Finite Group Databasebeta

← #14325957

Subgroups — #14325957

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×C3×D4×D5C211yesmaximal, characteristic
2C2×#91559C211yesmaximal, characteristic, complemented
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×D5×#217C211yesmaximal, characteristic, complemented
5C22×#6665C211yesmaximal, characteristic, complemented
6#11751321C211yesmaximal, characteristic, complemented
7C5×#5220C211yesmaximal, characteristic, complemented
8#11749489C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11749488C211yesmaximal, characteristic, complemented
11#11749488C211yesmaximal, characteristic, complemented
12#11748896C211yesmaximal, characteristic, complemented
13#11748896C211yesmaximal, characteristic, complemented
14#11748738C211yesmaximal, characteristic, complemented
15#11748702C211yesmaximal, characteristic, complemented
16#10606609—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C24×C3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×Dic15C2211yescharacteristic, complemented
21C23×C5×Dic3C2211yescharacteristic, complemented
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C2×C3×D4×D5—24no—
25C2×C3×D4×D5—24no—
26C2×C3×D4×D5C418yescomplemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic, complemented
31C2×#6719C2211yescharacteristic, complemented
32C2×#6719C2211yescharacteristic, complemented
33C2×#6719C2211yescharacteristic, complemented
34C2×C5×#217C2211yescharacteristic, complemented
35C2×C5×#217C2211yescharacteristic, complemented
36C2×C5×#217C2211yescharacteristic, complemented
37#91559—24no—
38Dic3×C22⋊D5—24no—
39D5×#217—24no—
40C2×#6668C2211yescharacteristic, complemented
41C2×#6668C2211yescharacteristic, complemented
42C2×#6665—24no—
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic, complemented
48C2×#6665C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic, complemented
50C2×#6665C2211yescharacteristic, complemented
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×Dic3×Dic5C2211yescharacteristic, complemented
54C2×Dic3×Dic5C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57C5×C3⋊#95C2211yescharacteristic, complemented
58C5×C3⋊#95C2211yescharacteristic, complemented
59D4×#217—51nomaximal, Hall
60C22×D4×D5D311yescharacteristic
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#65244—31no—
71#64956—31no—
72#64955—31no—
73#64954—31no—
74#64954—31no—
75C24×C3×C5C2311yescharacteristic
76C24×C3×C5C2311yescharacteristic
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5—22no—
81C23×C3×D5—22no—
82C23×C3×D5—22no—
83C23×C3×D5—22no—
84C23×C3×D5—22no—
85C23×C3×D5—41no—
86C23×C3×D5—41no—
87C23×C3×D5—41no—
88C23×C3×D5—41no—
89C23×C3×D5C2×C414yescomplemented
90C23×C3×D5C2×C414yescomplemented
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C2×C3×C5×D4—22no—
95C2×C3×C5×D4—22no—
96C2×C3×C5×D4C2×C414yescomplemented
97C22×C3×C4×C5C2311yescharacteristic
98C22×Dic15—22no—
99C22×Dic15—22no—
