Finite Group Databasebeta

← C19×#14814 #18020773

Subgroups — C19×#14814 #18020773

Order 4864.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#397C211yesmaximal, characteristic, complemented
2C2×C19×#387C211yesmaximal, characteristic, complemented
3C2×C19×#386C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C19C211yesmaximal, characteristic, complemented
5C19×#1443C211yesmaximal, characteristic, complemented
6C19×#1443C211yesmaximal, 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×#1434C211yesmaximal, characteristic, complemented
15C19×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C19C2211yescharacteristic
17C24×C4×C19C2211yescharacteristic
18C22×C4⋊C4×C19C2211yescharacteristic
19C22×C4⋊C4×C19C2211yescharacteristic
20C22×C22⋊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×C42×C19C2211yescharacteristic
32C22×C42×C19C2211yescharacteristic
33C19×#397—24no—
34C19×#387—24no—
35C19×#386—24no—
36C4×C22⋊C4×C19—24no—
37C2×C19×#95C2211yescharacteristic
38C2×C19×#95C2211yescharacteristic
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—22no—
61C22×D4×C19—22no—
62C22×D4×C19—41no—
63C22×D4×C19—41no—
64C23×C4×C19—22no—
65C23×C4×C19—22no—
66C23×C4×C19—22no—
67C23×C4×C19—22no—
68C23×C4×C19—22no—
69C23×C4×C19—41no—
70C23×C4×C19—41no—
71C23×C4×C19C2311yescharacteristic
72C23×C4×C19C2311yescharacteristic
73C23×C4×C19C2311yescharacteristic
74C23×C4×C19C2311yescharacteristic
75C23×C4×C19C2311yescharacteristic
76C23×C4×C19C2311yescharacteristic
77C23×C4×C19C2311yescharacteristic
78C23×C4×C19C2311yescharacteristic
79C23×C4×C19C2311yescharacteristic
80C23×C4×C19C2311yescharacteristic
81C23×C4×C19C2311yescharacteristic
82C23×C4×C19C2311yescharacteristic
83C23×C4×C19C2311yescharacteristic
84C2×C4⋊C4×C19—22no—
85C2×C4⋊C4×C19—22no—
86C2×C4⋊C4×C19—22no—
87C2×C4⋊C4×C19—22no—
88C2×C4⋊C4×C19—22no—
89C2×C4⋊C4×C19—41no—
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—22no—
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×C42×C19—22no—
124C2×C42×C19—22no—
125C2×C42×C19—22no—
126C2×C42×C19—22no—
127C2×C42×C19—41no—
128C2×C42×C19—41no—
129C19×#95—22no—
130C19×#95—22no—
131C19×#95—22no—
132C19×#95—22no—
133C19×#95—22no—
134C19×#95—22no—
135C19×#95—22no—
136C19×#95—22no—
137C19×#95—22no—
138C19×#95—41no—
139C19×#95—41no—
140C19×#95—41no—
141C19×#95—41no—
142C19×#95—41no—
143C19×#95—41no—
144C19×#95—41no—
145C19×#95D414yes—
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#4112yes—
174C24×C19#4112yes—
175C24×C19#4112yes—
176C24×C19#4112yes—
177C24×C19C2411yescharacteristic
178C2×D4×C19—28no—
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—28no—
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×C19—21no—
266C22×C4×C19—44no—
267C22×C4×C19—44no—
268C22×C4×C19—44no—
269C22×C4×C19—44no—
270C22×C4×C19—44no—
271C22×C4×C19—44no—
272C22×C4×C19C2×D412yes—
273C22×C4×C19C2×D412yes—
274C22×C4×C19C2×D412yes—
275C22×C4×C19C2×D412yes—
276C22×C4×C19C2×D412yes—
277C22×C4×C19C2×D412yes—
278C22×C4×C19#4112yes—
279C22×C4×C19#4112yes—
280C22×C4×C19#4112yes—
281C22×C4×C19#4112yes—
282C22×C4×C19#4112yes—
283C4⋊C4×C19—28no—
284C4⋊C4×C19—44no—
285C22⋊C4×C19—28no—
286C22⋊C4×C19—28no—
287C22⋊C4×C19—44no—
288C22⋊C4×C19—44no—
289C22⋊C4×C19—44no—
290C22⋊C4×C19—44no—
291C22⋊C4×C19—44no—
292C22⋊C4×C19—44no—
293C22⋊C4×C19—44no—
294C22⋊C4×C19—44no—
295C22⋊C4×C19—44no—
296C42×C19—44no—
297C42×C19—44no—
298#14814C1911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
310C23×C19—22no—
311C23×C19—22no—
312C23×C19—22no—
313C23×C19—22no—
