Finite Group Databasebeta

← C3×AGL(1,𝔽5)×#217 #72230127

Subgroups — C3×AGL(1,𝔽5)×#217 #72230127

Order 2880.

1268 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×C3×#6763C211yesmaximal, characteristic
3C2×C3×Dic3×AGL(1,𝔽5)C212yesmaximal, complemented
4C3×D5×#217C211yesmaximal, characteristic
5C3×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal, complemented
6C3×C22⋊C4×AGL(1,𝔽5)—31nomaximal
7AGL(1,𝔽5)×#217C311yesmaximal, characteristic, direct product factor
8C23×C32×D5C2211yescharacteristic
9C22×C3×ΓL(1,𝔽16)C2212yes—
10C22×C32×AGL(1,𝔽5)—24no—
11C22×C32×AGL(1,𝔽5)C414yescomplemented
12C22×C32×AGL(1,𝔽5)C2211yescharacteristic
13C22×C32×AGL(1,𝔽5)C2211yescharacteristic
14C2×C3×D5×Dic3C2212yes—
15C3×#6763C414yescomplemented
16C3×Dic3×AGL(1,𝔽5)—24no—
17C3×#6719C411yescharacteristic, complemented
18C3×C5×#217C411yescharacteristic, complemented
19C3×#6665C412yescomplemented
20C3×C4×#217—51nomaximal, Hall
21C23×C3×AGL(1,𝔽5)—21no—
22C23×C3×AGL(1,𝔽5)D311yescharacteristic
23C23×C3×AGL(1,𝔽5)C2×C311yescharacteristic
24C2×#6763C2×C311yescharacteristic
25C2×C3×C22⋊AGL(1,𝔽5)—31no—
26C2×C3×C4×AGL(1,𝔽5)—32no—
27C2×Dic3×AGL(1,𝔽5)C2×C312yescomplemented
28C3×D5×C22⋊C4—31no—
29D5×#217C2×C311yescharacteristic
30C3×(C2×AGL(1,𝔽5))⋊C4—32no—
31(C2×AGL(1,𝔽5))⋊Dic3C2×C312yescomplemented
32C23×C32×C5C2×C411yescharacteristic
33C22×C32×D5—22no—
34C22×C32×D5—22no—
35C22×C32×D5C2×C411yescharacteristic
36C22×C32×D5C2×C412yes—
37C22×C32×D5C2×C412yes—
38C22×C32×D5C2311yescharacteristic
39C2×C3×ΓL(1,𝔽16)—22no—
40C2×C3×ΓL(1,𝔽16)—22no—
41C2×C3×ΓL(1,𝔽16)C2×C414yescomplemented
42C2×C32×AGL(1,𝔽5)—22no—
43C2×C32×AGL(1,𝔽5)—28no—
44C2×C32×AGL(1,𝔽5)C2×C412yes—
45C2×C32×AGL(1,𝔽5)C2×C412yes—
46C2×C32×AGL(1,𝔽5)D414yes—
47C2×C3×Dic15C2×C412yescomplemented
48C2×C3×C5×Dic3C2×C412yescomplemented
49C3×D5×Dic3—22no—
50C3×D5×Dic3—22no—
51C22⋊C4×AGL(1,𝔽5)—31noHall
52C23×C32×C4—51no—
53C2×C3×#217—51no—
54C2×C3×#217—51no—
55C2×C3×C4×Dic3—52no—
56C3×C3⋊#95—52no—
57C23×C3×D5—21no—
58C23×C3×D5C2×D311yescharacteristic
59C23×C3×D5C22×C311yescharacteristic
60C22×ΓL(1,𝔽16)C22×C312yes—
61C22×C3×AGL(1,𝔽5)—24no—
62C22×C3×AGL(1,𝔽5)—24no—
63C22×C3×AGL(1,𝔽5)—21no—
64C22×C3×AGL(1,𝔽5)—24no—
65C22×C3×AGL(1,𝔽5)—24no—
66C22×C3×AGL(1,𝔽5)—24no—
67C22×C3×AGL(1,𝔽5)—21no—
68C22×C3×AGL(1,𝔽5)—32no—
69C22×C3×AGL(1,𝔽5)Dic314yescomplemented
70C22×C3×AGL(1,𝔽5)C3×C414yescomplemented
71C22×C3×AGL(1,𝔽5)C2×D311yescharacteristic
72C22×C3×AGL(1,𝔽5)C2×D311yescharacteristic
73C22×C3×AGL(1,𝔽5)C22×C311yescharacteristic
74C22×C3×AGL(1,𝔽5)C22×C311yescharacteristic
75C2×C3×C4×D5—32no—
76C2×D5×Dic3C22×C312yes—
77#6763C3×C414yescomplemented
78C3×C22⋊AGL(1,𝔽5)—34no—
79C3×C4×AGL(1,𝔽5)—64no—
80Dic3×AGL(1,𝔽5)—24no—
81C3×C5×C22⋊C4—31no—
