Finite Group Databasebeta

← C2×C19×#2418 #18040607

Subgroups — C2×C19×#2418 #18040607

Order 4864.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C19×#123C211yesmaximal, characteristic, complemented
2C22×C19×#120C211yesmaximal, characteristic
3C22×C4×D4×C19C211yesmaximal, characteristic, complemented
4C23×C22⋊C4×C19C211yesmaximal, characteristic, complemented
5C19×#2418C2116yesmaximal, direct product factor
6C2×C19×#399C211yesmaximal, characteristic, complemented
7C2×C19×#397C211yesmaximal, characteristic, complemented
8C2×C19×#394C211yesmaximal, characteristic, complemented
9C2×C19×#394C211yesmaximal, characteristic, complemented
10C2×C19×#388C211yesmaximal, characteristic, complemented
11C2×C19×#388C211yesmaximal, characteristic, complemented
12C2×C19×#386C211yesmaximal, characteristic, complemented
13C2×C19×#386C211yesmaximal, characteristic, complemented
14C2×C19×#385C211yesmaximal, characteristic, complemented
15C2×C19×#380C211yesmaximal, characteristic, complemented
16C2×C19×#379C211yesmaximal, characteristic, complemented
17C26×C19C2211yescharacteristic
18C23×D4×C19C2211yescharacteristic
19C23×D4×C19C2211yescharacteristic
20C23×D4×C19C2211yescharacteristic
21C24×C4×C19C2211yescharacteristic
22C24×C4×C19C2211yescharacteristic
23C24×C4×C19C2211yescharacteristic, complemented
24C2×C19×#123—28no—
25C2×C19×#123C2218yescomplemented
26C2×C19×#120—28no—
27C2×C19×#120C2218yes—
28C2×C4×D4×C19—28no—
29C2×C4×D4×C19C2218yescomplemented
30C22×C4⋊C4×C19C2211yescharacteristic, complemented
31C22×C4⋊C4×C19C2211yescharacteristic, complemented
32C22×C4⋊C4×C19C2211yescharacteristic, complemented
33C22×C4⋊C4×C19C2211yescharacteristic, complemented
34C22×C4⋊C4×C19C2211yescharacteristic, complemented
35C22×C22⋊C4×C19—28no—
36C22×C22⋊C4×C19C2211yescharacteristic
37C22×C22⋊C4×C19C2211yescharacteristic
38C22×C22⋊C4×C19C2211yescharacteristic
39C22×C22⋊C4×C19C2211yescharacteristic
40C22×C22⋊C4×C19C2211yescharacteristic
41C22×C22⋊C4×C19C2211yescharacteristic
42C22×C22⋊C4×C19C2211yescharacteristic
43C22×C22⋊C4×C19C2211yescharacteristic
44C22×C22⋊C4×C19C2211yescharacteristic
45C22×C22⋊C4×C19C2211yescharacteristic
46C22×C22⋊C4×C19C2211yescharacteristic
47C22×C22⋊C4×C19C2211yescharacteristic
48C22×C22⋊C4×C19C2211yescharacteristic
49C22×C22⋊C4×C19C2218yescomplemented
50C22×C22⋊C4×C19C2211yescharacteristic, complemented
51C22×C22⋊C4×C19C2211yescharacteristic, complemented
52C22×C22⋊C4×C19C2211yescharacteristic, complemented
53C22×C42×C19C2211yescharacteristic, complemented
54C19×#399C2218yescomplemented
55C19×#397C2218yescomplemented
56C19×#394C2218yescomplemented
57C19×#394C2218yescomplemented
58C19×#388C2218yescomplemented
59C19×#388C2218yescomplemented
60C19×#386C2218yescomplemented
61C19×#386C2218yescomplemented
62C19×#385C2218yescomplemented
63C19×#380C2218yescomplemented
64C19×#379C2218yescomplemented
65C2×C19×#95C2211yescharacteristic, complemented
66C2×C19×#95C2211yescharacteristic, complemented
67C2×C19×#95C2211yescharacteristic, complemented
