Finite Group Databasebeta

← C2×#10610412 #12969988

Subgroups — C2×#10610412 #12969988

Order 1280.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66167C211yesmaximal, characteristic
2C2×#66159C211yesmaximal, characteristic, complemented
3C2×C5×#408C211yesmaximal, characteristic, complemented
4C2×#65426C211yesmaximal, characteristic, complemented
5C2×#65423C211yesmaximal, characteristic, complemented
6C2×#65405C211yesmaximal, characteristic, complemented
7C2×#65403C211yesmaximal, characteristic, complemented
8#10610412C2116yesmaximal, direct product factor
9C2×#65028C211yesmaximal, characteristic, complemented
10C2×#65027C211yesmaximal, characteristic, complemented
11C2×#65022C211yesmaximal, characteristic, complemented
12C2×#65022C211yesmaximal, characteristic, complemented
13C2×#65011C211yesmaximal, characteristic, complemented
14C2×#65012C211yesmaximal, characteristic, complemented
15C2×#65026C211yesmaximal, characteristic, complemented
16C2×#65010C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic
21C23×C5×C8C2211yescharacteristic
22#66167—24no—
23#66167C2218yes—
24#66159—24no—
25#66159C2218yescomplemented
26C2×#4092—21no—
27C2×#4090—21no—
28C2×#4085—21no—
29C2×#4085—21no—
30C2×#4084—21no—
31C2×#4082—21no—
32C2×#4081—21no—
33C2×#4081—21no—
34C2×#4076C2211yescharacteristic
35C2×#4076C2211yescharacteristic
36C2×#4072C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C2×#4070C2211yescharacteristic
39C2×#4070C2211yescharacteristic
40C2×#4070C2211yescharacteristic
41C2×#4070C2211yescharacteristic
42C2×#4070C2211yescharacteristic
43C2×#4070C2211yescharacteristic
44C22×Dic20C2211yescharacteristic
45C22×Dic20C2211yescharacteristic
46C22×#677C2211yescharacteristic
47C22×#677C2211yescharacteristic
48C5×#408C2218yescomplemented
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×C5×C22⋊C8C2211yescharacteristic
52C2×C5×C22⋊C8C2211yescharacteristic
53#65426C2218yescomplemented
54#65423C2218yescomplemented
55#65405C2218yescomplemented
56#65403C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3949C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3948C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2211yescharacteristic
69#65028C2218yescomplemented
70#65027C2218yescomplemented
71#65026C2218yescomplemented
72#65022C2218yescomplemented
73#65022C2218yescomplemented
74#65012C2218yescomplemented
75#65011C2218yescomplemented
76#65010C2218yescomplemented
77C2×#3201—51nomaximal, Sylow
78C2×C5×#41—42no—
79C2×C5×#41—42no—
80C2×C5×#41D414yes—
81C2×C5×#41C2314yes—
82C22×C5×Q8D411yescharacteristic
83C22×C5×D4D411yescharacteristic
84C22×C5×D4D411yescharacteristic
85C22×C5×D4D411yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C22×C22⋊D5—21no—
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C23×Dic5—21no—
93C23×Dic5—21no—
94C2×#709—22no—
95C2×#709—42no—
96C2×#709—42no—
97C2×#709C2314yes—
98C22×D20C2311yescharacteristic
99C22×C4×D5—21no—
100C22×Dic10—21no—
101C22×Dic10—22no—
102C22×Dic10—42no—
103C22×Dic10—42no—
104C22×Dic10C2311yescharacteristic
105C22×Dic10C2311yescharacteristic
106C22×Dic10C2311yescharacteristic
107C22×Dic10C2314yes—
108C2×C5×M16—42no—
109C2×C5×M16C2314yes—
110C22×C5×C8—42no—
111C22×C5×C8C2311yescharacteristic
