Finite Group Databasebeta

← C2×#11754059 #14509986

Subgroups — C2×#11754059 #14509986

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×#92026C211yesmaximal, characteristic, complemented
3C2×D8×D15C211yesmaximal, characteristic, complemented
4C2×C5×#911C211yesmaximal, characteristic, complemented
5C2×C3×#4057C211yesmaximal, characteristic, complemented
6C2×#91500C211yesmaximal, characteristic, complemented
7C2×#91498C211yesmaximal, characteristic, complemented
8C2×#91495C211yesmaximal, characteristic, complemented
9C2×#91492C211yesmaximal, characteristic, complemented
10C2×D3×#686C211yesmaximal, characteristic, complemented
11C2×D5×#213C211yesmaximal, characteristic, complemented
12#11754059C2116yesmaximal, direct product factor
13C2×#91276C211yesmaximal, characteristic, complemented
14C2×#91268C211yesmaximal, characteristic, complemented
15C2×#91253C211yesmaximal, characteristic, complemented
16C2×#91249C211yesmaximal, characteristic, complemented
17C2×#66108—31nomaximal, Hall
18C2×D4×D15C2211yescharacteristic, complemented
19C2×D4×D15C2211yescharacteristic, complemented
20C2×C5×#237C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic, complemented
22C2×C3×#711C2211yescharacteristic, complemented
23C2×C3×D4×D5C2211yescharacteristic, complemented
24C2×#6790—21no—
25C2×#6790—21no—
26C2×D3×C22⋊D5—21no—
27C2×D5×#67—21no—
28C22×#1203—21no—
29C22×#1202—21no—
30C2×#6782—21no—
31C2×#6779—21no—
32#92027—24no—
33#92027C2218yescomplemented
34#92026—24no—
35#92026C2218yescomplemented
36C2×D3×D20C2211yescharacteristic, complemented
37C2×D5×D12C2211yescharacteristic, complemented
38C2×#6773C2211yescharacteristic, complemented
39C2×#6771C2211yescharacteristic
40C2×#6769C2211yescharacteristic, complemented
41C2×#6768C2211yescharacteristic, complemented
42C2×#6766C2211yescharacteristic, complemented
43C2×C3×C5×D8C2211yescharacteristic, complemented
44C2×#6715C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46D8×D15C2218yescomplemented
47C2×D120C2211yescharacteristic, complemented
48C2×C8×D15C2211yescharacteristic, complemented
49C2×C5×#214C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#911C2218yescomplemented
52C2×C5×#204C2211yescharacteristic, complemented
53C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
54C2×C3×#687C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4057C2218yescomplemented
57C2×C3×#677C2211yescharacteristic, complemented
58C2×C3×#676C2211yescharacteristic, complemented
59#91500C2218yescomplemented
60#91498C2218yescomplemented
61#91495C2218yescomplemented
62#91492C2218yescomplemented
63D3×#686C2218yescomplemented
64D5×#213C2218yescomplemented
65C2×#6661C2211yescharacteristic, complemented
66C2×#6660C2211yescharacteristic, complemented
67C2×#6658C2211yescharacteristic, complemented
68C2×#6654C2211yescharacteristic, complemented
69C2×#6653C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6651C2211yescharacteristic, complemented
72C2×D3×#168C2211yescharacteristic, complemented
73C2×D5×C3⋊C8C2211yescharacteristic, complemented
74#91276C2218yescomplemented
75#91268C2218yescomplemented
76#91253C2218yescomplemented
77#91249C2218yescomplemented
78C2×#5774—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×#4057D311yescharacteristic, complemented
91C2×D5×D8—31no—
92C2×D5×D8—31no—
93C2×#4054—31no—
94C2×#4053—31no—
95C23×D15—21no—
