Finite Group Databasebeta

← C19×#18434 #18024393

Subgroups — C19×#18434 #18024393

Order 4864.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3560C211yesmaximal, characteristic, complemented
2C19×#3213C211yesmaximal, characteristic, complemented
3C19×#3211C211yesmaximal, characteristic, complemented
4C19×#2662C211yesmaximal, characteristic, complemented
5C19×#1606C211yesmaximal, characteristic, complemented
6C19×#1604C211yesmaximal, characteristic, complemented
7C19×#1603C211yesmaximal, characteristic, complemented
8C19×#1601C211yesmaximal, characteristic, complemented
9C19×#1600C211yesmaximal, characteristic, complemented
10C19×#1598C211yesmaximal, characteristic, complemented
11C19×#1597C211yesmaximal, characteristic, complemented
12C19×#1595C211yesmaximal, characteristic, complemented
13C19×#1509C211yesmaximal, characteristic, complemented
14C19×#1502C211yesmaximal, characteristic, complemented
15C19×#1473C211yesmaximal, characteristic, complemented
16C19×#563—21no—
17C19×#560—21no—
18C19×#553—21no—
19C19×#553—21no—
20C19×#551—21no—
21C19×#547—21no—
22C19×#546—21no—
23C19×#546—21no—
24C19×#542—21no—
25C19×#539—21no—
26C19×#539C2211yescharacteristic
27C19×#538—21no—
28C19×#538—21no—
29C19×#538C2211yescharacteristic
30C19×#537C2211yescharacteristic
31C19×#534C2211yescharacteristic
32C19×#532C2211yescharacteristic
33C19×#529C2211yescharacteristic
34C2×C19×#126C2211yescharacteristic
35C2×C19×#124C2211yescharacteristic, complemented
36C19×#496—21no—
37C19×#495—21no—
38C19×#489—21no—
39C19×#488—21no—
40C19×#464—21no—
41C19×#463—21no—
42C19×#463—21no—
43C19×#463—21no—
44C19×#451C2211yescharacteristic, complemented
45C19×#450C2211yescharacteristic, complemented
46C19×#448C2211yescharacteristic
47C19×#448C2211yescharacteristic
48C19×#448C2211yescharacteristic, complemented
49C19×#447C2211yescharacteristic
50C19×#447C2211yescharacteristic
51C19×#447C2211yescharacteristic, complemented
52C19×#432C2211yescharacteristic, complemented
53C19×#431C2211yescharacteristic, complemented
54C19×#396—21no—
55C19×#395C2211yescharacteristic, complemented
56C19×#394—21no—
57C19×#394C2211yescharacteristic, complemented
58C19×#393C2211yescharacteristic
59C19×#392C2211yescharacteristic
60C19×#390—21no—
61C19×#388—21no—
62C4×C4⋊C4×C19C2211yescharacteristic, complemented
63C19×#328C2211yescharacteristic, complemented
64C19×#328C2211yescharacteristic, complemented
65C19×#327C2211yescharacteristic
66C19×#327C2211yescharacteristic
67C19×#327C2211yescharacteristic
68C19×#327C2211yescharacteristic
69C19×#327C2211yescharacteristic, complemented
70C19×#327C2211yescharacteristic, complemented
71C19×#324C2211yescharacteristic, complemented
72C19×#324C2211yescharacteristic, complemented
73C19×#323C2211yescharacteristic
74C19×#323C2211yescharacteristic
75C2×#41×C19—21no—
76C2×#41×C19—21no—
