Finite Group Databasebeta

← C2×#13088407 #72230273

Subgroups — C2×#13088407 #72230273

Order 2880.

1908 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×ΓL(1,𝔽16)⋊D3C211yesmaximal, characteristic
2C22×C3⋊D3×AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×D5×#624C211yesmaximal, characteristic
4C2×Dic3⋊ΓL(1,𝔽16)C212yesmaximal, complemented
5C2×C3×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
6#13088407C218yesmaximal, direct product factor
7C2×D3×C4⋊AGL(1,𝔽5)—32nomaximal
8C22×D5×C3⋊D3C2211yescharacteristic
9C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
10C22×C3×ΓL(1,𝔽16)C2212yes—
11C22×C32×AGL(1,𝔽5)C2211yescharacteristic
12C2×ΓL(1,𝔽16)⋊D3—24no—
13C2×ΓL(1,𝔽16)⋊D3C2214yes—
14C2×C3⋊D3×AGL(1,𝔽5)—24no—
15C2×C3⋊D3×AGL(1,𝔽5)C2214yes—
16C2×#67155C411yescharacteristic, complemented
17C2×#67149C412yescomplemented
18C2×C5×#624C411yescharacteristic, complemented
19C2×C3×D5×Dic3C2212yes—
20D5×#624C414yescomplemented
21D5×#624C2214yes—
22Dic3⋊ΓL(1,𝔽16)C2218yescomplemented
23C3×Dic3⋊AGL(1,𝔽5)C2218yescomplemented
24C2×#63883—51nomaximal, Hall
25C22×D3×AGL(1,𝔽5)—32no—
26C22×D3×AGL(1,𝔽5)—32no—
27C22×D3×AGL(1,𝔽5)—61no—
28C2×C4×D3×D5—32no—
29C2×C4⋊ΓL(1,𝔽16)—32no—
30C2×C3×C4⋊AGL(1,𝔽5)—32no—
31C2×Dic3⋊AGL(1,𝔽5)—32no—
32C2×Dic3⋊AGL(1,𝔽5)D312yescomplemented
33D3×C4⋊AGL(1,𝔽5)—316no—
34C22×C3⋊D15C2×C411yescharacteristic
35C22×C5×C3⋊D3C2×C411yescharacteristic
36C22×C32×D5C2311yescharacteristic
37C2×D5×C3⋊D3C2×C412yes—
38C2×D5×C3⋊D3D414yes—
39C2×D5×C3⋊D3Q814yes—
40C2×D5×C3⋊D3C2312yes—
41C2×C3⋊ΓL(1,𝔽16)—22no—
42C2×C3⋊ΓL(1,𝔽16)C2312yes—
43C2×C3×ΓL(1,𝔽16)—24no—
44C2×C3×ΓL(1,𝔽16)C2314yes—
45C2×C32×AGL(1,𝔽5)—22no—
46C2×C32×AGL(1,𝔽5)C2312yes—
47ΓL(1,𝔽16)⋊D3—28no—
48C3⋊D3×AGL(1,𝔽5)—28no—
49C2×C3×Dic15C2×C412yescomplemented
50C2×C3×C5×Dic3C2×C412yescomplemented
51#67155C2×C414yescomplemented
52#67149C2×C418yescomplemented
53C5×#624C2×C414yescomplemented
54C3×D5×Dic3C2×C414yescomplemented
55C3×D5×Dic3C2314yes—
56C22×C4⋊AGL(1,𝔽5)—91noHall
57C22×C4×C3⋊D3—51no—
58C22×#624—51no—
59C22×#624—51no—
60C2×C3×Dic3⋊C4—52no—
61C2×Dic3⋊Dic3—52no—
62#63883—58no—
63C22×D3×D5—32no—
64C22×D3×D5—61no—
65C22×ΓL(1,𝔽16)—32no—
66C22×ΓL(1,𝔽16)—61no—
67C22×ΓL(1,𝔽16)C2×D312yes—
68C22×C3×AGL(1,𝔽5)—21no—
69C22×C3×AGL(1,𝔽5)—32no—
70C22×C3×AGL(1,𝔽5)C2×D312yes—
71C2×D3×AGL(1,𝔽5)—38no—
72C2×D3×AGL(1,𝔽5)—38no—
73C2×D3×AGL(1,𝔽5)—68no—
