Finite Group Databasebeta

← #12267228

Subgroups — #12267228

Order 1280.

3700 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65882C211yesmaximal, characteristic, complemented
2C2×C4×D4×D5C211yesmaximal, characteristic, complemented
3C2×#65858C212yesmaximal, complemented
4C5×#2293C211yesmaximal, characteristic, complemented
5#10614004C212yesmaximal, complemented
6#10608172C211yesmaximal, characteristic, complemented
7#10608167C211yesmaximal, characteristic, complemented
8#10608048C211yesmaximal, characteristic, complemented
9#10608045C211yesmaximal, characteristic, complemented
10#10607951C211yesmaximal, characteristic, complemented
11#10607942C211yesmaximal, characteristic, complemented
12#10607742C211yesmaximal, characteristic, complemented
13#10607730C211yesmaximal, characteristic, complemented
14#10607589C212yesmaximal, complemented
15#10607577C212yesmaximal, complemented
16#10607258C212yesmaximal, complemented
17#10607244C212yesmaximal, complemented
18C4×#4041C211yesmaximal, characteristic, complemented
19C4×#4041C211yesmaximal, characteristic, complemented
20#10605311C212yesmaximal, complemented
21C4×#4028C212yesmaximal, complemented
22C4×#4020C211yesmaximal, characteristic, complemented
23C42×D20C211yesmaximal, characteristic, complemented
24C22×D4×D5C2211yescharacteristic
25C22×#709C2212yescomplemented
26C23×C4×D5C2212yes—
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2212yescomplemented
29C2×#4086C2211yescharacteristic
30C2×#4084C2211yescharacteristic
31C2×D4×Dic5C2211yescharacteristic
32C2×C4×C22⋊D5C2212yes—
33C2×C4×C22⋊D5C2212yescomplemented
34#65882—28no—
35C4×D4×D5—28no—
36#65858—216no—
37C2×#4043C2212yes—
38C2×#4043C2212yescomplemented
39C2×#4041C2212yes—
40C2×#4041C2211yescharacteristic
41C2×#4041C2211yescharacteristic
42C2×#4041C2212yescomplemented
43C2×#4041C2211yescharacteristic, complemented
44C2×#4039C2211yescharacteristic
45C2×D5×C4⋊C4C2211yescharacteristic
46C2×#4034C2211yescharacteristic, complemented
47C2×#4032C2212yescomplemented
48C2×#4032C2212yescomplemented
49C2×#4031C2212yescomplemented
50C2×#4030C2212yescomplemented
51C2×#4028C2212yes—
52C2×#4028C2212yes—
53C2×#4028C2212yes—
54C2×#4027C2212yes—
55C2×D5×C22⋊C4C2212yes—
56C2×#4020C2211yescharacteristic
57C2×C4×D20C2212yes—
58C2×C4×D20C2211yescharacteristic
59C2×C4×D20C2211yescharacteristic
60C2×C4×D20C2211yescharacteristic
61C2×C4×D20C2211yescharacteristic
62C2×C4×D20C2212yescomplemented
63C2×C4×D20C2212yescomplemented
64C2×C4×D20C2211yescharacteristic, complemented
65C2×C4×D20C2212yescomplemented
66C2×C42×D5C2211yescharacteristic
67C2×C42×D5C2211yescharacteristic, complemented
68C5×#390C2211yescharacteristic
69C5×#390C2211yescharacteristic
70C5×#389C2211yescharacteristic, complemented
71C5×#389C2211yescharacteristic, complemented
72C5×#388C2212yescomplemented
73C5×#388C2212yescomplemented
74C4×C5×C4⋊C4C2211yescharacteristic, complemented
75C4×C5×C22⋊C4C2212yescomplemented
76C43×C5C2211yescharacteristic, complemented
77#65283C2212yescomplemented
78#65283C2212yescomplemented
79#65280C2212yescomplemented
80#65277C2211yescharacteristic
81#65277C2211yescharacteristic, complemented
82#65276C2211yescharacteristic
83#65276C2211yescharacteristic, complemented
84#65274C2211yescharacteristic, complemented
85#65274C2211yescharacteristic, complemented
86#65272C2212yescomplemented
87#65250C2212yes—
88#65250C2212yescomplemented
89#65250C2212yescomplemented
90#65250C2212yescomplemented
91#65249C2212yes—
92#65249C2212yes—
93#65249C2212yes—
94#65247C2212yescomplemented
95#65244C2212yes—
96#65242C2212yescomplemented
97#65239C2212yescomplemented
98#65228C2211yescharacteristic
99#65228C2211yescharacteristic, complemented
