Finite Group Databasebeta

← #14326259

Subgroups — #14326259

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#872C211yesmaximal, characteristic, complemented
2C2×D3×#685C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4#11751041C211yesmaximal, characteristic, complemented
5C3×C4×#685C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic
7#11748891C211yesmaximal, characteristic, complemented
8#11748887C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11748854C211yesmaximal, characteristic, complemented
12#11748777C211yesmaximal, characteristic, complemented
13#11748727C211yesmaximal, characteristic, complemented
14#11748703C211yesmaximal, characteristic, complemented
15#11748669C211yesmaximal, characteristic, complemented
16#10614002—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C5×#872—24no—
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45D3×#685C418yescomplemented
46D5×(C2×D3)⋊C4—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#73574—51nomaximal, Hall
56C2×C5×#117—31no—
57C22×#685—31no—
58C2×D5×C22⋊C4—31no—
59#65500—31no—
60#65279—31no—
61#65279—31no—
62#65278—31no—
63#65278—31no—
64#65244—31no—
65#65231—31no—
66C22⋊C4×Dic5—31no—
67#65229—31no—
68#65229—31no—
69C4×#685—31no—
70C4×#685D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×D3×D5—22no—
75C22×D3×D5—22no—
76C22×D3×D5—22no—
77C22×D3×D5—22no—
78C22×D3×D5—41no—
79C22×D3×D5—41no—
80C22×D3×D5C2×C414yes—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3C2×C414yescomplemented
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—41no—
99C2×D3×Dic5—41no—
100C2×D3×Dic5—41no—
101C2×D3×Dic5C2×C414yescomplemented
102C2×D5×Dic3—22no—
103C2×D5×Dic3—22no—
104C2×D5×Dic3—41no—
105C3×C42×C5—22no—
106#6714—22no—
107#6714—41no—
108#6714C2×C414yescomplemented
109#6712—41no—
110C5×(C2×D3)⋊C4—22no—
111C5×(C2×D3)⋊C4D414yes—
112C5×Dic3⋊C4—22no—
113C5×Dic3⋊C4—22no—
114C4×C5×Dic3—22no—
115C3×#685—22no—
116C3×#685C2×C414yes—
117C3×C4×Dic5—41no—
118#6669—41no—
119#6667—22no—
120#6667—41no—
121#6667C2×C414yescomplemented
122(C2×D3)⋊Dic5—22no—
123(C2×D3)⋊Dic5—22no—
124#6665—22no—
125#6665C2×C414yes—
126Dic3×Dic5—41no—
127C22×(C2×D3)⋊C4—51no—
128C2×D3×C22⋊C4—51no—
129C2×#872D511yescharacteristic, complemented
130C3×C4×C22⋊C4—51no—
131#5210—51no—
132#4955—51no—
133#4946—51no—
134Dic3×C22⋊C4—51no—
135#4940—51no—
136#4940—51no—
137C4×(C2×D3)⋊C4—51no—
138#4669—51no—
139#4669—51no—
140#4667—51no—
141#4664—51no—
142C24×D5—31no—
143C23×C4×C5—31no—
144C23×Dic5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C5×#117—64no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C42×C5—31no—
153C2×C42×C5C2×D311yescharacteristic, complemented
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—38no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×#683—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5C2×D311yescharacteristic, complemented
171D5×C22⋊C4—64no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic, complemented
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15C22×C412yes—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3C22×C412yes—
194C22×C5×D3C2×D412yes—
195C22×C5×D3#4112yes—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5C22×C412yes—
201C22×C3×D5#4112yes—
202C22×C3×D5#4112yes—
203C2×D3×D5—28no—
204C2×D3×D5—28no—
205C2×D3×D5—44no—
206C2×D3×D5—44no—
207C2×D3×D5—44no—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
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×C5C22×C412yes—
218C2×C3×C4×C5C2×D412yes—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3C22×C412yes—
236C2×C5×Dic3C2×D412yes—
237C4×C5×D3—28no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5C22×C412yes—
247C3×C4×D5—44no—
248D3×Dic5—44no—
249D5×Dic3—44no—
250C24×D3—51no—
251C23×C3×C4—51no—
252C23×Dic3—51no—
253C22×C4×D3—51no—
254C22×C4×D3C2×D511yescharacteristic
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C42—51no—
258C2×C3×C42C2×D511yescharacteristic, complemented
259C2×#217—51no—
260C2×#217—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×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—104no—
270C2×(C2×D3)⋊C4C2×D511yescharacteristic
271C2×(C2×D3)⋊C4C2×D511yescharacteristic
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4C2×D511yescharacteristic, complemented
275C2×Dic3⋊C4C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3C2×D511yescharacteristic, complemented
278D3×C22⋊C4—58no—
279#872—24no—
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C23×D5—31no—
290C23×D5—34no—
291C23×D5—62no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—34no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—31no—
308C22×Dic5—34no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—121no—
312C22×Dic5—121no—
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—22no—
317C2×C4×D5—22no—
318C2×C4×D5—41no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—121no—
322C5×C4⋊C4—62no—
323C5×C4⋊C4—62no—
324C5×C22⋊C4—34no—
325C5×C22⋊C4—62no—