314C23×C19—22no—
315C23×C19—22no—
316C23×C19—22no—
317C23×C19—22no—
318C23×C19—22no—
319C23×C19—22no—
320C23×C19—22no—
321C23×C19—22no—
322C23×C19—22no—
323C23×C19—22no—
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×C19—41no—
366C23×C19—41no—
367C23×C19—41no—
368C23×C19#12614yes—
369C23×C19C22×D411yescharacteristic
370C23×C19C22×D411yescharacteristic
371C23×C19C2×#4111yescharacteristic
372C23×C19C2×#4111yescharacteristic
373C23×C19C2×#4111yescharacteristic
374C23×C19C2×#4111yescharacteristic
375C23×C19C2×#4111yescharacteristic
376C23×C19C2×#4111yescharacteristic
377C23×C19C2×#4111yescharacteristic
378C23×C19C2×#4111yescharacteristic
379C23×C19C2×#4111yescharacteristic
380C23×C19H(5,𝔽2)11yescharacteristic
381C23×C19H(5,𝔽2)11yescharacteristic
382C23×C19H(5,𝔽2)11yescharacteristic
383C23×C19H(5,𝔽2)11yescharacteristic
384D4×C19—416no—
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—22no—
415C2×C4×C19—416no—
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×C4×C19—41no—
473C2×C4×C19—41no—
474C2×C4×C19—41no—
475C2×C4×C19—41no—
476C2×C4×C19#12414yes—
477C2×#397C2×C1911yescharacteristic, complemented
478C2×#387C2×C1911yescharacteristic, complemented
479C2×#386C2×C1911yescharacteristic
480C2×C4×C22⋊C4C2×C1911yescharacteristic, complemented
481#1443C2×C1911yescharacteristic, complemented
482#1443C2×C1911yescharacteristic, complemented
483#1439C2×C1911yescharacteristic, complemented
484#1439C2×C1911yescharacteristic, complemented
485#1439C2×C1911yescharacteristic, complemented
486#1438C2×C1911yescharacteristic
487#1438C2×C1911yescharacteristic
488#1437C2×C1911yescharacteristic, complemented
489#1437C2×C1911yescharacteristic, complemented
490#1434C2×C1911yescharacteristic, complemented
491C22⋊#95C2×C1911yescharacteristic, complemented
492C22×C19—24no—
493C22×C19—24no—
494C22×C19—24no—
495C22×C19—42no—
496C22×C19—42no—
497C22×C19—42no—
498C22×C19—42no—
499C22×C19—42no—
500C22×C19—42no—
501C22×C19—42no—
502C22×C19—42no—
503C22×C19—42no—
504C22×C19—42no—
505C22×C19—42no—
506C22×C19—42no—
507C22×C19—42no—
508C22×C19—42no—
509C22×C19—42no—
510C22×C19—42no—
511C22×C19—42no—
512C22×C19—42no—
513C22×C19—42no—
514C22×C19—81no—
515C22×C19—81no—
516C22×C19—81no—
517C22×C19—81no—
518C22×C19—81no—
519C22×C19—81no—
520C22×C19—81no—
521C22×C19—81no—
522C22×C19#52511yescharacteristic
523C22×C19#52511yescharacteristic
524C22×C19#52511yescharacteristic
525C22×C19#52511yescharacteristic
526C22×C19#52511yescharacteristic
527C22×C19C2×#12411yescharacteristic
528C22×C19C2×#12611yescharacteristic
529C22×C19#52911yescharacteristic
530C22×C19#52911yescharacteristic
531C22×C19#52911yescharacteristic
532C22×C19#52911yescharacteristic
533C22×C19#52911yescharacteristic
534C22×C19#52911yescharacteristic
535C22×C19#53811yescharacteristic
536C22×C19#53811yescharacteristic
537C22×C19#53811yescharacteristic
538C22×C19#53811yescharacteristic
539C22×C19#54011yescharacteristic
540C22×C19#54011yescharacteristic
541C22×C19D4211yescharacteristic
542C22×C19#54611yescharacteristic
543C22×C19#54611yescharacteristic
544C22×C19#54611yescharacteristic
545C22×C19#54611yescharacteristic
546C22×C19#55011yescharacteristic
547C22×C19#55011yescharacteristic
548C22×C19#55111yescharacteristic
549C22×C19#55111yescharacteristic
550C22×C19#55111yescharacteristic
551C22×C19#55111yescharacteristic
552C22×C19#55111yescharacteristic
553C22×C19#55311yescharacteristic
554C22×C19#55311yescharacteristic
555C22×C19#55311yescharacteristic
556C22×C19#55311yescharacteristic
557C4×C19—24no—
558C4×C19—42no—
