Finite Group Databasebeta

← C101×#24861 #38807012

Subgroups — C101×#24861 #38807012

Order 25856.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C101C211yesmaximal, characteristic, complemented
2C22×#102×C101C211yesmaximal, characteristic, complemented
3C101×#2408C211yesmaximal, characteristic
4D4×C4⋊C4×C101C211yesmaximal, characteristic, complemented
5C101×#2093C211yesmaximal, characteristic, complemented
6C101×#2071C211yesmaximal, characteristic, complemented
7C101×#2033C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1925C211yesmaximal, characteristic, complemented
10C101×#1925C211yesmaximal, characteristic, complemented
11C101×#1874C211yesmaximal, characteristic, complemented
12C101×#1869C211yesmaximal, characteristic, complemented
13C101×#1852C211yesmaximal, characteristic, complemented
14C101×#1808C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18C2×#121×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×#120×C101—21no—
21C2×C4×D4×C101—21no—
22C2×C4×D4×C101C2211yescharacteristic
23C22×C4⋊C4×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic, complemented
25#480×C101—24no—
26C2×#107×C101C2211yescharacteristic, complemented
27C2×#107×C101C2211yescharacteristic, complemented
28C2×#107×C101C2211yescharacteristic, complemented
29C2×#107×C101C2211yescharacteristic, complemented
30C2×#102×C101—24no—
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×C22⋊C8×C101C2211yescharacteristic, complemented
41C2×C22⋊C8×C101C2211yescharacteristic, complemented
42#394×C101—21no—
43#392×C101—21no—
44#390×C101C2211yescharacteristic
45#390×C101C2211yescharacteristic
46#389×C101—21no—
47#385×C101—21no—
48#385×C101—21no—
49#384×C101C2211yescharacteristic, complemented
50#380×C101C2211yescharacteristic
51#380×C101C2211yescharacteristic
52#380×C101C2211yescharacteristic, complemented
53#379×C101—21no—
54C4×C4⋊C4×C101C2211yescharacteristic, complemented
55#340×C101C2211yescharacteristic, complemented
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#336×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61C25×C101—21no—
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—22no—
68C22×D4×C101—22no—
69C22×D4×C101—41no—
70C22×D4×C101—41no—
71C22×D4×C101D411yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101—21no—
75C23×C4×C101—21no—
76C23×C4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C22×C8×C101—22no—
79C22×C8×C101—22no—
80C22×C8×C101—41no—
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85#121×C101—22no—
86#121×C101—22no—
87#121×C101—41no—
88#121×C101—41no—
89#120×C101—44no—
90C4×D4×C101—22no—
91C4×D4×C101—22no—
92C4×D4×C101—44no—
93C2×C4⋊C4×C101—22no—
94C2×C4⋊C4×C101—22no—
95C2×C4⋊C4×C101—21no—
96C2×C4⋊C4×C101—21no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101—41no—
100C2×C4⋊C4×C101—41no—
101C2×C4⋊C4×C101D411yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C4⋊C4×C101C2311yescharacteristic
104C2×C4⋊C4×C101C2311yescharacteristic
105C2×C4⋊C4×C101C2311yescharacteristic
106C2×C4⋊C4×C101C2311yescharacteristic
107C2×C4⋊C4×C101C2311yescharacteristic
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101—21no—
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101D411yescharacteristic
118C2×C22⋊C4×C101D411yescharacteristic
119C2×C42×C101—21no—
120C2×C42×C101C2311yescharacteristic
121#107×C101—22no—
122#107×C101—22no—
123#107×C101—41no—
124#107×C101—41no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—22no—
129#102×C101—22no—
130#102×C101—41no—
131#102×C101—41no—
132#102×C101D414yescomplemented
133C22⋊C8×C101—22no—
134C22⋊C8×C101—22no—
135C22⋊C8×C101—41no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101—21no—
139#95×C101—21no—
140C24×C101—21no—
141C24×C101—21no—
142C24×C101—42no—
143C24×C101—42no—
144C24×C101—42no—
145C24×C101—42no—
146C24×C101—42no—
147C24×C101—81no—
148C24×C101—81no—
149C24×C101C2×D411yescharacteristic
150C24×C101C2×D411yescharacteristic
