Finite Group Databasebeta

← C2×#11754055 #14509985

Subgroups — C2×#11754055 #14509985

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92026C211yesmaximal, characteristic, complemented
2C2×#92025C211yesmaximal, characteristic, complemented
3C2×#91800C211yesmaximal, characteristic, complemented
4C2×C5×#911C211yesmaximal, characteristic, complemented
5C2×C3×D5×D8C211yesmaximal, characteristic, complemented
6C2×#91497C211yesmaximal, characteristic, complemented
7C2×#91493C211yesmaximal, characteristic, complemented
8C2×#91491C211yesmaximal, characteristic, complemented
9C2×#91489C211yesmaximal, characteristic, complemented
10C2×#91481C211yesmaximal, characteristic, complemented
11C2×D3×#686C211yesmaximal, characteristic, complemented
12#11754055C2116yesmaximal, direct product factor
13C2×#91269C211yesmaximal, characteristic, complemented
14C2×#91266C211yesmaximal, characteristic, complemented
15C2×#91258C211yesmaximal, characteristic, complemented
16C2×#91254C211yesmaximal, characteristic, complemented
17C2×#66108—31nomaximal, Hall
18C2×#6819C2211yescharacteristic, complemented
19C2×D4×D15C2211yescharacteristic, complemented
20C2×C5×#237C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic, complemented
22C2×C3×D4×D5C2211yescharacteristic, complemented
23C2×C3×D4×D5C2211yescharacteristic, complemented
24C2×#6790—21no—
25C2×D3×C22⋊D5—21no—
26C2×D5×#67—21no—
27C2×D5×#67—21no—
28C22×#1202—21no—
29C22×#1201—21no—
30C2×#6780—21no—
31C2×#6779—21no—
32#92026—24no—
33#92026C2218yescomplemented
34#92025—24no—
35#92025C2218yescomplemented
36C2×#6777C2211yescharacteristic, complemented
37C2×D3×D20C2211yescharacteristic, complemented
38C2×#6773C2211yescharacteristic, complemented
39C2×#6772C2211yescharacteristic, complemented
40C2×#6771C2211yescharacteristic
41C2×#6766C2211yescharacteristic, complemented
42C2×#6765C2211yescharacteristic, complemented
43C2×C3×C5×D8C2211yescharacteristic, complemented
44C2×#6716C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46#91800C2218yescomplemented
47C2×#6706C2211yescharacteristic, complemented
48C2×#6705C2211yescharacteristic, complemented
49C2×C5×#214C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#911C2218yescomplemented
52C2×C5×#204C2211yescharacteristic, complemented
53C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
54C2×C3×#686C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×D5×D8C2218yescomplemented
57C2×C3×D40C2211yescharacteristic, complemented
58C2×C3×C8×D5C2211yescharacteristic, complemented
59#91497C2218yescomplemented
60#91493C2218yescomplemented
61#91491C2218yescomplemented
62#91489C2218yescomplemented
63#91481C2218yescomplemented
64D3×#686C2218yescomplemented
65C2×#6663C2211yescharacteristic, complemented
66C2×#6657C2211yescharacteristic, complemented
67C2×#6655C2211yescharacteristic, complemented
68C2×#6654C2211yescharacteristic, complemented
69C2×#6653C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6649C2211yescharacteristic, complemented
72C2×#6648C2211yescharacteristic, complemented
73C2×D3×#168C2211yescharacteristic, complemented
74#91269C2218yescomplemented
75#91266C2218yescomplemented
76#91258C2218yescomplemented
77#91254C2218yescomplemented
78C2×#5757—51nomaximal, Hall
79C2×#4149—31no—
80C2×#4144—31no—
81C2×C5×AGL(1,ℤ/8)—31no—
82C2×#4096—31no—
83C22×#686—31no—
84#66108—316no—
85C2×#4062—31no—
86C2×#4062—31no—
87C2×#4060—31no—
88C2×#4060—31no—
89C2×#4057—31no—
90C2×#4057—31no—
91C2×D5×D8—31no—
92C2×D5×D8D311yescharacteristic, complemented
