Finite Group Databasebeta

← AGL(1,𝔽5)×#1004 #14479253

Subgroups — AGL(1,𝔽5)×#1004 #14479253

Order 1920.

3320 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#1004C211yesmaximal, characteristic
2#11756987C211yesmaximal, characteristic, complemented
3C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4#11756871C214yesmaximal, complemented
5C2×AGL(1,𝔽5)×#67C214yesmaximal, complemented
6#11756846C214yesmaximal, complemented
7#11756845C214yesmaximal, complemented
8AGL(1,𝔽5)×#237C214yesmaximal, complemented
9D3×D4×AGL(1,𝔽5)C214yesmaximal, complemented
10#11756836C212yesmaximal, complemented
11AGL(1,𝔽5)×#235C212yesmaximal, complemented
12AGL(1,𝔽5)×H(5,𝔽2)—31nomaximal, Hall
13C23×C3×AGL(1,𝔽5)C2212yescomplemented
14C22×D3×AGL(1,𝔽5)C2214yescomplemented
15#92095C411yescharacteristic, complemented
16C5×#1004C411yescharacteristic, complemented
17C2×C3×D4×D5C2211yescharacteristic
18#92049C414yescomplemented
19C2×D5×#67C2214yes—
20#92026C414yescomplemented
21#92025C414yescomplemented
22D5×#237C2214yes—
23D3×D4×D5C2214yes—
24#92017C412yescomplemented
25D5×#235C2212yes—
26C2×#6763C2214yescomplemented
27D4×ΓL(1,𝔽16)C2214yescomplemented
28D4×ΓL(1,𝔽16)C2214yescomplemented
29#91989C2212yescomplemented
30C2×C3×C22⋊AGL(1,𝔽5)C2212yescomplemented
31C3×D4×AGL(1,𝔽5)C2214yescomplemented
32C3×D4×AGL(1,𝔽5)C2214yescomplemented
33C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
34C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic, complemented
35#67⋊AGL(1,𝔽5)C2218yescomplemented
36#67⋊AGL(1,𝔽5)C2218yescomplemented
37D3×C22⋊AGL(1,𝔽5)C2218yescomplemented
38AGL(1,𝔽5)×#67C2214yescomplemented
39AGL(1,𝔽5)×#67C2214yescomplemented
40AGL(1,𝔽5)×#67C2218yescomplemented
41AGL(1,𝔽5)×#67C2218yescomplemented
42AGL(1,𝔽5)×#67C2218yescomplemented
43C2×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
44C2×(C2×D3)⋊AGL(1,𝔽5)C2214yescomplemented
45#91923C2218yescomplemented
46C2×Dic3×AGL(1,𝔽5)C2214yescomplemented
47#91921C2214yescomplemented
48D3×C4⋊AGL(1,𝔽5)C2214yescomplemented
49AGL(1,𝔽5)×D12C2212yescomplemented
50AGL(1,𝔽5)×D12C2212yescomplemented
51C4×D3×AGL(1,𝔽5)C2214yescomplemented
52#91909C2214yescomplemented
53ΓL(1,𝔽16)⋊Q8C2214yescomplemented
54#91907C2214yescomplemented
55AGL(1,𝔽5)×Dic6C2212yescomplemented
56AGL(1,𝔽5)×Dic6C2212yescomplemented
57C4×#1004—51nomaximal, Hall
58D5×H(5,𝔽2)—31no—
59#66266—34no—
60#66266—32no—
61#41×AGL(1,𝔽5)—34no—
62#41×AGL(1,𝔽5)—32no—
63#66258—31no—
64#66258—34no—
65#66258—34no—
66C2×D4×AGL(1,𝔽5)—34no—
67C2×D4×AGL(1,𝔽5)—34no—
68C2×D4×AGL(1,𝔽5)D311yescharacteristic, complemented
69C23×C3×D5C2312yes—
70C22×D3×D5C2314yes—
71C22×ΓL(1,𝔽16)C2314yes—
72C22×ΓL(1,𝔽16)C2314yes—
73C22×C3×AGL(1,𝔽5)—44no—
74C22×C3×AGL(1,𝔽5)C2314yes—
75C22×C3×AGL(1,𝔽5)C2311yescharacteristic
76C22×C3×AGL(1,𝔽5)C2314yes—
77C22×C3×AGL(1,𝔽5)C2311yescharacteristic
78C22×C3×AGL(1,𝔽5)C2312yes—
79C2×D3×AGL(1,𝔽5)—48no—
80C2×D3×AGL(1,𝔽5)C2314yes—
81C2×D3×AGL(1,𝔽5)C2314yes—
82C2×D3×AGL(1,𝔽5)C2318yes—
83C2×C3×C5×D4C2×C411yescharacteristic, complemented
84C2×#1220C2×C414yescomplemented
85#6819C2×C414yescomplemented
86D4×D15C2×C414yescomplemented
87#6817C2×C412yescomplemented
