Finite Group Databasebeta

← C2×#11754083 #14509987

Subgroups — C2×#11754083 #14509987

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×#92035C211yesmaximal, characteristic, complemented
2C2×#92025C211yesmaximal, characteristic, complemented
3C2×#91805C211yesmaximal, characteristic, complemented
4C2×C5×#914C211yesmaximal, characteristic, complemented
5C2×C3×#4060C211yesmaximal, characteristic, complemented
6C2×#91517C211yesmaximal, characteristic, complemented
7C2×#91514C211yesmaximal, characteristic, complemented
8C2×#91506C211yesmaximal, characteristic, complemented
9C2×#91482C211yesmaximal, characteristic, complemented
10C2×D3×#686C211yesmaximal, characteristic, complemented
11C2×D5×#213C211yesmaximal, characteristic, complemented
12#11754083C2116yesmaximal, direct product factor
13C2×#91268C211yesmaximal, characteristic, complemented
14C2×#91256C211yesmaximal, characteristic, complemented
15C2×#91254C211yesmaximal, characteristic, complemented
16C2×#91250C211yesmaximal, characteristic, complemented
17C2×#66108—31nomaximal, Hall
18C2×#6821C2211yescharacteristic, complemented
19C2×#6819C2211yescharacteristic, complemented
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic, complemented
22C2×C3×#713C2211yescharacteristic, complemented
23C2×C3×D4×D5C2211yescharacteristic, complemented
24C2×D3×C22⋊D5—21no—
25C2×D5×#67—21no—
26C22×#1201—21no—
27C2×#6780—21no—
28#92035—24no—
29#92035C2218yescomplemented
30#92025—24no—
31#92025C2218yescomplemented
32C2×#6777—21no—
33C2×#6777C2211yescharacteristic, complemented
34C2×#6777C2211yescharacteristic, complemented
35C2×D3×D20—21no—
36C2×D3×D20C2211yescharacteristic, complemented
37C2×D5×D12—21no—
38C2×D5×D12C2211yescharacteristic, complemented
39C2×#6772C2211yescharacteristic, complemented
40C2×#6771—21no—
41C2×#6771C2211yescharacteristic
42C2×#6765C2211yescharacteristic, complemented
43C2×C3×C5×SD16C2211yescharacteristic, complemented
44C2×#6718C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46#91805C2218yescomplemented
47C2×#6706C2211yescharacteristic, complemented
48C2×C8×D15C2211yescharacteristic, complemented
49C2×C5×#215C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#914C2218yescomplemented
52C2×C5×D24C2211yescharacteristic, complemented
53C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
54C2×C3×#688C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4060C2218yescomplemented
57C2×C3×D40C2211yescharacteristic, complemented
58C2×C3×#676C2211yescharacteristic, complemented
59#91517C2218yescomplemented
60#91514C2218yescomplemented
61#91506C2218yescomplemented
62#91482C2218yescomplemented
63D3×#686C2218yescomplemented
64D5×#213C2218yescomplemented
65C2×#6659C2211yescharacteristic, complemented
66C2×#6657C2211yescharacteristic, complemented
67C2×#6654C2211yescharacteristic, complemented
68C2×#6653C2211yescharacteristic, complemented
