Finite Group Databasebeta

← C3×#10604253 #14280010

Subgroups — C3×#10604253 #14280010

Order 1920.

1656 conjugacy classes of subgroups.

The subgroup lattice has 732 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#10604253C311yesmaximal, 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)C418yescomplemented
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×#1437—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—22no—
37C23×C3×D5—22no—
38C23×C3×D5—22no—
39C23×C3×D5C2×C411yescharacteristic
40C23×C3×D5C2×C414yes—
41C23×C3×D5C2311yescharacteristic
42C22×C3×AGL(1,𝔽5)—22no—
43C22×C3×AGL(1,𝔽5)—22no—
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)C2×C414yes—
53C22×C3×AGL(1,𝔽5)C2×C414yes—
54C22×C3×AGL(1,𝔽5)D414yes—
55C22×C3×AGL(1,𝔽5)D414yes—
56C22×C3×C4×C5C2×C411yescharacteristic
57C22×C3×C4×C5C2×C411yescharacteristic
58C22×C3×Dic5C2×C411yescharacteristic
59C22×C3×Dic5C2×C411yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5—21no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5D412yes—
68C3×C22⋊AGL(1,𝔽5)—216no—
69C3×C4×AGL(1,𝔽5)—28no—
70C3×C5×C22⋊C4—22no—
71C3×C22⋊Dic5—22no—
72C3×#685—22no—
73C3×#685—22no—
74C22×C3×C22⋊C4—52no—
75C22×C3×C22⋊C4—51no—
76C22×C3×C42—51no—
77C2×C3×#95—52no—
78C2×C3×#95—51no—
79C24×D5C22×C311yescharacteristic
80C23×AGL(1,𝔽5)C22×C312yes—
81C23×AGL(1,𝔽5)C22×C312yes—
82C22×C4×D5C22×C311yescharacteristic
83C22×C4×D5C22×C311yescharacteristic
84C2×C22⋊AGL(1,𝔽5)—24no—
85C2×C22⋊AGL(1,𝔽5)—24no—
86C2×C22⋊AGL(1,𝔽5)C3×C418yescomplemented
87C2×C4×AGL(1,𝔽5)—24no—
88C2×C4×AGL(1,𝔽5)—22no—
89C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
90C2×C22⋊Dic5C3×C411yescharacteristic, complemented
91C2×#685C3×C411yescharacteristic, complemented
92C2×#685C3×C411yescharacteristic, complemented
93D5×C22⋊C4—22no—
94D5×C22⋊C4—22no—
95(C2×AGL(1,𝔽5))⋊C4—24no—
96(C2×AGL(1,𝔽5))⋊C4—22no—
97#1437—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5C4212yescomplemented
103C23×C3×C5C22×C411yescharacteristic
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—24no—
109C22×C3×D5—24no—
110C22×C3×D5—24no—
111C22×C3×D5—24no—
112C22×C3×D5—24no—
113C22×C3×D5—24no—
114C22×C3×D5—41no—
115C22×C3×D5—42no—
116C22×C3×D5—42no—
117C22×C3×D5—42no—
118C22×C3×D5—41no—
119C22×C3×D5—42no—
120C22×C3×D5—42no—
121C22×C3×D5—41no—
122C22×C3×D5—42no—
123C22×C3×D5—41no—
124C22×C3×D5C4212yescomplemented
125C22×C3×D5C22×C412yes—
126C22×C3×D5C2×D412yes—
127C22×C3×D5C2×D412yes—
128C22×C3×D5C2×D411yescharacteristic
129C22×C3×D5C2×D411yescharacteristic
130C22×C3×D5#4112yes—
131C22×C3×D5#4112yes—
132C22×C3×D5#4112yes—
133C2×C3×AGL(1,𝔽5)—24no—
134C2×C3×AGL(1,𝔽5)—24no—
135C2×C3×AGL(1,𝔽5)—24no—
136C2×C3×AGL(1,𝔽5)—24no—
