Finite Group Databasebeta

← C19×#13376 #18019335

Subgroups — C19×#13376 #18019335

Order 4864.

640 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C19×#2748C211yesmaximal, characteristic, complemented
2C19×#1792C211yesmaximal, characteristic
3C19×#1790C211yesmaximal, characteristic
4C19×#1790C211yesmaximal, characteristic
5C19×#1393C211yesmaximal, characteristic, complemented
6C19×#1390C211yesmaximal, characteristic, complemented
7C19×#1390C211yesmaximal, characteristic, complemented
8C2×C19×H(5,𝔽2)C2211yescharacteristic
9C2×C19×#104—21no—
10C19×#417—21no—
11C2×C19×#100C2211yescharacteristic
12C2×C19×#99—21no—
13C2×C19×#99—21no—
14C2×C19×#99C2211yescharacteristic
15C2×C19×#99C2211yescharacteristic
16C19×#399—21no—
17C19×#398—21no—
18C19×#396—21no—
19C19×#390C2211yescharacteristic
20C19×#387—21no—
21C19×#386—21no—
22C19×#386—21no—
23C19×#386C2211yescharacteristic
24C19×#386C2211yescharacteristic
25C19×#385—21no—
26C19×#380—21no—
27C19×H(5,𝔽2)—21no—
28C19×H(5,𝔽2)—21no—
29C19×H(5,𝔽2)—21no—
30C19×H(5,𝔽2)—42no—
31C19×H(5,𝔽2)Q812yes—
32C2×#41×C19—21no—
33C2×#41×C19—41no—
34C22×D4×C19—21no—
35C22×D4×C19—21no—
36C22×D4×C19—41no—
37C22×D4×C19C2311yescharacteristic
38C23×C4×C19D411yescharacteristic
39C23×C4×C19D411yescharacteristic
40C2×M16×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C22⋊C4×C19—41no—
54C2×C22⋊C4×C19—41no—
55C2×C22⋊C4×C19D411yescharacteristic
56C2×C22⋊C4×C19D411yescharacteristic
57C2×C42×C19D411yescharacteristic
58C19×#104—42no—
59C19×#103—41no—
60C19×#102—41no—
61C19×#100—21no—
62C19×#100—21no—
63C19×#99—21no—
64C19×#99—21no—
65C19×#99—21no—
66C19×#99—21no—
67C19×#99—42no—
68C19×#99—42no—
69C19×#95—21no—
70C19×#95—21no—
71C19×#95—21no—
72C19×#95—21no—
73C19×#95—21no—
74C19×#95—41no—
75C19×#95—41no—
76C24×C19—21no—
77C24×C19—21no—
78C24×C19C2×D411yescharacteristic
79C24×C19C2×D411yescharacteristic
80#41×C19—22no—
81#41×C19—22no—
82#41×C19—42no—
83#41×C19—41no—
84#41×C19—42no—
85#41×C19—42no—
86#41×C19—42no—
87#41×C19—41no—
88C2×Q8×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—22no—
91C2×D4×C19—22no—
92C2×D4×C19—22no—
93C2×D4×C19—22no—
94C2×D4×C19—41no—
95C2×D4×C19—41no—
96C2×D4×C19—42no—
97C2×D4×C19—42no—
98C2×D4×C19—41no—
99C2×D4×C19—41no—
100C2×D4×C19—41no—
101C2×D4×C19—41no—
102C2×D4×C19—42no—
103C2×D4×C19—42no—
104C2×D4×C19—41no—
105C2×D4×C19—41no—
106C2×D4×C19—41no—
107C2×D4×C19C2×Q811yescharacteristic
108C2×D4×C19#4111yescharacteristic
109C2×D4×C19#4111yescharacteristic
110C2×D4×C19#4111yescharacteristic
111C22×C4×C19—21no—
112C22×C4×C19—21no—
113C22×C4×C19—21no—
114C22×C4×C19—21no—
115C22×C4×C19—21no—
116C22×C4×C19—21no—
117C22×C4×C19—21no—
118C22×C4×C19—21no—
119C22×C4×C19—41no—
120C22×C4×C19—42no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19—41no—
125C22×C4×C19—81no—
126C22×C4×C19C2×D411yescharacteristic
127M16×C19—41no—
128M16×C19—41no—
129C2×C8×C19—41no—
130C4⋊C4×C19—41no—
131C4⋊C4×C19—42no—
132C4⋊C4×C19—81no—
133C4⋊C4×C19—81no—
134C4⋊C4×C19—81no—
135C4⋊C4×C19—81no—
136C22⋊C4×C19—42no—
137C22⋊C4×C19—41no—
138C22⋊C4×C19—41no—
