Finite Group Databasebeta

← C2×#11756521 #14510020

Subgroups — C2×#11756521 #14510020

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92098C211yesmaximal, characteristic, complemented
2C2×#92095C211yesmaximal, characteristic, complemented
3C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
4C2×#91831C211yesmaximal, characteristic, complemented
5C2×#91821C211yesmaximal, characteristic, complemented
6#11756521C2116yesmaximal, direct product factor
7C2×#91805C212yesmaximal, complemented
8C2×#91804C212yesmaximal, complemented
9C2×#91803C212yesmaximal, complemented
10C2×SD16×D15C212yesmaximal, complemented
11C2×#91793C211yesmaximal, characteristic, complemented
12C2×#91790C211yesmaximal, characteristic, complemented
13C2×#66096—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic, complemented
15C22×C3×C5×D4C2211yescharacteristic
16C22×#1220—22no—
17#92098—24no—
18#92098C2218yescomplemented
19C2×#6821—21no—
20C2×#6821C2212yescomplemented
21C2×Q8×D15—21no—
22C2×Q8×D15C2212yescomplemented
23#92095—24no—
24#92095C2218yescomplemented
25C2×#6819—21no—
26C2×#6819C2212yes—
27C2×D4×D15—21no—
28C2×D4×D15C2212yes—
29C2×#6817—22no—
30C2×#6817C2211yescharacteristic
31C2×#6817C2211yescharacteristic
32C2×#6817C2211yescharacteristic, complemented
33C2×C3×C5×SD16C2212yescomplemented
34C2×C3×C5×SD16C2212yescomplemented
35C2×C3×C5×SD16C2218yescomplemented
36C22×C3×C5×C8C2211yescharacteristic, complemented
37C2×#6718C2212yescomplemented
38#91831C2218yescomplemented
39C2×#6717C2212yescomplemented
40C2×#6716C2212yescomplemented
41#91821C2218yescomplemented
42C2×#6715C2212yescomplemented
43C2×#6710C2211yescharacteristic, complemented
44#91805C22116yescomplemented
45#91804C22116yescomplemented
46#91803C22116yescomplemented
47SD16×D15C22116yescomplemented
48C2×Dic60C2211yescharacteristic, complemented
49#91793C2218yescomplemented
50C2×D120C2211yescharacteristic, complemented
51C2×#6706C2211yescharacteristic, complemented
52C2×#6706C2211yescharacteristic, complemented
53#91790C2218yescomplemented
54C2×#6705C2212yescomplemented
55C2×C8×D15C2212yescomplemented
56C2×#5762—51nomaximal, Hall
57C2×#4147—31no—
58C2×#4144—31no—
59C22×C5×SD16D311yescharacteristic, complemented
60C2×#4088—31no—
61C2×#4078—31no—
62#66096—316no—
63C2×#4062—32no—
64C2×#4061—32no—
65C2×#4060—32no—
66C2×D5×SD16—32no—
67C2×#4050—31no—
68C2×#4047—31no—
69C24×C3×C5—21no—
70C23×D15—22no—
71C2×C3×C5×Q8—21no—
72C2×C3×C5×Q8—22no—
73C2×C3×C5×Q8C2312yes—
74C2×C3×C5×Q8C2314yescomplemented
75C2×C3×C5×D4—21no—
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4C2312yes—
78C2×C3×C5×D4C2314yes—
79C22×C3×C4×C5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—21no—
83C2×#1220—22no—
84C2×#1220—216no—
85C2×#1220—22no—
86C2×#1220D412yes—
87C22×Dic15—22no—
88#6821—28no—
89#6821—24no—
