Finite Group Databasebeta

← C19×#34392 #18040351

Subgroups — C19×#34392 #18040351

Order 4864.

2090 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#529C211yesmaximal, characteristic
2C19×#2376C214yesmaximal, complemented
3C19×#2363C212yesmaximal
4C19×#2362C212yesmaximal, complemented
5C19×#2357C211yesmaximal, characteristic, complemented
6C19×#2356C211yesmaximal, characteristic, complemented
7C19×#2351C211yesmaximal, characteristic, complemented
8C19×#2349C211yesmaximal, characteristic, complemented
9C19×#2347C212yesmaximal, complemented
10C19×#2343C212yesmaximal, complemented
11C19×#2334C214yesmaximal, complemented
12C19×#2330C212yesmaximal, complemented
13C19×#2326C212yesmaximal, complemented
14C19×#2319C212yesmaximal, complemented
15C19×#2318C212yesmaximal, complemented
16C19×#2285C211yesmaximal, characteristic, complemented
17C19×#2283C211yesmaximal, characteristic, complemented
18C19×#529C4116yescomplemented
19C2×C19×#126C2212yes—
20C2×C19×#125C2211yescharacteristic
21C2×C19×#124C2211yescharacteristic
22C2×C19×#123C2212yes—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×#121C2211yescharacteristic
25C2×C4×Q8×C19C2212yes—
26C2×C4×Q8×C19C2211yescharacteristic
27C2×C4×D4×C19C2212yes—
28C2×C4×D4×C19C2211yescharacteristic
29C2×C4×D4×C19C2212yes—
30C2×C19×#117C2212yes—
31C2×C19×#117C2212yes—
32C22×C42×C19C2211yescharacteristic
33C19×#391C2212yes—
34C19×#390C2214yes—
35C19×#390C2212yes—
36C19×#389C2214yes—
37C19×#389C2214yes—
38C19×#389C2212yes—
39C19×#389C2212yes—
40C19×#389C2214yes—
41C19×#388C2214yes—
42C19×#388C2214yes—
43C19×#388C2214yes—
44C19×#388C2214yes—
45C19×#388C2214yes—
46C19×#388C2214yes—
47C19×#387C2214yes—
48C19×#387C2214yes—
49C19×#387C2214yes—
50C19×#387C2214yes—
51C19×#386C2214yes—
52C19×#385C2214yes—
53C19×#385C2214yes—
54C19×#385C2214yes—
55C19×#384C2212yes—
56C19×#383C2211yescharacteristic
57C19×#383C2211yescharacteristic
58C19×#383C2212yes—
59C19×#382C2212yes—
60C19×#382C2211yescharacteristic
61C19×#382C2211yescharacteristic
62C19×#382C2212yes—
63C19×#381C2211yescharacteristic
64C19×#381C2211yescharacteristic
65C19×#381C2212yes—
66C19×#380C2212yes—
67C19×#380C2212yes—
68C19×#380C2212yes—
69C19×#380C2212yes—
70C4×C4⋊C4×C19C2211yescharacteristic
71C4×C4⋊C4×C19C2211yescharacteristic
72C4×C4⋊C4×C19C2212yes—
73C4×C4⋊C4×C19C2212yes—
74C4×C4⋊C4×C19C2212yes—
75C4×C4⋊C4×C19C2212yes—
76C4×C4⋊C4×C19C2212yes—
77C4×C4⋊C4×C19C2214yes—
78C4×C22⋊C4×C19C2212yes—
79C4×C22⋊C4×C19C2212yes—
80C4×C22⋊C4×C19C2214yes—