137C2×C3×AGL(1,𝔽5)—24no—
138C2×C3×AGL(1,𝔽5)—24no—
139C2×C3×AGL(1,𝔽5)—24no—
140C2×C3×AGL(1,𝔽5)—24no—
141C2×C3×AGL(1,𝔽5)—24no—
142C2×C3×AGL(1,𝔽5)—42no—
143C2×C3×AGL(1,𝔽5)—42no—
144C2×C3×AGL(1,𝔽5)—42no—
145C2×C3×AGL(1,𝔽5)—42no—
146C2×C3×AGL(1,𝔽5)C22⋊C418yescomplemented
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22⋊C412yescomplemented
151C2×C3×Dic5—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22⋊C412yescomplemented
155C3×C4×D5—22no—
156C3×C4×D5—24no—
157C3×C4×D5—22no—
158C3×C4×D5—42no—
159C3×C4×D5—41no—
160C3×C4×D5—41no—
161C25×C3—51no—
162C23×C3×C4—52no—
163C23×C3×C4—51no—
164C23×C3×C4—52no—
165C23×C3×C4—51no—
166C2×C3×C22⋊C4—58no—
167C2×C3×C22⋊C4—51no—
168C2×C3×C22⋊C4—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—102no—
171C2×C3×C22⋊C4—102no—
172C2×C3×C22⋊C4—104no—
173C2×C3×C22⋊C4—104no—
174C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
175C2×C3×C42—104no—
176C2×C3×C42—102no—
177C3×#95—104no—
178C3×#95—102no—
179C24×C5C2×C3×C411yescharacteristic
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—21no—
183C23×D5—21no—
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5C2×C3×C411yescharacteristic
188C23×D5C2×C3×C414yes—
189C23×D5C23×C311yescharacteristic
190C22×AGL(1,𝔽5)—22no—
191C22×AGL(1,𝔽5)—22no—
192C22×AGL(1,𝔽5)—22no—
193C22×AGL(1,𝔽5)—22no—
194C22×AGL(1,𝔽5)—22no—
195C22×AGL(1,𝔽5)—22no—
196C22×AGL(1,𝔽5)—22no—
197C22×AGL(1,𝔽5)—22no—
198C22×AGL(1,𝔽5)—22no—
199C22×AGL(1,𝔽5)—22no—
200C22×AGL(1,𝔽5)C2×C3×C414yes—
201C22×AGL(1,𝔽5)C2×C3×C414yes—
202C22×AGL(1,𝔽5)C3×D414yes—
203C22×AGL(1,𝔽5)C3×D414yes—
204C22×C4×C5C2×C3×C411yescharacteristic
205C22×C4×C5C2×C3×C411yescharacteristic
206C22×Dic5C2×C3×C411yescharacteristic
207C22×Dic5C2×C3×C411yescharacteristic
208C2×C4×D5—22no—
209C2×C4×D5—22no—
210C2×C4×D5—22no—
211C2×C4×D5—21no—
212C2×C4×D5—21no—
213C2×C4×D5—22no—
214C2×C4×D5C3×D412yes—
215C2×C4×D5C3×D412yes—
216C22⋊AGL(1,𝔽5)—216no—
217C4×AGL(1,𝔽5)—28no—
218C5×C22⋊C4—22no—
219C22⋊Dic5—22no—
220#685—22no—
221#685—22no—
222C22×C22⋊C4—52no—
223C22×C22⋊C4—51no—
224C22×C42—51no—
225C2×#95—52no—
226C2×#95—51no—
227C22×C3×C5—24no—
228C22×C3×C5—22no—
229C22×C3×C5—41no—
230C22×C3×C5—42no—
231C22×C3×C5—41no—
232C22×C3×C5C2×C4211yescharacteristic
233C22×C3×C5C2×C22⋊C411yescharacteristic
234C22×C3×C5#11711yescharacteristic
235C22×C3×C5C4×D412yes—
236C22×C3×C5C4×D412yes—
237C2×C3×D5—24no—
238C2×C3×D5—22no—
239C2×C3×D5—41no—
240C2×C3×D5—42no—
241C2×C3×D5—41no—
242C2×C3×D5—44no—
243C2×C3×D5—44no—
244C2×C3×D5—44no—
245C2×C3×D5—44no—
246C2×C3×D5C2×C22⋊C412yes—
247C2×C3×D5#11712yes—
248C2×C3×D5C4×D412yes—
249C2×C3×D5C4×D412yes—
250C2×C3×D5C4×D412yes—
251C2×C3×D5C4×D412yes—
