Finite Group Databasebeta

← C101×#13097 #38795248

Subgroups — C101×#13097 #38795248

Order 25856.

650 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3009C211yesmaximal, characteristic
2C101×#2888C211yesmaximal, characteristic
3C101×#2135C211yesmaximal, characteristic, complemented
4C101×#2123C211yesmaximal, characteristic, complemented
5C101×#1795C211yesmaximal, characteristic
6C101×#1395C211yesmaximal, characteristic, complemented
7C101×#1392C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C101C2211yescharacteristic
9C2×#137×C101C411yescharacteristic, complemented
10C22×SD16×C101C411yescharacteristic, complemented
11#568×C101—21no—
12#536×C101C2211yescharacteristic
13#452×C101—21no—
14#452×C101—21no—
15#450×C101—21no—
16#450×C101—21no—
17#421×C101—21no—
18#418×C101—21no—
19#418×C101C411yescharacteristic, complemented
20#416×C101C411yescharacteristic, complemented
21#413×C101—22no—
22#413×C101C2211yescharacteristic
23#413×C101C2211yescharacteristic
24#413×C101C2211yescharacteristic
25C2×#100×C101—21no—
26C2×#100×C101—22no—
27#410×C101C2211yescharacteristic
28#408×C101C2211yescharacteristic
29#356×C101—22no—
30#352×C101—22no—
31H(5,𝔽2)×C101—42no—
32H(5,𝔽2)×C101—42no—
33C2×#41×C101—21no—
34C2×#41×C101C2×C411yescharacteristic
35C2×#41×C101D411yescharacteristic
36C2×#41×C101D411yescharacteristic
37C2×#41×C101C2311yescharacteristic
38C22×Q8×C101C2×C411yescharacteristic
39C22×D4×C101—21no—
40C22×D4×C101—21no—
41C22×D4×C101—21no—
42C22×D4×C101C2×C411yescharacteristic
43C22×D4×C101D411yescharacteristic
44C22×D4×C101D411yescharacteristic
45#137×C101—42no—
46C2×Q16×C101—21no—
47C2×SD16×C101—21no—
48C2×SD16×C101—21no—
49C2×SD16×C101—21no—
50C2×SD16×C101—42no—
51#131×C101—42no—
52#131×C101—42no—
53C2×M16×C101—24no—
54C2×M16×C101—21no—
55C2×M16×C101—21no—
56C2×M16×C101—21no—
57C2×M16×C101C2×C411yescharacteristic
58C22×C8×C101C2×C411yescharacteristic
59C4⋊Q8×C101—21no—
60#124×C101—21no—
61#123×C101—21no—
62#123×C101—21no—
63C22⋊Q8×C101—21no—
64C22⋊Q8×C101—21no—
65#117×C101—21no—
66#117×C101C2×C411yescharacteristic
67#104×C101—42no—
68#103×C101—21no—
69#102×C101—21no—
70#102×C101—21no—
71#102×C101—21no—
72#102×C101—42no—
73#101×C101—21no—
74#101×C101—21no—
75#101×C101D412yes—
76#100×C101—24no—
77#100×C101—21no—
78#100×C101—21no—
79#100×C101D412yes—
80#99×C101—21no—
81#99×C101—21no—
82C22⋊C8×C101—21no—
83C22⋊C8×C101—21no—
84C24×C101—21no—
85C24×C101—21no—
86C24×C101—21no—
87#41×C101—22no—
88#41×C101—22no—
89#41×C101—22no—
90#41×C101—22no—
91#41×C101—41no—
92#41×C101—41no—
93#41×C101—41no—
94#41×C101—41no—
95#41×C101—44no—
96C2×Q8×C101—21no—
97C2×Q8×C101—21no—
98C2×Q8×C101—41no—
99C2×Q8×C101—41no—
100C2×Q8×C101C22⋊C411yescharacteristic
101C2×Q8×C101C2×D411yescharacteristic
102C2×D4×C101—21no—
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101—21no—
106C2×D4×C101—21no—
107C2×D4×C101—21no—
108C2×D4×C101—21no—
109C2×D4×C101—21no—
110C2×D4×C101—41no—
111C2×D4×C101—41no—
112C2×D4×C101—41no—
113C2×D4×C101—41no—
114C2×D4×C101—44no—
115C2×D4×C101—44no—
116C2×D4×C101—44no—
117C2×D4×C101C22⋊C411yescharacteristic
118C2×D4×C101C22⋊C411yescharacteristic
119C2×D4×C101C22⋊C411yescharacteristic
120C2×D4×C101C2×D411yescharacteristic
121C2×D4×C101#4111yescharacteristic
122C2×D4×C101#4111yescharacteristic
123C22×C4×C101—21no—
124C22×C4×C101—21no—
125C22×C4×C101—21no—
126C22×C4×C101—21no—
127C22×C4×C101C22×C411yescharacteristic
128C22×C4×C101C2×D411yescharacteristic
129C22×C4×C101C2×D411yescharacteristic
130Q16×C101—42no—
131SD16×C101—42no—
132SD16×C101—42no—
133SD16×C101—42no—
134M16×C101—22no—
135M16×C101—22no—
136M16×C101—44no—
137M16×C101—41no—
138M16×C101—41no—
139M16×C101—41no—
140M16×C101—41no—
141M16×C101—41no—
