Finite Group Databasebeta

← C139×#25400 #48019996

Subgroups — C139×#25400 #48019996

Order 35584.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C139C211yesmaximal, characteristic, complemented
2C2×#465×C139C211yesmaximal, characteristic, complemented
3C2×#461×C139C211yesmaximal, characteristic, complemented
4C2×#435×C139C211yesmaximal, characteristic, complemented
5#2542×C139C211yesmaximal, characteristic, complemented
6#2535×C139C211yesmaximal, characteristic
7#2036×C139C211yesmaximal, characteristic, complemented
8#2035×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1960×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1894×C139C211yesmaximal, characteristic, complemented
14#1892×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20C2×C4⋊Q8×C139C2211yescharacteristic
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×C22⋊Q8×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29#468×C139—24no—
30#465×C139—24no—
31#461×C139—24no—
32#435×C139—24no—
33C2×#107×C139C2211yescharacteristic
34C2×#106×C139C2211yescharacteristic
35C2×C4⋊C8×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#103×C139C2211yescharacteristic
41C2×#103×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×#97×C139C2211yescharacteristic
47#399×C139—21no—
48#399×C139—21no—
49#397×C139—21no—
50#392×C139—21no—
51#390×C139—21no—
52#386×C139—21no—
53#386×C139—21no—
54#384×C139—21no—
55#382×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58C4×C4⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×Q8×C139C2311yescharacteristic
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139D411yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C23×C4×C139—21no—
70C23×C4×C139C2311yescharacteristic
71C23×C4×C139C2311yescharacteristic
72C2×SD16×C139—22no—
73C2×SD16×C139—22no—
74C2×SD16×C139—22no—
75C2×SD16×C139—22no—
76C2×SD16×C139—41no—
77C2×SD16×C139—41no—
78C2×M16×C139—22no—
79C2×M16×C139—22no—
80C2×M16×C139—41no—
81C22×C8×C139—22no—
82C22×C8×C139—22no—
83C22×C8×C139—41no—
84C22×C8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C4⋊Q8×C139—22no—
89C4⋊Q8×C139—22no—
90C22⋊Q8×C139—22no—
91C22⋊Q8×C139—22no—
92C22⋊Q8×C139—22no—
93C22⋊Q8×C139—22no—
94C22⋊Q8×C139—41no—
95C22⋊Q8×C139—41no—
96C22⋊Q8×C139—41no—
97C22⋊Q8×C139—41no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—41no—
101#121×C139—41no—
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139D411yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
127C2×C22⋊C4×C139D411yescharacteristic
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C42×C139—21no—
130C2×C42×C139C2311yescharacteristic
131#107×C139—22no—
132#106×C139—22no—
133C4⋊C8×C139D414yescomplemented
134#103×C139—22no—
135#103×C139—22no—
136#103×C139—22no—
137#103×C139—22no—
138#103×C139—41no—
139#103×C139—41no—
140#102×C139—22no—
141#102×C139D414yescomplemented
142C22⋊C8×C139—22no—
143C22⋊C8×C139—22no—
144#97×C139—22no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150C24×C139—21no—
151C24×C139C2×D411yescharacteristic
152C24×C139C2×D411yescharacteristic
153C2×Q8×C139—21no—
154C2×Q8×C139—21no—
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—21no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×D4×C139—22no—
166C2×D4×C139—22no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—41no—
173C2×D4×C139—42no—
174C2×D4×C139—42no—
175C2×D4×C139—42no—
176C2×D4×C139—42no—
177C2×D4×C139—81no—
178C2×D4×C139—81no—
179C2×D4×C139C2×D412yes—
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—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—21no—
