Finite Group Databasebeta

← C2×#11754109 #14510114

Subgroups — C2×#11754109 #14510114

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92035C211yesmaximal, characteristic, complemented
2C2×#92029C211yesmaximal, characteristic, complemented
3C2×#91808C211yesmaximal, characteristic, complemented
4C2×C5×#918C211yesmaximal, characteristic, complemented
5C2×C3×#4064C211yesmaximal, characteristic, complemented
6C2×#91519C211yesmaximal, characteristic, complemented
7C2×#91516C211yesmaximal, characteristic, complemented
8C2×#91512C211yesmaximal, characteristic, complemented
9C2×#91506C211yesmaximal, characteristic, complemented
10C2×D3×#688C211yesmaximal, characteristic, complemented
11C2×D5×#215C211yesmaximal, characteristic, complemented
12#11754109C2116yesmaximal, direct product factor
13C2×#91268C211yesmaximal, characteristic, complemented
14C2×#91255C211yesmaximal, characteristic, complemented
15C2×#91253C211yesmaximal, characteristic, complemented
16C2×#91249C211yesmaximal, characteristic, complemented
17C2×#66112—31nomaximal, Hall
18C2×#6821C2211yescharacteristic
19C2×#6821C2211yescharacteristic, complemented
20C2×C5×#239C2211yescharacteristic
21C2×C5×D3×Q8C2211yescharacteristic, complemented
22C2×C3×#713C2211yescharacteristic
23C2×C3×Q8×D5C2211yescharacteristic, complemented
24#92035—24no—
25#92035C2218yescomplemented
26#92029—24no—
27#92029C2218yescomplemented
28C2×#6777—21no—
29C2×#6777C2211yescharacteristic
30C2×D3×D20—21no—
31C2×D3×D20C2211yescharacteristic
32C2×D5×D12—21no—
33C2×D5×D12C2211yescharacteristic
34C2×#6773—21no—
35C2×#6773C2211yescharacteristic, complemented
36C2×#6771—21no—
37C2×#6771—21no—
38C2×#6771C2211yescharacteristic
39C2×D15⋊Q8—21no—
40C2×D15⋊Q8C2211yescharacteristic, complemented
41C2×#6769—21no—
42C2×#6769C2211yescharacteristic, complemented
43C2×C3×C5×Q16C2211yescharacteristic, complemented
44C2×#6717C2211yescharacteristic, complemented
45C2×#6717C2211yescharacteristic, complemented
46#91808C2218yescomplemented
47C2×D120C2211yescharacteristic, complemented
48C2×C8×D15C2211yescharacteristic, complemented
49C2×C5×#216C2211yescharacteristic, complemented
50C2×C5×#215C2211yescharacteristic, complemented
51C5×#918C2218yescomplemented
52C2×C5×#204C2211yescharacteristic, complemented
53C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
54C2×C3×#689C2211yescharacteristic, complemented
55C2×C3×#688C2211yescharacteristic, complemented
56C3×#4064C2218yescomplemented
57C2×C3×#677C2211yescharacteristic, complemented
58C2×C3×#676C2211yescharacteristic, complemented
59#91519C2218yescomplemented
60#91516C2218yescomplemented
61#91512C2218yescomplemented
62#91506C2218yescomplemented
63D3×#688C2218yescomplemented
64D5×#215C2218yescomplemented
65C2×#6660C2211yescharacteristic, complemented
66C2×#6658C2211yescharacteristic, complemented
67C2×#6656C2211yescharacteristic, complemented
68C2×#6655C2211yescharacteristic, complemented
69C2×#6654C2211yescharacteristic, complemented
70C2×#6653C2211yescharacteristic, complemented
71C2×#6651C2211yescharacteristic, complemented
72C2×D3×#168C2211yescharacteristic, complemented
73C2×D5×C3⋊C8C2211yescharacteristic, complemented
74#91268C2218yescomplemented
75#91255C2218yescomplemented
76#91253C2218yescomplemented
77#91249C2218yescomplemented
78C2×#5778—51nomaximal, Hall
79C2×#4149—31no—
80C2×#4147—31no—
81C2×C5×#137—31no—