69C2×#6652C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6651C2211yescharacteristic, complemented
72C2×D3×#168C2211yescharacteristic, complemented
73C2×D5×C3⋊C8C2211yescharacteristic, complemented
74#91268C2218yescomplemented
75#91256C2218yescomplemented
76#91254C2218yescomplemented
77#91250C2218yescomplemented
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×#4060D311yescharacteristic, complemented
89C2×#4057—31no—
90C2×#4057—31no—
91C2×D5×D8—31no—
92C2×D5×D8—31no—
93C2×#4054—31no—
94C2×#4053—31no—
95C23×C5×D3—21no—
96C23×C3×D5—21no—
97C22×D3×D5—21no—
98C22×D3×D5—21no—
99C22×D3×D5—21no—
100C22×D3×D5—21no—
101C2×C3×C5×Q8C2311yescharacteristic
102C2×C3×C5×D4C2311yescharacteristic
103C2×#1220—21no—
104C22×Dic15—21no—
105#6821—22no—
106#6821C2314yescomplemented
107#6819—22no—
108#6819C2314yescomplemented
109C2×D60—21no—
110C2×D60C2311yescharacteristic
111C2×C4×D15—21no—
112C2×C4×D15C2311yescharacteristic
113C2×Dic30C2311yescharacteristic
114C2×C5×#67—21no—
115C5×#239—22no—
116C5×#239C2314yescomplemented
117C5×D3×D4—22no—
118C5×D3×D4C2314yescomplemented
119C2×C5×D12—21no—
120C2×C5×D12C2311yescharacteristic
121C2×C5×D12C2311yescharacteristic
122C2×C4×C5×D3—21no—
123C2×C4×C5×D3C2311yescharacteristic
124C2×C3×C22⋊D5—21no—
125C3×#713—22no—
126C3×#713C2314yescomplemented
127C3×D4×D5—22no—
128C3×D4×D5C2314yescomplemented
129C2×C3×D20—21no—
130C2×C3×D20C2311yescharacteristic
131C2×C3×D20C2311yescharacteristic
132C2×C3×C4×D5—21no—
133C2×C3×C4×D5C2311yescharacteristic
134D3×C22⋊D5—28no—
135D5×#67—28no—
136C2×#1204D411yescharacteristic
137C2×#1203—21no—
138C2×#1203D411yescharacteristic
139C2×#1202—21no—
140C2×#1202D411yescharacteristic
141C2×#1201—21no—
142C2×#1201—21no—
143C2×#1201—21no—
144C2×#1201—21no—
145C2×#1201—28no—
146C2×#1201D411yescharacteristic
147C2×D3×Dic5—21no—
148#6780—28no—
149C2×D5×Dic3—21no—
150#6777—22no—
151#6777—22no—
152#6777—28no—
153#6777C2314yescomplemented
154#6777C2314yescomplemented
155D3×D20—22no—
156D3×D20—28no—
157D3×D20C2314yescomplemented
158D5×D12—22no—
159D5×D12—28no—
160D5×D12C2314yescomplemented
161#6772—22no—
162#6772C2314yescomplemented
163#6771—28no—
164#6771D414yes—
165#6771C2314yes—
166#6765—22no—
167#6765C2314yescomplemented
168C3×C5×SD16C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6718C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173#6706C2314yescomplemented
174C8×D15C2314yescomplemented
175C5×#215C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×D24C2314yescomplemented
179C5×ΓL(1,𝔽25)C2314yescomplemented
180C3×#688C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×D40C2314yescomplemented
184C3×#676C2314yescomplemented
185#6659C2314yescomplemented
186#6657C2314yescomplemented
187#6654C2314yescomplemented
188#6653C2314yescomplemented
189#6652C2314yescomplemented
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×#914D511yescharacteristic, complemented
