Finite Group Databasebeta

← C2×#11754056 #14509984

Subgroups — C2×#11754056 #14509984

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×#92027C211yesmaximal, characteristic, complemented
2C2×#92025C211yesmaximal, characteristic, complemented
3C2×#91800C211yesmaximal, characteristic, complemented
4C2×C5×D3×D8C211yesmaximal, characteristic, complemented
5C2×C3×#4057C211yesmaximal, characteristic, complemented
6C2×#91499C211yesmaximal, characteristic, complemented
7C2×#91496C211yesmaximal, characteristic, complemented
8C2×#91494C211yesmaximal, characteristic, complemented
9C2×#91490C211yesmaximal, characteristic, complemented
10C2×#91481C211yesmaximal, characteristic, complemented
11C2×D5×#213C211yesmaximal, characteristic, complemented
12#11754056C2116yesmaximal, direct product factor
13C2×#91272C211yesmaximal, characteristic, complemented
14C2×#91267C211yesmaximal, characteristic, complemented
15C2×#91257C211yesmaximal, characteristic, complemented
16C2×#91250C211yesmaximal, characteristic, complemented
17C2×#66091—31nomaximal, Hall
18C2×#6819C2211yescharacteristic, complemented
19C2×D4×D15C2211yescharacteristic, complemented
20C2×C5×D3×D4C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic, complemented
22C2×C3×#711C2211yescharacteristic, complemented
23C2×C3×D4×D5C2211yescharacteristic, complemented
24C2×#6790—21no—
25C2×D3×C22⋊D5—21no—
26C2×D3×C22⋊D5—21no—
27C2×D5×#67—21no—
28C22×#1203—21no—
29C22×#1201—21no—
30C2×#6782—21no—
31C2×#6780—21no—
32#92027—24no—
33#92027C2218yescomplemented
34#92025—24no—
35#92025C2218yescomplemented
36C2×#6777C2211yescharacteristic, complemented
37C2×D5×D12C2211yescharacteristic, complemented
38C2×#6772C2211yescharacteristic, complemented
39C2×#6771C2211yescharacteristic
40C2×#6769C2211yescharacteristic, complemented
41C2×#6768C2211yescharacteristic, 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×#213C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×D3×D8C2218yescomplemented
52C2×C5×D24C2211yescharacteristic, complemented
53C2×C5×D3×C8C2211yescharacteristic, complemented
54C2×C3×#687C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4057C2218yescomplemented
57C2×C3×#677C2211yescharacteristic, complemented
58C2×C3×#676C2211yescharacteristic, complemented
59#91499C2218yescomplemented
60#91496C2218yescomplemented
61#91494C2218yescomplemented
62#91490C2218yescomplemented
63#91481C2218yescomplemented
64D5×#213C2218yescomplemented
65C2×#6662C2211yescharacteristic, complemented
66C2×#6659C2211yescharacteristic, complemented
67C2×#6656C2211yescharacteristic, complemented
68C2×#6654C2211yescharacteristic, complemented
69C2×#6653C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6650C2211yescharacteristic, complemented
72C2×#6648C2211yescharacteristic, complemented
73C2×D5×C3⋊C8C2211yescharacteristic, complemented
74#91272C2218yescomplemented
75#91267C2218yescomplemented
76#91257C2218yescomplemented
77#91250C2218yescomplemented
78C2×#5774—51nomaximal, Hall