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×C139C2×D411yescharacteristic
203C22×C4×C139C2×D411yescharacteristic
204C22×C4×C139C2×D411yescharacteristic
205C22×C4×C139C2×D411yescharacteristic
206C22×C4×C139C2411yescharacteristic
207SD16×C139—44no—
208SD16×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—44no—
220C2×C8×C139C2×D412yes—
221C2×C8×C139C2×D412yes—
222C2×C8×C139C2×D412yes—
223C4⋊C4×C139—22no—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—21no—
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—42no—
233C4⋊C4×C139—42no—
234C4⋊C4×C139—42no—
235C4⋊C4×C139—42no—
236C4⋊C4×C139—42no—
237C4⋊C4×C139—42no—
238C4⋊C4×C139C2×D412yes—
239C4⋊C4×C139#4112yes—
240C22⋊C4×C139—22no—
241C22⋊C4×C139—22no—
242C22⋊C4×C139—42no—
243C22⋊C4×C139—42no—
244C22⋊C4×C139—42no—
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—42no—
252C42×C139C2×D412yes—
253C42×C139#4112yes—
254C23×C139—21no—
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—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139#13712yes—
275C23×C139C22×D411yescharacteristic
276Q8×C139—41no—
277Q8×C139—41no—
278Q8×C139—41no—
279Q8×C139—41no—
280Q8×C139—41no—
281Q8×C139—41no—
282Q8×C139—41no—
283Q8×C139—41no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—44no—
287D4×C139—41no—
288D4×C139—41no—
289D4×C139—84no—
290D4×C139—84no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—22no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—22no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—41no—
304C2×C4×C139—41no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
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—84no—
331C2×C4×C139#12112yes—
332C2×C4×C139#12112yes—
333C2×C4×C139C22×D411yescharacteristic
334C2×C4×C139C22×D411yescharacteristic
335C2×C4×C139C2×#4111yescharacteristic
336C2×C4×C139C2×#4111yescharacteristic
337C2×C4×C139H(5,𝔽2)11yescharacteristic
338C2×C4×C139H(5,𝔽2)11yescharacteristic
339C8×C139—22no—
340C8×C139—22no—
341C8×C139—22no—
342C8×C139—41no—
343C22×C139—22no—
344C22×C139—22no—
345C22×C139—22no—
346C22×C139—41no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—41no—
350C22×C139—41no—
351C22×C139—42no—
352C22×C139—42no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—42no—
356C22×C139—41no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—41no—
360C22×C139—81no—
361C22×C139—81no—
362C22×C139—81no—
363C22×C139—81no—
364C22×C139C2×#12111yescharacteristic
365C22×C139D4211yescharacteristic
366C22×C139#54611yescharacteristic
367C22×C139C2×#13711yescharacteristic
368C22×C139#57511yescharacteristic
369C22×C139#57711yescharacteristic
370C22×C139#57711yescharacteristic
371C4×C139—22no—
372C4×C139—22no—
373C4×C139—41no—
374C4×C139—41no—
375C4×C139—42no—
376C4×C139—42no—
377C4×C139—81no—
378C4×C139—81no—
379C4×C139—81no—
380C4×C139—81no—
381C4×C139—81no—
382C4×C139#53211yescharacteristic
383C4×C139#54011yescharacteristic
384C4×C139D4211yescharacteristic
385C4×C139#55011yescharacteristic
386C2×C139—42no—
387C2×C139—81no—
388C2×C139—82no—
389C2×C139#242811yescharacteristic
390C2×C139#305611yescharacteristic
391C2×C139#305711yescharacteristic
392C2×C139#326611yescharacteristic
393C2×C139#326711yescharacteristic
394C2×C139#330711yescharacteristic
395C2×C139#332011yescharacteristic
396#25400C13911yesmaximal, characteristic, direct product factor, Sylow
397C139#2540011yescharacteristic, direct product factor, Sylow
398C2×#468C2×C13911yescharacteristic, complemented
399C2×#465C2×C13911yescharacteristic, complemented
400C2×#461C2×C13911yescharacteristic, complemented
