Finite Group Databasebeta

← #14325962

Subgroups — #14325962

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic
2C2×D5×#217C211yesmaximal, characteristic, complemented
3C2×D3×#685C211yesmaximal, characteristic, complemented
4C2×#91442C211yesmaximal, characteristic, complemented
5C2×#91441C211yesmaximal, characteristic, complemented
6#11751058C211yesmaximal, characteristic, complemented
7C5×#4956C211yesmaximal, characteristic, complemented
8C3×#65244C211yesmaximal, characteristic, complemented
9#11749519C211yesmaximal, characteristic, complemented
10#11749483C211yesmaximal, characteristic, complemented
11#11748940C211yesmaximal, characteristic, complemented
12#11748885C211yesmaximal, characteristic, complemented
13#11748884C211yesmaximal, characteristic, complemented
14#11748872C211yesmaximal, characteristic, complemented
15#11748872C211yesmaximal, characteristic, complemented
16#10606609—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C2×D5×#67—24no—
23C2×D5×#67—24no—
24C2×D5×#67C418yescomplemented
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic, complemented
28C22×D5×Dic3C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic, complemented
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×#6719C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×#6714C2211yescharacteristic, complemented
35C2×#6712C2211yescharacteristic, complemented
36C2×C4×Dic15C2211yescharacteristic, complemented
37C2×C5×#217C2211yescharacteristic, complemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44D5×#217—24no—
45C2×#6669C2211yescharacteristic, complemented
46C2×#6667C2211yescharacteristic, complemented
47C2×#6667C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×Dic3×Dic5C2211yescharacteristic, complemented
52D3×#685—24no—
53#91442—24no—
54#91441—24no—
55C5×C3⋊#95C2211yescharacteristic, complemented
56C5×C3⋊#95C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59#73850—51nomaximal, Hall
60C22×D4×D5—31no—
61C2×C4×C22⋊D5—31no—
62C22×#685—31no—
63C2×#4027—31no—
64C2×D5×C22⋊C4—31no—
65C5×#386—31no—
66#65509—31no—
67#65246—31no—
68#65246—31no—
69#65244—31no—
70#65244D311yescharacteristic, complemented
71#64956—31no—
72#64955—31no—
73#64954—31no—
74#64954—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5—22no—
81C23×C3×D5—22no—
82C23×C3×D5—41no—
83C23×C3×D5—41no—
84C23×C3×D5C2×C414yescomplemented
85C23×C3×D5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×D3×D5—22no—
88C22×D3×D5—22no—
89C22×D3×D5—22no—
90C22×D3×D5—22no—
91C22×D3×D5—41no—
92C22×D3×D5—41no—
93C22×D3×D5C2×C414yescomplemented
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—22no—
97C2×#1220—22no—
98C2×#1220C2×C414yescomplemented
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×C5×#67—22no—
103C2×C5×#67—22no—
104C2×C5×#67C2×C414yescomplemented
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3—22no—
109C2×C4×C5×D3—22no—
110C2×C4×C5×D3—41no—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113D5×#67—232no—
114C2×#1202—22no—
115C2×#1202—22no—
116C2×#1202C2×C414yescomplemented
117C2×#1201C2×C414yes—
