Finite Group Databasebeta

← #72254811

Subgroups — #72254811

Order 4320.

1252 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×ΓL(1,𝔽16)⋊Dic3C211yesmaximal, characteristic, complemented
2D5×#6289C211yesmaximal, characteristic
3#72254765C211yesmaximal, characteristic, complemented
4C3×Dic3×ΓL(1,𝔽16)C212yesmaximal, complemented
5C2×ΓL(1,𝔽16)⋊(C3⋊D3)C212yesmaximal
6C4×ΓL(1,𝔽16)⋊D3—31nomaximal
7AGL(1,𝔽5)×#624—32nomaximal
8C2×D5×C3⋊(C3⋊D3)C2211yescharacteristic
9C2×C3×C3⋊ΓL(1,𝔽16)C2212yes—
10C2×C32×ΓL(1,𝔽16)C2212yes—
11ΓL(1,𝔽16)⋊(C3⋊D3)C418yescomplemented
12#11762088C411yescharacteristic, complemented
13#11762082C411yescharacteristic, complemented
14#11762075C411yescharacteristic, complemented
15C5×#6289C411yescharacteristic, complemented
16C3×D5×C3⋊Dic3C2211yescharacteristic
17C32×D5×Dic3C2211yescharacteristic
18#11722900—51nomaximal, Hall
19C2×ΓL(1,𝔽16)⋊D3—32no—
20C2×ΓL(1,𝔽16)⋊D3—32no—
21C2×ΓL(1,𝔽16)⋊D3—62no—
22C2×C3⋊D3×AGL(1,𝔽5)—32no—
23C4×D5×C3⋊D3—31no—
24C3×C4×ΓL(1,𝔽16)—32no—
25D5×#624—32no—
26D5×#624—61no—
27ΓL(1,𝔽16)⋊Dic3—31no—
28ΓL(1,𝔽16)⋊Dic3D311yescharacteristic, complemented
29Dic3×ΓL(1,𝔽16)—32no—
30Dic3×ΓL(1,𝔽16)D312yescomplemented
31C3×Dic3×AGL(1,𝔽5)—32no—
32C3×Dic3×AGL(1,𝔽5)—32no—
33C2×C3⋊(C3⋊D15)C2×C411yescharacteristic
34C2×C5×C3⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C33×D5C2311yescharacteristic
36D5×C3⋊(C3⋊D3)C2×C414yes—
37C3×C3⋊ΓL(1,𝔽16)C2×C414yescomplemented
38C32×ΓL(1,𝔽16)C2×C414yescomplemented
39C3×C3⋊Dic15C2×C411yescharacteristic, complemented
40C3×C5×C3⋊Dic3C2×C411yescharacteristic, complemented
41C32×Dic15C2×C411yescharacteristic, complemented
42C32×C5×Dic3C2×C411yescharacteristic, complemented
43C4×D3×AGL(1,𝔽5)—91no—
44C4×D3×AGL(1,𝔽5)—92no—
45C2×#6289—52no—
46C2×#6289—51no—
47#88813—51no—
48C3×Dic32—52no—
49C3×Dic32—51no—
50C2×D5×C3⋊D3—32no—
51C2×D5×C3⋊D3—31no—
52C2×D5×C3⋊D3—61no—
53C2×D5×C3⋊D3—62no—
54C2×D5×C3⋊D3—121no—
55C2×C3⋊ΓL(1,𝔽16)C2×D312yes—
56C2×C3×ΓL(1,𝔽16)—22no—
57C2×C3×ΓL(1,𝔽16)—32no—
58C2×C3×ΓL(1,𝔽16)—32no—
59C2×C3×ΓL(1,𝔽16)—62no—
60C2×C3×ΓL(1,𝔽16)C2×D312yes—
61C2×C3×ΓL(1,𝔽16)C2×D312yes—
62C2×C32×AGL(1,𝔽5)—32no—
63ΓL(1,𝔽16)⋊D3—38no—
64ΓL(1,𝔽16)⋊D3—38no—
65ΓL(1,𝔽16)⋊D3—68no—
66C3⋊D3×AGL(1,𝔽5)—38no—
67C4×C3⋊D15—31no—
68C4×C5×C3⋊D3—31no—
69C32×C4×D5—31no—
70#67155—32no—
71#67155—61no—
72#67149—32no—
73#67149—32no—
74#67149—61no—
75#67149—61no—
76C5×#624—32no—
77C5×#624—61no—
78#67137—31no—
79C3⋊D3×Dic5—31no—
80D5×C3⋊Dic3C2×D311yescharacteristic
