Finite Group Databasebeta

← C19×#22167 #18028126

Subgroups — C19×#22167 #18028126

Order 4864.

744 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3035C211yesmaximal, characteristic
2C19×#2932C211yesmaximal, characteristic, complemented
3C19×#2923C211yesmaximal, characteristic, complemented
4C19×#1980C211yesmaximal, characteristic, complemented
5C19×#1975C211yesmaximal, characteristic, complemented
6C19×#1974C211yesmaximal, characteristic, complemented
7C19×#1950C211yesmaximal, characteristic, complemented
8C19×#1938C211yesmaximal, characteristic, complemented
9C19×#1937C211yesmaximal, characteristic, complemented
10C19×#1876C211yesmaximal, characteristic, complemented
11C19×#1876C211yesmaximal, characteristic, complemented
12C19×#1866C211yesmaximal, characteristic, complemented
13C19×#1866C211yesmaximal, characteristic, complemented
14C19×#1806C211yesmaximal, characteristic, complemented
15C19×#1771C211yesmaximal, characteristic, complemented
16C2×C19×#135C2211yescharacteristic
17C2×C19×#135C2211yescharacteristic
18C2×C19×#131C2211yescharacteristic
19C2×C19×#131C2211yescharacteristic
20C19×#532C2211yescharacteristic
21C4×#41×C19C2211yescharacteristic
22C19×#464C411yescharacteristic, complemented
23C19×#464C411yescharacteristic, complemented
24C19×#463C411yescharacteristic, complemented
25C19×#463C411yescharacteristic, complemented
26C19×#462C411yescharacteristic, complemented
27C19×#461C411yescharacteristic, complemented
28C19×#460C411yescharacteristic, complemented
29C19×#459C411yescharacteristic, complemented
30C19×#435—21no—
31C19×#435—21no—
32C19×#435—21no—
33C19×#435—21no—
34C19×#433—21no—
35C19×#433—21no—
36C19×#432—21no—
37C19×#432—21no—
38C2×C19×#108C2211yescharacteristic
39C2×C19×#108C2211yescharacteristic
40C19×#424C2211yescharacteristic
41C19×#424C2211yescharacteristic
42C19×#423C2211yescharacteristic
43C2×C19×C4⋊C8C2211yescharacteristic
44C2×C19×#104C2211yescharacteristic
45C2×C19×#104C2211yescharacteristic
46C2×C19×#104C2211yescharacteristic
47C2×C19×#104C2211yescharacteristic
48C2×C19×#104C2211yescharacteristic
49C2×C19×#104C2211yescharacteristic
50C19×#416C2211yescharacteristic
51C19×#416C2211yescharacteristic
52C19×#408C2211yescharacteristic
53C19×#408C2211yescharacteristic
54C19×#408C2211yescharacteristic
55C19×#408C2211yescharacteristic
56C4×M16×C19C2211yescharacteristic
57C2×C19×#97C2211yescharacteristic
58C2×C19×#97C2211yescharacteristic
59C2×C4×C8×C19C2211yescharacteristic
60C4×C4⋊C4×C19C2211yescharacteristic
61C19×#341C2211yescharacteristic
62C19×#341C2211yescharacteristic
63C19×#339C2211yescharacteristic
64C19×#339C2211yescharacteristic
65C19×#336C2211yescharacteristic
66C19×#336C2211yescharacteristic
67C2×#41×C19C2311yescharacteristic
68C2×#41×C19C2311yescharacteristic
69C2×#41×C19C2311yescharacteristic
70C19×#135—41no—
71C19×#135—41no—
72C19×#135—41no—
73C19×#135—41no—
74C2×Q16×C19C2×C411yescharacteristic
75C2×Q16×C19C2×C411yescharacteristic
76C2×SD16×C19C2×C411yescharacteristic
77C2×SD16×C19C2×C411yescharacteristic
78C2×SD16×C19C2×C411yescharacteristic
79C2×SD16×C19C2×C411yescharacteristic
80C2×D8×C19C2×C411yescharacteristic
81C2×D8×C19C2×C411yescharacteristic