68C2×C19×#95C2211yescharacteristic, complemented
69C2×C19×#95C2211yescharacteristic, complemented
70C2×C19×#95C2211yescharacteristic, complemented
71C25×C19—24no—
72C25×C19—24no—
73C25×C19—24no—
74C25×C19—24no—
75C25×C19—24no—
76C25×C19—42no—
77C25×C19—42no—
78C25×C19C2311yescharacteristic
79C25×C19C2311yescharacteristic
80C25×C19C2311yescharacteristic
81C25×C19C2314yes—
82C25×C19C2311yescharacteristic
83C22×D4×C19—24no—
84C22×D4×C19—24no—
85C22×D4×C19—24no—
86C22×D4×C19—24no—
87C22×D4×C19—24no—
88C22×D4×C19—24no—
89C22×D4×C19—42no—
90C22×D4×C19—42no—
91C22×D4×C19D418yes—
92C22×D4×C19C2314yes—
93C22×D4×C19C2314yes—
94C22×D4×C19C2314yes—
95C23×C4×C19—24no—
96C23×C4×C19—24no—
97C23×C4×C19—24no—
98C23×C4×C19—24no—
99C23×C4×C19—24no—
100C23×C4×C19—24no—
101C23×C4×C19—42no—
102C23×C4×C19—42no—
103C23×C4×C19—42no—
104C23×C4×C19C2311yescharacteristic
105C23×C4×C19C2311yescharacteristic
106C23×C4×C19C2311yescharacteristic
107C23×C4×C19C2311yescharacteristic
108C23×C4×C19C2311yescharacteristic
109C23×C4×C19C2311yescharacteristic
110C23×C4×C19C2311yescharacteristic
111C23×C4×C19C2311yescharacteristic
112C23×C4×C19C2314yes—
113C23×C4×C19C2314yes—
114C23×C4×C19C2311yescharacteristic
115C23×C4×C19C2311yescharacteristic
116C23×C4×C19C2311yescharacteristic
117C23×C4×C19C2314yescomplemented
118C19×#123—232no—
119C19×#120—232no—
120C4×D4×C19—232no—
121C2×C4⋊C4×C19—24no—
122C2×C4⋊C4×C19—24no—
123C2×C4⋊C4×C19—24no—
124C2×C4⋊C4×C19—42no—
125C2×C4⋊C4×C19—42no—
126C2×C4⋊C4×C19C2314yescomplemented
127C2×C4⋊C4×C19C2314yescomplemented
128C2×C4⋊C4×C19C2314yescomplemented
129C2×C4⋊C4×C19C2314yescomplemented
130C2×C4⋊C4×C19C2314yescomplemented
131C2×C22⋊C4×C19—24no—
132C2×C22⋊C4×C19—24no—
133C2×C22⋊C4×C19—24no—
134C2×C22⋊C4×C19—24no—
135C2×C22⋊C4×C19—24no—
136C2×C22⋊C4×C19—24no—
137C2×C22⋊C4×C19—24no—
138C2×C22⋊C4×C19—24no—
139C2×C22⋊C4×C19—24no—
140C2×C22⋊C4×C19—24no—
141C2×C22⋊C4×C19—24no—
142C2×C22⋊C4×C19—24no—
143C2×C22⋊C4×C19—232no—
144C2×C22⋊C4×C19—42no—
145C2×C22⋊C4×C19—42no—
146C2×C22⋊C4×C19—42no—
147C2×C22⋊C4×C19D418yescomplemented
148C2×C22⋊C4×C19C2314yes—
149C2×C22⋊C4×C19C2314yes—
150C2×C22⋊C4×C19C2314yes—
151C2×C22⋊C4×C19C2314yes—
152C2×C22⋊C4×C19C2314yes—
153C2×C22⋊C4×C19C2314yes—
154C2×C22⋊C4×C19C2314yes—
155C2×C22⋊C4×C19C2314yes—
156C2×C22⋊C4×C19C2314yes—
157C2×C22⋊C4×C19C2314yes—
158C2×C22⋊C4×C19C2314yes—
159C2×C22⋊C4×C19C2314yes—
160C2×C22⋊C4×C19C2314yes—
161C2×C22⋊C4×C19C2314yescomplemented
162C2×C22⋊C4×C19C2314yescomplemented
163C2×C22⋊C4×C19C2314yescomplemented
164C2×C42×C19—24no—
165C2×C42×C19C2314yescomplemented
166C19×#95C2314yescomplemented
167C19×#95C2314yescomplemented
168C19×#95C2314yescomplemented
169C19×#95C2314yescomplemented
170C19×#95C2314yescomplemented
171C19×#95C2314yescomplemented
172C24×C19—22no—
173C24×C19—22no—
174C24×C19—22no—
175C24×C19—22no—
176C24×C19—232no—
177C24×C19—28no—
178C24×C19—22no—
179C24×C19—22no—
180C24×C19—22no—
181C24×C19—22no—
182C24×C19—22no—
183C24×C19—22no—
184C24×C19—22no—
185C24×C19—28no—
186C24×C19—28no—