77C22×Q8×C19C2311yescharacteristic
78C22×D4×C19—21no—
79C22×D4×C19—21no—
80C22×D4×C19C2311yescharacteristic
81C2×Q16×C19—21no—
82C2×SD16×C19—21no—
83C2×SD16×C19—21no—
84C2×SD16×C19—21no—
85C2×SD16×C19—21no—
86C2×D8×C19—21no—
87C2×D8×C19—21no—
88C2×D8×C19—21no—
89C19×C4⋊Q8—21no—
90C19×C4⋊Q8D411yescharacteristic, complemented
91C19×#127D411yescharacteristic, complemented
92C19×#126—21no—
93C19×#126—21no—
94C19×#126—21no—
95C19×#126—21no—
96C19×#126—21no—
97C19×#126—21no—
98C19×#126—21no—
99C19×#126—21no—
100C19×#126—21no—
101C19×#125—21no—
102C19×#125—21no—
103C19×#125D411yescharacteristic, complemented
104C19×#124—21no—
105C19×#124—21no—
106C19×#124—21no—
107C19×#124—21no—
108C19×#124—21no—
109C19×#124—21no—
110C19×#124—21no—
111C19×#124—21no—
112C19×#124D411yescharacteristic, complemented
113C19×#123—21no—
114C19×#123—21no—
115C19×#123—21no—
116C19×#123—21no—
117C19×#123—21no—
118C19×#123—21no—
119C19×#123—21no—
120C19×#123—21no—
121C19×#123—21no—
122C19×#123—21no—
123C19×#123—21no—
124C19×#123—21no—
125C19×C22⋊Q8—21no—
126C19×C22⋊Q8—21no—
127C19×C22⋊Q8—21no—
128C19×C22⋊Q8—21no—
129C19×C22⋊Q8—21no—
130C19×C22⋊Q8—21no—
131C19×C22⋊Q8—21no—
132C19×C22⋊Q8C2311yescharacteristic
133C19×#121—21no—
134C19×#121—21no—
135C19×#121—21no—
136C19×#121—21no—
137C19×#121—21no—
138C19×#121—21no—
139C19×#121—21no—
140C19×#121—21no—
141C19×#121—21no—
142C19×#121—21no—
143C19×#121—21no—
144C19×#121—21no—
145C19×#121C2311yescharacteristic
146C19×#121C2311yescharacteristic
147C19×#121C2311yescharacteristic
148C19×#120—21no—
149C19×#120—21no—
150C19×#120—21no—
151C19×#120—21no—
152C19×#120—21no—
153C4×Q8×C19D411yescharacteristic, complemented
154C4×D4×C19—21no—
155C4×D4×C19—21no—
156C4×D4×C19—21no—
157C4×D4×C19—21no—
158C4×D4×C19—21no—
159C4×D4×C19—21no—
160C4×D4×C19—21no—
161C4×D4×C19—21no—
162C4×D4×C19D411yescharacteristic, complemented
163C4×D4×C19D411yescharacteristic, complemented
164C4×D4×C19D411yescharacteristic, complemented
165C19×#117—21no—
166C19×#117—21no—
167C2×C4⋊C4×C19—21no—
168C2×C4⋊C4×C19—21no—
169C2×C4⋊C4×C19—21no—
170C2×C4⋊C4×C19D411yescharacteristic
171C2×C4⋊C4×C19D411yescharacteristic
172C2×C4⋊C4×C19C2311yescharacteristic
173C2×C22⋊C4×C19—21no—
174C2×C22⋊C4×C19—21no—
175C2×C22⋊C4×C19—21no—
176C2×C22⋊C4×C19—21no—
177C2×C22⋊C4×C19—21no—
178C2×C22⋊C4×C19—21no—
179C2×C22⋊C4×C19—21no—
180C2×C22⋊C4×C19—21no—
181C2×C22⋊C4×C19D411yescharacteristic
182C2×C22⋊C4×C19D411yescharacteristic
183C2×C22⋊C4×C19C2311yescharacteristic
184C2×C42×C19—21no—
185C2×C42×C19C2311yescharacteristic
186C19×C4⋊C8—21no—
187C19×C4⋊C8—21no—
188C19×#103—21no—
189C19×#103—21no—
190C19×#103—21no—
191C19×#103—21no—
192C19×#102—21no—
193C19×#102—21no—
194C19×#102—21no—
195C19×#102—21no—
196C19×C22⋊C8C2311yescharacteristic
197C19×C22⋊C8C2311yescharacteristic
198C19×C22⋊C8C2311yescharacteristic
