Finite Group Databasebeta

← C2×#11754089 #14509989

Subgroups — C2×#11754089 #14509989

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×#92026C211yesmaximal, characteristic, complemented
3C2×#91803C211yesmaximal, characteristic, complemented
4C2×C5×#916C211yesmaximal, characteristic, complemented
5C2×C3×#4060C211yesmaximal, characteristic, complemented
6C2×#91521C211yesmaximal, characteristic, complemented
7C2×#91516C211yesmaximal, characteristic, complemented
8C2×#91504C211yesmaximal, characteristic, complemented
9C2×#91481C211yesmaximal, characteristic, complemented
10C2×#91480C211yesmaximal, characteristic, complemented
11C2×D5×#213C211yesmaximal, characteristic, complemented
12#11754089C2116yesmaximal, direct product factor
13C2×#91267C211yesmaximal, characteristic, complemented
14C2×#91258C211yesmaximal, characteristic, complemented
15C2×D3×D40C211yesmaximal, characteristic, complemented
16C2×#91249C211yesmaximal, characteristic, complemented
17C2×#66103—31nomaximal, Hall
18C2×#6821C2211yescharacteristic, complemented
19C2×D4×D15C2211yescharacteristic, complemented
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×#237C2211yescharacteristic, complemented
22C2×C3×#713C2211yescharacteristic, complemented
23C2×C3×D4×D5C2211yescharacteristic, complemented
24C2×#6790—21no—
25C2×D5×#67—21no—
26C22×#1202—21no—
27C2×#6779—21no—
28#92035—24no—
29#92035C2218yescomplemented
30#92026—24no—
31#92026C2218yescomplemented
32C2×#6777—21no—
33C2×#6777C2211yescharacteristic, complemented
34C2×D3×D20—21no—
35C2×D3×D20C2211yescharacteristic, complemented
36C2×D3×D20C2211yescharacteristic, complemented
37C2×D5×D12—21no—
38C2×D5×D12C2211yescharacteristic, complemented
39C2×#6773C2211yescharacteristic, complemented
40C2×#6771—21no—
41C2×#6771C2211yescharacteristic
42C2×#6766C2211yescharacteristic, complemented
43C2×C3×C5×SD16C2211yescharacteristic, complemented
44C2×#6717C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46#91803C2218yescomplemented
47C2×D120C2211yescharacteristic, complemented
48C2×#6705C2211yescharacteristic, complemented
49C2×C5×#216C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#916C2218yescomplemented
52C2×C5×#204C2211yescharacteristic, complemented
53C2×C5×D3×C8C2211yescharacteristic, complemented
54C2×C3×#688C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4060C2218yescomplemented
57C2×C3×D40C2211yescharacteristic, complemented
58C2×C3×#676C2211yescharacteristic, complemented
59#91521C2218yescomplemented
60#91516C2218yescomplemented
61#91504C2218yescomplemented
62#91481C2218yescomplemented
63#91480C2218yescomplemented
64D5×#213C2218yescomplemented
65C2×#6660C2211yescharacteristic, complemented
66C2×#6655C2211yescharacteristic, complemented
67C2×#6654C2211yescharacteristic, complemented
68C2×#6653C2211yescharacteristic, complemented
69C2×#6653C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6650C2211yescharacteristic, complemented
72C2×#6648C2211yescharacteristic, complemented
73C2×D5×C3⋊C8C2211yescharacteristic, complemented
74#91267C2218yescomplemented
75#91258C2218yescomplemented
76D3×D40C2218yescomplemented
77#91249C2218yescomplemented
78C2×#5774—51nomaximal, Hall
79C2×#4149—31no—
