Finite Group Databasebeta

← C4×D32×AGL(1,𝔽5) #72230264

Subgroups — C4×D32×AGL(1,𝔽5) #72230264

Order 2880.

2100 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×AGL(1,𝔽5)C212yesmaximal
2C4×D32×D5C211yesmaximal, characteristic
3C4×ΓL(1,𝔽16)⋊D3C211yesmaximal, characteristic, complemented
4C4×D3×ΓL(1,𝔽16)C212yesmaximal, complemented
5C4×C3⋊D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6C3×C4×D3×AGL(1,𝔽5)C212yesmaximal, complemented
7AGL(1,𝔽5)×#624C212yesmaximal, complemented
8D3×Dic3×AGL(1,𝔽5)C214yesmaximal, complemented
9C2×C4×D3×AGL(1,𝔽5)—32nomaximal
10C2×D32×D5C2211yescharacteristic
11C2×ΓL(1,𝔽16)⋊D3C2212yes—
12C2×D3×ΓL(1,𝔽16)C2214yes—
13C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
14C2×C3×D3×AGL(1,𝔽5)C2214yes—
15D32×AGL(1,𝔽5)C4116yesdirect product factor
16C4×(C3⋊D3)⋊D5C411yescharacteristic, complemented
17C4×D3×D15C412yescomplemented
18C4×C5×D32C411yescharacteristic, complemented
19C4×D5×C3⋊D3C2211yescharacteristic
20C3×C4×D3×D5C2212yes—
21C4×C3⋊ΓL(1,𝔽16)C2211yescharacteristic, complemented
22C3×C4×ΓL(1,𝔽16)C2212yescomplemented
23C32×C4×AGL(1,𝔽5)C2211yescharacteristic, complemented
24#10624022C411yescharacteristic, complemented
25D3×#1200C412yescomplemented
26D32×Dic5C411yescharacteristic, complemented
27D5×#624C2211yescharacteristic
28D3×D5×Dic3C2212yes—
29ΓL(1,𝔽16)⋊Dic3C2212yescomplemented
30Dic3×ΓL(1,𝔽16)C2214yescomplemented
31AGL(1,𝔽5)×C3⋊Dic3C2212yescomplemented
32C3×Dic3×AGL(1,𝔽5)C2214yescomplemented
33C42×D32—51nomaximal, Hall
34C22×D3×AGL(1,𝔽5)—34no—
35C2×C4×D3×D5—32no—
36C2×C4×ΓL(1,𝔽16)—32no—
37C2×C3×C4×AGL(1,𝔽5)—32no—
38C2×Dic3×AGL(1,𝔽5)—34no—
39C4×D3×AGL(1,𝔽5)—34no—
40C4×D3×AGL(1,𝔽5)—32no—
41C4×D3×AGL(1,𝔽5)—32no—
42C4×D3×AGL(1,𝔽5)—32no—
43C4×D3×AGL(1,𝔽5)—34no—
44C4×D3×AGL(1,𝔽5)—61no—
45C4×D3×AGL(1,𝔽5)D312yesdirect product factor
46C2×(C3⋊D3)⋊D5C2×C411yescharacteristic
47C2×D3×D15C2×C412yes—
48C2×C5×D32C2×C411yescharacteristic
49C2×D5×C3⋊D3C2311yescharacteristic
50C2×C3×D3×D5C2312yes—
51C2×C3⋊ΓL(1,𝔽16)C2312yes—
52C2×C3×ΓL(1,𝔽16)C2314yes—
53C2×C32×AGL(1,𝔽5)C2312yes—
54D32×D5C2×C418yes—
55ΓL(1,𝔽16)⋊D3C2×C418yescomplemented
56D3×ΓL(1,𝔽16)C2×C4116yescomplemented
57C3⋊D3×AGL(1,𝔽5)C2×C418yescomplemented
58C3×D3×AGL(1,𝔽5)C2×C4116yescomplemented
59C4×C3⋊D15C2×C411yescharacteristic, complemented
60C4×C5×C3⋊D3C2×C411yescharacteristic, complemented
