Finite Group Databasebeta

← C2×#11754703 #14509994

Subgroups — C2×#11754703 #14509994

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×#92017C211yesmaximal, characteristic, complemented
3C2×C5×#932C211yesmaximal, characteristic, complemented
4C22×C3×#686C211yesmaximal, characteristic, complemented
5C2×#91498C212yesmaximal, complemented
6C2×#91497C212yesmaximal, complemented
7#11754703C2116yesmaximal, direct product factor
8C2×#91482C212yesmaximal, complemented
9C2×#91481C212yesmaximal, complemented
10C2×#91312C211yesmaximal, characteristic, complemented
11C2×#91303C211yesmaximal, characteristic, complemented
12C2×#91290C211yesmaximal, characteristic, complemented
13C2×#66108—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
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—
33C2×C5×#214C2212yescomplemented
34C5×#932C2218yescomplemented
35C2×C5×#213C2212yescomplemented
36C2×C5×#208C2211yescharacteristic, complemented
37C2×C3×#686C2212yescomplemented
38C2×C3×#686C2212yescomplemented
39C2×C3×#686C2218yescomplemented
40C22×C3×#168C2211yescharacteristic, complemented
41#91498C22116yescomplemented
42#91497C22116yescomplemented
43#91482C22116yescomplemented
44#91481C22116yescomplemented
45C2×#6663C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48#91312C2218yescomplemented
49C2×#6657C2212yescomplemented
50#91303C2218yescomplemented
51C2×#6654C2211yescharacteristic, complemented
52C2×#6653C2212yescomplemented
53C2×#6651C2212yescomplemented
54#91290C2218yescomplemented
55C2×#6648C2212yescomplemented
56C2×#5757—51nomaximal, Hall
57C2×#4149—31no—
58C2×#4144—31no—
59C2×C5×AGL(1,ℤ/8)—31no—
60C2×#4096—31no—
61C22×#686D311yescharacteristic, complemented
62#66108—316no—
63C2×#4062—32no—
64C2×#4060—32no—
65C2×#4057—32no—
66C2×D5×D8—32no—
67C2×#4054—31no—
68C2×#4053—31no—
69C24×C3×C5—21no—
70C23×D15—22no—
71C23×C3×D5—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×#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×#214C2318yescomplemented
121C5×#213C2318yescomplemented
122C5×#208C2314yescomplemented
123C2×C5×C3⋊C8C2312yes—
124C3×#686C2318yescomplemented
125C3×#686C2318yescomplemented
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2314yescomplemented
129#6663C2314yescomplemented
130#6660C2314yescomplemented
131#6659C2314yescomplemented
132#6657C2318yescomplemented
133#6654C2314yescomplemented
134#6653C2318yescomplemented
135#6651C2318yescomplemented
136#6648C2318yescomplemented
137C2×#1004—51no—
138C2×#1004—51no—
139C22×C3×D8—51no—
140C2×#932—51no—
141C2×#932D511yescharacteristic, complemented
142#5757—516no—
143C2×#912—52no—
144C2×#911—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#904—51no—
148C2×#901—51no—
149C2×C5×#41—31no—
150C22×C5×D4C2×D311yescharacteristic, complemented
151C22×C22⋊D5—62no—
152#4149—38no—
153#4149—64no—
154C2×#713—32no—
155#4144—38no—
156#4144—64no—
157C2×#711—32no—
158C2×#711—61no—
159C2×D4×D5—32no—
160C2×D4×D5—32no—
161C2×D4×D5—61no—
162C2×D4×D5—62no—
163C2×#709—31no—
164C2×#709—31no—
165C2×#709—61no—
166C22×D20—61no—
167C22×D20C2×D311yescharacteristic, complemented
168C5×AGL(1,ℤ/8)—38no—
169C2×C5×SD16—32no—
170C2×C5×D8—32no—
171C2×C5×M16—31no—
172#4096—38no—