80C2×#4149—31no—
81C2×C5×#135—31no—
82C2×#4095—31no—
83C2×#4095—31no—
84#66103—316no—
85C2×#4065—31no—
86C2×#4065—31no—
87C2×#4060—31no—
88C2×#4060—31no—
89C2×#4060—31no—
90C2×#4060D311yescharacteristic, complemented
91C2×D5×D8—31no—
92C2×D5×D8—31no—
93C22×D40—31no—
94C2×#4047—31no—
95C23×D15—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—
104#6821—22no—
105#6821C2314yescomplemented
106D4×D15—22no—
107D4×D15C2314yescomplemented
108C2×D60—21no—
109C2×D60C2311yescharacteristic
110C2×D60C2311yescharacteristic
111C2×C4×D15—21no—
112C2×C4×D15C2311yescharacteristic
113C2×C5×#67—21no—
114C22×C5×Dic3—21no—
115C5×#239—22no—
116C5×#239C2314yescomplemented
117C5×#237—22no—
118C5×#237C2314yescomplemented
119C2×C5×D12—21no—
120C2×C5×D12C2311yescharacteristic
121C2×C4×C5×D3—21no—
122C2×C4×C5×D3C2311yescharacteristic
123C2×C5×Dic6C2311yescharacteristic
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
134#6790—28no—
135D5×#67—28no—
136C2×#1204D411yescharacteristic
137C2×#1203—21no—
138C2×#1203D411yescharacteristic
139C2×#1202—21no—
140C2×#1202—21no—
141C2×#1202—21no—
142C2×#1202—21no—
143C2×#1202—28no—
144C2×#1202D411yescharacteristic
145C2×#1201—21no—
146C2×#1201D411yescharacteristic
147C2×#1200—21no—
148#6779—28no—
149C2×D5×Dic3—21no—
150#6777—22no—
151#6777—28no—
152#6777C2314yescomplemented
153D3×D20—22no—
154D3×D20—22no—
155D3×D20—28no—
156D3×D20C2314yescomplemented
157D3×D20C2314yescomplemented
158D5×D12—22no—
159D5×D12—28no—
160D5×D12C2314yescomplemented
161#6773—22no—
162#6773C2314yescomplemented
163#6771—28no—
164#6771D414yes—
165#6771C2314yes—
166#6766—22no—
167#6766C2314yescomplemented
168C3×C5×SD16C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6717C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173D120C2314yescomplemented
174#6705C2314yescomplemented
175C5×#216C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×#204C2314yescomplemented
179C5×D3×C8C2314yescomplemented
180C3×#688C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×D40C2314yescomplemented
184C3×#676C2314yescomplemented
185#6660C2314yescomplemented
186#6655C2314yescomplemented
187#6654C2314yescomplemented
188#6653C2314yescomplemented
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×#916D511yescharacteristic, complemented
202C2×#914—51no—
203C2×#914—51no—
204C2×#911—51no—
205C2×#911—51no—
206C2×D3×D8—51no—
207C2×D3×D8—51no—
208C2×#908—51no—
209C2×#907—51no—
210C2×C5×#41—31no—
211C2×C5×#41—31no—
212#4149—38no—
213#4149—38no—
214#4149—64no—
215#4149—64no—
216C2×#713—31no—
217C2×#713—31no—
218C2×#713—31no—
219C2×#713C2×D311yescharacteristic, complemented
220C2×D4×D5—31no—
221C2×D4×D5—31no—
222C2×D4×D5—31no—
223C2×D4×D5—61no—
224C2×D4×D5—61no—
225C2×D4×D5—61no—
226C2×D4×D5—61no—
227C2×D4×D5C2×D311yescharacteristic, complemented
228C2×#709—31no—
229C2×#709—61no—
230C2×#709—61no—
231C22×D20—31no—
232C22×D20—31no—
233C22×D20—61no—
234C22×D20—61no—
235C5×#135—38no—
236C2×C5×Q16—31no—
237C2×C5×SD16—31no—
238C2×C5×SD16C2×D311yescharacteristic, complemented
239C2×C5×D8—31no—
240C22×C5×C8—31no—
241#4095—38no—
242#4095—38no—
243C2×#688—31no—
244C2×#688—31no—
245C2×#688—31no—
246C2×#688C2×D311yescharacteristic, complemented
