Finite Group Databasebeta

← C103×#24475 #39929750

Subgroups — C103×#24475 #39929750

Order 26368.

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
1C103×#3585C211yesmaximal, characteristic
2C103×#3069C211yesmaximal, characteristic, complemented
3C103×#3040C211yesmaximal, characteristic, complemented
4C103×#3022C211yesmaximal, characteristic, complemented
5C2×#455×C103C211yesmaximal, characteristic, complemented
6C103×#2901C211yesmaximal, characteristic, complemented
7C103×#2050C211yesmaximal, characteristic, complemented
8C103×#2048C211yesmaximal, characteristic, complemented
9C103×#2009C211yesmaximal, characteristic, complemented
10C103×#2003C211yesmaximal, characteristic, complemented
11C103×#1906C211yesmaximal, characteristic, complemented
12C103×#1903C211yesmaximal, characteristic, complemented
13C103×#1902C211yesmaximal, characteristic, complemented
14C103×#1861C211yesmaximal, characteristic, complemented
15C103×#1795C211yesmaximal, characteristic, complemented
16#585×C103C2211yescharacteristic
17C2×H(5,𝔽2)×C103C2211yescharacteristic
18#577×C103—22no—
19#577×C103—22no—
20#576×C103—22no—
21#576×C103—22no—
22#575×C103—22no—
23#575×C103C2211yescharacteristic
24#575×C103C2211yescharacteristic
25C2×#137×C103C2211yescharacteristic
26C2×#137×C103C2211yescharacteristic, complemented
27C2×#137×C103C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C103—22no—
29C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
31#568×C103C2211yescharacteristic
32#568×C103C2211yescharacteristic, complemented
33#536×C103C2211yescharacteristic, complemented
34C2×#124×C103C2211yescharacteristic, complemented
35C4×#41×C103C2211yescharacteristic, complemented
36#473×C103—22no—
37#471×C103—22no—
38#464×C103—22no—
39#463×C103—22no—
40#456×C103—22no—
41#455×C103—22no—
42#455×C103—22no—
43#455×C103—22no—
44#430×C103C2211yescharacteristic, complemented
45#423×C103C2211yescharacteristic, complemented
46#421×C103—22no—
47#421×C103C2211yescharacteristic
48#421×C103C2211yescharacteristic
49#421×C103C2211yescharacteristic, complemented
50#421×C103C2211yescharacteristic, complemented
51C2×#104×C103—22no—
52C2×#104×C103C2211yescharacteristic
53C2×#104×C103C2211yescharacteristic, complemented
54C2×#104×C103C2211yescharacteristic, complemented
55#419×C103C2211yescharacteristic, complemented
56#418×C103C2211yescharacteristic, complemented
57#418×C103C2211yescharacteristic, complemented
58#413×C103C2211yescharacteristic, complemented
59#413×C103C2211yescharacteristic, complemented
60C2×#101×C103C2211yescharacteristic, complemented
61C2×#100×C103C2211yescharacteristic, complemented
62#410×C103C2211yescharacteristic, complemented
63#344×C103C2211yescharacteristic, complemented
64#344×C103C2211yescharacteristic, complemented
65#339×C103C2211yescharacteristic, complemented
66#338×C103C2211yescharacteristic, complemented
672−1+4×C103—21no—
682−1+4×C103—21no—
692−1+4×C103D412yes—
70H(5,𝔽2)×C103—22no—
71H(5,𝔽2)×C103—21no—
72H(5,𝔽2)×C103—22no—
73H(5,𝔽2)×C103—21no—
74H(5,𝔽2)×C103—22no—
75H(5,𝔽2)×C103—41no—
76H(5,𝔽2)×C103—41no—
77H(5,𝔽2)×C103D412yes—
78C2×#41×C103—22no—
79C2×#41×C103—22no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—41no—
