Finite Group Databasebeta

← C3×#10604344 #14280133

Subgroups — C3×#10604344 #14280133

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 616 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×D5×C4⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
5C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
6#10604344C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×AGL(1,𝔽5)C2212yes—
8C23×C3×AGL(1,𝔽5)C2212yes—
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)—24no—
13C2×C3×C4⋊AGL(1,𝔽5)—22no—
14C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
15C2×C3×C4⋊Dic5C411yescharacteristic, complemented
16C2×C3×#683C411yescharacteristic, complemented
17C2×C3×#683C411yescharacteristic, complemented
18C3×D5×C4⋊C4—22no—
19C3×D5×C4⋊C4—22no—
20C3×(C2×AGL(1,𝔽5))⋊C4—24no—
21C3×(C2×AGL(1,𝔽5))⋊C4—22no—
22C3×(C2×AGL(1,𝔽5))⋊C4—24no—
23C3×#1441—51nomaximal, Hall
24C22×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic
25C2×D5×C4⋊C4C2×C311yescharacteristic
26C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yes—
27C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
28C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yes—
29C23×C3×D5C2311yescharacteristic
30C22×C3×AGL(1,𝔽5)—22no—
31C22×C3×AGL(1,𝔽5)—22no—
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)—22no—
39C22×C3×AGL(1,𝔽5)—22no—
40C22×C3×AGL(1,𝔽5)—22no—
41C22×C3×AGL(1,𝔽5)—22no—
42C22×C3×AGL(1,𝔽5)D414yes—
43C22×C3×AGL(1,𝔽5)Q814yes—
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×C3×C4×C5C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C22×C3×Dic5C2×C411yescharacteristic
49C22×C3×Dic5C2×C411yescharacteristic
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—22no—
56C2×C3×C4×D5—22no—
57C2×C3×C4×D5—21no—
58C2×C3×C4×D5—21no—
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5D412yes—
62C2×C3×C4×D5D412yes—
63C2×C3×C4×D5Q812yes—
64C3×C4⋊AGL(1,𝔽5)—28no—
65C3×C5×C4⋊C4—22no—
66C3×C4⋊Dic5—22no—
67C3×#683—22no—
68C3×#683—22no—
69C22×C3×C4⋊C4—51no—
70C22×C3×C4⋊C4—51no—
71C2×C3×#95—52no—
72C2×C3×#95—51no—
73C2×C3×#95—52no—
74C23×AGL(1,𝔽5)C22×C312yes—
75C23×AGL(1,𝔽5)C22×C312yes—
76C22×C4×D5C22×C311yescharacteristic
77C22×C4×D5C22×C311yescharacteristic
78C22×C4×D5C22×C311yescharacteristic
79C2×C4⋊AGL(1,𝔽5)—24no—
80C2×C4⋊AGL(1,𝔽5)—22no—
81C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
82C2×C4⋊Dic5C3×C411yescharacteristic, complemented
83C2×#683C3×C411yescharacteristic, complemented
84C2×#683C3×C411yescharacteristic, complemented
85D5×C4⋊C4—22no—
86D5×C4⋊C4—22no—
87(C2×AGL(1,𝔽5))⋊C4—24no—
88(C2×AGL(1,𝔽5))⋊C4—22no—
89(C2×AGL(1,𝔽5))⋊C4—24no—
90#1441—51noSylow
91C23×C3×C5C22×C411yescharacteristic
92C22×C3×D5C2×D412yes—
93C22×C3×D5C2×D411yescharacteristic
94C22×C3×D5C2×D411yescharacteristic
95C22×C3×D5C2×D411yescharacteristic
96C22×C3×D5C2×Q812yes—
97C22×C3×D5C2×Q811yescharacteristic