81C19×#376C2212yes—
82C19×#376C2212yes—
83C2×C19×#95C2212yes—
84C22×Q8×C19C2311yescharacteristic
85C22×D4×C19C2311yescharacteristic
86C22×D4×C19C2312yes—
87C23×C4×C19C2311yescharacteristic
88C23×C4×C19C2314yes—
89C23×C4×C19C2312yes—
90C23×C4×C19C2311yescharacteristic
91C23×C4×C19C2311yescharacteristic
92C19×#126C2×C4116yescomplemented
93C19×#125C2×C418yescomplemented
94C19×#124C2×C418yes—
95C19×#123C2×C4116yescomplemented
96C19×C22⋊Q8C2×C418yescomplemented
97C19×#121C2×C418yes—
98C4×Q8×C19—44no—
99C4×Q8×C19C2×C418yescomplemented
100C4×D4×C19—44no—
101C4×D4×C19C2×C418yes—
102C4×D4×C19C2×C4116yescomplemented
103C19×#117—44no—
104C19×#117C2×C4116yescomplemented
105C2×C4⋊C4×C19C2312yes—
106C2×C4⋊C4×C19C2312yes—
107C2×C4⋊C4×C19C2312yes—
108C2×C4⋊C4×C19C2312yes—
109C2×C4⋊C4×C19C2314yes—
110C2×C4⋊C4×C19C2314yes—
111C2×C4⋊C4×C19C2314yes—
112C2×C4⋊C4×C19C2314yes—
113C2×C4⋊C4×C19C2314yes—
114C2×C4⋊C4×C19C2312yes—
115C2×C4⋊C4×C19C2311yescharacteristic
116C2×C4⋊C4×C19C2311yescharacteristic
117C2×C4⋊C4×C19C2312yes—
118C2×C4⋊C4×C19C2312yes—
119C2×C4⋊C4×C19C2312yes—
120C2×C22⋊C4×C19C2312yes—
121C2×C22⋊C4×C19C2312yes—
122C2×C22⋊C4×C19C2314yes—
123C2×C22⋊C4×C19C2314yes—
124C2×C22⋊C4×C19C2314yes—
125C2×C22⋊C4×C19C2314yes—
126C2×C22⋊C4×C19C2312yes—
127C2×C22⋊C4×C19C2312yes—
128C2×C22⋊C4×C19C2312yes—
129C2×C22⋊C4×C19C2312yes—
130C2×C22⋊C4×C19C2312yes—
131C2×C42×C19C2×C418yescomplemented
132C2×C42×C19C2312yes—
133C2×C42×C19C2312yes—
134C2×C42×C19C2314yes—
135C2×C42×C19C2314yes—
136C2×C42×C19C2314yes—
137C2×C42×C19C2314yes—
138C2×C42×C19C2311yescharacteristic
139C2×C42×C19C2312yes—
140C2×C42×C19C2311yescharacteristic
141C2×C42×C19C2311yescharacteristic
142C2×C42×C19C2311yescharacteristic
143C19×#95C2311yescharacteristic
144C19×#95C2312yes—
145C19×#95C2314yes—
146C19×#95C2311yescharacteristic
147C19×#95C2312yes—
148C19×#95C2312yes—
149C19×#95C2312yes—
150C19×#95C2312yes—
151C19×#95C2314yes—
152C19×#95C2312yes—
153C19×#95C2311yescharacteristic
154C19×#95C2312yes—
155C19×#95C2312yes—
156C19×#95C2314yes—
157C19×#95C2311yescharacteristic
158C19×#95C2312yes—
159C19×#95C2312yes—
160C19×#95C2314yes—
161C19×#95C2314yes—
162C19×#95C2314yes—
163C24×C19C2411yescharacteristic
164C24×C19C2412yes—
165C2×Q8×C19—22no—
166C2×Q8×C19—22no—
167C2×Q8×C19C22×C414yes—
168C2×D4×C19—22no—
169C2×D4×C19—22no—
170C2×D4×C19—44no—
171C2×D4×C19C22×C414yes—
172C2×D4×C19C22×C418yes—
173C22×C4×C19—22no—
174C22×C4×C19—22no—
175C22×C4×C19—44no—
176C22×C4×C19—42no—
177C22×C4×C19—42no—
