Finite Group Databasebeta

← C2×#11755330 #14510006

Subgroups — C2×#11755330 #14510006

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92100C211yesmaximal, characteristic, complemented
2C2×#92017C211yesmaximal, characteristic, complemented
3C2×C5×#950C211yesmaximal, characteristic, complemented
4C2×C3×#4095C211yesmaximal, characteristic, complemented
5#11755330C2116yesmaximal, direct product factor
6C2×#91521C212yesmaximal, complemented
7C2×#91506C212yesmaximal, complemented
8C2×#91498C212yesmaximal, complemented
9C2×#91481C212yesmaximal, complemented
10C2×#91305C211yesmaximal, characteristic, complemented
11C22×#6653C211yesmaximal, characteristic, complemented
12C2×#91291C211yesmaximal, characteristic, complemented
13C2×#66103—31nomaximal, Hall
14C2×C3×C5×#41C2211yescharacteristic, complemented
15#92100—24no—
16#92100C2218yescomplemented
17C2×#6821C2212yescomplemented
18C2×D4×D15—22no—
19C2×D4×D15C2212yescomplemented
20C2×#6817—21no—
21C2×#6817C2211yescharacteristic
22C22×D60—21no—
23C22×D60C2211yescharacteristic, complemented
24C2×C5×#235C2211yescharacteristic, complemented
25C22×C3×D20C2211yescharacteristic, complemented
26C2×D5×#67—22no—
27#92017—24no—
28#92017C2218yescomplemented
29C2×#6777C2212yescomplemented
30C2×D3×D20—21no—
31C2×#6766C2212yescomplemented
32C2×#6765—21no—
33C5×#950C2218yescomplemented
34C2×C5×#216C2211yescharacteristic, complemented
35C2×C5×#215C2211yescharacteristic, complemented
36C2×C5×#214C2211yescharacteristic, complemented
37C2×C5×#213C2211yescharacteristic, complemented
38C22×C5×C3⋊C8C2211yescharacteristic, complemented
39C3×#4095C2218yescomplemented
40C2×C3×#688C2212yescomplemented
41C2×C3×#686C2212yescomplemented
42C2×C3×#681C2211yescharacteristic, complemented
43#91521C22116yescomplemented
44#91506C22116yescomplemented
45#91498C22116yescomplemented
46#91481C22116yescomplemented
47C2×#6660C2212yescomplemented
48#91305C2218yescomplemented
49C2×#6654C2212yescomplemented
50C2×#6653C2212yescomplemented
51C2×#6653C2212yescomplemented
52C2×#6653C2218yescomplemented
53C2×#6651C2212yescomplemented
54#91291C2218yescomplemented
55C2×#6648C2212yescomplemented
56C2×#5774—51nomaximal, Hall
57C2×#4149—31no—
58C2×#4149—31no—
59C2×C5×#135—31no—
60C2×#4095—31no—
61C2×#4095D311yescharacteristic, complemented
62#66103—316no—
63C2×#4065—32no—
64C2×#4060—32no—
65C2×#4060—32no—
66C2×D5×D8—32no—
67C22×D40—31no—
68C2×#4047—31no—
69C23×D15—21no—
70C23×D15—22no—
71C23×C3×D5—21no—
72C22×D3×D5—22no—
73C3×C5×#41—22no—
74C3×C5×#41C2314yescomplemented
75C2×C3×C5×Q8C2311yescharacteristic
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—22no—
81C2×#1220D412yes—
82#6821—24no—
83#6821C2318yescomplemented
84D4×D15—216no—
85D4×D15—24no—
86D4×D15C2318yescomplemented
87#6817—28no—
88#6817D414yes—
89#6817C2314yes—
90C2×D60—22no—
91C2×D60—21no—
92C2×D60—22no—
93C2×D60—28no—
