Finite Group Databasebeta

← C139×#23580 #48018176

Subgroups — C139×#23580 #48018176

Order 35584.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C139C211yesmaximal, characteristic, complemented
2C2×#442×C139C211yesmaximal, characteristic, complemented
3C2×C4×D8×C139C211yesmaximal, characteristic, complemented
4#2324×C139C211yesmaximal, characteristic, complemented
5#2059×C139C211yesmaximal, characteristic, complemented
6#2041×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2025×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1999×C139C211yesmaximal, characteristic, complemented
12#1999×C139C211yesmaximal, characteristic, complemented
13#1762×C139C211yesmaximal, characteristic, complemented
14C4×#102×C139C211yesmaximal, characteristic, complemented
15#1750×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18#540×C139—24no—
19#540×C139—24no—
20C2×#127×C139C2211yescharacteristic
21C2×#125×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×#123×C139—21no—
24C2×#121×C139—21no—
25C2×#121×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×#117×C139C2211yescharacteristic
33#442×C139—24no—
34C4×D8×C139—24no—
35C2×#107×C139C2211yescharacteristic
36C2×#106×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×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×#97×C139C2211yescharacteristic
48C2×C4×C8×C139C2211yescharacteristic
49#390×C139—21no—
50#390×C139C2211yescharacteristic
51#389×C139C2211yescharacteristic
52#388×C139—21no—
53#386×C139—21no—
54#385×C139—21no—
55#380×C139C2211yescharacteristic
56C4×C4⋊C4×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×C139—21no—
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139—21no—
73C23×C4×C139—21no—
74C23×C4×C139C2311yescharacteristic
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—22no—
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85#127×C139—22no—
86#127×C139—22no—
87#125×C139—22no—
88#125×C139—22no—
89#123×C139—28no—
90#123×C139—28no—
91#121×C139—28no—
92#121×C139—28no—
93#121×C139—22no—
94#121×C139—22no—
95#121×C139—22no—
96#121×C139—22no—
97#121×C139—22no—
98#121×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102C4×D4×C139—22no—
103C4×D4×C139D414yescomplemented
104C4×D4×C139D414yescomplemented
105#117×C139—22no—
106#117×C139—22no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139D411yescharacteristic
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
126C2×C22⋊C4×C139D411yescharacteristic
127C2×C22⋊C4×C139D411yescharacteristic
128C2×C42×C139—21no—
129C2×C42×C139C2311yescharacteristic
130C2×C42×C139C2311yescharacteristic
131#107×C139—22no—
132#106×C139—22no—
133#102×C139—22no—
134#102×C139—22no—
135#102×C139—22no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141C22⋊C8×C139—22no—
142C22⋊C8×C139—22no—
143#97×C139—22no—
144C4×C8×C139—22no—
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—24no—
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—81no—
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×C139C2×D412yes—
183C2×D4×C139C2×D412yes—
184C2×D4×C139#4112yes—
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—24no—
195C22×C4×C139—24no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—42no—
199C22×C4×C139—81no—
200C22×C4×C139—81no—
201C22×C4×C139—81no—
202C22×C4×C139—81no—
203C22×C4×C139—81no—
204C22×C4×C139—81no—
205C22×C4×C139C2×D411yescharacteristic
206C22×C4×C139C2×D411yescharacteristic
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2411yescharacteristic
211D8×C139—28no—
212D8×C139—28no—
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—
224C2×C8×C139#4112yes—
225C4⋊C4×C139—24no—
226C4⋊C4×C139—24no—
227C4⋊C4×C139—22no—
228C4⋊C4×C139—22no—
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×C139C2×D412yes—
238C4⋊C4×C139C2×D412yes—
239C4⋊C4×C139#4112yes—
240C22⋊C4×C139—24no—
241C22⋊C4×C139—24no—
242C22⋊C4×C139—24no—
243C22⋊C4×C139—24no—
244C22⋊C4×C139—24no—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—22no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—81no—
249C22⋊C4×C139—81no—
250C22⋊C4×C139—81no—
251C42×C139—21no—
252C42×C139—21no—
253C42×C139—81no—
