Finite Group Databasebeta

← #14324037

Subgroups — #14324037

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91784C211yesmaximal, characteristic
2C2×#91782C211yesmaximal, characteristic, complemented
3C2×C4×D60C211yesmaximal, characteristic, complemented
4C3×C5×#387C211yesmaximal, characteristic, complemented
5#11751090C211yesmaximal, characteristic, complemented
6#11751081C211yesmaximal, characteristic, complemented
7#11751041C211yesmaximal, characteristic, complemented
8#11750770C211yesmaximal, characteristic, complemented
9#11750769C211yesmaximal, characteristic, complemented
10#11750768C211yesmaximal, characteristic, complemented
11#11750766C211yesmaximal, characteristic, complemented
12#11750766C211yesmaximal, characteristic, complemented
13#11750766C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15D15×#95C211yesmaximal, characteristic, complemented
16#10607029—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91784C418yescomplemented
43#91782—24no—
44C4×D60—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#75298—51nomaximal, Hall
56C2×#4041—31no—
57C2×#4039—31no—
58C2×C4×D20—31no—
59C5×#387D311yescharacteristic, complemented
60#65278—31no—
61#65270—31no—
62#65229—31no—
63#64958—31no—
64#64957—31no—
65#64956—31no—
66#64954—31no—
67#64954—31no—
68#64954—31no—
69#64954—31no—
70D5×#95—31no—
71C23×D15C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×D15C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×D60—22no—
87C2×D60—22no—
88C2×D60—22no—
89C2×D60—22no—
90C2×D60—41no—
91C2×D60—41no—
92C2×D60C2×C414yescomplemented
93C2×D60C2×C414yescomplemented
94C2×D60C2×C414yescomplemented
95C2×C4×D15—22no—
96C2×C4×D15—22no—
97C2×C4×D15—22no—
98C2×C4×D15—41no—
99C2×C4×D15—41no—
100C2×C4×D15—41no—
101C2×C4×D15—41no—
102C2×C4×D15—41no—
103C2×C4×D15—41no—
104C2×C4×D15—41no—
105C2×C4×D15—41no—
106C2×C4×D15—41no—
107C2×C4×D15—41no—
108C2×C4×D15C2×C414yescomplemented
109C2×C4×D15D414yescomplemented
110C3×C5×C4⋊C4—22no—
111C3×C5×C4⋊C4C2×C414yescomplemented
112C3×C42×C5—22no—
113#6714—22no—
114#6714—22no—
115#6714—22no—
116#6714—22no—
117#6714—41no—
118#6714—41no—
119#6714—41no—
120#6714—41no—
121#6714C2×C414yescomplemented
122#6714C2×C414yescomplemented
123C4⋊Dic15—22no—
124#6712—41no—
125#6712—41no—
126C4×Dic15—22no—
127C2×#895—51no—
128C2×#893—51no—
129C2×C4×D12—51no—
130C3×#387D511yescharacteristic, complemented
131#4989—51no—
132#4980—51no—
133#4940—51no—
134#4669—51no—
135#4668—51no—
136#4667—51no—
137#4665—51no—
138#4665—51no—
139#4665—51no—
140#4665—51no—
141D3×#95—51no—
142C22×D20—31no—
143C22×D20—31no—
144C22×D20—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C22×C4×D5—31no—
148C22×C4×D5—31no—
149C22×C4×D5—31no—
150C2×C5×C4⋊C4C2×D311yescharacteristic
151C2×C5×C4⋊C4C2×D311yescharacteristic
152C2×C42×C5C2×D311yescharacteristic
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×C4⋊Dic5—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×C4×Dic5—31no—
167#4041—38no—
168#4039—64no—
169C4×D20—64no—
170C5×#95C2×D311yescharacteristic
171C5×#95C2×D311yescharacteristic
172C5×#95C2×D311yescharacteristic
