Finite Group Databasebeta

← C139×#20746 #48015342

Subgroups — C139×#20746 #48015342

Order 35584.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C139C211yesmaximal, characteristic
2C2×#433×C139C211yesmaximal, characteristic, complemented
3#2314×C139C211yesmaximal, characteristic, complemented
4#1824×C139C211yesmaximal, characteristic, complemented
5#1823×C139C211yesmaximal, characteristic, complemented
6#1805×C139C211yesmaximal, characteristic, complemented
7#1804×C139C211yesmaximal, characteristic, complemented
8#1803×C139C211yesmaximal, characteristic, complemented
9#1802×C139C211yesmaximal, characteristic, complemented
10#1788×C139C211yesmaximal, characteristic
11#1788×C139C211yesmaximal, characteristic
12#1763×C139C211yesmaximal, characteristic, complemented
13#1762×C139C211yesmaximal, characteristic, complemented
14C4×#103×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17#520×C139—24no—
18#520×C139C418yescomplemented
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×D4×C139—21no—
22C2×C4×D4×C139—21no—
23C2×C4×D4×C139C2211yescharacteristic
24C2×C4×D4×C139C2211yescharacteristic
25C2×#117×C139—21no—
26C2×#117×C139C2211yescharacteristic
27C22×C4⋊C4×C139—21no—
28C22×C4⋊C4×C139C2211yescharacteristic
29#433×C139—24no—
30C2×C4⋊C8×C139C2211yescharacteristic
31C2×C4⋊C8×C139C2211yescharacteristic
32C2×#103×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×C22⋊C8×C139C2211yescharacteristic
41C2×C22⋊C8×C139C2211yescharacteristic
42C2×#97×C139C2211yescharacteristic
43C2×C4×C8×C139C2211yescharacteristic
44#388×C139—21no—
45#388×C139—21no—
46#387×C139—21no—
47#387×C139—21no—
48#384×C139C2211yescharacteristic
49#382×C139C2211yescharacteristic
50#380×C139C2211yescharacteristic
51#380×C139C2211yescharacteristic
52C4×C4⋊C4×C139C2211yescharacteristic
53C4×C4⋊C4×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62C2×#41×C139—22no—
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139C2×C414yes—
68C22×Q8×C139C2311yescharacteristic
69C22×D4×C139—21no—
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139—21no—
73C23×C4×C139—21no—
74C23×C4×C139—21no—
75C23×C4×C139C2311yescharacteristic
76C22×C8×C139C2311yescharacteristic
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C4×Q8×C139—22no—
81C4×Q8×C139—22no—
82C4×Q8×C139C2×C414yes—
83C4×Q8×C139C2×C414yes—
84C4×D4×C139—28no—
85C4×D4×C139—28no—
86C4×D4×C139—22no—
87C4×D4×C139—22no—
88C4×D4×C139C2×C414yes—
89C4×D4×C139C2×C414yes—
90#117×C139—28no—
91#117×C139C2×C414yes—
92#117×C139D414yes—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139—22no—
97C2×C4⋊C4×C139—28no—
98C2×C4⋊C4×C139—21no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139C2×C414yes—
101C2×C4⋊C4×C139D411yescharacteristic
102C2×C4⋊C4×C139D411yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C4⋊C4×C139C2311yescharacteristic
108C2×C4⋊C4×C139C2311yescharacteristic
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139D411yescharacteristic
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C42×C139—21no—
116C2×C42×C139—21no—
117C2×C42×C139—21no—
118C2×C42×C139—21no—
119C2×C42×C139C2311yescharacteristic
120C2×C42×C139C2311yescharacteristic
121C4⋊C8×C139—22no—
122C4⋊C8×C139—22no—
123#103×C139—22no—
124#103×C139—22no—
125#103×C139—22no—
126#103×C139—22no—
127#102×C139—22no—
128#102×C139—22no—
129#102×C139—22no—
130#102×C139—22no—
131C22⋊C8×C139—22no—
132C22⋊C8×C139—22no—
133#97×C139—22no—
134C4×C8×C139—22no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139—21no—
139#95×C139—21no—
140#95×C139—21no—
141C24×C139—21no—
142C24×C139C2×D411yescharacteristic
143#41×C139—28no—
144#41×C139—28no—
145#41×C139—28no—
146#41×C139—28no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139C22×C412yes—
151C2×Q8×C139#4112yes—
152C2×Q8×C139#4112yes—
153C2×D4×C139—24no—
154C2×D4×C139—24no—
