Finite Group Databasebeta

← C139×#25508 #48020104

Subgroups — C139×#25508 #48020104

Order 35584.

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×C139C211yesmaximal, characteristic, complemented
2C2×#469×C139C211yesmaximal, characteristic, complemented
3C2×#466×C139C211yesmaximal, characteristic, complemented
4#2624×C139C211yesmaximal, characteristic, complemented
5#2059×C139C211yesmaximal, characteristic, complemented
6#2041×C139C211yesmaximal, characteristic, complemented
7#2025×C139C211yesmaximal, characteristic, complemented
8#2011×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1893×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1864×C139C211yesmaximal, characteristic, complemented
14#1862×C139C211yesmaximal, characteristic, complemented
15#1729×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20#540×C139—24no—
21#540×C139—24no—
22C2×#127×C139C2211yescharacteristic
23C2×#125×C139C2211yescharacteristic
24C2×#123×C139—21no—
25C2×#123×C139—21no—
26C2×#121×C139—21no—
27C2×#121×C139—21no—
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C2×#117×C139C2211yescharacteristic
34#469×C139—24no—
35#466×C139—24no—
36C2×#107×C139C2211yescharacteristic
37C2×#106×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46#399×C139—21no—
47#397×C139—21no—
48#394×C139—21no—
49#394×C139—21no—
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#389×C139C2211yescharacteristic
54#380×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139—21no—
73C23×C4×C139C2311yescharacteristic
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—22no—
78C2×D8×C139—41no—
79C2×D8×C139—41no—
80C2×M16×C139—22no—
81C2×M16×C139—22no—
82C2×M16×C139—41no—
83C22×C8×C139—22no—
84C22×C8×C139—22no—
85C22×C8×C139—41no—
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90#127×C139—22no—
91#127×C139—22no—
92#125×C139—22no—
93#125×C139—22no—
94#123×C139—28no—
95#123×C139—28no—
96#121×C139—28no—
97#121×C139—28no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139D414yes—
103#121×C139D414yes—
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108#117×C139—22no—
109#117×C139—22no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139D411yescharacteristic
115C2×C4⋊C4×C139D411yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139D411yescharacteristic
132C2×C22⋊C4×C139D411yescharacteristic
133C2×C42×C139C2311yescharacteristic
134C2×C42×C139C2311yescharacteristic
135#107×C139—22no—
136#106×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144#102×C139—41no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139—21no—
151C24×C139C2×D411yescharacteristic
152C2×D4×C139—24no—
153C2×D4×C139—24no—
154C2×D4×C139—24no—
155C2×D4×C139—24no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—42no—
173C2×D4×C139—81no—
174C2×D4×C139—81no—
175C2×D4×C139—81no—
176C2×D4×C139—81no—
177C2×D4×C139—81no—
178C2×D4×C139—81no—
179C2×D4×C139—81no—
180C2×D4×C139—81no—
181C2×D4×C139—81no—
182C2×D4×C139—81no—
183C2×D4×C139C2×D412yes—
184C2×D4×C139C2×D412yes—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—24no—
192C22×C4×C139—24no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—81no—
197C22×C4×C139—81no—
198C22×C4×C139—81no—
199C22×C4×C139—81no—
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D411yescharacteristic
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139C2×D411yescharacteristic
204C22×C4×C139C2×D411yescharacteristic
205C22×C4×C139C2×D412yes—
206C22×C4×C139C2×D412yes—
207C22×C4×C139C2411yescharacteristic
208D8×C139—44no—
209D8×C139—44no—
210M16×C139—44no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139—21no—
220C2×C8×C139—21no—
221C2×C8×C139—44no—
222C2×C8×C139#4112yes—
223C2×C8×C139#4112yes—
224C4⋊C4×C139—24no—
225C4⋊C4×C139—24no—
226C4⋊C4×C139—22no—
227C4⋊C4×C139—22no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—81no—
237C4⋊C4×C139—81no—
238C4⋊C4×C139C2×D412yes—
239C4⋊C4×C139C2×D412yes—
240C22⋊C4×C139—24no—
241C22⋊C4×C139—24no—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—22no—
244C22⋊C4×C139—24no—
245C22⋊C4×C139—24no—
246C22⋊C4×C139—42no—
247C22⋊C4×C139—81no—
248C22⋊C4×C139—81no—
249C22⋊C4×C139—81no—
250C22⋊C4×C139—81no—
251C22⋊C4×C139—81no—
252C42×C139—21no—
253C42×C139—21no—
254C42×C139—21no—