100C22×Dic15—41no—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×C5×Dic3—22no—
106C22×C5×Dic3—22no—
107C22×C5×Dic3—41no—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C2×C3×C22⋊D5—22no—
113C2×C3×C22⋊D5—22no—
114C2×C3×C22⋊D5C2×C414yes—
115C2×C3×C22⋊D5C2×C414yescomplemented
116C2×C3×C22⋊D5D414yes—
117C2×C3×C22⋊D5D414yes—
118C22×C3×Dic5C2311yescharacteristic
119C3×D4×D5—232no—
120C2×C3×D20—22no—
121C2×C3×D20—22no—
122C2×C3×D20C2×C414yescomplemented
123C2×C3×C4×D5—22no—
124C2×C3×C4×D5—22no—
125C2×C3×C4×D5C2×C414yescomplemented
126C2×D5×Dic3—22no—
127C2×D5×Dic3—22no—
128C2×D5×Dic3—22no—
129C2×D5×Dic3—22no—
130C2×D5×Dic3—41no—
131C2×D5×Dic3—41no—
132#6719—22no—
133#6719—22no—
134#6719—41no—
135C5×#217—22no—
136C5×#217—22no—
137C5×#217—41no—
138#6668—22no—
139#6668—22no—
140#6665—22no—
141#6665—22no—
142#6665—22no—
143#6665—22no—
144#6665—22no—
145#6665—22no—
146#6665—22no—
147#6665—41no—
148#6665—41no—
149#6665D414yescomplemented
150Dic3×Dic5—22no—
151Dic3×Dic5—22no—
152C23×C3×D4—51no—
153C22×#217—51no—
154C22×#217—51no—
155C2×D4×Dic3—51no—
156C2×D4×Dic3—51no—
157#5247—51no—
158#5247—51no—
159#5221—51no—
160#5221—51no—
161#5220—51no—
162#5220—51no—
163#5220—51no—
164#5220D511yescharacteristic, complemented
165#5212—51no—
166C4×#217—51no—
167C24×D5C2×D311yescharacteristic
168C24×D5C2×D311yescharacteristic
169C22×C5×D4C2×D311yescharacteristic
170C23×C4×C5—31no—
171C22×C22⋊D5C2×D311yescharacteristic
172C22×C22⋊D5C2×D311yescharacteristic
173C23×Dic5—31no—
174C2×D4×D5—24no—
175C2×D4×D5—24no—
176C2×D4×D5Dic318yescomplemented
177C22×D20C2×D311yescharacteristic
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C4×C22⋊D5—64no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—64no—
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×C5—21no—
217C23×C3×C5—21no—
218C23×C3×C5—21no—
219C23×C3×C5—21no—
220C23×C3×C5C22×C412yes—
221C23×C3×C5C22×C412yes—
222C23×C3×C5C2×D412yes—
223C23×C3×C5C2×D412yes—
224C23×C3×C5C2411yescharacteristic
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5—21no—
230C22×C3×D5—21no—
231C22×C3×D5—21no—
232C22×C3×D5—21no—
233C22×C3×D5—28no—
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—28no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—44no—
247C22×C3×D5—44no—
248C22×C3×D5—44no—
249C22×C3×D5—44no—
250C22×C3×D5—44no—
251C22×C3×D5—44no—
252C22×C3×D5—44no—
253C22×C3×D5C22×C412yes—
254C22×C3×D5C22×C412yes—
255C22×C3×D5C22×C412yes—
256C22×C3×D5C2×D412yes—
257C22×C3×D5C2×D412yes—
258C22×C3×D5C2×D412yes—
259C22×C3×D5#4112yes—
260C3×C5×D4—28no—
261C2×C3×C4×C5—21no—
262C2×C3×C4×C5—21no—
263C2×C3×C4×C5C22×C412yes—
264C2×Dic15—21no—
265C2×Dic15—21no—
266C2×Dic15—21no—
267C2×Dic15—21no—
268C2×Dic15—21no—
269C2×Dic15—21no—
270C2×Dic15—21no—
271C2×Dic15—21no—
272C2×Dic15—21no—
273C2×Dic15—21no—
274C2×Dic15—21no—
275C2×Dic15—44no—
276C2×Dic15C2×D412yescomplemented
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×Dic3—21no—
285C2×C5×Dic3—21no—
286C2×C5×Dic3—21no—
