Finite Group Databasebeta

← C139×#24124 #48018720

Subgroups — C139×#24124 #48018720

Order 35584.

1216 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×#478×C139C211yesmaximal, characteristic, complemented
3C2×C4×D8×C139C211yesmaximal, characteristic, complemented
4#2535×C139C211yesmaximal, characteristic, complemented
5#2034×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#1999×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1991×C139C211yesmaximal, characteristic, complemented
10#1954×C139C211yesmaximal, characteristic, complemented
11#1875×C139C211yesmaximal, characteristic, complemented
12#1874×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1852×C139C211yesmaximal, characteristic, complemented
15#1804×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17#553×C139—24no—
18#553×C139—24no—
19C2×#126×C139—21no—
20C2×#125×C139C2211yescharacteristic
21C2×#123×C139—21no—
22C2×#121×C139—21no—
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×C4×D4×C139—21no—
28C2×C4×D4×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×#117×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2211yescharacteristic
33#478×C139—24no—
34C4×D8×C139—24no—
35C2×#107×C139C2211yescharacteristic
36C2×#107×C139C2211yescharacteristic
37C2×#106×C139C2211yescharacteristic
38C2×C4⋊C8×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
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C4×C8×C139C2211yescharacteristic
50#397×C139—21no—
51#392×C139—21no—
52#386×C139—21no—
53#386×C139—21no—
54#382×C139C2211yescharacteristic
55#380×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×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×C139—21no—
73C23×C4×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—22no—
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82#126×C139—28no—
83#125×C139—22no—
84#125×C139D414yescomplemented
85#123×C139—28no—
86#121×C139—28no—
87#121×C139—22no—
88#121×C139—22no—
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—41no—
94#121×C139—41no—
95C4×D4×C139—28no—
96C4×D4×C139—22no—
97C4×D4×C139—22no—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139D414yescomplemented
102#117×C139—22no—
103#117×C139—22no—
104C2×C4⋊C4×C139—21no—
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—22no—
108C2×C4⋊C4×C139—22no—
109C2×C4⋊C4×C139D411yescharacteristic
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
126C2×C22⋊C4×C139D411yescharacteristic
127C2×C42×C139—21no—
128C2×C42×C139C2311yescharacteristic
129#107×C139—22no—
130#107×C139—22no—
131#106×C139—22no—
132C4⋊C8×C139—22no—
133#102×C139—22no—
134#102×C139—22no—
135#102×C139—22no—
136#102×C139—22no—
137#102×C139—41no—
138#102×C139—41no—
139C22⋊C8×C139—22no—
140C22⋊C8×C139—22no—
141C22⋊C8×C139—41no—
142C22⋊C8×C139—41no—
143C4×C8×C139—22no—
144#95×C139—21no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139C2×D411yescharacteristic
151C24×C139C2×D411yescharacteristic
152C2×D4×C139—24no—
153C2×D4×C139—22no—
154C2×D4×C139—24no—
155C2×D4×C139—22no—
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—42no—
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×C139C2×D412yes—
178C2×D4×C139#4112yes—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—24no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
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—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—24no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—42no—
200C22×C4×C139—81no—
201C22×C4×C139—81no—
202C22×C4×C139—81no—
203C22×C4×C139—81no—
204C22×C4×C139—81no—
205C22×C4×C139—81no—
206C22×C4×C139C2×D411yescharacteristic
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2411yescharacteristic
211D8×C139—28no—
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—21no—
222C2×C8×C139—21no—
223C2×C8×C139#4112yes—
224C4⋊C4×C139—24no—
225C4⋊C4×C139—24no—
226C4⋊C4×C139—24no—
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—21no—
237C4⋊C4×C139C2×D412yes—
238C4⋊C4×C139C2×D412yes—
239C4⋊C4×C139C2×D412yes—
240C22⋊C4×C139—24no—
241C22⋊C4×C139—24no—
242C22⋊C4×C139—24no—
