Finite Group Databasebeta

← C19×#15508 #18021467

Subgroups — C19×#15508 #18021467

Order 4864.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#400C211yesmaximal, characteristic, complemented
2C2×C19×#396C211yesmaximal, characteristic, complemented
3C2×C19×#390C211yesmaximal, characteristic
4C2×C19×#386C211yesmaximal, characteristic
5C19×#1444C211yesmaximal, characteristic, complemented
6C19×#1439C211yesmaximal, characteristic, complemented
7C19×#1439C211yesmaximal, characteristic, complemented
8C19×#1439C211yesmaximal, characteristic, complemented
9C19×#1439C211yesmaximal, characteristic, complemented
10C19×#1439C211yesmaximal, characteristic, complemented
11C19×#1438C211yesmaximal, characteristic
12C19×#1436C211yesmaximal, characteristic, complemented
13C19×#1434C211yesmaximal, characteristic, complemented
14C19×C22⋊#95C211yesmaximal, characteristic, complemented
15C19×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C19C2211yescharacteristic
17C24×C4×C19C2211yescharacteristic
18C22×C4⋊C4×C19C2211yescharacteristic
19C22×C4⋊C4×C19C2211yescharacteristic
20C22×C4⋊C4×C19C2211yescharacteristic
21C22×C4⋊C4×C19C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C19C2211yescharacteristic
34C22×C42×C19C2211yescharacteristic
35C19×#400—24no—
36C19×#396—24no—
37C19×#390—24no—
38C19×#386—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—22no—
61C22×D4×C19—41no—
62C22×D4×C19—41no—
63C22×D4×C19Q814yes—
64C23×C4×C19—22no—
65C23×C4×C19—22no—
66C23×C4×C19—22no—
67C23×C4×C19—41no—
68C23×C4×C19—41no—
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—22no—
90C2×C4⋊C4×C19—22no—
91C2×C4⋊C4×C19—41no—
92C2×C4⋊C4×C19—41no—
93C2×C4⋊C4×C19—41no—
94C2×C4⋊C4×C19—41no—
95C2×C4⋊C4×C19—41no—
96C2×C4⋊C4×C19—41no—
97C2×C4⋊C4×C19—41no—
98C2×C4⋊C4×C19—41no—
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—22no—
114C2×C22⋊C4×C19—22no—
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×C19—41no—
125C2×C22⋊C4×C19—41no—
126C2×C22⋊C4×C19—41no—
127C2×C22⋊C4×C19—41no—
128C2×C22⋊C4×C19—41no—
129C2×C22⋊C4×C19—41no—
130C2×C22⋊C4×C19—41no—
131C2×C22⋊C4×C19D414yes—
132C2×C42×C19—22no—
133C2×C42×C19—22no—
134C2×C42×C19—41no—
135C19×#95—22no—
136C19×#95—22no—
137C19×#95—22no—
138C19×#95—22no—
139C19×#95—22no—
140C19×#95—22no—
141C19×#95—22no—
142C19×#95—22no—
143C19×#95—22no—
144C19×#95—22no—
145C19×#95—41no—
146C19×#95—41no—
147C19×#95—41no—
148C19×#95—41no—
149C19×#95—41no—
150C19×#95D414yes—
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×C19—21no—
176C24×C19—21no—
177C24×C19C2×D412yes—
178C24×C19C2×Q812yes—
179C24×C19C2×Q812yes—
180C24×C19#4112yes—
181C24×C19C2411yescharacteristic
182C2×D4×C19—28no—
183C2×D4×C19—28no—
184C2×D4×C19—44no—
185C2×D4×C19—44no—
186C2×D4×C19—44no—
187C2×D4×C19—44no—
188C2×D4×C19—44no—
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×C19—21no—
266C22×C4×C19—21no—
267C22×C4×C19—21no—
268C22×C4×C19—21no—
269C22×C4×C19—44no—
270C22×C4×C19—44no—
271C22×C4×C19—44no—
272C22×C4×C19—44no—
273C22×C4×C19—44no—
274C22×C4×C19—44no—
275C22×C4×C19—44no—
276C22×C4×C19C2×D412yes—
277C22×C4×C19C2×D412yes—
278C22×C4×C19C2×D412yes—
279C22×C4×C19C2×D412yes—
280C22×C4×C19C2×D412yes—
281C22×C4×C19C2×Q812yes—
282C22×C4×C19#4112yes—
283C22×C4×C19#4112yes—
284C22×C4×C19#4112yes—
285C22×C4×C19#4112yes—
286C22×C4×C19#4112yes—
287C4⋊C4×C19—44no—
288C4⋊C4×C19—44no—
289C4⋊C4×C19—44no—
290C4⋊C4×C19—44no—
291C4⋊C4×C19—44no—
292C22⋊C4×C19—44no—
293C22⋊C4×C19—44no—
294C22⋊C4×C19—44no—
295C22⋊C4×C19—44no—
296C22⋊C4×C19—44no—
297C22⋊C4×C19—44no—
298C22⋊C4×C19—44no—
299C22⋊C4×C19—44no—
300C22⋊C4×C19—44no—
301C22⋊C4×C19—44no—
