Finite Group Databasebeta

← #14322608

Subgroups — #14322608

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91561C211yesmaximal, characteristic
2#11751056C211yesmaximal, characteristic
3C5×#4944C211yesmaximal, characteristic, complemented
4C3×#65233C211yesmaximal, characteristic, complemented
5#11749502C211yesmaximal, characteristic
6#11749486C211yesmaximal, characteristic, complemented
7#11749479C211yesmaximal, characteristic, complemented
8#11748882C211yesmaximal, characteristic, complemented
9#11748881C211yesmaximal, characteristic, complemented
10#11748876C211yesmaximal, characteristic, complemented
11#11748875C211yesmaximal, characteristic, complemented
12#11748728C211yesmaximal, characteristic, complemented
13#11748727C211yesmaximal, characteristic, complemented
14#11748671C211yesmaximal, characteristic, complemented
15#11748668C211yesmaximal, characteristic, complemented
16#10607556—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
29C2×C4×C5×Dic3C2211yescharacteristic, complemented
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic, complemented
33C2×C3×C4×Dic5C2211yescharacteristic, complemented
34#91561C418yescomplemented
35C2×Dic3⋊Dic5C2211yescharacteristic, complemented
36C2×#6668C2211yescharacteristic, complemented
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C5×C3⋊#95C2211yescharacteristic, complemented
46C5×C3⋊#95C2211yescharacteristic, complemented
47C3×#3963C2211yescharacteristic, complemented
48C3×#3963C2211yescharacteristic, complemented
49#90994C2211yescharacteristic, complemented
50#90994C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75825—51nomaximal, Hall
54C2×D5×C22⋊C4—31no—
55C5×#388—31no—
56#65279—31no—
57#65276—31no—
58#65244—31no—
59#65244—31no—
60#65240—31no—
61#65234—31no—
62#65233D311yescharacteristic, complemented
63#65229—31no—
64C4×#685—31no—
65#64959—31no—
66#64958—31no—
67#64956—31no—
68#64955—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15—22no—
71C23×D15—22no—
72C23×D15—41no—
73C23×D15—41no—
74C23×D15—41no—
75C23×D15—41no—
76C23×D15C2×C414yes—
77C23×D15C2311yescharacteristic
78C23×D15C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×#1200—41no—
92C2×#1200—41no—
93C2×#1200—41no—
94C2×#1200—41no—
95C2×#1200C2×C414yes—
96C2×#1200C2×C414yes—
97C3×C5×C22⋊C4—41no—
98#6719—41no—
99#6714—22no—
100#6714—22no—
101#6714—41no—
102#6714—41no—
103C5×#217—41no—
104C5×#217C2×C414yes—
105C5×Dic3⋊C4—41no—
106C4×C5×Dic3—41no—
107C3×C22⋊Dic5—41no—
108C3×C22⋊Dic5C2×C414yes—
109C3×#683—41no—
110C3×C4×Dic5—41no—
111Dic3⋊Dic5—41no—
112#6668—41no—
113#6667—22no—
114#6667—22no—
115#6667—41no—
116#6667—41no—
117#6667C2×C414yes—
118#6667C2×C414yes—
119Dic3×Dic5—41no—
120Dic3×Dic5—41no—
121C2×D3×C22⋊C4—51no—
122C3×#388—51no—
123#4990—51no—
124#4987—51no—
125#4955—51no—
126#4955—51no—
127#4951—51no—
128#4945—51no—
129#4944D511yescharacteristic, complemented
130#4940—51no—
131C4×(C2×D3)⋊C4—51no—
132#4670—51no—
133#4669—51no—
134#4667—51no—
135#4666—51no—
136C24×D5—31no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4C2×D311yescharacteristic
143C2×C42×C5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5C2×D311yescharacteristic
146C2×C22⋊Dic5C2×D311yescharacteristic