155C2×D4×C139—24no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139C22×C412yes—
160C2×D4×C139#4112yes—
161C2×D4×C139#4112yes—
162C22×C4×C139—24no—
163C22×C4×C139—24no—
164C22×C4×C139—21no—
165C22×C4×C139—24no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—24no—
173C22×C4×C139—24no—
174C22×C4×C139—24no—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—81no—
180C22×C4×C139—81no—
181C22×C4×C139—81no—
182C22×C4×C139—81no—
183C22×C4×C139—81no—
184C22×C4×C139—81no—
185C22×C4×C139C22×C412yes—
186C22×C4×C139C2×D411yescharacteristic
187C22×C4×C139C2×D411yescharacteristic
188C22×C4×C139C2×D411yescharacteristic
189C22×C4×C139C2×D411yescharacteristic
190C22×C4×C139C2×D411yescharacteristic
191C22×C4×C139C2×D412yes—
192C22×C4×C139C2411yescharacteristic
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
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—
205C4⋊C4×C139—24no—
206C4⋊C4×C139—24no—
207C4⋊C4×C139—24no—
208C4⋊C4×C139—21no—
209C4⋊C4×C139—21no—
210C4⋊C4×C139—21no—
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—81no—
219C4⋊C4×C139—81no—
220C4⋊C4×C139C22⋊C414yes—
221C4⋊C4×C139C22⋊C414yes—
222C4⋊C4×C139C22×C412yes—
223C4⋊C4×C139C22×C412yes—
224C22⋊C4×C139—24no—
225C22⋊C4×C139—24no—
226C22⋊C4×C139—81no—
227C22⋊C4×C139—81no—
228C22⋊C4×C139C22⋊C414yes—
229C22⋊C4×C139C22⋊C414yes—
230C42×C139—24no—
231C42×C139—24no—
232C42×C139—81no—
233C42×C139—81no—
234C42×C139C22×C412yes—
235C42×C139C22×C412yes—
236C42×C139C2×D412yes—
237C42×C139C2×D412yes—
238C23×C139—22no—
239C23×C139—21no—
240C23×C139—21no—
241C23×C139—22no—
242C23×C139—22no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—41no—
248C23×C139—41no—
249C23×C139—41no—
250C23×C139—41no—
251C23×C139C2×C22⋊C412yes—
252C23×C139C22×D411yescharacteristic
253Q8×C139—22no—
254Q8×C139—22no—
255Q8×C139—22no—
256Q8×C139#11714yes—
257D4×C139—216no—
258D4×C139—22no—
259D4×C139—22no—
260D4×C139—22no—
261D4×C139#11714yes—
262C2×C4×C139—216no—
263C2×C4×C139—22no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—22no—
267C2×C4×C139—22no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—21no—
274C2×C4×C139—21no—
275C2×C4×C139—21no—
276C2×C4×C139—22no—
277C2×C4×C139—22no—
278C2×C4×C139—22no—
279C2×C4×C139—22no—
280C2×C4×C139—22no—
281C2×C4×C139—22no—
282C2×C4×C139—41no—
283C2×C4×C139—41no—
284C2×C4×C139—41no—
285C2×C4×C139—41no—
286C2×C4×C139—41no—
287C2×C4×C139—41no—
288C2×C4×C139—41no—
289C2×C4×C139—41no—
290C2×C4×C139—41no—
291C2×C4×C139—41no—
292C2×C4×C139—41no—
293C2×C4×C139—41no—
294C2×C4×C139—41no—
295C2×C4×C139—41no—
296C2×C4×C139—41no—
297C2×C4×C139—41no—
298C2×C4×C139—84no—
299C2×C4×C139—84no—
300C2×C4×C139—84no—
301C2×C4×C139C2×C22⋊C412yes—
302C2×C4×C139C2×C22⋊C412yes—
303C2×C4×C139C2×C22⋊C412yes—
304C2×C4×C139C2×C22⋊C412yes—
305C2×C4×C139C2×C22⋊C412yes—
306C2×C4×C139C23×C411yescharacteristic
307C2×C4×C139C22×D411yescharacteristic
308C2×C4×C139C2×#4111yescharacteristic
309C2×C4×C139C2×#4111yescharacteristic
310C2×C4×C139C2×#4111yescharacteristic
311C2×C4×C139C2×#4111yescharacteristic
312C8×C139—41no—
313C8×C139—41no—
314C8×C139—41no—
315C8×C139—41no—
316C22×C139—22no—
317C22×C139—22no—
318C22×C139—22no—
319C22×C139—24no—
320C22×C139—41no—
321C22×C139—42no—
322C22×C139—41no—
323C22×C139—42no—
324C22×C139—41no—
325C22×C139—42no—
326C22×C139—41no—
327C22×C139—42no—
328C22×C139—42no—
329C22×C139—42no—
330C22×C139C22×C22⋊C411yescharacteristic
331C22×C139#52511yescharacteristic
332C22×C139#52511yescharacteristic
333C22×C139#57611yescharacteristic
334C22×C139#57711yescharacteristic
335C22×C139#57711yescharacteristic
336C22×C139#57811yescharacteristic
337C4×C139—22no—
338C4×C139—22no—
339C4×C139—22no—
340C4×C139—22no—
341C4×C139—22no—
342C4×C139—24no—
343C4×C139—42no—
344C4×C139—42no—
345C4×C139—81no—
346C4×C139—81no—
347C4×C139—81no—
348C4×C139—81no—
349C4×C139C2×#11711yescharacteristic
350C4×C139C2×#11711yescharacteristic
