Finite Group Databasebeta

← C3×#10604254 #14280063

Subgroups — C3×#10604254 #14280063

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊AGL(1,𝔽5)C212yesmaximal
2C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal, complemented
5C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
6#10604254C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×D5C2211yescharacteristic
8C23×C3×AGL(1,𝔽5)C2212yes—
9C23×C3×AGL(1,𝔽5)C2212yes—
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C22⋊AGL(1,𝔽5)—24no—
13C2×C3×C22⋊AGL(1,𝔽5)—24no—
14C2×C3×C22⋊AGL(1,𝔽5)—24no—
15C2×C3×C4⋊AGL(1,𝔽5)—24no—
16C2×C3×C4⋊AGL(1,𝔽5)—22no—
17C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
18C2×C3×C22⋊Dic5C411yescharacteristic, complemented
19C2×C3×#685C411yescharacteristic, complemented
20C2×C3×#685C411yescharacteristic, complemented
21C3×D5×C22⋊C4—22no—
22C3×D5×C22⋊C4—22no—
23C3×(C2×AGL(1,𝔽5))⋊C4—24no—
24C3×(C2×AGL(1,𝔽5))⋊C4—22no—
25C3×#1439—51nomaximal, Hall
26C22×C22⋊AGL(1,𝔽5)C2×C312yes—
27C22×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
28C2×D5×C22⋊C4C2×C311yescharacteristic
29C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yescomplemented
30C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic, complemented
31C24×C3×C5C2×C411yescharacteristic
32C23×C3×D5—22no—
33C23×C3×D5—22no—
34C23×C3×D5—21no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C23×C3×D5—21no—
38C23×C3×D5—22no—
39C23×C3×D5—22no—
40C23×C3×D5C2×C411yescharacteristic
41C23×C3×D5D412yes—
42C23×C3×D5Q812yes—
43C23×C3×D5C2311yescharacteristic
44C22×C3×AGL(1,𝔽5)—22no—
45C22×C3×AGL(1,𝔽5)—22no—
46C22×C3×AGL(1,𝔽5)—22no—
47C22×C3×AGL(1,𝔽5)—22no—
48C22×C3×AGL(1,𝔽5)—22no—
49C22×C3×AGL(1,𝔽5)—22no—
50C22×C3×AGL(1,𝔽5)—22no—
51C22×C3×AGL(1,𝔽5)—22no—
52C22×C3×AGL(1,𝔽5)—22no—
53C22×C3×AGL(1,𝔽5)—22no—
54C22×C3×AGL(1,𝔽5)—22no—
55C22×C3×AGL(1,𝔽5)—22no—
56C22×C3×AGL(1,𝔽5)D414yes—
57C22×C3×AGL(1,𝔽5)D414yes—
58C22×C3×C4×C5C2×C411yescharacteristic
59C22×C3×C4×C5C2×C411yescharacteristic
60C22×C3×Dic5C2×C411yescharacteristic
61C22×C3×Dic5C2×C411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5D412yes—
69C2×C3×C4×D5D412yes—
70C3×C22⋊AGL(1,𝔽5)—216no—
71C3×C4⋊AGL(1,𝔽5)—28no—
72C3×C5×C22⋊C4—22no—
73C3×C22⋊Dic5—22no—
74C3×#685—22no—
75C3×#685—22no—
76C22×C3×C4⋊C4—51no—
77C22×C3×C22⋊C4—51no—
78C22×C3×C22⋊C4—52no—
79C2×C3×#95—51no—
80C2×C3×#95—52no—
81C24×D5C22×C311yescharacteristic
82C23×AGL(1,𝔽5)C22×C312yes—
83C23×AGL(1,𝔽5)C22×C312yes—
84C22×C4×D5C22×C311yescharacteristic
85C22×C4×D5C22×C311yescharacteristic
86C2×C22⋊AGL(1,𝔽5)—24no—
87C2×C22⋊AGL(1,𝔽5)—24no—
88C2×C22⋊AGL(1,𝔽5)—24no—
89C2×C4⋊AGL(1,𝔽5)—24no—
90C2×C4⋊AGL(1,𝔽5)—22no—
91C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
92C2×C22⋊Dic5C3×C411yescharacteristic, complemented
93C2×#685C3×C411yescharacteristic, complemented
94C2×#685C3×C411yescharacteristic, complemented
95D5×C22⋊C4—22no—
96D5×C22⋊C4—22no—
97(C2×AGL(1,𝔽5))⋊C4—24no—
98(C2×AGL(1,𝔽5))⋊C4—22no—
99#1439—51noSylow
100C23×C3×C5—21no—
101C23×C3×C5—21no—
102C23×C3×C5—22no—
103C23×C3×C5—22no—