118C2×#1201D414yes—
119C2×#1201D414yes—
120C2×D3×Dic5—22no—
121C2×D3×Dic5—22no—
122C2×D3×Dic5—41no—
123C2×D5×Dic3—22no—
124C2×D5×Dic3—22no—
125C2×D5×Dic3—22no—
126C2×D5×Dic3—22no—
127C2×D5×Dic3—22no—
128C2×D5×Dic3—22no—
129C2×D5×Dic3—41no—
130C2×D5×Dic3—41no—
131C2×D5×Dic3C2×C414yescomplemented
132C3×C5×C22⋊C4—41no—
133#6719—22no—
134#6714—22no—
135#6714—41no—
136#6712—22no—
137C4×Dic15—22no—
138C5×#217—22no—
139C5×(C2×D3)⋊C4—22no—
140C3×C22⋊Dic5—41no—
141C3×#685—22no—
142C3×#685—22no—
143C3×#685—22no—
144C3×#685—22no—
145#6669—22no—
146#6667—22no—
147#6667—41no—
148(C2×D3)⋊Dic5—22no—
149#6665—22no—
150#6665D414yescomplemented
151Dic3×Dic5—22no—
152C23×#67—51no—
153C22×#217—51no—
154C2×#67⋊C4—51no—
155C2×#67⋊C4—51no—
156C2×D3×C22⋊C4—51no—
157C3×#379—51no—
158#4958—51no—
159#4958—51no—
160#4957—51no—
161#4957—51no—
162#4956—51no—
163#4956D511yescharacteristic, complemented
164#4955—51no—
165#4942—51no—
166Dic3×C22⋊C4—51no—
167C24×D5—31no—
168C24×D5C2×D311yescharacteristic
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C23×Dic5—31no—
174C2×D4×D5—38no—
175C2×D4×D5—64no—
176C2×D4×D5—64no—
177C22×D20—31no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5C2×D311yescharacteristic, complemented
187C4×C22⋊D5—64no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—64no—
195C2×#685C2×D311yescharacteristic
196C2×#685C2×D311yescharacteristic
197C2×#685C2×D311yescharacteristic, complemented
198C2×#685C2×D311yescharacteristic, complemented
199C2×#683—31no—
200C2×#683—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203#4027—64no—
204D5×C22⋊C4—64no—
205C5×#95—31no—
206C5×#95—31no—
207#3963—31no—
208#3963—31no—
209D4×C22⋊C4—151noSylow
210C23×C3×C5—21no—
211C23×C3×C5—21no—
212C23×C3×C5—21no—
213C23×C3×C5—21no—
214C23×C3×C5—21no—
215C23×C3×C5—21no—
216C23×C3×C5C22×C412yes—
217C23×C3×C5C2411yescharacteristic
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—21no—
221C22×D15—21no—
222C22×D15—21no—
223C22×D15—21no—
224C22×D15C22×C412yes—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3C22×C412yes—
230C22×C5×D3C2×D412yes—
231C22×C5×D3C2×D412yes—
232C22×C3×D5—21no—
233C22×C3×D5—21no—
234C22×C3×D5—21no—
235C22×C3×D5—21no—
236C22×C3×D5—21no—
237C22×C3×D5—21no—
238C22×C3×D5—21no—
239C22×C3×D5—21no—
240C22×C3×D5—28no—
241C22×C3×D5—28no—
242C22×C3×D5—44no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—44no—
247C22×C3×D5C22×C412yes—
248C22×C3×D5C22×C412yes—
249C22×C3×D5C2×D412yes—
250C22×C3×D5C2×D412yes—
251C22×C3×D5C2×D412yes—
252C22×C3×D5#4112yes—
253C2×D3×D5—28no—
254C2×D3×D5—28no—
255C2×D3×D5—44no—
256C2×D3×D5—44no—
257C2×D3×D5—44no—
258C2×D3×D5—44no—
259C2×D3×D5—44no—
260C2×C3×C4×C5—21no—
261C2×C3×C4×C5—21no—
262C2×C3×C4×C5—21no—
263C2×C3×C4×C5—21no—
264C2×C3×C4×C5—21no—
265C2×C3×C4×C5—21no—
266#1220—28no—
267C2×Dic15—21no—
268C2×Dic15—21no—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15C22×C412yes—
273C2×Dic15C2×D412yes—
274C2×Dic15C2×D412yes—
275C2×Dic15C2×D412yescomplemented
276C5×#67—28no—
277C2×C5×Dic3—21no—
278C2×C5×Dic3—21no—
279C2×C5×Dic3—21no—
280C2×C5×Dic3—21no—
281C2×C5×Dic3—21no—
