Finite Group Databasebeta

← C139×#25553 #48020149

Subgroups — C139×#25553 #48020149

Order 35584.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C139C211yesmaximal, characteristic, complemented
2C2×#480×C139C211yesmaximal, characteristic, complemented
3C2×#469×C139C211yesmaximal, characteristic, complemented
4#2414×C139C211yesmaximal, characteristic, complemented
5#2059×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#2025×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1879×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1875×C139C211yesmaximal, characteristic, complemented
12#1870×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1736×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18#553×C139—24no—
19#553×C139—24no—
20C2×#126×C139—21no—
21C2×#125×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×#121×C139—21no—
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×C4×D4×C139—21no—
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×#117×C139C2211yescharacteristic
32C2×#117×C139C2211yescharacteristic
33C22×C4⋊C4×C139C2211yescharacteristic
34#480×C139—24no—
35#469×C139—24no—
36C2×#107×C139C2211yescharacteristic
37C2×#107×C139C2211yescharacteristic
38C2×#106×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48#394×C139—21no—
49#392×C139—21no—
50#390×C139—21no—
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#388×C139—21no—
54#380×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×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×C139D411yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C23×C4×C139—21no—
71C23×C4×C139—21no—
72C23×C4×C139C2311yescharacteristic
73C23×C4×C139C2311yescharacteristic
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—41no—
77C2×M16×C139—22no—
78C2×M16×C139—22no—
79C2×M16×C139—41no—
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84#126×C139—28no—
85#125×C139—22no—
86#125×C139—22no—
87#123×C139—28no—
88#121×C139—28no—
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—22no—
94#121×C139—22no—
95#121×C139—41no—
96#121×C139D414yescomplemented
97C4×D4×C139—28no—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102#117×C139—22no—
103#117×C139—22no—
104#117×C139—22no—
105#117×C139—41no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139D414yescomplemented
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
130C2×C22⋊C4×C139D411yescharacteristic
131C2×C42×C139—21no—
132C2×C42×C139—21no—
133C2×C42×C139C2311yescharacteristic
134#107×C139—22no—
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—41no—
143C22⋊C8×C139—22no—
144C22⋊C8×C139—22no—
145C22⋊C8×C139—41no—
146#95×C139—21no—
147#95×C139—21no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139C2×D411yescharacteristic
151C24×C139C2×D411yescharacteristic
152C2×D4×C139—22no—
153C2×D4×C139—24no—
154C2×D4×C139—24no—
155C2×D4×C139—21no—
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—41no—
167C2×D4×C139—41no—
168C2×D4×C139—42no—
169C2×D4×C139—42no—
170C2×D4×C139—42no—
171C2×D4×C139—42no—
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×C139C2×D412yes—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—24no—
188C22×C4×C139—24no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—81no—
198C22×C4×C139—81no—
199C22×C4×C139—81no—
200C22×C4×C139—81no—
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—
209M16×C139—44no—
210C2×C8×C139—21no—
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#4112yes—
222C4⋊C4×C139—24no—
223C4⋊C4×C139—24no—
224C4⋊C4×C139—24no—
225C4⋊C4×C139—22no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
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—81no—
235C4⋊C4×C139C2×D412yes—
236C4⋊C4×C139C2×D412yes—
237C4⋊C4×C139C2×D412yes—
238C4⋊C4×C139#4112yes—
239C22⋊C4×C139—24no—
240C22⋊C4×C139—24no—
241C22⋊C4×C139—24no—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—24no—
244C22⋊C4×C139—22no—
245C22⋊C4×C139—42no—
246C22⋊C4×C139—42no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—81no—
250C22⋊C4×C139—81no—
251C42×C139—24no—
252C42×C139—21no—
253C42×C139—21no—
254C42×C139—42no—
255C23×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—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
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#12012yes—
283C23×C139C22×D411yescharacteristic
