Finite Group Databasebeta

← C139×#22335 #48016931

Subgroups — C139×#22335 #48016931

Order 35584.

864 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C139C211yesmaximal, characteristic
2#1955×C139C211yesmaximal, characteristic, complemented
3#1954×C139C211yesmaximal, characteristic, complemented
4#1924×C139C211yesmaximal, characteristic, complemented
5#1924×C139C211yesmaximal, characteristic, complemented
6#1917×C139C211yesmaximal, characteristic, complemented
7#1916×C139C211yesmaximal, characteristic, complemented
8#1870×C139C211yesmaximal, characteristic, complemented
9#1870×C139C211yesmaximal, characteristic, complemented
10#1869×C139C211yesmaximal, characteristic, complemented
11#1869×C139C211yesmaximal, characteristic, complemented
12#1817×C139C211yesmaximal, characteristic, complemented
13#1753×C139C211yesmaximal, characteristic, complemented
14#1752×C139C211yesmaximal, characteristic, complemented
15#1749×C139C211yesmaximal, characteristic, complemented
16C22×M16×C139C2211yescharacteristic
17C23×C8×C139C2211yescharacteristic
18C2×#121×C139C411yescharacteristic
19C2×C4×D4×C139C2211yescharacteristic
20C2×C4×D4×C139C2211yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C22×C42×C139C2211yescharacteristic
23C2×C4⋊C8×C139C2211yescharacteristic
24C2×C4⋊C8×C139C2211yescharacteristic
25C2×C22⋊C8×C139C2211yescharacteristic
26C2×C22⋊C8×C139C2211yescharacteristic
27C2×C22⋊C8×C139C2211yescharacteristic
28C2×C22⋊C8×C139C2211yescharacteristic
29C2×C22⋊C8×C139C2211yescharacteristic
30C2×C22⋊C8×C139C2211yescharacteristic
31C2×C22⋊C8×C139C2211yescharacteristic
32C2×C22⋊C8×C139C2211yescharacteristic
33C2×C22⋊C8×C139C2211yescharacteristic
34C2×C22⋊C8×C139C2211yescharacteristic
35C2×#97×C139C2211yescharacteristic
36C2×#97×C139C2211yescharacteristic
37C2×#97×C139C2211yescharacteristic
38C2×C4×C8×C139C2211yescharacteristic
39#390×C139C411yescharacteristic
40#389×C139C411yescharacteristic
41#388×C139C411yescharacteristic
42#388×C139C411yescharacteristic
43#386×C139C411yescharacteristic
44#386×C139C411yescharacteristic
45#380×C139C411yescharacteristic
46C4×C4⋊C4×C139C2211yescharacteristic
47C4×C22⋊C4×C139C2211yescharacteristic
48C4×C22⋊C4×C139C2211yescharacteristic
49#336×C139C2211yescharacteristic
50#336×C139C2211yescharacteristic
51#336×C139C2211yescharacteristic
52#336×C139C2211yescharacteristic
53#336×C139C2211yescharacteristic
54#336×C139C2211yescharacteristic
55#336×C139C2211yescharacteristic
56#336×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C22×D4×C139C2×C411yescharacteristic
60C22×D4×C139C2×C411yescharacteristic
61C22×D4×C139C2×C411yescharacteristic
62C23×C4×C139C2×C411yescharacteristic
63C23×C4×C139C2×C411yescharacteristic
64C23×C4×C139C2311yescharacteristic
65C23×C4×C139C2311yescharacteristic
66C23×C4×C139C2311yescharacteristic
67C2×M16×C139—22no—
68C2×M16×C139—41no—
69C2×M16×C139—41no—
70C22×C8×C139—22no—
71C22×C8×C139—41no—
72C22×C8×C139—41no—
73C22×C8×C139C2311yescharacteristic
74C22×C8×C139C2311yescharacteristic
75C22×C8×C139C2311yescharacteristic
76C22×C8×C139C2311yescharacteristic
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81#121×C139—24no—
82C4×D4×C139—41no—
83C4×D4×C139—41no—
84C4×D4×C139—41no—
85C4×D4×C139—41no—
86C4×D4×C139—41no—
87C4×D4×C139—41no—
88C2×C4⋊C4×C139C2×C411yescharacteristic
89C2×C4⋊C4×C139C2×C411yescharacteristic
90C2×C4⋊C4×C139C2×C411yescharacteristic
91C2×C4⋊C4×C139C2×C411yescharacteristic