282C2×C5×Dic3—21no—
283C2×C5×Dic3—21no—
284C2×C5×Dic3C22×C412yes—
285C2×C5×Dic3C2×D412yescomplemented
286C4×C5×D3—44no—
287C2×C3×Dic5—21no—
288C2×C3×Dic5—21no—
289C2×C3×Dic5—21no—
290C2×C3×Dic5—21no—
291C2×C3×Dic5—21no—
292C2×C3×Dic5—21no—
293#1202—28no—
294#1201C22⋊C4116yescomplemented
295D3×Dic5—44no—
296D5×Dic3—28no—
297D5×Dic3—44no—
298D5×Dic3—44no—
299C25×C3—51no—
300C24×D3—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—58no—
304C22×#67—51no—
305C22×#67—104no—
306C22×#67—104no—
307C22×#67C2×D511yescharacteristic
308C23×Dic3—51no—
309C23×Dic3—51no—
310C23×Dic3—51no—
311C22×C4×D3—51no—
312C22×C4×D3C2×D511yescharacteristic, complemented
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4—51no—
316C2×C3×C22⋊C4—51no—
317C2×C3×C22⋊C4—51no—
318C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
319C2×#217—51no—
320C2×#217—51no—
321C2×#217—51no—
322C2×#217—104no—
323C2×#217C2×D511yescharacteristic, complemented
324C2×(C2×D3)⋊C4—51no—
325C2×(C2×D3)⋊C4—51no—
326C2×(C2×D3)⋊C4—51no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
330C2×Dic3⋊C4—51no—
331C2×Dic3⋊C4—51no—
332C2×C4×Dic3—51no—
333C2×C4×Dic3—51no—
334#67⋊C4—104no—
335#67⋊C4—104no—
336D3×C22⋊C4—104no—
337C3⋊#95—51no—
338C3⋊#95—51no—
339C3⋊#95C2×D511yescharacteristic, complemented
340C3⋊#95C2×D511yescharacteristic, complemented
341C24×C5—31no—
342C24×C5C22×D311yescharacteristic
343C23×D5—22no—
344C23×D5—22no—
345C23×D5—22no—
346C23×D5—22no—
347C23×D5—31no—
348C23×D5—34no—
349C23×D5—41no—
350C23×D5—41no—
351C23×D5—62no—
352C23×D5—62no—
353C23×D5—62no—
354C23×D5—62no—
355C23×D5—121no—
356C23×D5—121no—
357C23×D5C4×D314yescomplemented
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D311yescharacteristic
360C2×C5×D4—34no—
361C2×C5×D4—62no—
362C2×C5×D4—62no—
363C22×C4×C5—31no—
364C22×C4×C5—31no—
365C22×C4×C5—31no—
366C22×C4×C5—62no—
367C22×C4×C5—62no—
368C22×C4×C5—121no—
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C2×C22⋊D5—34no—
372C2×C22⋊D5—34no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—62no—
376C2×C22⋊D5—62no—
377C22×Dic5—31no—
378C22×Dic5—31no—
379C22×Dic5—31no—
380C22×Dic5—62no—
381C22×Dic5—62no—
382C22×Dic5—121no—
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385D4×D5—632no—
386C2×D20—34no—
387C2×D20—62no—
388C2×D20—62no—
389C2×C4×D5—34no—
390C2×C4×D5—62no—
391C2×C4×D5—62no—
392C2×C4×D5—62no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—62no—
396C2×C4×D5—121no—
397C2×C4×D5—121no—
398C5×C22⋊C4—41no—
399C5×C22⋊C4—62no—
400C5×C22⋊C4—62no—
401C22⋊Dic5—41no—
402C22⋊Dic5—62no—
403C22⋊Dic5—62no—
404#685—22no—
405#685—22no—
406#685—22no—
407#685—22no—
408#685—34no—
409#685—62no—
410#685—62no—
411#685—62no—
412#685—121no—
413#685—121no—
414#683—62no—
415#683—62no—
416C4×Dic5—62no—
417C4×Dic5—62no—
418C23×D4—151no—
419C2×C4×D4—151no—
420C2×C4×D4—151no—
421C22×C22⋊C4—151no—
422C22×C22⋊C4—151no—
423#390—151no—
424#390—151no—
425#386—31no—
426#386—151no—
427#386—151no—
428#386—151no—
429#380—151no—
430#379—51no—
431#379—151no—
432C4×C22⋊C4—151no—
433C22×C3×C5—22no—
434C22×C3×C5—22no—
435C22×C3×C5—22no—