199C19×C22⋊C8C2311yescharacteristic
200C19×#97—21no—
201C4×C8×C19—21no—
202C19×#95—21no—
203C19×#95—21no—
204C19×#95C2311yescharacteristic
205C19×#95C2311yescharacteristic
206C24×C19—21no—
207C24×C19—21no—
208C24×C19C2×D411yescharacteristic
209#41×C19—81no—
210#41×C19—81no—
211#41×C19—81no—
212#41×C19—81no—
213C2×Q8×C19—21no—
214C2×Q8×C19—21no—
215C2×Q8×C19—21no—
216C2×Q8×C19—21no—
217C2×Q8×C19—81no—
218C2×Q8×C19C2×D411yescharacteristic
219C2×D4×C19—21no—
220C2×D4×C19—21no—
221C2×D4×C19—21no—
222C2×D4×C19—21no—
223C2×D4×C19—21no—
224C2×D4×C19—21no—
225C2×D4×C19—21no—
226C2×D4×C19—21no—
227C2×D4×C19—21no—
228C2×D4×C19—21no—
229C2×D4×C19—21no—
230C2×D4×C19—21no—
231C2×D4×C19—21no—
232C2×D4×C19—21no—
233C2×D4×C19—42no—
234C2×D4×C19—81no—
235C2×D4×C19—81no—
236C2×D4×C19—81no—
237C2×D4×C19—81no—
238C2×D4×C19—81no—
239C2×D4×C19C2×D411yescharacteristic
240C2×D4×C19C2×D411yescharacteristic
241C2×D4×C19C2×D411yescharacteristic
242C22×C4×C19—21no—
243C22×C4×C19—21no—
244C22×C4×C19—21no—
245C22×C4×C19—21no—
246C22×C4×C19—21no—
247C22×C4×C19—21no—
248C22×C4×C19—21no—
249C22×C4×C19—21no—
250C22×C4×C19—21no—
251C22×C4×C19—21no—
252C22×C4×C19—21no—
253C22×C4×C19C2×D411yescharacteristic
254C22×C4×C19C2×D411yescharacteristic
255C22×C4×C19C2×D411yescharacteristic
256C22×C4×C19C2×D411yescharacteristic
257C22×C4×C19C2×D411yescharacteristic
258C22×C4×C19C2411yescharacteristic
259Q16×C19—81no—
260SD16×C19—81no—
261SD16×C19—81no—
262SD16×C19—81no—
263SD16×C19—81no—
264D8×C19—81no—
265D8×C19—81no—
266D8×C19—81no—
267C2×C8×C19—21no—
268C2×C8×C19—21no—
269C2×C8×C19—21no—
270C2×C8×C19—21no—
271C4⋊C4×C19—21no—
272C4⋊C4×C19—21no—
273C4⋊C4×C19—21no—
274C4⋊C4×C19—21no—
275C4⋊C4×C19—21no—
276C4⋊C4×C19—21no—
277C4⋊C4×C19—21no—
278C4⋊C4×C19—21no—
279C4⋊C4×C19—21no—
280C4⋊C4×C19—21no—
281C4⋊C4×C19—21no—
282C4⋊C4×C19—21no—
283C4⋊C4×C19—21no—
284C4⋊C4×C19—21no—
285C4⋊C4×C19—21no—
286C4⋊C4×C19—21no—
287C4⋊C4×C19—21no—
288C4⋊C4×C19—42no—
289C4⋊C4×C19—81no—
290C4⋊C4×C19C2×D411yescharacteristic
291C4⋊C4×C19C2×D411yescharacteristic
292C4⋊C4×C19C2×D411yescharacteristic
293C4⋊C4×C19C2×D411yescharacteristic
294C22⋊C4×C19—21no—
295C22⋊C4×C19—21no—
296C22⋊C4×C19—21no—
297C22⋊C4×C19—21no—
298C22⋊C4×C19—21no—
299C22⋊C4×C19—21no—
300C22⋊C4×C19—21no—
301C22⋊C4×C19—21no—
302C22⋊C4×C19—21no—
303C22⋊C4×C19—21no—
304C22⋊C4×C19—21no—
305C22⋊C4×C19—21no—
306C22⋊C4×C19—21no—
307C22⋊C4×C19—21no—
308C22⋊C4×C19—21no—
309C22⋊C4×C19—21no—
310C22⋊C4×C19—21no—
311C22⋊C4×C19—21no—
312C22⋊C4×C19—21no—
313C22⋊C4×C19—21no—
314C22⋊C4×C19—21no—
315C22⋊C4×C19—21no—
316C22⋊C4×C19—21no—
317C22⋊C4×C19—21no—
318C22⋊C4×C19—21no—
319C22⋊C4×C19—42no—
320C22⋊C4×C19—41no—
321C22⋊C4×C19—41no—
322C22⋊C4×C19—41no—
323C22⋊C4×C19—41no—
324C22⋊C4×C19—81no—
325C22⋊C4×C19—81no—
326C22⋊C4×C19—81no—
327C42×C19—21no—
328C42×C19—21no—
329C42×C19—21no—
330C42×C19—81no—