247C2×#686—31no—
248C2×#686—31no—
249C2×#686—31no—
250C2×#686C2×D311yescharacteristic, complemented
251C2×#681—31no—
252#4065—38no—
253#4065—38no—
254#4060—38no—
255#4060—38no—
256#4060—38no—
257#4060C2×D318yescomplemented
258D5×D8—38no—
259D5×D8—38no—
260C2×D40—31no—
261C2×D40—31no—
262C2×D40—31no—
263C2×D40—38no—
264C2×D40C2×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—
272C22×D15—21no—
273C22×D15—21no—
274C22×D15—24no—
275C22×D15—82no—
276C22×D15C2×D411yescharacteristic
277C22×C5×D3—21no—
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×Dic15C2×D411yescharacteristic
300D60—24no—
301D60—21no—
302D60—21no—
303D60C2412yes—
304D60C2412yes—
305C4×D15—24no—
306C4×D15C2×D412yes—
307C4×D15C2412yes—
308C5×#67—24no—
309C2×C5×Dic3—21no—
310C2×C5×Dic3—24no—
311C2×C5×Dic3C2×D411yescharacteristic
312C5×D12—24no—
313C5×D12—21no—
314C5×D12C2412yes—
315C4×C5×D3—24no—
316C4×C5×D3C2×D412yes—
317C4×C5×D3C2412yes—
318C5×Dic6—21no—
319C5×Dic6C2412yes—
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#1202—24no—
335#1202—24no—
336#1202—24no—
337#1202C2×D414yes—
338#1201—24no—
339#1201C2×D414yes—
340#1200—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—101no—
358C2×#237C2×D511yescharacteristic, complemented
359C2×D3×D4—51no—
360C2×D3×D4—51no—
361C2×D3×D4—51no—
362C2×D3×D4—51no—
363C2×D3×D4—101no—
364C2×D3×D4—101no—
365C2×D3×D4—101no—
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×#216C2×D511yescharacteristic, complemented
379C2×#215—51no—
380C2×#214—51no—
381C2×#213—51no—
382C2×#213—51no—
383C2×#213—58no—
384C2×#213—51no—
385C2×#213—51no—
386C2×#213C2×D511yescharacteristic, complemented
387C22×C3⋊C8—51no—
388#916—58no—
389#916C2×D518yescomplemented
390#914—58no—
391#914—58no—
392#911—58no—
393#911—58no—
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)—51no—
404C2×D3×C8—51no—
405C2×D3×C8C2×D511yescharacteristic, complemented
406C23×D5—21no—
407C23×D5—61no—
408C23×D5—61no—
409C23×D5—61no—
410C23×D5—61no—
411C23×D5—61no—
412C5×#41—34no—
413C5×#41—34no—
414C5×#41—62no—
415C5×#41—62no—
416C2×C5×Q8—31no—
417C2×C5×Q8C22×D311yescharacteristic
418C2×C5×D4—31no—
419C2×C5×D4—61no—
420C2×C5×D4—61no—
421C2×C5×D4C22×D311yescharacteristic
422C22×C4×C5—31no—
423C22×C4×C5—61no—
424C22×C4×C5—61no—
425C2×C22⋊D5—21no—
426C2×C22⋊D5—31no—
427C2×C22⋊D5—31no—
428C2×C22⋊D5—61no—
429C2×C22⋊D5—61no—
430C2×C22⋊D5—61no—
431#713—22no—
432#713—34no—
433#713—34no—
434#713—34no—
435#713—62no—
436#713—62no—
437#713—62no—
438#713C22×D314yescomplemented
439D4×D5—22no—
440D4×D5—34no—
441D4×D5—34no—
442D4×D5—34no—
443D4×D5—68no—
444D4×D5—62no—
445D4×D5—62no—
446D4×D5—68no—
447D4×D5—68no—
448D4×D5—68no—
449D4×D5—62no—
450D4×D5C22×D314yescomplemented
451#709—34no—
452#709—34no—
453#709—68no—
454#709—68no—
455C2×D20—21no—
456C2×D20—31no—
457C2×D20—31no—
458C2×D20—31no—
459C2×D20—34no—
460C2×D20—34no—
461C2×D20—68no—
462C2×D20—62no—
463C2×D20—62no—
464C2×D20—68no—
465C2×D20—61no—
466C2×D20—61no—
467C2×D20—61no—
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×D5—61no—
477C2×C4×D5C22×D311yescharacteristic
478C2×Dic10—31no—
479C5×Q16—34no—
480C5×SD16—34no—
481C5×SD16C22×D314yescomplemented
482C5×D8—34no—
483C2×C5×C8—31no—
484C2×C5×C8—34no—
