Finite Group Databasebeta

← C2×#10618216 #13007545

Subgroups — C2×#10618216 #13007545

Order 1280.

11510 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4150C211yesmaximal, characteristic, complemented
2C23×#711C211yesmaximal, characteristic, complemented
3C2×C5×#535C211yesmaximal, characteristic, complemented
4C2×#66162C211yesmaximal, characteristic, complemented
5C2×#66139C211yesmaximal, characteristic, complemented
6#10618216C2132yesmaximal, direct product factor
7C2×#66052C214yesmaximal, complemented
8C2×#66011C214yesmaximal, complemented
9C2×#65933C214yesmaximal, complemented
10C2×#65932C214yesmaximal, complemented
11C2×#65926C214yesmaximal, complemented
12C2×#65920C214yesmaximal, complemented
13C2×#65858C211yesmaximal, characteristic, complemented
14C2×#65850C211yesmaximal, characteristic, complemented
15C22×C5×#41C2211yescharacteristic
16C23×C5×D4C2211yescharacteristic
17C23×C22⋊D5C2212yes—
18C24×Dic5C2212yes—
19C2×#4150—216no—
20C2×#4150C22116yescomplemented
21C22×Q8×D5C2212yescomplemented
22C22×#711—216no—
23C22×#711C2214yes—
24C22×#711C2214yes—
25C22×#711C2214yes—
26C22×#711C22116yescomplemented
27C22×#711C2212yescomplemented
28C22×#709C2211yescharacteristic
29C22×#709C2212yescomplemented
30C23×C4×D5C2211yescharacteristic
31C23×Dic10C2211yescharacteristic
32C23×Dic10C2212yescomplemented
33C5×#535C22116yescomplemented
34C2×C5×#127C2212yescomplemented
35C2×C5×#124C2212yescomplemented
36C2×C5×#121C2214yescomplemented
37C2×C5×#120C2214yes—
38C2×C5×#117C2211yescharacteristic
39C2×#4099C2214yes—
40#66162C22116yescomplemented
41C2×#4092C2212yescomplemented
42#66139C22116yescomplemented
43C2×#4086C2212yescomplemented
44C2×#4086C2218yescomplemented
45C2×#4085C2218yescomplemented
46C2×#4085C2218yescomplemented
47C2×#4084C2214yescomplemented
48C2×#4084C2212yescomplemented
49C2×#4083C2212yes—
50C2×#4082C2212yescomplemented
51C2×#4081C2212yes—
52C2×D4×Dic5C2218yescomplemented
53C2×C4×C22⋊D5C2214yescomplemented
54C2×#4072C2211yescharacteristic
55#66052C22164yescomplemented
56#66011C22164yescomplemented
57#65933C22164yescomplemented
58#65932C22164yescomplemented
59#65926C22164yescomplemented
60#65920C22164yescomplemented
61#65858C22116yescomplemented
62#65850C22116yescomplemented
63C2×#4043C2212yescomplemented
64C2×#4041C2212yescomplemented
65C2×#4033C2214yescomplemented
66C2×#4032C2212yes—
67C2×#4031C2218yescomplemented
68C2×#4030C2218yescomplemented
69C2×#4028C2212yes—
70C2×#4027C2218yescomplemented
71C2×#4024C2218yescomplemented
72C2×#4023C2214yes—
73C2×C4×D20C2214yescomplemented
74C2×C4×Dic10C2214yescomplemented
75C2×#3487—51nomaximal, Sylow
76C25×C5C2312yes—
77C24×D5C2311yescharacteristic
78C2×C5×#41—28no—
79C2×C5×#41C2318yes—