96C23×D15—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—
105D4×D15—22no—
106D4×D15—22no—
107D4×D15C2314yescomplemented
108D4×D15C2314yescomplemented
109C2×D60C2311yescharacteristic
110C2×D60C2311yescharacteristic
111C2×C4×D15C2311yescharacteristic
112C2×C5×#67—21no—
113C2×C5×#67—21no—
114C22×C5×Dic3—21no—
115C5×#237—22no—
116C5×#237C2314yescomplemented
117C5×D3×D4—22no—
118C5×D3×D4C2314yescomplemented
119C2×C5×D12C2311yescharacteristic
120C2×C4×C5×D3C2311yescharacteristic
121C2×C5×Dic6C2311yescharacteristic
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—
133#6790—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×#1202—21no—
143C2×#1202—21no—
144C2×#1202—21no—
145C2×#1202—28no—
146C2×#1202D411yescharacteristic
147C2×#1201D411yescharacteristic
148C2×#1200—21no—
149C2×#1200—21no—
150#6782—28no—
151C2×D3×Dic5—21no—
152#6779—28no—
153C2×D5×Dic3—21no—
154D3×D20—22no—
155D3×D20C2314yescomplemented
156D5×D12—22no—
157D5×D12C2314yescomplemented
158#6773—22no—
159#6773C2314yescomplemented
160#6771D414yes—
161#6771C2314yes—
162#6769—22no—
163#6769C2314yescomplemented
164#6768—22no—
165#6768C2314yescomplemented
166#6766—22no—
167#6766C2314yescomplemented
168C3×C5×D8C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6715C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173D120C2314yescomplemented
174C8×D15C2314yescomplemented
175C5×#214C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×#204C2314yescomplemented
179C5×ΓL(1,𝔽25)C2314yescomplemented
180C3×#687C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×#677C2314yescomplemented
184C3×#676C2314yescomplemented
185#6661C2314yescomplemented
186#6660C2314yescomplemented
187#6658C2314yescomplemented
188#6654C2314yescomplemented
189#6653C2314yescomplemented
190#6652C2314yescomplemented
191#6651C2314yescomplemented
192D3×#168C2314yescomplemented
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×#911D511yescharacteristic, complemented
206C2×D3×D8—51no—
207C2×D3×D8—51no—
208C2×#908—51no—
209C2×#907—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—61no—
222C2×#711C2×D311yescharacteristic, complemented
223C2×D4×D5—31no—
224C2×D4×D5—31no—
225C2×D4×D5—31no—
226C2×D4×D5—61no—
227C2×D4×D5—61no—
228C2×D4×D5—61no—
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×#687C2×D311yescharacteristic, complemented
245C2×#686—31no—
246C2×#686—31no—
247C2×#686—31no—
248C2×#686—38no—
249C2×#686—31no—
250C2×#686C2×D311yescharacteristic, complemented
251C22×#168—31no—
252#4062—38no—
253#4062—38no—
254#4060—38no—
255#4060—38no—
256#4057—38no—
257#4057C2×D318yescomplemented
258D5×D8—38no—
259D5×D8—38no—
260#4054—38no—
261#4053—38no—
262C2×D40—31no—
263C2×D40—31no—
264C2×#677—31no—
265C2×#677C2×D311yescharacteristic, complemented
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—21no—
275C22×D15—24no—
276C22×D15—24no—
277C22×D15—82no—
278C22×D15—82no—
279C22×D15C2×D411yescharacteristic
280C22×C5×D3—21no—
281C22×C5×D3—24no—
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×Dic15C2×D411yescharacteristic
300D60—21no—
301D60—21no—
302D60C2412yes—
303D60C2412yes—
304C4×D15C2×D412yes—
305C4×D15C2412yes—
306C5×#67—24no—
307C5×#67—24no—
308C2×C5×Dic3—21no—
309C2×C5×Dic3—24no—
310C2×C5×Dic3C2×D411yescharacteristic
311C5×D12—21no—
312C5×D12C2412yes—
313C4×C5×D3C2×D412yes—
314C4×C5×D3C2412yes—
315C5×Dic6—21no—
316C5×Dic6C2412yes—
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#1202—24no—
