Finite Group Databasebeta

← D3×AGL(1,𝔽5)×#97 #72277215

Subgroups — D3×AGL(1,𝔽5)×#97 #72277215

Order 3840.

3580 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#65676C211yesmaximal, characteristic
2C2×D3×#3992C212yesmaximal
3D3×D5×#97C211yesmaximal, characteristic
4C2×D3×C8×AGL(1,𝔽5)C212yesmaximal
5C42×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
6#14294227C211yesmaximal, characteristic, complemented
7AGL(1,𝔽5)×#803C211yesmaximal, characteristic, complemented
8#14294225C212yesmaximal, complemented
9AGL(1,𝔽5)×#815C212yesmaximal, complemented
10#97×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
11C3×AGL(1,𝔽5)×#97C211yesmaximal, characteristic, complemented
12C2×AGL(1,𝔽5)×#97—31nomaximal, Hall
13C2×C4×D3×AGL(1,𝔽5)C414yes—
14C2×C4×D3×AGL(1,𝔽5)C2211yescharacteristic
15C2×C4×D3×AGL(1,𝔽5)C2211yescharacteristic
16C2×D3×D5⋊C8C2212yes—
17C2×D3×C8×D5C2212yes—
18C42×D3×D5C2211yescharacteristic
19C2×#91221C2212yes—
20C2×C8×ΓL(1,𝔽16)C2212yes—
21C42×ΓL(1,𝔽16)C2211yescharacteristic
22#11752335C2211yescharacteristic
23C2×C3×#3992C2212yes—
24C2×C3×C8×AGL(1,𝔽5)C2212yes—
25C3×C42×AGL(1,𝔽5)C2211yescharacteristic
26C3×#65676C2211yescharacteristic
27#11751873C414yescomplemented
28D3×#4002C414yescomplemented
29C4×Dic3×AGL(1,𝔽5)C414yes—
30C4×Dic3×AGL(1,𝔽5)C2211yescharacteristic
31C4×Dic3×AGL(1,𝔽5)C2211yescharacteristic
32#11751788C2212yes—
33C2×#91150C2212yes—
34C2×#91149C2212yes—
35C2×ΓL(1,𝔽16)⋊C8C2212yes—
36C2×AGL(1,𝔽5)×C3⋊C8C2212yes—
37D3×#3992C4116yescomplemented
38D3×C8×AGL(1,𝔽5)C4116yescomplemented
39D15×#97C411yescharacteristic, complemented
40C5×D3×#97C411yescharacteristic, complemented
41C3×D5×#97C2211yescharacteristic
42#11747603C412yescomplemented
43D3×#3947C412yescomplemented
44D5×#815C2212yes—
45#11746983C411yescharacteristic, complemented
46D3×#3935C411yescharacteristic, complemented
47D5×#803C2211yescharacteristic
48C4×D3×#97—51nomaximal, Hall
49C22×#3992—32no—
50C22×C8×AGL(1,𝔽5)—32no—
51C2×C42×AGL(1,𝔽5)—31no—
52C2×#65676—31no—
53C2×D5×#97—31no—
54AGL(1,𝔽5)×#97—31no—
55AGL(1,𝔽5)×#97—32no—
56AGL(1,𝔽5)×#97—32no—
57AGL(1,𝔽5)×#97—31no—
58AGL(1,𝔽5)×#97—31no—
59AGL(1,𝔽5)×#97D311yescharacteristic, direct product factor
60C22×D3×AGL(1,𝔽5)C2×C412yes—
61C22×D3×AGL(1,𝔽5)C2×C412yes—
62C2×C4×D3×D5C2×C412yes—
63C2×C4×D3×D5C2311yescharacteristic
64C2×C4×ΓL(1,𝔽16)C2×C414yes—
65C2×C4×ΓL(1,𝔽16)C2311yescharacteristic
66C2×C4×ΓL(1,𝔽16)C2311yescharacteristic
67C2×D5⋊(C3⋊C8)C2312yes—
68C2×C3×C4×AGL(1,𝔽5)C2×C414yes—
69C2×C3×C4×AGL(1,𝔽5)C2311yescharacteristic
70C2×C3×C4×AGL(1,𝔽5)C2311yescharacteristic
71C2×C3×D5⋊C8C2312yes—
72C2×#6738C2×C414yes—
73C2×D3×#170C2×C414yes—
74C2×Dic3×AGL(1,𝔽5)C2×C414yes—
75C2×Dic3×AGL(1,𝔽5)C2×C414yes—
76C2×Dic3×AGL(1,𝔽5)C2×C412yes—
77C2×Dic3×AGL(1,𝔽5)C2×C412yes—
78C4×D3×AGL(1,𝔽5)—216no—
79C4×D3×AGL(1,𝔽5)C2×C418yes—
80C4×D3×AGL(1,𝔽5)C2×C418yes—
81D3×D5⋊C8C2×C418yes—
82D3×D5⋊C8C2×C418yes—
83C2×C8×D15C2×C412yes—
84C42×D15C2×C411yescharacteristic
85C2×C5×D3×C8C2×C412yes—
86C42×C5×D3C2×C411yescharacteristic
87C2×C3×C8×D5C2312yes—
88C3×C42×D5C2311yescharacteristic
89C4×#1200C2×C411yescharacteristic
90C4×#1200C2×C412yes—
