Finite Group Databasebeta

← C2×#11754093 #14509988

Subgroups — C2×#11754093 #14509988

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×#92027C211yesmaximal, characteristic, complemented
3C2×#91803C211yesmaximal, characteristic, complemented
4C2×C5×#914C211yesmaximal, characteristic, complemented
5C2×C3×#4062C211yesmaximal, characteristic, complemented
6C2×#91523C211yesmaximal, characteristic, complemented
7C2×#91519C211yesmaximal, characteristic, complemented
8C2×#91502C211yesmaximal, characteristic, complemented
9C2×#91481C211yesmaximal, characteristic, complemented
10C2×D3×#686C211yesmaximal, characteristic, complemented
11C2×#91478C211yesmaximal, characteristic, complemented
12#11754093C2116yesmaximal, direct product factor
13C2×#91266C211yesmaximal, characteristic, complemented
14C2×#91257C211yesmaximal, characteristic, complemented
15C2×#91253C211yesmaximal, characteristic, complemented
16C2×D5×D24C211yesmaximal, characteristic, complemented
17C2×#66108—31nomaximal, Hall
18C2×#6821C2211yescharacteristic, complemented
19C2×D4×D15C2211yescharacteristic, complemented
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×D3×D4C2211yescharacteristic, complemented
22C2×C3×#713C2211yescharacteristic, complemented
23C2×C3×#711C2211yescharacteristic, complemented
24C2×#6790—21no—
25C2×D3×C22⋊D5—21no—
26C22×#1203—21no—
27C2×#6782—21no—
28#92035—24no—
29#92035C2218yescomplemented
30#92027—24no—
31#92027C2218yescomplemented
32C2×#6777—21no—
33C2×#6777C2211yescharacteristic, complemented
34C2×D3×D20—21no—
35C2×D3×D20C2211yescharacteristic, complemented
36C2×D5×D12—21no—
37C2×D5×D12C2211yescharacteristic, complemented
38C2×D5×D12C2211yescharacteristic, complemented
39C2×#6771—21no—
40C2×#6771C2211yescharacteristic
41C2×#6769C2211yescharacteristic, complemented
42C2×#6768C2211yescharacteristic, complemented
43C2×C3×C5×SD16C2211yescharacteristic, complemented
44C2×#6717C2211yescharacteristic, complemented
45C2×#6715C2211yescharacteristic, complemented
46#91803C2218yescomplemented
47C2×D120C2211yescharacteristic, complemented
48C2×#6705C2211yescharacteristic, complemented
49C2×C5×#215C2211yescharacteristic, complemented
50C2×C5×#213C2211yescharacteristic, complemented
51C5×#914C2218yescomplemented
52C2×C5×D24C2211yescharacteristic, complemented
53C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
54C2×C3×#689C2211yescharacteristic, complemented
55C2×C3×#686C2211yescharacteristic, complemented
56C3×#4062C2218yescomplemented
57C2×C3×#677C2211yescharacteristic, complemented
58C2×C3×C8×D5C2211yescharacteristic, complemented
59#91523C2218yescomplemented
60#91519C2218yescomplemented
61#91502C2218yescomplemented
62#91481C2218yescomplemented
63D3×#686C2218yescomplemented
64#91478C2218yescomplemented
65C2×#6658C2211yescharacteristic, complemented
66C2×#6656C2211yescharacteristic, complemented
67C2×#6654C2211yescharacteristic, complemented
68C2×#6654C2211yescharacteristic, complemented
69C2×#6653C2211yescharacteristic, complemented
70C2×#6652C2211yescharacteristic, complemented
71C2×#6649C2211yescharacteristic, complemented