82C2×#4096—31no—
83C22×#688—31no—
84#66112—316no—
85C2×#4065—31no—
86C2×#4065—31no—
87C2×#4064—31no—
88C2×#4064D311yescharacteristic, complemented
89C2×#4060—31no—
90C2×#4060—31no—
91C2×D5×SD16—31no—
92C2×D5×SD16—31no—
93C2×#4054—31no—
94C2×#4053—31no—
95C22×D3×D5—21no—
96C22×D3×D5—21no—
97C22×D3×D5—21no—
98C2×C3×C5×Q8C2311yescharacteristic
99C2×C3×C5×Q8C2311yescharacteristic
100#6821—22no—
101#6821—22no—
102#6821C2314yes—
103#6821C2314yescomplemented
104C2×D60—21no—
105C2×D60—21no—
106C2×D60C2311yescharacteristic
107C2×D60C2311yescharacteristic
108C2×C4×D15—21no—
109C2×C4×D15—21no—
110C2×C4×D15C2311yescharacteristic
111C5×#239—22no—
112C5×#239C2314yes—
113C5×D3×Q8—22no—
114C5×D3×Q8C2314yescomplemented
115C2×C5×D12—21no—
116C2×C5×D12C2311yescharacteristic
117C2×C4×C5×D3—21no—
118C2×C4×C5×D3—21no—
119C2×C4×C5×D3C2311yescharacteristic
120C2×C5×Dic6—21no—
121C2×C5×Dic6C2311yescharacteristic
122C3×#713—22no—
123C3×#713C2314yes—
124C3×Q8×D5—22no—
125C3×Q8×D5C2314yescomplemented
126C2×C3×D20—21no—
127C2×C3×D20C2311yescharacteristic
128C2×C3×C4×D5—21no—
129C2×C3×C4×D5—21no—
130C2×C3×C4×D5C2311yescharacteristic
131C2×C3×Dic10—21no—
132C2×C3×Dic10C2311yescharacteristic
133C2×#1204—21no—
134C2×#1204D411yescharacteristic
135C2×#1203—21no—
136C2×#1203—21no—
137C2×#1203D411yescharacteristic
138C2×#1202—21no—
139C2×#1202—21no—
140C2×#1202D411yescharacteristic
141C2×#1201—21no—
142C2×#1201D411yescharacteristic
143C2×#1200—21no—
144C2×#1200—21no—
145C2×#1200—21no—
146#6777—22no—
147#6777—28no—
148#6777C2314yes—
149D3×D20—22no—
150D3×D20—28no—
151D3×D20C2314yes—
152D5×D12—22no—
153D5×D12—28no—
154D5×D12C2314yes—
155#6773—22no—
156#6773—28no—
157#6773C2314yescomplemented
158#6771—28no—
159#6771—28no—
160#6771D414yes—
161#6771C2314yes—
162D15⋊Q8—22no—
163D15⋊Q8—28no—
164D15⋊Q8C2314yescomplemented
165#6769—22no—
166#6769—28no—
167#6769C2314yescomplemented
168C3×C5×Q16C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6717C2314yescomplemented
171#6717C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173D120C2314yescomplemented
174C8×D15C2314yescomplemented
175C5×#216C2314yescomplemented
176C5×#215C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×#204C2314yescomplemented
179C5×ΓL(1,𝔽25)C2314yescomplemented
180C3×#689C2314yescomplemented
181C3×#688C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×#677C2314yescomplemented
184C3×#676C2314yescomplemented
185#6660C2314yescomplemented
186#6658C2314yescomplemented
187#6656C2314yescomplemented
188#6655C2314yescomplemented
189#6654C2314yescomplemented
190#6653C2314yescomplemented
191#6651C2314yescomplemented
192D3×#168C2314yescomplemented
193D5×C3⋊C8C2314yescomplemented
194C2×#1009—51no—
195C2×#1007—51no—
196C2×C3×#137—51no—
197C2×#950—51no—
198C22×#215—51no—
199#5778—516no—
200C2×#919—51no—
201C2×#919—51no—
202C2×#918—51no—
203C2×#918D511yescharacteristic, complemented
204C2×#914—51no—
205C2×#914—51no—
206C2×D3×SD16—51no—
207C2×D3×SD16—51no—
208C2×#908—51no—
209C2×#907—51no—
210C2×C5×#41—31no—
211C22×C5×Q8—31no—
212#4149—38no—
213#4149—64no—
214#4147—38no—
215#4147—64no—
216C2×#713—31no—
217C2×#713—31no—
218C2×#713—31no—
219C2×#713—61no—
220C2×#713C2×D311yescharacteristic
221C2×Q8×D5—31no—
222C2×Q8×D5—61no—
223C2×Q8×D5C2×D311yescharacteristic, complemented
224C2×D4×D5—31no—
225C2×D4×D5—31no—
226C2×D4×D5—61no—
227C2×D4×D5—61no—
228C2×#709—31no—