173C2×#689—31no—
174C2×#688—31no—
175C2×#687—31no—
176C2×#686—31no—
177C2×#686C2×D312yescomplemented
178C2×#686C2×D312yescomplemented
179C2×#686C2×D318yescomplemented
180C22×#168C2×D311yescharacteristic, complemented
181#4062—316no—
182#4060—316no—
183#4057—316no—
184D5×D8—316no—
185#4054—38no—
186#4053—38no—
187C2×D40—32no—
188C2×#677—32no—
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—21no—
201C22×C3×D5—22no—
202C22×C3×D5—24no—
203C22×C3×D5—82no—
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×#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×#168C2412yes—
243C3×#168C2412yes—
244C5×C3⋊C8C2414yes—
245C22×C3×D4—51no—
246C22×C3×D4C2×D511yescharacteristic, complemented
247C22×#67—102no—
248C22×#67—102no—
249#1004—58no—
250#1004—58no—
251#1004—104no—
252#1004—104no—
253C2×#237—52no—
254C2×#237—52no—
255C2×#237—101no—
256C2×#237—101no—
257C2×D3×D4—52no—
258C2×D3×D4—52no—
259C2×D3×D4—101no—
260C2×D3×D4—101no—
261C2×#235—51no—
262C2×#235—51no—
263C2×#235C2×D511yescharacteristic, complemented
264C2×C3×D8—52no—
265C2×C3×D8—52no—
266C2×C3×D8—58no—
267C22×C3×C8—51no—
268C2×#214—52no—
269C2×#214C2×D512yescomplemented
270#932—58no—
271#932C2×D518yescomplemented
272C2×#213—52no—
273C2×#213C2×D512yescomplemented
274C2×#208C2×D511yescharacteristic, complemented
275#912—516no—
276#911—516no—
277#911—516no—
278D3×D8—516no—
279C2×Dic12—51no—
280#904—58no—
281C2×D24—51no—
282C2×#204—51no—
283C2×#204—51no—
284#901—58no—
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C24×C5—21no—
288C23×D5—21no—
289C23×D5—62no—
290C23×D5—62no—
291C5×#41—34no—
292C5×#41—62no—
293C2×C5×Q8—31no—
294C2×C5×D4—21no—
295C2×C5×D4—22no—
296C2×C5×D4—31no—
297C2×C5×D4—61no—
298C2×C5×D4C22×D312yes—
299C2×C5×D4C22×D314yescomplemented
300C22×C4×C5—61no—
301C22×C4×C5C22×D311yescharacteristic
302C2×C22⋊D5—32no—
303C2×C22⋊D5—62no—
304C2×C22⋊D5—62no—
305C2×C22⋊D5—616no—
306C2×C22⋊D5—62no—
307C2×C22⋊D5—61no—
308C22×Dic5—62no—
309#713—38no—
310#713—64no—
311#711—38no—
312#711—68no—
313#711—64no—
314D4×D5—38no—
315D4×D5—38no—
316D4×D5—64no—
317D4×D5—64no—
318D4×D5—68no—
319D4×D5—616no—
320#709—34no—
321#709—34no—
322#709—34no—
323#709—68no—
324#709—62no—
325C2×D20—21no—
326C2×D20—22no—
327C2×D20—31no—
328C2×D20—31no—
329C2×D20—68no—
330C2×D20—62no—
331C2×D20C22×D312yes—
332C2×D20C22×D314yescomplemented
333C2×C4×D5—32no—
334C2×C4×D5—62no—
335C2×C4×D5—61no—
336C2×Dic10—31no—
337C2×Dic10—31no—
338C5×SD16—38no—
339C5×D8—38no—
340C5×M16—34no—
341C2×C5×C8—32no—
342#689—34no—
343#688—34no—
344#687—34no—
345#686—34no—
346#686C22×D318yescomplemented
347#686C22×D318yescomplemented
348C2×#168C22×D311yescharacteristic
349C2×#168C22×D311yescharacteristic
350C2×#168C22×D314yescomplemented
351D40—38no—
352#677—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)—31no—
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—51no—
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—22no—
379C2×C5×D3—42no—
380C2×C3×D5—24no—
381C2×C3×D5—44no—
382C2×C3×D5—84no—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387Dic15—22no—
388Dic15C22×D414yes—
389C5×Dic3—22no—
390C24×C3—21no—
391C24×C3—101no—
392C23×D3—102no—
393C23×D3—102no—
394C2×C3×D4—21no—
