Finite Group Databasebeta

← C19×#14428 #18020387

Subgroups — C19×#14428 #18020387

Order 4864.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#390C211yesmaximal, characteristic
2C2×C19×#388C211yesmaximal, characteristic, complemented
3C2×C19×#386C211yesmaximal, characteristic
4C19×#1442C211yesmaximal, characteristic, complemented
5C19×#1440C211yesmaximal, characteristic, complemented
6C19×#1440C211yesmaximal, characteristic, complemented
7C19×#1440C211yesmaximal, characteristic, complemented
8C19×#1439C211yesmaximal, characteristic, complemented
9C19×#1438C211yesmaximal, characteristic
10C19×#1437C211yesmaximal, characteristic, complemented
11C19×#1436C211yesmaximal, characteristic, complemented
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×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×#390—24no—
34C19×#388—24no—
35C19×#386C418yescomplemented
36C2×C19×#95C2211yescharacteristic
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
54C25×C19C2311yescharacteristic
55C25×C19C2311yescharacteristic
56C22×D4×C19—22no—
57C22×D4×C19—22no—
58C22×D4×C19—22no—
59C22×D4×C19—22no—
60C22×D4×C19—41no—
61C22×D4×C19—41no—
62C22×D4×C19C2×C414yes—
63C23×C4×C19—41no—
64C23×C4×C19—41no—
65C23×C4×C19—41no—
66C23×C4×C19—41no—
67C23×C4×C19—41no—
68C23×C4×C19—41no—
69C23×C4×C19C2×C414yes—
70C23×C4×C19C2311yescharacteristic
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
83C2×C4⋊C4×C19—22no—
84C2×C4⋊C4×C19—22no—
85C2×C4⋊C4×C19—22no—
86C2×C4⋊C4×C19—22no—
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—41no—
101C2×C22⋊C4×C19—41no—
102C2×C22⋊C4×C19—41no—
103C2×C22⋊C4×C19—41no—
104C2×C22⋊C4×C19—41no—
105C2×C22⋊C4×C19—41no—
106C2×C22⋊C4×C19—41no—
107C2×C22⋊C4×C19—41no—
108C2×C22⋊C4×C19—41no—
109C2×C22⋊C4×C19—41no—
110C2×C22⋊C4×C19—41no—
111C2×C22⋊C4×C19—41no—
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×C19C2×C414yes—
119C2×C22⋊C4×C19C2×C414yes—
120C2×C22⋊C4×C19C2×C414yes—
121C2×C22⋊C4×C19D414yes—
122C2×C42×C19—22no—
123C2×C42×C19—22no—
124C2×C42×C19—22no—
125C2×C42×C19—41no—
126C2×C42×C19—41no—
127C2×C42×C19—41no—
128C19×#95—22no—
129C19×#95—22no—
130C19×#95—22no—
131C19×#95—22no—
132C19×#95—22no—
133C19×#95—41no—
134C19×#95—41no—
135C19×#95—41no—
136C19×#95—41no—
137C19×#95—41no—
138C19×#95—41no—
139C19×#95—41no—
140C19×#95—41no—
141C19×#95—41no—
142C19×#95—41no—
143C19×#95—41no—
144C19×#95C2×C414yes—
145C19×#95C2×C414yes—
146C24×C19—21no—
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×C19C22×C412yes—
173C24×C19C22×C412yes—
174C24×C19C2×D412yes—
175C24×C19#4112yes—
176C24×C19C2411yescharacteristic
177C2×D4×C19—28no—
178C2×D4×C19—28no—
179C2×D4×C19—44no—
180C2×D4×C19—44no—
181C2×D4×C19—44no—
182C2×D4×C19—44no—
183C2×D4×C19—44no—
184C22×C4×C19—21no—
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—44no—
265C22×C4×C19—44no—
266C22×C4×C19—44no—
267C22×C4×C19—44no—
268C22×C4×C19—44no—
269C22×C4×C19—44no—
270C22×C4×C19—44no—
271C22×C4×C19C22×C412yes—
272C22×C4×C19C22×C412yes—
273C22×C4×C19C22×C412yes—
274C22×C4×C19C22×C412yes—
275C22×C4×C19C22×C412yes—
276C22×C4×C19C2×D412yes—
277C22×C4×C19C2×D412yes—
278C22×C4×C19#4112yes—
279C22×C4×C19#4112yes—
280C22×C4×C19#4112yes—
281C22×C4×C19#4112yes—
282C4⋊C4×C19—44no—
283C4⋊C4×C19—44no—
284C22⋊C4×C19—28no—
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—
292C22⋊C4×C19—44no—
293C22⋊C4×C19—44no—
294C22⋊C4×C19—44no—
295C42×C19—44no—