252C2×C3×D5#12011yescharacteristic
253C2×C3×D5#12112yes—
254C2×C3×D5#12112yes—
255C2×C3×D5#12112yes—
256C2×C3×D5#12312yes—
257C2×C3×D5#12311yescharacteristic
258C2×C3×D5#12411yescharacteristic
259C2×C3×D5#12412yes—
260C2×C3×D5#12612yes—
261C2×C3×D5#12711yescharacteristic
262C3×AGL(1,𝔽5)—28no—
263C3×AGL(1,𝔽5)—44no—
264C3×C4×C5—22no—
265C3×C4×C5—41no—
266C3×Dic5—22no—
267C3×Dic5—41no—
268C24×C3—51no—
269C24×C3—54no—
270C24×C3—51no—
271C24×C3—102no—
272C24×C3—102no—
273C24×C3—101no—
274C24×C3—101no—
275C24×C3—102no—
276C24×C3—102no—
277C24×C3—102no—
278C24×C3C2×AGL(1,𝔽5)11yescharacteristic
279C22×C3×C4—54no—
280C22×C3×C4—54no—
281C22×C3×C4—54no—
282C22×C3×C4—51no—
283C22×C3×C4—52no—
284C22×C3×C4—52no—
285C22×C3×C4—54no—
286C22×C3×C4—51no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4—102no—
290C22×C3×C4—101no—
291C22×C3×C4—101no—
292C22×C3×C4—102no—
293C22×C3×C4—102no—
294C22×C3×C4—102no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4—102no—
298C22×C3×C4—102no—
299C22×C3×C4—102no—
300C22×C3×C4—102no—
301C22×C3×C4—102no—
302C22×C3×C4—102no—
303C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
304C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
305C3×C22⋊C4—22no—
306C3×C22⋊C4—102no—
307C3×C22⋊C4—102no—
308C3×C22⋊C4—1016no—
309C3×C22⋊C4—102no—
310C3×C42—108no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5C3×C4212yescomplemented
316C23×C5C22×C3×C411yescharacteristic
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—24no—
322C22×D5—24no—
323C22×D5—24no—
324C22×D5—24no—
325C22×D5—24no—
326C22×D5—24no—
327C22×D5—41no—
328C22×D5—42no—
329C22×D5—42no—
330C22×D5—42no—
331C22×D5—41no—
332C22×D5—42no—
333C22×D5—42no—
334C22×D5—41no—
335C22×D5—42no—
336C22×D5—41no—
337C22×D5C3×C4212yescomplemented
338C22×D5C22×C3×C412yes—
339C22×D5C2×C3×D412yes—
340C22×D5C2×C3×D412yes—
341C22×D5C2×C3×D411yescharacteristic
342C22×D5C2×C3×D411yescharacteristic
343C22×D5C3×#4112yes—
344C22×D5C3×#4112yes—
345C22×D5C3×#4112yes—
346C2×AGL(1,𝔽5)—24no—
347C2×AGL(1,𝔽5)—24no—
348C2×AGL(1,𝔽5)—24no—
349C2×AGL(1,𝔽5)—24no—
350C2×AGL(1,𝔽5)—24no—
351C2×AGL(1,𝔽5)—24no—
352C2×AGL(1,𝔽5)—24no—
353C2×AGL(1,𝔽5)—24no—
354C2×AGL(1,𝔽5)—24no—
355C2×AGL(1,𝔽5)—42no—
356C2×AGL(1,𝔽5)—42no—
357C2×AGL(1,𝔽5)—42no—
358C2×AGL(1,𝔽5)—42no—
359C2×AGL(1,𝔽5)C3×C22⋊C418yescomplemented
360C2×C4×C5—22no—
361C2×C4×C5—21no—
362C2×C4×C5—22no—
363C2×C4×C5C3×C22⋊C412yescomplemented
364C2×Dic5—22no—
365C2×Dic5—21no—
366C2×Dic5—22no—
367C2×Dic5C3×C22⋊C412yescomplemented
368C4×D5—22no—
369C4×D5—24no—
370C4×D5—22no—
371C4×D5—42no—
372C4×D5—41no—
373C4×D5—41no—
374C25—51no—
375C23×C4—52no—
376C23×C4—51no—
377C23×C4—52no—
378C23×C4—51no—
379C2×C22⋊C4—58no—
380C2×C22⋊C4—51no—
