Finite Group Databasebeta

← C3×#10603800 #14279895

Subgroups — C3×#10603800 #14279895

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
5C3×D5×#95C211yesmaximal, characteristic
6#10603800C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×AGL(1,𝔽5)C2212yes—
8C23×C3×AGL(1,𝔽5)C2211yescharacteristic
9C23×C3×AGL(1,𝔽5)C2211yescharacteristic
10C22×C3×C4×D5C2212yes—
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C4×AGL(1,𝔽5)—24no—
13C2×C3×C4×AGL(1,𝔽5)C414yescomplemented
14C3×(C2×AGL(1,𝔽5))⋊C4—24no—
15C3×(C2×AGL(1,𝔽5))⋊C4—24no—
16C3×(C2×AGL(1,𝔽5))⋊C4C414yescomplemented
17C3×C5×#95C411yescharacteristic, complemented
18C3×#3963C411yescharacteristic, complemented
19C3×#3963C412yescomplemented
20C3×#1434—51nomaximal, Hall
21C22×C4×AGL(1,𝔽5)C2×C311yescharacteristic
22C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yes—
23C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yes—
24C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
25D5×#95C2×C311yescharacteristic
26C23×C3×D5C2311yescharacteristic
27C22×C3×AGL(1,𝔽5)—22no—
28C22×C3×AGL(1,𝔽5)—22no—
29C22×C3×AGL(1,𝔽5)—22no—
30C22×C3×AGL(1,𝔽5)—21no—
31C22×C3×AGL(1,𝔽5)—21no—
32C22×C3×AGL(1,𝔽5)—22no—
33C22×C3×AGL(1,𝔽5)—22no—
34C22×C3×AGL(1,𝔽5)—22no—
35C22×C3×AGL(1,𝔽5)—22no—
36C22×C3×AGL(1,𝔽5)—22no—
37C22×C3×AGL(1,𝔽5)—22no—
38C22×C3×AGL(1,𝔽5)C2×C414yes—
39C22×C3×AGL(1,𝔽5)C2×C412yes—
40C22×C3×AGL(1,𝔽5)C2×C412yes—
41C22×C3×AGL(1,𝔽5)D414yes—
42C22×C3×AGL(1,𝔽5)D412yes—
43C22×C3×AGL(1,𝔽5)Q812yes—
44C22×C3×C4×C5C2×C412yes—
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×C3×Dic5C2×C412yes—
47C22×C3×Dic5C2×C411yescharacteristic
48C2×C3×C4×D5—22no—
49C2×C3×C4×D5—22no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—22no—
52C2×C3×C4×D5—22no—
53C2×C3×C4×D5—22no—
54C2×C3×C4×D5—22no—
55C2×C3×C4×D5—22no—
56C2×C3×C4×D5C2×C412yes—
57C2×C3×C4×D5C2×C412yes—
58C3×C4×AGL(1,𝔽5)—28no—
59C22×C3×C42—51no—
60C2×C3×#95—51no—
61C2×C3×#95—51no—
62C2×C3×#95—52no—
63C2×C3×#95—52no—
64C23×AGL(1,𝔽5)C22×C312yes—
65C23×AGL(1,𝔽5)C22×C311yescharacteristic
66C23×AGL(1,𝔽5)C22×C311yescharacteristic
67C22×C4×D5C22×C312yes—
68C22×C4×D5C22×C311yescharacteristic
69C2×C4×AGL(1,𝔽5)—24no—
70C2×C4×AGL(1,𝔽5)C3×C414yescomplemented
71(C2×AGL(1,𝔽5))⋊C4—24no—
72(C2×AGL(1,𝔽5))⋊C4—24no—
73(C2×AGL(1,𝔽5))⋊C4C3×C414yescomplemented
74C5×#95C3×C411yescharacteristic, complemented
75#3963C3×C411yescharacteristic, complemented
76#3963C3×C412yescomplemented
77#1434—51noSylow
78C23×C3×C5C22×C411yescharacteristic
79C22×C3×D5C22×C411yescharacteristic
80C22×C3×D5C22×C411yescharacteristic
81C22×C3×D5C2×D412yes—
82C22×C3×D5C2×D411yescharacteristic
83C22×C3×D5C2×Q811yescharacteristic
84C22×C3×D5#4112yes—