90#6821C2318yescomplemented
91Q8×D15—24no—
92Q8×D15—28no—
93Q8×D15C2318yescomplemented
94#6819—24no—
95#6819—28no—
96#6819C2318yes—
97D4×D15—28no—
98D4×D15—24no—
99D4×D15C2318yes—
100#6817—22no—
101#6817—22no—
102#6817—216no—
103#6817D414yes—
104#6817C2314yes—
105#6817C2314yes—
106#6817C2314yescomplemented
107C2×D60—22no—
108C2×D60D411yescharacteristic
109C2×D60C2311yescharacteristic
110C2×D60C2311yescharacteristic
111C2×C4×D15—22no—
112C2×C4×D15—21no—
113C2×C4×D15—21no—
114C2×C4×D15—22no—
115C2×C4×D15C2312yes—
116C2×Dic30—22no—
117C2×Dic30D411yescharacteristic
118C2×Dic30C2311yescharacteristic
119C2×Dic30C2311yescharacteristic
120C3×C5×SD16C2318yescomplemented
121C3×C5×SD16C2318yescomplemented
122C2×C3×C5×C8C2311yescharacteristic
123C2×C3×C5×C8C2311yescharacteristic
124C2×C3×C5×C8C2314yescomplemented
125#6718C2318yescomplemented
126#6717C2318yescomplemented
127#6716C2318yescomplemented
128#6715C2318yescomplemented
129#6710C2314yescomplemented
130C2×C3⋊#168C2312yes—
131Dic60C2314yescomplemented
132D120C2314yescomplemented
133#6706C2314yescomplemented
134#6706C2314yescomplemented
135#6705C2318yescomplemented
136C8×D15C2318yescomplemented
137C2×#1007—51no—
138C2×#1004—51no—
139C22×C3×SD16D511yescharacteristic, complemented
140C2×#942—51no—
141C2×#932—51no—
142#5762—516no—
143C2×#916—52no—
144C2×#915—52no—
145C2×#914—52no—
146C2×D3×SD16—52no—
147C2×#904—51no—
148C2×#901—51no—
149C22×C5×Q8C2×D311yescharacteristic, complemented
150C22×C5×D4C2×D311yescharacteristic
151C22×C22⋊D5—62no—
152#4147—38no—
153#4147—64no—
154C2×#713—32no—
155C2×#713—61no—
156C2×Q8×D5—32no—
157C2×Q8×D5—61no—
158#4144—38no—
159#4144—64no—
160C2×#711—32no—
161C2×#711—61no—
162C2×D4×D5—32no—
163C2×D4×D5—61no—
164C2×#709—31no—
165C2×#709—31no—
166C2×#709—31no—
167C2×#709—62no—
168C2×C5×SD16C2×D312yescomplemented
169C2×C5×SD16C2×D312yescomplemented
170C2×C5×SD16C2×D318yescomplemented
171C22×C5×C8C2×D311yescharacteristic, complemented
172C2×#689—32no—
173#4088—38no—
174C2×#688—32no—
175C2×#687—32no—
176#4078—38no—
177C2×#686—32no—
178C2×#681—31no—
179#4062—316no—
180#4061—316no—
181#4060—316no—
182D5×SD16—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×#577—151noSylow
192C23×C3×C5—22no—
193C23×C3×C5—24no—
194C23×C3×C5—82no—
195C23×C3×C5C2×D411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—28no—
199C22×D15—84no—
200C22×D15C2×D412yes—
201C3×C5×Q8—22no—
202C3×C5×Q8—24no—
203C3×C5×Q8C2414yes—
204C3×C5×D4—22no—
205C3×C5×D4—24no—
206C3×C5×D4C2414yes—
207C2×C3×C4×C5—22no—
208C2×C3×C4×C5—24no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5C2411yescharacteristic
212C2×C3×C4×C5C2412yes—
213#1220—24no—
214#1220—24no—
215#1220—28no—
216#1220—28no—
217#1220C2×D418yes—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—28no—
221C2×Dic15C2×D412yes—