74C2×D3×AGL(1,𝔽5)—64no—
75C2×D3×AGL(1,𝔽5)—64no—
76C2×D3×AGL(1,𝔽5)—68no—
77C2×D3×AGL(1,𝔽5)—64no—
78C2×C4×D15—32no—
79C2×C4×C5×D3—32no—
80C2×C3×C4×D5—32no—
81C2×#1200—32no—
82C2×D3×Dic5—32no—
83C2×D5×Dic3C2×D312yes—
84C4×D3×D5—38no—
85C4×D3×D5—38no—
86C4⋊ΓL(1,𝔽16)—38no—
87C3×C4⋊AGL(1,𝔽5)—38no—
88Dic3⋊AGL(1,𝔽5)—38no—
89Dic3⋊AGL(1,𝔽5)C2×D318yescomplemented
90C2×D3×C4⋊C4—152no—
91C22×C32×C5C22×C411yescharacteristic
92C2×C3⋊D15C4⋊C414yescomplemented
93C2×C3⋊D15C22×C412yes—
94C2×C5×C3⋊D3C4⋊C414yescomplemented
95C2×C5×C3⋊D3C22×C412yes—
96C2×C32×D5C22×C411yescharacteristic
97C2×C32×D5C2×D412yes—
98C2×C32×D5C2×Q812yes—
99C2×C32×D5C2411yescharacteristic
100D5×C3⋊D3C4⋊C418yescomplemented
101D5×C3⋊D3C2×D414yes—
102D5×C3⋊D3C2×Q814yes—
103C3⋊ΓL(1,𝔽16)—22no—
104C3×ΓL(1,𝔽16)—24no—
105C32×AGL(1,𝔽5)—22no—
106C3×Dic15C22×C414yescomplemented
107C3×C5×Dic3C22×C414yescomplemented
108C23×AGL(1,𝔽5)—91no—
109C23×AGL(1,𝔽5)—91no—
110C22×C4×D5—91no—
111C2×C4⋊AGL(1,𝔽5)—32no—
112C2×C4⋊AGL(1,𝔽5)—98no—
113C2×C4⋊AGL(1,𝔽5)—92no—
114C23×C3⋊D3—51no—
115C22×C32×C4—51no—
116C22×C3⋊Dic3—51no—
117C2×C4×C3⋊D3—54no—
118C2×C4×C3⋊D3—104no—
119C22×C3×Dic3—52no—
120C22×C3×Dic3—52no—
121C2×#624—51no—
122C2×#624—52no—
123C2×#624—54no—
124C2×#624—54no—
125C2×#624—54no—
126C2×#624—104no—
127C2×#624AGL(1,𝔽5)11yescharacteristic, complemented
128C3×Dic3⋊C4—58no—
129Dic3⋊Dic3—58no—
130C22×D15—32no—
131C22×D15—61no—
132C22×C5×D3—32no—
133C22×C5×D3—61no—
134C22×C3×D5—21no—
135C22×C3×D5C22×D312yes—
136C2×D3×D5—34no—
137C2×D3×D5—38no—
138C2×D3×D5—38no—
139C2×D3×D5—34no—
140C2×D3×D5—62no—
141C2×D3×D5—64no—
142C2×D3×D5—64no—
143C2×D3×D5—62no—
144C2×ΓL(1,𝔽16)—24no—
145C2×ΓL(1,𝔽16)—34no—
146C2×ΓL(1,𝔽16)—62no—
147C2×ΓL(1,𝔽16)—62no—
148C2×ΓL(1,𝔽16)—64no—
149C2×ΓL(1,𝔽16)—62no—
150C2×ΓL(1,𝔽16)C22×D314yes—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—24no—
154C2×C3×AGL(1,𝔽5)—22no—
155C2×C3×AGL(1,𝔽5)—34no—
156C2×C3×AGL(1,𝔽5)—64no—
157C2×C3×AGL(1,𝔽5)C22×D314yes—
158D3×AGL(1,𝔽5)—616no—
159D3×AGL(1,𝔽5)—68no—
160D3×AGL(1,𝔽5)—68no—
161D3×AGL(1,𝔽5)—616no—
162C2×C3×C4×C5—32no—
163C2×Dic15C4×D312yescomplemented
164C4×D15—38no—
165C2×C5×Dic3C4×D312yescomplemented
166C4×C5×D3—38no—
167C2×C3×Dic5—32no—
168C3×C4×D5—34no—
169C3×C4×D5—34no—
170#1200—38no—
171D3×Dic5—38no—
172D5×Dic3C4×D314yescomplemented
173D5×Dic3C22×D314yes—
174C22×C4×D3—152no—
175C22×C4×D3—152no—
176C22×C4×D3—152no—