395C2×C3×D4—22no—
396C2×C3×D4—52no—
397C2×C3×D4—54no—
398C2×C3×D4—101no—
399C2×C3×D4—102no—
400C2×C3×D4C22×D512yes—
401C2×C3×D4C22×D514yescomplemented
402C22×C3×C4C22×D511yescharacteristic
403C2×#67—21no—
404C2×#67—52no—
405C2×#67—102no—
406C2×#67—102no—
407C2×#67—102no—
408C2×#67—1016no—
409C2×#67—1016no—
410C2×#67—102no—
411C2×#67—101no—
412C22×Dic3—102no—
413C22×Dic3—102no—
414#237—58no—
415#237—58no—
416#237—104no—
417#237—108no—
418#237—108no—
419#237—104no—
420D3×D4—58no—
421D3×D4—58no—
422D3×D4—108no—
423D3×D4—104no—
424D3×D4—104no—
425D3×D4—108no—
426#235—22no—
427#235—54no—
428#235—54no—
429#235—54no—
430#235—102no—
431#235C22×D514yescomplemented
432C2×D12—51no—
433C2×D12—51no—
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—52no—
437C2×C4×D3—101no—
438C2×Dic6—51no—
439C2×Dic6—51no—
440C2×Dic6C22×D511yescharacteristic
441C3×D8—58no—
442C3×D8—58no—
443C2×C3×C8—51no—
444C2×C3×C8—51no—
445C2×C3×C8—54no—
446#214—58no—
447#214C22×D518yescomplemented
448#213—58no—
449#213C22×D518yescomplemented
450#208C22×D514yescomplemented
451C2×C3⋊C8C22×D512yes—
452Dic12—54no—
453D24—54no—
454#204—54no—
455#204—54no—
456ΓL(1,𝔽25)—58no—
457D3×C8—58no—
458C23×C5—22no—
459C23×C5—24no—
460C23×C5—61no—
461C23×C5—82no—
462C23×C5D3×D411yescharacteristic
463C22×D5—22no—
464C22×D5—24no—
465C22×D5—32no—
466C22×D5—68no—
467C22×D5—68no—
468C22×D5—61no—
469C22×D5—82no—
470C22×D5—244no—
471C22×D5—244no—
472C5×Q8—32no—
473C5×Q8—61no—
474C5×D4—22no—
475C5×D4—24no—
476C5×D4—32no—
477C5×D4—64no—
478C5×D4—61no—
479C5×D4C23×D314yes—
480C2×C4×C5—61no—
481C2×C4×C5—64no—
482C2×C4×C5D3×D411yescharacteristic
483C2×C4×C5D3×D412yes—
484C2×C4×C5C23×D311yescharacteristic
485C2×C4×C5C23×D312yes—
486C22⋊D5—38no—
487C22⋊D5—68no—
488C22⋊D5—68no—
489C22⋊D5—68no—
490C22⋊D5—64no—
491C2×Dic5—32no—
492C2×Dic5—68no—
493C2×Dic5—61no—
494D20—24no—
495D20—22no—
496D20—34no—
497D20—32no—
498D20—68no—
499D20—61no—
500D20C23×D314yes—
501C4×D5—34no—
502C4×D5—34no—
503C4×D5—68no—
504C4×D5—64no—
505Dic10—34no—
506Dic10—32no—
507Dic10—61no—
508C5×C8—34no—
509#168C23×D312yes—
510#168C23×D312yes—
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—151no—
520C2×#41—301no—
521C2×#41—301no—
522C22×D4—51no—
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)—38no—
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—32no—
538C2×SD16—152no—
539C2×SD16—151no—
540C2×SD16—151no—
541C2×D8—32no—
542C2×D8—52no—
543C2×D8—52no—
544C2×D8—58no—
545C2×D8—152no—
546C2×D8—151no—
547C2×D8—1516no—
548#131—158no—
549C2×M16—31no—
550C2×M16—152no—
551C22×C8—51no—
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—44no—
560C5×D3—42no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—82no—
564C23×C3—102no—
565C23×C3—104no—
566C23×C3—402no—
567C23×C3D4×D511yescharacteristic
568C22×D3—21no—
569C22×D3—52no—
570C22×D3—108no—
571C22×D3—108no—
572C22×D3—101no—
573C22×D3—404no—
574C22×D3—404no—
575C3×D4—22no—
576C3×D4—24no—
577C3×D4—54no—
578C3×D4—102no—
579C3×D4—104no—
580C3×D4C23×D514yes—
581C2×C3×C4D4×D511yescharacteristic
582C2×C3×C4D4×D512yes—
583C2×C3×C4C23×D511yescharacteristic
584C2×C3×C4C23×D512yes—
585#67—24no—
586#67—58no—
587#67—108no—
588#67—108no—
589#67—108no—
590#67—108no—
