Finite Group Databasebeta

← #14323967

Subgroups — #14323967

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91409C211yesmaximal, characteristic
2C2×#91396C211yesmaximal, characteristic, complemented
3C2×#91393C211yesmaximal, characteristic, complemented
4#11751090C211yesmaximal, characteristic, complemented
5C5×#4976C211yesmaximal, characteristic, complemented
6C3×#65277C211yesmaximal, characteristic, complemented
7#11748917C211yesmaximal, characteristic, complemented
8#11748913C211yesmaximal, characteristic, complemented
9#11748912C211yesmaximal, characteristic, complemented
10#11748896C211yesmaximal, characteristic, complemented
11#11748891C211yesmaximal, characteristic, complemented
12#11748878C211yesmaximal, characteristic, complemented
13#11748829C211yesmaximal, characteristic, complemented
14#11748708C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10607929—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46#91409C418yescomplemented
47#91396—24no—
48#91393—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#76296—51nomaximal, Hall
56C2×#4041—31no—
57C2×#4039—31no—
58C2×#4018—31no—
59C5×#389—31no—
60#65278—31no—
61#65278—31no—
62#65277—31no—
63#65277D311yescharacteristic, complemented
64#65276—31no—
65C4⋊C4×Dic5—31no—
66#65228—31no—
67#64958—31no—
68#64958—31no—
69#64954—31no—
70#64954—31no—
71C23×D15C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C2×C4×D15—22no—
81C2×C4×D15—41no—
82C2×C4×D15—41no—
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×D20—41no—
90C2×C3×D20—41no—
91C2×C3×D20C2×C414yescomplemented
92C2×#1202—22no—
93C2×#1202—22no—
94C2×#1202—41no—
95C2×#1202—41no—
96C2×#1202C2×C414yes—
97C2×#1202C2×C414yescomplemented
98C2×D5×Dic3—22no—
99C2×D5×Dic3—22no—
100C2×D5×Dic3—22no—
101C2×D5×Dic3—41no—
102C2×D5×Dic3—41no—
103C2×D5×Dic3C2×C414yescomplemented
104C3×C5×C4⋊C4—41no—
105#6714—41no—
106#6714C2×C414yescomplemented
107#6712—22no—
108C5×Dic3⋊C4—22no—
109C5×Dic3⋊C4—41no—
110C5×Dic3⋊C4C2×C414yescomplemented
111C4×C5×Dic3—22no—
112C3×#685—22no—
113C3×#685—22no—
114C3×#685—41no—
115C3×#685—41no—
116C3×C4×Dic5—41no—
117Dic3⋊Dic5—22no—
118#6669—22no—
119#6667—22no—
120#6667—41no—
121#6665—22no—
122#6665—41no—
123#6665—41no—
124#6665C2×C414yescomplemented
125Dic3×Dic5—41no—
126Dic3×Dic5D414yescomplemented
127C2×#939—51no—
128C2×#67⋊C4—51no—
129C2×#877—51no—
130C3×#390—51no—
131#5220—51no—
132#4989—51no—
133#4976D511yescharacteristic, complemented
134#4957—51no—
135#4957—51no—
136#4956—51no—
137#4946—51no—
138#4945—51no—
139#4942—51no—
140#4940—51no—
141C4×Dic3⋊C4—51no—
142C22×D20—31no—
143C22×D20—31no—
144C22×D20C2×D311yescharacteristic
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C22×C4×D5—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—31no—
151C2×C5×C4⋊C4C2×D311yescharacteristic
152C2×C42×C5—31no—
153C2×#685—31no—
154C2×#685—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×#685C2×D311yescharacteristic
164C2×#685C2×D311yescharacteristic
165C2×C4⋊Dic5—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5C2×D311yescharacteristic
171#4041—38no—
172#4039—64no—
173#4018—64no—
174C5×#95—31no—
175C5×#95—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2324—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×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5C22×C412yes—
202C22×C3×D5C22×C412yes—
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×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C22×C412yes—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C22×C412yes—
220C2×Dic15C2×D412yes—
221C4×D15—44no—
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×Dic3C22×C412yes—
231C2×C5×Dic3C22×C412yes—
232C2×C5×Dic3C2×D412yes—
233C2×C5×Dic3#4112yes—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5C2×D412yes—
240C3×D20—44no—
241#1202—28no—
242#1202—44no—
243D5×Dic3—28no—
244D5×Dic3—44no—
245C22×C3×D4—51no—
246C22×#67—51no—
247C22×#67—51no—