82#6719C3×C411yescharacteristic, complemented
83C5×#217C3×C411yescharacteristic, complemented
84C3×C22⋊Dic5—31no—
85C3×#685—32no—
86#6665C3×C412yescomplemented
87C3×C4×C22⋊C4—151no—
88C4×#217—51no—
89C22×C32×C5—22no—
90C22×C32×C5C4212yescomplemented
91C22×C32×C5C22×C411yescharacteristic
92C2×C32×D5—22no—
93C2×C32×D5—22no—
94C2×C32×D5—22no—
95C2×C32×D5—24no—
96C2×C32×D5C4212yescomplemented
97C2×C32×D5C22×C411yescharacteristic
98C2×C32×D5C22×C411yescharacteristic
99C2×C32×D5C2×D412yes—
100C2×C32×D5#4112yes—
101C3×ΓL(1,𝔽16)—24no—
102C32×AGL(1,𝔽5)—22no—
103C32×AGL(1,𝔽5)C22⋊C414yescomplemented
104C3×Dic15—22no—
105C3×C5×Dic3—22no—
106C23×AGL(1,𝔽5)C3×D311yescharacteristic
107C2×C22⋊AGL(1,𝔽5)—31no—
108C2×C4×AGL(1,𝔽5)—32no—
109D5×C22⋊C4—31no—
110(C2×AGL(1,𝔽5))⋊C4—32no—
111C24×C32—51no—
112C22×C32×C4—51no—
113C22×C32×C4—54no—
114C22×C32×C4—51no—
115C22×C32×C4—104no—
116C22×C3×Dic3—52no—
117C22×C3×Dic3—52no—
118C3×#217—54no—
119C3×#217—51no—
120C3×#217—52no—
121C3×#217AGL(1,𝔽5)11yescharacteristic, direct product factor
122C3×C4×Dic3—104no—
123C23×C3×C5—21no—
124C23×C3×C5C4×D311yescharacteristic
125C23×C3×C5C2×C3×C411yescharacteristic
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5—21no—
131C22×C3×D5—22no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5—21no—
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5C4×D311yescharacteristic
139C22×C3×D5C4×D312yes—
140C22×C3×D5C2×Dic312yes—
141C22×C3×D5C2×C3×C411yescharacteristic
142C22×C3×D5C2×C3×C412yes—
143C22×C3×D5C2×C3×C412yes—
144C22×C3×D5C22×D311yescharacteristic
145C22×C3×D5C23×C311yescharacteristic
146C2×ΓL(1,𝔽16)—22no—
147C2×ΓL(1,𝔽16)—22no—
148C2×ΓL(1,𝔽16)C2×C3×C414yescomplemented
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—28no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—28no—
153C2×C3×AGL(1,𝔽5)—22no—
154C2×C3×AGL(1,𝔽5)—24no—
155C2×C3×AGL(1,𝔽5)—22no—
156C2×C3×AGL(1,𝔽5)—22no—
157C2×C3×AGL(1,𝔽5)—28no—
158C2×C3×AGL(1,𝔽5)—28no—
159C2×C3×AGL(1,𝔽5)—22no—
160C2×C3×AGL(1,𝔽5)—34no—
161C2×C3×AGL(1,𝔽5)—62no—
162C2×C3×AGL(1,𝔽5)—62no—
163C2×C3×AGL(1,𝔽5)C2×Dic312yes—
164C2×C3×AGL(1,𝔽5)C2×Dic312yes—
165C2×C3×AGL(1,𝔽5)#6714yes—
166C2×C3×AGL(1,𝔽5)C2×C3×C412yes—
167C2×C3×AGL(1,𝔽5)C2×C3×C412yes—
168C2×C3×AGL(1,𝔽5)C3×D414yes—
169C2×C3×C4×C5—32no—
170C2×Dic15C2×C3×C412yescomplemented
171C2×C5×Dic3C2×C3×C412yescomplemented
172C2×C3×Dic5—32no—
173C3×C4×D5—62no—
174C3×C4×D5—62no—
175D5×Dic3—22no—
176D5×Dic3—22no—
177C23×C3×C4—51no—
178C23×C3×C4—51no—
179C23×C3×C4—101no—
180C2×C3×C22⋊C4—151no—
181C2×C3×C22⋊C4—151no—
182C2×C3×C42—152no—
183C2×#217—51no—
184C2×#217—51no—
185C2×C4×Dic3—52no—
186C3×#95—152no—
187C3⋊#95—52no—
188C2×C32×C5—22no—
189C2×C32×C5C2×C4211yescharacteristic
190C2×C32×C5C4×D412yes—