591#67—104no—
592C2×Dic3—21no—
593C2×Dic3—52no—
594C2×Dic3—108no—
595C2×Dic3—108no—
596C2×Dic3—101no—
597D12—21no—
598D12—54no—
599D12—52no—
600D12—101no—
601D12C23×D512yes—
602C4×D3—24no—
603C4×D3—54no—
604C4×D3—54no—
605C4×D3—104no—
606Dic6—21no—
607Dic6—54no—
608Dic6—52no—
609Dic6—101no—
610Dic6C23×D512yes—
611C3×C8—52no—
612C3×C8—52no—
613C3⋊C8C23×D514yes—
614C22×C5—22no—
615C22×C5—24no—
616C22×C5—44no—
617C22×C5—62no—
618C22×C5—84no—
619C22×C5—122no—
620C22×C5C2×D3×D412yes—
621C22×C5C2×D3×D411yescharacteristic
622C2×D5—24no—
623C2×D5—34no—
624C2×D5—44no—
625C2×D5—64no—
626C2×D5—62no—
627C2×D5—84no—
628C2×D5—122no—
629C2×D5—248no—
630C2×D5—248no—
631C4×C5—62no—
632C4×C5C2×D3×D412yes—
633C4×C5C2×D3×D411yescharacteristic
634C4×C5C24×D311yescharacteristic
635Dic5—34no—
636Dic5—62no—
637C24—21no—
638C24—101no—
639C24—302no—
640C24—302no—
641#41—34no—
642#41—62no—
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—31no—
654C2×Q8—151no—
655C2×Q8—151no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—31no—
659C2×D4—52no—
660C2×D4—54no—
661C2×D4—61no—
662C2×D4—101no—
663C2×D4—102no—
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—61no—
683C22×C4—152no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—301no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—38no—
690SD16—158no—
691SD16—154no—
692SD16—154no—
693D8—38no—
694D8—58no—
695D8—58no—
696D8—158no—
697D8—154no—
698M16—34no—
699M16—158no—
700C2×C8—32no—
701C2×C8—51no—
702C2×C8—51no—
703C2×C8—54no—
704C2×C8—158no—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—44no—
709C22×C3—84no—
710C22×C3—104no—
711C22×C3—204no—
712C22×C3—404no—
713C22×C3C2×D4×D512yes—
714C22×C3C2×D4×D511yescharacteristic
715C2×D3—22no—
716C2×D3—42no—
717C2×D3—54no—
718C2×D3—104no—
719C2×D3—102no—
720C2×D3—202no—
721C2×D3—408no—
722C2×D3—408no—
723C3×C4C2×D4×D511yescharacteristic
724C3×C4C2×D4×D512yes—
725C3×C4C24×D511yescharacteristic
726Dic3—22no—
727Dic3—54no—
728Dic3—102no—
729C2×C5—22no—
730C2×C5—44no—
731C2×C5—122no—
732C2×C5#575712yescomplemented
733C2×C5C22×D3×D411yescharacteristic
734D5—44no—
735D5—64no—
736D5—122no—
737C23—22no—
738C23—24no—
739C23—61no—
740C23—82no—
741C23—102no—
742C23—104no—
743C23—152no—
744C23—308no—
745C23—308no—
746C23—301no—
747C23—402no—
748C23—1204no—
749C23—1204no—
750C23#679011yescharacteristic
751Q8—32no—
752Q8—61no—
753Q8—154no—
754Q8—152no—
755Q8—301no—
756D4—22no—
757D4—24no—
758D4—32no—
759D4—54no—
760D4—64no—
761D4—61no—
762D4—104no—
763D4—102no—
764D4—158no—
765D4—154no—
766D4—152no—
767D4—308no—
768D4—308no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—301no—
773D4C22×D3×D514yes—
774C2×C4—61no—
775C2×C4—64no—
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—34no—
788C8—52no—
789C8—52no—
790C2×C3—22no—
791C2×C3—44no—
792C2×C3—204no—
793C2×C3#6610812yescomplemented
794C2×C3C22×D4×D511yescharacteristic
795D3—42no—
796D3—104no—
797D3—202no—
798C5C2×#575711yescharacteristic, complemented, Sylow
799C22—22no—
800C22—24no—
801C22—44no—
802C22—62no—
803C22—84no—
804C22—104no—
805C22—122no—
806C22—154no—
807C22—204no—
808C22—304no—
809C22—302no—
810C22—404no—
811C22—602no—
812C22—1208no—
813C22—1208no—
814C22C2×#679012yes—
