Finite Group Databasebeta

← C103×#25440 #39930715

Subgroups — C103×#25440 #39930715

Order 26368.

914 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3154C211yesmaximal, characteristic, complemented
2C2×#471×C103C211yesmaximal, characteristic, complemented
3C103×#3063C211yesmaximal, characteristic, complemented
4C103×#3062C211yesmaximal, characteristic, complemented
5C103×#3060C211yesmaximal, characteristic, complemented
6C2×#443×C103C211yesmaximal, characteristic, complemented
7C103×#2038C211yesmaximal, characteristic, complemented
8C103×#2037C211yesmaximal, characteristic, complemented
9C103×#2007C211yesmaximal, characteristic, complemented
10C103×#2006C211yesmaximal, characteristic, complemented
11C103×#1968C211yesmaximal, characteristic, complemented
12C103×#1951C211yesmaximal, characteristic, complemented
13C103×#1908C211yesmaximal, characteristic, complemented
14C103×#1907C211yesmaximal, characteristic, complemented
15C103×#1764C211yesmaximal, characteristic, complemented
16C2×#137×C103C2211yescharacteristic
17C2×#137×C103C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
20C2×#135×C103C2211yescharacteristic
21C22×SD16×C103C2211yescharacteristic
22C2×#131×C103C2211yescharacteristic
23C2×#131×C103C2211yescharacteristic
24C2×#131×C103C2211yescharacteristic
25#537×C103C2211yescharacteristic
26#537×C103C2211yescharacteristic
27#536×C103C2211yescharacteristic
28#535×C103C2211yescharacteristic
29#497×C103—21no—
30#496×C103—21no—
31#495×C103—21no—
32#492×C103—21no—
33#471×C103—24no—
34#470×C103—21no—
35#470×C103—21no—
36#469×C103—21no—
37#469×C103—21no—
38#468×C103—21no—
39#468×C103—21no—
40#467×C103—21no—
41#466×C103—21no—
42#465×C103—21no—
43#465×C103—21no—
44#465×C103—21no—
45#465×C103—21no—
46#443×C103—24no—
47C2×#108×C103C2211yescharacteristic
48#428×C103C2211yescharacteristic
49#428×C103C2211yescharacteristic
50C2×#106×C103C2211yescharacteristic
51C2×#104×C103C2211yescharacteristic
52C2×#104×C103C2211yescharacteristic
53C2×#104×C103C2211yescharacteristic
54#417×C103C2211yescharacteristic
55#417×C103C2211yescharacteristic
56#416×C103C2211yescharacteristic
57C2×#103×C103C2211yescharacteristic
58C2×#102×C103C2211yescharacteristic
59C2×#101×C103C2211yescharacteristic
60C2×#100×C103C2211yescharacteristic
61#405×C103C2211yescharacteristic
62C2×C4×C8×C103C2211yescharacteristic
63#391×C103C2211yescharacteristic
64#390×C103C2211yescharacteristic
65#343×C103C2211yescharacteristic
66#343×C103C2211yescharacteristic
67#341×C103C2211yescharacteristic
68#339×C103C2211yescharacteristic
69C2×#41×C103C2311yescharacteristic
70C2×#41×C103C2311yescharacteristic
71C2×#41×C103C2311yescharacteristic
72C22×Q8×C103C2311yescharacteristic
73C22×D4×C103C2311yescharacteristic
74#137×C103—22no—
75#137×C103—22no—
76#137×C103—41no—
77#137×C103—41no—
78AGL(1,ℤ/8)×C103—22no—
79AGL(1,ℤ/8)×C103—22no—
80AGL(1,ℤ/8)×C103—41no—
81AGL(1,ℤ/8)×C103—41no—
82#135×C103—22no—
83#135×C103—22no—
84C2×Q16×C103—21no—
85C2×Q16×C103—21no—
86C2×Q16×C103D411yescharacteristic
87C2×SD16×C103—21no—
88C2×SD16×C103—21no—
89C2×SD16×C103—21no—
90C2×SD16×C103—21no—
91C2×SD16×C103—22no—
92C2×SD16×C103—21no—
93C2×SD16×C103—21no—
94C2×SD16×C103—22no—