83C2×#41×C103C2311yescharacteristic
84C2×#41×C103C2311yescharacteristic
85C2×#41×C103C2311yescharacteristic
86C2×#41×C103C2311yescharacteristic
87C22×Q8×C103C2311yescharacteristic
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—41no—
91C22×D4×C103C2311yescharacteristic
92#137×C103—24no—
93#137×C103—21no—
94#137×C103—21no—
95#137×C103—21no—
96#137×C103—22no—
97#137×C103—22no—
98#137×C103—22no—
99#137×C103—22no—
100#137×C103—22no—
101#137×C103—41no—
102#137×C103D412yes—
103AGL(1,ℤ/8)×C103—24no—
104AGL(1,ℤ/8)×C103—24no—
105AGL(1,ℤ/8)×C103—24no—
106AGL(1,ℤ/8)×C103—22no—
107AGL(1,ℤ/8)×C103—22no—
108AGL(1,ℤ/8)×C103—21no—
109AGL(1,ℤ/8)×C103—22no—
110AGL(1,ℤ/8)×C103—21no—
111AGL(1,ℤ/8)×C103—21no—
112AGL(1,ℤ/8)×C103—22no—
113AGL(1,ℤ/8)×C103D412yes—
114#135×C103—24no—
115#135×C103—24no—
116#135×C103—22no—
117#135×C103—22no—
118C2×Q16×C103—21no—
119C2×Q16×C103—21no—
120C2×Q16×C103—21no—
121C2×SD16×C103—24no—
122C2×SD16×C103—21no—
123C2×SD16×C103—21no—
124C2×SD16×C103—21no—
125C2×SD16×C103—21no—
126C2×SD16×C103D412yes—
127C2×D8×C103—24no—
128C2×D8×C103—21no—
129C2×D8×C103D412yes—
130#131×C103—22no—
131#131×C103—22no—
132#131×C103—22no—
133#131×C103—41no—
134C2×M16×C103—22no—
135C2×M16×C103—22no—
136C2×M16×C103C2311yescharacteristic
137C2×M16×C103C2311yescharacteristic
138C2×M16×C103C2311yescharacteristic
139C2×M16×C103C2311yescharacteristic
140C2×M16×C103C2311yescharacteristic
141C2×M16×C103C2311yescharacteristic
142C4⋊Q8×C103—21no—
143#124×C103—21no—
144#124×C103—22no—
145#124×C103—21no—
146#124×C103—21no—
147#123×C103—41no—
148C22⋊Q8×C103—41no—
149C4×Q8×C103—21no—
150C4×D4×C103—21no—
151C4×D4×C103—41no—
152#117×C103—21no—
153#117×C103C2311yescharacteristic
154#117×C103C2311yescharacteristic
155C2×C22⋊C4×C103—41no—
156C2×C42×C103—21no—
157C2×C42×C103C2311yescharacteristic
158#108×C103—22no—
159C4⋊C8×C103—22no—
160#104×C103—22no—
161#104×C103—22no—
162#104×C103—22no—
163#104×C103—22no—
164#104×C103—21no—
165#104×C103—21no—
166#104×C103—21no—
167#104×C103—21no—
168#104×C103D412yes—
169#104×C103D412yes—
170#103×C103—22no—
171#102×C103—22no—
172#102×C103—41no—
173#101×C103—21no—
174#101×C103—21no—
175#101×C103—22no—
176#100×C103—21no—
177#100×C103—21no—
178#100×C103—22no—
179#99×C103—41no—
180C24×C103—21no—
181C24×C103—41no—
182#41×C103—21no—
183#41×C103—21no—
184#41×C103—21no—
185#41×C103—21no—
186#41×C103—24no—
187#41×C103—22no—
188#41×C103—22no—
189#41×C103—22no—
190#41×C103—22no—
191#41×C103—21no—
192#41×C103—21no—
193#41×C103—21no—
194#41×C103—21no—
195#41×C103—21no—
196#41×C103—21no—
197#41×C103—21no—
198#41×C103—21no—
199#41×C103—42no—
200#41×C103—42no—
201#41×C103—42no—
202#41×C103—42no—
203#41×C103—42no—
204#41×C103—42no—
205#41×C103—41no—
206#41×C103—41no—
207#41×C103—42no—
208#41×C103C2×D412yes—
209#41×C103C2×D412yes—
210#41×C103C2×D412yes—
211#41×C103C2×D412yes—
212C2×Q8×C103—22no—
213C2×Q8×C103—22no—
214C2×Q8×C103—21no—
215C2×Q8×C103—21no—
216C2×Q8×C103—21no—
217C2×Q8×C103—21no—
218C2×Q8×C103—21no—
219C2×Q8×C103—21no—
220C2×Q8×C103—41no—
221C2×Q8×C103C2×D411yescharacteristic
222C2×Q8×C103C2×D411yescharacteristic
223C2×Q8×C103C2×D411yescharacteristic