81C3×D5×Dic3—21no—
82C3×D5×Dic3—32no—
83C3×D5×Dic3—61no—
84C3×D5×Dic3C2×D312yes—
85C4×#624—152no—
86C4×#624—151no—
87C2×C33×C5C22×C411yescharacteristic
88C3⋊(C3⋊D15)C4212yescomplemented
89C5×C3⋊(C3⋊D3)C4212yescomplemented
90C33×D5C22×C412yes—
91C2×D3×AGL(1,𝔽5)—92no—
92C2×D3×AGL(1,𝔽5)—92no—
93C2×D3×AGL(1,𝔽5)—92no—
94C2×D3×AGL(1,𝔽5)—182no—
95C4×D3×D5—92no—
96C4×D3×D5—91no—
97C4×D3×D5—181no—
98C4×ΓL(1,𝔽16)—32no—
99C4×ΓL(1,𝔽16)—91no—
100C3×C4×AGL(1,𝔽5)—92no—
101C3×C4×AGL(1,𝔽5)—91no—
102Dic3×AGL(1,𝔽5)—32no—
103Dic3×AGL(1,𝔽5)—32no—
104Dic3×AGL(1,𝔽5)—92no—
105C22×C3⋊(C3⋊D3)—51no—
106C2×C3×C3⋊Dic3—52no—
107C2×C3×C3⋊Dic3—51no—
108C2×C32×Dic3—52no—
109C2×C32×Dic3—51no—
110#6289—58no—
111#6289—51no—
112#6289—51no—
113#6289—51no—
114#6289AGL(1,𝔽5)11yescharacteristic, complemented
115C2×C3⋊D15—31no—
116C2×C3⋊D15—32no—
117C2×C3⋊D15—61no—
118C2×C3⋊D15—62no—
119C2×C3⋊D15—121no—
120C2×C5×C3⋊D3—31no—
121C2×C5×C3⋊D3—32no—
122C2×C5×C3⋊D3—61no—
123C2×C5×C3⋊D3—62no—
124C2×C5×C3⋊D3—121no—
125C2×C32×D5—21no—
126C2×C32×D5—22no—
127C2×C32×D5—41no—
128C2×C32×D5C22×D312yes—
129C2×C32×D5C22×D311yescharacteristic
130D5×C3⋊D3—34no—
131D5×C3⋊D3—34no—
132D5×C3⋊D3—34no—
133D5×C3⋊D3—64no—
134D5×C3⋊D3—64no—
135D5×C3⋊D3—64no—
136D5×C3⋊D3—124no—
137C3⋊ΓL(1,𝔽16)C4×D314yescomplemented
138C3×ΓL(1,𝔽16)—24no—
139C3×ΓL(1,𝔽16)—34no—
140C3×ΓL(1,𝔽16)—34no—
141C3×ΓL(1,𝔽16)—64no—
142C3×ΓL(1,𝔽16)C4×D314yescomplemented
143C3×ΓL(1,𝔽16)C4×D314yescomplemented
144C32×AGL(1,𝔽5)—34no—
145C32×C4×C5—31no—
146C3⋊Dic15C4×D311yescharacteristic, complemented
147C5×C3⋊Dic3C4×D311yescharacteristic, complemented
148C3×Dic15—21no—
149C3×Dic15—32no—
150C3×Dic15—61no—
151C3×Dic15C4×D312yescomplemented
152C3×C5×Dic3—21no—
153C3×C5×Dic3—32no—
154C3×C5×Dic3—61no—
155C3×C5×Dic3C4×D312yescomplemented
156C32×Dic5—31no—
157C2×C4×AGL(1,𝔽5)—271noHall
158C2×C4×C3⋊D3—151no—
159C2×C4×C3⋊D3—152no—
160C2×#624—152no—
161C2×#624—152no—
162C2×#624—152no—
163C2×#624—301no—
164C2×#624—302no—
165C3×C4×Dic3—152no—
166C3×C4×Dic3—152no—
167C3×C4×Dic3—152no—
168Dic32—52no—
169Dic32—51no—
170Dic32—152no—
171Dic32—151no—
172C33×C5C2×C4211yescharacteristic, complemented, Hall
173C2×D3×D5—91no—
174C2×D3×D5—92no—
175C2×D3×D5—181no—
176C2×D3×D5—182no—
177C2×D3×D5—361no—
178C2×ΓL(1,𝔽16)—32no—
179C2×ΓL(1,𝔽16)—32no—
180C2×ΓL(1,𝔽16)—62no—
181C2×ΓL(1,𝔽16)D3212yes—
182C2×C3×AGL(1,𝔽5)—32no—
183C2×C3×AGL(1,𝔽5)—32no—
184C2×C3×AGL(1,𝔽5)—62no—
185C2×C3×AGL(1,𝔽5)—92no—
186D3×AGL(1,𝔽5)—98no—
187D3×AGL(1,𝔽5)—98no—