255C42×C139—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—22no—
263C23×C139—22no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139#12012yes—
284C23×C139C22×D411yescharacteristic
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—84no—
298D4×C139—84no—
299D4×C139—84no—
300D4×C139—84no—
301D4×C139—84no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—22no—
305C2×C4×C139—22no—
306C2×C4×C139—22no—
307C2×C4×C139—22no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—22no—
313C2×C4×C139—22no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—84no—
336C2×C4×C139—84no—
337C2×C4×C139#12012yes—
338C2×C4×C139C22×D411yescharacteristic
339C2×C4×C139C22×D411yescharacteristic
340C2×C4×C139C2×#4111yescharacteristic
341C2×C4×C139C2×#4111yescharacteristic
342C2×C4×C139H(5,𝔽2)11yescharacteristic
343C2×C4×C1392−1+411yescharacteristic
344C8×C139—22no—
345C8×C139—22no—
346C8×C139—41no—
347C8×C139—41no—
348C22×C139—22no—
349C22×C139—22no—
350C22×C139—22no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—42no—
356C22×C139—42no—
357C22×C139—42no—
358C22×C139—42no—
359C22×C139—42no—
360C22×C139—42no—
361C22×C139—81no—
362C22×C139—81no—
363C22×C139—81no—
364C22×C139—81no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139—81no—
368C22×C139—81no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139C2×#12011yescharacteristic
377C22×C139#53211yescharacteristic
378C22×C139#53711yescharacteristic
379C22×C139#57611yescharacteristic
380C22×C139#57611yescharacteristic
381C22×C139#57611yescharacteristic
382C22×C139#57711yescharacteristic
383C4×C139—22no—
384C4×C139—41no—
385C4×C139—41no—
386C4×C139—42no—
387C4×C139—41no—
388C4×C139—41no—
389C4×C139—42no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139—81no—
393C4×C139#54611yescharacteristic
394C4×C139#54611yescharacteristic
395C4×C139#54711yescharacteristic
396C4×C139#54711yescharacteristic
397C2×C139—42no—
398C2×C139—82no—
399C2×C139—82no—
400C2×C139—161no—
401C2×C139#243011yescharacteristic
402C2×C139#300811yescharacteristic
403C2×C139#301211yescharacteristic
404C2×C139#317611yescharacteristic
405C2×C139#317911yescharacteristic
406C2×C139#325711yescharacteristic
407C2×C139#325911yescharacteristic
408#25508C13911yesmaximal, characteristic, direct product factor, Sylow
409C139#2550811yescharacteristic, direct product factor, Sylow
410C2×#540C2×C13911yescharacteristic, complemented
411C2×#469C2×C13911yescharacteristic, complemented
412C2×#466C2×C13911yescharacteristic, complemented
413#2624C2×C13911yescharacteristic, complemented
414#2059C2×C13911yescharacteristic, complemented
415#2041C2×C13911yescharacteristic, complemented
416#2025C2×C13911yescharacteristic, complemented
417#2011C2×C13911yescharacteristic, complemented
418#1895C2×C13911yescharacteristic, complemented
419#1893C2×C13911yescharacteristic, complemented
420#1879C2×C13911yescharacteristic, complemented
421#1879C2×C13911yescharacteristic, complemented
422#1864C2×C13911yescharacteristic, complemented
423#1862C2×C13911yescharacteristic, complemented
424#1729C2×C13911yescharacteristic, complemented
425C22×D8C22×C13911yescharacteristic
426C22×D8C22×C13911yescharacteristic
427C22×M16C22×C13911yescharacteristic
428C23×C8C22×C13911yescharacteristic
429#540—24no—
430#540—24no—
431C2×#127C22×C13911yescharacteristic
432C2×#125C22×C13911yescharacteristic
433C2×#123—21no—
434C2×#123—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C13911yescharacteristic
438C2×#121C22×C13911yescharacteristic
439C2×#121C22×C13911yescharacteristic
440C2×C4×D4C22×C13911yescharacteristic
441C2×C4×D4C22×C13911yescharacteristic
442C2×#117C22×C13911yescharacteristic
443#469—24no—
444#466—24no—
445C2×#107C22×C13911yescharacteristic
446C2×#106C22×C13911yescharacteristic
447C2×#102C22×C13911yescharacteristic
448C2×#102C22×C13911yescharacteristic
449C2×#102C22×C13911yescharacteristic
450C2×#102C22×C13911yescharacteristic
451C2×#102C22×C13911yescharacteristic
452C2×#102C22×C13911yescharacteristic
453C2×#102C22×C13911yescharacteristic
454C2×#102C22×C13911yescharacteristic
455#399—21no—
456#397—21no—
457#394—21no—
458#394—21no—
459#390C22×C13911yescharacteristic
460#390C22×C13911yescharacteristic
461#389C22×C13911yescharacteristic
462#389C22×C13911yescharacteristic
