Finite Group Databasebeta

← C19×#15565 #18021524

Subgroups — C19×#15565 #18021524

Order 4864.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#397C211yesmaximal, characteristic, complemented
2C2×C19×#394C211yesmaximal, characteristic
3C2×C19×#388C211yesmaximal, characteristic, complemented
4C2×C19×#388C211yesmaximal, characteristic, complemented
5C19×#1441C211yesmaximal, characteristic, complemented
6C19×#1441C211yesmaximal, characteristic, complemented
7C19×#1439C211yesmaximal, characteristic, complemented
8C19×#1439C211yesmaximal, characteristic, complemented
9C19×#1439C211yesmaximal, characteristic, complemented
10C19×#1438C211yesmaximal, characteristic
11C19×#1438C211yesmaximal, characteristic
12C19×#1437C211yesmaximal, characteristic, complemented
13C19×#1437C211yesmaximal, characteristic, complemented
14C19×#1436C211yesmaximal, characteristic, complemented
15C19×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C19C2211yescharacteristic
17C22×C4⋊C4×C19C2211yescharacteristic
18C22×C4⋊C4×C19C2211yescharacteristic
19C22×C4⋊C4×C19C2211yescharacteristic
20C22×C4⋊C4×C19C2211yescharacteristic
21C22×C22⋊C4×C19C2211yescharacteristic
22C22×C22⋊C4×C19C2211yescharacteristic
23C22×C22⋊C4×C19C2211yescharacteristic
24C22×C22⋊C4×C19C2211yescharacteristic
25C22×C22⋊C4×C19C2211yescharacteristic
26C22×C22⋊C4×C19C2211yescharacteristic
27C22×C22⋊C4×C19C2211yescharacteristic
28C22×C22⋊C4×C19C2211yescharacteristic
29C22×C22⋊C4×C19C2211yescharacteristic
30C22×C22⋊C4×C19C2211yescharacteristic
31C22×C22⋊C4×C19C2211yescharacteristic
32C22×C22⋊C4×C19C2211yescharacteristic
33C22×C42×C19C2211yescharacteristic
34C22×C42×C19C2211yescharacteristic
35C19×#397—24no—
36C19×#394—24no—
37C19×#388—24no—
38C19×#388—24no—
39C2×C19×#95C2211yescharacteristic
40C2×C19×#95C2211yescharacteristic
41C2×C19×#95C2211yescharacteristic
42C2×C19×#95C2211yescharacteristic
43C2×C19×#95C2211yescharacteristic
44C2×C19×#95C2211yescharacteristic
45C2×C19×#95C2211yescharacteristic
46C2×C19×#95C2211yescharacteristic
47C2×C19×#95C2211yescharacteristic
48C2×C19×#95C2211yescharacteristic
49C2×C19×#95C2211yescharacteristic
50C2×C19×#95C2211yescharacteristic
51C2×C19×#95C2211yescharacteristic
52C2×C19×#95C2211yescharacteristic
53C2×C19×#95C2211yescharacteristic
54C2×C19×#95C2211yescharacteristic
55C25×C19C2311yescharacteristic
56C25×C19C2311yescharacteristic
57C22×D4×C19—22no—
58C22×D4×C19—22no—
59C22×D4×C19—22no—
60C22×D4×C19—41no—
61C22×D4×C19—41no—
62C22×D4×C19—41no—
63C22×D4×C19—41no—
64C23×C4×C19C2311yescharacteristic
65C23×C4×C19C2311yescharacteristic
66C23×C4×C19C2311yescharacteristic
67C23×C4×C19C2311yescharacteristic
68C23×C4×C19C2311yescharacteristic
69C23×C4×C19C2311yescharacteristic
70C23×C4×C19C2311yescharacteristic
71C23×C4×C19C2311yescharacteristic
72C23×C4×C19C2311yescharacteristic
73C23×C4×C19C2311yescharacteristic
