Finite Group Databasebeta

← C101×#25508 #38807659

Subgroups — C101×#25508 #38807659

Order 25856.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C101C211yesmaximal, characteristic, complemented
2C2×#469×C101C211yesmaximal, characteristic, complemented
3C2×#466×C101C211yesmaximal, characteristic, complemented
4C101×#2624C211yesmaximal, characteristic, complemented
5C101×#2059C211yesmaximal, characteristic, complemented
6C101×#2041C211yesmaximal, characteristic, complemented
7C101×#2025C211yesmaximal, characteristic, complemented
8C101×#2011C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1893C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1864C211yesmaximal, characteristic, complemented
14C101×#1862C211yesmaximal, characteristic, complemented
15C101×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20#540×C101—24no—
21#540×C101—24no—
22C2×#127×C101C2211yescharacteristic
23C2×#125×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×#123×C101—21no—
26C2×#121×C101—21no—
27C2×#121×C101—21no—
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×C4×D4×C101C2211yescharacteristic
32C2×C4×D4×C101C2211yescharacteristic
33C2×#117×C101C2211yescharacteristic
34#469×C101—24no—
35#466×C101—24no—
36C2×#107×C101C2211yescharacteristic
37C2×#106×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46#399×C101—21no—
47#397×C101—21no—
48#394×C101—21no—
49#394×C101—21no—
50#390×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#389×C101C2211yescharacteristic
54#380×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101C2311yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
71C23×C4×C101—21no—
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—22no—
78C2×D8×C101—41no—
79C2×D8×C101—41no—
80C2×M16×C101—22no—
81C2×M16×C101—22no—
82C2×M16×C101—41no—
83C22×C8×C101—22no—
84C22×C8×C101—22no—
85C22×C8×C101—41no—
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90#127×C101—22no—
91#127×C101—22no—
92#125×C101—22no—
93#125×C101—22no—
94#123×C101—28no—
95#123×C101—28no—
96#121×C101—28no—
97#121×C101—28no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101D414yes—
103#121×C101D414yes—
104C4×D4×C101—22no—
105C4×D4×C101—22no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108#117×C101—22no—
109#117×C101—22no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101—21no—
114C2×C4⋊C4×C101D411yescharacteristic
115C2×C4⋊C4×C101D411yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
120C2×C4⋊C4×C101C2311yescharacteristic
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C22⋊C4×C101D411yescharacteristic
133C2×C42×C101C2311yescharacteristic
134C2×C42×C101C2311yescharacteristic
135#107×C101—22no—
136#106×C101—22no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—41no—
144#102×C101—41no—
145#95×C101—21no—
146#95×C101—21no—
147#95×C101—21no—
148C24×C101—21no—
149C24×C101—21no—
150C24×C101—21no—
151C24×C101C2×D411yescharacteristic
152C2×D4×C101—24no—
153C2×D4×C101—24no—
154C2×D4×C101—24no—
155C2×D4×C101—24no—
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—21no—
165C2×D4×C101—21no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—42no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101—81no—
177C2×D4×C101—81no—
178C2×D4×C101—81no—
179C2×D4×C101—81no—
180C2×D4×C101—81no—
181C2×D4×C101—81no—
182C2×D4×C101—81no—
183C2×D4×C101C2×D412yes—
184C2×D4×C101C2×D412yes—
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—24no—
192C22×C4×C101—24no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—81no—
197C22×C4×C101—81no—
198C22×C4×C101—81no—
199C22×C4×C101—81no—
200C22×C4×C101C2×D411yescharacteristic
201C22×C4×C101C2×D411yescharacteristic
202C22×C4×C101C2×D411yescharacteristic
203C22×C4×C101C2×D411yescharacteristic
204C22×C4×C101C2×D411yescharacteristic
205C22×C4×C101C2×D412yes—
206C22×C4×C101C2×D412yes—
207C22×C4×C101C2411yescharacteristic
208D8×C101—44no—
209D8×C101—44no—
210M16×C101—44no—
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—21no—
220C2×C8×C101—21no—
221C2×C8×C101—44no—
222C2×C8×C101#4112yes—
223C2×C8×C101#4112yes—
224C4⋊C4×C101—24no—
225C4⋊C4×C101—24no—
226C4⋊C4×C101—22no—
227C4⋊C4×C101—22no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—81no—
237C4⋊C4×C101—81no—
238C4⋊C4×C101C2×D412yes—
239C4⋊C4×C101C2×D412yes—
240C22⋊C4×C101—24no—
241C22⋊C4×C101—24no—
242C22⋊C4×C101—22no—
243C22⋊C4×C101—22no—
244C22⋊C4×C101—24no—
245C22⋊C4×C101—24no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—81no—
248C22⋊C4×C101—81no—
249C22⋊C4×C101—81no—
250C22⋊C4×C101—81no—
