Finite Group Databasebeta

← C139×#25375 #48019971

Subgroups — C139×#25375 #48019971

Order 35584.

1004 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#495×C139C211yesmaximal, characteristic
2C2×#464×C139C211yesmaximal, characteristic, complemented
3C2×#464×C139C211yesmaximal, characteristic, complemented
4C2×#461×C139C211yesmaximal, characteristic, complemented
5#2545×C139C211yesmaximal, characteristic, complemented
6#2367×C139C211yesmaximal, characteristic, complemented
7#2055×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2016×C139C211yesmaximal, characteristic, complemented
10#2012×C139C211yesmaximal, characteristic
11#1983×C139C211yesmaximal, characteristic, complemented
12#1939×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic
14#1878×C139C211yesmaximal, characteristic, complemented
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139C2211yescharacteristic
17C22×Q16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21C22×D8×C139C2211yescharacteristic
22C2×C4⋊Q8×C139C2211yescharacteristic
23C2×#124×C139C2211yescharacteristic
24C2×#124×C139C2211yescharacteristic
25C2×#124×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29#495×C139—24no—
30#464×C139—24no—
31#464×C139—24no—
32#461×C139—24no—
33C2×C4⋊C8×C139C2211yescharacteristic
34C2×C4⋊C8×C139C2211yescharacteristic
35C2×C4⋊C8×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#103×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×C4×C8×C139C2211yescharacteristic
45#396×C139—21no—
46#396×C139—21no—
47#391×C139C2211yescharacteristic
48#391×C139C2211yescharacteristic
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#388×C139—21no—
52#388×C139—21no—
53#388×C139—21no—
54#388×C139—21no—
55#385×C139—21no—
56C4×C4⋊C4×C139C2211yescharacteristic
57C4×C4⋊C4×C139C2211yescharacteristic
58C4×C22⋊C4×C139—21no—
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×Q8×C139C2311yescharacteristic
65C22×Q8×C139C2311yescharacteristic
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C23×C4×C139—21no—
69C2×Q16×C139—22no—
70C2×Q16×C139—22no—
71C2×Q16×C139—22no—
72C2×Q16×C139—22no—
73C2×Q16×C139—41no—
74C2×Q16×C139—41no—
75C2×SD16×C139—22no—
76C2×SD16×C139—22no—
77C2×SD16×C139—22no—
78C2×SD16×C139—22no—
79C2×SD16×C139—22no—
80C2×SD16×C139—22no—
81C2×SD16×C139—41no—
82C2×SD16×C139—41no—
83C2×SD16×C139—41no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—41no—
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91C4⋊Q8×C139—22no—
92C4⋊Q8×C139—41no—
93#124×C139—22no—
94#124×C139—22no—
95#124×C139—22no—
96#124×C139—22no—
97#124×C139—41no—
98#124×C139D414yes—
99C4×Q8×C139—22no—
100C4×Q8×C139—22no—
101C4×Q8×C139—22no—
102C4×Q8×C139—41no—
103C4×D4×C139—22no—
104C4×D4×C139—41no—
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139D411yescharacteristic
110C2×C4⋊C4×C139D411yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
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×C42×C139—21no—
126C2×C42×C139—21no—
127C2×C42×C139—21no—
128C2×C42×C139C2311yescharacteristic
129C2×C42×C139C2311yescharacteristic
130C2×C42×C139C2311yescharacteristic
131C4⋊C8×C139—22no—
132C4⋊C8×C139—22no—
133C4⋊C8×C139—22no—
134#103×C139—22no—
135#103×C139—22no—
136#103×C139—22no—
137#103×C139—41no—
138#103×C139D414yes—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—41no—
142C4×C8×C139—22no—
143#95×C139—21no—
144#95×C139—21no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139D411yescharacteristic
149#95×C139D411yescharacteristic
150C24×C139—21no—
151C24×C139—21no—