74C23×C4×C19C2311yescharacteristic
75C23×C4×C19C2311yescharacteristic
76C23×C4×C19C2311yescharacteristic
77C2×C4⋊C4×C19—22no—
78C2×C4⋊C4×C19—22no—
79C2×C4⋊C4×C19—22no—
80C2×C4⋊C4×C19—22no—
81C2×C4⋊C4×C19—22no—
82C2×C4⋊C4×C19—22no—
83C2×C4⋊C4×C19—22no—
84C2×C4⋊C4×C19—41no—
85C2×C4⋊C4×C19—41no—
86C2×C4⋊C4×C19—41no—
87C2×C4⋊C4×C19—41no—
88C2×C4⋊C4×C19—41no—
89C2×C22⋊C4×C19—22no—
90C2×C22⋊C4×C19—22no—
91C2×C22⋊C4×C19—22no—
92C2×C22⋊C4×C19—22no—
93C2×C22⋊C4×C19—22no—
94C2×C22⋊C4×C19—22no—
95C2×C22⋊C4×C19—22no—
96C2×C22⋊C4×C19—22no—
97C2×C22⋊C4×C19—22no—
98C2×C22⋊C4×C19—22no—
99C2×C22⋊C4×C19—22no—
100C2×C22⋊C4×C19—22no—
101C2×C22⋊C4×C19—22no—
102C2×C22⋊C4×C19—22no—
103C2×C22⋊C4×C19—22no—
104C2×C22⋊C4×C19—22no—
105C2×C22⋊C4×C19—22no—
106C2×C22⋊C4×C19—22no—
107C2×C22⋊C4×C19—22no—
108C2×C22⋊C4×C19—22no—
109C2×C22⋊C4×C19—22no—
110C2×C22⋊C4×C19—22no—
111C2×C22⋊C4×C19—22no—
112C2×C22⋊C4×C19—41no—
113C2×C22⋊C4×C19—41no—
114C2×C22⋊C4×C19—41no—
115C2×C22⋊C4×C19—41no—
116C2×C22⋊C4×C19—41no—
117C2×C22⋊C4×C19—41no—
118C2×C22⋊C4×C19—41no—
119C2×C22⋊C4×C19—41no—
120C2×C22⋊C4×C19—41no—
121C2×C22⋊C4×C19—41no—
122C2×C22⋊C4×C19—41no—
123C2×C22⋊C4×C19—41no—
124C2×C22⋊C4×C19D414yes—
125C2×C42×C19—22no—
126C2×C42×C19—22no—
127C2×C42×C19—22no—
128C2×C42×C19—41no—
129C2×C42×C19—41no—
130C2×C42×C19—41no—
131C19×#95—22no—
132C19×#95—22no—
133C19×#95—22no—
134C19×#95—22no—
135C19×#95—22no—
136C19×#95—22no—
137C19×#95—22no—
138C19×#95—22no—
139C19×#95—22no—
140C19×#95—41no—
141C19×#95—41no—
142C19×#95—41no—
143C19×#95—41no—
144C19×#95—41no—
145C19×#95—41no—
146C19×#95D414yescomplemented
147C24×C19—21no—
148C24×C19—21no—
149C24×C19—21no—
150C24×C19—21no—
151C24×C19—21no—
152C24×C19—21no—
153C24×C19—21no—
154C24×C19—21no—
155C24×C19—21no—
156C24×C19—21no—
157C24×C19—21no—
158C24×C19—21no—
159C24×C19—21no—
160C24×C19—21no—
161C24×C19—21no—
162C24×C19—21no—
163C24×C19—21no—
164C24×C19—21no—
165C24×C19—21no—
166C24×C19—21no—
167C24×C19—21no—
168C24×C19—21no—
169C24×C19—21no—
170C24×C19—21no—
171C24×C19—21no—
172C24×C19—21no—
173C24×C19—21no—
174C24×C19—21no—
175C24×C19C2×D412yes—
176C24×C19#4112yes—
177C24×C19C2411yescharacteristic
178C2×D4×C19—44no—
179C2×D4×C19—44no—
180C2×D4×C19—44no—
181C2×D4×C19—44no—
182C2×D4×C19—44no—
183C2×D4×C19—44no—
184C2×D4×C19—44no—
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—21no—
193C22×C4×C19—21no—
194C22×C4×C19—21no—
195C22×C4×C19—21no—
196C22×C4×C19—21no—
197C22×C4×C19—21no—
198C22×C4×C19—21no—
199C22×C4×C19—21no—
200C22×C4×C19—21no—
201C22×C4×C19—21no—
202C22×C4×C19—21no—
203C22×C4×C19—21no—
204C22×C4×C19—21no—
205C22×C4×C19—21no—
206C22×C4×C19—21no—
207C22×C4×C19—21no—
208C22×C4×C19—21no—
209C22×C4×C19—21no—
210C22×C4×C19—21no—
211C22×C4×C19—21no—
212C22×C4×C19—21no—
213C22×C4×C19—21no—
214C22×C4×C19—21no—
215C22×C4×C19—21no—
216C22×C4×C19—21no—
217C22×C4×C19—21no—