229C2×#709—31no—
230C2×#709—61no—
231C2×#709—61no—
232C2×#709—61no—
233C22×D20—31no—
234C22×D20—61no—
235C5×#137—38no—
236C2×C5×Q16—31no—
237C2×C5×Q16C2×D311yescharacteristic, complemented
238C2×C5×SD16—31no—
239C2×C5×SD16—31no—
240C2×C5×M16—31no—
241#4096—38no—
242C2×#689C2×D311yescharacteristic, complemented
243C2×#688—31no—
244C2×#688—31no—
245C2×#688—31no—
246C2×#688—38no—
247C2×#688—31no—
248C2×#688C2×D311yescharacteristic, complemented
249C2×#687—31no—
250C2×#686—31no—
251C22×#168—31no—
252#4065—38no—
253#4065—38no—
254#4064—38no—
255#4064C2×D318yescomplemented
256#4060—38no—
257#4060—38no—
258D5×SD16—38no—
259D5×SD16—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×#577—151noSylow
271C22×D15—21no—
272C22×D15—21no—
273C22×D15C2×D411yescharacteristic
274C22×C5×D3—21no—
275C22×C5×D3C2×D411yescharacteristic
276C22×C3×D5—21no—
277C22×C3×D5C2×D411yescharacteristic
278C2×D3×D5—24no—
279C2×D3×D5—24no—
280C2×D3×D5—24no—
281C2×D3×D5—82no—
282C2×D3×D5—82no—
283C2×D3×D5—82no—
284C3×C5×Q8—21no—
285C3×C5×Q8—21no—
286C3×C5×Q8C2412yes—
287C3×C5×Q8C2412yes—
288C2×C3×C4×C5—21no—
289C2×C3×C4×C5—21no—
290C2×C3×C4×C5C2411yescharacteristic
291C2×Dic15C2×D411yescharacteristic
292D60—24no—
293D60—24no—
294D60—21no—
295D60—21no—
296D60C2412yes—
297D60C2412yes—
298C4×D15—24no—
299C4×D15—24no—
300C4×D15C2×D412yes—
301C4×D15C2412yes—
302C2×C5×Dic3—21no—
303C2×C5×Dic3C2×D411yescharacteristic
304C5×D12—24no—
305C5×D12—21no—
306C5×D12C2412yes—
307C4×C5×D3—24no—
308C4×C5×D3—24no—
309C4×C5×D3C2×D412yes—
310C4×C5×D3C2412yes—
311C5×Dic6—21no—
312C5×Dic6—24no—
313C5×Dic6C2412yes—
314C2×C3×Dic5—21no—
315C2×C3×Dic5C2×D411yescharacteristic
316C3×D20—24no—
317C3×D20—21no—
318C3×D20C2412yes—
319C3×C4×D5—24no—
320C3×C4×D5—24no—
321C3×C4×D5C2×D412yes—
322C3×C4×D5C2412yes—
323C3×Dic10—21no—
324C3×Dic10—24no—
325C3×Dic10C2412yes—
326#1204—24no—
327#1204C2×D414yes—
328#1203—24no—
329#1203—24no—
330#1203C2×D414yes—
331#1202—24no—
332#1202—24no—
333#1202C2×D414yes—
334#1201—24no—
335#1201C2×D414yes—
336#1200—24no—
337#1200—24no—
338#1200—24no—
339C3×C5×C8C2412yes—
340C3⋊#168C2412yes—
341C3×#168C2412yes—
342C5×C3⋊C8C2412yes—
343C2×C3×#41—51no—
344C22×C3×Q8—51no—
345#1009—58no—
346#1009—104no—
347#1007—58no—
348#1007—104no—
349C2×#239—51no—
350C2×#239—51no—
351C2×#239—51no—
352C2×#239—101no—
353C2×#239C2×D511yescharacteristic
354C2×D3×Q8—51no—
355C2×D3×Q8—101no—
356C2×D3×Q8C2×D511yescharacteristic, complemented
357C2×D3×D4—51no—
358C2×D3×D4—51no—
359C2×D3×D4—101no—
360C2×D3×D4—101no—
361C2×#235—51no—
362C2×#235—51no—
363C2×#235—101no—
364C2×#235—101no—
365C2×#235—101no—
366C22×D12—51no—
367C22×D12—101no—
368C3×#137—58no—
369C2×C3×Q16—51no—
370C2×C3×Q16C2×D511yescharacteristic, complemented
371C2×C3×SD16—51no—
372C2×C3×SD16—51no—
373C2×C3×M16—51no—
374#950—58no—
375C2×#216C2×D511yescharacteristic, complemented
376C2×#215—51no—
377C2×#215—51no—
378C2×#215—51no—
379C2×#215—58no—
380C2×#215—51no—
381C2×#215C2×D511yescharacteristic, complemented
382C2×#214—51no—
383C2×#213—51no—
384C22×C3⋊C8—51no—
385#919—58no—
386#919—58no—
387#918—58no—
388#918C2×D518yescomplemented
389#914—58no—
390#914—58no—
391D3×SD16—58no—
392D3×SD16—58no—
393#908—58no—
394#907—58no—
395C2×D24—51no—
396C2×D24—51no—
397C2×#204—51no—
398C2×#204C2×D511yescharacteristic, complemented
399C2×ΓL(1,𝔽25)—51no—
400C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