187C24×C19—22no—
188C24×C19—22no—
189C24×C19—22no—
190C24×C19—22no—
191C24×C19—22no—
192C24×C19—22no—
193C24×C19—22no—
194C24×C19—22no—
195C24×C19—22no—
196C24×C19—22no—
197C24×C19—22no—
198C24×C19—28no—
199C24×C19—28no—
200C24×C19—44no—
201C24×C19—44no—
202C24×C19—416no—
203C24×C19—416no—
204C24×C19—416no—
205C24×C19—416no—
206C24×C19—416no—
207C24×C19—416no—
208C24×C19C2×D414yes—
209C24×C19C2×D414yes—
210C24×C19C2×D414yes—
211C24×C19#4114yes—
212C24×C19#4114yes—
213C24×C19#4114yes—
214C24×C19C2412yes—
215C24×C19C2412yes—
216C24×C19C2412yes—
217C24×C19C2412yes—
218C24×C19C2411yescharacteristic
219C2×D4×C19—232no—
220C2×D4×C19—28no—
221C2×D4×C19—28no—
222C2×D4×C19—28no—
223C2×D4×C19—28no—
224C2×D4×C19—28no—
225C2×D4×C19—28no—
226C2×D4×C19—44no—
227C2×D4×C19—44no—
228C2×D4×C19—416no—
229C2×D4×C19—416no—
230C2×D4×C19C2×D4116yes—
231C22×C4×C19—22no—
232C22×C4×C19—22no—
233C22×C4×C19—22no—
234C22×C4×C19—22no—
235C22×C4×C19—22no—
236C22×C4×C19—22no—
237C22×C4×C19—22no—
238C22×C4×C19—22no—
239C22×C4×C19—22no—
240C22×C4×C19—22no—
241C22×C4×C19—22no—
242C22×C4×C19—22no—
243C22×C4×C19—22no—
244C22×C4×C19—22no—
245C22×C4×C19—22no—
246C22×C4×C19—22no—
247C22×C4×C19—28no—
248C22×C4×C19—28no—
249C22×C4×C19—22no—
250C22×C4×C19—22no—
251C22×C4×C19—22no—
252C22×C4×C19—22no—
253C22×C4×C19—28no—
254C22×C4×C19—22no—
255C22×C4×C19—22no—
256C22×C4×C19—22no—
257C22×C4×C19—22no—
258C22×C4×C19—22no—
259C22×C4×C19—22no—
260C22×C4×C19—22no—
261C22×C4×C19—22no—
262C22×C4×C19—22no—
263C22×C4×C19—22no—
264C22×C4×C19—28no—
265C22×C4×C19—28no—
266C22×C4×C19—28no—
267C22×C4×C19—44no—
268C22×C4×C19—44no—
269C22×C4×C19—44no—
270C22×C4×C19—416no—
271C22×C4×C19—416no—
272C22×C4×C19—416no—
273C22×C4×C19C2×D414yes—
274C22×C4×C19C2×D414yes—
275C22×C4×C19C2×D414yes—
276C22×C4×C19C2412yes—
277C22×C4×C19C2412yes—
278C22×C4×C19C2412yes—
279C22×C4×C19C2412yes—
280C22×C4×C19C2412yes—
281C22×C4×C19C2412yes—
282C22×C4×C19C2412yes—
283C22×C4×C19C2412yes—
284C22×C4×C19C2412yes—
285C22×C4×C19C2412yes—
286C22×C4×C19C2412yes—
287C4⋊C4×C19—28no—
288C4⋊C4×C19—28no—
289C4⋊C4×C19—28no—
290C4⋊C4×C19—44no—
291C4⋊C4×C19—44no—
292C22⋊C4×C19—28no—
293C22⋊C4×C19—28no—
294C22⋊C4×C19—28no—
295C22⋊C4×C19—28no—
296C22⋊C4×C19—28no—
297C22⋊C4×C19—28no—
298C22⋊C4×C19—28no—
299C22⋊C4×C19—28no—
300C22⋊C4×C19—28no—
301C22⋊C4×C19—28no—
302C22⋊C4×C19—28no—
303C22⋊C4×C19—28no—
304C22⋊C4×C19—44no—
305C22⋊C4×C19—44no—
306C22⋊C4×C19—44no—
307C22⋊C4×C19C2×D4116yescomplemented
308C42×C19—28no—
309C2×#2418C1911yesmaximal, characteristic, direct product factor, Sylow
310C23×C19—28no—
311C23×C19—28no—
312C23×C19—28no—
313C23×C19—28no—
314C23×C19—28no—
315C23×C19—28no—
316C23×C19—22no—
317C23×C19—22no—
318C23×C19—22no—
319C23×C19—22no—
320C23×C19—232no—
321C23×C19—28no—
322C23×C19—28no—
323C23×C19—28no—
324C23×C19—28no—
325C23×C19—28no—
326C23×C19—28no—
327C23×C19—28no—
328C23×C19—28no—
329C23×C19—28no—
330C23×C19—22no—
331C23×C19—22no—
332C23×C19—22no—
333C23×C19—22no—
334C23×C19—22no—
335C23×C19—22no—
336C23×C19—22no—