173C5×#95C2×D311yescharacteristic
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2325—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15C22×C412yes—
199C22×D15C22×C412yes—
200C22×D15C22×C412yes—
201C22×D15C2×D412yes—
202C22×D15#4112yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C22×C412yes—
221C2×C3×C4×C5C22×C412yes—
222C2×C3×C4×C5C22×C412yes—
223C2×C3×C4×C5C2×D412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15C22×C412yes—
238C2×Dic15C2×D412yes—
239D60—28no—
240D60—28no—
241D60—44no—
242C4×D15—44no—
243C4×D15—44no—
244C4×D15—44no—
245C4×D15—44no—
246C4×D15—44no—
247C22×D12—51no—
248C22×D12—51no—
249C22×D12—51no—
250C22×C4×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4C2×D511yescharacteristic
256C2×C3×C4⋊C4C2×D511yescharacteristic
257C2×C3×C42C2×D511yescharacteristic
258C2×(C2×D3)⋊C4—51no—
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×C4⋊Dic3—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×C4×Dic3—51no—
272#895—58no—
273#893—104no—
274C4×D12—104no—
275C3×#95C2×D511yescharacteristic
276C3×#95C2×D511yescharacteristic
277C3×#95C2×D511yescharacteristic
278C3×#95C2×D511yescharacteristic
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C23×D5—31no—
286C23×D5—31no—
287C23×D5—31no—
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C22×C4×C5C22×D311yescharacteristic
295C22×Dic5—31no—
296C22×Dic5—31no—
297C22×Dic5—31no—
298C22×Dic5—31no—
299C22×Dic5—31no—
300C2×D20—34no—
301C2×D20—34no—
302C2×D20—34no—
303C2×D20—62no—
304C2×D20—62no—
305C2×D20—62no—
306C2×D20—62no—
307C2×D20—121no—
308C2×D20—121no—
309C2×C4×D5—34no—
310C2×C4×D5—34no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—121no—
315C2×C4×D5—121no—
316C2×C4×D5—121no—
317C2×C4×D5—121no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—22no—
325C5×C4⋊C4C4×D314yescomplemented
326C42×C5—22no—
327#685—34no—
328#685—34no—
329#685—62no—
330#685—62no—
331#685—62no—
332#685—62no—
333#685—121no—
334#685—121no—
335#685—121no—
336#685—121no—
337C4⋊Dic5—62no—
338#683—121no—
339#683—121no—
340C4×Dic5—62no—
341C2×#121—151no—
342C2×C4×D4—151no—
343C2×C4×D4—151no—
344#388—151no—
345#388—151no—
346#387—151no—
347#387D1511yescharacteristic, complemented
348#386—151no—
349#386—151no—
350#386—151no—
351#386—151no—
352#385—151no—
353#385—151no—
354#380—151no—
355C2×#95—151no—
356C22×C3×C5C23×C411yescharacteristic
357C22×C3×C5C22×D411yescharacteristic
358C22×C3×C5C2×#4111yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C5H(5,𝔽2)11yescharacteristic
361C22×C3×C5H(5,𝔽2)11yescharacteristic
362C22×C3×C52−1+411yescharacteristic
363C2×D15—22no—
364C2×D15—22no—
365C2×D15—22no—
366C2×D15—22no—
367C2×D15—22no—
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15—22no—
373C2×D15—22no—
374C2×D15—22no—
375C2×D15—41no—
376C2×D15—41no—
377C2×D15—41no—
378C2×D15—41no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15C4×D414yes—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—22no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×C4×C5—41no—
391Dic15—22no—
392Dic15—22no—
393Dic15—41no—
394Dic15—41no—
395Dic15—41no—