88C2×C5×#67C2×C414yescomplemented
89C5×#237C2×C414yescomplemented
90C5×D3×D4C2×C414yescomplemented
91C5×#235C2×C412yescomplemented
92C2×C3×C22⋊D5C2×C412yescomplemented
93C3×D4×D5C2×C414yescomplemented
94C3×D4×D5C2314yes—
95C2×C3×D20C2×C411yescharacteristic, complemented
96C2×C3×C4×D5C2311yescharacteristic
97#6790C2×C418yescomplemented
98D3×C22⋊D5C2×C418yescomplemented
99D5×#67C2×C418yescomplemented
100D5×#67C2×C418yescomplemented
101D5×#67C2314yes—
102D5×#67C2318yes—
103C2×#1202C2×C414yescomplemented
104C2×#1201C2×C414yescomplemented
105#6782C2×C414yescomplemented
106#6780C2×C418yescomplemented
107#6779C2×C418yescomplemented
108C2×D5×Dic3C2314yes—
109#6777C2×C414yescomplemented
110D3×D20C2×C414yescomplemented
111D5×D12C2312yes—
112C4×D3×D5C2314yes—
113#6773C2×C412yescomplemented
114#6772C2×C412yescomplemented
115#6771C2×C414yescomplemented
116#6766C2×C414yescomplemented
117#6765C2×C414yescomplemented
118D5×Dic6C2312yes—
119#6763C2318yes—
120#6763C2314yes—
121C4⋊ΓL(1,𝔽16)C2312yes—
122C4⋊ΓL(1,𝔽16)C2312yes—
123C4×ΓL(1,𝔽16)C2314yes—
124C3×C22⋊AGL(1,𝔽5)C2318yes—
125C3×C4⋊AGL(1,𝔽5)C2314yes—
126C3×C4×AGL(1,𝔽5)C2312yes—
127C3×C4×AGL(1,𝔽5)C2312yes—
128Dic3⋊AGL(1,𝔽5)C2314yes—
129Dic3⋊AGL(1,𝔽5)C2314yes—
130Dic3⋊AGL(1,𝔽5)C2318yes—
131(C2×D3)⋊AGL(1,𝔽5)C2318yes—
132(C2×D3)⋊AGL(1,𝔽5)C2314yes—
133(C2×D3)⋊AGL(1,𝔽5)C2314yes—
134Dic3×AGL(1,𝔽5)C2314yes—
135Dic3×AGL(1,𝔽5)C2314yes—
136Dic3×AGL(1,𝔽5)C2318yes—
137C2×#1004—51no—
138C2×C3×C4×D4—51no—
139#5798—51no—
140C2×C4×#67—54no—
141#5546—54no—
142#5545—54no—
143C4×D3×D4—54no—
144C4×#237—54no—
145#5504—52no—
146#5486—54no—
147C4×#235—52no—
148C23×AGL(1,𝔽5)—34no—
149C23×AGL(1,𝔽5)C2×D312yescomplemented
150C5×H(5,𝔽2)—31no—
151#4149—34no—
152#4149—32no—
153D5×#41—34no—
154D5×#41—32no—
155#4144—31no—
156#4144—34no—
157#4144—34no—
158C2×D4×D5—34no—
159C2×D4×D5—34no—
160C2×D4×D5C2×D311yescharacteristic
161C2×C22⋊AGL(1,𝔽5)—34no—
162C2×C22⋊AGL(1,𝔽5)—34no—
163C2×C22⋊AGL(1,𝔽5)—38no—
164C2×C22⋊AGL(1,𝔽5)C2×D312yescomplemented
165Q8×AGL(1,𝔽5)—34no—
166Q8×AGL(1,𝔽5)—32no—
167Q8×AGL(1,𝔽5)—32no—
168D4×AGL(1,𝔽5)—38no—
169D4×AGL(1,𝔽5)—34no—
170D4×AGL(1,𝔽5)—38no—
171D4×AGL(1,𝔽5)—38no—
172D4×AGL(1,𝔽5)—34no—
173D4×AGL(1,𝔽5)—34no—
174D4×AGL(1,𝔽5)—34no—
175D4×AGL(1,𝔽5)—38no—
176D4×AGL(1,𝔽5)—38no—
177D4×AGL(1,𝔽5)—34no—
178D4×AGL(1,𝔽5)—32no—
179D4×AGL(1,𝔽5)—32no—
180D4×AGL(1,𝔽5)C2×D314yescomplemented
181D4×AGL(1,𝔽5)C2×D314yescomplemented
182#4130—32no—
183#4130—38no—
184#4130—34no—
185#4130—34no—
186C2×C4⋊AGL(1,𝔽5)—34no—
187C2×C4⋊AGL(1,𝔽5)—34no—
188C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic, complemented
189C2×C4×AGL(1,𝔽5)—34no—
190C2×C4×AGL(1,𝔽5)—34no—
191C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic, complemented
192C4×H(5,𝔽2)—151noSylow
193C23×C3×C5C22×C412yescomplemented
194C22×D15C22×C414yescomplemented
195C22×C5×D3C22×C414yescomplemented
196C22×C3×D5—42no—
197C22×C3×D5—42no—
198C22×C3×D5C22×C414yescomplemented
199C22×C3×D5C22×C412yescomplemented
200C22×C3×D5C2414yes—
201C22×C3×D5C2411yescharacteristic
202C2×D3×D5—44no—
203C2×D3×D5—44no—
204C2×D3×D5C22×C418yescomplemented
205C2×D3×D5C2414yes—