351C4×C139#52511yescharacteristic
352C4×C139#52511yescharacteristic
353C2×C139—42no—
354C2×C139—44no—
355C2×C139#228011yescharacteristic
356C2×C139#289711yescharacteristic
357C2×C139#289811yescharacteristic
358C2×C139#311911yescharacteristic
359C2×C139#312011yescharacteristic
360C2×C139#312411yescharacteristic
361C2×C139#312511yescharacteristic
362#20746C13911yesmaximal, characteristic, direct product factor, Sylow
363C139#2074611yescharacteristic, direct product factor, Sylow
364C2×#520C2×C13911yescharacteristic
365C2×#433C2×C13911yescharacteristic, complemented
366#2314C2×C13911yescharacteristic, complemented
367#1824C2×C13911yescharacteristic, complemented
368#1823C2×C13911yescharacteristic, complemented
369#1805C2×C13911yescharacteristic, complemented
370#1804C2×C13911yescharacteristic, complemented
371#1803C2×C13911yescharacteristic, complemented
372#1802C2×C13911yescharacteristic, complemented
373#1788C2×C13911yescharacteristic
374#1788C2×C13911yescharacteristic
375#1763C2×C13911yescharacteristic, complemented
376#1762C2×C13911yescharacteristic, complemented
377C4×#103C2×C13911yescharacteristic, complemented
378C4×#102C2×C13911yescharacteristic, complemented
379C22×#41C22×C13911yescharacteristic
380#520—24no—
381#520C4×C13918yescomplemented
382C2×C4×Q8C22×C13911yescharacteristic
383C2×C4×Q8C22×C13911yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4—21no—
386C2×C4×D4C22×C13911yescharacteristic
387C2×C4×D4C22×C13911yescharacteristic
388C2×#117—21no—
389C2×#117C22×C13911yescharacteristic
390C22×C4⋊C4—21no—
391C22×C4⋊C4C22×C13911yescharacteristic
392#433—24no—
393C2×C4⋊C8C22×C13911yescharacteristic
394C2×C4⋊C8C22×C13911yescharacteristic
395C2×#103C22×C13911yescharacteristic
396C2×#103C22×C13911yescharacteristic
397C2×#103C22×C13911yescharacteristic
398C2×#103C22×C13911yescharacteristic
399C2×#102C22×C13911yescharacteristic
400C2×#102C22×C13911yescharacteristic
401C2×#102C22×C13911yescharacteristic
402C2×#102C22×C13911yescharacteristic
403C2×C22⋊C8C22×C13911yescharacteristic
404C2×C22⋊C8C22×C13911yescharacteristic
405C2×#97C22×C13911yescharacteristic
406C2×C4×C8C22×C13911yescharacteristic
407#388—21no—
408#388—21no—
409#387—21no—
410#387—21no—
411#384C22×C13911yescharacteristic
412#382C22×C13911yescharacteristic
413#380C22×C13911yescharacteristic
414#380C22×C13911yescharacteristic
415C4×C4⋊C4C22×C13911yescharacteristic
416C4×C4⋊C4C22×C13911yescharacteristic
417#340C22×C13911yescharacteristic
418#340C22×C13911yescharacteristic
419#340C22×C13911yescharacteristic
420#340C22×C13911yescharacteristic
421#340C22×C13911yescharacteristic
422#340C22×C13911yescharacteristic
423#340C22×C13911yescharacteristic
424#340C22×C13911yescharacteristic
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41C2×C4×C13914yes—
431C22×Q8C23×C13911yescharacteristic
432C22×D4—21no—
433C22×D4C23×C13911yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C13911yescharacteristic
439C22×C8C23×C13911yescharacteristic
440C22×C8C23×C13911yescharacteristic
441C22×C8C23×C13911yescharacteristic
442C22×C8C23×C13911yescharacteristic
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8C2×C4×C13914yes—
446C4×Q8C2×C4×C13914yes—
447C4×D4—28no—
448C4×D4—28no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4C2×C4×C13914yes—
452C4×D4C2×C4×C13914yes—
453#117—28no—
454#117C2×C4×C13914yes—
455#117D4×C13914yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4C2×C4×C13914yes—
464C2×C4⋊C4D4×C13911yescharacteristic
465C2×C4⋊C4D4×C13911yescharacteristic
466C2×C4⋊C4C23×C13911yescharacteristic
467C2×C4⋊C4C23×C13911yescharacteristic
468C2×C4⋊C4C23×C13911yescharacteristic
469C2×C4⋊C4C23×C13911yescharacteristic
470C2×C4⋊C4C23×C13911yescharacteristic
471C2×C4⋊C4C23×C13911yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4D4×C13911yescharacteristic