191C32×D5—22no—
192C32×D5C2×C22⋊C411yescharacteristic
193C32×D5#11711yescharacteristic
194C32×D5C4×D412yes—
195C23×D5C2×C3×D311yescharacteristic
196C22×AGL(1,𝔽5)—24no—
197C22×AGL(1,𝔽5)—32no—
198C22×AGL(1,𝔽5)C3×Dic314yescomplemented
199C22×AGL(1,𝔽5)C2×C3×D311yescharacteristic
200C22×AGL(1,𝔽5)C2×C3×D311yescharacteristic
201C2×C4×D5—32no—
202C22⋊AGL(1,𝔽5)—34no—
203C4×AGL(1,𝔽5)—64no—
204C5×C22⋊C4—31no—
205C22⋊Dic5—31no—
206#685—32no—
207C23×C32—51no—
208C23×C32—52no—
209C23×C32—52no—
210C23×C32—51no—
211C23×C32—102no—
212C23×C32—102no—
213C23×C32C2×AGL(1,𝔽5)11yescharacteristic
214C2×C32×C4—52no—
215C2×C32×C4—54no—
216C2×C32×C4—52no—
217C2×C32×C4—108no—
218C2×C32×C4—102no—
219C2×C3×Dic3—54no—
220C2×C3×Dic3—52no—
221C2×C3×Dic3—102no—
222C2×C3×Dic3—102no—
223C2×C3×Dic3—102no—
224C2×C3×Dic3—102no—
225C2×C3×Dic3C2×AGL(1,𝔽5)12yescomplemented
226C4×C22⋊C4—151noSylow
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—21no—
233C22×C3×C5C4×Dic312yescomplemented
234C22×C3×C5C3×C4212yescomplemented
235C22×C3×C5C2×C4×D311yescharacteristic
236C22×C3×C5C22×C3×C411yescharacteristic
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—22no—
241C2×C3×D5—24no—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—24no—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5—24no—
249C2×C3×D5—22no—
250C2×C3×D5—22no—
251C2×C3×D5—22no—
252C2×C3×D5—24no—
253C2×C3×D5—22no—
254C2×C3×D5—21no—
255C2×C3×D5—22no—
256C2×C3×D5—21no—
257C2×C3×D5—22no—
258C2×C3×D5C4×Dic312yescomplemented
259C2×C3×D5C3×C4212yescomplemented
260C2×C3×D5C2×C4×D311yescharacteristic
261C2×C3×D5#23512yes—
262C2×C3×D5C22×Dic311yescharacteristic
263C2×C3×D5C2×#6712yes—
264C2×C3×D5C22×C3×C411yescharacteristic
265C2×C3×D5C22×C3×C411yescharacteristic
266C2×C3×D5C2×C3×D412yes—
267C2×C3×D5C3×#4112yes—
268ΓL(1,𝔽16)—24no—
269C3×AGL(1,𝔽5)—22no—
270C3×AGL(1,𝔽5)—22no—
271C3×AGL(1,𝔽5)—22no—
272C3×AGL(1,𝔽5)—22no—
273C3×AGL(1,𝔽5)—24no—
274C3×AGL(1,𝔽5)—64no—
275C3×AGL(1,𝔽5)#21714yesdirect product factor
276C3×AGL(1,𝔽5)C3×C22⋊C414yescomplemented
277C3×C4×C5—62no—
278Dic15—22no—
279C3×Dic5—62no—
280C5×Dic3—22no—
281C24×C3—51no—
282C24×C3—51no—
283C24×C3—101no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—54no—
289C22×C3×C4—54no—
290C22×C3×C4—101no—
291C22×C3×C4—101no—
292C22×C3×C4—104no—
293C22×C3×C4—104no—
294C22×C3×C4—104no—
295C22×C3×C4—104no—
296C22×C3×C4—104no—
297C22×C3×C4—152no—
298C22×C3×C4—152no—
299C22×Dic3—52no—
300C22×Dic3—52no—
301C3×C22⋊C4—31no—
302C3×C22⋊C4—152no—
303C3×C22⋊C4—154no—
304C3×C22⋊C4—151no—
305C3×C42—304no—
306#217—54no—
307#217—51no—
308#217—52no—
309#217C3×AGL(1,𝔽5)11yescharacteristic, direct product factor
310C4×Dic3—104no—
311C32×C5C4×C22⋊C411yescharacteristic, complemented, Hall