61C3×C4×D15C2×C412yescomplemented
62C3×C4×C5×D3C2×C412yescomplemented
63C32×C4×D5C2311yescharacteristic
64#67155C2×C411yescharacteristic, complemented
65#67154C2×C412yescomplemented
66#67149C2×C412yescomplemented
67D3×Dic15C2×C412yescomplemented
68Dic3×D15C2×C412yescomplemented
69C5×#624C2×C411yescharacteristic, complemented
70C5×D3×Dic3C2×C412yescomplemented
71#67137C2×C411yescharacteristic, complemented
72C3⋊D3×Dic5C2×C411yescharacteristic, complemented
73D5×C3⋊Dic3C2311yescharacteristic
74C3×#1200C2×C412yescomplemented
75C3×D3×Dic5C2×C412yescomplemented
76C3×D5×Dic3C2312yes—
77C22×C4×AGL(1,𝔽5)—91noHall
78C2×C4×D32—52no—
79C2×C4×D32—51no—
80C42×C3⋊D3—51no—
81C3×C42×D3—52no—
82C4×#624—52no—
83C4×#624—51no—
84C4×D3×Dic3—54no—
85C4×D3×Dic3—52no—
86C22×D3×D5—32no—
87C22×ΓL(1,𝔽16)—34no—
88C22×C3×AGL(1,𝔽5)—34no—
89C2×D3×AGL(1,𝔽5)—34no—
90C2×D3×AGL(1,𝔽5)—34no—
91C2×D3×AGL(1,𝔽5)—34no—
92C2×D3×AGL(1,𝔽5)—332no—
93C2×D3×AGL(1,𝔽5)—62no—
94C2×D3×AGL(1,𝔽5)C2×D314yes—
95C2×C4×D15—32no—
96C2×C4×C5×D3—32no—
97C2×C3×C4×D5—32no—
98C2×#1200—32no—
99C2×D3×Dic5—32no—
100C2×D5×Dic3—32no—
101C4×D3×D5—32no—
102C4×D3×D5—32no—
103C4×D3×D5—32no—
104C4×D3×D5—32no—
105C4×D3×D5—32no—
106C4×D3×D5—32no—
107C4×D3×D5—32no—
108C4×D3×D5—61no—
109C4×D3×D5C2×D312yes—
110C4×ΓL(1,𝔽16)—34no—
111C4×ΓL(1,𝔽16)—32no—
112C4×ΓL(1,𝔽16)—61no—
113C4×ΓL(1,𝔽16)C2×D312yescomplemented
114C3×C4×AGL(1,𝔽5)—21no—
115C3×C4×AGL(1,𝔽5)—34no—
116C3×C4×AGL(1,𝔽5)—32no—
117C3×C4×AGL(1,𝔽5)C2×D312yescomplemented
118Dic3×AGL(1,𝔽5)—34no—
119Dic3×AGL(1,𝔽5)—34no—
120Dic3×AGL(1,𝔽5)—34no—
121Dic3×AGL(1,𝔽5)—62no—
122Dic3×AGL(1,𝔽5)C2×D314yescomplemented
123C2×C42×D3—152no—
124C2×C3⋊D15C22×C411yescharacteristic
125C2×C5×C3⋊D3C22×C411yescharacteristic
126C2×C3×D15C22×C412yes—
127C2×C3×C5×D3C22×C412yes—
128C2×C32×D5C2411yescharacteristic
129(C3⋊D3)⋊D5C4214yescomplemented
130D3×D15C4218yescomplemented
131C5×D32C4214yescomplemented
132D5×C3⋊D3C22×C414yes—
133C3×D3×D5C22×C418yes—
134C3⋊ΓL(1,𝔽16)C22×C414yescomplemented
135C3×ΓL(1,𝔽16)C22×C418yescomplemented
136C32×AGL(1,𝔽5)C22×C414yescomplemented
137C32×C4×C5C22×C411yescharacteristic, complemented
138C3⋊Dic15C22×C411yescharacteristic, complemented
139C5×C3⋊Dic3C22×C411yescharacteristic, complemented
140C3×Dic15C22×C412yescomplemented
141C3×C5×Dic3C22×C412yescomplemented
142C32×Dic5C22×C411yescharacteristic, complemented