204C2×#911—51no—
205C2×#911—51no—
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×#713C2×D311yescharacteristic, complemented
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—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×SD16C2×D311yescharacteristic, complemented
238C2×C5×D8—31no—
239C2×C5×D8—31no—
240C2×C5×M16—31no—
241#4096—38no—
242C2×#689—31no—
243C2×#688C2×D311yescharacteristic, complemented
244C2×#687—31no—
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#4060C2×D318yescomplemented
256#4057—38no—
257#4057—38no—
258D5×D8—38no—
259D5×D8—38no—
260#4054—38no—
261#4053—38no—
262C2×D40—31no—
263C2×D40C2×D311yescharacteristic, complemented
264C2×#677—31no—
265C2×#677—31no—
266C2×#676—31no—
267C2×#676C2×D311yescharacteristic, complemented
268C2×C8×D5—31no—
269C2×C8×D5—31no—
270C2×#576—151noSylow
271C23×C3×C5—21no—
272C22×D15—21no—
273C22×D15C2×D411yescharacteristic
274C22×C5×D3—21no—
275C22×C5×D3—21no—
276C22×C5×D3—24no—
277C22×C5×D3—82no—
278C22×C5×D3C2×D411yescharacteristic
279C22×C3×D5—21no—
280C22×C3×D5—21no—
281C22×C3×D5—24no—
282C22×C3×D5—82no—
283C22×C3×D5C2×D411yescharacteristic
284C2×D3×D5—24no—
285C2×D3×D5—24no—
286C2×D3×D5—24no—
287C2×D3×D5—24no—
288C2×D3×D5—82no—
289C2×D3×D5—82no—
290C2×D3×D5—82no—
291C2×D3×D5—82no—
292C3×C5×Q8—21no—
293C3×C5×Q8C2412yes—
294C3×C5×D4—21no—
295C3×C5×D4C2412yes—
296C2×C3×C4×C5—21no—
297C2×C3×C4×C5C2411yescharacteristic
298#1220—24no—
299C2×Dic15—21no—
300C2×Dic15—24no—
301C2×Dic15C2×D411yescharacteristic
302D60—24no—
303D60—21no—
304D60C2412yes—
305C4×D15—24no—
306C4×D15C2×D412yes—
307C4×D15C2412yes—
308Dic30—21no—
309Dic30C2412yes—
310C5×#67—24no—
311C2×C5×Dic3C2×D411yescharacteristic
312C5×D12—24no—
313C5×D12—21no—
314C5×D12—21no—
315C5×D12C2412yes—
316C5×D12C2412yes—
317C4×C5×D3—24no—
318C4×C5×D3C2×D412yes—
319C4×C5×D3C2412yes—
320C3×C22⋊D5—24no—
321C2×C3×Dic5C2×D411yescharacteristic
322C3×D20—24no—
323C3×D20—21no—
324C3×D20—21no—
325C3×D20C2412yes—
326C3×D20C2412yes—
327C3×C4×D5—24no—
328C3×C4×D5C2×D412yes—
329C3×C4×D5C2412yes—
330#1204C2×D414yes—
331#1203—24no—
332#1203C2×D414yes—
333#1202—24no—
334#1202C2×D414yes—
335#1201—24no—
336#1201—24no—
337#1201—24no—
338#1201—24no—
339#1201C2×D414yes—
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×#239C2×D511yescharacteristic, complemented
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—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×SD16C2×D511yescharacteristic, complemented
374C2×C3×D8—51no—
375C2×C3×D8—51no—
376C2×C3×M16—51no—
377#950—58no—
378C2×#216—51no—
379C2×#215C2×D511yescharacteristic, complemented
380C2×#214—51no—
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#914C2×D518yescomplemented
392#911—58no—
393#911—58no—
394D3×D8—58no—
395D3×D8—58no—
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)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×Q8C22×D311yescharacteristic