177C22×C4×D3—301no—
178C2×C3×C4⋊C4—152no—
179C2×C4⋊Dic3—152no—
180C2×Dic3⋊C4—52no—
181C2×Dic3⋊C4—152no—
182D3×C4⋊C4—1516no—
183C2×C32×C5C2×C4⋊C412yescomplemented
184C2×C32×C5C23×C411yescharacteristic
185C3⋊D15C2×C4⋊C414yescomplemented
186C5×C3⋊D3C2×C4⋊C414yescomplemented
187C32×D5C2×C4⋊C412yescomplemented
188C32×D5C22×D411yescharacteristic
189C32×D5C22×Q811yescharacteristic
190C23×D5—91no—
191C22×AGL(1,𝔽5)—32no—
192C22×AGL(1,𝔽5)—94no—
193C22×AGL(1,𝔽5)—91no—
194C22×AGL(1,𝔽5)—94no—
195C22×AGL(1,𝔽5)—184no—
196C22×AGL(1,𝔽5)—184no—
197C22×AGL(1,𝔽5)D3211yescharacteristic
198C22×C4×C5—91no—
199C22×Dic5—91no—
200C2×C4×D5—32no—
201C2×C4×D5—94no—
202C2×C4×D5—94no—
203C2×C4×D5—92no—
204C4⋊AGL(1,𝔽5)—38no—
205C4⋊AGL(1,𝔽5)—98no—
206C23×C32—51no—
207C22×C3⋊D3—51no—
208C22×C3⋊D3—54no—
209C22×C3⋊D3—54no—
210C22×C3⋊D3—52no—
211C22×C3⋊D3—52no—
212C22×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic
213C2×C32×C4—52no—
214C2×C32×C4—102no—
215C2×C3⋊Dic3—52no—
216C2×C3⋊Dic3—102no—
217C4×C3⋊D3—108no—
218C2×C3×Dic3—52no—
219C2×C3×Dic3—54no—
220C2×C3×Dic3—54no—
221C2×C3×Dic3—54no—
222C2×C3×Dic3—104no—
223C2×C3×Dic3C2×AGL(1,𝔽5)12yescomplemented
224#624—54no—
225#624—58no—
226#624—108no—
227#624C2×AGL(1,𝔽5)14yescomplemented
228C22×C4⋊C4—451noSylow
229C22×C3×C5—21no—
230C22×C3×C5C2×C4×D312yes—
231C2×D15—38no—
232C2×D15—34no—
233C2×D15—64no—
234C2×D15—62no—
235C2×C5×D3—38no—
236C2×C5×D3—34no—
237C2×C5×D3—64no—
238C2×C5×D3—62no—
239C2×C3×D5—21no—
240C2×C3×D5—22no—
241C2×C3×D5—21no—
242C2×C3×D5—22no—
243C2×C3×D5C2×C4×D312yes—
244C2×C3×D5D3×D414yes—
245C2×C3×D5D3×Q814yes—
246C2×C3×D5C23×D312yes—
247D3×D5—316no—
248D3×D5—38no—
249D3×D5—38no—
250D3×D5—68no—
251D3×D5—64no—
252D3×D5—64no—
253ΓL(1,𝔽16)—24no—
254ΓL(1,𝔽16)—62no—
255ΓL(1,𝔽16)—62no—
256ΓL(1,𝔽16)—64no—
257C3×AGL(1,𝔽5)—22no—
258C3×AGL(1,𝔽5)—22no—
259C3×AGL(1,𝔽5)—24no—
260C3×AGL(1,𝔽5)—64no—
261C3×C4×C5—34no—
262Dic15C2×C4×D314yescomplemented
263C3×Dic5—34no—
264C5×Dic3C2×C4×D314yescomplemented
265C23×D3—152no—
266C23×D3—301no—
267C22×C3×C4—52no—
268C22×C3×C4—101no—
269C22×C3×C4—152no—
270C22×C3×C4—152no—
271C22×Dic3—52no—
272C22×Dic3—52no—
273C22×Dic3—152no—
274C22×Dic3—301no—
275C2×C4×D3—32no—
276C2×C4×D3—158no—
277C2×C4×D3—158no—
278C2×C4×D3—152no—
279C2×C4×D3—152no—
280C2×C4×D3—152no—
281C2×C4×D3—158no—
282C2×C4×D3—158no—
283C2×C4×D3—304no—
284C2×C4×D3—308no—
285C2×C4×D3—308no—