142C2×C8×C101—21no—
143C2×C8×C101—21no—
144C2×C8×C101—44no—
145C2×C8×C101—41no—
146C2×C8×C101—41no—
147C2×C8×C101—41no—
148C2×C8×C101—41no—
149C4⋊C4×C101—21no—
150C4⋊C4×C101—41no—
151C4⋊C4×C101—41no—
152C4⋊C4×C101—41no—
153C22⋊C4×C101—21no—
154C22⋊C4×C101—41no—
155C22⋊C4×C101—41no—
156C22⋊C4×C101—41no—
157C42×C101—21no—
158C42×C101—41no—
159C23×C101—21no—
160C23×C101—21no—
161C23×C101—21no—
162C23×C101—42no—
163C23×C101—42no—
164C23×C101—42no—
165C23×C101—161no—
166C23×C101—161no—
167C23×C101—161no—
168C23×C101C4×D411yescharacteristic
169C23×C101#12111yescharacteristic
170C23×C101#12311yescharacteristic
171Q8×C101—21no—
172Q8×C101—41no—
173Q8×C101—41no—
174Q8×C101—41no—
175Q8×C101—81no—
176Q8×C101#9912yes—
177D4×C101—24no—
178D4×C101—21no—
179D4×C101—21no—
180D4×C101—21no—
181D4×C101—21no—
182D4×C101—21no—
183D4×C101—41no—
184D4×C101—41no—
185D4×C101—41no—
186D4×C101—42no—
187D4×C101—42no—
188D4×C101—42no—
189D4×C101—42no—
190D4×C101—42no—
191D4×C101#9912yes—
192C2×C4×C101—24no—
193C2×C4×C101—21no—
194C2×C4×C101—21no—
195C2×C4×C101—21no—
196C2×C4×C101—21no—
197C2×C4×C101—21no—
198C2×C4×C101—21no—
199C2×C4×C101—21no—
200C2×C4×C101—42no—
201C2×C4×C101—42no—
202C2×C4×C101—41no—
203C2×C4×C101—41no—
204C2×C4×C101—81no—
205C2×C4×C101—81no—
206C2×C4×C101C2×C22⋊C411yescharacteristic
207C2×C4×C101C4×D411yescharacteristic
208C2×C4×C101#12011yescharacteristic
209C2×C4×C101#12111yescharacteristic
210C8×C101—42no—
211C8×C101—42no—
212C8×C101—41no—
213C8×C101—41no—
214C8×C101—81no—
215C22×C101—21no—
216C22×C101—21no—
217C22×C101—21no—
218C22×C101—22no—
219C22×C101—41no—
220C22×C101—41no—
221C22×C101—41no—
222C22×C101—41no—
223C22×C101—41no—
224C22×C101—81no—
225C22×C101—81no—
226C22×C101—81no—
227C22×C101—162no—
228C22×C101—162no—
229C22×C101—162no—
230C22×C101#38611yescharacteristic
231C4×C101—21no—
232C4×C101—21no—
233C4×C101—22no—
234C4×C101—21no—
235C4×C101—81no—
236C4×C101—81no—
237C4×C101—161no—
238C4×C101C2×#9911yescharacteristic
239C4×C101C2×#9911yescharacteristic
240#13097C10111yesmaximal, characteristic, direct product factor, Sylow
241C2×C101—21no—
242C2×C101—41no—
243C2×C101—41no—
244C2×C101—41no—
245C2×C101—42no—
246C2×C101—81no—
247C2×C101—81no—
248C2×C101#189811yescharacteristic
249#3009C2×C10111yescharacteristic
250#2888C2×C10111yescharacteristic
251#2135C2×C10111yescharacteristic, complemented
252#2123C2×C10111yescharacteristic, complemented
253#1795C2×C10111yescharacteristic
254#1395C2×C10111yescharacteristic, complemented
255#1392C2×C10111yescharacteristic, complemented
256C101#1309711yescharacteristic, direct product factor, Sylow
257C2×H(5,𝔽2)C22×C10111yescharacteristic
258C2×#137C4×C10111yescharacteristic, complemented
259C22×SD16C4×C10111yescharacteristic, complemented
260#568—21no—
261#536C22×C10111yescharacteristic
262#452—21no—
263#452—21no—
264#450—21no—
265#450—21no—
266#421—21no—
267#418—21no—
268#418C4×C10111yescharacteristic, complemented
269#416C4×C10111yescharacteristic, complemented
270#413—22no—
271#413C22×C10111yescharacteristic
272#413C22×C10111yescharacteristic
273#413C22×C10111yescharacteristic
274C2×#100—21no—
275C2×#100—22no—
276#410C22×C10111yescharacteristic
277#408C22×C10111yescharacteristic
278#356—22no—
279#352—22no—
280H(5,𝔽2)—42no—
281H(5,𝔽2)—42no—
282C2×#41—21no—
283C2×#41C2×C4×C10111yescharacteristic
284C2×#41D4×C10111yescharacteristic
285C2×#41D4×C10111yescharacteristic
286C2×#41C23×C10111yescharacteristic
287C22×Q8C2×C4×C10111yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×C4×C10111yescharacteristic
292C22×D4D4×C10111yescharacteristic
293C22×D4D4×C10111yescharacteristic
294#137—42no—
295C2×Q16—21no—
296C2×SD16—21no—
297C2×SD16—21no—
298C2×SD16—21no—
299C2×SD16—42no—