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683C2×D311yescharacteristic, complemented
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5C2×D311yescharacteristic, complemented
163D5×C22⋊C4—38no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963C2×D311yescharacteristic, complemented
171#3963C2×D311yescharacteristic, complemented
172#2312—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5C2411yescharacteristic
181C22×D15—21no—
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—28no—
192C22×D15—44no—
193C22×D15—44no—
194C22×D15—44no—
195C22×D15—44no—
196C22×D15—44no—
197C22×D15—44no—
198C22×D15C22×C412yes—
199C22×D15C22×C412yes—
200C22×D15#4112yes—
201C22×D15#4112yes—
202C2×C3×C4×C5—21no—
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×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3C22×C412yes—
225C2×C5×Dic3C22×C412yes—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5C22×C412yes—
237C2×C3×Dic5C22×C412yes—
238#1200—44no—
239#1200—44no—
240C24×D3—51no—
241C22×C4×D3—51no—
242C22×C4×D3—51no—
243C2×C3×C4⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C22⋊C4—51no—
246C2×C3×C22⋊C4C2×D511yescharacteristic
247C2×C3×C42—51no—
248C2×#217—51no—
249C2×#217C2×D511yescharacteristic
250C2×#217C2×D511yescharacteristic
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×(C2×D3)⋊C4—51no—
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×C4⋊Dic3—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4C2×D511yescharacteristic, complemented
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266C2×C4×Dic3C2×D511yescharacteristic, complemented
267D3×C22⋊C4—58no—
268C3×#95—51no—
269C3×#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95C2×D511yescharacteristic, complemented
275C3⋊#95C2×D511yescharacteristic, complemented
276C24×C5C22×D311yescharacteristic
277C23×D5—31no—
278C23×D5—31no—
279C23×D5—34no—
280C23×D5—62no—
281C23×D5—62no—
282C23×D5—121no—
283C23×D5—121no—
284C23×D5—121no—
285C23×D5—121no—
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5—31no—
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5C22×D311yescharacteristic
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—121no—
301C2×C4×D5—121no—
302C2×C4×D5—121no—
303C2×C4×D5—121no—
304C5×C4⋊C4—121no—
305C5×C22⋊C4—34no—
306C5×C22⋊C4—41no—
307C5×C22⋊C4—121no—
308C42×C5—121no—
309C22⋊Dic5—41no—
310C22⋊Dic5—121no—
311C22⋊Dic5C4×D314yes—
312#685—34no—
313#685—34no—
314#685—62no—
315#685—62no—
316#685—62no—
317#685—62no—
318#685—121no—
319#685—121no—
320#685—121no—
321#685—121no—
322C4⋊Dic5—121no—
323#683—41no—
324#683—121no—
325C4×Dic5—41no—
326C4×Dic5—121no—
327C4×Dic5—121no—
328C22×C22⋊C4—151no—
329#388—31no—
330#388—51no—
331#388—151no—
332#388—151no—
333#388—151no—
334#388—151no—
335#388—151no—
336#388—151no—
337#380—151no—
338#380—151no—
339#379—151no—
340#379—151no—
341C4×C22⋊C4—151no—
342C4×C22⋊C4—151no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C23×C411yescharacteristic
351C22×C3×C5C2×#4111yescharacteristic
352C22×C3×C5C2×#4111yescharacteristic
353C22×C3×C5H(5,𝔽2)11yescharacteristic
354C22×C3×C5H(5,𝔽2)11yescharacteristic
355C22×C3×C5H(5,𝔽2)11yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C2×D15—22no—
358C2×D15—22no—