188D3×AGL(1,𝔽5)—98no—
189D3×AGL(1,𝔽5)—188no—
190C4×D15—92no—
191C4×D15—91no—
192C4×D15—181no—
193C4×C5×D3—92no—
194C4×C5×D3—91no—
195C4×C5×D3—181no—
196C3×C4×D5—32no—
197C3×C4×D5—61no—
198C3×C4×D5—91no—
199#1200—92no—
200#1200—91no—
201#1200—181no—
202D3×Dic5—92no—
203D3×Dic5—91no—
204D3×Dic5—181no—
205D5×Dic3—32no—
206D5×Dic3—61no—
207D5×Dic3D3211yescharacteristic
208C22×C33—51no—
209C2×C3⋊(C3⋊D3)—51no—
210C2×C3⋊(C3⋊D3)—54no—
211C2×C3⋊(C3⋊D3)C2×AGL(1,𝔽5)11yescharacteristic
212C3×C3⋊Dic3—54no—
213C3×C3⋊Dic3—51no—
214C3×C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
215C32×Dic3—54no—
216C32×Dic3—51no—
217C32×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
218C42×D3—451no—
219C42×D3—452no—
220C2×C32×C5—22no—
221C2×C32×C5—21no—
222C2×C32×C5—41no—
223C2×C32×C5C2×C4×D311yescharacteristic
224C2×C32×C5C2×C4×D312yes—
225C3⋊D15—34no—
226C3⋊D15—32no—
227C3⋊D15—64no—
228C3⋊D15—62no—
229C3⋊D15—122no—
230C5×C3⋊D3—34no—
231C5×C3⋊D3—32no—
232C5×C3⋊D3—64no—
233C5×C3⋊D3—62no—
234C5×C3⋊D3—122no—
235C32×D5—22no—
236C32×D5—22no—
237C32×D5—22no—
238C32×D5—42no—
239C32×D5C2×C4×D312yes—
240C32×D5C2×C4×D312yes—
241C32×D5C2×C4×D312yes—
242C22×AGL(1,𝔽5)—272no—
243C2×C4×D5—271no—
244C4×AGL(1,𝔽5)—92no—
245C4×AGL(1,𝔽5)—91no—
246C4×AGL(1,𝔽5)—271no—
247C22×C3⋊D3—152no—
248C22×C3⋊D3—151no—
249C22×C3⋊D3—301no—
250C22×C3⋊D3—302no—
251C22×C3⋊D3—601no—
252C2×C32×C4—151no—
253C2×C32×C4—152no—
254C2×C3⋊Dic3—52no—
255C2×C3⋊Dic3—51no—
256C4×C3⋊D3—31no—
257C4×C3⋊D3—151no—
258C4×C3⋊D3—151no—
259C4×C3⋊D3—158no—
260C4×C3⋊D3—151no—
261C2×C3×Dic3—52no—
262C2×C3×Dic3—52no—
263C2×C3×Dic3—52no—
264C2×C3×Dic3—101no—
265C2×C3×Dic3—102no—
266C2×C3×Dic3—152no—
267C2×C3×Dic3—152no—
268C2×C3×Dic3—152no—
269C2×C3×Dic3—301no—
270C2×C3×Dic3—302no—
271#624—32no—
272#624—61no—
273#624—152no—
274#624—152no—
275#624—158no—
276#624—158no—
277#624—152no—
278#624—301no—
279#624—301no—
280#624—301no—
281#624—308no—
282C2×D15—92no—
283C2×D15—91no—
284C2×D15—181no—
285C2×D15—182no—
286C2×D15—361no—
287C2×C5×D3—92no—
288C2×C5×D3—91no—
289C2×C5×D3—181no—
290C2×C5×D3—182no—
291C2×C5×D3—361no—
292C2×C3×D5—21no—
293C2×C3×D5—22no—
294C2×C3×D5—41no—
295C2×C3×D5C2×D3211yescharacteristic
296C2×C3×D5C2×D3212yes—
297D3×D5—94no—
298D3×D5—94no—
299D3×D5—94no—
300D3×D5—184no—
301D3×D5—184no—
302D3×D5—184no—
303D3×D5—364no—
304ΓL(1,𝔽16)—34no—
305ΓL(1,𝔽16)—34no—
306ΓL(1,𝔽16)—64no—
307ΓL(1,𝔽16)#62414yescomplemented
308C3×AGL(1,𝔽5)—34no—
309C3×AGL(1,𝔽5)—34no—
310C3×AGL(1,𝔽5)—64no—