401C2×D3×C8—51no—
402C2×D3×C8—51no—
403C23×D5—61no—
404C23×D5—61no—
405C23×D5—61no—
406C5×#41—34no—
407C5×#41—62no—
408C2×C5×Q8—34no—
409C2×C5×Q8—31no—
410C2×C5×Q8—61no—
411C2×C5×Q8—62no—
412C2×C5×Q8C22×D311yescharacteristic
413C2×C5×Q8C22×D311yescharacteristic
414C2×C5×D4—31no—
415C2×C5×D4—61no—
416C22×C4×C5—31no—
417C22×C4×C5—61no—
418C22×C4×C5—61no—
419C2×C22⋊D5—31no—
420C2×C22⋊D5—31no—
421C2×C22⋊D5—61no—
422C2×C22⋊D5—61no—
423C2×C22⋊D5—61no—
424#713—22no—
425#713—34no—
426#713—34no—
427#713—34no—
428#713—68no—
429#713—62no—
430#713—62no—
431#713—62no—
432#713C22×D314yes—
433Q8×D5—22no—
434Q8×D5—34no—
435Q8×D5—68no—
436Q8×D5—62no—
437Q8×D5C22×D314yescomplemented
438D4×D5—34no—
439D4×D5—34no—
440D4×D5—68no—
441D4×D5—62no—
442D4×D5—68no—
443D4×D5—62no—
444#709—34no—
445#709—34no—
446#709—34no—
447#709—68no—
448#709—62no—
449#709—68no—
450#709—68no—
451C2×D20—21no—
452C2×D20—31no—
453C2×D20—31no—
454C2×D20—31no—
455C2×D20—34no—
456C2×D20—68no—
457C2×D20—62no—
458C2×D20—61no—
459C2×D20—61no—
460C2×D20—61no—
461C2×D20—61no—
462C2×D20C22×D311yescharacteristic
463C2×C4×D5—21no—
464C2×C4×D5—21no—
465C2×C4×D5—31no—
466C2×C4×D5—61no—
467C2×C4×D5—61no—
468C2×C4×D5—61no—
469C2×C4×D5—61no—
470C2×C4×D5—61no—
471C2×C4×D5C22×D311yescharacteristic
472C2×Dic10—21no—
473C2×Dic10—31no—
474C2×Dic10—61no—
475C2×Dic10C22×D311yescharacteristic
476C5×Q16—34no—
477C5×Q16C22×D314yescomplemented
478C5×SD16—34no—
479C5×SD16—34no—
480C5×M16—34no—
481C2×C5×C8—31no—
482C2×C5×C8C22×D311yescharacteristic
483#689C22×D314yescomplemented
484#688—34no—
485#688—34no—
486#688—34no—
487#688—34no—
488#688C22×D314yescomplemented
489#687—34no—
490#686—34no—
491C2×#168—31no—
492C2×#168—34no—
493C2×#168C22×D311yescharacteristic
494D40—34no—
495D40—34no—
496#677—34no—
497#677C22×D314yescomplemented
498#676—34no—
499#676C22×D314yescomplemented
500C8×D5—34no—
501C8×D5—34no—
502C2×2−1+4—151no—
503C2×H(5,𝔽2)—151no—
504#577—1516no—
505C2×#137—31no—
506C2×#137—51no—
507C2×#137—151no—
508C2×AGL(1,ℤ/8)—151no—
509C2×AGL(1,ℤ/8)—151no—
510C2×AGL(1,ℤ/8)—151no—
511C2×#135—151no—
512C2×#135—151no—
513C2×#135—151no—
514C22×SD16—151no—
515C22×SD16—151no—
516C22×SD16—151no—
517C2×#131—151no—
518C22×C3×C5C22×D411yescharacteristic
519C2×D15—22no—
520C2×D15—22no—
521C2×D15—22no—
522C2×D15—42no—
523C2×D15—42no—
524C2×D15C22×D412yes—
525C2×C5×D3—22no—
526C2×C5×D3—22no—
527C2×C5×D3—42no—
528C2×C5×D3C22×D412yes—
529C2×C3×D5—22no—
530C2×C3×D5—22no—
531C2×C3×D5—42no—
532C2×C3×D5C22×D412yes—
533D3×D5—84no—
534D3×D5—84no—
535D3×D5—84no—
536C3×C4×C5—22no—
537C3×C4×C5—22no—
538C3×C4×C5C22×D411yescharacteristic
539C3×C4×C5C2511yescharacteristic
540Dic15C22×D412yes—
541C3×Dic5—22no—
542C3×Dic5C22×D412yes—
543C5×Dic3—22no—
544C5×Dic3C22×D412yes—
545C23×D3—101no—
546C23×D3—101no—
547C23×D3—101no—
548C3×#41—54no—
549C3×#41—102no—
550C2×C3×Q8—54no—
551C2×C3×Q8—51no—
552C2×C3×Q8—101no—
553C2×C3×Q8—102no—
554C2×C3×Q8C22×D511yescharacteristic
555C2×C3×Q8C22×D511yescharacteristic
556C2×C3×D4—51no—
557C2×C3×D4—101no—
558C22×C3×C4—51no—
559C22×C3×C4—101no—
560C22×C3×C4—101no—
561C2×#67—51no—
562C2×#67—51no—
563C2×#67—101no—
564C2×#67—101no—
565C2×#67—101no—
566#239—22no—
567#239—54no—
568#239—54no—
569#239—54no—
570#239—108no—
571#239—102no—
572#239—102no—
573#239—102no—
574#239C22×D514yes—
575D3×Q8—22no—
576D3×Q8—54no—
577D3×Q8—108no—