72C2×#6648C2211yescharacteristic, complemented
73C2×D3×#168C2211yescharacteristic, complemented
74#91266C2218yescomplemented
75#91257C2218yescomplemented
76#91253C2218yescomplemented
77D5×D24C2218yescomplemented
78C2×#5769—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×#4062D311yescharacteristic, complemented
87C2×#4060—31no—
88C2×#4060—31no—
89C2×#4057—31no—
90C2×#4057—31no—
91C2×D5×D8—31no—
92C2×D5×D8—31no—
93C2×#4054—31no—
94C2×#4053—31no—
95C23×D15—21no—
96C23×C5×D3—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—
114C5×#239—22no—
115C5×#239C2314yescomplemented
116C5×D3×D4—22no—
117C5×D3×D4C2314yescomplemented
118C2×C5×D12—21no—
119C2×C5×D12C2311yescharacteristic
120C2×C5×D12C2311yescharacteristic
121C2×C4×C5×D3—21no—
122C2×C4×C5×D3C2311yescharacteristic
123C2×C3×C22⋊D5—21no—
124C22×C3×Dic5—21no—
125C3×#713—22no—
126C3×#713C2314yescomplemented
127C3×#711—22no—
128C3×#711C2314yescomplemented
129C2×C3×D20—21no—
130C2×C3×D20C2311yescharacteristic
131C2×C3×C4×D5—21no—
132C2×C3×C4×D5C2311yescharacteristic
133C2×C3×Dic10C2311yescharacteristic
134#6790—28no—
135D3×C22⋊D5—28no—
136C2×#1204D411yescharacteristic
137C2×#1203—21no—
138C2×#1203—21no—
139C2×#1203—21no—
140C2×#1203—21no—
141C2×#1203—28no—
142C2×#1203D411yescharacteristic
143C2×#1202—21no—
144C2×#1202D411yescharacteristic
145C2×#1201—21no—
146C2×#1201D411yescharacteristic
147C2×#1200—21no—
148#6782—28no—
149C2×D3×Dic5—21no—
150#6777—22no—
151#6777—28no—
152#6777C2314yescomplemented
153D3×D20—22no—
154D3×D20—28no—
155D3×D20C2314yescomplemented
156D5×D12—22no—
157D5×D12—22no—
158D5×D12—28no—
159D5×D12C2314yescomplemented
160D5×D12C2314yescomplemented
161#6771—28no—
162#6771D414yes—
163#6771C2314yes—
164#6769—22no—
165#6769C2314yescomplemented
166#6768—22no—
167#6768C2314yescomplemented
168C3×C5×SD16C2314yescomplemented
169C2×C3×C5×C8C2311yescharacteristic
170#6717C2314yescomplemented
171#6715C2314yescomplemented
172C2×C3⋊#168C2311yescharacteristic
173D120C2314yescomplemented
174#6705C2314yescomplemented
175C5×#215C2314yescomplemented
176C5×#213C2314yescomplemented
177C2×C5×C3⋊C8C2311yescharacteristic
178C5×D24C2314yescomplemented
179C5×ΓL(1,𝔽25)C2314yescomplemented
180C3×#689C2314yescomplemented
181C3×#686C2314yescomplemented
182C2×C3×#168C2311yescharacteristic
183C3×#677C2314yescomplemented
184C3×C8×D5C2314yescomplemented
185#6658C2314yescomplemented
186#6656C2314yescomplemented
187#6654C2314yescomplemented
188#6654C2314yescomplemented
189#6653C2314yescomplemented
190#6652C2314yescomplemented
191#6649C2314yescomplemented
192#6648C2314yescomplemented
193D3×#168C2314yescomplemented
194C2×#1009—51no—
195C2×#1009—51no—
196C2×C3×#135—51no—
197C2×#949—51no—
198C2×#949—51no—
199#5769—516no—
200C2×#919—51no—
201C2×#919—51no—
202C2×#914—51no—
203C2×#914—51no—
204C2×#914—51no—
205C2×#914D511yescharacteristic, complemented
206C2×D3×D8—51no—
207C2×D3×D8—51no—
208C22×D24—51no—
209C2×#901—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—61no—
222C2×#711C2×D311yescharacteristic, complemented
223C2×D4×D5—31no—
224C2×D4×D5—31no—
225C2×D4×D5—31no—
226C2×D4×D5—31no—
227C2×D4×D5—61no—