311C3×AGL(1,𝔽5)—94no—
312C3×C4×C5—32no—
313C3×C4×C5—61no—
314C3×C4×C5—91no—
315Dic15—32no—
316Dic15—61no—
317Dic15#62411yescharacteristic, complemented
318C3×Dic5—32no—
319C3×Dic5—61no—
320C3×Dic5—91no—
321C5×Dic3—32no—
322C5×Dic3—61no—
323C5×Dic3#62411yescharacteristic, complemented
324C2×C33—52no—
325C2×C33C22×AGL(1,𝔽5)11yescharacteristic
326C3⋊(C3⋊D3)—52no—
327C3⋊(C3⋊D3)C4×AGL(1,𝔽5)12yescomplemented
328C2×C4×D3—451no—
329C2×C4×D3—452no—
330C2×C4×D3—452no—
331C2×C4×D3—452no—
332C2×C4×D3—452no—
333C2×C4×D3—901no—
334C2×C4×D3—902no—
335C3×C42—452no—
336C3×C42—451no—
337C4×Dic3—152no—
338C4×Dic3—152no—
339C4×Dic3—152no—
340C4×Dic3—452no—
341C4×Dic3—451no—
342C32×C5—22no—
343C32×C5—21no—
344C32×C5—41no—
345C32×C5C42×D311yescharacteristic, complemented
346C32×C5C42×D312yescomplemented
347C22×D5—271no—
348C2×AGL(1,𝔽5)—32no—
349C2×AGL(1,𝔽5)—92no—
350C2×AGL(1,𝔽5)—278no—
351C2×C4×C5—271no—
352C2×Dic5—271no—
353C4×D5—31no—
354C4×D5—91no—
355C4×D5—271no—
356C4×D5—271no—
357C22×C32—51no—
358C22×C32—52no—
359C22×C32—102no—
360C22×C32—101no—
361C22×C32—201no—
362C2×C3⋊D3—32no—
363C2×C3⋊D3—31no—
364C2×C3⋊D3—61no—
365C2×C3⋊D3—62no—
366C2×C3⋊D3—121no—
367C2×C3⋊D3—154no—
368C2×C3⋊D3—154no—
369C2×C3⋊D3—154no—
370C2×C3⋊D3—152no—
371C2×C3⋊D3—151no—
372C2×C3⋊D3—304no—
373C2×C3⋊D3—304no—
374C2×C3⋊D3—304no—
375C2×C3⋊D3—301no—
376C2×C3⋊D3—302no—
377C2×C3⋊D3—604no—
378C2×C3⋊D3—601no—
379C32×C4—31no—
380C32×C4—154no—
381C32×C4—151no—
382C3⋊Dic3—54no—
383C3⋊Dic3—51no—
384C3⋊Dic3D3×AGL(1,𝔽5)11yescharacteristic, complemented
385C3×Dic3—21no—
386C3×Dic3—32no—
387C3×Dic3—54no—
388C3×Dic3—54no—
389C3×Dic3—52no—
390C3×Dic3—61no—
391C3×Dic3—101no—
392C3×Dic3—104no—
393C3×Dic3—154no—
394C3×Dic3—154no—
395C3×Dic3—152no—
396C3×Dic3—301no—
397C3×Dic3—304no—
398C3×Dic3D3×AGL(1,𝔽5)12yescomplemented
399C2×C42—1351noSylow
400C2×C3×C5—21no—
401C2×C3×C5—22no—
402C2×C3×C5—41no—
403C2×C3×C5C4×D3212yes—
404C2×C3×C5C2×#62411yescharacteristic
405D15—94no—
406D15—92no—
407D15—184no—
408D15—182no—
409D15—362no—
410C3×D5—22no—
411C3×D5—22no—
412C3×D5—22no—
413C3×D5—42no—
414C3×D5C4×D3212yes—
415C3×D5C4×D3212yes—
416C3×D5C2×#62412yes—
417C5×D3—94no—
418C5×D3—92no—
419C5×D3—184no—
420C5×D3—182no—
421C5×D3—362no—
422C33C2×C4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
423C22×D3—452no—
424C22×D3—451no—
425C22×D3—901no—
426C22×D3—902no—
427C22×D3—1801no—
428C2×C3×C4—152no—
429C2×C3×C4—152no—
430C2×C3×C4—152no—
431C2×C3×C4—301no—