100#65228C2212yescomplemented
101#65228C2212yescomplemented
102C4×#685C2211yescharacteristic
103C4×#685C2211yescharacteristic
104C4×#685C2211yescharacteristic
105C4×#685C2211yescharacteristic, complemented
106C4×#685C2212yescomplemented
107C4×#685C2212yescomplemented
108C4×#685C2211yescharacteristic, complemented
109C4×#685C2211yescharacteristic, complemented
110#65224C2211yescharacteristic, complemented
111C4×C4⋊Dic5C2211yescharacteristic, complemented
112C4×C4⋊Dic5C2211yescharacteristic, complemented
113C4×C4⋊Dic5C2211yescharacteristic, complemented
114#64962C2212yescomplemented
115#64961C2212yescomplemented
116#64960C2212yescomplemented
117#64959C2212yescomplemented
118#64959C2212yescomplemented
119#64957C2212yes—
120#64957C2212yescomplemented
121#64954C2212yes—
122#64954C2212yes—
123#64954C2212yescomplemented
124#64954C2212yescomplemented
125#64945C2212yescomplemented
126#34681—51nomaximal, Sylow
127C24×D5C2312yes—
128C22×C5×D4C2311yescharacteristic
129C23×C4×C5C2312yes—
130C22×C22⋊D5C2312yes—
131C22×C22⋊D5C2312yes—
132C22×C22⋊D5C2312yes—
133C22×C22⋊D5C2312yes—
134C23×Dic5C2312yes—
135C2×D4×D5—24no—
136C2×D4×D5—24no—
137C2×D4×D5—24no—
138C2×#709—28no—
139C2×#709—28no—
140C2×#709—44no—
141C22×D20C2312yes—
142C22×D20C2311yescharacteristic
143C22×D20C2312yes—
144C22×D20C2312yes—
145C22×D20C2312yes—
146C22×D20C2312yes—
147C22×D20C2311yescharacteristic
148C22×D20C2311yescharacteristic
149C22×C4×D5—28no—
150C22×C4×D5—28no—
151C22×C4×D5—44no—
152C22×C4×D5C2311yescharacteristic
153C22×C4×D5C2312yes—
154C22×C4×D5C2312yes—
155C22×C4×D5C2311yescharacteristic
156C22×C4×D5C2311yescharacteristic
157C22×C4×D5C2312yes—
158C22×C4×D5C2312yes—
159C22×C4×D5C2311yescharacteristic
160C22×C4×D5C2311yescharacteristic
161C22×C4×D5C2311yescharacteristic
162C22×Dic10C2312yes—
163C4×C5×D4D418yescomplemented
164C5×#117—28no—
165C2×C5×C4⋊C4C2312yes—
166C2×C5×C4⋊C4C2312yes—
167C2×C5×C4⋊C4C2311yescharacteristic
168C2×C5×C4⋊C4C2311yescharacteristic
169C2×C5×C4⋊C4C2311yescharacteristic
170C2×C5×C22⋊C4C2312yes—
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2312yes—
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2312yes—
175C2×C42×C5C2311yescharacteristic
176C2×C42×C5C2311yescharacteristic
177C2×C42×C5C2311yescharacteristic
178C2×C42×C5C2311yescharacteristic
179C2×C42×C5C2312yes—
180C2×C42×C5C2311yescharacteristic
181C2×C42×C5C2311yescharacteristic
182C2×C42×C5C2311yescharacteristic
183C2×C22⋊Dic5C2312yes—
184C2×C22⋊Dic5C2312yes—
185#4086—24no—
186#4084—24no—
187D4×Dic5—24no—
188C4×C22⋊D5—28no—
189C4×C22⋊D5—28no—
190C2×#685C2312yes—
191C2×#685C2312yes—
192C2×#685C2312yes—
193C2×#685C2312yes—
194C2×#685C2312yes—
195C2×#685C2312yes—
196C2×#685C2312yes—
197C2×#685C2312yes—
198C2×#685C2312yes—
199C2×#685C2312yes—
200C2×#685C2311yescharacteristic
201C2×#685C2311yescharacteristic
202C2×#685C2311yescharacteristic
203C2×#685C2312yes—
204C2×#685C2312yes—
205C2×#685C2312yes—
206C2×#685C2312yes—
207C2×#685C2312yes—
208C2×#685C2312yes—
209C2×#685C2311yescharacteristic
210C2×#685C2311yescharacteristic
211C2×#685C2311yescharacteristic
212C2×C4⋊Dic5C2311yescharacteristic
213C2×C4⋊Dic5C2311yescharacteristic
214C2×C4⋊Dic5C2312yes—
215C2×C4⋊Dic5C2311yescharacteristic
216C2×C4⋊Dic5C2312yes—
217C2×C4⋊Dic5C2312yes—
218C2×C4⋊Dic5C2311yescharacteristic
219C2×C4⋊Dic5C2312yes—
220C2×C4⋊Dic5C2311yescharacteristic
221C2×#683C2312yes—
222C2×#683C2312yes—
223C2×C4×Dic5C2311yescharacteristic
224C2×C4×Dic5C2311yescharacteristic
225C2×C4×Dic5C2311yescharacteristic
226C2×C4×Dic5C2311yescharacteristic
227C2×C4×Dic5C2311yescharacteristic
228C2×C4×Dic5C2311yescharacteristic
229#4043—28no—
230#4043—28no—
231#4041—28no—