359C2×D15—22no—
360C2×D15—22no—
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—22no—
365C2×D15—22no—
366C2×D15—416no—
367C2×D15—41no—
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—41no—
371C2×D15#11714yes—
372C3×C4×C5—41no—
373C3×C4×C5—41no—
374Dic15—41no—
375Dic15—41no—
376C3×Dic5—22no—
377C3×Dic5—22no—
378C3×Dic5—41no—
379C3×Dic5—41no—
380C5×Dic3—22no—
381C5×Dic3—22no—
382C5×Dic3—41no—
383C5×Dic3—41no—
384C24×C3C22×D511yescharacteristic
385C23×D3—51no—
386C23×D3—51no—
387C23×D3—54no—
388C23×D3—102no—
389C23×D3—102no—
390C23×D3—201no—
391C23×D3—201no—
392C23×D3—201no—
393C23×D3—201no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3C22×D511yescharacteristic
403C22×Dic3C22×D511yescharacteristic
404C22×Dic3C22×D511yescharacteristic
405C22×Dic3C22×D511yescharacteristic
406C2×C4×D3—54no—
407C2×C4×D3—54no—
408C2×C4×D3—201no—
409C2×C4×D3—201no—
410C2×C4×D3—201no—
411C2×C4×D3—201no—
412C3×C4⋊C4—201no—
413C3×C22⋊C4—41no—
414C3×C22⋊C4—54no—
415C3×C22⋊C4—201no—
416C3×C42—201no—
417#217—41no—
418#217—201no—
419#217C4×D514yes—
420(C2×D3)⋊C4—54no—
421(C2×D3)⋊C4—54no—
422(C2×D3)⋊C4—102no—
423(C2×D3)⋊C4—102no—
424(C2×D3)⋊C4—102no—
425(C2×D3)⋊C4—102no—
426(C2×D3)⋊C4—201no—
427(C2×D3)⋊C4—201no—
428(C2×D3)⋊C4—201no—
429(C2×D3)⋊C4—201no—
430C4⋊Dic3—201no—
431Dic3⋊C4—41no—
432Dic3⋊C4—201no—
433C4×Dic3—41no—
434C4×Dic3—201no—
435C4×Dic3—201no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5C2×C4×D312yes—
443C23×C5C23×D311yescharacteristic
444C22×D5—32no—
445C22×D5—32no—
446C22×D5—32no—
447C22×D5—32no—
448C22×D5—68no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5—61no—
454C22×D5—61no—
455C22×D5—61no—
456C22×D5—61no—
457C22×D5—61no—
458C22×D5—61no—
459C22×D5—124no—
460C22×D5—124no—
461C22×D5—124no—
462C22×D5—124no—
463C22×D5—124no—
464C22×D5—124no—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—32no—
472C2×C4×C5—32no—
473C2×C4×C5—61no—
474C2×C4×C5—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—61no—
494C2×Dic5—61no—
495C2×Dic5—61no—
496C2×Dic5—61no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5C2×C4×D312yes—
500C2×Dic5C2×C4×D312yes—
501C4×D5—124no—
502C4×D5—124no—
503C25—151no—
504C23×C4—151no—
505C23×C4—151no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—151no—
509C2×C4⋊C4—151no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—158no—
515C2×C22⋊C4—151no—
516C2×C22⋊C4—151no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4D3×D511yescharacteristic
527C2×C42—31no—
528C2×C42—51no—
529C2×C42—151no—
530C2×C42—151no—
531#95—31no—
532#95—31no—
533#95—51no—
534#95—51no—
535#95—151no—
536#95—151no—
537#95—151no—
538#95—151no—
539C2×C3×C5—42no—
540C2×C3×C5C2×#11711yescharacteristic
541C2×C3×C5#51811yescharacteristic
542C2×C3×C5#51811yescharacteristic
543C2×C3×C5#53811yescharacteristic
544C2×C3×C5#53811yescharacteristic
545C2×C3×C5#53811yescharacteristic
546C2×C3×C5#53811yescharacteristic
547D15—24no—
548D15—42no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3C2×C4×D512yes—
556C23×C3C23×D511yescharacteristic
557C22×D3—52no—
558C22×D3—52no—
559C22×D3—52no—
560C22×D3—52no—
561C22×D3—108no—
562C22×D3—101no—
563C22×D3—101no—
564C22×D3—101no—
565C22×D3—101no—
566C22×D3—101no—
567C22×D3—101no—
568C22×D3—101no—
