Finite Group Databasebeta

← C101×#24475 #38806626

Subgroups — C101×#24475 #38806626

Order 25856.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3585C211yesmaximal, characteristic
2C101×#3069C211yesmaximal, characteristic, complemented
3C101×#3040C211yesmaximal, characteristic, complemented
4C101×#3022C211yesmaximal, characteristic, complemented
5C2×#455×C101C211yesmaximal, characteristic, complemented
6C101×#2901C211yesmaximal, characteristic, complemented
7C101×#2050C211yesmaximal, characteristic, complemented
8C101×#2048C211yesmaximal, characteristic, complemented
9C101×#2009C211yesmaximal, characteristic, complemented
10C101×#2003C211yesmaximal, characteristic, complemented
11C101×#1906C211yesmaximal, characteristic, complemented
12C101×#1903C211yesmaximal, characteristic, complemented
13C101×#1902C211yesmaximal, characteristic, complemented
14C101×#1861C211yesmaximal, characteristic, complemented
15C101×#1795C211yesmaximal, characteristic, complemented
16#585×C101C2211yescharacteristic
17C2×H(5,𝔽2)×C101C2211yescharacteristic
18#577×C101—22no—
19#577×C101—22no—
20#576×C101—22no—
21#576×C101—22no—
22#575×C101—22no—
23#575×C101C2211yescharacteristic
24#575×C101C2211yescharacteristic
25C2×#137×C101C2211yescharacteristic
26C2×#137×C101C2211yescharacteristic, complemented
27C2×#137×C101C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C101—22no—
29C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
31#568×C101C2211yescharacteristic
32#568×C101C2211yescharacteristic, complemented
33#536×C101C2211yescharacteristic, complemented
34C2×#124×C101C2211yescharacteristic, complemented
35C4×#41×C101C2211yescharacteristic, complemented
36#473×C101—22no—
37#471×C101—22no—
38#464×C101—22no—
39#463×C101—22no—
40#456×C101—22no—
41#455×C101—22no—
42#455×C101—22no—
43#455×C101—22no—
44#430×C101C2211yescharacteristic, complemented
45#423×C101C2211yescharacteristic, complemented
46#421×C101—22no—
47#421×C101C2211yescharacteristic
48#421×C101C2211yescharacteristic
49#421×C101C2211yescharacteristic, complemented
50#421×C101C2211yescharacteristic, complemented
51C2×#104×C101—22no—
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic, complemented
54C2×#104×C101C2211yescharacteristic, complemented
55#419×C101C2211yescharacteristic, complemented
56#418×C101C2211yescharacteristic, complemented
57#418×C101C2211yescharacteristic, complemented
58#413×C101C2211yescharacteristic, complemented
59#413×C101C2211yescharacteristic, complemented
60C2×#101×C101C2211yescharacteristic, complemented
61C2×#100×C101C2211yescharacteristic, complemented
62#410×C101C2211yescharacteristic, complemented
63#344×C101C2211yescharacteristic, complemented
64#344×C101C2211yescharacteristic, complemented
65#339×C101C2211yescharacteristic, complemented
66#338×C101C2211yescharacteristic, complemented
672−1+4×C101—21no—
682−1+4×C101—21no—
692−1+4×C101D412yes—
70H(5,𝔽2)×C101—22no—
71H(5,𝔽2)×C101—21no—
72H(5,𝔽2)×C101—22no—
73H(5,𝔽2)×C101—21no—
74H(5,𝔽2)×C101—22no—
75H(5,𝔽2)×C101—41no—
76H(5,𝔽2)×C101—41no—
77H(5,𝔽2)×C101D412yes—
78C2×#41×C101—22no—
79C2×#41×C101—22no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—41no—
83C2×#41×C101C2311yescharacteristic
84C2×#41×C101C2311yescharacteristic
85C2×#41×C101C2311yescharacteristic
86C2×#41×C101C2311yescharacteristic
87C22×Q8×C101C2311yescharacteristic
88C22×D4×C101—21no—
89C22×D4×C101—21no—
90C22×D4×C101—41no—
91C22×D4×C101C2311yescharacteristic
92#137×C101—24no—
93#137×C101—21no—
94#137×C101—21no—
95#137×C101—21no—
96#137×C101—22no—
97#137×C101—22no—
98#137×C101—22no—
99#137×C101—22no—
100#137×C101—22no—
101#137×C101—41no—
102#137×C101D412yes—
103AGL(1,ℤ/8)×C101—24no—
104AGL(1,ℤ/8)×C101—24no—
105AGL(1,ℤ/8)×C101—24no—
106AGL(1,ℤ/8)×C101—22no—