112C22×C5×C8C2311yescharacteristic
113C22×C5×C8C2311yescharacteristic
114C22×C5×C8C2311yescharacteristic
115C22×C5×C8C2314yes—
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5—21no—
123#4092—28no—
124#4090—28no—
125#4085—28no—
126#4085—28no—
127#4084—28no—
128#4082—28no—
129#4081—28no—
130#4081—28no—
131#4076—22no—
132#4076—22no—
133#4076C2314yes—
134#4076C2314yes—
135C2×#685—21no—
136C2×#685—21no—
137#4072—22no—
138#4072C2314yes—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5—22no—
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2314yes—
146#4070—22no—
147#4070—22no—
148#4070—22no—
149#4070—22no—
150#4070—22no—
151#4070—22no—
152#4070C2314yes—
153#4070C2314yes—
154#4070C2314yes—
155#4070C2314yes—
156#4070C2314yes—
157#4070C2314yes—
158C2×#683—21no—
159C2×#683—21no—
160C2×#683—21no—
161C2×#683—21no—
162C2×#683—21no—
163C2×#683—21no—
164C2×C4×Dic5—21no—
165C2×Dic20—42no—
166C2×Dic20—42no—
167C2×Dic20C2314yes—
168C2×Dic20C2314yes—
169C2×#677—42no—
170C2×#677—42no—
171C2×#677C2314yes—
172C2×#677C2314yes—
173C5×C22⋊C8C2314yes—
174C5×C22⋊C8C2314yes—
175C5×C22⋊C8C2314yes—
176C5×C22⋊C8C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3950C2314yes—
180#3950C2314yes—
181#3949C2314yes—
182#3949C2314yes—
183#3948C2314yes—
184#3948C2314yes—
185#3948C2314yes—
186#3948C2314yes—
187#3948C2314yes—
188#3948C2314yes—
189C2×#537—51no—
190C2×#536—51no—
191#3201—516no—
192C2×#484—51no—
193C2×#485—51no—
194C2×#482—51no—
195C2×#483—51no—
196C2×#470—51no—
197C2×#468—51no—
198C2×#467—51no—
199C2×#465—51no—
200C2×#452—51no—
201C2×#452—51no—
202C2×#451—51no—
203C2×#448—51no—
204C2×#408D511yescharacteristic, complemented
205C24×C5C2×D411yescharacteristic
206C24×C5C2×D411yescharacteristic
207C24×C5C2×D411yescharacteristic
208C23×D5—21no—
209C5×#41—48no—
210C5×#41—44no—
211C5×#41—44no—
212C2×C5×Q8—42no—
213C2×C5×Q8C2×D414yes—
214C2×C5×D4—42no—
215C2×C5×D4—42no—
216C2×C5×D4—42no—
217C2×C5×D4C2×D414yes—
218C2×C5×D4C2×D414yes—
219C2×C5×D4C2×D414yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D412yes—
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2411yescharacteristic
236C2×C22⋊D5—24no—
237C2×C22⋊D5—24no—
238C2×C22⋊D5—24no—
239C2×C22⋊D5—44no—
240C2×C22⋊D5—82no—
241C2×C22⋊D5—82no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—24no—
250C22×Dic5—24no—
251C22×Dic5—44no—
252C22×Dic5—82no—
253#709—44no—
254#709—44no—
255#709—48no—
256C2×D20—22no—
257C2×D20—22no—
258C2×D20—21no—
259C2×D20C2412yes—
260C2×C4×D5—24no—
261C2×C4×D5—44no—
262C2×Dic10—22no—
263C2×Dic10—22no—
264C2×Dic10—22no—
265C2×Dic10—22no—
266C2×Dic10—22no—
267C2×Dic10—22no—
268C2×Dic10—21no—
269C2×Dic10—21no—
270C2×Dic10—24no—
271C2×Dic10—21no—
272C2×Dic10—44no—
273C2×Dic10—44no—
274C2×Dic10—44no—
275C2×Dic10—48no—
276C2×Dic10C2412yes—
277C2×Dic10C2412yes—
278C2×Dic10C2412yes—
279C5×M16—44no—
280C2×C5×C8—22no—
281C2×C5×C8—22no—
282C2×C5×C8—22no—
283C2×C5×C8—22no—
284C2×C5×C8—44no—
285C2×C5×C8C2412yes—
286C2×C5×C8C2412yes—
287C2×C5×C8C2412yes—
288C2×C5×C8C2412yes—
289C22⋊Dic5—24no—
290C22⋊Dic5—24no—
291C22⋊Dic5—24no—
292C22⋊Dic5—24no—
293C22⋊Dic5—24no—
294C22⋊Dic5—24no—
295C22⋊Dic5—24no—
296#685—24no—
297#685—24no—
298C4⋊Dic5—21no—
299C4⋊Dic5—21no—
300C4⋊Dic5—21no—
301C4⋊Dic5—21no—
302C4⋊Dic5—24no—