93C2×#4054—31no—
94C2×#4053—31no—
95C23×D15—21no—
96C23×C5×D3—21no—
97C23×C3×D5—21no—
98C23×C3×D5—21no—
99C22×D3×D5—21no—
100C22×D3×D5—21no—
101C2×C3×C5×D4C2311yescharacteristic
102C2×C3×C5×D4C2311yescharacteristic
103C2×#1220—21no—
104C2×#1220—21no—
105C22×Dic15—21no—
106#6819—22no—
107#6819C2314yescomplemented
108D4×D15—22no—
109D4×D15C2314yescomplemented
110C2×D60C2311yescharacteristic
111C2×C4×D15C2311yescharacteristic
112C2×Dic30C2311yescharacteristic
113C2×C5×#67—21no—
114C2×C5×#67—21no—
115C22×C5×Dic3—21no—
116C5×#237—22no—
117C5×#237C2314yescomplemented
118C5×D3×D4—22no—
119C5×D3×D4C2314yescomplemented
120C2×C5×D12C2311yescharacteristic
121C2×C4×C5×D3C2311yescharacteristic
122C2×C5×Dic6C2311yescharacteristic
123C2×C3×C22⋊D5—21no—
124C2×C3×C22⋊D5—21no—
125C3×D4×D5—22no—
126C3×D4×D5—22no—
127C3×D4×D5C2314yescomplemented
128C3×D4×D5C2314yescomplemented
129C2×C3×D20C2311yescharacteristic
130C2×C3×D20C2311yescharacteristic
131C2×C3×C4×D5C2311yescharacteristic
132#6790—28no—
133D3×C22⋊D5—28no—
134D5×#67—28no—
135D5×#67—28no—
136C2×#1204D411yescharacteristic
137C2×#1203D411yescharacteristic
138C2×#1202—21no—
139C2×#1202—21no—
140C2×#1202—21no—
141C2×#1202—28no—
142C2×#1202D411yescharacteristic
143C2×#1201—21no—
144C2×#1201—21no—
145C2×#1201—21no—
146C2×#1201—28no—
147C2×#1201D411yescharacteristic
148C2×#1200—21no—
149C2×D3×Dic5—21no—
150#6780—28no—
151#6779—28no—
152C2×D5×Dic3—21no—
153C2×D5×Dic3—21no—
154#6777—22no—
155#6777C2314yescomplemented
156D3×D20—22no—
157D3×D20C2314yescomplemented
158#6773—22no—
159#6773C2314yescomplemented
160#6772—22no—
161#6772C2314yescomplemented
162#6771D414yes—
163#6771C2314yes—
164#6766—22no—
165#6766C2314yescomplemented
166#6765—22no—
167#6765C2314yescomplemented
168C3×C5×D8C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6716C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173#6706C2314yescomplemented
174#6705C2314yescomplemented
175C5×#214C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×#204C2314yescomplemented
179C5×ΓL(1,𝔽25)C2314yescomplemented
180C3×#686C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×D40C2314yescomplemented
184C3×C8×D5C2314yescomplemented
185#6663C2314yescomplemented
186#6657C2314yescomplemented
187#6655C2314yescomplemented
188#6654C2314yescomplemented
189#6653C2314yescomplemented
190#6652C2314yescomplemented
191#6649C2314yescomplemented
192#6648C2314yescomplemented
193D3×#168C2314yescomplemented
194C2×#1004—51no—
195C2×#1004—51no—
196C22×C3×D8—51no—
197C2×#932—51no—
198C2×#932—51no—
199#5757—516no—
200C2×#912—51no—
201C2×#912—51no—
202C2×#911—51no—
203C2×#911—51no—
204C2×#911—51no—
205C2×#911D511yescharacteristic, complemented
206C2×D3×D8—51no—
207C2×D3×D8—51no—
208C2×#904—51no—
209C2×#901—51no—
210C2×C5×#41—31no—
211C22×C5×D4—31no—
212C22×C22⋊D5—61no—
213C22×C22⋊D5—61no—
214#4149—38no—
215#4149—64no—
216C2×#713—31no—
217C2×#713—31no—
218#4144—38no—
219#4144—64no—
220C2×#711—31no—
221C2×#711—31no—
222C2×#711—61no—
223C2×D4×D5—31no—
224C2×D4×D5—31no—
225C2×D4×D5—61no—
226C2×D4×D5—61no—
227C2×D4×D5—61no—
228C2×D4×D5C2×D311yescharacteristic, complemented
229C2×D4×D5C2×D311yescharacteristic, complemented
230C2×#709—31no—
231C2×#709—31no—
232C2×#709—61no—
233C22×D20—31no—
234C22×D20—61no—
235C5×AGL(1,ℤ/8)—38no—
236C2×C5×SD16—31no—
237C2×C5×SD16—31no—
238C2×C5×D8—31no—
239C2×C5×D8C2×D311yescharacteristic, complemented
240C2×C5×M16—31no—
241#4096—38no—
242C2×#689—31no—
243C2×#688—31no—
244C2×#687—31no—
245C2×#686—31no—
246C2×#686—31no—
247C2×#686—38no—