107AGL(1,ℤ/8)×C101—22no—
108AGL(1,ℤ/8)×C101—21no—
109AGL(1,ℤ/8)×C101—22no—
110AGL(1,ℤ/8)×C101—21no—
111AGL(1,ℤ/8)×C101—21no—
112AGL(1,ℤ/8)×C101—22no—
113AGL(1,ℤ/8)×C101D412yes—
114#135×C101—24no—
115#135×C101—24no—
116#135×C101—22no—
117#135×C101—22no—
118C2×Q16×C101—21no—
119C2×Q16×C101—21no—
120C2×Q16×C101—21no—
121C2×SD16×C101—24no—
122C2×SD16×C101—21no—
123C2×SD16×C101—21no—
124C2×SD16×C101—21no—
125C2×SD16×C101—21no—
126C2×SD16×C101D412yes—
127C2×D8×C101—24no—
128C2×D8×C101—21no—
129C2×D8×C101D412yes—
130#131×C101—22no—
131#131×C101—22no—
132#131×C101—22no—
133#131×C101—41no—
134C2×M16×C101—22no—
135C2×M16×C101—22no—
136C2×M16×C101C2311yescharacteristic
137C2×M16×C101C2311yescharacteristic
138C2×M16×C101C2311yescharacteristic
139C2×M16×C101C2311yescharacteristic
140C2×M16×C101C2311yescharacteristic
141C2×M16×C101C2311yescharacteristic
142C4⋊Q8×C101—21no—
143#124×C101—21no—
144#124×C101—22no—
145#124×C101—21no—
146#124×C101—21no—
147#123×C101—41no—
148C22⋊Q8×C101—41no—
149C4×Q8×C101—21no—
150C4×D4×C101—21no—
151C4×D4×C101—41no—
152#117×C101—21no—
153#117×C101C2311yescharacteristic
154#117×C101C2311yescharacteristic
155C2×C22⋊C4×C101—41no—
156C2×C42×C101—21no—
157C2×C42×C101C2311yescharacteristic
158#108×C101—22no—
159C4⋊C8×C101—22no—
160#104×C101—22no—
161#104×C101—22no—
162#104×C101—22no—
163#104×C101—22no—
164#104×C101—21no—
165#104×C101—21no—
166#104×C101—21no—
167#104×C101—21no—
168#104×C101D412yes—
169#104×C101D412yes—
170#103×C101—22no—
171#102×C101—22no—
172#102×C101—41no—
173#101×C101—21no—
174#101×C101—21no—
175#101×C101—22no—
176#100×C101—21no—
177#100×C101—21no—
178#100×C101—22no—
179#99×C101—41no—
180C24×C101—21no—
181C24×C101—41no—
182#41×C101—21no—
183#41×C101—21no—
184#41×C101—21no—
185#41×C101—21no—
186#41×C101—24no—
187#41×C101—22no—
188#41×C101—22no—
189#41×C101—22no—
190#41×C101—22no—
191#41×C101—21no—
192#41×C101—21no—
193#41×C101—21no—
194#41×C101—21no—
195#41×C101—21no—
196#41×C101—21no—
197#41×C101—21no—
198#41×C101—21no—
199#41×C101—42no—
200#41×C101—42no—
201#41×C101—42no—
202#41×C101—42no—
203#41×C101—42no—
204#41×C101—42no—
205#41×C101—41no—
206#41×C101—41no—
207#41×C101—42no—
208#41×C101C2×D412yes—
209#41×C101C2×D412yes—
210#41×C101C2×D412yes—
211#41×C101C2×D412yes—
212C2×Q8×C101—22no—
213C2×Q8×C101—22no—
214C2×Q8×C101—21no—
215C2×Q8×C101—21no—
216C2×Q8×C101—21no—
217C2×Q8×C101—21no—
218C2×Q8×C101—21no—
219C2×Q8×C101—21no—
220C2×Q8×C101—41no—
221C2×Q8×C101C2×D411yescharacteristic
222C2×Q8×C101C2×D411yescharacteristic
223C2×Q8×C101C2×D411yescharacteristic
224C2×Q8×C101#4111yescharacteristic
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—24no—
228C2×D4×C101—22no—
229C2×D4×C101—22no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—21no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—21no—
236C2×D4×C101—21no—
237C2×D4×C101—42no—
238C2×D4×C101—41no—
239C2×D4×C101—41no—
240C2×D4×C101—42no—
241C2×D4×C101—42no—
242C2×D4×C101—41no—
243C2×D4×C101—44no—
244C2×D4×C101—42no—
245C2×D4×C101—42no—
246C2×D4×C101—44no—
247C2×D4×C101—42no—
248C2×D4×C101C2×D411yescharacteristic
249C2×D4×C101C2×D411yescharacteristic
250C2×D4×C101C2×D412yes—
251C2×D4×C101C2×D411yescharacteristic
252C2×D4×C101#4111yescharacteristic
253C22×C4×C101—21no—
254C22×C4×C101—21no—
255C22×C4×C101—21no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—21no—
259C22×C4×C101—41no—
260C22×C4×C101—42no—
261C22×C4×C101—41no—
262C22×C4×C101C2411yescharacteristic
263Q16×C101—22no—
264Q16×C101—22no—
265Q16×C101—42no—
266Q16×C101—42no—
267Q16×C101—42no—
268SD16×C101—24no—
269SD16×C101—22no—
270SD16×C101—22no—
271SD16×C101—22no—
272SD16×C101—24no—
273SD16×C101—22no—
274SD16×C101—42no—
275SD16×C101—42no—
276SD16×C101—42no—
277D8×C101—24no—
278D8×C101—22no—
