Finite Group Databasebeta

← C139×#24567 #48019163

Subgroups — C139×#24567 #48019163

Order 35584.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C139C211yesmaximal, characteristic, complemented
2C2×#408×C139C211yesmaximal, characteristic, complemented
3#2615×C139C211yesmaximal, characteristic
4#2311×C139C211yesmaximal, characteristic, complemented
5#2077×C139C211yesmaximal, characteristic, complemented
6#2075×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1893×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1853×C139C211yesmaximal, characteristic, complemented
13#1825×C139C211yesmaximal, characteristic, complemented
14#1809×C139C211yesmaximal, characteristic, complemented
15#1807×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×#117×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24#482×C139—24no—
25C2×#107×C139C2211yescharacteristic
26C2×#106×C139C2211yescharacteristic
27C2×#106×C139C2211yescharacteristic
28C2×#106×C139C2211yescharacteristic
29C2×#102×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33#408×C139—24no—
34C2×C22⋊C8×C139C2211yescharacteristic
35C2×C22⋊C8×C139C2211yescharacteristic
36C2×C22⋊C8×C139C2211yescharacteristic
37C2×C22⋊C8×C139C2211yescharacteristic
38#393×C139—21no—
39#392×C139—21no—
40#392×C139—21no—
41#392×C139—21no—
42#391×C139—21no—
43#390×C139—21no—
44#386×C139—21no—
45#386×C139—21no—
46#380×C139C2211yescharacteristic
47#380×C139C2211yescharacteristic
48#380×C139C2211yescharacteristic
49#380×C139C2211yescharacteristic
50#380×C139C2211yescharacteristic
51#380×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61C2×#41×C139—22no—
62C2×#41×C139—22no—
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—41no—
66C2×#41×C139—41no—
67C22×Q8×C139D411yescharacteristic
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139D411yescharacteristic
73C22×D4×C139D411yescharacteristic
74C22×D4×C139C2311yescharacteristic
75C23×C4×C139—21no—
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C23×C4×C139C2311yescharacteristic
79C2×M16×C139—22no—
80C2×M16×C139—22no—
81C2×M16×C139—41no—
82C22×C8×C139—22no—
83C22×C8×C139—22no—
84C22×C8×C139—41no—
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—41no—
94#121×C139—41no—
95#117×C139—22no—
96#117×C139—22no—
97C2×C4⋊C4×C139—21no—
98C2×C4⋊C4×C139—41no—
99C2×C4⋊C4×C139—41no—
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C42×C139—21no—
119#107×C139—22no—
120#106×C139—22no—
121#106×C139—41no—
122#106×C139—41no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—41no—
126#102×C139—41no—
127C22⋊C8×C139—22no—
128C22⋊C8×C139—22no—
129C22⋊C8×C139—22no—
130C22⋊C8×C139D414yescomplemented
131#95×C139—21no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138C24×C139—21no—
139C24×C139C2×D411yescharacteristic
140C24×C139C2×D411yescharacteristic
141C24×C139C2×D411yescharacteristic
142#41×C139—44no—
143#41×C139—44no—
144#41×C139—44no—
145#41×C139—44no—
146C2×Q8×C139—22no—
147C2×Q8×C139—22no—
148C2×Q8×C139—41no—
149C2×D4×C139—22no—
150C2×D4×C139—22no—
151C2×D4×C139—22no—
152C2×D4×C139—22no—
153C2×D4×C139—22no—
154C2×D4×C139—22no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—41no—
162C2×D4×C139—41no—
163C2×D4×C139—41no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—42no—
167C2×D4×C139—81no—
168C2×D4×C139—81no—
169C2×D4×C139—81no—
170C2×D4×C139—81no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C22×C4×C139—21no—
174C22×C4×C139—21no—
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—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—42no—
195C22×C4×C139—81no—
196C22×C4×C139—81no—
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2×D412yes—
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139#4112yes—
202C22×C4×C139#4112yes—
203C22×C4×C139#4112yes—
204C22×C4×C139C2411yescharacteristic
205M16×C139—44no—
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×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—44no—
217C2×C8×C139C2×D412yes—
218C2×C8×C139C2×D412yes—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
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—21no—
233C4⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—81no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139—81no—
241C22⋊C4×C139—81no—
242C22⋊C4×C139—81no—