222D60—28no—
223D60—21no—
224D60—21no—
225D60C2×D414yes—
226D60C2412yes—
227D60C2412yes—
228C4×D15—28no—
229C4×D15—24no—
230C4×D15—24no—
231C4×D15—28no—
232C4×D15C2×D414yes—
233C4×D15C2414yes—
234Dic30—21no—
235Dic30—21no—
236Dic30—28no—
237Dic30C2×D414yes—
238Dic30C2412yes—
239Dic30C2412yes—
240C3×C5×C8C2412yes—
241C3×C5×C8C2412yes—
242C3⋊#168C2414yes—
243C22×C3×Q8C2×D511yescharacteristic, complemented
244C22×C3×D4C2×D511yescharacteristic
245C22×#67—102no—
246#1007—58no—
247#1007—104no—
248C2×#239—52no—
249C2×#239—101no—
250C2×D3×Q8—52no—
251C2×D3×Q8—101no—
252#1004—58no—
253#1004—104no—
254C2×#237—52no—
255C2×#237—101no—
256C2×D3×D4—52no—
257C2×D3×D4—101no—
258C2×#235—51no—
259C2×#235—51no—
260C2×#235—51no—
261C2×#235—102no—
262C2×C3×SD16C2×D512yescomplemented
263C2×C3×SD16C2×D512yescomplemented
264C2×C3×SD16C2×D518yescomplemented
265C22×C3×C8C2×D511yescharacteristic, complemented
266C2×#216—52no—
267#942—58no—
268C2×#215—52no—
269C2×#214—52no—
270#932—58no—
271C2×#213—52no—
272C2×#208—51no—
273#916—516no—
274#915—516no—
275#914—516no—
276D3×SD16—516no—
277C2×Dic12—51no—
278#904—58no—
279C2×D24—51no—
280C2×#204—51no—
281C2×#204—51no—
282#901—58no—
283C2×ΓL(1,𝔽25)—52no—
284C2×D3×C8—52no—
285C24×C5—21no—
286C23×D5—62no—
287C2×C5×Q8—21no—
288C2×C5×Q8—22no—
289C2×C5×Q8C22×D312yes—
290C2×C5×Q8C22×D314yescomplemented
291C2×C5×D4—21no—
292C2×C5×D4—22no—
293C2×C5×D4C22×D312yes—
294C2×C5×D4C22×D314yes—
295C22×C4×C5—21no—
296C22×C4×C5C22×D311yescharacteristic
297C2×C22⋊D5—32no—
298C2×C22⋊D5—62no—
299C2×C22⋊D5—616no—
300C2×C22⋊D5—62no—
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303C22×Dic5—62no—
304#713—38no—
305#713—64no—
306#713—68no—
307Q8×D5—38no—
308Q8×D5—68no—
309Q8×D5—64no—
310#711—38no—
311#711—68no—
312#711—64no—
313D4×D5—38no—
314D4×D5—64no—
315D4×D5—68no—
316#709—34no—
317#709—34no—
318#709—34no—
319#709—34no—
320#709—616no—
321#709—62no—
322#709—62no—
323C2×D20—31no—
324C2×D20—31no—
325C2×D20—31no—
326C2×D20—62no—
327C2×C4×D5—32no—
328C2×C4×D5—62no—
329C2×C4×D5—62no—
330C2×C4×D5—61no—
331C2×C4×D5—61no—
332C2×Dic10—31no—
333C2×Dic10—31no—
334C2×Dic10—31no—
335C2×Dic10—62no—
336C5×SD16C22×D318yescomplemented
337C5×SD16C22×D318yescomplemented
338C2×C5×C8C22×D311yescharacteristic
339C2×C5×C8C22×D311yescharacteristic
340C2×C5×C8C22×D314yescomplemented
341#689—38no—
342#688—38no—
343#687—38no—
344#686—38no—
345#681—34no—
346C2×#168—32no—
347Dic20—34no—
348D40—34no—
349#677—34no—
350#677—34no—
351#676—38no—
352C8×D5—38no—
353C2×2−1+4—151no—
354C2×H(5,𝔽2)—151no—
355#577—1516no—
356C2×#137—151no—
357C2×#137—152no—
358C2×AGL(1,ℤ/8)—151no—
359C2×AGL(1,ℤ/8)—152no—
360C2×#135—152no—
361C2×#135—151no—
362C22×SD16—152no—
363C22×SD16D1511yescharacteristic, complemented
364C2×#131—151no—
365C22×C3×C5—22no—
366C22×C3×C5—24no—