206C2×ΓL(1,𝔽16)—44no—
207C2×ΓL(1,𝔽16)—44no—
208C2×ΓL(1,𝔽16)C2414yes—
209C2×ΓL(1,𝔽16)C2414yes—
210C2×C3×AGL(1,𝔽5)—28no—
211C2×C3×AGL(1,𝔽5)—22no—
212C2×C3×AGL(1,𝔽5)—42no—
213C2×C3×AGL(1,𝔽5)—44no—
214C2×C3×AGL(1,𝔽5)—41no—
215C2×C3×AGL(1,𝔽5)C2412yes—
216C2×C3×AGL(1,𝔽5)C2414yes—
217C2×C3×AGL(1,𝔽5)C2411yescharacteristic
218C2×C3×AGL(1,𝔽5)C2411yescharacteristic
219D3×AGL(1,𝔽5)—28no—
220D3×AGL(1,𝔽5)—48no—
221D3×AGL(1,𝔽5)—44no—
222C3×C5×D4C22×C414yescomplemented
223C2×C3×C4×C5C22×C411yescharacteristic, complemented
224#1220C22×C418yescomplemented
225#1220C22×C414yescomplemented
226C2×Dic15C22×C414yescomplemented
227D60C22×C412yescomplemented
228C4×D15C22×C414yescomplemented
229Dic30C22×C412yescomplemented
230C5×#67C22×C418yescomplemented
231C5×#67C22×C414yescomplemented
232C2×C5×Dic3C22×C414yescomplemented
233C5×D12C22×C412yescomplemented
234C4×C5×D3C22×C414yescomplemented
235C5×Dic6C22×C412yescomplemented
236C3×C22⋊D5C22×C418yescomplemented
237C2×C3×Dic5C22×C411yescharacteristic, complemented
238C3×D20C22×C414yescomplemented
239C3×C4×D5C22×C412yescomplemented
240C3×C4×D5C2412yes—
241#1204C22×C414yescomplemented
242#1203C22×C414yescomplemented
243#1202C22×C418yescomplemented
244#1202C22×C414yescomplemented
245#1201C22×C418yescomplemented
246#1201C22×C414yescomplemented
247#1200C22×C414yescomplemented
248D3×Dic5C22×C414yescomplemented
249D5×Dic3C22×C418yescomplemented
250D5×Dic3C2414yes—
251C22×C3×D4—51no—
252C23×C3×C4—52no—
253C22×#67—54no—
254#1004—51no—
255#1004—54no—
256#1004—54no—
257#1004—54no—
258#1004—52no—
259#1004AGL(1,𝔽5)11yescharacteristic, direct product factor
260C2×#237—54no—
261C2×D3×D4—54no—
262C2×#235—52no—
263C22×C4×D3—54no—
264C3×C4×D4—54no—
265C3×C4×D4—54no—
266C2×C3×C4⋊C4—51no—
267C2×C3×C22⋊C4—52no—
268C2×C3×C42—51no—
269C2×#217—54no—
270D4×Dic3—54no—
271D4×Dic3—54no—
272C4×#67—54no—
273C4×#67—54no—
274C4×#67—58no—
275C4×#67—58no—
276C4×#67—58no—
277C2×(C2×D3)⋊C4—54no—
278#926—52no—
279C2×Dic3⋊C4—54no—
280C2×C4×Dic3—54no—
281#893—54no—
282#892—54no—
283D3×C4⋊C4—54no—
284#887—54no—
285#67⋊C4—58no—
286#67⋊C4—58no—
287D3×C22⋊C4—58no—
288#877—58no—
289C4×D12—52no—
290C4×D12—52no—
291#872—54no—
292C42×D3—54no—
293C4×Dic6—52no—
294C4×Dic6—52no—
295C23×D5—34no—
296C23×D5C22×D312yes—
297C22×AGL(1,𝔽5)—34no—
298C22×AGL(1,𝔽5)—34no—
299C22×AGL(1,𝔽5)—34no—
300C22×AGL(1,𝔽5)—34no—
301C22×AGL(1,𝔽5)—38no—
302C22×AGL(1,𝔽5)—44no—
303C22×AGL(1,𝔽5)—128no—
304C22×AGL(1,𝔽5)C22×D314yes—
305C22×AGL(1,𝔽5)C22×D311yescharacteristic
306C22×AGL(1,𝔽5)C22×D311yescharacteristic
307C22×AGL(1,𝔽5)C22×D314yes—
308C22×AGL(1,𝔽5)C22×D312yes—
309C5×#41—34no—
310C5×#41—32no—
311C2×C5×D4—34no—
312C2×C5×D4—34no—
313C2×C5×D4C4×D311yescharacteristic, complemented
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—38no—
317C2×C22⋊D5C4×D312yescomplemented
318#713—34no—
319#713—32no—
320Q8×D5—32no—
321#711—34no—
322#711—38no—
323#711—34no—
324#711—32no—
325D4×D5—38no—
326D4×D5—38no—
327D4×D5—34no—
328D4×D5—38no—
329D4×D5—34no—
330D4×D5—38no—
331D4×D5—34no—
332D4×D5—32no—
333D4×D5C4×D314yescomplemented
334D4×D5C22×D314yes—
335#709—32no—
336#709—38no—
337#709—34no—
338#709—34no—