578D3×Q8—102no—
579D3×Q8C22×D514yescomplemented
580D3×D4—54no—
581D3×D4—54no—
582D3×D4—108no—
583D3×D4—102no—
584D3×D4—108no—
585D3×D4—102no—
586#235—54no—
587#235—54no—
588#235—54no—
589#235—108no—
590#235—102no—
591#235—108no—
592#235—108no—
593C2×D12—21no—
594C2×D12—51no—
595C2×D12—51no—
596C2×D12—51no—
597C2×D12—54no—
598C2×D12—108no—
599C2×D12—102no—
600C2×D12—101no—
601C2×D12—101no—
602C2×D12—101no—
603C2×D12—101no—
604C2×D12C22×D511yescharacteristic
605C2×C4×D3—21no—
606C2×C4×D3—21no—
607C2×C4×D3—51no—
608C2×C4×D3—101no—
609C2×C4×D3—101no—
610C2×C4×D3—101no—
611C2×C4×D3—101no—
612C2×C4×D3—101no—
613C2×C4×D3C22×D511yescharacteristic
614C2×Dic6—21no—
615C2×Dic6—51no—
616C2×Dic6—101no—
617C2×Dic6C22×D511yescharacteristic
618C3×Q16—54no—
619C3×Q16C22×D514yescomplemented
620C3×SD16—54no—
621C3×SD16—54no—
622C3×M16—54no—
623C2×C3×C8—51no—
624C2×C3×C8C22×D511yescharacteristic
625#216C22×D514yescomplemented
626#215—54no—
627#215—54no—
628#215—54no—
629#215—54no—
630#215C22×D514yescomplemented
631#214—54no—
632#213—54no—
633C2×C3⋊C8—51no—
634C2×C3⋊C8—54no—
635C2×C3⋊C8C22×D511yescharacteristic
636D24—54no—
637D24—54no—
638#204—54no—
639#204C22×D514yescomplemented
640ΓL(1,𝔽25)—54no—
641ΓL(1,𝔽25)C22×D514yescomplemented
642D3×C8—54no—
643D3×C8—54no—
644C23×C5—31no—
645C23×C5—61no—
646C22×D5—21no—
647C22×D5—31no—
648C22×D5—64no—
649C22×D5—64no—
650C22×D5—61no—
651C22×D5—61no—
652C22×D5—64no—
653C22×D5—242no—
654C22×D5—242no—
655C22×D5—242no—
656C22×D5D3×D411yescharacteristic
657C5×Q8—21no—
658C5×Q8—21no—
659C5×Q8—32no—
660C5×Q8—64no—
661C5×Q8—61no—
662C5×Q8C23×D312yes—
663C5×Q8C23×D312yes—
664C5×D4—32no—
665C5×D4—64no—
666C5×D4—61no—
667C2×C4×C5—21no—
668C2×C4×C5—21no—
669C2×C4×C5—31no—
670C2×C4×C5—32no—
671C2×C4×C5—32no—
672C2×C4×C5—64no—
673C2×C4×C5—64no—
674C2×C4×C5—61no—
675C2×C4×C5C23×D311yescharacteristic
676C22⋊D5—34no—
677C22⋊D5—34no—
678C22⋊D5—64no—
679C22⋊D5—64no—
680C22⋊D5—64no—
681C2×Dic5—21no—
682C2×Dic5—31no—
683C2×Dic5D3×D411yescharacteristic
684D20—24no—
685D20—21no—
686D20—34no—
687D20—32no—
688D20—32no—
689D20—64no—
690D20—64no—
691D20—64no—
692D20—64no—
693D20—61no—
694D20—61no—
695D20C23×D312yes—
696C4×D5—24no—
697C4×D5—24no—
698C4×D5—32no—
699C4×D5—32no—
700C4×D5—64no—
701C4×D5—64no—
702C4×D5—64no—
703C4×D5—64no—
704C4×D5—64no—
705C4×D5D3×D412yes—
706C4×D5C23×D312yes—
707Dic10—21no—
708Dic10—24no—
709Dic10—34no—
710Dic10—64no—
711Dic10C23×D312yes—
712C5×C8—32no—
713C5×C8C23×D312yes—
714#168—32no—
715#168C23×D312yes—
7162−1+4—158no—
7172−1+4—304no—
718H(5,𝔽2)—158no—
719H(5,𝔽2)—304no—
720C2×#41—31no—
721C2×#41—51no—
722C2×#41—151no—
723C2×#41—151no—
724C2×#41—151no—
725C2×#41—151no—
726C2×#41—151no—
727C2×#41—301no—
728C2×#41—301no—
729C2×#41—301no—
730C2×#41—301no—
731C22×Q8—31no—
732C22×Q8—51no—
733C22×Q8—151no—
734C22×Q8—301no—
735C22×D4—151no—
736C22×D4—151no—
737C22×D4—151no—
738C22×D4—301no—
739C22×D4—301no—
740C22×D4—301no—
741#137—38no—
742#137—58no—
743#137—158no—
744AGL(1,ℤ/8)—158no—
745AGL(1,ℤ/8)—158no—
746AGL(1,ℤ/8)—158no—
747#135—158no—
748#135—158no—
749#135—158no—
750C2×Q16—31no—
751C2×Q16—51no—
752C2×Q16D3×D511yescharacteristic, complemented
753C2×SD16—31no—
754C2×SD16—31no—
755C2×SD16—51no—
756C2×SD16—51no—
757C2×SD16—151no—
758C2×SD16—151no—
759C2×SD16—158no—
760C2×SD16—158no—
761C2×SD16—158no—
762C2×SD16—151no—
763C2×SD16—151no—
764C2×SD16—151no—