287C2×C5×Dic3—21no—
288C2×C5×Dic3—44no—
289C2×C5×Dic3C2×D412yescomplemented
290C3×C22⋊D5—28no—
291C3×C22⋊D5C22⋊C4116yescomplemented
292C2×C3×Dic5C22×C412yes—
293C2×C3×Dic5C2×D412yes—
294C2×C3×Dic5C2×D412yes—
295C3×D20—28no—
296C3×C4×D5—28no—
297D5×Dic3—44no—
298D5×Dic3—44no—
299C25×C3—51no—
300C25×C3—51no—
301C22×C3×D4—51no—
302C22×C3×D4—51no—
303C22×C3×D4—58no—
304C22×C3×D4—51no—
305C22×C3×D4—104no—
306C22×C3×D4—104no—
307C22×C3×D4C2×D511yescharacteristic
308C23×C3×C4—51no—
309C23×Dic3—51no—
310C23×Dic3—51no—
311C23×Dic3—51no—
312C23×Dic3C2×D511yescharacteristic, complemented
313C2×#217—51no—
314C2×#217—51no—
315C2×#217—51no—
316C2×#217—51no—
317C2×#217—51no—
318C2×#217—51no—
319C2×#217—51no—
320C2×#217—51no—
321C2×#217—51no—
322C2×#217—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217—104no—
327C2×#217—104no—
328C2×#217C2×D511yescharacteristic, complemented
329C2×#217C2×D511yescharacteristic, complemented
330C2×#217C2×D511yescharacteristic, complemented
331D4×Dic3—104no—
332D4×Dic3—104no—
333C2×C4⋊Dic3—51no—
334C2×C4⋊Dic3—51no—
335C2×C4×Dic3—51no—
336C2×C4×Dic3—51no—
337C3⋊#95—51no—
338C3⋊#95—51no—
339C3⋊#95C2×D511yescharacteristic, complemented
340C3⋊#95C2×D511yescharacteristic, complemented
341C24×C5C22×D311yescharacteristic
342C24×C5C22×D311yescharacteristic
343C23×D5—22no—
344C23×D5—22no—
345C23×D5—22no—
346C23×D5—22no—
347C23×D5—22no—
348C23×D5—22no—
349C23×D5—22no—
350C23×D5—22no—
351C23×D5—41no—
352C23×D5—41no—
353C23×D5—41no—
354C23×D5—41no—
355C23×D5C2×Dic314yescomplemented
356C23×D5C2×Dic314yescomplemented
357C23×D5C22×D311yescharacteristic
358C23×D5C22×D311yescharacteristic
359C23×D5C22×D311yescharacteristic
360C2×C5×D4—22no—
361C2×C5×D4—22no—
362C2×C5×D4C2×Dic314yescomplemented
363C22×C4×C5—31no—
364C22×C4×C5—31no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—62no—
368C22×C4×C5—62no—
369C22×C4×C5—121no—
370C22×C4×C5C22×D311yescharacteristic
371C2×C22⋊D5—22no—
372C2×C22⋊D5—22no—
373C2×C22⋊D5C2×Dic314yes—
374C2×C22⋊D5C2×Dic314yescomplemented
375C2×C22⋊D5#6714yes—
376C2×C22⋊D5#6714yes—
377C22×Dic5—31no—
378C22×Dic5—31no—
379C22×Dic5—31no—
380C22×Dic5—31no—
381C22×Dic5—62no—
382C22×Dic5—62no—
383C22×Dic5—121no—
384C22×Dic5C22×D311yescharacteristic
385D4×D5—232no—
386C2×D20—22no—
387C2×D20—22no—
388C2×D20C2×Dic314yescomplemented
389C2×C4×D5—22no—
390C2×C4×D5—22no—
391C2×C4×D5—62no—
392C2×C4×D5—62no—
393C2×C4×D5—62no—
394C2×C4×D5—62no—
395C2×C4×D5—121no—
396C2×C4×D5—121no—
397C2×C4×D5C2×Dic314yescomplemented
398C5×C22⋊C4—62no—
399C5×C22⋊C4—62no—
400C5×C22⋊C4—121no—
401C22⋊Dic5—62no—
402C22⋊Dic5—62no—
403C22⋊Dic5—121no—
404#685—34no—
405#685—62no—
406#685—62no—
407#685—62no—
408#685—62no—
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—51no—
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—151no—
431#379—151no—
432C4×C22⋊C4—151no—
433C22×C3×C5—22no—
434C22×C3×C5—22no—
435C22×C3×C5—22no—
436C22×C3×C5—22no—
437C22×C3×C5—22no—