279D8×C101—22no—
280D8×C101—24no—
281M16×C101—24no—
282M16×C101—21no—
283M16×C101—21no—
284M16×C101—21no—
285M16×C101—21no—
286M16×C101—21no—
287M16×C101—21no—
288M16×C101—21no—
289M16×C101—21no—
290M16×C101—21no—
291M16×C101—21no—
292M16×C101—42no—
293M16×C101C2×D412yes—
294M16×C101C2×D412yes—
295C2×C8×C101—24no—
296C2×C8×C101—21no—
297C2×C8×C101—21no—
298C2×C8×C101—21no—
299C2×C8×C101—21no—
300C2×C8×C101—21no—
301C2×C8×C101—42no—
302C2×C8×C101C2×D412yes—
303C4⋊C4×C101—21no—
304C4⋊C4×C101—21no—
305C4⋊C4×C101—41no—
306C4⋊C4×C101—42no—
307C22⋊C4×C101—21no—
308C22⋊C4×C101—21no—
309C22⋊C4×C101—42no—
310C22⋊C4×C101—42no—
311C22⋊C4×C101—41no—
312C22⋊C4×C101—42no—
313C42×C101—21no—
314C42×C101—21no—
315C42×C101—21no—
316C42×C101—41no—
317C42×C101C2×D411yescharacteristic
318C42×C101C2×D411yescharacteristic
319C23×C101—21no—
320C23×C101—21no—
321C23×C101—21no—
322C23×C101—22no—
323C23×C101—21no—
324C23×C101—42no—
325C23×C101—44no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—82no—
329C23×C101—162no—
330C23×C101H(5,𝔽2)11yescharacteristic
331Q8×C101—21no—
332Q8×C101—21no—
333Q8×C101—21no—
334Q8×C101—21no—
335Q8×C101—21no—
336Q8×C101—21no—
337Q8×C101—42no—
338Q8×C101—41no—
339Q8×C101—41no—
340Q8×C101—41no—
341Q8×C101—41no—
342Q8×C101#12012yes—
343Q8×C101#12112yes—
344D4×C101—22no—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—21no—
349D4×C101—21no—
350D4×C101—22no—
351D4×C101—21no—
352D4×C101—21no—
353D4×C101—21no—
354D4×C101—21no—
355D4×C101—22no—
356D4×C101—42no—
357D4×C101—42no—
358D4×C101—44no—
359D4×C101—42no—
360D4×C101—44no—
361D4×C101—41no—
362D4×C101—41no—
363D4×C101—41no—
364D4×C101—41no—
365D4×C101—41no—
366D4×C101—41no—
367D4×C101#12012yes—
368D4×C101#12112yes—
369C2×C4×C101—21no—
370C2×C4×C101—21no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—22no—
374C2×C4×C101—22no—
375C2×C4×C101—21no—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—42no—
380C2×C4×C101—42no—
381C2×C4×C101—42no—
382C2×C4×C101—44no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—81no—
393C2×C4×C101—82no—
394C2×C4×C101C22×D411yescharacteristic
395C2×C4×C101C22×D411yescharacteristic
396C2×C4×C101C22×D411yescharacteristic
397C2×C4×C101C22×D411yescharacteristic
398C2×C4×C101C2×#4111yescharacteristic
399C2×C4×C101H(5,𝔽2)11yescharacteristic
400C8×C101—22no—
401C8×C101—22no—
402C8×C101—22no—
403C8×C101—41no—
404C8×C101—41no—
405C8×C101—41no—
406C22×C101—22no—
407C22×C101—22no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—42no—
411C22×C101—41no—
412C22×C101—81no—
413C22×C101—81no—
414C22×C101—81no—
415C22×C101—82no—
416C22×C101—81no—
417C22×C101—82no—
418C22×C101—161no—
419C22×C101—162no—
420C22×C101—164no—
421C22×C101#53411yescharacteristic
422C22×C101D4211yescharacteristic
423C22×C101#54611yescharacteristic
424C4×C101—22no—
425C4×C101—22no—
426C4×C101—41no—
427C4×C101—41no—
428C4×C101—41no—
429C4×C101—41no—
430C4×C101—81no—
431C4×C101—81no—
432C4×C101—81no—
433C4×C101C2×#12011yescharacteristic
434C4×C101C2×#12111yescharacteristic
435C4×C101D4211yescharacteristic
436C4×C101#54611yescharacteristic
437#24475C10111yesmaximal, characteristic, direct product factor, Sylow
438C2×C101—21no—
439C2×C101—21no—
440C2×C101—21no—
441C2×C101—42no—
442C2×C101—42no—
443C2×C101—82no—
444C2×C101—81no—
445C2×C101—81no—
446C2×C101#241011yescharacteristic
447#3585C2×C10111yescharacteristic
448#3069C2×C10111yescharacteristic, complemented
449#3040C2×C10111yescharacteristic, complemented
450#3022C2×C10111yescharacteristic, complemented
451C2×#455C2×C10111yescharacteristic, complemented
452#2901C2×C10111yescharacteristic, complemented
453#2050C2×C10111yescharacteristic, complemented
454#2048C2×C10111yescharacteristic, complemented
455#2009C2×C10111yescharacteristic, complemented