765C2×SD16—151no—
766C2×D8—151no—
767C2×D8—151no—
768C2×D8—151no—
769#131—158no—
770C2×M16—31no—
771C2×M16—51no—
772C2×M16—151no—
773C22×C8—151no—
774C22×C8—151no—
775C22×C8—151no—
776C2×C3×C5#57712yescomplemented
777C2×C3×C5C23×D411yescharacteristic
778D15—22no—
779D15—42no—
780D15—42no—
781C3×D5—22no—
782C3×D5—42no—
783C5×D3—22no—
784C5×D3—42no—
785C23×C3—51no—
786C23×C3—101no—
787C22×D3—21no—
788C22×D3—51no—
789C22×D3—104no—
790C22×D3—104no—
791C22×D3—101no—
792C22×D3—101no—
793C22×D3—104no—
794C22×D3—402no—
795C22×D3—402no—
796C22×D3—402no—
797C22×D3D4×D511yescharacteristic
798C3×Q8—21no—
799C3×Q8—21no—
800C3×Q8—52no—
801C3×Q8—104no—
802C3×Q8—101no—
803C3×Q8C23×D512yes—
804C3×Q8C23×D512yes—
805C3×D4—52no—
806C3×D4—104no—
807C3×D4—101no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—51no—
811C2×C3×C4—52no—
812C2×C3×C4—52no—
813C2×C3×C4—104no—
814C2×C3×C4—104no—
815C2×C3×C4—101no—
816C2×C3×C4C23×D511yescharacteristic
817#67—54no—
818#67—54no—
819#67—104no—
820#67—104no—
821#67—104no—
822C2×Dic3—21no—
823C2×Dic3—51no—
824C2×Dic3D4×D511yescharacteristic
825D12—24no—
826D12—21no—
827D12—54no—
828D12—52no—
829D12—52no—
830D12—104no—
831D12—104no—
832D12—104no—
833D12—104no—
834D12—101no—
835D12—101no—
836D12C23×D512yes—
837C4×D3—24no—
838C4×D3—24no—
839C4×D3—52no—
840C4×D3—52no—
841C4×D3—104no—
842C4×D3—104no—
843C4×D3—104no—
844C4×D3—104no—
845C4×D3—104no—
846C4×D3D4×D512yes—
847C4×D3C23×D512yes—
848Dic6—21no—
849Dic6—24no—
850Dic6—54no—
851Dic6—104no—
852Dic6C23×D512yes—
853C3×C8—52no—
854C3×C8C23×D512yes—
855C3⋊C8—52no—
856C3⋊C8C23×D512yes—
857C22×C5—32no—
858C22×C5—62no—
859C22×C5—62no—
860C22×C5—122no—
861C22×C5C2×D3×D411yescharacteristic
862C2×D5—22no—
863C2×D5—22no—
864C2×D5—32no—
865C2×D5—42no—
866C2×D5—62no—
867C2×D5—62no—
868C2×D5—62no—
869C2×D5—122no—
870C2×D5—122no—
871C2×D5—244no—
872C2×D5—244no—
873C2×D5—244no—
874C2×D5C2×D3×D412yes—
875C4×C5—22no—
876C4×C5—22no—
877C4×C5—32no—
878C4×C5—62no—
879C4×C5C2×D3×D411yescharacteristic
880C4×C5C24×D311yescharacteristic
881Dic5—22no—
882Dic5—32no—
883Dic5C2×D3×D412yes—
884C24—301no—
885C24—301no—
886C24—301no—
887#41—34no—
888#41—54no—
889#41—62no—
890#41—102no—
891#41—154no—
892#41—154no—
893#41—154no—
894#41—154no—
895#41—154no—
896#41—154no—
897#41—302no—
898#41—302no—
899#41—308no—
900#41—308no—
901#41—308no—
902#41—308no—
903#41—302no—
904#41—302no—
905C2×Q8—34no—
906C2×Q8—31no—
907C2×Q8—54no—
908C2×Q8—51no—
909C2×Q8—61no—
910C2×Q8—62no—
911C2×Q8—101no—
912C2×Q8—102no—
913C2×Q8—151no—
914C2×Q8—154no—
915C2×Q8—301no—
916C2×Q8—302no—
917C2×Q8—308no—
918C2×Q8C2×D3×D511yescharacteristic
919C2×Q8C2×D3×D511yescharacteristic
920C2×D4—31no—
921C2×D4—51no—
922C2×D4—61no—
923C2×D4—101no—
924C2×D4—154no—
925C2×D4—151no—
926C2×D4—154no—
927C2×D4—151no—
928C2×D4—154no—
929C2×D4—151no—
930C2×D4—151no—
931C2×D4—151no—
932C2×D4—301no—
933C2×D4—301no—
934C2×D4—302no—
935C2×D4—301no—
936C2×D4—302no—
937C2×D4—301no—
938C2×D4—308no—
939C2×D4—301no—
940C2×D4—308no—
941C2×D4—301no—
942C2×D4—302no—
943C2×D4—301no—
944C2×D4—308no—
945C22×C4—31no—
946C22×C4—51no—
947C22×C4—61no—
948C22×C4—61no—
949C22×C4—101no—
950C22×C4—101no—
951C22×C4—151no—
952C22×C4—301no—
953C22×C4—301no—
954C22×C4—301no—
955C22×C4—301no—
956C22×C4—301no—
957Q16—34no—
958Q16—54no—
959Q16C2×D3×D514yescomplemented
960SD16—34no—
961SD16—34no—
962SD16—54no—
963SD16—54no—