178C22×C4×C19—44no—
179C22×C4×C19—44no—
180C22×C4×C19—44no—
181C22×C4×C19C22×C414yes—
182C22×C4×C19C22×C414yes—
183C22×C4×C19C22×C414yes—
184C22×C4×C19C22×C418yes—
185C22×C4×C19C2412yes—
186C22×C4×C19C2414yes—
187C22×C4×C19C2412yes—
188C22×C4×C19C2412yes—
189C22×C4×C19C2414yes—
190C22×C4×C19C2412yes—
191C22×C4×C19C2411yescharacteristic
192C22×C4×C19C2411yescharacteristic
193C22×C4×C19C2412yes—
194C22×C4×C19C2412yes—
195C22×C4×C19C2412yes—
196C22×C4×C19C2411yescharacteristic
197C22×C4×C19C2411yescharacteristic
198C22×C4×C19C2411yescharacteristic
199C22×C4×C19C2411yescharacteristic
200C4⋊C4×C19—24no—
201C4⋊C4×C19—24no—
202C4⋊C4×C19—44no—
203C4⋊C4×C19—44no—
204C4⋊C4×C19—42no—
205C4⋊C4×C19—44no—
206C4⋊C4×C19—44no—
207C4⋊C4×C19—42no—
208C4⋊C4×C19—44no—
209C4⋊C4×C19C22×C418yes—
210C4⋊C4×C19C22×C418yes—
211C4⋊C4×C19C22×C414yes—
212C4⋊C4×C19C22×C418yes—
213C4⋊C4×C19C22×C414yes—
214C4⋊C4×C19C22×C418yes—
215C22⋊C4×C19—42no—
216C22⋊C4×C19—44no—
217C22⋊C4×C19—42no—
218C22⋊C4×C19—44no—
219C22⋊C4×C19—44no—
220C22⋊C4×C19—44no—
221C22⋊C4×C19C22×C418yes—
222C22⋊C4×C19C22×C418yes—
223C22⋊C4×C19C22×C418yes—
224C22⋊C4×C19C22×C418yes—
225C22⋊C4×C19C22×C418yes—
226C42×C19—24no—
227C42×C19—24no—
228C42×C19—44no—
229C42×C19—44no—
230C42×C19—44no—
231C42×C19—44no—
232C42×C19C22×C414yes—
233C42×C19C22×C414yes—
234C42×C19C22×C414yes—
235C42×C19C22×C414yes—
236C42×C19C22×C418yes—
237#34392C1911yesmaximal, characteristic, direct product factor, Sylow
238C23×C19—21no—
239C23×C19—22no—
240C23×C19—21no—
241C23×C19—22no—
242C23×C19—22no—
243C23×C19—24no—
244C23×C19—24no—
245C23×C19—22no—
246C23×C19C23×C414yes—
247C23×C19C23×C412yes—
248C23×C19C2511yescharacteristic
249Q8×C19—28no—
250D4×C19—28no—
251D4×C19—48no—
252C2×C4×C19—21no—
253C2×C4×C19—22no—
254C2×C4×C19—21no—
255C2×C4×C19—22no—
256C2×C4×C19—24no—
257C2×C4×C19—24no—
258C2×C4×C19—22no—
259C2×C4×C19—22no—
260C2×C4×C19—22no—
261C2×C4×C19—22no—
262C2×C4×C19—28no—
263C2×C4×C19—22no—
264C2×C4×C19—22no—
265C2×C4×C19—24no—
266C2×C4×C19—24no—
267C2×C4×C19—22no—
268C2×C4×C19—22no—
269C2×C4×C19—22no—
270C2×C4×C19—22no—
271C2×C4×C19—24no—
272C2×C4×C19—24no—
273C2×C4×C19—22no—
274C2×C4×C19—22no—
275C2×C4×C19—22no—
276C2×C4×C19—24no—
277C2×C4×C19—22no—
278C2×C4×C19—22no—
279C2×C4×C19—24no—
280C2×C4×C19—22no—
281C2×C4×C19—44no—
282C2×C4×C19—48no—
283C2×C4×C19—44no—
284C2×C4×C19—88no—
285C2×C4×C19C23×C412yes—
286C2×C4×C19C23×C412yes—
287C2×C4×C19C23×C412yes—
288C2×C4×C19C23×C412yes—
289C2×C4×C19C23×C412yes—
290C2×C4×C19C23×C414yes—