339C2×D20—34no—
340C2×D20—34no—
341C2×D20C4×D311yescharacteristic, complemented
342C2×C4×D5—34no—
343C2×C4×D5—34no—
344C2×C4×D5C22×D311yescharacteristic
345C22⋊AGL(1,𝔽5)—34no—
346C22⋊AGL(1,𝔽5)—38no—
347C22⋊AGL(1,𝔽5)—38no—
348C22⋊AGL(1,𝔽5)—34no—
349C22⋊AGL(1,𝔽5)—34no—
350C22⋊AGL(1,𝔽5)C22×D318yes—
351C4⋊AGL(1,𝔽5)—38no—
352C4⋊AGL(1,𝔽5)—34no—
353C4⋊AGL(1,𝔽5)—34no—
354C4⋊AGL(1,𝔽5)—32no—
355C4⋊AGL(1,𝔽5)—32no—
356C4⋊AGL(1,𝔽5)C22×D314yes—
357C4×AGL(1,𝔽5)—34no—
358C4×AGL(1,𝔽5)—38no—
359C4×AGL(1,𝔽5)—34no—
360C4×AGL(1,𝔽5)—34no—
361C4×AGL(1,𝔽5)C22×D312yes—
362C4×AGL(1,𝔽5)C22×D312yes—
363C2×H(5,𝔽2)—151no—
364#520—152no—
365#520—154no—
366#518—154no—
367#518—154no—
368#518—151no—
369C4×#41—152no—
370C4×#41—154no—
371C2×C4×D4—51no—
372C2×C4×D4—154no—
373C2×C4×D4—154no—
374C22×C3×C5—42no—
375C22×C3×C5C23×C411yescharacteristic
376C22×C3×C5C23×C414yes—
377C2×D15—44no—
378C2×D15C23×C414yes—
379C2×C5×D3—44no—
380C2×C5×D3C23×C414yes—
381C2×C3×D5—21no—
382C2×C3×D5—24no—
383C2×C3×D5—21no—
384C2×C3×D5—24no—
385C2×C3×D5—42no—
386C2×C3×D5—44no—
387C2×C3×D5C23×C414yes—
388C2×C3×D5C23×C411yescharacteristic
389C2×C3×D5C2511yescharacteristic
390D3×D5—24no—
391D3×D5—24no—
392D3×D5—48no—
393ΓL(1,𝔽16)—24no—
394ΓL(1,𝔽16)—24no—
395C3×AGL(1,𝔽5)—24no—
396C3×AGL(1,𝔽5)—21no—
397C3×AGL(1,𝔽5)—22no—
398C3×AGL(1,𝔽5)H(5,𝔽2)12yescomplemented
399C3×C4×C5C23×C412yes—
400Dic15C23×C414yes—
401C3×Dic5C23×C412yes—
402C5×Dic3C23×C414yes—
403C24×C3—52no—
404C23×D3—54no—
405C2×C3×D4—52no—
406C2×C3×D4—54no—
407C2×C3×D4—54no—
408C2×C3×D4—51no—
409C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
410C22×C3×C4—51no—
411C22×C3×C4—54no—
412C22×C3×C4—51no—
413C22×C3×C4—54no—
414C22×C3×C4—51no—
415C22×C3×C4—52no—
416C22×C3×C4—204no—
417C2×#67—54no—
418C2×#67—54no—
419C2×#67—58no—
420C2×#67—58no—
421C2×#67—58no—
422C2×#67—54no—
423C2×#67—54no—
424C2×#67C2×AGL(1,𝔽5)14yescomplemented
425C22×Dic3—54no—
426C22×Dic3—54no—
427C22×Dic3—54no—
428#237—54no—
429#237—58no—
430#237—58no—
431#237—54no—
432#237—54no—
433#237C2×AGL(1,𝔽5)14yescomplemented
434D3×D4—58no—
435D3×D4—54no—
436D3×D4—58no—
437D3×D4—54no—
438D3×D4—54no—
439D3×D4C2×AGL(1,𝔽5)14yescomplemented
440#235—52no—
441#235—54no—
442#235—52no—
443#235—54no—
444#235—52no—
445#235C2×AGL(1,𝔽5)12yescomplemented
446C2×D12—52no—
447C2×C4×D3—54no—
448C2×C4×D3—54no—
449C2×C4×D3—54no—
450C2×C4×D3—58no—
451C2×C4×D3—208no—
452C2×Dic6—52no—
453C3×C4⋊C4—54no—
454C3×C22⋊C4—58no—
455C3×C42—52no—
456C3×C42—52no—
457#217—58no—
458#217—54no—
459(C2×D3)⋊C4—54no—
460(C2×D3)⋊C4—54no—
461(C2×D3)⋊C4—58no—
462C4⋊Dic3—52no—
463C4⋊Dic3—52no—
464Dic3⋊C4—54no—
465Dic3⋊C4—54no—
466Dic3⋊C4—58no—
467C4×Dic3—54no—
468C4×Dic3—54no—
469C4×Dic3—58no—
470C4×Dic3—54no—
471C23×C5—34no—
472C23×C5C2×C4×D312yescomplemented
473C22×D5—34no—
474C22×D5—34no—
475C22×D5—38no—
476C22×D5—42no—
477C22×D5—42no—
478C22×D5—124no—
479C22×D5—124no—
480C22×D5C2×C4×D314yescomplemented
481C22×D5C2×C4×D312yescomplemented
482C22×D5C23×D311yescharacteristic
483C22×D5C23×D314yes—
484C2×AGL(1,𝔽5)—22no—
485C2×AGL(1,𝔽5)—28no—
486C2×AGL(1,𝔽5)—34no—
487C2×AGL(1,𝔽5)—34no—
488C2×AGL(1,𝔽5)—44no—
489C2×AGL(1,𝔽5)—42no—