485C2×C5×C8C22×D311yescharacteristic
486#688—34no—
487#688—34no—
488#688—34no—
489#688C22×D314yescomplemented
490#686—34no—
491#686—34no—
492#686—34no—
493#686C22×D314yescomplemented
494#681—34no—
495C2×#168—31no—
496C2×#168C22×D311yescharacteristic
497D40—34no—
498D40—34no—
499D40—34no—
500D40C22×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—31no—
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—22no—
527C2×D15—42no—
528C2×D15—42no—
529C2×D15—84no—
530C2×D15C22×D412yes—
531C2×C5×D3—22no—
532C2×C5×D3—22no—
533C2×C5×D3—42no—
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
549Dic15C22×D412yes—
550C3×Dic5C22×D412yes—
551C5×Dic3—22no—
552C5×Dic3C22×D412yes—
553C24×C3—101no—
554C23×D3—101no—
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—108no—
575C2×#67—101no—
576C2×#67—101no—
577C2×#67—101no—
578C2×#67—101no—
579C2×#67—108no—
580C2×#67—101no—
581C2×#67—101no—
582C22×Dic3—21no—
583C22×Dic3—101no—
584#239—22no—
585#239—54no—
586#239—102no—
587#239C22×D514yescomplemented
588#237—22no—
589#237—54no—
590#237—102no—
591#237—108no—
592#237C22×D514yescomplemented
593D3×D4—54no—
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×D4—102no—
604#235—54no—
605#235—54no—
606#235—54no—
607#235—102no—
608#235—108no—
609C2×D12—21no—
610C2×D12—51no—
611C2×D12—51no—
612C2×D12—51no—
613C2×D12—54no—
614C2×D12—108no—
615C2×D12—102no—
616C2×D12—101no—
617C2×D12—101no—
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×Dic6C22×D511yescharacteristic
626C3×SD16—54no—
627C3×SD16C22×D514yescomplemented
628C3×D8—54no—
629C3×D8—54no—
630C3×M16—54no—
631C2×C3×C8—51no—
632C2×C3×C8C22×D511yescharacteristic
633#216C22×D514yescomplemented
634#215—54no—
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—
645D24—54no—
646#204—54no—
647#204C22×D514yescomplemented
648ΓL(1,𝔽25)—54no—
649ΓL(1,𝔽25)—54no—
650D3×C8—54no—
651D3×C8C22×D514yescomplemented
652C23×C5—21no—
653C23×C5—31no—
654C23×C5—61no—
655C22×D5—21no—
656C22×D5—21no—
657C22×D5—24no—
658C22×D5—31no—
659C22×D5—64no—
660C22×D5—64no—
661C22×D5—64no—
662C22×D5—64no—
663C22×D5—61no—
664C22×D5—61no—
665C22×D5—64no—
666C22×D5—82no—
667C22×D5—242no—
668C22×D5—242no—
669C22×D5—242no—
670C22×D5—242no—
671C22×D5—242no—
672C22×D5D3×D411yescharacteristic
673C5×Q8—21no—
674C5×Q8—32no—
675C5×Q8—61no—
676C5×Q8C23×D312yes—
677C5×D4—21no—
678C5×D4—32no—
679C5×D4—64no—
680C5×D4—64no—
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×C5—64no—
689C2×C4×C5—61no—
690C2×C4×C5C23×D311yescharacteristic
691C22⋊D5—24no—
692C22⋊D5—34no—
693C22⋊D5—34no—
694C22⋊D5—64no—
695C22⋊D5—64no—
696C22⋊D5—64no—
697C2×Dic5—31no—
698C2×Dic5D3×D411yescharacteristic
699D20—24no—
700D20—21no—
701D20—21no—
702D20—34no—
703D20—32no—
704D20—32no—
705D20—64no—
706D20—64no—
707D20—64no—
708D20—64no—
709D20—64no—
710D20—61no—
711D20—61no—
712D20C23×D312yes—
713D20C23×D312yes—
714C4×D5—24no—
715C4×D5—32no—
716C4×D5—32no—
717C4×D5—64no—
718C4×D5—64no—
719C4×D5—64no—
720C4×D5D3×D412yes—
721C4×D5C23×D312yes—
722Dic10—34no—
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—31no—
733C2×#41—51no—
734C2×#41—151no—
735C2×#41—151no—
736C2×#41—151no—
737C2×#41—151no—
738C2×#41—301no—
739C2×#41—301no—
740C22×D4—51no—