438C22×C3×C5—22no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—41no—
443C22×C3×C5—41no—
444C22×C3×C5—41no—
445C22×C3×C5—41no—
446C22×C3×C5C2×C22⋊C414yescomplemented
447C22×C3×C5C23×C411yescharacteristic
448C22×C3×C5C22×D411yescharacteristic
449C22×C3×C5C22×D411yescharacteristic
450C22×C3×C5C22×D411yescharacteristic
451C22×C3×C5C2×#4111yescharacteristic
452C22×C3×C5H(5,𝔽2)11yescharacteristic
453C22×C3×C5H(5,𝔽2)11yescharacteristic
454C2×C3×D5—22no—
455C2×C3×D5—22no—
456C2×C3×D5—22no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
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—416no—
470C2×C3×D5—416no—
471C2×C3×D5—41no—
472C2×C3×D5—41no—
473C2×C3×D5—41no—
474C2×C3×D5—41no—
475C2×C3×D5C2×C22⋊C414yescomplemented
476C2×C3×D5C4×D414yescomplemented
477C3×C4×C5—22no—
478Dic15—22no—
479Dic15—41no—
480Dic15—41no—
481Dic15—41no—
482C3×Dic5C2×C22⋊C414yescomplemented
483C5×Dic3—22no—
484C5×Dic3—41no—
485C5×Dic3—41no—
486C5×Dic3—41no—
487C24×C3—51no—
488C24×C3—51no—
489C24×C3—51no—
490C24×C3—54no—
491C24×C3—54no—
492C24×C3—102no—
493C24×C3—102no—
494C24×C3—102no—
495C24×C3—102no—
496C24×C3—102no—
497C24×C3—102no—
498C24×C3—102no—
499C24×C3—102no—
500C24×C3—201no—
501C24×C3—201no—
502C24×C3—201no—
503C24×C3—201no—
504C24×C3C22×D511yescharacteristic
505C24×C3C22×D511yescharacteristic
506C2×C3×D4—22no—
507C2×C3×D4—22no—
508C2×C3×D4—54no—
509C2×C3×D4—54no—
510C2×C3×D4—54no—
511C2×C3×D4—54no—
512C2×C3×D4—54no—
513C2×C3×D4—102no—
514C2×C3×D4—102no—
515C2×C3×D4—102no—
516C2×C3×D4—102no—
517C2×C3×D4—1032no—
518C2×C3×D4C4×D514yescomplemented
519C22×C3×C4—51no—
520C22×C3×C4—54no—
521C22×C3×C4—102no—
522C22×C3×C4—102no—
523C22×C3×C4C22×D511yescharacteristic
524C22×Dic3—22no—
525C22×Dic3—22no—
526C22×Dic3—41no—
527C22×Dic3—51no—
528C22×Dic3—51no—
529C22×Dic3—51no—
530C22×Dic3—51no—
531C22×Dic3—102no—
532C22×Dic3—102no—
533C22×Dic3—102no—
534C22×Dic3—102no—
535C22×Dic3—102no—
536C22×Dic3—102no—
537C22×Dic3—201no—
538C22×Dic3—201no—
539C22×Dic3—201no—
540C22×Dic3C22×D511yescharacteristic
541C22×Dic3C22×D511yescharacteristic
542C22×Dic3C22×D511yescharacteristic
543C22×Dic3C22×D511yescharacteristic
544#217—22no—
545#217—22no—
546#217—41no—
547#217—54no—
548#217—102no—
549#217—102no—
550#217—102no—
551#217—102no—
552#217—102no—
553#217—102no—
554#217—102no—
555#217—102no—
556#217—102no—
557#217—201no—
558#217—201no—
559#217—201no—
560C4⋊Dic3—102no—
561C4⋊Dic3—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—21no—
571C23×C5—21no—
572C23×C5—21no—
573C23×C5—21no—
574C23×C5C22×Dic312yes—
575C23×C5C22×Dic312yes—
576C23×C5C2×#6712yes—
577C23×C5C2×#6712yes—
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—21no—
589C22×D5—21no—
590C22×D5—21no—
591C22×D5—21no—
592C22×D5—21no—
593C22×D5—21no—
594C22×D5—28no—
595C22×D5—28no—
596C22×D5—28no—
597C22×D5—44no—
598C22×D5—44no—
599C22×D5—44no—
600C22×D5—44no—
601C22×D5—44no—
602C22×D5—44no—
603C22×D5—44no—
604C22×D5—44no—
605C22×D5—44no—
606C22×D5—44no—
607C22×D5D3×D412yes—