401C2×#435C2×C13911yescharacteristic, complemented
402#2542C2×C13911yescharacteristic, complemented
403#2535C2×C13911yescharacteristic
404#2036C2×C13911yescharacteristic, complemented
405#2035C2×C13911yescharacteristic, complemented
406#2000C2×C13911yescharacteristic, complemented
407#2000C2×C13911yescharacteristic, complemented
408#1960C2×C13911yescharacteristic, complemented
409#1949C2×C13911yescharacteristic, complemented
410#1894C2×C13911yescharacteristic, complemented
411#1892C2×C13911yescharacteristic, complemented
412#1762C2×C13911yescharacteristic, complemented
413C22×SD16C22×C13911yescharacteristic
414C22×SD16C22×C13911yescharacteristic
415C22×M16C22×C13911yescharacteristic
416C23×C8C22×C13911yescharacteristic
417C2×C4⋊Q8C22×C13911yescharacteristic
418C2×C22⋊Q8C22×C13911yescharacteristic
419C2×C22⋊Q8C22×C13911yescharacteristic
420C2×C22⋊Q8C22×C13911yescharacteristic
421C2×C22⋊Q8C22×C13911yescharacteristic
422C2×#121C22×C13911yescharacteristic
423C2×#121C22×C13911yescharacteristic
424C2×C4×D4C22×C13911yescharacteristic
425C2×C4×D4C22×C13911yescharacteristic
426#468—24no—
427#465—24no—
428#461—24no—
429#435—24no—
430C2×#107C22×C13911yescharacteristic
431C2×#106C22×C13911yescharacteristic
432C2×C4⋊C8C22×C13911yescharacteristic
433C2×#103C22×C13911yescharacteristic
434C2×#103C22×C13911yescharacteristic
435C2×#103C22×C13911yescharacteristic
436C2×#103C22×C13911yescharacteristic
437C2×#103C22×C13911yescharacteristic
438C2×#103C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×C22⋊C8C22×C13911yescharacteristic
442C2×C22⋊C8C22×C13911yescharacteristic
443C2×#97C22×C13911yescharacteristic
444#399—21no—
445#399—21no—
446#397—21no—
447#392—21no—
448#390—21no—
449#386—21no—
450#386—21no—
451#384—21no—
452#382C22×C13911yescharacteristic
453#380C22×C13911yescharacteristic
454#380C22×C13911yescharacteristic
455C4×C4⋊C4C22×C13911yescharacteristic
456#340C22×C13911yescharacteristic
457#340C22×C13911yescharacteristic
458#340C22×C13911yescharacteristic
459#340C22×C13911yescharacteristic
460C22×Q8C23×C13911yescharacteristic
461C22×Q8C23×C13911yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4D4×C13911yescharacteristic
465C22×D4C23×C13911yescharacteristic
466C23×C4—21no—
467C23×C4C23×C13911yescharacteristic
468C23×C4C23×C13911yescharacteristic
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16—41no—
474C2×SD16—41no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—41no—
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—41no—
481C22×C8C23×C13911yescharacteristic
482C22×C8C23×C13911yescharacteristic
483C22×C8C23×C13911yescharacteristic
484C22×C8C23×C13911yescharacteristic
485C4⋊Q8—22no—
486C4⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—41no—
492C22⋊Q8—41no—
493C22⋊Q8—41no—
494C22⋊Q8—41no—
495#121—22no—
496#121—22no—
497#121—41no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4D4×C13911yescharacteristic
510C2×C4⋊C4C23×C13911yescharacteristic
511C2×C4⋊C4C23×C13911yescharacteristic
512C2×C4⋊C4C23×C13911yescharacteristic
513C2×C4⋊C4C23×C13911yescharacteristic
514C2×C4⋊C4C23×C13911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4D4×C13911yescharacteristic
525C2×C22⋊C4D4×C13911yescharacteristic
526C2×C42—21no—
527C2×C42C23×C13911yescharacteristic
528#107—22no—
529#106—22no—
530C4⋊C8D4×C13914yescomplemented
531#103—22no—
532#103—22no—
533#103—22no—
534#103—22no—
535#103—41no—
536#103—41no—
537#102—22no—
538#102D4×C13914yescomplemented
539C22⋊C8—22no—
540C22⋊C8—22no—
541#97—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547C24—21no—
548C24C2×D4×C13911yescharacteristic