243C22⋊C4×C139—81no—
244C22⋊C4×C139—81no—
245C42×C139—42no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
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—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139#12112yes—
273C23×C139#12312yes—
274C23×C139C22×D411yescharacteristic
275Q8×C139—44no—
276D4×C139—44no—
277D4×C139—44no—
278D4×C139—44no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
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—22no—
291C2×C4×C139—22no—
292C2×C4×C139—22no—
293C2×C4×C139—22no—
294C2×C4×C139—22no—
295C2×C4×C139—22no—
296C2×C4×C139—22no—
297C2×C4×C139—22no—
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—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—84no—
327C2×C4×C139#12112yes—
328C2×C4×C139#12312yes—
329C2×C4×C139C22×D411yescharacteristic
330C2×C4×C139C2×#4111yescharacteristic
331C2×C4×C139C2×#4111yescharacteristic
332C2×C4×C139C2×#4111yescharacteristic
333C2×C4×C139H(5,𝔽2)11yescharacteristic
334C2×C4×C139H(5,𝔽2)11yescharacteristic
335C8×C139—22no—
336C8×C139—22no—
337C8×C139—41no—
338C8×C139—41no—
339C22×C139—22no—
340C22×C139—22no—
341C22×C139—22no—
342C22×C139—22no—
343C22×C139—22no—
344C22×C139—22no—
345C22×C139—41no—
346C22×C139—41no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—41no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—41no—
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×C139—81no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139C2×#12111yescharacteristic
368C22×C139C2×#12311yescharacteristic
369C22×C139#53411yescharacteristic
370C22×C139#57611yescharacteristic
371C22×C139#57711yescharacteristic
372C22×C139#57711yescharacteristic
373C22×C139#57711yescharacteristic
374C4×C139—22no—
375C4×C139—22no—
376C4×C139—41no—
377C4×C139—81no—
378C4×C139—81no—
379C4×C139—81no—
380C4×C139—81no—
381C4×C139—81no—
382C4×C139—81no—
383C4×C139—81no—
384C4×C139#54611yescharacteristic
385C4×C139#54611yescharacteristic
386C4×C139#55111yescharacteristic
387C4×C139#55111yescharacteristic
388C2×C139—42no—
389C2×C139—42no—
390C2×C139—81no—
391C2×C139—161no—
392C2×C139#241211yescharacteristic
393C2×C139#306011yescharacteristic
394C2×C139#306211yescharacteristic
395C2×C139#309611yescharacteristic
396C2×C139#309911yescharacteristic
397C2×C139#319811yescharacteristic
398C2×C139#320011yescharacteristic
399#24567C13911yesmaximal, characteristic, direct product factor, Sylow
400C139#2456711yescharacteristic, direct product factor, Sylow
401C2×#482C2×C13911yescharacteristic, complemented
402C2×#408C2×C13911yescharacteristic, complemented
403#2615C2×C13911yescharacteristic
404#2311C2×C13911yescharacteristic, complemented
405#2077C2×C13911yescharacteristic, complemented
406#2075C2×C13911yescharacteristic, complemented
407#2034C2×C13911yescharacteristic, complemented
408#2034C2×C13911yescharacteristic, complemented
409#1895C2×C13911yescharacteristic, complemented
410#1893C2×C13911yescharacteristic, complemented
411#1874C2×C13911yescharacteristic, complemented
412#1853C2×C13911yescharacteristic, complemented
413#1825C2×C13911yescharacteristic, complemented
414#1809C2×C13911yescharacteristic, complemented
415#1807C2×C13911yescharacteristic, complemented
416C22×#41C22×C13911yescharacteristic
417C22×M16C22×C13911yescharacteristic
418C23×C8C22×C13911yescharacteristic
419C2×#121C22×C13911yescharacteristic
420C2×#121C22×C13911yescharacteristic
421C2×#121C22×C13911yescharacteristic
422C2×#117C22×C13911yescharacteristic
423C22×C4⋊C4C22×C13911yescharacteristic
424#482—24no—
425C2×#107C22×C13911yescharacteristic
426C2×#106C22×C13911yescharacteristic
427C2×#106C22×C13911yescharacteristic
428C2×#106C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433#408—24no—
434C2×C22⋊C8C22×C13911yescharacteristic
435C2×C22⋊C8C22×C13911yescharacteristic
436C2×C22⋊C8C22×C13911yescharacteristic
437C2×C22⋊C8C22×C13911yescharacteristic
438#393—21no—
439#392—21no—
440#392—21no—
441#392—21no—
442#391—21no—
443#390—21no—
444#386—21no—
445#386—21no—
446#380C22×C13911yescharacteristic
447#380C22×C13911yescharacteristic
448#380C22×C13911yescharacteristic
449#380C22×C13911yescharacteristic
450#380C22×C13911yescharacteristic
451#380C22×C13911yescharacteristic
452#380C22×C13911yescharacteristic
453#340C22×C13911yescharacteristic