254C42×C139C2×D412yes—
255C42×C139C2×D412yes—
256C23×C139—21no—
257C23×C139—22no—
258C23×C139—22no—
259C23×C139—22no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
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—41no—
284C23×C139C22×D411yescharacteristic
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—22no—
290D4×C139—22no—
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—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—22no—
310C2×C4×C139—22no—
311C2×C4×C139—21no—
312C2×C4×C139—22no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
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—84no—
337C2×C4×C139#12012yes—
338C2×C4×C139#12012yes—
339C2×C4×C139C22×D411yescharacteristic
340C2×C4×C139C22×D411yescharacteristic
341C2×C4×C139C2×#4111yescharacteristic
342C2×C4×C139C2×#4111yescharacteristic
343C2×C4×C139C2×#4111yescharacteristic
344C2×C4×C139C2×#4111yescharacteristic
345C8×C139—22no—
346C8×C139—22no—
347C8×C139—41no—
348C8×C139—41no—
349C22×C139—41no—
350C22×C139—42no—
351C22×C139—41no—
352C22×C139—42no—
353C22×C139—41no—
354C22×C139—42no—
355C22×C139—42no—
356C22×C139—42no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—42no—
360C22×C139—41no—
361C22×C139—42no—
362C22×C139—42no—
363C22×C139—41no—
364C22×C139—42no—
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×C139—81no—
377C22×C139C2×#12011yescharacteristic
378C22×C139#52511yescharacteristic
379C22×C139#53211yescharacteristic
380C22×C139#57611yescharacteristic
381C22×C139#57611yescharacteristic
382C22×C139#57611yescharacteristic
383C22×C139#57711yescharacteristic
384C4×C139—22no—
385C4×C139—22no—
386C4×C139—42no—
387C4×C139—41no—
388C4×C139—41no—
389C4×C139—42no—
390C4×C139—41no—
391C4×C139—42no—
392C4×C139—81no—
393C4×C139—81no—
394C4×C139#52511yescharacteristic
395C4×C139#52511yescharacteristic
396C4×C139#53211yescharacteristic
397C4×C139#53211yescharacteristic
398C2×C139—81no—
399C2×C139—82no—
400C2×C139—82no—
401C2×C139—82no—
402C2×C139#238811yescharacteristic
403C2×C139#300811yescharacteristic
404C2×C139#301211yescharacteristic
405C2×C139#311911yescharacteristic
406C2×C139#312211yescharacteristic
407C2×C139#317611yescharacteristic
408C2×C139#317911yescharacteristic
409#23580C13911yesmaximal, characteristic, direct product factor, Sylow
410C139#2358011yescharacteristic, direct product factor, Sylow
411C2×#540C2×C13911yescharacteristic, complemented
412C2×#442C2×C13911yescharacteristic, complemented
413C2×C4×D8C2×C13911yescharacteristic, complemented
414#2324C2×C13911yescharacteristic, complemented
415#2059C2×C13911yescharacteristic, complemented
416#2041C2×C13911yescharacteristic, complemented
417#2034C2×C13911yescharacteristic, complemented
418#2033C2×C13911yescharacteristic, complemented
419#2025C2×C13911yescharacteristic, complemented
420#2011C2×C13911yescharacteristic, complemented
421#1999C2×C13911yescharacteristic, complemented
422#1999C2×C13911yescharacteristic, complemented
423#1762C2×C13911yescharacteristic, complemented
424C4×#102C2×C13911yescharacteristic, complemented
425#1750C2×C13911yescharacteristic, complemented
426C22×D8C22×C13911yescharacteristic
427C22×D8C22×C13911yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C13911yescharacteristic
431C2×#125C22×C13911yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C13911yescharacteristic
437C2×#121C22×C13911yescharacteristic
438C2×#121C22×C13911yescharacteristic
439C2×C4×D4C22×C13911yescharacteristic
440C2×C4×D4C22×C13911yescharacteristic
441C2×C4×D4C22×C13911yescharacteristic
442C2×#117C22×C13911yescharacteristic
443#442—24no—
444C4×D8—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
455C2×C22⋊C8C22×C13911yescharacteristic
456C2×C22⋊C8C22×C13911yescharacteristic
457C2×#97C22×C13911yescharacteristic
458C2×C4×C8C22×C13911yescharacteristic
459#390—21no—
460#390C22×C13911yescharacteristic
461#389C22×C13911yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C13911yescharacteristic
466C4×C4⋊C4C22×C13911yescharacteristic
467#340C22×C13911yescharacteristic
468#340C22×C13911yescharacteristic
469#340C22×C13911yescharacteristic
470#340C22×C13911yescharacteristic