224C2×Q8×C103#4111yescharacteristic
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—24no—
228C2×D4×C103—22no—
229C2×D4×C103—22no—
230C2×D4×C103—21no—
231C2×D4×C103—21no—
232C2×D4×C103—21no—
233C2×D4×C103—21no—
234C2×D4×C103—21no—
235C2×D4×C103—21no—
236C2×D4×C103—21no—
237C2×D4×C103—42no—
238C2×D4×C103—41no—
239C2×D4×C103—41no—
240C2×D4×C103—42no—
241C2×D4×C103—42no—
242C2×D4×C103—41no—
243C2×D4×C103—44no—
244C2×D4×C103—42no—
245C2×D4×C103—42no—
246C2×D4×C103—44no—
247C2×D4×C103—42no—
248C2×D4×C103C2×D411yescharacteristic
249C2×D4×C103C2×D411yescharacteristic
250C2×D4×C103C2×D412yes—
251C2×D4×C103C2×D411yescharacteristic
252C2×D4×C103#4111yescharacteristic
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—21no—
258C22×C4×C103—21no—
259C22×C4×C103—41no—
260C22×C4×C103—42no—
261C22×C4×C103—41no—
262C22×C4×C103C2411yescharacteristic
263Q16×C103—22no—
264Q16×C103—22no—
265Q16×C103—42no—
266Q16×C103—42no—
267Q16×C103—42no—
268SD16×C103—24no—
269SD16×C103—22no—
270SD16×C103—22no—
271SD16×C103—22no—
272SD16×C103—24no—
273SD16×C103—22no—
274SD16×C103—42no—
275SD16×C103—42no—
276SD16×C103—42no—
277D8×C103—24no—
278D8×C103—22no—
279D8×C103—22no—
280D8×C103—24no—
281M16×C103—24no—
282M16×C103—21no—
283M16×C103—21no—
284M16×C103—21no—
285M16×C103—21no—
286M16×C103—21no—
287M16×C103—21no—
288M16×C103—21no—
289M16×C103—21no—
290M16×C103—21no—
291M16×C103—21no—
292M16×C103—42no—
293M16×C103C2×D412yes—
294M16×C103C2×D412yes—
295C2×C8×C103—24no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103—21no—
300C2×C8×C103—21no—
301C2×C8×C103—42no—
302C2×C8×C103C2×D412yes—
303C4⋊C4×C103—21no—
304C4⋊C4×C103—21no—
305C4⋊C4×C103—41no—
306C4⋊C4×C103—42no—
307C22⋊C4×C103—21no—
308C22⋊C4×C103—21no—
309C22⋊C4×C103—42no—
310C22⋊C4×C103—42no—
311C22⋊C4×C103—41no—
312C22⋊C4×C103—42no—
313C42×C103—21no—
314C42×C103—21no—
315C42×C103—21no—
316C42×C103—41no—
317C42×C103C2×D411yescharacteristic
318C42×C103C2×D411yescharacteristic
319C23×C103—21no—
320C23×C103—21no—
321C23×C103—21no—
322C23×C103—22no—
323C23×C103—21no—
324C23×C103—42no—
325C23×C103—44no—
326C23×C103—41no—
327C23×C103—41no—
328C23×C103—82no—
329C23×C103—162no—
330C23×C103H(5,𝔽2)11yescharacteristic
331Q8×C103—21no—
332Q8×C103—21no—
333Q8×C103—21no—
334Q8×C103—21no—
335Q8×C103—21no—
336Q8×C103—21no—
337Q8×C103—42no—
338Q8×C103—41no—
339Q8×C103—41no—
340Q8×C103—41no—
341Q8×C103—41no—
342Q8×C103#12012yes—
343Q8×C103#12112yes—
344D4×C103—22no—
345D4×C103—22no—
346D4×C103—22no—
347D4×C103—22no—
348D4×C103—21no—
349D4×C103—21no—
350D4×C103—22no—
351D4×C103—21no—
352D4×C103—21no—
353D4×C103—21no—
354D4×C103—21no—
355D4×C103—22no—
356D4×C103—42no—
357D4×C103—42no—
358D4×C103—44no—
359D4×C103—42no—
360D4×C103—44no—
361D4×C103—41no—
362D4×C103—41no—
363D4×C103—41no—
364D4×C103—41no—
365D4×C103—41no—
366D4×C103—41no—
367D4×C103#12012yes—
368D4×C103#12112yes—
369C2×C4×C103—21no—
370C2×C4×C103—21no—
371C2×C4×C103—22no—
372C2×C4×C103—22no—
373C2×C4×C103—22no—
374C2×C4×C103—22no—
375C2×C4×C103—21no—
376C2×C4×C103—21no—
377C2×C4×C103—21no—
378C2×C4×C103—21no—
379C2×C4×C103—42no—
380C2×C4×C103—42no—
381C2×C4×C103—42no—
382C2×C4×C103—44no—