151C2×D4×C101—22no—
152C2×D4×C101—22no—
153C2×D4×C101—28no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—21no—
164C2×D4×C101—44no—
165C2×D4×C101—44no—
166C2×D4×C101—42no—
167C2×D4×C101—42no—
168C2×D4×C101—44no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—42no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101D814yes—
177C2×D4×C101C2×D412yes—
178C2×D4×C101#4112yes—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—42no—
196C22×C4×C101—42no—
197C22×C4×C101—42no—
198C22×C4×C101—42no—
199C22×C4×C101—81no—
200C22×C4×C101—81no—
201C22×C4×C101C2×D411yescharacteristic
202C22×C4×C101C2×D411yescharacteristic
203C22×C4×C101C2×D411yescharacteristic
204C22×C4×C101C2×D411yescharacteristic
205C22×C4×C101#4112yes—
206C22×C4×C101#4112yes—
207C22×C4×C101C2411yescharacteristic
208C2×C8×C101—21no—
209C2×C8×C101—21no—
210C2×C8×C101—21no—
211C2×C8×C101—21no—
212C2×C8×C101—21no—
213C2×C8×C101—21no—
214C2×C8×C101—21no—
215C2×C8×C101—21no—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—44no—
220C2×C8×C101C2×D412yes—
221C4⋊C4×C101—22no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—21no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—42no—
234C4⋊C4×C101—42no—
235C4⋊C4×C101—42no—
236C4⋊C4×C101—81no—
237C4⋊C4×C101C2×D412yes—
238C22⋊C4×C101—22no—
239C22⋊C4×C101—22no—
240C22⋊C4×C101—42no—
241C22⋊C4×C101—42no—
242C22⋊C4×C101—42no—
243C22⋊C4×C101—42no—
244C22⋊C4×C101—42no—
245C22⋊C4×C101—42no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—81no—
248C22⋊C4×C101—81no—
249C42×C101—21no—
250C42×C101—21no—
251C42×C101—42no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—21no—
255C23×C101—21no—
256C23×C101—21no—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—22no—
263C23×C101—22no—
264C23×C101—48no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—41no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—84no—
278C23×C101—84no—
279C23×C101—84no—
280C23×C101—84no—
281C23×C101—84no—
282C23×C101—84no—
283C23×C101#12312yes—
284C23×C101C2×D812yes—
285C23×C101C2×D812yes—
286C23×C101#13712yes—
287C23×C101C22×D411yescharacteristic
288D4×C101—28no—
289D4×C101—22no—
290D4×C101—22no—
291D4×C101—22no—
292D4×C101—22no—
293D4×C101—48no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—41no—
298D4×C101—84no—
299D4×C101—84no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—22no—
305C2×C4×C101—22no—
306C2×C4×C101—22no—
307C2×C4×C101—22no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—22no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—84no—
337C2×C4×C101—84no—
338C2×C4×C101#12312yes—
339C2×C4×C101C2×D812yes—
340C2×C4×C101C22×D411yescharacteristic
341C2×C4×C101C2×#4111yescharacteristic
342C2×C4×C101C2×#4111yescharacteristic
343C2×C4×C101C2×#4111yescharacteristic
344C2×C4×C101H(5,𝔽2)11yescharacteristic
345C2×C4×C101H(5,𝔽2)11yescharacteristic
346C8×C101—22no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C22×C101—22no—
351C22×C101—22no—
352C22×C101—22no—
353C22×C101—22no—
354C22×C101—22no—
355C22×C101—22no—
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—816no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101#48014yescomplemented
379C22×C101C2×#12311yescharacteristic
380C22×C101D4211yescharacteristic
381C22×C101#54611yescharacteristic
382C22×C101C22×D811yescharacteristic
383C22×C101C2×#13711yescharacteristic
384C22×C101#57611yescharacteristic
385C22×C101#57711yescharacteristic
386C4×C101—22no—
387C4×C101—22no—
388C4×C101—41no—
389C4×C101—41no—
390C4×C101—42no—
391C4×C101—81no—
392C4×C101—81no—
393C4×C101—81no—
394C4×C101—81no—
395C4×C101—81no—
396C4×C101#52511yescharacteristic
397C4×C101#53811yescharacteristic
398C4×C101#54611yescharacteristic
399C4×C101#55111yescharacteristic
400#24861C10111yesmaximal, characteristic, direct product factor, Sylow
401C2×C101—24no—
402C2×C101—42no—
403C2×C101—82no—
404C2×C101—82no—
405C2×C101#241811yescharacteristic
406C2×C101C2×#48011yescharacteristic
