Finite Group Databasebeta

← C19×#13347 #18019306

Subgroups — C19×#13347 #18019306

Order 4864.

830 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#458C211yesmaximal, characteristic, complemented
2C2×C19×#453C211yesmaximal, characteristic
3C19×#2709C211yesmaximal, characteristic, complemented
4C2×C19×#353C211yesmaximal, characteristic, complemented
5C2×C19×#352C211yesmaximal, characteristic, complemented
6C19×#1790C211yesmaximal, characteristic, complemented
7C19×#1390C211yesmaximal, characteristic, complemented
8C2×C19×H(5,𝔽2)C2211yescharacteristic
9C2×C19×AGL(1,ℤ/8)—21no—
10C2×C19×#127C2211yescharacteristic
11C2×C19×#123—21no—
12C2×C19×#123C2211yescharacteristic
13C19×#458—22no—
14C19×#458—22no—
15C19×#453—22no—
16C19×#453—22no—
17C2×C19×#104—21no—
18C2×C19×#100C2211yescharacteristic
19C2×C19×#99—21no—
20C2×C19×#99—21no—
21C2×C19×#99C2211yescharacteristic
22C2×C19×#99C2211yescharacteristic
23C19×#394—21no—
24C19×#394—21no—
25C19×#394—21no—
26C19×#387—21no—
27C19×#386—21no—
28C19×#386—21no—
29C19×#386—21no—
30C19×#386C2211yescharacteristic
31C19×#353—22no—
32C19×#352—22no—
33C19×H(5,𝔽2)—21no—
34C19×H(5,𝔽2)—21no—
35C19×H(5,𝔽2)—21no—
36C19×H(5,𝔽2)—42no—
37C19×H(5,𝔽2)D412yes—
38C2×#41×C19—21no—
39C2×#41×C19—41no—
40C22×D4×C19—21no—
41C22×D4×C19—21no—
42C22×D4×C19—21no—
43C22×D4×C19—21no—
44C22×D4×C19—41no—
45C22×D4×C19D411yescharacteristic
46C22×D4×C19C2311yescharacteristic
47C23×C4×C19D411yescharacteristic
48C23×C4×C19D411yescharacteristic
49C19×AGL(1,ℤ/8)—24no—
50C19×AGL(1,ℤ/8)—42no—
51C2×SD16×C19—41no—
52C2×D8×C19—41no—
53C2×M16×C19—21no—
54C19×#127—21no—
55C19×#127—21no—
56C19×#127—21no—
57C19×#127—21no—
58C19×#123—24no—
59C19×#123—21no—
60C19×#123—21no—
61C19×#123—21no—
62C19×#123—21no—
63C19×#123—42no—
64C2×C4⋊C4×C19—21no—
65C2×C4⋊C4×C19—21no—
66C2×C4⋊C4×C19—41no—
67C2×C22⋊C4×C19—21no—
68C2×C22⋊C4×C19—21no—
69C2×C22⋊C4×C19—21no—
70C2×C22⋊C4×C19—21no—
71C2×C22⋊C4×C19—21no—
72C2×C22⋊C4×C19—21no—
73C2×C22⋊C4×C19—21no—
74C2×C22⋊C4×C19—21no—
75C2×C22⋊C4×C19—41no—
76C2×C22⋊C4×C19—41no—
77C2×C22⋊C4×C19D411yescharacteristic
78C2×C22⋊C4×C19D411yescharacteristic
79C2×C42×C19D411yescharacteristic
80C19×#104—24no—
81C19×#100—21no—
82C19×#100D412yes—
83C19×#99—24no—
84C19×#99—21no—
85C19×#99—21no—
86C19×#99—21no—
87C19×#99—42no—
88C19×#99D412yes—
89C19×#95—21no—
90C19×#95—21no—
91C19×#95—21no—
92C19×#95—21no—
93C19×#95—41no—
94C24×C19—21no—
95C24×C19—21no—
96C24×C19—21no—
97C24×C19C2×D411yescharacteristic
98C24×C19C2×D411yescharacteristic
99#41×C19—22no—
100#41×C19—22no—
101#41×C19—42no—
102#41×C19—41no—
103#41×C19—42no—
104#41×C19—42no—
105#41×C19—42no—
106#41×C19—41no—
107C2×Q8×C19—21no—
108C2×D4×C19—21no—
109C2×D4×C19—22no—
110C2×D4×C19—22no—
111C2×D4×C19—22no—
112C2×D4×C19—22no—
113C2×D4×C19—21no—
114C2×D4×C19—21no—
115C2×D4×C19—41no—
116C2×D4×C19—41no—
117C2×D4×C19—41no—