436C22×C3×C5—41no—
437C22×C3×C5—41no—
438C22×C3×C5—41no—
439C22×C3×C5—41no—
440C22×C3×C5C23×C411yescharacteristic
441C22×C3×C5C22×D411yescharacteristic
442C22×C3×C5C22×D411yescharacteristic
443C22×C3×C5C22×D411yescharacteristic
444C22×C3×C5C2×#4111yescharacteristic
445C22×C3×C5H(5,𝔽2)11yescharacteristic
446C22×C3×C5H(5,𝔽2)11yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—41no—
451C2×D15—41no—
452C2×D15—41no—
453C2×D15—41no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3C2×C22⋊C414yescomplemented
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—22no—
468C2×C3×D5—22no—
469C2×C3×D5—22no—
470C2×C3×D5—22no—
471C2×C3×D5—22no—
472C2×C3×D5—22no—
473C2×C3×D5—416no—
474C2×C3×D5C2×C22⋊C414yescomplemented
475C2×C3×D5C4×D414yescomplemented
476D3×D5—416no—
477C3×C4×C5—41no—
478C3×C4×C5—41no—
479Dic15—22no—
480Dic15—41no—
481Dic15C2×C22⋊C414yescomplemented
482C3×Dic5—41no—
483C3×Dic5—41no—
484C5×Dic3—22no—
485C5×Dic3—22no—
486C5×Dic3—41no—
487C24×C3—51no—
488C24×C3—51no—
489C24×C3—54no—
490C24×C3—102no—
491C24×C3—102no—
492C24×C3—102no—
493C24×C3—102no—
494C24×C3—201no—
495C24×C3—201no—
496C24×C3C22×D511yescharacteristic
497C23×D3—51no—
498C23×D3—54no—
499C23×D3—102no—
500C23×D3—102no—
501C23×D3—102no—
502C23×D3—102no—
503C23×D3—201no—
504C23×D3—201no—
505C23×D3C22×D511yescharacteristic
506C22×C3×C4—51no—
507C22×C3×C4—51no—
508C22×C3×C4C22×D511yescharacteristic
509C22×C3×C4C22×D511yescharacteristic
510C2×#67—22no—
511C2×#67—22no—
512C2×#67—54no—
513C2×#67—54no—
514C2×#67—54no—
515C2×#67—54no—
516C2×#67—54no—
517C2×#67—102no—
518C2×#67—102no—
519C2×#67—102no—
520C2×#67—102no—
521C2×#67—1032no—
522C2×#67C4×D514yescomplemented
523C22×Dic3—51no—
524C22×Dic3—51no—
525C22×Dic3—54no—
526C22×Dic3—51no—
527C22×Dic3—102no—
528C22×Dic3—102no—
529C22×Dic3—102no—
530C22×Dic3—102no—
531C22×Dic3—102no—
532C22×Dic3—102no—
533C22×Dic3—201no—
534C22×Dic3—201no—
535C22×Dic3C22×D511yescharacteristic
536C22×Dic3C22×D511yescharacteristic
537C22×Dic3C22×D511yescharacteristic
538C2×C4×D3—22no—
539C2×C4×D3—22no—
540C2×C4×D3—41no—
541C2×C4×D3—102no—
542C2×C4×D3—102no—
543C2×C4×D3—201no—
544C3×C22⋊C4—41no—
545C3×C22⋊C4—102no—
546C3×C22⋊C4—102no—
547C3×C22⋊C4—102no—
548C3×C22⋊C4—102no—
549C3×C22⋊C4—201no—
550#217—22no—
551#217—54no—
552#217—102no—
553#217—102no—
554(C2×D3)⋊C4—22no—
555(C2×D3)⋊C4—102no—
556(C2×D3)⋊C4—102no—
557(C2×D3)⋊C4—102no—
558(C2×D3)⋊C4—201no—
559(C2×D3)⋊C4—201no—
560Dic3⋊C4—102no—
561Dic3⋊C4—102no—
562C4×Dic3—102no—
563C4×Dic3—102no—
564C23×C5—21no—
565C23×C5—21no—
566C23×C5—21no—
567C23×C5—21no—
568C23×C5—21no—
569C23×C5—21no—
570C23×C5—32no—
571C23×C5—32no—
572C23×C5—32no—
573C23×C5—61no—
574C23×C5—61no—
575C23×C5—61no—
576C23×C5—61no—
577C23×C5C2×C4×D312yes—
578C23×C5C23×D311yescharacteristic
579C22×D5—21no—
580C22×D5—21no—
581C22×D5—21no—
582C22×D5—21no—
583C22×D5—21no—
584C22×D5—21no—
585C22×D5—21no—
586C22×D5—21no—
587C22×D5—28no—
588C22×D5—28no—
589C22×D5—32no—
590C22×D5—44no—
591C22×D5—44no—
592C22×D5—44no—
593C22×D5—44no—
594C22×D5—44no—
595C22×D5—68no—
596C22×D5—61no—
597C22×D5—61no—