143C23×AGL(1,𝔽5)—92no—
144C22×C4×D5—91no—
145C2×C4×AGL(1,𝔽5)—32no—
146C2×C4×AGL(1,𝔽5)—92no—
147C2×C4×AGL(1,𝔽5)—91no—
148C2×C4×AGL(1,𝔽5)—92no—
149C2×C4×AGL(1,𝔽5)—94no—
150C2×C4×AGL(1,𝔽5)—91no—
151C22×D32—51no—
152C2×C4×C3⋊D3—52no—
153C2×C4×C3⋊D3—51no—
154C2×C3×C4×D3—54no—
155C2×C3×C4×D3—52no—
156C2×#624—52no—
157C2×#624—51no—
158C2×D3×Dic3—54no—
159C2×D3×Dic3—52no—
160C4×D32—516no—
161C4×D32—51no—
162C4×D32—51no—
163C4×D32—52no—
164C4×D32—51no—
165C4×D32—52no—
166C4×D32AGL(1,𝔽5)11yescharacteristic, direct product factor
167C32×C42—51no—
168C4×C3⋊Dic3—51no—
169C4×C3⋊Dic3—52no—
170C3×C4×Dic3—52no—
171C3×C4×Dic3—54no—
172Dic32—54no—
173Dic32—52no—
174C22×D15—32no—
175C22×C5×D3—32no—
176C22×C3×D5—32no—
177C2×D3×D5—32no—
178C2×D3×D5—32no—
179C2×D3×D5—32no—
180C2×D3×D5—316no—
181C2×D3×D5—61no—
182C2×D3×D5C22×D312yes—
183C2×ΓL(1,𝔽16)—34no—
184C2×ΓL(1,𝔽16)—316no—
185C2×ΓL(1,𝔽16)—62no—
186C2×ΓL(1,𝔽16)C22×D314yes—
187C2×C3×AGL(1,𝔽5)—22no—
188C2×C3×AGL(1,𝔽5)—34no—
189C2×C3×AGL(1,𝔽5)—316no—
190C2×C3×AGL(1,𝔽5)C22×D314yes—
191D3×AGL(1,𝔽5)—316no—
192D3×AGL(1,𝔽5)—316no—
193D3×AGL(1,𝔽5)—316no—
194D3×AGL(1,𝔽5)—68no—
195D3×AGL(1,𝔽5)C4×D3116yesdirect product factor
196C2×C3×C4×C5—32no—
197C2×Dic15—32no—
198C4×D15—32no—
199C4×D15—32no—
200C4×D15—32no—
201C4×D15—61no—
202C4×D15C4×D312yescomplemented
203C2×C5×Dic3—32no—
204C4×C5×D3—32no—
205C4×C5×D3—32no—
206C4×C5×D3—32no—
207C4×C5×D3—61no—
208C4×C5×D3C4×D312yescomplemented
209C2×C3×Dic5—32no—
210C3×C4×D5—21no—
211C3×C4×D5—32no—
212C3×C4×D5—32no—
213C3×C4×D5—32no—
214C3×C4×D5C22×D312yes—
215#1200—32no—
216#1200—32no—
217#1200—32no—
218#1200—61no—
219#1200C4×D312yescomplemented
220D3×Dic5—32no—
221D3×Dic5—32no—
222D3×Dic5—32no—
223D3×Dic5—61no—
224D3×Dic5C4×D312yescomplemented
225D5×Dic3—32no—
226D5×Dic3—32no—
227D5×Dic3—32no—
228D5×Dic3—61no—
229D5×Dic3C22×D312yes—
230C22×C4×D3—152no—
231C22×C4×D3—154no—
232C2×C3×C42—152no—
233C2×C4×Dic3—154no—
234C2×C4×Dic3—152no—
235C42×D3—52no—
236C42×D3—154no—
237C42×D3—152no—
238C42×D3—152no—
239C42×D3—152no—
240C42×D3—154no—
241C42×D3—301no—
242C2×C32×C5C23×C411yescharacteristic
243C3⋊D15C2×C4212yescomplemented
244C5×C3⋊D3C2×C4212yescomplemented
245C3×D15C2×C4214yescomplemented
246C3×C5×D3C2×C4214yescomplemented
247C32×D5C23×C412yes—
248C23×D5—91no—
249C22×AGL(1,𝔽5)—34no—
250C22×AGL(1,𝔽5)—92no—