471#336C22×C13911yescharacteristic
472#336C22×C13911yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C13911yescharacteristic
479C22×D4C23×C13911yescharacteristic
480C22×D4C23×C13911yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C13911yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C13911yescharacteristic
492C22×C8C23×C13911yescharacteristic
493C22×C8C23×C13911yescharacteristic
494C22×C8C23×C13911yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C13914yescomplemented
514C4×D4D4×C13914yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C13911yescharacteristic
521C2×C4⋊C4D4×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⋊C4D4×C13911yescharacteristic
537C2×C22⋊C4D4×C13911yescharacteristic
538C2×C42—21no—
539C2×C42C23×C13911yescharacteristic
540C2×C42C23×C13911yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C13911yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
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—21no—
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—
594C2×D4#41×C13912yes—
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—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C13911yescharacteristic
616C22×C4C2×D4×C13911yescharacteristic
617C22×C4C2×D4×C13911yescharacteristic
618C22×C4C2×D4×C13911yescharacteristic
619C22×C4C2×D4×C13911yescharacteristic
620C22×C4C24×C13911yescharacteristic
621D8—28no—
622D8—28no—
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—21no—
632C2×C8—21no—
633C2×C8#41×C13912yes—
634C2×C8#41×C13912yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C13912yes—
648C4⋊C4C2×D4×C13912yes—
649C4⋊C4#41×C13912yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C13912yes—
665C42C2×D4×C13912yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
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—41no—
693C23—41no—
694C23C22×D4×C13911yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C13912yes—
748C2×C4#120×C13912yes—
749C2×C4C22×D4×C13911yescharacteristic
750C2×C4C22×D4×C13911yescharacteristic
751C2×C4C2×#41×C13911yescharacteristic
752C2×C4C2×#41×C13911yescharacteristic
753C2×C4C2×#41×C13911yescharacteristic
754C2×C4C2×#41×C13911yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C13911yescharacteristic
788C22#525×C13911yescharacteristic
789C22#532×C13911yescharacteristic
790C22#576×C13911yescharacteristic
791C22#576×C13911yescharacteristic
792C22#576×C13911yescharacteristic
793C22#577×C13911yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#525×C13911yescharacteristic
805C4#525×C13911yescharacteristic
806C4#532×C13911yescharacteristic
807C4#532×C13911yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2#2388×C13911yescharacteristic
813C2#3008×C13911yescharacteristic
814C2#3012×C13911yescharacteristic
815C2#3119×C13911yescharacteristic
816C2#3122×C13911yescharacteristic
817C2#3176×C13911yescharacteristic
818C2#3179×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×#442×C139C2semidirect
3. C2×C4×D8×C139C2semidirect
4. #2324×C139C2semidirect
5. #2059×C139C2semidirect
6. #2041×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #2025×C139C2semidirect
10. #2011×C139C2semidirect
11. #1999×C139C2semidirect
12. #1999×C139C2semidirect
13. #1762×C139C2semidirect
14. C4×#102×C139C2semidirect
15. #1750×C139C2semidirect
103. C4×D4×C139D4semidirect
104. C4×D4×C139D4semidirect
409. #23580C139direct (N × H)
410. C139#23580direct (N × H)
411. C2×#540C2×C139semidirect
412. C2×#442C2×C139semidirect
413. C2×C4×D8C2×C139semidirect
414. #2324C2×C139semidirect
415. #2059C2×C139semidirect
416. #2041C2×C139semidirect
417. #2034C2×C139semidirect
418. #2033C2×C139semidirect
419. #2025C2×C139semidirect
420. #2011C2×C139semidirect
421. #1999C2×C139semidirect
422. #1999C2×C139semidirect
423. #1762C2×C139semidirect
424. C4×#102C2×C139semidirect
425. #1750C2×C139semidirect
513. C4×D4D4×C139semidirect
514. C4×D4D4×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×#442×C1392
C2×C4×D8×C1392
#2324×C1392
#2059×C1392
#2041×C1392
#2034×C1392
#2033×C1392
#2025×C1392
#2011×C1392
#1999×C1392
#1762×C1392
C4×#102×C1392
#1750×C1392
#23580139