741C22×D4—151no—
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)—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—38no—
759#135—158no—
760#135—158no—
761C2×Q16—31no—
762C2×SD16—31no—
763C2×SD16—51no—
764C2×SD16—151no—
765C2×SD16—151no—
766C2×SD16—151no—
767C2×SD16D3×D511yescharacteristic, complemented
768C2×D8—31no—
769C2×D8—51no—
770C2×D8—51no—
771C2×D8—158no—
772C2×D8—151no—
773C2×D8—151no—
774C2×D8—151no—
775C2×D8—158no—
776C2×D8—158no—
777C2×D8—151no—
778C2×D8—151no—
779C2×D8—151no—
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#57612yescomplemented
789C2×C3×C5C23×D411yescharacteristic
790D15—22no—
791D15—42no—
792D15—42no—
793C3×D5—22no—
794C3×D5—42no—
795C3×D5—42no—
796C5×D3—22no—
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—51no—
806C22×D3—104no—
807C22×D3—104no—
808C22×D3—104no—
809C22×D3—101no—
810C22×D3—101no—
811C22×D3—104no—
812C22×D3—104no—
813C22×D3—402no—
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—21no—
845C2×Dic3—24no—
846C2×Dic3—51no—
847C2×Dic3—104no—
848C2×Dic3D4×D511yescharacteristic
849D12—24no—
850D12—21no—
851D12—54no—
852D12—52no—
853D12—52no—
854D12—104no—
855D12—104no—
856D12—101no—
857D12—101no—
858D12C23×D512yes—
859C4×D3—24no—
860C4×D3—52no—
861C4×D3—52no—
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—32no—
875C22×C5—42no—
876C22×C5—62no—
877C22×C5—62no—
878C22×C5—122no—
879C22×C5C2×D3×D411yescharacteristic
880C2×D5—22no—
881C2×D5—22no—
882C2×D5—22no—
883C2×D5—32no—
884C2×D5—42no—
885C2×D5—42no—
886C2×D5—62no—
887C2×D5—62no—
888C2×D5—62no—
889C2×D5—84no—
890C2×D5—122no—
891C2×D5—122no—
892C2×D5—244no—
893C2×D5—244no—
894C2×D5—244no—
895C2×D5—244no—
896C2×D5—244no—
897C2×D5C2×D3×D412yes—
898C4×C5—22no—
899C4×C5—32no—
900C4×C5—62no—
901C4×C5C2×D3×D411yescharacteristic
902C4×C5C24×D311yescharacteristic
903Dic5—32no—
904Dic5C2×D3×D412yes—
905C24—101no—
906C24—301no—
907C24—301no—
908C24—301no—
909C24—301no—
910C24—301no—
911#41—34no—
912#41—34no—
913#41—54no—
914#41—62no—
915#41—62no—
916#41—102no—
917#41—154no—
918#41—154no—
919#41—154no—
920#41—154no—
921#41—154no—
922#41—302no—
923#41—308no—
924#41—308no—
925#41—302no—
926#41—302no—
927C2×Q8—31no—
928C2×Q8—151no—
929C2×Q8C2×D3×D511yescharacteristic
930C2×D4—31no—
931C2×D4—54no—
932C2×D4—51no—
933C2×D4—51no—
934C2×D4—61no—
935C2×D4—61no—
936C2×D4—101no—
937C2×D4—102no—
938C2×D4—101no—
939C2×D4—154no—
940C2×D4—154no—
941C2×D4—151no—
942C2×D4—154no—
943C2×D4—151no—
944C2×D4—154no—
945C2×D4—151no—
946C2×D4—154no—
947C2×D4—151no—
948C2×D4—151no—
949C2×D4—301no—
950C2×D4—302no—
951C2×D4—302no—
952C2×D4—301no—
953C2×D4—301no—
954C2×D4—302no—
955C2×D4—301no—
956C2×D4—308no—
957C2×D4—308no—
958C2×D4—301no—
959C2×D4—301no—
960C2×D4—308no—
961C2×D4—302no—
962C2×D4—302no—
963C2×D4—301no—
964C2×D4—301no—
965C2×D4—308no—
966C2×D4—308no—
967C2×D4—308no—
968C2×D4C2×D3×D511yescharacteristic
969C22×C4—31no—
970C22×C4—51no—
971C22×C4—61no—
972C22×C4—61no—
973C22×C4—101no—
974C22×C4—151no—
975C22×C4—301no—
976C22×C4—301no—
977C22×C4—301no—
978Q16—34no—
979SD16—34no—
980SD16—54no—
981SD16—154no—
982SD16—154no—
983SD16—154no—
984SD16C2×D3×D514yescomplemented
985D8—34no—
986D8—54no—
987D8—54no—