334#1202—24no—
335#1202—24no—
336#1202C2×D414yes—
337#1201C2×D414yes—
338#1200—24no—
339#1200—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—101no—
358C2×#237C2×D511yescharacteristic, complemented
359C2×D3×D4—51no—
360C2×D3×D4—51no—
361C2×D3×D4—51no—
362C2×D3×D4—101no—
363C2×D3×D4—101no—
364C2×D3×D4—101no—
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×#214C2×D511yescharacteristic, complemented
381C2×#213—51no—
382C2×#213—51no—
383C2×#213—51no—
384C2×#213—58no—
385C2×#213—51no—
386C2×#213C2×D511yescharacteristic, complemented
387C22×C3⋊C8—51no—
388#916—58no—
389#916—58no—
390#914—58no—
391#914—58no—
392#911—58no—
393#911C2×D518yescomplemented
394D3×D8—58no—
395D3×D8—58no—
396#908—58no—
397#907—58no—
398C2×D24—51no—
399C2×D24—51no—
400C2×#204—51no—
401C2×#204C2×D511yescharacteristic, complemented
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—61no—
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—68no—
429C2×C22⋊D5—61no—
430C2×C22⋊D5—61no—
431C2×C22⋊D5—61no—
432C2×C22⋊D5—61no—
433C2×C22⋊D5—68no—
434C2×C22⋊D5—61no—
435C22×Dic5—21no—
436C22×Dic5—61no—
437#713—34no—
438#713—34no—
439#713—62no—
440#713—62no—
441#711—22no—
442#711—34no—
443#711—62no—
444#711—68no—
445#711C22×D314yescomplemented
446D4×D5—22no—
447D4×D5—34no—
448D4×D5—34no—
449D4×D5—34no—
450D4×D5—62no—
451D4×D5—62no—
452D4×D5—68no—
453D4×D5—68no—
454D4×D5—68no—
455D4×D5—62no—
456D4×D5C22×D314yescomplemented
457#709—34no—
458#709—34no—
459#709—34no—
460#709—62no—
461#709—68no—
462C2×D20—31no—
463C2×D20—31no—
464C2×D20—31no—
465C2×D20—34no—
466C2×D20—62no—
467C2×D20—68no—
468C2×D20—61no—
469C2×D20—61no—
470C2×D20—61no—
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×Dic10C22×D311yescharacteristic
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#687C22×D314yescomplemented
489#686—34no—
490#686—34no—
491#686—34no—
492#686—34no—
493#686C22×D314yescomplemented
494C2×#168—31no—
495C2×#168—34no—
496C2×#168C22×D311yescharacteristic
497D40—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)—31no—
509C2×AGL(1,ℤ/8)—51no—
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—151no—
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—22no—
529C2×D15—42no—
530C2×D15—42no—
531C2×D15—84no—
532C2×D15—84no—
533C2×D15C22×D412yes—
534C2×C5×D3—22no—
535C2×C5×D3—22no—
536C2×C5×D3—42no—
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
548Dic15C22×D412yes—
549C3×Dic5—22no—
550C3×Dic5C22×D412yes—
551C5×Dic3—22no—
552C5×Dic3C22×D412yes—
553C24×C3—101no—
554C23×D3—21no—
555C23×D3—101no—
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—108no—
576C2×#67—101no—
577C2×#67—101no—
578C2×#67—101no—
579C2×#67—101no—
580C2×#67—108no—
581C2×#67—101no—
582C22×Dic3—21no—
583C22×Dic3—101no—
584#239—54no—
585#239—54no—
586#239—102no—
587#239—102no—
588#237—22no—
589#237—54no—
590#237—102no—
591#237—108no—
592#237C22×D514yescomplemented
593D3×D4—22no—
594D3×D4—54no—
595D3×D4—54no—
596D3×D4—54no—
597D3×D4—102no—
598D3×D4—102no—
599D3×D4—108no—
600D3×D4—108no—
601D3×D4—108no—
602D3×D4—102no—
603D3×D4C22×D514yescomplemented
604#235—54no—
605#235—54no—
606#235—54no—
607#235—102no—
608#235—108no—
609C2×D12—51no—
610C2×D12—51no—
611C2×D12—51no—
612C2×D12—54no—
613C2×D12—102no—
614C2×D12—108no—
615C2×D12—101no—
616C2×D12—101no—
617C2×D12—101no—
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×Dic6C22×D511yescharacteristic