118C2×D4×C19—41no—
119C2×D4×C19—42no—
120C2×D4×C19—42no—
121C2×D4×C19—42no—
122C2×D4×C19—42no—
123C2×D4×C19—41no—
124C2×D4×C19—41no—
125C2×D4×C19—41no—
126C2×D4×C19—41no—
127C2×D4×C19—42no—
128C2×D4×C19—42no—
129C2×D4×C19—41no—
130C2×D4×C19—41no—
131C2×D4×C19—41no—
132C2×D4×C19—41no—
133C2×D4×C19—41no—
134C2×D4×C19—41no—
135C2×D4×C19—41no—
136C2×D4×C19—81no—
137C2×D4×C19—81no—
138C2×D4×C19C2×D411yescharacteristic
139C2×D4×C19C2×D411yescharacteristic
140C2×D4×C19C2×D411yescharacteristic
141C2×D4×C19#4111yescharacteristic
142C22×C4×C19—21no—
143C22×C4×C19—21no—
144C22×C4×C19—21no—
145C22×C4×C19—21no—
146C22×C4×C19—21no—
147C22×C4×C19—21no—
148C22×C4×C19—21no—
149C22×C4×C19—21no—
150C22×C4×C19—21no—
151C22×C4×C19—41no—
152C22×C4×C19—41no—
153C22×C4×C19—41no—
154C22×C4×C19—41no—
155C22×C4×C19—41no—
156C22×C4×C19—41no—
157C22×C4×C19—81no—
158C22×C4×C19C2×D411yescharacteristic
159SD16×C19—44no—
160D8×C19—44no—
161M16×C19—22no—
162M16×C19—41no—
163C2×C8×C19—41no—
164C4⋊C4×C19—42no—
165C4⋊C4×C19—44no—
166C4⋊C4×C19—41no—
167C4⋊C4×C19—41no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C22⋊C4×C19—41no—
172C22⋊C4×C19—44no—
173C22⋊C4×C19—41no—
174C22⋊C4×C19—41no—
175C22⋊C4×C19—41no—
176C22⋊C4×C19—41no—
177C22⋊C4×C19—41no—
178C22⋊C4×C19—81no—
179C22⋊C4×C19—81no—
180C22⋊C4×C19—81no—
181C22⋊C4×C19—81no—
182C22⋊C4×C19—81no—
183C22⋊C4×C19—82no—
184C42×C19—21no—
185C42×C19—21no—
186#13347C1911yesmaximal, characteristic, direct product factor, Sylow
187C23×C19—21no—
188C23×C19—21no—
189C23×C19—21no—
190C23×C19—21no—
191C23×C19—22no—
192C23×C19—22no—
193C23×C19—41no—
194C23×C19—41no—
195C23×C19—41no—
196C23×C19—41no—
197C23×C19—41no—
198C23×C19—41no—
199C23×C19—41no—
200C23×C19—41no—
201C23×C19—41no—
202C23×C19—41no—
203C23×C19—41no—
204C23×C19—41no—
205C23×C19—41no—
206C23×C19—41no—
207C23×C19—81no—
208C23×C19—81no—
209C23×C19—81no—
210C23×C19—81no—
211C23×C19#12011yescharacteristic
212C23×C19#12011yescharacteristic
213C23×C19#12111yescharacteristic
214C23×C19#12111yescharacteristic
215C23×C19#12711yescharacteristic
216Q8×C19—22no—
217Q8×C19—41no—
218D4×C19—22no—
219D4×C19—41no—
220D4×C19—41no—
221D4×C19—41no—
222D4×C19—41no—
223D4×C19—41no—
224D4×C19—42no—
225D4×C19—42no—
226D4×C19—42no—
227D4×C19—42no—
228D4×C19—42no—
229D4×C19—42no—
230D4×C19—42no—
231D4×C19—81no—
232D4×C19—82no—
233D4×C19—82no—
234D4×C19—82no—
235D4×C19—82no—
236C2×C4×C19—21no—
237C2×C4×C19—21no—
238C2×C4×C19—22no—
239C2×C4×C19—22no—
240C2×C4×C19—22no—
241C2×C4×C19—42no—
242C2×C4×C19—42no—
243C2×C4×C19—41no—
244C2×C4×C19—41no—
245C2×C4×C19—41no—
246C2×C4×C19—41no—
247C2×C4×C19—41no—
248C2×C4×C19—42no—
249C2×C4×C19—42no—
250C2×C4×C19—41no—
251C2×C4×C19—41no—
252C2×C4×C19—41no—
253C2×C4×C19—41no—
254C2×C4×C19—41no—
255C2×C4×C19—41no—
256C2×C4×C19—42no—
257C2×C4×C19—41no—
258C2×C4×C19—41no—
259C2×C4×C19—41no—
260C2×C4×C19—41no—