291C2×C4×C19C23×C414yes—
292C2×C4×C19C23×C414yes—
293C2×C4×C19C23×C412yes—
294C2×C4×C19H(5,𝔽2)12yes—
295C2×C4×C192−1+412yes—
296C2×#529C2×C1911yescharacteristic
297#2376C2×C1914yescomplemented
298#2363C2×C1912yes—
299#2362C2×C1912yescomplemented
300#2357C2×C1911yescharacteristic, complemented
301#2356C2×C1911yescharacteristic, complemented
302#2351C2×C1911yescharacteristic, complemented
303#2349C2×C1911yescharacteristic, complemented
304#2347C2×C1912yescomplemented
305#2343C2×C1912yescomplemented
306#2334C2×C1914yescomplemented
307#2330C2×C1912yescomplemented
308#2326C2×C1912yescomplemented
309#2319C2×C1912yescomplemented
310#2318C2×C1912yescomplemented
311#2285C2×C1911yescharacteristic, complemented
312#2283C2×C1911yescharacteristic, complemented
313C22×C19—22no—
314C22×C19—24no—
315C22×C19—22no—
316C22×C19—22no—
317C22×C19—24no—
318C22×C19—24no—
319C22×C19—44no—
320C22×C19—42no—
321C22×C19—42no—
322C22×C19—44no—
323C22×C19C24×C411yescharacteristic
324C22×C19C2×H(5,𝔽2)11yescharacteristic
325C22×C19C2×2−1+411yescharacteristic
326C22×C19#58512yes—
327C22×C19#58512yes—
328C4×C19—22no—
329C4×C19—24no—
330C4×C19—22no—
331C4×C19—24no—
332C4×C19—22no—
333C4×C19—22no—
334C4×C19—22no—
335C4×C19—24no—
336C4×C19—42no—
337C4×C19—44no—
338C4×C19—44no—
339C4×C19—42no—
340C4×C19—42no—
341C4×C19—42no—
342C4×C19#52014yes—
343#529C4×C19116yescomplemented
344C2×#126C22×C1912yes—
345C2×#125C22×C1911yescharacteristic
346C2×#124C22×C1911yescharacteristic
347C2×#123C22×C1912yes—
348C2×C22⋊Q8C22×C1911yescharacteristic
349C2×#121C22×C1911yescharacteristic
350C2×C4×Q8C22×C1912yes—
351C2×C4×Q8C22×C1911yescharacteristic
352C2×C4×D4C22×C1912yes—
353C2×C4×D4C22×C1911yescharacteristic
354C2×C4×D4C22×C1912yes—
355C2×#117C22×C1912yes—
356C2×#117C22×C1912yes—
357C22×C42C22×C1911yescharacteristic
358#391C22×C1912yes—
359#390C22×C1914yes—
360#390C22×C1912yes—
361#389C22×C1914yes—
362#389C22×C1914yes—
363#389C22×C1912yes—
364#389C22×C1912yes—
365#389C22×C1914yes—
366#388C22×C1914yes—
367#388C22×C1914yes—
368#388C22×C1914yes—
369#388C22×C1914yes—
370#388C22×C1914yes—
371#388C22×C1914yes—
372#387C22×C1914yes—
373#387C22×C1914yes—
374#387C22×C1914yes—
375#387C22×C1914yes—
376#386C22×C1914yes—
377#385C22×C1914yes—
378#385C22×C1914yes—
379#385C22×C1914yes—
380#384C22×C1912yes—
381#383C22×C1912yes—
382#383C22×C1911yescharacteristic
383#383C22×C1911yescharacteristic
384#382C22×C1912yes—
385#382C22×C1912yes—
386#382C22×C1911yescharacteristic
387#382C22×C1911yescharacteristic