139C22⋊C4×C19—41no—
140C22⋊C4×C19—41no—
141C22⋊C4×C19—41no—
142C22⋊C4×C19—41no—
143C22⋊C4×C19—81no—
144C22⋊C4×C19—81no—
145C22⋊C4×C19—81no—
146C22⋊C4×C19—82no—
147C22⋊C4×C19—82no—
148C42×C19—41no—
149#13376C1911yesmaximal, characteristic, direct product factor, Sylow
150C23×C19—21no—
151C23×C19—21no—
152C23×C19—21no—
153C23×C19—21no—
154C23×C19—22no—
155C23×C19—22no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—41no—
162C23×C19—41no—
163C23×C19—81no—
164C23×C19—81no—
165C23×C19—81no—
166C23×C19—81no—
167C23×C19#12011yescharacteristic
168C23×C19C22⋊Q811yescharacteristic
169C23×C19C22⋊Q811yescharacteristic
170C23×C19#12411yescharacteristic
171C23×C19#12411yescharacteristic
172Q8×C19—22no—
173Q8×C19—41no—
174D4×C19—22no—
175D4×C19—41no—
176D4×C19—41no—
177D4×C19—41no—
178D4×C19—41no—
179D4×C19—41no—
180D4×C19—42no—
181D4×C19—42no—
182D4×C19—42no—
183D4×C19—42no—
184D4×C19—42no—
185D4×C19—42no—
186C2×C4×C19—21no—
187C2×C4×C19—21no—
188C2×C4×C19—22no—
189C2×C4×C19—22no—
190C2×C4×C19—22no—
191C2×C4×C19—42no—
192C2×C4×C19—42no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—41no—
198C2×C4×C19—42no—
199C2×C4×C19—41no—
200C2×C4×C19—41no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—41no—
208C2×C4×C19—41no—
209C2×C4×C19—42no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—81no—
216C2×C4×C19—81no—
217C2×C4×C19—81no—
218C2×C4×C19—81no—
219C2×C4×C19—81no—
220C2×C4×C19—81no—
221C2×C4×C19—81no—
222C2×C4×C19—81no—
223C2×C4×C19C22⋊Q811yescharacteristic
224C2×C4×C19#12411yescharacteristic
225C8×C19—81no—
226#2748C2×C1911yescharacteristic, complemented
227#1792C2×C1911yescharacteristic
228#1790C2×C1911yescharacteristic
229#1790C2×C1911yescharacteristic
230#1393C2×C1911yescharacteristic, complemented
231#1390C2×C1911yescharacteristic, complemented
232#1390C2×C1911yescharacteristic, complemented
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—41no—
240C22×C19—41no—
241C22×C19—41no—
242C22×C19—41no—
243C22×C19—41no—
244C22×C19—41no—
245C22×C19—41no—
246C22×C19—41no—
247C22×C19—42no—
248C22×C19—81no—
249C22×C19—81no—
250C22×C19—82no—
251C22×C19—82no—
252C22×C19—81no—
253C22×C19—81no—
254C22×C19—161no—
255C22×C19—161no—
256C22×C19#39311yescharacteristic
257C22×C19B(4,𝔽2)11yescharacteristic
258C22×C19B(4,𝔽2)11yescharacteristic
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—42no—
262C4×C19—42no—
263C4×C19—81no—
264C4×C19—81no—
265C4×C19—81no—
266C4×C19—81no—
267C4×C19—81no—
268C4×C19—161no—
269C4×C19—161no—
270C2×H(5,𝔽2)C22×C1911yescharacteristic
271C2×#104—21no—
272#417—21no—
273C2×#100C22×C1911yescharacteristic
274C2×#99—21no—
275C2×#99—21no—
276C2×#99C22×C1911yescharacteristic
277C2×#99C22×C1911yescharacteristic
278#399—21no—
279#398—21no—
280#396—21no—
281#390C22×C1911yescharacteristic
282#387—21no—
283#386—21no—
284#386—21no—
285#386C22×C1911yescharacteristic
286#386C22×C1911yescharacteristic
287#385—21no—
288#380—21no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—41no—
292C2×C19—41no—
293C2×C19—41no—
294C2×C19—41no—
295C2×C19—82no—
296C2×C19#202911yescharacteristic