94C2×D60D411yescharacteristic
95C2×D60C2312yes—
96C2×D60C2314yescomplemented
97C2×C4×D15—22no—
98C2×C4×D15C2312yes—
99C2×Dic30D411yescharacteristic
100C2×C5×#67—21no—
101C5×#235—22no—
102C5×#235C2314yescomplemented
103C2×C5×D12C2311yescharacteristic
104C2×C4×C5×D3—21no—
105C2×C5×Dic6C2311yescharacteristic
106C2×C3×D20—21no—
107C2×C3×D20—22no—
108C2×C3×D20C2312yes—
109C2×C3×D20C2314yescomplemented
110D5×#67—216no—
111C2×#1202—22no—
112C2×#1201—22no—
113C2×D5×Dic3—22no—
114#6777—24no—
115#6777C2318yescomplemented
116D3×D20—28no—
117#6766—24no—
118#6766C2318yescomplemented
119#6765—28no—
120C5×#216C2314yescomplemented
121C5×#215C2314yescomplemented
122C5×#214C2314yescomplemented
123C5×#213C2314yescomplemented
124C2×C5×C3⋊C8C2311yescharacteristic
125C2×C5×C3⋊C8C2311yescharacteristic
126C2×C5×C3⋊C8C2314yescomplemented
127C3×#688C2318yescomplemented
128C3×#686C2318yescomplemented
129C3×#681C2314yescomplemented
130C2×C3×#168C2312yes—
131#6660C2318yescomplemented
132#6654C2318yescomplemented
133#6653C2318yescomplemented
134#6653C2318yescomplemented
135#6651C2318yescomplemented
136#6648C2318yescomplemented
137C2×#1009—51no—
138C2×#1004—51no—
139C2×C3×AGL(1,ℤ/8)—51no—
140C2×#950D511yescharacteristic, complemented
141C22×#213—51no—
142#5774—516no—
143C2×#916—52no—
144C2×#914—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#908—51no—
148C2×#907—51no—
149C2×C5×#41—31no—
150C2×C5×#41C2×D311yescharacteristic, complemented
151#4149—38no—
152#4149—38no—
153#4149—64no—
154#4149—64no—
155C2×#713—32no—
156C2×#713—32no—
157C2×D4×D5—32no—
158C2×D4×D5—32no—
159C2×D4×D5—62no—
160C2×D4×D5—62no—
161C2×#709—31no—
162C2×#709—61no—
163C2×#709—61no—
164C22×D20—31no—
165C22×D20—61no—
166C22×D20—61no—
167C22×D20C2×D311yescharacteristic, complemented
168C5×#135—38no—
169C2×C5×Q16—31no—
170C2×C5×SD16—31no—
171C2×C5×SD16—31no—
172C2×C5×D8—31no—
173C22×C5×C8—31no—
174#4095—38no—
175#4095C2×D318yescomplemented
176C2×#688—32no—
177C2×#688C2×D312yescomplemented
178C2×#686—32no—
179C2×#686C2×D312yescomplemented
180C2×#681C2×D311yescharacteristic, complemented
181#4065—316no—
182#4060—316no—
183#4060—316no—
184D5×D8—316no—
185C2×D40—32no—
186C2×D40—32no—
187C2×D40—38no—
188#4047—38no—
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#576—151noSylow
192C23×C3×C5—21no—
193C23×C3×C5C2×D411yescharacteristic
194C22×D15—22no—
195C22×D15—24no—
196C22×D15—28no—
197C22×D15—84no—
198C22×D15—82no—
199C22×D15C2×D412yes—
200C22×C5×D3—21no—
201C22×C3×D5—22no—
202C22×C3×D5—24no—
203C22×C3×D5—82no—
204C2×D3×D5—28no—
205C2×D3×D5—84no—
206C3×C5×Q8—21no—
207C3×C5×Q8C2412yes—
208C3×C5×D4—24no—
209C3×C5×D4—21no—
210C3×C5×D4C2412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—24no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D412yes—
215C2×C3×C4×C5C2411yescharacteristic
216C2×C3×C4×C5C2412yes—
217#1220—28no—
218#1220C2×D418yes—
219C2×Dic15C2×D412yes—