396C23×D3—51no—
397C23×D3—51no—
398C23×D3—51no—
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C22×Dic3—51no—
407C22×Dic3—51no—
408C22×Dic3—51no—
409C22×Dic3—51no—
410C22×Dic3—51no—
411C2×D12—54no—
412C2×D12—54no—
413C2×D12—54no—
414C2×D12—102no—
415C2×D12—102no—
416C2×D12—102no—
417C2×D12—102no—
418C2×D12—201no—
419C2×D12—201no—
420C2×C4×D3—54no—
421C2×C4×D3—54no—
422C2×C4×D3—102no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—201no—
426C2×C4×D3—201no—
427C2×C4×D3—201no—
428C2×C4×D3—201no—
429C2×C4×D3—201no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C2×C4×D3—201no—
435C3×C4⋊C4—22no—
436C3×C4⋊C4C4×D514yescomplemented
437C3×C42—22no—
438(C2×D3)⋊C4—54no—
439(C2×D3)⋊C4—54no—
440(C2×D3)⋊C4—102no—
441(C2×D3)⋊C4—102no—
442(C2×D3)⋊C4—102no—
443(C2×D3)⋊C4—102no—
444(C2×D3)⋊C4—201no—
445(C2×D3)⋊C4—201no—
446(C2×D3)⋊C4—201no—
447(C2×D3)⋊C4—201no—
448C4⋊Dic3—102no—
449Dic3⋊C4—201no—
450Dic3⋊C4—201no—
451C4×Dic3—102no—
452C23×C5C23×D311yescharacteristic
453C22×D5—32no—
454C22×D5—32no—
455C22×D5—32no—
456C22×D5—32no—
457C22×D5—32no—
458C22×D5—61no—
459C22×D5—61no—
460C22×D5—61no—
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—61no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C22×D5—61no—
473C22×D5—61no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5C2×C4×D312yes—
492C2×C4×C5C2×C4×D312yes—
493C2×C4×C5C2×C4×D312yes—
494C2×C4×C5D3×D412yes—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510D20—68no—
511D20—68no—
512D20—124no—
513C4×D5—124no—
514C4×D5—124no—
515C4×D5—124no—
516C4×D5—124no—
517C4×D5—124no—
518C22×D4—151no—
519C22×D4—151no—
520C22×D4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524C23×C4—151no—
525C23×C4—151no—
526#121—158no—
527C4×D4—304no—
528C4×D4—304no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4C2×D1511yescharacteristic
533C2×C4⋊C4C2×D1511yescharacteristic
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C42—151no—
545C2×C42C2×D1511yescharacteristic
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552#95C2×D1511yescharacteristic
553#95C2×D1511yescharacteristic
554#95C2×D1511yescharacteristic
555#95C2×D1511yescharacteristic
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5#51811yescharacteristic
558C2×C3×C5#52011yescharacteristic
559C2×C3×C5#53411yescharacteristic
560C2×C3×C5#53711yescharacteristic
561C2×C3×C5#53811yescharacteristic
562C2×C3×C5#53911yescharacteristic
563D15—24no—
564D15—42no—
565D15—42no—
566C23×C3C23×D511yescharacteristic
567C22×D3—52no—
568C22×D3—52no—
569C22×D3—52no—
570C22×D3—52no—
571C22×D3—52no—
572C22×D3—101no—
573C22×D3—101no—
574C22×D3—101no—
575C22×D3—101no—
576C22×D3—101no—
577C22×D3—101no—
578C22×D3—101no—
579C22×D3—101no—
580C22×D3—101no—
581C22×D3—101no—
582C22×D3—101no—
583C22×D3—101no—
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—101no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4C2×C4×D512yes—
606C2×C3×C4C2×C4×D512yes—
607C2×C3×C4C2×C4×D512yes—
608C2×C3×C4D4×D512yes—
609C2×Dic3—52no—
610C2×Dic3—52no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—101no—
624D12—108no—
625D12—108no—
626D12—204no—