91C4×D3×Dic5C2×C411yescharacteristic
92C4×D3×Dic5C2×C412yes—
93C4×D5×Dic3C2×C412yes—
94C4×D5×Dic3C2311yescharacteristic
95C2×#6648C2×C412yes—
96C2×D3×#168C2×C412yes—
97C2×D5×C3⋊C8C2312yes—
98D3×C8×D5C2×C418yes—
99D3×C8×D5C2×C418yes—
100#91231C2×C414yescomplemented
101#91221C2×C418yescomplemented
102C8×ΓL(1,𝔽16)C2×C418yescomplemented
103C3×#4002C2×C414yescomplemented
104C3×#3992C2×C418yescomplemented
105C3×C8×AGL(1,𝔽5)C2×C418yescomplemented
106#91169C2×C418yescomplemented
107#91150C2×C418yescomplemented
108#91149C2×C418yescomplemented
109ΓL(1,𝔽16)⋊C8C2×C418yescomplemented
110AGL(1,𝔽5)×C3⋊C8C2×C418yescomplemented
111C3×C5×#97C2×C411yescharacteristic, complemented
112#91099C2×C412yescomplemented
113#91087C2×C411yescharacteristic, complemented
114C5×#815C2×C412yescomplemented
115C5×#803C2×C411yescharacteristic, complemented
116C3×#3947C2×C412yescomplemented
117C3×#3935C2×C411yescharacteristic, complemented
118#90954C2×C412yescomplemented
119#90953C2×C412yescomplemented
120#90952C2×C412yescomplemented
121C2×D3×#97—52no—
122C2×D3×#97—51no—
123C2×D3×#97—51no—
124C2×C4×D3×C8—52no—
125C43×D3—51no—
126C3×C4×#97—51no—
127Dic3×#97—51no—
128Dic3×#97—52no—
129Dic3×#97—51no—
130C4×#815—52no—
131C4×#803—51no—
132C22×C4×AGL(1,𝔽5)—31no—
133C22×C4×AGL(1,𝔽5)—31no—
134C22×C4×AGL(1,𝔽5)—34no—
135C22×D5⋊C8—32no—
136C22×C8×D5—32no—
137C2×C42×D5—31no—
138C2×#4002—34no—
139C2×#3992—32no—
140C2×#3992—316no—
141C2×#3992—32no—
142C2×#3992—32no—
143C2×#3992C2×D312yes—
144C2×C8×AGL(1,𝔽5)—32no—
145C2×C8×AGL(1,𝔽5)—316no—
146C2×C8×AGL(1,𝔽5)—32no—
147C2×C8×AGL(1,𝔽5)—32no—
148C2×C8×AGL(1,𝔽5)C2×D312yes—
149C42×AGL(1,𝔽5)—31no—
150C42×AGL(1,𝔽5)—34no—
151C42×AGL(1,𝔽5)—31no—
152C42×AGL(1,𝔽5)—31no—
153C42×AGL(1,𝔽5)C2×D311yescharacteristic
154#65676—31no—
155#65676—34no—
156#65676—32no—
157#65676C2×D311yescharacteristic
158C2×C5×#97—31no—
159C2×#3947—32no—
160C2×#3935—31no—
161D5×#97—32no—
162D5×#97—31no—
163D5×#97—31no—
164D5×#97—32no—
165D5×#97—31no—
166D5×#97C2×D311yescharacteristic
167C2×C4×#97—151noSylow
168C22×D3×D5C22×C411yescharacteristic
169C22×ΓL(1,𝔽16)C22×C412yes—
170C22×ΓL(1,𝔽16)C22×C412yes—
171C22×C3×AGL(1,𝔽5)C22×C412yes—
172C22×C3×AGL(1,𝔽5)C22×C412yes—
173C2×D3×AGL(1,𝔽5)—28no—
174C2×D3×AGL(1,𝔽5)C4218yes—
175C2×D3×AGL(1,𝔽5)C4218yes—
176C2×D3×AGL(1,𝔽5)M16116yes—
177C2×C4×D15C4212yes—
178C2×C4×D15C22×C411yescharacteristic
179C2×C4×C5×D3C4212yes—
180C2×C4×C5×D3C22×C411yescharacteristic
181C2×C3×C4×D5C22×C412yes—
182C2×C3×C4×D5C2411yescharacteristic
183C2×#1200C4212yes—
184C2×#1200C22×C411yescharacteristic
185C2×D3×Dic5C4212yes—
186C2×D3×Dic5C22×C411yescharacteristic
187C2×D5×Dic3C22×C412yes—
188C2×D5×Dic3C22×C411yescharacteristic
189C4×D3×D5—28no—
190C4×D3×D5C22×C414yes—
191C4×D3×D5C22×C414yes—
192C2×C3⋊#170C22×C414yes—
193C4×ΓL(1,𝔽16)—28no—
194C4×ΓL(1,𝔽16)C22×C414yes—
195C4×ΓL(1,𝔽16)C22×C414yes—
196D5⋊(C3⋊C8)C22×C414yes—
197D5⋊(C3⋊C8)C22×C414yes—
198C2×C3×#170C22×C414yes—
199C3×C4×AGL(1,𝔽5)—28no—
200C3×C4×AGL(1,𝔽5)C22×C414yes—
201C3×C4×AGL(1,𝔽5)C22×C414yes—
202C3×D5⋊C8C22×C414yes—
203C3×D5⋊C8C22×C414yes—
204#6738C42116yescomplemented
205D3×#170C42116yescomplemented