367C22×C3×C5—44no—
368C22×C3×C5—84no—
369C22×C3×C5C22×D412yes—
370C22×C3×C5C22×D411yescharacteristic
371C2×D15—24no—
372C2×D15—22no—
373C2×D15—22no—
374C2×D15—42no—
375C2×D15—42no—
376C2×D15—88no—
377C2×D15C22×D414yes—
378C3×C4×C5—24no—
379C3×C4×C5C22×D411yescharacteristic
380C3×C4×C5C22×D412yes—
381C3×C4×C5C2511yescharacteristic
382Dic15—22no—
383Dic15—22no—
384Dic15C22×D414yes—
385C24×C3—21no—
386C23×D3—102no—
387C2×C3×Q8—21no—
388C2×C3×Q8—22no—
389C2×C3×Q8C22×D512yes—
390C2×C3×Q8C22×D514yescomplemented
391C2×C3×D4—21no—
392C2×C3×D4—22no—
393C2×C3×D4C22×D512yes—
394C2×C3×D4C22×D514yes—
395C22×C3×C4—21no—
396C22×C3×C4C22×D511yescharacteristic
397C2×#67—52no—
398C2×#67—102no—
399C2×#67—1016no—
400C2×#67—102no—
401C2×#67—101no—
402C2×#67—101no—
403C22×Dic3—102no—
404#239—58no—
405#239—104no—
406#239—108no—
407D3×Q8—58no—
408D3×Q8—108no—
409D3×Q8—104no—
410#237—58no—
411#237—108no—
412#237—104no—
413D3×D4—58no—
414D3×D4—104no—
415D3×D4—108no—
416#235—54no—
417#235—54no—
418#235—54no—
419#235—54no—
420#235—1016no—
421#235—102no—
422#235—102no—
423C2×D12—51no—
424C2×D12—51no—
425C2×D12—51no—
426C2×D12—102no—
427C2×C4×D3—52no—
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—101no—
431C2×C4×D3—101no—
432C2×Dic6—51no—
433C2×Dic6—51no—
434C2×Dic6—51no—
435C2×Dic6—102no—
436C3×SD16C22×D518yescomplemented
437C3×SD16C22×D518yescomplemented
438C2×C3×C8C22×D511yescharacteristic
439C2×C3×C8C22×D511yescharacteristic
440C2×C3×C8C22×D514yescomplemented
441#216—58no—
442#215—58no—
443#214—58no—
444#213—58no—
445#208—54no—
446C2×C3⋊C8—52no—
447Dic12—54no—
448D24—54no—
449#204—54no—
450#204—54no—
451ΓL(1,𝔽25)—58no—
452D3×C8—58no—
453C23×C5—22no—
454C23×C5—24no—
455C23×C5—82no—
456C23×C5D3×D411yescharacteristic
457C22×D5—32no—
458C22×D5—68no—
459C22×D5—61no—
460C22×D5—61no—
461C22×D5—244no—
462C5×Q8—22no—
463C5×Q8—24no—
464C5×Q8C23×D314yes—
465C5×D4—24no—
466C5×D4—22no—
467C5×D4C23×D314yes—
468C2×C4×C5—22no—
469C2×C4×C5—24no—
470C2×C4×C5D3×D411yescharacteristic
471C2×C4×C5D3×D412yes—
472C2×C4×C5C23×D311yescharacteristic
473C2×C4×C5C23×D312yes—
474C22⋊D5—38no—
475C22⋊D5—68no—
476C22⋊D5—68no—
477C22⋊D5—64no—
478C22⋊D5—64no—
479C2×Dic5—32no—
480C2×Dic5—68no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483D20—34no—
484D20—32no—
485D20—32no—
486D20—68no—
487D20—61no—
488D20—61no—
489C4×D5—34no—
490C4×D5—34no—
491C4×D5—68no—
492C4×D5—68no—
493C4×D5—64no—
494C4×D5—64no—
495Dic10—34no—
496Dic10—32no—
497Dic10—32no—
498Dic10—68no—
499Dic10—61no—
500Dic10—61no—
501C5×C8C23×D312yes—
502C5×C8C23×D312yes—
503#168—34no—
5042−1+4—158no—
5052−1+4—304no—
506H(5,𝔽2)—158no—
507H(5,𝔽2)—304no—
508C2×#41—151no—
509C2×#41—152no—
510C2×#41—152no—
511C2×#41—151no—
512C2×#41—151no—
513C2×#41—302no—
514C2×#41—301no—
515C2×#41—301no—
516C22×Q8—152no—
517C22×Q8—301no—