232#4041—24no—
233#4041—24no—
234#4041—24no—
235#4041—28no—
236#4039—24no—
237D5×C4⋊C4—24no—
238#4034—24no—
239#4032—28no—
240#4032—28no—
241#4031—28no—
242#4030—28no—
243#4028—28no—
244#4028—28no—
245#4028—28no—
246#4027—28no—
247D5×C22⋊C4—28no—
248#4020—24no—
249C4×D20—28no—
250C4×D20—28no—
251C4×D20—24no—
252C4×D20—24no—
253C4×D20—24no—
254C4×D20—28no—
255C4×D20—24no—
256C4×D20—44no—
257C4×D20D418yescomplemented
258C42×D5—24no—
259C42×D5—24no—
260C5×#95C2312yes—
261C5×#95C2312yes—
262C5×#95C2312yes—
263#3963C2311yescharacteristic
264#3963C2312yes—
265#3963C2312yes—
266#3963C2311yescharacteristic
267#3963C2312yes—
268#3963C2311yescharacteristic
269#3963C2312yes—
270#3963C2311yescharacteristic
271#3963C2311yescharacteristic
272#3963C2311yescharacteristic
273C2×#532—51no—
274C2×#525—52no—
275C22×C4×D4—51no—
276#2472—52no—
277#2464—52no—
278#2461—52no—
279#2452—51no—
280#2445—51no—
281#2440—51no—
282#2433—51no—
283#2428—51no—
284#2424—52no—
285#2422—51no—
286#2416—51no—
287#2408—51no—
288#2392—52no—
289#2388—52no—
290C4×#127—51no—
291C4×#121—51no—
292C4×#121—51no—
293C4×#120—52no—
294#2293D511yescharacteristic, complemented
295C42×D4—51no—
296C24×C5C2412yes—
297C23×D5—24no—
298C23×D5—24no—
299C23×D5—24no—
300C23×D5—24no—
301C23×D5—24no—
302C23×D5—42no—
303C23×D5—42no—
304C23×D5C2412yes—
305C23×D5C2411yescharacteristic
306C23×D5C2412yes—
307C23×D5C2411yescharacteristic
308C2×C5×D4—22no—
309C2×C5×D4—22no—
310C2×C5×D4C2×D414yes—
311C22×C4×C5—24no—
312C22×C4×C5—24no—
313C22×C4×C5C2×D418yes—
314C22×C4×C5C2411yescharacteristic
315C22×C4×C5C2412yes—
316C22×C4×C5C2412yes—
317C22×C4×C5C2411yescharacteristic
318C22×C4×C5C2411yescharacteristic
319C22×C4×C5C2411yescharacteristic
320C22×C4×C5C2412yes—
321C22×C4×C5C2411yescharacteristic
322C22×C4×C5C2411yescharacteristic
323C22×C4×C5C2411yescharacteristic
324C2×C22⋊D5—24no—
325C2×C22⋊D5—24no—
326C2×C22⋊D5—24no—
327C2×C22⋊D5—24no—
328C2×C22⋊D5—24no—
329C2×C22⋊D5—24no—
330C2×C22⋊D5—24no—
331C2×C22⋊D5—24no—
332C2×C22⋊D5—24no—
333C2×C22⋊D5—42no—
334C2×C22⋊D5—42no—
335C2×C22⋊D5—42no—
336C22×Dic5—24no—
337C22×Dic5—24no—
338C22×Dic5—42no—
339C22×Dic5C2411yescharacteristic
340C22×Dic5C2411yescharacteristic
341C22×Dic5C2412yes—
342C22×Dic5C2412yes—
343C22×Dic5C2411yescharacteristic
344C22×Dic5C2411yescharacteristic
345C22×Dic5C2411yescharacteristic
346C22×Dic5C2411yescharacteristic
347D4×D5—232no—
348#709—432no—
349C2×D20—22no—
350C2×D20—22no—
351C2×D20—22no—
352C2×D20—22no—
353C2×D20—24no—
354C2×D20—24no—
355C2×D20—24no—
356C2×D20—24no—
357C2×D20—24no—
358C2×D20—24no—
359C2×D20—24no—
360C2×D20—24no—
361C2×D20—24no—
362C2×D20—24no—
363C2×D20—22no—
364C2×D20—22no—
365C2×D20—24no—
366C2×D20—22no—
367C2×D20—42no—
368C2×D20—42no—
369C2×D20—42no—
370C2×D20—42no—
371C2×D20C2×D414yes—
372C2×D20#4114yescomplemented
373C2×C4×D5—22no—
374C2×C4×D5—22no—
375C2×C4×D5—22no—
376C2×C4×D5—22no—
377C2×C4×D5—22no—
378C2×C4×D5—22no—
379C2×C4×D5—24no—
380C2×C4×D5—22no—
381C2×C4×D5—24no—
382C2×C4×D5—24no—
383C2×C4×D5—24no—
384C2×C4×D5—24no—
385C2×C4×D5—24no—
386C2×C4×D5—24no—
387C2×C4×D5—22no—
388C2×C4×D5—22no—
389C2×C4×D5—22no—
390C2×C4×D5—22no—
391C2×C4×D5—22no—
392C2×C4×D5—24no—
393C2×C4×D5—24no—
394C2×C4×D5—24no—
395C2×C4×D5—22no—
396C2×C4×D5—432no—
397C2×C4×D5—42no—
398C2×C4×D5—42no—
399C2×C4×D5—41no—
400C2×C4×D5—41no—
401C2×C4×D5C2×D414yes—
402C2×C4×D5C2×D414yescomplemented
403C2×C4×D5#4114yescomplemented
404C2×Dic10—24no—
405C2×Dic10—24no—
406C2×Dic10—42no—
407C5×C4⋊C4—24no—
408C5×C4⋊C4—24no—
409C5×C4⋊C4—22no—
410C5×C4⋊C4—22no—
411C5×C4⋊C4C2×D414yes—
412C5×C22⋊C4—24no—
413C5×C22⋊C4—24no—
414C5×C22⋊C4—24no—
415C5×C22⋊C4—42no—
416C5×C22⋊C4C2×D418yes—
417C42×C5—24no—