477C2×C22⋊C4D4×C13911yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C13911yescharacteristic
483C2×C42C23×C13911yescharacteristic
484C4⋊C8—22no—
485C4⋊C8—22no—
486#103—22no—
487#103—22no—
488#103—22no—
489#103—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#97—22no—
497C4×C8—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C24—21no—
505C24C2×D4×C13911yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×C4×C13912yes—
514C2×Q8#41×C13912yes—
515C2×Q8#41×C13912yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4C22×C4×C13912yes—
523C2×D4#41×C13912yes—
524C2×D4#41×C13912yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4C22×C4×C13912yes—
549C22×C4C2×D4×C13911yescharacteristic
550C22×C4C2×D4×C13911yescharacteristic
551C22×C4C2×D4×C13911yescharacteristic
552C22×C4C2×D4×C13911yescharacteristic
553C22×C4C2×D4×C13911yescharacteristic
554C22×C4C2×D4×C13912yes—
555C22×C4C24×C13911yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4C22⋊C4×C13914yes—
584C4⋊C4C22⋊C4×C13914yes—
585C4⋊C4C22×C4×C13912yes—
586C4⋊C4C22×C4×C13912yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4C22⋊C4×C13914yes—
592C22⋊C4C22⋊C4×C13914yes—
593C42—24no—
594C42—24no—
595C42—81no—
596C42—81no—
597C42C22×C4×C13912yes—
598C42C22×C4×C13912yes—
599C42C2×D4×C13912yes—
600C42C2×D4×C13912yes—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C2×C22⋊C4×C13912yes—
615C23C22×D4×C13911yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#117×C13914yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#117×C13914yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4C2×C22⋊C4×C13912yes—
665C2×C4C2×C22⋊C4×C13912yes—
666C2×C4C2×C22⋊C4×C13912yes—
667C2×C4C2×C22⋊C4×C13912yes—
668C2×C4C2×C22⋊C4×C13912yes—
669C2×C4C23×C4×C13911yescharacteristic
670C2×C4C22×D4×C13911yescharacteristic
671C2×C4C2×#41×C13911yescharacteristic
672C2×C4C2×#41×C13911yescharacteristic
673C2×C4C2×#41×C13911yescharacteristic
674C2×C4C2×#41×C13911yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—22no—
680C22—24no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22C22×C22⋊C4×C13911yescharacteristic
694C22#525×C13911yescharacteristic
695C22#525×C13911yescharacteristic
696C22#576×C13911yescharacteristic
697C22#577×C13911yescharacteristic
698C22#577×C13911yescharacteristic
699C22#578×C13911yescharacteristic
700C4—22no—
701C4—24no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C2×#117×C13911yescharacteristic
713C4C2×#117×C13911yescharacteristic
714C4#525×C13911yescharacteristic
715C4#525×C13911yescharacteristic
716C2—42no—
717C2—44no—
718C2#2280×C13911yescharacteristic
719C2#2897×C13911yescharacteristic
720C2#2898×C13911yescharacteristic
721C2#3119×C13911yescharacteristic
722C2#3120×C13911yescharacteristic
723C2#3124×C13911yescharacteristic
724C2#3125×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC22×#41×C139C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#433×C139C2semidirect
3. #2314×C139C2semidirect
4. #1824×C139C2semidirect
5. #1823×C139C2semidirect
6. #1805×C139C2semidirect
7. #1804×C139C2semidirect
8. #1803×C139C2semidirect
9. #1802×C139C2semidirect
12. #1763×C139C2semidirect
13. #1762×C139C2semidirect
14. C4×#103×C139C2semidirect
15. C4×#102×C139C2semidirect
18. #520×C139C4semidirect
362. #20746C139direct (N × H)
363. C139#20746direct (N × H)
365. C2×#433C2×C139semidirect
366. #2314C2×C139semidirect
367. #1824C2×C139semidirect
368. #1823C2×C139semidirect
369. #1805C2×C139semidirect
370. #1804C2×C139semidirect
371. #1803C2×C139semidirect
372. #1802C2×C139semidirect
375. #1763C2×C139semidirect
376. #1762C2×C139semidirect
377. C4×#103C2×C139semidirect
378. C4×#102C2×C139semidirect
381. #520C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1392
C2×#433×C1392
#2314×C1392
#1824×C1392
#1823×C1392
#1805×C1392
#1804×C1392
#1803×C1392
#1802×C1392
#1788×C1392
#1763×C1392
#1762×C1392
C4×#103×C1392
C4×#102×C1392
#20746139