104C23×C3×C5C4⋊C412yescomplemented
105C23×C3×C5C22×C411yescharacteristic
106C22×C3×D5—21no—
107C22×C3×D5—21no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—24no—
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—24no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—41no—
119C22×C3×D5—42no—
120C22×C3×D5—42no—
121C22×C3×D5—42no—
122C22×C3×D5—41no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C22×C3×D5—41no—
126C22×C3×D5—42no—
127C22×C3×D5—41no—
128C22×C3×D5C4⋊C412yescomplemented
129C22×C3×D5C2×D412yes—
130C22×C3×D5C2×D411yescharacteristic
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×D411yescharacteristic
133C22×C3×D5C2×D411yescharacteristic
134C22×C3×D5C2×Q811yescharacteristic
135C22×C3×D5#4111yescharacteristic
136C22×C3×D5#4112yes—
137C22×C3×D5#4111yescharacteristic
138C22×C3×D5#4112yes—
139C2×C3×AGL(1,𝔽5)—24no—
140C2×C3×AGL(1,𝔽5)—24no—
141C2×C3×AGL(1,𝔽5)—24no—
142C2×C3×AGL(1,𝔽5)—24no—
143C2×C3×AGL(1,𝔽5)—24no—
144C2×C3×AGL(1,𝔽5)—24no—
145C2×C3×AGL(1,𝔽5)—42no—
146C2×C3×AGL(1,𝔽5)—42no—
147C2×C3×AGL(1,𝔽5)—42no—
148C2×C3×AGL(1,𝔽5)—42no—
149C2×C3×AGL(1,𝔽5)—42no—
150C2×C3×AGL(1,𝔽5)—42no—
151C2×C3×AGL(1,𝔽5)—42no—
152C2×C3×AGL(1,𝔽5)—42no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5C22⋊C412yescomplemented
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22⋊C412yescomplemented
161C3×C4×D5—22no—
162C3×C4×D5—24no—
163C3×C4×D5—22no—
164C3×C4×D5—42no—
165C3×C4×D5—41no—
166C3×C4×D5—41no—
167C25×C3—51no—
168C23×C3×C4—51no—
169C23×C3×C4—52no—
170C23×C3×C4—52no—
171C23×C3×C4—51no—
172C2×C3×C4⋊C4—102no—
173C2×C3×C4⋊C4—104no—
174C2×C3×C22⋊C4—51no—
175C2×C3×C22⋊C4—51no—
176C2×C3×C22⋊C4—51no—
177C2×C3×C22⋊C4—102no—
178C2×C3×C22⋊C4—102no—
179C2×C3×C22⋊C4—104no—
180C2×C3×C22⋊C4—104no—
181C2×C3×C22⋊C4—104no—
182C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
183C3×#95—102no—
184C3×#95—104no—
185C24×C5C2×C3×C411yescharacteristic
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—21no—
189C23×D5—21no—
190C23×D5—21no—
191C23×D5—21no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5C2×C3×C411yescharacteristic
195C23×D5C3×D412yes—
196C23×D5C3×Q812yes—
197C23×D5C23×C311yescharacteristic
198C22×AGL(1,𝔽5)—22no—
199C22×AGL(1,𝔽5)—22no—
200C22×AGL(1,𝔽5)—22no—
201C22×AGL(1,𝔽5)—22no—
202C22×AGL(1,𝔽5)—22no—
203C22×AGL(1,𝔽5)—22no—
204C22×AGL(1,𝔽5)—22no—
205C22×AGL(1,𝔽5)—22no—
206C22×AGL(1,𝔽5)—22no—
207C22×AGL(1,𝔽5)—22no—
208C22×AGL(1,𝔽5)—22no—
209C22×AGL(1,𝔽5)—22no—
210C22×AGL(1,𝔽5)C3×D414yes—
211C22×AGL(1,𝔽5)C3×D414yes—
212C22×C4×C5C2×C3×C411yescharacteristic
213C22×C4×C5C2×C3×C411yescharacteristic
214C22×Dic5C2×C3×C411yescharacteristic
215C22×Dic5C2×C3×C411yescharacteristic
216C2×C4×D5—22no—
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5—21no—
220C2×C4×D5—21no—
221C2×C4×D5—22no—
222C2×C4×D5C3×D412yes—
223C2×C4×D5C3×D412yes—
224C22⋊AGL(1,𝔽5)—216no—
225C4⋊AGL(1,𝔽5)—28no—
226C5×C22⋊C4—22no—
227C22⋊Dic5—22no—
228#685—22no—
229#685—22no—
230C22×C4⋊C4—51no—
231C22×C22⋊C4—51no—
232C22×C22⋊C4—52no—
233C2×#95—51no—