206Dic3×AGL(1,𝔽5)—28no—
207Dic3×AGL(1,𝔽5)—28no—
208Dic3×AGL(1,𝔽5)C4218yes—
209Dic3×AGL(1,𝔽5)C4218yes—
210C2×C3×C5×C8C22×C412yes—
211C3×C42×C5C22×C411yescharacteristic
212C4×Dic15C4212yes—
213C4×Dic15C22×C411yescharacteristic
214C2×C3⋊#168C22×C412yes—
215C8×D15C4218yescomplemented
216C4×C5×Dic3C4212yes—
217C4×C5×Dic3C22×C411yescharacteristic
218C2×C5×C3⋊C8C22×C412yes—
219C5×D3×C8C4218yescomplemented
220C3×C4×Dic5C22×C411yescharacteristic
221C3×C4×Dic5C22×C412yes—
222C2×C3×#168C22×C412yes—
223C3×C8×D5C22×C414yes—
224C3×C8×D5C22×C414yes—
225Dic3×Dic5C4212yes—
226Dic3×Dic5C4212yes—
227Dic3×Dic5C22×C412yes—
228#6648C4218yescomplemented
229D3×#168C4218yescomplemented
230D5×C3⋊C8C22×C414yes—
231D5×C3⋊C8C22×C414yes—
232C22×D3×C8—52no—
233C22×D3×C8—52no—
234C2×C42×D3—51no—
235C2×C42×D3—51no—
236C2×C42×D3—51no—
237C2×C42×D3—54no—
238C2×C3×#97—51no—
239C2×C3×#97—52no—
240C2×C3×#97—51no—
241C2×C3×C4×C8—52no—
242C3×C43—51no—
243C2×#815—52no—
244C2×#815—52no—
245C2×#815—52no—
246C2×#815—52no—
247C2×C8×Dic3—52no—
248C2×C8×Dic3—52no—
249C42×Dic3—51no—
250C42×Dic3—54no—
251C42×Dic3—51no—
252C42×Dic3—51no—
253C2×#803—52no—
254C2×#803—51no—
255C2×#803—51no—
256C2×C4×C3⋊C8—52no—
257D3×#97—54no—
258D3×#97—54no—
259D3×#97—516no—
260D3×#97—52no—
261D3×#97—51no—
262D3×#97—51no—
263D3×#97—52no—
264D3×#97—51no—
265D3×#97AGL(1,𝔽5)11yescharacteristic, direct product factor
266C4×D3×C8—516no—
267C23×AGL(1,𝔽5)—32no—
268C23×AGL(1,𝔽5)—32no—
269C22×C4×D5—31no—
270C22×C4×D5—32no—
271C22×#170—34no—
272C2×C4×AGL(1,𝔽5)—32no—
273C2×C4×AGL(1,𝔽5)—32no—
274C2×C4×AGL(1,𝔽5)—31no—
275C2×C4×AGL(1,𝔽5)—31no—
276C2×C4×AGL(1,𝔽5)—38no—
277C2×C4×AGL(1,𝔽5)—38no—
278C2×C4×AGL(1,𝔽5)—34no—
279C2×C4×AGL(1,𝔽5)—34no—
280C2×C4×AGL(1,𝔽5)—34no—
281C2×C4×AGL(1,𝔽5)—616no—
282C2×C4×AGL(1,𝔽5)C4×D314yes—
283C2×C4×AGL(1,𝔽5)C22×D311yescharacteristic
284C2×C4×AGL(1,𝔽5)C22×D311yescharacteristic
285C2×D5⋊C8—32no—
286C2×D5⋊C8—34no—
287C2×D5⋊C8—38no—
288C2×D5⋊C8—38no—
289C2×D5⋊C8C22×D312yes—
290C22×C5×C8—32no—
291C2×C42×C5—31no—
292C2×C4×Dic5—31no—
293C2×C4×Dic5—32no—
294C22×#168—32no—
295C2×C8×D5—32no—
296C2×C8×D5—32no—
297C2×C8×D5—32no—
298C2×C8×D5—38no—
299C2×C8×D5—38no—
300C2×C8×D5C22×D312yes—
301C42×D5—32no—
302C42×D5—31no—
303C42×D5—31no—
304C42×D5—32no—
305C42×D5—31no—
306C42×D5C22×D311yescharacteristic
307#4002—38no—
308#4002—34no—
309#4002C4×D314yescomplemented
310#3992—38no—
311#3992—38no—
312#3992—38no—
313#3992C4×D318yescomplemented
314C8×AGL(1,𝔽5)—38no—
315C8×AGL(1,𝔽5)—38no—
316C8×AGL(1,𝔽5)—38no—
317C8×AGL(1,𝔽5)C4×D318yescomplemented
318C5×#97—32no—
319C5×#97—31no—
320C5×#97C4×D311yescharacteristic, complemented
321#3947—32no—
322#3947—32no—
323#3947—32no—
324#3947C4×D312yescomplemented
325#3935—31no—
326#3935—32no—
327#3935C4×D311yescharacteristic, complemented
328C22×#97—151no—
329C22×#97—152no—
330C22×#97—151no—
331C22×C4×C8—152no—
332C2×C43—151no—
333C4×#97—51no—
334C4×#97—151no—
335C4×#97—152no—
336C4×#97—151no—
337C4×#97—152no—
338C4×#97—151no—
339C22×D15C2×C4211yescharacteristic
340C22×C5×D3C2×C4211yescharacteristic
341C22×C3×D5C23×C411yescharacteristic
342C2×D3×D5C2×C4212yes—