228C2×D4×D5—61no—
229C2×D4×D5—61no—
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×#689C2×D311yescharacteristic, complemented
243C2×#688—31no—
244C2×#687—31no—
245C2×#686—31no—
246C2×#686—31no—
247C2×#686—38no—
248C2×#686—31no—
249C2×#686—31no—
250C2×#686C2×D311yescharacteristic, complemented
251C22×#168—31no—
252#4062—38no—
253#4062C2×D318yescomplemented
254#4060—38no—
255#4060—38no—
256#4057—38no—
257#4057—38no—
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×#676—31no—
268C2×C8×D5—31no—
269C2×C8×D5C2×D311yescharacteristic, complemented
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×D3—21no—
279C22×C5×D3—24no—
280C22×C5×D3—82no—
281C22×C5×D3C2×D411yescharacteristic
282C22×C3×D5—21no—
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×Dic3C2×D411yescharacteristic
310C5×D12—24no—
311C5×D12—21no—
312C5×D12—21no—
313C5×D12C2412yes—
314C5×D12C2412yes—
315C4×C5×D3—24no—
316C4×C5×D3C2×D412yes—
317C4×C5×D3C2412yes—
318C3×C22⋊D5—24no—
319C2×C3×Dic5—21no—
320C2×C3×Dic5—24no—
321C2×C3×Dic5C2×D411yescharacteristic
322C3×D20—24no—
323C3×D20—21no—
324C3×D20C2412yes—
325C3×C4×D5—24no—
326C3×C4×D5C2×D412yes—
327C3×C4×D5C2412yes—
328C3×Dic10—21no—
329C3×Dic10C2412yes—
330#1204C2×D414yes—
331#1203—24no—
332#1203—24no—
333#1203—24no—
334#1203—24no—
335#1203C2×D414yes—
336#1202—24no—
337#1202C2×D414yes—
338#1201—24no—
339#1201C2×D414yes—
340#1200—24no—
341D3×Dic5—24no—
342C3×C5×C8C2412yes—
343C3⋊#168C2412yes—
344C3×#168C2412yes—
345C5×C3⋊C8C2412yes—
346C2×C3×#41—51no—
347C2×C3×#41—51no—
348#1009—58no—
349#1009—58no—
350#1009—104no—
351#1009—104no—
352C2×#239—51no—
353C2×#239—51no—
354C2×#239—51no—
355C2×#239C2×D511yescharacteristic, complemented
356C2×D3×D4—51no—
357C2×D3×D4—51no—
358C2×D3×D4—51no—
359C2×D3×D4—101no—
360C2×D3×D4—101no—
361C2×D3×D4—101no—
362C2×D3×D4—101no—
363C2×D3×D4C2×D511yescharacteristic, complemented
364C2×#235—51no—
365C2×#235—101no—
366C2×#235—101no—
367C22×D12—51no—
368C22×D12—51no—
369C22×D12—101no—
370C22×D12—101no—
371C3×#135—58no—
372C2×C3×Q16—51no—
373C2×C3×SD16—51no—
374C2×C3×SD16C2×D511yescharacteristic, complemented
375C2×C3×D8—51no—
376C22×C3×C8—51no—
377#949—58no—
378#949—58no—
379C2×#215—51no—
380C2×#215—51no—
381C2×#215—51no—
382C2×#215C2×D511yescharacteristic, complemented
383C2×#213—51no—
384C2×#213—51no—
385C2×#213—51no—
386C2×#213C2×D511yescharacteristic, complemented
387C2×#208—51no—
388#919—58no—
389#919—58no—
390#914—58no—
391#914—58no—
392#914—58no—
393#914C2×D518yescomplemented
394D3×D8—58no—
395D3×D8—58no—
396C2×D24—51no—
397C2×D24—51no—
398C2×D24—51no—
399C2×D24—58no—
400C2×D24C2×D511yescharacteristic, complemented
401#901—58no—
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—61no—
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—68no—
428C2×C22⋊D5—61no—
429C2×C22⋊D5—61no—
430C2×C22⋊D5—61no—
431C2×C22⋊D5—61no—
432C2×C22⋊D5—68no—
433C2×C22⋊D5—61no—
434C2×C22⋊D5—61no—
435C22×Dic5—21no—
436C22×Dic5—61no—
437#713—22no—
438#713—34no—
439#713—62no—
440#713C22×D314yescomplemented
441#711—22no—
442#711—34no—
443#711—62no—
444#711—68no—
445#711C22×D314yescomplemented