85C22×C3×D5#4112yes—
86C22×C3×D5#4111yescharacteristic
87C22×C3×D5#4112yes—
88C22×C3×D5#4111yescharacteristic
89C2×C3×AGL(1,𝔽5)—22no—
90C2×C3×AGL(1,𝔽5)—22no—
91C2×C3×AGL(1,𝔽5)—22no—
92C2×C3×AGL(1,𝔽5)—22no—
93C2×C3×AGL(1,𝔽5)—24no—
94C2×C3×AGL(1,𝔽5)—24no—
95C2×C3×AGL(1,𝔽5)—24no—
96C2×C3×AGL(1,𝔽5)—24no—
97C2×C3×AGL(1,𝔽5)—24no—
98C2×C3×AGL(1,𝔽5)—24no—
99C2×C3×AGL(1,𝔽5)—24no—
100C2×C3×AGL(1,𝔽5)—42no—
101C2×C3×AGL(1,𝔽5)—42no—
102C2×C3×AGL(1,𝔽5)—42no—
103C2×C3×AGL(1,𝔽5)—42no—
104C2×C3×AGL(1,𝔽5)C22⋊C414yes—
105C2×C3×AGL(1,𝔽5)C4⋊C414yes—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5C4212yes—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5C4212yes—
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—24no—
119C3×C4×D5—42no—
120C3×C4×D5—42no—
121C3×C4×D5—42no—
122C3×C4×D5—42no—
123C23×C3×C4—51no—
124C23×C3×C4—51no—
125C23×C3×C4—51no—
126C23×C3×C4—52no—
127C23×C3×C4—52no—
128C2×C3×C42—54no—
129C2×C3×C42—104no—
130C3×#95—54no—
131C3×#95—52no—
132C3×#95—51no—
133C3×#95—104no—
134C3×#95—104no—
135C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
136C23×D5C23×C311yescharacteristic
137C22×AGL(1,𝔽5)—22no—
138C22×AGL(1,𝔽5)—22no—
139C22×AGL(1,𝔽5)—22no—
140C22×AGL(1,𝔽5)—21no—
141C22×AGL(1,𝔽5)—21no—
142C22×AGL(1,𝔽5)—22no—
143C22×AGL(1,𝔽5)—22no—
144C22×AGL(1,𝔽5)—22no—
145C22×AGL(1,𝔽5)—22no—
146C22×AGL(1,𝔽5)—22no—
147C22×AGL(1,𝔽5)—22no—
148C22×AGL(1,𝔽5)C2×C3×C414yes—
149C22×AGL(1,𝔽5)C2×C3×C412yes—
150C22×AGL(1,𝔽5)C2×C3×C412yes—
151C22×AGL(1,𝔽5)C3×D414yes—
152C22×AGL(1,𝔽5)C3×D412yes—
153C22×AGL(1,𝔽5)C3×Q812yes—
154C22×C4×C5C2×C3×C412yes—
155C22×C4×C5C2×C3×C411yescharacteristic
156C22×Dic5C2×C3×C412yes—
157C22×Dic5C2×C3×C411yescharacteristic
158C2×C4×D5—22no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5C2×C3×C412yes—
167C2×C4×D5C2×C3×C412yes—
168C4×AGL(1,𝔽5)—28no—
169C22×C42—51no—
170C2×#95—51no—
171C2×#95—51no—
172C2×#95—52no—
173C2×#95—52no—
174C22×C3×C5C2×C4211yescharacteristic
175C22×C3×C5#11712yes—
176C22×C3×C5C4×D412yes—
177C22×C3×C5C4×D411yescharacteristic
178C22×C3×C5C4×Q811yescharacteristic
179C2×C3×D5C2×C22⋊C411yescharacteristic
180C2×C3×D5C2×C4⋊C411yescharacteristic
181C2×C3×D5#11711yescharacteristic
182C2×C3×D5#11711yescharacteristic
183C2×C3×D5#11711yescharacteristic
184C2×C3×D5#11711yescharacteristic
185C2×C3×D5#11712yes—
186C2×C3×D5C4×D412yes—
187C2×C3×D5C4×D411yescharacteristic
188C2×C3×D5C4×Q811yescharacteristic
189C2×C3×D5#12112yes—
190C2×C3×D5C22⋊Q812yes—
191C2×C3×D5#12312yes—
192C2×C3×D5#12312yes—
193C2×C3×D5#12412yes—
194C2×C3×D5#12512yes—
195C2×C3×D5#12612yes—
196C2×C3×D5#12612yes—
197C3×AGL(1,𝔽5)—24no—
198C3×AGL(1,𝔽5)—24no—
199C3×AGL(1,𝔽5)—44no—
200C3×C4×C5—22no—
201C3×C4×C5—42no—