286C2×C4×D3—304no—
287C2×C4×D3—304no—
288C3×C4⋊C4—158no—
289C4⋊Dic3—158no—
290Dic3⋊C4—58no—
291Dic3⋊C4—158no—
292C32×C5C22×C4⋊C411yescharacteristic, complemented, Hall
293C23×C5—91no—
294C22×D5—91no—
295C22×D5—92no—
296C22×D5—94no—
297C22×D5—92no—
298C22×D5—94no—
299C22×D5C2×D3211yescharacteristic
300C2×AGL(1,𝔽5)—22no—
301C2×AGL(1,𝔽5)—34no—
302C2×AGL(1,𝔽5)—64no—
303C2×AGL(1,𝔽5)—92no—
304C2×AGL(1,𝔽5)—188no—
305C2×AGL(1,𝔽5)—188no—
306C2×AGL(1,𝔽5)—182no—
307C2×AGL(1,𝔽5)C2×D3212yes—
308C2×C4×C5—32no—
309C2×C4×C5—94no—
310C2×Dic5—32no—
311C2×Dic5—94no—
312C4×D5—34no—
313C4×D5—34no—
314C4×D5—98no—
315C22×C32—52no—
316C22×C32—52no—
317C22×C32—51no—
318C22×C32—51no—
319C22×C32C22×AGL(1,𝔽5)11yescharacteristic
320C2×C3⋊D3—54no—
321C2×C3⋊D3—52no—
322C2×C3⋊D3—58no—
323C2×C3⋊D3—54no—
324C2×C3⋊D3—54no—
325C2×C3⋊D3C4⋊AGL(1,𝔽5)14yescomplemented
326C2×C3⋊D3C22×AGL(1,𝔽5)12yes—
327C32×C4—102no—
328C3⋊Dic3—102no—
329C3×Dic3—54no—
330C3×Dic3—104no—
331C3×Dic3C22×AGL(1,𝔽5)14yescomplemented
332C23×C4—451no—
333C23×C4—451no—
334C23×C4—451no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—458no—
337C2×C4⋊C4—452no—
338C2×C3×C5—21no—
339C2×C3×C5—22no—
340C2×C3×C5D3×C4⋊C414yescomplemented
341C2×C3×C5C22×C4×D312yes—
342D15—38no—
343D15—64no—
344C3×D5—21no—
345C3×D5—21no—
346C3×D5—22no—
347C3×D5D3×C4⋊C414yescomplemented
348C3×D5C2×D3×D412yes—
349C3×D5C2×D3×Q812yes—
350C5×D3—38no—
351C5×D3—64no—
352C23×C3—52no—
353C23×C3—101no—
354C22×D3—32no—
355C22×D3—61no—
356C22×D3—154no—
357C22×D3—154no—
358C22×D3—158no—
359C22×D3—158no—
360C22×D3—152no—
361C22×D3—302no—
362C22×D3—304no—
363C22×D3—302no—
364C22×D3—304no—
365C22×D3—301no—
366C2×C3×C4—32no—
367C2×C3×C4—54no—
368C2×C3×C4—102no—
369C2×C3×C4—104no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—154no—
373C2×C3×C4—154no—
374C2×C3×C4—152no—
375C2×C3×C4—154no—
376C2×C3×C4—304no—
377C2×Dic3—52no—
378C2×Dic3—54no—
379C2×Dic3—54no—
380C2×Dic3—54no—
381C2×Dic3—104no—
382C2×Dic3—154no—
383C2×Dic3—302no—
384C2×Dic3—304no—
385C2×Dic3—302no—
386C2×Dic3—302no—
387C2×Dic3D3×AGL(1,𝔽5)12yescomplemented
388C4×D3—38no—
389C4×D3—158no—
390C4×D3—158no—
391C4×D3—158no—
392C4×D3—3016no—
393C4×D3—3016no—
394C4×D3—308no—
395C4×D3—308no—
396C22×C5—92no—
397C22×C5—94no—
398C22×C5C4×D3211yescharacteristic
399C2×D5—92no—
400C2×D5—94no—
401C2×D5—94no—
402C2×D5—94no—
403C2×D5—98no—
404C2×D5#379712yes—