248C2×#686—31no—
249C2×#686C2×D311yescharacteristic, complemented
250C2×#686C2×D311yescharacteristic, complemented
251C22×#168—31no—
252#4062—38no—
253#4062—38no—
254#4060—38no—
255#4060—38no—
256#4057—38no—
257#4057—38no—
258D5×D8—38no—
259D5×D8C2×D318yescomplemented
260#4054—38no—
261#4053—38no—
262C2×D40—31no—
263C2×D40C2×D311yescharacteristic, complemented
264C2×#677—31no—
265C2×#677—31no—
266C2×#676—31no—
267C2×#676—31no—
268C2×C8×D5—31no—
269C2×C8×D5C2×D311yescharacteristic, complemented
270C2×#576—151noSylow
271C23×C3×C5—21no—
272C23×C3×C5—21no—
273C22×D15—21no—
274C22×D15—24no—
275C22×D15—82no—
276C22×D15C2×D411yescharacteristic
277C22×C5×D3—21no—
278C22×C5×D3—24no—
279C22×C5×D3—82no—
280C22×C5×D3C2×D411yescharacteristic
281C22×C3×D5—21no—
282C22×C3×D5—21no—
283C22×C3×D5—24no—
284C22×C3×D5—24no—
285C22×C3×D5—82no—
286C22×C3×D5—82no—
287C22×C3×D5C2×D411yescharacteristic
288C2×D3×D5—24no—
289C2×D3×D5—24no—
290C2×D3×D5—82no—
291C2×D3×D5—82no—
292C3×C5×D4—21no—
293C3×C5×D4—21no—
294C3×C5×D4C2412yes—
295C3×C5×D4C2412yes—
296C2×C3×C4×C5C2411yescharacteristic
297#1220—24no—
298#1220—24no—
299C2×Dic15—21no—
300C2×Dic15—24no—
301C2×Dic15C2×D411yescharacteristic
302D60—21no—
303D60C2412yes—
304C4×D15C2×D412yes—
305C4×D15C2412yes—
306Dic30—21no—
307Dic30C2412yes—
308C5×#67—24no—
309C5×#67—24no—
310C2×C5×Dic3—21no—
311C2×C5×Dic3—24no—
312C2×C5×Dic3C2×D411yescharacteristic
313C5×D12—21no—
314C5×D12C2412yes—
315C4×C5×D3C2×D412yes—
316C4×C5×D3C2412yes—
317C5×Dic6—21no—
318C5×Dic6C2412yes—
319C3×C22⋊D5—24no—
320C3×C22⋊D5—24no—
321C2×C3×Dic5C2×D411yescharacteristic
322C3×D20—21no—
323C3×D20—21no—
324C3×D20C2412yes—
325C3×D20C2412yes—
326C3×C4×D5C2×D412yes—
327C3×C4×D5C2412yes—
328#1204C2×D414yes—
329#1203C2×D414yes—
330#1202—24no—
331#1202—24no—
332#1202—24no—
333#1202C2×D414yes—
334#1201—24no—
335#1201—24no—
336#1201—24no—
337#1201C2×D414yes—
338#1200—24no—
339D3×Dic5—24no—
340D5×Dic3—24no—
341D5×Dic3—24no—
342C3×C5×C8C2412yes—
343C3⋊#168C2412yes—
344C3×#168C2412yes—
345C5×C3⋊C8C2412yes—
346C22×C3×D4—51no—
347C22×C3×D4—51no—
348C22×#67—101no—
349C22×#67—101no—
350C22×#67—101no—
351C22×#67—101no—
352#1004—58no—
353#1004—58no—
354#1004—104no—
355#1004—104no—
356C2×#237—51no—
357C2×#237—51no—
358C2×#237—51no—
359C2×#237—101no—
360C2×#237—101no—
361C2×#237C2×D511yescharacteristic, complemented
362C2×D3×D4—51no—
363C2×D3×D4—51no—
364C2×D3×D4—51no—
365C2×D3×D4—101no—
366C2×D3×D4—101no—
367C2×D3×D4C2×D511yescharacteristic, complemented
368C2×#235—51no—
369C2×#235—51no—
370C2×#235—51no—
371C2×C3×D8—51no—
372C2×C3×D8—51no—
373C2×C3×D8—58no—
374C2×C3×D8—51no—
375C2×C3×D8C2×D511yescharacteristic, complemented
376C22×C3×C8—51no—
377C2×#214—51no—
378C2×#214—51no—
379C2×#214—51no—
380C2×#214C2×D511yescharacteristic, complemented
381#932—58no—
382#932—58no—
383C2×#213—51no—
384C2×#213—51no—
385C2×#213—51no—
386C2×#213C2×D511yescharacteristic, complemented
387C2×#208—51no—
388#912—58no—
389#912—58no—
390#911—58no—
391#911—58no—
392#911—58no—
393#911C2×D518yescomplemented
394D3×D8—58no—
395D3×D8—58no—
396C2×Dic12—51no—
397#904—58no—
398C2×D24—51no—
399C2×#204—51no—
400C2×#204C2×D511yescharacteristic, complemented
401#901—58no—
402C2×ΓL(1,𝔽25)—51no—
403C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
404C2×D3×C8—51no—
405C2×D3×C8—51no—
406C24×C5—61no—
407C23×D5—21no—
408C23×D5—21no—
409C23×D5—61no—
410C23×D5—61no—
411C23×D5—61no—
412C5×#41—34no—
413C5×#41—62no—
414C2×C5×Q8—31no—
415C2×C5×D4—34no—
416C2×C5×D4—31no—
417C2×C5×D4—62no—