220D60—28no—
221D60—24no—
222D60—22no—
223D60C2×D414yes—
224D60C2414yes—
225C4×D15—28no—
226C4×D15C2×D414yes—
227C4×D15C2414yes—
228Dic30C2×D414yes—
229C5×#67—24no—
230C2×C5×Dic3—21no—
231C5×D12—21no—
232C5×D12C2412yes—
233C4×C5×D3—24no—
234C5×Dic6—21no—
235C5×Dic6C2412yes—
236C3×D20—24no—
237C3×D20—22no—
238C3×D20C2414yes—
239#1202—28no—
240#1201—28no—
241D5×Dic3—28no—
242C3×#168C2414yes—
243C5×C3⋊C8C2412yes—
244C5×C3⋊C8C2412yes—
245C2×C3×#41C2×D511yescharacteristic, complemented
246C22×C3×D4—51no—
247C22×#67—102no—
248#1009—58no—
249#1009—104no—
250C2×#239—52no—
251#1004—58no—
252#1004—104no—
253C2×#237—52no—
254C2×#237—101no—
255C2×D3×D4—52no—
256C2×D3×D4—52no—
257C2×D3×D4—101no—
258C2×D3×D4—102no—
259C2×#235—51no—
260C2×#235—101no—
261C2×#235C2×D511yescharacteristic, complemented
262C22×D12—51no—
263C22×D12—101no—
264C3×AGL(1,ℤ/8)—58no—
265C2×C3×SD16—52no—
266C2×C3×D8—52no—
267C2×C3×M16—51no—
268#950C2×D518yescomplemented
269C2×#216C2×D511yescharacteristic, complemented
270C2×#215C2×D511yescharacteristic, complemented
271C2×#214C2×D511yescharacteristic, complemented
272C2×#213—52no—
273C2×#213—52no—
274C2×#213—58no—
275C2×#213C2×D511yescharacteristic, complemented
276C22×C3⋊C8C2×D511yescharacteristic, complemented
277#916—516no—
278#914—516no—
279#911—516no—
280D3×D8—516no—
281#908—58no—
282#907—58no—
283C2×D24—52no—
284C2×#204—52no—
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C23×D5—21no—
288C23×D5—62no—
289C23×D5—62no—
290C23×D5—61no—
291C5×#41—22no—
292C5×#41—34no—
293C5×#41—62no—
294C5×#41C22×D314yescomplemented
295C2×C5×Q8—31no—
296C2×C5×Q8C22×D311yescharacteristic
297C2×C5×D4—21no—
298C2×C5×D4—31no—
299C2×C5×D4—61no—
300C2×C5×D4C22×D311yescharacteristic
301C22×C4×C5—21no—
302C22×C4×C5—61no—
303C22×C4×C5C22×D311yescharacteristic
304C2×C22⋊D5—32no—
305C2×C22⋊D5—62no—
306C2×C22⋊D5—62no—
307#713—38no—
308#713—38no—
309#713—64no—
310#713—64no—
311D4×D5—38no—
312D4×D5—38no—
313D4×D5—64no—
314D4×D5—64no—
315D4×D5—616no—
316D4×D5—616no—
317#709—34no—
318#709—34no—
319#709—68no—
320#709—68no—
321C2×D20—21no—
322C2×D20—22no—
323C2×D20—31no—
324C2×D20—32no—
325C2×D20—34no—
326C2×D20—68no—
327C2×D20—68no—
328C2×D20—62no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—62no—
332C2×D20C22×D312yes—
333C2×D20C22×D314yescomplemented
334C2×C4×D5—32no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×Dic10—31no—
338C5×Q16—34no—
339C5×SD16—34no—
340C5×SD16—34no—
341C5×D8—34no—
342C2×C5×C8—31no—
343C2×C5×C8—31no—
344C2×C5×C8—34no—
345#688—38no—
346#688C22×D318yescomplemented
347#686—38no—
348#686C22×D318yescomplemented
349#681C22×D314yescomplemented
350C2×#168C22×D312yes—
351D40—38no—
352D40—38no—
353#676—38no—
354C8×D5—38no—
355C2×H(5,𝔽2)—151no—
356C2×H(5,𝔽2)—151no—
357#576—1516no—
358C2×AGL(1,ℤ/8)—51no—
359C2×AGL(1,ℤ/8)—151no—
360C2×AGL(1,ℤ/8)—152no—
361C2×AGL(1,ℤ/8)—152no—