248C23×Dic3—51no—
249C23×Dic3—51no—
250C22×C4×D3—51no—
251C2×C3×C4⋊C4C2×D511yescharacteristic
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C42—51no—
257C2×#217—51no—
258C2×#217—51no—
259C2×#217—51no—
260C2×#217—51no—
261#939—58no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4C2×D511yescharacteristic
270C2×Dic3⋊C4C2×D511yescharacteristic
271C2×Dic3⋊C4C2×D511yescharacteristic
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3C2×D511yescharacteristic
275#67⋊C4—104no—
276#877—104no—
277C3⋊#95—51no—
278C3⋊#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95C2×D511yescharacteristic
282C3⋊#95C2×D511yescharacteristic
283C23×D5—31no—
284C23×D5C22×D311yescharacteristic
285C23×D5C22×D311yescharacteristic
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×C4×C5C22×D311yescharacteristic
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×D20—34no—
299C2×D20—34no—
300C2×D20—41no—
301C2×D20—41no—
302C2×D20—62no—
303C2×D20—62no—
304C2×D20—121no—
305C2×D20—121no—
306C2×D20C4×D314yescomplemented
307C2×C4×D5—34no—
308C2×C4×D5—62no—
309C2×C4×D5—62no—
310C2×C4×D5—62no—
311C2×C4×D5—62no—
312C2×C4×D5—121no—
313C2×C4×D5—121no—
314C2×C4×D5—121no—
315C2×C4×D5—121no—
316C5×C4⋊C4—34no—
317C5×C4⋊C4—41no—
318C5×C4⋊C4—62no—
319C5×C4⋊C4—121no—
320C42×C5—62no—
321#685—22no—
322#685—22no—
323#685—34no—
324#685—34no—
325#685—41no—
326#685—41no—
327#685—62no—
328#685—62no—
329#685—121no—
330#685—121no—
331#685—121no—
332#685—121no—
333C4⋊Dic5—62no—
334#683—62no—
335#683—62no—
336C4×Dic5—34no—
337C4×Dic5—41no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—51no—
343#390—151no—
344#390—151no—
345#389—31no—
346#388—151no—
347#388—151no—
348#386—151no—
349#386—151no—
350#385—151no—
351#385—151no—
352#380—151no—
353C4×C4⋊C4—151no—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C2×#4111yescharacteristic
357C22×C3×C5H(5,𝔽2)11yescharacteristic
358C22×C3×C5H(5,𝔽2)11yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C52−1+411yescharacteristic
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—41no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C2×C3×D5—22no—
369C2×C3×D5—22no—
370C2×C3×D5—22no—
371C2×C3×D5—22no—
372C2×C3×D5—22no—
373C2×C3×D5—22no—
374C2×C3×D5—41no—
375C2×C3×D5—41no—
376C2×C3×D5—41no—
377C2×C3×D5—41no—
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C3×C4×C5—22no—
383C3×C4×C5—41no—
384C3×C4×C5—41no—
385Dic15—22no—
386Dic15—22no—
387Dic15—41no—
388C3×Dic5—22no—
389C3×Dic5—41no—
390C5×Dic3—22no—
391C5×Dic3—41no—
392C5×Dic3—41no—
393C5×Dic3C4×D414yes—
394C24×C3—51no—
395C24×C3—51no—
396C23×D3—51no—
397C2×C3×D4—54no—
398C2×C3×D4—201no—
399C2×C3×D4—201no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—54no—
406C2×#67—54no—
407C2×#67—102no—
408C2×#67—102no—
409C2×#67—201no—
410C2×#67—201no—
411C22×Dic3—51no—
412C22×Dic3—51no—
413C22×Dic3—54no—
414C22×Dic3—51no—
415C22×Dic3—102no—
416C22×Dic3—102no—
417C22×Dic3—102no—
418C22×Dic3—201no—
419C22×Dic3—201no—
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C22×Dic3C22×D511yescharacteristic
423C22×Dic3C22×D511yescharacteristic
424C2×C4×D3—102no—
425C2×C4×D3—201no—
426C2×C4×D3—201no—
427C3×C4⋊C4—41no—
428C3×C22⋊C4—102no—
429C3×C22⋊C4—102no—
430C3×C22⋊C4—201no—
431C3×C22⋊C4—201no—
432C3×C42—201no—
433#217—54no—
434#217—102no—
435#217—201no—
436#217—201no—
437(C2×D3)⋊C4—54no—
438(C2×D3)⋊C4—102no—
439(C2×D3)⋊C4—201no—
440(C2×D3)⋊C4—201no—
441Dic3⋊C4—22no—
442Dic3⋊C4—41no—
443Dic3⋊C4—102no—
444Dic3⋊C4—102no—
445Dic3⋊C4—102no—
446Dic3⋊C4C4×D514yescomplemented
447C4×Dic3—22no—
448C4×Dic3—54no—
449C4×Dic3—201no—
450C23×C5C23×D311yescharacteristic
451C22×D5—21no—
452C22×D5—21no—
453C22×D5—21no—
454C22×D5—21no—
455C22×D5—21no—
456C22×D5—21no—
457C22×D5—21no—
458C22×D5—21no—
459C22×D5—21no—
460C22×D5—21no—
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—32no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5C2×C4×D312yes—