92C2×C4⋊C4×C139C2×C411yescharacteristic
93C2×C22⋊C4×C139C2×C411yescharacteristic
94C2×C22⋊C4×C139C2×C411yescharacteristic
95C2×C22⋊C4×C139C2×C411yescharacteristic
96C2×C22⋊C4×C139C2×C411yescharacteristic
97C2×C22⋊C4×C139C2×C411yescharacteristic
98C2×C22⋊C4×C139C2×C411yescharacteristic
99C2×C22⋊C4×C139C2×C411yescharacteristic
100C2×C22⋊C4×C139C2×C411yescharacteristic
101C2×C22⋊C4×C139C2×C411yescharacteristic
102C2×C22⋊C4×C139C2×C411yescharacteristic
103C2×C42×C139—41no—
104C2×C42×C139—41no—
105C2×C42×C139C2×C411yescharacteristic
106C2×C42×C139C2×C411yescharacteristic
107C2×C42×C139C2311yescharacteristic
108C2×C42×C139C2311yescharacteristic
109C2×C42×C139C2311yescharacteristic
110C2×C42×C139C2311yescharacteristic
111C4⋊C8×C139—41no—
112C4⋊C8×C139—41no—
113C22⋊C8×C139—22no—
114C22⋊C8×C139—22no—
115C22⋊C8×C139—22no—
116C22⋊C8×C139—22no—
117C22⋊C8×C139—41no—
118C22⋊C8×C139—41no—
119C22⋊C8×C139—41no—
120C22⋊C8×C139—41no—
121C22⋊C8×C139—41no—
122C22⋊C8×C139—41no—
123#97×C139—41no—
124#97×C139—41no—
125#97×C139—41no—
126C4×C8×C139—41no—
127#95×C139C2×C411yescharacteristic
128#95×C139C2×C411yescharacteristic
129#95×C139C2×C411yescharacteristic
130#95×C139C2×C411yescharacteristic
131#95×C139C2×C411yescharacteristic
132#95×C139C2×C411yescharacteristic
133C24×C139C22×C411yescharacteristic
134C24×C139C22×C411yescharacteristic
135C24×C139C22×C411yescharacteristic
136C2×D4×C139—22no—
137C2×D4×C139—22no—
138C2×D4×C139—22no—
139C2×D4×C139—41no—
140C2×D4×C139—41no—
141C2×D4×C139—41no—
142C2×D4×C139—41no—
143C2×D4×C139—41no—
144C2×D4×C139M1614yescomplemented
145C22×C4×C139—22no—
146C22×C4×C139—22no—
147C22×C4×C139—21no—
148C22×C4×C139—21no—
149C22×C4×C139—21no—
150C22×C4×C139—21no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—21no—
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—21no—
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—41no—
166C22×C4×C139—41no—
167C22×C4×C139—41no—
168C22×C4×C139—41no—
169C22×C4×C139C22×C411yescharacteristic
170C22×C4×C139C22×C411yescharacteristic
171C22×C4×C139C22×C411yescharacteristic
172C22×C4×C139C22×C411yescharacteristic
173C22×C4×C139C22×C411yescharacteristic
174C22×C4×C139C22×C411yescharacteristic
175C22×C4×C139C22×C411yescharacteristic
176C22×C4×C139C22×C411yescharacteristic
177C22×C4×C139C22×C411yescharacteristic
178C22×C4×C139C22×C411yescharacteristic
179C22×C4×C139C22×C411yescharacteristic
180C22×C4×C139C2411yescharacteristic
181M16×C139—44no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
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—44no—
205C2×C8×C139#4112yes—
206C2×C8×C139#4112yes—
207C4⋊C4×C139—22no—
208C4⋊C4×C139—22no—
209C4⋊C4×C139—41no—
210C4⋊C4×C139—41no—
211C4⋊C4×C139—41no—
212C22⋊C4×C139—22no—
213C22⋊C4×C139—22no—
214C22⋊C4×C139—41no—
215C22⋊C4×C139—41no—
216C22⋊C4×C139—41no—
217C22⋊C4×C139—41no—
218C22⋊C4×C139—41no—
219C22⋊C4×C139—41no—
220C22⋊C4×C139—41no—
221C22⋊C4×C139—41no—
222C42×C139—21no—
223C42×C139—21no—
224C42×C139—21no—
225C42×C139—21no—
226C42×C139—21no—
227C42×C139—21no—
228C42×C139—21no—
229C42×C139—21no—
230C42×C139—41no—
231C42×C139—41no—
232C23×C139—21no—
233C23×C139—21no—
234C23×C139—21no—
235C23×C139—21no—
236C23×C139—21no—
237C23×C139—21no—
238C23×C139—21no—
239C23×C139—21no—
240C23×C139—21no—
241C23×C139—21no—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139C2×M1612yes—
252C23×C139C2×M1612yes—
253C23×C139C23×C411yescharacteristic