297C2×C19#219711yescharacteristic
298C2×C19#220011yescharacteristic
299H(5,𝔽2)—21no—
300H(5,𝔽2)—21no—
301H(5,𝔽2)—21no—
302H(5,𝔽2)—42no—
303H(5,𝔽2)Q8×C1912yes—
304C2×#41—21no—
305C2×#41—41no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—41no—
309C22×D4C23×C1911yescharacteristic
310C23×C4D4×C1911yescharacteristic
311C23×C4D4×C1911yescharacteristic
312C2×M16—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4D4×C1911yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4D4×C1911yescharacteristic
328C2×C22⋊C4D4×C1911yescharacteristic
329C2×C42D4×C1911yescharacteristic
330#104—42no—
331#103—41no—
332#102—41no—
333#100—21no—
334#100—21no—
335#99—21no—
336#99—21no—
337#99—21no—
338#99—21no—
339#99—42no—
340#99—42no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—41no—
347#95—41no—
348C19#1337611yescharacteristic, direct product factor, Sylow
349C24—21no—
350C24—21no—
351C24C2×D4×C1911yescharacteristic
352C24C2×D4×C1911yescharacteristic
353#41—22no—
354#41—22no—
355#41—42no—
356#41—41no—
357#41—42no—
358#41—42no—
359#41—42no—
360#41—41no—
361C2×Q8—21no—
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4C2×Q8×C1911yescharacteristic
381C2×D4#41×C1911yescharacteristic
382C2×D4#41×C1911yescharacteristic
383C2×D4#41×C1911yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—81no—
399C22×C4C2×D4×C1911yescharacteristic
400M16—41no—
401M16—41no—
402C2×C8—41no—
403C4⋊C4—41no—
404C4⋊C4—42no—
405C4⋊C4—81no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C4⋊C4—81no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C22⋊C4—82no—
420C22⋊C4—82no—
421C42—41no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—81no—
436C23—81no—
437C23—81no—
438C23—81no—
439C23C19×#12011yescharacteristic
440C23C19×C22⋊Q811yescharacteristic
441C23C19×C22⋊Q811yescharacteristic
442C23C19×#12411yescharacteristic
443C23C19×#12411yescharacteristic
444Q8—22no—
445Q8—41no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4C19×C22⋊Q811yescharacteristic
496C2×C4C19×#12411yescharacteristic
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22—81no—
518C22—81no—
519C22—161no—
520C22—161no—
521C22C19×#39311yescharacteristic
522C22C19×B(4,𝔽2)11yescharacteristic
523C22C19×B(4,𝔽2)11yescharacteristic
524C4—21no—
525C4—21no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—161no—
534C4—161no—
535C2—21no—
536C2—21no—
537C2—41no—
538C2—41no—
539C2—41no—
540C2—41no—
541C2—82no—
542C2C19×#202911yescharacteristic
543C2C19×#219711yescharacteristic
544C2C19×#220011yescharacteristic
subgroupG/H
center, socleC22×C19B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C19
prime radicalC2×C19×H(5,𝔽2)C22
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. C19×#2748C2semidirect
5. C19×#1393C2semidirect
6. C19×#1390C2semidirect
7. C19×#1390C2semidirect
149. #13376C19direct (N × H)
226. #2748C2×C19semidirect
230. #1393C2×C19semidirect
231. #1390C2×C19semidirect
232. #1390C2×C19semidirect
348. C19#13376direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#27482
C19×#17922
C19×#17902
C19×#13932
C19×#13902
#1337619