407C2×C101#309611yescharacteristic
408C2×C101#326611yescharacteristic
409C2×C101D4×D811yescharacteristic
410C2×C101#329411yescharacteristic
411C2×C101#331411yescharacteristic
412C2×#480C2×C10111yescharacteristic, complemented
413C22×#102C2×C10111yescharacteristic, complemented
414#2408C2×C10111yescharacteristic
415D4×C4⋊C4C2×C10111yescharacteristic, complemented
416#2093C2×C10111yescharacteristic, complemented
417#2071C2×C10111yescharacteristic, complemented
418#2033C2×C10111yescharacteristic, complemented
419#2033C2×C10111yescharacteristic, complemented
420#1925C2×C10111yescharacteristic, complemented
421#1925C2×C10111yescharacteristic, complemented
422#1874C2×C10111yescharacteristic, complemented
423#1869C2×C10111yescharacteristic, complemented
424#1852C2×C10111yescharacteristic, complemented
425#1808C2×C10111yescharacteristic, complemented
426#1786C2×C10111yescharacteristic, complemented
427C101#2486111yescharacteristic, direct product factor, Sylow
428C23×D4C22×C10111yescharacteristic
429C23×C8C22×C10111yescharacteristic
430C2×#121C22×C10111yescharacteristic
431C2×#121C22×C10111yescharacteristic
432C2×#120—21no—
433C2×C4×D4—21no—
434C2×C4×D4C22×C10111yescharacteristic
435C22×C4⋊C4C22×C10111yescharacteristic
436C22×C4⋊C4C22×C10111yescharacteristic, complemented
437#480—24no—
438C2×#107C22×C10111yescharacteristic, complemented
439C2×#107C22×C10111yescharacteristic, complemented
440C2×#107C22×C10111yescharacteristic, complemented
441C2×#107C22×C10111yescharacteristic, complemented
442C2×#102—24no—
443C2×#102C22×C10111yescharacteristic
444C2×#102C22×C10111yescharacteristic
445C2×#102C22×C10111yescharacteristic
446C2×#102C22×C10111yescharacteristic
447C2×#102C22×C10111yescharacteristic
448C2×#102C22×C10111yescharacteristic
449C2×#102C22×C10111yescharacteristic
450C2×#102C22×C10111yescharacteristic
451C2×C22⋊C8C22×C10111yescharacteristic
452C2×C22⋊C8C22×C10111yescharacteristic, complemented
453C2×C22⋊C8C22×C10111yescharacteristic, complemented
454#394—21no—
455#392—21no—
456#390C22×C10111yescharacteristic
457#390C22×C10111yescharacteristic
458#389—21no—
459#385—21no—
460#385—21no—
461#384C22×C10111yescharacteristic, complemented
462#380C22×C10111yescharacteristic
463#380C22×C10111yescharacteristic
464#380C22×C10111yescharacteristic, complemented
465#379—21no—
466C4×C4⋊C4C22×C10111yescharacteristic, complemented
467#340C22×C10111yescharacteristic, complemented
468#340C22×C10111yescharacteristic, complemented
469#340C22×C10111yescharacteristic, complemented
470#340C22×C10111yescharacteristic, complemented
471#336C22×C10111yescharacteristic, complemented
472#336C22×C10111yescharacteristic, complemented
473C25—21no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4D4×C10111yescharacteristic
484C22×D4C23×C10111yescharacteristic
485C22×D4C23×C10111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C10111yescharacteristic
489C23×C4C23×C10111yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8C23×C10111yescharacteristic
494C22×C8C23×C10111yescharacteristic
495C22×C8C23×C10111yescharacteristic
496C22×C8C23×C10111yescharacteristic
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#120—44no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—44no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C10111yescharacteristic
514C2×C4⋊C4C23×C10111yescharacteristic
515C2×C4⋊C4C23×C10111yescharacteristic
516C2×C4⋊C4C23×C10111yescharacteristic
517C2×C4⋊C4C23×C10111yescharacteristic
518C2×C4⋊C4C23×C10111yescharacteristic
519C2×C4⋊C4C23×C10111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4D4×C10111yescharacteristic
530C2×C22⋊C4D4×C10111yescharacteristic
531C2×C42—21no—
532C2×C42C23×C10111yescharacteristic
533#107—22no—
534#107—22no—
535#107—41no—
536#107—41no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543#102—41no—
544#102D4×C10114yescomplemented
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C10111yescharacteristic