432C2×C3×C4—302no—
433C2×C3×C4—451no—
434C2×C3×C4—452no—
435C2×Dic3—52no—
436C2×Dic3—51no—
437C2×Dic3—152no—
438C2×Dic3—152no—
439C2×Dic3—152no—
440C2×Dic3—301no—
441C2×Dic3—302no—
442C4×D3—92no—
443C4×D3—91no—
444C4×D3—181no—
445C4×D3—452no—
446C4×D3—451no—
447C4×D3—451no—
448C4×D3—458no—
449C4×D3—452no—
450C4×D3—452no—
451C4×D3—458no—
452C4×D3—458no—
453C4×D3—451no—
454C4×D3—901no—
455C4×D3—901no—
456C4×D3—901no—
457C4×D3—908no—
458C22×C5—271no—
459C2×D5—271no—
460C2×D5—274no—
461C2×D5D3311yescharacteristic
462AGL(1,𝔽5)—34no—
463AGL(1,𝔽5)—94no—
464C4×C5—31no—
465C4×C5—91no—
466Dic5—31no—
467Dic5—91no—
468C2×C32—22no—
469C2×C32—21no—
470C2×C32—41no—
471C2×C32—52no—
472C2×C32—52no—
473C2×C32—52no—
474C2×C32—102no—
475C2×C32—102no—
476C2×C32—102no—
477C2×C32—202no—
478C2×C32C2×D3×AGL(1,𝔽5)11yescharacteristic
479C2×C32C2×D3×AGL(1,𝔽5)12yes—
480C3⋊D3—32no—
481C3⋊D3—34no—
482C3⋊D3—64no—
483C3⋊D3—62no—
484C3⋊D3—122no—
485C3⋊D3—152no—
486C3⋊D3—154no—
487C3⋊D3—304no—
488C3⋊D3—302no—
489C3⋊D3—602no—
490C22×C4—1351no—
491C22×C4—1352no—
492C42—452no—
493C42—451no—
494C42—1351no—
495C3×C5—22no—
496C3×C5—21no—
497C3×C5—41no—
498C3×C5C4×#62412yescomplemented
499C3×C5C4×#62411yescharacteristic, complemented
500C22×C3—52no—
501C22×C3—51no—
502C22×C3—101no—
503C22×C3—102no—
504C22×C3—201no—
505C2×D3—92no—
506C2×D3—91no—
507C2×D3—181no—
508C2×D3—182no—
509C2×D3—361no—
510C2×D3—454no—
511C2×D3—454no—
512C2×D3—454no—
513C2×D3—452no—
514C2×D3—451no—
515C2×D3—904no—
516C2×D3—904no—
517C2×D3—904no—
518C2×D3—901no—
519C2×D3—902no—
520C2×D3—1804no—
521C2×D3—1801no—
522C3×C4—32no—
523C3×C4—61no—
524C3×C4—91no—
525C3×C4—154no—
526C3×C4—154no—
527C3×C4—152no—
528C3×C4—301no—
529C3×C4—304no—
530C3×C4—454no—
531C3×C4—451no—
532Dic3—32no—
533Dic3—54no—
534Dic3—51no—
535Dic3—61no—
536Dic3—154no—
537Dic3—154no—
538Dic3—152no—
539Dic3—301no—
540Dic3—304no—
541Dic3ΓL(1,𝔽16)⋊D311yescharacteristic, complemented
542C2×C5—272no—
543C2×C5D3×#62411yescharacteristic
544D5—272no—
545D5D3×#62412yes—
546C32—22no—
547C32—21no—
548C32—41no—
549C32C4×D3×AGL(1,𝔽5)11yescharacteristic, complemented
550C32C4×D3×AGL(1,𝔽5)12yescomplemented
551C23—1351no—
552C2×C4—151no—
553C2×C4—152no—
554C2×C4—271no—
555C2×C4—451no—
556C2×C4—452no—
557C2×C4—1351no—
558C2×C4—1351no—
559C2×C4—1351no—
560C2×C4—1358no—
561C2×C3—21no—
562C2×C3—22no—
563C2×C3—41no—
564C2×C3—52no—
565C2×C3—52no—
566C2×C3—52no—
567C2×C3—102no—
568C2×C3—102no—
569C2×C3—102no—
570C2×C3—202no—
