Finite Group Databasebeta

← C2×AGL(1,𝔽5)×#237 #14478944

Subgroups — C2×AGL(1,𝔽5)×#237 #14478944

Order 1920.

3456 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
1C2×D5×#237C211yesmaximal, characteristic
2C2×D4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C2×#67⋊AGL(1,𝔽5)C212yesmaximal, complemented
5C2×AGL(1,𝔽5)×#67C212yesmaximal, complemented
6C2×#91923C212yesmaximal, complemented
7C22×Dic3×AGL(1,𝔽5)C212yesmaximal, complemented
8AGL(1,𝔽5)×#237C2116yesmaximal, direct product factor
9C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
11C2×#91907C211yesmaximal, characteristic, complemented
12C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic, complemented
13C2×#41×AGL(1,𝔽5)—31nomaximal, Hall
14C23×ΓL(1,𝔽16)C2212yes—
15C23×C3×AGL(1,𝔽5)C2212yes—
16C22×D3×AGL(1,𝔽5)C2211yescharacteristic
17C22×D3×AGL(1,𝔽5)C2211yescharacteristic
18C2×#6819C411yescharacteristic, complemented
19C2×C5×#237C411yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×D5×#67C2212yes—
22C2×#6780C412yescomplemented
23C2×#6779C412yescomplemented
24C22×D5×Dic3C2212yes—
25D5×#237C418yescomplemented
26D5×#237C2218yes—
27C2×C4×D3×D5C2211yescharacteristic
28C2×#6766C411yescharacteristic, complemented
29C2×#6765C411yescharacteristic, complemented
30C2×D5×Dic6C2211yescharacteristic
31C2×#6763C2212yes—
32D4×ΓL(1,𝔽16)C2218yescomplemented
33C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
34C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
35C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
36C3×D4×AGL(1,𝔽5)C2218yescomplemented
37C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
38C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
39#67⋊AGL(1,𝔽5)C22116yescomplemented
40AGL(1,𝔽5)×#67C22116yescomplemented
41C2×Dic3⋊AGL(1,𝔽5)C2212yes—
42C2×Dic3⋊AGL(1,𝔽5)C2212yes—
43C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
44#91923C22116yescomplemented
45C2×Dic3×AGL(1,𝔽5)C2212yes—
46C2×Dic3×AGL(1,𝔽5)C2212yes—
47C2×Dic3×AGL(1,𝔽5)C2212yes—
48C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
49C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
50C2×Dic3×AGL(1,𝔽5)C22116yescomplemented
51C4×D3×AGL(1,𝔽5)C2218yescomplemented
52ΓL(1,𝔽16)⋊Q8C2218yescomplemented
53#91907C2218yescomplemented
54AGL(1,𝔽5)×Dic6C2218yescomplemented
55C2×C4×#237—51nomaximal, Hall
56C2×D5×#41—31no—
57#41×AGL(1,𝔽5)—316no—
58C2×Q8×AGL(1,𝔽5)—31no—
59C2×Q8×AGL(1,𝔽5)—31no—
60C2×D4×AGL(1,𝔽5)—32no—
61C2×D4×AGL(1,𝔽5)—31no—
62C2×D4×AGL(1,𝔽5)—32no—
63C2×D4×AGL(1,𝔽5)D311yescharacteristic, complemented
64C2×#4130—32no—
65C2×#4130—31no—
66C22×C4×AGL(1,𝔽5)—32no—
67C22×C4×AGL(1,𝔽5)—31no—
68C23×C3×D5C2312yes—
69C22×D3×D5C2311yescharacteristic
70C22×ΓL(1,𝔽16)—28no—
71C22×ΓL(1,𝔽16)C2312yes—
72C22×ΓL(1,𝔽16)C2311yescharacteristic
73C22×ΓL(1,𝔽16)C2318yes—
74C22×ΓL(1,𝔽16)C2311yescharacteristic
75C22×C3×AGL(1,𝔽5)—28no—
76C22×C3×AGL(1,𝔽5)C2312yes—
77C22×C3×AGL(1,𝔽5)C2311yescharacteristic
78C22×C3×AGL(1,𝔽5)C2318yes—
79C22×C3×AGL(1,𝔽5)C2311yescharacteristic
80C2×D3×AGL(1,𝔽5)—24no—