598C22×D5—61no—
599C22×D5—61no—
600C22×D5—61no—
601C22×D5—61no—
602C22×D5—68no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5C2×C4×D312yes—
609C22×D5C2×C4×D312yes—
610C22×D5D3×D412yes—
611C22×D5D3×D412yes—
612C22×D5D3×D412yes—
613C22×D5#23712yes—
614C5×D4—68no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—21no—
620C2×C4×C5—21no—
621C2×C4×C5—32no—
622C2×C4×C5—32no—
623C2×C4×C5—61no—
624C2×C4×C5—61no—
625C2×C4×C5—61no—
626C2×C4×C5—61no—
627C2×C4×C5—61no—
628C2×C4×C5—61no—
629C2×C4×C5—61no—
630C2×C4×C5—124no—
631C22⋊D5—316no—
632C22⋊D5—68no—
633C2×Dic5—21no—
634C2×Dic5—21no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—21no—
638C2×Dic5—21no—
639C2×Dic5—32no—
640C2×Dic5—32no—
641C2×Dic5—32no—
642C2×Dic5—32no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—61no—
646C2×Dic5—61no—
647C2×Dic5—61no—
648C2×Dic5—124no—
649D20—68no—
650C4×D5—68no—
651C4×D5—124no—
652C4×D5—124no—
653C25—51no—
654C25—151no—
655C22×D4—31no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—304no—
661C22×D4—304no—
662C23×C4—31no—
663C23×C4—151no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667C4×D4—304no—
668C4×D4—304no—
669C2×C4⋊C4—151no—
670C2×C4⋊C4—151no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—51no—
674C2×C22⋊C4—51no—
675C2×C22⋊C4—51no—
676C2×C22⋊C4—51no—
677C2×C22⋊C4—51no—
678C2×C22⋊C4—151no—
679C2×C22⋊C4—151no—
680C2×C22⋊C4—151no—
681C2×C22⋊C4—151no—
682C2×C22⋊C4—151no—
683C2×C22⋊C4—151no—
684C2×C22⋊C4—151no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—304no—
687C2×C22⋊C4—304no—
688C2×C22⋊C4D3×D511yescharacteristic, complemented
689C2×C42—151no—
690C2×C42—151no—
691#95—31no—
692#95—31no—
693#95—151no—
694#95—151no—
695C2×C3×C5—42no—
696C2×C3×C5C22×C22⋊C411yescharacteristic
697C2×C3×C5C2×C4×D411yescharacteristic
698C2×C3×C5#51811yescharacteristic
699C2×C3×C5D4211yescharacteristic
700C2×C3×C5D4211yescharacteristic
701C2×C3×C5#54611yescharacteristic
702C2×C3×C5#54611yescharacteristic
703D15—42no—
704C3×D5—24no—
705C3×D5—24no—
706C5×D3—24no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—52no—
714C23×C3—52no—
715C23×C3—52no—
716C23×C3—52no—
717C23×C3—52no—
718C23×C3—52no—
719C23×C3—108no—
720C23×C3—108no—
721C23×C3—101no—
722C23×C3—101no—
723C23×C3—101no—
724C23×C3—101no—
725C23×C3—101no—
726C23×C3—101no—
727C23×C3—101no—
728C23×C3—101no—
729C23×C3—204no—
730C23×C3—204no—
731C23×C3—204no—
732C23×C3—204no—
733C23×C3—204no—
734C23×C3C2×C4×D512yes—
735C23×C3C23×D511yescharacteristic
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—52no—
741C22×D3—108no—
742C22×D3—101no—
743C22×D3—101no—
744C22×D3—101no—
745C22×D3—101no—
746C22×D3—101no—
747C22×D3—101no—
748C22×D3—108no—
749C22×D3—204no—
750C22×D3—204no—
751C22×D3—204no—
752C22×D3—204no—
753C22×D3—204no—
754C22×D3C2×C4×D512yes—
755C22×D3D4×D512yes—
756C22×D3D4×D512yes—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—101no—
764C2×C3×C4—101no—
765C2×C3×C4—101no—
766C2×C3×C4—101no—
767C2×C3×C4—101no—
768C2×C3×C4—101no—
769#67—28no—
770#67—516no—
771#67—108no—
772#67—108no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—52no—