383C2×C4×C103—41no—
384C2×C4×C103—41no—
385C2×C4×C103—41no—
386C2×C4×C103—41no—
387C2×C4×C103—41no—
388C2×C4×C103—41no—
389C2×C4×C103—41no—
390C2×C4×C103—41no—
391C2×C4×C103—41no—
392C2×C4×C103—81no—
393C2×C4×C103—82no—
394C2×C4×C103C22×D411yescharacteristic
395C2×C4×C103C22×D411yescharacteristic
396C2×C4×C103C22×D411yescharacteristic
397C2×C4×C103C22×D411yescharacteristic
398C2×C4×C103C2×#4111yescharacteristic
399C2×C4×C103H(5,𝔽2)11yescharacteristic
400C8×C103—22no—
401C8×C103—22no—
402C8×C103—22no—
403C8×C103—41no—
404C8×C103—41no—
405C8×C103—41no—
406C22×C103—22no—
407C22×C103—22no—
408C22×C103—41no—
409C22×C103—41no—
410C22×C103—42no—
411C22×C103—41no—
412C22×C103—81no—
413C22×C103—81no—
414C22×C103—81no—
415C22×C103—82no—
416C22×C103—81no—
417C22×C103—82no—
418C22×C103—161no—
419C22×C103—162no—
420C22×C103—164no—
421C22×C103#53411yescharacteristic
422C22×C103D4211yescharacteristic
423C22×C103#54611yescharacteristic
424C4×C103—22no—
425C4×C103—22no—
426C4×C103—41no—
427C4×C103—41no—
428C4×C103—41no—
429C4×C103—41no—
430C4×C103—81no—
431C4×C103—81no—
432C4×C103—81no—
433C4×C103C2×#12011yescharacteristic
434C4×C103C2×#12111yescharacteristic
435C4×C103D4211yescharacteristic
436C4×C103#54611yescharacteristic
437#24475C10311yesmaximal, characteristic, direct product factor, Sylow
438C2×C103—21no—
439C2×C103—21no—
440C2×C103—21no—
441C2×C103—42no—
442C2×C103—42no—
443C2×C103—82no—
444C2×C103—81no—
445C2×C103—81no—
446C2×C103#241011yescharacteristic
447#3585C2×C10311yescharacteristic
448#3069C2×C10311yescharacteristic, complemented
449#3040C2×C10311yescharacteristic, complemented
450#3022C2×C10311yescharacteristic, complemented
451C2×#455C2×C10311yescharacteristic, complemented
452#2901C2×C10311yescharacteristic, complemented
453#2050C2×C10311yescharacteristic, complemented
454#2048C2×C10311yescharacteristic, complemented
455#2009C2×C10311yescharacteristic, complemented
456#2003C2×C10311yescharacteristic, complemented
457#1906C2×C10311yescharacteristic, complemented
458#1903C2×C10311yescharacteristic, complemented
459#1902C2×C10311yescharacteristic, complemented
460#1861C2×C10311yescharacteristic, complemented
461#1795C2×C10311yescharacteristic, complemented
462C103#2447511yescharacteristic, direct product factor, Sylow
463#585C22×C10311yescharacteristic
464C2×H(5,𝔽2)C22×C10311yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C10311yescharacteristic
471#575C22×C10311yescharacteristic
472C2×#137C22×C10311yescharacteristic
473C2×#137C22×C10311yescharacteristic, complemented
474C2×#137C22×C10311yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
477C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
478#568C22×C10311yescharacteristic
479#568C22×C10311yescharacteristic, complemented
480#536C22×C10311yescharacteristic, complemented
481C2×#124C22×C10311yescharacteristic, complemented
482C4×#41C22×C10311yescharacteristic, 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×C10311yescharacteristic, complemented
492#423C22×C10311yescharacteristic, complemented
493#421—22no—
494#421C22×C10311yescharacteristic
495#421C22×C10311yescharacteristic
496#421C22×C10311yescharacteristic, complemented