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#214C22×D514yescomplemented
636#213—54no—
637#213—54no—
638#213—54no—
639#213—54no—
640#213C22×D514yescomplemented
641C2×C3⋊C8—51no—
642C2×C3⋊C8—54no—
643C2×C3⋊C8C22×D511yescharacteristic
644D24—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—24no—
660C22×D5—31no—
661C22×D5—64no—
662C22×D5—64no—
663C22×D5—64no—
664C22×D5—61no—
665C22×D5—61no—
666C22×D5—64no—
667C22×D5—82no—
668C22×D5—242no—
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—21no—
699C2×Dic5—24no—
700C2×Dic5—31no—
701C2×Dic5—64no—
702C2×Dic5D3×D411yescharacteristic
703D20—21no—
704D20—34no—
705D20—32no—
706D20—32no—
707D20—64no—
708D20—64no—
709D20—64no—
710D20—61no—
711D20—61no—
712D20C23×D312yes—
713C4×D5—32no—
714C4×D5—32no—
715C4×D5—64no—
716C4×D5—64no—
717C4×D5—64no—
718C4×D5D3×D412yes—
719C4×D5C23×D312yes—
720Dic10—21no—
721Dic10—34no—
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—31no—
732C2×#41—51no—
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—151no—
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)—58no—
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—51no—
765C2×SD16—51no—
766C2×SD16—151no—
767C2×SD16—151no—
768C2×D8—31no—
769C2×D8—51no—
770C2×D8—151no—
771C2×D8—151no—
772C2×D8—158no—
773C2×D8—158no—
774C2×D8—151no—
775C2×D8—151no—
776C2×D8—151no—
777C2×D8—158no—
778C2×D8—151no—
779C2×D8D3×D511yescharacteristic, complemented
780#131—158no—
781C2×M16—31no—
782C2×M16—51no—
783C2×M16—151no—
784C22×C8—151no—
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—
793D15—42no—
794C3×D5—22no—
795C3×D5—42no—
796C5×D3—22no—
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—24no—
806C22×D3—51no—
807C22×D3—82no—
808C22×D3—104no—
809C22×D3—104no—
810C22×D3—104no—
811C22×D3—101no—
812C22×D3—101no—
813C22×D3—104no—
814C22×D3—402no—
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—21no—
845C2×Dic3—24no—
846C2×Dic3—51no—
847C2×Dic3—104no—
848C2×Dic3D4×D511yescharacteristic
849D12—21no—
850D12—54no—
851D12—52no—
852D12—52no—
853D12—104no—
854D12—104no—
855D12—104no—
856D12—101no—
857D12—101no—
858D12C23×D512yes—
859C4×D3—52no—
860C4×D3—52no—
861C4×D3—104no—
862C4×D3—104no—
863C4×D3—104no—
864C4×D3D4×D512yes—
865C4×D3C23×D512yes—
866Dic6—21no—
867Dic6—54no—
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—32no—
886C2×D5—42no—
887C2×D5—62no—
888C2×D5—62no—
889C2×D5—62no—
890C2×D5—84no—
891C2×D5—122no—
892C2×D5—122no—
893C2×D5—244no—
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—22no—
903Dic5—32no—
904Dic5C2×D3×D412yes—
905C24—61no—
906C24—101no—
907C24—301no—
908C24—301no—
909C24—301no—
910C24—301no—
911#41—34no—
912#41—54no—
913#41—62no—
914#41—102no—
915#41—154no—
916#41—154no—
917#41—154no—
918#41—154no—
919#41—154no—
920#41—154no—
921#41—302no—
922#41—302no—
923#41—308no—
924#41—308no—
925#41—302no—
926#41—302no—
927C2×Q8—31no—
928C2×Q8—51no—
929C2×Q8—151no—
930C2×D4—34no—
931C2×D4—31no—
932C2×D4—54no—
933C2×D4—51no—
934C2×D4—62no—
935C2×D4—61no—
936C2×D4—61no—
937C2×D4—102no—
938C2×D4—101no—
939C2×D4—101no—
940C2×D4—154no—
941C2×D4—151no—
942C2×D4—154no—
943C2×D4—151no—
944C2×D4—151no—
945C2×D4—154no—
946C2×D4—154no—
947C2×D4—151no—
948C2×D4—151no—
949C2×D4—302no—
950C2×D4—301no—
951C2×D4—302no—
952C2×D4—301no—
953C2×D4—308no—
954C2×D4—301no—
955C2×D4—301no—
956C2×D4—308no—
957C2×D4—301no—