781C2×Dic3—52no—
782C2×Dic3—52no—
783C2×Dic3—52no—
784C2×Dic3—108no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—204no—
791C2×Dic3—204no—
792C2×Dic3C2×C4×D512yes—
793C2×Dic3D4×D512yescomplemented
794C4×D3—44no—
795C4×D3—204no—
796C22×C5—22no—
797C22×C5—22no—
798C22×C5—22no—
799C22×C5—34no—
800C22×C5—41no—
801C22×C5—41no—
802C22×C5—41no—
803C22×C5—41no—
804C22×C5—62no—
805C22×C5—62no—
806C22×C5—62no—
807C22×C5—62no—
808C22×C5—62no—
809C22×C5—62no—
810C22×C5C22×C4×D311yescharacteristic
811C22×C5C2×D3×D411yescharacteristic
812C22×C5C2×D3×D411yescharacteristic
813C22×C5C2×D3×D411yescharacteristic
814C22×C5C2×#23711yescharacteristic
815C22×C5#100411yescharacteristic
816C22×C5#100411yescharacteristic
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—22no—
820C2×D5—22no—
821C2×D5—22no—
822C2×D5—22no—
823C2×D5—22no—
824C2×D5—22no—
825C2×D5—22no—
826C2×D5—22no—
827C2×D5—22no—
828C2×D5—22no—
829C2×D5—416no—
830C2×D5—62no—
831C2×D5—62no—
832C2×D5—62no—
833C2×D5—1216no—
834C2×D5—121no—
835C2×D5—121no—
836C2×D5—121no—
837C2×D5—121no—
838C2×D5D3×C22⋊C414yescomplemented
839C2×D5#67⋊C414yescomplemented
840C4×C5—41no—
841C4×C5—41no—
842C4×C5—62no—
843C4×C5—62no—
844C4×C5—121no—
845Dic5—34no—
846Dic5—41no—
847Dic5—41no—
848Dic5—62no—
849Dic5—121no—
850C24—31no—
851C24—51no—
852C24—51no—
853C24—54no—
854C24—102no—
855C24—102no—
856C24—102no—
857C24—102no—
858C24—154no—
859C24—151no—
860C24—201no—
861C24—201no—
862C24—302no—
863C24—302no—
864C24—302no—
865C24—302no—
866C24—601no—
867C24—601no—
868C24C2×D3×D511yescharacteristic
869C2×D4—34no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—154no—
873C2×D4—154no—
874C2×D4—154no—
875C2×D4—154no—
876C2×D4—154no—
877C2×D4—302no—
878C2×D4—302no—
879C2×D4—302no—
880C2×D4—302no—
881C2×D4—3032no—
882C22×C4—31no—
883C22×C4—31no—
884C22×C4—31no—
885C22×C4—51no—
886C22×C4—51no—
887C22×C4—62no—
888C22×C4—62no—
889C22×C4—121no—
890C22×C4—154no—
891C22×C4—151no—
892C22×C4—151no—
893C22×C4—151no—
894C22×C4—302no—
895C22×C4—302no—
896C22×C4—302no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—302no—
902C22×C4—601no—
903C22×C4—601no—
904C22×C4—601no—
905C22×C4C2×D3×D511yescharacteristic
906C22×C4C2×D3×D511yescharacteristic
907C4⋊C4—302no—
908C4⋊C4—302no—
909C22⋊C4—41no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—102no—
913C22⋊C4—102no—
914C22⋊C4—102no—
915C22⋊C4—102no—
916C22⋊C4—154no—
917C22⋊C4—201no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—302no—
922C22⋊C4—302no—
923C22⋊C4—601no—
924C22⋊C4—601no—
925C42—302no—
926C42—302no—
927C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—22no—
931C22×C3—41no—
932C22×C3—41no—
933C22×C3—41no—
934C22×C3—41no—
935C22×C3—54no—
936C22×C3—54no—
937C22×C3—102no—
938C22×C3—102no—
939C22×C3—102no—
940C22×C3—102no—
941C22×C3—102no—
942C22×C3—102no—
943C22×C3—102no—
944C22×C3—102no—
945C22×C3—102no—
946C22×C3—102no—
947C22×C3—102no—
948C22×C3—102no—
949C22×C3—2016no—
950C22×C3C22×C4×D511yescharacteristic
951C22×C3C2×D4×D511yescharacteristic
952C22×C3C2×D4×D511yescharacteristic
953C22×C3C2×D4×D511yescharacteristic