218C22×C4×C19—21no—
219C22×C4×C19—21no—
220C22×C4×C19—21no—
221C22×C4×C19—21no—
222C22×C4×C19—21no—
223C22×C4×C19—21no—
224C22×C4×C19—21no—
225C22×C4×C19—21no—
226C22×C4×C19—21no—
227C22×C4×C19—21no—
228C22×C4×C19—21no—
229C22×C4×C19—21no—
230C22×C4×C19—21no—
231C22×C4×C19—21no—
232C22×C4×C19—21no—
233C22×C4×C19—21no—
234C22×C4×C19—21no—
235C22×C4×C19—21no—
236C22×C4×C19—21no—
237C22×C4×C19—21no—
238C22×C4×C19—21no—
239C22×C4×C19—21no—
240C22×C4×C19—21no—
241C22×C4×C19—21no—
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×C19—21no—
254C22×C4×C19—21no—
255C22×C4×C19—21no—
256C22×C4×C19—21no—
257C22×C4×C19—21no—
258C22×C4×C19—21no—
259C22×C4×C19—21no—
260C22×C4×C19—21no—
261C22×C4×C19—21no—
262C22×C4×C19—21no—
263C22×C4×C19—21no—
264C22×C4×C19—21no—
265C22×C4×C19C2×D412yes—
266C22×C4×C19C2×D412yes—
267C22×C4×C19C2×D412yes—
268C22×C4×C19C2×D412yes—
269C22×C4×C19C2×D412yes—
270C22×C4×C19#4112yes—
271C22×C4×C19#4112yes—
272C22×C4×C19#4112yes—
273C22×C4×C19#4112yes—
274C22×C4×C19#4112yes—
275C22×C4×C19#4112yes—
276C4⋊C4×C19—44no—
277C4⋊C4×C19—44no—
278C4⋊C4×C19—44no—
279C4⋊C4×C19—44no—
280C22⋊C4×C19—28no—
281C22⋊C4×C19—28no—
282C22⋊C4×C19—44no—
283C22⋊C4×C19—44no—
284C22⋊C4×C19—44no—
285C22⋊C4×C19—44no—
286C22⋊C4×C19—44no—
287C22⋊C4×C19—44no—
288C22⋊C4×C19—44no—
289C22⋊C4×C19—44no—
290C22⋊C4×C19—44no—
291C22⋊C4×C19—44no—
292C42×C19—44no—
293C42×C19—44no—
294#15565C1911yesmaximal, characteristic, direct product factor, Sylow
295C23×C19—22no—
296C23×C19—22no—
297C23×C19—22no—
298C23×C19—22no—
299C23×C19—22no—
300C23×C19—22no—
301C23×C19—22no—
302C23×C19—22no—
303C23×C19—22no—
304C23×C19—22no—
305C23×C19—22no—
306C23×C19—22no—
307C23×C19—22no—
308C23×C19—22no—
309C23×C19—41no—
310C23×C19—41no—
311C23×C19—41no—
312C23×C19—41no—
313C23×C19—41no—
314C23×C19—41no—
315C23×C19—41no—
316C23×C19—41no—
317C23×C19—41no—
318C23×C19—41no—
319C23×C19—41no—
320C23×C19—41no—
321C23×C19—41no—
322C23×C19—41no—
323C23×C19—41no—
324C23×C19—41no—
325C23×C19—41no—
326C23×C19—41no—
327C23×C19—41no—
328C23×C19—41no—
329C23×C19—41no—
330C23×C19—41no—
331C23×C19—41no—
332C23×C19—41no—
333C23×C19—41no—
334C23×C19—41no—
335C23×C19—41no—
336C23×C19—41no—
337C23×C19—41no—
338C23×C19—41no—
339C23×C19—41no—
340C23×C19—41no—
341C23×C19—41no—
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—41no—
352C23×C19—41no—
353C23×C19—41no—
354C23×C19—41no—
355C23×C19—41no—
356C23×C19—41no—
357C23×C19—41no—
358C23×C19—41no—
359C23×C19—41no—
360C23×C19—41no—
361C23×C19—41no—
362C23×C19—41no—
363C23×C19—41no—
364C23×C19—41no—
365C23×C19C22×D411yescharacteristic
366C23×C19C22×D411yescharacteristic
367C23×C19C2×#4111yescharacteristic
368C23×C19C2×#4111yescharacteristic
369C23×C19C2×#4111yescharacteristic
370C23×C19C2×#4111yescharacteristic
371C23×C19C2×#4111yescharacteristic
372C23×C19C2×#4111yescharacteristic