415C2×C5×D4—34no—
416C2×C5×D4—31no—
417C2×C5×D4—31no—
418C2×C5×D4—61no—
419C2×C5×D4—62no—
420C2×C5×D4—61no—
421C2×C5×D4C22×D311yescharacteristic
422C22×C4×C5—31no—
423C22×C4×C5—61no—
424C2×C22⋊D5—21no—
425C2×C22⋊D5—31no—
426C2×C22⋊D5—31no—
427C2×C22⋊D5—61no—
428C2×C22⋊D5—61no—
429C2×C22⋊D5—68no—
430C2×C22⋊D5—68no—
431C2×C22⋊D5—61no—
432C2×C22⋊D5—61no—
433C2×C22⋊D5—61no—
434C2×C22⋊D5—61no—
435C22×Dic5—61no—
436C22×Dic5—61no—
437#713—22no—
438#713—34no—
439#713—62no—
440#713C22×D314yescomplemented
441#711—34no—
442#711—34no—
443#711—68no—
444#711—62no—
445#711—62no—
446D4×D5—22no—
447D4×D5—34no—
448D4×D5—34no—
449D4×D5—34no—
450D4×D5—68no—
451D4×D5—62no—
452D4×D5—62no—
453D4×D5—68no—
454D4×D5—68no—
455D4×D5—62no—
456D4×D5C22×D314yescomplemented
457#709—34no—
458#709—34no—
459#709—34no—
460#709—68no—
461#709—62no—
462C2×D20—21no—
463C2×D20—31no—
464C2×D20—31no—
465C2×D20—34no—
466C2×D20—68no—
467C2×D20—62no—
468C2×D20—61no—
469C2×D20—61no—
470C2×D20C22×D311yescharacteristic
471C2×D20C22×D311yescharacteristic
472C2×C4×D5—21no—
473C2×C4×D5—31no—
474C2×C4×D5—61no—
475C2×C4×D5—61no—
476C2×C4×D5C22×D311yescharacteristic
477C2×Dic10—31no—
478C2×Dic10—31no—
479C5×SD16—34no—
480C5×SD16C22×D314yescomplemented
481C5×D8—34no—
482C5×D8—34no—
483C5×M16—34no—
484C2×C5×C8—31no—
485C2×C5×C8C22×D311yescharacteristic
486#689—34no—
487#688C22×D314yescomplemented
488#687—34no—
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—
498D40C22×D314yescomplemented
499#677—34no—
500#677—34no—
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—42no—
523C22×C3×C5C22×D411yescharacteristic
524C2×D15—22no—
525C2×D15—22no—
526C2×D15—42no—
527C2×D15C22×D412yes—
528C2×C5×D3—22no—
529C2×C5×D3—22no—
530C2×C5×D3—22no—
531C2×C5×D3—42no—
532C2×C5×D3—42no—
533C2×C5×D3—84no—
534C2×C5×D3C22×D412yes—
535C2×C3×D5—22no—
536C2×C3×D5—22no—
537C2×C3×D5—22no—
538C2×C3×D5—42no—
539C2×C3×D5—42no—
540C2×C3×D5—84no—
541C2×C3×D5C22×D412yes—
542D3×D5—84no—
543D3×D5—84no—
544D3×D5—84no—
545D3×D5—84no—
546C3×C4×C5—22no—
547C3×C4×C5C22×D411yescharacteristic
548C3×C4×C5C2511yescharacteristic
549Dic15—22no—
550Dic15C22×D412yes—
551C3×Dic5C22×D412yes—
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×Q8C22×D511yescharacteristic
562C2×C3×D4—54no—
563C2×C3×D4—51no—
564C2×C3×D4—51no—
565C2×C3×D4—101no—
566C2×C3×D4—102no—
567C2×C3×D4—101no—
568C2×C3×D4C22×D511yescharacteristic
569C22×C3×C4—51no—
570C22×C3×C4—101no—
571C2×#67—21no—
572C2×#67—51no—
573C2×#67—51no—
574C2×#67—101no—
575C2×#67—101no—
576C2×#67—108no—
577C2×#67—108no—
578C2×#67—101no—
579C2×#67—101no—
580C2×#67—101no—
581C2×#67—101no—
582C22×Dic3—101no—
583C22×Dic3—101no—
584#239—22no—
585#239—54no—
586#239—102no—
587#239C22×D514yescomplemented
588#237—54no—
589#237—54no—
590#237—108no—
591#237—102no—
592#237—102no—
593D3×D4—22no—
594D3×D4—54no—
595D3×D4—54no—
596D3×D4—54no—
597D3×D4—108no—
598D3×D4—102no—