405C2×D5C4×D3211yescharacteristic
406C2×D5#381112yes—
407C2×D5C22×D3211yescharacteristic
408AGL(1,𝔽5)—22no—
409AGL(1,𝔽5)—64no—
410AGL(1,𝔽5)—182no—
411C4×C5—34no—
412Dic5—34no—
413C2×C32—52no—
414C2×C32—51no—
415C2×C32—51no—
416C2×C32C2×C4⋊AGL(1,𝔽5)12yescomplemented
417C2×C32C23×AGL(1,𝔽5)11yescharacteristic
418C3⋊D3—54no—
419C3⋊D3C2×C4⋊AGL(1,𝔽5)14yescomplemented
420C24—451no—
421C22×C4—51no—
422C22×C4—91no—
423C22×C4—152no—
424C22×C4—152no—
425C22×C4—452no—
426C22×C4—454no—
427C22×C4—454no—
428C22×C4—454no—
429C22×C4—451no—
430C22×C4—454no—
431C22×C4—451no—
432C22×C4—904no—
433C22×C4—904no—
434C4⋊C4—158no—
435C4⋊C4—458no—
436C3×C5—21no—
437C3×C5C2×D3×C4⋊C412yescomplemented
438C22×C3—21no—
439C22×C3—54no—
440C22×C3—54no—
441C22×C3—52no—
442C22×C3—52no—
443C22×C3—101no—
444C22×C3—102no—
445C22×C3—101no—
446C22×C3—102no—
447C22×C3C2×D3×AGL(1,𝔽5)12yes—
448C2×D3—38no—
449C2×D3—34no—
450C2×D3—64no—
451C2×D3—62no—
452C2×D3—158no—
453C2×D3—1516no—
454C2×D3—158no—
455C2×D3—158no—
456C2×D3—154no—
457C2×D3—304no—
458C2×D3—308no—
459C2×D3—304no—
460C2×D3—302no—
461C2×D3—304no—
462C3×C4—34no—
463C3×C4—104no—
464C3×C4—102no—
465C3×C4—102no—
466C3×C4—154no—
467C3×C4—304no—
468Dic3—54no—
469Dic3—104no—
470Dic3—304no—
471Dic3—302no—
472Dic3—302no—
473Dic3C2×D3×AGL(1,𝔽5)14yescomplemented
474C2×C5—94no—
475C2×C5#6388312yescomplemented
476C2×C5C2×C4×D3211yescharacteristic
477D5—94no—
478D5#6388312yescomplemented
479D5C2×#379711yescharacteristic
480D5C2×#381111yescharacteristic
481C32C22×C4⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
482C23—51no—
483C23—91no—
484C23—452no—
485C23—452no—
486C23—454no—
487C23—454no—
488C23—451no—
489C2×C4—32no—
490C2×C4—52no—
491C2×C4—94no—
492C2×C4—102no—
493C2×C4—154no—
494C2×C4—154no—
495C2×C4—152no—
496C2×C4—154no—
497C2×C4—304no—
498C2×C4—458no—
499C2×C4—454no—
500C2×C4—452no—
501C2×C4—908no—
502C2×C4—908no—
503C2×C4—902no—
504C2×C3—21no—
505C2×C3—22no—
506C2×C3—52no—
507C2×C3—54no—
508C2×C3—52no—
509C2×C3—101no—
510C2×C3—101no—
511C2×C3—102no—
512C2×C3D3×C4⋊AGL(1,𝔽5)14yescomplemented
513C2×C3C22×D3×AGL(1,𝔽5)12yes—
514D3—38no—
515D3—64no—
516D3—158no—
517D3—304no—
518C5C2×#6388311yescharacteristic, complemented, Sylow
519C22—51no—
520C22—51no—
521C22—52no—
522C22—52no—
523C22—92no—
524C22—94no—
525C22—454no—
526C22—454no—
527C22—458no—
528C22—452no—
529C22—454no—
530C22D32×AGL(1,𝔽5)11yescharacteristic