608C22×D5#23712yes—
609C22×D5C22×Dic312yes—
610C22×D5C22×Dic312yes—
611C22×D5C22×Dic312yes—
612C22×D5C2×#6712yes—
613C22×D5C2×#6712yes—
614C5×D4—28no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—32no—
618C2×C4×C5—61no—
619C2×C4×C5—61no—
620C2×C4×C5—61no—
621C2×C4×C5—61no—
622C2×C4×C5—61no—
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—124no—
630C2×C4×C5C22×Dic312yes—
631C22⋊D5—28no—
632C22⋊D5#217116yescomplemented
633C2×Dic5—32no—
634C2×Dic5—61no—
635C2×Dic5—61no—
636C2×Dic5—61no—
637C2×Dic5—61no—
638C2×Dic5—61no—
639C2×Dic5—61no—
640C2×Dic5—61no—
641C2×Dic5—61no—
642C2×Dic5—61no—
643C2×Dic5—61no—
644C2×Dic5—61no—
645C2×Dic5—124no—
646C2×Dic5C22×Dic312yes—
647C2×Dic5C2×#6712yes—
648C2×Dic5C2×#6712yes—
649D20—28no—
650C4×D5—28no—
651C4×D5—124no—
652C4×D5—124no—
653C25—51no—
654C25—51no—
655C22×D4—51no—
656C22×D4—51no—
657C22×D4—58no—
658C22×D4—51no—
659C22×D4—104no—
660C22×D4—104no—
661C22×D4D3×D511yescharacteristic
662C23×C4—31no—
663C23×C4—51no—
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—31no—
674C2×C22⋊C4—151no—
675C2×C22⋊C4—151no—
676C2×C22⋊C4—151no—
677C2×C22⋊C4—151no—
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—151no—
687C2×C22⋊C4—304no—
688C2×C22⋊C4—304no—
689C2×C42—151no—
690C2×C42—151no—
691#95—31no—
692#95—31no—
693#95—151no—
694#95—151no—
695C2×C3×C5—24no—
696C2×C3×C5—42no—
697C2×C3×C5C22×C22⋊C411yescharacteristic
698C2×C3×C5C2×C4×D411yescharacteristic
699C2×C3×C5#51811yescharacteristic
700C2×C3×C5D4211yescharacteristic
701C2×C3×C5D4211yescharacteristic
702C2×C3×C5#54611yescharacteristic
703C2×C3×C5#54611yescharacteristic
704C3×D5—24no—
705C3×D5—24no—
706C3×D5—42no—
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—52no—
718C23×C3—52no—
719C23×C3—52no—
720C23×C3—52no—
721C23×C3—52no—
722C23×C3—52no—
723C23×C3—52no—
724C23×C3—108no—
725C23×C3—108no—
726C23×C3—108no—
727C23×C3—101no—
728C23×C3—101no—
729C23×C3—101no—
730C23×C3—101no—
731C23×C3—101no—
732C23×C3—101no—
733C23×C3—101no—
734C23×C3—101no—
735C23×C3—101no—
736C23×C3—101no—
737C23×C3—101no—
738C23×C3—101no—
739C23×C3—101no—
740C23×C3—101no—
741C23×C3—108no—
742C23×C3—204no—
743C23×C3—204no—
744C23×C3—204no—
745C23×C3—204no—
746C23×C3—204no—
747C23×C3—204no—
748C23×C3—204no—
749C23×C3—204no—
750C23×C3—204no—
751C23×C3—204no—
752C23×C3C2×C4×D512yes—
753C23×C3C2×C4×D512yes—
754C23×C3D4×D512yes—
755C23×C3D4×D512yes—
756C23×C3C23×D511yescharacteristic
757C3×D4—28no—
758C3×D4—516no—
759C3×D4—108no—
760C3×D4—108no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—52no—
764C2×C3×C4—52no—
765C2×C3×C4—52no—
766C2×C3×C4—108no—
767C2×C3×C4C2×C4×D512yes—
768C2×Dic3—21no—
769C2×Dic3—21no—
770C2×Dic3—21no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—44no—
780C2×Dic3—52no—
781C2×Dic3—101no—
782C2×Dic3—101no—
783C2×Dic3—101no—
784C2×Dic3—101no—
785C2×Dic3—101no—
786C2×Dic3—101no—
787C2×Dic3—101no—
788C2×Dic3—101no—
789C2×Dic3—101no—
790C2×Dic3—101no—
791C2×Dic3—101no—
792C2×Dic3—204no—