337C23×C19—22no—
338C23×C19—22no—
339C23×C19—22no—
340C23×C19—22no—
341C23×C19—22no—
342C23×C19—22no—
343C23×C19—22no—
344C23×C19—22no—
345C23×C19—22no—
346C23×C19—22no—
347C23×C19—22no—
348C23×C19—416no—
349C23×C19—416no—
350C23×C19—416no—
351C23×C19—416no—
352C23×C19—4128no—
353C23×C19—416no—
354C23×C19—44no—
355C23×C19—44no—
356C23×C19—416no—
357C23×C19—44no—
358C23×C19—44no—
359C23×C19—44no—
360C23×C19—44no—
361C23×C19—44no—
362C23×C19—44no—
363C23×C19—44no—
364C23×C19—44no—
365C23×C19—44no—
366C23×C19—44no—
367C23×C19#123116yescomplemented
368C23×C19C22×D414yes—
369C23×C19C22×D414yes—
370C23×C19C22×D414yes—
371C23×C19C22×D412yes—
372C23×C19C22×D412yes—
373C23×C19C2×#4114yes—
374C23×C19C2×#4114yes—
375C23×C19C2×#4114yes—
376C23×C19C2×#4112yes—
377C23×C19C2×#4112yes—
378C23×C19C2×#4112yes—
379C23×C19H(5,𝔽2)12yes—
380C23×C19H(5,𝔽2)12yes—
381C23×C19C2511yescharacteristic
382D4×C19—232no—
383D4×C19—416no—
384D4×C19—416no—
385C2×C4×C19—28no—
386C2×C4×C19—28no—
387C2×C4×C19—28no—
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—22no—
416C2×C4×C19—22no—
417C2×C4×C19—22no—
418C2×C4×C19—416no—
419C2×C4×C19—416no—
420C2×C4×C19—416no—
421C2×C4×C19—44no—
422C2×C4×C19—44no—
423C2×C4×C19—44no—
424C2×C4×C19—44no—
425C2×C4×C19—44no—
426C2×C4×C19—44no—
427C2×C4×C19—44no—
428C2×C4×C19—44no—
429C2×C4×C19C22×D414yes—
430C2×C4×C19C22×D414yes—
431C2×C4×C19C22×D414yes—
432C22×#123C2×C1911yescharacteristic, complemented
433C22×#120C2×C1911yescharacteristic
434C22×C4×D4C2×C1911yescharacteristic, complemented
435C23×C22⋊C4C2×C1911yescharacteristic, complemented
436#2418C2×C19116yesdirect product factor
437C2×#399C2×C1911yescharacteristic, complemented
438C2×#397C2×C1911yescharacteristic, complemented
439C2×#394C2×C1911yescharacteristic, complemented
440C2×#394C2×C1911yescharacteristic, complemented
441C2×#388C2×C1911yescharacteristic, complemented
442C2×#388C2×C1911yescharacteristic, complemented
443C2×#386C2×C1911yescharacteristic, complemented
444C2×#386C2×C1911yescharacteristic, complemented
445C2×#385C2×C1911yescharacteristic, complemented
446C2×#380C2×C1911yescharacteristic, complemented
447C2×#379C2×C1911yescharacteristic, complemented
448C22×C19—24no—
449C22×C19—232no—
450C22×C19—24no—
451C22×C19—24no—
452C22×C19—24no—
453C22×C19—24no—
454C22×C19—24no—
455C22×C19—24no—
456C22×C19—24no—
457C22×C19—24no—
458C22×C19—24no—
459C22×C19—24no—
460C22×C19—24no—
461C22×C19—24no—
462C22×C19—24no—
463C22×C19—24no—
464C22×C19—464no—
465C22×C19—42no—
466C22×C19—42no—
467C22×C19—42no—
468C22×C19—416no—
469C22×C19—416no—
470C22×C19—416no—
471C22×C19—42no—
472C22×C19—42no—
473C22×C19—42no—
474C22×C19—42no—
475C22×C19—42no—
476C22×C19—42no—
477C22×C19—42no—
478C22×C19—42no—
479C22×C19—42no—
480C22×C19C2×#12314yes—
481C22×C19C2×#12318yescomplemented
482C22×C19#52514yes—
483C22×C19#53814yes—
484C22×C19D4214yes—
485C22×C19#54614yes—
486C22×C19#54614yes—
487C22×C19#55114yes—
488C22×C19C23×D411yescharacteristic
489C22×C19C23×D411yescharacteristic
