Finite Group Databasebeta

← #14326359

Subgroups — #14326359

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×#91561C211yesmaximal, characteristic
2C2×#91561C211yesmaximal, characteristic
3C2×#91403C211yesmaximal, characteristic, complemented
4#11751056C211yesmaximal, characteristic
5C5×#4945C211yesmaximal, characteristic, complemented
6C3×#65233C211yesmaximal, characteristic, complemented
7#11749486C211yesmaximal, characteristic, complemented
8#11749478C211yesmaximal, characteristic, complemented
9#11748895C211yesmaximal, characteristic, complemented
10#11748894C211yesmaximal, characteristic, complemented
11#11748889C211yesmaximal, characteristic, complemented
12#11748882C211yesmaximal, characteristic, complemented
13#11748881C211yesmaximal, characteristic, complemented
14#11748875C211yesmaximal, characteristic, complemented
15#11748875C211yesmaximal, characteristic, complemented
16#10607563—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic, complemented
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36#91561—24no—
37#91561C418yescomplemented
38C2×Dic3⋊Dic5C2211yescharacteristic, complemented
39C2×#6668C2211yescharacteristic, complemented
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91403—24no—
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75833—51nomaximal, Hall
56C2×D5×C22⋊C4—31no—
57C2×D5×C22⋊C4—31no—
58C2×#4018—31no—
59C5×#388—31no—
60#65278—31no—
61#65276—31no—
62#65244—31no—
63#65240—31no—
64#65234—31no—
65#65233D311yescharacteristic, complemented
66C4×#685—31no—
67#64957—31no—
68#64955—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15—22no—
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15C2×C414yes—
79C23×D15C2311yescharacteristic
80C23×D15C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×#1200—22no—
94C2×#1200—22no—
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98C2×#1200—22no—
99C2×#1200—41no—
100C2×#1200—41no—
101C2×#1200—41no—
102C2×#1200—41no—
103C2×#1200C2×C414yescomplemented
104C2×#1200C2×C414yescomplemented
105C3×C5×C22⋊C4—41no—
106#6719—41no—
107#6714—22no—
108#6714—22no—
109#6714—22no—
110#6714—22no—
111C5×#217—22no—
112C5×#217C2×C414yescomplemented
113C5×Dic3⋊C4—41no—
114C4×C5×Dic3—22no—
115C3×C22⋊Dic5—22no—
116C3×C22⋊Dic5C2×C414yescomplemented
117C3×#683—22no—
118C3×C4×Dic5—41no—
119Dic3⋊Dic5—41no—
120#6668—22no—
121#6667—22no—
122#6667C2×C414yes—
123#6667C2×C414yes—
124#6667D414yes—
125Dic3×Dic5—22no—
126Dic3×Dic5—41no—
127C2×#892—51no—
128C2×D3×C22⋊C4—51no—
129C2×D3×C22⋊C4—51no—
130C3×#388—51no—
131#4989—51no—
132#4955—51no—
133#4951—51no—
134#4945D511yescharacteristic, complemented
135#4944—51no—
136C4×(C2×D3)⋊C4—51no—
137C4×(C2×D3)⋊C4—51no—
138#4668—51no—
139#4667—51no—
140#4666—51no—
141#4664—51no—
142C24×D5—31no—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5C2×D311yescharacteristic
154C2×C22⋊Dic5C2×D311yescharacteristic
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×#683C2×D311yescharacteristic, complemented
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5C2×D311yescharacteristic, complemented
169D5×C22⋊C4—38no—
170D5×C22⋊C4—64no—
171#4018—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×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
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—28no—
198C22×D15—28no—
199C22×D15—44no—
200C22×D15—44no—
201C22×D15—44no—
202C22×D15—44no—
203C22×D15—44no—
204C22×D15C22×C412yes—
205C22×D15C22×C412yes—
206C22×D15C2×D412yes—
207C22×D15#4112yes—
208C22×D15#4112yes—
209C22×D15#4112yes—
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×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3C22×C412yes—
232C2×C5×Dic3C22×C412yes—
233C2×C5×Dic3C2×D412yes—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5C22×C412yes—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C2×D412yes—
246#1200—28no—
247#1200—44no—
248#1200—44no—
249#1200—44no—
250C24×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42—51no—
260C2×#217—51no—
261C2×#217C2×D511yescharacteristic
262C2×#217C2×D511yescharacteristic
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—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4C2×D511yescharacteristic, complemented
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3C2×D511yescharacteristic, complemented
277#892—104no—
278D3×C22⋊C4—58no—
279D3×C22⋊C4—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×C5C22×D311yescharacteristic