471C22×D5C2×C4×D312yes—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—32no—
481C2×C4×C5—32no—
482C2×C4×C5—32no—
483C2×C4×C5—32no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5—61no—
488C2×C4×C5—61no—
489C2×C4×C5—61no—
490C2×C4×C5—61no—
491C2×C4×C5—61no—
492C2×C4×C5C2×C4×D312yes—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5D3×D412yes—
508D20—44no—
509D20—68no—
510D20—124no—
511C4×D5—68no—
512C4×D5—124no—
513C4×D5—124no—
514C22×D4—51no—
515C22×D4—151no—
516C22×D4—151no—
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520#121—158no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4D3×D511yescharacteristic
530C2×C22⋊C4—51no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C42—31no—
543C2×C42—51no—
544C2×C42—151no—
545C2×C42—151no—
546#95—31no—
547#95—31no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5C2×C4×D411yescharacteristic
553C2×C3×C5#51811yescharacteristic
554C2×C3×C5#52011yescharacteristic
555C2×C3×C5#53511yescharacteristic
556C2×C3×C5#53711yescharacteristic
557C2×C3×C5#54011yescharacteristic
558C2×C3×C5#54211yescharacteristic
559D15—42no—
560C3×D5—42no—
561C3×D5—42no—
562C23×C3—52no—
563C23×C3—52no—
564C23×C3—101no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—101no—
568C23×C3—101no—
569C23×C3—101no—
570C23×C3—101no—
571C23×C3—101no—
572C23×C3—101no—
573C23×C3—101no—
574C23×C3—101no—
575C23×C3—101no—
576C23×C3C23×D511yescharacteristic
577C22×D3—52no—
578C22×D3—101no—
579C22×D3—101no—
580C22×D3—101no—
581C22×D3—101no—
582C22×D3—101no—
583C22×D3—101no—
584C3×D4—204no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—52no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4C2×C4×D512yes—
600#67—108no—
601#67—204no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—52no—
611C2×Dic3—52no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—108no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—204no—
621C2×Dic3C2×C4×D512yes—
622C2×Dic3C2×C4×D512yes—
623C2×Dic3D4×D512yes—
624C2×Dic3#71312yes—
625C4×D3—204no—
626C22×C5C22×C4×D311yescharacteristic
627C22×C5C2×D3×D411yescharacteristic
628C22×C5#100411yescharacteristic
629C22×C5#100411yescharacteristic
630C22×C5#100411yescharacteristic
631C22×C5D3×#4111yescharacteristic
632C22×C5#101011yescharacteristic
633C2×D5—22no—
634C2×D5—22no—
635C2×D5—22no—
636C2×D5—22no—
637C2×D5—22no—
638C2×D5—22no—
639C2×D5—41no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—41no—
645C2×D5—41no—
646C2×D5—41no—
647C2×D5—62no—
648C2×D5—62no—
649C2×D5—62no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C4×C5—22no—
655C4×C5—34no—
656C4×C5—41no—
657C4×C5—41no—
658C4×C5—62no—
659C4×C5—121no—
660C4×C5—121no—
661Dic5—22no—
662Dic5—41no—
663Dic5—62no—
664Dic5—62no—
665Dic5—121no—
666C24—51no—
667C24—51no—
668C24—151no—
669C2×D4—54no—
670C2×D4—154no—
671C2×D4—154no—
672C2×D4—201no—
673C2×D4—201no—
674C2×D4—302no—
675C2×D4—302no—
676C2×D4—601no—
677C2×D4—601no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—154no—
685C22×C4—151no—
686C22×C4—151no—
687C22×C4—151no—
688C22×C4—302no—
689C22×C4—302no—
690C22×C4—302no—
691C22×C4—302no—
692C22×C4—601no—
693C22×C4—601no—
694C22×C4—601no—
695C22×C4—601no—
696C22×C4C2×D3×D511yescharacteristic
697C22×C4C2×D3×D511yescharacteristic
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—41no—
701C4⋊C4—62no—
702C4⋊C4—121no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C22⋊C4—102no—
707C22⋊C4—102no—
708C22⋊C4—154no—
709C22⋊C4—154no—
710C22⋊C4—201no—
711C22⋊C4—201no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C22⋊C4—601no—
717C22⋊C4—601no—
718C42—62no—
719C42—154no—
720C42—201no—
721C42—601no—
722C3×C5#232411yescharacteristic, complemented, Hall
723C22×C3—102no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—102no—
727C22×C3—102no—
728C22×C3—102no—
729C22×C3—201no—
730C22×C3—201no—
731C22×C3—201no—
732C22×C3—201no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3C22×C4×D511yescharacteristic