80C22×C5×Q8C2311yescharacteristic
81C22×C5×D4—28no—
82C22×C5×D4C2312yes—
83C22×C5×D4C2312yes—
84C22×C5×D4C2312yes—
85C22×C5×D4C2311yescharacteristic
86C22×C5×D4C2318yes—
87C22×C5×D4C2318yes—
88C23×C4×C5C2312yes—
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—216no—
91C22×C22⋊D5C2312yes—
92C22×C22⋊D5C2318yes—
93C22×C22⋊D5C2314yes—
94C22×C22⋊D5C23116yes—
95C22×C22⋊D5C2318yes—
96C22×C22⋊D5C2314yes—
97C23×Dic5—216no—
98C23×Dic5C2318yes—
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2314yes—
101C23×Dic5C23116yes—
102C23×Dic5C2312yes—
103#4150—2128no—
104C2×Q8×D5—216no—
105C2×Q8×D5C23116yescomplemented
106C2×#711—232no—
107C2×#711—232no—
108C2×#711—232no—
109C2×#711—216no—
110C2×#711—2128no—
111C2×#711C23132yes—
112C2×#711C23132yes—
113C2×#711C23132yes—
114C2×#711C23116yescomplemented
115C2×#709—28no—
116C2×#709—216no—
117C2×#709C2318yes—
118C2×#709C23116yescomplemented
119C22×D20C2311yescharacteristic
120C22×D20C2314yes—
121C22×C4×D5—28no—
122C22×C4×D5C2312yes—
123C22×C4×D5C2312yes—
124C22×C4×D5C2314yes—
125C22×C4×D5C2312yes—
126C22×C4×D5C2318yes—
127C22×Dic10—216no—
128C22×Dic10D4116yescomplemented
129C22×Dic10C2314yes—
130C22×Dic10C2311yescharacteristic
131C22×Dic10C2312yes—
132C22×Dic10C2312yes—
133C22×Dic10C2318yes—
134C22×Dic10C23116yescomplemented
135C5×#127C23116yescomplemented
136C5×#124C23116yescomplemented
137C5×#121C23132yescomplemented
138C5×#120C23132yes—
139C5×#117C2318yes—
140C2×C5×C4⋊C4C2312yes—
141C2×C5×C22⋊C4C2312yes—
142C2×C5×C22⋊C4C2318yes—
143C2×C42×C5C2312yes—
144#4099C23132yes—
145C2×C22⋊Dic5C2312yes—
146C2×C22⋊Dic5C2318yes—
147C2×C22⋊Dic5C2314yes—
148#4092C23116yescomplemented
149#4086C23164yescomplemented
150#4086C23116yescomplemented
151#4085C23164yescomplemented
152#4085C23164yescomplemented
153#4084C23116yescomplemented
154#4084C23132yescomplemented
155#4083C23116yes—
156#4082C23116yescomplemented
157#4081C23116yes—
158D4×Dic5C23164yescomplemented
159C4×C22⋊D5C23132yescomplemented
160C2×#685C2314yes—
161C2×#685C2314yes—
162C2×#685C2314yes—
163#4072C2318yes—
164C2×C4⋊Dic5C2312yes—
165C2×C4⋊Dic5C2314yes—
166C2×#683C2318yes—
167C2×#683C2314yes—
168C2×C4×Dic5C2318yes—
169C2×C4×Dic5C2312yes—
170#4043C23116yescomplemented
171#4041C23116yescomplemented
172#4033C23132yescomplemented
173#4032C23116yes—
174#4031C23164yescomplemented
175#4030C23164yescomplemented
176#4028C23116yes—
177#4027C23164yescomplemented
178#4024C23164yescomplemented
179#4023C23132yes—
180C4×D20C23132yescomplemented
181C4×Dic10C23132yescomplemented
182C22×2−1+4—51no—
183C23×#41—51no—
184#3487—532no—
185C2×#550—54no—
186C2×#550—54no—
187C2×#548—54no—
188C2×#548—54no—
189C2×#535—51no—
190C2×#535—54no—
191C2×#535D511yescharacteristic, complemented