490C2×AGL(1,𝔽5)—41no—
491C2×AGL(1,𝔽5)—68no—
492C2×AGL(1,𝔽5)—124no—
493C2×AGL(1,𝔽5)—128no—
494C2×AGL(1,𝔽5)—124no—
495C2×AGL(1,𝔽5)—124no—
496C2×AGL(1,𝔽5)C23×D312yes—
497C2×AGL(1,𝔽5)C23×D314yes—
498C2×AGL(1,𝔽5)C23×D311yescharacteristic
499C2×AGL(1,𝔽5)C23×D311yescharacteristic
500C5×Q8—32no—
501C5×D4—38no—
502C5×D4—34no—
503C5×D4—32no—
504C5×D4C2×C4×D314yescomplemented
505C2×C4×C5—34no—
506C2×C4×C5—34no—
507C2×C4×C5C2×C4×D311yescharacteristic, complemented
508C22⋊D5—38no—
509C22⋊D5—34no—
510C22⋊D5—38no—
511C22⋊D5—34no—
512C22⋊D5—34no—
513C22⋊D5C2×C4×D318yescomplemented
514C2×Dic5—34no—
515C2×Dic5—34no—
516C2×Dic5C2×C4×D311yescharacteristic, complemented
517D20—38no—
518D20—34no—
519D20—32no—
520D20C2×C4×D314yescomplemented
521C4×D5—38no—
522C4×D5—34no—
523C4×D5—34no—
524C4×D5—34no—
525C4×D5C2×C4×D312yescomplemented
526C4×D5C23×D312yes—
527Dic10—32no—
528Dic10—34no—
529H(5,𝔽2)—31no—
530H(5,𝔽2)—154no—
531H(5,𝔽2)—154no—
532H(5,𝔽2)—154no—
533H(5,𝔽2)—152no—
534H(5,𝔽2)—151no—
535C2×#41—152no—
536C2×#41—154no—
537C22×D4—51no—
538C22×D4—154no—
539C22×D4—154no—
540C23×C4—52no—
541C23×C4—154no—
542C4×Q8—152no—
543C4×Q8—152no—
544C4×Q8—154no—
545C4×D4—54no—
546C4×D4—54no—
547C4×D4—152no—
548C4×D4—152no—
549C4×D4—158no—
550C4×D4—158no—
551C4×D4—154no—
552C4×D4—154no—
553C4×D4—158no—
554C4×D4—158no—
555C4×D4—158no—
556C4×D4—154no—
557C4×D4—154no—
558C4×D4—154no—
559#117—154no—
560#117—158no—
561#117—154no—
562#117—152no—
563C2×C4⋊C4—51no—
564C2×C4⋊C4—154no—
565C2×C4⋊C4—154no—
566C2×C22⋊C4—52no—
567C2×C22⋊C4—158no—
568C2×C22⋊C4—154no—
569C2×C22⋊C4—154no—
570C2×C42—51no—
571C2×C42—154no—
572C2×C42—154no—
573C2×C3×C5—21no—
574C2×C3×C5—24no—
575C2×C3×C5C24×C411yescharacteristic
576D15—24no—
577C3×D5—24no—
578C3×D5—21no—
579C3×D5C2×H(5,𝔽2)11yescharacteristic
580C3×D5#58511yescharacteristic
581C5×D3—24no—
582C23×C3—51no—
583C23×C3—54no—
584C23×C3—52no—
585C23×C3—54no—
586C23×C3—202no—
587C23×C3—202no—
588C23×C3C22×AGL(1,𝔽5)12yescomplemented
589C22×D3—54no—
590C22×D3—54no—
591C22×D3—58no—
592C22×D3—204no—
593C22×D3—204no—
594C22×D3C22×AGL(1,𝔽5)14yescomplemented
595C3×D4—58no—
596C3×D4—54no—
597C3×D4C22×AGL(1,𝔽5)14yescomplemented
598C2×C3×C4—51no—
599C2×C3×C4—51no—
600C2×C3×C4—52no—
601C2×C3×C4—52no—
602C2×C3×C4—52no—
603C2×C3×C4—54no—
604C2×C3×C4—51no—
605C2×C3×C4—108no—
606C2×C3×C4—102no—
607C2×C3×C4—201no—
608C2×C3×C4—202no—
609C2×C3×C4—204no—
610C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic, complemented
611#67—54no—
612#67—58no—
613#67—54no—
614#67—58no—
615#67—54no—
616#67—58no—
617#67C22×AGL(1,𝔽5)14yescomplemented
618#67C22×AGL(1,𝔽5)18yescomplemented
619C2×Dic3—54no—
620C2×Dic3—58no—
621C2×Dic3—54no—
622C2×Dic3—54no—
623C2×Dic3—54no—
624C2×Dic3—204no—
625C2×Dic3—204no—
626C2×Dic3C22×AGL(1,𝔽5)14yescomplemented
627D12—54no—
628D12—52no—
629D12C22×AGL(1,𝔽5)12yescomplemented
630C4×D3—54no—
631C4×D3—54no—
632C4×D3—54no—
633C4×D3—108no—
634C4×D3—204no—
635C4×D3—208no—
636C4×D3C22×AGL(1,𝔽5)14yescomplemented
637Dic6—52no—
638Dic6—54no—
639Dic6C22×AGL(1,𝔽5)12yescomplemented
640C22×C5—34no—
641C22×C5—42no—
642C22×C5—124no—
643C22×C5C22×C4×D314yes—
