Finite Group Databasebeta

← C3×AGL(1,𝔽5)×#99 #14295380

Subgroups — C3×AGL(1,𝔽5)×#99 #14295380

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic
2C3×D5⋊#99C211yesmaximal, characteristic
3C3×C22⋊C4×AGL(1,𝔽5)C212yesmaximal, complemented
4C3×D5×#99C211yesmaximal, characteristic
5C3×#64866C212yesmaximal, complemented
6AGL(1,𝔽5)×#99C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×AGL(1,𝔽5)C411yescharacteristic, complemented
8C23×C3×AGL(1,𝔽5)C2211yescharacteristic
9C2×C3×D4×D5C2211yescharacteristic
10C2×C3×C22⋊AGL(1,𝔽5)C411yescharacteristic, complemented
11C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
12C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
13C3×D4×AGL(1,𝔽5)—22no—
14C3×D4×AGL(1,𝔽5)—22no—
15C2×C3×C4⋊AGL(1,𝔽5)C411yescharacteristic, complemented
16C2×C3×C4×AGL(1,𝔽5)—22no—
17C2×C3×C4×AGL(1,𝔽5)C411yescharacteristic, complemented
18C3×D5×C22⋊C4C2212yes—
19C3×#4011C412yescomplemented
20C3×(C2×AGL(1,𝔽5))⋊C4—22no—
21C3×#3999C412yescomplemented
22C3×C5×#99C411yescharacteristic, complemented
23C3×#3966C411yescharacteristic, complemented
24C3×#3938C412yescomplemented
25C3×C4×#99—51nomaximal, Hall
26C2×D4×AGL(1,𝔽5)C2×C311yescharacteristic
27D5⋊#99C2×C311yescharacteristic
28C22⋊C4×AGL(1,𝔽5)C2×C312yescomplemented
29D5×#99C2×C311yescharacteristic
30#64866C2×C312yescomplemented
31C23×C3×D5C2×C411yescharacteristic
32C23×C3×D5C2311yescharacteristic
33C22×C3×AGL(1,𝔽5)—22no—
34C22×C3×AGL(1,𝔽5)—21no—
35C22×C3×AGL(1,𝔽5)—21no—
36C22×C3×AGL(1,𝔽5)—42no—
37C22×C3×AGL(1,𝔽5)—42no—
38C22×C3×AGL(1,𝔽5)C2×C411yescharacteristic
39C22×C3×AGL(1,𝔽5)C2×C411yescharacteristic
40C22×C3×AGL(1,𝔽5)C2×C411yescharacteristic
41C22×C3×AGL(1,𝔽5)C2×C411yescharacteristic
42C22×C3×AGL(1,𝔽5)D412yes—
43C22×C3×AGL(1,𝔽5)D412yes—
44C2×C3×C5×D4C2×C411yescharacteristic
45C2×C3×C22⋊D5C2×C411yescharacteristic
46C2×C3×C22⋊D5C2×C411yescharacteristic
47C3×D4×D5—22no—
48C3×D4×D5—22no—
49C2×C3×D20C2×C411yescharacteristic
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5C2×C411yescharacteristic
52C3×C22⋊AGL(1,𝔽5)—22no—
53C3×C22⋊AGL(1,𝔽5)—22no—
54C3×C22⋊AGL(1,𝔽5)—22no—
55C3×C22⋊AGL(1,𝔽5)C2×C414yescomplemented
56C3×C4⋊AGL(1,𝔽5)—22no—
57C3×C4×AGL(1,𝔽5)—21no—
58C3×C4×AGL(1,𝔽5)—21no—
59C3×C4×AGL(1,𝔽5)—44no—
60C3×C5×C22⋊C4C2×C412yescomplemented
61C3×C22⋊Dic5C2×C412yescomplemented
62C3×#685—22no—
63C2×C3×C4×D4—51no—
64C2×C3×#99—51no—
65C2×C3×#99—51no—
66C3×C4×C22⋊C4—52no—
67C3×#342—52no—
68C23×AGL(1,𝔽5)C3×C411yescharacteristic, complemented
69C23×AGL(1,𝔽5)C22×C311yescharacteristic
