Finite Group Databasebeta

← C2×Dic3×C4⋊AGL(1,𝔽5) #14319474

Subgroups — C2×Dic3×C4⋊AGL(1,𝔽5) #14319474

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic
2C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C22×Dic3×AGL(1,𝔽5)C212yesmaximal
4C2×C4×D5×Dic3C211yesmaximal, characteristic
5C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal
6Dic3×C4⋊AGL(1,𝔽5)C218yesmaximal, direct product factor
7C2×C4×C4⋊AGL(1,𝔽5)—31nomaximal, Hall
8C23×ΓL(1,𝔽16)C2212yes—
9C23×C3×AGL(1,𝔽5)C2212yes—
10C22×C3×C4×D5C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C22×D5×Dic3C2211yescharacteristic
13C2×C4⋊ΓL(1,𝔽16)C418yescomplemented
14C2×C4⋊ΓL(1,𝔽16)C2214yes—
15C2×C3×C4⋊AGL(1,𝔽5)C418yescomplemented
16C2×C3×C4⋊AGL(1,𝔽5)C2214yes—
17C2×Dic3×AGL(1,𝔽5)—28no—
18C2×Dic3×AGL(1,𝔽5)C2218yes—
19C2×C4×Dic15C411yescharacteristic, complemented
20C2×C4×C5×Dic3C411yescharacteristic, complemented
21C2×Dic3×Dic5C411yescharacteristic, complemented
22C2×Dic3×Dic5C411yescharacteristic, complemented
23C4×D5×Dic3C414yescomplemented
24C4×D5×Dic3C2214yes—
25(C2×AGL(1,𝔽5))⋊Dic3C2218yes—
26C2×Dic3×C4⋊C4—51nomaximal, Hall
27C22×C4⋊AGL(1,𝔽5)—31no—
28C22×C4⋊AGL(1,𝔽5)D311yescharacteristic
29C22×C4×AGL(1,𝔽5)—32no—
30C2×C42×D5—31no—
31C2×(C2×AGL(1,𝔽5))⋊C4—32no—
32C4×C4⋊AGL(1,𝔽5)—38no—
33C23×C3×D5C2311yescharacteristic
34C22×ΓL(1,𝔽16)—24no—
35C22×ΓL(1,𝔽16)—24no—
36C22×ΓL(1,𝔽16)C2×C418yes—
37C22×ΓL(1,𝔽16)C2314yes—
38C22×C3×AGL(1,𝔽5)—24no—
39C22×C3×AGL(1,𝔽5)—24no—
40C22×C3×AGL(1,𝔽5)C2×C418yes—
41C22×C3×AGL(1,𝔽5)C2314yes—
42C22×C3×C4×C5C2×C411yescharacteristic
43C22×Dic15C2×C411yescharacteristic
44C22×Dic15C2×C411yescharacteristic
45C22×C5×Dic3C2×C411yescharacteristic
46C22×C5×Dic3C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C412yes—
49C2×C3×C4×D5C2×C414yes—
50C2×C3×C4×D5C2×C414yes—
51C2×C3×C4×D5C2312yes—
52C2×D5×Dic3—22no—
53C2×D5×Dic3—22no—
54C2×D5×Dic3C2×C412yes—
55C2×D5×Dic3C2×C412yes—
56C2×D5×Dic3D414yes—
57C2×D5×Dic3Q814yes—
58C2×D5×Dic3C2312yes—
59C2×D5×Dic3C2312yes—
60C4⋊ΓL(1,𝔽16)C2×C4116yescomplemented
61C3×C4⋊AGL(1,𝔽5)C2×C4116yescomplemented
62Dic3×AGL(1,𝔽5)—216no—
63C4×Dic15C2×C414yescomplemented
64C4×C5×Dic3C2×C414yescomplemented
65Dic3×Dic5C2×C414yescomplemented
66Dic3×Dic5C2×C414yescomplemented
67C22×C3×C4⋊C4—51no—
68C22×C4⋊Dic3—51no—
69C22×C4×Dic3—51no—
70C22×C4×Dic3—52no—
71C2×C3⋊#95—52no—
72Dic3×C4⋊C4—58no—
73C23×AGL(1,𝔽5)—32no—
74C23×AGL(1,𝔽5)C2×D312yes—
75C22×C4×D5—31no—