490C22×C19C22×#4111yescharacteristic
491C22×C19C22×#4111yescharacteristic
492C22×C19C22×#4111yescharacteristic
493C22×C19C2×H(5,𝔽2)11yescharacteristic
494C22×C19C2×H(5,𝔽2)11yescharacteristic
495C4×C19—24no—
496C4×C19—24no—
497C4×C19—24no—
498C4×C19—42no—
499C4×C19—42no—
500C4×C19—42no—
501C4×C19—42no—
502C4×C19—42no—
503C4×C19—42no—
504C4×C19—42no—
505C4×C19—42no—
506C26C22×C1911yescharacteristic
507C23×D4C22×C1911yescharacteristic
508C23×D4C22×C1911yescharacteristic
509C23×D4C22×C1911yescharacteristic
510C24×C4C22×C1911yescharacteristic
511C24×C4C22×C1911yescharacteristic
512C24×C4C22×C1911yescharacteristic, complemented
513C2×#123—28no—
514C2×#123C22×C1918yescomplemented
515C2×#120—28no—
516C2×#120C22×C1918yes—
517C2×C4×D4—28no—
518C2×C4×D4C22×C1918yescomplemented
519C22×C4⋊C4C22×C1911yescharacteristic, complemented
520C22×C4⋊C4C22×C1911yescharacteristic, complemented
521C22×C4⋊C4C22×C1911yescharacteristic, complemented
522C22×C4⋊C4C22×C1911yescharacteristic, complemented
523C22×C4⋊C4C22×C1911yescharacteristic, complemented
524C22×C22⋊C4—28no—
525C22×C22⋊C4C22×C1911yescharacteristic
526C22×C22⋊C4C22×C1911yescharacteristic
527C22×C22⋊C4C22×C1911yescharacteristic
528C22×C22⋊C4C22×C1911yescharacteristic
529C22×C22⋊C4C22×C1911yescharacteristic
530C22×C22⋊C4C22×C1911yescharacteristic
531C22×C22⋊C4C22×C1911yescharacteristic
532C22×C22⋊C4C22×C1911yescharacteristic
533C22×C22⋊C4C22×C1911yescharacteristic
534C22×C22⋊C4C22×C1911yescharacteristic
535C22×C22⋊C4C22×C1911yescharacteristic
536C22×C22⋊C4C22×C1911yescharacteristic
537C22×C22⋊C4C22×C1911yescharacteristic
538C22×C22⋊C4C22×C1918yescomplemented
539C22×C22⋊C4C22×C1911yescharacteristic, complemented
540C22×C22⋊C4C22×C1911yescharacteristic, complemented
541C22×C22⋊C4C22×C1911yescharacteristic, complemented
542C22×C42C22×C1911yescharacteristic, complemented
543#399C22×C1918yescomplemented
544#397C22×C1918yescomplemented
545#394C22×C1918yescomplemented
546#394C22×C1918yescomplemented
547#388C22×C1918yescomplemented
548#388C22×C1918yescomplemented
549#386C22×C1918yescomplemented
550#386C22×C1918yescomplemented
551#385C22×C1918yescomplemented
552#380C22×C1918yescomplemented
553#379C22×C1918yescomplemented
554C2×#95C22×C1911yescharacteristic, complemented
555C2×#95C22×C1911yescharacteristic, complemented
556C2×#95C22×C1911yescharacteristic, complemented
557C2×#95C22×C1911yescharacteristic, complemented
558C2×#95C22×C1911yescharacteristic, complemented
559C2×#95C22×C1911yescharacteristic, complemented
560C2×C19—28no—
561C2×C19—44no—
562C2×C19—44no—
563C2×C19—44no—
564C2×C19#241818yesdirect product factor
565C2×C19C22×#12311yescharacteristic
566C2×C19C2×#52511yescharacteristic
567C2×C19C2×#53811yescharacteristic
568C2×C19C2×D4211yescharacteristic
569C2×C19C2×#54611yescharacteristic
570C2×C19C2×#54611yescharacteristic
571C2×C19C2×#55111yescharacteristic
572C25—24no—
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—42no—
578C25—42no—
579C25C23×C1911yescharacteristic
580C25C23×C1911yescharacteristic
