
460C23×C4—151no—
461#123—158no—
462C2×C4⋊C4—151no—
463C2×C4⋊C4—151no—
464C2×C4⋊C4—151no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4C2×D1511yescharacteristic
471C2×C22⋊C4—151no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4C2×D1511yescharacteristic
479C2×C22⋊C4C2×D1511yescharacteristic
480C2×C22⋊C4C2×D1511yescharacteristic
481C2×C42—151no—
482C2×C42—151no—
483C2×C42C2×D1511yescharacteristic
484#95—151no—
485#95—151no—
486#95—151no—
487#95—151no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95C2×D1511yescharacteristic
493#95C2×D1511yescharacteristic
494C2×C3×C5—42no—
495C2×C3×C5#51811yescharacteristic
496C2×C3×C5#52011yescharacteristic
497C2×C3×C5#52011yescharacteristic
498C2×C3×C5#56011yescharacteristic
499C2×C3×C5#56211yescharacteristic
500C2×C3×C5#56211yescharacteristic
501C2×C3×C5#56311yescharacteristic
502D15—42no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3C2×C4×D512yes—
510C23×C3C23×D511yescharacteristic
511C22×D3—52no—
512C22×D3—101no—
513C22×D3—101no—
514C22×D3—101no—
515C22×D3—101no—
516C22×D3—101no—
517C22×D3—101no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4C2×C4×D512yes—
535C2×C3×C4C2×C4×D512yes—
536#67—204no—
537C2×Dic3—52no—
538C2×Dic3—52no—
539C2×Dic3—52no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—204no—
559C4×D3—204no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5C22×C4×D311yescharacteristic
568C22×C5#100411yescharacteristic
569C22×C5#100411yescharacteristic
570C22×C5#100911yescharacteristic
571C22×C5#100911yescharacteristic
572C22×C5#101011yescharacteristic
573C22×C5#101011yescharacteristic
574C2×D5—62no—
575C2×D5—62no—
576C2×D5—62no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—41no—
584C4×C5—41no—
585C4×C5—41no—
586C4×C5—41no—
587Dic5—62no—
588Dic5—62no—
589Dic5—62no—
590Dic5—121no—
591Dic5—121no—
592Dic5—121no—
593Dic5—121no—
594C24—151no—
595C24C22×D1511yescharacteristic
596C2×D4—154no—
597C2×D4—601no—
598C2×D4—601no—
599C22×C4—151no—
600C22×C4—151no—
601C22×C4—151no—
602C22×C4—154no—
603C22×C4—151no—
604C22×C4—151no—
605C22×C4—151no—
606C22×C4—151no—
607C22×C4—601no—
608C22×C4—601no—
609C22×C4—601no—
610C22×C4—601no—
611C22×C4—601no—
612C22×C4C22×D1511yescharacteristic
613C22×C4C22×D1511yescharacteristic
614C22×C4C22×D1511yescharacteristic
615C22×C4C22×D1511yescharacteristic
616C22×C4C22×D1511yescharacteristic
617C22×C4C22×D1511yescharacteristic
618C4⋊C4—41no—
619C4⋊C4—154no—
620C4⋊C4—154no—
621C4⋊C4—601no—
622C4⋊C4—601no—
623C4⋊C4—601no—
624C4⋊C4—601no—
625C4⋊C4—601no—
626C4⋊C4—601no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—154no—
630C22⋊C4—154no—
631C22⋊C4—601no—
632C22⋊C4—601no—
633C22⋊C4—601no—
634C22⋊C4—601no—
635C22⋊C4—601no—
636C22⋊C4C4×D1514yes—
637C42—41no—
638C42—601no—
639C42—601no—
640C3×C5#237611yescharacteristic, complemented, Hall
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3C22×C4×D511yescharacteristic
649C22×C3#414411yescharacteristic
650C22×C3#414411yescharacteristic
651C22×C3#414911yescharacteristic
652C22×C3#414911yescharacteristic
653C22×C3#415011yescharacteristic
654C22×C3#415011yescharacteristic
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—102no—
658C2×D3—201no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668Dic3—102no—
669Dic3—102no—
670Dic3—102no—
671Dic3—201no—
672Dic3—201no—
673Dic3—201no—
674Dic3—201no—
675C2×C5—42no—
676C2×C5#552311yescharacteristic
677C2×C5#554511yescharacteristic
678C2×C5#554611yescharacteristic
679C2×C5#562111yescharacteristic
680C2×C5#566611yescharacteristic
681C2×C5#568411yescharacteristic
682C2×C5#571211yescharacteristic
683D5—122no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—152no—
691C23—301no—
692C23—301no—
693C23—301no—
694C23—301no—
695C23—301no—
696C23—301no—
697C23C2×C4×D1512yes—
698C23C23×D1511yescharacteristic
699D4—604no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
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—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—152no—
717C2×C4—152no—
718C2×C4—152no—
719C2×C4—301no—
720C2×C4—301no—
721C2×C4—301no—
722C2×C4—301no—
723C2×C4—301no—
724C2×C4—301no—
725C2×C4—301no—
726C2×C4—301no—
727C2×C4—301no—
728C2×C4—301no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—604no—
738C2×C4—604no—
739C2×C4C2×C4×D1512yes—
740C2×C4C2×C4×D1512yes—
741C2×C3—42no—
742C2×C3#6585711yescharacteristic
743C2×C3#6587911yescharacteristic
744C2×C3#6588011yescharacteristic
745C2×C3#6595511yescharacteristic
746C2×C3#6600011yescharacteristic
747C2×C3#6601811yescharacteristic
748C2×C3#6604611yescharacteristic
749D3—202no—
750C5#7584111yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—302no—
759C22—302no—
760C22—302no—
761C22—601no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22C22×C4×D1511yescharacteristic
766C22#9209511yescharacteristic
767C22#9209511yescharacteristic
768C22#9210011yescharacteristic
769C22#9210011yescharacteristic
770C22#9210111yescharacteristic
771C22#9210111yescharacteristic
772C4—22no—
773C4—22no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—302no—
779C4—302no—
780C4—302no—
781C4—601no—
782C4—601no—
783C4—601no—
784C4—601no—
785C3#1060757211yescharacteristic, complemented, Sylow
786C2—42no—
787C2—602no—
788C2#1175628211yescharacteristic
789C2#1175630411yescharacteristic
790C2#1175630511yescharacteristic
791C2#1175638011yescharacteristic
792C2#1175642511yescharacteristic
793C2#1175644311yescharacteristic
794C2#1175647111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#388D15
hypocenterC3×C5#2376
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. #11751088C2semidirect
4. #11751079C2semidirect
7. #11751051C2semidirect
8. #11751047C2semidirect
9. #11751046C2semidirect
10. #11751041C2semidirect
11. #11751029C2semidirect
12. #11750771C2semidirect
13. #11750768C2semidirect
14. #11750755C2semidirect
15. #11750748C2semidirect
42. #91772C4semidirect
55. C5×#388D3semidirect
92. C2×C4×D15C2×C4semidirect
104. #6714C2×C4semidirect
107. C4⋊Dic15C2×C4semidirect
112. #6712C2×C4semidirect
116. C3×#388D5semidirect
313. #388D15semidirect
640. C3×C5#2376semidirect
750. C5#75841semidirect
785. C3#10607572semidirect

Maximal subgroups

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

subgroupindex
C2×#917722
C3×C5×#3882
#117510882
#117510792
#117510592
#117510582
#117510512
#117510472
#117510462
#117510412
#117510292
#117507712
#117507682
#117507552
#117507482
#106075723
#758415