326C42×C5—22no—
327C42×C5—62no—
328C22⋊Dic5—62no—
329C22⋊Dic5—62no—
330#685—22no—
331#685—34no—
332#685—34no—
333#685—34no—
334#685—62no—
335#685—62no—
336#685—62no—
337#685—121no—
338#685—121no—
339#685C4×D314yes—
340#683—121no—
341#683—121no—
342C4×Dic5—41no—
343C4×Dic5—121no—
344C2×#117—31no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—151no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—51no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5C23×C411yescharacteristic
360C22×C3×C5C22×D411yescharacteristic
361C22×C3×C5C2×#4111yescharacteristic
362C22×C3×C5C2×#4111yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C2×D15—22no—
367C2×D15—22no—
368C2×D15—22no—
369C2×D15—41no—
370C2×D15—41no—
371C2×D15—41no—
372C2×D15—41no—
373C2×C5×D3—22no—
374C2×C5×D3—22no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3C4×D414yes—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5#11714yescomplemented
387D3×D5—416no—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390C3×C4×C5—41no—
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3—51no—
401C23×D3—51no—
402C23×D3—54no—
403C23×D3—102no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—201no—
408C23×D3—201no—
409C23×D3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—102no—
414C22×C3×C4—102no—
415C22×C3×C4—201no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3—51no—
422C22×Dic3—102no—
423C22×Dic3—102no—
424C22×Dic3—201no—
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C22×Dic3C22×D511yescharacteristic
428C2×C4×D3—22no—
429C2×C4×D3—22no—
430C2×C4×D3—54no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3C4×D514yescomplemented
434C3×C22⋊C4—54no—
435C3×C22⋊C4—102no—
436C3×C42—22no—
437C3×C42—201no—
438#217—54no—
439#217—102no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—54no—
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—102no—
444(C2×D3)⋊C4—102no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—201no—
448(C2×D3)⋊C4—201no—
449(C2×D3)⋊C4C22⋊D514yes—
450Dic3⋊C4—22no—
451Dic3⋊C4—22no—
452Dic3⋊C4—201no—
453Dic3⋊C4—201no—
454C4×Dic3—22no—
455C4×Dic3—201no—
456C23×C5—32no—
457C23×C5—32no—
458C23×C5—32no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—61no—
462C23×C5—61no—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—32no—
469C22×D5—68no—
470C22×D5—61no—
471C22×D5—61no—
472C22×D5—61no—
473C22×D5—61no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—68no—
477C22×D5—124no—
478C22×D5—124no—
479C22×D5—124no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5C2×C4×D312yes—
483C22×D5#23512yes—
484C22×D5#23512yes—
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×C5—21no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
494C2×C4×C5—68no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5C2×C4×D312yes—
503C2×C4×C5D3×D412yes—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—32no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—124no—
522C2×Dic5C2×C4×D312yes—
523C4×D5—44no—
524C4×D5—124no—
525C25—151no—
526C23×C4—31no—
527C23×C4—51no—
528C23×C4—151no—
529C23×C4—151no—
530#117—64no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—158no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—151no—
550C2×C22⋊C4—304no—
551C2×C42—31no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42D3×D511yescharacteristic, complemented
555#95—51no—
556#95—51no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5C2×#11711yescharacteristic
564C2×C3×C5C2×C4×D411yescharacteristic
565C2×C3×C5#51811yescharacteristic
566C2×C3×C5#54611yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#55111yescharacteristic
569C2×C3×C5#55111yescharacteristic
570D15—42no—
571C3×D5—24no—
572C5×D3—24no—
573C23×C3—52no—
574C23×C3—52no—
575C23×C3—52no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3C23×D511yescharacteristic
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—52no—
586C22×D3—108no—
587C22×D3—101no—
588C22×D3—101no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—108no—
594C22×D3—204no—
595C22×D3—204no—
596C22×D3—204no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3C2×C4×D512yes—
600C22×D3#70912yes—
601C22×D3C2×C22⋊D512yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—52no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—204no—
619C2×C3×C4C2×C4×D512yes—
620C2×C3×C4C2×C22⋊D512yes—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—52no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—204no—
638C2×Dic3C2×C4×D512yes—
639C2×Dic3C2×C22⋊D512yes—
640C4×D3—28no—
641C4×D3—204no—
642C22×C5—34no—
643C22×C5—62no—
644C22×C5—62no—
645C22×C5—62no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×#23511yescharacteristic
651C22×C5C2×#23511yescharacteristic
652C22×C5C2×D3×D411yescharacteristic
653C22×C5#100411yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—1216no—
666C2×D5—121no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5#87214yescomplemented
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—41no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—41no—