418C2×C5×D4—61no—
419C2×C5×D4—61no—
420C2×C5×D4C22×D311yescharacteristic
421C2×C5×D4C22×D311yescharacteristic
422C22×C4×C5—31no—
423C22×C4×C5—61no—
424C2×C22⋊D5—21no—
425C2×C22⋊D5—21no—
426C2×C22⋊D5—31no—
427C2×C22⋊D5—31no—
428C2×C22⋊D5—61no—
429C2×C22⋊D5—61no—
430C2×C22⋊D5—68no—
431C2×C22⋊D5—68no—
432C2×C22⋊D5—61no—
433C2×C22⋊D5—61no—
434C2×C22⋊D5—61no—
435C22×Dic5—61no—
436C22×Dic5—61no—
437#713—34no—
438#713—34no—
439#713—62no—
440#713—62no—
441#711—34no—
442#711—34no—
443#711—68no—
444#711—62no—
445#711—62no—
446D4×D5—22no—
447D4×D5—22no—
448D4×D5—34no—
449D4×D5—34no—
450D4×D5—62no—
451D4×D5—62no—
452D4×D5—68no—
453D4×D5—68no—
454D4×D5—68no—
455D4×D5C22×D314yescomplemented
456D4×D5C22×D314yescomplemented
457#709—34no—
458#709—34no—
459#709—34no—
460#709—68no—
461#709—62no—
462C2×D20—31no—
463C2×D20—31no—
464C2×D20—34no—
465C2×D20—62no—
466C2×D20—68no—
467C2×D20—61no—
468C2×D20—61no—
469C2×D20—61no—
470C2×D20C22×D311yescharacteristic
471C2×D20C22×D311yescharacteristic
472C2×C4×D5—31no—
473C2×C4×D5—61no—
474C2×C4×D5—61no—
475C2×C4×D5—61no—
476C2×C4×D5C22×D311yescharacteristic
477C2×Dic10—31no—
478C2×Dic10—31no—
479C5×SD16—34no—
480C5×SD16—34no—
481C5×D8—34no—
482C5×D8C22×D314yescomplemented
483C5×M16—34no—
484C2×C5×C8—31no—
485C2×C5×C8C22×D311yescharacteristic
486#689—34no—
487#688—34no—
488#687—34no—
489#686—34no—
490#686—34no—
491#686—34no—
492#686C22×D314yescomplemented
493#686C22×D314yescomplemented
494C2×#168—31no—
495C2×#168—34no—
496C2×#168C22×D311yescharacteristic
497D40—34no—
498D40C22×D314yescomplemented
499#677—34no—
500#677—34no—
501#676—34no—
502#676—34no—
503C8×D5—34no—
504C8×D5C22×D314yescomplemented
505C2×H(5,𝔽2)—151no—
506C2×H(5,𝔽2)—151no—
507#576—1516no—
508C2×AGL(1,ℤ/8)—31no—
509C2×AGL(1,ℤ/8)—151no—
510C2×AGL(1,ℤ/8)—151no—
511C2×AGL(1,ℤ/8)—151no—
512C2×AGL(1,ℤ/8)—151no—
513C2×AGL(1,ℤ/8)—151no—
514C2×#135—151no—
515C2×#135—151no—
516C2×#135—151no—
517C22×D8—51no—
518C22×D8—151no—
519C22×D8—151no—
520C2×#131—151no—
521C22×C3×C5—22no—
522C22×C3×C5—22no—
523C22×C3×C5—42no—
524C22×C3×C5—42no—
525C22×C3×C5C22×D411yescharacteristic
526C2×D15—22no—
527C2×D15—22no—
528C2×D15—42no—
529C2×D15—84no—
530C2×D15C22×D412yes—
531C2×C5×D3—22no—
532C2×C5×D3—22no—
533C2×C5×D3—42no—
534C2×C5×D3—84no—
535C2×C5×D3C22×D412yes—
536C2×C3×D5—22no—
537C2×C3×D5—22no—
538C2×C3×D5—22no—
539C2×C3×D5—42no—
540C2×C3×D5—42no—
541C2×C3×D5—84no—
542C2×C3×D5—84no—
543C2×C3×D5C22×D412yes—
544D3×D5—84no—
545D3×D5—84no—
546C3×C4×C5C22×D411yescharacteristic
547C3×C4×C5C2511yescharacteristic
548Dic15—22no—
549Dic15C22×D412yes—
550C3×Dic5C22×D412yes—
551C5×Dic3—22no—
552C5×Dic3C22×D412yes—
553C24×C3—101no—
554C24×C3—101no—
555C23×D3—21no—
556C23×D3—101no—
557C23×D3—101no—
558C23×D3—101no—
559C2×C3×D4—54no—
560C2×C3×D4—54no—
561C2×C3×D4—51no—
562C2×C3×D4—51no—
563C2×C3×D4—102no—
564C2×C3×D4—102no—
565C2×C3×D4—101no—
566C2×C3×D4—101no—
567C2×C3×D4C22×D511yescharacteristic
568C2×C3×D4C22×D511yescharacteristic
569C22×C3×C4—51no—
570C2×#67—21no—
571C2×#67—21no—
572C2×#67—51no—
573C2×#67—51no—
574C2×#67—108no—
575C2×#67—101no—
576C2×#67—101no—
577C2×#67—101no—
578C2×#67—101no—
579C2×#67—108no—
580C2×#67—108no—
581C2×#67—108no—
582C2×#67—101no—
583C2×#67—101no—
584C2×#67—101no—
585C2×#67—101no—
586C22×Dic3—21no—
587C22×Dic3—101no—
588C22×Dic3—101no—
589C22×Dic3—101no—
590#237—22no—
591#237—54no—
592#237—54no—
593#237—54no—
594#237—102no—
595#237—108no—
596#237—108no—
597#237—102no—
598#237—102no—
599#237C22×D514yescomplemented
600D3×D4—22no—
601D3×D4—54no—