152C2×Q8×C139—21no—
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×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139C2×D412yes—
169C2×Q8×C139C2×D412yes—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139C2×D412yes—
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—42no—
189C22×C4×C139—42no—
190C22×C4×C139—81no—
191C22×C4×C139C2×D411yescharacteristic
192C22×C4×C139C2×D411yescharacteristic
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2411yescharacteristic
198Q16×C139—44no—
199Q16×C139—44no—
200SD16×C139—44no—
201SD16×C139—44no—
202SD16×C139—44no—
203D8×C139—44no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139C2×D412yes—
215C2×C8×C139#4112yes—
216C4⋊C4×C139—22no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—41no—
223C4⋊C4×C139—42no—
224C4⋊C4×C139—42no—
225C4⋊C4×C139—42no—
226C4⋊C4×C139—42no—
227C4⋊C4×C139C2×D412yes—
228C22⋊C4×C139—24no—
229C22⋊C4×C139—24no—
230C22⋊C4×C139—42no—
231C22⋊C4×C139—42no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—81no—
239C42×C139—21no—
240C42×C139—21no—
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—42no—
244C42×C139—42no—
245C42×C139—81no—
246C42×C139C2×D412yes—
247C42×C139#4112yes—
248C23×C139—22no—
249C23×C139—41no—
250C23×C139—41no—
251C23×C139—41no—
252C23×C139—41no—
253C23×C139—41no—
254C23×C139—41no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139C22×D411yescharacteristic
263Q8×C139—22no—
264Q8×C139—22no—
265Q8×C139—22no—
266Q8×C139—22no—
267Q8×C139—41no—
268Q8×C139—41no—
269Q8×C139—41no—
270Q8×C139—41no—
271Q8×C139—41no—
272Q8×C139—41no—
273Q8×C139—41no—
274Q8×C139—41no—
275D4×C139—22no—
276D4×C139—22no—
277D4×C139—41no—
278D4×C139—41no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
283C2×C4×C139—21no—
284C2×C4×C139—21no—
285C2×C4×C139—21no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—21no—
289C2×C4×C139—22no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—22no—
294C2×C4×C139—22no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—41no—
302C2×C4×C139—41no—
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—84no—
317C2×C4×C139#12112yes—
318C2×C4×C139#12112yes—
319C2×C4×C139#13512yes—
320C2×C4×C139C22×D411yescharacteristic
321C2×C4×C139C22×D411yescharacteristic
322C2×C4×C139C2×#4111yescharacteristic
323C2×C4×C139C2×#4111yescharacteristic
324C2×C4×C139H(5,𝔽2)11yescharacteristic
325C2×C4×C139H(5,𝔽2)11yescharacteristic
326C8×C139—22no—
327C8×C139—22no—
328C8×C139—41no—
329C8×C139—41no—
330C22×C139—42no—
331C22×C139—42no—
332C22×C139—42no—
333C22×C139—81no—
334C22×C139—81no—
335C22×C139—81no—
336C22×C139—81no—
337C22×C139—81no—
338C22×C139—81no—
339C22×C139—81no—
340C22×C139—81no—
341C22×C139—81no—
342C22×C139—81no—
343C22×C139—81no—
344C22×C139C2×#12111yescharacteristic
345C22×C139D4211yescharacteristic
346C22×C139#55011yescharacteristic
347C22×C139C2×#13511yescharacteristic
348C22×C139#57511yescharacteristic
349C22×C139#57711yescharacteristic
350C22×C139#57811yescharacteristic
351C4×C139—22no—
352C4×C139—22no—
353C4×C139—22no—
354C4×C139—42no—
355C4×C139—42no—
356C4×C139—41no—
357C4×C139—41no—
358C4×C139—41no—
359C4×C139—42no—
360C4×C139—81no—
361C4×C139—81no—
362C4×C139—81no—
363C4×C139#53211yescharacteristic
364C4×C139#54011yescharacteristic
365C4×C139D4211yescharacteristic
366C4×C139#54611yescharacteristic
367C2×C139—82no—
368C2×C139—161no—
369C2×C139#242811yescharacteristic
370C2×C139#303511yescharacteristic
371C2×C139#304611yescharacteristic
372C2×C139#327711yescharacteristic
373C2×C139#328211yescharacteristic