388#381C22×C1911yescharacteristic
389#381C22×C1911yescharacteristic
390#381C22×C1912yes—
391#380C22×C1912yes—
392#380C22×C1912yes—
393#380C22×C1912yes—
394#380C22×C1912yes—
395C4×C4⋊C4C22×C1912yes—
396C4×C4⋊C4C22×C1912yes—
397C4×C4⋊C4C22×C1912yes—
398C4×C4⋊C4C22×C1912yes—
399C4×C4⋊C4C22×C1914yes—
400C4×C4⋊C4C22×C1912yes—
401C4×C4⋊C4C22×C1911yescharacteristic
402C4×C4⋊C4C22×C1911yescharacteristic
403C4×C22⋊C4C22×C1912yes—
404C4×C22⋊C4C22×C1914yes—
405C4×C22⋊C4C22×C1912yes—
406#376C22×C1912yes—
407#376C22×C1912yes—
408C2×#95C22×C1912yes—
409C2×C19—42no—
410C2×C19—44no—
411C2×C19C2×#52011yescharacteristic
412C2×C19#342811yescharacteristic
413C2×C19#342811yescharacteristic
414C2×C19#356212yes—
415C2×C19#356512yes—
416C22×Q8C23×C1911yescharacteristic
417C22×D4C23×C1911yescharacteristic
418C22×D4C23×C1912yes—
419C23×C4C23×C1911yescharacteristic
420C23×C4C23×C1914yes—
421C23×C4C23×C1912yes—
422C23×C4C23×C1911yescharacteristic
423C23×C4C23×C1911yescharacteristic
424#126C2×C4×C19116yescomplemented
425#125C2×C4×C1918yescomplemented
426#124C2×C4×C1918yes—
427#123C2×C4×C19116yescomplemented
428C22⋊Q8C2×C4×C1918yescomplemented
429#121C2×C4×C1918yes—
430C4×Q8—44no—
431C4×Q8C2×C4×C1918yescomplemented
432C4×D4—44no—
433C4×D4C2×C4×C1918yes—
434C4×D4C2×C4×C19116yescomplemented
435#117—44no—
436#117C2×C4×C19116yescomplemented
437C2×C4⋊C4C23×C1912yes—
438C2×C4⋊C4C23×C1912yes—
439C2×C4⋊C4C23×C1914yes—
440C2×C4⋊C4C23×C1912yes—
441C2×C4⋊C4C23×C1912yes—
442C2×C4⋊C4C23×C1914yes—
443C2×C4⋊C4C23×C1914yes—
444C2×C4⋊C4C23×C1914yes—
445C2×C4⋊C4C23×C1914yes—
446C2×C4⋊C4C23×C1912yes—
447C2×C4⋊C4C23×C1912yes—
448C2×C4⋊C4C23×C1911yescharacteristic
449C2×C4⋊C4C23×C1912yes—
450C2×C4⋊C4C23×C1911yescharacteristic
451C2×C4⋊C4C23×C1912yes—
452C2×C22⋊C4C23×C1914yes—
453C2×C22⋊C4C23×C1914yes—
454C2×C22⋊C4C23×C1912yes—
455C2×C22⋊C4C23×C1912yes—
456C2×C22⋊C4C23×C1914yes—
457C2×C22⋊C4C23×C1914yes—
458C2×C22⋊C4C23×C1912yes—
459C2×C22⋊C4C23×C1912yes—
460C2×C22⋊C4C23×C1912yes—
461C2×C22⋊C4C23×C1912yes—
462C2×C22⋊C4C23×C1912yes—
463C2×C42C2×C4×C1918yescomplemented
464C2×C42C23×C1912yes—
465C2×C42C23×C1912yes—
466C2×C42C23×C1914yes—
467C2×C42C23×C1914yes—
468C2×C42C23×C1914yes—
469C2×C42C23×C1914yes—
470C2×C42C23×C1911yescharacteristic
471C2×C42C23×C1912yes—
472C2×C42C23×C1911yescharacteristic
473C2×C42C23×C1911yescharacteristic
474C2×C42C23×C1911yescharacteristic
475#95C23×C1911yescharacteristic
476#95C23×C1912yes—
477#95C23×C1914yes—
478#95C23×C1911yescharacteristic