303C4⋊Dic5C2412yes—
304C4⋊Dic5C2412yes—
305C4⋊Dic5C2412yes—
306C4⋊Dic5C2412yes—
307#683—24no—
308#683—24no—
309#683—24no—
310#683—24no—
311#683—24no—
312#683—24no—
313C4×Dic5—24no—
314Dic20—44no—
315Dic20—44no—
316#677—44no—
317#677—44no—
318C22×#41—51no—
319C22×#41C2×D511yescharacteristic
320C23×Q8—51no—
321C22×Q16—51no—
322C22×Q16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×M16C2×D511yescharacteristic
326C23×C8C2×D511yescharacteristic
327#537—58no—
328#537—104no—
329#536—58no—
330#536—104no—
331C2×C4⋊Q8—101no—
332C2×#124—101no—
333C2×#123—101no—
334C2×#123—101no—
335C2×C22⋊Q8—51no—
336C2×C22⋊Q8—51no—
337C2×C22⋊Q8—51no—
338C2×C22⋊Q8—51no—
339C2×C22⋊Q8—51no—
340C2×C22⋊Q8—51no—
341C2×C22⋊Q8—101no—
342C2×#121—51no—
343C2×#121—51no—
344C2×#121—101no—
345C2×#121—101no—
346C2×#121—101no—
347C2×#117—51no—
348C22×C4⋊C4—51no—
349#485—58no—
350#484—58no—
351#483—58no—
352#482—58no—
353#470—58no—
354#468—58no—
355#467—58no—
356#465—58no—
357#452—58no—
358#452—58no—
359#451—58no—
360#448—58no—
361C2×#107—51no—
362C2×#107—51no—
363C2×#106—51no—
364C2×#106—51no—
365C2×#103—51no—
366C2×#103—51no—
367C2×#103—51no—
368C2×#103—51no—
369C2×#103—51no—
370C2×#103—51no—
371C2×#102—51no—
372C2×#102—51no—
373#408C2×D518yescomplemented
374C2×C22⋊C8C2×D511yescharacteristic
375C2×C22⋊C8C2×D511yescharacteristic
376C2×C22⋊C8C2×D511yescharacteristic
377C2×C22⋊C8C2×D511yescharacteristic
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5C22×D412yes—
388C23×C5C22×D412yes—
389C23×C5C22×D412yes—
390C23×C5C22×D411yescharacteristic
391C22×D5—22no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—42no—
395C5×Q8—44no—
396C5×D4—44no—
397C5×D4—44no—
398C5×D4—44no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—24no—
403C2×C4×C5—24no—
404C2×C4×C5—24no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D411yescharacteristic
415C2×C4×C5H(5,𝔽2)12yes—
416C2×C4×C5H(5,𝔽2)12yes—
417C2×C4×C5C2511yescharacteristic
418C22⋊D5—48no—
419C22⋊D5—84no—
420C22⋊D5—84no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—48no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432C2×Dic5—42no—
433C2×Dic5—42no—
434C2×Dic5—42no—
435C2×Dic5—42no—
436C2×Dic5—84no—
437D20—22no—
438D20—22no—
439D20—42no—
440C4×D5—48no—
441Dic10—22no—
442Dic10—22no—
443Dic10—22no—
444Dic10—22no—
445Dic10—22no—
446Dic10—22no—
447Dic10—48no—
448Dic10—42no—
449Dic10—42no—
450Dic10—42no—
451C5×C8—22no—
452C5×C8—22no—
453C5×C8—22no—
454C5×C8—22no—
455C2×#41—42no—
456C2×#41—42no—
457C2×#41—54no—
458C2×#41—102no—
459C2×#41—202no—
460C2×#41—202no—
461C2×#41D2014yes—
462C2×#41C22×D514yes—
463C22×Q8—51no—
464C22×Q8—51no—
465C22×Q8—51no—
466C22×Q8—54no—
467C22×Q8—101no—
468C22×Q8—102no—
469C22×Q8—202no—
470C22×Q8—202no—
471C22×Q8D2011yescharacteristic
472C22×D4—51no—
473C22×D4—101no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4D2011yescharacteristic
477C22×D4D2011yescharacteristic
478C22×D4D2011yescharacteristic
479C23×C4—101no—
480C23×C4—101no—
481C23×C4—101no—
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C2×Q16—54no—
486C2×Q16—54no—
487C2×Q16—202no—
488C2×Q16—202no—
489C2×SD16—54no—
490C2×SD16—54no—
491C2×SD16—202no—
492C2×SD16—202no—
493C2×M16—42no—
494C2×M16C22×D514yes—
495C22×C8—42no—