81C2×D3×AGL(1,𝔽5)—24no—
82C2×D3×AGL(1,𝔽5)C2314yes—
83C2×D3×AGL(1,𝔽5)C2314yes—
84C2×C3×C5×D4C2×C411yescharacteristic, complemented
85C2×#1220C2×C412yescomplemented
86C22×Dic15C2×C412yescomplemented
87#6819C2×C418yescomplemented
88C2×C4×D15C2×C411yescharacteristic, complemented
89C2×Dic30C2×C411yescharacteristic, complemented
90C2×C5×#67C2×C412yescomplemented
91C22×C5×Dic3C2×C412yescomplemented
92C5×#237C2×C418yescomplemented
93C2×C4×C5×D3C2×C411yescharacteristic, complemented
94C2×C5×Dic6C2×C411yescharacteristic, complemented
95C2×C3×C22⋊D5C2×C412yescomplemented
96C3×D4×D5C2×C414yescomplemented
97C3×D4×D5C2314yes—
98C2×C3×D20C2×C411yescharacteristic, complemented
99C2×C3×C4×D5C2311yescharacteristic
100D5×#67C2×C418yescomplemented
101D5×#67C2318yes—
102C2×#1204C2×C412yescomplemented
103C2×#1202C2×C412yescomplemented
104C2×#1201C2×C412yescomplemented
105C2×#1200C2×C411yescharacteristic, complemented
106C2×D3×Dic5C2×C411yescharacteristic, complemented
107#6780C2×C4116yescomplemented
108#6779C2×C4116yescomplemented
109C2×D5×Dic3C2×C418yescomplemented
110C2×D5×Dic3C2×C412yescomplemented
111C2×D5×Dic3C2×C412yescomplemented
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2312yes—
114C2×D5×Dic3C2318yes—
115C4×D3×D5C2×C414yescomplemented
116C4×D3×D5C2314yes—
117#6766C2×C418yescomplemented
118#6765C2×C418yescomplemented
119D5×Dic6C2×C414yescomplemented
120D5×Dic6C2314yes—
121#6763C2318yes—
122C4⋊ΓL(1,𝔽16)C2314yes—
123C4×ΓL(1,𝔽16)C2314yes—
124C3×C22⋊AGL(1,𝔽5)C2318yes—
125C3×C4⋊AGL(1,𝔽5)C2314yes—
126C3×C4×AGL(1,𝔽5)C2314yes—
127Dic3⋊AGL(1,𝔽5)C2318yes—
128Dic3⋊AGL(1,𝔽5)C2318yes—
129(C2×D3)⋊AGL(1,𝔽5)C2318yes—
130Dic3×AGL(1,𝔽5)C2318yes—
131Dic3×AGL(1,𝔽5)C2318yes—
132Dic3×AGL(1,𝔽5)C2318yes—
133Dic3×AGL(1,𝔽5)C2314yes—
134Dic3×AGL(1,𝔽5)C2314yes—
135C22×#237—51no—
136C2×C3×C4×D4—51no—
137C2×D4×Dic3—51no—
138C2×C4×#67—52no—
139C22×C4×Dic3—52no—
140C4×#237—516no—
141C2×#892—51no—
142C2×#887—51no—
143C2×#67⋊C4—52no—
144C2×#877—52no—
145C2×C42×D3—51no—
146C2×C4×Dic6—51no—
147C23×AGL(1,𝔽5)—32no—
148C23×AGL(1,𝔽5)—31no—
149C23×AGL(1,𝔽5)—31no—
150C23×AGL(1,𝔽5)C2×D312yes—
151C2×C5×#41—31no—
152D5×#41—38no—
153D5×#41—38no—
154C2×#713—31no—
155C2×Q8×D5—31no—
156C2×#711—31no—
157C2×#711—32no—
158C2×D4×D5—32no—
159C2×D4×D5C2×D311yescharacteristic
160C2×#709—32no—
161C2×#709—31no—
162C22×C4×D5—32no—
163C22×C4×D5—31no—
164C2×C22⋊AGL(1,𝔽5)—32no—
165C2×C22⋊AGL(1,𝔽5)—32no—
166C2×C22⋊AGL(1,𝔽5)C2×D312yes—
167Q8×AGL(1,𝔽5)—38no—
168Q8×AGL(1,𝔽5)—38no—
169D4×AGL(1,𝔽5)—316no—
170D4×AGL(1,𝔽5)—38no—
171D4×AGL(1,𝔽5)—316no—
172D4×AGL(1,𝔽5)C2×D318yescomplemented
173#4130—316no—
174#4130—38no—
175C2×C4⋊AGL(1,𝔽5)—32no—
176C2×C4⋊AGL(1,𝔽5)—32no—
177C2×C4⋊AGL(1,𝔽5)—31no—
178C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
179C2×C4×AGL(1,𝔽5)—31no—
180C2×C4×AGL(1,𝔽5)—32no—
181C2×C4×AGL(1,𝔽5)—31no—
182C2×C4×AGL(1,𝔽5)—32no—
183C2×C4×AGL(1,𝔽5)—32no—
184C2×C4×AGL(1,𝔽5)—316no—
185C2×C4×AGL(1,𝔽5)—31no—
186C2×C4×AGL(1,𝔽5)—38no—
187C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