446D4×D5—34no—
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×D5—62no—
457#709—34no—
458#709—34no—
459#709—34no—
460#709—62no—
461#709—68no—
462C2×D20—21no—
463C2×D20—31no—
464C2×D20—31no—
465C2×D20—31no—
466C2×D20—34no—
467C2×D20—68no—
468C2×D20—62no—
469C2×D20—61no—
470C2×D20—61no—
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×Dic10C22×D311yescharacteristic
479C5×SD16—34no—
480C5×SD16C22×D314yescomplemented
481C5×D8—34no—
482C5×D8—34no—
483C5×M16—34no—
484C2×C5×C8—31no—
485C2×C5×C8C22×D311yescharacteristic
486#689C22×D314yescomplemented
487#688—34no—
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—
498D40—34no—
499#677—34no—
500#677C22×D314yescomplemented
501#676—34no—
502#676—34no—
503C8×D5—34no—
504C8×D5C22×D314yescomplemented
505C2×H(5,𝔽2)—151no—
506C2×H(5,𝔽2)—151no—
507#576—1516no—
508C2×AGL(1,ℤ/8)—31no—
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—51no—
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—22no—
534C2×C5×D3—42no—
535C2×C5×D3—42no—
536C2×C5×D3—84no—
537C2×C5×D3C22×D412yes—
538C2×C3×D5—22no—
539C2×C3×D5—22no—
540C2×C3×D5—42no—
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×Dic5—22no—
551C3×Dic5C22×D412yes—
552C5×Dic3C22×D412yes—
553C23×D3—21no—
554C23×D3—101no—
555C23×D3—101no—
556C23×D3—101no—
557C23×D3—101no—
558C23×D3—101no—
559C3×#41—54no—
560C3×#41—54no—
561C3×#41—102no—
562C3×#41—102no—
563C2×C3×Q8—51no—
564C2×C3×Q8C22×D511yescharacteristic
565C2×C3×D4—51no—
566C2×C3×D4—101no—
567C2×C3×D4—101no—
568C2×C3×D4C22×D511yescharacteristic
569C22×C3×C4—51no—
570C22×C3×C4—101no—
571C22×C3×C4—101no—
572C2×#67—21no—
573C2×#67—51no—
574C2×#67—51no—
575C2×#67—101no—
576C2×#67—101no—
577C2×#67—101no—
578#239—22no—
579#239—54no—
580#239—54no—
581#239—54no—
582#239—102no—
583#239—102no—
584#239—102no—
585#239C22×D514yescomplemented
586D3×D4—22no—
587D3×D4—54no—
588D3×D4—54no—
589D3×D4—54no—
590D3×D4—108no—
591D3×D4—102no—
592D3×D4—102no—
593D3×D4—108no—
594D3×D4—108no—
595D3×D4—108no—
596D3×D4—102no—
597D3×D4C22×D514yescomplemented
598#235—54no—
599#235—54no—
600#235—108no—
601#235—108no—
602C2×D12—21no—
603C2×D12—51no—
604C2×D12—51no—
605C2×D12—51no—
606C2×D12—54no—
607C2×D12—54no—
608C2×D12—108no—
609C2×D12—102no—
610C2×D12—102no—
611C2×D12—108no—
612C2×D12—101no—
613C2×D12—101no—
614C2×D12—101no—
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×D3—101no—
624C2×C4×D3C22×D511yescharacteristic
625C2×Dic6—51no—
626C3×Q16—54no—
627C3×SD16—54no—
628C3×SD16C22×D514yescomplemented
629C3×D8—54no—
630C2×C3×C8—51no—
631C2×C3×C8—54no—
632C2×C3×C8C22×D511yescharacteristic
633#215—54no—
634#215—54no—
635#215—54no—
636#215C22×D514yescomplemented
637#213—54no—
638#213—54no—
639#213—54no—
640#213C22×D514yescomplemented
641#208—54no—
642C2×C3⋊C8—51no—
643C2×C3⋊C8C22×D511yescharacteristic
644D24—54no—
645D24—54no—
646D24—54no—
647D24C22×D514yescomplemented
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—31no—
660C22×D5—64no—
661C22×D5—64no—
662C22×D5—64no—
663C22×D5—61no—
664C22×D5—61no—
665C22×D5—64no—
666C22×D5—64no—
667C22×D5—242no—
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—21no—