362C2×#135—31no—
363C2×#135—152no—
364C22×D8—151no—
365C22×D8—152no—
366C2×#131—151no—
367C22×C3×C5—22no—
368C22×C3×C5—22no—
369C22×C3×C5—42no—
370C22×C3×C5C22×D412yes—
371C22×C3×C5C22×D411yescharacteristic
372C2×D15—24no—
373C2×D15—24no—
374C2×D15—44no—
375C2×D15—88no—
376C2×D15—84no—
377C2×D15C22×D414yes—
378C2×C5×D3—22no—
379C2×C5×D3—42no—
380C2×C3×D5—24no—
381C2×C3×D5—44no—
382C2×C3×D5—84no—
383D3×D5—88no—
384C3×C4×C5—22no—
385C3×C4×C5C22×D411yescharacteristic
386C3×C4×C5C22×D412yes—
387C3×C4×C5C2511yescharacteristic
388Dic15C22×D414yes—
389C5×Dic3—22no—
390C24×C3—101no—
391C23×D3—102no—
392C23×D3—102no—
393C23×D3—101no—
394C3×#41—22no—
395C3×#41C22×D514yescomplemented
396C2×C3×Q8C22×D511yescharacteristic
397C2×C3×D4—21no—
398C2×C3×D4—52no—
399C2×C3×D4—54no—
400C2×C3×D4—101no—
401C2×C3×D4—102no—
402C2×C3×D4C22×D511yescharacteristic
403C22×C3×C4—21no—
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—21no—
406C2×#67—52no—
407C2×#67—102no—
408C2×#67—102no—
409C2×#67—102no—
410C2×#67—1016no—
411C22×Dic3—102no—
412#239—58no—
413#239—104no—
414#237—58no—
415#237—104no—
416#237—108no—
417D3×D4—58no—
418D3×D4—58no—
419D3×D4—108no—
420D3×D4—104no—
421D3×D4—104no—
422D3×D4—1016no—
423#235—22no—
424#235—54no—
425#235—54no—
426#235—108no—
427#235C22×D514yescomplemented
428C2×D12—51no—
429C2×D12—52no—
430C2×D12—54no—
431C2×D12—108no—
432C2×D12—102no—
433C2×D12—101no—
434C2×D12—102no—
435C2×D12C22×D511yescharacteristic
436C2×C4×D3—21no—
437C2×C4×D3—52no—
438C2×C4×D3—102no—
439C2×Dic6—51no—
440C2×Dic6C22×D511yescharacteristic
441C3×SD16—58no—
442C3×D8—58no—
443C3×M16—54no—
444C2×C3×C8—52no—
445#216C22×D514yescomplemented
446#215C22×D514yescomplemented
447#214C22×D514yescomplemented
448#213—58no—
449#213—58no—
450#213C22×D514yescomplemented
451C2×C3⋊C8C22×D511yescharacteristic
452C2×C3⋊C8C22×D511yescharacteristic
453C2×C3⋊C8C22×D514yescomplemented
454D24—58no—
455#204—58no—
456ΓL(1,𝔽25)—58no—
457D3×C8—58no—
458C23×C5—21no—
459C23×C5—61no—
460C23×C5D3×D411yescharacteristic
461C22×D5—22no—
462C22×D5—24no—
463C22×D5—32no—
464C22×D5—68no—
465C22×D5—68no—
466C22×D5—62no—
467C22×D5—64no—
468C22×D5—82no—
469C22×D5—244no—
470C22×D5—244no—
471C22×D5—242no—
472C5×Q8—21no—
473C5×Q8—32no—
474C5×Q8—61no—
475C5×Q8C23×D312yes—
476C5×D4—24no—
477C5×D4—21no—
478C5×D4—32no—
479C5×D4—64no—
480C5×D4—61no—
481C5×D4C23×D312yes—
482C2×C4×C5—21no—
483C2×C4×C5—24no—
484C2×C4×C5—61no—
485C2×C4×C5—64no—
486C2×C4×C5D3×D411yescharacteristic
487C2×C4×C5D3×D412yes—
488C2×C4×C5C23×D311yescharacteristic
489C2×C4×C5C23×D312yes—
490C22⋊D5—38no—
491C22⋊D5—68no—
492C22⋊D5—68no—
493C2×Dic5—32no—
494D20—24no—
495D20—22no—
496D20—34no—
497D20—34no—
498D20—68no—
499D20—68no—
500D20—64no—
501D20—62no—
502D20C23×D314yes—
503C4×D5—34no—
504C4×D5—34no—
505C4×D5—68no—
506C4×D5—68no—
507Dic10—34no—
508C5×C8—32no—
509C5×C8—32no—
510#168C23×D314yes—