192C2×#525—51no—
193C2×#525—54no—
194C2×#525—51no—
195C2×#519—51no—
196C24×C5—28no—
197C24×C5—48no—
198C24×C5C2414yes—
199C24×C5C2412yes—
200C24×C5C2411yescharacteristic
201C24×C5C2418yes—
202C23×D5—24no—
203C23×D5—44no—
204C23×D5C2412yes—
205C23×D5C2412yes—
206C23×D5C2414yes—
207C5×#41—232no—
208C2×C5×Q8—24no—
209C2×C5×Q8C2414yes—
210C2×C5×D4—28no—
211C2×C5×D4—28no—
212C2×C5×D4—28no—
213C2×C5×D4—232no—
214C2×C5×D4—24no—
215C2×C5×D4—416no—
216C2×C5×D4C2418yes—
217C2×C5×D4C2418yes—
218C2×C5×D4C2418yes—
219C2×C5×D4C2414yes—
220C2×C5×D4C24132yes—
221C22×C4×C5—28no—
222C22×C4×C5C2×D418yes—
223C22×C4×C5C2414yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2418yes—
226C22×C4×C5C2411yescharacteristic
227C22×C4×C5C2411yescharacteristic
228C22×C4×C5C2414yes—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—216no—
231C2×C22⋊D5—232no—
232C2×C22⋊D5—264no—
233C2×C22⋊D5—416no—
234C2×C22⋊D5—48no—
235C2×C22⋊D5C2418yes—
236C2×C22⋊D5C24116yes—
237C2×C22⋊D5C24132yes—
238C2×C22⋊D5C24132yes—
239C2×C22⋊D5C24116yes—
240C22×Dic5—24no—
241C22×Dic5—216no—
242C22×Dic5—232no—
243C22×Dic5—264no—
244C22×Dic5C2×D4116yes—
245C22×Dic5C2412yes—
246C22×Dic5C2414yes—
247C22×Dic5C2412yes—
248C22×Dic5C24116yes—
249C22×Dic5C2414yes—
250C22×Dic5C24132yes—
251C22×Dic5C2414yes—
252C22×Dic5C2418yes—
253Q8×D5—264no—
254#711—2128no—
255#711—2128no—
256#711—2128no—
257#711—264no—
258#709—232no—
259#709—264no—
260C2×D20—24no—
261C2×D20—48no—
262C2×D20C2414yes—
263C2×D20C24116yes—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—232no—
267C2×C4×D5—28no—
268C2×C4×D5—216no—
269C2×C4×D5C2418yes—
270C2×C4×D5C2418yes—
271C2×C4×D5C2418yes—
272C2×C4×D5C24116yes—
273C2×Dic10—24no—
274C2×Dic10—216no—
275C2×Dic10—264no—
276C2×Dic10C2×D4116yes—
277C2×Dic10C2×D4116yes—
278C2×Dic10C2×D4164yescomplemented
279C2×Dic10C2414yes—
280C2×Dic10C24116yes—
281C2×Dic10C2418yes—
282C2×Dic10C2418yes—
283C5×C4⋊C4C2418yes—
284C5×C22⋊C4C2418yes—
285C5×C22⋊C4C24132yes—
286C42×C5C2418yes—
287C22⋊Dic5C2418yes—
288C22⋊Dic5C24132yes—
289C22⋊Dic5C24116yes—
290#685C24116yes—
291#685C24116yes—
292#685C24116yes—
293C4⋊Dic5C2418yes—
294C4⋊Dic5C24116yes—
295#683C24132yes—
296#683C24116yes—
297C4×Dic5C24132yes—
298C4×Dic5C2418yes—
299C2×2−1+4—516no—
300C2×2−1+4—1016no—
301C22×#41—54no—
302C22×#41—54no—
303C22×#41—516no—
304C22×#41—54no—
305C22×#41—52no—
306C22×#41—51no—
307C22×#41—52no—
308C22×#41—1016no—
309C22×#41C2×D511yescharacteristic
310C23×Q8—52no—
311C23×Q8—51no—
312C23×Q8—52no—
313C23×D4—52no—
314C23×D4C2×D511yescharacteristic
315C24×C4—52no—
316C24×C4—51no—
317#550—564no—
318#550—564no—
319#548—564no—
320#548—564no—
321#535—516no—
322#535—564no—
323#535C2×D5116yescomplemented
