Finite Group Databasebeta

← C2×#11754704 #14509991

Subgroups — C2×#11754704 #14509991

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×#92095C211yesmaximal, characteristic, complemented
2C2×#92018C211yesmaximal, characteristic, complemented
3C22×C5×#213C211yesmaximal, characteristic, complemented
4C2×C3×#4078C211yesmaximal, characteristic, complemented
5C2×#91500C212yesmaximal, complemented
6C2×#91499C212yesmaximal, complemented
7#11754704C2116yesmaximal, direct product factor
8C2×#91482C212yesmaximal, complemented
9C2×#91481C212yesmaximal, complemented
10C2×#91311C211yesmaximal, characteristic, complemented
11C2×#91304C211yesmaximal, characteristic, complemented
12C2×#91291C211yesmaximal, characteristic, complemented
13C2×#66091—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic, complemented
15C22×#1220—22no—
16#92095—24no—
17#92095C2218yescomplemented
18C2×#6819—21no—
19C2×#6819C2212yescomplemented
20C2×D4×D15—21no—
21C2×D4×D15C2212yescomplemented
22C2×#6817C2211yescharacteristic
23C2×#6817C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C2×C3×#709C2211yescharacteristic, complemented
26C2×D3×C22⋊D5—22no—
27#92018—24no—
28#92018C2218yescomplemented
29C2×#6777C2212yescomplemented
30C2×D5×D12—21no—
31C2×#6772—21no—
32C2×#6768C2212yescomplemented
33C2×C5×#213C2212yescomplemented
34C2×C5×#213C2212yescomplemented
35C2×C5×#213C2218yescomplemented
36C22×C5×C3⋊C8C2211yescharacteristic, complemented
37C2×C3×#687C2212yescomplemented
38C3×#4078C2218yescomplemented
39C2×C3×#686C2212yescomplemented
40C2×C3×#681C2211yescharacteristic, complemented
41#91500C22116yescomplemented
42#91499C22116yescomplemented
43#91482C22116yescomplemented
44#91481C22116yescomplemented
45C2×#6662C2211yescharacteristic, complemented
46C2×#6659C2212yescomplemented
47C2×#6658C2211yescharacteristic, complemented
48#91311C2218yescomplemented
49C2×#6657C2211yescharacteristic, complemented
50#91304C2218yescomplemented
51C2×#6654C2212yescomplemented
52C2×#6653C2211yescharacteristic, complemented
53C2×#6651C2212yescomplemented
54#91291C2218yescomplemented
55C2×#6648C2212yescomplemented
56C2×#5774—51nomaximal, Hall
57C2×#4144—31no—
58C2×#4144—31no—
59C22×C5×D8—31no—
60C2×#4078—31no—
61C2×#4078D311yescharacteristic, complemented
62#66091—316no—
63C2×#4058—32no—
64C2×#4057—32no—
65C2×#4057—32no—
66C2×D5×D8—32no—
67C2×#4050—31no—
68C2×#4047—31no—
69C24×C3×C5—21no—
70C23×D15—22no—
71C23×C5×D3—21no—
72C22×D3×D5—22no—
73C2×C3×C5×D4—21no—
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4C2312yes—
76C2×C3×C5×D4C2314yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79C2×#1220—22no—
80C2×#1220—216no—
81C2×#1220—22no—
82C2×#1220D412yes—
83C22×Dic15—22no—
84#6819—24no—
85#6819—28no—
86#6819C2318yescomplemented
87D4×D15—28no—
88D4×D15—24no—
89D4×D15C2318yescomplemented
90#6817—22no—
91#6817D414yes—
92#6817C2314yes—
93#6817C2314yescomplemented
94C2×D60D411yescharacteristic
95C2×D60C2311yescharacteristic
96C2×C4×D15—21no—
97C2×C4×D15C2312yes—
98C2×Dic30D411yescharacteristic
99C2×Dic30C2311yescharacteristic
100C2×C5×D12—21no—
101C2×C5×D12—22no—
102C2×C5×D12C2312yes—