571C2×C3D32×AGL(1,𝔽5)12yes—
572C2×C3C2×ΓL(1,𝔽16)⋊D311yescharacteristic
573D3—94no—
574D3—92no—
575D3—182no—
576D3—184no—
577D3—362no—
578D3—454no—
579D3—452no—
580D3—904no—
581D3—902no—
582D3—1802no—
583C5#1172290011yescharacteristic, complemented, Sylow
584C22—51no—
585C22—271no—
586C22—1354no—
587C22—1351no—
588C4—31no—
589C4—91no—
590C4—154no—
591C4—151no—
592C4—454no—
593C4—451no—
594C3—21no—
595C3—22no—
596C3—41no—
597C3AGL(1,𝔽5)×#62412yescomplemented
598C3C4×ΓL(1,𝔽16)⋊D311yescharacteristic, complemented
599C2—52no—
600C2—272no—
601C2—1352no—
602C2D3×ΓL(1,𝔽16)⋊D311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×ΓL(1,𝔽16)⋊D3
commutator, hypocenterC33×C5C2×C42
Fitting, socleC2×C33×C5C22×C4
prime radicalC2×D5×C3⋊(C3⋊D3)C22
cosocleC2×C33×D5C23
LCSG ▷ C33×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×ΓL(1,𝔽16)⋊Dic3C2semidirect
3. #72254765C2semidirect
4. C3×Dic3×ΓL(1,𝔽16)C2semidirect
11. ΓL(1,𝔽16)⋊(C3⋊D3)C4semidirect
12. #11762088C4semidirect
13. #11762082C4semidirect
14. #11762075C4semidirect
15. C5×#6289C4semidirect
28. ΓL(1,𝔽16)⋊Dic3D3semidirect
30. Dic3×ΓL(1,𝔽16)D3semidirect
37. C3×C3⋊ΓL(1,𝔽16)C2×C4semidirect
38. C32×ΓL(1,𝔽16)C2×C4semidirect
39. C3×C3⋊Dic15C2×C4semidirect
40. C3×C5×C3⋊Dic3C2×C4semidirect
41. C32×Dic15C2×C4semidirect
42. C32×C5×Dic3C2×C4semidirect
88. C3⋊(C3⋊D15)C42semidirect
89. C5×C3⋊(C3⋊D3)C42semidirect
114. #6289AGL(1,𝔽5)semidirect
137. C3⋊ΓL(1,𝔽16)C4×D3semidirect
142. C3×ΓL(1,𝔽16)C4×D3semidirect
143. C3×ΓL(1,𝔽16)C4×D3semidirect
146. C3⋊Dic15C4×D3semidirect
147. C5×C3⋊Dic3C4×D3semidirect
151. C3×Dic15C4×D3semidirect
155. C3×C5×Dic3C4×D3semidirect
172. C33×C5C2×C42semidirect
214. C3×C3⋊Dic3C2×AGL(1,𝔽5)semidirect
217. C32×Dic3C2×AGL(1,𝔽5)semidirect
307. ΓL(1,𝔽16)#624semidirect
317. Dic15#624semidirect
323. C5×Dic3#624semidirect
327. C3⋊(C3⋊D3)C4×AGL(1,𝔽5)semidirect
345. C32×C5C42×D3semidirect
346. C32×C5C42×D3semidirect
384. C3⋊Dic3D3×AGL(1,𝔽5)semidirect
398. C3×Dic3D3×AGL(1,𝔽5)semidirect
422. C33C2×C4×AGL(1,𝔽5)semidirect
498. C3×C5C4×#624semidirect
499. C3×C5C4×#624semidirect
541. Dic3ΓL(1,𝔽16)⋊D3semidirect
549. C32C4×D3×AGL(1,𝔽5)semidirect
550. C32C4×D3×AGL(1,𝔽5)semidirect
583. C5#11722900semidirect
597. C3AGL(1,𝔽5)×#624semidirect
598. C3C4×ΓL(1,𝔽16)⋊D3semidirect

Maximal subgroups

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

subgroupindex
C3×ΓL(1,𝔽16)⋊Dic32
D5×#62892
#722547652
C3×Dic3×ΓL(1,𝔽16)2
C2×ΓL(1,𝔽16)⋊(C3⋊D3)2
C4×ΓL(1,𝔽16)⋊D33
AGL(1,𝔽5)×#6243
#117229005