559C4×C19—42no—
560C4×C19—42no—
561C4×C19—42no—
562C4×C19—42no—
563C4×C19—42no—
564C4×C19—42no—
565C4×C19—42no—
566C4×C19—81no—
567C4×C19—81no—
568C4×C19—81no—
569C4×C19—81no—
570C23×D4C22×C1911yescharacteristic
571C24×C4C22×C1911yescharacteristic
572C22×C4⋊C4C22×C1911yescharacteristic
573C22×C4⋊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×C22⋊C4C22×C1911yescharacteristic
583C22×C22⋊C4C22×C1911yescharacteristic
584C22×C22⋊C4C22×C1911yescharacteristic
585C22×C42C22×C1911yescharacteristic
586C22×C42C22×C1911yescharacteristic
587#397—24no—
588#387—24no—
589#386—24no—
590C4×C22⋊C4—24no—
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×#95C22×C1911yescharacteristic
605C2×#95C22×C1911yescharacteristic
606C2×#95C22×C1911yescharacteristic
607C2×#95C22×C1911yescharacteristic
608C2×#95C22×C1911yescharacteristic
609C2×C19—44no—
610C2×C19—82no—
611C2×C19#239811yescharacteristic
612C2×C19#245611yescharacteristic
613C2×C19#245611yescharacteristic
614C2×C19#245711yescharacteristic
615C2×C19#246711yescharacteristic
616C2×C19#247111yescharacteristic
617C2×C19#247111yescharacteristic
618C2×C19#247211yescharacteristic
619C2×C19#248011yescharacteristic
620C2×C19#249011yescharacteristic
621C2×C19#251011yescharacteristic
622C2×C19#257611yescharacteristic
623C2×C19#257811yescharacteristic
624C2×C19#264811yescharacteristic
625C2×C19#285211yescharacteristic
626C25C23×C1911yescharacteristic
627C25C23×C1911yescharacteristic
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4C23×C1911yescharacteristic
643C23×C4C23×C1911yescharacteristic
644C23×C4C23×C1911yescharacteristic
645C23×C4C23×C1911yescharacteristic
646C23×C4C23×C1911yescharacteristic
647C23×C4C23×C1911yescharacteristic
648C23×C4C23×C1911yescharacteristic
649C23×C4C23×C1911yescharacteristic
650C23×C4C23×C1911yescharacteristic
651C23×C4C23×C1911yescharacteristic
652C23×C4C23×C1911yescharacteristic
653C23×C4C23×C1911yescharacteristic
654C23×C4C23×C1911yescharacteristic
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—41no—
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—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
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⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C42—22no—
695C2×C42—22no—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—41no—
699C2×C42—41no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95D4×C1914yes—
717#95D4×C1914yescomplemented
718C19#1481411yescharacteristic, direct product factor, Sylow
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—
742C24—21no—
743C24—21no—
744C24—21no—
745C24#41×C1912yes—
746C24#41×C1912yes—
747C24#41×C1912yes—
748C24#41×C1912yes—
749C24C24×C1911yescharacteristic
750C2×D4—28no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—28no—
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×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4C2×D4×C1912yes—
845C22×C4C2×D4×C1912yes—
846C22×C4C2×D4×C1912yes—
847C22×C4C2×D4×C1912yes—
848C22×C4C2×D4×C1912yes—
849C22×C4C2×D4×C1912yes—
850C22×C4#41×C1912yes—
851C22×C4#41×C1912yes—
852C22×C4#41×C1912yes—
853C22×C4#41×C1912yes—
854C22×C4#41×C1912yes—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C42—44no—
869C42—44no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
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—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23C19×#12614yes—
940C23C22×D4×C1911yescharacteristic
941C23C22×D4×C1911yescharacteristic
942C23C2×#41×C1911yescharacteristic