331C42×C19C2×D411yescharacteristic
332C42×C19C2×D411yescharacteristic
333C42×C19C2×D411yescharacteristic
334C42×C19C2×D411yescharacteristic
335#18434C1911yesmaximal, characteristic, direct product factor, Sylow
336C23×C19—21no—
337C23×C19—21no—
338C23×C19—21no—
339C23×C19—21no—
340C23×C19—21no—
341C23×C19—21no—
342C23×C19—41no—
343C23×C19—41no—
344C23×C19—41no—
345C23×C19—41no—
346C23×C19—41no—
347C23×C19—41no—
348C23×C19—41no—
349C23×C19—41no—
350C23×C19—41no—
351C23×C19—81no—
352C23×C19—81no—
353C23×C19—81no—
354C23×C19C22×D411yescharacteristic
355Q8×C19—41no—
356Q8×C19—41no—
357Q8×C19—41no—
358Q8×C19—41no—
359Q8×C19—41no—
360Q8×C19—81no—
361Q8×C19—81no—
362D4×C19—41no—
363D4×C19—41no—
364D4×C19—41no—
365D4×C19—41no—
366D4×C19—41no—
367D4×C19—41no—
368D4×C19—41no—
369D4×C19—41no—
370D4×C19—41no—
371D4×C19—41no—
372D4×C19—41no—
373D4×C19—41no—
374D4×C19—41no—
375D4×C19—81no—
376D4×C19—81no—
377D4×C19—81no—
378D4×C19—81no—
379D4×C19—81no—
380D4×C19—81no—
381D4×C19—81no—
382D4×C19—81no—
383D4×C19—81no—
384D4×C19—84no—
385C2×C4×C19—21no—
386C2×C4×C19—21no—
387C2×C4×C19—22no—
388C2×C4×C19—21no—
389C2×C4×C19—21no—
390C2×C4×C19—21no—
391C2×C4×C19—21no—
392C2×C4×C19—21no—
393C2×C4×C19—21no—
394C2×C4×C19—21no—
395C2×C4×C19—21no—
396C2×C4×C19—21no—
397C2×C4×C19—21no—
398C2×C4×C19—41no—
399C2×C4×C19—41no—
400C2×C4×C19—41no—
401C2×C4×C19—41no—
402C2×C4×C19—41no—
403C2×C4×C19—41no—
404C2×C4×C19—41no—
405C2×C4×C19—41no—
406C2×C4×C19—41no—
407C2×C4×C19—41no—
408C2×C4×C19—41no—
409C2×C4×C19—41no—
410C2×C4×C19—81no—
411C2×C4×C19—81no—
412C2×C4×C19—81no—
413C2×C4×C19—81no—
414C2×C4×C19—81no—
415C2×C4×C19—81no—
416C2×C4×C19—81no—
417C2×C4×C19—81no—
418C2×C4×C19#12011yescharacteristic
419C2×C4×C19#12011yescharacteristic
420C2×C4×C19#12011yescharacteristic
421C2×C4×C19#12011yescharacteristic
422C2×C4×C19C22×D411yescharacteristic
423C2×C4×C19C22×D411yescharacteristic
424C8×C19—41no—
425C8×C19—41no—
426C8×C19—41no—
427C8×C19—41no—
428#3560C2×C1911yescharacteristic, complemented
429#3213C2×C1911yescharacteristic, complemented
430#3211C2×C1911yescharacteristic, complemented
431#2662C2×C1911yescharacteristic, complemented
432#1606C2×C1911yescharacteristic, complemented
433#1604C2×C1911yescharacteristic, complemented
434#1603C2×C1911yescharacteristic, complemented
435#1601C2×C1911yescharacteristic, complemented
436#1600C2×C1911yescharacteristic, complemented
437#1598C2×C1911yescharacteristic, complemented
438#1597C2×C1911yescharacteristic, complemented
439#1595C2×C1911yescharacteristic, complemented
440#1509C2×C1911yescharacteristic, complemented
441#1502C2×C1911yescharacteristic, complemented
442#1473C2×C1911yescharacteristic, complemented
443C22×C19—21no—
444C22×C19—21no—
445C22×C19—41no—
446C22×C19—41no—
447C22×C19—41no—
448C22×C19—41no—
449C22×C19—41no—
450C22×C19—41no—
451C22×C19—41no—