243C22⋊C4×C139—24no—
244C22⋊C4×C139—22no—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—42no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—81no—
250C22⋊C4×C139—81no—
251C42×C139—24no—
252C42×C139C2×D412yes—
253C42×C139C2×D412yes—
254C23×C139—21no—
255C23×C139—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—22no—
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#13512yes—
282C23×C139C22×D411yescharacteristic
283D4×C139—22no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—44no—
288D4×C139—48no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—84no—
294D4×C139—84no—
295D4×C139—84no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—22no—
302C2×C4×C139—22no—
303C2×C4×C139—21no—
304C2×C4×C139—22no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—41no—
310C2×C4×C139—41no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
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—84no—
333C2×C4×C139—84no—
334C2×C4×C139—84no—
335C2×C4×C139#12012yes—
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—42no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—42no—
362C22×C139—41no—
363C22×C139—42no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—42no—
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×C139C2×#13511yescharacteristic
379C22×C139#57511yescharacteristic
380C22×C139#57611yescharacteristic
381C22×C139#57611yescharacteristic
382C4×C139—22no—
383C4×C139—22no—
384C4×C139—41no—
385C4×C139—41no—
386C4×C139—42no—
387C4×C139—42no—
388C4×C139—42no—
389C4×C139—81no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139#52511yescharacteristic
393C4×C139#53711yescharacteristic
394C4×C139#54811yescharacteristic
395C4×C139#55011yescharacteristic
396C2×C139—42no—
397C2×C139—81no—
398C2×C139—82no—
399C2×C139—82no—
400C2×C139#240711yescharacteristic
401C2×C139#300211yescharacteristic
402C2×C139#300811yescharacteristic
403C2×C139#329711yescharacteristic
404C2×C139#332211yescharacteristic
405C2×C139#333911yescharacteristic
406C2×C139#335511yescharacteristic
407#24124C13911yesmaximal, characteristic, direct product factor, Sylow
408C139#2412411yescharacteristic, direct product factor, Sylow
409C2×#553C2×C13911yescharacteristic, complemented
410C2×#478C2×C13911yescharacteristic, complemented
411C2×C4×D8C2×C13911yescharacteristic, complemented
412#2535C2×C13911yescharacteristic, complemented
413#2034C2×C13911yescharacteristic, complemented
414#2033C2×C13911yescharacteristic, complemented
415#1999C2×C13911yescharacteristic, complemented
416#1999C2×C13911yescharacteristic, complemented
417#1991C2×C13911yescharacteristic, complemented
418#1954C2×C13911yescharacteristic, complemented
419#1875C2×C13911yescharacteristic, complemented
420#1874C2×C13911yescharacteristic, complemented
421#1854C2×C13911yescharacteristic, complemented
422#1852C2×C13911yescharacteristic, complemented
423#1804C2×C13911yescharacteristic, complemented
424C22×D8C22×C13911yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C13911yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C13911yescharacteristic
432C2×#121C22×C13911yescharacteristic
433C2×#121C22×C13911yescharacteristic
434C2×#121C22×C13911yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C13911yescharacteristic
437C2×C4×D4C22×C13911yescharacteristic
438C2×C4×D4C22×C13911yescharacteristic
439C2×#117C22×C13911yescharacteristic
440C22×C4⋊C4C22×C13911yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C13911yescharacteristic
444C2×#107C22×C13911yescharacteristic
445C2×#106C22×C13911yescharacteristic
446C2×C4⋊C8C22×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
456C2×C22⋊C8C22×C13911yescharacteristic
457C2×C4×C8C22×C13911yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C13911yescharacteristic
463#380C22×C13911yescharacteristic
464#380C22×C13911yescharacteristic
465#340C22×C13911yescharacteristic
466#340C22×C13911yescharacteristic
467#340C22×C13911yescharacteristic
468#340C22×C13911yescharacteristic
469#340C22×C13911yescharacteristic
470#340C22×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×C4—21no—