312C23×C5C3×C4×D311yescharacteristic
313C22×D5—22no—
314C22×D5—22no—
315C22×D5C3×C4×D311yescharacteristic
316C22×D5C3×C4×D312yes—
317C22×D5C2×C3×Dic312yes—
318C22×D5C22×C3×D311yescharacteristic
319C2×AGL(1,𝔽5)—22no—
320C2×AGL(1,𝔽5)—28no—
321C2×AGL(1,𝔽5)—34no—
322C2×AGL(1,𝔽5)—62no—
323C2×AGL(1,𝔽5)—62no—
324C2×AGL(1,𝔽5)C2×C3×Dic312yes—
325C2×AGL(1,𝔽5)C2×C3×Dic312yes—
326C2×AGL(1,𝔽5)C3×#6714yes—
327C2×C4×C5—32no—
328C2×Dic5—32no—
329C4×D5—62no—
330C4×D5—62no—
331C22×C32—22no—
332C22×C32—51no—
333C22×C32—51no—
334C22×C32—52no—
335C22×C32—52no—
336C22×C32—52no—
337C22×C32—102no—
338C22×C32—102no—
339C22×C32—104no—
340C22×C32—102no—
341C22×C32C4×AGL(1,𝔽5)12yescomplemented
342C22×C32C22×AGL(1,𝔽5)11yescharacteristic
343C32×C4—54no—
344C32×C4—102no—
345C3×Dic3—22no—
346C3×Dic3—104no—
347C3×Dic3—102no—
348C23×C4—51no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C42—152no—
352#95—152no—
353C2×C3×C5—22no—
354C2×C3×C5—22no—
355C2×C3×C5—22no—
356C2×C3×C5—22no—
357C2×C3×C5—21no—
358C2×C3×C5—22no—
359C2×C3×C5C2×C4×Dic311yescharacteristic
360C2×C3×C5C4×#6712yes—
361C2×C3×C5C2×C3×C4211yescharacteristic
362C2×C3×C5C3×C4×D412yes—
363C3×D5—22no—
364C3×D5—22no—
365C3×D5—22no—
366C3×D5—22no—
367C3×D5—21no—
368C3×D5—22no—
369C3×D5—21no—
370C3×D5#92611yescharacteristic
371C3×D5C4×#6712yes—
372C3×D5C2×#21711yescharacteristic
373C3×D5C2×C3×C22⋊C411yescharacteristic
374C3×D5C3×#11711yescharacteristic
375C3×D5C3×C4×D412yes—
376C23×C3—21no—
377C23×C3—51no—
378C23×C3—51no—
379C23×C3—52no—
380C23×C3—52no—
381C23×C3—52no—
382C23×C3—52no—
383C23×C3—51no—
384C23×C3—51no—
385C23×C3—102no—
386C23×C3—101no—
387C23×C3—102no—
388C23×C3—101no—
389C23×C3—102no—
390C23×C3—102no—
391C23×C3—102no—
392C23×C3—102no—
393C23×C3—102no—
394C23×C3—102no—
395C23×C3—102no—
396C23×C3—102no—
397C23×C3D3×AGL(1,𝔽5)11yescharacteristic
398C23×C3C2×C3×AGL(1,𝔽5)11yescharacteristic
399C2×C3×C4—32no—
400C2×C3×C4—52no—
401C2×C3×C4—54no—
402C2×C3×C4—52no—
403C2×C3×C4—54no—
404C2×C3×C4—52no—
405C2×C3×C4—52no—
406C2×C3×C4—104no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4—108no—
410C2×C3×C4—108no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—108no—
414C2×C3×C4—102no—
415C2×C3×C4—108no—
416C2×C3×C4—102no—
417C2×C3×C4—154no—
418C2×C3×C4—152no—
419C2×C3×C4—302no—
420C2×C3×C4—302no—
421C2×C3×C4—302no—
422C2×C3×C4—302no—
423C2×Dic3—54no—
424C2×Dic3—52no—
425C2×Dic3—102no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3C2×C3×AGL(1,𝔽5)12yescomplemented
430C22×C5—22no—
431C22×C5C3×C4×Dic312yescomplemented
432C22×C5C2×C3×C4×D311yescharacteristic
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—24no—
436C2×D5—22no—
437C2×D5C3×C4×Dic312yescomplemented
438C2×D5C2×C3×C4×D311yescharacteristic