103C2×C5×D12C2314yescomplemented
104C2×C3×C22⋊D5—21no—
105C3×#709—22no—
106C3×#709C2314yescomplemented
107C2×C3×D20C2311yescharacteristic
108C2×C3×C4×D5—21no—
109C2×C3×Dic10C2311yescharacteristic
110D3×C22⋊D5—216no—
111C2×#1203—22no—
112C2×#1201—22no—
113C2×D3×Dic5—22no—
114#6777—24no—
115#6777C2318yescomplemented
116D5×D12—28no—
117#6772—28no—
118#6768—24no—
119#6768C2318yescomplemented
120C5×#213C2318yescomplemented
121C5×#213C2318yescomplemented
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C2×C5×C3⋊C8C2314yescomplemented
125C3×#687C2318yescomplemented
126C3×#686C2318yescomplemented
127C3×#681C2314yescomplemented
128C2×C3×#168C2312yes—
129#6662C2314yescomplemented
130#6659C2318yescomplemented
131#6658C2314yescomplemented
132#6657C2314yescomplemented
133#6654C2318yescomplemented
134#6653C2314yescomplemented
135#6651C2318yescomplemented
136#6648C2318yescomplemented
137C2×#1009—51no—
138C2×#1004—51no—
139C2×C3×AGL(1,ℤ/8)—51no—
140C2×#950—51no—
141C22×#213D511yescharacteristic, complemented
142#5774—516no—
143C2×#916—52no—
144C2×#914—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#908—51no—
148C2×#907—51no—
149C22×C5×D4—31no—
150C22×C5×D4C2×D311yescharacteristic, complemented
151C22×C22⋊D5—62no—
152C22×C22⋊D5—62no—
153#4144—38no—
154#4144—38no—
155#4144—64no—
156#4144—64no—
157C2×#711—32no—
158C2×#711—32no—
159C2×#711—61no—
160C2×#711—61no—
161C2×D4×D5—32no—
162C2×D4×D5—32no—
163C2×D4×D5—61no—
164C2×D4×D5—61no—
165C2×#709—31no—
166C2×#709—31no—
167C2×#709C2×D311yescharacteristic, complemented
168C2×C5×D8—32no—
169C2×C5×D8—32no—
170C2×C5×D8—38no—
171C22×C5×C8—31no—
172C2×#687—32no—
173C2×#687C2×D312yescomplemented
174#4078—38no—
175#4078C2×D318yescomplemented
176C2×#686—32no—
177C2×#686C2×D312yescomplemented
178C2×#681C2×D311yescharacteristic, complemented
179#4058—316no—
180#4057—316no—
181#4057—316no—
182D5×D8—316no—
183C2×Dic20—31no—
184#4050—38no—
185C2×D40—31no—
186C2×#677—31no—
187C2×#677—31no—
188#4047—38no—
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#576—151noSylow
192C23×C3×C5—22no—
193C23×C3×C5—24no—
194C23×C3×C5—82no—
195C23×C3×C5C2×D411yescharacteristic
196C22×D15—21no—
197C22×D15—28no—
198C22×D15—84no—
199C22×D15C2×D412yes—
200C22×C5×D3—22no—
201C22×C5×D3—24no—
202C22×C5×D3—82no—
203C22×C3×D5—21no—
204C2×D3×D5—28no—
205C2×D3×D5—84no—
206C3×C5×D4—22no—
207C3×C5×D4—24no—
208C3×C5×D4C2414yes—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5C2411yescharacteristic
212C2×C3×C4×C5C2412yes—
213#1220—24no—
214#1220—28no—
215#1220—28no—
216#1220C2×D418yes—
217C2×Dic15—21no—
218C2×Dic15—28no—
219C2×Dic15C2×D412yes—
220D60—21no—
221D60C2×D414yes—
222D60C2412yes—
223C4×D15—24no—
224C4×D15C2×D414yes—
225C4×D15C2414yes—
226Dic30—21no—
227Dic30C2×D414yes—
228Dic30C2412yes—
229C5×D12—22no—
230C5×D12—24no—
231C5×D12C2414yes—
232C3×C22⋊D5—24no—
233C2×C3×Dic5—21no—
234C3×D20—21no—
235C3×D20C2412yes—
236C3×C4×D5—24no—
237C3×Dic10—21no—
238C3×Dic10C2412yes—
239#1203—28no—
240#1201—28no—
241D3×Dic5—28no—
242C3×#168C2414yes—
243C5×C3⋊C8C2412yes—
244C5×C3⋊C8C2412yes—
245C2×C3×#41—51no—
246C22×C3×D4C2×D511yescharacteristic, complemented