679Dic5—41no—
680Dic5—62no—
681Dic5—121no—
682Dic5—121no—
683C24—31no—
684C24—51no—
685C24—154no—
686C24—151no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—302no—
691C24—601no—
692C24—601no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—102no—
703C22×C4—102no—
704C22×C4—154no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—201no—
709C22×C4—302no—
710C22×C4—302no—
711C22×C4—601no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—54no—
723C22⋊C4—62no—
724C22⋊C4—102no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—601no—
734C22⋊C4—601no—
735C42—22no—
736C42—62no—
737C42—201no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—54no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3C22×C4×D511yescharacteristic
748C22×C3C2×#70911yescharacteristic
749C22×C3D5×#4111yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3#414911yescharacteristic
752C22×C3#414911yescharacteristic
753C22×C3C22×C22⋊D511yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—2016no—
764C2×D3—201no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3C4×C22⋊D514yes—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—41no—
772C3×C4—102no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—41no—
778Dic3—102no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—64no—
782C2×C5C2×#87211yescharacteristic
783C2×C5#549011yescharacteristic
784C2×C5#552711yescharacteristic
785C2×C5C4×D3×D411yescharacteristic
786C2×C5#554511yescharacteristic
787C2×C5#555011yescharacteristic
788C2×C5#555611yescharacteristic
789D5—24no—
790D5—122no—
791C23—32no—
792C23—32no—
793C23—32no—
794C23—52no—
795C23—52no—
796C23—52no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—152no—
806C23—308no—
807C23—308no—
808C23—301no—
809C23—301no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—301no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23—604no—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—52no—
830C2×C4—68no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—152no—
847C2×C4—204no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—604no—
857C2×C4—604no—
858C2×C4C4×D3×D512yes—
859C2×C4D3×C22⋊D512yes—
860C2×C3—104no—
861C2×C3D5×#11711yescharacteristic
862C2×C3#6585511yescharacteristic
863C2×C3#6586111yescharacteristic
864C2×C3#6586111yescharacteristic
865C2×C3C2×C4×C22⋊D511yescharacteristic
866C2×C3#6616311yescharacteristic
867C2×C3#6616311yescharacteristic
868D3—24no—
869D3—202no—
870C5#7357411yescharacteristic, complemented, Sylow
871C22—34no—
872C22—54no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—102no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—302no—
886C22—302no—
887C22—302no—
888C22—6016no—
889C22—601no—
890C22—601no—
891C22—601no—
892C22—601no—
893C22C2×C4×D3×D511yescharacteristic
894C22D5×#23511yescharacteristic
895C22D5×#23511yescharacteristic
896C22D3×#70911yescharacteristic
897C22#9201711yescharacteristic
898C22#9201911yescharacteristic
899C22C2×D3×C22⋊D511yescharacteristic
900C4—22no—
901C4—22no—
902C4—41no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—121no—
907C4—201no—
908C4—201no—
909C4—302no—
910C4—601no—
911C4—601no—
912C3#1061400211yescharacteristic, complemented, Sylow
913C2—64no—
914C2—104no—
915C2—602no—
916C2D5×#87211yescharacteristic
917C2#1175272711yescharacteristic
918C2#1175275711yescharacteristic
919C2#1175275911yescharacteristic
920C2C4×D3×C22⋊D511yescharacteristic
921C2#1175465011yescharacteristic
922C2#1175465111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C5×#872C2semidirect
4. #11751041C2semidirect
5. C3×C4×#685C2semidirect
7. #11748891C2semidirect
8. #11748887C2semidirect
9. Dic3×#685C2semidirect
10. Dic5×(C2×D3)⋊C4C2semidirect
11. #11748854C2semidirect
12. #11748777C2semidirect
13. #11748727C2semidirect
14. #11748703C2semidirect
15. #11748669C2semidirect
22. C2×C3×C42×C5C22semidirect
26. C2×#6712C22semidirect
29. C2×C5×Dic3⋊C4C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
31. C2×C4×C5×Dic3C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C2×#6669C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. D3×#685C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
70. C4×#685D3semidirect
92. C2×C4×C5×D3C2×C4semidirect
101. C2×D3×Dic5C2×C4semidirect
108. #6714C2×C4semidirect
121. #6667C2×C4semidirect
129. C2×#872D5semidirect
153. C2×C42×C5C2×D3semidirect
170. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
258. C2×C3×C42C2×D5semidirect
274. C2×Dic3⋊C4C2×D5semidirect
275. C2×Dic3⋊C4C2×D5semidirect
277. C2×C4×Dic3C2×D5semidirect
386. C2×C3×D5#117semidirect
433. C2×C4×D3C4×D5semidirect
554. C2×C42D3×D5semidirect
670. C2×D5#872semidirect
739. C3×C5#2342semidirect
870. C5#73574semidirect
912. C3#10614002semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
#117510412
C3×C4×#6852
#117489402
#117488912
#117488872
Dic3×#6852
Dic5×(C2×D3)⋊C42
#117488542
#117487772
#117487272
#117487032
#117486692
#106140023
#735745