79C2×#4144—31no—
80C2×#4144—31no—
81C22×C5×D8—31no—
82C2×#4078—31no—
83C2×#4078—31no—
84#66091—316no—
85C2×#4058—31no—
86C2×#4058—31no—
87C2×#4057—31no—
88C2×#4057—31no—
89C2×#4057—31no—
90C2×#4057D311yescharacteristic, complemented
91C2×D5×D8—31no—
92C2×D5×D8—31no—
93C2×#4050—31no—
94C2×#4047—31no—
95C23×D15—21no—
96C23×C5×D3—21no—
97C23×C5×D3—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—
115C5×D3×D4—22no—
116C5×D3×D4—22no—
117C5×D3×D4C2314yescomplemented
118C5×D3×D4C2314yescomplemented
119C2×C5×D12C2311yescharacteristic
120C2×C5×D12C2311yescharacteristic
121C2×C4×C5×D3C2311yescharacteristic
122C2×C3×C22⋊D5—21no—
123C2×C3×C22⋊D5—21no—
124C22×C3×Dic5—21no—
125C3×#711—22no—
126C3×#711C2314yescomplemented
127C3×D4×D5—22no—
128C3×D4×D5C2314yescomplemented
129C2×C3×D20C2311yescharacteristic
130C2×C3×C4×D5C2311yescharacteristic
131C2×C3×Dic10C2311yescharacteristic
132#6790—28no—
133D3×C22⋊D5—28no—
134D3×C22⋊D5—28no—
135D5×#67—28no—
136C2×#1204D411yescharacteristic
137C2×#1203—21no—
138C2×#1203—21no—
139C2×#1203—21no—
140C2×#1203—28no—
141C2×#1203D411yescharacteristic
142C2×#1202D411yescharacteristic
143C2×#1201—21no—
144C2×#1201—21no—
145C2×#1201—21no—
146C2×#1201—28no—
147C2×#1201D411yescharacteristic
148C2×#1200—21no—
149#6782—28no—
150C2×D3×Dic5—21no—
151C2×D3×Dic5—21no—
152#6780—28no—
153C2×D5×Dic3—21no—
154#6777—22no—
155#6777C2314yescomplemented
156D5×D12—22no—
157D5×D12C2314yescomplemented
158#6772—22no—
159#6772C2314yescomplemented
160#6771D414yes—
161#6771C2314yes—
162#6769—22no—
163#6769C2314yescomplemented
164#6768—22no—
165#6768C2314yescomplemented
166#6765—22no—
167#6765C2314yescomplemented
168C3×C5×D8C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6716C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173#6706C2314yescomplemented
174#6705C2314yescomplemented
175C5×#213C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×D24C2314yescomplemented
179C5×D3×C8C2314yescomplemented
180C3×#687C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×#677C2314yescomplemented
184C3×#676C2314yescomplemented
185#6662C2314yescomplemented
186#6659C2314yescomplemented
187#6656C2314yescomplemented
188#6654C2314yescomplemented
189#6653C2314yescomplemented
190#6652C2314yescomplemented
191#6650C2314yescomplemented
192#6648C2314yescomplemented
193D5×C3⋊C8C2314yescomplemented
194C2×#1009—51no—
195C2×#1004—51no—
196C2×C3×AGL(1,ℤ/8)—51no—
197C2×#950—51no—
198C22×#213—51no—
199#5774—516no—
200C2×#916—51no—
201C2×#916—51no—
202C2×#914—51no—
203C2×#914—51no—
204C2×#911—51no—
205C2×#911—51no—
206C2×D3×D8—51no—
207C2×D3×D8D511yescharacteristic, complemented
208C2×#908—51no—
209C2×#907—51no—
210C22×C5×D4—31no—
211C22×C5×D4—31no—
212C22×C22⋊D5—61no—
213C22×C22⋊D5—61no—
214C22×C22⋊D5—61no—
215C22×C22⋊D5—61no—
216#4144—38no—
217#4144—38no—
218#4144—64no—
219#4144—64no—
220C2×#711—31no—
221C2×#711—31no—
222C2×#711—31no—
223C2×#711—61no—
224C2×#711—61no—
225C2×#711C2×D311yescharacteristic, complemented