70C2×D4×D5C22×C311yescharacteristic
71C2×C22⋊AGL(1,𝔽5)C3×C411yescharacteristic, complemented
72C2×C22⋊AGL(1,𝔽5)C22×C311yescharacteristic
73C2×C22⋊AGL(1,𝔽5)C22×C312yes—
74D4×AGL(1,𝔽5)—22no—
75D4×AGL(1,𝔽5)—22no—
76C2×C4⋊AGL(1,𝔽5)C3×C411yescharacteristic, complemented
77C2×C4×AGL(1,𝔽5)—22no—
78C2×C4×AGL(1,𝔽5)C3×C411yescharacteristic, complemented
79D5×C22⋊C4C22×C312yes—
80#4011C3×C412yescomplemented
81(C2×AGL(1,𝔽5))⋊C4—22no—
82#3999C3×C412yescomplemented
83C5×#99C3×C411yescharacteristic, complemented
84#3966C3×C411yescharacteristic, complemented
85#3938C3×C412yescomplemented
86C4×#99—51noSylow
87C23×C3×C5C4211yescharacteristic, complemented
88C23×C3×C5C22×C411yescharacteristic
89C22×C3×D5—21no—
90C22×C3×D5—21no—
91C22×C3×D5—41no—
92C22×C3×D5—41no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C22×C3×D5C4211yescharacteristic, complemented
96C22×C3×D5C22×C411yescharacteristic
97C22×C3×D5C22×C411yescharacteristic
98C22×C3×D5C2×D412yes—
99C22×C3×D5#4112yes—
100C2×C3×AGL(1,𝔽5)—24no—
101C2×C3×AGL(1,𝔽5)—22no—
102C2×C3×AGL(1,𝔽5)—21no—
103C2×C3×AGL(1,𝔽5)—21no—
104C2×C3×AGL(1,𝔽5)—24no—
105C2×C3×AGL(1,𝔽5)—41no—
106C2×C3×AGL(1,𝔽5)—42no—
107C2×C3×AGL(1,𝔽5)—42no—
108C2×C3×AGL(1,𝔽5)—42no—
109C2×C3×AGL(1,𝔽5)—42no—
110C2×C3×AGL(1,𝔽5)—42no—
111C2×C3×AGL(1,𝔽5)—41no—
112C2×C3×AGL(1,𝔽5)—41no—
113C2×C3×AGL(1,𝔽5)C22⋊C411yescharacteristic
114C2×C3×AGL(1,𝔽5)C22⋊C412yes—
115C2×C3×AGL(1,𝔽5)C22⋊C411yescharacteristic
116C3×C5×D4—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5C4211yescharacteristic, complemented
119C3×C22⋊D5—22no—
120C3×C22⋊D5—22no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5C4211yescharacteristic, complemented
123C3×D20—22no—
124C3×C4×D5—21no—
125C3×C4×D5—21no—
126C3×C4×D5—42no—
127C3×C4×D5—42no—
128C22×C3×D4—51no—
129C23×C3×C4—51no—
130C23×C3×C4—51no—
131C3×C4×D4—102no—
132C3×C4×D4—102no—
133C2×C3×C4⋊C4—51no—
134C2×C3×C22⋊C4—52no—
135C2×C3×C22⋊C4—52no—
136C2×C3×C22⋊C4—51no—
137C2×C3×C22⋊C4—51no—
138C2×C3×C42—51no—
139C2×C3×C42—102no—
140C3×#99—52no—
141C3×#99—52no—
142C3×#99—51no—
143C3×#99—52no—
144C3×#99AGL(1,𝔽5)11yescharacteristic, direct product factor
145C3×#95—102no—
146C23×D5C2×C3×C411yescharacteristic
147C23×D5C23×C311yescharacteristic
148C22×AGL(1,𝔽5)—22no—
149C22×AGL(1,𝔽5)—21no—
150C22×AGL(1,𝔽5)—21no—
151C22×AGL(1,𝔽5)—42no—
152C22×AGL(1,𝔽5)—42no—
153C22×AGL(1,𝔽5)C2×C3×C411yescharacteristic
154C22×AGL(1,𝔽5)C2×C3×C411yescharacteristic
155C22×AGL(1,𝔽5)C2×C3×C411yescharacteristic
156C22×AGL(1,𝔽5)C2×C3×C411yescharacteristic