456#2003C2×C10111yescharacteristic, complemented
457#1906C2×C10111yescharacteristic, complemented
458#1903C2×C10111yescharacteristic, complemented
459#1902C2×C10111yescharacteristic, complemented
460#1861C2×C10111yescharacteristic, complemented
461#1795C2×C10111yescharacteristic, complemented
462C101#2447511yescharacteristic, direct product factor, Sylow
463#585C22×C10111yescharacteristic
464C2×H(5,𝔽2)C22×C10111yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C10111yescharacteristic
471#575C22×C10111yescharacteristic
472C2×#137C22×C10111yescharacteristic
473C2×#137C22×C10111yescharacteristic, complemented
474C2×#137C22×C10111yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
477C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
478#568C22×C10111yescharacteristic
479#568C22×C10111yescharacteristic, complemented
480#536C22×C10111yescharacteristic, complemented
481C2×#124C22×C10111yescharacteristic, complemented
482C4×#41C22×C10111yescharacteristic, complemented
483#473—22no—
484#471—22no—
485#464—22no—
486#463—22no—
487#456—22no—
488#455—22no—
489#455—22no—
490#455—22no—
491#430C22×C10111yescharacteristic, complemented
492#423C22×C10111yescharacteristic, complemented
493#421—22no—
494#421C22×C10111yescharacteristic
495#421C22×C10111yescharacteristic
496#421C22×C10111yescharacteristic, complemented
497#421C22×C10111yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C10111yescharacteristic
500C2×#104C22×C10111yescharacteristic, complemented
501C2×#104C22×C10111yescharacteristic, complemented
502#419C22×C10111yescharacteristic, complemented
503#418C22×C10111yescharacteristic, complemented
504#418C22×C10111yescharacteristic, complemented
505#413C22×C10111yescharacteristic, complemented
506#413C22×C10111yescharacteristic, complemented
507C2×#101C22×C10111yescharacteristic, complemented
508C2×#100C22×C10111yescharacteristic, complemented
509#410C22×C10111yescharacteristic, complemented
510#344C22×C10111yescharacteristic, complemented
511#344C22×C10111yescharacteristic, complemented
512#339C22×C10111yescharacteristic, complemented
513#338C22×C10111yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C10112yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C10112yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C10111yescharacteristic
531C2×#41C23×C10111yescharacteristic
532C2×#41C23×C10111yescharacteristic
533C2×#41C23×C10111yescharacteristic
534C22×Q8C23×C10111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C10111yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C10112yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C10112yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C10112yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C10112yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C10111yescharacteristic
584C2×M16C23×C10111yescharacteristic
585C2×M16C23×C10111yescharacteristic
586C2×M16C23×C10111yescharacteristic
587C2×M16C23×C10111yescharacteristic
588C2×M16C23×C10111yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C10111yescharacteristic
601#117C23×C10111yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C10111yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C10112yes—
616#104D4×C10112yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C10112yes—
656#41C2×D4×C10112yes—
657#41C2×D4×C10112yes—
658#41C2×D4×C10112yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C10111yescharacteristic
669C2×Q8C2×D4×C10111yescharacteristic
670C2×Q8C2×D4×C10111yescharacteristic
671C2×Q8#41×C10111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C10111yescharacteristic
696C2×D4C2×D4×C10111yescharacteristic
697C2×D4C2×D4×C10112yes—
698C2×D4C2×D4×C10111yescharacteristic