251C22×AGL(1,𝔽5)—916no—
252C22×AGL(1,𝔽5)—94no—
253C22×AGL(1,𝔽5)—92no—
254C22×C4×C5—91no—
255C22×Dic5—91no—
256C2×C4×D5—32no—
257C2×C4×D5—91no—
258C2×C4×D5—91no—
259C2×C4×D5—91no—
260C2×C4×D5—92no—
261C2×C4×D5—92no—
262C2×C4×D5—92no—
263C2×C4×D5—91no—
264C4×AGL(1,𝔽5)—34no—
265C4×AGL(1,𝔽5)—32no—
266C4×AGL(1,𝔽5)—94no—
267C4×AGL(1,𝔽5)—92no—
268C4×AGL(1,𝔽5)—92no—
269C4×AGL(1,𝔽5)—91no—
270C4×AGL(1,𝔽5)D3211yescharacteristic, direct product factor
271C22×C3⋊D3—51no—
272C22×C3×D3—52no—
273C2×D32—51no—
274C2×D32—52no—
275C2×D32—58no—
276C2×D32C2×AGL(1,𝔽5)11yescharacteristic
277C2×C32×C4—52no—
278C2×C32×C4—51no—
279C2×C3⋊Dic3—52no—
280C2×C3⋊Dic3—51no—
281C4×C3⋊D3—58no—
282C4×C3⋊D3—51no—
283C4×C3⋊D3—51no—
284C4×C3⋊D3—51no—
285C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
286C2×C3×Dic3—54no—
287C2×C3×Dic3—52no—
288C3×C4×D3—516no—
289C3×C4×D3—52no—
290C3×C4×D3—52no—
291C3×C4×D3—52no—
292C3×C4×D3C2×AGL(1,𝔽5)12yescomplemented
293#624—58no—
294#624—51no—
295#624—52no—
296#624C2×AGL(1,𝔽5)11yescharacteristic, complemented
297D3×Dic3—516no—
298D3×Dic3—52no—
299D3×Dic3—52no—
300D3×Dic3—52no—
301D3×Dic3C2×AGL(1,𝔽5)12yescomplemented
302C22×C42—451noSylow
303C22×C3×C5—32no—
304C2×D15—32no—
305C2×D15—38no—
306C2×D15—61no—
307C2×D15C2×C4×D312yes—
308C2×C5×D3—32no—
309C2×C5×D3—38no—
310C2×C5×D3—61no—
311C2×C5×D3C2×C4×D312yes—
312C2×C3×D5—21no—
313C2×C3×D5—32no—
314C2×C3×D5—38no—
315C2×C3×D5C23×D312yes—
316D3×D5—38no—
317D3×D5—38no—
318D3×D5—38no—
319D3×D5—64no—
320D3×D5C2×C4×D318yes—
321ΓL(1,𝔽16)—38no—
322ΓL(1,𝔽16)—64no—
323ΓL(1,𝔽16)C2×C4×D318yescomplemented
324C3×AGL(1,𝔽5)—24no—
325C3×AGL(1,𝔽5)—38no—
326C3×AGL(1,𝔽5)C2×C4×D318yescomplemented
327C3×C4×C5—21no—
328C3×C4×C5—32no—
329C3×C4×C5C2×C4×D312yescomplemented
330Dic15—32no—
331Dic15—61no—
332Dic15C2×C4×D312yescomplemented
333C3×Dic5—21no—
334C3×Dic5—32no—
335C3×Dic5C2×C4×D312yescomplemented
336C5×Dic3—32no—
337C5×Dic3—61no—
338C5×Dic3C2×C4×D312yescomplemented
339C23×D3—152no—
340C22×C3×C4—152no—
341C22×C3×C4—154no—
342C22×Dic3—152no—
343C22×Dic3—154no—
344C2×C4×D3—32no—
345C2×C4×D3—54no—
346C2×C4×D3—52no—
347C2×C4×D3—152no—
348C2×C4×D3—152no—
349C2×C4×D3—152no—
350C2×C4×D3—152no—
351C2×C4×D3—152no—
352C2×C4×D3—152no—
353C2×C4×D3—152no—
354C2×C4×D3—152no—
355C2×C4×D3—152no—
356C2×C4×D3—1532no—
357C2×C4×D3—154no—
358C2×C4×D3—154no—
359C2×C4×D3—154no—