202C3×Dic5—22no—
203C3×Dic5—42no—
204C24×C3—51no—
205C22×C3×C4—52no—
206C22×C3×C4—54no—
207C22×C3×C4—52no—
208C22×C3×C4—52no—
209C22×C3×C4—52no—
210C22×C3×C4—51no—
211C22×C3×C4—52no—
212C22×C3×C4—52no—
213C22×C3×C4—54no—
214C22×C3×C4—52no—
215C22×C3×C4—102no—
216C22×C3×C4—102no—
217C22×C3×C4—102no—
218C22×C3×C4—102no—
219C22×C3×C4—102no—
220C22×C3×C4—102no—
221C22×C3×C4—102no—
222C22×C3×C4—102no—
223C22×C3×C4—102no—
224C22×C3×C4—102no—
225C22×C3×C4—102no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C22×C3×C4—102no—
229C22×C3×C4—102no—
230C22×C3×C4—102no—
231C22×C3×C4—102no—
232C22×C3×C4—102no—
233C22×C3×C4—102no—
234C22×C3×C4C2×AGL(1,𝔽5)12yes—
235C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
236C3×C42—108no—
237C23×C5C22×C3×C411yescharacteristic
238C22×D5C22×C3×C411yescharacteristic
239C22×D5C22×C3×C411yescharacteristic
240C22×D5C2×C3×D412yes—
241C22×D5C2×C3×D411yescharacteristic
242C22×D5C2×C3×Q811yescharacteristic
243C22×D5C3×#4112yes—
244C22×D5C3×#4112yes—
245C22×D5C3×#4111yescharacteristic
246C22×D5C3×#4112yes—
247C22×D5C3×#4111yescharacteristic
248C2×AGL(1,𝔽5)—22no—
249C2×AGL(1,𝔽5)—22no—
250C2×AGL(1,𝔽5)—22no—
251C2×AGL(1,𝔽5)—22no—
252C2×AGL(1,𝔽5)—24no—
253C2×AGL(1,𝔽5)—24no—
254C2×AGL(1,𝔽5)—24no—
255C2×AGL(1,𝔽5)—24no—
256C2×AGL(1,𝔽5)—24no—
257C2×AGL(1,𝔽5)—24no—
258C2×AGL(1,𝔽5)—24no—
259C2×AGL(1,𝔽5)—42no—
260C2×AGL(1,𝔽5)—42no—
261C2×AGL(1,𝔽5)—42no—
262C2×AGL(1,𝔽5)—42no—
263C2×AGL(1,𝔽5)C3×C22⋊C414yes—
264C2×AGL(1,𝔽5)C3×C4⋊C414yes—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5C3×C4212yes—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5C3×C4212yes—
275C4×D5—22no—
276C4×D5—22no—
277C4×D5—24no—
278C4×D5—42no—
279C4×D5—42no—
280C4×D5—42no—
281C4×D5—42no—
282C23×C4—51no—
283C23×C4—51no—
284C23×C4—51no—
285C23×C4—52no—
286C23×C4—52no—
287C2×C42—54no—
288C2×C42—104no—
289#95—54no—
290#95—52no—
291#95—51no—
292#95—104no—
293#95—104no—
294#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
295C2×C3×C5#37611yescharacteristic
296C2×C3×C5C4×C22⋊C411yescharacteristic
297C2×C3×C5C4×C4⋊C411yescharacteristic
298C2×C3×C5#38712yes—
299C2×C3×C5#38812yes—
300C3×D5#38011yescharacteristic
301C3×D5#38111yescharacteristic
302C3×D5#38211yescharacteristic
303C3×D5#38311yescharacteristic
304C3×D5#38712yes—
305C3×D5#38812yes—
306C23×C3—51no—
307C23×C3—51no—
308C23×C3—52no—
309C23×C3—52no—
310C23×C3—52no—
311C23×C3—51no—
312C23×C3—52no—
313C23×C3—51no—
314C23×C3—51no—
315C23×C3—51no—
316C23×C3C22×AGL(1,𝔽5)11yescharacteristic
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—54no—
322C2×C3×C4—54no—
323C2×C3×C4—52no—
324C2×C3×C4—102no—
325C2×C3×C4—102no—
326C2×C3×C4—104no—