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—44no—
287D4×C139—48no—
288D4×C139—41no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—84no—
295D4×C139—84no—
296D4×C139—84no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—22no—
300C2×C4×C139—22no—
301C2×C4×C139—22no—
302C2×C4×C139—22no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—22no—
306C2×C4×C139—21no—
307C2×C4×C139—22no—
308C2×C4×C139—22no—
309C2×C4×C139—22no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
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—84no—
335C2×C4×C139—84no—
336C2×C4×C139#12012yes—
337C2×C4×C139C22×D411yescharacteristic
338C2×C4×C139C22×D411yescharacteristic
339C2×C4×C139C2×#4111yescharacteristic
340C2×C4×C139C2×#4111yescharacteristic
341C2×C4×C139H(5,𝔽2)11yescharacteristic
342C2×C4×C1392−1+411yescharacteristic
343C8×C139—22no—
344C8×C139—41no—
345C8×C139—41no—
346C8×C139—41no—
347C22×C139—22no—
348C22×C139—22no—
349C22×C139—22no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—41no—
356C22×C139—41no—
357C22×C139—42no—
358C22×C139—41no—
359C22×C139—42no—
360C22×C139—42no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—41no—
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×C139C2×#12011yescharacteristic
376C22×C139#54611yescharacteristic
377C22×C139#54711yescharacteristic
378C22×C139#57511yescharacteristic
379C22×C139#57511yescharacteristic
380C22×C139#57611yescharacteristic
381C22×C139#57611yescharacteristic
382C4×C139—22no—
383C4×C139—41no—
384C4×C139—41no—
385C4×C139—42no—
386C4×C139—41no—
387C4×C139—42no—
388C4×C139—42no—
389C4×C139—42no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139#53211yescharacteristic
393C4×C139#53711yescharacteristic
394C4×C139#54611yescharacteristic
395C4×C139#54711yescharacteristic
396C2×C139—42no—
397C2×C139—81no—
398C2×C139—82no—
399C2×C139—161no—
400C2×C139#243011yescharacteristic
401C2×C139#300511yescharacteristic
402C2×C139#300811yescharacteristic
403C2×C139#330911yescharacteristic
404C2×C139#332211yescharacteristic
405C2×C139#334711yescharacteristic
406C2×C139#335511yescharacteristic
407#25553C13911yesmaximal, characteristic, direct product factor, Sylow
408C139#2555311yescharacteristic, direct product factor, Sylow
409C2×#553C2×C13911yescharacteristic, complemented
410C2×#480C2×C13911yescharacteristic, complemented
411C2×#469C2×C13911yescharacteristic, complemented
412#2414C2×C13911yescharacteristic, complemented
413#2059C2×C13911yescharacteristic, complemented
414#2033C2×C13911yescharacteristic, complemented
415#2025C2×C13911yescharacteristic, complemented
416#1999C2×C13911yescharacteristic, complemented
417#1879C2×C13911yescharacteristic, complemented
418#1875C2×C13911yescharacteristic, complemented
419#1875C2×C13911yescharacteristic, complemented
420#1870C2×C13911yescharacteristic, complemented
421#1862C2×C13911yescharacteristic, complemented
422#1854C2×C13911yescharacteristic, complemented
423#1736C2×C13911yescharacteristic, complemented
424C22×D8C22×C13911yescharacteristic
425C22×M16C22×C13911yescharacteristic
426#553—24no—
427#553—24no—
428C2×#126—21no—
429C2×#125C22×C13911yescharacteristic
430C2×#123—21no—
431C2×#121—21no—
432C2×#121C22×C13911yescharacteristic
433C2×#121C22×C13911yescharacteristic
434C2×#121C22×C13911yescharacteristic
435C2×#121C22×C13911yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C22×C13911yescharacteristic
438C2×C4×D4C22×C13911yescharacteristic
439C2×#117C22×C13911yescharacteristic
440C2×#117C22×C13911yescharacteristic
441C22×C4⋊C4C22×C13911yescharacteristic
442#480—24no—
443#469—24no—
444C2×#107C22×C13911yescharacteristic
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×C22⋊C8C22×C13911yescharacteristic
454C2×C22⋊C8C22×C13911yescharacteristic
455C2×C22⋊C8C22×C13911yescharacteristic
456#394—21no—
457#392—21no—
458#390—21no—
459#390C22×C13911yescharacteristic
460#389C22×C13911yescharacteristic
461#388—21no—
462#380C22×C13911yescharacteristic
463#340C22×C13911yescharacteristic
464#340C22×C13911yescharacteristic
465#340C22×C13911yescharacteristic
466#340C22×C13911yescharacteristic
467#340C22×C13911yescharacteristic
468#340C22×C13911yescharacteristic
469#336C22×C13911yescharacteristic
470#336C22×C13911yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C13911yescharacteristic