343C2×D3×D5C2×C4212yes—
344C2×D3×D5C2×M1618yes—
345C2×ΓL(1,𝔽16)—24no—
346C2×ΓL(1,𝔽16)C2×C4214yes—
347C2×ΓL(1,𝔽16)C2×C4214yes—
348C2×ΓL(1,𝔽16)C2×M1618yes—
349C2×C3×AGL(1,𝔽5)—24no—
350C2×C3×AGL(1,𝔽5)C2×C4214yes—
351C2×C3×AGL(1,𝔽5)C2×C4214yes—
352C2×C3×AGL(1,𝔽5)C2×M1618yes—
353D3×AGL(1,𝔽5)—216no—
354D3×AGL(1,𝔽5)#97132yesdirect product factor
355C2×C3×C4×C5C2×C4212yes—
356C2×C3×C4×C5C23×C411yescharacteristic
357C2×Dic15C2×C4212yes—
358C2×Dic15C2×C4211yescharacteristic
359C4×D15—24no—
360C4×D15C2×C4214yes—
361C2×C5×Dic3C2×C4212yes—
362C2×C5×Dic3C2×C4211yescharacteristic
363C4×C5×D3—24no—
364C4×C5×D3C2×C4214yes—
365C2×C3×Dic5C2×C4212yes—
366C2×C3×Dic5C23×C411yescharacteristic
367C3×C4×D5—24no—
368C3×C4×D5C23×C412yes—
369C3×C4×D5C23×C412yes—
370#1200—24no—
371#1200C2×C4214yes—
372D3×Dic5—24no—
373D3×Dic5C2×C4214yes—
374D5×Dic3—24no—
375D5×Dic3C2×C4212yes—
376D5×Dic3C2×C4212yes—
377C3⋊#170C2×C4218yescomplemented
378C3×#170C2×C4218yescomplemented
379C3×C5×C8C2×C4214yescomplemented
380C3⋊#168C2×C4214yescomplemented
381C3×#168C2×C4214yescomplemented
382C5×C3⋊C8C2×C4214yescomplemented
383C22×C4×D3—52no—
384C22×C4×D3—51no—
385C22×C4×D3—52no—
386C22×C4×D3—52no—
387C22×C3×C8—52no—
388C22×C3×C8—52no—
389C2×C3×C42—51no—
390C2×C3×C42—51no—
391C2×C3×C42—51no—
392C2×C3×C42—54no—
393C2×C4×Dic3—52no—
394C2×C4×Dic3—52no—
395C2×C4×Dic3—51no—
396C2×C4×Dic3—51no—
397C2×C4×Dic3—52no—
398C2×C4×Dic3—51no—
399C2×C4×Dic3—54no—
400C2×C4×Dic3—54no—
401C2×C4×Dic3—54no—
402C22×C3⋊C8—52no—
403C22×C3⋊C8—52no—
404C2×D3×C8—58no—
405C2×D3×C8—58no—
406C2×D3×C8—54no—
407C2×D3×C8—54no—
408C2×D3×C8—52no—
409C2×D3×C8—52no—
410C2×D3×C8—52no—
411C2×D3×C8—58no—
412C2×D3×C8—58no—
413C2×D3×C8C2×AGL(1,𝔽5)12yes—
414C42×D3—58no—
415C42×D3—58no—
416C42×D3—52no—
417C42×D3—51no—
418C42×D3—51no—
419C42×D3—52no—
420C42×D3—51no—
421C42×D3—1016no—
422C42×D3C2×AGL(1,𝔽5)11yescharacteristic
423C3×#97—58no—
424C3×#97—54no—
425C3×#97—52no—
426C3×#97—51no—
427C3×#97C2×AGL(1,𝔽5)11yescharacteristic, complemented
428C3×C4×C8—58no—
429#815—58no—
430#815—58no—
431#815—58no—
432#815—52no—
433#815—52no—
434#815—52no—
435#815C2×AGL(1,𝔽5)12yescomplemented
436C8×Dic3—58no—
437C8×Dic3—58no—
438#803—58no—
439#803—54no—
440#803—51no—
441#803—52no—
442#803C2×AGL(1,𝔽5)11yescharacteristic, complemented
443C4×C3⋊C8—58no—
444C23×D5—31no—
445C22×AGL(1,𝔽5)—32no—
446C22×AGL(1,𝔽5)—38no—
447C22×AGL(1,𝔽5)—316no—
448C22×AGL(1,𝔽5)—32no—
449C22×AGL(1,𝔽5)—38no—
450C22×AGL(1,𝔽5)—68no—
451C22×AGL(1,𝔽5)C2×C4×D312yes—
452C22×AGL(1,𝔽5)C2×C4×D312yes—
453C22×C4×C5—31no—
454C22×C4×C5—32no—
455C22×Dic5—31no—
456C22×Dic5—32no—
457C2×C4×D5—31no—
458C2×C4×D5—31no—
459C2×C4×D5—31no—
460C2×C4×D5—34no—
461C2×C4×D5—34no—
462C2×C4×D5—32no—
463C2×C4×D5—32no—
464C2×C4×D5—32no—
465C2×C4×D5—68no—
466C2×C4×D5C2×C4×D312yes—
467C2×C4×D5C23×D311yescharacteristic
468C2×#170—34no—
469C2×#170—316no—
470C2×#170C2×C4×D314yes—
471C4×AGL(1,𝔽5)—28no—
472C4×AGL(1,𝔽5)—38no—
473C4×AGL(1,𝔽5)—38no—
474C4×AGL(1,𝔽5)—34no—
475C4×AGL(1,𝔽5)—34no—
476C4×AGL(1,𝔽5)—68no—
477C4×AGL(1,𝔽5)—68no—
478C4×AGL(1,𝔽5)—68no—
479C4×AGL(1,𝔽5)C2×C4×D314yes—
480C4×AGL(1,𝔽5)C2×C4×D314yes—
