Finite Group Databasebeta

← C139×#24662 #48019258

Subgroups — C139×#24662 #48019258

Order 35584.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C139C211yesmaximal, characteristic, complemented
2C2×#433×C139C211yesmaximal, characteristic, complemented
3#2619×C139C211yesmaximal, characteristic, complemented
4#2324×C139C211yesmaximal, characteristic, complemented
5#2034×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#1999×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1982×C139C211yesmaximal, characteristic, complemented
10#1972×C139C211yesmaximal, characteristic, complemented
11#1970×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1936×C139C211yesmaximal, characteristic, complemented
14#1934×C139C211yesmaximal, characteristic, complemented
15#1804×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C2×#127×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C2×#117×C139C2211yescharacteristic
24#459×C139—24no—
25#433×C139—24no—
26C2×#107×C139C2211yescharacteristic
27C2×#106×C139C2211yescharacteristic
28C2×C4⋊C8×C139C2211yescharacteristic
29C2×C4⋊C8×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×#97×C139C2211yescharacteristic
41C2×C4×C8×C139C2211yescharacteristic
42#394×C139—21no—
43#394×C139—21no—
44#392×C139—21no—
45#392×C139—21no—
46#390×C139—21no—
47#390×C139C2211yescharacteristic
48#390×C139C2211yescharacteristic
49#390×C139C2211yescharacteristic
50#389×C139C2211yescharacteristic
51#388×C139—21no—
52#386×C139—21no—
53#385×C139—21no—
54#382×C139C2211yescharacteristic
55#380×C139C2211yescharacteristic
56C4×C4⋊C4×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C23×C4×C139—21no—
70C23×C4×C139C2311yescharacteristic
71C2×D8×C139—22no—
72C2×D8×C139—22no—
73C2×D8×C139—22no—
74C2×D8×C139—22no—
75C2×D8×C139—41no—
76C2×D8×C139—41no—
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81#127×C139—22no—
82#127×C139—22no—
83#121×C139—22no—
84#121×C139—22no—
85#121×C139—41no—
86#121×C139—41no—
87#121×C139—41no—
88#121×C139—41no—
89C4×D4×C139—22no—
90C4×D4×C139—22no—
91#117×C139—22no—
92#117×C139—22no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139D411yescharacteristic
95C2×C4⋊C4×C139D411yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139D411yescharacteristic
113C2×C22⋊C4×C139D411yescharacteristic
114C2×C42×C139—21no—
115C2×C42×C139C2311yescharacteristic
116C2×C42×C139C2311yescharacteristic
117#107×C139—41no—
118#106×C139—41no—
119C4⋊C8×C139—22no—
120C4⋊C8×C139D414yescomplemented
121#102×C139—22no—
122#102×C139—22no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—41no—
126#102×C139—41no—
127#102×C139—41no—
128#102×C139—41no—
129C22⋊C8×C139—22no—
130C22⋊C8×C139—22no—
131#97×C139—22no—
132C4×C8×C139—22no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138C24×C139—21no—
139C24×C139—21no—
140C24×C139—21no—
141C24×C139C2×D411yescharacteristic
142C2×D4×C139—24no—
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—42no—
161C2×D4×C139—42no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—81no—
165C2×D4×C139—81no—
166C2×D4×C139—81no—
167C2×D4×C139—81no—
168C2×D4×C139—81no—
169C2×D4×C139—81no—
170C2×D4×C139—81no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139—81no—
174C2×D4×C139#4112yes—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
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—42no—
187C22×C4×C139—81no—
188C22×C4×C139—81no—
189C22×C4×C139C2×D411yescharacteristic
190C22×C4×C139C2×D411yescharacteristic
191C22×C4×C139C2×D411yescharacteristic
192C22×C4×C139C2×D411yescharacteristic
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139C2411yescharacteristic
195D8×C139—44no—
196D8×C139—44no—
197C2×C8×C139—21no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139—21no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139C2×D412yes—
208C2×C8×C139C2×D412yes—
209C4⋊C4×C139—22no—
210C4⋊C4×C139—22no—
211C4⋊C4×C139—21no—
212C4⋊C4×C139—21no—
213C4⋊C4×C139—21no—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—81no—
221C4⋊C4×C139#4112yes—
222C22⋊C4×C139—24no—
223C22⋊C4×C139—22no—
224C22⋊C4×C139—22no—
225C22⋊C4×C139—42no—
226C22⋊C4×C139—42no—
227C22⋊C4×C139—42no—
228C22⋊C4×C139—81no—
229C22⋊C4×C139—81no—
230C22⋊C4×C139—81no—
231C22⋊C4×C139—81no—
232C22⋊C4×C139—81no—
233C22⋊C4×C139—81no—
234C22⋊C4×C139—81no—
235C42×C139—21no—
236C42×C139—21no—
237C42×C139—81no—