98C22×C3×D5#4111yescharacteristic
99C22×C3×D5#4111yescharacteristic
100C22×C3×D5#4112yes—
101C22×C3×D5#4112yes—
102C2×C3×AGL(1,𝔽5)—24no—
103C2×C3×AGL(1,𝔽5)—24no—
104C2×C3×AGL(1,𝔽5)—24no—
105C2×C3×AGL(1,𝔽5)—24no—
106C2×C3×AGL(1,𝔽5)—24no—
107C2×C3×AGL(1,𝔽5)—24no—
108C2×C3×AGL(1,𝔽5)—42no—
109C2×C3×AGL(1,𝔽5)—42no—
110C2×C3×AGL(1,𝔽5)—42no—
111C2×C3×AGL(1,𝔽5)—42no—
112C2×C3×AGL(1,𝔽5)—42no—
113C2×C3×AGL(1,𝔽5)—42no—
114C2×C3×AGL(1,𝔽5)—42no—
115C2×C3×AGL(1,𝔽5)—42no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5C22⋊C412yes—
122C2×C3×C4×C5C4⋊C412yescomplemented
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5C22⋊C412yes—
129C2×C3×Dic5C4⋊C412yescomplemented
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×C4×D5—24no—
134C3×C4×D5—22no—
135C3×C4×D5—22no—
136C3×C4×D5—22no—
137C3×C4×D5—41no—
138C3×C4×D5—42no—
139C3×C4×D5—41no—
140C23×C3×C4—51no—
141C23×C3×C4—51no—
142C23×C3×C4—52no—
143C23×C3×C4—52no—
144C23×C3×C4—51no—
145C2×C3×C4⋊C4—51no—
146C2×C3×C4⋊C4—51no—
147C2×C3×C4⋊C4—51no—
148C2×C3×C4⋊C4—102no—
149C2×C3×C4⋊C4—102no—
150C2×C3×C4⋊C4—102no—
151C2×C3×C4⋊C4—104no—
152C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
153C3×#95—104no—
154C3×#95—102no—
155C3×#95—104no—
156C23×D5C23×C311yescharacteristic
157C22×AGL(1,𝔽5)—22no—
158C22×AGL(1,𝔽5)—22no—
159C22×AGL(1,𝔽5)—22no—
160C22×AGL(1,𝔽5)—22no—
161C22×AGL(1,𝔽5)—22no—
162C22×AGL(1,𝔽5)—22no—
163C22×AGL(1,𝔽5)—22no—
164C22×AGL(1,𝔽5)—22no—
165C22×AGL(1,𝔽5)—22no—
166C22×AGL(1,𝔽5)—22no—
167C22×AGL(1,𝔽5)—22no—
168C22×AGL(1,𝔽5)—22no—
169C22×AGL(1,𝔽5)C3×D414yes—
170C22×AGL(1,𝔽5)C3×Q814yes—
171C22×C4×C5C2×C3×C411yescharacteristic
172C22×C4×C5C2×C3×C411yescharacteristic
173C22×C4×C5C2×C3×C411yescharacteristic
174C22×Dic5C2×C3×C411yescharacteristic
175C22×Dic5C2×C3×C411yescharacteristic
176C22×Dic5C2×C3×C411yescharacteristic
177C2×C4×D5—22no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—22no—
183C2×C4×D5—22no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—22no—
187C2×C4×D5C3×D412yes—
188C2×C4×D5C3×D412yes—
189C2×C4×D5C3×D412yes—
190C2×C4×D5C3×Q812yes—
191C4⋊AGL(1,𝔽5)—28no—
192C5×C4⋊C4—22no—
193C4⋊Dic5—22no—
194#683—22no—
195#683—22no—
196C22×C4⋊C4—51no—
197C22×C4⋊C4—51no—
198C2×#95—51no—
199C2×#95—52no—
200C2×#95—52no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5C2×C4⋊C411yescharacteristic
203C22×C3×C5#11711yescharacteristic
204C22×C3×C5C4×D412yes—
205C22×C3×C5C4×Q812yes—
206C2×C3×D5#12011yescharacteristic
207C2×C3×D5#12112yes—
208C2×C3×D5#12111yescharacteristic
209C2×C3×D5#12111yescharacteristic
210C2×C3×D5#12112yes—
211C2×C3×D5C22⋊Q812yes—
212C2×C3×D5C22⋊Q811yescharacteristic
213C2×C3×D5C22⋊Q812yes—
214C2×C3×D5C22⋊Q812yes—
215C2×C3×D5C22⋊Q811yescharacteristic
216C2×C3×D5#12312yes—
217C2×C3×D5#12311yescharacteristic
218C2×C3×D5#12411yescharacteristic
219C2×C3×D5#12512yes—
220C2×C3×D5#12512yes—
221C2×C3×D5#12612yes—