296C42×C19—44no—
297#14428C1911yesmaximal, characteristic, direct product factor, Sylow
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—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—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×C19—41no—
366C23×C19—41no—
367C23×C19C4×D414yes—
368C23×C19C23×C411yescharacteristic
369C23×C19C22×D411yescharacteristic
370C23×C19C2×#4111yescharacteristic
371C23×C19C2×#4111yescharacteristic
372C23×C19C2×#4111yescharacteristic
373C23×C19C2×#4111yescharacteristic
374C23×C19C2×#4111yescharacteristic
375C23×C19H(5,𝔽2)11yescharacteristic
376C23×C19H(5,𝔽2)11yescharacteristic
377C23×C19H(5,𝔽2)11yescharacteristic
378C23×C19H(5,𝔽2)11yescharacteristic
379C23×C19H(5,𝔽2)11yescharacteristic
380C23×C19H(5,𝔽2)11yescharacteristic
381C23×C19H(5,𝔽2)11yescharacteristic
382C23×C192−1+411yescharacteristic
383D4×C19—416no—
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—416no—
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×C4×C19—41no—
473C2×C4×C19—41no—
474C2×C4×C19—41no—
475C2×C4×C19#11714yes—
476C2×#390C2×C1911yescharacteristic
477C2×#388C2×C1911yescharacteristic, complemented
478C2×#386C2×C1911yescharacteristic
479#1442C2×C1911yescharacteristic, complemented
480#1440C2×C1911yescharacteristic, complemented
481#1440C2×C1911yescharacteristic, complemented
482#1440C2×C1911yescharacteristic, complemented
483#1439C2×C1911yescharacteristic, complemented
484#1438C2×C1911yescharacteristic
485#1437C2×C1911yescharacteristic, complemented
486#1436C2×C1911yescharacteristic, complemented
487#1436C2×C1911yescharacteristic, complemented
488#1434C2×C1911yescharacteristic, complemented
489C22⋊#95C2×C1911yescharacteristic, complemented
490C22⋊#95C2×C1911yescharacteristic, complemented
491C22×C19—24no—
492C22×C19—24no—
493C22×C19—24no—
494C22×C19—42no—
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—81no—
514C22×C19—81no—
515C22×C19—81no—
516C22×C19—81no—
517C22×C19—81no—
518C22×C19—81no—
519C22×C19—81no—
520C22×C19—81no—
521C22×C19C2×#11711yescharacteristic
522C22×C19C2×C4×D411yescharacteristic
523C22×C19C4×#4111yescharacteristic
524C22×C19#51811yescharacteristic
525C22×C19#51811yescharacteristic
526C22×C19#51811yescharacteristic
527C22×C19#52011yescharacteristic
528C22×C19#53411yescharacteristic
529C22×C19#53711yescharacteristic
530C22×C19#53811yescharacteristic
531C22×C19#53811yescharacteristic
532C22×C19#53911yescharacteristic
533C22×C19#53911yescharacteristic
534C22×C19#54011yescharacteristic
535C22×C19#54011yescharacteristic
536C22×C19#54011yescharacteristic
537C22×C19#54211yescharacteristic
538C22×C19#54211yescharacteristic
539C22×C19#54211yescharacteristic
540C22×C19#54611yescharacteristic
541C22×C19#54611yescharacteristic
542C22×C19#54611yescharacteristic
543C22×C19#54611yescharacteristic
544C22×C19#55111yescharacteristic
545C22×C19#55111yescharacteristic
546C22×C19#55311yescharacteristic
547C22×C19#55311yescharacteristic
548C22×C19#55311yescharacteristic
549C22×C19#55311yescharacteristic
550C22×C19#55911yescharacteristic
551C22×C19#55911yescharacteristic
552C22×C19#56011yescharacteristic
553C22×C19#56011yescharacteristic
554C22×C19#56011yescharacteristic
555C22×C19H(3,𝔽4)11yescharacteristic
556C4×C19—24no—
557C4×C19—42no—
558C4×C19—42no—
559C4×C19—42no—
560C4×C19—42no—
561C4×C19—42no—
562C4×C19—42no—
563C4×C19—42no—
564C4×C19—42no—
565C4×C19—81no—
566C4×C19—81no—