238C42×C139C2×D412yes—
239C42×C139#4112yes—
240C23×C139—21no—
241C23×C139—22no—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—41no—
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×C139—41no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139C22×D411yescharacteristic
269D4×C139—22no—
270D4×C139—22no—
271D4×C139—41no—
272D4×C139—41no—
273D4×C139—41no—
274D4×C139—41no—
275D4×C139—41no—
276D4×C139—41no—
277D4×C139—41no—
278D4×C139—41no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—84no—
282D4×C139—84no—
283D4×C139—84no—
284D4×C139—84no—
285D4×C139—84no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
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—41no—
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—41no—
317C2×C4×C139—41no—
318C2×C4×C139—84no—
319C2×C4×C139#12112yes—
320C2×C4×C139#12112yes—
321C2×C4×C139C22×D411yescharacteristic
322C2×C4×C139C2×#4111yescharacteristic
323C2×C4×C139C2×#4111yescharacteristic
324C2×C4×C139C2×#4111yescharacteristic
325C2×C4×C139H(5,𝔽2)11yescharacteristic
326C2×C4×C139H(5,𝔽2)11yescharacteristic
327C8×C139—22no—
328C8×C139—22no—
329C8×C139—41no—
330C8×C139—41no—
331C22×C139—41no—
332C22×C139—42no—
333C22×C139—41no—
334C22×C139—42no—
335C22×C139—41no—
336C22×C139—42no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139—41no—
340C22×C139—41no—
341C22×C139—81no—
342C22×C139—81no—
343C22×C139—81no—
344C22×C139—81no—
345C22×C139—81no—
346C22×C139—81no—
347C22×C139—81no—
348C22×C139—81no—
349C22×C139—81no—
350C22×C139—81no—
351C22×C139—81no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—81no—
359C22×C139C2×#12111yescharacteristic
360C22×C139#52511yescharacteristic
361C22×C139#53511yescharacteristic
362C22×C139#57611yescharacteristic
363C22×C139#57611yescharacteristic
364C22×C139#57611yescharacteristic
365C22×C139#57711yescharacteristic
366C4×C139—22no—
367C4×C139—22no—
368C4×C139—42no—
369C4×C139—41no—
370C4×C139—41no—
371C4×C139—41no—
372C4×C139—81no—
373C4×C139—81no—
374C4×C139—81no—
375C4×C139—81no—
376C4×C139#54611yescharacteristic
377C4×C139#55011yescharacteristic
378C4×C139#55311yescharacteristic
379C4×C139#55511yescharacteristic
380C2×C139—81no—
381C2×C139—82no—
382C2×C139—161no—
383C2×C139—161no—
384C2×C139#241411yescharacteristic
385C2×C139#305811yescharacteristic
386C2×C139#306211yescharacteristic
387C2×C139#311911yescharacteristic
388C2×C139#312211yescharacteristic
389C2×C139#322011yescharacteristic
390C2×C139#322411yescharacteristic
391#24662C13911yesmaximal, characteristic, direct product factor, Sylow
392C139#2466211yescharacteristic, direct product factor, Sylow
393C2×#459C2×C13911yescharacteristic, complemented
394C2×#433C2×C13911yescharacteristic, complemented
395#2619C2×C13911yescharacteristic, complemented
396#2324C2×C13911yescharacteristic, complemented
397#2034C2×C13911yescharacteristic, complemented
398#2033C2×C13911yescharacteristic, complemented
399#1999C2×C13911yescharacteristic, complemented
400#1999C2×C13911yescharacteristic, complemented
401#1982C2×C13911yescharacteristic, complemented
402#1972C2×C13911yescharacteristic, complemented
403#1970C2×C13911yescharacteristic, complemented
404#1949C2×C13911yescharacteristic, complemented
405#1936C2×C13911yescharacteristic, complemented
406#1934C2×C13911yescharacteristic, complemented
407#1804C2×C13911yescharacteristic, complemented
408C22×D8C22×C13911yescharacteristic
409C22×D8C22×C13911yescharacteristic
410C2×#127C22×C13911yescharacteristic
411C2×#121C22×C13911yescharacteristic
412C2×#121C22×C13911yescharacteristic
413C2×#121C22×C13911yescharacteristic
414C2×C4×D4C22×C13911yescharacteristic
415C2×#117C22×C13911yescharacteristic
416#459—24no—
417#433—24no—
418C2×#107C22×C13911yescharacteristic
419C2×#106C22×C13911yescharacteristic
420C2×C4⋊C8C22×C13911yescharacteristic
421C2×C4⋊C8C22×C13911yescharacteristic
422C2×#102C22×C13911yescharacteristic
423C2×#102C22×C13911yescharacteristic
424C2×#102C22×C13911yescharacteristic
425C2×#102C22×C13911yescharacteristic
426C2×#102C22×C13911yescharacteristic
427C2×#102C22×C13911yescharacteristic
428C2×#102C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×C22⋊C8C22×C13911yescharacteristic
431C2×C22⋊C8C22×C13911yescharacteristic
432C2×#97C22×C13911yescharacteristic
433C2×C4×C8C22×C13911yescharacteristic
434#394—21no—
435#394—21no—
436#392—21no—