699C2×Dic5—24no—
700C2×Dic5—31no—
701C2×Dic5—64no—
702C2×Dic5D3×D411yescharacteristic
703D20—24no—
704D20—21no—
705D20—34no—
706D20—32no—
707D20—32no—
708D20—64no—
709D20—64no—
710D20—61no—
711D20—61no—
712D20C23×D312yes—
713C4×D5—24no—
714C4×D5—32no—
715C4×D5—32no—
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—51no—
734C2×#41—151no—
735C2×#41—151no—
736C2×#41—151no—
737C2×#41—151no—
738C2×#41—301no—
739C2×#41—301no—
740C22×D4—31no—
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)—38no—
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—58no—
759#135—158no—
760#135—158no—
761C2×Q16—51no—
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—151no—
772C2×D8—158no—
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—31no—
782C2×M16—151no—
783C2×M16—151no—
784C22×C8—51no—
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—
795C5×D3—22no—
796C5×D3—42no—
797C5×D3—42no—
798C23×C3—21no—
799C23×C3—51no—
800C23×C3—101no—
801C22×D3—21no—
802C22×D3—21no—
803C22×D3—24no—
804C22×D3—51no—
805C22×D3—82no—
806C22×D3—104no—
807C22×D3—104no—
808C22×D3—104no—
809C22×D3—104no—
810C22×D3—101no—
811C22×D3—101no—
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×Q8—52no—
821C3×Q8—101no—
822C3×Q8C23×D512yes—
823C3×D4—21no—
824C3×D4—52no—
825C3×D4—104no—
826C3×D4—104no—
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×C4—104no—
835C2×C3×C4—101no—
836C2×C3×C4C23×D511yescharacteristic
837#67—24no—
838#67—54no—
839#67—54no—
840#67—104no—
841#67—104no—
842#67—104no—
843C2×Dic3—51no—
844C2×Dic3D4×D511yescharacteristic
845D12—24no—
846D12—21no—
847D12—21no—
848D12—54no—
849D12—52no—
850D12—52no—
851D12—104no—
852D12—104no—
853D12—104no—
854D12—104no—
855D12—104no—
856D12—101no—
857D12—101no—
858D12C23×D512yes—
859D12C23×D512yes—
860C4×D3—24no—
861C4×D3—52no—
862C4×D3—52no—
863C4×D3—104no—
864C4×D3—104no—
865C4×D3—104no—
866C4×D3D4×D512yes—
867C4×D3C23×D512yes—
868Dic6—54no—
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—32no—
886C2×D5—42no—
887C2×D5—62no—
888C2×D5—62no—
889C2×D5—62no—
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×C5C2×D3×D411yescharacteristic
901C4×C5C24×D311yescharacteristic
902Dic5—22no—
903Dic5—32no—
904Dic5C2×D3×D412yes—
905C24—61no—
906C24—301no—
907C24—301no—
908C24—301no—
909C24—301no—
910C24—301no—
911#41—34no—
912#41—54no—
913#41—54no—
914#41—62no—
915#41—102no—
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—51no—
928C2×Q8—151no—
929C2×Q8C2×D3×D511yescharacteristic
930C2×D4—34no—
931C2×D4—31no—
932C2×D4—31no—
933C2×D4—51no—
934C2×D4—61no—
935C2×D4—62no—
936C2×D4—61no—
937C2×D4—101no—
938C2×D4—101no—
939C2×D4—154no—
940C2×D4—151no—
941C2×D4—154no—
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—301no—
952C2×D4—302no—
953C2×D4—302no—
954C2×D4—301no—
955C2×D4—301no—
956C2×D4—308no—
957C2×D4—308no—
958C2×D4—308no—
959C2×D4—301no—
960C2×D4—301no—
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—101no—
973C22×C4—101no—
974C22×C4—151no—
975C22×C4—301no—
976C22×C4—301no—
977C22×C4—301no—
978Q16—54no—
979SD16—34no—
980SD16—54no—
981SD16—154no—
982SD16—154no—