157C22×AGL(1,𝔽5)C3×D412yes—
158C22×AGL(1,𝔽5)C3×D412yes—
159C2×C5×D4C2×C3×C411yescharacteristic
160C2×C22⋊D5C2×C3×C411yescharacteristic
161C2×C22⋊D5C2×C3×C411yescharacteristic
162D4×D5—22no—
163D4×D5—22no—
164C2×D20C2×C3×C411yescharacteristic
165C2×C4×D5—22no—
166C2×C4×D5C2×C3×C411yescharacteristic
167C22⋊AGL(1,𝔽5)—22no—
168C22⋊AGL(1,𝔽5)—22no—
169C22⋊AGL(1,𝔽5)—22no—
170C22⋊AGL(1,𝔽5)C2×C3×C414yescomplemented
171C4⋊AGL(1,𝔽5)—22no—
172C4×AGL(1,𝔽5)—21no—
173C4×AGL(1,𝔽5)—21no—
174C4×AGL(1,𝔽5)—44no—
175C5×C22⋊C4C2×C3×C412yescomplemented
176C22⋊Dic5C2×C3×C412yescomplemented
177#685—22no—
178C2×C4×D4—51no—
179C2×#99—51no—
180C2×#99—51no—
181C4×C22⋊C4—52no—
182#342—52no—
183C22×C3×C5—21no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C4211yescharacteristic
187C22×C3×C5C4×D412yes—
188C2×C3×D5—22no—
189C2×C3×D5—21no—
190C2×C3×D5—22no—
191C2×C3×D5—21no—
192C2×C3×D5—21no—
193C2×C3×D5—41no—
194C2×C3×D5—42no—
195C2×C3×D5—42no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C2×C3×D5—41no—
199C2×C3×D5C2×C22⋊C411yescharacteristic
200C2×C3×D5#11711yescharacteristic
201C2×C3×D5C4×D412yes—
202C3×AGL(1,𝔽5)—21no—
203C3×AGL(1,𝔽5)—22no—
204C3×AGL(1,𝔽5)—44no—
205C3×AGL(1,𝔽5)—41no—
206C3×AGL(1,𝔽5)—41no—
207C3×AGL(1,𝔽5)#9912yesdirect product factor
208C3×C4×C5—21no—
209C3×C4×C5—42no—
210C3×Dic5—21no—
211C3×Dic5—42no—
212C24×C3—51no—
213C24×C3—51no—
214C2×C3×D4—51no—
215C2×C3×D4—51no—
216C2×C3×D4—51no—
217C2×C3×D4—102no—
218C2×C3×D4—102no—
219C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
220C22×C3×C4—51no—
221C22×C3×C4—52no—
222C22×C3×C4—52no—
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—102no—
228C22×C3×C4—101no—
229C22×C3×C4—101no—
230C22×C3×C4—102no—
231C22×C3×C4—202no—
232C22×C3×C4—202no—
233C3×C4⋊C4—102no—
234C3×C22⋊C4—54no—
235C3×C22⋊C4—52no—
236C3×C22⋊C4—102no—
237C3×C22⋊C4—102no—
238C3×C22⋊C4—102no—
239C3×C22⋊C4—102no—
240C3×C22⋊C4C2×AGL(1,𝔽5)12yescomplemented
241C3×C42—101no—
242C3×C42—101no—
243C3×C42—204no—
244C23×C5C3×C4211yescharacteristic, complemented
245C23×C5C22×C3×C411yescharacteristic
246C22×D5—21no—
247C22×D5—21no—
248C22×D5—41no—
249C22×D5—41no—
250C22×D5—41no—
251C22×D5—41no—
252C22×D5C3×C4211yescharacteristic, complemented
253C22×D5C22×C3×C411yescharacteristic
254C22×D5C22×C3×C411yescharacteristic
255C22×D5C2×C3×D412yes—
256C22×D5C3×#4112yes—
257C2×AGL(1,𝔽5)—24no—
258C2×AGL(1,𝔽5)—22no—
259C2×AGL(1,𝔽5)—21no—
260C2×AGL(1,𝔽5)—21no—
261C2×AGL(1,𝔽5)—24no—
262C2×AGL(1,𝔽5)—41no—
263C2×AGL(1,𝔽5)—42no—
264C2×AGL(1,𝔽5)—42no—