324C2×#127—58no—
325C2×#127—52no—
326C2×#127C2×D512yescomplemented
327C2×#124—52no—
328C2×#124—58no—
329C2×#124C2×D512yescomplemented
330#525—516no—
331#525—564no—
332#525—516no—
333C2×#123—52no—
334C2×#123—52no—
335C2×C22⋊Q8—52no—
336C2×C22⋊Q8—52no—
337C2×C22⋊Q8—58no—
338C2×#121—52no—
339C2×#121—54no—
340C2×#121—58no—
341C2×#121—58no—
342C2×#121—52no—
343C2×#121—58no—
344C2×#121C2×D514yescomplemented
345C2×#120—54no—
346C2×#120—52no—
347C2×#120—52no—
348C2×#120C2×D514yes—
349#519—516no—
350C2×C4×Q8—54no—
351C2×C4×Q8—54no—
352C2×C4×D4—58no—
353C2×C4×D4—54no—
354C2×C4×D4—58no—
355C2×C4×D4—54no—
356C2×#117—51no—
357C2×#117—54no—
358C2×#117C2×D511yescharacteristic
359C23×C5—24no—
360C23×C5—24no—
361C23×C5—216no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—216no—
365C23×C5—416no—
366C23×C5—432no—
367C23×C5C22×D414yes—
368C23×C5C2518yes—
369C23×C5C2514yes—
370C23×C5C2512yes—
371C23×C5C2511yescharacteristic
372C22×D5—24no—
373C22×D5—28no—
374C22×D5—24no—
375C22×D5—24no—
376C22×D5—28no—
377C22×D5—24no—
378C22×D5—48no—
379C22×D5—416no—
380C22×D5C2514yes—
381C22×D5C2514yes—
382C5×Q8—28no—
383C5×D4—216no—
384C5×D4—216no—
385C5×D4—216no—
386C5×D4—28no—
387C5×D4—432no—
388C2×C4×C5—24no—
389C2×C4×C5—28no—
390C2×C4×C5—216no—
391C2×C4×C5C22×D414yes—
392C2×C4×C5C22×D414yes—
393C2×C4×C5C22×D4116yes—
394C2×C4×C5C2518yes—
395C2×C4×C5C2514yes—
396C2×C4×C5C2512yes—
397C2×C4×C5C2512yes—
398C22⋊D5—216no—
399C22⋊D5—232no—
400C22⋊D5—264no—
401C22⋊D5—432no—
402C22⋊D5—416no—
403C2×Dic5—24no—
404C2×Dic5—28no—
405C2×Dic5—24no—
406C2×Dic5—28no—
407C2×Dic5—232no—
408C2×Dic5—264no—
409C2×Dic5C22×D4116yes—
410C2×Dic5C22×D4132yes—
411C2×Dic5C2518yes—
412C2×Dic5C2514yes—
413C2×Dic5C2514yes—
414C2×Dic5C2518yes—
415D20—28no—
416D20—416no—
417C4×D5—216no—
418C4×D5—216no—
419C4×D5—216no—
420C4×D5—232no—
421Dic10—28no—
422Dic10—232no—
423Dic10C22×D4132yes—
424Dic10C22×D4132yes—
425C25—51no—
426C25C22×D512yes—
4272−1+4—10128no—
428C2×#41—28no—
429C2×#41—532no—
430C2×#41—532no—
431C2×#41—532no—
432C2×#41—516no—
433C2×#41—58no—
434C2×#41—516no—
435C2×#41—1016no—
436C2×#41—1032no—
437C2×#41—1032no—
438C2×#41—1032no—
439C2×#41—10128no—
440C2×#41—1016no—
441C2×#41—108no—
442C2×#41C22×D518yes—
443C22×Q8—516no—
444C22×Q8—516no—
445C22×Q8—52no—
446C22×Q8—52no—
447C22×Q8—58no—
448C22×Q8—54no—
449C22×Q8—51no—
450C22×Q8—516no—
451C22×Q8—1016no—
452C22×Q8—1016no—
453C22×Q8C22×D511yescharacteristic
454C22×D4—28no—
455C22×D4—52no—
456C22×D4—58no—
457C22×D4—54no—
458C22×D4—516no—
459C22×D4—54no—
460C22×D4—58no—
461C22×D4—51no—
462C22×D4—54no—
463C22×D4—1016no—
464C22×D4C22×D512yes—
465C22×D4C22×D512yes—
466C22×D4C22×D511yescharacteristic
467C22×D4C22×D512yes—
468C22×D4C22×D518yes—