188C2×C4×#41—151noSylow
189C23×C3×C5C22×C412yes—
190C22×D15C22×C411yescharacteristic
191C22×C5×D3C22×C411yescharacteristic
192C22×C3×D5—24no—
193C22×C3×D5—24no—
194C22×C3×D5C22×C412yes—
195C22×C3×D5C22×C414yes—
196C22×C3×D5C2414yes—
197C22×C3×D5C2411yescharacteristic
198C2×D3×D5—22no—
199C2×D3×D5—22no—
200C2×D3×D5C22×C412yes—
201C2×D3×D5C2412yes—
202C2×ΓL(1,𝔽16)—22no—
203C2×ΓL(1,𝔽16)—24no—
204C2×ΓL(1,𝔽16)—216no—
205C2×ΓL(1,𝔽16)#4114yescomplemented
206C2×ΓL(1,𝔽16)C2414yes—
207C2×ΓL(1,𝔽16)C2412yes—
208C2×ΓL(1,𝔽16)C2412yes—
209C2×C3×AGL(1,𝔽5)—22no—
210C2×C3×AGL(1,𝔽5)—24no—
211C2×C3×AGL(1,𝔽5)—216no—
212C2×C3×AGL(1,𝔽5)#4114yescomplemented
213C2×C3×AGL(1,𝔽5)C2414yes—
214C2×C3×AGL(1,𝔽5)C2412yes—
215C2×C3×AGL(1,𝔽5)C2412yes—
216D3×AGL(1,𝔽5)—28no—
217D3×AGL(1,𝔽5)—28no—
218C3×C5×D4C22×C414yescomplemented
219C2×C3×C4×C5C22×C411yescharacteristic
220#1220C22×C418yescomplemented
221C2×Dic15C22×C411yescharacteristic
222C2×Dic15C22×C412yes—
223C2×Dic15C22×C418yescomplemented
224C4×D15C22×C414yescomplemented
225Dic30C22×C414yescomplemented
226C5×#67C22×C418yescomplemented
227C2×C5×Dic3C22×C411yescharacteristic
228C2×C5×Dic3C22×C412yes—
229C2×C5×Dic3C22×C418yescomplemented
230C4×C5×D3C22×C414yescomplemented
231C5×Dic6C22×C414yescomplemented
232C3×C22⋊D5C22×C418yescomplemented
233C2×C3×Dic5C22×C411yescharacteristic
234C3×D20C22×C414yescomplemented
235C3×C4×D5C22×C412yes—
236C3×C4×D5C2412yes—
237#1204C22×C418yescomplemented
238#1202C22×C418yescomplemented
239#1201C22×C418yescomplemented
240#1200C22×C414yescomplemented
241D3×Dic5C22×C414yescomplemented
242D5×Dic3C22×C414yes—
243D5×Dic3C22×C412yes—
244D5×Dic3C22×C418yescomplemented
245D5×Dic3C22×C418yescomplemented
246D5×Dic3C2412yes—
247D5×Dic3C2414yes—
248C22×C3×D4—51no—
249C23×C3×C4—52no—
250C22×#67—52no—
251C23×Dic3—52no—
252C23×Dic3—52no—
253C2×#237—51no—
254C2×#237—52no—
255C2×#237—52no—
256C2×#237—58no—
257C2×#237—58no—
258C2×#237—51no—
259C2×#237—51no—
260C2×#237AGL(1,𝔽5)11yescharacteristic, direct product factor
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×Dic6—51no—
265C3×C4×D4—58no—
266C2×C3×C4⋊C4—51no—
267C2×C3×C22⋊C4—52no—
268C2×C3×C42—51no—
269C2×#217—52no—
270D4×Dic3—58no—
271C4×#67—516no—
272C2×(C2×D3)⋊C4—52no—
273C2×C4⋊Dic3—51no—
274C2×Dic3⋊C4—52no—
275C2×Dic3⋊C4—52no—
276C2×C4×Dic3—52no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279C2×C4×Dic3—52no—
280C2×C4×Dic3—52no—
281C2×C4×Dic3—516no—
282C2×C4×Dic3—51no—
283#892—58no—
284#887—58no—
285#67⋊C4—516no—
286#877—516no—
287C42×D3—58no—
288C4×Dic6—58no—
289C23×D5—31no—
290C23×D5C22×D312yes—
291C22×AGL(1,𝔽5)—28no—
292C22×AGL(1,𝔽5)—31no—
293C22×AGL(1,𝔽5)—31no—
294C22×AGL(1,𝔽5)—32no—
295C22×AGL(1,𝔽5)—38no—
296C22×AGL(1,𝔽5)—34no—
297C22×AGL(1,𝔽5)—34no—
298C22×AGL(1,𝔽5)—64no—
299C22×AGL(1,𝔽5)—68no—
300C22×AGL(1,𝔽5)—64no—
301C22×AGL(1,𝔽5)C22×D312yes—
302C22×AGL(1,𝔽5)C22×D318yes—
303C22×AGL(1,𝔽5)C22×D311yescharacteristic
304C22×AGL(1,𝔽5)C22×D311yescharacteristic
305C5×#41—38no—
306C2×C5×Q8—31no—
307C2×C5×D4—32no—
308C2×C5×D4C4×D311yescharacteristic, complemented