265C2×AGL(1,𝔽5)—42no—
266C2×AGL(1,𝔽5)—42no—
267C2×AGL(1,𝔽5)—42no—
268C2×AGL(1,𝔽5)—41no—
269C2×AGL(1,𝔽5)—41no—
270C2×AGL(1,𝔽5)C3×C22⋊C411yescharacteristic
271C2×AGL(1,𝔽5)C3×C22⋊C412yes—
272C2×AGL(1,𝔽5)C3×C22⋊C411yescharacteristic
273C5×D4—22no—
274C2×C4×C5—22no—
275C2×C4×C5C3×C4211yescharacteristic, complemented
276C22⋊D5—22no—
277C22⋊D5—22no—
278C2×Dic5—22no—
279C2×Dic5C3×C4211yescharacteristic, complemented
280D20—22no—
281C4×D5—21no—
282C4×D5—21no—
283C4×D5—42no—
284C4×D5—42no—
285C22×D4—51no—
286C23×C4—51no—
287C23×C4—51no—
288C4×D4—102no—
289C4×D4—102no—
290C2×C4⋊C4—51no—
291C2×C22⋊C4—52no—
292C2×C22⋊C4—52no—
293C2×C22⋊C4—51no—
294C2×C22⋊C4—51no—
295C2×C42—51no—
296C2×C42—102no—
297#99—52no—
298#99—52no—
299#99—51no—
300#99—52no—
301#99C3×AGL(1,𝔽5)11yescharacteristic, direct product factor
302#95—102no—
303C2×C3×C5—22no—
304C2×C3×C5—21no—
305C2×C3×C5—41no—
306C2×C3×C5C4×C22⋊C411yescharacteristic
307C3×D5—22no—
308C3×D5—21no—
309C3×D5—41no—
310C3×D5C2×#9911yescharacteristic
311C3×D5#41011yescharacteristic
312C23×C3—51no—
313C23×C3—52no—
314C23×C3—51no—
315C23×C3—52no—
316C23×C3—51no—
317C23×C3—101no—
318C23×C3—101no—
319C23×C3—201no—
320C23×C3—201no—
321C23×C3—201no—
322C23×C3—201no—
323C23×C3C4×AGL(1,𝔽5)11yescharacteristic, complemented
324C23×C3C22×AGL(1,𝔽5)11yescharacteristic
325C3×D4—22no—
326C3×D4—102no—
327C3×D4—102no—
328C3×D4—102no—
329C2×C3×C4—22no—
330C2×C3×C4—51no—
331C2×C3×C4—51no—
332C2×C3×C4—52no—
333C2×C3×C4—51no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—104no—
337C2×C3×C4—102no—
338C2×C3×C4—101no—
339C2×C3×C4—104no—
340C2×C3×C4—101no—
341C2×C3×C4—102no—
342C2×C3×C4—202no—
343C2×C3×C4—202no—
344C2×C3×C4—202no—
345C2×C3×C4—201no—
346C2×C3×C4—202no—
347C2×C3×C4—202no—
348C2×C3×C4—202no—
349C2×C3×C4—202no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic, complemented
353C22×C5—21no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5C2×C3×C4211yescharacteristic
357C22×C5C3×C4×D412yes—
358C2×D5—22no—
359C2×D5—21no—
360C2×D5—22no—
361C2×D5—21no—
362C2×D5—21no—
363C2×D5—41no—
364C2×D5—42no—
365C2×D5—42no—
366C2×D5—41no—
367C2×D5—41no—
368C2×D5—41no—
369C2×D5C2×C3×C22⋊C411yescharacteristic
370C2×D5C3×#11711yescharacteristic
371C2×D5C3×C4×D412yes—
372AGL(1,𝔽5)—21no—
373AGL(1,𝔽5)—22no—
374AGL(1,𝔽5)—44no—
375AGL(1,𝔽5)—41no—
376AGL(1,𝔽5)—41no—
377AGL(1,𝔽5)C3×#9912yesdirect product factor
378C4×C5—21no—
379C4×C5—42no—
380Dic5—21no—
381Dic5—42no—
382C24—51no—
383C24—51no—
384C2×D4—51no—
385C2×D4—51no—