983SD16—154no—
984SD16C2×D3×D514yescomplemented
985D8—34no—
986D8—34no—
987D8—54no—
988D8—154no—
989D8—154no—
990D8—154no—
991D8—154no—
992D8—154no—
993D8—154no—
994M16—34no—
995M16—154no—
996M16—154no—
997C2×C8—31no—
998C2×C8—51no—
999C2×C8—54no—
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—202no—
1011C22×C3C2×D4×D511yescharacteristic
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—42no—
1016C2×D3—42no—
1017C2×D3—52no—
1018C2×D3—84no—
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×C4—102no—
1033C3×C4C2×D4×D511yescharacteristic
1034C3×C4C24×D511yescharacteristic
1035Dic3—52no—
1036Dic3C2×D4×D512yes—
1037C2×C5—42no—
1038C2×C5—62no—
1039C2×C5—122no—
1040C2×C5—122no—
1041C2×C5#576912yescomplemented
1042C2×C5C22×D3×D411yescharacteristic
1043D5—22no—
1044D5—42no—
1045D5—62no—
1046D5—122no—
1047D5—122no—
1048C23—21no—
1049C23—31no—
1050C23—51no—
1051C23—64no—
1052C23—61no—
1053C23—61no—
1054C23—101no—
1055C23—151no—
1056C23—242no—
1057C23—304no—
1058C23—304no—
1059C23—304no—
1060C23—304no—
1061C23—304no—
1062C23—301no—
1063C23—301no—
1064C23—1202no—
1065C23—1202no—
1066C23—1202no—
1067C23—1202no—
1068C23—1202no—
1069Q8—21no—
1070Q8—52no—
1071Q8—101no—
1072Q8—154no—
1073Q8C22×D3×D512yes—
1074D4—21no—
1075D4—32no—
1076D4—32no—
1077D4—52no—
1078D4—64no—
1079D4—64no—
1080D4—61no—
1081D4—61no—
1082D4—104no—
1083D4—104no—
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—104no—
1110C2×C4—104no—
1111C2×C4—101no—
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#6610812yescomplemented
1127C2×C3C22×D4×D511yescharacteristic
1128D3—22no—
1129D3—42no—
1130D3—42no—
1131D3—102no—
1132D3—202no—
1133D3—202no—
1134C5C2×#576911yescharacteristic, complemented, Sylow
1135C22—22no—
1136C22—32no—
1137C22—42no—
1138C22—52no—
1139C22—62no—
1140C22—62no—
1141C22—62no—
1142C22—102no—
1143C22—102no—
1144C22—122no—
1145C22—122no—
1146C22—152no—
1147C22—202no—
1148C22—244no—
1149C22—302no—
1150C22—302no—
1151C22—302no—
1152C22—602no—
1153C22—602no—
1154C22—1204no—
1155C22—1204no—
1156C22—1204no—
1157C22—1204no—
1158C22—1204no—
1159C22D3×D4×D511yescharacteristic
1160C4—22no—
1161C4—32no—
1162C4—52no—
1163C4—102no—
1164C4—152no—
1165C4D3×D4×D511yescharacteristic
1166C4C23×D3×D511yescharacteristic
1167C3C2×#6610811yescharacteristic, complemented, Sylow
1168C2—42no—
1169C2—62no—
1170C2—102no—
1171C2—122no—
1172C2—122no—
1173C2—202no—
1174C2—302no—
1175C2—602no—
1176C2—602no—
1177C2#1175409312yesdirect 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×#92027C2semidirect
3. C2×#91803C2semidirect
4. C2×C5×#914C2semidirect
5. C2×C3×#4062C2semidirect
6. C2×#91523C2semidirect
7. C2×#91519C2semidirect
8. C2×#91502C2semidirect
9. C2×#91481C2semidirect
10. C2×D3×#686C2semidirect
11. C2×#91478C2semidirect
12. #11754093C2direct (N × H)
13. C2×#91266C2semidirect
14. C2×#91257C2semidirect
15. C2×#91253C2semidirect
16. C2×D5×D24C2semidirect
18. C2×#6821C22semidirect
19. C2×D4×D15C22semidirect
20. C2×C5×#239C22semidirect
21. C2×C5×D3×D4C22semidirect
22. C2×C3×#713C22semidirect
23. C2×C3×#711C22semidirect
29. #92035C22semidirect
31. #92027C22semidirect