95C2×SD16×C103D411yescharacteristic
96C2×SD16×C103D411yescharacteristic
97C2×D8×C103—21no—
98C2×D8×C103—21no—
99C2×D8×C103D411yescharacteristic
100#131×C103—22no—
101#131×C103—22no—
102#131×C103—22no—
103#131×C103—22no—
104#131×C103—41no—
105#131×C103—41no—
106C2×M16×C103—21no—
107C2×M16×C103—21no—
108C2×M16×C103—21no—
109C2×M16×C103C2311yescharacteristic
110C2×M16×C103C2311yescharacteristic
111C2×M16×C103C2311yescharacteristic
112C2×M16×C103C2311yescharacteristic
113C22×C8×C103—21no—
114C22×C8×C103—21no—
115C22×C8×C103—21no—
116C22×C8×C103C2311yescharacteristic
117C22×C8×C103C2311yescharacteristic
118C4⋊Q8×C103—21no—
119#127×C103—21no—
120#124×C103—21no—
121#124×C103—21no—
122#123×C103—41no—
123C22⋊Q8×C103—21no—
124C22⋊Q8×C103—21no—
125C22⋊Q8×C103—21no—
126C22⋊Q8×C103—21no—
127C22⋊Q8×C103—21no—
128C22⋊Q8×C103—21no—
129#121×C103—21no—
130#121×C103—21no—
131#121×C103—21no—
132#121×C103—21no—
133#121×C103—21no—
134#121×C103—21no—
135#121×C103—41no—
136#121×C103—41no—
137#120×C103—41no—
138#117×C103C2311yescharacteristic
139C2×C4⋊C4×C103C2311yescharacteristic
140C2×C4⋊C4×C103C2311yescharacteristic
141C2×C22⋊C4×C103—41no—
142C2×C42×C103C2311yescharacteristic
143#108×C103D414yescomplemented
144#107×C103—21no—
145#107×C103—21no—
146#106×C103—21no—
147#106×C103—21no—
148#106×C103—21no—
149#106×C103—21no—
150#104×C103—22no—
151#104×C103—22no—
152#104×C103—22no—
153#103×C103—21no—
154#103×C103—21no—
155#103×C103—21no—
156#103×C103—21no—
157#103×C103D411yescharacteristic
158#103×C103D411yescharacteristic
159#102×C103—21no—
160#102×C103—21no—
161#102×C103—21no—
162#102×C103—21no—
163#102×C103D411yescharacteristic
164#102×C103D411yescharacteristic
165#101×C103—22no—
166#100×C103—22no—
167#97×C103—21no—
168C4×C8×C103—22no—
169C4×C8×C103—21no—
170#95×C103—41no—
171C24×C103—21no—
172#41×C103—21no—
173#41×C103—21no—
174#41×C103—21no—
175#41×C103—21no—
176#41×C103—21no—
177#41×C103—21no—
178#41×C103—21no—
179#41×C103—21no—
180#41×C103—21no—
181#41×C103—21no—
182#41×C103—21no—
183#41×C103—21no—
184C2×Q8×C103—21no—
185C2×Q8×C103—21no—
186C2×Q8×C103—21no—
187C2×Q8×C103—21no—
188C2×Q8×C103—21no—
189C2×Q8×C103—21no—
190C2×Q8×C103C2×D411yescharacteristic
191C2×Q8×C103C2×D411yescharacteristic
192C2×Q8×C103C2×D411yescharacteristic
193C2×D4×C103—21no—
194C2×D4×C103—21no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—21no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—41no—
203C2×D4×C103—41no—
204C2×D4×C103—41no—
205C2×D4×C103—41no—
206C2×D4×C103C2×D411yescharacteristic
207C2×D4×C103C2×D411yescharacteristic
208C2×D4×C103C2×D411yescharacteristic
209C22×C4×C103—21no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103C2411yescharacteristic
217Q16×C103—22no—
218Q16×C103—42no—
219Q16×C103—42no—
220SD16×C103—22no—
221SD16×C103—22no—
222SD16×C103—42no—
223SD16×C103—42no—
224SD16×C103—42no—
225SD16×C103—42no—
226SD16×C103—42no—
227SD16×C103—42no—
228D8×C103—22no—
229D8×C103—42no—
230D8×C103—42no—
231M16×C103—21no—
232M16×C103—21no—
233M16×C103—21no—
234M16×C103—21no—
235M16×C103—21no—
236M16×C103—42no—
237M16×C103—42no—
238M16×C103—42no—
239M16×C103C2×D412yes—
240M16×C103C2×D412yes—
241M16×C103#4112yes—