76C22×C4×D5—31no—
77C22×C4×D5C2×D311yescharacteristic
78C2×C4⋊AGL(1,𝔽5)—38no—
79C2×C4⋊AGL(1,𝔽5)—34no—
80C2×C4⋊AGL(1,𝔽5)Dic318yesdirect product factor
81C2×C4⋊AGL(1,𝔽5)C2×D314yes—
82C2×C4×AGL(1,𝔽5)—38no—
83C2×C4×AGL(1,𝔽5)—68no—
84C2×C42×C5—31no—
85C2×C4×Dic5—31no—
86C2×C4×Dic5—31no—
87C2×C4×Dic5—31no—
88C42×D5—34no—
89C42×D5—34no—
90(C2×AGL(1,𝔽5))⋊C4—38no—
91C2×C4×C4⋊C4—151noSylow
92C23×C3×C5C22×C411yescharacteristic
93C22×C3×D5C22×C411yescharacteristic
94C22×C3×D5C22×C412yes—
95C22×C3×D5C22×C412yes—
96C22×C3×D5C2×D412yes—
97C22×C3×D5C2×Q812yes—
98C22×C3×D5#4112yes—
99C22×C3×D5#4112yes—
100C22×C3×D5C2411yescharacteristic
101C2×ΓL(1,𝔽16)—216no—
102C2×ΓL(1,𝔽16)—24no—
103C2×ΓL(1,𝔽16)—24no—
104C2×ΓL(1,𝔽16)C22×C418yes—
105C2×C3×AGL(1,𝔽5)—216no—
106C2×C3×AGL(1,𝔽5)—24no—
107C2×C3×AGL(1,𝔽5)—24no—
108C2×C3×AGL(1,𝔽5)C22×C418yes—
109C2×C3×C4×C5C4214yescomplemented
110C2×C3×C4×C5C22×C412yes—
111C2×Dic15—22no—
112C2×Dic15C4⋊C414yescomplemented
113C2×Dic15C22×C412yes—
114C2×Dic15C22×C412yes—
115C2×C5×Dic3—22no—
116C2×C5×Dic3C4⋊C414yescomplemented
117C2×C5×Dic3C22×C412yes—
118C2×C5×Dic3C22×C412yes—
119C2×C3×Dic5C4214yescomplemented
120C2×C3×Dic5C22×C412yes—
121C3×C4×D5C4218yescomplemented
122C3×C4×D5C22×C414yes—
123C3×C4×D5C22×C414yes—
124D5×Dic3—24no—
125D5×Dic3—22no—
126D5×Dic3—22no—
127D5×Dic3C4⋊C418yescomplemented
128D5×Dic3C2×D414yes—
129D5×Dic3C2×Q814yes—
130C23×C3×C4—51no—
131C23×C3×C4—52no—
132C23×Dic3—51no—
133C23×Dic3—52no—
134C23×Dic3—51no—
135C2×C3×C4⋊C4—58no—
136C2×C3×C4⋊C4—54no—
137C2×C4⋊Dic3—58no—
138C2×C4⋊Dic3—54no—
139C2×C4×Dic3—51no—
140C2×C4×Dic3—51no—
141C2×C4×Dic3—51no—
142C2×C4×Dic3—54no—
143C2×C4×Dic3—54no—
144C2×C4×Dic3—58no—
145C2×C4×Dic3—108no—
146C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
147C3⋊#95—58no—
148C23×D5C22×D311yescharacteristic
149C22×AGL(1,𝔽5)—24no—
150C22×AGL(1,𝔽5)—24no—
151C22×AGL(1,𝔽5)—38no—
152C22×AGL(1,𝔽5)—34no—
153C22×AGL(1,𝔽5)—64no—
154C22×AGL(1,𝔽5)—64no—
155C22×AGL(1,𝔽5)C2×Dic318yes—
156C22×AGL(1,𝔽5)C22×D314yes—
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5C4×D311yescharacteristic
160C22×Dic5—31no—
161C22×Dic5—31no—
162C22×Dic5C4×D311yescharacteristic
163C2×C4×D5—32no—
164C2×C4×D5—34no—
165C2×C4×D5—34no—
166C2×C4×D5—32no—
167C2×C4×D5—32no—
168C2×C4×D5—32no—
169C2×C4×D5—62no—
170C2×C4×D5—62no—
171C2×C4×D5C4×D312yes—
172C2×C4×D5C4×D314yes—
173C2×C4×D5C2×Dic314yes—
174C2×C4×D5C22×D312yes—