602D3×D4—54no—
603D3×D4—54no—
604D3×D4—102no—
605D3×D4—102no—
606D3×D4—108no—
607D3×D4—108no—
608D3×D4—102no—
609D3×D4C22×D514yescomplemented
610#235—54no—
611#235—54no—
612#235—54no—
613#235—54no—
614#235—102no—
615#235—102no—
616C2×D12—51no—
617C2×D12—51no—
618C2×D12C22×D511yescharacteristic
619C2×C4×D3—51no—
620C2×C4×D3—101no—
621C2×C4×D3—101no—
622C2×C4×D3C22×D511yescharacteristic
623C2×Dic6—51no—
624C2×Dic6—51no—
625C2×Dic6C22×D511yescharacteristic
626C3×D8—54no—
627C3×D8—54no—
628C3×D8—54no—
629C3×D8C22×D514yescomplemented
630C2×C3×C8—51no—
631C2×C3×C8—54no—
632C2×C3×C8C22×D511yescharacteristic
633#214—54no—
634#214—54no—
635#214—54no—
636#214C22×D514yescomplemented
637#213—54no—
638#213—54no—
639#213—54no—
640#213C22×D514yescomplemented
641#208—54no—
642C2×C3⋊C8—51no—
643C2×C3⋊C8C22×D511yescharacteristic
644Dic12—54no—
645D24—54no—
646#204—54no—
647#204C22×D514yescomplemented
648ΓL(1,𝔽25)—54no—
649ΓL(1,𝔽25)C22×D514yescomplemented
650D3×C8—54no—
651D3×C8—54no—
652C23×C5—21no—
653C23×C5—21no—
654C23×C5—31no—
655C23×C5—64no—
656C23×C5—61no—
657C23×C5—242no—
658C22×D5—21no—
659C22×D5—21no—
660C22×D5—24no—
661C22×D5—24no—
662C22×D5—31no—
663C22×D5—64no—
664C22×D5—64no—
665C22×D5—64no—
666C22×D5—61no—
667C22×D5—82no—
668C22×D5—82no—
669C22×D5—242no—
670C22×D5—242no—
671C22×D5—242no—
672C22×D5D3×D411yescharacteristic
673C5×Q8—32no—
674C5×Q8—61no—
675C5×D4—21no—
676C5×D4—21no—
677C5×D4—32no—
678C5×D4—64no—
679C5×D4—64no—
680C5×D4—61no—
681C5×D4C23×D312yes—
682C5×D4C23×D312yes—
683C2×C4×C5—31no—
684C2×C4×C5—32no—
685C2×C4×C5—32no—
686C2×C4×C5—64no—
687C2×C4×C5—61no—
688C2×C4×C5C23×D311yescharacteristic
689C22⋊D5—24no—
690C22⋊D5—24no—
691C22⋊D5—34no—
692C22⋊D5—34no—
693C22⋊D5—64no—
694C22⋊D5—64no—
695C22⋊D5—64no—
696C22⋊D5—64no—
697C22⋊D5—64no—
698C2×Dic5—31no—
699C2×Dic5—64no—
700C2×Dic5—61no—
701C2×Dic5—64no—
702C2×Dic5D3×D411yescharacteristic
703D20—21no—
704D20—21no—
705D20—34no—
706D20—32no—
707D20—64no—
708D20—64no—
709D20—64no—
710D20—61no—
711D20C23×D312yes—
712D20C23×D312yes—
713C4×D5—32no—
714C4×D5—32no—
715C4×D5—64no—
716C4×D5—64no—
717C4×D5—64no—
718C4×D5D3×D412yes—
719C4×D5C23×D312yes—
720Dic10—34no—
721Dic10—32no—
722Dic10—61no—
723C5×C8—32no—
724C5×C8C23×D312yes—
725#168—32no—
726#168C23×D312yes—
727H(5,𝔽2)—158no—
728H(5,𝔽2)—158no—
729H(5,𝔽2)—304no—
730H(5,𝔽2)—304no—
731C2×#41—31no—
732C2×#41—151no—
733C2×#41—151no—
734C2×#41—151no—
735C2×#41—151no—
736C2×#41—151no—
737C2×#41—151no—
738C2×#41—301no—
739C2×#41—301no—
740C22×D4—31no—
741C22×D4—51no—
742C22×D4—51no—
743C22×D4—151no—
744C22×D4—151no—
745C22×D4—151no—
746C22×D4—301no—
747C22×D4—301no—
748C22×D4—301no—
749C22×D4—301no—
750C22×D4—301no—
751C22×D4—301no—
752AGL(1,ℤ/8)—38no—
753AGL(1,ℤ/8)—158no—
754AGL(1,ℤ/8)—158no—
755AGL(1,ℤ/8)—158no—
756AGL(1,ℤ/8)—158no—
757AGL(1,ℤ/8)—158no—
758#135—158no—
759#135—158no—
760#135—158no—
761C2×Q16—151no—
762C2×SD16—31no—
763C2×SD16—31no—
764C2×SD16—151no—
765C2×SD16—151no—
766C2×SD16—151no—
767C2×SD16—151no—
768C2×D8—31no—
769C2×D8—51no—
770C2×D8—51no—
771C2×D8—58no—
772C2×D8—51no—
773C2×D8—151no—
774C2×D8—151no—
775C2×D8—158no—
776C2×D8—158no—
777C2×D8—151no—
778C2×D8—151no—
779C2×D8D3×D511yescharacteristic, complemented
780#131—158no—
781C2×M16—31no—
782C2×M16—151no—
783C2×M16—151no—
784C22×C8—51no—
785C22×C8—151no—
786C22×C8—151no—
787C2×C3×C5—42no—
788C2×C3×C5—42no—
789C2×C3×C5#57612yescomplemented
790C2×C3×C5C23×D411yescharacteristic
791D15—22no—
792D15—42no—
793C3×D5—22no—
794C3×D5—42no—
795C3×D5—42no—