476C22×D4C23×C13911yescharacteristic
477C22×D4C23×C13911yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C13911yescharacteristic
481C23×C4C23×C13911yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C13911yescharacteristic
489C22×C8C23×C13911yescharacteristic
490C22×C8C23×C13911yescharacteristic
491C22×C8C23×C13911yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C13914yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C13911yescharacteristic
520C2×C4⋊C4D4×C13914yescomplemented
521C2×C4⋊C4C23×C13911yescharacteristic
522C2×C4⋊C4C23×C13911yescharacteristic
523C2×C4⋊C4C23×C13911yescharacteristic
524C2×C4⋊C4C23×C13911yescharacteristic
525C2×C4⋊C4C23×C13911yescharacteristic
526C2×C4⋊C4C23×C13911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
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⋊C4D4×C13911yescharacteristic
538C2×C22⋊C4D4×C13911yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C13911yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C13911yescharacteristic
559C24C2×D4×C13911yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
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—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C13912yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
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—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×C13912yes—
614C22×C4C2×D4×C13912yes—
615C22×C4C24×C13911yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
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#41×C13912yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
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—81no—
643C4⋊C4C2×D4×C13912yes—
644C4⋊C4C2×D4×C13912yes—
645C4⋊C4C2×D4×C13912yes—
646C4⋊C4#41×C13912yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
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#120×C13912yes—
691C23C22×D4×C13911yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
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—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4#120×C13912yes—
745C2×C4C22×D4×C13911yescharacteristic
746C2×C4C22×D4×C13911yescharacteristic
747C2×C4C2×#41×C13911yescharacteristic
748C2×C4C2×#41×C13911yescharacteristic
749C2×C4H(5,𝔽2)×C13911yescharacteristic
750C2×C42−1+4×C13911yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C13911yescharacteristic
784C22#546×C13911yescharacteristic
785C22#547×C13911yescharacteristic
786C22#575×C13911yescharacteristic
787C22#575×C13911yescharacteristic
788C22#576×C13911yescharacteristic
789C22#576×C13911yescharacteristic
790C4—22no—
791C4—42no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4#532×C13911yescharacteristic
801C4#537×C13911yescharacteristic
802C4#546×C13911yescharacteristic
803C4#547×C13911yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2#2430×C13911yescharacteristic
809C2#3005×C13911yescharacteristic
810C2#3008×C13911yescharacteristic
811C2#3309×C13911yescharacteristic
812C2#3322×C13911yescharacteristic
813C2#3347×C13911yescharacteristic
814C2#3355×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C139C2semidirect
2. C2×#480×C139C2semidirect
3. C2×#469×C139C2semidirect
4. #2414×C139C2semidirect
5. #2059×C139C2semidirect
6. #2033×C139C2semidirect
7. #2025×C139C2semidirect
8. #1999×C139C2semidirect
9. #1879×C139C2semidirect
10. #1875×C139C2semidirect
11. #1875×C139C2semidirect
12. #1870×C139C2semidirect
13. #1862×C139C2semidirect
14. #1854×C139C2semidirect
15. #1736×C139C2semidirect
96. #121×C139D4semidirect
112. C2×C4⋊C4×C139D4semidirect
407. #25553C139direct (N × H)
408. C139#25553direct (N × H)
409. C2×#553C2×C139semidirect
410. C2×#480C2×C139semidirect
411. C2×#469C2×C139semidirect
412. #2414C2×C139semidirect
413. #2059C2×C139semidirect
414. #2033C2×C139semidirect
415. #2025C2×C139semidirect
416. #1999C2×C139semidirect
417. #1879C2×C139semidirect
418. #1875C2×C139semidirect
419. #1875C2×C139semidirect
420. #1870C2×C139semidirect
421. #1862C2×C139semidirect
422. #1854C2×C139semidirect
423. #1736C2×C139semidirect
504. #121D4×C139semidirect
520. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1392
C2×#480×C1392
C2×#469×C1392
#2414×C1392
#2059×C1392
#2033×C1392
#2025×C1392
#1999×C1392
#1879×C1392
#1875×C1392
#1870×C1392
#1862×C1392
#1854×C1392
#1736×C1392
#25553139