452C22×C19—41no—
453C22×C19—41no—
454C22×C19—41no—
455C22×C19—41no—
456C22×C19—41no—
457C22×C19—81no—
458C22×C19—81no—
459C22×C19—81no—
460C22×C19—81no—
461C22×C19—81no—
462C22×C19—81no—
463C22×C19—81no—
464C22×C19—81no—
465C22×C19—81no—
466C22×C19—162no—
467C22×C19C2×#12011yescharacteristic
468C22×C19#57611yescharacteristic
469C22×C19#57711yescharacteristic
470C4×C19—21no—
471C4×C19—21no—
472C4×C19—21no—
473C4×C19—21no—
474C4×C19—21no—
475C4×C19—21no—
476C4×C19—42no—
477C4×C19—41no—
478C4×C19—41no—
479C4×C19—41no—
480C4×C19—41no—
481C4×C19—41no—
482C4×C19—41no—
483C4×C19—41no—
484C4×C19—41no—
485C4×C19—81no—
486C4×C19—81no—
487#563—21no—
488#560—21no—
489#553—21no—
490#553—21no—
491#551—21no—
492#547—21no—
493#546—21no—
494#546—21no—
495#542—21no—
496#539—21no—
497#539C22×C1911yescharacteristic
498#538—21no—
499#538—21no—
500#538C22×C1911yescharacteristic
501#537C22×C1911yescharacteristic
502#534C22×C1911yescharacteristic
503#532C22×C1911yescharacteristic
504#529C22×C1911yescharacteristic
505C2×#126C22×C1911yescharacteristic
506C2×#124C22×C1911yescharacteristic, complemented
507#496—21no—
508#495—21no—
509#489—21no—
510#488—21no—
511#464—21no—
512#463—21no—
513#463—21no—
514#463—21no—
515#451C22×C1911yescharacteristic, complemented
516#450C22×C1911yescharacteristic, complemented
517#448C22×C1911yescharacteristic
518#448C22×C1911yescharacteristic
519#448C22×C1911yescharacteristic, complemented
520#447C22×C1911yescharacteristic
521#447C22×C1911yescharacteristic
522#447C22×C1911yescharacteristic, complemented
523#432C22×C1911yescharacteristic, complemented
524#431C22×C1911yescharacteristic, complemented
525#396—21no—
526#395C22×C1911yescharacteristic, complemented
527#394—21no—
528#394C22×C1911yescharacteristic, complemented
529#393C22×C1911yescharacteristic
530#392C22×C1911yescharacteristic
531#390—21no—
532#388—21no—
533C4×C4⋊C4C22×C1911yescharacteristic, complemented
534#328C22×C1911yescharacteristic, complemented
535#328C22×C1911yescharacteristic, complemented
536#327C22×C1911yescharacteristic
537#327C22×C1911yescharacteristic
538#327C22×C1911yescharacteristic
539#327C22×C1911yescharacteristic
540#327C22×C1911yescharacteristic, complemented
541#327C22×C1911yescharacteristic, complemented
542#324C22×C1911yescharacteristic, complemented
543#324C22×C1911yescharacteristic, complemented
544#323C22×C1911yescharacteristic
545#323C22×C1911yescharacteristic
546C2×C19—21no—
547C2×C19—21no—
548C2×C19—81no—
549C2×C19—81no—
550C2×C19—81no—
551C2×C19—81no—
552C2×C19—161no—
553C2×C19#301211yescharacteristic
554C2×C19#301811yescharacteristic
555C2×C19#302711yescharacteristic
556C2×#41—21no—
557C2×#41—21no—
558C22×Q8C23×C1911yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4C23×C1911yescharacteristic
562C2×Q16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×D8—21no—