82C19×#131—41no—
83C19×#131—41no—
84C19×#131—41no—
85C19×#131—41no—
86C2×M16×C19—21no—
87C2×M16×C19—21no—
88C2×M16×C19C2311yescharacteristic
89C2×M16×C19C2311yescharacteristic
90C2×M16×C19C2311yescharacteristic
91C2×M16×C19C2311yescharacteristic
92C22×C8×C19—21no—
93C22×C8×C19—21no—
94C22×C8×C19C2311yescharacteristic
95C22×C8×C19C2311yescharacteristic
96C22×C8×C19C2311yescharacteristic
97C22×C8×C19C2311yescharacteristic
98C19×C4⋊Q8C2×C411yescharacteristic
99C19×#127C2×C411yescharacteristic
100C19×#124C2×C411yescharacteristic
101C19×#124C2×C411yescharacteristic
102C19×#121—21no—
103C19×#121—21no—
104C4×Q8×C19C2×C411yescharacteristic
105C4×Q8×C19C2×C411yescharacteristic
106C4×D4×C19—21no—
107C4×D4×C19—21no—
108C4×D4×C19—21no—
109C4×D4×C19—21no—
110C4×D4×C19C2×C411yescharacteristic
111C4×D4×C19C2×C411yescharacteristic
112C19×#117—21no—
113C19×#117C2311yescharacteristic
114C2×C4⋊C4×C19—21no—
115C2×C42×C19—21no—
116C2×C42×C19C2311yescharacteristic
117C2×C42×C19C2311yescharacteristic
118C2×C42×C19C2311yescharacteristic
119C19×#108—41no—
120C19×#108—41no—
121C19×C4⋊C8—21no—
122C19×C4⋊C8—21no—
123C19×C4⋊C8—21no—
124C19×C4⋊C8—21no—
125C19×C4⋊C8—21no—
126C19×C4⋊C8—21no—
127C19×C4⋊C8C2×C411yescharacteristic
128C19×C4⋊C8C2×C411yescharacteristic
129C19×C4⋊C8C2×C411yescharacteristic
130C19×C4⋊C8C2×C411yescharacteristic
131C19×#104—41no—
132C19×#104—41no—
133C19×#104—41no—
134C19×#104—41no—
135C19×#104—41no—
136C19×#104—41no—
137C19×#103C2×C411yescharacteristic
138C19×#103C2×C411yescharacteristic
139C19×#103C2×C411yescharacteristic
140C19×#103C2×C411yescharacteristic
141C19×#102C2×C411yescharacteristic
142C19×#102C2×C411yescharacteristic
143C19×#102C2×C411yescharacteristic
144C19×#102C2×C411yescharacteristic
145C19×C22⋊C8—21no—
146C19×C22⋊C8—21no—
147C19×C22⋊C8—21no—
148C19×C22⋊C8—21no—
149C19×C22⋊C8—21no—
150C19×C22⋊C8—21no—
151C19×C22⋊C8—21no—
152C19×C22⋊C8—21no—
153C19×#97—21no—
154C19×#97—41no—
155C19×#97D411yescharacteristic
156C19×#97D411yescharacteristic
157C19×#97D411yescharacteristic
158C19×#97D411yescharacteristic
159C4×C8×C19—21no—
160C4×C8×C19—41no—
161C19×#95—21no—
162#41×C19—21no—
163#41×C19—21no—
164#41×C19—21no—
165#41×C19—21no—
166#41×C19—21no—
167#41×C19—21no—
168#41×C19—21no—
169#41×C19—21no—
170#41×C19—21no—
171#41×C19—21no—
172#41×C19—21no—
173#41×C19—21no—
174C2×Q8×C19C22×C411yescharacteristic
175C2×Q8×C19C22×C411yescharacteristic
176C2×Q8×C19C22×C411yescharacteristic
177C2×D4×C19—21no—
178C2×D4×C19—21no—
179C2×D4×C19—21no—
180C2×D4×C19—21no—
181C2×D4×C19—21no—
182C2×D4×C19C22×C411yescharacteristic
183C2×D4×C19C22×C411yescharacteristic
184C2×D4×C19C22×C411yescharacteristic
185C22×C4×C19—21no—
186C22×C4×C19—21no—
187C22×C4×C19—21no—
188C22×C4×C19—21no—
189C22×C4×C19—21no—
190C22×C4×C19—21no—
191C22×C4×C19—21no—
192C22×C4×C19#4111yescharacteristic
193C22×C4×C19#4111yescharacteristic
194C22×C4×C19C2411yescharacteristic
195Q16×C19—41no—
196Q16×C19—41no—
197SD16×C19—41no—
198SD16×C19—41no—
199SD16×C19—41no—
200SD16×C19—41no—
201D8×C19—41no—
202D8×C19—41no—
203M16×C19—21no—
204M16×C19—21no—
205M16×C19—21no—
206M16×C19—21no—
207M16×C19—21no—
208M16×C19—21no—
209M16×C19—21no—