793C2×Dic3—204no—
794C2×Dic3—204no—
795C2×Dic3D4×D512yescomplemented
796C22×C5—22no—
797C22×C5—22no—
798C22×C5—22no—
799C22×C5—22no—
800C22×C5—22no—
801C22×C5—22no—
802C22×C5—22no—
803C22×C5—22no—
804C22×C5—22no—
805C22×C5—41no—
806C22×C5—41no—
807C22×C5—41no—
808C22×C5—41no—
809C22×C5C2×#21714yescomplemented
810C22×C5C2×D3×D411yescharacteristic
811C22×C5C2×#23711yescharacteristic
812C22×C5#100411yescharacteristic
813C22×C5#100411yescharacteristic
814C22×C5C23×Dic311yescharacteristic
815C22×C5C22×#6711yescharacteristic
816C22×C5C22×#6711yescharacteristic
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—22no—
830C2×D5—22no—
831C2×D5—22no—
832C2×D5—416no—
833C2×D5—416no—
834C2×D5—41no—
835C2×D5—41no—
836C2×D5—41no—
837C2×D5—41no—
838C2×D5D4×Dic314yescomplemented
839C2×D5C2×#21714yescomplemented
840C4×C5—22no—
841C4×C5—62no—
842C4×C5—121no—
843C4×C5—121no—
844C4×C5—121no—
845Dic5—62no—
846Dic5—121no—
847Dic5—121no—
848Dic5—121no—
849Dic5C2×#21714yescomplemented
850C24—51no—
851C24—51no—
852C24—51no—
853C24—54no—
854C24—54no—
855C24—102no—
856C24—102no—
857C24—102no—
858C24—102no—
859C24—102no—
860C24—102no—
861C24—102no—
862C24—102no—
863C24—201no—
864C24—201no—
865C24—201no—
866C24—201no—
867C24C2×D3×D511yescharacteristic
868C24C2×D3×D511yescharacteristic
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—54no—
872C2×D4—54no—
873C2×D4—54no—
874C2×D4—54no—
875C2×D4—54no—
876C2×D4—102no—
877C2×D4—102no—
878C2×D4—102no—
879C2×D4—102no—
880C2×D4—1032no—
881C2×D4D5×Dic314yescomplemented
882C22×C4—31no—
883C22×C4—31no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—51no—
887C22×C4—54no—
888C22×C4—62no—
889C22×C4—62no—
890C22×C4—102no—
891C22×C4—102no—
892C22×C4—121no—
893C22×C4—151no—
894C22×C4—151no—
895C22×C4—151no—
896C22×C4—151no—
897C22×C4—302no—
898C22×C4—302no—
899C22×C4—302no—
900C22×C4—302no—
901C22×C4—302no—
902C22×C4—302no—
903C22×C4—601no—
904C22×C4—601no—
905C22×C4—601no—
906C22×C4C2×D3×D511yescharacteristic
907C4⋊C4—302no—
908C4⋊C4—302no—
909C22⋊C4—62no—
910C22⋊C4—62no—
911C22⋊C4—121no—
912C22⋊C4—154no—
913C22⋊C4—302no—
914C22⋊C4—302no—
915C22⋊C4—302no—
916C22⋊C4—302no—
917C22⋊C4—302no—
918C22⋊C4—302no—
919C22⋊C4—302no—
920C22⋊C4—302no—
921C22⋊C4—302no—
922C22⋊C4—601no—
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—22no—
932C22×C3—22no—
933C22×C3—22no—
934C22×C3—22no—
935C22×C3—22no—
936C22×C3—22no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
941C22×C3—54no—
942C22×C3—54no—
943C22×C3—102no—
944C22×C3—102no—
945C22×C3—102no—
946C22×C3—102no—
947C22×C3—102no—
948C22×C3—102no—
949C22×C3—102no—
950C22×C3—102no—
951C22×C3—102no—
952C22×C3—102no—
953C22×C3—102no—
954C22×C3—102no—
955C22×C3—102no—
956C22×C3—102no—
957C22×C3—102no—
958C22×C3—2016no—
959C22×C3—2016no—
960C22×C3—201no—
961C22×C3—201no—
962C22×C3—201no—
963C22×C3—201no—
964C22×C3D5×C22⋊C414yescomplemented
965C22×C3C22×C4×D511yescharacteristic
966C22×C3C2×D4×D511yescharacteristic