251C22⋊C4×C101—81no—
252C42×C101—21no—
253C42×C101—21no—
254C42×C101—21no—
255C42×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—41no—
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—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101#12012yes—
284C23×C101C22×D411yescharacteristic
285D4×C101—22no—
286D4×C101—22no—
287D4×C101—22no—
288D4×C101—22no—
289D4×C101—41no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—84no—
298D4×C101—84no—
299D4×C101—84no—
300D4×C101—84no—
301D4×C101—84no—
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—21no—
312C2×C4×C101—22no—
313C2×C4×C101—22no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
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—84no—
336C2×C4×C101—84no—
337C2×C4×C101#12012yes—
338C2×C4×C101C22×D411yescharacteristic
339C2×C4×C101C22×D411yescharacteristic
340C2×C4×C101C2×#4111yescharacteristic
341C2×C4×C101C2×#4111yescharacteristic
342C2×C4×C101H(5,𝔽2)11yescharacteristic
343C2×C4×C1012−1+411yescharacteristic
344C8×C101—22no—
345C8×C101—22no—
346C8×C101—41no—
347C8×C101—41no—
348C22×C101—22no—
349C22×C101—22no—
350C22×C101—22no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—42no—
357C22×C101—42no—
358C22×C101—42no—
359C22×C101—42no—
360C22×C101—42no—
361C22×C101—81no—
362C22×C101—81no—
363C22×C101—81no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101C2×#12011yescharacteristic
377C22×C101#53211yescharacteristic
378C22×C101#53711yescharacteristic
379C22×C101#57611yescharacteristic
380C22×C101#57611yescharacteristic
381C22×C101#57611yescharacteristic
382C22×C101#57711yescharacteristic
383C4×C101—22no—
384C4×C101—41no—
385C4×C101—41no—
386C4×C101—42no—
387C4×C101—41no—
388C4×C101—41no—
389C4×C101—42no—
390C4×C101—81no—
391C4×C101—81no—
392C4×C101—81no—
393C4×C101#54611yescharacteristic
394C4×C101#54611yescharacteristic
395C4×C101#54711yescharacteristic
396C4×C101#54711yescharacteristic
397#25508C10111yesmaximal, characteristic, direct product factor, Sylow
398C2×C101—42no—
399C2×C101—82no—
400C2×C101—82no—
401C2×C101—161no—
402C2×C101#243011yescharacteristic
403C2×C101#300811yescharacteristic
404C2×C101#301211yescharacteristic
405C2×C101#317611yescharacteristic
406C2×C101#317911yescharacteristic
407C2×C101#325711yescharacteristic
408C2×C101#325911yescharacteristic
409C2×#540C2×C10111yescharacteristic, complemented
410C2×#469C2×C10111yescharacteristic, complemented
411C2×#466C2×C10111yescharacteristic, complemented
412#2624C2×C10111yescharacteristic, complemented
413#2059C2×C10111yescharacteristic, complemented
414#2041C2×C10111yescharacteristic, complemented
415#2025C2×C10111yescharacteristic, complemented
416#2011C2×C10111yescharacteristic, complemented
417#1895C2×C10111yescharacteristic, complemented
418#1893C2×C10111yescharacteristic, complemented
419#1879C2×C10111yescharacteristic, complemented
420#1879C2×C10111yescharacteristic, complemented
421#1864C2×C10111yescharacteristic, complemented
422#1862C2×C10111yescharacteristic, complemented
423#1729C2×C10111yescharacteristic, complemented
424C101#2550811yescharacteristic, direct product factor, Sylow
425C22×D8C22×C10111yescharacteristic
426C22×D8C22×C10111yescharacteristic
427C22×M16C22×C10111yescharacteristic
428C23×C8C22×C10111yescharacteristic
429#540—24no—
430#540—24no—
431C2×#127C22×C10111yescharacteristic
432C2×#125C22×C10111yescharacteristic
433C2×#123—21no—
434C2×#123—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C10111yescharacteristic
438C2×#121C22×C10111yescharacteristic
439C2×#121C22×C10111yescharacteristic
440C2×C4×D4C22×C10111yescharacteristic
441C2×C4×D4C22×C10111yescharacteristic
442C2×#117C22×C10111yescharacteristic
443#469—24no—
444#466—24no—
445C2×#107C22×C10111yescharacteristic
446C2×#106C22×C10111yescharacteristic
447C2×#102C22×C10111yescharacteristic
448C2×#102C22×C10111yescharacteristic
449C2×#102C22×C10111yescharacteristic
450C2×#102C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×#102C22×C10111yescharacteristic
454C2×#102C22×C10111yescharacteristic
455#399—21no—
456#397—21no—
457#394—21no—
458#394—21no—
459#390C22×C10111yescharacteristic
460#390C22×C10111yescharacteristic
461#389C22×C10111yescharacteristic
462#389C22×C10111yescharacteristic
463#380C22×C10111yescharacteristic
464#340C22×C10111yescharacteristic
465#340C22×C10111yescharacteristic
466#340C22×C10111yescharacteristic
467#340C22×C10111yescharacteristic
468#336C22×C10111yescharacteristic
469#336C22×C10111yescharacteristic
470#336C22×C10111yescharacteristic