175C4⋊AGL(1,𝔽5)—316no—
176C4⋊AGL(1,𝔽5)C2×Dic3116yesdirect product factor
177C4×AGL(1,𝔽5)—616no—
178C42×C5—34no—
179C4×Dic5—34no—
180C4×Dic5—34no—
181C4×Dic5—34no—
182C22×C4⋊C4—51no—
183C22×C4⋊C4—151no—
184C22×C42—151no—
185C22×C42—152no—
186C4×C4⋊C4—158no—
187C2×#95—152no—
188C22×C3×C5C2×C4212yes—
189C22×C3×C5C2×C4⋊C412yes—
190C22×C3×C5#11712yes—
191C22×C3×C5C23×C411yescharacteristic
192C2×C3×D5C2×C4212yes—
193C2×C3×D5C2×C4⋊C412yes—
194C2×C3×D5#11712yes—
195C2×C3×D5C4×D414yes—
196C2×C3×D5C4×D414yes—
197C2×C3×D5C4×Q814yes—
198C2×C3×D5C4×Q814yes—
199C2×C3×D5C23×C411yescharacteristic
200C2×C3×D5C23×C411yescharacteristic
201C2×C3×D5C22×D411yescharacteristic
202C2×C3×D5C22×Q811yescharacteristic
203C2×C3×D5C2×#4111yescharacteristic
204C2×C3×D5C2×#4111yescharacteristic
205ΓL(1,𝔽16)—28no—
206C3×AGL(1,𝔽5)—28no—
207C3×C4×C5C2×C4214yescomplemented
208Dic15—22no—
209Dic15C2×C4⋊C414yescomplemented
210C3×Dic5C2×C4214yescomplemented
211C5×Dic3—22no—
212C5×Dic3C2×C4⋊C414yescomplemented
213C24×C3—51no—
214C22×C3×C4—51no—
215C22×C3×C4—54no—
216C22×C3×C4—54no—
217C22×C3×C4—52no—
218C22×C3×C4—52no—
219C22×C3×C4—54no—
220C22×C3×C4—58no—
221C22×C3×C4—104no—
222C22×C3×C4—104no—
223C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
224C22×Dic3—51no—
225C22×Dic3—54no—
226C22×Dic3—54no—
227C22×Dic3—52no—
228C22×Dic3—52no—
229C22×Dic3—54no—
230C22×Dic3—58no—
231C22×Dic3—51no—
232C22×Dic3—52no—
233C22×Dic3—52no—
234C22×Dic3—102no—
235C22×Dic3—102no—
236C22×Dic3—104no—
237C22×Dic3—104no—
238C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
239C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
240C3×C4⋊C4—516no—
241C4⋊Dic3—516no—
242C4×Dic3—54no—
243C4×Dic3—54no—
244C4×Dic3—54no—
245C4×Dic3—1016no—
246C4×Dic3C2×AGL(1,𝔽5)14yescomplemented
247C23×C5C2×C4×D311yescharacteristic
248C22×D5C2×C4×D312yes—
249C22×D5C2×C4×D311yescharacteristic
250C22×D5D3×D412yes—
251C22×D5#23712yes—
252C22×D5D3×Q812yes—
253C22×D5#23912yes—
254C22×D5C22×Dic312yes—
255C22×D5C23×D311yescharacteristic
256C2×AGL(1,𝔽5)—216no—
257C2×AGL(1,𝔽5)—24no—
258C2×AGL(1,𝔽5)—24no—
259C2×AGL(1,𝔽5)—38no—
260C2×AGL(1,𝔽5)—616no—
261C2×AGL(1,𝔽5)—64no—
262C2×AGL(1,𝔽5)—64no—
263C2×AGL(1,𝔽5)C22×Dic318yes—
264C2×C4×C5—34no—
265C2×C4×C5—32no—
266C2×C4×C5—32no—
267C2×C4×C5—62no—
268C2×C4×C5C4×Dic314yescomplemented
269C2×C4×C5C2×C4×D312yes—
270C2×Dic5—34no—
271C2×Dic5—32no—
272C2×Dic5—32no—
273C2×Dic5—62no—
274C2×Dic5C4×Dic314yescomplemented