954C22×C3#414411yescharacteristic
955C22×C3D5×#4111yescharacteristic
956C22×C3#414911yescharacteristic
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—22no—
962C2×D3—22no—
963C2×D3—102no—
964C2×D3—102no—
965C2×D3—102no—
966C2×D3—2016no—
967C2×D3—201no—
968C2×D3—201no—
969C2×D3—201no—
970C2×D3—201no—
971C2×D3D5×C22⋊C414yescomplemented
972C3×C4—41no—
973C3×C4—41no—
974C3×C4—201no—
975C3×C4—201no—
976Dic3—22no—
977Dic3—22no—
978Dic3—41no—
979Dic3—54no—
980Dic3—102no—
981Dic3—201no—
982C2×C5—42no—
983C2×C5—64no—
984C2×C5C2×D3×C22⋊C411yescharacteristic
985C2×C5C2×#67⋊C411yescharacteristic
986C2×C5#548611yescharacteristic
987C2×C5#559011yescharacteristic
988C2×C5#559011yescharacteristic
989C2×C5#559111yescharacteristic
990C2×C5#559111yescharacteristic
991D5—24no—
992D5—24no—
993D5—122no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—32no—
1001C23—32no—
1002C23—32no—
1003C23—52no—
1004C23—52no—
1005C23—52no—
1006C23—52no—
1007C23—52no—
1008C23—52no—
1009C23—61no—
1010C23—61no—
1011C23—61no—
1012C23—61no—
1013C23—108no—
1014C23—108no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—101no—
1022C23—101no—
1023C23—152no—
1024C23—204no—
1025C23—204no—
1026C23—204no—
1027C23—204no—
1028C23—204no—
1029C23—308no—
1030C23—308no—
1031C23—301no—
1032C23—301no—
1033C23—301no—
1034C23—301no—
1035C23—301no—
1036C23—301no—
1037C23—604no—
1038C23—604no—
1039C23—604no—
1040C23—604no—
1041C23—604no—
1042C23C4×D3×D512yes—
1043C23C22×D3×D511yescharacteristic
1044D4—68no—
1045D4—1516no—
1046D4—308no—
1047D4—308no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—32no—
1055C2×C4—32no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—101no—
1064C2×C4—101no—
1065C2×C4—101no—
1066C2×C4—101no—
1067C2×C4—101no—
1068C2×C4—101no—
1069C2×C4—124no—
1070C2×C4—152no—
1071C2×C4—152no—
1072C2×C4—152no—
1073C2×C4—152no—
1074C2×C4—308no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—301no—
1080C2×C4—604no—
1081C2×C4—604no—
1082C2×C4—604no—
1083C2×C3—42no—
1084C2×C3—104no—
1085C2×C3—104no—
1086C2×C3C2×D5×C22⋊C411yescharacteristic
1087C2×C3C4×D4×D511yescharacteristic
1088C2×C3#6587911yescharacteristic
1089C2×C3#6592411yescharacteristic
1090C2×C3#6594311yescharacteristic
1091C2×C3#6594411yescharacteristic
1092C2×C3#6598811yescharacteristic
1093D3—24no—
1094D3—202no—
1095C5#7385011yescharacteristic, complemented, Sylow
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—34no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—54no—
1105C22—54no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—102no—
1113C22—102no—
1114C22—102no—
1115C22—102no—
1116C22—102no—
1117C22—102no—
1118C22—102no—
1119C22—102no—
1120C22—102no—
1121C22—102no—
1122C22—102no—
1123C22—102no—
1124C22—2016no—
1125C22—302no—
1126C22—302no—
1127C22—302no—
1128C22—6016no—
1129C22—601no—
1130C22—601no—
1131C22—601no—
1132C22—601no—
1133C22C2×C4×D3×D511yescharacteristic
1134C22#9201711yescharacteristic
1135C22D3×D4×D511yescharacteristic
1136C22D3×D4×D511yescharacteristic
1137C22D3×D4×D511yescharacteristic
1138C22D5×#23711yescharacteristic