511H(5,𝔽2)—158no—
512H(5,𝔽2)—158no—
513H(5,𝔽2)—304no—
514H(5,𝔽2)—304no—
515C2×#41—31no—
516C2×#41—151no—
517C2×#41—152no—
518C2×#41—152no—
519C2×#41—301no—
520C2×#41—301no—
521C2×#41D3×D511yescharacteristic, complemented
522C22×D4—51no—
523C22×D4—152no—
524C22×D4—152no—
525C22×D4—151no—
526C22×D4—301no—
527C22×D4—301no—
528C22×D4—302no—
529C22×D4—302no—
530AGL(1,ℤ/8)—58no—
531AGL(1,ℤ/8)—158no—
532AGL(1,ℤ/8)—1516no—
533AGL(1,ℤ/8)—1516no—
534#135—38no—
535#135—1516no—
536C2×Q16—31no—
537C2×SD16—31no—
538C2×SD16—31no—
539C2×SD16—52no—
540C2×SD16—152no—
541C2×D8—31no—
542C2×D8—52no—
543C2×D8—152no—
544C2×D8—152no—
545C2×D8—158no—
546C2×D8—152no—
547C2×D8—1516no—
548#131—158no—
549C2×M16—51no—
550C2×M16—152no—
551C22×C8—31no—
552C22×C8—152no—
553C2×C3×C5—22no—
554C2×C3×C5—42no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—24no—
558D15—44no—
559C3×D5—44no—
560C5×D3—42no—
561C23×C3—21no—
562C23×C3—102no—
563C23×C3—104no—
564C23×C3—402no—
565C23×C3D4×D511yescharacteristic
566C22×D3—21no—
567C22×D3—52no—
568C22×D3—108no—
569C22×D3—108no—
570C22×D3—102no—
571C22×D3—104no—
572C22×D3—404no—
573C22×D3—404no—
574C22×D3—402no—
575C3×Q8—21no—
576C3×Q8C23×D512yes—
577C3×D4—24no—
578C3×D4—21no—
579C3×D4—54no—
580C3×D4—102no—
581C3×D4—104no—
582C3×D4C23×D512yes—
583C2×C3×C4—21no—
584C2×C3×C4—24no—
585C2×C3×C4D4×D511yescharacteristic
586C2×C3×C4D4×D512yes—
587C2×C3×C4C23×D511yescharacteristic
588C2×C3×C4C23×D512yes—
589#67—24no—
590#67—58no—
591#67—108no—
592#67—108no—
593#67—108no—
594C2×Dic3—21no—
595C2×Dic3—52no—
596C2×Dic3—108no—
597D12—21no—
598D12—54no—
599D12—54no—
600D12—108no—
601D12—104no—
602D12—102no—
603D12C23×D512yes—
604C4×D3—24no—
605C4×D3—54no—
606C4×D3—54no—
607C4×D3—108no—
608Dic6—21no—
609Dic6—54no—
610Dic6C23×D512yes—
611C3×C8—54no—
612C3⋊C8C23×D512yes—
613C3⋊C8C23×D512yes—
614C22×C5—22no—
615C22×C5—22no—
616C22×C5—42no—
617C22×C5—62no—
618C22×C5—122no—
619C22×C5C2×D3×D412yes—
620C22×C5C2×D3×D411yescharacteristic
621C2×D5—24no—
622C2×D5—34no—
623C2×D5—44no—
624C2×D5—64no—
625C2×D5—64no—
626C2×D5—84no—
627C2×D5—124no—
628C2×D5—248no—
629C2×D5—248no—
630C2×D5—244no—
631C4×C5—22no—
632C4×C5—62no—
633C4×C5C2×D3×D412yes—
634C4×C5C2×D3×D411yescharacteristic
635C4×C5C24×D311yescharacteristic
636Dic5—34no—
637C24—101no—
638C24—302no—
639C24—302no—
640C24—301no—
641#41—22no—
642#41—34no—
643#41—62no—
644#41—154no—
645#41—154no—
646#41—158no—
647#41—158no—
648#41—308no—
649#41—308no—
650#41—304no—
651#41—304no—
652#41C2×D3×D514yescomplemented
653C2×Q8—31no—
654C2×Q8—151no—
655C2×Q8C2×D3×D511yescharacteristic
656C2×D4—21no—
657C2×D4—31no—
658C2×D4—52no—
659C2×D4—54no—
660C2×D4—61no—
661C2×D4—101no—
662C2×D4—102no—
663C2×D4—158no—
664C2×D4—152no—
665C2×D4—158no—
666C2×D4—151no—
667C2×D4—152no—
668C2×D4—154no—
669C2×D4—308no—
670C2×D4—302no—
671C2×D4—308no—
672C2×D4—302no—
673C2×D4—304no—
674C2×D4—304no—