275C2×Dic5C2×C4×D312yes—
276C4×D5—38no—
277C4×D5—34no—
278C4×D5—34no—
279C4×D5—64no—
280C4×D5—62no—
281C4×D5—62no—
282C4×D5C4×Dic318yescomplemented
283C4×D5C2×C4×D314yes—
284C4×D5C22×Dic314yes—
285C23×C4—51no—
286C23×C4—52no—
287C23×C4—151no—
288C23×C4—151no—
289C23×C4—152no—
290C2×C4⋊C4—58no—
291C2×C4⋊C4—54no—
292C2×C4⋊C4—154no—
293C2×C4⋊C4—158no—
294C2×C42—31no—
295C2×C42—154no—
296C2×C42—154no—
297C2×C42—151no—
298C2×C42—151no—
299C2×C42—151no—
300C2×C42—158no—
301C2×C42—308no—
302#95—158no—
303C2×C3×C5C4×C4⋊C414yescomplemented
304C2×C3×C5C22×C4211yescharacteristic
305C2×C3×C5C22×C4⋊C411yescharacteristic
306C2×C3×C5C2×#11711yescharacteristic
307C3×D5C4×C4⋊C414yescomplemented
308C3×D5C2×C4×D411yescharacteristic
309C3×D5C2×C4×D411yescharacteristic
310C3×D5C2×C4×Q811yescharacteristic
311C3×D5C2×C4×Q811yescharacteristic
312C23×C3—52no—
313C23×C3—52no—
314C23×C3—52no—
315C23×C3—52no—
316C23×C3—52no—
317C23×C3—52no—
318C23×C3—51no—
319C23×C3—51no—
320C23×C3C22×AGL(1,𝔽5)11yescharacteristic
321C2×C3×C4—54no—
322C2×C3×C4—52no—
323C2×C3×C4—58no—
324C2×C3×C4—54no—
325C2×C3×C4—54no—
326C2×C3×C4—58no—
327C2×C3×C4—104no—
328C2×C3×C4—1016no—
329C2×C3×C4—104no—
330C2×C3×C4C4×AGL(1,𝔽5)14yescomplemented
331C2×C3×C4C22×AGL(1,𝔽5)12yes—
332C2×Dic3—22no—
333C2×Dic3—54no—
334C2×Dic3—52no—
335C2×Dic3—58no—
336C2×Dic3—54no—
337C2×Dic3—54no—
338C2×Dic3—58no—
339C2×Dic3—52no—
340C2×Dic3—104no—
341C2×Dic3—102no—
342C2×Dic3—102no—
343C2×Dic3—104no—
344C2×Dic3—1016no—
345C2×Dic3—104no—
346C2×Dic3—102no—
347C2×Dic3C4⋊AGL(1,𝔽5)14yesdirect product factor
348C2×Dic3C22×AGL(1,𝔽5)12yes—
349C2×Dic3C22×AGL(1,𝔽5)12yes—
350C22×C5D3×C4⋊C412yes—
351C22×C5#89212yes—
352C22×C5C2×C4×Dic312yes—
353C22×C5C22×C4×D311yescharacteristic
354C2×D5#88714yes—
355C2×D5D3×C4⋊C412yes—
356C2×D5#89212yes—
357C2×D5#89314yes—
358C2×D5C2×C4×Dic312yes—
359C2×D5D4×Dic314yes—
360C2×D5Q8×Dic314yes—
361C2×D5C22×C4×D311yescharacteristic
362C2×D5C2×D3×D411yescharacteristic
363C2×D5C2×#23711yescharacteristic
364C2×D5C2×D3×Q811yescharacteristic
365C2×D5C2×#23911yescharacteristic
366C2×D5C23×Dic311yescharacteristic
367AGL(1,𝔽5)—28no—
368AGL(1,𝔽5)—68no—
369C4×C5—34no—
370C4×C5—62no—
371C4×C5C2×C4×Dic314yescomplemented
372Dic5—34no—
373Dic5—62no—
374Dic5C2×C4×Dic314yescomplemented
375C24—51no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—51no—
379C22×C4—54no—
380C22×C4—54no—
381C22×C4—52no—
382C22×C4—52no—