469C22×D4C22×D518yes—
470C23×C4—52no—
471C23×C4—54no—
472C23×C4—58no—
473C23×C4—51no—
474C23×C4—516no—
475C23×C4—54no—
476C23×C4—52no—
477C23×C4—52no—
478C23×C4—52no—
479C23×C4—58no—
480C23×C4—1016no—
481C23×C4—108no—
482C23×C4C22×D512yes—
483C23×C4C22×D511yescharacteristic
484#127—564no—
485#127—516no—
486#127C22×D5116yescomplemented
487#124—516no—
488#124—564no—
489#124C22×D5116yescomplemented
490#123—516no—
491#123—516no—
492C22⋊Q8—516no—
493C22⋊Q8—516no—
494C22⋊Q8—564no—
495#121—516no—
496#121—564no—
497#121—532no—
498#121—564no—
499#121—516no—
500#121—564no—
501#121C22×D5132yescomplemented
502#120—532no—
503#120—516no—
504#120—516no—
505#120C22×D5132yes—
506C4×Q8—532no—
507C4×Q8—532no—
508C4×D4—564no—
509C4×D4—532no—
510C4×D4—564no—
511C4×D4—532no—
512#117—58no—
513#117—532no—
514#117C22×D518yes—
515C2×C4⋊C4—58no—
516C2×C4⋊C4—52no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—54no—
519C2×C4⋊C4C22×D512yes—
520C2×C22⋊C4—52no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—58no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4C22×D512yes—
527C2×C22⋊C4C22×D518yes—
528C2×C42—58no—
529C2×C42—52no—
530C2×C42C22×D512yes—
531C22×C5—24no—
532C22×C5—28no—
533C22×C5—24no—
534C22×C5—28no—
535C22×C5—28no—
536C22×C5—216no—
537C22×C5—432no—
538C22×C5—48no—
539C22×C5—416no—
540C22×C5C23×D414yes—
541C22×C5C23×D412yes—
542C22×C5#58514yes—
543C22×C5C2611yescharacteristic
544C2×D5—24no—
545C2×D5—24no—
546C2×D5—24no—
547C2×D5—28no—
548C2×D5—24no—
549C2×D5—416no—
550C2×D5—48no—
551C2×D5—48no—
552C4×C5—24no—
553C4×C5—28no—
554C4×C5C23×D414yes—
555C4×C5C23×D414yes—
556Dic5—24no—
557Dic5—24no—
558Dic5—28no—
559Dic5C23×D4116yes—
560C24—28no—
561C24—48no—
562C24—52no—
563C24—52no—
564C24—54no—
565C24—104no—
566C24—204no—
567C24C23×D514yes—
568C24C23×D512yes—
569C24C23×D511yescharacteristic
570C24C23×D518yes—
571#41—232no—
572#41—1064no—
573#41—10128no—
574#41—10128no—
575#41—10128no—
576#41—1064no—
577#41—1032no—
578C2×Q8—24no—
579C2×Q8—516no—
580C2×Q8—516no—
581C2×Q8—564no—
582C2×Q8—58no—
583C2×Q8—58no—
584C2×Q8—516no—
585C2×Q8—54no—
586C2×Q8—1016no—
587C2×Q8—1064no—
588C2×Q8—1064no—
589C2×Q8—104no—
590C2×Q8C23×D514yes—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—232no—
595C2×D4—24no—
596C2×D4—416no—
597C2×D4—58no—
598C2×D4—532no—
599C2×D4—516no—
600C2×D4—516no—
601C2×D4—532no—
602C2×D4—54no—
603C2×D4—516no—
604C2×D4—1032no—
605C2×D4—1064no—
606C2×D4—1016no—
607C2×D4—108no—
608C2×D4—104no—
609C2×D4—208no—
610C2×D4—208no—
611C2×D4—2016no—
612C2×D4C23×D518yes—
613C2×D4C23×D518yes—
614C2×D4C23×D514yes—
615C2×D4C23×D518yes—
616C2×D4C23×D5132yes—
617C22×C4—28no—
618C22×C4—516no—
619C22×C4—58no—
620C22×C4—54no—
621C22×C4—516no—
622C22×C4—532no—