562C24C2×D4×C10111yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4D8×C10114yes—
589C2×D4C2×D4×C10112yes—
590C2×D4#41×C10112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C10111yescharacteristic
614C22×C4C2×D4×C10111yescharacteristic
615C22×C4C2×D4×C10111yescharacteristic
616C22×C4C2×D4×C10111yescharacteristic
617C22×C4#41×C10112yes—
618C22×C4#41×C10112yes—
619C22×C4C24×C10111yescharacteristic
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C10112yes—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C10112yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#123×C10112yes—
696C23C2×D8×C10112yes—
697C23C2×D8×C10112yes—
698C23#137×C10112yes—
699C23C22×D4×C10111yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4#123×C10112yes—
751C2×C4C2×D8×C10112yes—
752C2×C4C22×D4×C10111yescharacteristic
753C2×C4C2×#41×C10111yescharacteristic
754C2×C4C2×#41×C10111yescharacteristic
755C2×C4C2×#41×C10111yescharacteristic
756C2×C4H(5,𝔽2)×C10111yescharacteristic
757C2×C4H(5,𝔽2)×C10111yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22#480×C10114yescomplemented
791C22C2×#123×C10111yescharacteristic
792C22D42×C10111yescharacteristic
793C22#546×C10111yescharacteristic
794C22C22×D8×C10111yescharacteristic
795C22C2×#137×C10111yescharacteristic
796C22#576×C10111yescharacteristic
797C22#577×C10111yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4#525×C10111yescharacteristic
809C4#538×C10111yescharacteristic
810C4#546×C10111yescharacteristic
811C4#551×C10111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C101×#241811yescharacteristic
817C2C2×#480×C10111yescharacteristic
818C2C101×#309611yescharacteristic
819C2C101×#326611yescharacteristic
820C2D4×D8×C10111yescharacteristic
821C2C101×#329411yescharacteristic
822C2C101×#331411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#480×C101C2semidirect
2. C22×#102×C101C2semidirect
4. D4×C4⋊C4×C101C2semidirect
5. C101×#2093C2semidirect
6. C101×#2071C2semidirect
7. C101×#2033C2semidirect
8. C101×#2033C2semidirect
9. C101×#1925C2semidirect
10. C101×#1925C2semidirect
11. C101×#1874C2semidirect
12. C101×#1869C2semidirect
13. C101×#1852C2semidirect
14. C101×#1808C2semidirect
15. C101×#1786C2semidirect
24. C22×C4⋊C4×C101C22semidirect
26. C2×#107×C101C22semidirect
27. C2×#107×C101C22semidirect
28. C2×#107×C101C22semidirect
29. C2×#107×C101C22semidirect
40. C2×C22⋊C8×C101C22semidirect
41. C2×C22⋊C8×C101C22semidirect
49. #384×C101C22semidirect
52. #380×C101C22semidirect
54. C4×C4⋊C4×C101C22semidirect
55. #340×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #336×C101C22semidirect
60. #336×C101C22semidirect
132. #102×C101D4semidirect
378. C22×C101#480semidirect
400. #24861C101direct (N × H)
412. C2×#480C2×C101semidirect
413. C22×#102C2×C101semidirect
415. D4×C4⋊C4C2×C101semidirect
416. #2093C2×C101semidirect
417. #2071C2×C101semidirect
418. #2033C2×C101semidirect
419. #2033C2×C101semidirect
420. #1925C2×C101semidirect
421. #1925C2×C101semidirect
422. #1874C2×C101semidirect
423. #1869C2×C101semidirect
424. #1852C2×C101semidirect
425. #1808C2×C101semidirect
426. #1786C2×C101semidirect
427. C101#24861direct (N × H)
436. C22×C4⋊C4C22×C101semidirect
438. C2×#107C22×C101semidirect
439. C2×#107C22×C101semidirect
440. C2×#107C22×C101semidirect
441. C2×#107C22×C101semidirect
452. C2×C22⋊C8C22×C101semidirect
453. C2×C22⋊C8C22×C101semidirect
461. #384C22×C101semidirect
464. #380C22×C101semidirect
466. C4×C4⋊C4C22×C101semidirect
467. #340C22×C101semidirect
468. #340C22×C101semidirect
469. #340C22×C101semidirect
470. #340C22×C101semidirect
471. #336C22×C101semidirect
472. #336C22×C101semidirect
544. #102D4×C101semidirect
790. C22#480×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1012
C22×#102×C1012
C101×#24082
D4×C4⋊C4×C1012
C101×#20932
C101×#20712
C101×#20332
C101×#19252
C101×#18742
C101×#18692
C101×#18522
C101×#18082
C101×#17862
#24861101