Finite Group Databasebeta

← #14326348

Subgroups — #14326348

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×#91473C211yesmaximal, characteristic
2C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#91402C211yesmaximal, characteristic, complemented
4C4×#6714C211yesmaximal, characteristic, complemented
5C5×#4940C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic, complemented
7#11748940C211yesmaximal, characteristic
8#11748890C211yesmaximal, characteristic, complemented
9#11748889C211yesmaximal, characteristic, complemented
10#11748884C211yesmaximal, characteristic, complemented
11#11748863C211yesmaximal, characteristic, complemented
12#11748794C211yesmaximal, characteristic, complemented
13#11748721C211yesmaximal, characteristic, complemented
14#11748714C211yesmaximal, characteristic, complemented
15#11748703C211yesmaximal, characteristic, complemented
16#10607564—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic, complemented
33C2×Dic3⋊Dic5C2211yescharacteristic, complemented
34C2×#6669C2211yescharacteristic, complemented
35C2×#6669C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44#91473C418yescomplemented
45D5×(C2×D3)⋊C4—24no—
46#91402—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#73574—51nomaximal, Hall
56C2×#4038—31no—
57C2×D5×C22⋊C4—31no—
58C2×D5×C22⋊C4—31no—
59C5×#388—31no—
60#65278—31no—
61#65244—31no—
62#65240—31no—
63#65234—31no—
64#65233—31no—
65C4×#685—31no—
66C4×#685D311yescharacteristic, complemented
67#64957—31no—
68#64956—31no—
69#64955—31no—
70#64953—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
87C2×C4×D15—41no—
88C2×C4×D15—41no—
89C2×C4×D15C2×C414yescomplemented
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
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×#1200—22no—
100C2×#1200—22no—
101C2×#1200C2×C414yescomplemented
102C2×D5×Dic3—22no—
103C2×D5×Dic3—22no—
104C2×D5×Dic3—41no—
105C3×C42×C5—41no—
106#6714—22no—
107#6714D414yes—
108C4×Dic15—41no—
109C5×(C2×D3)⋊C4—22no—
110C5×(C2×D3)⋊C4—41no—
111C5×(C2×D3)⋊C4C2×C414yescomplemented
112C5×Dic3⋊C4—22no—
113C3×#685—22no—
114C3×#685C2×C414yes—
115C3×C4×Dic5—22no—
116Dic3⋊Dic5—22no—
117#6669—41no—
118#6669—41no—
119#6667—22no—
120#6667—22no—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—41no—
123(C2×D3)⋊Dic5C2×C414yescomplemented
124#6665—22no—
125#6665C2×C414yes—
126Dic3×Dic5—22no—
127C22×(C2×D3)⋊C4—51no—
128C2×D3×C22⋊C4—51no—
129C2×#872—51no—
130C3×C4×C22⋊C4—51no—
131#5210—51no—
132#4955—51no—
133#4946—51no—
134Dic3×C22⋊C4—51no—
135#4940—51no—
136#4940D511yescharacteristic, complemented
137C4×(C2×D3)⋊C4—51no—
138#4669—51no—
139#4669—51no—
140#4667—51no—
141#4664—51no—
142C24×D5—31no—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C42×C5C2×D311yescharacteristic, complemented
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685C2×D311yescharacteristic
162C2×#685C2×D311yescharacteristic
163C2×C4⋊Dic5—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5C2×D311yescharacteristic, complemented
169#4038—64no—
170D5×C22⋊C4—38no—
171D5×C22⋊C4—64no—
172C5×#95—31no—
173C5×#95—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×D15C22×C412yes—
187C22×D15C2×D412yes—
188C22×D15#4112yes—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3C22×C412yes—
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×Dic15C22×C412yes—
227C2×Dic15C2×D412yes—
228C4×D15—44no—
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×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3C22×C412yes—
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—
248#1200—28no—
249D5×Dic3—44no—
250C24×D3—51no—
251C23×C3×C4—51no—
252C23×Dic3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
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—104no—
269C2×(C2×D3)⋊C4C2×D511yescharacteristic
270C2×(C2×D3)⋊C4C2×D511yescharacteristic
271C2×(C2×D3)⋊C4C2×D511yescharacteristic
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278D3×C22⋊C4—58no—
279#872—104no—
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
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—31no—
301C22×C4×C5C22×D311yescharacteristic
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×C4×D5—22no—
311C2×C4×D5—22no—
312C2×C4×D5—34no—
313C2×C4×D5—34no—
314C2×C4×D5—41no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—62no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—62no—
325C5×C22⋊C4—121no—
326C42×C5—41no—
327C22⋊Dic5—34no—
328C22⋊Dic5—62no—
329C22⋊Dic5—121no—
330#685—22no—
331#685—34no—
332#685—34no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685—62no—
337#685C4×D314yes—
338C4⋊Dic5—62no—
339#683—121no—
340#683—121no—
341C4×Dic5—22no—
342C4×Dic5—62no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—31no—
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—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15C4×D414yes—
373C2×C5×D3—22no—
374C2×C5×D3—22no—
375C2×C5×D3—22no—
376C2×C5×D3—41no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
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—22no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—41no—
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—54no—
429C2×C4×D3—54no—
430C2×C4×D3—102no—
431C2×C4×D3—102no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C22⋊C4—54no—
435C3×C22⋊C4—102no—
436C3×C42—41no—
437C3×C42—102no—
438#217—54no—
439#217—102no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—41no—
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—102no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—102no—
448(C2×D3)⋊C4—201no—
449(C2×D3)⋊C4C4×D514yescomplemented
450Dic3⋊C4—22no—
451Dic3⋊C4—102no—
452Dic3⋊C4—201no—
453Dic3⋊C4—201no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—32no—
457C23×C5—61no—
458C23×C5—61no—
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—32no—
470C22×D5—32no—
471C22×D5—68no—
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—61no—
494C2×C4×C5—61no—