497#421C22×C10311yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C10311yescharacteristic
500C2×#104C22×C10311yescharacteristic, complemented
501C2×#104C22×C10311yescharacteristic, complemented
502#419C22×C10311yescharacteristic, complemented
503#418C22×C10311yescharacteristic, complemented
504#418C22×C10311yescharacteristic, complemented
505#413C22×C10311yescharacteristic, complemented
506#413C22×C10311yescharacteristic, complemented
507C2×#101C22×C10311yescharacteristic, complemented
508C2×#100C22×C10311yescharacteristic, complemented
509#410C22×C10311yescharacteristic, complemented
510#344C22×C10311yescharacteristic, complemented
511#344C22×C10311yescharacteristic, complemented
512#339C22×C10311yescharacteristic, complemented
513#338C22×C10311yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C10312yes—
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×C10312yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C10311yescharacteristic
531C2×#41C23×C10311yescharacteristic
532C2×#41C23×C10311yescharacteristic
533C2×#41C23×C10311yescharacteristic
534C22×Q8C23×C10311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C10311yescharacteristic
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×C10312yes—
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×C10312yes—
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×C10312yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C10312yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C10311yescharacteristic
584C2×M16C23×C10311yescharacteristic
585C2×M16C23×C10311yescharacteristic
586C2×M16C23×C10311yescharacteristic
587C2×M16C23×C10311yescharacteristic
588C2×M16C23×C10311yescharacteristic
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×C10311yescharacteristic
601#117C23×C10311yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C10311yescharacteristic
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×C10312yes—
616#104D4×C10312yes—
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×C10312yes—
656#41C2×D4×C10312yes—
657#41C2×D4×C10312yes—
658#41C2×D4×C10312yes—
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×C10311yescharacteristic
669C2×Q8C2×D4×C10311yescharacteristic
670C2×Q8C2×D4×C10311yescharacteristic
671C2×Q8#41×C10311yescharacteristic
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×C10311yescharacteristic
696C2×D4C2×D4×C10311yescharacteristic
697C2×D4C2×D4×C10312yes—
698C2×D4C2×D4×C10311yescharacteristic
699C2×D4#41×C10311yescharacteristic
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×C10311yescharacteristic
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×C10312yes—
741M16C2×D4×C10312yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C10312yes—
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×C10311yescharacteristic
765C42C2×D4×C10311yescharacteristic
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)×C10311yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C10312yes—
790Q8#121×C10312yes—
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×C10312yes—
815D4#121×C10312yes—
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×C10311yescharacteristic