1139C22#9204911yescharacteristic
1140C4—41no—
1141C4—41no—
1142C4—62no—
1143C4—62no—
1144C4—121no—
1145C4—154no—
1146C4—201no—
1147C4—201no—
1148C4—302no—
1149C4—601no—
1150C3#1060660911yescharacteristic, complemented, Sylow
1151C2—42no—
1152C2—64no—
1153C2—104no—
1154C2—104no—
1155C2—602no—
1156C2D3×D5×C22⋊C411yescharacteristic
1157C2D5×#67⋊C411yescharacteristic
1158C2#1175322911yescharacteristic
1159C2#1175323011yescharacteristic
1160C2#1175462511yescharacteristic
1161C2#1175503411yescharacteristic
1162C2#1175503511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×#67C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5D4×C22⋊C4
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
2. C2×D5×#217C2semidirect
3. C2×D3×#685C2semidirect
4. C2×#91442C2semidirect
5. C2×#91441C2semidirect
6. #11751058C2semidirect
7. C5×#4956C2semidirect
8. C3×#65244C2semidirect
9. #11749519C2semidirect
10. #11749483C2semidirect
11. #11748940C2semidirect
12. #11748885C2semidirect
13. #11748884C2semidirect
14. #11748872C2semidirect
15. #11748872C2semidirect
21. C22×C4×C5×D3C22semidirect
24. C2×D5×#67C4semidirect
27. C22×D3×Dic5C22semidirect
29. C22×D5×Dic3C22semidirect
30. C22×D5×Dic3C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
32. C2×#6719C22semidirect
33. C2×#6714C22semidirect
34. C2×#6714C22semidirect
35. C2×#6712C22semidirect
36. C2×C4×Dic15C22semidirect
37. C2×C5×#217C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C3×C22⋊Dic5C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
45. C2×#6669C22semidirect
46. C2×#6667C22semidirect
47. C2×#6667C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×Dic3×Dic5C22semidirect
55. C5×C3⋊#95C22semidirect
56. C5×C3⋊#95C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
70. #65244D3semidirect
84. C23×C3×D5C2×C4semidirect
93. C22×D3×D5C2×C4semidirect
98. C2×#1220C2×C4semidirect
104. C2×C5×#67C2×C4semidirect
116. C2×#1202C2×C4semidirect
131. C2×D5×Dic3C2×C4semidirect
150. #6665D4semidirect
163. #4956D5semidirect
183. C2×C5×C22⋊C4C2×D3semidirect
186. C2×C22⋊Dic5C2×D3semidirect
197. C2×#685C2×D3semidirect
198. C2×#685C2×D3semidirect
275. C2×Dic15C2×D4semidirect
285. C2×C5×Dic3C2×D4semidirect
294. #1201C22⋊C4semidirect
312. C22×C4×D3C2×D5semidirect
318. C2×C3×C22⋊C4C2×D5semidirect
323. C2×#217C2×D5semidirect
329. C2×(C2×D3)⋊C4C2×D5semidirect
339. C3⋊#95C2×D5semidirect
340. C3⋊#95C2×D5semidirect
357. C23×D5C4×D3semidirect
460. C2×C5×D3C2×C22⋊C4semidirect
474. C2×C3×D5C2×C22⋊C4semidirect
475. C2×C3×D5C4×D4semidirect
481. Dic15C2×C22⋊C4semidirect
522. C2×#67C4×D5semidirect
688. C2×C22⋊C4D3×D5semidirect
793. C2×Dic3D4×D5semidirect
838. C2×D5D3×C22⋊C4semidirect
839. C2×D5#67⋊C4semidirect
927. C3×C5D4×C22⋊C4semidirect
971. C2×D3D5×C22⋊C4semidirect
1095. C5#73850semidirect
1150. C3#10606609semidirect

Maximal subgroups

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

subgroupindex
C22×D5×#672
C2×D5×#2172
C2×D3×#6852
C2×#914422
C2×#914412
#117510582
C5×#49562
C3×#652442
#117495192
#117494832
#117489402
#117488852
#117488842
#117488722
#106066093
#738505