374C2×C139#339311yescharacteristic
375C2×C139#340111yescharacteristic
376#25375C13911yesmaximal, characteristic, direct product factor, Sylow
377C139#2537511yescharacteristic, direct product factor, Sylow
378C2×#495C2×C13911yescharacteristic
379C2×#464C2×C13911yescharacteristic, complemented
380C2×#464C2×C13911yescharacteristic, complemented
381C2×#461C2×C13911yescharacteristic, complemented
382#2545C2×C13911yescharacteristic, complemented
383#2367C2×C13911yescharacteristic, complemented
384#2055C2×C13911yescharacteristic, complemented
385#2055C2×C13911yescharacteristic, complemented
386#2016C2×C13911yescharacteristic, complemented
387#2012C2×C13911yescharacteristic
388#1983C2×C13911yescharacteristic, complemented
389#1939C2×C13911yescharacteristic, complemented
390#1879C2×C13911yescharacteristic
391#1878C2×C13911yescharacteristic, complemented
392C4×#103C2×C13911yescharacteristic, complemented
393C22×Q16C22×C13911yescharacteristic
394C22×Q16C22×C13911yescharacteristic
395C22×SD16C22×C13911yescharacteristic
396C22×SD16C22×C13911yescharacteristic
397C22×SD16C22×C13911yescharacteristic
398C22×D8C22×C13911yescharacteristic
399C2×C4⋊Q8C22×C13911yescharacteristic
400C2×#124C22×C13911yescharacteristic
401C2×#124C22×C13911yescharacteristic
402C2×#124C22×C13911yescharacteristic
403C2×C4×Q8C22×C13911yescharacteristic
404C2×C4×Q8C22×C13911yescharacteristic
405C2×C4×D4C22×C13911yescharacteristic
406#495—24no—
407#464—24no—
408#464—24no—
409#461—24no—
410C2×C4⋊C8C22×C13911yescharacteristic
411C2×C4⋊C8C22×C13911yescharacteristic
412C2×C4⋊C8C22×C13911yescharacteristic
413C2×#103C22×C13911yescharacteristic
414C2×#103C22×C13911yescharacteristic
415C2×#103C22×C13911yescharacteristic
416C2×#103C22×C13911yescharacteristic
417C2×#103C22×C13911yescharacteristic
418C2×#102C22×C13911yescharacteristic
419C2×#102C22×C13911yescharacteristic
420C2×#102C22×C13911yescharacteristic
421C2×C4×C8C22×C13911yescharacteristic
422#396—21no—
423#396—21no—
424#391C22×C13911yescharacteristic
425#391C22×C13911yescharacteristic
426#390C22×C13911yescharacteristic
427#390C22×C13911yescharacteristic
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#385—21no—
433C4×C4⋊C4C22×C13911yescharacteristic
434C4×C4⋊C4C22×C13911yescharacteristic
435C4×C22⋊C4—21no—
436#340C22×C13911yescharacteristic
437#340C22×C13911yescharacteristic
438#336C22×C13911yescharacteristic
439#336C22×C13911yescharacteristic
440C22×Q8C23×C13911yescharacteristic
441C22×Q8C23×C13911yescharacteristic
442C22×Q8C23×C13911yescharacteristic
443C22×D4C23×C13911yescharacteristic
444C22×D4C23×C13911yescharacteristic
445C23×C4—21no—
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—41no—
451C2×Q16—41no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×SD16—41no—
460C2×SD16—41no—
461C2×D8—22no—
462C2×D8—22no—
463C2×D8—41no—
464C22×C8C23×C13911yescharacteristic
465C22×C8C23×C13911yescharacteristic
466C22×C8C23×C13911yescharacteristic
467C22×C8C23×C13911yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—41no—
470#124—22no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124—41no—
475#124D4×C13914yes—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—41no—
480C4×D4—22no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C13911yescharacteristic
487C2×C4⋊C4D4×C13911yescharacteristic
488C2×C4⋊C4C23×C13911yescharacteristic
489C2×C4⋊C4C23×C13911yescharacteristic
490C2×C4⋊C4C23×C13911yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42C23×C13911yescharacteristic
506C2×C42C23×C13911yescharacteristic