33. C2×#6777C22semidirect
35. C2×D3×D20C22semidirect
37. C2×D5×D12C22semidirect
38. C2×D5×D12C22semidirect
41. C2×#6769C22semidirect
42. C2×#6768C22semidirect
43. C2×C3×C5×SD16C22semidirect
44. C2×#6717C22semidirect
45. C2×#6715C22semidirect
46. #91803C22semidirect
47. C2×D120C22semidirect
48. C2×#6705C22semidirect
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×#689C22semidirect
55. C2×C3×#686C22semidirect
56. C3×#4062C22semidirect
57. C2×C3×#677C22semidirect
58. C2×C3×C8×D5C22semidirect
59. #91523C22semidirect
60. #91519C22semidirect
61. #91502C22semidirect
62. #91481C22semidirect
63. D3×#686C22semidirect
64. #91478C22semidirect
65. C2×#6658C22semidirect
66. C2×#6656C22semidirect
67. C2×#6654C22semidirect
68. C2×#6654C22semidirect
69. C2×#6653C22semidirect
70. C2×#6652C22semidirect
71. C2×#6649C22semidirect
72. C2×#6648C22semidirect
73. C2×D3×#168C22semidirect
74. #91266C22semidirect
75. #91257C22semidirect
76. #91253C22semidirect
77. D5×D24C22semidirect
86. C2×#4062D3semidirect
105. #6821C23semidirect
107. D4×D15C23semidirect
115. C5×#239C23semidirect
117. C5×D3×D4C23semidirect
126. C3×#713C23semidirect
128. C3×#711C23semidirect
152. #6777C23semidirect
155. D3×D20C23semidirect
159. D5×D12C23semidirect
160. D5×D12C23semidirect
165. #6769C23semidirect
167. #6768C23semidirect
168. C3×C5×SD16C23semidirect
170. #6717C23semidirect
171. #6715C23semidirect
173. D120C23semidirect
174. #6705C23semidirect
175. C5×#215C23semidirect
176. C5×#213C23semidirect
178. C5×D24C23semidirect
179. C5×ΓL(1,𝔽25)C23semidirect
180. C3×#689C23semidirect
181. C3×#686C23semidirect
183. C3×#677C23semidirect
184. C3×C8×D5C23semidirect
185. #6658C23semidirect
186. #6656C23semidirect
187. #6654C23semidirect
188. #6654C23semidirect
189. #6653C23semidirect
190. #6652C23semidirect
191. #6649C23semidirect
192. #6648C23semidirect
193. D3×#168C23semidirect
205. C2×#914D5semidirect
217. C2×#713C2×D3semidirect
222. C2×#711C2×D3semidirect
237. C2×C5×SD16C2×D3semidirect
242. C2×#689C2×D3semidirect
250. C2×#686C2×D3semidirect
253. #4062C2×D3semidirect
265. C2×#677C2×D3semidirect
269. C2×C8×D5C2×D3semidirect
355. C2×#239C2×D5semidirect
363. C2×D3×D4C2×D5semidirect
374. C2×C3×SD16C2×D5semidirect
382. C2×#215C2×D5semidirect
386. C2×#213C2×D5semidirect
393. #914C2×D5semidirect
400. C2×D24C2×D5semidirect
403. C2×ΓL(1,𝔽25)C2×D5semidirect
440. #713C22×D3semidirect
445. #711C22×D3semidirect
480. C5×SD16C22×D3semidirect
486. #689C22×D3semidirect
493. #686C22×D3semidirect
500. #677C22×D3semidirect
504. C8×D5C22×D3semidirect
585. #239C22×D5semidirect
597. D3×D4C22×D5semidirect
628. C3×SD16C22×D5semidirect
636. #215C22×D5semidirect
640. #213C22×D5semidirect
647. 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#5769semidirect
1126. C2×C3#66108semidirect
1134. C5C2×#5769semidirect
1167. C3C2×#66108semidirect
1177. C2#11754093direct (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×#920272
C2×#918032
C2×C5×#9142
C2×C3×#40622
C2×#915232
C2×#915192
C2×#915022
C2×#914812
C2×D3×#6862
C2×#914782
#117540932
C2×#912662
C2×#912572
C2×#912532
C2×D5×D242
C2×#661083
C2×#57695