675C2×D4—302no—
676C2×D4—302no—
677C2×D4—3016no—
678C2×D4—3016no—
679C2×D4—301no—
680C2×D4—302no—
681C2×D4C2×D3×D511yescharacteristic
682C22×C4—21no—
683C22×C4—61no—
684C22×C4—152no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—34no—
689SD16—34no—
690SD16—34no—
691SD16—58no—
692SD16—158no—
693D8—34no—
694D8—58no—
695D8—158no—
696D8—158no—
697D8—158no—
698M16—54no—
699M16—158no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—34no—
703C2×C8—52no—
704C2×C8—158no—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—42no—
709C22×C3—104no—
710C22×C3—204no—
711C22×C3—404no—
712C22×C3C2×D4×D512yes—
713C22×C3C2×D4×D511yescharacteristic
714C2×D3—22no—
715C2×D3—42no—
716C2×D3—54no—
717C2×D3—104no—
718C2×D3—104no—
719C2×D3—204no—
720C2×D3—408no—
721C2×D3—408no—
722C2×D3—404no—
723C3×C4—22no—
724C3×C4C2×D4×D511yescharacteristic
725C3×C4C2×D4×D512yes—
726C3×C4C24×D511yescharacteristic
727Dic3—22no—
728Dic3—54no—
729C2×C5—22no—
730C2×C5—42no—
731C2×C5—122no—
732C2×C5#577412yescomplemented
733C2×C5C22×D3×D411yescharacteristic
734D5—44no—
735D5—64no—
736D5—124no—
737C23—21no—
738C23—61no—
739C23—102no—
740C23—104no—
741C23—152no—
742C23—308no—
743C23—308no—
744C23—302no—
745C23—304no—
746C23—402no—
747C23—1202no—
748C23—1204no—
749C23—1204no—
750C23#679011yescharacteristic
751Q8—21no—
752Q8—32no—
753Q8—61no—
754Q8—154no—
755Q8C22×D3×D512yes—
756D4—24no—
757D4—21no—
758D4—32no—
759D4—54no—
760D4—64no—
761D4—61no—
762D4—104no—
763D4—102no—
764D4—158no—
765D4—154no—
766D4—154no—
767D4—308no—
768D4—308no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—302no—
773D4C22×D3×D512yes—
774C2×C4—21no—
775C2×C4—24no—
776C2×C4—61no—
777C2×C4—64no—
778C2×C4—152no—
779C2×C4—154no—
780C2×C4—154no—
781C2×C4—308no—
782C2×C4—308no—
783C2×C4#679012yes—
784C2×C4#679011yescharacteristic
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D511yescharacteristic
787C8—32no—
788C8—32no—
789C8—54no—
790C2×C3—22no—
791C2×C3—42no—
792C2×C3—204no—
793C2×C3#6610312yescomplemented
794C2×C3C22×D4×D511yescharacteristic
795D3—42no—
796D3—104no—
797D3—204no—
798C5C2×#577411yescharacteristic, complemented, Sylow
799C22—22no—
800C22—22no—
801C22—42no—
802C22—62no—
803C22—104no—
804C22—122no—
805C22—154no—
806C22—204no—
807C22—304no—
808C22—304no—
809C22—404no—
810C22—604no—
811C22—1204no—
812C22—1208no—
813C22—1208no—
814C22C2×#679012yes—
815C22C2×#679011yescharacteristic
816C4—22no—
817C4—62no—
818C4—154no—
819C4C2×#679012yes—
820C4C2×#679011yescharacteristic
821C4C23×D3×D511yescharacteristic
822C3C2×#6610311yescharacteristic, complemented, Sylow
823C2—22no—
824C2—42no—
825C2—122no—
826C2—204no—
827C2—304no—
828C2—604no—
829C2#1175533012yesdirect product factor
830C2C22×#679011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#92100C2semidirect
2. C2×#92017C2semidirect
3. C2×C5×#950C2semidirect
4. C2×C3×#4095C2semidirect