569C22×D3—101no—
570C22×D3—101no—
571C22×D3—101no—
572C22×D3—204no—
573C22×D3—204no—
574C22×D3—204no—
575C22×D3—204no—
576C22×D3—204no—
577C22×D3—204no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—52no—
585C2×C3×C4—52no—
586C2×C3×C4—101no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3C2×C4×D512yes—
613C2×Dic3C2×C4×D512yes—
614C4×D3—204no—
615C4×D3—204no—
616C22×C5—22no—
617C22×C5—22no—
618C22×C5—22no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5—41no—
623C22×C5C22×C4×D311yescharacteristic
624C22×C5#100411yescharacteristic
625C22×C5#100411yescharacteristic
626C22×C5D3×#4111yescharacteristic
627C22×C5D3×#4111yescharacteristic
628C22×C5#100911yescharacteristic
629C22×C5#100911yescharacteristic
630C2×D5—34no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—62no—
634C2×D5—62no—
635C2×D5—62no—
636C2×D5—62no—
637C2×D5—62no—
638C2×D5—62no—
639C2×D5—62no—
640C2×D5—1216no—
641C2×D5—121no—
642C2×D5—121no—
643C2×D5—121no—
644C2×D5—121no—
645C4×C5—41no—
646C4×C5—41no—
647C4×C5—62no—
648C4×C5—62no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—22no—
653Dic5—41no—
654Dic5—41no—
655Dic5—121no—
656Dic5—121no—
657C24—151no—
658C24—151no—
659C24—154no—
660C24—302no—
661C24—302no—
662C24—601no—
663C24—601no—
664C24—601no—
665C24—601no—
666C24C2×D3×D511yescharacteristic
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—51no—
675C22×C4—154no—
676C22×C4—154no—
677C22×C4—151no—
678C22×C4—151no—
679C22×C4—601no—
680C22×C4—601no—
681C22×C4—601no—
682C22×C4—601no—
683C22×C4C2×D3×D511yescharacteristic
684C22×C4C2×D3×D511yescharacteristic
685C4⋊C4—121no—
686C4⋊C4—201no—
687C4⋊C4—601no—
688C4⋊C4—601no—
689C22⋊C4—34no—
690C22⋊C4—41no—
691C22⋊C4—54no—
692C22⋊C4—121no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—201no—
696C22⋊C4—302no—
697C22⋊C4—302no—
698C22⋊C4—302no—
699C22⋊C4—302no—
700C22⋊C4—601no—
701C22⋊C4—601no—
702C22⋊C4—601no—
703C22⋊C4—601no—
704C22⋊C4—601no—
705C42—121no—
706C42—201no—
707C42—601no—
708C42—601no—
709C3×C5#231211yescharacteristic, complemented, Hall
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3C22×C4×D511yescharacteristic
718C22×C3#414411yescharacteristic
719C22×C3#414411yescharacteristic
720C22×C3D5×#4111yescharacteristic
721C22×C3D5×#4111yescharacteristic
722C22×C3#414911yescharacteristic
723C22×C3#414911yescharacteristic
724C2×D3—54no—
725C2×D3—102no—
726C2×D3—102no—
727C2×D3—102no—
728C2×D3—102no—
729C2×D3—102no—
730C2×D3—102no—
731C2×D3—102no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—2016no—
735C2×D3—201no—
736C2×D3—201no—
737C2×D3—201no—
738C2×D3—201no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—102no—
742C3×C4—102no—
743C3×C4—201no—
744C3×C4—201no—
745Dic3—22no—
746Dic3—22no—
747Dic3—41no—
748Dic3—41no—
749Dic3—201no—
750Dic3—201no—
751C2×C5—42no—
752C2×C5D3×#11711yescharacteristic
753C2×C5#554511yescharacteristic
754C2×C5#554511yescharacteristic
755C2×C5#561311yescharacteristic
756C2×C5#565711yescharacteristic
757C2×C5#567811yescharacteristic
758C2×C5#570411yescharacteristic
759D5—64no—
760D5—122no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—152no—
768C23—152no—
769C23—152no—
770C23—152no—
771C23—308no—
772C23—301no—
773C23—301no—
774C23—301no—