481D5⋊C8—34no—
482D5⋊C8—34no—
483D5⋊C8—316no—
484D5⋊C8C2×C4×D314yes—
485D5⋊C8C2×C4×D314yes—
486C2×C5×C8—32no—
487C2×C5×C8—38no—
488C2×C5×C8C2×C4×D312yes—
489C42×C5—32no—
490C42×C5—31no—
491C42×C5C2×C4×D311yescharacteristic
492C4×Dic5—32no—
493C4×Dic5—31no—
494C4×Dic5—32no—
495C4×Dic5—32no—
496C4×Dic5—32no—
497C4×Dic5C2×C4×D311yescharacteristic
498C4×Dic5C2×C4×D312yes—
499C2×#168—32no—
500C2×#168—38no—
501C2×#168C2×C4×D312yes—
502C8×D5—34no—
503C8×D5—34no—
504C8×D5—38no—
505C8×D5—38no—
506C8×D5C2×C4×D314yes—
507C8×D5C2×C4×D314yes—
508C23×C8—152no—
509C23×C8—152no—
510C22×C42—151no—
511C22×C42—151no—
512C22×C42—151no—
513C22×C42—154no—
514C2×#97—31no—
515C2×#97—51no—
516C2×#97—52no—
517C2×#97—51no—
518C2×#97—152no—
519C2×#97—151no—
520C2×#97—151no—
521C2×#97—152no—
522C2×#97—151no—
523C2×#97—152no—
524C2×#97—154no—
525C2×#97—1516no—
526C2×#97—154no—
527C2×#97—151no—
528C2×#97—152no—
529C2×#97—152no—
530C2×#97—152no—
531C2×#97—152no—
532C2×#97—151no—
533C2×C4×C8—52no—
534C2×C4×C8—1516no—
535C2×C4×C8—152no—
536C2×C4×C8—152no—
537C2×C4×C8—152no—
538C43—51no—
539C43—151no—
540C43—151no—
541C43—151no—
542C43—154no—
543C22×C3×C5C22×C4211yescharacteristic
544C2×D15C4312yes—
545C2×D15C4×M1614yes—
546C2×C5×D3C4312yes—
547C2×C5×D3C4×M1614yes—
548C2×C3×D5C22×C4211yescharacteristic
549C2×C3×D5C22×C4211yescharacteristic
550C2×C3×D5C22×M1614yes—
551D3×D5C2×#9718yes—
552D3×D5C4×M1618yes—
553ΓL(1,𝔽16)—24no—
554ΓL(1,𝔽16)C2×#9718yescomplemented
555C3×AGL(1,𝔽5)—24no—
556C3×AGL(1,𝔽5)C2×#9718yescomplemented
557C3×C4×C5—22no—
558C3×C4×C5C22×C4212yes—
559Dic15—22no—
560Dic15C4312yes—
561C3×Dic5—22no—
562C3×Dic5C22×C4212yes—
563C5×Dic3—22no—
564C5×Dic3C4312yes—
565C23×D3—51no—
566C22×C3×C4—52no—
567C22×C3×C4—51no—
568C22×C3×C4—52no—
569C22×C3×C4—52no—
570C22×Dic3—52no—
571C22×Dic3—51no—
572C22×Dic3—52no—
573C22×Dic3—52no—
574C2×C4×D3—58no—
575C2×C4×D3—516no—
576C2×C4×D3—51no—
577C2×C4×D3—51no—
578C2×C4×D3—51no—
579C2×C4×D3—54no—
580C2×C4×D3—54no—
581C2×C4×D3—58no—
582C2×C4×D3—52no—
583C2×C4×D3—52no—
584C2×C4×D3—52no—
585C2×C4×D3—108no—
586C2×C4×D3—108no—
587C2×C4×D3C4×AGL(1,𝔽5)12yes—
588C2×C4×D3C22×AGL(1,𝔽5)11yescharacteristic
589C2×C3×C8—54no—
590C2×C3×C8—54no—
591C2×C3×C8—54no—
592C2×C3×C8—52no—
593C2×C3×C8—54no—
594C2×C3×C8—54no—
595C2×C3×C8C22×AGL(1,𝔽5)12yes—
596C3×C42—54no—
597C3×C42—54no—
598C3×C42—52no—
599C3×C42—51no—
600C3×C42—108no—
601C3×C42C22×AGL(1,𝔽5)11yescharacteristic
602C4×Dic3—54no—
603C4×Dic3—54no—
604C4×Dic3—58no—
605C4×Dic3—58no—
606C4×Dic3—52no—
607C4×Dic3—51no—
608C4×Dic3—52no—
609C4×Dic3—52no—
610C4×Dic3—52no—
611C4×Dic3—108no—
612C4×Dic3—108no—
613C4×Dic3—108no—
614C4×Dic3C4×AGL(1,𝔽5)12yes—
615C4×Dic3C22×AGL(1,𝔽5)11yescharacteristic
616C2×C3⋊C8—54no—
617C2×C3⋊C8—54no—
618C2×C3⋊C8—54no—
619C2×C3⋊C8—52no—
620C2×C3⋊C8—54no—
621C2×C3⋊C8—54no—
622C2×C3⋊C8C22×AGL(1,𝔽5)12yes—
623D3×C8—516no—
624D3×C8—516no—
625D3×C8—58no—
626D3×C8—58no—
627D3×C8—58no—
628D3×C8C4×AGL(1,𝔽5)18yescomplemented
629C23×C5—31no—
630C22×D5—31no—
631C22×D5—32no—
632C22×D5—32no—
633C22×D5—38no—
634C22×D5C22×C4×D311yescharacteristic
635C2×AGL(1,𝔽5)—24no—