518C22×Q8C2×D1511yescharacteristic, complemented
519C22×D4—152no—
520C22×D4—301no—
521C22×D4—302no—
522C22×D4C2×D1511yescharacteristic
523#137—158no—
524#137—1516no—
525AGL(1,ℤ/8)—158no—
526AGL(1,ℤ/8)—1516no—
527#135—1516no—
528#135—158no—
529C2×Q16—152no—
530C2×Q16—151no—
531C2×SD16—152no—
532C2×SD16—152no—
533C2×SD16—1516no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16C2×D1512yescomplemented
537C2×SD16C2×D1512yescomplemented
538C2×SD16C2×D1518yescomplemented
539C2×D8—152no—
540C2×D8—151no—
541#131—158no—
542C2×M16—151no—
543C2×M16—152no—
544C22×C8—152no—
545C22×C8C2×D1511yescharacteristic, complemented
546C2×C3×C5—22no—
547C2×C3×C5—44no—
548C2×C3×C5#57712yescomplemented
549C2×C3×C5C23×D411yescharacteristic
550D15—24no—
551D15—42no—
552D15—42no—
553C23×C3—22no—
554C23×C3—24no—
555C23×C3—82no—
556C23×C3D4×D511yescharacteristic
557C22×D3—52no—
558C22×D3—108no—
559C22×D3—101no—
560C22×D3—101no—
561C22×D3—404no—
562C3×Q8—22no—
563C3×Q8—24no—
564C3×Q8C23×D514yes—
565C3×D4—24no—
566C3×D4—22no—
567C3×D4C23×D514yes—
568C2×C3×C4—22no—
569C2×C3×C4—24no—
570C2×C3×C4D4×D511yescharacteristic
571C2×C3×C4D4×D512yes—
572C2×C3×C4C23×D511yescharacteristic
573C2×C3×C4C23×D512yes—
574#67—58no—
575#67—108no—
576#67—108no—
577#67—104no—
578#67—104no—
579C2×Dic3—52no—
580C2×Dic3—108no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583D12—54no—
584D12—52no—
585D12—52no—
586D12—108no—
587D12—101no—
588D12—101no—
589C4×D3—54no—
590C4×D3—54no—
591C4×D3—108no—
592C4×D3—108no—
593C4×D3—104no—
594C4×D3—104no—
595Dic6—54no—
596Dic6—52no—
597Dic6—52no—
598Dic6—108no—
599Dic6—101no—
600Dic6—101no—
601C3×C8C23×D512yes—
602C3×C8C23×D512yes—
603C3⋊C8—54no—
604C22×C5—22no—
605C22×C5—24no—
606C22×C5—44no—
607C22×C5—84no—
608C22×C5C2×D3×D412yes—
609C22×C5C2×D3×D411yescharacteristic
610C2×D5—34no—
611C2×D5—64no—
612C2×D5—62no—
613C2×D5—62no—
614C2×D5—122no—
615C2×D5—122no—
616C2×D5—248no—
617C4×C5—24no—
618C4×C5C2×D3×D412yes—
619C4×C5C2×D3×D411yescharacteristic
620C4×C5C24×D311yescharacteristic
621Dic5—34no—
622Dic5—62no—
623Dic5—62no—
624C24—21no—
625C24—302no—
626#41—154no—
627#41—154no—
628#41—158no—
629#41—158no—
630#41—154no—
631#41—154no—
632#41—3016no—
633#41—304no—
634#41—304no—
635#41—308no—
636#41—308no—
637#41—302no—
638#41—302no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—151no—
642C2×Q8—158no—
643C2×Q8—151no—
644C2×Q8—151no—
645C2×Q8—302no—
646C2×Q8—304no—
647C2×Q8—308no—
648C2×Q8C22×D1512yes—
649C2×Q8C22×D1514yescomplemented
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—152no—
653C2×D4—158no—
654C2×D4—151no—
655C2×D4—151no—
656C2×D4—151no—
657C2×D4—302no—
658C2×D4—304no—
659C2×D4—302no—
660C2×D4—308no—
661C2×D4—3016no—
662C2×D4—302no—
663C2×D4—301no—
664C2×D4—301no—
665C2×D4C22×D1512yes—
666C2×D4C22×D1514yes—
667C22×C4—21no—