302C22⋊C4×C19—44no—
303C42×C19—44no—
304#15508C1911yesmaximal, characteristic, direct product factor, Sylow
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—22no—
325C23×C19—22no—
326C23×C19—22no—
327C23×C19—22no—
328C23×C19—22no—
329C23×C19—22no—
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—41no—
369C23×C19—41no—
370C23×C19—41no—
371C23×C19—41no—
372C23×C19—41no—
373C23×C19—41no—
374C23×C19C22⋊Q814yes—
375C23×C19C22×D411yescharacteristic
376C23×C19C22×D411yescharacteristic
377C23×C19C22×Q811yescharacteristic
378C23×C19C2×#4111yescharacteristic
379C23×C19C2×#4111yescharacteristic
380C23×C19C2×#4111yescharacteristic
381C23×C19C2×#4111yescharacteristic
382C23×C19C2×#4111yescharacteristic
383C23×C19C2×#4111yescharacteristic
384C23×C19H(5,𝔽2)11yescharacteristic
385C23×C19H(5,𝔽2)11yescharacteristic
386C23×C19H(5,𝔽2)11yescharacteristic
387C23×C19H(5,𝔽2)11yescharacteristic
388C23×C19H(5,𝔽2)11yescharacteristic
389C23×C19H(5,𝔽2)11yescharacteristic
390D4×C19—416no—
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—22no—
416C2×C4×C19—22no—
417C2×C4×C19—22no—
418C2×C4×C19—22no—
419C2×C4×C19—22no—
420C2×C4×C19—22no—
421C2×C4×C19—416no—
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—41no—
477C2×C4×C19—41no—
478C2×C4×C19—41no—
479C2×C4×C19—41no—
480C2×C4×C19—41no—
481C2×C4×C19—41no—
482C2×C4×C19C22⋊Q814yes—
483C2×#400C2×C1911yescharacteristic, complemented
484C2×#396C2×C1911yescharacteristic, complemented
485C2×#390C2×C1911yescharacteristic
486C2×#386C2×C1911yescharacteristic
487#1444C2×C1911yescharacteristic, complemented
488#1439C2×C1911yescharacteristic, complemented
489#1439C2×C1911yescharacteristic, complemented
490#1439C2×C1911yescharacteristic, complemented
491#1439C2×C1911yescharacteristic, complemented
492#1439C2×C1911yescharacteristic, complemented
493#1438C2×C1911yescharacteristic
494#1436C2×C1911yescharacteristic, complemented
495#1434C2×C1911yescharacteristic, complemented
496C22⋊#95C2×C1911yescharacteristic, complemented
497C22⋊#95C2×C1911yescharacteristic, complemented
498C22×C19—24no—
499C22×C19—24no—
500C22×C19—24no—
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—42no—
515C22×C19—42no—
516C22×C19—42no—
517C22×C19—42no—
518C22×C19—42no—
519C22×C19—42no—
520C22×C19—81no—
521C22×C19—81no—
522C22×C19—81no—
523C22×C19—81no—
524C22×C19—81no—
525C22×C19—81no—
526C22×C19—81no—
527C22×C19—81no—
528C22×C19C2×C22⋊Q811yescharacteristic
529C22×C19C2×C22⋊Q811yescharacteristic
530C22×C19#52911yescharacteristic
531C22×C19#52911yescharacteristic
532C22×C19#53211yescharacteristic
533C22×C19#53211yescharacteristic
534C22×C19#53411yescharacteristic
535C22×C19#53511yescharacteristic
536C22×C19#53811yescharacteristic
537C22×C19#53811yescharacteristic
538C22×C19#53811yescharacteristic
539C22×C19#53811yescharacteristic
540C22×C19#54011yescharacteristic
541C22×C19#54011yescharacteristic
542C22×C19#54311yescharacteristic
543C22×C19D4211yescharacteristic
544C22×C19#54611yescharacteristic
545C22×C19#54611yescharacteristic
546C22×C19#54611yescharacteristic
547C22×C19#54611yescharacteristic
548C22×C19#54611yescharacteristic
549C22×C19#55011yescharacteristic
550C22×C19#55111yescharacteristic
551C22×C19#55111yescharacteristic
552C22×C19#55111yescharacteristic
553C22×C19#55311yescharacteristic
554C22×C19#55311yescharacteristic
555C22×C19#55311yescharacteristic
556C22×C19#55411yescharacteristic
557C22×C19#55411yescharacteristic
558C22×C19#55411yescharacteristic
559C22×C19#55411yescharacteristic
560C22×C19#55511yescharacteristic
561C22×C19#56011yescharacteristic
562C22×C19#56011yescharacteristic
563C4×C19—24no—