439C2×D5C3×#23512yes—
440C2×D5C22×C3×Dic311yescharacteristic
441C2×D5C2×C3×#6712yes—
442AGL(1,𝔽5)—22no—
443AGL(1,𝔽5)—64no—
444AGL(1,𝔽5)C3×#21714yesdirect product factor
445C4×C5—62no—
446Dic5—62no—
447C2×C32—22no—
448C2×C32—51no—
449C2×C32—51no—
450C2×C32—52no—
451C2×C32—102no—
452C2×C32C2×C4×AGL(1,𝔽5)11yescharacteristic
453C2×C32D4×AGL(1,𝔽5)12yes—
454C24—51no—
455C22×C4—51no—
456C22×C4—51no—
457C22×C4—54no—
458C22×C4—104no—
459C22×C4—152no—
460C22×C4—152no—
461C22⋊C4—31no—
462C22⋊C4—152no—
463C22⋊C4—154no—
464C22⋊C4—151no—
465C42—304no—
466C3×C5—21no—
467C3×C5C4×#21711yescharacteristic, complemented
468C3×C5C3×C4×C22⋊C411yescharacteristic, complemented
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—51no—
476C22×C3—51no—
477C22×C3—52no—
478C22×C3—52no—
479C22×C3—51no—
480C22×C3—51no—
481C22×C3—52no—
482C22×C3—52no—
483C22×C3—52no—
484C22×C3—52no—
485C22×C3—102no—
486C22×C3—101no—
487C22×C3—102no—
488C22×C3—101no—
489C22×C3—102no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—104no—
493C22×C3—102no—
494C22×C3—104no—
495C22×C3—102no—
496C22×C3—102no—
497C22×C3—102no—
498C22×C3—102no—
499C22×C3—104no—
500C22×C3—102no—
501C22×C3—102no—
502C22×C3—104no—
503C22×C3—102no—
504C22×C3—102no—
505C22×C3—102no—
506C22×C3Dic3×AGL(1,𝔽5)12yescomplemented
507C22×C3C3×C4×AGL(1,𝔽5)12yescomplemented
508C22×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
509C22×C3C22×C3×AGL(1,𝔽5)11yescharacteristic
510C3×C4—54no—
511C3×C4—54no—
512C3×C4—62no—
513C3×C4—104no—
514C3×C4—102no—
515C3×C4—102no—
516C3×C4—102no—
517C3×C4—102no—
518C3×C4—304no—
519C3×C4—302no—
520Dic3—22no—
521Dic3—104no—
522Dic3—102no—
523C2×C5—22no—
524C2×C5C2×C3×C4×Dic311yescharacteristic
525C2×C5C3×C4×#6712yes—
526D5—22no—
527D5C3×#92611yescharacteristic
528D5C3×C4×#6712yes—
529D5C2×C3×#21711yescharacteristic
530C32C22⋊C4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
531C23—51no—
532C23—51no—
533C23—52no—
534C23—52no—
535C23—102no—
536C23—102no—
537C23C3×D3×AGL(1,𝔽5)11yescharacteristic
538C2×C4—32no—
539C2×C4—54no—
540C2×C4—52no—
541C2×C4—52no—
542C2×C4—108no—
543C2×C4—102no—
544C2×C4—154no—
545C2×C4—152no—
546C2×C4—302no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—22no—
553C2×C3—22no—
554C2×C3—21no—
555C2×C3—22no—
556C2×C3—52no—
557C2×C3—51no—
558C2×C3—51no—
559C2×C3—51no—
560C2×C3—52no—
561C2×C3—51no—
562C2×C3—101no—
563C2×C3—102no—
564C2×C3—101no—
565C2×C3—102no—
566C2×C3—102no—
567C2×C3—102no—
568C2×C3—102no—
569C2×C3C2×Dic3×AGL(1,𝔽5)11yescharacteristic
570C2×C3AGL(1,𝔽5)×#6712yes—
571C2×C3C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
572C2×C3C3×D4×AGL(1,𝔽5)12yes—
573C5C3×C4×#21711yescharacteristic, complemented, Sylow
574C22—22no—
575C22—51no—
