Finite Group Databasebeta

← #14326331

Subgroups — #14326331

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×#892C211yesmaximal, characteristic, complemented
2C2×D3×#685C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4#11751091C211yesmaximal, characteristic, complemented
5C3×#65278C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic
7#11748899C211yesmaximal, characteristic, complemented
8#11748886C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10#11748874C211yesmaximal, characteristic, complemented
11#11748777C211yesmaximal, characteristic, complemented
12#11748730C211yesmaximal, characteristic, complemented
13#11748728C211yesmaximal, characteristic, complemented
14C4×#6665C211yesmaximal, characteristic, complemented
15#11748685C211yesmaximal, 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×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C5×#892—24no—
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic, complemented
36C2×#6668C2211yescharacteristic, 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#74595—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#65278D311yescharacteristic, complemented
64#65244—31no—
65#65231—31no—
66C22⋊C4×Dic5—31no—
67#65229—31no—
68#65229—31no—
69C4×#685—31no—
70C4×#685—31no—
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×C5×C4⋊C4—22no—
106#6714—22no—
107#6714—41no—
108#6714C2×C414yescomplemented
109C4×Dic15—41no—
110C5×(C2×D3)⋊C4—22no—
111C5×(C2×D3)⋊C4D414yes—
112C5×C4⋊Dic3—22no—
113C4×C5×Dic3—22no—
114C4×C5×Dic3—22no—
115C3×#685—22no—
116C3×#685C2×C414yes—
117C3×#683—41no—
118#6668—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×#892D511yescharacteristic, complemented
129C2×D3×C22⋊C4—51no—
130C3×#385—51no—
131C4×#217—51no—
132#4990—51no—
133#4990—51no—
134#4987—51no—
135#4955—51no—
136#4950—51no—
137Dic3×C22⋊C4—51no—
138#4670—51no—
139#4670—51no—
140#4666—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⋊C4C2×D311yescharacteristic, complemented
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C42×C5—31no—
153C2×C42×C5—31no—
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×#683C2×D311yescharacteristic, complemented
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
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×C4⋊C4—51no—
256C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
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×C4⋊Dic3—51no—
273C2×C4⋊Dic3C2×D511yescharacteristic, complemented
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3C2×D511yescharacteristic, complemented
277C2×C4×Dic3C2×D511yescharacteristic, complemented
278#892—24no—
279D3×C22⋊C4—58no—
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—22no—
323C5×C4⋊C4—62no—
324C5×C22⋊C4—34no—
325C5×C22⋊C4—62no—
326C42×C5—62no—
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—41no—
341#683—121no—
342C4×Dic5—121no—
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—51no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
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×C4⋊C4—22no—
435C3×C4⋊C4—201no—
436C3×C22⋊C4—54no—
437C3×C22⋊C4—102no—
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—
450C4⋊Dic3—22no—
451C4⋊Dic3—201no—
452C4×Dic3—22no—
453C4×Dic3—22no—
454C4×Dic3—201no—
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#23712yes—
484C22×D5#23912yes—
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—51no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4D3×D511yescharacteristic, complemented
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—31no—
553C2×C42—151no—
554C2×C42—151no—
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×D3×D411yescharacteristic
651C22×C5C2×#23711yescharacteristic
652C22×C5#100411yescharacteristic
653C22×C5C2×#23911yescharacteristic
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#89214yescomplemented
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—22no—
718C4⋊C4—62no—
719C4⋊C4—201no—
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—62no—
736C42—62no—
737C42—601no—
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×#89211yescharacteristic
783C2×C5C4×D3×D411yescharacteristic
784C2×C5#554511yescharacteristic
785C2×C5#559111yescharacteristic
786C2×C5#563011yescharacteristic
787C2×C5#563711yescharacteristic
788C2×C5#565811yescharacteristic
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#7459511yescharacteristic, 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
894C22D3×#70911yescharacteristic
895C22D5×#23711yescharacteristic
896C22#9202611yescharacteristic
897C22D5×#23911yescharacteristic
898C22#9203511yescharacteristic
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×#89211yescharacteristic
917C2#1175383911yescharacteristic
918C2#1175390311yescharacteristic
919C2#1175391011yescharacteristic
920C2C4×D3×C22⋊D511yescharacteristic
921C2#1175506611yescharacteristic
922C2#1175527711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#892C2semidirect
4. #11751091C2semidirect
5. C3×#65278C2semidirect
7. #11748899C2semidirect
8. #11748886C2semidirect
9. Dic3×#685C2semidirect
10. #11748874C2semidirect
11. #11748777C2semidirect
12. #11748730C2semidirect
13. #11748728C2semidirect
14. C4×#6665C2semidirect
15. #11748685C2semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
31. C2×C4×C5×Dic3C22semidirect
35. C2×C3×#683C22semidirect
36. C2×#6668C22semidirect
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
63. #65278D3semidirect
92. C2×C4×C5×D3C2×C4semidirect
101. C2×D3×Dic5C2×C4semidirect
108. #6714C2×C4semidirect
121. #6667C2×C4semidirect
128. C2×#892D5semidirect
149. C2×C5×C4⋊C4C2×D3semidirect
168. C2×#683C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
256. C2×C3×C4⋊C4C2×D5semidirect
273. C2×C4⋊Dic3C2×D5semidirect
276. C2×C4×Dic3C2×D5semidirect
277. C2×C4×Dic3C2×D5semidirect
386. C2×C3×D5#117semidirect
433. C2×C4×D3C4×D5semidirect
534. C2×C4⋊C4D3×D5semidirect
670. C2×D5#892semidirect
739. C3×C5#2342semidirect
870. C5#74595semidirect
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×#8922
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
#117510912
C3×#652782
#117489402
#117488992
#117488862
Dic3×#6852
#117488742
#117487772
#117487302
#117487282
C4×#66652
#117486852
#106140023
#745955