234C2×#95—52no—
235C22×C3×C5—22no—
236C22×C3×C5—24no—
237C22×C3×C5—41no—
238C22×C3×C5—42no—
239C22×C3×C5—41no—
240C22×C3×C5C2×C22⋊C411yescharacteristic
241C22×C3×C5C2×C4⋊C411yescharacteristic
242C22×C3×C5#11711yescharacteristic
243C22×C3×C5C4×D412yes—
244C22×C3×C5C4×D412yes—
245C2×C3×D5—22no—
246C2×C3×D5—24no—
247C2×C3×D5—41no—
248C2×C3×D5—42no—
249C2×C3×D5—41no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C2×C3×D5—44no—
253C2×C3×D5—44no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5#12011yescharacteristic
257C2×C3×D5#12012yes—
258C2×C3×D5#12112yes—
259C2×C3×D5#12111yescharacteristic
260C2×C3×D5#12111yescharacteristic
261C2×C3×D5#12112yes—
262C2×C3×D5#12112yes—
263C2×C3×D5C22⋊Q812yes—
264C2×C3×D5C22⋊Q811yescharacteristic
265C2×C3×D5C22⋊Q811yescharacteristic
266C2×C3×D5C22⋊Q812yes—
267C2×C3×D5#12312yes—
268C2×C3×D5#12312yes—
269C2×C3×D5#12311yescharacteristic
270C2×C3×D5#12412yes—
271C2×C3×D5#12411yescharacteristic
272C2×C3×D5#12612yes—
273C2×C3×D5#12711yescharacteristic
274C3×AGL(1,𝔽5)—44no—
275C3×AGL(1,𝔽5)—44no—
276C3×C4×C5—22no—
277C3×C4×C5—41no—
278C3×Dic5—22no—
279C3×Dic5—41no—
280C24×C3—51no—
281C24×C3—52no—
282C24×C3—52no—
283C24×C3—51no—
284C24×C3—102no—
285C24×C3—102no—
286C24×C3—101no—
287C24×C3—101no—
288C24×C3—101no—
289C24×C3—101no—
290C24×C3—102no—
291C24×C3—102no—
292C24×C3C2×AGL(1,𝔽5)11yescharacteristic
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—52no—
296C22×C3×C4—54no—
297C22×C3×C4—54no—
298C22×C3×C4—51no—
299C22×C3×C4—102no—
300C22×C3×C4—102no—
301C22×C3×C4—102no—
302C22×C3×C4—101no—
303C22×C3×C4—101no—
304C22×C3×C4—102no—
305C22×C3×C4—102no—
306C22×C3×C4—102no—
307C22×C3×C4—102no—
308C22×C3×C4—102no—
309C22×C3×C4—102no—
310C22×C3×C4—102no—
311C22×C3×C4—102no—
312C22×C3×C4—102no—
313C22×C3×C4—102no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
318C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
319C3×C4⋊C4—108no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—102no—
322C3×C22⋊C4—102no—
323C3×C22⋊C4—1016no—
324C3×C22⋊C4—102no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5C3×C4⋊C412yescomplemented
330C23×C5C22×C3×C411yescharacteristic
331C22×D5—21no—
332C22×D5—21no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—24no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—24no—
341C22×D5—24no—
342C22×D5—24no—
343C22×D5—41no—
344C22×D5—42no—
345C22×D5—42no—
346C22×D5—42no—
347C22×D5—41no—
348C22×D5—42no—
349C22×D5—42no—
350C22×D5—41no—
351C22×D5—42no—
352C22×D5—41no—
353C22×D5C3×C4⋊C412yescomplemented
354C22×D5C2×C3×D412yes—
355C22×D5C2×C3×D411yescharacteristic
356C22×D5C2×C3×D412yes—
357C22×D5C2×C3×D411yescharacteristic
358C22×D5C2×C3×D411yescharacteristic
359C22×D5C2×C3×Q811yescharacteristic
360C22×D5C3×#4111yescharacteristic
361C22×D5C3×#4112yes—
362C22×D5C3×#4111yescharacteristic
363C22×D5C3×#4112yes—
364C2×AGL(1,𝔽5)—24no—
365C2×AGL(1,𝔽5)—24no—
366C2×AGL(1,𝔽5)—24no—
367C2×AGL(1,𝔽5)—24no—
368C2×AGL(1,𝔽5)—24no—
369C2×AGL(1,𝔽5)—24no—
370C2×AGL(1,𝔽5)—42no—
371C2×AGL(1,𝔽5)—42no—