327C2×C3×C4—102no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—104no—
331C2×C3×C4—104no—
332C2×C3×C4—102no—
333C2×C3×C4—104no—
334C2×C3×C4—104no—
335C2×C3×C4—102no—
336C2×C3×C4—104no—
337C2×C3×C4—104no—
338C2×C3×C4—104no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—202no—
343C2×C3×C4—202no—
344C2×C3×C4—202no—
345C2×C3×C4—202no—
346C2×C3×C4—202no—
347C2×C3×C4—202no—
348C2×C3×C4—202no—
349C2×C3×C4—202no—
350C2×C3×C4C4×AGL(1,𝔽5)12yes—
351C22×C5C2×C3×C4211yescharacteristic
352C22×C5C3×#11712yes—
353C22×C5C3×C4×D412yes—
354C22×C5C3×C4×D411yescharacteristic
355C22×C5C3×C4×Q811yescharacteristic
356C2×D5C2×C3×C22⋊C411yescharacteristic
357C2×D5C2×C3×C4⋊C411yescharacteristic
358C2×D5C3×#11711yescharacteristic
359C2×D5C3×#11711yescharacteristic
360C2×D5C3×#11711yescharacteristic
361C2×D5C3×#11711yescharacteristic
362C2×D5C3×#11712yes—
363C2×D5C3×C4×D412yes—
364C2×D5C3×C4×D411yescharacteristic
365C2×D5C3×C4×Q811yescharacteristic
366C2×D5C3×#12112yes—
367C2×D5C3×C22⋊Q812yes—
368C2×D5C3×#12312yes—
369C2×D5C3×#12312yes—
370C2×D5C3×#12412yes—
371C2×D5C3×#12512yes—
372C2×D5C3×#12612yes—
373C2×D5C3×#12612yes—
374AGL(1,𝔽5)—24no—
375AGL(1,𝔽5)—24no—
376AGL(1,𝔽5)—44no—
377C4×C5—22no—
378C4×C5—42no—
379Dic5—22no—
380Dic5—42no—
381C24—51no—
382C22×C4—52no—
383C22×C4—54no—
384C22×C4—52no—
385C22×C4—52no—
386C22×C4—52no—
387C22×C4—51no—
388C22×C4—52no—
389C22×C4—52no—
390C22×C4—54no—
391C22×C4—52no—
392C22×C4—102no—
393C22×C4—102no—
394C22×C4—102no—
395C22×C4—102no—
396C22×C4—102no—
397C22×C4—102no—
398C22×C4—102no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4—102no—
403C22×C4—101no—
404C22×C4—101no—
405C22×C4—102no—
406C22×C4—102no—
407C22×C4—102no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4C2×C3×AGL(1,𝔽5)12yes—
412C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
413C42—108no—
414C3×C5#143411yescharacteristic, complemented, Hall
415C22×C3—51no—
416C22×C3—51no—
417C22×C3—52no—
418C22×C3—51no—
419C22×C3—51no—
420C22×C3—52no—
421C22×C3—52no—
422C22×C3—52no—
423C22×C3—52no—
424C22×C3—52no—
425C22×C3—51no—
426C22×C3—51no—
427C22×C3—51no—
428C22×C3—51no—
429C22×C3—52no—
430C22×C3—52no—
431C22×C3—52no—
432C22×C3—52no—
433C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
434C22×C3#413012yes—
435C22×C3D4×AGL(1,𝔽5)12yes—
436C22×C3D4×AGL(1,𝔽5)11yescharacteristic
437C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
438C3×C4—22no—
439C3×C4—42no—
440C3×C4—104no—
441C3×C4—104no—
442C3×C4—102no—
443C3×C4—204no—
444C3×C4—202no—
445C2×C5C3×#37611yescharacteristic
446C2×C5C3×C4×C22⋊C411yescharacteristic
447C2×C5C3×C4×C4⋊C411yescharacteristic
448C2×C5C3×#38712yes—
449C2×C5C3×#38812yes—
450D5C3×#38011yescharacteristic
451D5C3×#38111yescharacteristic