644C22×C5C22×C4×D311yescharacteristic
645C2×D5—21no—
646C2×D5—24no—
647C2×D5—21no—
648C2×D5—24no—
649C2×D5—34no—
650C2×D5—44no—
651C2×D5—42no—
652C2×D5—64no—
653C2×D5—64no—
654C2×D5—128no—
655C2×D5—124no—
656C2×D5C22×C4×D314yes—
657C2×D5C22×C4×D311yescharacteristic
658C2×D5C24×D311yescharacteristic
659AGL(1,𝔽5)—21no—
660AGL(1,𝔽5)—24no—
661AGL(1,𝔽5)—22no—
662AGL(1,𝔽5)—64no—
663AGL(1,𝔽5)—64no—
664AGL(1,𝔽5)#100412yesdirect product factor
665C4×C5—34no—
666C4×C5C22×C4×D312yes—
667Dic5—34no—
668Dic5C22×C4×D312yes—
669C24—52no—
670C24—154no—
671#41—34no—
672#41—32no—
673#41—154no—
674#41—158no—
675#41—154no—
676#41—154no—
677#41—152no—
678#41—152no—
679#41—158no—
680#41—154no—
681#41—154no—
682#41—152no—
683C2×Q8—152no—
684C2×D4—34no—
685C2×D4—34no—
686C2×D4—52no—
687C2×D4—54no—
688C2×D4—54no—
689C2×D4—51no—
690C2×D4—154no—
691C2×D4—154no—
692C2×D4—152no—
693C2×D4—158no—
694C2×D4—154no—
695C2×D4—158no—
696C2×D4—154no—
697C2×D4—158no—
698C2×D4—158no—
699C2×D4—158no—
700C2×D4—154no—
701C2×D4—154no—
702C2×D4—154no—
703C2×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—54no—
707C22×C4—51no—
708C22×C4—52no—
709C22×C4—54no—
710C22×C4—154no—
711C22×C4—154no—
712C22×C4—154no—
713C22×C4—154no—
714C22×C4—158no—
715C22×C4—154no—
716C22×C4—154no—
717C22×C4—204no—
718C22×C4—608no—
719C4⋊C4—54no—
720C4⋊C4—154no—
721C4⋊C4—158no—
722C4⋊C4—152no—
723C4⋊C4—154no—
724C4⋊C4—152no—
725C22⋊C4—58no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—158no—
729C22⋊C4—158no—
730C22⋊C4—154no—
731C42—52no—
732C42—52no—
733C42—154no—
734C42—154no—
735C42—154no—
736C42—158no—
737C3×C5C4×H(5,𝔽2)11yescharacteristic, complemented, Hall
738C22×C3—42no—
739C22×C3—51no—
740C22×C3—54no—
741C22×C3—51no—
742C22×C3—104no—
743C22×C3—104no—
744C22×C3—101no—
745C22×C3—101no—
746C22×C3—204no—
747C22×C3—202no—
748C22×C3C23×AGL(1,𝔽5)14yes—
749C22×C3C23×AGL(1,𝔽5)11yescharacteristic
750C2×D3—44no—
751C2×D3—54no—
752C2×D3—104no—
753C2×D3—104no—
754C2×D3—208no—
755C2×D3—204no—
756C2×D3C23×AGL(1,𝔽5)14yes—
757C3×C4—52no—
758C3×C4—52no—
759C3×C4—104no—
760C3×C4—102no—
761C3×C4—101no—
762C3×C4C23×AGL(1,𝔽5)12yes—
763Dic3—54no—
764Dic3—104no—
765Dic3—104no—
766Dic3C23×AGL(1,𝔽5)14yes—
767C2×C5—21no—
768C2×C5—24no—
769C2×C5—64no—
770C2×C5C23×C4×D311yescharacteristic
771D5—21no—
772D5—24no—
773D5—64no—
774D5C2×#100411yescharacteristic
775D5#596411yescharacteristic
776C23—34no—
777C23—54no—
778C23—51no—
779C23—54no—
780C23—52no—
781C23—154no—
782C23—158no—
783C23—154no—
784C23—202no—
785C23—202no—
786C23—604no—
787C23—604no—
788C23C2×D3×AGL(1,𝔽5)12yescomplemented
789Q8—32no—
790Q8—154no—
791Q8—152no—
792D4—38no—
793D4—34no—
794D4—32no—
795D4—58no—
796D4—54no—
797D4—154no—
798D4—158no—
799D4—154no—
800D4—154no—
801D4—158no—
802D4—158no—
803D4—154no—
804D4—152no—
805D4C2×D3×AGL(1,𝔽5)14yescomplemented
806C2×C4—34no—
807C2×C4—34no—
808C2×C4—51no—
809C2×C4—51no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—51no—
814C2×C4—54no—
815C2×C4—102no—
816C2×C4—108no—
817C2×C4—154no—
818C2×C4—154no—
819C2×C4—158no—
820C2×C4—154no—
821C2×C4—154no—
822C2×C4—154no—
823C2×C4—154no—
824C2×C4—154no—
825C2×C4—204no—
