Finite Group Databasebeta

← D3×C4⋊C4×AGL(1,𝔽5) #14319475

Subgroups — D3×C4⋊C4×AGL(1,𝔽5) #14319475

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×C4×D3×AGL(1,𝔽5)C212yesmaximal
3C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
4D3×D5×C4⋊C4C211yesmaximal, characteristic
5C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
6C3×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
7D3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal
8#11751846C211yesmaximal, characteristic, complemented
9AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#11751833C212yesmaximal, complemented
11AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal, complemented
12C2×C4⋊C4×AGL(1,𝔽5)—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C22×D3×AGL(1,𝔽5)C2211yescharacteristic
15C22×D3×AGL(1,𝔽5)C2211yescharacteristic
16C2×C4×D3×D5C2212yes—
17C2×C4×D3×D5C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
19C2×C4×ΓL(1,𝔽16)C2212yes—
20C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4×AGL(1,𝔽5)C2212yes—
23C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
28C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
29D3×C4⋊AGL(1,𝔽5)C418yescomplemented
30C4×D3×AGL(1,𝔽5)—28no—
31C4×D3×AGL(1,𝔽5)C418yescomplemented
32C4⋊C4×D15C411yescharacteristic, complemented
33C5×D3×C4⋊C4C411yescharacteristic, complemented
34C3×D5×C4⋊C4C2211yescharacteristic
35#91437C411yescharacteristic, complemented
36D3×C4⋊Dic5C411yescharacteristic, complemented
37D5×C4⋊Dic3C2211yescharacteristic
38#91404C412yescomplemented
39D3×#683C412yescomplemented
40D5×Dic3⋊C4C2212yes—
41#91235C2212yes—
42C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
45C4×D3×C4⋊C4—51nomaximal, Hall
46C22×C4⋊AGL(1,𝔽5)—31no—
47C22×C4×AGL(1,𝔽5)—31no—
48C22×C4×AGL(1,𝔽5)—32no—
49C2×D5×C4⋊C4—31no—
50C2×(C2×AGL(1,𝔽5))⋊C4—32no—
51C4⋊C4×AGL(1,𝔽5)—31no—
52C4⋊C4×AGL(1,𝔽5)—32no—
53C4⋊C4×AGL(1,𝔽5)—31no—
54C4⋊C4×AGL(1,𝔽5)—32no—
55C4⋊C4×AGL(1,𝔽5)—31no—
56C4⋊C4×AGL(1,𝔽5)D311yescharacteristic, direct product factor
57C22×D3×D5C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2312yes—
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2312yes—
62C22×C3×AGL(1,𝔽5)C2311yescharacteristic
63C22×C3×AGL(1,𝔽5)C2311yescharacteristic
64C2×D3×AGL(1,𝔽5)—24no—
65C2×D3×AGL(1,𝔽5)—22no—
66C2×D3×AGL(1,𝔽5)—22no—
67C2×D3×AGL(1,𝔽5)—24no—
68C2×D3×AGL(1,𝔽5)C2×C414yes—
69C2×D3×AGL(1,𝔽5)C2×C418yes—
70C2×D3×AGL(1,𝔽5)C2×C414yes—
71C2×D3×AGL(1,𝔽5)D414yes—
72C2×D3×AGL(1,𝔽5)Q814yes—
73C2×C4×D15C2×C412yes—
74C2×C4×D15C2×C411yescharacteristic
75C2×C4×C5×D3C2×C412yes—