373C23×C19C2×#4111yescharacteristic
374C23×C19H(5,𝔽2)11yescharacteristic
375C23×C19H(5,𝔽2)11yescharacteristic
376C23×C19H(5,𝔽2)11yescharacteristic
377C23×C19H(5,𝔽2)11yescharacteristic
378C23×C19H(5,𝔽2)11yescharacteristic
379C23×C192−1+411yescharacteristic
380D4×C19—416no—
381C2×C4×C19—22no—
382C2×C4×C19—22no—
383C2×C4×C19—22no—
384C2×C4×C19—22no—
385C2×C4×C19—22no—
386C2×C4×C19—22no—
387C2×C4×C19—22no—
388C2×C4×C19—22no—
389C2×C4×C19—22no—
390C2×C4×C19—22no—
391C2×C4×C19—22no—
392C2×C4×C19—22no—
393C2×C4×C19—22no—
394C2×C4×C19—22no—
395C2×C4×C19—22no—
396C2×C4×C19—22no—
397C2×C4×C19—22no—
398C2×C4×C19—22no—
399C2×C4×C19—22no—
400C2×C4×C19—22no—
401C2×C4×C19—22no—
402C2×C4×C19—22no—
403C2×C4×C19—22no—
404C2×C4×C19—22no—
405C2×C4×C19—22no—
406C2×C4×C19—22no—
407C2×C4×C19—22no—
408C2×C4×C19—22no—
409C2×C4×C19—22no—
410C2×C4×C19—22no—
411C2×C4×C19—22no—
412C2×C4×C19—22no—
413C2×C4×C19—22no—
414C2×C4×C19—41no—
415C2×C4×C19—41no—
416C2×C4×C19—41no—
417C2×C4×C19—41no—
418C2×C4×C19—41no—
419C2×C4×C19—41no—
420C2×C4×C19—41no—
421C2×C4×C19—41no—
422C2×C4×C19—41no—
423C2×C4×C19—41no—
424C2×C4×C19—41no—
425C2×C4×C19—41no—
426C2×C4×C19—41no—
427C2×C4×C19—41no—
428C2×C4×C19—41no—
429C2×C4×C19—41no—
430C2×C4×C19—41no—
431C2×C4×C19—41no—
432C2×C4×C19—41no—
433C2×C4×C19—41no—
434C2×C4×C19—41no—
435C2×C4×C19—41no—
436C2×C4×C19—41no—
437C2×C4×C19—41no—
438C2×C4×C19—41no—
439C2×C4×C19—41no—
440C2×C4×C19—41no—
441C2×C4×C19—41no—
442C2×C4×C19—41no—
443C2×C4×C19—41no—
444C2×C4×C19—41no—
445C2×C4×C19—41no—
446C2×C4×C19—41no—
447C2×C4×C19—41no—
448C2×C4×C19—41no—
449C2×C4×C19—41no—
450C2×C4×C19—41no—
451C2×C4×C19—41no—
452C2×C4×C19—41no—
453C2×C4×C19—41no—
454C2×C4×C19—41no—
455C2×C4×C19—41no—
456C2×C4×C19—41no—
457C2×C4×C19—41no—
458C2×C4×C19—41no—
459C2×C4×C19—41no—
460C2×C4×C19—41no—
461C2×C4×C19—41no—
462C2×C4×C19—41no—
463C2×C4×C19—41no—
464C2×C4×C19—41no—
465C2×C4×C19—41no—
466C2×C4×C19—41no—
467C2×C4×C19—41no—
468C2×C4×C19—41no—
469C2×C4×C19—41no—
470C2×C4×C19—41no—
471C2×C4×C19—41no—
472C2×#397C2×C1911yescharacteristic, complemented
473C2×#394C2×C1911yescharacteristic
474C2×#388C2×C1911yescharacteristic, complemented
475C2×#388C2×C1911yescharacteristic, complemented
476#1441C2×C1911yescharacteristic, complemented
477#1441C2×C1911yescharacteristic, complemented
478#1439C2×C1911yescharacteristic, complemented
479#1439C2×C1911yescharacteristic, complemented
480#1439C2×C1911yescharacteristic, complemented
481#1438C2×C1911yescharacteristic
482#1438C2×C1911yescharacteristic
483#1437C2×C1911yescharacteristic, complemented
484#1437C2×C1911yescharacteristic, complemented
485#1436C2×C1911yescharacteristic, complemented
486#1434C2×C1911yescharacteristic, complemented
487C22×C19—42no—
488C22×C19—42no—
489C22×C19—42no—
490C22×C19—42no—
491C22×C19—42no—
492C22×C19—42no—
493C22×C19—42no—
494C22×C19—42no—
495C22×C19—42no—