452D5C3×#38211yescharacteristic
453D5C3×#38311yescharacteristic
454D5C3×#38712yes—
455D5C3×#38812yes—
456C23—51no—
457C23—51no—
458C23—52no—
459C23—52no—
460C23—52no—
461C23—51no—
462C23—52no—
463C23—51no—
464C23—51no—
465C23—51no—
466C23C22×C3×AGL(1,𝔽5)11yescharacteristic
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—54no—
472C2×C4—54no—
473C2×C4—52no—
474C2×C4—102no—
475C2×C4—104no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—104no—
481C2×C4—104no—
482C2×C4—102no—
483C2×C4—104no—
484C2×C4—104no—
485C2×C4—102no—
486C2×C4—104no—
487C2×C4—104no—
488C2×C4—104no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—202no—
493C2×C4—202no—
494C2×C4—202no—
495C2×C4—202no—
496C2×C4—202no—
497C2×C4—202no—
498C2×C4—202no—
499C2×C4—202no—
500C2×C4C3×C4×AGL(1,𝔽5)12yes—
501C2×C3—51no—
502C2×C3—51no—
503C2×C3—52no—
504C2×C3—51no—
505C2×C3—51no—
506C2×C3—52no—
507C2×C3#6568611yescharacteristic
508C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
509C2×C3#6570012yes—
510C2×C3C4⋊C4×AGL(1,𝔽5)11yescharacteristic
511C2×C3#6571112yes—
512C5C3×#143411yescharacteristic, complemented, Sylow
513C22—51no—
514C22—51no—
515C22—52no—
516C22—51no—
517C22—52no—
518C22—51no—
519C22—52no—
520C22—52no—
521C22—52no—
522C22—52no—
523C22—51no—
524C22—51no—
525C22—51no—
526C22—51no—
527C22—52no—
528C22—52no—
529C22—52no—
530C22—52no—
531C22C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
532C22C3×#413012yes—
533C22C3×D4×AGL(1,𝔽5)12yes—
534C22C3×D4×AGL(1,𝔽5)11yescharacteristic
535C22C3×Q8×AGL(1,𝔽5)11yescharacteristic
536C4—22no—
537C4—42no—
538C4—104no—
539C4—104no—
540C4—102no—
541C4—204no—
542C4—202no—
543C3#1060380011yescharacteristic, direct product factor, Sylow
544C2—51no—
545C2—51no—
546C2—52no—
547C2—51no—
548C2—51no—
549C2—52no—
550C2C3×#6568611yescharacteristic
551C2C3×C22⋊C4×AGL(1,𝔽5)11yescharacteristic
552C2C3×#6570012yes—
553C2C3×C4⋊C4×AGL(1,𝔽5)11yescharacteristic
554C2C3×#6571112yes—
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×#1434
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
6. #10603800C3direct (N × H)
13. C2×C3×C4×AGL(1,𝔽5)C4semidirect
16. C3×(C2×AGL(1,𝔽5))⋊C4C4semidirect
17. C3×C5×#95C4semidirect
18. C3×#3963C4semidirect
19. C3×#3963C4semidirect
70. C2×C4×AGL(1,𝔽5)C3×C4semidirect
73. (C2×AGL(1,𝔽5))⋊C4C3×C4semidirect
74. C5×#95C3×C4semidirect
75. #3963C3×C4semidirect
76. #3963C3×C4semidirect
135. C3×#95AGL(1,𝔽5)semidirect
294. #95C3×AGL(1,𝔽5)semidirect
414. C3×C5#1434semidirect
512. C5C3×#1434semidirect
543. C3#10603800direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×AGL(1,𝔽5)2
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C3×D5×#952
#106038003
C3×#14345