815C22C2×#679011yescharacteristic
816C4—62no—
817C4—154no—
818C4—302no—
819C4C2×#679012yes—
820C4C2×#679011yescharacteristic
821C4C23×D3×D511yescharacteristic
822C3C2×#6610811yescharacteristic, complemented, Sylow
823C2—22no—
824C2—44no—
825C2—122no—
826C2—204no—
827C2—304no—
828C2—602no—
829C2#1175470312yesdirect 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×#92017C2semidirect
3. C2×C5×#932C2semidirect
4. C22×C3×#686C2semidirect
5. C2×#91498C2semidirect
6. C2×#91497C2semidirect
7. #11754703C2direct (N × H)
8. C2×#91482C2semidirect
9. C2×#91481C2semidirect
10. C2×#91312C2semidirect
11. C2×#91303C2semidirect
12. C2×#91290C2semidirect
14. C22×C3×C5×D4C22semidirect
17. #92095C22semidirect
19. C2×#6819C22semidirect
21. C2×D4×D15C22semidirect
23. C2×#6817C22semidirect
24. C2×C5×#235C22semidirect
25. C22×C3×D20C22semidirect
28. #92017C22semidirect
29. C2×#6777C22semidirect
31. C2×#6766C22semidirect
33. C2×C5×#214C22semidirect
34. C5×#932C22semidirect
35. C2×C5×#213C22semidirect
36. C2×C5×#208C22semidirect
37. C2×C3×#686C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
40. C22×C3×#168C22semidirect
41. #91498C22semidirect
42. #91497C22semidirect
43. #91482C22semidirect
44. #91481C22semidirect
45. C2×#6663C22semidirect
46. C2×#6660C22semidirect
47. C2×#6659C22semidirect
48. #91312C22semidirect
49. C2×#6657C22semidirect
50. #91303C22semidirect
51. C2×#6654C22semidirect
52. C2×#6653C22semidirect
53. C2×#6651C22semidirect
54. #91290C22semidirect
55. C2×#6648C22semidirect
61. C22×#686D3semidirect
76. C2×C3×C5×D4C23semidirect
86. #6819C23semidirect
89. D4×D15C23semidirect
93. #6817C23semidirect
102. C5×#235C23semidirect
109. C2×C3×D20C23semidirect
115. #6777C23semidirect
118. #6766C23semidirect
120. C5×#214C23semidirect
121. C5×#213C23semidirect
122. C5×#208C23semidirect
124. C3×#686C23semidirect
125. C3×#686C23semidirect
128. C2×C3×#168C23semidirect
129. #6663C23semidirect
130. #6660C23semidirect
131. #6659C23semidirect
132. #6657C23semidirect
133. #6654C23semidirect
134. #6653C23semidirect
135. #6651C23semidirect
136. #6648C23semidirect
141. C2×#932D5semidirect
150. C22×C5×D4C2×D3semidirect
167. C22×D20C2×D3semidirect
177. C2×#686C2×D3semidirect
178. C2×#686C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C22×#168C2×D3semidirect
246. C22×C3×D4C2×D5semidirect
263. C2×#235C2×D5semidirect
269. C2×#214C2×D5semidirect
271. #932C2×D5semidirect
273. C2×#213C2×D5semidirect
274. C2×#208C2×D5semidirect
299. C2×C5×D4C22×D3semidirect
332. C2×D20C22×D3semidirect
346. #686C22×D3semidirect
347. #686C22×D3semidirect
350. C2×#168C22×D3semidirect
401. C2×C3×D4C22×D5semidirect
431. #235C22×D5semidirect
447. #214C22×D5semidirect
449. #213C22×D5semidirect
450. #208C22×D5semidirect
529. C22×D4D3×D5semidirect
555. C2×C3×C5#576semidirect
681. C2×D4C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
732. C2×C5#5757semidirect
793. C2×C3#66108semidirect
798. C5C2×#5757semidirect
822. C3C2×#66108semidirect
829. C2#11754703direct (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×#920172
C2×C5×#9322
C22×C3×#6862
C2×#914982
C2×#914972
#117547032
C2×#914822
C2×#914812
C2×#913122
C2×#913032
C2×#912902
C2×#661083
C2×#57575