496C22×C19—42no—
497C22×C19—42no—
498C22×C19—42no—
499C22×C19—42no—
500C22×C19—42no—
501C22×C19—81no—
502C22×C19—81no—
503C22×C19—81no—
504C22×C19—81no—
505C22×C19—81no—
506C22×C19—81no—
507C22×C19—81no—
508C22×C19—81no—
509C22×C19—81no—
510C22×C19—81no—
511C22×C19—81no—
512C22×C19—81no—
513C22×C19—81no—
514C22×C19—81no—
515C22×C19—81no—
516C22×C19—81no—
517C22×C19#52511yescharacteristic
518C22×C19#52511yescharacteristic
519C22×C19#52911yescharacteristic
520C22×C19#52911yescharacteristic
521C22×C19#53211yescharacteristic
522C22×C19#53211yescharacteristic
523C22×C19#53411yescharacteristic
524C22×C19#53711yescharacteristic
525C22×C19#53811yescharacteristic
526C22×C19#53811yescharacteristic
527C22×C19#53811yescharacteristic
528C22×C19#53811yescharacteristic
529C22×C19#53911yescharacteristic
530C22×C19#54011yescharacteristic
531C22×C19#54211yescharacteristic
532C22×C19D4211yescharacteristic
533C22×C19#54611yescharacteristic
534C22×C19#54611yescharacteristic
535C22×C19#54611yescharacteristic
536C22×C19#54611yescharacteristic
537C22×C19#54711yescharacteristic
538C22×C19#55011yescharacteristic
539C22×C19#55111yescharacteristic
540C22×C19#55111yescharacteristic
541C22×C19#55111yescharacteristic
542C22×C19#55211yescharacteristic
543C22×C19#55311yescharacteristic
544C22×C19#55311yescharacteristic
545C22×C19#55311yescharacteristic
546C22×C19#55511yescharacteristic
547C22×C19#55511yescharacteristic
548C22×C19#55611yescharacteristic
549C22×C19#55911yescharacteristic
550C22×C19#56011yescharacteristic
551C22×C19#56211yescharacteristic
552C4×C19—42no—
553C4×C19—42no—
554C4×C19—42no—
555C4×C19—42no—
556C4×C19—42no—
557C4×C19—42no—
558C4×C19—42no—
559C4×C19—42no—
560C4×C19—42no—
561C4×C19—42no—
562C4×C19—42no—
563C4×C19—81no—
564C4×C19—81no—
565C23×D4C22×C1911yescharacteristic
566C22×C4⋊C4C22×C1911yescharacteristic
567C22×C4⋊C4C22×C1911yescharacteristic
568C22×C4⋊C4C22×C1911yescharacteristic
569C22×C4⋊C4C22×C1911yescharacteristic
570C22×C22⋊C4C22×C1911yescharacteristic
571C22×C22⋊C4C22×C1911yescharacteristic
572C22×C22⋊C4C22×C1911yescharacteristic
573C22×C22⋊C4C22×C1911yescharacteristic
574C22×C22⋊C4C22×C1911yescharacteristic
575C22×C22⋊C4C22×C1911yescharacteristic
576C22×C22⋊C4C22×C1911yescharacteristic
577C22×C22⋊C4C22×C1911yescharacteristic
578C22×C22⋊C4C22×C1911yescharacteristic
579C22×C22⋊C4C22×C1911yescharacteristic
580C22×C22⋊C4C22×C1911yescharacteristic
581C22×C22⋊C4C22×C1911yescharacteristic
582C22×C42C22×C1911yescharacteristic
583C22×C42C22×C1911yescharacteristic
584#397—24no—
585#394—24no—
586#388—24no—
587#388—24no—
588C2×#95C22×C1911yescharacteristic
589C2×#95C22×C1911yescharacteristic
590C2×#95C22×C1911yescharacteristic
591C2×#95C22×C1911yescharacteristic
592C2×#95C22×C1911yescharacteristic
593C2×#95C22×C1911yescharacteristic
594C2×#95C22×C1911yescharacteristic
595C2×#95C22×C1911yescharacteristic