599D3×D4—102no—
600D3×D4—108no—
601D3×D4—108no—
602D3×D4—102no—
603D3×D4C22×D514yescomplemented
604#235—54no—
605#235—54no—
606#235—54no—
607#235—108no—
608#235—102no—
609C2×D12—21no—
610C2×D12—51no—
611C2×D12—51no—
612C2×D12—54no—
613C2×D12—108no—
614C2×D12—102no—
615C2×D12—101no—
616C2×D12—101no—
617C2×D12C22×D511yescharacteristic
618C2×D12C22×D511yescharacteristic
619C2×C4×D3—21no—
620C2×C4×D3—51no—
621C2×C4×D3—101no—
622C2×C4×D3—101no—
623C2×C4×D3C22×D511yescharacteristic
624C2×Dic6—51no—
625C2×Dic6—51no—
626C3×SD16—54no—
627C3×SD16C22×D514yescomplemented
628C3×D8—54no—
629C3×D8—54no—
630C3×M16—54no—
631C2×C3×C8—51no—
632C2×C3×C8C22×D511yescharacteristic
633#216—54no—
634#215C22×D514yescomplemented
635#214—54no—
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—
645D24C22×D514yescomplemented
646#204—54no—
647#204—54no—
648ΓL(1,𝔽25)—54no—
649ΓL(1,𝔽25)C22×D514yescomplemented
650D3×C8—54no—
651D3×C8—54no—
652C23×C5—21no—
653C23×C5—31no—
654C23×C5—64no—
655C23×C5—61no—
656C23×C5—61no—
657C23×C5—242no—
658C22×D5—21no—
659C22×D5—21no—
660C22×D5—24no—
661C22×D5—31no—
662C22×D5—64no—
663C22×D5—64no—
664C22×D5—64no—
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—21no—
674C5×Q8C23×D312yes—
675C5×D4—21no—
676C5×D4—32no—
677C5×D4—32no—
678C5×D4—64no—
679C5×D4—64no—
680C5×D4—61no—
681C5×D4—61no—
682C5×D4C23×D312yes—
683C2×C4×C5—21no—
684C2×C4×C5—31no—
685C2×C4×C5—32no—
686C2×C4×C5—32no—
687C2×C4×C5—64no—
688C2×C4×C5C23×D311yescharacteristic
689C22⋊D5—24no—
690C22⋊D5—34no—
691C22⋊D5—34no—
692C22⋊D5—64no—
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—24no—
704D20—21no—
705D20—21no—
706D20—34no—
707D20—32no—
708D20—64no—
709D20—64no—
710D20—61no—
711D20C23×D312yes—
712D20C23×D312yes—
713C4×D5—24no—
714C4×D5—32no—
715C4×D5—32no—
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—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—51no—
764C2×SD16—151no—
765C2×SD16—151no—
766C2×SD16—151no—
767C2×SD16D3×D511yescharacteristic, complemented
768C2×D8—31no—
769C2×D8—31no—
770C2×D8—51no—
771C2×D8—51no—
772C2×D8—151no—
773C2×D8—151no—
774C2×D8—158no—
775C2×D8—158no—
776C2×D8—158no—
777C2×D8—151no—
778C2×D8—151no—
779C2×D8—151no—
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#57612yescomplemented
789C2×C3×C5C23×D411yescharacteristic
790D15—22no—
791D15—42no—
792C3×D5—22no—
793C3×D5—42no—
794C3×D5—42no—
795C5×D3—22no—
796C5×D3—42no—
797C5×D3—42no—
798C23×C3—21no—
799C23×C3—51no—
800C23×C3—104no—
801C23×C3—101no—
802C23×C3—101no—
803C23×C3—402no—
804C22×D3—21no—
805C22×D3—21no—
806C22×D3—24no—
807C22×D3—51no—
808C22×D3—82no—
809C22×D3—104no—
810C22×D3—104no—
811C22×D3—104no—
812C22×D3—101no—
813C22×D3—104no—
814C22×D3—402no—
815C22×D3—402no—
816C22×D3—402no—
817C22×D3—402no—
818C22×D3D4×D511yescharacteristic
819C3×Q8—21no—
820C3×Q8C23×D512yes—
821C3×D4—21no—
822C3×D4—52no—
823C3×D4—52no—
824C3×D4—104no—