372C2×AGL(1,𝔽5)—42no—
373C2×AGL(1,𝔽5)—42no—
374C2×AGL(1,𝔽5)—42no—
375C2×AGL(1,𝔽5)—42no—
376C2×AGL(1,𝔽5)—42no—
377C2×AGL(1,𝔽5)—42no—
378C2×C4×C5—22no—
379C2×C4×C5—21no—
380C2×C4×C5—22no—
381C2×C4×C5C3×C22⋊C412yescomplemented
382C2×Dic5—22no—
383C2×Dic5—21no—
384C2×Dic5—22no—
385C2×Dic5C3×C22⋊C412yescomplemented
386C4×D5—22no—
387C4×D5—24no—
388C4×D5—22no—
389C4×D5—42no—
390C4×D5—41no—
391C4×D5—41no—
392C25—51no—
393C23×C4—51no—
394C23×C4—52no—
395C23×C4—52no—
396C23×C4—51no—
397C2×C4⋊C4—102no—
398C2×C4⋊C4—104no—
399C2×C22⋊C4—51no—
400C2×C22⋊C4—51no—
401C2×C22⋊C4—51no—
402C2×C22⋊C4—102no—
403C2×C22⋊C4—102no—
404C2×C22⋊C4—104no—
405C2×C22⋊C4—104no—
406C2×C22⋊C4—104no—
407C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
408#95—102no—
409#95—104no—
410C2×C3×C5—42no—
411C2×C3×C5#38011yescharacteristic
412C2×C3×C5#38512yes—
413C2×C3×C5#38611yescharacteristic
414C2×C3×C5#38812yes—
415C2×C3×C5#39011yescharacteristic
416C3×D5—42no—
417C3×D5#39211yescharacteristic
418C3×D5#39311yescharacteristic
419C3×D5#39412yes—
420C3×D5#39612yes—
421C3×D5#39711yescharacteristic
422C3×D5#39911yescharacteristic
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—21no—
427C23×C3—51no—
428C23×C3—51no—
429C23×C3—51no—
430C23×C3—51no—
431C23×C3—52no—
432C23×C3—52no—
433C23×C3—52no—
434C23×C3—52no—
435C23×C3—51no—
436C23×C3—51no—
437C23×C3—52no—
438C23×C3—104no—
439C23×C3—104no—
440C23×C3—104no—
441C23×C3—104no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3—101no—
447C23×C3—102no—
448C23×C3—102no—
449C23×C3—101no—
450C23×C3—202no—
451C23×C3—202no—
452C23×C3—202no—
453C23×C3—202no—
454C23×C3—201no—
455C23×C3—202no—
456C23×C3—201no—
457C23×C3—202no—
458C23×C3—201no—
459C23×C3—201no—
460C23×C3C4⋊AGL(1,𝔽5)12yescomplemented
461C23×C3C22×AGL(1,𝔽5)11yescharacteristic
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—52no—
466C2×C3×C4—102no—
467C2×C3×C4—104no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—104no—
471C2×C3×C4—104no—
472C2×C3×C4—104no—
473C2×C3×C4—104no—
474C2×C3×C4—104no—
475C2×C3×C4—104no—
476C2×C3×C4—102no—
477C2×C3×C4—101no—
478C2×C3×C4—202no—
479C2×C3×C4—201no—
480C2×C3×C4—201no—
481C2×C3×C4—202no—
482C2×C3×C4—202no—
483C2×C3×C4—202no—
484C2×C3×C4—202no—
485C2×C3×C4—202no—
486C2×C3×C4—202no—
487C2×C3×C4—202no—
488C2×C3×C4—202no—
489C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
490C22×C5—22no—
491C22×C5—24no—
492C22×C5—41no—
493C22×C5—42no—
494C22×C5—41no—
495C22×C5C2×C3×C22⋊C411yescharacteristic
496C22×C5C2×C3×C4⋊C411yescharacteristic
497C22×C5C3×#11711yescharacteristic
498C22×C5C3×C4×D412yes—
499C22×C5C3×C4×D412yes—
500C2×D5—22no—
501C2×D5—24no—
502C2×D5—41no—
503C2×D5—42no—
504C2×D5—41no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—44no—
508C2×D5—44no—
509C2×D5—42no—
510C2×D5—42no—
511C2×D5C3×#12011yescharacteristic
512C2×D5C3×#12012yes—
513C2×D5C3×#12112yes—
514C2×D5C3×#12111yescharacteristic
515C2×D5C3×#12111yescharacteristic
516C2×D5C3×#12112yes—
517C2×D5C3×#12112yes—
518C2×D5C3×C22⋊Q812yes—
519C2×D5C3×C22⋊Q811yescharacteristic