242C2×C8×C103—21no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—42no—
249C2×C8×C103—42no—
250C2×C8×C103—42no—
251C2×C8×C103C2×D411yescharacteristic
252C2×C8×C103C2×D411yescharacteristic
253C2×C8×C103C2×D411yescharacteristic
254C2×C8×C103C2×D412yes—
255C2×C8×C103C2×D411yescharacteristic
256C2×C8×C103#4112yes—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—41no—
262C4⋊C4×C103—41no—
263C4⋊C4×C103—41no—
264C4⋊C4×C103—41no—
265C4⋊C4×C103C2×D411yescharacteristic
266C4⋊C4×C103C2×D411yescharacteristic
267C22⋊C4×C103—21no—
268C22⋊C4×C103—41no—
269C22⋊C4×C103—41no—
270C22⋊C4×C103—41no—
271C22⋊C4×C103—41no—
272C22⋊C4×C103—41no—
273C22⋊C4×C103—41no—
274C22⋊C4×C103—41no—
275C22⋊C4×C103—41no—
276C22⋊C4×C103—82no—
277C42×C103—21no—
278C42×C103—21no—
279C42×C103—21no—
280C23×C103—21no—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—41no—
284C23×C103—41no—
285C23×C103—41no—
286C23×C103—81no—
287C23×C103—81no—
288C23×C103H(5,𝔽2)11yescharacteristic
289Q8×C103—21no—
290Q8×C103—21no—
291Q8×C103—21no—
292Q8×C103—21no—
293Q8×C103—21no—
294Q8×C103—21no—
295Q8×C103—41no—
296Q8×C103—41no—
297Q8×C103—41no—
298Q8×C103—41no—
299D4×C103—21no—
300D4×C103—21no—
301D4×C103—21no—
302D4×C103—21no—
303D4×C103—21no—
304D4×C103—21no—
305D4×C103—41no—
306D4×C103—41no—
307D4×C103—41no—
308D4×C103—41no—
309D4×C103—41no—
310D4×C103—41no—
311D4×C103—41no—
312D4×C103—41no—
313D4×C103—41no—
314D4×C103—41no—
315D4×C103—161no—
316D4×C103—161no—
317D4×C103—161no—
318D4×C103—161no—
319C2×C4×C103—22no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—41no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
331C2×C4×C103—41no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—41no—
336C2×C4×C103—41no—
337C2×C4×C103—41no—
338C2×C4×C103—81no—
339C2×C4×C103—81no—
340C2×C4×C103C22×D411yescharacteristic
341C2×C4×C103C22×D411yescharacteristic
342C2×C4×C103C22×D411yescharacteristic
343C2×C4×C103C2×#4111yescharacteristic
344C2×C4×C103C2×#4111yescharacteristic
345C2×C4×C103H(5,𝔽2)11yescharacteristic
346C8×C103—21no—
347C8×C103—21no—
348C8×C103—22no—
349C8×C103—22no—
350C8×C103—22no—
351C8×C103—41no—
352C8×C103#12112yes—
353C8×C103#12112yes—
354C22×C103—21no—
355C22×C103—21no—
356C22×C103—41no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—41no—
361C22×C103—41no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—41no—
365C22×C103—82no—
366C22×C103—81no—
367C22×C103—81no—
368C22×C103—81no—
369C22×C103—161no—
370C22×C103#54011yescharacteristic
371C22×C103D4211yescharacteristic
372C22×C103#55011yescharacteristic
373C4×C103—42no—
374C4×C103—41no—
375C4×C103—41no—
376C4×C103—41no—
377C4×C103—41no—
378C4×C103—41no—
379C4×C103—81no—
380C4×C103—81no—
381C4×C103—81no—
382C4×C103C2×#12111yescharacteristic
383C4×C103#53211yescharacteristic
384C4×C103D4211yescharacteristic
385C4×C103#54611yescharacteristic
386#25440C10311yesmaximal, characteristic, direct product factor, Sylow
387C2×C103—21no—
388C2×C103—21no—
389C2×C103—81no—
390C2×C103—81no—
391C2×C103—81no—
392C2×C103—161no—
393C2×C103#242811yescharacteristic
394C2×C103#329011yescharacteristic
395C2×C103#329111yescharacteristic
396#3154C2×C10311yescharacteristic, complemented
397C2×#471C2×C10311yescharacteristic, complemented