309C22×C4×C5—32no—
310C22×C4×C5—31no—
311C2×C22⋊D5—32no—
312C2×C22⋊D5—32no—
313C2×C22⋊D5C4×D312yescomplemented
314C22×Dic5—32no—
315C22×Dic5—31no—
316#713—38no—
317Q8×D5—34no—
318Q8×D5—34no—
319#711—38no—
320#711—316no—
321D4×D5—38no—
322D4×D5—38no—
323D4×D5C4×D314yescomplemented
324D4×D5C22×D314yes—
325#709—316no—
326#709—38no—
327C2×D20—32no—
328C2×D20C4×D311yescharacteristic, complemented
329C2×C4×D5—32no—
330C2×C4×D5—32no—
331C2×C4×D5—38no—
332C2×C4×D5—31no—
333C2×C4×D5—32no—
334C2×C4×D5—38no—
335C2×C4×D5—31no—
336C2×C4×D5—31no—
337C2×C4×D5—34no—
338C2×C4×D5—34no—
339C2×C4×D5C22×D311yescharacteristic
340C2×Dic10—31no—
341C2×Dic10—32no—
342C22⋊AGL(1,𝔽5)—38no—
343C22⋊AGL(1,𝔽5)—38no—
344C22⋊AGL(1,𝔽5)C22×D318yes—
345C4⋊AGL(1,𝔽5)—38no—
346C4⋊AGL(1,𝔽5)—38no—
347C4⋊AGL(1,𝔽5)—34no—
348C4⋊AGL(1,𝔽5)C22×D314yes—
349C4×AGL(1,𝔽5)—34no—
350C4×AGL(1,𝔽5)—38no—
351C4×AGL(1,𝔽5)—34no—
352C4×AGL(1,𝔽5)—38no—
353C4×AGL(1,𝔽5)—38no—
354C4×AGL(1,𝔽5)—34no—
355C4×AGL(1,𝔽5)C22×D314yes—
356C22×#41—151no—
357C4×#41—1516no—
358C2×C4×Q8—151no—
359C2×C4×Q8—151no—
360C2×C4×D4—51no—
361C2×C4×D4—152no—
362C2×C4×D4—152no—
363C2×C4×D4—151no—
364C2×#117—152no—
365C2×#117—151no—
366C22×C42—151no—
367C22×C42—152no—
368C22×C3×C5—24no—
369C22×C3×C5C23×C414yes—
370C22×C3×C5C23×C411yescharacteristic
371C2×D15—22no—
372C2×D15C23×C412yes—
373C2×C5×D3—22no—
374C2×C5×D3C23×C412yes—
375C2×C3×D5—24no—
376C2×C3×D5—28no—
377C2×C3×D5—24no—
378C2×C3×D5—24no—
379C2×C3×D5C23×C414yes—
380C2×C3×D5C23×C411yescharacteristic
381C2×C3×D5C2×#4112yes—
382C2×C3×D5C2×#4112yes—
383C2×C3×D5C2511yescharacteristic
384D3×D5—24no—
385D3×D5—22no—
386D3×D5—22no—
387ΓL(1,𝔽16)—22no—
388ΓL(1,𝔽16)—24no—
389ΓL(1,𝔽16)C2×#4114yescomplemented
390C3×AGL(1,𝔽5)—22no—
391C3×AGL(1,𝔽5)—24no—
392C3×AGL(1,𝔽5)C2×#4114yescomplemented
393C3×C4×C5C23×C412yes—
394Dic15C23×C412yes—
395Dic15C23×C414yes—
396C3×Dic5C23×C412yes—
397C5×Dic3C23×C412yes—
398C5×Dic3C23×C414yes—
399C24×C3—52no—
400C23×D3—51no—
401C2×C3×D4—52no—
402C2×C3×D4—54no—
403C2×C3×D4—54no—
404C2×C3×D4—51no—
405C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
406C22×C3×C4—51no—
407C22×C3×C4—51no—
408C22×C3×C4—52no—
409C22×C3×C4—58no—
410C22×C3×C4—51no—
411C22×C3×C4—108no—
412C2×#67—52no—
413C2×#67—52no—
414C2×#67—58no—
415C2×#67—58no—
416C2×#67—52no—
417C2×#67C2×AGL(1,𝔽5)12yescomplemented
418C22×Dic3—51no—
419C22×Dic3—52no—
420C22×Dic3—52no—
421C22×Dic3—52no—
422C22×Dic3—51no—
423C22×Dic3—52no—
424C22×Dic3—58no—
425C22×Dic3—58no—
426C22×Dic3—58no—
427C22×Dic3—51no—
428C22×Dic3—52no—
429C22×Dic3—108no—
430C22×Dic3C2×AGL(1,𝔽5)12yescomplemented
431#237—58no—
432#237—516no—
433#237—516no—
434#237—58no—
435#237—58no—
436#237C2×AGL(1,𝔽5)18yesdirect product factor
437C2×C4×D3—51no—
438C2×C4×D3—51no—
439C2×C4×D3—51no—
440C2×C4×D3—54no—
441C2×C4×D3—54no—
442C2×C4×D3—54no—
443C2×C4×D3—54no—
444C2×C4×D3—104no—
445C2×C4×D3—104no—
446C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
447C2×Dic6—51no—
448C2×Dic6—52no—
449C2×Dic6—54no—
450C2×Dic6—54no—