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—51no—
261C2×#235—101no—
262C22×D12—101no—
263C22×D12C2×D511yescharacteristic, complemented
264C3×AGL(1,ℤ/8)—58no—
265C2×C3×SD16—52no—
266C2×C3×D8—52no—
267C2×C3×M16—51no—
268#950—58no—
269C2×#216—51no—
270C2×#215—51no—
271C2×#214—51no—
272C2×#213—51no—
273C2×#213C2×D512yescomplemented
274C2×#213C2×D512yescomplemented
275C2×#213C2×D518yescomplemented
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—
287C24×C5—21no—
288C24×C5—61no—
289C23×D5—62no—
290C23×D5—62no—
291C2×C5×D4—21no—
292C2×C5×D4—22no—
293C2×C5×D4—32no—
294C2×C5×D4—34no—
295C2×C5×D4—61no—
296C2×C5×D4—62no—
297C2×C5×D4C22×D312yes—
298C2×C5×D4C22×D314yescomplemented
299C22×C4×C5C22×D311yescharacteristic
300C2×C22⋊D5—21no—
301C2×C22⋊D5—32no—
302C2×C22⋊D5—62no—
303C2×C22⋊D5—62no—
304C2×C22⋊D5—62no—
305C2×C22⋊D5—616no—
306C2×C22⋊D5—616no—
307C2×C22⋊D5—62no—
308C2×C22⋊D5—61no—
309C22×Dic5—62no—
310C22×Dic5—62no—
311#711—38no—
312#711—38no—
313#711—64no—
314#711—68no—
315#711—68no—
316#711—64no—
317D4×D5—38no—
318D4×D5—38no—
319D4×D5—68no—
320D4×D5—64no—
321D4×D5—64no—
322D4×D5—68no—
323#709—22no—
324#709—34no—
325#709—34no—
326#709—34no—
327#709—62no—
328#709C22×D314yescomplemented
329C2×D20—31no—
330C2×D20—31no—
331C2×D20C22×D311yescharacteristic
332C2×C4×D5—21no—
333C2×C4×D5—32no—
334C2×C4×D5—61no—
335C2×Dic10—31no—
336C2×Dic10—31no—
337C2×Dic10C22×D311yescharacteristic
338C5×D8—38no—
339C5×D8—38no—
340C2×C5×C8—31no—
341C2×C5×C8—31no—
342C2×C5×C8—34no—
343#687—38no—
344#687C22×D318yescomplemented
345#686—38no—
346#686C22×D318yescomplemented
347#681C22×D314yescomplemented
348C2×#168C22×D312yes—
349Dic20—34no—
350D40—34no—
351#677—34no—
352#677—34no—
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—151no—
363C2×#135—152no—
364C22×D8—31no—
365C22×D8—152no—
366C2×#131—151no—
367C22×C3×C5—22no—
368C22×C3×C5—24no—
369C22×C3×C5—44no—
370C22×C3×C5—84no—
371C22×C3×C5C22×D412yes—
372C22×C3×C5C22×D411yescharacteristic
373C2×D15—24no—
374C2×D15—22no—
375C2×D15—42no—
376C2×D15—88no—
377C2×D15C22×D414yes—
378C2×C5×D3—24no—
379C2×C5×D3—44no—
380C2×C5×D3—84no—
381C2×C3×D5—22no—
382C2×C3×D5—42no—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387Dic15—22no—
388Dic15C22×D414yes—
389C3×Dic5—22no—
390C24×C3—21no—
391C23×D3—21no—
392C23×D3—102no—
393C23×D3—102no—
394C3×#41—54no—
395C3×#41—102no—
396C2×C3×Q8—51no—
397C2×C3×D4—21no—
398C2×C3×D4—22no—
399C2×C3×D4—51no—
400C2×C3×D4—101no—
401C2×C3×D4C22×D512yes—
402C2×C3×D4C22×D514yescomplemented
403C22×C3×C4—101no—
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—52no—
406C2×#67—102no—
407C2×#67—102no—
408C2×#67—1016no—
409C2×#67—102no—
410C2×#67—101no—
411C22×Dic3—102no—
412#239—58no—
413#239—104no—
414#237—58no—
415#237—108no—
416#237—104no—
417D3×D4—58no—
418D3×D4—58no—
419D3×D4—104no—
420D3×D4—104no—
421D3×D4—108no—
422D3×D4—1016no—
423#235—54no—
424#235—54no—
425#235—54no—
426#235—108no—
427#235—102no—
428C2×D12—21no—
429C2×D12—22no—
430C2×D12—51no—
431C2×D12—51no—
432C2×D12—108no—
433C2×D12—102no—
434C2×D12C22×D512yes—
435C2×D12C22×D514yescomplemented