381C2×C22⋊C4—51no—
382C2×C22⋊C4—51no—
383C2×C22⋊C4—102no—
384C2×C22⋊C4—102no—
385C2×C22⋊C4—104no—
386C2×C22⋊C4—104no—
387C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
388C2×C42—104no—
389C2×C42—102no—
390#95—104no—
391#95—102no—
392C2×C3×C5—42no—
393C2×C3×C5C4×C22⋊C412yes—
394C2×C3×C5C4×C22⋊C411yescharacteristic
395C2×C3×C5#38611yescharacteristic
396C2×C3×C5#38812yes—
397C2×C3×C5#39011yescharacteristic
398C3×D5—42no—
399C3×D5#38612yes—
400C3×D5#38812yes—
401C3×D5#38812yes—
402C3×D5#39012yes—
403C23×C3—21no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—52no—
408C23×C3—52no—
409C23×C3—52no—
410C23×C3—52no—
411C23×C3—52no—
412C23×C3—52no—
413C23×C3—51no—
414C23×C3—51no—
415C23×C3—52no—
416C23×C3—104no—
417C23×C3—104no—
418C23×C3—104no—
419C23×C3—104no—
420C23×C3—104no—
421C23×C3—104no—
422C23×C3—101no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—101no—
426C23×C3—202no—
427C23×C3—202no—
428C23×C3—202no—
429C23×C3—202no—
430C23×C3—201no—
431C23×C3—202no—
432C23×C3—201no—
433C23×C3—202no—
434C23×C3—201no—
435C23×C3—201no—
436C23×C3C4×AGL(1,𝔽5)12yescomplemented
437C23×C3C22×AGL(1,𝔽5)11yescharacteristic
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—58no—
442C2×C3×C4—52no—
443C2×C3×C4—102no—
444C2×C3×C4—104no—
445C2×C3×C4—102no—
446C2×C3×C4—104no—
447C2×C3×C4—104no—
448C2×C3×C4—104no—
449C2×C3×C4—104no—
450C2×C3×C4—104no—
451C2×C3×C4—104no—
452C2×C3×C4—102no—
453C2×C3×C4—104no—
454C2×C3×C4—104no—
455C2×C3×C4—104no—
456C2×C3×C4—102no—
457C2×C3×C4—101no—
458C2×C3×C4—202no—
459C2×C3×C4—201no—
460C2×C3×C4—201no—
461C2×C3×C4—202no—
462C2×C3×C4—202no—
463C2×C3×C4—202no—
464C2×C3×C4—202no—
465C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
466C22×C5—24no—
467C22×C5—22no—
468C22×C5—41no—
469C22×C5—42no—
470C22×C5—41no—
471C22×C5C2×C3×C4211yescharacteristic
472C22×C5C2×C3×C22⋊C411yescharacteristic
473C22×C5C3×#11711yescharacteristic
474C22×C5C3×C4×D412yes—
475C22×C5C3×C4×D412yes—
476C2×D5—24no—
477C2×D5—22no—
478C2×D5—41no—
479C2×D5—42no—
480C2×D5—41no—
481C2×D5—44no—
482C2×D5—44no—
483C2×D5—44no—
484C2×D5—44no—
485C2×D5C2×C3×C22⋊C412yes—
486C2×D5C3×#11712yes—
487C2×D5C3×C4×D412yes—
488C2×D5C3×C4×D412yes—
489C2×D5C3×C4×D412yes—
490C2×D5C3×C4×D412yes—
491C2×D5C3×#12011yescharacteristic
492C2×D5C3×#12112yes—
493C2×D5C3×#12112yes—
494C2×D5C3×#12112yes—
495C2×D5C3×#12312yes—
496C2×D5C3×#12311yescharacteristic
497C2×D5C3×#12411yescharacteristic
498C2×D5C3×#12412yes—
499C2×D5C3×#12612yes—
500C2×D5C3×#12711yescharacteristic
501AGL(1,𝔽5)—28no—
502AGL(1,𝔽5)—44no—
503C4×C5—22no—
504C4×C5—41no—
505Dic5—22no—
506Dic5—41no—
507C24—51no—
508C24—54no—
509C24—51no—
510C24—102no—
511C24—102no—