596C2×#95C22×C1911yescharacteristic
597C2×#95C22×C1911yescharacteristic
598C2×#95C22×C1911yescharacteristic
599C2×#95C22×C1911yescharacteristic
600C2×#95C22×C1911yescharacteristic
601C2×#95C22×C1911yescharacteristic
602C2×#95C22×C1911yescharacteristic
603C2×#95C22×C1911yescharacteristic
604C2×C19—82no—
605C2×C19—82no—
606C2×C19#245611yescharacteristic
607C2×C19#245911yescharacteristic
608C2×C19#247411yescharacteristic
609C2×C19#253111yescharacteristic
610C2×C19#255311yescharacteristic
611C2×C19#255411yescharacteristic
612C2×C19#255511yescharacteristic
613C2×C19#260111yescharacteristic
614C2×C19#260211yescharacteristic
615C2×C19#267111yescharacteristic
616C2×C19#269711yescharacteristic
617C2×C19#270511yescharacteristic
618C2×C19#275611yescharacteristic
619C2×C19#277911yescharacteristic
620C2×C19#280811yescharacteristic
621C25C23×C1911yescharacteristic
622C25C23×C1911yescharacteristic
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C23×C4C23×C1911yescharacteristic
631C23×C4C23×C1911yescharacteristic
632C23×C4C23×C1911yescharacteristic
633C23×C4C23×C1911yescharacteristic
634C23×C4C23×C1911yescharacteristic
635C23×C4C23×C1911yescharacteristic
636C23×C4C23×C1911yescharacteristic
637C23×C4C23×C1911yescharacteristic
638C23×C4C23×C1911yescharacteristic
639C23×C4C23×C1911yescharacteristic
640C23×C4C23×C1911yescharacteristic
641C23×C4C23×C1911yescharacteristic
642C23×C4C23×C1911yescharacteristic
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4D4×C1914yes—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95D4×C1914yescomplemented
713C19#1556511yescharacteristic, direct product factor, Sylow
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C2×D4×C1912yes—
743C24#41×C1912yes—
744C24C24×C1911yescharacteristic
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4C2×D4×C1912yes—
833C22×C4C2×D4×C1912yes—
834C22×C4C2×D4×C1912yes—
835C22×C4C2×D4×C1912yes—
836C22×C4C2×D4×C1912yes—
837C22×C4#41×C1912yes—
838C22×C4#41×C1912yes—
839C22×C4#41×C1912yes—
840C22×C4#41×C1912yes—
841C22×C4#41×C1912yes—
842C22×C4#41×C1912yes—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C42—44no—
860C42—44no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23C22×D4×C1911yescharacteristic
932C23C22×D4×C1911yescharacteristic
933C23C2×#41×C1911yescharacteristic
934C23C2×#41×C1911yescharacteristic
935C23C2×#41×C1911yescharacteristic
936C23C2×#41×C1911yescharacteristic
937C23C2×#41×C1911yescharacteristic
938C23C2×#41×C1911yescharacteristic
939C23C2×#41×C1911yescharacteristic
940C23C19×H(5,𝔽2)11yescharacteristic
941C23C19×H(5,𝔽2)11yescharacteristic
942C23C19×H(5,𝔽2)11yescharacteristic
943C23C19×H(5,𝔽2)11yescharacteristic
944C23C19×H(5,𝔽2)11yescharacteristic
945C23C19×2−1+411yescharacteristic
946D4—416no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22C19×#52511yescharacteristic