222C2×C3×D5C4⋊Q812yes—
223C2×C3×D5C4⋊Q811yescharacteristic
224C3×AGL(1,𝔽5)—44no—
225C3×AGL(1,𝔽5)—44no—
226C3×C4×C5—22no—
227C3×C4×C5—22no—
228C3×C4×C5—41no—
229C3×Dic5—22no—
230C3×Dic5—22no—
231C3×Dic5—41no—
232C24×C3—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—52no—
236C22×C3×C4—52no—
237C22×C3×C4—52no—
238C22×C3×C4—52no—
239C22×C3×C4—54no—
240C22×C3×C4—54no—
241C22×C3×C4—51no—
242C22×C3×C4—102no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×C3×C4—101no—
246C22×C3×C4—101no—
247C22×C3×C4—102no—
248C22×C3×C4—102no—
249C22×C3×C4—101no—
250C22×C3×C4—101no—
251C22×C3×C4—102no—
252C22×C3×C4—102no—
253C22×C3×C4—102no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C22×C3×C4—102no—
257C22×C3×C4—102no—
258C22×C3×C4—102no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4—102no—
262C22×C3×C4—102no—
263C22×C3×C4—102no—
264C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
265C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
266C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
267C3×C4⋊C4—22no—
268C3×C4⋊C4—102no—
269C3×C4⋊C4—102no—
270C3×C4⋊C4—108no—
271C3×C4⋊C4—102no—
272C23×C5C22×C3×C411yescharacteristic
273C22×D5C2×C3×D412yes—
274C22×D5C2×C3×D411yescharacteristic
275C22×D5C2×C3×D411yescharacteristic
276C22×D5C2×C3×D411yescharacteristic
277C22×D5C2×C3×Q812yes—
278C22×D5C2×C3×Q811yescharacteristic
279C22×D5C3×#4111yescharacteristic
280C22×D5C3×#4111yescharacteristic
281C22×D5C3×#4112yes—
282C22×D5C3×#4112yes—
283C2×AGL(1,𝔽5)—24no—
284C2×AGL(1,𝔽5)—24no—
285C2×AGL(1,𝔽5)—24no—
286C2×AGL(1,𝔽5)—24no—
287C2×AGL(1,𝔽5)—24no—
288C2×AGL(1,𝔽5)—24no—
289C2×AGL(1,𝔽5)—42no—
290C2×AGL(1,𝔽5)—42no—
291C2×AGL(1,𝔽5)—42no—
292C2×AGL(1,𝔽5)—42no—
293C2×AGL(1,𝔽5)—42no—
294C2×AGL(1,𝔽5)—42no—
295C2×AGL(1,𝔽5)—42no—
296C2×AGL(1,𝔽5)—42no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5C3×C22⋊C412yes—
303C2×C4×C5C3×C4⋊C412yescomplemented
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—22no—
307C2×Dic5—21no—
308C2×Dic5—22no—
309C2×Dic5C3×C22⋊C412yes—
310C2×Dic5C3×C4⋊C412yescomplemented
311C4×D5—22no—
312C4×D5—22no—
313C4×D5—22no—
314C4×D5—24no—
315C4×D5—22no—
316C4×D5—22no—
317C4×D5—22no—
318C4×D5—41no—
319C4×D5—42no—
320C4×D5—41no—
321C23×C4—51no—
322C23×C4—51no—
323C23×C4—52no—
324C23×C4—52no—
325C23×C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—102no—
330C2×C4⋊C4—102no—
331C2×C4⋊C4—102no—
332C2×C4⋊C4—104no—
333C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
334#95—104no—
335#95—102no—
336#95—104no—
337C2×C3×C5#38011yescharacteristic
338C2×C3×C5#38611yescharacteristic
339C2×C3×C5#38712yes—
340C2×C3×C5#38912yes—
341C2×C3×C5#39111yescharacteristic
342C3×D5#39411yescharacteristic
343C3×D5#39511yescharacteristic
344C3×D5#39612yes—
345C3×D5#39811yescharacteristic
346C3×D5#39812yes—
347C3×D5#40011yescharacteristic
348C23×C3—51no—
349C23×C3—51no—