436C2×C4×D3—52no—
437C2×C4×D3—102no—
438C2×C4×D3—101no—
439C2×Dic6—51no—
440C2×Dic6—51no—
441C3×SD16—58no—
442C3×D8—58no—
443C3×M16—54no—
444C2×C3×C8—52no—
445#216—54no—
446#215—54no—
447#214—54no—
448#213—54no—
449#213C22×D518yescomplemented
450#213C22×D518yescomplemented
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—22no—
459C23×C5—24no—
460C23×C5—62no—
461C23×C5—64no—
462C23×C5—82no—
463C23×C5—242no—
464C23×C5D3×D411yescharacteristic
465C22×D5—21no—
466C22×D5—32no—
467C22×D5—68no—
468C22×D5—68no—
469C22×D5—61no—
470C22×D5—244no—
471C22×D5—244no—
472C5×D4—22no—
473C5×D4—24no—
474C5×D4—34no—
475C5×D4—62no—
476C5×D4—64no—
477C5×D4C23×D314yes—
478C2×C4×C5D3×D411yescharacteristic
479C2×C4×C5D3×D412yes—
480C2×C4×C5C23×D311yescharacteristic
481C2×C4×C5C23×D312yes—
482C22⋊D5—24no—
483C22⋊D5—38no—
484C22⋊D5—68no—
485C22⋊D5—68no—
486C22⋊D5—68no—
487C22⋊D5—68no—
488C22⋊D5—64no—
489C2×Dic5—21no—
490C2×Dic5—32no—
491C2×Dic5—68no—
492C2×Dic5—68no—
493C2×Dic5—61no—
494D20—21no—
495D20—34no—
496D20—32no—
497D20—61no—
498D20C23×D312yes—
499C4×D5—24no—
500C4×D5—34no—
501C4×D5—34no—
502C4×D5—64no—
503Dic10—21no—
504Dic10—34no—
505Dic10—32no—
506Dic10—61no—
507Dic10C23×D312yes—
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—51no—
516C2×#41—151no—
517C2×#41—152no—
518C2×#41—152no—
519C2×#41—151no—
520C2×#41—301no—
521C2×#41—301no—
522C22×D4—31no—
523C22×D4—152no—
524C22×D4—152no—
525C22×D4—301no—
526C22×D4—301no—
527C22×D4—302no—
528C22×D4—302no—
529C22×D4D3×D511yescharacteristic, complemented
530AGL(1,ℤ/8)—58no—
531AGL(1,ℤ/8)—158no—
532AGL(1,ℤ/8)—1516no—
533AGL(1,ℤ/8)—1516no—
534#135—158no—
535#135—1516no—
536C2×Q16—151no—
537C2×SD16—52no—
538C2×SD16—151no—
539C2×SD16—151no—
540C2×SD16—152no—
541C2×D8—32no—
542C2×D8—32no—
543C2×D8—38no—
544C2×D8—52no—
545C2×D8—151no—
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—44no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—24no—
558D15—42no—
559C3×D5—42no—
560C5×D3—44no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—82no—
564C23×C3—101no—
565C23×C3D4×D511yescharacteristic
566C22×D3—22no—
567C22×D3—24no—
568C22×D3—52no—
569C22×D3—82no—
570C22×D3—108no—
571C22×D3—108no—
572C22×D3—101no—
573C22×D3—404no—
574C22×D3—404no—
575C3×Q8—52no—
576C3×Q8—101no—
577C3×D4—22no—
578C3×D4—24no—
579C3×D4—52no—
580C3×D4—104no—
581C3×D4—101no—
582C3×D4C23×D514yes—
583C2×C3×C4—101no—
584C2×C3×C4—104no—
585C2×C3×C4D4×D511yescharacteristic
586C2×C3×C4D4×D512yes—
587C2×C3×C4C23×D511yescharacteristic
588C2×C3×C4C23×D512yes—
589#67—58no—
590#67—108no—
591#67—108no—
592#67—108no—
593#67—104no—
594C2×Dic3—52no—
595C2×Dic3—108no—
596C2×Dic3—101no—
597D12—24no—
598D12—22no—
599D12—54no—
600D12—52no—
601D12—108no—
602D12—101no—
603D12C23×D514yes—
604C4×D3—54no—
605C4×D3—54no—
606C4×D3—108no—
607C4×D3—104no—
608Dic6—54no—
609Dic6—52no—
610Dic6—101no—
611C3×C8—54no—
612C3⋊C8C23×D512yes—
613C3⋊C8C23×D512yes—
614C22×C5—22no—
615C22×C5—24no—
616C22×C5—44no—
617C22×C5—64no—
618C22×C5—84no—
619C22×C5—124no—
620C22×C5—244no—
621C22×C5C2×D3×D412yes—
622C22×C5C2×D3×D411yescharacteristic
623C2×D5—22no—
624C2×D5—34no—