254D4×C139—44no—
255D4×C139—44no—
256D4×C139—44no—
257C2×C4×C139—21no—
258C2×C4×C139—21no—
259C2×C4×C139—21no—
260C2×C4×C139—21no—
261C2×C4×C139—21no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
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—21no—
277C2×C4×C139—21no—
278C2×C4×C139—21no—
279C2×C4×C139—21no—
280C2×C4×C139—21no—
281C2×C4×C139—21no—
282C2×C4×C139—21no—
283C2×C4×C139—21no—
284C2×C4×C139—21no—
285C2×C4×C139—21no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—44no—
289C2×C4×C139—44no—
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—41no—
299C2×C4×C139—41no—
300C2×C4×C139—41no—
301C2×C4×C139—41no—
302C2×C4×C139C2×M1612yes—
303C2×C4×C139#13112yes—
304C2×C4×C139C2×#4111yescharacteristic
305C2×C4×C139C2×#4111yescharacteristic
306C2×C4×C139H(5,𝔽2)11yescharacteristic
307C2×C4×C139H(5,𝔽2)11yescharacteristic
308C2×C4×C139H(5,𝔽2)11yescharacteristic
309C2×C4×C139H(5,𝔽2)11yescharacteristic
310C8×C139—22no—
311C8×C139—22no—
312C8×C139—41no—
313C8×C139—41no—
314C8×C139—41no—
315C8×C139—41no—
316C8×C139—41no—
317C8×C139—41no—
318C22×C139—22no—
319C22×C139—22no—
320C22×C139—22no—
321C22×C139—22no—
322C22×C139—22no—
323C22×C139—22no—
324C22×C139—41no—
325C22×C139—41no—
326C22×C139—41no—
327C22×C139—41no—
328C22×C139—41no—
329C22×C139—41no—
330C22×C139—41no—
331C22×C139—41no—
332C22×C139—41no—
333C22×C139—41no—
334C22×C139—41no—
335C22×C139—41no—
336C22×C139—41no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139C4×#4111yescharacteristic
340C22×C139#51811yescharacteristic
341C22×C139#51811yescharacteristic
342C22×C139C22×M1611yescharacteristic
343C22×C139C2×#13111yescharacteristic
344C22×C139#56811yescharacteristic
345C22×C139#56811yescharacteristic
346C4×C139—22no—
347C4×C139—22no—
348C4×C139—41no—
349C4×C139—41no—
350C4×C139—41no—
351C4×C139—41no—
352C4×C139—41no—
353C4×C139—41no—
354C4×C139—41no—
355C4×C139—41no—
356C4×C139—41no—
357C4×C139#53811yescharacteristic
358C4×C139#53811yescharacteristic
359C4×C139#54011yescharacteristic
360C4×C139#54011yescharacteristic
361C2×C139—42no—
362C2×C139—42no—
363C2×C139—81no—
364C2×C139#233311yescharacteristic
365C2×C139#296911yescharacteristic
366C2×C139#297011yescharacteristic
367C2×C139#297311yescharacteristic
368C2×C139#297411yescharacteristic
369C2×C139#297811yescharacteristic
370C2×C139#298111yescharacteristic
371#22335C13911yesmaximal, characteristic, direct product factor, Sylow
372C139#2233511yescharacteristic, direct product factor, Sylow
373C4×#121C2×C13911yescharacteristic
374#1955C2×C13911yescharacteristic, complemented
375#1954C2×C13911yescharacteristic, complemented
376#1924C2×C13911yescharacteristic, complemented
377#1924C2×C13911yescharacteristic, complemented
378#1917C2×C13911yescharacteristic, complemented
379#1916C2×C13911yescharacteristic, complemented
380#1870C2×C13911yescharacteristic, complemented
381#1870C2×C13911yescharacteristic, complemented
382#1869C2×C13911yescharacteristic, complemented
383#1869C2×C13911yescharacteristic, complemented
384#1817C2×C13911yescharacteristic, complemented
385#1753C2×C13911yescharacteristic, complemented
386#1752C2×C13911yescharacteristic, complemented
387#1749C2×C13911yescharacteristic, complemented
388C22×M16C22×C13911yescharacteristic
389C23×C8C22×C13911yescharacteristic
390C2×#121C4×C13911yescharacteristic
391C2×C4×D4C22×C13911yescharacteristic
392C2×C4×D4C22×C13911yescharacteristic