289C23×D5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—62no—
296C23×D5—121no—
297C23×D5—121no—
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5C22×D311yescharacteristic
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×C4×D5—34no—
311C2×C4×D5—34no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—121no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—41no—
325C5×C22⋊C4—62no—
326C42×C5—62no—
327C22⋊Dic5—22no—
328C22⋊Dic5—121no—
329C22⋊Dic5C4×D314yescomplemented
330#685—34no—
331#685—34no—
332#685—34no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685—62no—
337#685—62no—
338C4⋊Dic5—121no—
339#683—22no—
340#683—62no—
341C4×Dic5—41no—
342C4×Dic5—62no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—31no—
348#388—51no—
349#388—151no—
350#388—151no—
351#385—151no—
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×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×D15—22no—
374C2×D15—22no—
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—416no—
386C2×D15#11714yescomplemented
387C2×D15C4×D414yes—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390Dic15—41no—
391Dic15—41no—
392C3×Dic5—22no—
393C3×Dic5—22no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C5×Dic3—22no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3C22×D511yescharacteristic
401C23×D3—51no—
402C23×D3—51no—
403C23×D3—54no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—102no—
408C23×D3—201no—
409C23×D3—201no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—54no—
423C2×C4×D3—54no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C4⋊C4—102no—
435C3×C22⋊C4—41no—
436C3×C22⋊C4—54no—
437C3×C22⋊C4—102no—
438C3×C42—201no—
439#217—22no—
440#217—201no—
441#217C4×D514yescomplemented
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—54no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—102no—
448(C2×D3)⋊C4—102no—
449(C2×D3)⋊C4—102no—
450C4⋊Dic3—102no—
451Dic3⋊C4—41no—
452Dic3⋊C4—201no—
453C4×Dic3—22no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C2×C4×D312yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—32no—
465C22×D5—32no—
466C22×D5—32no—
467C22×D5—32no—
468C22×D5—32no—
469C22×D5—32no—
470C22×D5—68no—
471C22×D5—68no—
472C22×D5—61no—
473C22×D5—61no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—61no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5—124no—
483C22×D5—124no—
484C22×D5—124no—
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—32no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
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×C5—61no—
502C2×C4×C5—61no—
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—21no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5C2×C4×D312yes—
519C2×Dic5C2×C4×D312yes—
520C2×Dic5D3×D412yes—
521C4×D5—68no—
522C4×D5—124no—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—151no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—51no—
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—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—31no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42—151no—
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×C5—42no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571D15—24no—
572D15—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3C2×C4×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—52no—
583C22×D3—52no—
584C22×D3—52no—
585C22×D3—52no—
586C22×D3—52no—
587C22×D3—108no—
588C22×D3—108no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—101no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3—204no—
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—52no—
609C2×C3×C4—52no—
610C2×C3×C4—52no—
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—101no—
619C2×C3×C4—101no—
620C2×Dic3—21no—
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—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3C2×C4×D512yes—
636C2×Dic3C2×C4×D512yes—
637C2×Dic3D4×D512yes—
638C4×D3—108no—
639C4×D3—204no—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×D3×D411yescharacteristic
651C22×C5#100411yescharacteristic
652C22×C5D3×#4111yescharacteristic
653C22×C5D3×#4111yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—34no—
657C2×D5—34no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—62no—
670C2×D5—1216no—
671C4×C5—41no—
672C4×C5—41no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—41no—
681Dic5—121no—