226C2×D4×D5—31no—
227C2×D4×D5—31no—
228C2×D4×D5—31no—
229C2×D4×D5—61no—
230C2×D4×D5—61no—
231C2×D4×D5C2×D311yescharacteristic, complemented
232C2×#709—31no—
233C2×#709—31no—
234C2×#709—31no—
235C2×C5×D8—31no—
236C2×C5×D8—31no—
237C2×C5×D8—38no—
238C2×C5×D8—31no—
239C2×C5×D8C2×D311yescharacteristic, complemented
240C22×C5×C8—31no—
241C2×#687—31no—
242C2×#687—31no—
243C2×#687—31no—
244C2×#687C2×D311yescharacteristic, complemented
245#4078—38no—
246#4078—38no—
247C2×#686—31no—
248C2×#686—31no—
249C2×#686—31no—
250C2×#686C2×D311yescharacteristic, complemented
251C2×#681—31no—
252#4058—38no—
253#4058—38no—
254#4057—38no—
255#4057—38no—
256#4057—38no—
257#4057C2×D318yescomplemented
258D5×D8—38no—
259D5×D8—38no—
260C2×Dic20—31no—
261#4050—38no—
262C2×D40—31no—
263C2×#677—31no—
264C2×#677C2×D311yescharacteristic, complemented
265#4047—38no—
266C2×#676—31no—
267C2×#676C2×D311yescharacteristic, complemented
268C2×C8×D5—31no—
269C2×C8×D5—31no—
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—21no—
279C22×C5×D3—24no—
280C22×C5×D3—24no—
281C22×C5×D3—82no—
282C22×C5×D3—82no—
283C22×C5×D3C2×D411yescharacteristic
284C22×C3×D5—21no—
285C22×C3×D5—24no—
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×Dic3C2×D411yescharacteristic
311C5×D12—21no—
312C5×D12—21no—
313C5×D12C2412yes—
314C5×D12C2412yes—
315C4×C5×D3C2×D412yes—
316C4×C5×D3C2412yes—
317C3×C22⋊D5—24no—
318C3×C22⋊D5—24no—
319C2×C3×Dic5—21no—
320C2×C3×Dic5—24no—
321C2×C3×Dic5C2×D411yescharacteristic
322C3×D20—21no—
323C3×D20C2412yes—
324C3×C4×D5C2×D412yes—
325C3×C4×D5C2412yes—
326C3×Dic10—21no—
327C3×Dic10C2412yes—
328#1204C2×D414yes—
329#1203—24no—
330#1203—24no—
331#1203—24no—
332#1203C2×D414yes—
333#1202C2×D414yes—
334#1201—24no—
335#1201—24no—
336#1201—24no—
337#1201C2×D414yes—
338#1200—24no—
339D3×Dic5—24no—
340D3×Dic5—24no—
341D5×Dic3—24no—
342C3×C5×C8C2412yes—
343C3⋊#168C2412yes—
344C3×#168C2412yes—
345C5×C3⋊C8C2412yes—
346C2×C3×#41—51no—
347C22×C3×D4—51no—
348C22×#67—101no—
349C22×#67—101no—
350#1009—58no—
351#1009—104no—
352C2×#239—51no—
353C2×#239—51no—
354#1004—58no—
355#1004—104no—
356C2×#237—51no—
357C2×#237—51no—
358C2×#237—101no—
359C2×D3×D4—51no—
360C2×D3×D4—51no—
361C2×D3×D4—101no—
362C2×D3×D4—101no—
363C2×D3×D4—101no—
364C2×D3×D4C2×D511yescharacteristic, complemented
365C2×D3×D4C2×D511yescharacteristic, complemented
366C2×#235—51no—
367C2×#235—51no—
368C2×#235—101no—
369C22×D12—51no—
370C22×D12—101no—
371C3×AGL(1,ℤ/8)—58no—
372C2×C3×SD16—51no—
373C2×C3×SD16—51no—
374C2×C3×D8—51no—
375C2×C3×D8C2×D511yescharacteristic, complemented
376C2×C3×M16—51no—
377#950—58no—
378C2×#216—51no—
379C2×#215—51no—
380C2×#214—51no—
381C2×#213—51no—
382C2×#213—51no—
383C2×#213—58no—
384C2×#213—51no—
385C2×#213C2×D511yescharacteristic, complemented
386C2×#213C2×D511yescharacteristic, complemented
387C22×C3⋊C8—51no—
388#916—58no—
389#916—58no—
390#914—58no—
391#914—58no—
392#911—58no—
393#911—58no—
394D3×D8—58no—
395D3×D8C2×D518yescomplemented