967C22×C3C2×D4×D511yescharacteristic
968C22×C3C2×D4×D511yescharacteristic
969C22×C3#414411yescharacteristic
970C22×C3D5×#4111yescharacteristic
971C22×C3#414911yescharacteristic
972C3×C4—22no—
973C3×C4—54no—
974Dic3—22no—
975Dic3—41no—
976Dic3—41no—
977Dic3—41no—
978Dic3—102no—
979Dic3—201no—
980Dic3—201no—
981Dic3—201no—
982C2×C5—24no—
983C2×C5—42no—
984C2×C5C2×D4×Dic311yescharacteristic
985C2×C5#579811yescharacteristic
986C2×C5D4×#6711yescharacteristic
987C2×C5D4×#6711yescharacteristic
988C2×C5#580611yescharacteristic
989C2×C5#580611yescharacteristic
990C2×C5C22×#21711yescharacteristic
991D5—24no—
992D5—24no—
993D5—42no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—52no—
1005C23—52no—
1006C23—52no—
1007C23—52no—
1008C23—52no—
1009C23—52no—
1010C23—52no—
1011C23—108no—
1012C23—108no—
1013C23—108no—
1014C23—101no—
1015C23—101no—
1016C23—101no—
1017C23—101no—
1018C23—101no—
1019C23—101no—
1020C23—101no—
1021C23—101no—
1022C23—101no—
1023C23—101no—
1024C23—101no—
1025C23—101no—
1026C23—101no—
1027C23—101no—
1028C23—108no—
1029C23—204no—
1030C23—204no—
1031C23—204no—
1032C23—204no—
1033C23—204no—
1034C23—204no—
1035C23—204no—
1036C23—204no—
1037C23—204no—
1038C23—204no—
1039C23C2×D5×Dic312yes—
1040C23C2×D5×Dic312yes—
1041C23D5×#6712yes—
1042C23D5×#6712yes—
1043C23C22×D3×D511yescharacteristic
1044D4—28no—
1045D4—516no—
1046D4—108no—
1047D4—108no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—32no—
1051C2×C4—52no—
1052C2×C4—52no—
1053C2×C4—52no—
1054C2×C4—61no—
1055C2×C4—61no—
1056C2×C4—61no—
1057C2×C4—61no—
1058C2×C4—61no—
1059C2×C4—61no—
1060C2×C4—61no—
1061C2×C4—61no—
1062C2×C4—61no—
1063C2×C4—61no—
1064C2×C4—61no—
1065C2×C4—108no—
1066C2×C4—124no—
1067C2×C4—152no—
1068C2×C4—301no—
1069C2×C4—301no—
1070C2×C4—301no—
1071C2×C4—301no—
1072C2×C4—301no—
1073C2×C4—301no—
1074C2×C4—301no—
1075C2×C4—301no—
1076C2×C4—301no—
1077C2×C4—301no—
1078C2×C4—301no—
1079C2×C4—604no—
1080C2×C4—604no—
1081C2×C4—604no—
1082C2×C4C2×D5×Dic312yes—
1083C2×C3—24no—
1084C2×C3—42no—
1085C2×C3—104no—
1086C2×C3—104no—
1087C2×C3—202no—
1088C2×C3C2×D5×C22⋊C411yescharacteristic
1089C2×C3C4×D4×D511yescharacteristic
1090C2×C3#6587911yescharacteristic
1091C2×C3#6592411yescharacteristic
1092C2×C3#6594311yescharacteristic
1093C2×C3#6594411yescharacteristic
1094C2×C3#6598811yescharacteristic
1095C5D4×#21711yescharacteristic, complemented, Sylow
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—54no—
1110C22—54no—
1111C22—102no—
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—102no—
1125C22—102no—
1126C22—2016no—
1127C22—2016no—
1128C22—201no—
1129C22—201no—
1130C22—201no—
1131C22—201no—
1132C22D5×#21714yescomplemented
1133C22D3×D4×D511yescharacteristic
1134C22D5×#23711yescharacteristic
1135C22#9202511yescharacteristic
1136C22#9202611yescharacteristic
1137C22C22×D5×Dic311yescharacteristic
1138C22C2×D5×#6711yescharacteristic
1139C22C2×D5×#6711yescharacteristic
1140C4—22no—
1141C4—54no—
1142C4—62no—
1143C4—121no—