418C42×C5—22no—
419C42×C5—22no—
420C42×C5—22no—
421C42×C5—22no—
422C42×C5—41no—
423C42×C5C2×D414yes—
424C42×C5C2×D414yescomplemented
425C22⋊Dic5—24no—
426C22⋊Dic5—24no—
427#685—24no—
428#685—24no—
429#685—22no—
430#685—24no—
431#685—24no—
432#685—24no—
433#685—24no—
434#685—24no—
435#685—24no—
436#685—24no—
437#685—22no—
438#685—24no—
439#685—24no—
440#685—22no—
441#685—24no—
442#685—24no—
443#685—42no—
444#685—42no—
445#685—42no—
446#685C2×D414yes—
447#685C2×D414yescomplemented
448#685#4114yescomplemented
449C4⋊Dic5—24no—
450C4⋊Dic5—22no—
451C4⋊Dic5—22no—
452C4⋊Dic5—24no—
453C4⋊Dic5—24no—
454C4⋊Dic5—22no—
455C4⋊Dic5—22no—
456C4⋊Dic5—42no—
457C4⋊Dic5C2×D414yescomplemented
458#683—24no—
459#683—24no—
460C4×Dic5—22no—
461C4×Dic5—22no—
462C4×Dic5—22no—
463C4×Dic5—22no—
464C4×Dic5—22no—
465C4×Dic5—22no—
466C22×#41—52no—
467C23×D4—51no—
468C24×C4—52no—
469#532—108no—
470C2×C4⋊Q8—51no—
471C2×#127—51no—
472C2×#127—51no—
473C2×#124—52no—
474#525—1016no—
475C2×#123—52no—
476C2×#123—52no—
477C2×C22⋊Q8—52no—
478C2×C22⋊Q8—52no—
479C2×#121—51no—
480C2×#121—51no—
481C2×#121—52no—
482C2×#121—51no—
483C2×#121—52no—
484C2×#121—51no—
485C2×#121—52no—
486C2×#120—52no—
487C2×#120—52no—
488C2×#120—52no—
489C2×C4×D4—51no—
490C2×C4×D4—52no—
491C2×C4×D4—52no—
492C2×C4×D4—51no—
493C2×C4×D4—52no—
494C2×C4×D4—51no—
495C2×C4×D4—51no—
496C2×C4×D4—52no—
497C2×C4×D4—51no—
498C2×C4×D4—51no—
499C2×C4×D4—52no—
500C2×C4×D4—51no—
501C2×C4×D4—52no—
502C2×C4×D4—52no—
503C2×C4×D4—108no—
504C2×C4×D4C2×D511yescharacteristic
505C2×#117C2×D512yescomplemented
506C22×C4⋊C4—51no—
507C22×C22⋊C4—52no—
508C22×C42—51no—
509C22×C42—51no—
510#398—52no—
511#397—52no—
512#396—52no—
513#396—52no—
514#395—52no—
515#394—52no—
516#394—52no—
517#394—52no—
518#394—52no—
519#394—52no—
520#394—52no—
521#393—52no—
522#392—52no—
523#392—52no—
524#392—52no—
525#392—52no—
526#390—51no—
527#390—51no—
528#390—51no—
529#390—51no—
530#390—52no—
531#390—52no—
532#390C2×D511yescharacteristic
533#390C2×D511yescharacteristic
534#389—51no—
535#389—51no—
536#389C2×D511yescharacteristic, complemented
537#389C2×D511yescharacteristic, complemented
538#388—52no—
539#388—52no—
540#388C2×D512yescomplemented
541#388C2×D512yescomplemented
542#386—52no—
543#386—52no—
544#386—52no—
545#386—52no—
546#386—52no—
547#385—52no—
548#385—52no—
549#385—52no—
550#384—51no—
551#380—51no—
552#380—51no—
553#379—52no—
554C4×C4⋊C4—51no—
555C4×C4⋊C4—51no—
556C4×C4⋊C4—51no—
557C4×C4⋊C4C2×D511yescharacteristic, complemented
558C4×C22⋊C4—51no—
559C4×C22⋊C4—52no—
560C4×C22⋊C4—52no—
561C4×C22⋊C4—51no—
562C4×C22⋊C4—51no—
563C4×C22⋊C4—51no—
564C4×C22⋊C4—51no—
565C4×C22⋊C4—51no—
566C4×C22⋊C4C2×D512yescomplemented
567C43C2×D511yescharacteristic, complemented
568C23×C5—22no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5C22×D414yes—
575C23×C5C2511yescharacteristic
576C22×D5—21no—
577C22×D5—21no—
578C22×D5—21no—
579C22×D5—21no—
580C22×D5—216no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—21no—
584C22×D5—21no—
585C22×D5—21no—
586C22×D5—22no—
587C22×D5—21no—
588C22×D5—22no—
589C22×D5—22no—
590C22×D5—21no—
591C22×D5—21no—
592C22×D5—22no—
593C22×D5—22no—
594C22×D5—22no—
595C22×D5—22no—
596C22×D5—22no—
597C22×D5—22no—
598C22×D5—22no—
599C22×D5—22no—
600C22×D5—48no—
601C22×D5—48no—
602C22×D5—48no—
603C22×D5—48no—
604C22×D5—48no—
605C22×D5—48no—
606C22×D5C22×D412yes—
607C22×D5C22×D412yes—
608C22×D5C2×#4114yes—
609C22×D5C2×#4112yes—
610C22×D5C2×#4112yes—
611C5×D4—28no—
612C2×C4×C5—22no—
613C2×C4×C5—21no—
614C2×C4×C5—21no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—22no—
620C2×C4×C5—21no—
621C2×C4×C5—21no—
622C2×C4×C5—216no—
623C2×C4×C5—22no—
624C2×C4×C5—22no—