393C2×C4×D4C22×C13911yescharacteristic
394C22×C42C22×C13911yescharacteristic
395C2×C4⋊C8C22×C13911yescharacteristic
396C2×C4⋊C8C22×C13911yescharacteristic
397C2×C22⋊C8C22×C13911yescharacteristic
398C2×C22⋊C8C22×C13911yescharacteristic
399C2×C22⋊C8C22×C13911yescharacteristic
400C2×C22⋊C8C22×C13911yescharacteristic
401C2×C22⋊C8C22×C13911yescharacteristic
402C2×C22⋊C8C22×C13911yescharacteristic
403C2×C22⋊C8C22×C13911yescharacteristic
404C2×C22⋊C8C22×C13911yescharacteristic
405C2×C22⋊C8C22×C13911yescharacteristic
406C2×C22⋊C8C22×C13911yescharacteristic
407C2×#97C22×C13911yescharacteristic
408C2×#97C22×C13911yescharacteristic
409C2×#97C22×C13911yescharacteristic
410C2×C4×C8C22×C13911yescharacteristic
411#390C4×C13911yescharacteristic
412#389C4×C13911yescharacteristic
413#388C4×C13911yescharacteristic
414#388C4×C13911yescharacteristic
415#386C4×C13911yescharacteristic
416#386C4×C13911yescharacteristic
417#380C4×C13911yescharacteristic
418C4×C4⋊C4C22×C13911yescharacteristic
419C4×C22⋊C4C22×C13911yescharacteristic
420C4×C22⋊C4C22×C13911yescharacteristic
421#336C22×C13911yescharacteristic
422#336C22×C13911yescharacteristic
423#336C22×C13911yescharacteristic
424#336C22×C13911yescharacteristic
425#336C22×C13911yescharacteristic
426#336C22×C13911yescharacteristic
427#336C22×C13911yescharacteristic
428#336C22×C13911yescharacteristic
429#336C22×C13911yescharacteristic
430#336C22×C13911yescharacteristic
431C22×D4C2×C4×C13911yescharacteristic
432C22×D4C2×C4×C13911yescharacteristic
433C22×D4C2×C4×C13911yescharacteristic
434C23×C4C2×C4×C13911yescharacteristic
435C23×C4C2×C4×C13911yescharacteristic
436C23×C4C23×C13911yescharacteristic
437C23×C4C23×C13911yescharacteristic
438C23×C4C23×C13911yescharacteristic
439C2×M16—22no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—22no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C13911yescharacteristic
446C22×C8C23×C13911yescharacteristic
447C22×C8C23×C13911yescharacteristic
448C22×C8C23×C13911yescharacteristic
449C22×C8C23×C13911yescharacteristic
450C22×C8C23×C13911yescharacteristic
451C22×C8C23×C13911yescharacteristic
452C22×C8C23×C13911yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C13911yescharacteristic
461C2×C4⋊C4C2×C4×C13911yescharacteristic
462C2×C4⋊C4C2×C4×C13911yescharacteristic
463C2×C4⋊C4C2×C4×C13911yescharacteristic
464C2×C4⋊C4C2×C4×C13911yescharacteristic
465C2×C22⋊C4C2×C4×C13911yescharacteristic
466C2×C22⋊C4C2×C4×C13911yescharacteristic
467C2×C22⋊C4C2×C4×C13911yescharacteristic
468C2×C22⋊C4C2×C4×C13911yescharacteristic
469C2×C22⋊C4C2×C4×C13911yescharacteristic
470C2×C22⋊C4C2×C4×C13911yescharacteristic
471C2×C22⋊C4C2×C4×C13911yescharacteristic
472C2×C22⋊C4C2×C4×C13911yescharacteristic
473C2×C22⋊C4C2×C4×C13911yescharacteristic
474C2×C22⋊C4C2×C4×C13911yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C13911yescharacteristic
478C2×C42C2×C4×C13911yescharacteristic
479C2×C42C23×C13911yescharacteristic
480C2×C42C23×C13911yescharacteristic
481C2×C42C23×C13911yescharacteristic
482C2×C42C23×C13911yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495#97—41no—
496#97—41no—
497#97—41no—
498C4×C8—41no—
499#95C2×C4×C13911yescharacteristic
500#95C2×C4×C13911yescharacteristic
501#95C2×C4×C13911yescharacteristic
502#95C2×C4×C13911yescharacteristic
503#95C2×C4×C13911yescharacteristic
504#95C2×C4×C13911yescharacteristic
505C24C22×C4×C13911yescharacteristic
506C24C22×C4×C13911yescharacteristic