210M16×C19—21no—
211M16×C19—42no—
212M16×C19—42no—
213C2×C8×C19—21no—
214C2×C8×C19—21no—
215C2×C8×C19—21no—
216C2×C8×C19—21no—
217C2×C8×C19—21no—
218C2×C8×C19—21no—
219C2×C8×C19—21no—
220C2×C8×C19—21no—
221C2×C8×C19—21no—
222C2×C8×C19—21no—
223C2×C8×C19—21no—
224C2×C8×C19—21no—
225C2×C8×C19—42no—
226C2×C8×C19—42no—
227C2×C8×C19C22×C411yescharacteristic
228C2×C8×C19C22×C411yescharacteristic
229C2×C8×C19C22×C411yescharacteristic
230C2×C8×C19C22×C411yescharacteristic
231C2×C8×C19C2×D411yescharacteristic
232C2×C8×C19C2×D411yescharacteristic
233C2×C8×C19C2×D411yescharacteristic
234C2×C8×C19C2×D411yescharacteristic
235C4⋊C4×C19—21no—
236C4⋊C4×C19—21no—
237C4⋊C4×C19—21no—
238C4⋊C4×C19—21no—
239C4⋊C4×C19—42no—
240C4⋊C4×C19C22×C411yescharacteristic
241C4⋊C4×C19C22×C411yescharacteristic
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—
249C42×C19—21no—
250C42×C19—21no—
251C42×C19—21no—
252C42×C19—21no—
253C42×C19—21no—
254C42×C19—21no—
255C42×C19—21no—
256C42×C19C22×C411yescharacteristic
257C42×C19C22×C411yescharacteristic
258C42×C19C2×D411yescharacteristic
259C42×C19C2×D411yescharacteristic
260#22167C1911yesmaximal, characteristic, direct product factor, Sylow
261C23×C19—21no—
262C23×C19—21no—
263C23×C19—21no—
264C23×C19C2×#4111yescharacteristic
265Q8×C19—21no—
266Q8×C19—21no—
267Q8×C19—21no—
268Q8×C19—21no—
269Q8×C19—21no—
270Q8×C19—21no—
271D4×C19—21no—
272D4×C19—21no—
273D4×C19—21no—
274D4×C19—21no—
275D4×C19—21no—
276D4×C19—21no—
277D4×C19—41no—
278D4×C19—41no—
279D4×C19—41no—
280D4×C19—41no—
281D4×C19—41no—
282D4×C19—41no—
283D4×C19—81no—
284D4×C19—81no—
285C2×C4×C19—22no—
286C2×C4×C19—21no—
287C2×C4×C19—21no—
288C2×C4×C19—21no—
289C2×C4×C19—21no—
290C2×C4×C19—21no—
291C2×C4×C19—41no—
292C2×C4×C19—41no—
293C2×C4×C19—41no—
294C2×C4×C19—41no—
295C2×C4×C19—41no—
296C2×C4×C19—41no—
297C2×C4×C19—41no—
298C2×C4×C19—41no—
299C2×C4×C19—41no—
300C2×C4×C19—41no—
301C2×C4×C19—41no—
302C2×C4×C19—41no—
303C2×C4×C19—41no—
304C2×C4×C19—81no—
305C2×C4×C19—81no—
306C2×C4×C19C4×D411yescharacteristic
307C2×C4×C19C4×D411yescharacteristic
308C2×C4×C19C4×D411yescharacteristic
309C2×C4×C19C4×D411yescharacteristic
310C2×C4×C19C23×C411yescharacteristic
311C2×C4×C19C22×D411yescharacteristic
312C2×C4×C19H(5,𝔽2)11yescharacteristic
313C2×C4×C19H(5,𝔽2)11yescharacteristic
314C2×C4×C19H(5,𝔽2)11yescharacteristic
315C2×C4×C192−1+411yescharacteristic
316C8×C19—21no—
317C8×C19—21no—
318C8×C19—21no—
319C8×C19—21no—
320C8×C19—21no—
321C8×C19—21no—
322C8×C19—21no—
323C8×C19—21no—
324C8×C19—41no—
325C8×C19—41no—
326C8×C19—41no—
327C8×C19—41no—
328#3035C2×C1911yescharacteristic
329#2932C2×C1911yescharacteristic, complemented
330#2923C2×C1911yescharacteristic, complemented
331#1980C2×C1911yescharacteristic, complemented
332#1975C2×C1911yescharacteristic, complemented
333#1974C2×C1911yescharacteristic, complemented
334#1950C2×C1911yescharacteristic, complemented
335#1938C2×C1911yescharacteristic, complemented
336#1937C2×C1911yescharacteristic, complemented
337#1876C2×C1911yescharacteristic, complemented
338#1876C2×C1911yescharacteristic, complemented
339#1866C2×C1911yescharacteristic, complemented
340#1866C2×C1911yescharacteristic, complemented