568C2×D8—21no—
569C2×D8—21no—
570C4⋊Q8—21no—
571C4⋊Q8D4×C1911yescharacteristic, complemented
572#127D4×C1911yescharacteristic, complemented
573#126—21no—
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#125—21no—
583#125—21no—
584#125D4×C1911yescharacteristic, complemented
585#124—21no—
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124D4×C1911yescharacteristic, complemented
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C23×C1911yescharacteristic
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121C23×C1911yescharacteristic
627#121C23×C1911yescharacteristic
628#121C23×C1911yescharacteristic
629#120—21no—
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634C4×Q8D4×C1911yescharacteristic, complemented
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4D4×C1911yescharacteristic, complemented
644C4×D4D4×C1911yescharacteristic, complemented
645C4×D4D4×C1911yescharacteristic, complemented
646#117—21no—
647#117—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4D4×C1911yescharacteristic
652C2×C4⋊C4D4×C1911yescharacteristic
653C2×C4⋊C4C23×C1911yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C1911yescharacteristic
663C2×C22⋊C4D4×C1911yescharacteristic
664C2×C22⋊C4C23×C1911yescharacteristic
665C2×C42—21no—
666C2×C42C23×C1911yescharacteristic
667C4⋊C8—21no—
668C4⋊C8—21no—
669#103—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#102—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677C22⋊C8C23×C1911yescharacteristic
678C22⋊C8C23×C1911yescharacteristic
679C22⋊C8C23×C1911yescharacteristic
680C22⋊C8C23×C1911yescharacteristic
681#97—21no—
682C4×C8—21no—
683#95—21no—
684#95—21no—
685#95C23×C1911yescharacteristic
686#95C23×C1911yescharacteristic
687C19#1843411yescharacteristic, direct product factor, Sylow
688C24—21no—
689C24—21no—
690C24C2×D4×C1911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C1911yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C1911yescharacteristic
722C2×D4C2×D4×C1911yescharacteristic
723C2×D4C2×D4×C1911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C1911yescharacteristic
736C22×C4C2×D4×C1911yescharacteristic
737C22×C4C2×D4×C1911yescharacteristic
738C22×C4C2×D4×C1911yescharacteristic
739C22×C4C2×D4×C1911yescharacteristic
740C22×C4C24×C1911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C1911yescharacteristic
773C4⋊C4C2×D4×C1911yescharacteristic
774C4⋊C4C2×D4×C1911yescharacteristic
775C4⋊C4C2×D4×C1911yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C1911yescharacteristic
814C42C2×D4×C1911yescharacteristic
815C42C2×D4×C1911yescharacteristic
816C42C2×D4×C1911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C1911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4C19×#12011yescharacteristic
900C2×C4C19×#12011yescharacteristic
901C2×C4C19×#12011yescharacteristic
902C2×C4C19×#12011yescharacteristic