636C2×AGL(1,𝔽5)—34no—
637C2×AGL(1,𝔽5)—38no—
638C2×AGL(1,𝔽5)—332no—
639C2×AGL(1,𝔽5)—34no—
640C2×AGL(1,𝔽5)—616no—
641C2×AGL(1,𝔽5)—64no—
642C2×AGL(1,𝔽5)C42×D314yes—
643C2×AGL(1,𝔽5)C42×D314yes—
644C2×AGL(1,𝔽5)D3×M1618yes—
645C2×C4×C5—31no—
646C2×C4×C5—34no—
647C2×C4×C5—32no—
648C2×C4×C5—64no—
649C2×C4×C5C42×D312yes—
650C2×C4×C5C22×C4×D311yescharacteristic
651C2×Dic5—31no—
652C2×Dic5—34no—
653C2×Dic5—32no—
654C2×Dic5—64no—
655C2×Dic5C42×D312yes—
656C2×Dic5C22×C4×D311yescharacteristic
657C4×D5—24no—
658C4×D5—32no—
659C4×D5—32no—
660C4×D5—34no—
661C4×D5—34no—
662C4×D5—64no—
663C4×D5—64no—
664C4×D5—64no—
665C4×D5C22×C4×D312yes—
666C4×D5C22×C4×D312yes—
667#170—38no—
668#170C42×D318yescomplemented
669C5×C8—34no—
670C5×C8C42×D314yescomplemented
671#168—34no—
672#168C42×D314yescomplemented
673C23×C4—151no—
674C23×C4—152no—
675C23×C4—152no—
676C23×C4—152no—
677C22×C8—32no—
678C22×C8—52no—
679C22×C8—52no—
680C22×C8—158no—
681C22×C8—152no—
682C22×C8—158no—
683C22×C8—152no—
684C22×C8—152no—
685C22×C8—158no—
686C22×C8—158no—
687C22×C8—154no—
688C22×C8—154no—
689C22×C8—152no—
690C22×C8—152no—
691C2×C42—31no—
692C2×C42—51no—
693C2×C42—51no—
694C2×C42—51no—
695C2×C42—54no—
696C2×C42—152no—
697C2×C42—151no—
698C2×C42—151no—
699C2×C42—152no—
700C2×C42—152no—
701C2×C42—151no—
702C2×C42—158no—
703C2×C42—158no—
704C2×C42—151no—
705C2×C42—151no—
706C2×C42—152no—
707C2×C42—152no—
708C2×C42—151no—
709C2×C42—154no—
710C2×C42—154no—
711C2×C42—154no—
712C2×C42—3016no—
713#97—32no—
714#97—31no—
715#97—58no—
716#97—54no—
717#97—52no—
718#97—51no—
719#97—152no—
720#97—152no—
721#97—158no—
722#97—154no—
723#97—152no—
724#97—158no—
725#97—158no—
726#97—158no—
727#97—152no—
728#97—151no—
729#97D3×AGL(1,𝔽5)11yescharacteristic, direct product factor
730C4×C8—58no—
731C4×C8—158no—
732C4×C8—158no—
733C4×C8—158no—
734C2×C3×C5C2×C4311yescharacteristic
735C2×C3×C5C2×C4×M1612yes—
736D15C4×#9714yescomplemented
737C3×D5C22×#9712yes—
738C3×D5C2×C4×M1612yes—
739C5×D3C4×#9714yescomplemented
740C23×C3—51no—
741C22×D3—51no—
742C22×D3—52no—
743C22×D3—52no—
744C22×D3—58no—
745C22×D3C2×C4×AGL(1,𝔽5)11yescharacteristic
746C2×C3×C4—54no—
747C2×C3×C4—58no—
748C2×C3×C4—51no—
749C2×C3×C4—52no—
750C2×C3×C4—52no—
751C2×C3×C4—54no—
752C2×C3×C4—52no—
753C2×C3×C4—104no—
754C2×C3×C4—104no—
755C2×C3×C4C2×C4×AGL(1,𝔽5)12yes—
756C2×C3×C4C23×AGL(1,𝔽5)11yescharacteristic
757C2×Dic3—54no—
758C2×Dic3—58no—
759C2×Dic3—51no—
760C2×Dic3—52no—
761C2×Dic3—52no—
762C2×Dic3—54no—
763C2×Dic3—52no—
764C2×Dic3—104no—
765C2×Dic3—104no—
766C2×Dic3C2×C4×AGL(1,𝔽5)12yes—
767C2×Dic3C2×C4×AGL(1,𝔽5)11yescharacteristic
768C4×D3—24no—
769C4×D3—532no—
770C4×D3—54no—
771C4×D3—54no—
772C4×D3—54no—
773C4×D3—104no—
774C4×D3—104no—
775C4×D3—1016no—
776C4×D3—104no—
777C4×D3C2×C4×AGL(1,𝔽5)14yes—
778C3×C8—58no—
779C3×C8—54no—
780C3×C8C2×C4×AGL(1,𝔽5)14yescomplemented
781C3⋊C8—58no—
782C3⋊C8—54no—
783C3⋊C8C2×C4×AGL(1,𝔽5)14yescomplemented
784C22×C5—32no—
785C22×C5—34no—
786C22×C5C2×C42×D311yescharacteristic
787C2×D5—32no—
788C2×D5—34no—
789C2×D5—38no—
790C2×D5—38no—
791C2×D5C2×C42×D311yescharacteristic
792C2×D5C2×C42×D311yescharacteristic