451C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
452C3×C4⋊C4—54no—
453C3×C22⋊C4—58no—
454C3×C42—54no—
455#217—58no—
456(C2×D3)⋊C4—58no—
457C4⋊Dic3—54no—
458Dic3⋊C4—58no—
459Dic3⋊C4—58no—
460C4×Dic3—58no—
461C4×Dic3—54no—
462C4×Dic3—54no—
463C4×Dic3—58no—
464C4×Dic3—58no—
465C4×Dic3—54no—
466C23×C5—31no—
467C23×C5C2×C4×D312yes—
468C22×D5—24no—
469C22×D5—24no—
470C22×D5—31no—
471C22×D5—32no—
472C22×D5—32no—
473C22×D5—62no—
474C22×D5—62no—
475C22×D5C2×C4×D312yes—
476C22×D5C2×C4×D314yes—
477C22×D5C23×D314yes—
478C22×D5C23×D311yescharacteristic
479C2×AGL(1,𝔽5)—24no—
480C2×AGL(1,𝔽5)—22no—
481C2×AGL(1,𝔽5)—216no—
482C2×AGL(1,𝔽5)—34no—
483C2×AGL(1,𝔽5)—32no—
484C2×AGL(1,𝔽5)—32no—
485C2×AGL(1,𝔽5)—34no—
486C2×AGL(1,𝔽5)—68no—
487C2×AGL(1,𝔽5)—616no—
488C2×AGL(1,𝔽5)—62no—
489C2×AGL(1,𝔽5)—64no—
490C2×AGL(1,𝔽5)—68no—
491C2×AGL(1,𝔽5)#23714yesdirect product factor
492C2×AGL(1,𝔽5)C23×D314yes—
493C2×AGL(1,𝔽5)C23×D312yes—
494C2×AGL(1,𝔽5)C23×D312yes—
495C5×Q8—34no—
496C5×D4—38no—
497C5×D4C2×C4×D314yescomplemented
498C2×C4×C5—32no—
499C2×C4×C5—31no—
500C2×C4×C5—38no—
501C2×C4×C5—34no—
502C2×C4×C5C2×C4×D311yescharacteristic
503C22⋊D5—38no—
504C22⋊D5—38no—
505C22⋊D5C2×C4×D318yescomplemented
506C2×Dic5—32no—
507C2×Dic5—31no—
508C2×Dic5—38no—
509C2×Dic5—34no—
510C2×Dic5C2×C4×D311yescharacteristic
511D20—38no—
512D20C2×C4×D314yescomplemented
513C4×D5—32no—
514C4×D5—34no—
515C4×D5—38no—
516C4×D5—38no—
517C4×D5—32no—
518C4×D5—34no—
519C4×D5—34no—
520C4×D5—34no—
521C4×D5C2×C4×D312yes—
522C4×D5C23×D312yes—
523Dic10—34no—
524Dic10—38no—
525C2×#41—31no—
526C2×#41—152no—
527C2×#41—151no—
528C2×#41—152no—
529C2×#41—151no—
530C2×#41—158no—
531C2×#41—158no—
532C2×#41—151no—
533C22×Q8—151no—
534C22×D4—51no—
535C22×D4—152no—
536C23×C4—52no—
537C23×C4—151no—
538C23×C4—152no—
539C23×C4—151no—
540C23×C4—151no—
541C23×C4—152no—
542C4×Q8—158no—
543C4×Q8—158no—
544C4×D4—58no—
545C4×D4—1516no—
546C4×D4—1516no—
547C4×D4—158no—
548#117—1516no—
549#117—158no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—152no—
552C2×C4⋊C4—152no—
553C2×C4⋊C4—151no—
554C2×C22⋊C4—52no—
555C2×C22⋊C4—152no—
556C2×C22⋊C4—152no—
557C2×C42—51no—
558C2×C42—158no—
559C2×C42—151no—
560C2×C42—152no—
561C2×C42—152no—
562C2×C42—151no—
563C2×C42—152no—
564C2×C42—1516no—
565C2×C42—151no—
566C2×C3×C5—24no—
567C2×C3×C5C4×#4112yescomplemented
568C2×C3×C5C24×C411yescharacteristic
569D15—22no—
570C3×D5—24no—
571C3×D5C4×#4112yescomplemented
572C3×D5C22×#4111yescharacteristic
573C3×D5C22×#4111yescharacteristic
574C5×D3—22no—
575C23×C3—51no—
576C23×C3—54no—
577C23×C3—52no—
578C23×C3—54no—
579C23×C3—104no—
580C23×C3—104no—
581C23×C3C22×AGL(1,𝔽5)12yes—
582C22×D3—51no—
583C22×D3—52no—
584C22×D3—52no—
585C22×D3—102no—
586C22×D3—102no—
587C22×D3C22×AGL(1,𝔽5)11yescharacteristic
588C3×D4—58no—
589C3×D4—54no—
590C3×D4C22×AGL(1,𝔽5)14yescomplemented
591C2×C3×C4—54no—
592C2×C3×C4—52no—
593C2×C3×C4—51no—
594C2×C3×C4—52no—
595C2×C3×C4—52no—
596C2×C3×C4—54no—
597C2×C3×C4—52no—
598C2×C3×C4—1016no—
599C2×C3×C4—102no—