360C2×C4×D3—152no—
361C2×C4×D3—301no—
362C2×C4×D3—302no—
363C3×C42—52no—
364C3×C42—101no—
365C3×C42—154no—
366C3×C42—152no—
367C4×Dic3—54no—
368C4×Dic3—52no—
369C4×Dic3—154no—
370C4×Dic3—154no—
371C4×Dic3—154no—
372C4×Dic3—154no—
373C4×Dic3—152no—
374C4×Dic3—302no—
375C4×Dic3—301no—
376C32×C5C22×C4211yescharacteristic, complemented, Hall
377C23×C5—91no—
378C22×D5—32no—
379C22×D5—91no—
380C22×D5—98no—
381C22×D5—92no—
382C22×D5—91no—
383C2×AGL(1,𝔽5)—34no—
384C2×AGL(1,𝔽5)—316no—
385C2×AGL(1,𝔽5)—98no—
386C2×AGL(1,𝔽5)—916no—
387C2×AGL(1,𝔽5)—92no—
388C2×AGL(1,𝔽5)—98no—
389C2×AGL(1,𝔽5)C2×D3212yes—
390C2×C4×C5—32no—
391C2×C4×C5—91no—
392C2×C4×C5—92no—
393C2×C4×C5—91no—
394C2×Dic5—32no—
395C2×Dic5—91no—
396C2×Dic5—92no—
397C2×Dic5—91no—
398C4×D5—32no—
399C4×D5—32no—
400C4×D5—32no—
401C4×D5—92no—
402C4×D5—92no—
403C4×D5—92no—
404C4×D5—91no—
405C4×D5—91no—
406C4×D5—91no—
407C4×D5C2×D3211yescharacteristic
408C22×C32—51no—
409C2×C3⋊D3—51no—
410C2×C3⋊D3—54no—
411C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
412C2×C3×D3—52no—
413C2×C3×D3—58no—
414C2×C3×D3C22×AGL(1,𝔽5)12yes—
415D32—54no—
416D32—58no—
417D32C4×AGL(1,𝔽5)14yesdirect product factor
418C32×C4—54no—
419C32×C4—51no—
420C32×C4C22×AGL(1,𝔽5)11yescharacteristic, complemented
421C3⋊Dic3—54no—
422C3⋊Dic3—51no—
423C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic, complemented
424C3×Dic3—58no—
425C3×Dic3—52no—
426C3×Dic3C22×AGL(1,𝔽5)12yescomplemented
427C23×C4—451no—
428C23×C4—452no—
429C2×C42—152no—
430C2×C42—451no—
431C2×C42—451no—
432C2×C42—452no—
433C2×C42—452no—
434C2×C42—454no—
435C2×C3×C5—21no—
436C2×C3×C5—34no—
437C2×C3×C5C22×C4×D312yes—
438D15—34no—
439D15—62no—
440D15C42×D314yescomplemented
441C3×D5—22no—
442C3×D5—34no—
443C3×D5C22×C4×D314yes—
444C5×D3—34no—
445C5×D3—62no—
446C5×D3C42×D314yescomplemented
447C23×C3—152no—
448C22×D3—32no—
449C22×D3—52no—
450C22×D3—152no—
451C22×D3—1516no—
452C22×D3—152no—
453C22×D3—152no—
454C22×D3—152no—
455C22×D3—301no—
456C2×C3×C4—32no—
457C2×C3×C4—54no—
458C2×C3×C4—52no—
459C2×C3×C4—101no—
460C2×C3×C4—102no—
461C2×C3×C4—152no—
462C2×C3×C4—152no—
463C2×C3×C4—152no—
464C2×C3×C4—1516no—
465C2×C3×C4—154no—
466C2×C3×C4—152no—
467C2×Dic3—32no—
468C2×Dic3—54no—
469C2×Dic3—52no—
470C2×Dic3—152no—
471C2×Dic3—152no—
472C2×Dic3—152no—
473C2×Dic3—1516no—
474C2×Dic3—154no—
475C2×Dic3—152no—