341#1806C2×C1911yescharacteristic, complemented
342#1771C2×C1911yescharacteristic, complemented
343C22×C19—21no—
344C22×C19—21no—
345C22×C19—41no—
346C22×C19—41no—
347C22×C19—41no—
348C22×C19—41no—
349C22×C19—41no—
350C22×C19—41no—
351C22×C19—41no—
352C22×C19—41no—
353C22×C19—41no—
354C22×C19C2×C4×D411yescharacteristic
355C22×C19#54011yescharacteristic
356C22×C19#54211yescharacteristic
357C4×C19—21no—
358C4×C19—21no—
359C4×C19—21no—
360C4×C19—21no—
361C4×C19—42no—
362C4×C19—41no—
363C4×C19—41no—
364C4×C19—41no—
365C4×C19—41no—
366C4×C19—41no—
367C4×C19—81no—
368C4×C19#51811yescharacteristic
369C4×C19#52011yescharacteristic
370C4×C19#53511yescharacteristic
371C4×C19#53711yescharacteristic
372C2×#135C22×C1911yescharacteristic
373C2×#135C22×C1911yescharacteristic
374C2×#131C22×C1911yescharacteristic
375C2×#131C22×C1911yescharacteristic
376#532C22×C1911yescharacteristic
377C4×#41C22×C1911yescharacteristic
378#464C4×C1911yescharacteristic, complemented
379#464C4×C1911yescharacteristic, complemented
380#463C4×C1911yescharacteristic, complemented
381#463C4×C1911yescharacteristic, complemented
382#462C4×C1911yescharacteristic, complemented
383#461C4×C1911yescharacteristic, complemented
384#460C4×C1911yescharacteristic, complemented
385#459C4×C1911yescharacteristic, complemented
386#435—21no—
387#435—21no—
388#435—21no—
389#435—21no—
390#433—21no—
391#433—21no—
392#432—21no—
393#432—21no—
394C2×#108C22×C1911yescharacteristic
395C2×#108C22×C1911yescharacteristic
396#424C22×C1911yescharacteristic
397#424C22×C1911yescharacteristic
398#423C22×C1911yescharacteristic
399C2×C4⋊C8C22×C1911yescharacteristic
400C2×#104C22×C1911yescharacteristic
401C2×#104C22×C1911yescharacteristic
402C2×#104C22×C1911yescharacteristic
403C2×#104C22×C1911yescharacteristic
404C2×#104C22×C1911yescharacteristic
405C2×#104C22×C1911yescharacteristic
406#416C22×C1911yescharacteristic
407#416C22×C1911yescharacteristic
408#408C22×C1911yescharacteristic
409#408C22×C1911yescharacteristic
410#408C22×C1911yescharacteristic
411#408C22×C1911yescharacteristic
412C4×M16C22×C1911yescharacteristic
413C2×#97C22×C1911yescharacteristic
414C2×#97C22×C1911yescharacteristic
415C2×C4×C8C22×C1911yescharacteristic
416C4×C4⋊C4C22×C1911yescharacteristic
417#341C22×C1911yescharacteristic
418#341C22×C1911yescharacteristic
419#339C22×C1911yescharacteristic
420#339C22×C1911yescharacteristic
421#336C22×C1911yescharacteristic
422#336C22×C1911yescharacteristic
423C2×C19—21no—
424C2×C19—21no—
425C2×C19—81no—
426C2×C19—81no—
427C2×C19—81no—
428C2×C19#232411yescharacteristic
429C2×C19#295611yescharacteristic
430C2×C19#295711yescharacteristic
431C2×#41C23×C1911yescharacteristic
432C2×#41C23×C1911yescharacteristic
433C2×#41C23×C1911yescharacteristic
434#135—41no—
435#135—41no—
436#135—41no—
437#135—41no—
438C2×Q16C2×C4×C1911yescharacteristic
439C2×Q16C2×C4×C1911yescharacteristic
440C2×SD16C2×C4×C1911yescharacteristic
441C2×SD16C2×C4×C1911yescharacteristic
442C2×SD16C2×C4×C1911yescharacteristic
443C2×SD16C2×C4×C1911yescharacteristic
444C2×D8C2×C4×C1911yescharacteristic
445C2×D8C2×C4×C1911yescharacteristic
446#131—41no—
447#131—41no—