520C2×D5C3×C22⋊Q811yescharacteristic
521C2×D5C3×C22⋊Q812yes—
522C2×D5C3×#12312yes—
523C2×D5C3×#12312yes—
524C2×D5C3×#12311yescharacteristic
525C2×D5C3×#12412yes—
526C2×D5C3×#12411yescharacteristic
527C2×D5C3×#12612yes—
528C2×D5C3×#12711yescharacteristic
529AGL(1,𝔽5)—44no—
530AGL(1,𝔽5)—44no—
531C4×C5—22no—
532C4×C5—41no—
533Dic5—22no—
534Dic5—41no—
535C24—51no—
536C24—52no—
537C24—52no—
538C24—51no—
539C24—102no—
540C24—102no—
541C24—101no—
542C24—101no—
543C24—101no—
544C24—101no—
545C24—102no—
546C24—102no—
547C24C2×C3×AGL(1,𝔽5)11yescharacteristic
548C22×C4—51no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—54no—
552C22×C4—54no—
553C22×C4—51no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
573C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
574C4⋊C4—108no—
575C22⋊C4—22no—
576C22⋊C4—102no—
577C22⋊C4—102no—
578C22⋊C4—1016no—
579C22⋊C4—102no—
580C3×C5#143911yescharacteristic, complemented, Hall
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—42no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—52no—
587C22×C3—52no—
588C22×C3—52no—
589C22×C3—52no—
590C22×C3—52no—
591C22×C3—52no—
592C22×C3—52no—
593C22×C3—52no—
594C22×C3—51no—
595C22×C3—51no—
596C22×C3—51no—
597C22×C3—51no—
598C22×C3—51no—
599C22×C3—52no—
600C22×C3—51no—
601C22×C3—52no—
602C22×C3—51no—
603C22×C3—51no—
604C22×C3—104no—
605C22×C3—102no—
606C22×C3—202no—
607C22×C3—204no—
608C22×C3—202no—
609C22×C3—204no—
610C22×C3—202no—
611C22×C3—202no—
612C22×C3—202no—
613C22×C3—201no—
614C22×C3—201no—
615C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
616C22×C3#413011yescharacteristic
617C22×C3D4×AGL(1,𝔽5)12yes—
618C22×C3D4×AGL(1,𝔽5)12yes—
619C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
620C3×C4—22no—
621C3×C4—41no—
622C3×C4—102no—
623C3×C4—204no—
624C3×C4—204no—
625C3×C4—201no—
626C2×C5—42no—
627C2×C5C3×#38011yescharacteristic
628C2×C5C3×#38512yes—
629C2×C5C3×#38611yescharacteristic
630C2×C5C3×#38812yes—
631C2×C5C3×#39011yescharacteristic
632D5—42no—
633D5C3×#39211yescharacteristic
634D5C3×#39311yescharacteristic
635D5C3×#39412yes—
636D5C3×#39612yes—
637D5C3×#39711yescharacteristic
638D5C3×#39911yescharacteristic
639C23—21no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—51no—
644C23—51no—
645C23—51no—
646C23—51no—
647C23—52no—
648C23—52no—
649C23—52no—
650C23—52no—
651C23—51no—
652C23—51no—
653C23—52no—
654C23—104no—
655C23—104no—
656C23—104no—
657C23—104no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—101no—
663C23—102no—
664C23—102no—
665C23—101no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—202no—
670C23—201no—
671C23—202no—
672C23—201no—
673C23—202no—
674C23—201no—
675C23—201no—
676C23C3×C4⋊AGL(1,𝔽5)12yescomplemented
677C23C22×C3×AGL(1,𝔽5)11yescharacteristic
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—52no—
682C2×C4—102no—
683C2×C4—104no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—104no—
687C2×C4—104no—
688C2×C4—104no—
689C2×C4—104no—
690C2×C4—104no—
691C2×C4—104no—
692C2×C4—102no—
693C2×C4—101no—