476C2×Dic3—301no—
477C2×Dic3—302no—
478C4×D3—32no—
479C4×D3—32no—
480C4×D3—32no—
481C4×D3—516no—
482C4×D3—52no—
483C4×D3—52no—
484C4×D3—52no—
485C4×D3—61no—
486C4×D3—152no—
487C4×D3—152no—
488C4×D3—152no—
489C4×D3—152no—
490C4×D3—1516no—
491C4×D3—152no—
492C4×D3—152no—
493C4×D3—1516no—
494C4×D3—1516no—
495C4×D3—152no—
496C4×D3—152no—
497C4×D3—152no—
498C4×D3—301no—
499C4×D3—301no—
500C4×D3—301no—
501C4×D3—308no—
502C4×D3D3×AGL(1,𝔽5)12yesdirect product factor
503C22×C5—32no—
504C22×C5—94no—
505C22×C5—91no—
506C2×D5—32no—
507C2×D5—38no—
508C2×D5—94no—
509C2×D5—98no—
510C2×D5—91no—
511C2×D5—94no—
512C2×D5C22×D3211yescharacteristic
513AGL(1,𝔽5)—38no—
514AGL(1,𝔽5)—94no—
515AGL(1,𝔽5)C4×D3214yesdirect product factor
516C4×C5—32no—
517C4×C5—91no—
518C4×C5C4×D3211yescharacteristic, complemented
519Dic5—32no—
520Dic5—91no—
521Dic5C4×D3211yescharacteristic, complemented
522C2×C32—52no—
523C2×C32C23×AGL(1,𝔽5)11yescharacteristic
524C3⋊D3—52no—
525C3⋊D3C2×C4×AGL(1,𝔽5)12yescomplemented
526C3×D3—54no—
527C3×D3C2×C4×AGL(1,𝔽5)14yescomplemented
528C24—451no—
529C22×C4—91no—
530C22×C4—152no—
531C22×C4—154no—
532C22×C4—452no—
533C22×C4—451no—
534C22×C4—452no—
535C22×C4—451no—
536C22×C4—451no—
537C22×C4—452no—
538C22×C4—451no—
539C22×C4—452no—
540C22×C4—451no—
541C22×C4—452no—
542C22×C4—4516no—
543C22×C4—454no—
544C42—51no—
545C42—154no—
546C42—152no—
547C42—452no—
548C42—451no—
549C42—454no—
550C42—452no—
551C3×C5—21no—
552C3×C5C2×C42×D312yescomplemented
553C22×C3—32no—
554C22×C3—52no—
555C22×C3—101no—
556C22×C3—158no—
557C22×C3—152no—
558C2×D3—32no—
559C2×D3—38no—
560C2×D3—52no—
561C2×D3—58no—
562C2×D3—61no—
563C2×D3—158no—
564C2×D3—158no—
565C2×D3—158no—
566C2×D3—152no—
567C2×D3—158no—
568C2×D3—304no—
569C2×D3—301no—
570C2×D3C2×D3×AGL(1,𝔽5)12yes—
571C3×C4—21no—
572C3×C4—32no—
573C3×C4—58no—
574C3×C4—52no—
575C3×C4—101no—
576C3×C4—104no—
577C3×C4—158no—
578C3×C4—152no—
579C3×C4C2×D3×AGL(1,𝔽5)12yescomplemented
580Dic3—32no—
581Dic3—58no—
582Dic3—52no—
583Dic3—61no—
584Dic3—158no—
585Dic3—152no—
586Dic3—301no—
587Dic3—304no—
588Dic3C2×D3×AGL(1,𝔽5)12yescomplemented
589C2×C5—34no—
590C2×C5—92no—
591C2×C5C2×C4×D3211yescharacteristic
592D5—34no—
593D5—92no—
594D5C2×C4×D3212yes—
595C32C22×C4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
596C23—91no—
597C23—152no—
598C23—452no—
599C23—451no—