383C22×C4—54no—
384C22×C4—58no—
385C22×C4—104no—
386C22×C4—104no—
387C22×C4—152no—
388C22×C4—152no—
389C22×C4—154no—
390C22×C4—154no—
391C22×C4—152no—
392C22×C4—152no—
393C22×C4—151no—
394C22×C4—154no—
395C22×C4—158no—
396C22×C4—151no—
397C22×C4—302no—
398C22×C4—302no—
399C22×C4—304no—
400C22×C4—304no—
401C22×C4D3×AGL(1,𝔽5)11yescharacteristic
402C4⋊C4—516no—
403C4⋊C4—1516no—
404C42—34no—
405C42—154no—
406C42—154no—
407C42—154no—
408C42—3016no—
409C3×C5C2×C4×C4⋊C411yescharacteristic, complemented, Hall
410C22×C3—54no—
411C22×C3—54no—
412C22×C3—54no—
413C22×C3—54no—
414C22×C3—52no—
415C22×C3—51no—
416C22×C3—51no—
417C22×C3—52no—
418C22×C3—51no—
419C22×C3—51no—
420C22×C3—52no—
421C22×C3—51no—
422C22×C3—51no—
423C22×C3C2×C4×AGL(1,𝔽5)12yes—
424C22×C3C2×C4⋊AGL(1,𝔽5)12yes—
425C22×C3#413012yes—
426C22×C3C23×AGL(1,𝔽5)11yescharacteristic
427C3×C4—54no—
428C3×C4—108no—
429C3×C4C2×C4×AGL(1,𝔽5)14yescomplemented
430Dic3—22no—
431Dic3—54no—
432Dic3—108no—
433Dic3—102no—
434Dic3C2×C4⋊AGL(1,𝔽5)14yesdirect product factor
435C2×C5Dic3×C4⋊C414yescomplemented
436C2×C5C2×D3×C4⋊C411yescharacteristic
437C2×C5C2×#89211yescharacteristic
438C2×C5C22×C4×Dic311yescharacteristic
439D5Dic3×C4⋊C414yescomplemented
440D5C2×#88711yescharacteristic
441D5C2×#89311yescharacteristic
442D5C2×D4×Dic311yescharacteristic
443D5C2×Q8×Dic311yescharacteristic
444C23—52no—
445C23—52no—
446C23—52no—
447C23—52no—
448C23—52no—
449C23—52no—
450C23—51no—
451C23—51no—
452C23C2×D3×AGL(1,𝔽5)11yescharacteristic
453C2×C4—34no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—54no—
457C2×C4—52no—
458C2×C4—54no—
459C2×C4—54no—
460C2×C4—58no—
461C2×C4—58no—
462C2×C4—62no—
463C2×C4—104no—
464C2×C4—104no—
465C2×C4—1016no—
466C2×C4—154no—
467C2×C4—158no—
468C2×C4—154no—
469C2×C4—154no—
470C2×C4—152no—
471C2×C4—158no—
472C2×C4—152no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—304no—
476C2×C4—304no—
477C2×C4—304no—
478C2×C4—3016no—
479C2×C4—302no—
480C2×C4Dic3×AGL(1,𝔽5)14yescomplemented
481C2×C4C2×D3×AGL(1,𝔽5)12yes—
482C2×C3—51no—
483C2×C3—51no—
484C2×C3—51no—
485C2×C3—51no—
486C2×C3—54no—
487C2×C3C4×C4⋊AGL(1,𝔽5)14yescomplemented
488C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
489C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
490C2×C3C2×#413011yescharacteristic
491C5C2×Dic3×C4⋊C411yescharacteristic, complemented, Sylow
492C22—51no—
493C22—51no—
494C22—52no—
495C22—51no—
496C22—52no—