1069C22C19×#52511yescharacteristic
1070C22C19×#52911yescharacteristic
1071C22C19×#52911yescharacteristic
1072C22C19×#53211yescharacteristic
1073C22C19×#53211yescharacteristic
1074C22C19×#53411yescharacteristic
1075C22C19×#53711yescharacteristic
1076C22C19×#53811yescharacteristic
1077C22C19×#53811yescharacteristic
1078C22C19×#53811yescharacteristic
1079C22C19×#53811yescharacteristic
1080C22C19×#53911yescharacteristic
1081C22C19×#54011yescharacteristic
1082C22C19×#54211yescharacteristic
1083C22D42×C1911yescharacteristic
1084C22C19×#54611yescharacteristic
1085C22C19×#54611yescharacteristic
1086C22C19×#54611yescharacteristic
1087C22C19×#54611yescharacteristic
1088C22C19×#54711yescharacteristic
1089C22C19×#55011yescharacteristic
1090C22C19×#55111yescharacteristic
1091C22C19×#55111yescharacteristic
1092C22C19×#55111yescharacteristic
1093C22C19×#55211yescharacteristic
1094C22C19×#55311yescharacteristic
1095C22C19×#55311yescharacteristic
1096C22C19×#55311yescharacteristic
1097C22C19×#55511yescharacteristic
1098C22C19×#55511yescharacteristic
1099C22C19×#55611yescharacteristic
1100C22C19×#55911yescharacteristic
1101C22C19×#56011yescharacteristic
1102C22C19×#56211yescharacteristic
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C2—82no—
1117C2—82no—
1118C2C19×#245611yescharacteristic
1119C2C19×#245911yescharacteristic
1120C2C19×#247411yescharacteristic
1121C2C19×#253111yescharacteristic
1122C2C19×#255311yescharacteristic
1123C2C19×#255411yescharacteristic
1124C2C19×#255511yescharacteristic
1125C2C19×#260111yescharacteristic
1126C2C19×#260211yescharacteristic
1127C2C19×#267111yescharacteristic
1128C2C19×#269711yescharacteristic
1129C2C19×#270511yescharacteristic
1130C2C19×#275611yescharacteristic
1131C2C19×#277911yescharacteristic
1132C2C19×#280811yescharacteristic
subgroupG/H
center, socleC24×C19C24
commutator, Frattini, cosocleC24C24×C19
prime radicalC23×D4×C19C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C19×#397C2semidirect
3. C2×C19×#388C2semidirect
4. C2×C19×#388C2semidirect
5. C19×#1441C2semidirect
6. C19×#1441C2semidirect
7. C19×#1439C2semidirect
8. C19×#1439C2semidirect
9. C19×#1439C2semidirect
12. C19×#1437C2semidirect
13. C19×#1437C2semidirect
14. C19×#1436C2semidirect
15. C19×#1434C2semidirect
146. C19×#95D4semidirect
294. #15565C19direct (N × H)
472. C2×#397C2×C19semidirect
474. C2×#388C2×C19semidirect
475. C2×#388C2×C19semidirect
476. #1441C2×C19semidirect
477. #1441C2×C19semidirect
478. #1439C2×C19semidirect
479. #1439C2×C19semidirect
480. #1439C2×C19semidirect
483. #1437C2×C19semidirect
484. #1437C2×C19semidirect
485. #1436C2×C19semidirect
486. #1434C2×C19semidirect
712. #95D4×C19semidirect
713. C19#15565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#3972
C2×C19×#3942
C2×C19×#3882
C19×#14412
C19×#14392
C19×#14382
C19×#14372
C19×#14362
C19×#14342
#1556519