627C4×D3—204no—
628C4×D3—204no—
629C4×D3—204no—
630C4×D3—204no—
631C4×D3—204no—
632C22×C5C22×C4×D311yescharacteristic
633C22×C5C2×D3×D411yescharacteristic
634C22×C5#100711yescharacteristic
635C22×C5D3×#4111yescharacteristic
636C22×C5#100911yescharacteristic
637C22×C5#100911yescharacteristic
638C22×C5#100911yescharacteristic
639C2×D5—34no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—62no—
645C2×D5—62no—
646C2×D5—62no—
647C2×D5—62no—
648C2×D5—62no—
649C2×D5—62no—
650C2×D5—62no—
651C2×D5—62no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—121no—
656C2×D5—121no—
657C2×D5—121no—
658C2×D5—121no—
659C2×D5—121no—
660C4×C5—22no—
661C4×C5—22no—
662C4×C5—22no—
663C4×C5—22no—
664C4×C5—41no—
665C4×C5—41no—
666C4×C5—41no—
667Dic5—62no—
668Dic5—62no—
669Dic5—121no—
670Dic5—121no—
671Dic5—121no—
672C24—151no—
673C24—151no—
674C24—151no—
675C2×D4—154no—
676C2×D4—154no—
677C2×D4—154no—
678C2×D4—302no—
679C2×D4—302no—
680C2×D4—302no—
681C2×D4—302no—
682C2×D4—601no—
683C2×D4—601no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—154no—
687C22×C4—154no—
688C22×C4—151no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—302no—
692C22×C4—302no—
693C22×C4—302no—
694C22×C4—601no—
695C22×C4—601no—
696C22×C4—601no—
697C22×C4—601no—
698C22×C4—601no—
699C22×C4—601no—
700C22×C4—601no—
701C22×C4—601no—
702C22×C4—601no—
703C22×C4—601no—
704C22×C4C22×D1511yescharacteristic
705C22×C4C22×D1511yescharacteristic
706C22×C4C22×D1511yescharacteristic
707C22×C4C22×D1511yescharacteristic
708C22×C4C22×D1511yescharacteristic
709C22×C4C22×D1511yescharacteristic
710C22×C4C22×D1511yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—302no—
713C4⋊C4—601no—
714C4⋊C4—601no—
715C4⋊C4C4×D1514yescomplemented
716C22⋊C4—154no—
717C22⋊C4—154no—
718C22⋊C4—302no—
719C22⋊C4—302no—
720C22⋊C4—302no—
721C22⋊C4—302no—
722C22⋊C4—601no—
723C22⋊C4—601no—
724C22⋊C4—601no—
725C22⋊C4—601no—
726C42—22no—
727C42—302no—
728C3×C5#232511yescharacteristic, complemented, Hall
729C22×C3C22×C4×D511yescharacteristic
730C22×C3C2×D4×D511yescharacteristic
731C22×C3#414711yescharacteristic
732C22×C3D5×#4111yescharacteristic
733C22×C3#414911yescharacteristic
734C22×C3#414911yescharacteristic
735C22×C3#414911yescharacteristic
736C2×D3—54no—
737C2×D3—102no—
738C2×D3—102no—
739C2×D3—102no—
740C2×D3—102no—
741C2×D3—102no—
742C2×D3—102no—
743C2×D3—102no—
744C2×D3—102no—
745C2×D3—102no—
746C2×D3—102no—
747C2×D3—102no—
748C2×D3—102no—
749C2×D3—201no—
750C2×D3—201no—
751C2×D3—201no—
752C2×D3—201no—
753C2×D3—201no—
754C2×D3—201no—
755C2×D3—201no—
756C2×D3—201no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764Dic3—102no—
765Dic3—102no—
766Dic3—201no—
767Dic3—201no—
768Dic3—201no—
769C2×C5#552111yescharacteristic
770C2×C5C4×D3×D411yescharacteristic
771C2×C5#557411yescharacteristic
772C2×C5#562911yescharacteristic
773C2×C5#565311yescharacteristic
774C2×C5#569211yescharacteristic
775C2×C5#570411yescharacteristic
776D5—64no—
777D5—122no—
778D5—122no—
779C23—152no—
780C23—152no—
781C23—152no—
782C23—152no—
783C23—152no—
784C23—301no—
785C23—301no—
786C23—301no—