261C2×C4×C19—41no—
262C2×C4×C19—41no—
263C2×C4×C19—81no—
264C2×C4×C19—81no—
265C2×C4×C19—81no—
266C2×C4×C19—81no—
267C2×C4×C19—81no—
268C2×C4×C19—81no—
269C2×C4×C19—81no—
270C2×C4×C19#12011yescharacteristic
271C2×C4×C19#12111yescharacteristic
272C8×C19—42no—
273C2×#458C2×C1911yescharacteristic, complemented
274C2×#453C2×C1911yescharacteristic
275#2709C2×C1911yescharacteristic, complemented
276C2×#353C2×C1911yescharacteristic, complemented
277C2×#352C2×C1911yescharacteristic, complemented
278#1790C2×C1911yescharacteristic, complemented
279#1390C2×C1911yescharacteristic, complemented
280C22×C19—21no—
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
284C22×C19—21no—
285C22×C19—21no—
286C22×C19—41no—
287C22×C19—41no—
288C22×C19—41no—
289C22×C19—41no—
290C22×C19—41no—
291C22×C19—41no—
292C22×C19—41no—
293C22×C19—41no—
294C22×C19—42no—
295C22×C19—81no—
296C22×C19—81no—
297C22×C19—81no—
298C22×C19—81no—
299C22×C19—81no—
300C22×C19—81no—
301C22×C19—82no—
302C22×C19—82no—
303C22×C19—81no—
304C22×C19—81no—
305C22×C19—81no—
306C22×C19—81no—
307C22×C19—81no—
308C22×C19—161no—
309C22×C19—161no—
310C22×C19#39211yescharacteristic
311C22×C19B(4,𝔽2)11yescharacteristic
312C22×C19B(4,𝔽2)11yescharacteristic
313C4×C19—21no—
314C4×C19—21no—
315C4×C19—42no—
316C4×C19—42no—
317C4×C19—81no—
318C4×C19—81no—
319C4×C19—82no—
320C4×C19—81no—
321C4×C19—81no—
322C4×C19—161no—
323C2×H(5,𝔽2)C22×C1911yescharacteristic
324C2×AGL(1,ℤ/8)—21no—
325C2×#127C22×C1911yescharacteristic
326C2×#123—21no—
327C2×#123C22×C1911yescharacteristic
328#458—22no—
329#458—22no—
330#453—22no—
331#453—22no—
332C2×#104—21no—
333C2×#100C22×C1911yescharacteristic
334C2×#99—21no—
335C2×#99—21no—
336C2×#99C22×C1911yescharacteristic
337C2×#99C22×C1911yescharacteristic
338#394—21no—
339#394—21no—
340#394—21no—
341#387—21no—
342#386—21no—
343#386—21no—
344#386—21no—
345#386C22×C1911yescharacteristic
346#353—22no—
347#352—22no—
348C2×C19—21no—
349C2×C19—21no—
350C2×C19—41no—
351C2×C19—41no—
352C2×C19—41no—
353C2×C19—41no—
354C2×C19—82no—
355C2×C19—161no—
356C2×C19#202111yescharacteristic
357C2×C19#219811yescharacteristic
358C2×C19#220011yescharacteristic
359H(5,𝔽2)—21no—
360H(5,𝔽2)—21no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—42no—
363H(5,𝔽2)D4×C1912yes—
364C2×#41—21no—
365C2×#41—41no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—41no—
371C22×D4D4×C1911yescharacteristic
372C22×D4C23×C1911yescharacteristic
373C23×C4D4×C1911yescharacteristic
374C23×C4D4×C1911yescharacteristic
375AGL(1,ℤ/8)—24no—
376AGL(1,ℤ/8)—42no—
377C2×SD16—41no—
378C2×D8—41no—
379C2×M16—21no—
380#127—21no—
381#127—21no—
382#127—21no—
383#127—21no—
384#123—24no—
385#123—21no—
386#123—21no—
387#123—21no—
388#123—21no—
389#123—42no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—41no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4D4×C1911yescharacteristic