448#131—41no—
449#131—41no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16C23×C1911yescharacteristic
453C2×M16C23×C1911yescharacteristic
454C2×M16C23×C1911yescharacteristic
455C2×M16C23×C1911yescharacteristic
456C22×C8—21no—
457C22×C8—21no—
458C22×C8C23×C1911yescharacteristic
459C22×C8C23×C1911yescharacteristic
460C22×C8C23×C1911yescharacteristic
461C22×C8C23×C1911yescharacteristic
462C4⋊Q8C2×C4×C1911yescharacteristic
463#127C2×C4×C1911yescharacteristic
464#124C2×C4×C1911yescharacteristic
465#124C2×C4×C1911yescharacteristic
466#121—21no—
467#121—21no—
468C4×Q8C2×C4×C1911yescharacteristic
469C4×Q8C2×C4×C1911yescharacteristic
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4C2×C4×C1911yescharacteristic
475C4×D4C2×C4×C1911yescharacteristic
476#117—21no—
477#117C23×C1911yescharacteristic
478C2×C4⋊C4—21no—
479C2×C42—21no—
480C2×C42C23×C1911yescharacteristic
481C2×C42C23×C1911yescharacteristic
482C2×C42C23×C1911yescharacteristic
483#108—41no—
484#108—41no—
485C4⋊C8—21no—
486C4⋊C8—21no—
487C4⋊C8—21no—
488C4⋊C8—21no—
489C4⋊C8—21no—
490C4⋊C8—21no—
491C4⋊C8C2×C4×C1911yescharacteristic
492C4⋊C8C2×C4×C1911yescharacteristic
493C4⋊C8C2×C4×C1911yescharacteristic
494C4⋊C8C2×C4×C1911yescharacteristic
495#104—41no—
496#104—41no—
497#104—41no—
498#104—41no—
499#104—41no—
500#104—41no—
501#103C2×C4×C1911yescharacteristic
502#103C2×C4×C1911yescharacteristic
503#103C2×C4×C1911yescharacteristic
504#103C2×C4×C1911yescharacteristic
505#102C2×C4×C1911yescharacteristic
506#102C2×C4×C1911yescharacteristic
507#102C2×C4×C1911yescharacteristic
508#102C2×C4×C1911yescharacteristic
509C22⋊C8—21no—
510C22⋊C8—21no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517#97—21no—
518#97—41no—
519#97D4×C1911yescharacteristic
520#97D4×C1911yescharacteristic
521#97D4×C1911yescharacteristic
522#97D4×C1911yescharacteristic
523C4×C8—21no—
524C4×C8—41no—
525#95—21no—
526C19#2216711yescharacteristic, direct product factor, Sylow
527#41—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539C2×Q8C22×C4×C1911yescharacteristic
540C2×Q8C22×C4×C1911yescharacteristic
541C2×Q8C22×C4×C1911yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4C22×C4×C1911yescharacteristic
548C2×D4C22×C4×C1911yescharacteristic
549C2×D4C22×C4×C1911yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4#41×C1911yescharacteristic
558C22×C4#41×C1911yescharacteristic
559C22×C4C24×C1911yescharacteristic
560Q16—41no—
561Q16—41no—
562SD16—41no—
563SD16—41no—
564SD16—41no—
565SD16—41no—
566D8—41no—
567D8—41no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—21no—
573M16—21no—
574M16—21no—
575M16—21no—
576M16—42no—
577M16—42no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—42no—
591C2×C8—42no—
592C2×C8C22×C4×C1911yescharacteristic
593C2×C8C22×C4×C1911yescharacteristic
594C2×C8C22×C4×C1911yescharacteristic
595C2×C8C22×C4×C1911yescharacteristic
596C2×C8C2×D4×C1911yescharacteristic
597C2×C8C2×D4×C1911yescharacteristic
598C2×C8C2×D4×C1911yescharacteristic
599C2×C8C2×D4×C1911yescharacteristic
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4C22×C4×C1911yescharacteristic
606C4⋊C4C22×C4×C1911yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42C22×C4×C1911yescharacteristic