454#340C22×C13911yescharacteristic
455#340C22×C13911yescharacteristic
456#340C22×C13911yescharacteristic
457#340C22×C13911yescharacteristic
458#340C22×C13911yescharacteristic
459#340C22×C13911yescharacteristic
460#340C22×C13911yescharacteristic
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C13911yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C13911yescharacteristic
472C22×D4D4×C13911yescharacteristic
473C22×D4D4×C13911yescharacteristic
474C22×D4C23×C13911yescharacteristic
475C23×C4—21no—
476C23×C4C23×C13911yescharacteristic
477C23×C4C23×C13911yescharacteristic
478C23×C4C23×C13911yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C13911yescharacteristic
486C22×C8C23×C13911yescharacteristic
487C22×C8C23×C13911yescharacteristic
488C22×C8C23×C13911yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—22no—
496#117—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4C23×C13911yescharacteristic
501C2×C4⋊C4C23×C13911yescharacteristic
502C2×C4⋊C4C23×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#107—22no—
520#106—22no—
521#106—41no—
522#106—41no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C13914yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C13911yescharacteristic
540C24C2×D4×C13911yescharacteristic
541C24C2×D4×C13911yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
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—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C13911yescharacteristic
598C22×C4C2×D4×C13911yescharacteristic
599C22×C4C2×D4×C13912yes—
600C22×C4C2×D4×C13911yescharacteristic
601C22×C4#41×C13912yes—
602C22×C4#41×C13912yes—
603C22×C4#41×C13912yes—
604C22×C4C24×C13911yescharacteristic
605M16—44no—
606C2×C8—21no—
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—
619C4⋊C4—21no—
620C4⋊C4—21no—
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—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C13912yes—
673C23#123×C13912yes—
674C23C22×D4×C13911yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
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—84no—
727C2×C4#121×C13912yes—
728C2×C4#123×C13912yes—
729C2×C4C22×D4×C13911yescharacteristic
730C2×C4C2×#41×C13911yescharacteristic
731C2×C4C2×#41×C13911yescharacteristic
732C2×C4C2×#41×C13911yescharacteristic
733C2×C4H(5,𝔽2)×C13911yescharacteristic
734C2×C4H(5,𝔽2)×C13911yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C13911yescharacteristic
768C22C2×#123×C13911yescharacteristic
769C22#534×C13911yescharacteristic
770C22#576×C13911yescharacteristic
771C22#577×C13911yescharacteristic
772C22#577×C13911yescharacteristic
773C22#577×C13911yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C13911yescharacteristic
785C4#546×C13911yescharacteristic
786C4#551×C13911yescharacteristic
787C4#551×C13911yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2#2412×C13911yescharacteristic
793C2#3060×C13911yescharacteristic
794C2#3062×C13911yescharacteristic
795C2#3096×C13911yescharacteristic
796C2#3099×C13911yescharacteristic
797C2#3198×C13911yescharacteristic
798C2#3200×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2615×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C139C2semidirect
2. C2×#408×C139C2semidirect
4. #2311×C139C2semidirect
5. #2077×C139C2semidirect
6. #2075×C139C2semidirect
7. #2034×C139C2semidirect
8. #2034×C139C2semidirect
9. #1895×C139C2semidirect
10. #1893×C139C2semidirect
11. #1874×C139C2semidirect
12. #1853×C139C2semidirect
13. #1825×C139C2semidirect
14. #1809×C139C2semidirect
15. #1807×C139C2semidirect
130. C22⋊C8×C139D4semidirect
399. #24567C139direct (N × H)
400. C139#24567direct (N × H)
401. C2×#482C2×C139semidirect
402. C2×#408C2×C139semidirect
404. #2311C2×C139semidirect
405. #2077C2×C139semidirect
406. #2075C2×C139semidirect
407. #2034C2×C139semidirect
408. #2034C2×C139semidirect
409. #1895C2×C139semidirect
410. #1893C2×C139semidirect
411. #1874C2×C139semidirect
412. #1853C2×C139semidirect
413. #1825C2×C139semidirect
414. #1809C2×C139semidirect
415. #1807C2×C139semidirect
530. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1392
C2×#408×C1392
#2615×C1392
#2311×C1392
#2077×C1392
#2075×C1392
#2034×C1392
#1895×C1392
#1893×C1392
#1874×C1392
#1853×C1392
#1825×C1392
#1809×C1392
#1807×C1392
#24567139