404C2×C22⋊C4D4×C1911yescharacteristic
405C2×C42D4×C1911yescharacteristic
406#104—24no—
407#100—21no—
408#100D4×C1912yes—
409#99—24no—
410#99—21no—
411#99—21no—
412#99—21no—
413#99—42no—
414#99D4×C1912yes—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—41no—
420C19#1334711yescharacteristic, direct product factor, Sylow
421C24—21no—
422C24—21no—
423C24—21no—
424C24C2×D4×C1911yescharacteristic
425C24C2×D4×C1911yescharacteristic
426#41—22no—
427#41—22no—
428#41—42no—
429#41—41no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—41no—
434C2×Q8—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4C2×D4×C1911yescharacteristic
466C2×D4C2×D4×C1911yescharacteristic
467C2×D4C2×D4×C1911yescharacteristic
468C2×D4#41×C1911yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—81no—
485C22×C4C2×D4×C1911yescharacteristic
486SD16—44no—
487D8—44no—
488M16—22no—
489M16—41no—
490C2×C8—41no—
491C4⋊C4—42no—
492C4⋊C4—44no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—44no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—82no—
511C42—21no—
512C42—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23C19×#12011yescharacteristic
538C23C19×#12011yescharacteristic
539C23C19×#12111yescharacteristic
540C23C19×#12111yescharacteristic
541C23C19×#12711yescharacteristic
542Q8—22no—
543Q8—41no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—81no—
558D4—82no—
559D4—82no—
560D4—82no—
561D4—82no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4C19×#12011yescharacteristic
597C2×C4C19×#12111yescharacteristic
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—82no—
621C22—82no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C19×#39211yescharacteristic
630C22C19×B(4,𝔽2)11yescharacteristic
631C22C19×B(4,𝔽2)11yescharacteristic
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—81no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4—161no—
642C2—21no—
643C2—21no—
644C2—41no—
645C2—41no—
646C2—41no—
647C2—41no—
648C2—82no—
649C2—161no—
650C2C19×#202111yescharacteristic
651C2C19×#219811yescharacteristic
652C2C19×#220011yescharacteristic
subgroupG/H
center, socleC22×C19B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C19
prime radicalC2×C19×#453C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C19 ◁ C22×D4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C19×#458C2semidirect
3. C19×#2709C2semidirect
4. C2×C19×#353C2semidirect
5. C2×C19×#352C2semidirect
6. C19×#1790C2semidirect
7. C19×#1390C2semidirect
186. #13347C19direct (N × H)
273. C2×#458C2×C19semidirect
275. #2709C2×C19semidirect
276. C2×#353C2×C19semidirect
277. C2×#352C2×C19semidirect
278. #1790C2×C19semidirect
279. #1390C2×C19semidirect
420. C19#13347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#4582
C2×C19×#4532
C19×#27092
C2×C19×#3532
C2×C19×#3522
C19×#17902
C19×#13902
#1334719