581C25C23×C1911yescharacteristic
582C25C23×C1914yes—
583C25C23×C1911yescharacteristic
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—42no—
591C22×D4—42no—
592C22×D4D4×C1918yes—
593C22×D4C23×C1914yes—
594C22×D4C23×C1914yes—
595C22×D4C23×C1914yes—
596C23×C4—24no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4—42no—
605C23×C4C23×C1911yescharacteristic
606C23×C4C23×C1911yescharacteristic
607C23×C4C23×C1911yescharacteristic
608C23×C4C23×C1911yescharacteristic
609C23×C4C23×C1911yescharacteristic
610C23×C4C23×C1911yescharacteristic
611C23×C4C23×C1911yescharacteristic
612C23×C4C23×C1911yescharacteristic
613C23×C4C23×C1914yes—
614C23×C4C23×C1914yes—
615C23×C4C23×C1911yescharacteristic
616C23×C4C23×C1911yescharacteristic
617C23×C4C23×C1911yescharacteristic
618C23×C4C23×C1914yescomplemented
619#123—232no—
620#120—232no—
621C4×D4—232no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4C23×C1914yescomplemented
628C2×C4⋊C4C23×C1914yescomplemented
629C2×C4⋊C4C23×C1914yescomplemented
630C2×C4⋊C4C23×C1914yescomplemented
631C2×C4⋊C4C23×C1914yescomplemented
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—232no—
645C2×C22⋊C4—42no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4D4×C1918yescomplemented
649C2×C22⋊C4C23×C1914yes—
650C2×C22⋊C4C23×C1914yes—
651C2×C22⋊C4C23×C1914yes—
652C2×C22⋊C4C23×C1914yes—
653C2×C22⋊C4C23×C1914yes—
654C2×C22⋊C4C23×C1914yes—
655C2×C22⋊C4C23×C1914yes—
656C2×C22⋊C4C23×C1914yes—
657C2×C22⋊C4C23×C1914yes—
658C2×C22⋊C4C23×C1914yes—
659C2×C22⋊C4C23×C1914yes—
660C2×C22⋊C4C23×C1914yes—
661C2×C22⋊C4C23×C1914yes—
662C2×C22⋊C4C23×C1914yescomplemented
663C2×C22⋊C4C23×C1914yescomplemented
664C2×C22⋊C4C23×C1914yescomplemented
665C2×C42—24no—
666C2×C42C23×C1914yescomplemented
667#95C23×C1914yescomplemented
668#95C23×C1914yescomplemented
669#95C23×C1914yescomplemented
670#95C23×C1914yescomplemented
671#95C23×C1914yescomplemented
672#95C23×C1914yescomplemented
673C19C2×#241811yescharacteristic, direct product factor, Sylow
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28no—
688C24—28no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—28no—
702C24—44no—
703C24—44no—
704C24—416no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24C2×D4×C1914yes—
711C24C2×D4×C1914yes—
712C24C2×D4×C1914yes—
713C24#41×C1914yes—
714C24#41×C1914yes—
715C24#41×C1914yes—
716C24C24×C1912yes—
717C24C24×C1912yes—
718C24C24×C1912yes—
719C24C24×C1912yes—
720C24C24×C1911yescharacteristic
721C2×D4—232no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4C2×D4×C19116yes—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4C2×D4×C1914yes—
776C22×C4C2×D4×C1914yes—
777C22×C4C2×D4×C1914yes—
778C22×C4C24×C1912yes—
779C22×C4C24×C1912yes—
780C22×C4C24×C1912yes—
781C22×C4C24×C1912yes—
782C22×C4C24×C1912yes—
783C22×C4C24×C1912yes—
784C22×C4C24×C1912yes—
785C22×C4C24×C1912yes—
786C22×C4C24×C1912yes—
787C22×C4C24×C1912yes—
788C22×C4C24×C1912yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4C2×D4×C19116yescomplemented