76C2×C4×C5×D3C2×C411yescharacteristic
77C2×C3×C4×D5C2312yes—
78C2×C3×C4×D5C2311yescharacteristic
79C2×#1200C2×C412yes—
80C2×#1200C2×C411yescharacteristic
81C2×D3×Dic5C2×C412yes—
82C2×D3×Dic5C2×C411yescharacteristic
83C2×D5×Dic3C2312yes—
84C2×D5×Dic3C2311yescharacteristic
85C4×D3×D5—24no—
86C4×D3×D5—24no—
87C4×D3×D5C2×C414yes—
88C4×D3×D5C2×C414yes—
89C4⋊ΓL(1,𝔽16)C2×C414yescomplemented
90C4×ΓL(1,𝔽16)—24no—
91C4×ΓL(1,𝔽16)C2×C414yescomplemented
92C3×C4⋊AGL(1,𝔽5)C2×C414yescomplemented
93C3×C4×AGL(1,𝔽5)—24no—
94C3×C4×AGL(1,𝔽5)C2×C414yescomplemented
95Dic3⋊AGL(1,𝔽5)C2×C418yescomplemented
96Dic3×AGL(1,𝔽5)—24no—
97Dic3×AGL(1,𝔽5)—24no—
98Dic3×AGL(1,𝔽5)C2×C414yescomplemented
99Dic3×AGL(1,𝔽5)C2×C414yescomplemented
100C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
101C4⋊Dic15C2×C411yescharacteristic, complemented
102#6712C2×C412yescomplemented
103C5×C4⋊Dic3C2×C411yescharacteristic, complemented
104C5×Dic3⋊C4C2×C412yescomplemented
105C3×C4⋊Dic5C2×C411yescharacteristic, complemented
106C3×#683C2×C412yescomplemented
107Dic3⋊Dic5C2×C412yescomplemented
108#6669C2×C412yescomplemented
109#6668C2×C412yescomplemented
110C2×D3×C4⋊C4—51no—
111C2×D3×C4⋊C4—51no—
112C2×C42×D3—51no—
113C2×C42×D3—52no—
114C3×C4×C4⋊C4—51no—
115Dic3×C4⋊C4—51no—
116Dic3×C4⋊C4—51no—
117C4×C4⋊Dic3—51no—
118C4×Dic3⋊C4—52no—
119D3×#95—52no—
120#4649—52no—
121C23×AGL(1,𝔽5)—31no—
122C23×AGL(1,𝔽5)—32no—
123C23×AGL(1,𝔽5)—31no—
124C22×C4×D5—31no—
125C22×C4×D5—32no—
126C2×C4⋊AGL(1,𝔽5)—32no—
127C2×C4⋊AGL(1,𝔽5)—31no—
128C2×C4⋊AGL(1,𝔽5)—38no—
129C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
130C2×C4×AGL(1,𝔽5)—31no—
131C2×C4×AGL(1,𝔽5)—31no—
132C2×C4×AGL(1,𝔽5)—31no—
133C2×C4×AGL(1,𝔽5)—38no—
134C2×C4×AGL(1,𝔽5)—32no—
135C2×C4×AGL(1,𝔽5)—32no—
136C2×C4×AGL(1,𝔽5)—32no—
137C2×C4×AGL(1,𝔽5)—68no—
138C2×C4×AGL(1,𝔽5)C2×D312yes—
139C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
140C2×C5×C4⋊C4—31no—
141C2×C4⋊Dic5—31no—
142C2×#683—32no—
143D5×C4⋊C4—32no—
144D5×C4⋊C4—31no—
145D5×C4⋊C4—31no—
146D5×C4⋊C4—31no—
147D5×C4⋊C4—32no—
148D5×C4⋊C4C2×D311yescharacteristic
149(C2×AGL(1,𝔽5))⋊C4—32no—
150(C2×AGL(1,𝔽5))⋊C4—32no—
151(C2×AGL(1,𝔽5))⋊C4—32no—
152(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
153C2×C4×C4⋊C4—151noSylow
154C22×D15C22×C411yescharacteristic
155C22×C5×D3C22×C411yescharacteristic
156C22×C3×D5C2411yescharacteristic
157C2×D3×D5C22×C412yes—
158C2×D3×D5C22×C412yes—
159C2×D3×D5C2×D412yes—
160C2×D3×D5C2×Q812yes—
161C2×D3×D5#4112yes—
162C2×D3×D5#4112yes—
163C2×ΓL(1,𝔽16)—22no—
164C2×ΓL(1,𝔽16)—21no—
165C2×ΓL(1,𝔽16)—21no—