668C22×C4—152no—
669C22×C4—302no—
670C22×C4—302no—
671C22×C4—302no—
672C22×C4—301no—
673C22×C4—301no—
674C22×C4C22×D1511yescharacteristic
675Q16—158no—
676Q16—154no—
677SD16—158no—
678SD16—158no—
679SD16—154no—
680SD16—154no—
681SD16C22×D1518yescomplemented
682SD16C22×D1518yescomplemented
683D8—158no—
684D8—154no—
685M16—154no—
686M16—158no—
687C2×C8—152no—
688C2×C8—158no—
689C2×C8C22×D1511yescharacteristic
690C2×C8C22×D1511yescharacteristic
691C2×C8C22×D1514yescomplemented
692C3×C5C2×#57711yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—24no—
695C22×C3—44no—
696C22×C3—84no—
697C22×C3C2×D4×D512yes—
698C22×C3C2×D4×D511yescharacteristic
699C2×D3—54no—
700C2×D3—104no—
701C2×D3—102no—
702C2×D3—102no—
703C2×D3—202no—
704C2×D3—202no—
705C2×D3—408no—
706C3×C4—24no—
707C3×C4C2×D4×D512yes—
708C3×C4C2×D4×D511yescharacteristic
709C3×C4C24×D511yescharacteristic
710Dic3—54no—
711Dic3—102no—
712Dic3—102no—
713C2×C5—22no—
714C2×C5—44no—
715C2×C5#576212yescomplemented
716C2×C5C22×D3×D411yescharacteristic
717D5—64no—
718D5—122no—
719D5—122no—
720C23—22no—
721C23—24no—
722C23—82no—
723C23—152no—
724C23—308no—
725C23—301no—
726C23—301no—
727C23—1204no—
728C23D4×D1511yescharacteristic
729Q8—22no—
730Q8—24no—
731Q8—154no—
732Q8—152no—
733Q8—152no—
734Q8—308no—
735Q8—301no—
736Q8—301no—
737Q8C23×D1514yes—
738D4—22no—
739D4—24no—
740D4—158no—
741D4—154no—
742D4—152no—
743D4—152no—
744D4—308no—
745D4—308no—
746D4—308no—
747D4—304no—
748D4—304no—
749D4—301no—
750D4—301no—
751D4C23×D1514yes—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—152no—
755C2×C4—154no—
756C2×C4—154no—
757C2×C4—308no—
758C2×C4—308no—
759C2×C4—308no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—304no—
763C2×C4—304no—
764C2×C4D4×D1512yes—
765C2×C4D4×D1511yescharacteristic
766C2×C4C23×D1512yes—
767C2×C4C23×D1511yescharacteristic
768C8—154no—
769C8C23×D1512yes—
770C8C23×D1512yes—
771C2×C3—22no—
772C2×C3—44no—
773C2×C3#6609612yescomplemented
774C2×C3C22×D4×D511yescharacteristic
775D3—104no—
776D3—202no—
777D3—202no—
778C5C2×#576211yescharacteristic, complemented, Sylow
779C22—22no—
780C22—24no—
781C22—44no—
782C22—84no—
783C22—154no—
784C22—304no—
785C22—302no—
786C22—302no—
787C22—602no—
788C22—602no—
789C22—1208no—
790C22C2×D4×D1512yes—
791C22C2×D4×D1511yescharacteristic
792C4—24no—
793C4—154no—
794C4—302no—
795C4—302no—
796C4C2×D4×D1511yescharacteristic
797C4C2×D4×D1512yes—
798C4C24×D1511yescharacteristic
799C3C2×#6609611yescharacteristic, complemented, Sylow
800C2—22no—
801C2—44no—
802C2—304no—
803C2—602no—
804C2—602no—
805C2#1175652112yesdirect product factor
806C2C22×D4×D1511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC22×C3×C5×SD16C2
socleC22×C3×C5C22×D4
hypercenterC22×SD16D15
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#92098C2semidirect