479#95C23×C1912yes—
480#95C23×C1912yes—
481#95C23×C1912yes—
482#95C23×C1912yes—
483#95C23×C1914yes—
484#95C23×C1912yes—
485#95C23×C1911yescharacteristic
486#95C23×C1912yes—
487#95C23×C1912yes—
488#95C23×C1914yes—
489#95C23×C1911yescharacteristic
490#95C23×C1912yes—
491#95C23×C1912yes—
492#95C23×C1914yes—
493#95C23×C1914yes—
494#95C23×C1914yes—
495C19#3439211yescharacteristic, direct product factor, Sylow
496C24C24×C1911yescharacteristic
497C24C24×C1912yes—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8C22×C4×C1914yes—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—44no—
504C2×D4C22×C4×C1914yes—
505C2×D4C22×C4×C1918yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4C22×C4×C1914yes—
515C22×C4C22×C4×C1914yes—
516C22×C4C22×C4×C1914yes—
517C22×C4C22×C4×C1918yes—
518C22×C4C24×C1912yes—
519C22×C4C24×C1912yes—
520C22×C4C24×C1912yes—
521C22×C4C24×C1914yes—
522C22×C4C24×C1912yes—
523C22×C4C24×C1914yes—
524C22×C4C24×C1911yescharacteristic
525C22×C4C24×C1911yescharacteristic
526C22×C4C24×C1912yes—
527C22×C4C24×C1912yes—
528C22×C4C24×C1912yes—
529C22×C4C24×C1911yescharacteristic
530C22×C4C24×C1911yescharacteristic
531C22×C4C24×C1911yescharacteristic
532C22×C4C24×C1911yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C4⋊C4—42no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—42no—
541C4⋊C4—44no—
542C4⋊C4C22×C4×C1918yes—
543C4⋊C4C22×C4×C1918yes—
544C4⋊C4C22×C4×C1914yes—
545C4⋊C4C22×C4×C1918yes—
546C4⋊C4C22×C4×C1914yes—
547C4⋊C4C22×C4×C1918yes—
548C22⋊C4—42no—
549C22⋊C4—44no—
550C22⋊C4—42no—
551C22⋊C4—44no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C22⋊C4C22×C4×C1918yes—
555C22⋊C4C22×C4×C1918yes—
556C22⋊C4C22×C4×C1918yes—
557C22⋊C4C22×C4×C1918yes—
558C22⋊C4C22×C4×C1918yes—
559C42—24no—
560C42—24no—
561C42—44no—
562C42—44no—
563C42—44no—
564C42—44no—
565C42C22×C4×C1914yes—
566C42C22×C4×C1914yes—
567C42C22×C4×C1914yes—
568C42C22×C4×C1914yes—
569C42C22×C4×C1918yes—
570C23—21no—
571C23—22no—
572C23—21no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23C23×C4×C1914yes—
579C23C23×C4×C1912yes—
580C23C25×C1911yescharacteristic
581Q8—28no—
582D4—28no—
583D4—48no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—28no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—44no—
614C2×C4—48no—
615C2×C4—44no—
616C2×C4—88no—
617C2×C4C23×C4×C1912yes—
618C2×C4C23×C4×C1912yes—
619C2×C4C23×C4×C1912yes—
620C2×C4C23×C4×C1912yes—
621C2×C4C23×C4×C1912yes—
622C2×C4C23×C4×C1914yes—
623C2×C4C23×C4×C1914yes—
624C2×C4C23×C4×C1914yes—