497C22—51no—
498C22—51no—
499C22—51no—
500C22—52no—
501C22—54no—
502C22—54no—
503C22—54no—
504C22—54no—
505C22#9190712yes—
506C22D3×C4⋊AGL(1,𝔽5)12yes—
507C22C2×Dic3×AGL(1,𝔽5)12yes—
508C22C22×D3×AGL(1,𝔽5)11yescharacteristic
509C4—34no—
510C4—54no—
511C4—62no—
512C4—108no—
513C4—154no—
514C4—308no—
515C4—302no—
516C4C2×Dic3×AGL(1,𝔽5)14yescomplemented
517C3C2×C4×C4⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
518C2—51no—
519C2—51no—
520C2—54no—
521C2—51no—
522C2—51no—
523C2Dic3×C4⋊AGL(1,𝔽5)14yesdirect product factor
524C2C2×#9190711yescharacteristic
525C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
526C2C22×Dic3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. Dic3×C4⋊AGL(1,𝔽5)C2direct (N × H)
13. C2×C4⋊ΓL(1,𝔽16)C4semidirect
15. C2×C3×C4⋊AGL(1,𝔽5)C4semidirect
19. C2×C4×Dic15C4semidirect
20. C2×C4×C5×Dic3C4semidirect
21. C2×Dic3×Dic5C4semidirect
22. C2×Dic3×Dic5C4semidirect
23. C4×D5×Dic3C4semidirect
60. C4⋊ΓL(1,𝔽16)C2×C4semidirect
61. C3×C4⋊AGL(1,𝔽5)C2×C4semidirect
63. C4×Dic15C2×C4semidirect
64. C4×C5×Dic3C2×C4semidirect
65. Dic3×Dic5C2×C4semidirect
66. Dic3×Dic5C2×C4semidirect
80. C2×C4⋊AGL(1,𝔽5)Dic3direct (N × H)
109. C2×C3×C4×C5C42semidirect
112. C2×Dic15C4⋊C4semidirect
116. C2×C5×Dic3C4⋊C4semidirect
119. C2×C3×Dic5C42semidirect
121. C3×C4×D5C42semidirect
127. D5×Dic3C4⋊C4semidirect
146. C2×C4×Dic3AGL(1,𝔽5)semidirect
176. C4⋊AGL(1,𝔽5)C2×Dic3direct (N × H)
207. C3×C4×C5C2×C42semidirect
209. Dic15C2×C4⋊C4semidirect
210. C3×Dic5C2×C42semidirect
212. C5×Dic3C2×C4⋊C4semidirect
246. C4×Dic3C2×AGL(1,𝔽5)semidirect
268. C2×C4×C5C4×Dic3semidirect
274. C2×Dic5C4×Dic3semidirect
282. C4×D5C4×Dic3semidirect
303. C2×C3×C5C4×C4⋊C4semidirect
307. C3×D5C4×C4⋊C4semidirect
330. C2×C3×C4C4×AGL(1,𝔽5)semidirect
347. C2×Dic3C4⋊AGL(1,𝔽5)direct (N × H)
371. C4×C5C2×C4×Dic3semidirect
374. Dic5C2×C4×Dic3semidirect
409. C3×C5C2×C4×C4⋊C4semidirect
429. C3×C4C2×C4×AGL(1,𝔽5)semidirect
434. Dic3C2×C4⋊AGL(1,𝔽5)direct (N × H)
435. C2×C5Dic3×C4⋊C4semidirect
439. D5Dic3×C4⋊C4semidirect
480. C2×C4Dic3×AGL(1,𝔽5)semidirect
487. C2×C3C4×C4⋊AGL(1,𝔽5)semidirect
491. C5C2×Dic3×C4⋊C4semidirect
516. C4C2×Dic3×AGL(1,𝔽5)semidirect
517. C3C2×C4×C4⋊AGL(1,𝔽5)semidirect
523. C2Dic3×C4⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊ΓL(1,𝔽16)2
C22×C3×C4⋊AGL(1,𝔽5)2
C22×Dic3×AGL(1,𝔽5)2
C2×C4×D5×Dic32
C2×(C2×AGL(1,𝔽5))⋊Dic32
Dic3×C4⋊AGL(1,𝔽5)2
C2×C4×C4⋊AGL(1,𝔽5)3
C2×Dic3×C4⋊C45