350C23×C3—51no—
351C23×C3—51no—
352C23×C3—52no—
353C23×C3—52no—
354C23×C3—52no—
355C23×C3—52no—
356C23×C3—51no—
357C23×C3—51no—
358C23×C3C22×AGL(1,𝔽5)11yescharacteristic
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—52no—
365C2×C3×C4—52no—
366C2×C3×C4—102no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—104no—
372C2×C3×C4—102no—
373C2×C3×C4—101no—
374C2×C3×C4—102no—
375C2×C3×C4—101no—
376C2×C3×C4—104no—
377C2×C3×C4—104no—
378C2×C3×C4—104no—
379C2×C3×C4—104no—
380C2×C3×C4—104no—
381C2×C3×C4—104no—
382C2×C3×C4—102no—
383C2×C3×C4—101no—
384C2×C3×C4—201no—
385C2×C3×C4—202no—
386C2×C3×C4—201no—
387C2×C3×C4—202no—
388C2×C3×C4—202no—
389C2×C3×C4—202no—
390C2×C3×C4—202no—
391C2×C3×C4—202no—
392C2×C3×C4—202no—
393C2×C3×C4—202no—
394C2×C3×C4—202no—
395C2×C3×C4C4⋊AGL(1,𝔽5)12yescomplemented
396C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
397C22×C5C2×C3×C22⋊C411yescharacteristic
398C22×C5C2×C3×C4⋊C411yescharacteristic
399C22×C5C3×#11711yescharacteristic
400C22×C5C3×C4×D412yes—
401C22×C5C3×C4×Q812yes—
402C2×D5C3×#12011yescharacteristic
403C2×D5C3×#12112yes—
404C2×D5C3×#12111yescharacteristic
405C2×D5C3×#12111yescharacteristic
406C2×D5C3×#12112yes—
407C2×D5C3×C22⋊Q812yes—
408C2×D5C3×C22⋊Q811yescharacteristic
409C2×D5C3×C22⋊Q812yes—
410C2×D5C3×C22⋊Q812yes—
411C2×D5C3×C22⋊Q811yescharacteristic
412C2×D5C3×#12312yes—
413C2×D5C3×#12311yescharacteristic
414C2×D5C3×#12411yescharacteristic
415C2×D5C3×#12512yes—
416C2×D5C3×#12512yes—
417C2×D5C3×#12612yes—
418C2×D5C3×C4⋊Q812yes—
419C2×D5C3×C4⋊Q811yescharacteristic
420AGL(1,𝔽5)—44no—
421AGL(1,𝔽5)—44no—
422C4×C5—22no—
423C4×C5—22no—
424C4×C5—41no—
425Dic5—22no—
426Dic5—22no—
427Dic5—41no—
428C24—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—52no—
434C22×C4—52no—
435C22×C4—54no—
436C22×C4—54no—
437C22×C4—51no—
438C22×C4—102no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
461C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
462C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
463C4⋊C4—22no—
464C4⋊C4—102no—
465C4⋊C4—102no—
466C4⋊C4—108no—
467C4⋊C4—102no—
468C3×C5#144111yescharacteristic, complemented, Hall
469C22×C3—52no—
470C22×C3—52no—
471C22×C3—52no—
472C22×C3—52no—
473C22×C3—52no—
474C22×C3—52no—
475C22×C3—52no—
476C22×C3—52no—
477C22×C3—51no—
478C22×C3—51no—
479C22×C3—51no—
480C22×C3—51no—
481C22×C3—51no—
482C22×C3—52no—
483C22×C3—51no—
484C22×C3—52no—
485C22×C3—51no—
486C22×C3—51no—
487C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
488C22×C3#413011yescharacteristic
489C22×C3D4×AGL(1,𝔽5)12yes—
490C22×C3Q8×AGL(1,𝔽5)12yes—
491C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—41no—
495C3×C4—102no—
496C3×C4—102no—
497C3×C4—204no—
498C3×C4—204no—
499C3×C4—201no—
500C2×C5C3×#38011yescharacteristic
501C2×C5C3×#38611yescharacteristic
502C2×C5C3×#38712yes—
503C2×C5C3×#38912yes—