793C2×D5C2×D3×M1614yes—
794AGL(1,𝔽5)—24no—
795AGL(1,𝔽5)—38no—
796AGL(1,𝔽5)—64no—
797AGL(1,𝔽5)D3×#9718yesdirect product factor
798C4×C5—22no—
799C4×C5—32no—
800C4×C5—62no—
801C4×C5C2×C42×D312yes—
802Dic5—22no—
803Dic5—32no—
804Dic5—62no—
805Dic5C2×C42×D312yes—
806C24—151no—
807C22×C4—31no—
808C22×C4—32no—
809C22×C4—52no—
810C22×C4—51no—
811C22×C4—52no—
812C22×C4—52no—
813C22×C4—151no—
814C22×C4—154no—
815C22×C4—154no—
816C22×C4—152no—
817C22×C4—151no—
818C22×C4—152no—
819C22×C4—151no—
820C22×C4—158no—
821C22×C4—1516no—
822C22×C4—152no—
823C22×C4—158no—
824C22×C4—152no—
825C22×C4—151no—
826C22×C4—152no—
827C22×C4—152no—
828C22×C4—308no—
829C22×C4—308no—
830C2×C8—32no—
831C2×C8—38no—
832C2×C8—54no—
833C2×C8—54no—
834C2×C8—54no—
835C2×C8—52no—
836C2×C8—54no—
837C2×C8—54no—
838C2×C8—158no—
839C2×C8—154no—
840C2×C8—154no—
841C2×C8—158no—
842C2×C8—1516no—
843C2×C8—1516no—
844C2×C8—154no—
845C2×C8—154no—
846C2×C8—154no—
847C2×C8—152no—
848C2×C8—158no—
849C2×C8C2×D3×AGL(1,𝔽5)12yes—
850C42—32no—
851C42—31no—
852C42—54no—
853C42—54no—
854C42—52no—
855C42—51no—
856C42—108no—
857C42—152no—
858C42—152no—
859C42—152no—
860C42—154no—
861C42—154no—
862C42—158no—
863C42—158no—
864C42—152no—
865C42—151no—
866C42—308no—
867C42—308no—
868C42—308no—
869C42C2×D3×AGL(1,𝔽5)11yescharacteristic
870C3×C5C2×C4×#9711yescharacteristic, complemented, Hall
871C22×C3—54no—
872C22×C3—51no—
873C22×C3—51no—
874C22×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
875C2×D3—54no—
876C2×D3—52no—
877C2×D3—58no—
878C2×D3—58no—
879C2×D3C42×AGL(1,𝔽5)12yes—
880C2×D3M16×AGL(1,𝔽5)14yes—
881C3×C4—22no—
882C3×C4—58no—
883C3×C4—52no—
884C3×C4—104no—
885C3×C4—102no—
886C3×C4C22×C4×AGL(1,𝔽5)12yes—
887Dic3—22no—
888Dic3—58no—
889Dic3—52no—
890Dic3—104no—
891Dic3—102no—
892Dic3C42×AGL(1,𝔽5)12yes—
893C2×C5—34no—
894C2×C5C43×D311yescharacteristic
895C2×C5C4×D3×M1612yes—
896D5—34no—
897D5C2×D3×#9712yes—
898D5C4×D3×M1612yes—
899C23—31no—
900C23—51no—
901C23—152no—
902C23—152no—
903C23—158no—
904C23—151no—
905C2×C4—31no—
906C2×C4—34no—
907C2×C4—32no—
908C2×C4—54no—
909C2×C4—58no—
910C2×C4—51no—
911C2×C4—52no—
912C2×C4—52no—
913C2×C4—54no—
914C2×C4—52no—
915C2×C4—64no—
916C2×C4—104no—
917C2×C4—104no—
918C2×C4—154no—
919C2×C4—152no—
920C2×C4—152no—
921C2×C4—154no—
922C2×C4—1532no—
923C2×C4—154no—
924C2×C4—158no—
925C2×C4—151no—
926C2×C4—154no—
927C2×C4—154no—
928C2×C4—152no—
929C2×C4—304no—
930C2×C4—304no—
931C2×C4—304no—
932C2×C4—304no—
933C2×C4—3016no—
934C2×C4—304no—
935C2×C4C4×D3×AGL(1,𝔽5)12yes—
936C2×C4C22×D3×AGL(1,𝔽5)11yescharacteristic
937C8—34no—
938C8—58no—
939C8—54no—
940C8—158no—
941C8—154no—
942C8C4×D3×AGL(1,𝔽5)14yescomplemented
943C2×C3—52no—
944C2×C3—52no—
945C2×C3C2×C42×AGL(1,𝔽5)11yescharacteristic
946C2×C3C2×M16×AGL(1,𝔽5)12yes—
947D3—54no—
948D3AGL(1,𝔽5)×#9714yesdirect product factor
949C5C4×D3×#9711yescharacteristic, complemented, Sylow
950C22—34no—
951C22—32no—
952C22—54no—
953C22—51no—
954C22—51no—
955C22—158no—
956C22—158no—
957C22—154no—
958C22—152no—
959C22C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
960C4—22no—
961C4—32no—
962C4—58no—
963C4—52no—
964C4—62no—