694C2×C4—202no—
695C2×C4—201no—
696C2×C4—201no—
697C2×C4—202no—
698C2×C4—202no—
699C2×C4—202no—
700C2×C4—202no—
701C2×C4—202no—
702C2×C4—202no—
703C2×C4—202no—
704C2×C4—202no—
705C2×C4C3×C22⋊AGL(1,𝔽5)12yescomplemented
706C2×C3—42no—
707C2×C3—51no—
708C2×C3—52no—
709C2×C3—51no—
710C2×C3—52no—
711C2×C3—51no—
712C2×C3—51no—
713C2×C3—202no—
714C2×C3#6569912yes—
715C2×C3#6570012yes—
716C2×C3#6576511yescharacteristic
717C2×C3#6577911yescharacteristic
718C2×C3#6578011yescharacteristic
719C5C3×#143911yescharacteristic, complemented, Sylow
720C22—24no—
721C22—22no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—52no—
726C22—52no—
727C22—52no—
728C22—52no—
729C22—52no—
730C22—52no—
731C22—52no—
732C22—52no—
733C22—51no—
734C22—51no—
735C22—51no—
736C22—51no—
737C22—51no—
738C22—52no—
739C22—51no—
740C22—52no—
741C22—51no—
742C22—51no—
743C22—104no—
744C22—102no—
745C22—202no—
746C22—204no—
747C22—202no—
748C22—204no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—201no—
753C22—201no—
754C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
755C22C3×#413011yescharacteristic
756C22C3×D4×AGL(1,𝔽5)12yes—
757C22C3×D4×AGL(1,𝔽5)12yes—
758C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
759C4—22no—
760C4—41no—
761C4—102no—
762C4—204no—
763C4—204no—
764C4—201no—
765C3#1060425411yescharacteristic, direct product factor, Sylow
766C2—42no—
767C2—51no—
768C2—52no—
769C2—51no—
770C2—52no—
771C2—51no—
772C2—51no—
773C2—202no—
774C2C3×#6569912yes—
775C2C3×#6570012yes—
776C2C3×#6576511yescharacteristic
777C2C3×#6577911yescharacteristic
778C2C3×#6578011yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC23×D5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1439
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊AGL(1,𝔽5)C2semidirect
4. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
5. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
6. #10604254C3direct (N × H)
17. C2×C3×C5×C22⋊C4C4semidirect
18. C2×C3×C22⋊Dic5C4semidirect
19. C2×C3×#685C4semidirect
20. C2×C3×#685C4semidirect
27. C22×C4⋊AGL(1,𝔽5)C2×C3semidirect
29. C2×(C2×AGL(1,𝔽5))⋊C4C2×C3semidirect
30. C2×(C2×AGL(1,𝔽5))⋊C4C2×C3semidirect
91. C2×C5×C22⋊C4C3×C4semidirect
92. C2×C22⋊Dic5C3×C4semidirect
93. C2×#685C3×C4semidirect
94. C2×#685C3×C4semidirect
104. C23×C3×C5C4⋊C4semidirect
128. C22×C3×D5C4⋊C4semidirect
156. C2×C3×C4×C5C22⋊C4semidirect
160. C2×C3×Dic5C22⋊C4semidirect
182. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
329. C23×C5C3×C4⋊C4semidirect
353. C22×D5C3×C4⋊C4semidirect
381. C2×C4×C5C3×C22⋊C4semidirect
385. C2×Dic5C3×C22⋊C4semidirect
407. C2×C22⋊C4C3×AGL(1,𝔽5)semidirect
460. C23×C3C4⋊AGL(1,𝔽5)semidirect
489. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
580. C3×C5#1439semidirect
676. C23C3×C4⋊AGL(1,𝔽5)semidirect
705. C2×C4C3×C22⋊AGL(1,𝔽5)semidirect
719. C5C3×#1439semidirect
765. C3#10604254direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊AGL(1,𝔽5)2
C22×C3×C4⋊AGL(1,𝔽5)2
C2×C3×D5×C22⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
#106042543
C3×#14395