625C2×C4×C5—21no—
626C2×C4×C5—22no—
627C2×C4×C5—22no—
628C2×C4×C5—22no—
629C2×C4×C5—21no—
630C2×C4×C5—22no—
631C2×C4×C5—21no—
632C2×C4×C5C22×D412yes—
633C2×C4×C5C22×D414yes—
634C2×C4×C5C22×D412yes—
635C2×C4×C5C22×D412yes—
636C2×C4×C5C22×D412yes—
637C2×C4×C5C22×D412yes—
638C2×C4×C5C22×D412yes—
639C2×C4×C5C2×#4112yes—
640C2×C4×C5C2×#4112yes—
641C2×C4×C5C2×#4112yes—
642C2×C4×C5H(5,𝔽2)12yes—
643C22⋊D5—216no—
644C22⋊D5—48no—
645C22⋊D5—48no—
646C22⋊D5—48no—
647C2×Dic5—21no—
648C2×Dic5—21no—
649C2×Dic5—21no—
650C2×Dic5—21no—
651C2×Dic5—21no—
652C2×Dic5—21no—
653C2×Dic5—21no—
654C2×Dic5—21no—
655C2×Dic5—21no—
656C2×Dic5—21no—
657C2×Dic5—22no—
658C2×Dic5—22no—
659C2×Dic5—22no—
660C2×Dic5—22no—
661C2×Dic5—21no—
662C2×Dic5—21no—
663C2×Dic5—21no—
664C2×Dic5—22no—
665C2×Dic5—22no—
666C2×Dic5—21no—
667C2×Dic5—48no—
668C2×Dic5C22×D412yes—
669C2×Dic5C22×D412yes—
670C2×Dic5C2×#4112yes—
671C2×Dic5C2×#4112yes—
672D20—28no—
673D20—28no—
674D20—48no—
675D20—48no—
676D20—48no—
677D20—48no—
678D20—48no—
679D20—44no—
680C4×D5—28no—
681C4×D5—28no—
682C4×D5—28no—
683C4×D5—44no—
684C4×D5—48no—
685C4×D5—44no—
686C4×D5—48no—
687C4×D5—44no—
688C4×D5—48no—
689C4×D5—48no—
690Dic10—48no—
691C25—52no—
692C2×#41—108no—
693C2×#41—108no—
694C2×#41—204no—
695C22×Q8—52no—
696C22×D4—52no—
697C22×D4—52no—
698C22×D4—52no—
699C22×D4—52no—
700C22×D4—51no—
701C22×D4—51no—
702C22×D4—52no—
703C22×D4—51no—
704C22×D4—52no—
705C22×D4—52no—
706C22×D4—52no—
707C22×D4—52no—
708C22×D4—104no—
709C22×D4—104no—
710C22×D4—104no—
711C22×D4C22×D511yescharacteristic
712C23×C4—51no—
713C23×C4—51no—
714C23×C4—51no—
715C23×C4—52no—
716C23×C4—51no—
717C23×C4—52no—
718C23×C4—52no—
719C23×C4—51no—
720C23×C4—52no—
721C23×C4—52no—
722C23×C4—51no—
723C23×C4—108no—
724C23×C4—108no—
725C23×C4—204no—
726C23×C4C22×D512yes—
727C4⋊Q8—104no—
728#127—104no—
729#127—104no—
730#124—108no—
731#123—108no—
732#123—108no—
733C22⋊Q8—108no—
734C22⋊Q8—108no—
735#121—108no—
736#121—104no—
737#121—108no—
738#121—104no—
739#121—104no—
740#121—104no—
741#121—108no—
742#120—108no—
743#120—108no—
744#120—108no—
745C4×D4—58no—
746C4×D4—104no—
747C4×D4—108no—
748C4×D4—108no—
749C4×D4—104no—
750C4×D4—104no—
751C4×D4—108no—
752C4×D4—108no—
753C4×D4—104no—
754C4×D4—108no—
755C4×D4—104no—
756C4×D4—104no—
757C4×D4—108no—
758C4×D4—204no—
759C4×D4D2018yescomplemented
760#117—28no—
761C2×C4⋊C4—51no—
762C2×C4⋊C4—51no—
763C2×C4⋊C4—52no—
764C2×C4⋊C4—51no—
765C2×C4⋊C4—52no—
766C2×C4⋊C4—52no—
767C2×C4⋊C4—52no—
768C2×C4⋊C4—52no—
769C2×C4⋊C4—51no—
770C2×C4⋊C4—51no—
771C2×C4⋊C4—52no—
772C2×C4⋊C4—104no—
773C2×C4⋊C4C22×D512yes—
774C2×C4⋊C4C22×D512yes—
775C2×C4⋊C4C22×D511yescharacteristic
776C2×C4⋊C4C22×D511yescharacteristic
777C2×C4⋊C4C22×D511yescharacteristic
778C2×C22⋊C4—51no—
779C2×C22⋊C4—51no—
780C2×C22⋊C4—51no—
781C2×C22⋊C4—52no—
782C2×C22⋊C4—52no—
783C2×C22⋊C4—52no—
784C2×C22⋊C4—52no—
785C2×C22⋊C4—52no—
786C2×C22⋊C4—52no—
787C2×C22⋊C4—52no—
788C2×C22⋊C4—52no—
789C2×C22⋊C4—52no—
790C2×C22⋊C4—52no—
791C2×C22⋊C4—52no—
792C2×C22⋊C4—52no—
793C2×C22⋊C4—51no—
794C2×C22⋊C4—51no—
795C2×C22⋊C4—51no—
796C2×C22⋊C4—52no—
797C2×C22⋊C4—52no—
798C2×C22⋊C4—52no—
799C2×C22⋊C4—52no—
800C2×C22⋊C4—52no—
801C2×C22⋊C4—52no—
802C2×C22⋊C4—108no—
803C2×C22⋊C4C22×D512yes—
804C2×C22⋊C4C22×D512yes—
805C2×C22⋊C4C22×D512yes—
806C2×C22⋊C4C22×D512yes—
807C2×C22⋊C4C22×D512yes—
808C2×C42—51no—
809C2×C42—51no—
810C2×C42—51no—
811C2×C42—51no—
812C2×C42—51no—
813C2×C42—51no—
814C2×C42—104no—
815C2×C42—104no—
816C2×C42C22×D511yescharacteristic
817C2×C42C22×D511yescharacteristic
818C2×C42C22×D511yescharacteristic
819C2×C42C22×D512yes—
820C2×C42C22×D511yescharacteristic
821C2×C42C22×D511yescharacteristic
822C2×C42C22×D511yescharacteristic