964SD16—154no—
965SD16—154no—
966SD16—154no—
967SD16—154no—
968SD16—154no—
969SD16—154no—
970D8—154no—
971D8—154no—
972D8—154no—
973M16—34no—
974M16—54no—
975M16—154no—
976C2×C8—31no—
977C2×C8—51no—
978C2×C8—154no—
979C2×C8—154no—
980C2×C8—151no—
981C2×C8—154no—
982C2×C8C2×D3×D511yescharacteristic
983C3×C5C2×#57711yescharacteristic, complemented, Hall
984C22×C3—52no—
985C22×C3—102no—
986C22×C3—102no—
987C22×C3—202no—
988C22×C3C2×D4×D511yescharacteristic
989C2×D3—22no—
990C2×D3—22no—
991C2×D3—42no—
992C2×D3—52no—
993C2×D3—102no—
994C2×D3—102no—
995C2×D3—102no—
996C2×D3—202no—
997C2×D3—202no—
998C2×D3—404no—
999C2×D3—404no—
1000C2×D3—404no—
1001C2×D3C2×D4×D512yes—
1002C3×C4—22no—
1003C3×C4—22no—
1004C3×C4—52no—
1005C3×C4—102no—
1006C3×C4C2×D4×D511yescharacteristic
1007C3×C4C24×D511yescharacteristic
1008Dic3—22no—
1009Dic3—52no—
1010Dic3C2×D4×D512yes—
1011C2×C5—62no—
1012C2×C5—122no—
1013C2×C5#577812yescomplemented
1014C2×C5C22×D3×D411yescharacteristic
1015D5—22no—
1016D5—42no—
1017D5—62no—
1018D5—122no—
1019D5—122no—
1020C23—31no—
1021C23—51no—
1022C23—61no—
1023C23—101no—
1024C23—151no—
1025C23—304no—
1026C23—304no—
1027C23—304no—
1028C23—301no—
1029C23—301no—
1030C23—1202no—
1031C23—1202no—
1032C23—1202no—
1033Q8—21no—
1034Q8—21no—
1035Q8—32no—
1036Q8—52no—
1037Q8—64no—
1038Q8—61no—
1039Q8—104no—
1040Q8—101no—
1041Q8—154no—
1042Q8—304no—
1043Q8C22×D3×D512yes—
1044Q8C22×D3×D512yes—
1045D4—32no—
1046D4—52no—
1047D4—64no—
1048D4—61no—
1049D4—104no—
1050D4—101no—
1051D4—154no—
1052D4—154no—
1053D4—154no—
1054D4—152no—
1055D4—152no—
1056D4—304no—
1057D4—304no—
1058D4—304no—
1059D4—304no—
1060D4—304no—
1061D4—304no—
1062D4—304no—
1063D4—301no—
1064D4—301no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—31no—
1068C2×C4—32no—
1069C2×C4—32no—
1070C2×C4—51no—
1071C2×C4—52no—
1072C2×C4—52no—
1073C2×C4—64no—
1074C2×C4—64no—
1075C2×C4—61no—
1076C2×C4—104no—
1077C2×C4—104no—
1078C2×C4—101no—
1079C2×C4—151no—
1080C2×C4—152no—
1081C2×C4—152no—
1082C2×C4—304no—
1083C2×C4—304no—
1084C2×C4—304no—
1085C2×C4—304no—
1086C2×C4—304no—
1087C2×C4C22×D3×D511yescharacteristic
1088C8—32no—
1089C8—52no—
1090C8—152no—
1091C8C22×D3×D512yes—
1092C2×C3—102no—
1093C2×C3—202no—
1094C2×C3#6611212yescomplemented
1095C2×C3C22×D4×D511yescharacteristic
1096D3—22no—
1097D3—42no—
1098D3—102no—
1099D3—202no—
1100D3—202no—
1101C5C2×#577811yescharacteristic, complemented, Sylow
1102C22—32no—
1103C22—52no—
1104C22—62no—
1105C22—62no—
1106C22—102no—
1107C22—102no—
1108C22—122no—
1109C22—152no—
1110C22—202no—
1111C22—302no—
1112C22—302no—
1113C22—302no—
1114C22—602no—
1115C22—602no—
1116C22—1204no—
1117C22—1204no—
1118C22—1204no—
1119C22D3×D4×D511yescharacteristic
1120C4—22no—
1121C4—22no—
1122C4—32no—
1123C4—52no—
1124C4—62no—
1125C4—102no—
1126C4—152no—
1127C4D3×D4×D511yescharacteristic
1128C4C23×D3×D511yescharacteristic
1129C3C2×#6611211yescharacteristic, complemented, Sylow
1130C2—62no—
1131C2—102no—
1132C2—122no—
1133C2—202no—
1134C2—302no—
1135C2—602no—
1136C2—602no—
1137C2#1175410912yesdirect product factor
1138C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
hypercenterC2×Q16D3×D5
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#92035C2semidirect
2. C2×#92029C2semidirect
3. C2×#91808C2semidirect
4. C2×C5×#918C2semidirect
5. C2×C3×#4064C2semidirect
6. C2×#91519C2semidirect
7. C2×#91516C2semidirect