623C22×C4—54no—
624C22×C4—54no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—516no—
628C22×C4—58no—
629C22×C4—58no—
630C22×C4—58no—
631C22×C4—1016no—
632C22×C4—1032no—
633C22×C4—1064no—
634C22×C4—1016no—
635C22×C4—104no—
636C22×C4—108no—
637C22×C4—108no—
638C22×C4—1032no—
639C22×C4—108no—
640C22×C4D4×D518yes—
641C22×C4C23×D518yes—
642C22×C4C23×D514yes—
643C22×C4C23×D512yes—
644C22×C4C23×D514yes—
645C22×C4C23×D511yescharacteristic
646C22×C4C23×D511yescharacteristic
647C4⋊C4—532no—
648C4⋊C4—58no—
649C4⋊C4—516no—
650C4⋊C4—516no—
651C4⋊C4C23×D518yes—
652C22⋊C4—58no—
653C22⋊C4—516no—
654C22⋊C4—532no—
655C22⋊C4—516no—
656C22⋊C4—516no—
657C22⋊C4—516no—
658C22⋊C4C23×D518yes—
659C22⋊C4C23×D5132yes—
660C42—532no—
661C42—58no—
662C42C23×D518yes—
663C2×C5—24no—
664C2×C5—44no—
665C2×C5—48no—
666C2×C5#348714yescomplemented
667C2×C5C24×D411yescharacteristic
668C2×C5C2×#58512yes—
669D5—44no—
670D5—44no—
671C23—24no—
672C23—24no—
673C23—216no—
674C23—28no—
675C23—28no—
676C23—216no—
677C23—416no—
678C23—432no—
679C23—54no—
680C23—54no—
681C23—104no—
682C23—108no—
683C23—104no—
684C23—108no—
685C23—104no—
686C23—104no—
687C23—208no—
688C23—2016no—
689C23C2×D4×D514yes—
690C23C24×D518yes—
691C23C24×D514yes—
692C23C24×D512yes—
693C23C24×D511yescharacteristic
694Q8—28no—
695Q8—532no—
696Q8—532no—
697Q8—1032no—
698Q8—108no—
699D4—216no—
700D4—216no—
701D4—216no—
702D4—28no—
703D4—432no—
704D4—1064no—
705D4—1032no—
706D4—1016no—
707D4—108no—
708D4—2016no—
709D4—2016no—
710D4—2032no—
711C2×C4—24no—
712C2×C4—28no—
713C2×C4—216no—
714C2×C4—516no—
715C2×C4—532no—
716C2×C4—58no—
717C2×C4—58no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—1032no—
721C2×C4—1064no—
722C2×C4—1032no—
723C2×C4—108no—
724C2×C4—104no—
725C2×C4—104no—
726C2×C4—108no—
727C2×C4—1016no—
728C2×C4—1016no—
729C2×C4—1016no—
730C2×C4C2×D4×D514yes—
731C2×C4C2×D4×D514yes—
732C2×C4C2×D4×D5116yes—
733C2×C4C24×D518yes—
734C2×C4C24×D514yes—
735C2×C4C24×D512yes—
736C2×C4C24×D512yes—
737C5C2×#348711yescharacteristic, complemented, Sylow
738C22—24no—
739C22—28no—
740C22—24no—
741C22—28no—
742C22—28no—
743C22—216no—
744C22—432no—
745C22—416no—
746C22—48no—
747C22—104no—
748C22—104no—
749C22—108no—
750C22—104no—
751C22—104no—
752C22—2016no—
753C22—208no—
754C22—208no—
755C22C22×D4×D514yes—
756C22C22×D4×D512yes—
757C22#6628514yes—
758C22C25×D511yescharacteristic
759C4—24no—
760C4—28no—
761C4—516no—
762C4—104no—
763C4—104no—
764C4—108no—
765C4C22×D4×D514yes—
766C4C22×D4×D514yes—
767C2—24no—
768C2—48no—
769C2—44no—
770C2—204no—
771C2—204no—
772C2#1061821614yesdirect product factor
773C2C23×D4×D511yescharacteristic
774C2C2×#6628512yes—
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#535C2