823C2×C42C22×D511yescharacteristic
824#95—51no—
825#95—51no—
826#95—51no—
827#95—51no—
828#95—51no—
829#95—51no—
830#95—52no—
831#95—52no—
832#95—52no—
833#95—52no—
834#95C22×D512yes—
835#95C22×D512yes—
836#95C22×D512yes—
837C22×C5—24no—
838C22×C5—24no—
839C22×C5—24no—
840C22×C5—42no—
841C22×C5—42no—
842C22×C5—42no—
843C22×C5—42no—
844C22×C5C23×D411yescharacteristic
845C22×C5C23×D411yescharacteristic
846C22×C5C22×#4111yescharacteristic
847C22×C5C22×#4111yescharacteristic
848C22×C5C22×#4111yescharacteristic
849C22×C5C2×H(5,𝔽2)11yescharacteristic
850C22×C5#58511yescharacteristic
851C2×D5—22no—
852C2×D5—22no—
853C2×D5—22no—
854C2×D5—22no—
855C2×D5—22no—
856C2×D5—22no—
857C2×D5—24no—
858C2×D5—22no—
859C2×D5—22no—
860C2×D5—24no—
861C2×D5—22no—
862C2×D5—24no—
863C2×D5—432no—
864C2×D5—41no—
865C2×D5—42no—
866C2×D5—41no—
867C2×D5—42no—
868C2×D5—42no—
869C2×D5—41no—
870C2×D5—42no—
871C2×D5—41no—
872C2×D5—42no—
873C2×D5—42no—
874C2×D5—42no—
875C2×D5—42no—
876C2×D5—42no—
877C2×D5—42no—
878C2×D5—42no—
879C2×D5#53214yescomplemented
880C4×C5—22no—
881C4×C5—24no—
882C4×C5—22no—
883C4×C5—22no—
884C4×C5—22no—
885C4×C5—42no—
886C4×C5—41no—
887C4×C5—42no—
888C4×C5#52514yescomplemented
889C4×C5D4214yes—
890Dic5—22no—
891Dic5—22no—
892Dic5—22no—
893Dic5—22no—
894Dic5—41no—
895Dic5—42no—
896Dic5—42no—
897Dic5—41no—
898C24—51no—
899C24—52no—
900C24—51no—
901C24—52no—
902C24—104no—
903C24—104no—
904C24—104no—
905C24—104no—
906C24—104no—
907C24—202no—
908C24—202no—
909C24C23×D512yes—
910#41—2032no—
911C2×Q8—104no—
912C2×Q8—104no—
913C2×Q8—202no—
914C2×D4—22no—
915C2×D4—22no—
916C2×D4—54no—
917C2×D4—54no—
918C2×D4—102no—
919C2×D4—102no—
920C2×D4—104no—
921C2×D4—104no—
922C2×D4—104no—
923C2×D4—104no—
924C2×D4—104no—
925C2×D4—104no—
926C2×D4—104no—
927C2×D4—104no—
928C2×D4—104no—
929C2×D4—104no—
930C2×D4—104no—
931C2×D4—1032no—
932C2×D4—104no—
933C2×D4—104no—
934C2×D4—104no—
935C2×D4—104no—
936C2×D4—104no—
937C2×D4—104no—
938C2×D4—102no—
939C2×D4—102no—
940C2×D4—104no—
941C2×D4—104no—
942C2×D4—102no—
943C2×D4—104no—
944C2×D4—102no—
945C2×D4—102no—
946C2×D4—202no—
947C2×D4—202no—
948C2×D4—202no—
949C2×D4—202no—
950C2×D4—202no—
951C2×D4—202no—
952C2×D4—202no—
953C2×D4C2×D2014yes—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—51no—
957C22×C4—51no—
958C22×C4—51no—
959C22×C4—51no—
960C22×C4—54no—
961C22×C4—54no—
962C22×C4—54no—
963C22×C4—51no—
964C22×C4—51no—
965C22×C4—52no—
966C22×C4—52no—
967C22×C4—102no—
968C22×C4—104no—
969C22×C4—102no—
970C22×C4—104no—
971C22×C4—104no—
972C22×C4—102no—
973C22×C4—102no—
974C22×C4—102no—
975C22×C4—102no—
976C22×C4—102no—
977C22×C4—102no—
978C22×C4—104no—
979C22×C4—102no—
980C22×C4—102no—
981C22×C4—102no—
982C22×C4—104no—
983C22×C4—104no—
984C22×C4—104no—
985C22×C4—104no—
986C22×C4—104no—
987C22×C4—104no—
988C22×C4—102no—
989C22×C4—102no—
990C22×C4—104no—
991C22×C4—104no—
992C22×C4—202no—
993C22×C4—202no—
994C22×C4—201no—
995C22×C4—201no—
996C22×C4—2032no—
997C22×C4—202no—
998C22×C4C2×D2018yes—
999C22×C4C23×D511yescharacteristic
1000C22×C4C23×D512yes—
1001C22×C4C23×D512yes—
1002C22×C4C23×D511yescharacteristic
1003C22×C4C23×D512yes—
1004C22×C4C23×D511yescharacteristic
1005C22×C4C23×D511yescharacteristic
1006C22×C4C23×D511yescharacteristic
1007C22×C4C23×D511yescharacteristic
1008C22×C4C23×D511yescharacteristic
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—54no—
1014C4⋊C4—104no—
1015C4⋊C4—104no—
1016C4⋊C4—102no—
1017C4⋊C4—102no—
1018C4⋊C4—104no—
1019C4⋊C4—102no—
1020C4⋊C4—104no—
1021C4⋊C4—102no—
1022C4⋊C4—104no—
1023C4⋊C4—202no—
1024C4⋊C4C2×D2014yes—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—42no—
1029C22⋊C4—54no—
1030C22⋊C4—54no—
1031C22⋊C4—54no—