738C22×C3C2×D4×D511yescharacteristic
739C22×C3#414411yescharacteristic
740C22×C3C2×#71311yescharacteristic
741C22×C3#414711yescharacteristic
742C22×C3#414911yescharacteristic
743C22×C3#414911yescharacteristic
744C2×D3—102no—
745C2×D3—102no—
746C2×D3—102no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—22no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—102no—
755C3×C4—201no—
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—102no—
760Dic3—102no—
761Dic3—201no—
762Dic3#403914yes—
763C2×C5#548611yescharacteristic
764C2×C5C4×D3×D411yescharacteristic
765C2×C5#554611yescharacteristic
766C2×C5#559711yescharacteristic
767C2×C5#561511yescharacteristic
768C2×C5#566911yescharacteristic
769C2×C5#571511yescharacteristic
770D5—42no—
771D5—42no—
772D5—122no—
773C23—52no—
774C23—52no—
775C23—101no—
776C23—101no—
777C23—101no—
778C23—101no—
779C23—101no—
780C23—101no—
781C23—101no—
782C23—101no—
783C23—101no—
784C23—101no—
785C23—101no—
786C23—101no—
787C23—152no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23—301no—
794C23C22×D3×D511yescharacteristic
795D4—204no—
796D4—308no—
797D4—604no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—52no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—152no—
825C2×C4—152no—
826C2×C4—308no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—604no—
835C2×C4—604no—
836C2×C4C4×D3×D512yes—
837C2×C3—202no—
838C2×C3—202no—
839C2×C3C2×#403911yescharacteristic
840C2×C3#6587911yescharacteristic
841C2×C3#6590811yescharacteristic
842C2×C3#6594111yescharacteristic
843C2×C3#6596311yescharacteristic
844C2×C3#6603211yescharacteristic
845C2×C3#6606711yescharacteristic
846D3—202no—
847C5#7629611yescharacteristic, complemented, Sylow
848C22—102no—
849C22—102no—
850C22—102no—
851C22—102no—
852C22—102no—
853C22—102no—
854C22—201no—
855C22—201no—
856C22—201no—
857C22—201no—
858C22—201no—
859C22—201no—
860C22—201no—
861C22—201no—
862C22—302no—
863C22—302no—
864C22—302no—
865C22—601no—
866C22—601no—
867C22—601no—
868C22—601no—
869C22C2×C4×D3×D511yescharacteristic
870C22#9201711yescharacteristic
871C22D3×D4×D511yescharacteristic
872C22#9202611yescharacteristic
873C22#9202811yescharacteristic
874C22D3×#71311yescharacteristic
875C22#9204911yescharacteristic
876C4—22no—
877C4—34no—
878C4—41no—
879C4—41no—
880C4—62no—
881C4—102no—
882C4—121no—
883C4—121no—
884C4—201no—
885C4—302no—
886C4—302no—
887C4—601no—
888C3#1060792911yescharacteristic, complemented, Sylow
889C2—202no—
890C2—202no—
891C2—602no—
892C2#1175340111yescharacteristic
893C2#1175341411yescharacteristic
894C2#1175377211yescharacteristic
895C2D3×#403911yescharacteristic
896C2#1175462511yescharacteristic
897C2#1175505111yescharacteristic
898C2#1175520511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91409C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2324
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
2. C2×#91396C2semidirect
3. C2×#91393C2semidirect
4. #11751090C2semidirect
5. C5×#4976C2semidirect
6. C3×#65277C2semidirect
7. #11748917C2semidirect
8. #11748913C2semidirect
9. #11748912C2semidirect
10. #11748896C2semidirect
11. #11748891C2semidirect
12. #11748878C2semidirect
13. #11748829C2semidirect
14. #11748708C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
46. #91409C4semidirect
63. #65277D3semidirect
91. C2×C3×D20C2×C4semidirect
97. C2×#1202C2×C4semidirect
103. C2×D5×Dic3C2×C4semidirect
106. #6714C2×C4semidirect
110. C5×Dic3⋊C4C2×C4semidirect
124. #6665C2×C4semidirect
126. Dic3×Dic5D4semidirect
133. #4976D5semidirect
306. C2×D20C4×D3semidirect
446. Dic3⋊C4C4×D5semidirect
722. C3×C5#2324semidirect
847. C5#76296semidirect
888. C3#10607929semidirect

Maximal subgroups

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

subgroupindex
C2×#914092
C2×#913962
C2×#913932
#117510902
C5×#49762
C3×#652772
#117489172
#117489132
#117489122
#117488962
#117488912
#117488782
#117488292
#117487082
Dic5×Dic3⋊C42
#106079293
#762965