600C2×C3×C4—104no—
601C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
602#67—58no—
603#67—58no—
604#67—58no—
605#67C22×AGL(1,𝔽5)18yescomplemented
606C2×Dic3—54no—
607C2×Dic3—52no—
608C2×Dic3—52no—
609C2×Dic3—51no—
610C2×Dic3—58no—
611C2×Dic3—54no—
612C2×Dic3—52no—
613C2×Dic3—58no—
614C2×Dic3—58no—
615C2×Dic3—52no—
616C2×Dic3—54no—
617C2×Dic3—52no—
618C2×Dic3—54no—
619C2×Dic3—1016no—
620C2×Dic3—102no—
621C2×Dic3—104no—
622C2×Dic3C22×AGL(1,𝔽5)12yes—
623C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
624C2×Dic3C22×AGL(1,𝔽5)18yescomplemented
625C4×D3—54no—
626C4×D3—54no—
627C4×D3—54no—
628C4×D3—108no—
629C4×D3—108no—
630C4×D3C22×AGL(1,𝔽5)14yescomplemented
631Dic6—54no—
632Dic6—58no—
633Dic6C22×AGL(1,𝔽5)14yescomplemented
634C22×C5—24no—
635C22×C5—32no—
636C22×C5—62no—
637C22×C5C22×C4×D314yes—
638C22×C5C22×C4×D311yescharacteristic
639C2×D5—24no—
640C2×D5—24no—
641C2×D5—24no—
642C2×D5—28no—
643C2×D5—32no—
644C2×D5—62no—
645C2×D5—62no—
646C2×D5—62no—
647C2×D5—64no—
648C2×D5C22×C4×D314yes—
649C2×D5C22×C4×D311yescharacteristic
650C2×D5C2×#23712yes—
651C2×D5D3×#4112yes—
652C2×D5C24×D311yescharacteristic
653AGL(1,𝔽5)—24no—
654AGL(1,𝔽5)—22no—
655AGL(1,𝔽5)—34no—
656AGL(1,𝔽5)—62no—
657AGL(1,𝔽5)—64no—
658AGL(1,𝔽5)C2×#23714yesdirect product factor
659C4×C5—34no—
660C4×C5—32no—
661C4×C5C22×C4×D312yes—
662Dic5—34no—
663Dic5—32no—
664Dic5C22×C4×D312yes—
665C24—52no—
666C24—151no—
667#41—38no—
668#41—1516no—
669#41—158no—
670#41—1516no—
671#41—158no—
672#41—158no—
673C2×Q8—31no—
674C2×Q8—152no—
675C2×Q8—154no—
676C2×Q8—154no—
677C2×Q8—151no—
678C2×D4—32no—
679C2×D4—52no—
680C2×D4—54no—
681C2×D4—54no—
682C2×D4—51no—
683C2×D4—152no—
684C2×D4—158no—
685C2×D4—158no—
686C2×D4—152no—
687C2×D4—152no—
688C2×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
689C22×C4—32no—
690C22×C4—31no—
691C22×C4—51no—
692C22×C4—51no—
693C22×C4—51no—
694C22×C4—52no—
695C22×C4—58no—
696C22×C4—108no—
697C22×C4—154no—
698C22×C4—151no—
699C22×C4—154no—
700C22×C4—151no—
701C22×C4—152no—
702C22×C4—158no—
703C22×C4—158no—
704C22×C4—152no—
705C22×C4—152no—
706C22×C4—151no—
707C22×C4—154no—
708C22×C4—154no—
709C22×C4—151no—
710C22×C4—152no—
711C22×C4—151no—
712C22×C4—152no—
713C22×C4—151no—
714C22×C4—158no—
715C22×C4—304no—
716C22×C4—304no—
717C22×C4—308no—
718C4⋊C4—54no—
719C4⋊C4—158no—
720C4⋊C4—158no—
721C4⋊C4—154no—
722C22⋊C4—58no—
723C22⋊C4—158no—
724C22⋊C4—158no—
725C42—54no—
726C42—154no—
727C42—154no—
728C42—158no—
729C42—158no—
730C42—154no—
731C42—158no—
732C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
733C22×C3—24no—
734C22×C3—52no—
735C22×C3—52no—
736C22×C3—51no—
737C22×C3—51no—
738C22×C3—54no—
739C22×C3—104no—
740C22×C3—104no—
741C22×C3—108no—
742C22×C3—104no—
743C22×C3C23×AGL(1,𝔽5)14yes—
744C22×C3C23×AGL(1,𝔽5)11yescharacteristic
745C2×D3—22no—
746C2×D3—52no—
747C2×D3—102no—
748C2×D3—102no—
749C2×D3—104no—
750C2×D3—102no—
751C2×D3C23×AGL(1,𝔽5)12yes—
752C3×C4—54no—
753C3×C4—52no—
754C3×C4—102no—
755C3×C4—104no—
756C3×C4C23×AGL(1,𝔽5)12yes—
757Dic3—54no—