564C4×C19—42no—
565C4×C19—42no—
566C4×C19—42no—
567C4×C19—42no—
568C4×C19—42no—
569C4×C19—42no—
570C4×C19—42no—
571C4×C19—42no—
572C4×C19—81no—
573C4×C19—81no—
574C4×C19—81no—
575C4×C19—81no—
576C23×D4C22×C1911yescharacteristic
577C24×C4C22×C1911yescharacteristic
578C22×C4⋊C4C22×C1911yescharacteristic
579C22×C4⋊C4C22×C1911yescharacteristic
580C22×C4⋊C4C22×C1911yescharacteristic
581C22×C4⋊C4C22×C1911yescharacteristic
582C22×C4⋊C4C22×C1911yescharacteristic
583C22×C22⋊C4C22×C1911yescharacteristic
584C22×C22⋊C4C22×C1911yescharacteristic
585C22×C22⋊C4C22×C1911yescharacteristic
586C22×C22⋊C4C22×C1911yescharacteristic
587C22×C22⋊C4C22×C1911yescharacteristic
588C22×C22⋊C4C22×C1911yescharacteristic
589C22×C22⋊C4C22×C1911yescharacteristic
590C22×C22⋊C4C22×C1911yescharacteristic
591C22×C22⋊C4C22×C1911yescharacteristic
592C22×C22⋊C4C22×C1911yescharacteristic
593C22×C22⋊C4C22×C1911yescharacteristic
594C22×C42C22×C1911yescharacteristic
595#400—24no—
596#396—24no—
597#390—24no—
598#386—24no—
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×#95C22×C1911yescharacteristic
610C2×#95C22×C1911yescharacteristic
611C2×#95C22×C1911yescharacteristic
612C2×#95C22×C1911yescharacteristic
613C2×#95C22×C1911yescharacteristic
614C2×#95C22×C1911yescharacteristic
615C2×C19—44no—
616C2×C19—82no—
617C2×C19#243711yescharacteristic
618C2×C19#245011yescharacteristic
619C2×C19#245411yescharacteristic
620C2×C19#252611yescharacteristic
621C2×C19#255411yescharacteristic
622C2×C19#255511yescharacteristic
623C2×C19#255911yescharacteristic
624C2×C19#256411yescharacteristic
625C2×C19#256611yescharacteristic
626C2×C19#267311yescharacteristic
627C2×C19#268511yescharacteristic
628C2×C19#268811yescharacteristic
629C2×C19#274911yescharacteristic
630C2×C19#278011yescharacteristic
631C2×C19#278411yescharacteristic
632C25C23×C1911yescharacteristic
633C25C23×C1911yescharacteristic
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4Q8×C1914yes—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4C23×C1911yescharacteristic
649C23×C4C23×C1911yescharacteristic
650C23×C4C23×C1911yescharacteristic
651C23×C4C23×C1911yescharacteristic
652C23×C4C23×C1911yescharacteristic
653C23×C4C23×C1911yescharacteristic
654C23×C4C23×C1911yescharacteristic
655C23×C4C23×C1911yescharacteristic
656C23×C4C23×C1911yescharacteristic
657C23×C4C23×C1911yescharacteristic
658C23×C4C23×C1911yescharacteristic
659C23×C4C23×C1911yescharacteristic
660C23×C4C23×C1911yescharacteristic
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
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—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4D4×C1914yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95D4×C1914yes—
728C19#1550811yescharacteristic, direct product factor, Sylow
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—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24C2×D4×C1912yes—
756C24C2×Q8×C1912yes—
757C24C2×Q8×C1912yes—
758C24#41×C1912yes—
759C24C24×C1911yescharacteristic
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
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—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4C2×D4×C1912yes—
855C22×C4C2×D4×C1912yes—
856C22×C4C2×D4×C1912yes—
857C22×C4C2×D4×C1912yes—
858C22×C4C2×D4×C1912yes—
859C22×C4C2×Q8×C1912yes—
860C22×C4#41×C1912yes—
861C22×C4#41×C1912yes—
862C22×C4#41×C1912yes—
863C22×C4#41×C1912yes—
864C22×C4#41×C1912yes—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—44no—
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—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23C19×C22⋊Q814yes—