825C3×D4—104no—
826C3×D4—101no—
827C3×D4—101no—
828C3×D4C23×D512yes—
829C2×C3×C4—21no—
830C2×C3×C4—51no—
831C2×C3×C4—52no—
832C2×C3×C4—52no—
833C2×C3×C4—104no—
834C2×C3×C4C23×D511yescharacteristic
835#67—24no—
836#67—54no—
837#67—54no—
838#67—104no—
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—24no—
850D12—21no—
851D12—21no—
852D12—54no—
853D12—52no—
854D12—104no—
855D12—104no—
856D12—101no—
857D12C23×D512yes—
858D12C23×D512yes—
859C4×D3—24no—
860C4×D3—52no—
861C4×D3—52no—
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—32no—
875C22×C5—42no—
876C22×C5—62no—
877C22×C5—62no—
878C22×C5—62no—
879C22×C5—122no—
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—122no—
893C2×D5—244no—
894C2×D5—244no—
895C2×D5—244no—
896C2×D5—244no—
897C2×D5C2×D3×D412yes—
898C4×C5—22no—
899C4×C5—32no—
900C4×C5C2×D3×D411yescharacteristic
901C4×C5C24×D311yescharacteristic
902Dic5—32no—
903Dic5—62no—
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—302no—
925#41—302no—
926#41—308no—
927C2×Q8—151no—
928C2×Q8—151no—
929C2×Q8C2×D3×D511yescharacteristic
930C2×D4—34no—
931C2×D4—31no—
932C2×D4—31no—
933C2×D4—54no—
934C2×D4—51no—
935C2×D4—51no—
936C2×D4—61no—
937C2×D4—62no—
938C2×D4—61no—
939C2×D4—101no—
940C2×D4—102no—
941C2×D4—101no—
942C2×D4—154no—
943C2×D4—151no—
944C2×D4—154no—
945C2×D4—151no—
946C2×D4—154no—
947C2×D4—154no—
948C2×D4—151no—
949C2×D4—151no—
950C2×D4—301no—
951C2×D4—302no—
952C2×D4—301no—
953C2×D4—302no—
954C2×D4—301no—
955C2×D4—308no—
956C2×D4—308no—
957C2×D4—302no—
958C2×D4—302no—
959C2×D4—301no—
960C2×D4—301no—
961C2×D4—308no—
962C2×D4—308no—
963C2×D4—308no—
964C2×D4—308no—
965C2×D4—301no—
966C2×D4—301no—
967C2×D4—301no—
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—54no—
981SD16—154no—
982SD16—154no—
983SD16—154no—
984SD16C2×D3×D514yescomplemented
985D8—34no—
986D8—34no—
987D8—54no—
988D8—54no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8—154no—
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—42no—
1007C22×C3—52no—
1008C22×C3—102no—
1009C22×C3—102no—
1010C22×C3—102no—
1011C22×C3—202no—
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—102no—
1023C2×D3—102no—
1024C2×D3—202no—
1025C2×D3—404no—
1026C2×D3—404no—
1027C2×D3—404no—
1028C2×D3—404no—
1029C2×D3C2×D4×D512yes—
1030C3×C4—22no—
1031C3×C4—52no—
1032C3×C4C2×D4×D511yescharacteristic
1033C3×C4C24×D511yescharacteristic
1034Dic3—52no—
1035Dic3—102no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—62no—
1039C2×C5—122no—
1040C2×C5—122no—
1041C2×C5#577412yescomplemented
1042C2×C5C22×D3×D411yescharacteristic
1043D5—22no—
1044D5—42no—
1045D5—42no—
1046D5—62no—
1047D5—122no—
1048C23—21no—
1049C23—31no—
1050C23—51no—
1051C23—64no—
1052C23—61no—
1053C23—61no—
1054C23—104no—
1055C23—101no—
1056C23—101no—
1057C23—151no—
1058C23—242no—
1059C23—304no—
1060C23—304no—
1061C23—304no—
1062C23—304no—
1063C23—301no—
1064C23—402no—