549C24C2×D4×C13911yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4C2×D4×C13912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
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—21no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4C2×D4×C13911yescharacteristic
600C22×C4C2×D4×C13911yescharacteristic
601C22×C4C2×D4×C13911yescharacteristic
602C22×C4C2×D4×C13911yescharacteristic
603C22×C4C24×C13911yescharacteristic
604SD16—44no—
605SD16—44no—
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C13912yes—
618C2×C8C2×D4×C13912yes—
619C2×C8C2×D4×C13912yes—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4C2×D4×C13912yes—
636C4⋊C4#41×C13912yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C42—42no—
649C42C2×D4×C13912yes—
650C42#41×C13912yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#137×C13912yes—
672C23C22×D4×C13911yescharacteristic
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—44no—
684D4—41no—
685D4—41no—
686D4—84no—
687D4—84no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
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—84no—
728C2×C4#121×C13912yes—
729C2×C4#121×C13912yes—
730C2×C4C22×D4×C13911yescharacteristic
731C2×C4C22×D4×C13911yescharacteristic
732C2×C4C2×#41×C13911yescharacteristic
733C2×C4C2×#41×C13911yescharacteristic
734C2×C4H(5,𝔽2)×C13911yescharacteristic
735C2×C4H(5,𝔽2)×C13911yescharacteristic
736C8—22no—
737C8—22no—
738C8—22no—
739C8—41no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—42no—
753C22—42no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22C2×#121×C13911yescharacteristic
762C22D42×C13911yescharacteristic
763C22#546×C13911yescharacteristic
764C22C2×#137×C13911yescharacteristic
765C22#575×C13911yescharacteristic
766C22#577×C13911yescharacteristic
767C22#577×C13911yescharacteristic
768C4—22no—
769C4—22no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4#532×C13911yescharacteristic
780C4#540×C13911yescharacteristic
781C4D42×C13911yescharacteristic
782C4#550×C13911yescharacteristic
783C2—42no—
784C2—81no—
785C2—82no—
786C2#2428×C13911yescharacteristic
787C2#3056×C13911yescharacteristic
788C2#3057×C13911yescharacteristic
789C2#3266×C13911yescharacteristic
790C2#3267×C13911yescharacteristic
791C2#3307×C13911yescharacteristic
792C2#3320×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2535×C139C2
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×#468×C139C2semidirect
2. C2×#465×C139C2semidirect
3. C2×#461×C139C2semidirect
4. C2×#435×C139C2semidirect
5. #2542×C139C2semidirect
7. #2036×C139C2semidirect
8. #2035×C139C2semidirect
9. #2000×C139C2semidirect
10. #2000×C139C2semidirect
11. #1960×C139C2semidirect
12. #1949×C139C2semidirect
13. #1894×C139C2semidirect
14. #1892×C139C2semidirect
15. #1762×C139C2semidirect
133. C4⋊C8×C139D4semidirect
141. #102×C139D4semidirect
396. #25400C139direct (N × H)
397. C139#25400direct (N × H)
398. C2×#468C2×C139semidirect
399. C2×#465C2×C139semidirect
400. C2×#461C2×C139semidirect
401. C2×#435C2×C139semidirect
402. #2542C2×C139semidirect
404. #2036C2×C139semidirect
405. #2035C2×C139semidirect
406. #2000C2×C139semidirect
407. #2000C2×C139semidirect
408. #1960C2×C139semidirect
409. #1949C2×C139semidirect
410. #1894C2×C139semidirect
411. #1892C2×C139semidirect
412. #1762C2×C139semidirect
530. C4⋊C8D4×C139semidirect
538. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1392
C2×#465×C1392
C2×#461×C1392
C2×#435×C1392
#2542×C1392
#2535×C1392
#2036×C1392
#2035×C1392
#2000×C1392
#1960×C1392
#1949×C1392
#1894×C1392
#1892×C1392
#1762×C1392
#25400139