810C42—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—4128no—
854C23—416no—
855C23—44no—
856C23—44no—
857C23—416no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23C19×#123116yescomplemented
869C23C22×D4×C1914yes—
870C23C22×D4×C1914yes—
871C23C22×D4×C1914yes—
872C23C22×D4×C1912yes—
873C23C22×D4×C1912yes—
874C23C2×#41×C1914yes—
875C23C2×#41×C1914yes—
876C23C2×#41×C1914yes—
877C23C2×#41×C1912yes—
878C23C2×#41×C1912yes—
879C23C2×#41×C1912yes—
880C23C19×H(5,𝔽2)12yes—
881C23C19×H(5,𝔽2)12yes—
882C23C25×C1911yescharacteristic
883D4—232no—
884D4—416no—
885D4—416no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—416no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4C22×D4×C1914yes—
931C2×C4C22×D4×C1914yes—
932C2×C4C22×D4×C1914yes—
933C22—24no—
934C22—232no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—464no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—416no—
954C22—416no—
955C22—416no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22C2×C19×#12314yes—
966C22C2×C19×#12318yescomplemented
967C22C19×#52514yes—
968C22C19×#53814yes—
969C22D42×C1914yes—
970C22C19×#54614yes—
971C22C19×#54614yes—
972C22C19×#55114yes—
973C22C23×D4×C1911yescharacteristic
974C22C23×D4×C1911yescharacteristic
975C22C22×#41×C1911yescharacteristic
976C22C22×#41×C1911yescharacteristic
977C22C22×#41×C1911yescharacteristic
978C22C2×C19×H(5,𝔽2)11yescharacteristic
979C22C2×C19×H(5,𝔽2)11yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2C19×#241818yesdirect product factor
996C2C22×C19×#12311yescharacteristic
997C2C2×C19×#52511yescharacteristic
998C2C2×C19×#53811yescharacteristic
999C2C2×D42×C1911yescharacteristic
1000C2C2×C19×#54611yescharacteristic
1001C2C2×C19×#54611yescharacteristic
1002C2C2×C19×#55111yescharacteristic
subgroupG/H
center, socleC24×C19C24
commutator, Frattini, cosocleC23C25×C19
prime radicalC22×C19×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C19×#123C2semidirect
3. C22×C4×D4×C19C2semidirect
4. C23×C22⋊C4×C19C2semidirect
5. C19×#2418C2direct (N × H)
6. C2×C19×#399C2semidirect
7. C2×C19×#397C2semidirect
8. C2×C19×#394C2semidirect
9. C2×C19×#394C2semidirect
10. C2×C19×#388C2semidirect
11. C2×C19×#388C2semidirect
12. C2×C19×#386C2semidirect
13. C2×C19×#386C2semidirect
14. C2×C19×#385C2semidirect
15. C2×C19×#380C2semidirect
16. C2×C19×#379C2semidirect
23. C24×C4×C19C22semidirect
25. C2×C19×#123C22semidirect
29. C2×C4×D4×C19C22semidirect
30. C22×C4⋊C4×C19C22semidirect
31. C22×C4⋊C4×C19C22semidirect
32. C22×C4⋊C4×C19C22semidirect
33. C22×C4⋊C4×C19C22semidirect
34. C22×C4⋊C4×C19C22semidirect
49. C22×C22⋊C4×C19C22semidirect
50. C22×C22⋊C4×C19C22semidirect
51. C22×C22⋊C4×C19C22semidirect
52. C22×C22⋊C4×C19C22semidirect
53. C22×C42×C19C22semidirect
54. C19×#399C22semidirect
55. C19×#397C22semidirect
56. C19×#394C22semidirect
57. C19×#394C22semidirect
58. C19×#388C22semidirect
59. C19×#388C22semidirect
60. C19×#386C22semidirect
61. C19×#386C22semidirect
62. C19×#385C22semidirect
63. C19×#380C22semidirect
64. C19×#379C22semidirect
65. C2×C19×#95C22semidirect