socleC23×C5C25
hypercenterC2×#535D5
hypocenterC5C2×#3487
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#4150C2semidirect
2. C23×#711C2semidirect
3. C2×C5×#535C2semidirect
4. C2×#66162C2semidirect
5. C2×#66139C2semidirect
6. #10618216C2direct (N × H)
7. C2×#66052C2semidirect
8. C2×#66011C2semidirect
9. C2×#65933C2semidirect
10. C2×#65932C2semidirect
11. C2×#65926C2semidirect
12. C2×#65920C2semidirect
13. C2×#65858C2semidirect
14. C2×#65850C2semidirect
20. C2×#4150C22semidirect
21. C22×Q8×D5C22semidirect
26. C22×#711C22semidirect
27. C22×#711C22semidirect
29. C22×#709C22semidirect
32. C23×Dic10C22semidirect
33. C5×#535C22semidirect
34. C2×C5×#127C22semidirect
35. C2×C5×#124C22semidirect
36. C2×C5×#121C22semidirect
40. #66162C22semidirect
41. C2×#4092C22semidirect
42. #66139C22semidirect
43. C2×#4086C22semidirect
44. C2×#4086C22semidirect
45. C2×#4085C22semidirect
46. C2×#4085C22semidirect
47. C2×#4084C22semidirect
48. C2×#4084C22semidirect
50. C2×#4082C22semidirect
52. C2×D4×Dic5C22semidirect
53. C2×C4×C22⋊D5C22semidirect
55. #66052C22semidirect
56. #66011C22semidirect
57. #65933C22semidirect
58. #65932C22semidirect
59. #65926C22semidirect
60. #65920C22semidirect
61. #65858C22semidirect
62. #65850C22semidirect
63. C2×#4043C22semidirect
64. C2×#4041C22semidirect
65. C2×#4033C22semidirect
67. C2×#4031C22semidirect
68. C2×#4030C22semidirect
70. C2×#4027C22semidirect
71. C2×#4024C22semidirect
73. C2×C4×D20C22semidirect
74. C2×C4×Dic10C22semidirect
105. C2×Q8×D5C23semidirect
114. C2×#711C23semidirect
118. C2×#709C23semidirect
128. C22×Dic10D4semidirect
134. C22×Dic10C23semidirect
135. C5×#127C23semidirect
136. C5×#124C23semidirect
137. C5×#121C23semidirect
148. #4092C23semidirect
149. #4086C23semidirect
150. #4086C23semidirect
151. #4085C23semidirect
152. #4085C23semidirect
153. #4084C23semidirect
154. #4084C23semidirect
156. #4082C23semidirect
158. D4×Dic5C23semidirect
159. C4×C22⋊D5C23semidirect
170. #4043C23semidirect
171. #4041C23semidirect
172. #4033C23semidirect
174. #4031C23semidirect
175. #4030C23semidirect
177. #4027C23semidirect
178. #4024C23semidirect
180. C4×D20C23semidirect
181. C4×Dic10C23semidirect
191. C2×#535D5semidirect
278. C2×Dic10C2×D4semidirect
323. #535C2×D5semidirect
326. C2×#127C2×D5semidirect
329. C2×#124C2×D5semidirect
344. C2×#121C2×D5semidirect
486. #127C22×D5semidirect
489. #124C22×D5semidirect
501. #121C22×D5semidirect
666. C2×C5#3487semidirect
737. C5C2×#3487semidirect
772. C2#10618216direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41502
C23×#7112
C2×C5×#5352
C2×#661622
C2×#661392
#106182162
C2×#660522
C2×#660112
C2×#659332
C2×#659322
C2×#659262
C2×#659202
C2×#658582
C2×#658502
C2×#34875