988D8—154no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8—154no—
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—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—42no—
1018C2×D3—52no—
1019C2×D3—102no—
1020C2×D3—102no—
1021C2×D3—102no—
1022C2×D3—202no—
1023C2×D3—202no—
1024C2×D3—404no—
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—22no—
1035Dic3—52no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—62no—
1039C2×C5—122no—
1040C2×C5#577412yescomplemented
1041C2×C5C22×D3×D411yescharacteristic
1042D5—22no—
1043D5—42no—
1044D5—42no—
1045D5—62no—
1046D5—122no—
1047D5—122no—
1048C23—21no—
1049C23—31no—
1050C23—51no—
1051C23—61no—
1052C23—104no—
1053C23—101no—
1054C23—101no—
1055C23—151no—
1056C23—304no—
1057C23—304no—
1058C23—304no—
1059C23—304no—
1060C23—304no—
1061C23—301no—
1062C23—301no—
1063C23—402no—
1064C23—1202no—
1065C23—1202no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—21no—
1070Q8—32no—
1071Q8—61no—
1072Q8—154no—
1073Q8C22×D3×D512yes—
1074D4—21no—
1075D4—32no—
1076D4—52no—
1077D4—52no—
1078D4—64no—
1079D4—64no—
1080D4—61no—
1081D4—104no—
1082D4—104no—
1083D4—101no—
1084D4—101no—
1085D4—154no—
1086D4—154no—
1087D4—154no—
1088D4—152no—
1089D4—152no—
1090D4—304no—
1091D4—304no—
1092D4—304no—
1093D4—304no—
1094D4—304no—
1095D4—304no—
1096D4—304no—
1097D4—304no—
1098D4—301no—
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—64no—
1110C2×C4—61no—
1111C2×C4—104no—
1112C2×C4—151no—
1113C2×C4—152no—
1114C2×C4—152no—
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—102no—
1125C2×C3—202no—
1126C2×C3—202no—
1127C2×C3#6610312yescomplemented
1128C2×C3C22×D4×D511yescharacteristic
1129D3—22no—
1130D3—42no—
1131D3—102no—
1132D3—202no—
1133D3—202no—
1134C5C2×#577411yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—32no—
1137C22—42no—
1138C22—52no—
1139C22—62no—
1140C22—62no—
1141C22—102no—
1142C22—102no—
1143C22—102no—
1144C22—122no—
1145C22—152no—
1146C22—202no—
1147C22—202no—
1148C22—302no—
1149C22—302no—
1150C22—302no—
1151C22—404no—
1152C22—602no—
1153C22—602no—
1154C22—1204no—
1155C22—1204no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—22no—
1161C4—32no—
1162C4—52no—
1163C4—62no—
1164C4—152no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6610311yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—62no—
1170C2—102no—
1171C2—122no—
1172C2—202no—
1173C2—202no—
1174C2—302no—
1175C2—602no—
1176C2—602no—
1177C2#1175408912yesdirect 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×#92026C2semidirect
3. C2×#91803C2semidirect
4. C2×C5×#916C2semidirect
5. C2×C3×#4060C2semidirect
6. C2×#91521C2semidirect
7. C2×#91516C2semidirect
8. C2×#91504C2semidirect
9. C2×#91481C2semidirect
10. C2×#91480C2semidirect
11. C2×D5×#213C2semidirect
12. #11754089C2direct (N × H)
13. C2×#91267C2semidirect
14. C2×#91258C2semidirect
15. C2×D3×D40C2semidirect
16. C2×#91249C2semidirect
18. C2×#6821C22semidirect
19. C2×D4×D15C22semidirect
20. C2×C5×#239C22semidirect
21. C2×C5×#237C22semidirect
22. C2×C3×#713C22semidirect
23. C2×C3×D4×D5C22semidirect
29. #92035C22semidirect
31. #92026C22semidirect
33. C2×#6777C22semidirect
35. C2×D3×D20C22semidirect
36. C2×D3×D20C22semidirect
38. C2×D5×D12C22semidirect