386C2×D4—51no—
387C2×D4—102no—
388C2×D4—102no—
389C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
390C22×C4—51no—
391C22×C4—52no—
392C22×C4—52no—
393C22×C4—51no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—102no—
398C22×C4—101no—
399C22×C4—101no—
400C22×C4—102no—
401C22×C4—202no—
402C22×C4—202no—
403C4⋊C4—102no—
404C22⋊C4—54no—
405C22⋊C4—52no—
406C22⋊C4—102no—
407C22⋊C4—102no—
408C22⋊C4—102no—
409C22⋊C4—102no—
410C22⋊C4C2×C3×AGL(1,𝔽5)12yescomplemented
411C42—101no—
412C42—101no—
413C42—204no—
414C3×C5C4×#9911yescharacteristic, complemented, Hall
415C22×C3—21no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—51no—
419C22×C3—51no—
420C22×C3—52no—
421C22×C3—102no—
422C22×C3—101no—
423C22×C3—102no—
424C22×C3—101no—
425C22×C3—101no—
426C22×C3—202no—
427C22×C3—201no—
428C22×C3—201no—
429C22×C3—201no—
430C22×C3—201no—
431C22×C3—202no—
432C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
433C22×C3D4×AGL(1,𝔽5)12yes—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—52no—
437C3×C4—102no—
438C3×C4—101no—
439C3×C4—101no—
440C3×C4—202no—
441C3×C4—201no—
442C3×C4—201no—
443C3×C4—204no—
444C2×C5—22no—
445C2×C5—21no—
446C2×C5—41no—
447C2×C5C3×C4×C22⋊C411yescharacteristic
448D5—22no—
449D5—21no—
450D5—41no—
451D5C2×C3×#9911yescharacteristic
452D5C3×#41011yescharacteristic
453C23—51no—
454C23—52no—
455C23—51no—
456C23—52no—
457C23—51no—
458C23—101no—
459C23—101no—
460C23—201no—
461C23—201no—
462C23—201no—
463C23—201no—
464C23C3×C4×AGL(1,𝔽5)11yescharacteristic, complemented
465C23C22×C3×AGL(1,𝔽5)11yescharacteristic
466D4—22no—
467D4—102no—
468D4—102no—
469D4—102no—
470C2×C4—22no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—52no—
474C2×C4—51no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—104no—
478C2×C4—102no—
479C2×C4—101no—
480C2×C4—104no—
481C2×C4—101no—
482C2×C4—102no—
483C2×C4—202no—
484C2×C4—202no—
485C2×C4—202no—
486C2×C4—202no—
487C2×C4—201no—
488C2×C4—202no—
489C2×C4—202no—
490C2×C4—202no—
491C2×C4—201no—
492C2×C4—201no—
493C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic, complemented
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—41no—
497C2×C3—51no—
498C2×C3—51no—
499C2×C3—102no—
500C2×C3—101no—
501C2×C3—201no—
502C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
503C5C3×C4×#9911yescharacteristic, complemented, Sylow
504C22—21no—
505C22—41no—
506C22—41no—
507C22—51no—
508C22—52no—
509C22—51no—
510C22—102no—
511C22—101no—
512C22—102no—
513C22—101no—
514C22—101no—
515C22—202no—
516C22—201no—