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498C22×C8C22×D511yescharacteristic
499C22×C8C22×D511yescharacteristic
500C22×C8C22×D514yes—
501C4⋊Q8—108no—
502#124—108no—
503#123—108no—
504#123—108no—
505C22⋊Q8—54no—
506C22⋊Q8—54no—
507C22⋊Q8—54no—
508C22⋊Q8—54no—
509C22⋊Q8—54no—
510C22⋊Q8—54no—
511C22⋊Q8—108no—
512C22⋊Q8—102no—
513C22⋊Q8—102no—
514C22⋊Q8—102no—
515C22⋊Q8—102no—
516C22⋊Q8—102no—
517C22⋊Q8—102no—
518#121—54no—
519#121—54no—
520#121—108no—
521#121—108no—
522#121—108no—
523#121—102no—
524#121—102no—
525#117—54no—
526#117—102no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—54no—
530C2×C4⋊C4—51no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—102no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4—101no—
538C2×C4⋊C4—101no—
539C2×C4⋊C4—101no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C22⋊C4—101no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C42—101no—
550#107—54no—
551#107—54no—
552#106—54no—
553#106—54no—
554#103—54no—
555#103—54no—
556#103—54no—
557#103—54no—
558#103—54no—
559#103—54no—
560#102—54no—
561#102—54no—
562C22⋊C8C22×D514yes—
563C22⋊C8C22×D514yes—
564C22⋊C8C22×D514yes—
565C22⋊C8C22×D514yes—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—44no—
576C22×C5—44no—
577C22×C5—44no—
578C22×C5#53412yes—
579C22×C5#57712yes—
580C22×C5#57812yes—
581C22×C5C23×D411yescharacteristic
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—84no—
586C4×C5—22no—
587C4×C5—22no—
588C4×C5—22no—
589C4×C5#53412yes—
590C4×C5C2×H(5,𝔽2)11yescharacteristic
591C4×C5C2×H(5,𝔽2)11yescharacteristic
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595Dic5—42no—
596Dic5—42no—
597Dic5—42no—
598Dic5—42no—
599C24—101no—
600C24C2×D2011yescharacteristic
601C24C2×D2011yescharacteristic
602C24C2×D2011yescharacteristic
603#41—48no—
604#41—44no—
605#41—44no—
606#41—204no—
607#41—204no—
608#41—208no—
609C2×Q8—42no—
610C2×Q8—52no—
611C2×Q8—52no—
612C2×Q8—52no—
613C2×Q8—101no—
614C2×Q8—101no—
615C2×Q8—101no—
616C2×Q8—104no—
617C2×Q8—102no—
618C2×Q8—102no—
619C2×Q8—102no—
620C2×Q8—102no—
621C2×Q8—102no—
622C2×Q8—102no—
623C2×Q8—204no—
624C2×Q8—204no—
625C2×Q8—204no—
626C2×Q8—208no—
627C2×Q8C2×D2014yes—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—52no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—104no—
635C2×D4—101no—
636C2×D4—102no—
637C2×D4—102no—
638C2×D4—204no—
639C2×D4—402no—
640C2×D4—402no—
641C2×D4C2×D2014yes—
642C2×D4C2×D2014yes—
643C2×D4C2×D2014yes—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—104no—
651C22×C4—101no—
652C22×C4—101no—
653C22×C4—101no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—104no—
659C22×C4—104no—
660C22×C4—204no—
661C22×C4—204no—
662C22×C4—402no—
663C22×C4C2×D2012yes—
664C22×C4C2×D2012yes—
665C22×C4C2×D2012yes—
666C22×C4C2×D2011yescharacteristic
667C22×C4C2×D2011yescharacteristic
668C22×C4C2×D2011yescharacteristic
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D512yes—
672C22×C4C23×D511yescharacteristic
673Q16—204no—
674Q16—204no—
675SD16—204no—
676SD16—204no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D512yes—
684C2×C8C23×D512yes—
685C2×C8C23×D512yes—
686C2×C8C23×D512yes—
687C4⋊C4—52no—
688C4⋊C4—52no—
689C4⋊C4—52no—
690C4⋊C4—52no—
691C4⋊C4—104no—
692C4⋊C4—101no—
693C4⋊C4—101no—