1144C4—121no—
1145C4—121no—
1146C4—302no—
1147C4—601no—
1148C4—601no—
1149C4—601no—
1150C3#1060660911yescharacteristic, complemented, Sylow
1151C2—24no—
1152C2—42no—
1153C2—104no—
1154C2—104no—
1155C2—202no—
1156C2D4×D5×Dic311yescharacteristic
1157C2#1175478911yescharacteristic
1158C2#1175479111yescharacteristic
1159C2#1175491011yescharacteristic
1160C2#1175503111yescharacteristic
1161C2#1175503811yescharacteristic
1162C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
hypercenterC22×D4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91559C2semidirect
3. C2×Dic3×C22⋊D5C2semidirect
4. C2×D5×#217C2semidirect
5. C22×#6665C2semidirect
6. #11751321C2semidirect
7. C5×#5220C2semidirect
8. #11749489C2semidirect
9. #11749489C2semidirect
10. #11749488C2semidirect
11. #11749488C2semidirect
12. #11748896C2semidirect
13. #11748896C2semidirect
14. #11748738C2semidirect
15. #11748702C2semidirect
20. C23×Dic15C22semidirect
21. C23×C5×Dic3C22semidirect
26. C2×C3×D4×D5C4semidirect
29. C22×D5×Dic3C22semidirect
30. C22×D5×Dic3C22semidirect
31. C2×#6719C22semidirect
32. C2×#6719C22semidirect
33. C2×#6719C22semidirect
34. C2×C5×#217C22semidirect
35. C2×C5×#217C22semidirect
36. C2×C5×#217C22semidirect
40. C2×#6668C22semidirect
41. C2×#6668C22semidirect
47. C2×#6665C22semidirect
48. C2×#6665C22semidirect
49. C2×#6665C22semidirect
50. C2×#6665C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×Dic3×Dic5C22semidirect
54. C2×Dic3×Dic5C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
57. C5×C3⋊#95C22semidirect
58. C5×C3⋊#95C22semidirect
89. C23×C3×D5C2×C4semidirect
90. C23×C3×D5C2×C4semidirect
96. C2×C3×C5×D4C2×C4semidirect
115. C2×C3×C22⋊D5C2×C4semidirect
122. C2×C3×D20C2×C4semidirect
125. C2×C3×C4×D5C2×C4semidirect
149. #6665D4semidirect
164. #5220D5semidirect
176. C2×D4×D5Dic3semidirect
276. C2×Dic15C2×D4semidirect
289. C2×C5×Dic3C2×D4semidirect
291. C3×C22⋊D5C22⋊C4semidirect
312. C23×Dic3C2×D5semidirect
328. C2×#217C2×D5semidirect
329. C2×#217C2×D5semidirect
330. C2×#217C2×D5semidirect
339. C3⋊#95C2×D5semidirect
340. C3⋊#95C2×D5semidirect
355. C23×D5C2×Dic3semidirect
356. C23×D5C2×Dic3semidirect
362. C2×C5×D4C2×Dic3semidirect
374. C2×C22⋊D5C2×Dic3semidirect
388. C2×D20C2×Dic3semidirect
397. C2×C4×D5C2×Dic3semidirect
446. C22×C3×C5C2×C22⋊C4semidirect
475. C2×C3×D5C2×C22⋊C4semidirect
476. C2×C3×D5C4×D4semidirect
482. C3×Dic5C2×C22⋊C4semidirect
518. C2×C3×D4C4×D5semidirect
632. C22⋊D5#217semidirect
795. C2×Dic3D4×D5semidirect
809. C22×C5C2×#217semidirect
838. C2×D5D4×Dic3semidirect
839. C2×D5C2×#217semidirect
849. Dic5C2×#217semidirect
881. C2×D4D5×Dic3semidirect
927. C3×C5D4×C22⋊C4semidirect
964. C22×C3D5×C22⋊C4semidirect
1095. C5D4×#217semidirect
1132. C22D5×#217semidirect
1150. C3#10606609semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×#915592
C2×Dic3×C22⋊D52
C2×D5×#2172
C22×#66652
#117513212
C5×#52202
#117494892
#117494882
#117488962
#117487382
#117487022
#106066093
D4×#2175