517C22—201no—
518C22—201no—
519C22—201no—
520C22—202no—
521C22C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
522C22C3×D4×AGL(1,𝔽5)12yes—
523C4—21no—
524C4—42no—
525C4—52no—
526C4—101no—
527C4—102no—
528C4—101no—
529C4—202no—
530C4—201no—
531C4—201no—
532C4—204no—
533C3AGL(1,𝔽5)×#9911yescharacteristic, direct product factor, Sylow
534C2—22no—
535C2—21no—
536C2—41no—
537C2—51no—
538C2—51no—
539C2—102no—
540C2—101no—
541C2—201no—
542C2C3×C22⋊C4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#99C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C3×D4×D5C22
cosocleC23×D5C23×C3
hypercenterC3×#99AGL(1,𝔽5)
hypocenterC5C3×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

Complements

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

NH ≅ G/Ntype
3. C3×C22⋊C4×AGL(1,𝔽5)C2semidirect
5. C3×#64866C2semidirect
6. AGL(1,𝔽5)×#99C3direct (N × H)
7. C23×C3×AGL(1,𝔽5)C4semidirect
10. C2×C3×C22⋊AGL(1,𝔽5)C4semidirect
15. C2×C3×C4⋊AGL(1,𝔽5)C4semidirect
17. C2×C3×C4×AGL(1,𝔽5)C4semidirect
19. C3×#4011C4semidirect
21. C3×#3999C4semidirect
22. C3×C5×#99C4semidirect
23. C3×#3966C4semidirect
24. C3×#3938C4semidirect
28. C22⋊C4×AGL(1,𝔽5)C2×C3semidirect
30. #64866C2×C3semidirect
55. C3×C22⋊AGL(1,𝔽5)C2×C4semidirect
60. C3×C5×C22⋊C4C2×C4semidirect
61. C3×C22⋊Dic5C2×C4semidirect
68. C23×AGL(1,𝔽5)C3×C4semidirect
71. C2×C22⋊AGL(1,𝔽5)C3×C4semidirect
76. C2×C4⋊AGL(1,𝔽5)C3×C4semidirect
78. C2×C4×AGL(1,𝔽5)C3×C4semidirect
80. #4011C3×C4semidirect
82. #3999C3×C4semidirect
83. C5×#99C3×C4semidirect
84. #3966C3×C4semidirect
85. #3938C3×C4semidirect
87. C23×C3×C5C42semidirect
95. C22×C3×D5C42semidirect
118. C2×C3×C4×C5C42semidirect
122. C2×C3×Dic5C42semidirect
144. C3×#99AGL(1,𝔽5)direct (N × H)
170. C22⋊AGL(1,𝔽5)C2×C3×C4semidirect
175. C5×C22⋊C4C2×C3×C4semidirect
176. C22⋊Dic5C2×C3×C4semidirect
207. C3×AGL(1,𝔽5)#99direct (N × H)
240. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
244. C23×C5C3×C42semidirect
252. C22×D5C3×C42semidirect
275. C2×C4×C5C3×C42semidirect
279. C2×Dic5C3×C42semidirect
301. #99C3×AGL(1,𝔽5)direct (N × H)
323. C23×C3C4×AGL(1,𝔽5)semidirect
352. C2×C3×C4C4×AGL(1,𝔽5)semidirect
377. AGL(1,𝔽5)C3×#99direct (N × H)
410. C22⋊C4C2×C3×AGL(1,𝔽5)semidirect
414. C3×C5C4×#99semidirect
464. C23C3×C4×AGL(1,𝔽5)semidirect
493. C2×C4C3×C4×AGL(1,𝔽5)semidirect
503. C5C3×C4×#99semidirect
533. C3AGL(1,𝔽5)×#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×AGL(1,𝔽5)2
C3×D5⋊#992
C3×C22⋊C4×AGL(1,𝔽5)2
C3×D5×#992
C3×#648662
AGL(1,𝔽5)×#993
C3×C4×#995