396#908—58no—
397#907—58no—
398C2×D24—51no—
399C2×D24C2×D511yescharacteristic, complemented
400C2×#204—51no—
401C2×#204—51no—
402C2×ΓL(1,𝔽25)—51no—
403C2×ΓL(1,𝔽25)—51no—
404C2×D3×C8—51no—
405C2×D3×C8C2×D511yescharacteristic, complemented
406C24×C5—61no—
407C24×C5—61no—
408C23×D5—21no—
409C23×D5—61no—
410C23×D5—61no—
411C23×D5—61no—
412C2×C5×D4—34no—
413C2×C5×D4—34no—
414C2×C5×D4—31no—
415C2×C5×D4—31no—
416C2×C5×D4—62no—
417C2×C5×D4—62no—
418C2×C5×D4—61no—
419C2×C5×D4—61no—
420C2×C5×D4C22×D311yescharacteristic
421C2×C5×D4C22×D311yescharacteristic
422C22×C4×C5—31no—
423C2×C22⋊D5—21no—
424C2×C22⋊D5—21no—
425C2×C22⋊D5—31no—
426C2×C22⋊D5—31no—
427C2×C22⋊D5—68no—
428C2×C22⋊D5—61no—
429C2×C22⋊D5—61no—
430C2×C22⋊D5—61no—
431C2×C22⋊D5—61no—
432C2×C22⋊D5—68no—
433C2×C22⋊D5—68no—
434C2×C22⋊D5—68no—
435C2×C22⋊D5—61no—
436C2×C22⋊D5—61no—
437C2×C22⋊D5—61no—
438C2×C22⋊D5—61no—
439C22×Dic5—21no—
440C22×Dic5—61no—
441C22×Dic5—61no—
442C22×Dic5—61no—
443#711—22no—
444#711—34no—
445#711—34no—
446#711—34no—
447#711—62no—
448#711—68no—
449#711—68no—
450#711—62no—
451#711—62no—
452#711C22×D314yescomplemented
453D4×D5—22no—
454D4×D5—34no—
455D4×D5—34no—
456D4×D5—34no—
457D4×D5—62no—
458D4×D5—62no—
459D4×D5—68no—
460D4×D5—68no—
461D4×D5—62no—
462D4×D5C22×D314yescomplemented
463#709—34no—
464#709—34no—
465#709—34no—
466#709—34no—
467#709—62no—
468#709—62no—
469C2×D20—31no—
470C2×D20—31no—
471C2×D20C22×D311yescharacteristic
472C2×C4×D5—31no—
473C2×C4×D5—61no—
474C2×C4×D5—61no—
475C2×C4×D5C22×D311yescharacteristic
476C2×Dic10—31no—
477C2×Dic10—31no—
478C2×Dic10C22×D311yescharacteristic
479C5×D8—34no—
480C5×D8—34no—
481C5×D8—34no—
482C5×D8C22×D314yescomplemented
483C2×C5×C8—31no—
484C2×C5×C8—34no—
485C2×C5×C8C22×D311yescharacteristic
486#687—34no—
487#687—34no—
488#687—34no—
489#687C22×D314yescomplemented
490#686—34no—
491#686—34no—
492#686—34no—
493#686C22×D314yescomplemented
494#681—34no—
495C2×#168—31no—
496C2×#168C22×D311yescharacteristic
497Dic20—34no—
498D40—34no—
499#677—34no—
500#677C22×D314yescomplemented
501#676—34no—
502#676C22×D314yescomplemented
503C8×D5—34no—
504C8×D5—34no—
505C2×H(5,𝔽2)—151no—
506C2×H(5,𝔽2)—151no—
507#576—1516no—
508C2×AGL(1,ℤ/8)—51no—
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—31no—
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—22no—
534C2×C5×D3—42no—
535C2×C5×D3—42no—
536C2×C5×D3—84no—
537C2×C5×D3—84no—
538C2×C5×D3C22×D412yes—
539C2×C3×D5—22no—
540C2×C3×D5—22no—
541C2×C3×D5—42no—
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×Dic5—22no—
551C3×Dic5C22×D412yes—
552C5×Dic3C22×D412yes—
553C24×C3—101no—
554C23×D3—21no—
555C23×D3—21no—
556C23×D3—101no—
557C23×D3—101no—
558C23×D3—101no—
559C3×#41—54no—
560C3×#41—102no—
561C2×C3×Q8—51no—
562C2×C3×D4—54no—
563C2×C3×D4—51no—
564C2×C3×D4—102no—
565C2×C3×D4—101no—
566C2×C3×D4—101no—
567C2×C3×D4C22×D511yescharacteristic
568C2×C3×D4C22×D511yescharacteristic
569C22×C3×C4—51no—
570C22×C3×C4—101no—
571C2×#67—21no—
572C2×#67—21no—