758Dic3—54no—
759Dic3—52no—
760Dic3—102no—
761Dic3—104no—
762Dic3C23×AGL(1,𝔽5)14yes—
763Dic3C23×AGL(1,𝔽5)12yes—
764C2×C5—24no—
765C2×C5—62no—
766C2×C5C4×#23712yescomplemented
767C2×C5C23×C4×D311yescharacteristic
768D5—24no—
769D5—62no—
770D5C4×#23712yescomplemented
771D5C22×#23711yescharacteristic
772D5C2×D3×#4111yescharacteristic
773C23—31no—
774C23—51no—
775C23—54no—
776C23—54no—
777C23—52no—
778C23—104no—
779C23—104no—
780C23—152no—
781C23—152no—
782C23—151no—
783C23—302no—
784C23—302no—
785C23C2×D3×AGL(1,𝔽5)12yes—
786Q8—34no—
787Q8—158no—
788Q8—154no—
789D4—38no—
790D4—58no—
791D4—54no—
792D4—158no—
793D4—158no—
794D4—158no—
795D4C2×D3×AGL(1,𝔽5)14yescomplemented
796C2×C4—38no—
797C2×C4—31no—
798C2×C4—32no—
799C2×C4—34no—
800C2×C4—52no—
801C2×C4—54no—
802C2×C4—51no—
803C2×C4—52no—
804C2×C4—52no—
805C2×C4—52no—
806C2×C4—54no—
807C2×C4—1016no—
808C2×C4—104no—
809C2×C4—102no—
810C2×C4—154no—
811C2×C4—152no—
812C2×C4—154no—
813C2×C4—152no—
814C2×C4—154no—
815C2×C4—158no—
816C2×C4—158no—
817C2×C4—154no—
818C2×C4—152no—
819C2×C4—154no—
820C2×C4—158no—
821C2×C4—151no—
822C2×C4—152no—
823C2×C4—154no—
824C2×C4—154no—
825C2×C4—152no—
826C2×C4—308no—
827C2×C4—308no—
828C2×C4—3016no—
829C2×C4—302no—
830C2×C4—304no—
831C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
832C2×C3—24no—
833C2×C3—51no—
834C2×C3—51no—
835C2×C3—52no—
836C2×C3—104no—
837C2×C3#41×AGL(1,𝔽5)12yescomplemented
838C2×C3C24×AGL(1,𝔽5)11yescharacteristic
839D3—22no—
840D3—102no—
841C5C2×C4×#23711yescharacteristic, complemented, Sylow
842C22—24no—
843C22—32no—
844C22—52no—
845C22—52no—
846C22—51no—
847C22—51no—
848C22—54no—
849C22—62no—
850C22—104no—
851C22—104no—
852C22—108no—
853C22—104no—
854C22—152no—
855C22—302no—
856C22—302no—
857C22—304no—
858C22—302no—
859C22C22×D3×AGL(1,𝔽5)14yes—
860C22C22×D3×AGL(1,𝔽5)11yescharacteristic
861C4—32no—
862C4—34no—
863C4—54no—
864C4—52no—
865C4—104no—
866C4—102no—
867C4—154no—
868C4—152no—
869C4—154no—
870C4—302no—
871C4—304no—
872C4C22×D3×AGL(1,𝔽5)12yes—
873C3C2×#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
874C2—24no—
875C2—51no—
876C2—51no—
877C2—52no—
878C2—62no—
879C2—104no—
880C2—302no—
881C2AGL(1,𝔽5)×#23712yesdirect product factor
882C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#237C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D4×ΓL(1,𝔽16)C2semidirect
3. C2×C3×D4×AGL(1,𝔽5)C2semidirect
4. C2×#67⋊AGL(1,𝔽5)C2semidirect
5. C2×AGL(1,𝔽5)×#67C2semidirect
6. C2×#91923C2semidirect
7. C22×Dic3×AGL(1,𝔽5)C2semidirect
8. AGL(1,𝔽5)×#237C2direct (N × H)
9. C2×C4×D3×AGL(1,𝔽5)C2semidirect
10. C2×ΓL(1,𝔽16)⋊Q8C2semidirect
11. C2×#91907C2semidirect
12. C2×AGL(1,𝔽5)×Dic6C2semidirect
18. C2×#6819C4semidirect
19. C2×C5×#237C4semidirect
22. C2×#6780C4semidirect
23. C2×#6779C4semidirect
25. D5×#237C4semidirect
28. C2×#6766C4semidirect
29. C2×#6765C4semidirect
32. D4×ΓL(1,𝔽16)C22semidirect
36. C3×D4×AGL(1,𝔽5)C22semidirect
39. #67⋊AGL(1,𝔽5)C22semidirect
40. AGL(1,𝔽5)×#67C22semidirect
44. #91923C22semidirect
50. C2×Dic3×AGL(1,𝔽5)C22semidirect