943C23C2×#41×C1911yescharacteristic
944C23C2×#41×C1911yescharacteristic
945C23C2×#41×C1911yescharacteristic
946C23C2×#41×C1911yescharacteristic
947C23C2×#41×C1911yescharacteristic
948C23C2×#41×C1911yescharacteristic
949C23C2×#41×C1911yescharacteristic
950C23C2×#41×C1911yescharacteristic
951C23C19×H(5,𝔽2)11yescharacteristic
952C23C19×H(5,𝔽2)11yescharacteristic
953C23C19×H(5,𝔽2)11yescharacteristic
954C23C19×H(5,𝔽2)11yescharacteristic
955D4—416no—
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—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—416no—
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—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4C19×#12414yes—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C19×#52511yescharacteristic
1079C22C19×#52511yescharacteristic
1080C22C19×#52511yescharacteristic
1081C22C19×#52511yescharacteristic
1082C22C19×#52511yescharacteristic
1083C22C2×C19×#12411yescharacteristic
1084C22C2×C19×#12611yescharacteristic
1085C22C19×#52911yescharacteristic
1086C22C19×#52911yescharacteristic
1087C22C19×#52911yescharacteristic
1088C22C19×#52911yescharacteristic
1089C22C19×#52911yescharacteristic
1090C22C19×#52911yescharacteristic
1091C22C19×#53811yescharacteristic
1092C22C19×#53811yescharacteristic
1093C22C19×#53811yescharacteristic
1094C22C19×#53811yescharacteristic
1095C22C19×#54011yescharacteristic
1096C22C19×#54011yescharacteristic
1097C22D42×C1911yescharacteristic
1098C22C19×#54611yescharacteristic
1099C22C19×#54611yescharacteristic
1100C22C19×#54611yescharacteristic
1101C22C19×#54611yescharacteristic
1102C22C19×#55011yescharacteristic
1103C22C19×#55011yescharacteristic
1104C22C19×#55111yescharacteristic
1105C22C19×#55111yescharacteristic
1106C22C19×#55111yescharacteristic
1107C22C19×#55111yescharacteristic
1108C22C19×#55111yescharacteristic
1109C22C19×#55311yescharacteristic
1110C22C19×#55311yescharacteristic
1111C22C19×#55311yescharacteristic
1112C22C19×#55311yescharacteristic
1113C4—24no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C19×#239811yescharacteristic
1129C2C19×#245611yescharacteristic
1130C2C19×#245611yescharacteristic
1131C2C19×#245711yescharacteristic
1132C2C19×#246711yescharacteristic
1133C2C19×#247111yescharacteristic
1134C2C19×#247111yescharacteristic
1135C2C19×#247211yescharacteristic
1136C2C19×#248011yescharacteristic
1137C2C19×#249011yescharacteristic
1138C2C19×#251011yescharacteristic
1139C2C19×#257611yescharacteristic
1140C2C19×#257811yescharacteristic
1141C2C19×#264811yescharacteristic
1142C2C19×#285211yescharacteristic
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
2. C2×C19×#387C2semidirect
4. C2×C4×C22⋊C4×C19C2semidirect
5. C19×#1443C2semidirect
6. C19×#1443C2semidirect
7. C19×#1439C2semidirect
8. C19×#1439C2semidirect
9. C19×#1439C2semidirect
12. C19×#1437C2semidirect
13. C19×#1437C2semidirect
14. C19×#1434C2semidirect
15. C19×C22⋊#95C2semidirect
146. C19×#95D4semidirect
298. #14814C19direct (N × H)
477. C2×#397C2×C19semidirect
478. C2×#387C2×C19semidirect
480. C2×C4×C22⋊C4C2×C19semidirect
481. #1443C2×C19semidirect
482. #1443C2×C19semidirect
483. #1439C2×C19semidirect
484. #1439C2×C19semidirect
485. #1439C2×C19semidirect
488. #1437C2×C19semidirect
489. #1437C2×C19semidirect
490. #1434C2×C19semidirect
491. C22⋊#95C2×C19semidirect
717. #95D4×C19semidirect
718. C19#14814direct (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×#3872
C2×C19×#3862
C2×C4×C22⋊C4×C192
C19×#14432
C19×#14392
C19×#14382
C19×#14372
C19×#14342
C19×C22⋊#952
#1481419