573C2×#67—51no—
574C2×#67—51no—
575C2×#67—101no—
576C2×#67—101no—
577C2×#67—108no—
578C2×#67—108no—
579C2×#67—101no—
580C2×#67—101no—
581C2×#67—101no—
582C22×Dic3—101no—
583C22×Dic3—101no—
584#239—54no—
585#239—54no—
586#239—102no—
587#239—102no—
588#237—54no—
589#237—54no—
590#237—108no—
591#237—102no—
592#237—102no—
593D3×D4—22no—
594D3×D4—22no—
595D3×D4—54no—
596D3×D4—54no—
597D3×D4—102no—
598D3×D4—102no—
599D3×D4—108no—
600D3×D4—108no—
601D3×D4—108no—
602D3×D4C22×D514yescomplemented
603D3×D4C22×D514yescomplemented
604#235—54no—
605#235—54no—
606#235—54no—
607#235—108no—
608#235—102no—
609C2×D12—51no—
610C2×D12—51no—
611C2×D12—54no—
612C2×D12—102no—
613C2×D12—108no—
614C2×D12—101no—
615C2×D12—101no—
616C2×D12—101no—
617C2×D12C22×D511yescharacteristic
618C2×D12C22×D511yescharacteristic
619C2×C4×D3—51no—
620C2×C4×D3—101no—
621C2×C4×D3—101no—
622C2×C4×D3—101no—
623C2×C4×D3C22×D511yescharacteristic
624C2×Dic6—51no—
625C2×Dic6—51no—
626C3×SD16—54no—
627C3×SD16—54no—
628C3×D8—54no—
629C3×D8C22×D514yescomplemented
630C3×M16—54no—
631C2×C3×C8—51no—
632C2×C3×C8C22×D511yescharacteristic
633#216—54no—
634#215—54no—
635#214—54no—
636#213—54no—
637#213—54no—
638#213—54no—
639#213C22×D514yescomplemented
640#213C22×D514yescomplemented
641C2×C3⋊C8—51no—
642C2×C3⋊C8—54no—
643C2×C3⋊C8C22×D511yescharacteristic
644D24—54no—
645D24C22×D514yescomplemented
646#204—54no—
647#204—54no—
648ΓL(1,𝔽25)—54no—
649ΓL(1,𝔽25)—54no—
650D3×C8—54no—
651D3×C8C22×D514yescomplemented
652C23×C5—21no—
653C23×C5—21no—
654C23×C5—31no—
655C23×C5—64no—
656C23×C5—64no—
657C23×C5—61no—
658C23×C5—61no—
659C23×C5—242no—
660C23×C5—242no—
661C22×D5—21no—
662C22×D5—24no—
663C22×D5—31no—
664C22×D5—64no—
665C22×D5—64no—
666C22×D5—61no—
667C22×D5—64no—
668C22×D5—82no—
669C22×D5—242no—
670C22×D5—242no—
671C22×D5—242no—
672C22×D5D3×D411yescharacteristic
673C5×D4—21no—
674C5×D4—21no—
675C5×D4—32no—
676C5×D4—32no—
677C5×D4—64no—
678C5×D4—64no—
679C5×D4—61no—
680C5×D4—61no—
681C5×D4C23×D312yes—
682C5×D4C23×D312yes—
683C2×C4×C5—31no—
684C2×C4×C5—32no—
685C2×C4×C5—32no—
686C2×C4×C5C23×D311yescharacteristic
687C22⋊D5—24no—
688C22⋊D5—24no—
689C22⋊D5—34no—
690C22⋊D5—34no—
691C22⋊D5—64no—
692C22⋊D5—64no—
693C22⋊D5—64no—
694C22⋊D5—64no—
695C22⋊D5—64no—
696C22⋊D5—64no—
697C22⋊D5—64no—
698C22⋊D5—64no—
699C2×Dic5—21no—
700C2×Dic5—24no—
701C2×Dic5—31no—
702C2×Dic5—64no—
703C2×Dic5—64no—
704C2×Dic5—61no—
705C2×Dic5—64no—
706C2×Dic5D3×D411yescharacteristic
707D20—21no—
708D20—34no—
709D20—32no—
710D20—61no—
711D20C23×D312yes—
712C4×D5—32no—
713C4×D5—32no—
714C4×D5—64no—
715C4×D5—64no—
716C4×D5D3×D412yes—
717C4×D5C23×D312yes—
718Dic10—21no—
719Dic10—34no—
720Dic10—32no—
721Dic10—61no—
722Dic10C23×D312yes—
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—51no—
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—31no—
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)—58no—
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—51no—
763C2×SD16—51no—
764C2×SD16—151no—