39. C2×#6773C22semidirect
42. C2×#6766C22semidirect
43. C2×C3×C5×SD16C22semidirect
44. C2×#6717C22semidirect
45. C2×#6715C22semidirect
46. #91803C22semidirect
47. C2×D120C22semidirect
48. C2×#6705C22semidirect
49. C2×C5×#216C22semidirect
50. C2×C5×#213C22semidirect
51. C5×#916C22semidirect
52. C2×C5×#204C22semidirect
53. C2×C5×D3×C8C22semidirect
54. C2×C3×#688C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4060C22semidirect
57. C2×C3×D40C22semidirect
58. C2×C3×#676C22semidirect
59. #91521C22semidirect
60. #91516C22semidirect
61. #91504C22semidirect
62. #91481C22semidirect
63. #91480C22semidirect
64. D5×#213C22semidirect
65. C2×#6660C22semidirect
66. C2×#6655C22semidirect
67. C2×#6654C22semidirect
68. C2×#6653C22semidirect
69. C2×#6653C22semidirect
70. C2×#6652C22semidirect
71. C2×#6650C22semidirect
72. C2×#6648C22semidirect
73. C2×D5×C3⋊C8C22semidirect
74. #91267C22semidirect
75. #91258C22semidirect
76. D3×D40C22semidirect
77. #91249C22semidirect
90. C2×#4060D3semidirect
105. #6821C23semidirect
107. D4×D15C23semidirect
116. C5×#239C23semidirect
118. C5×#237C23semidirect
126. C3×#713C23semidirect
128. C3×D4×D5C23semidirect
152. #6777C23semidirect
156. D3×D20C23semidirect
157. D3×D20C23semidirect
160. D5×D12C23semidirect
162. #6773C23semidirect
167. #6766C23semidirect
168. C3×C5×SD16C23semidirect
170. #6717C23semidirect
171. #6715C23semidirect
173. D120C23semidirect
174. #6705C23semidirect
175. C5×#216C23semidirect
176. C5×#213C23semidirect
178. C5×#204C23semidirect
179. C5×D3×C8C23semidirect
180. C3×#688C23semidirect
181. C3×#686C23semidirect
183. C3×D40C23semidirect
184. C3×#676C23semidirect
185. #6660C23semidirect
186. #6655C23semidirect
187. #6654C23semidirect
188. #6653C23semidirect
189. #6653C23semidirect
190. #6652C23semidirect
191. #6650C23semidirect
192. #6648C23semidirect
193. D5×C3⋊C8C23semidirect
201. C2×#916D5semidirect
219. C2×#713C2×D3semidirect
227. C2×D4×D5C2×D3semidirect
238. C2×C5×SD16C2×D3semidirect
246. C2×#688C2×D3semidirect
250. C2×#686C2×D3semidirect
257. #4060C2×D3semidirect
264. C2×D40C2×D3semidirect
267. C2×#676C2×D3semidirect
353. C2×#239C2×D5semidirect
358. C2×#237C2×D5semidirect
373. C2×C3×SD16C2×D5semidirect
378. C2×#216C2×D5semidirect
386. C2×#213C2×D5semidirect
389. #916C2×D5semidirect
401. C2×#204C2×D5semidirect
405. C2×D3×C8C2×D5semidirect
438. #713C22×D3semidirect
450. D4×D5C22×D3semidirect
481. C5×SD16C22×D3semidirect
489. #688C22×D3semidirect
493. #686C22×D3semidirect
500. D40C22×D3semidirect
502. #676C22×D3semidirect
587. #239C22×D5semidirect
592. #237C22×D5semidirect
627. C3×SD16C22×D5semidirect
633. #216C22×D5semidirect
640. #213C22×D5semidirect
647. #204C22×D5semidirect
651. D3×C8C22×D5semidirect
767. C2×SD16D3×D5semidirect
788. C2×C3×C5#576semidirect
984. SD16C2×D3×D5semidirect
1004. C3×C5C2×#576semidirect
1040. C2×C5#5774semidirect
1127. C2×C3#66103semidirect
1134. C5C2×#5774semidirect
1167. C3C2×#66103semidirect
1177. C2#11754089direct (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×#920262
C2×#918032
C2×C5×#9162
C2×C3×#40602
C2×#915212
C2×#915162
C2×#915042
C2×#914812
C2×#914802
C2×D5×#2132
#117540892
C2×#912672
C2×#912582
C2×D3×D402
C2×#912492
C2×#661033
C2×#57745