398#3063C2×C10311yescharacteristic, complemented
399#3062C2×C10311yescharacteristic, complemented
400#3060C2×C10311yescharacteristic, complemented
401C2×#443C2×C10311yescharacteristic, complemented
402#2038C2×C10311yescharacteristic, complemented
403#2037C2×C10311yescharacteristic, complemented
404#2007C2×C10311yescharacteristic, complemented
405#2006C2×C10311yescharacteristic, complemented
406#1968C2×C10311yescharacteristic, complemented
407#1951C2×C10311yescharacteristic, complemented
408#1908C2×C10311yescharacteristic, complemented
409#1907C2×C10311yescharacteristic, complemented
410#1764C2×C10311yescharacteristic, complemented
411C103#2544011yescharacteristic, direct product factor, Sylow
412C2×#137C22×C10311yescharacteristic
413C2×#137C22×C10311yescharacteristic
414C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
415C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
416C2×#135C22×C10311yescharacteristic
417C22×SD16C22×C10311yescharacteristic
418C2×#131C22×C10311yescharacteristic
419C2×#131C22×C10311yescharacteristic
420C2×#131C22×C10311yescharacteristic
421#537C22×C10311yescharacteristic
422#537C22×C10311yescharacteristic
423#536C22×C10311yescharacteristic
424#535C22×C10311yescharacteristic
425#497—21no—
426#496—21no—
427#495—21no—
428#492—21no—
429#471—24no—
430#470—21no—
431#470—21no—
432#469—21no—
433#469—21no—
434#468—21no—
435#468—21no—
436#467—21no—
437#466—21no—
438#465—21no—
439#465—21no—
440#465—21no—
441#465—21no—
442#443—24no—
443C2×#108C22×C10311yescharacteristic
444#428C22×C10311yescharacteristic
445#428C22×C10311yescharacteristic
446C2×#106C22×C10311yescharacteristic
447C2×#104C22×C10311yescharacteristic
448C2×#104C22×C10311yescharacteristic
449C2×#104C22×C10311yescharacteristic
450#417C22×C10311yescharacteristic
451#417C22×C10311yescharacteristic
452#416C22×C10311yescharacteristic
453C2×#103C22×C10311yescharacteristic
454C2×#102C22×C10311yescharacteristic
455C2×#101C22×C10311yescharacteristic
456C2×#100C22×C10311yescharacteristic
457#405C22×C10311yescharacteristic
458C2×C4×C8C22×C10311yescharacteristic
459#391C22×C10311yescharacteristic
460#390C22×C10311yescharacteristic
461#343C22×C10311yescharacteristic
462#343C22×C10311yescharacteristic
463#341C22×C10311yescharacteristic
464#339C22×C10311yescharacteristic
465C2×#41C23×C10311yescharacteristic
466C2×#41C23×C10311yescharacteristic
467C2×#41C23×C10311yescharacteristic
468C22×Q8C23×C10311yescharacteristic
469C22×D4C23×C10311yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C10311yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C10311yescharacteristic
492C2×SD16D4×C10311yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C10311yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C10311yescharacteristic
506C2×M16C23×C10311yescharacteristic
507C2×M16C23×C10311yescharacteristic
508C2×M16C23×C10311yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C10311yescharacteristic
513C22×C8C23×C10311yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C10311yescharacteristic
535C2×C4⋊C4C23×C10311yescharacteristic
536C2×C4⋊C4C23×C10311yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C10311yescharacteristic