1032C22⋊C4—104no—
1033C22⋊C4—104no—
1034C22⋊C4—102no—
1035C22⋊C4—104no—
1036C22⋊C4—104no—
1037C22⋊C4—104no—
1038C22⋊C4—104no—
1039C22⋊C4—102no—
1040C22⋊C4—104no—
1041C22⋊C4—104no—
1042C22⋊C4—104no—
1043C22⋊C4—104no—
1044C22⋊C4—104no—
1045C22⋊C4—104no—
1046C22⋊C4—104no—
1047C22⋊C4—104no—
1048C22⋊C4—104no—
1049C22⋊C4—102no—
1050C22⋊C4—202no—
1051C22⋊C4—202no—
1052C22⋊C4—202no—
1053C22⋊C4C2×D2018yes—
1054C42—24no—
1055C42—22no—
1056C42—22no—
1057C42—22no—
1058C42—22no—
1059C42—41no—
1060C42—102no—
1061C42—102no—
1062C42—102no—
1063C42—102no—
1064C42—102no—
1065C42—102no—
1066C42C2×D2014yes—
1067C42D4×D514yescomplemented
1068C2×C5—44no—
1069C2×C5C2×#52511yescharacteristic
1070C2×C5C2×#53211yescharacteristic
1071C2×C5#346011yescharacteristic
1072C2×C5C2×D4211yescharacteristic
1073C2×C5D4×#4111yescharacteristic
1074C2×C5D4×#4111yescharacteristic
1075C2×C5#348111yescharacteristic
1076D5—24no—
1077D5—42no—
1078D5—44no—
1079D5—82no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—52no—
1087C23—52no—
1088C23—52no—
1089C23—52no—
1090C23—54no—
1091C23—1016no—
1092C23—101no—
1093C23—101no—
1094C23—101no—
1095C23—101no—
1096C23—102no—
1097C23—101no—
1098C23—102no—
1099C23—101no—
1100C23—101no—
1101C23—102no—
1102C23—101no—
1103C23—102no—
1104C23—102no—
1105C23—101no—
1106C23—101no—
1107C23—102no—
1108C23—102no—
1109C23—102no—
1110C23—102no—
1111C23—102no—
1112C23—102no—
1113C23—102no—
1114C23—102no—
1115C23—208no—
1116C23—208no—
1117C23—208no—
1118C23—208no—
1119C23—208no—
1120C23—208no—
1121C23C22×D2014yes—
1122C23C24×D511yescharacteristic
1123Q8—208no—
1124D4—28no—
1125D4—108no—
1126D4—1016no—
1127D4—108no—
1128D4—208no—
1129D4—208no—
1130D4—208no—
1131D4—208no—
1132D4—208no—
1133D4—208no—
1134D4—208no—
1135D4—208no—
1136D4—204no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—216no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—52no—
1158C2×C4—52no—
1159C2×C4—52no—
1160C2×C4—52no—
1161C2×C4—101no—
1162C2×C4—101no—
1163C2×C4—101no—
1164C2×C4—101no—
1165C2×C4—101no—
1166C2×C4—101no—
1167C2×C4—101no—
1168C2×C4—101no—
1169C2×C4—108no—
1170C2×C4—108no—
1171C2×C4—108no—
1172C2×C4—101no—
1173C2×C4—101no—
1174C2×C4—102no—
1175C2×C4—102no—
1176C2×C4—102no—
1177C2×C4—102no—
1178C2×C4—101no—
1179C2×C4—101no—
1180C2×C4—101no—
1181C2×C4—102no—
1182C2×C4—102no—
1183C2×C4—101no—
1184C2×C4—208no—
1185C2×C4—204no—
1186C2×C4—208no—
1187C2×C4—204no—
1188C2×C4—208no—
1189C2×C4—204no—
1190C2×C4—208no—
1191C2×C4—208no—
1192C2×C4C22×D2012yes—
1193C2×C4C22×D2014yes—
1194C2×C4C22×D2012yes—
1195C2×C4C22×D2012yes—
1196C2×C4C2×D4×D512yes—
1197C2×C4C2×D4×D512yes—
1198C2×C4C2×D4×D512yes—
1199C2×C4D5×#4112yes—
1200C2×C4D5×#4112yes—
1201C2×C4D5×#4112yes—
1202C2×C4#414912yes—
1203C5#3468111yescharacteristic, complemented, Sylow
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—54no—
1212C22—102no—
1213C22—102no—
1214C22—102no—
1215C22—102no—
1216C22—102no—
1217C22—102no—
1218C22—102no—
1219C22—104no—
1220C22—102no—
1221C22—104no—
1222C22—102no—
1223C22—104no—
1224C22—2032no—
1225C22—202no—
1226C22—201no—
1227C22—202no—
1228C22—201no—
1229C22—202no—
1230C22—202no—
1231C22—201no—
1232C22—201no—
1233C22—202no—
1234C22—202no—
1235C22—202no—
1236C22—202no—
1237C22—202no—
1238C22—202no—
1239C22—202no—
1240C22C23×D2011yescharacteristic
1241C22C22×D4×D511yescharacteristic
1242C22C2×D5×#4111yescharacteristic
1243C22C2×D5×#4111yescharacteristic
1244C22C2×D5×#4111yescharacteristic
1245C22C2×#414911yescharacteristic
1246C22#6628311yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—24no—
1250C4—22no—
1251C4—22no—
1252C4—42no—
1253C4—42no—
1254C4—41no—
1255C4—102no—
1256C4—102no—
1257C4—102no—
1258C4—102no—