481C23×C4C23×C13911yescharacteristic
482C23×C4C23×C13911yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C13911yescharacteristic
487C22×C8C23×C13911yescharacteristic
488C22×C8C23×C13911yescharacteristic
489C22×C8C23×C13911yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C13914yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C13914yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C13911yescharacteristic
518C2×C4⋊C4C23×C13911yescharacteristic
519C2×C4⋊C4C23×C13911yescharacteristic
520C2×C4⋊C4C23×C13911yescharacteristic
521C2×C4⋊C4C23×C13911yescharacteristic
522C2×C4⋊C4C23×C13911yescharacteristic
523C2×C4⋊C4C23×C13911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
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⋊C4D4×C13911yescharacteristic
534C2×C22⋊C4D4×C13911yescharacteristic
535C2×C42—21no—
536C2×C42C23×C13911yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C13911yescharacteristic
559C24C2×D4×C13911yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
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—42no—
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×D4C2×D4×C13912yes—
586C2×D4#41×C13912yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
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—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C13911yescharacteristic
615C22×C4C2×D4×C13911yescharacteristic
616C22×C4C2×D4×C13911yescharacteristic
617C22×C4C2×D4×C13911yescharacteristic
618C22×C4C24×C13911yescharacteristic
619D8—28no—
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#41×C13912yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
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⋊C4C2×D4×C13912yes—
646C4⋊C4C2×D4×C13912yes—
647C4⋊C4C2×D4×C13912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C13912yes—
661C42C2×D4×C13912yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
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#135×C13912yes—
690C23C22×D4×C13911yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
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—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C13912yes—
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—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
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
786C22C2×#135×C13911yescharacteristic
787C22#575×C13911yescharacteristic
788C22#576×C13911yescharacteristic
789C22#576×C13911yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C13911yescharacteristic
801C4#537×C13911yescharacteristic
802C4#548×C13911yescharacteristic
803C4#550×C13911yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2#2407×C13911yescharacteristic
809C2#3002×C13911yescharacteristic
810C2#3008×C13911yescharacteristic
811C2#3297×C13911yescharacteristic
812C2#3322×C13911yescharacteristic
813C2#3339×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×#478×C139C2semidirect
3. C2×C4×D8×C139C2semidirect
4. #2535×C139C2semidirect
5. #2034×C139C2semidirect
6. #2033×C139C2semidirect
7. #1999×C139C2semidirect
8. #1999×C139C2semidirect
9. #1991×C139C2semidirect
10. #1954×C139C2semidirect
11. #1875×C139C2semidirect
12. #1874×C139C2semidirect
13. #1854×C139C2semidirect
14. #1852×C139C2semidirect
15. #1804×C139C2semidirect
84. #125×C139D4semidirect
101. C4×D4×C139D4semidirect
407. #24124C139direct (N × H)
408. C139#24124direct (N × H)
409. C2×#553C2×C139semidirect
410. C2×#478C2×C139semidirect
411. C2×C4×D8C2×C139semidirect
412. #2535C2×C139semidirect
413. #2034C2×C139semidirect
414. #2033C2×C139semidirect
415. #1999C2×C139semidirect
416. #1999C2×C139semidirect
417. #1991C2×C139semidirect
418. #1954C2×C139semidirect
419. #1875C2×C139semidirect
420. #1874C2×C139semidirect
421. #1854C2×C139semidirect
422. #1852C2×C139semidirect
423. #1804C2×C139semidirect
492. #125D4×C139semidirect
509. C4×D4D4×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×#478×C1392
C2×C4×D8×C1392
#2535×C1392
#2034×C1392
#2033×C1392
#1999×C1392
#1991×C1392
#1954×C1392
#1875×C1392
#1874×C1392
#1854×C1392
#1852×C1392
#1804×C1392
#24124139