1065C23—1202no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—21no—
1070Q8—154no—
1071Q8—152no—
1072Q8—301no—
1073Q8C22×D3×D512yes—
1074D4—21no—
1075D4—32no—
1076D4—32no—
1077D4—52no—
1078D4—52no—
1079D4—64no—
1080D4—64no—
1081D4—61no—
1082D4—61no—
1083D4—104no—
1084D4—104no—
1085D4—101no—
1086D4—101no—
1087D4—154no—
1088D4—154no—
1089D4—154no—
1090D4—152no—
1091D4—304no—
1092D4—304no—
1093D4—304no—
1094D4—304no—
1095D4—304no—
1096D4—304no—
1097D4—304no—
1098D4—304no—
1099D4—301no—
1100D4C22×D3×D512yes—
1101C2×C4—21no—
1102C2×C4—31no—
1103C2×C4—32no—
1104C2×C4—32no—
1105C2×C4—51no—
1106C2×C4—52no—
1107C2×C4—52no—
1108C2×C4—64no—
1109C2×C4—104no—
1110C2×C4—151no—
1111C2×C4—152no—
1112C2×C4—152no—
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—102no—
1125C2×C3—202no—
1126C2×C3—202no—
1127C2×C3#6610812yescomplemented
1128C2×C3C22×D4×D511yescharacteristic
1129D3—22no—
1130D3—42no—
1131D3—42no—
1132D3—102no—
1133D3—202no—
1134C5C2×#577411yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—32no—
1137C22—42no—
1138C22—52no—
1139C22—62no—
1140C22—62no—
1141C22—62no—
1142C22—102no—
1143C22—102no—
1144C22—102no—
1145C22—122no—
1146C22—122no—
1147C22—152no—
1148C22—202no—
1149C22—202no—
1150C22—244no—
1151C22—302no—
1152C22—302no—
1153C22—404no—
1154C22—602no—
1155C22—1204no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—22no—
1161C4—32no—
1162C4—52no—
1163C4—152no—
1164C4—302no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6610811yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—62no—
1170C2—102no—
1171C2—122no—
1172C2—122no—
1173C2—202no—
1174C2—202no—
1175C2—302no—
1176C2—602no—
1177C2#1175408312yesdirect product factor
1178C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
hypercenterC2×SD16D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#92035C2semidirect
2. C2×#92025C2semidirect
3. C2×#91805C2semidirect
4. C2×C5×#914C2semidirect
5. C2×C3×#4060C2semidirect
6. C2×#91517C2semidirect
7. C2×#91514C2semidirect
8. C2×#91506C2semidirect
9. C2×#91482C2semidirect
10. C2×D3×#686C2semidirect
11. C2×D5×#213C2semidirect
12. #11754083C2direct (N × H)
13. C2×#91268C2semidirect
14. C2×#91256C2semidirect
15. C2×#91254C2semidirect
16. C2×#91250C2semidirect
18. C2×#6821C22semidirect
19. C2×#6819C22semidirect
20. C2×C5×#239C22semidirect
21. C2×C5×D3×D4C22semidirect
22. C2×C3×#713C22semidirect
23. C2×C3×D4×D5C22semidirect
29. #92035C22semidirect
31. #92025C22semidirect
33. C2×#6777C22semidirect
34. C2×#6777C22semidirect
36. C2×D3×D20C22semidirect
38. C2×D5×D12C22semidirect
39. C2×#6772C22semidirect
42. C2×#6765C22semidirect
43. C2×C3×C5×SD16C22semidirect
44. C2×#6718C22semidirect
45. C2×#6715C22semidirect
46. #91805C22semidirect
47. C2×#6706C22semidirect
48. C2×C8×D15C22semidirect
49. C2×C5×#215C22semidirect
50. C2×C5×#213C22semidirect
51. C5×#914C22semidirect
52. C2×C5×D24C22semidirect
53. C2×C5×ΓL(1,𝔽25)C22semidirect