567C4×C19—81no—
568C4×C19—81no—
569C23×D4C22×C1911yescharacteristic
570C24×C4C22×C1911yescharacteristic
571C22×C4⋊C4C22×C1911yescharacteristic
572C22×C4⋊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×C22⋊C4C22×C1911yescharacteristic
583C22×C22⋊C4C22×C1911yescharacteristic
584C22×C42C22×C1911yescharacteristic
585C22×C42C22×C1911yescharacteristic
586#390—24no—
587#388—24no—
588#386C4×C1918yescomplemented
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×#95C22×C1911yescharacteristic
605C2×#95C22×C1911yescharacteristic
606C2×#95C22×C1911yescharacteristic
607C2×C19—44no—
608C2×C19—82no—
609C2×C19#231911yescharacteristic
610C2×C19#232511yescharacteristic
611C2×C19#233511yescharacteristic
612C2×C19#234211yescharacteristic
613C2×C19#235711yescharacteristic
614C2×C19#236411yescharacteristic
615C2×C19#237511yescharacteristic
616C2×C19#268811yescharacteristic
617C2×C19#269111yescharacteristic
618C2×C19#270911yescharacteristic
619C2×C19#271211yescharacteristic
620C2×C19#275311yescharacteristic
621C2×C19#275711yescharacteristic
622C2×C19#279611yescharacteristic
623C2×C19#279711yescharacteristic
624C25C23×C1911yescharacteristic
625C25C23×C1911yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4C2×C4×C1914yes—
633C23×C4—41no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4C2×C4×C1914yes—
640C23×C4C23×C1911yescharacteristic
641C23×C4C23×C1911yescharacteristic
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
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
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—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
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⋊C4C2×C4×C1914yes—
689C2×C22⋊C4C2×C4×C1914yes—
690C2×C22⋊C4C2×C4×C1914yes—
691C2×C22⋊C4D4×C1914yes—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—41no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95C2×C4×C1914yes—
715#95C2×C4×C1914yes—
716C19#1442811yescharacteristic, direct product factor, Sylow
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—
742C24—21no—
743C24C22×C4×C1912yes—
744C24C22×C4×C1912yes—
745C24C2×D4×C1912yes—
746C24#41×C1912yes—
747C24C24×C1911yescharacteristic
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
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×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4C22×C4×C1912yes—
843C22×C4C22×C4×C1912yes—
844C22×C4C22×C4×C1912yes—
845C22×C4C22×C4×C1912yes—
846C22×C4C22×C4×C1912yes—
847C22×C4C2×D4×C1912yes—
848C22×C4C2×D4×C1912yes—
849C22×C4#41×C1912yes—
850C22×C4#41×C1912yes—
851C22×C4#41×C1912yes—
852C22×C4#41×C1912yes—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C42—44no—
867C42—44no—
868C23—22no—
869C23—22no—
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—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—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23C4×D4×C1914yes—
938C23C23×C4×C1911yescharacteristic
939C23C22×D4×C1911yescharacteristic
940C23C2×#41×C1911yescharacteristic
941C23C2×#41×C1911yescharacteristic
942C23C2×#41×C1911yescharacteristic
943C23C2×#41×C1911yescharacteristic
944C23C2×#41×C1911yescharacteristic
945C23C19×H(5,𝔽2)11yescharacteristic
946C23C19×H(5,𝔽2)11yescharacteristic
947C23C19×H(5,𝔽2)11yescharacteristic
948C23C19×H(5,𝔽2)11yescharacteristic
949C23C19×H(5,𝔽2)11yescharacteristic
950C23C19×H(5,𝔽2)11yescharacteristic