300#131—42no—
301#131—42no—
302C2×M16—24no—
303C2×M16—21no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16C2×C4×C10111yescharacteristic
307C22×C8C2×C4×C10111yescharacteristic
308C4⋊Q8—21no—
309#124—21no—
310#123—21no—
311#123—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314#117—21no—
315#117C2×C4×C10111yescharacteristic
316#104—42no—
317#103—21no—
318#102—21no—
319#102—21no—
320#102—21no—
321#102—42no—
322#101—21no—
323#101—21no—
324#101D4×C10112yes—
325#100—24no—
326#100—21no—
327#100—21no—
328#100D4×C10112yes—
329#99—21no—
330#99—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C24—21no—
334C24—21no—
335C24—21no—
336#41—22no—
337#41—22no—
338#41—22no—
339#41—22no—
340#41—41no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—44no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8C22⋊C4×C10111yescharacteristic
350C2×Q8C2×D4×C10111yescharacteristic
351C2×D4—21no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4—44no—
366C2×D4C22⋊C4×C10111yescharacteristic
367C2×D4C22⋊C4×C10111yescharacteristic
368C2×D4C22⋊C4×C10111yescharacteristic
369C2×D4C2×D4×C10111yescharacteristic
370C2×D4#41×C10111yescharacteristic
371C2×D4#41×C10111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4C22×C4×C10111yescharacteristic
377C22×C4C2×D4×C10111yescharacteristic
378C22×C4C2×D4×C10111yescharacteristic
379Q16—42no—
380SD16—42no—
381SD16—42no—
382SD16—42no—
383M16—22no—
384M16—22no—
385M16—44no—
386M16—41no—
387M16—41no—
388M16—41no—
389M16—41no—
390M16—41no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—44no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C4⋊C4—21no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C22⋊C4—21no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42—21no—
407C42—41no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—161no—
415C23—161no—
416C23—161no—
417C23C4×D4×C10111yescharacteristic
418C23#121×C10111yescharacteristic
419C23#123×C10111yescharacteristic
420Q8—21no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—81no—
425Q8#99×C10112yes—
426D4—24no—
427D4—21no—
428D4—21no—
429D4—21no—
430D4—21no—
431D4—21no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4#99×C10112yes—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4C2×C22⋊C4×C10111yescharacteristic
456C2×C4C4×D4×C10111yescharacteristic
457C2×C4#120×C10111yescharacteristic
458C2×C4#121×C10111yescharacteristic
459C8—42no—
460C8—42no—
461C8—41no—
462C8—41no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—162no—
477C22—162no—
478C22—162no—
479C22#386×C10111yescharacteristic
480C4—21no—
481C4—21no—
482C4—22no—
483C4—21no—
484C4—81no—
485C4—81no—
486C4—161no—
487C4C2×#99×C10111yescharacteristic
488C4C2×#99×C10111yescharacteristic
489C2—21no—
490C2—41no—
491C2—41no—
492C2—41no—
493C2—42no—
494C2—81no—
495C2—81no—
496C2C101×#189811yescharacteristic
subgroupG/H
center, socleC2×C101#1898
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×#41C23×C101
prime radicalC2×H(5,𝔽2)×C101C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×H(5,𝔽2)×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#2135C2semidirect
4. C101×#2123C2semidirect
6. C101×#1395C2semidirect
7. C101×#1392C2semidirect
9. C2×#137×C101C4semidirect
10. C22×SD16×C101C4semidirect
19. #418×C101C4semidirect
20. #416×C101C4semidirect
240. #13097C101direct (N × H)
251. #2135C2×C101semidirect
252. #2123C2×C101semidirect
254. #1395C2×C101semidirect
255. #1392C2×C101semidirect
256. C101#13097direct (N × H)
258. C2×#137C4×C101semidirect
259. C22×SD16C4×C101semidirect
268. #418C4×C101semidirect
269. #416C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30092
C101×#28882
C101×#21352
C101×#21232
C101×#17952
C101×#13952
C101×#13922
#13097101