958C2×D4—301no—
959C2×D4—302no—
960C2×D4—302no—
961C2×D4—301no—
962C2×D4—301no—
963C2×D4—308no—
964C2×D4—308no—
965C2×D4—308no—
966C2×D4—308no—
967C2×D4C2×D3×D511yescharacteristic
968C2×D4C2×D3×D511yescharacteristic
969C22×C4—31no—
970C22×C4—51no—
971C22×C4—61no—
972C22×C4—101no—
973C22×C4—151no—
974C22×C4—301no—
975C22×C4—301no—
976C22×C4—301no—
977C22×C4—301no—
978Q16—154no—
979SD16—34no—
980SD16—34no—
981SD16—54no—
982SD16—54no—
983SD16—154no—
984SD16—154no—
985D8—34no—
986D8—54no—
987D8—154no—
988D8—154no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8C2×D3×D514yescomplemented
994M16—34no—
995M16—54no—
996M16—154no—
997C2×C8—31no—
998C2×C8—51no—
999C2×C8—154no—
1000C2×C8—154no—
1001C2×C8—151no—
1002C2×C8—154no—
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—42no—
1018C2×D3—52no—
1019C2×D3—84no—
1020C2×D3—102no—
1021C2×D3—102no—
1022C2×D3—102no—
1023C2×D3—202no—
1024C2×D3—202no—
1025C2×D3—404no—
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—22no—
1035Dic3—52no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—42no—
1039C2×C5—62no—
1040C2×C5—122no—
1041C2×C5#577412yescomplemented
1042C2×C5C22×D3×D411yescharacteristic
1043D5—22no—
1044D5—42no—
1045D5—62no—
1046D5—122no—
1047D5—122no—
1048C23—21no—
1049C23—21no—
1050C23—31no—
1051C23—51no—
1052C23—64no—
1053C23—61no—
1054C23—104no—
1055C23—101no—
1056C23—151no—
1057C23—242no—
1058C23—304no—
1059C23—304no—
1060C23—304no—
1061C23—304no—
1062C23—301no—
1063C23—301no—
1064C23—402no—
1065C23—1202no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—32no—
1070Q8—52no—
1071Q8—61no—
1072Q8—101no—
1073Q8—154no—
1074D4—21no—
1075D4—21no—
1076D4—32no—
1077D4—52no—
1078D4—64no—
1079D4—64no—
1080D4—61no—
1081D4—104no—
1082D4—104no—
1083D4—101no—
1084D4—154no—
1085D4—154no—
1086D4—154no—
1087D4—152no—
1088D4—152no—
1089D4—304no—
1090D4—304no—
1091D4—304no—
1092D4—304no—
1093D4—304no—
1094D4—304no—
1095D4—304no—
1096D4—304no—
1097D4—301no—
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—104no—
1110C2×C4—101no—
1111C2×C4—151no—
1112C2×C4—152no—
1113C2×C4—152no—
1114C2×C4—304no—
1115C2×C4—304no—
1116C2×C4—304no—
1117C2×C4—304no—
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#6610812yescomplemented
1128C2×C3C22×D4×D511yescharacteristic
1129D3—22no—
1130D3—42no—
1131D3—102no—
1132D3—202no—
1133D3—202no—
1134C5C2×#577411yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—22no—
1137C22—32no—
1138C22—42no—
1139C22—42no—
1140C22—52no—
1141C22—62no—
1142C22—62no—
1143C22—102no—
1144C22—102no—
1145C22—122no—
1146C22—152no—
1147C22—202no—
1148C22—244no—
1149C22—302no—
1150C22—302no—
1151C22—302no—
1152C22—404no—
1153C22—602no—
1154C22—602no—
1155C22—1204no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—32no—
1161C4—52no—
1162C4—62no—
1163C4—102no—
1164C4—152no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6610811yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—42no—
1170C2—62no—
1171C2—102no—
1172C2—122no—
1173C2—202no—
1174C2—302no—
1175C2—602no—
1176C2—602no—
1177C2#1175405912yesdirect 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×#92026C2semidirect
3. C2×D8×D15C2semidirect
4. C2×C5×#911C2semidirect
5. C2×C3×#4057C2semidirect
6. C2×#91500C2semidirect
7. C2×#91498C2semidirect
8. C2×#91495C2semidirect
9. C2×#91492C2semidirect
10. C2×D3×#686C2semidirect
11. C2×D5×#213C2semidirect
12. #11754059C2direct (N × H)