471#336C22×C10111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C10111yescharacteristic
478C22×D4C23×C10111yescharacteristic
479C22×D4C23×C10111yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C10111yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8C23×C10111yescharacteristic
496C22×C8C23×C10111yescharacteristic
497C22×C8C23×C10111yescharacteristic
498C22×C8C23×C10111yescharacteristic
499#127—22no—
500#127—22no—
501#125—22no—
502#125—22no—
503#123—28no—
504#123—28no—
505#121—28no—
506#121—28no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121D4×C10114yes—
512#121D4×C10114yes—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10111yescharacteristic
524C2×C4⋊C4D4×C10111yescharacteristic
525C2×C4⋊C4C23×C10111yescharacteristic
526C2×C4⋊C4C23×C10111yescharacteristic
527C2×C4⋊C4C23×C10111yescharacteristic
528C2×C4⋊C4C23×C10111yescharacteristic
529C2×C4⋊C4C23×C10111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C10111yescharacteristic
541C2×C22⋊C4D4×C10111yescharacteristic
542C2×C42C23×C10111yescharacteristic
543C2×C42C23×C10111yescharacteristic
544#107—22no—
545#106—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C10111yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
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—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C10112yes—
593C2×D4C2×D4×C10112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C10111yescharacteristic
610C22×C4C2×D4×C10111yescharacteristic
611C22×C4C2×D4×C10111yescharacteristic
612C22×C4C2×D4×C10111yescharacteristic
613C22×C4C2×D4×C10111yescharacteristic
614C22×C4C2×D4×C10112yes—
615C22×C4C2×D4×C10112yes—
616C22×C4C24×C10111yescharacteristic
617D8—44no—
618D8—44no—
619M16—44no—
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—44no—
631C2×C8#41×C10112yes—
632C2×C8#41×C10112yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
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—81no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C10112yes—
648C4⋊C4C2×D4×C10112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
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—41no—
690C23—41no—
691C23—41no—
692C23#120×C10112yes—
693C23C22×D4×C10111yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
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—84no—
745C2×C4—84no—
746C2×C4#120×C10112yes—
747C2×C4C22×D4×C10111yescharacteristic
748C2×C4C22×D4×C10111yescharacteristic
749C2×C4C2×#41×C10111yescharacteristic
750C2×C4C2×#41×C10111yescharacteristic
751C2×C4H(5,𝔽2)×C10111yescharacteristic
752C2×C42−1+4×C10111yescharacteristic
753C8—22no—
754C8—22no—
755C8—41no—
756C8—41no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C10111yescharacteristic
786C22#532×C10111yescharacteristic
787C22#537×C10111yescharacteristic
788C22#576×C10111yescharacteristic
789C22#576×C10111yescharacteristic
790C22#576×C10111yescharacteristic
791C22#577×C10111yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C10111yescharacteristic
803C4#546×C10111yescharacteristic
804C4#547×C10111yescharacteristic
805C4#547×C10111yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C101×#243011yescharacteristic
811C2C101×#300811yescharacteristic
812C2C101×#301211yescharacteristic
813C2C101×#317611yescharacteristic
814C2C101×#317911yescharacteristic
815C2C101×#325711yescharacteristic
816C2C101×#325911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C101C2semidirect
2. C2×#469×C101C2semidirect
3. C2×#466×C101C2semidirect
4. C101×#2624C2semidirect
5. C101×#2059C2semidirect
6. C101×#2041C2semidirect
7. C101×#2025C2semidirect
8. C101×#2011C2semidirect
9. C101×#1895C2semidirect
10. C101×#1893C2semidirect
11. C101×#1879C2semidirect
12. C101×#1879C2semidirect
13. C101×#1864C2semidirect
14. C101×#1862C2semidirect
15. C101×#1729C2semidirect
397. #25508C101direct (N × H)
409. C2×#540C2×C101semidirect
410. C2×#469C2×C101semidirect
411. C2×#466C2×C101semidirect
412. #2624C2×C101semidirect
413. #2059C2×C101semidirect
414. #2041C2×C101semidirect
415. #2025C2×C101semidirect
416. #2011C2×C101semidirect
417. #1895C2×C101semidirect
418. #1893C2×C101semidirect
419. #1879C2×C101semidirect
420. #1879C2×C101semidirect
421. #1864C2×C101semidirect
422. #1862C2×C101semidirect
423. #1729C2×C101semidirect
424. C101#25508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#540×C1012
C2×#469×C1012
C2×#466×C1012
C101×#26242
C101×#20592
C101×#20412
C101×#20252
C101×#20112
C101×#18952
C101×#18932
C101×#18792
C101×#18642
C101×#18622
C101×#17292
#25508101