952C23C22×D4×C1911yescharacteristic
953C23C22×D4×C1911yescharacteristic
954C23C22×Q8×C1911yescharacteristic
955C23C2×#41×C1911yescharacteristic
956C23C2×#41×C1911yescharacteristic
957C23C2×#41×C1911yescharacteristic
958C23C2×#41×C1911yescharacteristic
959C23C2×#41×C1911yescharacteristic
960C23C2×#41×C1911yescharacteristic
961C23C19×H(5,𝔽2)11yescharacteristic
962C23C19×H(5,𝔽2)11yescharacteristic
963C23C19×H(5,𝔽2)11yescharacteristic
964C23C19×H(5,𝔽2)11yescharacteristic
965C23C19×H(5,𝔽2)11yescharacteristic
966C23C19×H(5,𝔽2)11yescharacteristic
967D4—416no—
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—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—416no—
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×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4C19×C22⋊Q814yes—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C2×C19×C22⋊Q811yescharacteristic
1091C22C2×C19×C22⋊Q811yescharacteristic
1092C22C19×#52911yescharacteristic
1093C22C19×#52911yescharacteristic
1094C22C19×#53211yescharacteristic
1095C22C19×#53211yescharacteristic
1096C22C19×#53411yescharacteristic
1097C22C19×#53511yescharacteristic
1098C22C19×#53811yescharacteristic
1099C22C19×#53811yescharacteristic
1100C22C19×#53811yescharacteristic
1101C22C19×#53811yescharacteristic
1102C22C19×#54011yescharacteristic
1103C22C19×#54011yescharacteristic
1104C22C19×#54311yescharacteristic
1105C22D42×C1911yescharacteristic
1106C22C19×#54611yescharacteristic
1107C22C19×#54611yescharacteristic
1108C22C19×#54611yescharacteristic
1109C22C19×#54611yescharacteristic
1110C22C19×#54611yescharacteristic
1111C22C19×#55011yescharacteristic
1112C22C19×#55111yescharacteristic
1113C22C19×#55111yescharacteristic
1114C22C19×#55111yescharacteristic
1115C22C19×#55311yescharacteristic
1116C22C19×#55311yescharacteristic
1117C22C19×#55311yescharacteristic
1118C22C19×#55411yescharacteristic
1119C22C19×#55411yescharacteristic
1120C22C19×#55411yescharacteristic
1121C22C19×#55411yescharacteristic
1122C22C19×#55511yescharacteristic
1123C22C19×#56011yescharacteristic
1124C22C19×#56011yescharacteristic
1125C4—24no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C2—44no—
1139C2—82no—
1140C2C19×#243711yescharacteristic
1141C2C19×#245011yescharacteristic
1142C2C19×#245411yescharacteristic
1143C2C19×#252611yescharacteristic
1144C2C19×#255411yescharacteristic
1145C2C19×#255511yescharacteristic
1146C2C19×#255911yescharacteristic
1147C2C19×#256411yescharacteristic
1148C2C19×#256611yescharacteristic
1149C2C19×#267311yescharacteristic
1150C2C19×#268511yescharacteristic
1151C2C19×#268811yescharacteristic
1152C2C19×#274911yescharacteristic
1153C2C19×#278011yescharacteristic
1154C2C19×#278411yescharacteristic
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×#400C2semidirect
2. C2×C19×#396C2semidirect
5. C19×#1444C2semidirect
6. C19×#1439C2semidirect
7. C19×#1439C2semidirect
8. C19×#1439C2semidirect
9. C19×#1439C2semidirect
10. C19×#1439C2semidirect
12. C19×#1436C2semidirect
13. C19×#1434C2semidirect
14. C19×C22⋊#95C2semidirect
15. C19×C22⋊#95C2semidirect
304. #15508C19direct (N × H)
483. C2×#400C2×C19semidirect
484. C2×#396C2×C19semidirect
487. #1444C2×C19semidirect
488. #1439C2×C19semidirect
489. #1439C2×C19semidirect
490. #1439C2×C19semidirect
491. #1439C2×C19semidirect
492. #1439C2×C19semidirect
494. #1436C2×C19semidirect
495. #1434C2×C19semidirect
496. C22⋊#95C2×C19semidirect
497. C22⋊#95C2×C19semidirect
728. C19#15508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#4002
C2×C19×#3962
C2×C19×#3902
C2×C19×#3862
C19×#14442
C19×#14392
C19×#14382
C19×#14362
C19×#14342
C19×C22⋊#952
#1550819