951C23C19×H(5,𝔽2)11yescharacteristic
952C23C19×2−1+411yescharacteristic
953D4—416no—
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—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—416no—
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—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4C19×#11714yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
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—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×C19×#11711yescharacteristic
1077C22C2×C4×D4×C1911yescharacteristic
1078C22C4×#41×C1911yescharacteristic
1079C22C19×#51811yescharacteristic
1080C22C19×#51811yescharacteristic
1081C22C19×#51811yescharacteristic
1082C22C19×#52011yescharacteristic
1083C22C19×#53411yescharacteristic
1084C22C19×#53711yescharacteristic
1085C22C19×#53811yescharacteristic
1086C22C19×#53811yescharacteristic
1087C22C19×#53911yescharacteristic
1088C22C19×#53911yescharacteristic
1089C22C19×#54011yescharacteristic
1090C22C19×#54011yescharacteristic
1091C22C19×#54011yescharacteristic
1092C22C19×#54211yescharacteristic
1093C22C19×#54211yescharacteristic
1094C22C19×#54211yescharacteristic
1095C22C19×#54611yescharacteristic
1096C22C19×#54611yescharacteristic
1097C22C19×#54611yescharacteristic
1098C22C19×#54611yescharacteristic
1099C22C19×#55111yescharacteristic
1100C22C19×#55111yescharacteristic
1101C22C19×#55311yescharacteristic
1102C22C19×#55311yescharacteristic
1103C22C19×#55311yescharacteristic
1104C22C19×#55311yescharacteristic
1105C22C19×#55911yescharacteristic
1106C22C19×#55911yescharacteristic
1107C22C19×#56011yescharacteristic
1108C22C19×#56011yescharacteristic
1109C22C19×#56011yescharacteristic
1110C22C19×H(3,𝔽4)11yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C2—44no—
1125C2—82no—
1126C2C19×#231911yescharacteristic
1127C2C19×#232511yescharacteristic
1128C2C19×#233511yescharacteristic
1129C2C19×#234211yescharacteristic
1130C2C19×#235711yescharacteristic
1131C2C19×#236411yescharacteristic
1132C2C19×#237511yescharacteristic
1133C2C19×#268811yescharacteristic
1134C2C19×#269111yescharacteristic
1135C2C19×#270911yescharacteristic
1136C2C19×#271211yescharacteristic
1137C2C19×#275311yescharacteristic
1138C2C19×#275711yescharacteristic
1139C2C19×#279611yescharacteristic
1140C2C19×#279711yescharacteristic
subgroupG/H
center, socleC24×C19C24
commutatorC23C23×C4×C19
Frattini, cosocleC24C24×C19
prime radicalC23×D4×C19C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C19×#388C2semidirect
4. C19×#1442C2semidirect
5. C19×#1440C2semidirect
6. C19×#1440C2semidirect
7. C19×#1440C2semidirect
8. C19×#1439C2semidirect
10. C19×#1437C2semidirect
11. C19×#1436C2semidirect
12. C19×#1436C2semidirect
13. C19×#1434C2semidirect
14. C19×C22⋊#95C2semidirect
15. C19×C22⋊#95C2semidirect
35. C19×#386C4semidirect
297. #14428C19direct (N × H)
477. C2×#388C2×C19semidirect
479. #1442C2×C19semidirect
480. #1440C2×C19semidirect
481. #1440C2×C19semidirect
482. #1440C2×C19semidirect
483. #1439C2×C19semidirect
485. #1437C2×C19semidirect
486. #1436C2×C19semidirect
487. #1436C2×C19semidirect
488. #1434C2×C19semidirect
489. C22⋊#95C2×C19semidirect
490. C22⋊#95C2×C19semidirect
588. #386C4×C19semidirect
716. C19#14428direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#3902
C2×C19×#3882
C2×C19×#3862
C19×#14422
C19×#14402
C19×#14392
C19×#14382
C19×#14372
C19×#14362
C19×#14342
C19×C22⋊#952
#1442819