539#108D4×C10314yescomplemented
540#107—21no—
541#107—21no—
542#106—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C10311yescharacteristic
554#103D4×C10311yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C10311yescharacteristic
560#102D4×C10311yescharacteristic
561#101—22no—
562#100—22no—
563#97—21no—
564C4×C8—22no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C10311yescharacteristic
587C2×Q8C2×D4×C10311yescharacteristic
588C2×Q8C2×D4×C10311yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C10311yescharacteristic
603C2×D4C2×D4×C10311yescharacteristic
604C2×D4C2×D4×C10311yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C10311yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C10312yes—
636M16C2×D4×C10312yes—
637M16#41×C10312yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C10311yescharacteristic
648C2×C8C2×D4×C10311yescharacteristic
649C2×C8C2×D4×C10311yescharacteristic
650C2×C8C2×D4×C10312yes—
651C2×C8C2×D4×C10311yescharacteristic
652C2×C8#41×C10312yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C10311yescharacteristic
662C4⋊C4C2×D4×C10311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C10311yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C10311yescharacteristic
737C2×C4C22×D4×C10311yescharacteristic
738C2×C4C22×D4×C10311yescharacteristic
739C2×C4C2×#41×C10311yescharacteristic
740C2×C4C2×#41×C10311yescharacteristic
741C2×C4H(5,𝔽2)×C10311yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C10312yes—
749C8#121×C10312yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22#540×C10311yescharacteristic
767C22D42×C10311yescharacteristic
768C22#550×C10311yescharacteristic
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C10311yescharacteristic
779C4#532×C10311yescharacteristic
780C4D42×C10311yescharacteristic
781C4#546×C10311yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C103×#242811yescharacteristic
789C2C103×#329011yescharacteristic
790C2C103×#329111yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3154C2semidirect
2. C2×#471×C103C2semidirect
3. C103×#3063C2semidirect
4. C103×#3062C2semidirect
5. C103×#3060C2semidirect
6. C2×#443×C103C2semidirect
7. C103×#2038C2semidirect
8. C103×#2037C2semidirect
9. C103×#2007C2semidirect
10. C103×#2006C2semidirect
11. C103×#1968C2semidirect
12. C103×#1951C2semidirect
13. C103×#1908C2semidirect
14. C103×#1907C2semidirect
15. C103×#1764C2semidirect
143. #108×C103D4semidirect
386. #25440C103direct (N × H)
396. #3154C2×C103semidirect
397. C2×#471C2×C103semidirect
398. #3063C2×C103semidirect
399. #3062C2×C103semidirect
400. #3060C2×C103semidirect
401. C2×#443C2×C103semidirect
402. #2038C2×C103semidirect
403. #2037C2×C103semidirect
404. #2007C2×C103semidirect
405. #2006C2×C103semidirect
406. #1968C2×C103semidirect
407. #1951C2×C103semidirect
408. #1908C2×C103semidirect
409. #1907C2×C103semidirect
410. #1764C2×C103semidirect
411. C103#25440direct (N × H)
539. #108D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31542
C2×#471×C1032
C103×#30632
C103×#30622
C103×#30602
C2×#443×C1032
C103×#20382
C103×#20372
C103×#20072
C103×#20062
C103×#19682
C103×#19512
C103×#19082
C103×#19072
C103×#17642
#25440103