787C23—301no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23—301no—
794C23—301no—
795C23—301no—
796C23—301no—
797C23—301no—
798C23—301no—
799C23—301no—
800C23C23×D1511yescharacteristic
801D4—308no—
802D4—308no—
803D4—604no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—152no—
822C2×C4—152no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—301no—
836C2×C4—604no—
837C2×C4—604no—
838C2×C4—604no—
839C2×C4—604no—
840C2×C4—604no—
841C2×C4C2×C4×D1512yes—
842C2×C4C2×C4×D1512yes—
843C2×C4C2×C4×D1512yes—
844C2×C4D4×D1512yes—
845C2×C3#6585511yescharacteristic
846C2×C3C4×D4×D511yescharacteristic
847C2×C3#6590811yescharacteristic
848C2×C3#6596311yescharacteristic
849C2×C3#6598711yescharacteristic
850C2×C3#6602611yescharacteristic
851C2×C3#6603811yescharacteristic
852D3—104no—
853D3—202no—
854D3—202no—
855C5#7529811yescharacteristic, complemented, Sylow
856C22—154no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—302no—
861C22—302no—
862C22—302no—
863C22—302no—
864C22—302no—
865C22—302no—
866C22—302no—
867C22—302no—
868C22—302no—
869C22—601no—
870C22—601no—
871C22—601no—
872C22—601no—
873C22—601no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22C22×C4×D1511yescharacteristic
878C22C2×D4×D1511yescharacteristic
879C22#9209811yescharacteristic
880C22#41×D1511yescharacteristic
881C22#9210011yescharacteristic
882C22#9210011yescharacteristic
883C22#9210011yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—302no—
892C4—302no—
893C4—601no—
894C4—601no—
895C4—601no—
896C3#1060702911yescharacteristic, complemented, Sylow
897C2—304no—
898C2—602no—
899C2—602no—
900C2#1175628011yescharacteristic
901C2C4×D4×D1511yescharacteristic
902C2#1175633311yescharacteristic
903C2#1175638811yescharacteristic
904C2#1175641211yescharacteristic
905C2#1175645111yescharacteristic
906C2#1175646311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#387C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91784C2
hypercenter#387D15
hypocenterC3×C5#2325
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×#91782C2semidirect
3. C2×C4×D60C2semidirect
4. C3×C5×#387C2semidirect
5. #11751090C2semidirect
6. #11751081C2semidirect
7. #11751041C2semidirect
8. #11750770C2semidirect
9. #11750769C2semidirect
10. #11750768C2semidirect
11. #11750766C2semidirect
12. #11750766C2semidirect
13. #11750766C2semidirect
14. #11750766C2semidirect
15. D15×#95C2semidirect
42. #91784C4semidirect
59. C5×#387D3semidirect
92. C2×D60C2×C4semidirect
93. C2×D60C2×C4semidirect
94. C2×D60C2×C4semidirect
108. C2×C4×D15C2×C4semidirect
109. C2×C4×D15D4semidirect
111. C3×C5×C4⋊C4C2×C4semidirect
121. #6714C2×C4semidirect
122. #6714C2×C4semidirect
130. C3×#387D5semidirect
325. C5×C4⋊C4C4×D3semidirect
347. #387D15semidirect
436. C3×C4⋊C4C4×D5semidirect
715. C4⋊C4C4×D15semidirect
728. C3×C5#2325semidirect
855. C5#75298semidirect
896. C3#10607029semidirect

Maximal subgroups

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

subgroupindex
C2×#917842
C2×#917822
C2×C4×D602
C3×C5×#3872
#117510902
#117510812
#117510412
#117507702
#117507692
#117507682
#117507662
D15×#952
#106070293
#752985