463#380C22×C13911yescharacteristic
464#340C22×C13911yescharacteristic
465#340C22×C13911yescharacteristic
466#340C22×C13911yescharacteristic
467#340C22×C13911yescharacteristic
468#336C22×C13911yescharacteristic
469#336C22×C13911yescharacteristic
470#336C22×C13911yescharacteristic
471#336C22×C13911yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C13911yescharacteristic
478C22×D4C23×C13911yescharacteristic
479C22×D4C23×C13911yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C13911yescharacteristic
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×C13911yescharacteristic
496C22×C8C23×C13911yescharacteristic
497C22×C8C23×C13911yescharacteristic
498C22×C8C23×C13911yescharacteristic
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×C13914yes—
512#121D4×C13914yes—
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×C13911yescharacteristic
524C2×C4⋊C4D4×C13911yescharacteristic
525C2×C4⋊C4C23×C13911yescharacteristic
526C2×C4⋊C4C23×C13911yescharacteristic
527C2×C4⋊C4C23×C13911yescharacteristic
528C2×C4⋊C4C23×C13911yescharacteristic
529C2×C4⋊C4C23×C13911yescharacteristic
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×C13911yescharacteristic
541C2×C22⋊C4D4×C13911yescharacteristic
542C2×C42C23×C13911yescharacteristic
543C2×C42C23×C13911yescharacteristic
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×C13911yescharacteristic
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×C13912yes—
593C2×D4C2×D4×C13912yes—
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×C13911yescharacteristic
610C22×C4C2×D4×C13911yescharacteristic
611C22×C4C2×D4×C13911yescharacteristic
612C22×C4C2×D4×C13911yescharacteristic
613C22×C4C2×D4×C13911yescharacteristic
614C22×C4C2×D4×C13912yes—
615C22×C4C2×D4×C13912yes—
616C22×C4C24×C13911yescharacteristic
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×C13912yes—
632C2×C8#41×C13912yes—
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×C13912yes—
648C4⋊C4C2×D4×C13912yes—
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×C13912yes—
693C23C22×D4×C13911yescharacteristic
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×C13912yes—
747C2×C4C22×D4×C13911yescharacteristic
748C2×C4C22×D4×C13911yescharacteristic
749C2×C4C2×#41×C13911yescharacteristic
750C2×C4C2×#41×C13911yescharacteristic
751C2×C4H(5,𝔽2)×C13911yescharacteristic
752C2×C42−1+4×C13911yescharacteristic
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×C13911yescharacteristic
786C22#532×C13911yescharacteristic
787C22#537×C13911yescharacteristic
788C22#576×C13911yescharacteristic
789C22#576×C13911yescharacteristic
790C22#576×C13911yescharacteristic
791C22#577×C13911yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C13911yescharacteristic
803C4#546×C13911yescharacteristic
804C4#547×C13911yescharacteristic
805C4#547×C13911yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2#2430×C13911yescharacteristic
811C2#3008×C13911yescharacteristic
812C2#3012×C13911yescharacteristic
813C2#3176×C13911yescharacteristic
814C2#3179×C13911yescharacteristic
815C2#3257×C13911yescharacteristic
816C2#3259×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C139C2semidirect
2. C2×#469×C139C2semidirect
3. C2×#466×C139C2semidirect
4. #2624×C139C2semidirect
5. #2059×C139C2semidirect
6. #2041×C139C2semidirect
7. #2025×C139C2semidirect
8. #2011×C139C2semidirect
9. #1895×C139C2semidirect
10. #1893×C139C2semidirect
11. #1879×C139C2semidirect
12. #1879×C139C2semidirect
13. #1864×C139C2semidirect
14. #1862×C139C2semidirect
15. #1729×C139C2semidirect
408. #25508C139direct (N × H)
409. C139#25508direct (N × H)
410. C2×#540C2×C139semidirect
411. C2×#469C2×C139semidirect
412. C2×#466C2×C139semidirect
413. #2624C2×C139semidirect
414. #2059C2×C139semidirect
415. #2041C2×C139semidirect
416. #2025C2×C139semidirect
417. #2011C2×C139semidirect
418. #1895C2×C139semidirect
419. #1893C2×C139semidirect
420. #1879C2×C139semidirect
421. #1879C2×C139semidirect
422. #1864C2×C139semidirect
423. #1862C2×C139semidirect
424. #1729C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1392
C2×#469×C1392
C2×#466×C1392
#2624×C1392
#2059×C1392
#2041×C1392
#2025×C1392
#2011×C1392
#1895×C1392
#1893×C1392
#1879×C1392
#1864×C1392
#1862×C1392
#1729×C1392
#25508139