2. C2×#92095C2semidirect
3. C22×C3×C5×SD16C2semidirect
4. C2×#91831C2semidirect
5. C2×#91821C2semidirect
6. #11756521C2direct (N × H)
7. C2×#91805C2semidirect
8. C2×#91804C2semidirect
9. C2×#91803C2semidirect
10. C2×SD16×D15C2semidirect
11. C2×#91793C2semidirect
12. C2×#91790C2semidirect
14. C22×C3×C5×Q8C22semidirect
18. #92098C22semidirect
20. C2×#6821C22semidirect
22. C2×Q8×D15C22semidirect
24. #92095C22semidirect
32. C2×#6817C22semidirect
33. C2×C3×C5×SD16C22semidirect
34. C2×C3×C5×SD16C22semidirect
35. C2×C3×C5×SD16C22semidirect
36. C22×C3×C5×C8C22semidirect
37. C2×#6718C22semidirect
38. #91831C22semidirect
39. C2×#6717C22semidirect
40. C2×#6716C22semidirect
41. #91821C22semidirect
42. C2×#6715C22semidirect
43. C2×#6710C22semidirect
44. #91805C22semidirect
45. #91804C22semidirect
46. #91803C22semidirect
47. SD16×D15C22semidirect
48. C2×Dic60C22semidirect
49. #91793C22semidirect
50. C2×D120C22semidirect
51. C2×#6706C22semidirect
52. C2×#6706C22semidirect
53. #91790C22semidirect
54. C2×#6705C22semidirect
55. C2×C8×D15C22semidirect
59. C22×C5×SD16D3semidirect
74. C2×C3×C5×Q8C23semidirect
90. #6821C23semidirect
93. Q8×D15C23semidirect
106. #6817C23semidirect
120. C3×C5×SD16C23semidirect
121. C3×C5×SD16C23semidirect
124. C2×C3×C5×C8C23semidirect
125. #6718C23semidirect
126. #6717C23semidirect
127. #6716C23semidirect
128. #6715C23semidirect
129. #6710C23semidirect
131. Dic60C23semidirect
132. D120C23semidirect
133. #6706C23semidirect
134. #6706C23semidirect
135. #6705C23semidirect
136. C8×D15C23semidirect
139. C22×C3×SD16D5semidirect
149. C22×C5×Q8C2×D3semidirect
168. C2×C5×SD16C2×D3semidirect
169. C2×C5×SD16C2×D3semidirect
170. C2×C5×SD16C2×D3semidirect
171. C22×C5×C8C2×D3semidirect
243. C22×C3×Q8C2×D5semidirect
262. C2×C3×SD16C2×D5semidirect
263. C2×C3×SD16C2×D5semidirect
264. C2×C3×SD16C2×D5semidirect
265. C22×C3×C8C2×D5semidirect
290. C2×C5×Q8C22×D3semidirect
336. C5×SD16C22×D3semidirect
337. C5×SD16C22×D3semidirect
340. C2×C5×C8C22×D3semidirect
363. C22×SD16D15semidirect
390. C2×C3×Q8C22×D5semidirect
436. C3×SD16C22×D5semidirect
437. C3×SD16C22×D5semidirect
440. C2×C3×C8C22×D5semidirect
518. C22×Q8C2×D15semidirect
536. C2×SD16C2×D15semidirect
537. C2×SD16C2×D15semidirect
538. C2×SD16C2×D15semidirect
545. C22×C8C2×D15semidirect
548. C2×C3×C5#577semidirect
649. C2×Q8C22×D15semidirect
681. SD16C22×D15semidirect
682. SD16C22×D15semidirect
691. C2×C8C22×D15semidirect
692. C3×C5C2×#577semidirect
715. C2×C5#5762semidirect
773. C2×C3#66096semidirect
778. C5C2×#5762semidirect
799. C3C2×#66096semidirect
805. C2#11756521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920982
C2×#920952
C22×C3×C5×SD162
C2×#918312
C2×#918212
#117565212
C2×#918052
C2×#918042
C2×#918032
C2×SD16×D152
C2×#917932
C2×#917902
C2×#660963
C2×#57625