765C2×SD16—151no—
766C2×SD16—151no—
767C2×SD16—151no—
768C2×D8—31no—
769C2×D8—31no—
770C2×D8—38no—
771C2×D8—31no—
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—51no—
782C2×M16—151no—
783C2×M16—151no—
784C22×C8—31no—
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—
795C5×D3—22no—
796C5×D3—42no—
797C5×D3—42no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—51no—
801C23×C3—104no—
802C23×C3—101no—
803C23×C3—402no—
804C22×D3—21no—
805C22×D3—21no—
806C22×D3—24no—
807C22×D3—24no—
808C22×D3—51no—
809C22×D3—82no—
810C22×D3—82no—
811C22×D3—104no—
812C22×D3—104no—
813C22×D3—104no—
814C22×D3—101no—
815C22×D3—402no—
816C22×D3—402no—
817C22×D3—402no—
818C22×D3D4×D511yescharacteristic
819C3×Q8—52no—
820C3×Q8—101no—
821C3×D4—21no—
822C3×D4—21no—
823C3×D4—52no—
824C3×D4—104no—
825C3×D4—104no—
826C3×D4—101no—
827C3×D4C23×D512yes—
828C3×D4C23×D512yes—
829C2×C3×C4—51no—
830C2×C3×C4—52no—
831C2×C3×C4—52no—
832C2×C3×C4—104no—
833C2×C3×C4—101no—
834C2×C3×C4C23×D511yescharacteristic
835#67—24no—
836#67—24no—
837#67—54no—
838#67—54no—
839#67—104no—
840#67—104no—
841#67—104no—
842#67—104no—
843#67—104no—
844C2×Dic3—51no—
845C2×Dic3—104no—
846C2×Dic3—101no—
847C2×Dic3—104no—
848C2×Dic3D4×D511yescharacteristic
849D12—21no—
850D12—21no—
851D12—54no—
852D12—52no—
853D12—104no—
854D12—104no—
855D12—104no—
856D12—101no—
857D12C23×D512yes—
858D12C23×D512yes—
859C4×D3—52no—
860C4×D3—52no—
861C4×D3—104no—
862C4×D3—104no—
863C4×D3—104no—
864C4×D3D4×D512yes—
865C4×D3C23×D512yes—
866Dic6—54no—
867Dic6—52no—
868Dic6—101no—
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—62no—
881C22×C5—122no—
882C22×C5—122no—
883C22×C5—244no—
884C22×C5—244no—
885C22×C5C2×D3×D411yescharacteristic
886C2×D5—22no—
887C2×D5—22no—
888C2×D5—32no—
889C2×D5—42no—
890C2×D5—62no—
891C2×D5—62no—
892C2×D5—84no—
893C2×D5—122no—
894C2×D5—244no—
895C2×D5—244no—
896C2×D5—244no—
897C2×D5C2×D3×D412yes—
898C4×C5—32no—
899C4×C5C2×D3×D411yescharacteristic
900C4×C5C24×D311yescharacteristic
901Dic5—22no—
902Dic5—32no—
903Dic5—62no—
904Dic5C2×D3×D412yes—
905C24—61no—
906C24—61no—
907C24—101no—
908C24—301no—
909C24—301no—
910C24—301no—
911#41—54no—
912#41—102no—
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—51no—
928C2×Q8—151no—
929C2×Q8—151no—
930C2×D4—34no—
931C2×D4—34no—
932C2×D4—31no—
933C2×D4—31no—
934C2×D4—54no—
935C2×D4—51no—
936C2×D4—62no—
937C2×D4—62no—
938C2×D4—61no—
939C2×D4—61no—
940C2×D4—102no—
941C2×D4—101no—
942C2×D4—101no—
943C2×D4—151no—
944C2×D4—154no—
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—101no—
972C22×C4—151no—
973C22×C4—301no—
974C22×C4—301no—
975C22×C4—301no—
976C22×C4—301no—
977C22×C4—301no—
978Q16—154no—
979SD16—54no—
980SD16—54no—
981SD16—154no—
982SD16—154no—
983SD16—154no—
984SD16—154no—
985D8—34no—
986D8—34no—
987D8—34no—
988D8—54no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8C2×D3×D514yescomplemented
994M16—54no—
995M16—154no—
996M16—154no—
997C2×C8—31no—
998C2×C8—34no—
999C2×C8—51no—