512C24—101no—
513C24—101no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24C2×C3×AGL(1,𝔽5)11yescharacteristic
518C22×C4—54no—
519C22×C4—54no—
520C22×C4—54no—
521C22×C4—51no—
522C22×C4—52no—
523C22×C4—52no—
524C22×C4—54no—
525C22×C4—51no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—101no—
530C22×C4—101no—
531C22×C4—102no—
532C22×C4—102no—
533C22×C4—102no—
534C22×C4—102no—
535C22×C4—102no—
536C22×C4—102no—
537C22×C4—102no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4—102no—
541C22×C4—102no—
542C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
543C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
544C22⋊C4—22no—
545C22⋊C4—102no—
546C22⋊C4—102no—
547C22⋊C4—1016no—
548C22⋊C4—102no—
549C42—108no—
550C3×C5#143711yescharacteristic, complemented, Hall
551C22×C3—24no—
552C22×C3—22no—
553C22×C3—42no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—52no—
557C22×C3—52no—
558C22×C3—52no—
559C22×C3—52no—
560C22×C3—52no—
561C22×C3—52no—
562C22×C3—52no—
563C22×C3—52no—
564C22×C3—52no—
565C22×C3—52no—
566C22×C3—51no—
567C22×C3—52no—
568C22×C3—51no—
569C22×C3—52no—
570C22×C3—51no—
571C22×C3—51no—
572C22×C3—104no—
573C22×C3—102no—
574C22×C3—204no—
575C22×C3—204no—
576C22×C3—204no—
577C22×C3—204no—
578C22×C3—202no—
579C22×C3—201no—
580C22×C3—201no—
581C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
582C22×C3#413011yescharacteristic
583C22×C3D4×AGL(1,𝔽5)12yes—
584C22×C3D4×AGL(1,𝔽5)12yes—
585C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
586C3×C4—22no—
587C3×C4—41no—
588C3×C4—108no—
589C3×C4—102no—
590C3×C4—204no—
591C3×C4—201no—
592C2×C5—42no—
593C2×C5C3×C4×C22⋊C412yes—
594C2×C5C3×C4×C22⋊C411yescharacteristic
595C2×C5C3×#38611yescharacteristic
596C2×C5C3×#38812yes—
597C2×C5C3×#39011yescharacteristic
598D5—42no—
599D5C3×#38612yes—
600D5C3×#38812yes—
601D5C3×#38812yes—
602D5C3×#39012yes—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—52no—
608C23—52no—
609C23—52no—
610C23—52no—
611C23—52no—
612C23—52no—
613C23—51no—
614C23—51no—
615C23—52no—
616C23—104no—
617C23—104no—
618C23—104no—
619C23—104no—
620C23—104no—
621C23—104no—
622C23—101no—
623C23—102no—
624C23—102no—
625C23—101no—
626C23—202no—
627C23—202no—
628C23—202no—
629C23—202no—
630C23—201no—
631C23—202no—
632C23—201no—
633C23—202no—
634C23—201no—
635C23—201no—
636C23C3×C4×AGL(1,𝔽5)12yescomplemented
637C23C22×C3×AGL(1,𝔽5)11yescharacteristic
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—58no—
642C2×C4—52no—
643C2×C4—102no—
644C2×C4—104no—
645C2×C4—102no—
646C2×C4—104no—
647C2×C4—104no—
648C2×C4—104no—
649C2×C4—104no—
650C2×C4—104no—
651C2×C4—104no—
652C2×C4—102no—
653C2×C4—104no—
654C2×C4—104no—
655C2×C4—104no—