54. C2×C3×#688C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4060C22semidirect
57. C2×C3×D40C22semidirect
58. C2×C3×#676C22semidirect
59. #91517C22semidirect
60. #91514C22semidirect
61. #91506C22semidirect
62. #91482C22semidirect
63. D3×#686C22semidirect
64. D5×#213C22semidirect
65. C2×#6659C22semidirect
66. C2×#6657C22semidirect
67. C2×#6654C22semidirect
68. C2×#6653C22semidirect
69. C2×#6652C22semidirect
70. C2×#6652C22semidirect
71. C2×#6651C22semidirect
72. C2×D3×#168C22semidirect
73. C2×D5×C3⋊C8C22semidirect
74. #91268C22semidirect
75. #91256C22semidirect
76. #91254C22semidirect
77. #91250C22semidirect
88. C2×#4060D3semidirect
106. #6821C23semidirect
108. #6819C23semidirect
116. C5×#239C23semidirect
118. C5×D3×D4C23semidirect
126. C3×#713C23semidirect
128. C3×D4×D5C23semidirect
153. #6777C23semidirect
154. #6777C23semidirect
157. D3×D20C23semidirect
160. D5×D12C23semidirect
162. #6772C23semidirect
167. #6765C23semidirect
168. C3×C5×SD16C23semidirect
170. #6718C23semidirect
171. #6715C23semidirect
173. #6706C23semidirect
174. C8×D15C23semidirect
175. C5×#215C23semidirect
176. C5×#213C23semidirect
178. C5×D24C23semidirect
179. C5×ΓL(1,𝔽25)C23semidirect
180. C3×#688C23semidirect
181. C3×#686C23semidirect
183. C3×D40C23semidirect
184. C3×#676C23semidirect
185. #6659C23semidirect
186. #6657C23semidirect
187. #6654C23semidirect
188. #6653C23semidirect
189. #6652C23semidirect
190. #6652C23semidirect
191. #6651C23semidirect
192. D3×#168C23semidirect
193. D5×C3⋊C8C23semidirect
203. C2×#914D5semidirect
217. C2×#713C2×D3semidirect
229. C2×D4×D5C2×D3semidirect
237. C2×C5×SD16C2×D3semidirect
243. C2×#688C2×D3semidirect
250. C2×#686C2×D3semidirect
255. #4060C2×D3semidirect
263. C2×D40C2×D3semidirect
267. C2×#676C2×D3semidirect
353. C2×#239C2×D5semidirect
365. C2×D3×D4C2×D5semidirect
373. C2×C3×SD16C2×D5semidirect
379. C2×#215C2×D5semidirect
386. C2×#213C2×D5semidirect
391. #914C2×D5semidirect
399. C2×D24C2×D5semidirect
403. C2×ΓL(1,𝔽25)C2×D5semidirect
440. #713C22×D3semidirect
456. D4×D5C22×D3semidirect
480. C5×SD16C22×D3semidirect
487. #688C22×D3semidirect
493. #686C22×D3semidirect
498. D40C22×D3semidirect
502. #676C22×D3semidirect
587. #239C22×D5semidirect
603. D3×D4C22×D5semidirect
627. C3×SD16C22×D5semidirect
634. #215C22×D5semidirect
640. #213C22×D5semidirect
645. D24C22×D5semidirect
649. ΓL(1,𝔽25)C22×D5semidirect
767. C2×SD16D3×D5semidirect
788. C2×C3×C5#576semidirect
984. SD16C2×D3×D5semidirect
1004. C3×C5C2×#576semidirect
1041. C2×C5#5774semidirect
1127. C2×C3#66108semidirect
1134. C5C2×#5774semidirect
1167. C3C2×#66108semidirect
1177. C2#11754083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920352
C2×#920252
C2×#918052
C2×C5×#9142
C2×C3×#40602
C2×#915172
C2×#915142
C2×#915062
C2×#914822
C2×D3×#6862
C2×D5×#2132
#117540832
C2×#912682
C2×#912562
C2×#912542
C2×#912502
C2×#661083
C2×#57745