826C2×C4—202no—
827C2×C4—201no—
828C2×C4—308no—
829C2×C4—608no—
830C2×C4—604no—
831C2×C4—604no—
832C2×C4—604no—
833C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic, complemented
834C2×C3—24no—
835C2×C3—21no—
836C2×C3—51no—
837C2×C3—51no—
838C2×C3—104no—
839C2×C3—101no—
840C2×C3C24×AGL(1,𝔽5)11yescharacteristic
841D3—24no—
842D3—104no—
843C5C4×#100411yescharacteristic, complemented, Sylow
844C22—34no—
845C22—42no—
846C22—51no—
847C22—51no—
848C22—54no—
849C22—101no—
850C22—104no—
851C22—101no—
852C22—104no—
853C22—124no—
854C22—154no—
855C22—202no—
856C22—204no—
857C22—304no—
858C22—304no—
859C22—604no—
860C22—608no—
861C22C22×D3×AGL(1,𝔽5)14yes—
862C22C22×D3×AGL(1,𝔽5)11yescharacteristic
863C4—34no—
864C4—52no—
865C4—52no—
866C4—101no—
867C4—104no—
868C4—102no—
869C4—154no—
870C4—304no—
871C4—304no—
872C4C22×D3×AGL(1,𝔽5)12yes—
873C3AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic, complemented, Sylow
874C2—21no—
875C2—24no—
876C2—51no—
877C2—51no—
878C2—64no—
879C2—101no—
880C2—104no—
881C2—304no—
882C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC2×C3×C5×D4C2×C4
prime radicalD5×#1004C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×H(5,𝔽2)
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11756987C2semidirect
3. C2×C3×D4×AGL(1,𝔽5)C2semidirect
4. #11756871C2semidirect
5. C2×AGL(1,𝔽5)×#67C2semidirect
6. #11756846C2semidirect
7. #11756845C2semidirect
8. AGL(1,𝔽5)×#237C2semidirect
9. D3×D4×AGL(1,𝔽5)C2semidirect
10. #11756836C2semidirect
11. AGL(1,𝔽5)×#235C2semidirect
13. C23×C3×AGL(1,𝔽5)C22semidirect
14. C22×D3×AGL(1,𝔽5)C22semidirect
15. #92095C4semidirect
16. C5×#1004C4semidirect
18. #92049C4semidirect
20. #92026C4semidirect
21. #92025C4semidirect
24. #92017C4semidirect
26. C2×#6763C22semidirect
27. D4×ΓL(1,𝔽16)C22semidirect
28. D4×ΓL(1,𝔽16)C22semidirect
29. #91989C22semidirect
30. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
31. C3×D4×AGL(1,𝔽5)C22semidirect
32. C3×D4×AGL(1,𝔽5)C22semidirect
33. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
34. C2×C3×C4×AGL(1,𝔽5)C22semidirect
35. #67⋊AGL(1,𝔽5)C22semidirect
36. #67⋊AGL(1,𝔽5)C22semidirect
37. D3×C22⋊AGL(1,𝔽5)C22semidirect
38. AGL(1,𝔽5)×#67C22semidirect
39. AGL(1,𝔽5)×#67C22semidirect
40. AGL(1,𝔽5)×#67C22semidirect
41. AGL(1,𝔽5)×#67C22semidirect
42. AGL(1,𝔽5)×#67C22semidirect
43. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
44. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
45. #91923C22semidirect
46. C2×Dic3×AGL(1,𝔽5)C22semidirect
47. #91921C22semidirect
48. D3×C4⋊AGL(1,𝔽5)C22semidirect
49. AGL(1,𝔽5)×D12C22semidirect
50. AGL(1,𝔽5)×D12C22semidirect
51. C4×D3×AGL(1,𝔽5)C22semidirect
52. #91909C22semidirect
53. ΓL(1,𝔽16)⋊Q8C22semidirect
54. #91907C22semidirect
55. AGL(1,𝔽5)×Dic6C22semidirect
56. AGL(1,𝔽5)×Dic6C22semidirect
68. C2×D4×AGL(1,𝔽5)D3semidirect
83. C2×C3×C5×D4C2×C4semidirect
84. C2×#1220C2×C4semidirect
85. #6819C2×C4semidirect
86. D4×D15C2×C4semidirect
87. #6817C2×C4semidirect
88. C2×C5×#67C2×C4semidirect
89. C5×#237C2×C4semidirect
90. C5×D3×D4C2×C4semidirect
91. C5×#235C2×C4semidirect
92. C2×C3×C22⋊D5C2×C4semidirect