622C42C22×C4×C1911yescharacteristic
623C42C2×D4×C1911yescharacteristic
624C42C2×D4×C1911yescharacteristic
625C23—21no—
626C23—21no—
627C23—21no—
628C23C2×#41×C1911yescharacteristic
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—21no—
634Q8—21no—
635D4—21no—
636D4—21no—
637D4—21no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—81no—
648D4—81no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4C4×D4×C1911yescharacteristic
671C2×C4C4×D4×C1911yescharacteristic
672C2×C4C4×D4×C1911yescharacteristic
673C2×C4C4×D4×C1911yescharacteristic
674C2×C4C23×C4×C1911yescharacteristic
675C2×C4C22×D4×C1911yescharacteristic
676C2×C4C19×H(5,𝔽2)11yescharacteristic
677C2×C4C19×H(5,𝔽2)11yescharacteristic
678C2×C4C19×H(5,𝔽2)11yescharacteristic
679C2×C4C19×2−1+411yescharacteristic
680C8—21no—
681C8—21no—
682C8—21no—
683C8—21no—
684C8—21no—
685C8—21no—
686C8—21no—
687C8—21no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—21no—
693C22—21no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×C4×D4×C1911yescharacteristic
704C22C19×#54011yescharacteristic
705C22C19×#54211yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—42no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4C19×#51811yescharacteristic
718C4C19×#52011yescharacteristic
719C4C19×#53511yescharacteristic
720C4C19×#53711yescharacteristic
721C2—21no—
722C2—21no—
723C2—81no—
724C2—81no—
725C2—81no—
726C2C19×#232411yescharacteristic
727C2C19×#295611yescharacteristic
728C2C19×#295711yescharacteristic
subgroupG/H
centerC2×C4×C19C22×D4
commutatorC2×C4C23×C4×C19
Frattini, cosocleC22×C4C24×C19
socleC22×C19C2×C4×D4
prime radicalC19×#3035C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ C2×C19×#97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2932C2semidirect
3. C19×#2923C2semidirect
4. C19×#1980C2semidirect
5. C19×#1975C2semidirect
6. C19×#1974C2semidirect
7. C19×#1950C2semidirect
8. C19×#1938C2semidirect
9. C19×#1937C2semidirect
10. C19×#1876C2semidirect
11. C19×#1876C2semidirect
12. C19×#1866C2semidirect
13. C19×#1866C2semidirect
14. C19×#1806C2semidirect
15. C19×#1771C2semidirect
22. C19×#464C4semidirect
23. C19×#464C4semidirect
24. C19×#463C4semidirect
25. C19×#463C4semidirect
26. C19×#462C4semidirect
27. C19×#461C4semidirect
28. C19×#460C4semidirect
29. C19×#459C4semidirect
260. #22167C19direct (N × H)
329. #2932C2×C19semidirect
330. #2923C2×C19semidirect
331. #1980C2×C19semidirect
332. #1975C2×C19semidirect
333. #1974C2×C19semidirect
334. #1950C2×C19semidirect
335. #1938C2×C19semidirect
336. #1937C2×C19semidirect
337. #1876C2×C19semidirect
338. #1876C2×C19semidirect
339. #1866C2×C19semidirect
340. #1866C2×C19semidirect
341. #1806C2×C19semidirect
342. #1771C2×C19semidirect
378. #464C4×C19semidirect
379. #464C4×C19semidirect
380. #463C4×C19semidirect
381. #463C4×C19semidirect
382. #462C4×C19semidirect
383. #461C4×C19semidirect
384. #460C4×C19semidirect
385. #459C4×C19semidirect
526. C19#22167direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#30352
C19×#29322
C19×#29232
C19×#19802
C19×#19752
C19×#19742
C19×#19502
C19×#19382
C19×#19372
C19×#18762
C19×#18662
C19×#18062
C19×#17712
#2216719