504C2×C5C3×#39111yescharacteristic
505D5C3×#39411yescharacteristic
506D5C3×#39511yescharacteristic
507D5C3×#39612yes—
508D5C3×#39811yescharacteristic
509D5C3×#39812yes—
510D5C3×#40011yescharacteristic
511C23—51no—
512C23—51no—
513C23—51no—
514C23—51no—
515C23—52no—
516C23—52no—
517C23—52no—
518C23—52no—
519C23—51no—
520C23—51no—
521C23C22×C3×AGL(1,𝔽5)11yescharacteristic
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—104no—
535C2×C4—102no—
536C2×C4—101no—
537C2×C4—102no—
538C2×C4—101no—
539C2×C4—104no—
540C2×C4—104no—
541C2×C4—104no—
542C2×C4—104no—
543C2×C4—104no—
544C2×C4—104no—
545C2×C4—102no—
546C2×C4—101no—
547C2×C4—201no—
548C2×C4—202no—
549C2×C4—201no—
550C2×C4—202no—
551C2×C4—202no—
552C2×C4—202no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—202no—
558C2×C4C3×C4⋊AGL(1,𝔽5)12yescomplemented
559C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
560C2×C3—51no—
561C2×C3—52no—
562C2×C3—51no—
563C2×C3—52no—
564C2×C3—51no—
565C2×C3—51no—
566C2×C3#6571112yes—
567C2×C3#6571212yes—
568C2×C3#6576511yescharacteristic
569C2×C3#6577911yescharacteristic
570C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
571C5C3×#144111yescharacteristic, complemented, Sylow
572C22—52no—
573C22—52no—
574C22—52no—
575C22—52no—
576C22—52no—
577C22—52no—
578C22—52no—
579C22—52no—
580C22—51no—
581C22—51no—
582C22—51no—
583C22—51no—
584C22—51no—
585C22—52no—
586C22—51no—
587C22—52no—
588C22—51no—
589C22—51no—
590C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
591C22C3×#413011yescharacteristic
592C22C3×D4×AGL(1,𝔽5)12yes—
593C22C3×Q8×AGL(1,𝔽5)12yes—
594C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
595C4—22no—
596C4—22no—
597C4—41no—
598C4—102no—
599C4—102no—
600C4—204no—
601C4—204no—
602C4—201no—
603C3#1060434411yescharacteristic, direct product factor, Sylow
604C2—51no—
605C2—52no—
606C2—51no—
607C2—52no—
608C2—51no—
609C2—51no—
610C2C3×#6571112yes—
611C2C3×#6571212yes—
612C2C3×#6576511yescharacteristic
613C2C3×#6577911yescharacteristic
614C2C3×(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1441
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10604344C3direct (N × H)
14. C2×C3×C5×C4⋊C4C4semidirect
15. C2×C3×C4⋊Dic5C4semidirect
16. C2×C3×#683C4semidirect
17. C2×C3×#683C4semidirect
81. C2×C5×C4⋊C4C3×C4semidirect
82. C2×C4⋊Dic5C3×C4semidirect
83. C2×#683C3×C4semidirect
84. C2×#683C3×C4semidirect
122. C2×C3×C4×C5C4⋊C4semidirect
129. C2×C3×Dic5C4⋊C4semidirect
152. C2×C3×C4⋊C4AGL(1,𝔽5)semidirect
303. C2×C4×C5C3×C4⋊C4semidirect
310. C2×Dic5C3×C4⋊C4semidirect
333. C2×C4⋊C4C3×AGL(1,𝔽5)semidirect
395. C2×C3×C4C4⋊AGL(1,𝔽5)semidirect
468. C3×C5#1441semidirect
558. C2×C4C3×C4⋊AGL(1,𝔽5)semidirect
571. C5C3×#1441semidirect
603. C3#10604344direct (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×D5×C4⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
#106043443
C3×#14415