842C2×C4C22×D4×C10311yescharacteristic
843C2×C4C22×D4×C10311yescharacteristic
844C2×C4C22×D4×C10311yescharacteristic
845C2×C4C2×#41×C10311yescharacteristic
846C2×C4H(5,𝔽2)×C10311yescharacteristic
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×C10311yescharacteristic
869C22D42×C10311yescharacteristic
870C22#546×C10311yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C10311yescharacteristic
881C4C2×#121×C10311yescharacteristic
882C4D42×C10311yescharacteristic
883C4#546×C10311yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C103×#241011yescharacteristic
subgroupG/H
center, socleC2×C103#2410
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3585C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3069C2semidirect
3. C103×#3040C2semidirect
4. C103×#3022C2semidirect
5. C2×#455×C103C2semidirect
6. C103×#2901C2semidirect
7. C103×#2050C2semidirect
8. C103×#2048C2semidirect
9. C103×#2009C2semidirect
10. C103×#2003C2semidirect
11. C103×#1906C2semidirect
12. C103×#1903C2semidirect
13. C103×#1902C2semidirect
14. C103×#1861C2semidirect
15. C103×#1795C2semidirect
26. C2×#137×C103C22semidirect
27. C2×#137×C103C22semidirect
32. #568×C103C22semidirect
33. #536×C103C22semidirect
34. C2×#124×C103C22semidirect
35. C4×#41×C103C22semidirect
44. #430×C103C22semidirect
45. #423×C103C22semidirect
49. #421×C103C22semidirect
50. #421×C103C22semidirect
53. C2×#104×C103C22semidirect
54. C2×#104×C103C22semidirect
55. #419×C103C22semidirect
56. #418×C103C22semidirect
57. #418×C103C22semidirect
58. #413×C103C22semidirect
59. #413×C103C22semidirect
60. C2×#101×C103C22semidirect
61. C2×#100×C103C22semidirect
62. #410×C103C22semidirect
63. #344×C103C22semidirect
64. #344×C103C22semidirect
65. #339×C103C22semidirect
66. #338×C103C22semidirect
437. #24475C103direct (N × H)
448. #3069C2×C103semidirect
449. #3040C2×C103semidirect
450. #3022C2×C103semidirect
451. C2×#455C2×C103semidirect
452. #2901C2×C103semidirect
453. #2050C2×C103semidirect
454. #2048C2×C103semidirect
455. #2009C2×C103semidirect
456. #2003C2×C103semidirect
457. #1906C2×C103semidirect
458. #1903C2×C103semidirect
459. #1902C2×C103semidirect
460. #1861C2×C103semidirect
461. #1795C2×C103semidirect
462. C103#24475direct (N × H)
473. C2×#137C22×C103semidirect
474. C2×#137C22×C103semidirect
479. #568C22×C103semidirect
480. #536C22×C103semidirect
481. C2×#124C22×C103semidirect
482. C4×#41C22×C103semidirect
491. #430C22×C103semidirect
492. #423C22×C103semidirect
496. #421C22×C103semidirect
497. #421C22×C103semidirect
500. C2×#104C22×C103semidirect
501. C2×#104C22×C103semidirect
502. #419C22×C103semidirect
503. #418C22×C103semidirect
504. #418C22×C103semidirect
505. #413C22×C103semidirect
506. #413C22×C103semidirect
507. C2×#101C22×C103semidirect
508. C2×#100C22×C103semidirect
509. #410C22×C103semidirect
510. #344C22×C103semidirect
511. #344C22×C103semidirect
512. #339C22×C103semidirect
513. #338C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35852
C103×#30692
C103×#30402
C103×#30222
C2×#455×C1032
C103×#29012
C103×#20502
C103×#20482
C103×#20092
C103×#20032
C103×#19062
C103×#19032
C103×#19022
C103×#18612
C103×#17952
#24475103