625C2×C4C23×C4×C1912yes—
626C2×C4C19×H(5,𝔽2)12yes—
627C2×C4C19×2−1+412yes—
628C22—22no—
629C22—24no—
630C22—22no—
631C22—22no—
632C22—24no—
633C22—24no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22C24×C4×C1911yescharacteristic
639C22C2×C19×H(5,𝔽2)11yescharacteristic
640C22C2×C19×2−1+411yescharacteristic
641C22C19×#58512yes—
642C22C19×#58512yes—
643C4—22no—
644C4—24no—
645C4—22no—
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—24no—
651C4—42no—
652C4—44no—
653C4—42no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4C19×#52014yes—
658C2—42no—
659C2—44no—
660C2C2×C19×#52011yescharacteristic
661C2C19×#342811yescharacteristic
662C2C19×#342811yescharacteristic
663C2C19×#356212yes—
664C2C19×#356512yes—
subgroupG/H
center, socleC23×C19C25
commutatorC22C24×C4×C19
Frattini, cosocleC23C25×C19
prime radicalC2×C19×#121C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2376C2semidirect
4. C19×#2362C2semidirect
5. C19×#2357C2semidirect
6. C19×#2356C2semidirect
7. C19×#2351C2semidirect
8. C19×#2349C2semidirect
9. C19×#2347C2semidirect
10. C19×#2343C2semidirect
11. C19×#2334C2semidirect
12. C19×#2330C2semidirect
13. C19×#2326C2semidirect
14. C19×#2319C2semidirect
15. C19×#2318C2semidirect
16. C19×#2285C2semidirect
17. C19×#2283C2semidirect
18. C19×#529C4semidirect
92. C19×#126C2×C4semidirect
93. C19×#125C2×C4semidirect
95. C19×#123C2×C4semidirect
96. C19×C22⋊Q8C2×C4semidirect
99. C4×Q8×C19C2×C4semidirect
102. C4×D4×C19C2×C4semidirect
104. C19×#117C2×C4semidirect
131. C2×C42×C19C2×C4semidirect
237. #34392C19direct (N × H)
297. #2376C2×C19semidirect
299. #2362C2×C19semidirect
300. #2357C2×C19semidirect
301. #2356C2×C19semidirect
302. #2351C2×C19semidirect
303. #2349C2×C19semidirect
304. #2347C2×C19semidirect
305. #2343C2×C19semidirect
306. #2334C2×C19semidirect
307. #2330C2×C19semidirect
308. #2326C2×C19semidirect
309. #2319C2×C19semidirect
310. #2318C2×C19semidirect
311. #2285C2×C19semidirect
312. #2283C2×C19semidirect
343. #529C4×C19semidirect
424. #126C2×C4×C19semidirect
425. #125C2×C4×C19semidirect
427. #123C2×C4×C19semidirect
428. C22⋊Q8C2×C4×C19semidirect
431. C4×Q8C2×C4×C19semidirect
434. C4×D4C2×C4×C19semidirect
436. #117C2×C4×C19semidirect
463. C2×C42C2×C4×C19semidirect
495. C19#34392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#5292
C19×#23762
C19×#23632
C19×#23622
C19×#23572
C19×#23562
C19×#23512
C19×#23492
C19×#23472
C19×#23432
C19×#23342
C19×#23302
C19×#23262
C19×#23192
C19×#23182
C19×#22852
C19×#22832
#3439219