576C22—51no—
577C22—52no—
578C22—52no—
579C22—52no—
580C22—102no—
581C22—104no—
582C22—102no—
583C22—102no—
584C22C3×Dic3×AGL(1,𝔽5)12yescomplemented
585C22C2×C3×D3×AGL(1,𝔽5)11yescharacteristic
586C4—54no—
587C4—62no—
588C4—102no—
589C4—304no—
590C4—302no—
591C3—21no—
592C3AGL(1,𝔽5)×#21711yescharacteristic, direct product factor
593C3C3×C22⋊C4×AGL(1,𝔽5)11yescharacteristic, complemented
594C2—22no—
595C2—51no—
596C2—52no—
597C2—51no—
598C2—102no—
599C2C2×C3×Dic3×AGL(1,𝔽5)11yescharacteristic
600C2C3×AGL(1,𝔽5)×#6712yes—
subgroupG/H
centerC22×C3C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C3×C42
FrattiniC22C2×C3×D3×AGL(1,𝔽5)
FittingC23×C32×C5C2×C4
socleC22×C32×C5C22×C4
prime radicalC23×C32×D5C22
cosocleC22×C3×D5C23×C3
hypercenterC23×C3D3×AGL(1,𝔽5)
hypocenterC3×C5C3×C4×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
3. C2×C3×Dic3×AGL(1,𝔽5)C2semidirect
5. C3×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
7. AGL(1,𝔽5)×#217C3direct (N × H)
11. C22×C32×AGL(1,𝔽5)C4semidirect
15. C3×#6763C4semidirect
17. C3×#6719C4semidirect
18. C3×C5×#217C4semidirect
19. C3×#6665C4semidirect
27. C2×Dic3×AGL(1,𝔽5)C2×C3semidirect
31. (C2×AGL(1,𝔽5))⋊Dic3C2×C3semidirect
41. C2×C3×ΓL(1,𝔽16)C2×C4semidirect
47. C2×C3×Dic15C2×C4semidirect
48. C2×C3×C5×Dic3C2×C4semidirect
69. C22×C3×AGL(1,𝔽5)Dic3semidirect
70. C22×C3×AGL(1,𝔽5)C3×C4semidirect
77. #6763C3×C4semidirect
82. #6719C3×C4semidirect
83. C5×#217C3×C4semidirect
86. #6665C3×C4semidirect
90. C22×C32×C5C42semidirect
96. C2×C32×D5C42semidirect
103. C32×AGL(1,𝔽5)C22⋊C4semidirect
121. C3×#217AGL(1,𝔽5)direct (N × H)
148. C2×ΓL(1,𝔽16)C2×C3×C4semidirect
170. C2×Dic15C2×C3×C4semidirect
171. C2×C5×Dic3C2×C3×C4semidirect
198. C22×AGL(1,𝔽5)C3×Dic3semidirect
225. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
233. C22×C3×C5C4×Dic3semidirect
234. C22×C3×C5C3×C42semidirect
258. C2×C3×D5C4×Dic3semidirect
259. C2×C3×D5C3×C42semidirect
275. C3×AGL(1,𝔽5)#217direct (N × H)
276. C3×AGL(1,𝔽5)C3×C22⋊C4semidirect
309. #217C3×AGL(1,𝔽5)direct (N × H)
311. C32×C5C4×C22⋊C4semidirect
341. C22×C32C4×AGL(1,𝔽5)semidirect
429. C2×Dic3C2×C3×AGL(1,𝔽5)semidirect
431. C22×C5C3×C4×Dic3semidirect
437. C2×D5C3×C4×Dic3semidirect
444. AGL(1,𝔽5)C3×#217direct (N × H)
467. C3×C5C4×#217semidirect
468. C3×C5C3×C4×C22⋊C4semidirect
506. C22×C3Dic3×AGL(1,𝔽5)semidirect
507. C22×C3C3×C4×AGL(1,𝔽5)semidirect
530. C32C22⋊C4×AGL(1,𝔽5)semidirect
573. C5C3×C4×#217semidirect
584. C22C3×Dic3×AGL(1,𝔽5)semidirect
592. C3AGL(1,𝔽5)×#217direct (N × H)
593. C3C3×C22⋊C4×AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C23×C32×AGL(1,𝔽5)2
C2×C3×#67632
C2×C3×Dic3×AGL(1,𝔽5)2
C3×D5×#2172
C3×(C2×AGL(1,𝔽5))⋊Dic32
C3×C22⋊C4×AGL(1,𝔽5)3
AGL(1,𝔽5)×#2173
C3×C4×#2175