903C2×C4C22×D4×C1911yescharacteristic
904C2×C4C22×D4×C1911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×C19×#12011yescharacteristic
934C22C19×#57611yescharacteristic
935C22C19×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C19×#301211yescharacteristic
961C2C19×#301811yescharacteristic
962C2C19×#302711yescharacteristic
subgroupG/H
center, socleC22×C19C2×#120
commutator, Frattini, cosocleC22×C4C24×C19
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3560C2semidirect
2. C19×#3213C2semidirect
3. C19×#3211C2semidirect
4. C19×#2662C2semidirect
5. C19×#1606C2semidirect
6. C19×#1604C2semidirect
7. C19×#1603C2semidirect
8. C19×#1601C2semidirect
9. C19×#1600C2semidirect
10. C19×#1598C2semidirect
11. C19×#1597C2semidirect
12. C19×#1595C2semidirect
13. C19×#1509C2semidirect
14. C19×#1502C2semidirect
15. C19×#1473C2semidirect
35. C2×C19×#124C22semidirect
44. C19×#451C22semidirect
45. C19×#450C22semidirect
48. C19×#448C22semidirect
51. C19×#447C22semidirect
52. C19×#432C22semidirect
53. C19×#431C22semidirect
55. C19×#395C22semidirect
57. C19×#394C22semidirect
62. C4×C4⋊C4×C19C22semidirect
63. C19×#328C22semidirect
64. C19×#328C22semidirect
69. C19×#327C22semidirect
70. C19×#327C22semidirect
71. C19×#324C22semidirect
72. C19×#324C22semidirect
90. C19×C4⋊Q8D4semidirect
91. C19×#127D4semidirect
103. C19×#125D4semidirect
112. C19×#124D4semidirect
153. C4×Q8×C19D4semidirect
162. C4×D4×C19D4semidirect
163. C4×D4×C19D4semidirect
164. C4×D4×C19D4semidirect
335. #18434C19direct (N × H)
428. #3560C2×C19semidirect
429. #3213C2×C19semidirect
430. #3211C2×C19semidirect
431. #2662C2×C19semidirect
432. #1606C2×C19semidirect
433. #1604C2×C19semidirect
434. #1603C2×C19semidirect
435. #1601C2×C19semidirect
436. #1600C2×C19semidirect
437. #1598C2×C19semidirect
438. #1597C2×C19semidirect
439. #1595C2×C19semidirect
440. #1509C2×C19semidirect
441. #1502C2×C19semidirect
442. #1473C2×C19semidirect
506. C2×#124C22×C19semidirect
515. #451C22×C19semidirect
516. #450C22×C19semidirect
519. #448C22×C19semidirect
522. #447C22×C19semidirect
523. #432C22×C19semidirect
524. #431C22×C19semidirect
526. #395C22×C19semidirect
528. #394C22×C19semidirect
533. C4×C4⋊C4C22×C19semidirect
534. #328C22×C19semidirect
535. #328C22×C19semidirect
540. #327C22×C19semidirect
541. #327C22×C19semidirect
542. #324C22×C19semidirect
543. #324C22×C19semidirect
571. C4⋊Q8D4×C19semidirect
572. #127D4×C19semidirect
584. #125D4×C19semidirect
593. #124D4×C19semidirect
634. C4×Q8D4×C19semidirect
643. C4×D4D4×C19semidirect
644. C4×D4D4×C19semidirect
645. C4×D4D4×C19semidirect
687. C19#18434direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35602
C19×#32132
C19×#32112
C19×#26622
C19×#16062
C19×#16042
C19×#16032
C19×#16012
C19×#16002
C19×#15982
C19×#15972
C19×#15952
C19×#15092
C19×#15022
C19×#14732
#1843419