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—202no—
1013C22×C3—404no—
1014C22×C3C2×D4×D511yescharacteristic
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—52no—
1021C2×D3—84no—
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×C4—102no—
1032C3×C4C2×D4×D511yescharacteristic
1033C3×C4C24×D511yescharacteristic
1034Dic3—52no—
1035Dic3—102no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—42no—
1039C2×C5—62no—
1040C2×C5—122no—
1041C2×C5—122no—
1042C2×C5#577412yescomplemented
1043C2×C5C22×D3×D411yescharacteristic
1044D5—22no—
1045D5—42no—
1046D5—62no—
1047D5—122no—
1048C23—21no—
1049C23—21no—
1050C23—31no—
1051C23—51no—
1052C23—64no—
1053C23—64no—
1054C23—61no—
1055C23—61no—
1056C23—104no—
1057C23—101no—
1058C23—151no—
1059C23—242no—
1060C23—242no—
1061C23—304no—
1062C23—304no—
1063C23—304no—
1064C23—301no—
1065C23—402no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—52no—
1070Q8—101no—
1071Q8—154no—
1072Q8—152no—
1073Q8—301no—
1074D4—21no—
1075D4—21no—
1076D4—32no—
1077D4—32no—
1078D4—52no—
1079D4—64no—
1080D4—64no—
1081D4—61no—
1082D4—61no—
1083D4—104no—
1084D4—104no—
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—104no—
1108C2×C4—101no—
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#6609112yescomplemented
1128C2×C3C22×D4×D511yescharacteristic
1129D3—22no—
1130D3—42no—
1131D3—42no—
1132D3—102no—
1133D3—202no—
1134C5C2×#577411yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—22no—
1137C22—32no—
1138C22—42no—
1139C22—42no—
1140C22—52no—
1141C22—62no—
1142C22—62no—
1143C22—62no—
1144C22—102no—
1145C22—102no—
1146C22—122no—
1147C22—122no—
1148C22—152no—
1149C22—202no—
1150C22—244no—
1151C22—244no—
1152C22—302no—
1153C22—302no—
1154C22—404no—
1155C22—602no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—32no—
1161C4—52no—
1162C4—102no—
1163C4—152no—
1164C4—302no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6609111yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—42no—
1170C2—62no—
1171C2—102no—
1172C2—122no—
1173C2—122no—
1174C2—202no—
1175C2—302no—
1176C2—602no—
1177C2#1175405612yesdirect 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×#92027C2semidirect
2. C2×#92025C2semidirect
3. C2×#91800C2semidirect
4. C2×C5×D3×D8C2semidirect
5. C2×C3×#4057C2semidirect
6. C2×#91499C2semidirect
7. C2×#91496C2semidirect
8. C2×#91494C2semidirect
9. C2×#91490C2semidirect
10. C2×#91481C2semidirect
11. C2×D5×#213C2semidirect
12. #11754056C2direct (N × H)
13. C2×#91272C2semidirect
14. C2×#91267C2semidirect
15. C2×#91257C2semidirect
16. C2×#91250C2semidirect
18. C2×#6819C22semidirect
19. C2×D4×D15C22semidirect
20. C2×C5×D3×D4C22semidirect
21. C2×C5×D3×D4C22semidirect
22. C2×C3×#711C22semidirect
23. C2×C3×D4×D5C22semidirect
33. #92027C22semidirect
35. #92025C22semidirect
36. C2×#6777C22semidirect
37. C2×D5×D12C22semidirect
38. C2×#6772C22semidirect
40. C2×#6769C22semidirect
41. C2×#6768C22semidirect
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×#213C22semidirect