600C23—458no—
601C23—451no—
602C2×C4—32no—
603C2×C4—52no—
604C2×C4—51no—
605C2×C4—91no—
606C2×C4—92no—
607C2×C4—91no—
608C2×C4—152no—
609C2×C4—152no—
610C2×C4—152no—
611C2×C4—1516no—
612C2×C4—154no—
613C2×C4—152no—
614C2×C4—452no—
615C2×C4—452no—
616C2×C4—451no—
617C2×C4—451no—
618C2×C4—458no—
619C2×C4—452no—
620C2×C4—451no—
621C2×C4—451no—
622C2×C4—458no—
623C2×C4—452no—
624C2×C4—4516no—
625C2×C4—452no—
626C2×C4—451no—
627C2×C3—21no—
628C2×C3—34no—
629C2×C3—54no—
630C2×C3—102no—
631C2×C3—154no—
632C2×C3C22×D3×AGL(1,𝔽5)12yes—
633D3—34no—
634D3—54no—
635D3—62no—
636D3—154no—
637D3—302no—
638D3C4×D3×AGL(1,𝔽5)14yesdirect product factor
639C5C42×D3211yescharacteristic, complemented, Sylow
640C22—32no—
641C22—51no—
642C22—94no—
643C22—91no—
644C22—158no—
645C22—152no—
646C22—458no—
647C22—454no—
648C22—454no—
649C22—451no—
650C4—32no—
651C4—54no—
652C4—51no—
653C4—91no—
654C4—158no—
655C4—152no—
656C4—454no—
657C4—451no—
658C4D32×AGL(1,𝔽5)11yescharacteristic, direct product factor
659C3—21no—
660C3C2×C4×D3×AGL(1,𝔽5)12yescomplemented
661C2—34no—
662C2—52no—
663C2—92no—
664C2—154no—
665C2—452no—
666C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC4D32×AGL(1,𝔽5)
commutator, hypocenterC32×C5C22×C42
FrattiniC2C2×D32×AGL(1,𝔽5)
FittingC32×C4×C5C22×C4
socleC2×C32×C5C23×C4
prime radicalC2×D32×D5C22
cosocleC2×C32×D5C24
LCSG ▷ C32×C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
3. C4×ΓL(1,𝔽16)⋊D3C2semidirect
4. C4×D3×ΓL(1,𝔽16)C2semidirect
5. C4×C3⋊D3×AGL(1,𝔽5)C2semidirect
6. C3×C4×D3×AGL(1,𝔽5)C2semidirect
7. AGL(1,𝔽5)×#624C2semidirect
8. D3×Dic3×AGL(1,𝔽5)C2semidirect
15. D32×AGL(1,𝔽5)C4direct (N × H)
16. C4×(C3⋊D3)⋊D5C4semidirect
17. C4×D3×D15C4semidirect
18. C4×C5×D32C4semidirect
21. C4×C3⋊ΓL(1,𝔽16)C22semidirect
22. C3×C4×ΓL(1,𝔽16)C22semidirect
23. C32×C4×AGL(1,𝔽5)C22semidirect
24. #10624022C4semidirect
25. D3×#1200C4semidirect
26. D32×Dic5C4semidirect
29. ΓL(1,𝔽16)⋊Dic3C22semidirect
30. Dic3×ΓL(1,𝔽16)C22semidirect
31. AGL(1,𝔽5)×C3⋊Dic3C22semidirect
32. C3×Dic3×AGL(1,𝔽5)C22semidirect
45. C4×D3×AGL(1,𝔽5)D3direct (N × H)
55. ΓL(1,𝔽16)⋊D3C2×C4semidirect
56. D3×ΓL(1,𝔽16)C2×C4semidirect
57. C3⋊D3×AGL(1,𝔽5)C2×C4semidirect
58. C3×D3×AGL(1,𝔽5)C2×C4semidirect
59. C4×C3⋊D15C2×C4semidirect
60. C4×C5×C3⋊D3C2×C4semidirect
61. C3×C4×D15C2×C4semidirect
62. C3×C4×C5×D3C2×C4semidirect