1259C4—201no—
1260C4—202no—
1261C4—202no—
1262C4—201no—
1263C4#6585814yescomplemented
1264C4D4×D2014yes—
1265C2—44no—
1266C2—104no—
1267C2—204no—
1268C2—202no—
1269C2—402no—
1270C2C2×#6585811yescharacteristic
1271C2C2×D4×D2011yescharacteristic
1272C2#41×D2011yescharacteristic
1273C2#1061804911yescharacteristic
1274C2#1061805411yescharacteristic
1275C2D5×#53211yescharacteristic
1276C2#1061813911yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutator, socle, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC5×#2293C2
hypercenter#2293D5
hypocenterC5#34681
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. C2×#65882C2semidirect
2. C2×C4×D4×D5C2semidirect
3. C2×#65858C2semidirect
4. C5×#2293C2semidirect
5. #10614004C2semidirect
6. #10608172C2semidirect
7. #10608167C2semidirect
8. #10608048C2semidirect
9. #10608045C2semidirect
10. #10607951C2semidirect
11. #10607942C2semidirect
12. #10607742C2semidirect
13. #10607730C2semidirect
14. #10607589C2semidirect
15. #10607577C2semidirect
16. #10607258C2semidirect
17. #10607244C2semidirect
18. C4×#4041C2semidirect
19. C4×#4041C2semidirect
20. #10605311C2semidirect
21. C4×#4028C2semidirect
22. C4×#4020C2semidirect
23. C42×D20C2semidirect
25. C22×#709C22semidirect
28. C2×C5×#117C22semidirect
33. C2×C4×C22⋊D5C22semidirect
38. C2×#4043C22semidirect
42. C2×#4041C22semidirect
43. C2×#4041C22semidirect
46. C2×#4034C22semidirect
47. C2×#4032C22semidirect
48. C2×#4032C22semidirect
49. C2×#4031C22semidirect
50. C2×#4030C22semidirect
62. C2×C4×D20C22semidirect
63. C2×C4×D20C22semidirect
64. C2×C4×D20C22semidirect
65. C2×C4×D20C22semidirect
67. C2×C42×D5C22semidirect
70. C5×#389C22semidirect
71. C5×#389C22semidirect
72. C5×#388C22semidirect
73. C5×#388C22semidirect
74. C4×C5×C4⋊C4C22semidirect
75. C4×C5×C22⋊C4C22semidirect
76. C43×C5C22semidirect
77. #65283C22semidirect
78. #65283C22semidirect
79. #65280C22semidirect
81. #65277C22semidirect
83. #65276C22semidirect
84. #65274C22semidirect
85. #65274C22semidirect
86. #65272C22semidirect
88. #65250C22semidirect
89. #65250C22semidirect
90. #65250C22semidirect
94. #65247C22semidirect
96. #65242C22semidirect
97. #65239C22semidirect
99. #65228C22semidirect
100. #65228C22semidirect
101. #65228C22semidirect
105. C4×#685C22semidirect
106. C4×#685C22semidirect
107. C4×#685C22semidirect
108. C4×#685C22semidirect
109. C4×#685C22semidirect
110. #65224C22semidirect
111. C4×C4⋊Dic5C22semidirect
112. C4×C4⋊Dic5C22semidirect
113. C4×C4⋊Dic5C22semidirect
114. #64962C22semidirect
115. #64961C22semidirect
116. #64960C22semidirect
117. #64959C22semidirect
118. #64959C22semidirect
120. #64957C22semidirect
123. #64954C22semidirect
124. #64954C22semidirect
125. #64945C22semidirect
163. C4×C5×D4D4semidirect
257. C4×D20D4semidirect
294. #2293D5semidirect
372. C2×D20#41semidirect
402. C2×C4×D5C2×D4semidirect
403. C2×C4×D5#41semidirect
424. C42×C5C2×D4semidirect
447. #685C2×D4semidirect
448. #685#41semidirect
457. C4⋊Dic5C2×D4semidirect
505. C2×#117C2×D5semidirect
536. #389C2×D5semidirect
537. #389C2×D5semidirect
540. #388C2×D5semidirect
541. #388C2×D5semidirect
557. C4×C4⋊C4C2×D5semidirect
566. C4×C22⋊C4C2×D5semidirect
567. C43C2×D5semidirect
759. C4×D4D20semidirect
879. C2×D5#532semidirect
888. C4×C5#525semidirect
1067. C42D4×D5semidirect
1203. C5#34681semidirect
1263. C4#65858semidirect

Maximal subgroups

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

subgroupindex
C2×#658822
C2×C4×D4×D52
C2×#658582
C5×#22932
#106140042
#106081722
#106081672
#106080482
#106080452
#106079512
#106079422
#106077422
#106077302
#106075892
#106075772
#106072582
#106072442
C4×#40412
#106053112
C4×#40282
C4×#40202
C42×D202
#346815