796C5×D3—22no—
797C5×D3—42no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—51no—
801C23×C3—104no—
802C23×C3—104no—
803C23×C3—101no—
804C23×C3—101no—
805C23×C3—402no—
806C23×C3—402no—
807C22×D3—21no—
808C22×D3—24no—
809C22×D3—51no—
810C22×D3—82no—
811C22×D3—104no—
812C22×D3—104no—
813C22×D3—101no—
814C22×D3—104no—
815C22×D3—402no—
816C22×D3—402no—
817C22×D3—402no—
818C22×D3D4×D511yescharacteristic
819C3×D4—21no—
820C3×D4—21no—
821C3×D4—52no—
822C3×D4—52no—
823C3×D4—104no—
824C3×D4—104no—
825C3×D4—101no—
826C3×D4—101no—
827C3×D4C23×D512yes—
828C3×D4C23×D512yes—
829C2×C3×C4—51no—
830C2×C3×C4—52no—
831C2×C3×C4—52no—
832C2×C3×C4C23×D511yescharacteristic
833#67—24no—
834#67—24no—
835#67—54no—
836#67—54no—
837#67—104no—
838#67—104no—
839#67—104no—
840#67—104no—
841#67—104no—
842#67—104no—
843#67—104no—
844#67—104no—
845C2×Dic3—21no—
846C2×Dic3—24no—
847C2×Dic3—51no—
848C2×Dic3—104no—
849C2×Dic3—104no—
850C2×Dic3—101no—
851C2×Dic3—104no—
852C2×Dic3D4×D511yescharacteristic
853D12—21no—
854D12—54no—
855D12—52no—
856D12—101no—
857D12C23×D512yes—
858C4×D3—52no—
859C4×D3—52no—
860C4×D3—104no—
861C4×D3—104no—
862C4×D3D4×D512yes—
863C4×D3C23×D512yes—
864Dic6—21no—
865Dic6—54no—
866Dic6—52no—
867Dic6—101no—
868Dic6C23×D512yes—
869C3×C8—52no—
870C3×C8C23×D512yes—
871C3⋊C8—52no—
872C3⋊C8C23×D512yes—
873C22×C5—22no—
874C22×C5—22no—
875C22×C5—32no—
876C22×C5—42no—
877C22×C5—42no—
878C22×C5—62no—
879C22×C5—62no—
880C22×C5—122no—
881C22×C5—244no—
882C22×C5C2×D3×D411yescharacteristic
883C2×D5—22no—
884C2×D5—22no—
885C2×D5—22no—
886C2×D5—32no—
887C2×D5—42no—
888C2×D5—42no—
889C2×D5—62no—
890C2×D5—62no—
891C2×D5—84no—
892C2×D5—84no—
893C2×D5—122no—
894C2×D5—244no—
895C2×D5—244no—
896C2×D5—244no—
897C2×D5C2×D3×D412yes—
898C4×C5—32no—
899C4×C5—62no—
900C4×C5C2×D3×D411yescharacteristic
901C4×C5C24×D311yescharacteristic
902Dic5—32no—
903Dic5—62no—
904Dic5C2×D3×D412yes—
905C24—61no—
906C24—101no—
907C24—101no—
908C24—301no—
909C24—301no—
910C24—301no—
911#41—34no—
912#41—62no—
913#41—154no—
914#41—154no—
915#41—154no—
916#41—154no—
917#41—154no—
918#41—154no—
919#41—154no—
920#41—302no—
921#41—302no—
922#41—302no—
923#41—308no—
924#41—302no—
925#41—302no—
926#41—308no—
927C2×Q8—31no—
928C2×Q8—151no—
929C2×Q8—151no—
930C2×D4—34no—
931C2×D4—31no—
932C2×D4—54no—
933C2×D4—54no—
934C2×D4—51no—
935C2×D4—51no—
936C2×D4—62no—
937C2×D4—61no—
938C2×D4—61no—
939C2×D4—102no—
940C2×D4—102no—
941C2×D4—101no—
942C2×D4—101no—
943C2×D4—154no—
944C2×D4—151no—
945C2×D4—151no—
946C2×D4—154no—
947C2×D4—151no—
948C2×D4—154no—
949C2×D4—151no—
950C2×D4—302no—
951C2×D4—301no—
952C2×D4—308no—
953C2×D4—301no—
954C2×D4—301no—
955C2×D4—302no—
956C2×D4—302no—
957C2×D4—301no—
958C2×D4—301no—
959C2×D4—308no—
960C2×D4—308no—
961C2×D4—308no—
962C2×D4—308no—
963C2×D4—308no—
964C2×D4—301no—
965C2×D4—301no—
966C2×D4—301no—
967C2×D4C2×D3×D511yescharacteristic
968C2×D4C2×D3×D511yescharacteristic
969C22×C4—31no—
970C22×C4—51no—
971C22×C4—61no—
972C22×C4—151no—
973C22×C4—301no—
974C22×C4—301no—
975C22×C4—301no—
976C22×C4—301no—
977C22×C4—301no—
978Q16—154no—
979SD16—34no—
980SD16—34no—
981SD16—154no—
982SD16—154no—
983SD16—154no—
984SD16—154no—
985D8—34no—
986D8—54no—
987D8—54no—
988D8—54no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8C2×D3×D514yescomplemented
994M16—34no—
995M16—154no—
996M16—154no—
997C2×C8—31no—
998C2×C8—51no—
999C2×C8—54no—
1000C2×C8—154no—
1001C2×C8—154no—
1002C2×C8—151no—
1003C2×C8C2×D3×D511yescharacteristic
1004C3×C5C2×#57611yescharacteristic, complemented, Hall