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×C5C2×C4×D312yes—
502C2×C4×C5D3×D412yes—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—32no—
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×Dic5C2×C4×D312yes—
521C4×D5—44no—
522C4×D5—68no—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—51no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—158no—
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—51no—
552C2×C42—151no—
553C2×C42—151no—
554C2×C42D3×D511yescharacteristic, complemented
555#95—31no—
556#95—31no—
557#95—51no—
558#95—51no—
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—24no—
571C3×D5—24no—
572C5×D3—42no—
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—21no—
586C22×D3—21no—
587C22×D3—52no—
588C22×D3—52no—
589C22×D3—52no—
590C22×D3—108no—
591C22×D3—108no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—204no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3C2×C4×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×C4D4×D512yes—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—204no—
639C2×Dic3C2×C4×D512yes—
640C4×D3—108no—
641C4×D3—204no—
642C22×C5—62no—
643C22×C5—62no—
644C22×C5—62no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
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—34no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—1216no—
670C2×D5#87214yescomplemented
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—41no—
674C4×C5—62no—
675C4×C5—121no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—41no—
679Dic5—41no—
680Dic5—62no—
681Dic5—62no—
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—31no—
696C22×C4—51no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—102no—
700C22×C4—102no—
701C22×C4—154no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—154no—
705C22×C4—151no—
706C22×C4—201no—
707C22×C4—302no—
708C22×C4—302no—
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—302no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—54no—
723C22⋊C4—62no—
724C22⋊C4—102no—
725C22⋊C4—121no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—302no—
734C22⋊C4—601no—
735C42—41no—
736C42—102no—
737C42—302no—
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×D4×D511yescharacteristic
749C22×C3#414411yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3D5×#4111yescharacteristic
752C22×C3D5×#4111yescharacteristic
753C22×C3#414911yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—54no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—102no—
768C2×D3—2016no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—41no—
772C3×C4—102no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—41no—
777Dic3—41no—
778Dic3—102no—
779Dic3—102no—
780Dic3—201no—
781C2×C5—122no—
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—64no—
791C23—32no—
792C23—52no—
793C23—52no—
794C23—52no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—152no—
806C23—152no—
807C23—152no—
808C23—308no—
809C23—308no—
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—52no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—101no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—152no—
846C2×C4—152no—
847C2×C4—204no—
848C2×C4—308no—
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×C4#677712yes—
860C2×C3—104no—
861C2×C3D5×#11711yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6594411yescharacteristic
865C2×C3#6599311yescharacteristic
866C2×C3#6601011yescharacteristic
867C2×C3#6603911yescharacteristic
868D3—42no—
869D3—104no—
870C5#7357411yescharacteristic, complemented, Sylow
871C22—54no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—102no—
876C22—102no—
877C22—102no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—154no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22C2×C4×D3×D511yescharacteristic
894C22C2×#677711yescharacteristic
895C22D5×#23511yescharacteristic
896C22D5×#23511yescharacteristic
897C22#9201611yescharacteristic
898C22#9201911yescharacteristic
899C22#9204911yescharacteristic
900C4—22no—
901C4—22no—
902C4—41no—
903C4—62no—
904C4—102no—
905C4—121no—
906C4—121no—
907C4—201no—
908C4—201no—
909C4—302no—
910C4—302no—
911C4—601no—
912C3#1060756411yescharacteristic, complemented, Sylow
913C2—104no—
914C2—122no—
915C2—304no—
916C2D5×#87211yescharacteristic
917C2C4×#677711yescharacteristic
918C2#1175274811yescharacteristic
919C2#1175276111yescharacteristic
920C2#1175462911yescharacteristic
921C2#1175467211yescharacteristic
922C2#1175467811yescharacteristic
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
3. C2×#91402C2semidirect
4. C4×#6714C2semidirect
5. C5×#4940C2semidirect
6. C3×C4×#685C2semidirect
8. #11748890C2semidirect
9. #11748889C2semidirect
10. #11748884C2semidirect
11. #11748863C2semidirect
12. #11748794C2semidirect
13. #11748721C2semidirect
14. #11748714C2semidirect
15. #11748703C2semidirect
22. C2×C3×C42×C5C22semidirect
25. C2×C4×Dic15C22semidirect
29. C2×C5×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic5C22semidirect
33. C2×Dic3⋊Dic5C22semidirect
34. C2×#6669C22semidirect
35. C2×#6669C22semidirect
43. C2×Dic3×Dic5C22semidirect
44. #91473C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
66. C4×#685D3semidirect
89. C2×C4×D15C2×C4semidirect
101. C2×#1200C2×C4semidirect
111. C5×(C2×D3)⋊C4C2×C4semidirect
123. (C2×D3)⋊Dic5C2×C4semidirect
136. #4940D5semidirect
151. C2×C42×C5C2×D3semidirect
168. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
258. C2×C3×C42C2×D5semidirect
275. C2×Dic3⋊C4C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
386. C2×C3×D5#117semidirect
449. (C2×D3)⋊C4C4×D5semidirect
554. C2×C42D3×D5semidirect
670. C2×D5#872semidirect
739. C3×C5#2342semidirect
870. C5#73574semidirect
912. C3#10607564semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#914022
C4×#67142
C5×#49402
C3×C4×#6852
#117489402
#117488902
#117488892
#117488842
#117488632
#117487942
#117487212
#117487142
#117487032
#106075643
#735745