699C2×D4#41×C10111yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C10111yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C10112yes—
741M16C2×D4×C10112yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C10112yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C10111yescharacteristic
765C42C2×D4×C10111yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C10111yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C10112yes—
790Q8#121×C10112yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C10112yes—
815D4#121×C10112yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C10111yescharacteristic
842C2×C4C22×D4×C10111yescharacteristic
843C2×C4C22×D4×C10111yescharacteristic
844C2×C4C22×D4×C10111yescharacteristic
845C2×C4C2×#41×C10111yescharacteristic
846C2×C4H(5,𝔽2)×C10111yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22#534×C10111yescharacteristic
869C22D42×C10111yescharacteristic
870C22#546×C10111yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C10111yescharacteristic
881C4C2×#121×C10111yescharacteristic
882C4D42×C10111yescharacteristic
883C4#546×C10111yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C101×#241011yescharacteristic
subgroupG/H
center, socleC2×C101#2410
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3585C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3069C2semidirect
3. C101×#3040C2semidirect
4. C101×#3022C2semidirect
5. C2×#455×C101C2semidirect
6. C101×#2901C2semidirect
7. C101×#2050C2semidirect
8. C101×#2048C2semidirect
9. C101×#2009C2semidirect
10. C101×#2003C2semidirect
11. C101×#1906C2semidirect
12. C101×#1903C2semidirect
13. C101×#1902C2semidirect
14. C101×#1861C2semidirect
15. C101×#1795C2semidirect
26. C2×#137×C101C22semidirect
27. C2×#137×C101C22semidirect
32. #568×C101C22semidirect
33. #536×C101C22semidirect
34. C2×#124×C101C22semidirect
35. C4×#41×C101C22semidirect
44. #430×C101C22semidirect
45. #423×C101C22semidirect
49. #421×C101C22semidirect
50. #421×C101C22semidirect
53. C2×#104×C101C22semidirect
54. C2×#104×C101C22semidirect
55. #419×C101C22semidirect
56. #418×C101C22semidirect
57. #418×C101C22semidirect
58. #413×C101C22semidirect
59. #413×C101C22semidirect
60. C2×#101×C101C22semidirect
61. C2×#100×C101C22semidirect
62. #410×C101C22semidirect
63. #344×C101C22semidirect
64. #344×C101C22semidirect
65. #339×C101C22semidirect
66. #338×C101C22semidirect
437. #24475C101direct (N × H)
448. #3069C2×C101semidirect
449. #3040C2×C101semidirect
450. #3022C2×C101semidirect
451. C2×#455C2×C101semidirect
452. #2901C2×C101semidirect
453. #2050C2×C101semidirect
454. #2048C2×C101semidirect
455. #2009C2×C101semidirect
456. #2003C2×C101semidirect
457. #1906C2×C101semidirect
458. #1903C2×C101semidirect
459. #1902C2×C101semidirect
460. #1861C2×C101semidirect
461. #1795C2×C101semidirect
462. C101#24475direct (N × H)
473. C2×#137C22×C101semidirect
474. C2×#137C22×C101semidirect
479. #568C22×C101semidirect
480. #536C22×C101semidirect
481. C2×#124C22×C101semidirect
482. C4×#41C22×C101semidirect
491. #430C22×C101semidirect
492. #423C22×C101semidirect
496. #421C22×C101semidirect
497. #421C22×C101semidirect
500. C2×#104C22×C101semidirect
501. C2×#104C22×C101semidirect
502. #419C22×C101semidirect
503. #418C22×C101semidirect
504. #418C22×C101semidirect
505. #413C22×C101semidirect
506. #413C22×C101semidirect
507. C2×#101C22×C101semidirect
508. C2×#100C22×C101semidirect
509. #410C22×C101semidirect
510. #344C22×C101semidirect
511. #344C22×C101semidirect
512. #339C22×C101semidirect
513. #338C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35852
C101×#30692
C101×#30402
C101×#30222
C2×#455×C1012
C101×#29012
C101×#20502
C101×#20482
C101×#20092
C101×#20032
C101×#19062
C101×#19032
C101×#19022
C101×#18612
C101×#17952
#24475101