775C23—301no—
776C23—301no—
777C23—301no—
778C23—301no—
779C23—301no—
780C23—301no—
781C23—301no—
782C23—604no—
783C23—604no—
784C23—604no—
785C23—604no—
786C23—604no—
787C23—604no—
788C23C4×D3×D512yes—
789C23C22×D3×D511yescharacteristic
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—52no—
799C2×C4—52no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—101no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C3—42no—
829C2×C3D5×#11711yescharacteristic
830C2×C3#6587911yescharacteristic
831C2×C3#6587911yescharacteristic
832C2×C3#6594711yescharacteristic
833C2×C3#6599111yescharacteristic
834C2×C3#6601211yescharacteristic
835C2×C3#6603811yescharacteristic
836D3—104no—
837D3—202no—
838C5#7582511yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—154no—
847C22—302no—
848C22—302no—
849C22—302no—
850C22—302no—
851C22—302no—
852C22—302no—
853C22—302no—
854C22—302no—
855C22—302no—
856C22—6016no—
857C22—601no—
858C22—601no—
859C22—601no—
860C22—601no—
861C22C2×C4×D3×D511yescharacteristic
862C22#9201911yescharacteristic
863C22#9202411yescharacteristic
864C22#9202411yescharacteristic
865C22#9202611yescharacteristic
866C22#9202711yescharacteristic
867C22#9204911yescharacteristic
868C4—41no—
869C4—41no—
870C4—62no—
871C4—62no—
872C4—102no—
873C4—102no—
874C4—121no—
875C4—121no—
876C4—201no—
877C4—201no—
878C4—601no—
879C4—601no—
880C3#1060755611yescharacteristic, complemented, Sylow
881C2—42no—
882C2—304no—
883C2—602no—
884C2#1175282511yescharacteristic
885C2#1175302711yescharacteristic
886C2#1175303811yescharacteristic
887C2#1175320411yescharacteristic
888C2#1175462911yescharacteristic
889C2#1175490111yescharacteristic
890C2#1175498111yescharacteristic
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#2312
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. C5×#4944C2semidirect
4. C3×#65233C2semidirect
6. #11749486C2semidirect
7. #11749479C2semidirect
8. #11748882C2semidirect
9. #11748881C2semidirect
10. #11748876C2semidirect
11. #11748875C2semidirect
12. #11748728C2semidirect
13. #11748727C2semidirect
14. #11748671C2semidirect
15. #11748668C2semidirect
28. C2×C5×Dic3⋊C4C22semidirect
29. C2×C4×C5×Dic3C22semidirect
32. C2×C3×#683C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. #91561C4semidirect
35. C2×Dic3⋊Dic5C22semidirect
36. C2×#6668C22semidirect
43. C2×Dic3×Dic5C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C5×C3⋊#95C22semidirect
46. C5×C3⋊#95C22semidirect
47. C3×#3963C22semidirect
48. C3×#3963C22semidirect
49. #90994C22semidirect
50. #90994C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
62. #65233D3semidirect
129. #4944D5semidirect
159. C2×#683C2×D3semidirect
162. C2×C4×Dic5C2×D3semidirect
170. #3963C2×D3semidirect
171. #3963C2×D3semidirect
263. C2×Dic3⋊C4C2×D5semidirect
266. C2×C4×Dic3C2×D5semidirect
274. C3⋊#95C2×D5semidirect
275. C3⋊#95C2×D5semidirect
709. C3×C5#2312semidirect
838. C5#75825semidirect
880. C3#10607556semidirect

Maximal subgroups

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

subgroupindex
C2×#915612
#117510562
C5×#49442
C3×#652332
#117495022
#117494862
#117494792
#117488822
#117488812
#117488762
#117488752
#117487282
#117487272
#117486712
#117486682
#106075563
#758255