93. C3×D4×D5C2×C4semidirect
95. C2×C3×D20C2×C4semidirect
97. #6790C2×C4semidirect
98. D3×C22⋊D5C2×C4semidirect
99. D5×#67C2×C4semidirect
100. D5×#67C2×C4semidirect
103. C2×#1202C2×C4semidirect
104. C2×#1201C2×C4semidirect
105. #6782C2×C4semidirect
106. #6780C2×C4semidirect
107. #6779C2×C4semidirect
109. #6777C2×C4semidirect
110. D3×D20C2×C4semidirect
113. #6773C2×C4semidirect
114. #6772C2×C4semidirect
115. #6771C2×C4semidirect
116. #6766C2×C4semidirect
117. #6765C2×C4semidirect
149. C23×AGL(1,𝔽5)C2×D3semidirect
164. C2×C22⋊AGL(1,𝔽5)C2×D3semidirect
180. D4×AGL(1,𝔽5)C2×D3semidirect
181. D4×AGL(1,𝔽5)C2×D3semidirect
188. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
191. C2×C4×AGL(1,𝔽5)C2×D3semidirect
193. C23×C3×C5C22×C4semidirect
194. C22×D15C22×C4semidirect
195. C22×C5×D3C22×C4semidirect
198. C22×C3×D5C22×C4semidirect
199. C22×C3×D5C22×C4semidirect
204. C2×D3×D5C22×C4semidirect
222. C3×C5×D4C22×C4semidirect
223. C2×C3×C4×C5C22×C4semidirect
224. #1220C22×C4semidirect
225. #1220C22×C4semidirect
226. C2×Dic15C22×C4semidirect
227. D60C22×C4semidirect
228. C4×D15C22×C4semidirect
229. Dic30C22×C4semidirect
230. C5×#67C22×C4semidirect
231. C5×#67C22×C4semidirect
232. C2×C5×Dic3C22×C4semidirect
233. C5×D12C22×C4semidirect
234. C4×C5×D3C22×C4semidirect
235. C5×Dic6C22×C4semidirect
236. C3×C22⋊D5C22×C4semidirect
237. C2×C3×Dic5C22×C4semidirect
238. C3×D20C22×C4semidirect
239. C3×C4×D5C22×C4semidirect
241. #1204C22×C4semidirect
242. #1203C22×C4semidirect
243. #1202C22×C4semidirect
244. #1202C22×C4semidirect
245. #1201C22×C4semidirect
246. #1201C22×C4semidirect
247. #1200C22×C4semidirect
248. D3×Dic5C22×C4semidirect
249. D5×Dic3C22×C4semidirect
259. #1004AGL(1,𝔽5)direct (N × H)
313. C2×C5×D4C4×D3semidirect
317. C2×C22⋊D5C4×D3semidirect
333. D4×D5C4×D3semidirect
341. C2×D20C4×D3semidirect
398. C3×AGL(1,𝔽5)H(5,𝔽2)semidirect
409. C2×C3×D4C2×AGL(1,𝔽5)semidirect
424. C2×#67C2×AGL(1,𝔽5)semidirect
433. #237C2×AGL(1,𝔽5)semidirect
439. D3×D4C2×AGL(1,𝔽5)semidirect
445. #235C2×AGL(1,𝔽5)semidirect
472. C23×C5C2×C4×D3semidirect
480. C22×D5C2×C4×D3semidirect
481. C22×D5C2×C4×D3semidirect
504. C5×D4C2×C4×D3semidirect
507. C2×C4×C5C2×C4×D3semidirect
513. C22⋊D5C2×C4×D3semidirect
516. C2×Dic5C2×C4×D3semidirect
520. D20C2×C4×D3semidirect
525. C4×D5C2×C4×D3semidirect
588. C23×C3C22×AGL(1,𝔽5)semidirect
594. C22×D3C22×AGL(1,𝔽5)semidirect
597. C3×D4C22×AGL(1,𝔽5)semidirect
610. C2×C3×C4C22×AGL(1,𝔽5)semidirect
617. #67C22×AGL(1,𝔽5)semidirect
618. #67C22×AGL(1,𝔽5)semidirect
626. C2×Dic3C22×AGL(1,𝔽5)semidirect
629. D12C22×AGL(1,𝔽5)semidirect
636. C4×D3C22×AGL(1,𝔽5)semidirect
639. Dic6C22×AGL(1,𝔽5)semidirect
664. AGL(1,𝔽5)#1004direct (N × H)
703. C2×D4D3×AGL(1,𝔽5)semidirect
737. C3×C5C4×H(5,𝔽2)semidirect
788. C23C2×D3×AGL(1,𝔽5)semidirect
805. D4C2×D3×AGL(1,𝔽5)semidirect
833. C2×C4C2×D3×AGL(1,𝔽5)semidirect
843. C5C4×#1004semidirect
873. C3AGL(1,𝔽5)×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
D5×#10042
#117569872
C2×C3×D4×AGL(1,𝔽5)2
#117568712
C2×AGL(1,𝔽5)×#672
#117568462
#117568452
AGL(1,𝔽5)×#2372
D3×D4×AGL(1,𝔽5)2
#117568362
AGL(1,𝔽5)×#2352
AGL(1,𝔽5)×H(5,𝔽2)3
C4×#10045