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—42no—
1008C22×C3—42no—
1009C22×C3—52no—
1010C22×C3—102no—
1011C22×C3—102no—
1012C22×C3—102no—
1013C22×C3—202no—
1014C22×C3—202no—
1015C22×C3—404no—
1016C22×C3—404no—
1017C22×C3C2×D4×D511yescharacteristic
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—42no—
1021C2×D3—52no—
1022C2×D3—84no—
1023C2×D3—102no—
1024C2×D3—102no—
1025C2×D3—202no—
1026C2×D3—404no—
1027C2×D3—404no—
1028C2×D3—404no—
1029C2×D3C2×D4×D512yes—
1030C3×C4—52no—
1031C3×C4C2×D4×D511yescharacteristic
1032C3×C4C24×D511yescharacteristic
1033Dic3—22no—
1034Dic3—52no—
1035Dic3—102no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—42no—
1039C2×C5—62no—
1040C2×C5—122no—
1041C2×C5#575712yescomplemented
1042C2×C5C22×D3×D411yescharacteristic
1043D5—22no—
1044D5—42no—
1045D5—42no—
1046D5—62no—
1047D5—122no—
1048C23—21no—
1049C23—21no—
1050C23—31no—
1051C23—51no—
1052C23—64no—
1053C23—61no—
1054C23—104no—
1055C23—104no—
1056C23—101no—
1057C23—101no—
1058C23—151no—
1059C23—242no—
1060C23—304no—
1061C23—304no—
1062C23—304no—
1063C23—301no—
1064C23—402no—
1065C23—402no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—32no—
1070Q8—61no—
1071Q8—154no—
1072Q8—152no—
1073Q8—301no—
1074D4—21no—
1075D4—21no—
1076D4—32no—
1077D4—52no—
1078D4—52no—
1079D4—64no—
1080D4—64no—
1081D4—61no—
1082D4—104no—
1083D4—104no—
1084D4—101no—
1085D4—101no—
1086D4—154no—
1087D4—154no—
1088D4—154no—
1089D4—152no—
1090D4—304no—
1091D4—304no—
1092D4—304no—
1093D4—304no—
1094D4—304no—
1095D4—304no—
1096D4—304no—
1097D4—304no—
1098D4—301no—
1099D4C22×D3×D512yes—
1100D4C22×D3×D512yes—
1101C2×C4—31no—
1102C2×C4—32no—
1103C2×C4—32no—
1104C2×C4—51no—
1105C2×C4—52no—
1106C2×C4—52no—
1107C2×C4—64no—
1108C2×C4—61no—
1109C2×C4—151no—
1110C2×C4—152no—
1111C2×C4—152no—
1112C2×C4—304no—
1113C2×C4—304no—
1114C2×C4—304no—
1115C2×C4—304no—
1116C2×C4—304no—
1117C2×C4—301no—
1118C2×C4C22×D3×D511yescharacteristic
1119C8—32no—
1120C8—52no—
1121C8—152no—
1122C8C22×D3×D512yes—
1123C2×C3—42no—
1124C2×C3—42no—
1125C2×C3—102no—
1126C2×C3—202no—
1127C2×C3—202no—
1128C2×C3#6610812yescomplemented
1129C2×C3C22×D4×D511yescharacteristic
1130D3—22no—
1131D3—42no—
1132D3—102no—
1133D3—202no—
1134C5C2×#575711yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—22no—
1137C22—32no—
1138C22—42no—
1139C22—42no—
1140C22—52no—
1141C22—62no—
1142C22—62no—
1143C22—102no—
1144C22—102no—
1145C22—102no—
1146C22—122no—
1147C22—152no—
1148C22—202no—
1149C22—202no—
1150C22—244no—
1151C22—302no—
1152C22—302no—
1153C22—404no—
1154C22—404no—
1155C22—602no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—32no—
1161C4—52no—
1162C4—62no—
1163C4—152no—
1164C4—302no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6610811yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—42no—
1170C2—62no—
1171C2—102no—
1172C2—122no—
1173C2—202no—
1174C2—202no—
1175C2—302no—
1176C2—602no—
1177C2#1175405512yesdirect product factor
1178C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
hypercenterC2×D8D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#92026C2semidirect
2. C2×#92025C2semidirect
3. C2×#91800C2semidirect
4. C2×C5×#911C2semidirect
5. C2×C3×D5×D8C2semidirect
6. C2×#91497C2semidirect
7. C2×#91493C2semidirect
8. C2×#91491C2semidirect
9. C2×#91489C2semidirect
10. C2×#91481C2semidirect
11. C2×D3×#686C2semidirect
12. #11754055C2direct (N × H)
13. C2×#91269C2semidirect
14. C2×#91266C2semidirect
15. C2×#91258C2semidirect
16. C2×#91254C2semidirect
18. C2×#6819C22semidirect