625C2×D5—42no—
626C2×D5—64no—
627C2×D5—62no—
628C2×D5—122no—
629C2×D5—248no—
630C2×D5—248no—
631C4×C5C2×D3×D411yescharacteristic
632C4×C5C2×D3×D412yes—
633C4×C5C24×D311yescharacteristic
634Dic5—22no—
635Dic5—34no—
636Dic5—62no—
637C24—21no—
638C24—61no—
639C24—302no—
640C24—302no—
641#41—54no—
642#41—102no—
643#41—154no—
644#41—154no—
645#41—158no—
646#41—158no—
647#41—154no—
648#41—308no—
649#41—304no—
650#41—304no—
651#41—308no—
652#41—302no—
653C2×Q8—51no—
654C2×Q8—151no—
655C2×Q8—151no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—32no—
659C2×D4—34no—
660C2×D4—51no—
661C2×D4—61no—
662C2×D4—62no—
663C2×D4—101no—
664C2×D4—158no—
665C2×D4—152no—
666C2×D4—158no—
667C2×D4—151no—
668C2×D4—151no—
669C2×D4—308no—
670C2×D4—302no—
671C2×D4—304no—
672C2×D4—304no—
673C2×D4—302no—
674C2×D4—302no—
675C2×D4—308no—
676C2×D4—3016no—
677C2×D4—3016no—
678C2×D4—302no—
679C2×D4—301no—
680C2×D4C2×D3×D512yes—
681C2×D4C2×D3×D514yescomplemented
682C22×C4—101no—
683C22×C4—152no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—301no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—58no—
690SD16—154no—
691SD16—154no—
692SD16—158no—
693D8—38no—
694D8—38no—
695D8—58no—
696D8—154no—
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—24no—
708C22×C3—44no—
709C22×C3—84no—
710C22×C3—102no—
711C22×C3—202no—
712C22×C3C2×D4×D512yes—
713C22×C3C2×D4×D511yescharacteristic
714C2×D3—24no—
715C2×D3—44no—
716C2×D3—54no—
717C2×D3—84no—
718C2×D3—104no—
719C2×D3—102no—
720C2×D3—202no—
721C2×D3—408no—
722C2×D3—408no—
723C3×C4—102no—
724C3×C4C2×D4×D512yes—
725C3×C4C2×D4×D511yescharacteristic
726C3×C4C24×D511yescharacteristic
727Dic3—54no—
728Dic3—102no—
729C2×C5—22no—
730C2×C5—44no—
731C2×C5—124no—
732C2×C5#577412yescomplemented
733C2×C5C22×D3×D411yescharacteristic
734D5—42no—
735D5—64no—
736D5—122no—
737C23—22no—
738C23—24no—
739C23—62no—
740C23—64no—
741C23—82no—
742C23—101no—
743C23—152no—
744C23—242no—
745C23—308no—
746C23—308no—
747C23—301no—
748C23—1204no—
749C23—1204no—
750C23#679011yescharacteristic
751Q8—52no—
752Q8—101no—
753Q8—154no—
754Q8—152no—
755Q8—301no—
756D4—22no—
757D4—24no—
758D4—34no—
759D4—52no—
760D4—64no—
761D4—62no—
762D4—104no—
763D4—101no—
764D4—158no—
765D4—154no—
766D4—152no—
767D4—308no—
768D4—308no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—301no—
773D4C22×D3×D514yes—
774C2×C4—101no—
775C2×C4—104no—
776C2×C4—152no—
777C2×C4—154no—
778C2×C4—154no—
779C2×C4—308no—
780C2×C4—308no—
781C2×C4—301no—
782C2×C4—304no—
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—44no—
792C2×C3—202no—
793C2×C3#6609112yescomplemented
794C2×C3C22×D4×D511yescharacteristic
795D3—44no—
796D3—104no—
797D3—202no—
798C5C2×#577411yescharacteristic, complemented, Sylow
799C22—22no—
800C22—24no—
801C22—44no—
802C22—64no—
803C22—84no—
804C22—102no—
805C22—124no—
806C22—154no—
807C22—202no—
808C22—244no—
809C22—304no—
810C22—302no—
811C22—602no—
812C22—1208no—
813C22—1208no—
814C22C2×#679012yes—
815C22C2×#679011yescharacteristic
816C4—102no—
817C4—154no—
818C4—302no—
819C4C2×#679012yes—
820C4C2×#679011yescharacteristic
821C4C23×D3×D511yescharacteristic