437#392—21no—
438#390—21no—
439#390C22×C13911yescharacteristic
440#390C22×C13911yescharacteristic
441#390C22×C13911yescharacteristic
442#389C22×C13911yescharacteristic
443#388—21no—
444#386—21no—
445#385—21no—
446#382C22×C13911yescharacteristic
447#380C22×C13911yescharacteristic
448C4×C4⋊C4C22×C13911yescharacteristic
449#340C22×C13911yescharacteristic
450#340C22×C13911yescharacteristic
451#340C22×C13911yescharacteristic
452#340C22×C13911yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C13911yescharacteristic
459C22×D4C23×C13911yescharacteristic
460C22×D4C23×C13911yescharacteristic
461C23×C4—21no—
462C23×C4C23×C13911yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C13911yescharacteristic
470C22×C8C23×C13911yescharacteristic
471C22×C8C23×C13911yescharacteristic
472C22×C8C23×C13911yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
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×C4⋊C4C23×C13911yescharacteristic
492C2×C4⋊C4C23×C13911yescharacteristic
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×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C13911yescharacteristic
505C2×C22⋊C4D4×C13911yescharacteristic
506C2×C42—21no—
507C2×C42C23×C13911yescharacteristic
508C2×C42C23×C13911yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C13914yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C13911yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4#41×C13912yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C13911yescharacteristic
582C22×C4C2×D4×C13911yescharacteristic
583C22×C4C2×D4×C13911yescharacteristic
584C22×C4C2×D4×C13911yescharacteristic
585C22×C4C2×D4×C13911yescharacteristic
586C22×C4C24×C13911yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C13912yes—
600C2×C8C2×D4×C13912yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C13912yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C13912yes—
631C42#41×C13912yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C13911yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
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—84no—
711C2×C4#121×C13912yes—
712C2×C4#121×C13912yes—
713C2×C4C22×D4×C13911yescharacteristic
714C2×C4C2×#41×C13911yescharacteristic
715C2×C4C2×#41×C13911yescharacteristic
716C2×C4C2×#41×C13911yescharacteristic
717C2×C4H(5,𝔽2)×C13911yescharacteristic
718C2×C4H(5,𝔽2)×C13911yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#121×C13911yescharacteristic
752C22#525×C13911yescharacteristic
753C22#535×C13911yescharacteristic
754C22#576×C13911yescharacteristic
755C22#576×C13911yescharacteristic
756C22#576×C13911yescharacteristic
757C22#577×C13911yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—42no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4#546×C13911yescharacteristic
769C4#550×C13911yescharacteristic
770C4#553×C13911yescharacteristic
771C4#555×C13911yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2#2414×C13911yescharacteristic
777C2#3058×C13911yescharacteristic
778C2#3062×C13911yescharacteristic
779C2#3119×C13911yescharacteristic
780C2#3122×C13911yescharacteristic
781C2#3220×C13911yescharacteristic
782C2#3224×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×#459×C139C2semidirect
2. C2×#433×C139C2semidirect
3. #2619×C139C2semidirect
4. #2324×C139C2semidirect
5. #2034×C139C2semidirect
6. #2033×C139C2semidirect
7. #1999×C139C2semidirect
8. #1999×C139C2semidirect
9. #1982×C139C2semidirect
10. #1972×C139C2semidirect
11. #1970×C139C2semidirect
12. #1949×C139C2semidirect
13. #1936×C139C2semidirect
14. #1934×C139C2semidirect
15. #1804×C139C2semidirect
120. C4⋊C8×C139D4semidirect
391. #24662C139direct (N × H)
392. C139#24662direct (N × H)
393. C2×#459C2×C139semidirect
394. C2×#433C2×C139semidirect
395. #2619C2×C139semidirect
396. #2324C2×C139semidirect
397. #2034C2×C139semidirect
398. #2033C2×C139semidirect
399. #1999C2×C139semidirect
400. #1999C2×C139semidirect
401. #1982C2×C139semidirect
402. #1972C2×C139semidirect
403. #1970C2×C139semidirect
404. #1949C2×C139semidirect
405. #1936C2×C139semidirect
406. #1934C2×C139semidirect
407. #1804C2×C139semidirect
512. C4⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1392
C2×#433×C1392
#2619×C1392
#2324×C1392
#2034×C1392
#2033×C1392
#1999×C1392
#1982×C1392
#1972×C1392
#1970×C1392
#1949×C1392
#1936×C1392
#1934×C1392
#1804×C1392
#24662139