507C24C22×C4×C13911yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4M16×C13914yescomplemented
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4C22×C4×C13911yescharacteristic
542C22×C4C22×C4×C13911yescharacteristic
543C22×C4C22×C4×C13911yescharacteristic
544C22×C4C22×C4×C13911yescharacteristic
545C22×C4C22×C4×C13911yescharacteristic
546C22×C4C22×C4×C13911yescharacteristic
547C22×C4C22×C4×C13911yescharacteristic
548C22×C4C22×C4×C13911yescharacteristic
549C22×C4C22×C4×C13911yescharacteristic
550C22×C4C22×C4×C13911yescharacteristic
551C22×C4C22×C4×C13911yescharacteristic
552C22×C4C24×C13911yescharacteristic
553M16—44no—
554C2×C8—21no—
555C2×C8—21no—
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—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8#41×C13912yes—
578C2×C8#41×C13912yes—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×M16×C13912yes—
624C23C2×M16×C13912yes—
625C23C23×C4×C13911yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
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—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4C2×M16×C13912yes—
675C2×C4#131×C13912yes—
676C2×C4C2×#41×C13911yescharacteristic
677C2×C4C2×#41×C13911yescharacteristic
678C2×C4H(5,𝔽2)×C13911yescharacteristic
679C2×C4H(5,𝔽2)×C13911yescharacteristic
680C2×C4H(5,𝔽2)×C13911yescharacteristic
681C2×C4H(5,𝔽2)×C13911yescharacteristic
682C8—22no—
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C4×#41×C13911yescharacteristic
712C22#518×C13911yescharacteristic
713C22#518×C13911yescharacteristic
714C22C22×M16×C13911yescharacteristic
715C22C2×#131×C13911yescharacteristic
716C22#568×C13911yescharacteristic
717C22#568×C13911yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#538×C13911yescharacteristic
730C4#538×C13911yescharacteristic
731C4#540×C13911yescharacteristic
732C4#540×C13911yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2#2333×C13911yescharacteristic
737C2#2969×C13911yescharacteristic
738C2#2970×C13911yescharacteristic
739C2#2973×C13911yescharacteristic
740C2#2974×C13911yescharacteristic
741C2#2978×C13911yescharacteristic
742C2#2981×C13911yescharacteristic
subgroupG/H
centerC22×C4×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC22×C4C24×C139
socleC23×C139C23×C4
prime radicalC2×#121×C139C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1955×C139C2semidirect
3. #1954×C139C2semidirect
4. #1924×C139C2semidirect
5. #1924×C139C2semidirect
6. #1917×C139C2semidirect
7. #1916×C139C2semidirect
8. #1870×C139C2semidirect
9. #1870×C139C2semidirect
10. #1869×C139C2semidirect
11. #1869×C139C2semidirect
12. #1817×C139C2semidirect
13. #1753×C139C2semidirect
14. #1752×C139C2semidirect
15. #1749×C139C2semidirect
144. C2×D4×C139M16semidirect
371. #22335C139direct (N × H)
372. C139#22335direct (N × H)
374. #1955C2×C139semidirect
375. #1954C2×C139semidirect
376. #1924C2×C139semidirect
377. #1924C2×C139semidirect
378. #1917C2×C139semidirect
379. #1916C2×C139semidirect
380. #1870C2×C139semidirect
381. #1870C2×C139semidirect
382. #1869C2×C139semidirect
383. #1869C2×C139semidirect
384. #1817C2×C139semidirect
385. #1753C2×C139semidirect
386. #1752C2×C139semidirect
387. #1749C2×C139semidirect
516. C2×D4M16×C139semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1392
#1955×C1392
#1954×C1392
#1924×C1392
#1917×C1392
#1916×C1392
#1870×C1392
#1869×C1392
#1817×C1392
#1753×C1392
#1752×C1392
#1749×C1392
#22335139