64. #67155C2×C4semidirect
65. #67154C2×C4semidirect
66. #67149C2×C4semidirect
67. D3×Dic15C2×C4semidirect
68. Dic3×D15C2×C4semidirect
69. C5×#624C2×C4semidirect
70. C5×D3×Dic3C2×C4semidirect
71. #67137C2×C4semidirect
72. C3⋊D3×Dic5C2×C4semidirect
74. C3×#1200C2×C4semidirect
75. C3×D3×Dic5C2×C4semidirect
113. C4×ΓL(1,𝔽16)C2×D3semidirect
117. C3×C4×AGL(1,𝔽5)C2×D3semidirect
122. Dic3×AGL(1,𝔽5)C2×D3semidirect
129. (C3⋊D3)⋊D5C42semidirect
130. D3×D15C42semidirect
131. C5×D32C42semidirect
134. C3⋊ΓL(1,𝔽16)C22×C4semidirect
135. C3×ΓL(1,𝔽16)C22×C4semidirect
136. C32×AGL(1,𝔽5)C22×C4semidirect
137. C32×C4×C5C22×C4semidirect
138. C3⋊Dic15C22×C4semidirect
139. C5×C3⋊Dic3C22×C4semidirect
140. C3×Dic15C22×C4semidirect
141. C3×C5×Dic3C22×C4semidirect
142. C32×Dic5C22×C4semidirect
166. C4×D32AGL(1,𝔽5)direct (N × H)
195. D3×AGL(1,𝔽5)C4×D3direct (N × H)
202. C4×D15C4×D3semidirect
208. C4×C5×D3C4×D3semidirect
219. #1200C4×D3semidirect
224. D3×Dic5C4×D3semidirect
243. C3⋊D15C2×C42semidirect
244. C5×C3⋊D3C2×C42semidirect
245. C3×D15C2×C42semidirect
246. C3×C5×D3C2×C42semidirect
270. C4×AGL(1,𝔽5)D32direct (N × H)
285. C4×C3⋊D3C2×AGL(1,𝔽5)semidirect
292. C3×C4×D3C2×AGL(1,𝔽5)semidirect
296. #624C2×AGL(1,𝔽5)semidirect
301. D3×Dic3C2×AGL(1,𝔽5)semidirect
323. ΓL(1,𝔽16)C2×C4×D3semidirect
326. C3×AGL(1,𝔽5)C2×C4×D3semidirect
329. C3×C4×C5C2×C4×D3semidirect
332. Dic15C2×C4×D3semidirect
335. C3×Dic5C2×C4×D3semidirect
338. C5×Dic3C2×C4×D3semidirect
376. C32×C5C22×C42semidirect
417. D32C4×AGL(1,𝔽5)direct (N × H)
420. C32×C4C22×AGL(1,𝔽5)semidirect
423. C3⋊Dic3C22×AGL(1,𝔽5)semidirect
426. C3×Dic3C22×AGL(1,𝔽5)semidirect
440. D15C42×D3semidirect
446. C5×D3C42×D3semidirect
502. C4×D3D3×AGL(1,𝔽5)direct (N × H)
515. AGL(1,𝔽5)C4×D32direct (N × H)
518. C4×C5C4×D32semidirect
521. Dic5C4×D32semidirect
525. C3⋊D3C2×C4×AGL(1,𝔽5)semidirect
527. C3×D3C2×C4×AGL(1,𝔽5)semidirect
552. C3×C5C2×C42×D3semidirect
579. C3×C4C2×D3×AGL(1,𝔽5)semidirect
588. Dic3C2×D3×AGL(1,𝔽5)semidirect
595. C32C22×C4×AGL(1,𝔽5)semidirect
638. D3C4×D3×AGL(1,𝔽5)direct (N × H)
639. C5C42×D32semidirect
658. C4D32×AGL(1,𝔽5)direct (N × H)
660. C3C2×C4×D3×AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C2×D32×AGL(1,𝔽5)2
C4×D32×D52
C4×ΓL(1,𝔽16)⋊D32
C4×D3×ΓL(1,𝔽16)2
C4×C3⋊D3×AGL(1,𝔽5)2
C3×C4×D3×AGL(1,𝔽5)2
AGL(1,𝔽5)×#6242
D3×Dic3×AGL(1,𝔽5)2
C2×C4×D3×AGL(1,𝔽5)3
C42×D325