19. C2×D4×D15C22semidirect
20. C2×C5×#237C22semidirect
21. C2×C5×D3×D4C22semidirect
22. C2×C3×D4×D5C22semidirect
23. C2×C3×D4×D5C22semidirect
33. #92026C22semidirect
35. #92025C22semidirect
36. C2×#6777C22semidirect
37. C2×D3×D20C22semidirect
38. C2×#6773C22semidirect
39. C2×#6772C22semidirect
41. C2×#6766C22semidirect
42. C2×#6765C22semidirect
43. C2×C3×C5×D8C22semidirect
44. C2×#6716C22semidirect
45. C2×#6715C22semidirect
46. #91800C22semidirect
47. C2×#6706C22semidirect
48. C2×#6705C22semidirect
49. C2×C5×#214C22semidirect
50. C2×C5×#213C22semidirect
51. C5×#911C22semidirect
52. C2×C5×#204C22semidirect
53. C2×C5×ΓL(1,𝔽25)C22semidirect
54. C2×C3×#686C22semidirect
55. C2×C3×#686C22semidirect
56. C3×D5×D8C22semidirect
57. C2×C3×D40C22semidirect
58. C2×C3×C8×D5C22semidirect
59. #91497C22semidirect
60. #91493C22semidirect
61. #91491C22semidirect
62. #91489C22semidirect
63. #91481C22semidirect
64. D3×#686C22semidirect
65. C2×#6663C22semidirect
66. C2×#6657C22semidirect
67. C2×#6655C22semidirect
68. C2×#6654C22semidirect
69. C2×#6653C22semidirect
70. C2×#6652C22semidirect
71. C2×#6649C22semidirect
72. C2×#6648C22semidirect
73. C2×D3×#168C22semidirect
74. #91269C22semidirect
75. #91266C22semidirect
76. #91258C22semidirect
77. #91254C22semidirect
92. C2×D5×D8D3semidirect
107. #6819C23semidirect
109. D4×D15C23semidirect
117. C5×#237C23semidirect
119. C5×D3×D4C23semidirect
127. C3×D4×D5C23semidirect
128. C3×D4×D5C23semidirect
155. #6777C23semidirect
157. D3×D20C23semidirect
159. #6773C23semidirect
161. #6772C23semidirect
165. #6766C23semidirect
167. #6765C23semidirect
168. C3×C5×D8C23semidirect
170. #6716C23semidirect
171. #6715C23semidirect
173. #6706C23semidirect
174. #6705C23semidirect
175. C5×#214C23semidirect
176. C5×#213C23semidirect
178. C5×#204C23semidirect
179. C5×ΓL(1,𝔽25)C23semidirect
180. C3×#686C23semidirect
181. C3×#686C23semidirect
183. C3×D40C23semidirect
184. C3×C8×D5C23semidirect
185. #6663C23semidirect
186. #6657C23semidirect
187. #6655C23semidirect
188. #6654C23semidirect
189. #6653C23semidirect
190. #6652C23semidirect
191. #6649C23semidirect
192. #6648C23semidirect
193. D3×#168C23semidirect
205. C2×#911D5semidirect
228. C2×D4×D5C2×D3semidirect
229. C2×D4×D5C2×D3semidirect
239. C2×C5×D8C2×D3semidirect
249. C2×#686C2×D3semidirect
250. C2×#686C2×D3semidirect
259. D5×D8C2×D3semidirect
263. C2×D40C2×D3semidirect
269. C2×C8×D5C2×D3semidirect
361. C2×#237C2×D5semidirect
367. C2×D3×D4C2×D5semidirect
375. C2×C3×D8C2×D5semidirect
380. C2×#214C2×D5semidirect
386. C2×#213C2×D5semidirect
393. #911C2×D5semidirect
400. C2×#204C2×D5semidirect
403. C2×ΓL(1,𝔽25)C2×D5semidirect
455. D4×D5C22×D3semidirect
456. D4×D5C22×D3semidirect
482. C5×D8C22×D3semidirect
492. #686C22×D3semidirect
493. #686C22×D3semidirect
498. D40C22×D3semidirect
504. C8×D5C22×D3semidirect
599. #237C22×D5semidirect
609. D3×D4C22×D5semidirect
629. C3×D8C22×D5semidirect
636. #214C22×D5semidirect
640. #213C22×D5semidirect
647. #204C22×D5semidirect
649. ΓL(1,𝔽25)C22×D5semidirect
779. C2×D8D3×D5semidirect
789. C2×C3×C5#576semidirect
993. D8C2×D3×D5semidirect
1004. C3×C5C2×#576semidirect
1041. C2×C5#5757semidirect
1128. C2×C3#66108semidirect
1134. C5C2×#5757semidirect
1167. C3C2×#66108semidirect
1177. C2#11754055direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920262
C2×#920252
C2×#918002
C2×C5×#9112
C2×C3×D5×D82
C2×#914972
C2×#914932
C2×#914912
C2×#914892
C2×#914812
C2×D3×#6862
#117540552
C2×#912692
C2×#912662
C2×#912582
C2×#912542
C2×#661083
C2×#57575