531C4—34no—
532C4—102no—
533C4—154no—
534C4—304no—
535C4—902no—
536C3—21no—
537C3C2×D3×C4⋊AGL(1,𝔽5)12yescomplemented
538C2—51no—
539C2—51no—
540C2—52no—
541C2—94no—
542C2—454no—
543C2#1308840712yesdirect product factor
544C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC22D32×AGL(1,𝔽5)
commutatorC2×C32×C5C23×C4
FrattiniC2C2×D32×AGL(1,𝔽5)
Fitting, socleC22×C32×C5C22×C4
prime radicalC22×D5×C3⋊D3C22
cosocleC2×C32×D5C24
hypocenterC32×C5C22×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
4. C2×Dic3⋊ΓL(1,𝔽16)C2semidirect
5. C2×C3×Dic3⋊AGL(1,𝔽5)C2semidirect
6. #13088407C2direct (N × H)
16. C2×#67155C4semidirect
17. C2×#67149C4semidirect
18. C2×C5×#624C4semidirect
20. D5×#624C4semidirect
22. Dic3⋊ΓL(1,𝔽16)C22semidirect
23. C3×Dic3⋊AGL(1,𝔽5)C22semidirect
32. C2×Dic3⋊AGL(1,𝔽5)D3semidirect
49. C2×C3×Dic15C2×C4semidirect
50. C2×C3×C5×Dic3C2×C4semidirect
51. #67155C2×C4semidirect
52. #67149C2×C4semidirect
53. C5×#624C2×C4semidirect
54. C3×D5×Dic3C2×C4semidirect
89. Dic3⋊AGL(1,𝔽5)C2×D3semidirect
92. C2×C3⋊D15C4⋊C4semidirect
94. C2×C5×C3⋊D3C4⋊C4semidirect
100. D5×C3⋊D3C4⋊C4semidirect
106. C3×Dic15C22×C4semidirect
107. C3×C5×Dic3C22×C4semidirect
127. C2×#624AGL(1,𝔽5)semidirect
163. C2×Dic15C4×D3semidirect
165. C2×C5×Dic3C4×D3semidirect
172. D5×Dic3C4×D3semidirect
183. C2×C32×C5C2×C4⋊C4semidirect
185. C3⋊D15C2×C4⋊C4semidirect
186. C5×C3⋊D3C2×C4⋊C4semidirect
187. C32×D5C2×C4⋊C4semidirect
223. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
227. #624C2×AGL(1,𝔽5)semidirect
262. Dic15C2×C4×D3semidirect
264. C5×Dic3C2×C4×D3semidirect
292. C32×C5C22×C4⋊C4semidirect
325. C2×C3⋊D3C4⋊AGL(1,𝔽5)semidirect
331. C3×Dic3C22×AGL(1,𝔽5)semidirect
340. C2×C3×C5D3×C4⋊C4semidirect
347. C3×D5D3×C4⋊C4semidirect
387. C2×Dic3D3×AGL(1,𝔽5)semidirect
416. C2×C32C2×C4⋊AGL(1,𝔽5)semidirect
419. C3⋊D3C2×C4⋊AGL(1,𝔽5)semidirect
437. C3×C5C2×D3×C4⋊C4semidirect
473. Dic3C2×D3×AGL(1,𝔽5)semidirect
475. C2×C5#63883semidirect
478. D5#63883semidirect
481. C32C22×C4⋊AGL(1,𝔽5)semidirect
512. C2×C3D3×C4⋊AGL(1,𝔽5)semidirect
518. C5C2×#63883semidirect
537. C3C2×D3×C4⋊AGL(1,𝔽5)semidirect
543. C2#13088407direct (N × H)

Maximal subgroups

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

subgroupindex
C22×ΓL(1,𝔽16)⋊D32
C22×C3⋊D3×AGL(1,𝔽5)2
C2×D5×#6242
C2×Dic3⋊ΓL(1,𝔽16)2
C2×C3×Dic3⋊AGL(1,𝔽5)2
#130884072
C2×D3×C4⋊AGL(1,𝔽5)3
C2×#638835