50. C2×C5×#213C22semidirect
51. C5×D3×D8C22semidirect
52. C2×C5×D24C22semidirect
53. C2×C5×D3×C8C22semidirect
54. C2×C3×#687C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4057C22semidirect
57. C2×C3×#677C22semidirect
58. C2×C3×#676C22semidirect
59. #91499C22semidirect
60. #91496C22semidirect
61. #91494C22semidirect
62. #91490C22semidirect
63. #91481C22semidirect
64. D5×#213C22semidirect
65. C2×#6662C22semidirect
66. C2×#6659C22semidirect
67. C2×#6656C22semidirect
68. C2×#6654C22semidirect
69. C2×#6653C22semidirect
70. C2×#6652C22semidirect
71. C2×#6650C22semidirect
72. C2×#6648C22semidirect
73. C2×D5×C3⋊C8C22semidirect
74. #91272C22semidirect
75. #91267C22semidirect
76. #91257C22semidirect
77. #91250C22semidirect
90. C2×#4057D3semidirect
107. #6819C23semidirect
109. D4×D15C23semidirect
117. C5×D3×D4C23semidirect
118. C5×D3×D4C23semidirect
126. C3×#711C23semidirect
128. C3×D4×D5C23semidirect
155. #6777C23semidirect
157. D5×D12C23semidirect
159. #6772C23semidirect
163. #6769C23semidirect
165. #6768C23semidirect
167. #6765C23semidirect
168. C3×C5×D8C23semidirect
170. #6716C23semidirect
171. #6715C23semidirect
173. #6706C23semidirect
174. #6705C23semidirect
175. C5×#213C23semidirect
176. C5×#213C23semidirect
178. C5×D24C23semidirect
179. C5×D3×C8C23semidirect
180. C3×#687C23semidirect
181. C3×#686C23semidirect
183. C3×#677C23semidirect
184. C3×#676C23semidirect
185. #6662C23semidirect
186. #6659C23semidirect
187. #6656C23semidirect
188. #6654C23semidirect
189. #6653C23semidirect
190. #6652C23semidirect
191. #6650C23semidirect
192. #6648C23semidirect
193. D5×C3⋊C8C23semidirect
207. C2×D3×D8D5semidirect
225. C2×#711C2×D3semidirect
231. C2×D4×D5C2×D3semidirect
239. C2×C5×D8C2×D3semidirect
244. C2×#687C2×D3semidirect
250. C2×#686C2×D3semidirect
257. #4057C2×D3semidirect
264. C2×#677C2×D3semidirect
267. C2×#676C2×D3semidirect
364. C2×D3×D4C2×D5semidirect
365. C2×D3×D4C2×D5semidirect
375. C2×C3×D8C2×D5semidirect
385. C2×#213C2×D5semidirect
386. C2×#213C2×D5semidirect
395. D3×D8C2×D5semidirect
399. C2×D24C2×D5semidirect
405. C2×D3×C8C2×D5semidirect
452. #711C22×D3semidirect
462. D4×D5C22×D3semidirect
482. C5×D8C22×D3semidirect
489. #687C22×D3semidirect
493. #686C22×D3semidirect
500. #677C22×D3semidirect
502. #676C22×D3semidirect
602. D3×D4C22×D5semidirect
603. D3×D4C22×D5semidirect
629. C3×D8C22×D5semidirect
639. #213C22×D5semidirect
640. #213C22×D5semidirect
645. D24C22×D5semidirect
651. D3×C8C22×D5semidirect
779. C2×D8D3×D5semidirect
789. C2×C3×C5#576semidirect
993. D8C2×D3×D5semidirect
1004. C3×C5C2×#576semidirect
1042. C2×C5#5774semidirect
1127. C2×C3#66091semidirect
1134. C5C2×#5774semidirect
1167. C3C2×#66091semidirect
1177. C2#11754056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920272
C2×#920252
C2×#918002
C2×C5×D3×D82
C2×C3×#40572
C2×#914992
C2×#914962
C2×#914942
C2×#914902
C2×#914812
C2×D5×#2132
#117540562
C2×#912722
C2×#912672
C2×#912572
C2×#912502
C2×#660913
C2×#57745