694C4⋊C4—101no—
695C4⋊C4—101no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—104no—
699C4⋊C4—104no—
700C4⋊C4—104no—
701C4⋊C4—104no—
702C22⋊C4—104no—
703C22⋊C4—104no—
704C22⋊C4—104no—
705C22⋊C4—104no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C42—104no—
712C2×C5—42no—
713C2×C5—42no—
714C2×C5—42no—
715C2×C5#320114yescomplemented
716C2×C5C2×#53411yescharacteristic
717C2×C5C2×#57711yescharacteristic
718C2×C5C2×#57811yescharacteristic
719D5—82no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—102no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23C22×D2012yes—
734C23C22×D2012yes—
735C23C22×D2012yes—
736C23C22×D2011yescharacteristic
737Q8—44no—
738Q8—102no—
739Q8—102no—
740Q8—102no—
741Q8—102no—
742Q8—102no—
743Q8—102no—
744Q8—208no—
745Q8—202no—
746Q8—202no—
747Q8—202no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—102no—
752D4—102no—
753D4—208no—
754D4—202no—
755D4—404no—
756D4—404no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—208no—
777C2×C4—208no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—202no—
783C2×C4—202no—
784C2×C4—202no—
785C2×C4—404no—
786C2×C4C22×D2012yes—
787C2×C4C22×D2012yes—
788C2×C4C22×D2012yes—
789C2×C4C22×D2011yescharacteristic
790C2×C4#414412yes—
791C2×C4#414412yes—
792C2×C4C24×D511yescharacteristic
793C8—22no—
794C8—22no—
795C8—22no—
796C8—22no—
797C5C2×#320111yescharacteristic, complemented, Sylow
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—202no—
811C22—202no—
812C22—202no—
813C22—404no—
814C22#6582712yes—
815C22#6608512yes—
816C22#6608712yes—
817C22C23×D2011yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—202no—
822C4—202no—
823C4—202no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4—202no—
828C4#6582712yes—
829C4C2×#414411yescharacteristic
830C4C2×#414411yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—402no—
835C2#1061041214yesdirect product factor
836C2C2×#6582711yescharacteristic
837C2C2×#6608511yescharacteristic
838C2C2×#6608711yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#408C2
socleC23×C5C22×D4
prime radicalC2×#66167C2
hypercenterC2×#408D5
hypocenterC5C2×#3201
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#66159C2semidirect
3. C2×C5×#408C2semidirect
4. C2×#65426C2semidirect
5. C2×#65423C2semidirect
6. C2×#65405C2semidirect
7. C2×#65403C2semidirect
8. #10610412C2direct (N × H)
9. C2×#65028C2semidirect
10. C2×#65027C2semidirect
11. C2×#65022C2semidirect
12. C2×#65022C2semidirect
13. C2×#65011C2semidirect
14. C2×#65012C2semidirect
15. C2×#65026C2semidirect
16. C2×#65010C2semidirect
25. #66159C22semidirect
48. C5×#408C22semidirect
53. #65426C22semidirect
54. #65423C22semidirect
55. #65405C22semidirect
56. #65403C22semidirect
69. #65028C22semidirect
70. #65027C22semidirect
71. #65026C22semidirect
72. #65022C22semidirect
73. #65022C22semidirect
74. #65012C22semidirect
75. #65011C22semidirect
76. #65010C22semidirect
204. C2×#408D5semidirect
373. #408C2×D5semidirect
715. C2×C5#3201semidirect
797. C5C2×#3201semidirect
835. C2#10610412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661672
C2×#661592
C2×C5×#4082
C2×#654262
C2×#654232
C2×#654052
C2×#654032
#106104122
C2×#650282
C2×#650272
C2×#650222
C2×#650112
C2×#650122
C2×#650262
C2×#650102
C2×#32015