5. #11755330C2direct (N × H)
6. C2×#91521C2semidirect
7. C2×#91506C2semidirect
8. C2×#91498C2semidirect
9. C2×#91481C2semidirect
10. C2×#91305C2semidirect
11. C22×#6653C2semidirect
12. C2×#91291C2semidirect
14. C2×C3×C5×#41C22semidirect
16. #92100C22semidirect
17. C2×#6821C22semidirect
19. C2×D4×D15C22semidirect
23. C22×D60C22semidirect
24. C2×C5×#235C22semidirect
25. C22×C3×D20C22semidirect
28. #92017C22semidirect
29. C2×#6777C22semidirect
31. C2×#6766C22semidirect
33. C5×#950C22semidirect
34. C2×C5×#216C22semidirect
35. C2×C5×#215C22semidirect
36. C2×C5×#214C22semidirect
37. C2×C5×#213C22semidirect
38. C22×C5×C3⋊C8C22semidirect
39. C3×#4095C22semidirect
40. C2×C3×#688C22semidirect
41. C2×C3×#686C22semidirect
42. C2×C3×#681C22semidirect
43. #91521C22semidirect
44. #91506C22semidirect
45. #91498C22semidirect
46. #91481C22semidirect
47. C2×#6660C22semidirect
48. #91305C22semidirect
49. C2×#6654C22semidirect
50. C2×#6653C22semidirect
51. C2×#6653C22semidirect
52. C2×#6653C22semidirect
53. C2×#6651C22semidirect
54. #91291C22semidirect
55. C2×#6648C22semidirect
61. C2×#4095D3semidirect
74. C3×C5×#41C23semidirect
83. #6821C23semidirect
86. D4×D15C23semidirect
96. C2×D60C23semidirect
102. C5×#235C23semidirect
109. C2×C3×D20C23semidirect
115. #6777C23semidirect
118. #6766C23semidirect
120. C5×#216C23semidirect
121. C5×#215C23semidirect
122. C5×#214C23semidirect
123. C5×#213C23semidirect
126. C2×C5×C3⋊C8C23semidirect
127. C3×#688C23semidirect
128. C3×#686C23semidirect
129. C3×#681C23semidirect
131. #6660C23semidirect
132. #6654C23semidirect
133. #6653C23semidirect
134. #6653C23semidirect
135. #6651C23semidirect
136. #6648C23semidirect
140. C2×#950D5semidirect
150. C2×C5×#41C2×D3semidirect
167. C22×D20C2×D3semidirect
175. #4095C2×D3semidirect
177. C2×#688C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C2×#681C2×D3semidirect
245. C2×C3×#41C2×D5semidirect
261. C2×#235C2×D5semidirect
268. #950C2×D5semidirect
269. C2×#216C2×D5semidirect
270. C2×#215C2×D5semidirect
271. C2×#214C2×D5semidirect
275. C2×#213C2×D5semidirect
276. C22×C3⋊C8C2×D5semidirect
294. C5×#41C22×D3semidirect
333. C2×D20C22×D3semidirect
346. #688C22×D3semidirect
348. #686C22×D3semidirect
349. #681C22×D3semidirect
395. C3×#41C22×D5semidirect
427. #235C22×D5semidirect
445. #216C22×D5semidirect
446. #215C22×D5semidirect
447. #214C22×D5semidirect
450. #213C22×D5semidirect
453. C2×C3⋊C8C22×D5semidirect
521. C2×#41D3×D5semidirect
555. C2×C3×C5#576semidirect
652. #41C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
732. C2×C5#5774semidirect
793. C2×C3#66103semidirect
798. C5C2×#5774semidirect
822. C3C2×#66103semidirect
829. C2#11755330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921002
C2×#920172
C2×C5×#9502
C2×C3×#40952
#117553302
C2×#915212
C2×#915062
C2×#914982
C2×#914812
C2×#913052
C22×#66532
C2×#912912
C2×#661033
C2×#57745