51. C4×D3×AGL(1,𝔽5)C22semidirect
52. ΓL(1,𝔽16)⋊Q8C22semidirect
53. #91907C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
63. C2×D4×AGL(1,𝔽5)D3semidirect
84. C2×C3×C5×D4C2×C4semidirect
85. C2×#1220C2×C4semidirect
86. C22×Dic15C2×C4semidirect
87. #6819C2×C4semidirect
88. C2×C4×D15C2×C4semidirect
89. C2×Dic30C2×C4semidirect
90. C2×C5×#67C2×C4semidirect
91. C22×C5×Dic3C2×C4semidirect
92. C5×#237C2×C4semidirect
93. C2×C4×C5×D3C2×C4semidirect
94. C2×C5×Dic6C2×C4semidirect
95. C2×C3×C22⋊D5C2×C4semidirect
96. C3×D4×D5C2×C4semidirect
98. C2×C3×D20C2×C4semidirect
100. D5×#67C2×C4semidirect
102. C2×#1204C2×C4semidirect
103. C2×#1202C2×C4semidirect
104. C2×#1201C2×C4semidirect
105. C2×#1200C2×C4semidirect
106. C2×D3×Dic5C2×C4semidirect
107. #6780C2×C4semidirect
108. #6779C2×C4semidirect
109. C2×D5×Dic3C2×C4semidirect
110. C2×D5×Dic3C2×C4semidirect
111. C2×D5×Dic3C2×C4semidirect
115. C4×D3×D5C2×C4semidirect
117. #6766C2×C4semidirect
118. #6765C2×C4semidirect
119. D5×Dic6C2×C4semidirect
172. D4×AGL(1,𝔽5)C2×D3semidirect
205. C2×ΓL(1,𝔽16)#41semidirect
212. C2×C3×AGL(1,𝔽5)#41semidirect
218. C3×C5×D4C22×C4semidirect
220. #1220C22×C4semidirect
223. C2×Dic15C22×C4semidirect
224. C4×D15C22×C4semidirect
225. Dic30C22×C4semidirect
226. C5×#67C22×C4semidirect
229. C2×C5×Dic3C22×C4semidirect
230. C4×C5×D3C22×C4semidirect
231. C5×Dic6C22×C4semidirect
232. C3×C22⋊D5C22×C4semidirect
234. C3×D20C22×C4semidirect
237. #1204C22×C4semidirect
238. #1202C22×C4semidirect
239. #1201C22×C4semidirect
240. #1200C22×C4semidirect
241. D3×Dic5C22×C4semidirect
244. D5×Dic3C22×C4semidirect
245. D5×Dic3C22×C4semidirect
260. C2×#237AGL(1,𝔽5)direct (N × H)
308. C2×C5×D4C4×D3semidirect
313. C2×C22⋊D5C4×D3semidirect
323. D4×D5C4×D3semidirect
328. C2×D20C4×D3semidirect
389. ΓL(1,𝔽16)C2×#41semidirect
392. C3×AGL(1,𝔽5)C2×#41semidirect
405. C2×C3×D4C2×AGL(1,𝔽5)semidirect
417. C2×#67C2×AGL(1,𝔽5)semidirect
430. C22×Dic3C2×AGL(1,𝔽5)semidirect
436. #237C2×AGL(1,𝔽5)direct (N × H)
446. C2×C4×D3C2×AGL(1,𝔽5)semidirect
451. C2×Dic6C2×AGL(1,𝔽5)semidirect
491. C2×AGL(1,𝔽5)#237direct (N × H)
497. C5×D4C2×C4×D3semidirect
505. C22⋊D5C2×C4×D3semidirect
512. D20C2×C4×D3semidirect
567. C2×C3×C5C4×#41semidirect
571. C3×D5C4×#41semidirect
590. C3×D4C22×AGL(1,𝔽5)semidirect
605. #67C22×AGL(1,𝔽5)semidirect
624. C2×Dic3C22×AGL(1,𝔽5)semidirect
630. C4×D3C22×AGL(1,𝔽5)semidirect
633. Dic6C22×AGL(1,𝔽5)semidirect
658. AGL(1,𝔽5)C2×#237direct (N × H)
688. C2×D4D3×AGL(1,𝔽5)semidirect
732. C3×C5C2×C4×#41semidirect
766. C2×C5C4×#237semidirect
770. D5C4×#237semidirect
795. D4C2×D3×AGL(1,𝔽5)semidirect
837. C2×C3#41×AGL(1,𝔽5)semidirect
841. C5C2×C4×#237semidirect
873. C3C2×#41×AGL(1,𝔽5)semidirect
881. C2AGL(1,𝔽5)×#237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#2372
C2×D4×ΓL(1,𝔽16)2
C2×C3×D4×AGL(1,𝔽5)2
C2×#67⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C2×#919232
C22×Dic3×AGL(1,𝔽5)2
AGL(1,𝔽5)×#2372
C2×C4×D3×AGL(1,𝔽5)2
C2×ΓL(1,𝔽16)⋊Q82
C2×#919072
C2×AGL(1,𝔽5)×Dic62
C2×#41×AGL(1,𝔽5)3
C2×C4×#2375