66. C2×C19×#95C22semidirect
67. C2×C19×#95C22semidirect
68. C2×C19×#95C22semidirect
69. C2×C19×#95C22semidirect
70. C2×C19×#95C22semidirect
117. C23×C4×C19C23semidirect
126. C2×C4⋊C4×C19C23semidirect
127. C2×C4⋊C4×C19C23semidirect
128. C2×C4⋊C4×C19C23semidirect
129. C2×C4⋊C4×C19C23semidirect
130. C2×C4⋊C4×C19C23semidirect
147. C2×C22⋊C4×C19D4semidirect
161. C2×C22⋊C4×C19C23semidirect
162. C2×C22⋊C4×C19C23semidirect
163. C2×C22⋊C4×C19C23semidirect
165. C2×C42×C19C23semidirect
166. C19×#95C23semidirect
167. C19×#95C23semidirect
168. C19×#95C23semidirect
169. C19×#95C23semidirect
170. C19×#95C23semidirect
171. C19×#95C23semidirect
307. C22⋊C4×C19C2×D4semidirect
309. C2×#2418C19direct (N × H)
367. C23×C19#123semidirect
432. C22×#123C2×C19semidirect
434. C22×C4×D4C2×C19semidirect
435. C23×C22⋊C4C2×C19semidirect
436. #2418C2×C19direct (N × H)
437. C2×#399C2×C19semidirect
438. C2×#397C2×C19semidirect
439. C2×#394C2×C19semidirect
440. C2×#394C2×C19semidirect
441. C2×#388C2×C19semidirect
442. C2×#388C2×C19semidirect
443. C2×#386C2×C19semidirect
444. C2×#386C2×C19semidirect
445. C2×#385C2×C19semidirect
446. C2×#380C2×C19semidirect
447. C2×#379C2×C19semidirect
481. C22×C19C2×#123semidirect
512. C24×C4C22×C19semidirect
514. C2×#123C22×C19semidirect
518. C2×C4×D4C22×C19semidirect
519. C22×C4⋊C4C22×C19semidirect
520. C22×C4⋊C4C22×C19semidirect
521. C22×C4⋊C4C22×C19semidirect
522. C22×C4⋊C4C22×C19semidirect
523. C22×C4⋊C4C22×C19semidirect
538. C22×C22⋊C4C22×C19semidirect
539. C22×C22⋊C4C22×C19semidirect
540. C22×C22⋊C4C22×C19semidirect
541. C22×C22⋊C4C22×C19semidirect
542. C22×C42C22×C19semidirect
543. #399C22×C19semidirect
544. #397C22×C19semidirect
545. #394C22×C19semidirect
546. #394C22×C19semidirect
547. #388C22×C19semidirect
548. #388C22×C19semidirect
549. #386C22×C19semidirect
550. #386C22×C19semidirect
551. #385C22×C19semidirect
552. #380C22×C19semidirect
553. #379C22×C19semidirect
554. C2×#95C22×C19semidirect
555. C2×#95C22×C19semidirect
556. C2×#95C22×C19semidirect
557. C2×#95C22×C19semidirect
558. C2×#95C22×C19semidirect
559. C2×#95C22×C19semidirect
564. C2×C19#2418direct (N × H)
618. C23×C4C23×C19semidirect
627. C2×C4⋊C4C23×C19semidirect
628. C2×C4⋊C4C23×C19semidirect
629. C2×C4⋊C4C23×C19semidirect
630. C2×C4⋊C4C23×C19semidirect
631. C2×C4⋊C4C23×C19semidirect
648. C2×C22⋊C4D4×C19semidirect
662. C2×C22⋊C4C23×C19semidirect
663. C2×C22⋊C4C23×C19semidirect
664. C2×C22⋊C4C23×C19semidirect
666. C2×C42C23×C19semidirect
667. #95C23×C19semidirect
668. #95C23×C19semidirect
669. #95C23×C19semidirect
670. #95C23×C19semidirect
671. #95C23×C19semidirect
672. #95C23×C19semidirect
673. C19C2×#2418direct (N × H)
809. C22⋊C4C2×D4×C19semidirect
868. C23C19×#123semidirect
966. C22C2×C19×#123semidirect
995. C2C19×#2418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C19×#1232
C22×C19×#1202
C22×C4×D4×C192
C23×C22⋊C4×C192
C19×#24182
C2×C19×#3992
C2×C19×#3972
C2×C19×#3942
C2×C19×#3882
C2×C19×#3862
C2×C19×#3852
C2×C19×#3802
C2×C19×#3792
C2×#241819