656C2×C4—102no—
657C2×C4—101no—
658C2×C4—202no—
659C2×C4—201no—
660C2×C4—201no—
661C2×C4—202no—
662C2×C4—202no—
663C2×C4—202no—
664C2×C4—202no—
665C2×C4C3×C22⋊AGL(1,𝔽5)12yescomplemented
666C2×C3—42no—
667C2×C3—52no—
668C2×C3—52no—
669C2×C3—52no—
670C2×C3—52no—
671C2×C3—202no—
672C2×C3C22⋊C4×AGL(1,𝔽5)12yes—
673C2×C3#6570012yes—
674C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
675C2×C3#6577911yescharacteristic
676C2×C3#6578011yescharacteristic
677C5C3×#143711yescharacteristic, complemented, Sylow
678C22—24no—
679C22—22no—
680C22—42no—
681C22—41no—
682C22—41no—
683C22—52no—
684C22—52no—
685C22—52no—
686C22—52no—
687C22—52no—
688C22—52no—
689C22—52no—
690C22—52no—
691C22—52no—
692C22—52no—
693C22—51no—
694C22—52no—
695C22—51no—
696C22—52no—
697C22—51no—
698C22—51no—
699C22—104no—
700C22—102no—
701C22—204no—
702C22—204no—
703C22—204no—
704C22—204no—
705C22—202no—
706C22—201no—
707C22—201no—
708C22C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
709C22C3×#413011yescharacteristic
710C22C3×D4×AGL(1,𝔽5)12yes—
711C22C3×D4×AGL(1,𝔽5)12yes—
712C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
713C4—22no—
714C4—41no—
715C4—108no—
716C4—102no—
717C4—204no—
718C4—201no—
719C3#1060425311yescharacteristic, direct product factor, Sylow
720C2—42no—
721C2—52no—
722C2—52no—
723C2—52no—
724C2—52no—
725C2—202no—
726C2C3×C22⋊C4×AGL(1,𝔽5)12yes—
727C2C3×#6570012yes—
728C2C3×C4×C22⋊AGL(1,𝔽5)11yescharacteristic
729C2C3×#6577911yescharacteristic
730C2C3×#6578011yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
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×#1437
LCSG ▷ C22×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. #10604253C3direct (N × H)
14. C2×C3×C22⋊AGL(1,𝔽5)C4semidirect
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
86. C2×C22⋊AGL(1,𝔽5)C3×C4semidirect
89. C2×C5×C22⋊C4C3×C4semidirect
90. C2×C22⋊Dic5C3×C4semidirect
91. C2×#685C3×C4semidirect
92. C2×#685C3×C4semidirect
102. C23×C3×C5C42semidirect
124. C22×C3×D5C42semidirect
146. C2×C3×AGL(1,𝔽5)C22⋊C4semidirect
150. C2×C3×C4×C5C22⋊C4semidirect
154. C2×C3×Dic5C22⋊C4semidirect
174. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
315. C23×C5C3×C42semidirect
337. C22×D5C3×C42semidirect
359. C2×AGL(1,𝔽5)C3×C22⋊C4semidirect
363. C2×C4×C5C3×C22⋊C4semidirect
367. C2×Dic5C3×C22⋊C4semidirect
387. C2×C22⋊C4C3×AGL(1,𝔽5)semidirect
436. C23×C3C4×AGL(1,𝔽5)semidirect
465. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
550. C3×C5#1437semidirect
636. C23C3×C4×AGL(1,𝔽5)semidirect
665. C2×C4C3×C22⋊AGL(1,𝔽5)semidirect
677. C5C3×#1437semidirect
719. C3#10604253direct (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
#106042533
C3×#14375