965C4—104no—
966C4—102no—
967C4—158no—
968C4—152no—
969C4—304no—
970C4—302no—
971C4C2×C4×D3×AGL(1,𝔽5)12yes—
972C3C2×AGL(1,𝔽5)×#9711yescharacteristic, complemented, Sylow
973C2—34no—
974C2—52no—
975C2—52no—
976C2—154no—
977C2C42×D3×AGL(1,𝔽5)11yescharacteristic
978C2D3×M16×AGL(1,𝔽5)12yes—
subgroupG/H
center, FrattiniC2×C4C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C43
FittingC3×C5×#97C2×C4
socleC22×C3×C5C22×C42
prime radicalC22×D3×D5C22×C4
cosocleC2×C3×C4×D5C24
hypercenter#97D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
6. #14294227C2semidirect
7. AGL(1,𝔽5)×#803C2semidirect
8. #14294225C2semidirect
9. AGL(1,𝔽5)×#815C2semidirect
10. #97×ΓL(1,𝔽16)C2semidirect
11. C3×AGL(1,𝔽5)×#97C2semidirect
27. #11751873C4semidirect
28. D3×#4002C4semidirect
37. D3×#3992C4semidirect
38. D3×C8×AGL(1,𝔽5)C4semidirect
39. D15×#97C4semidirect
40. C5×D3×#97C4semidirect
42. #11747603C4semidirect
43. D3×#3947C4semidirect
45. #11746983C4semidirect
46. D3×#3935C4semidirect
59. AGL(1,𝔽5)×#97D3direct (N × H)
100. #91231C2×C4semidirect
101. #91221C2×C4semidirect
102. C8×ΓL(1,𝔽16)C2×C4semidirect
103. C3×#4002C2×C4semidirect
104. C3×#3992C2×C4semidirect
105. C3×C8×AGL(1,𝔽5)C2×C4semidirect
106. #91169C2×C4semidirect
107. #91150C2×C4semidirect
108. #91149C2×C4semidirect
109. ΓL(1,𝔽16)⋊C8C2×C4semidirect
110. AGL(1,𝔽5)×C3⋊C8C2×C4semidirect
111. C3×C5×#97C2×C4semidirect
112. #91099C2×C4semidirect
113. #91087C2×C4semidirect
114. C5×#815C2×C4semidirect
115. C5×#803C2×C4semidirect
116. C3×#3947C2×C4semidirect
117. C3×#3935C2×C4semidirect
118. #90954C2×C4semidirect
119. #90953C2×C4semidirect
120. #90952C2×C4semidirect
204. #6738C42semidirect
205. D3×#170C42semidirect
215. C8×D15C42semidirect
219. C5×D3×C8C42semidirect
228. #6648C42semidirect
229. D3×#168C42semidirect
265. D3×#97AGL(1,𝔽5)direct (N × H)
309. #4002C4×D3semidirect
313. #3992C4×D3semidirect
317. C8×AGL(1,𝔽5)C4×D3semidirect
320. C5×#97C4×D3semidirect
324. #3947C4×D3semidirect
327. #3935C4×D3semidirect
354. D3×AGL(1,𝔽5)#97direct (N × H)
377. C3⋊#170C2×C42semidirect
378. C3×#170C2×C42semidirect
379. C3×C5×C8C2×C42semidirect
380. C3⋊#168C2×C42semidirect
381. C3×#168C2×C42semidirect
382. C5×C3⋊C8C2×C42semidirect
427. C3×#97C2×AGL(1,𝔽5)semidirect
435. #815C2×AGL(1,𝔽5)semidirect
442. #803C2×AGL(1,𝔽5)semidirect
554. ΓL(1,𝔽16)C2×#97semidirect
556. C3×AGL(1,𝔽5)C2×#97semidirect
628. D3×C8C4×AGL(1,𝔽5)semidirect
668. #170C42×D3semidirect
670. C5×C8C42×D3semidirect
672. #168C42×D3semidirect
729. #97D3×AGL(1,𝔽5)direct (N × H)
736. D15C4×#97semidirect
739. C5×D3C4×#97semidirect
780. C3×C8C2×C4×AGL(1,𝔽5)semidirect
783. C3⋊C8C2×C4×AGL(1,𝔽5)semidirect
797. AGL(1,𝔽5)D3×#97direct (N × H)
870. C3×C5C2×C4×#97semidirect
942. C8C4×D3×AGL(1,𝔽5)semidirect
948. D3AGL(1,𝔽5)×#97direct (N × H)
949. C5C4×D3×#97semidirect
972. C3C2×AGL(1,𝔽5)×#97semidirect

Maximal subgroups

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

subgroupindex
D3×#656762
C2×D3×#39922
D3×D5×#972
C2×D3×C8×AGL(1,𝔽5)2
C42×D3×AGL(1,𝔽5)2
#142942272
AGL(1,𝔽5)×#8032
#142942252
AGL(1,𝔽5)×#8152
#97×ΓL(1,𝔽16)2
C3×AGL(1,𝔽5)×#972
C2×AGL(1,𝔽5)×#973
C4×D3×#975