822C3C2×#6609111yescharacteristic, complemented, Sylow
823C2—22no—
824C2—44no—
825C2—124no—
826C2—202no—
827C2—304no—
828C2—602no—
829C2#1175470412yesdirect product factor
830C2C22×#679011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#92095C2semidirect
2. C2×#92018C2semidirect
3. C22×C5×#213C2semidirect
4. C2×C3×#4078C2semidirect
5. C2×#91500C2semidirect
6. C2×#91499C2semidirect
7. #11754704C2direct (N × H)
8. C2×#91482C2semidirect
9. C2×#91481C2semidirect
10. C2×#91311C2semidirect
11. C2×#91304C2semidirect
12. C2×#91291C2semidirect
14. C22×C3×C5×D4C22semidirect
17. #92095C22semidirect
19. C2×#6819C22semidirect
21. C2×D4×D15C22semidirect
23. C2×#6817C22semidirect
24. C22×C5×D12C22semidirect
25. C2×C3×#709C22semidirect
28. #92018C22semidirect
29. C2×#6777C22semidirect
32. C2×#6768C22semidirect
33. C2×C5×#213C22semidirect
34. C2×C5×#213C22semidirect
35. C2×C5×#213C22semidirect
36. C22×C5×C3⋊C8C22semidirect
37. C2×C3×#687C22semidirect
38. C3×#4078C22semidirect
39. C2×C3×#686C22semidirect
40. C2×C3×#681C22semidirect
41. #91500C22semidirect
42. #91499C22semidirect
43. #91482C22semidirect
44. #91481C22semidirect
45. C2×#6662C22semidirect
46. C2×#6659C22semidirect
47. C2×#6658C22semidirect
48. #91311C22semidirect
49. C2×#6657C22semidirect
50. #91304C22semidirect
51. C2×#6654C22semidirect
52. C2×#6653C22semidirect
53. C2×#6651C22semidirect
54. #91291C22semidirect
55. C2×#6648C22semidirect
61. C2×#4078D3semidirect
76. C2×C3×C5×D4C23semidirect
86. #6819C23semidirect
89. D4×D15C23semidirect
93. #6817C23semidirect
103. C2×C5×D12C23semidirect
106. C3×#709C23semidirect
115. #6777C23semidirect
119. #6768C23semidirect
120. C5×#213C23semidirect
121. C5×#213C23semidirect
124. C2×C5×C3⋊C8C23semidirect
125. C3×#687C23semidirect
126. C3×#686C23semidirect
127. C3×#681C23semidirect
129. #6662C23semidirect
130. #6659C23semidirect
131. #6658C23semidirect
132. #6657C23semidirect
133. #6654C23semidirect
134. #6653C23semidirect
135. #6651C23semidirect
136. #6648C23semidirect
141. C22×#213D5semidirect
150. C22×C5×D4C2×D3semidirect
167. C2×#709C2×D3semidirect
173. C2×#687C2×D3semidirect
175. #4078C2×D3semidirect
177. C2×#686C2×D3semidirect
178. C2×#681C2×D3semidirect
246. C22×C3×D4C2×D5semidirect
263. C22×D12C2×D5semidirect
273. C2×#213C2×D5semidirect
274. C2×#213C2×D5semidirect
275. C2×#213C2×D5semidirect
276. C22×C3⋊C8C2×D5semidirect
298. C2×C5×D4C22×D3semidirect
328. #709C22×D3semidirect
344. #687C22×D3semidirect
346. #686C22×D3semidirect
347. #681C22×D3semidirect
402. C2×C3×D4C22×D5semidirect
435. C2×D12C22×D5semidirect
449. #213C22×D5semidirect
450. #213C22×D5semidirect
453. C2×C3⋊C8C22×D5semidirect
529. C22×D4D3×D5semidirect
555. C2×C3×C5#576semidirect
681. C2×D4C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
732. C2×C5#5774semidirect
793. C2×C3#66091semidirect
798. C5C2×#5774semidirect
822. C3C2×#66091semidirect
829. C2#11754704direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920952
C2×#920182
C22×C5×#2132
C2×C3×#40782
C2×#915002
C2×#914992
#117547042
C2×#914822
C2×#914812
C2×#913112
C2×#913042
C2×#912912
C2×#660913
C2×#57745