507C2×C42C23×C13911yescharacteristic
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—41no—
515#103D4×C13914yes—
516#102—22no—
517#102—22no—
518#102—41no—
519C4×C8—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95D4×C13911yescharacteristic
526#95D4×C13911yescharacteristic
527C24—21no—
528C24—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8C2×D4×C13912yes—
546C2×Q8C2×D4×C13912yes—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4C2×D4×C13912yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—81no—
568C22×C4C2×D4×C13911yescharacteristic
569C22×C4C2×D4×C13911yescharacteristic
570C22×C4C2×D4×C13911yescharacteristic
571C22×C4C2×D4×C13911yescharacteristic
572C22×C4C2×D4×C13911yescharacteristic
573C22×C4C2×D4×C13911yescharacteristic
574C22×C4C24×C13911yescharacteristic
575Q16—44no—
576Q16—44no—
577SD16—44no—
578SD16—44no—
579SD16—44no—
580D8—44no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8C2×D4×C13912yes—
592C2×C8#41×C13912yes—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—41no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4C2×D4×C13912yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—42no—
621C42—42no—
622C42—81no—
623C42C2×D4×C13912yes—
624C42#41×C13912yes—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C22×D4×C13911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652D4—22no—
653D4—22no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4#121×C13912yes—
695C2×C4#121×C13912yes—
696C2×C4#135×C13912yes—
697C2×C4C22×D4×C13911yescharacteristic
698C2×C4C22×D4×C13911yescharacteristic
699C2×C4C2×#41×C13911yescharacteristic
700C2×C4C2×#41×C13911yescharacteristic
701C2×C4H(5,𝔽2)×C13911yescharacteristic
702C2×C4H(5,𝔽2)×C13911yescharacteristic
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#121×C13911yescharacteristic
722C22D42×C13911yescharacteristic
723C22#550×C13911yescharacteristic
724C22C2×#135×C13911yescharacteristic
725C22#575×C13911yescharacteristic
726C22#577×C13911yescharacteristic
727C22#578×C13911yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—41no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4#532×C13911yescharacteristic
741C4#540×C13911yescharacteristic
742C4D42×C13911yescharacteristic
743C4#546×C13911yescharacteristic
744C2—82no—
745C2—161no—
746C2#2428×C13911yescharacteristic
747C2#3035×C13911yescharacteristic
748C2#3046×C13911yescharacteristic
749C2#3277×C13911yescharacteristic
750C2#3282×C13911yescharacteristic
751C2#3393×C13911yescharacteristic
752C2#3401×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D8×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C139C2semidirect
3. C2×#464×C139C2semidirect
4. C2×#461×C139C2semidirect
5. #2545×C139C2semidirect
6. #2367×C139C2semidirect
7. #2055×C139C2semidirect
8. #2055×C139C2semidirect
9. #2016×C139C2semidirect
11. #1983×C139C2semidirect
12. #1939×C139C2semidirect
14. #1878×C139C2semidirect
15. C4×#103×C139C2semidirect
376. #25375C139direct (N × H)
377. C139#25375direct (N × H)
379. C2×#464C2×C139semidirect
380. C2×#464C2×C139semidirect
381. C2×#461C2×C139semidirect
382. #2545C2×C139semidirect
383. #2367C2×C139semidirect
384. #2055C2×C139semidirect
385. #2055C2×C139semidirect
386. #2016C2×C139semidirect
388. #1983C2×C139semidirect
389. #1939C2×C139semidirect
391. #1878C2×C139semidirect
392. C4×#103C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#495×C1392
C2×#464×C1392
C2×#461×C1392
#2545×C1392
#2367×C1392
#2055×C1392
#2016×C1392
#2012×C1392
#1983×C1392
#1939×C1392
#1879×C1392
#1878×C1392
C4×#103×C1392
#25375139