682Dic5—121no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—302no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—601no—
691C24—601no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—154no—
702C22×C4—154no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—302no—
706C22×C4—302no—
707C22×C4—302no—
708C22×C4—302no—
709C22×C4—302no—
710C22×C4—302no—
711C22×C4—601no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—102no—
718C4⋊C4—121no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—41no—
723C22⋊C4—54no—
724C22⋊C4—62no—
725C22⋊C4—102no—
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—62no—
736C42—201no—
737C42—302no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
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—54no—
755C2×D3—54no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—102no—
768C2×D3—2016no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—102no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—41no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—42no—
782C2×C5D3×#11711yescharacteristic
783C2×C5C4×D3×D411yescharacteristic
784C2×C5#554511yescharacteristic
785C2×C5#561011yescharacteristic
786C2×C5#565911yescharacteristic
787C2×C5#567611yescharacteristic
788C2×C5#570511yescharacteristic
789D5—64no—
790D5—64no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—152no—
798C23—152no—
799C23—152no—
800C23—152no—
801C23—152no—
802C23—152no—
803C23—308no—
804C23—308no—
805C23—301no—
806C23—301no—
807C23—301no—
808C23—301no—
809C23—301no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—604no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23C4×D3×D512yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—52no—
830C2×C4—52no—
831C2×C4—52no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—308no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—604no—
858C2×C4—604no—
859C2×C4—604no—
860C2×C3—42no—
861C2×C3D5×#11711yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6594611yescharacteristic
865C2×C3#6598811yescharacteristic
866C2×C3#6601311yescharacteristic
867C2×C3#6603911yescharacteristic
868D3—104no—
869D3—104no—
870C5#7583311yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—154no—
879C22—154no—
880C22—302no—
881C22—302no—
882C22—302no—
883C22—302no—
884C22—302no—
885C22—302no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22C2×C4×D3×D511yescharacteristic
894C22#9201911yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22#9202411yescharacteristic
897C22#9202411yescharacteristic
898C22#9202411yescharacteristic
899C22#9204911yescharacteristic
900C4—41no—
901C4—41no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—102no—
907C4—102no—
908C4—121no—
909C4—201no—
910C4—601no—
911C4—601no—
912C3#1060756311yescharacteristic, complemented, Sylow
913C2—42no—
914C2—304no—
915C2—304no—
916C2#1175282511yescharacteristic
917C2#1175303311yescharacteristic
918C2#1175320311yescharacteristic
919C2#1175326011yescharacteristic
920C2#1175462911yescharacteristic
921C2#1175489811yescharacteristic
922C2#1175504311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#91403C2semidirect
5. C5×#4945C2semidirect
6. C3×#65233C2semidirect
7. #11749486C2semidirect
8. #11749478C2semidirect
9. #11748895C2semidirect
10. #11748894C2semidirect
11. #11748889C2semidirect
12. #11748882C2semidirect
13. #11748881C2semidirect
14. #11748875C2semidirect
15. #11748875C2semidirect
30. C2×C5×Dic3⋊C4C22semidirect
31. C2×C4×C5×Dic3C22semidirect
34. C2×C3×#683C22semidirect
35. C2×C3×C4×Dic5C22semidirect
37. #91561C4semidirect
38. C2×Dic3⋊Dic5C22semidirect
39. C2×#6668C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
65. #65233D3semidirect
103. C2×#1200C2×C4semidirect
104. C2×#1200C2×C4semidirect
112. C5×#217C2×C4semidirect
116. C3×C22⋊Dic5C2×C4semidirect
134. #4945D5semidirect
165. C2×#683C2×D3semidirect
168. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
273. C2×Dic3⋊C4C2×D5semidirect
276. C2×C4×Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
329. C22⋊Dic5C4×D3semidirect
386. C2×D15#117semidirect
441. #217C4×D5semidirect
739. C3×C5#2342semidirect
870. C5#75833semidirect
912. C3#10607563semidirect

Maximal subgroups

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

subgroupindex
C2×#915612
C2×#914032
#117510562
C5×#49452
C3×#652332
#117494862
#117494782
#117488952
#117488942
#117488892
#117488822
#117488812
#117488752
#106075633
#758335