8. C2×#91512C2semidirect
9. C2×#91506C2semidirect
10. C2×D3×#688C2semidirect
11. C2×D5×#215C2semidirect
12. #11754109C2direct (N × H)
13. C2×#91268C2semidirect
14. C2×#91255C2semidirect
15. C2×#91253C2semidirect
16. C2×#91249C2semidirect
19. C2×#6821C22semidirect
21. C2×C5×D3×Q8C22semidirect
23. C2×C3×Q8×D5C22semidirect
25. #92035C22semidirect
27. #92029C22semidirect
35. C2×#6773C22semidirect
40. C2×D15⋊Q8C22semidirect
42. C2×#6769C22semidirect
43. C2×C3×C5×Q16C22semidirect
44. C2×#6717C22semidirect
45. C2×#6717C22semidirect
46. #91808C22semidirect
47. C2×D120C22semidirect
48. C2×C8×D15C22semidirect
49. C2×C5×#216C22semidirect
50. C2×C5×#215C22semidirect
51. C5×#918C22semidirect
52. C2×C5×#204C22semidirect
53. C2×C5×ΓL(1,𝔽25)C22semidirect
54. C2×C3×#689C22semidirect
55. C2×C3×#688C22semidirect
56. C3×#4064C22semidirect
57. C2×C3×#677C22semidirect
58. C2×C3×#676C22semidirect
59. #91519C22semidirect
60. #91516C22semidirect
61. #91512C22semidirect
62. #91506C22semidirect
63. D3×#688C22semidirect
64. D5×#215C22semidirect
65. C2×#6660C22semidirect
66. C2×#6658C22semidirect
67. C2×#6656C22semidirect
68. C2×#6655C22semidirect
69. C2×#6654C22semidirect
70. C2×#6653C22semidirect
71. C2×#6651C22semidirect
72. C2×D3×#168C22semidirect
73. C2×D5×C3⋊C8C22semidirect
74. #91268C22semidirect
75. #91255C22semidirect
76. #91253C22semidirect
77. #91249C22semidirect
88. C2×#4064D3semidirect
103. #6821C23semidirect
114. C5×D3×Q8C23semidirect
125. C3×Q8×D5C23semidirect
157. #6773C23semidirect
164. D15⋊Q8C23semidirect
167. #6769C23semidirect
168. C3×C5×Q16C23semidirect
170. #6717C23semidirect
171. #6717C23semidirect
173. D120C23semidirect
174. C8×D15C23semidirect
175. C5×#216C23semidirect
176. C5×#215C23semidirect
178. C5×#204C23semidirect
179. C5×ΓL(1,𝔽25)C23semidirect
180. C3×#689C23semidirect
181. C3×#688C23semidirect
183. C3×#677C23semidirect
184. C3×#676C23semidirect
185. #6660C23semidirect
186. #6658C23semidirect
187. #6656C23semidirect
188. #6655C23semidirect
189. #6654C23semidirect
190. #6653C23semidirect
191. #6651C23semidirect
192. D3×#168C23semidirect
193. D5×C3⋊C8C23semidirect
203. C2×#918D5semidirect
223. C2×Q8×D5C2×D3semidirect
237. C2×C5×Q16C2×D3semidirect
242. C2×#689C2×D3semidirect
248. C2×#688C2×D3semidirect
255. #4064C2×D3semidirect
265. C2×#677C2×D3semidirect
267. C2×#676C2×D3semidirect
356. C2×D3×Q8C2×D5semidirect
370. C2×C3×Q16C2×D5semidirect
375. C2×#216C2×D5semidirect
381. C2×#215C2×D5semidirect
388. #918C2×D5semidirect
398. C2×#204C2×D5semidirect
400. C2×ΓL(1,𝔽25)C2×D5semidirect
437. Q8×D5C22×D3semidirect
477. C5×Q16C22×D3semidirect
483. #689C22×D3semidirect
488. #688C22×D3semidirect
497. #677C22×D3semidirect
499. #676C22×D3semidirect
579. D3×Q8C22×D5semidirect
619. C3×Q16C22×D5semidirect
625. #216C22×D5semidirect
630. #215C22×D5semidirect
639. #204C22×D5semidirect
641. ΓL(1,𝔽25)C22×D5semidirect
752. C2×Q16D3×D5semidirect
776. C2×C3×C5#577semidirect
959. Q16C2×D3×D5semidirect
983. C3×C5C2×#577semidirect
1013. C2×C5#5778semidirect
1094. C2×C3#66112semidirect
1101. C5C2×#5778semidirect
1129. C3C2×#66112semidirect
1137. C2#11754109direct (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×#920292
C2×#918082
C2×C5×#9182
C2×C3×#40642
C2×#915192
C2×#915162
C2×#915122
C2×#915062
C2×D3×#6882
C2×D5×#2152
#117541092
C2×#912682
C2×#912552
C2×#912532
C2×#912492
C2×#661123
C2×#57785