13. C2×#91276C2semidirect
14. C2×#91268C2semidirect
15. C2×#91253C2semidirect
16. C2×#91249C2semidirect
18. C2×D4×D15C22semidirect
19. C2×D4×D15C22semidirect
20. C2×C5×#237C22semidirect
21. C2×C5×D3×D4C22semidirect
22. C2×C3×#711C22semidirect
23. C2×C3×D4×D5C22semidirect
33. #92027C22semidirect
35. #92026C22semidirect
36. C2×D3×D20C22semidirect
37. C2×D5×D12C22semidirect
38. C2×#6773C22semidirect
40. C2×#6769C22semidirect
41. C2×#6768C22semidirect
42. C2×#6766C22semidirect
43. C2×C3×C5×D8C22semidirect
44. C2×#6715C22semidirect
45. C2×#6715C22semidirect
46. D8×D15C22semidirect
47. C2×D120C22semidirect
48. C2×C8×D15C22semidirect
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×#687C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4057C22semidirect
57. C2×C3×#677C22semidirect
58. C2×C3×#676C22semidirect
59. #91500C22semidirect
60. #91498C22semidirect
61. #91495C22semidirect
62. #91492C22semidirect
63. D3×#686C22semidirect
64. D5×#213C22semidirect
65. C2×#6661C22semidirect
66. C2×#6660C22semidirect
67. C2×#6658C22semidirect
68. C2×#6654C22semidirect
69. C2×#6653C22semidirect
70. C2×#6652C22semidirect
71. C2×#6651C22semidirect
72. C2×D3×#168C22semidirect
73. C2×D5×C3⋊C8C22semidirect
74. #91276C22semidirect
75. #91268C22semidirect
76. #91253C22semidirect
77. #91249C22semidirect
90. C2×#4057D3semidirect
107. D4×D15C23semidirect
108. D4×D15C23semidirect
116. C5×#237C23semidirect
118. C5×D3×D4C23semidirect
126. C3×#711C23semidirect
128. C3×D4×D5C23semidirect
155. D3×D20C23semidirect
157. D5×D12C23semidirect
159. #6773C23semidirect
163. #6769C23semidirect
165. #6768C23semidirect
167. #6766C23semidirect
168. C3×C5×D8C23semidirect
170. #6715C23semidirect
171. #6715C23semidirect
173. D120C23semidirect
174. C8×D15C23semidirect
175. C5×#214C23semidirect
176. C5×#213C23semidirect
178. C5×#204C23semidirect
179. C5×ΓL(1,𝔽25)C23semidirect
180. C3×#687C23semidirect
181. C3×#686C23semidirect
183. C3×#677C23semidirect
184. C3×#676C23semidirect
185. #6661C23semidirect
186. #6660C23semidirect
187. #6658C23semidirect
188. #6654C23semidirect
189. #6653C23semidirect
190. #6652C23semidirect
191. #6651C23semidirect
192. D3×#168C23semidirect
193. D5×C3⋊C8C23semidirect
205. C2×#911D5semidirect
222. C2×#711C2×D3semidirect
229. C2×D4×D5C2×D3semidirect
239. C2×C5×D8C2×D3semidirect
244. C2×#687C2×D3semidirect
250. C2×#686C2×D3semidirect
257. #4057C2×D3semidirect
265. C2×#677C2×D3semidirect
267. C2×#676C2×D3semidirect
358. C2×#237C2×D5semidirect
365. C2×D3×D4C2×D5semidirect
375. C2×C3×D8C2×D5semidirect
380. C2×#214C2×D5semidirect
386. C2×#213C2×D5semidirect
393. #911C2×D5semidirect
401. C2×#204C2×D5semidirect
403. C2×ΓL(1,𝔽25)C2×D5semidirect
445. #711C22×D3semidirect
456. D4×D5C22×D3semidirect
482. C5×D8C22×D3semidirect
488. #687C22×D3semidirect
493. #686C22×D3semidirect
500. #677C22×D3semidirect
502. #676C22×D3semidirect
592. #237C22×D5semidirect
603. D3×D4C22×D5semidirect
629. C3×D8C22×D5semidirect
635. #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#5774semidirect
1127. C2×C3#66108semidirect
1134. C5C2×#5774semidirect
1167. C3C2×#66108semidirect
1177. C2#11754059direct (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×#920262
C2×D8×D152
C2×C5×#9112
C2×C3×#40572
C2×#915002
C2×#914982
C2×#914952
C2×#914922
C2×D3×#6862
C2×D5×#2132
#117540592
C2×#912762
C2×#912682
C2×#912532
C2×#912492
C2×#661083
C2×#57745