166C2×ΓL(1,𝔽16)—22no—
167C2×ΓL(1,𝔽16)C22×C412yes—
168C2×ΓL(1,𝔽16)C22×C414yes—
169C2×ΓL(1,𝔽16)C22×C412yes—
170C2×ΓL(1,𝔽16)C2×D412yes—
171C2×ΓL(1,𝔽16)C2×Q812yes—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—21no—
174C2×C3×AGL(1,𝔽5)—21no—
175C2×C3×AGL(1,𝔽5)—22no—
176C2×C3×AGL(1,𝔽5)C22×C412yes—
177C2×C3×AGL(1,𝔽5)C22×C414yes—
178C2×C3×AGL(1,𝔽5)C22×C412yes—
179C2×C3×AGL(1,𝔽5)C2×D412yes—
180C2×C3×AGL(1,𝔽5)C2×Q812yes—
181D3×AGL(1,𝔽5)—28no—
182D3×AGL(1,𝔽5)—216no—
183D3×AGL(1,𝔽5)C4⋊C4116yesdirect product factor
184C2×C3×C4×C5C22×C412yes—
185C2×C3×C4×C5C22×C411yescharacteristic
186C2×Dic15C22×C412yes—
187C2×Dic15C22×C411yescharacteristic
188C4×D15—24no—
189C4×D15C4214yescomplemented
190C2×C5×Dic3C22×C412yes—
191C2×C5×Dic3C22×C411yescharacteristic
192C4×C5×D3—24no—
193C4×C5×D3C4214yescomplemented
194C2×C3×Dic5C22×C412yes—
195C2×C3×Dic5C22×C411yescharacteristic
196C3×C4×D5—22no—
197C3×C4×D5—22no—
198C3×C4×D5C22×C412yes—
199C3×C4×D5C22×C412yes—
200#1200—24no—
201#1200C4214yescomplemented
202D3×Dic5—24no—
203D3×Dic5C4214yescomplemented
204D5×Dic3—22no—
205D5×Dic3—22no—
206D5×Dic3C22×C412yes—
207D5×Dic3C22×C412yes—
208C22×C4×D3—51no—
209C22×C4×D3—51no—
210C22×C4×D3—51no—
211C22×C4×D3—52no—
212C22×C4×D3—52no—
213C2×C3×C4⋊C4—51no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C42—51no—
216C2×C3×C42—52no—
217C2×C4⋊Dic3—51no—
218C2×C4⋊Dic3—51no—
219C2×Dic3⋊C4—52no—
220C2×Dic3⋊C4—52no—
221C2×C4×Dic3—51no—
222C2×C4×Dic3—51no—
223C2×C4×Dic3—51no—
224C2×C4×Dic3—52no—
225C2×C4×Dic3—52no—
226C2×C4×Dic3—52no—
227D3×C4⋊C4—58no—
228D3×C4⋊C4—52no—
229D3×C4⋊C4—51no—
230D3×C4⋊C4—51no—
231D3×C4⋊C4—51no—
232D3×C4⋊C4—52no—
233D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, direct product factor
234C42×D3—58no—
235C42×D3—108no—
236C3×#95—52no—
237C3⋊#95—52no—
238C3⋊#95—52no—
239C3⋊#95—52no—
240C23×D5—31no—
241C22×AGL(1,𝔽5)—31no—
242C22×AGL(1,𝔽5)—34no—
243C22×AGL(1,𝔽5)—34no—
244C22×AGL(1,𝔽5)—34no—
245C22×AGL(1,𝔽5)—32no—
246C22×AGL(1,𝔽5)—31no—
247C22×AGL(1,𝔽5)—34no—
248C22×AGL(1,𝔽5)—38no—
249C22×AGL(1,𝔽5)—64no—
250C22×AGL(1,𝔽5)—62no—
251C22×AGL(1,𝔽5)—64no—
252C22×AGL(1,𝔽5)—62no—
253C22×AGL(1,𝔽5)C22×D312yes—
254C22×AGL(1,𝔽5)C22×D311yescharacteristic
255C22×AGL(1,𝔽5)C22×D311yescharacteristic
256C22×C4×C5—31no—
257C22×C4×C5—32no—
258C22×Dic5—31no—
259C22×Dic5—32no—
260C2×C4×D5—31no—
261C2×C4×D5—31no—
262C2×C4×D5—31no—
263C2×C4×D5—34no—
264C2×C4×D5—34no—
265C2×C4×D5—32no—
266C2×C4×D5—32no—
267C2×C4×D5—32no—
268C2×C4×D5—64no—
269C2×C4×D5—64no—
270C2×C4×D5C22×D312yes—
271C2×C4×D5C22×D311yescharacteristic
272C4⋊AGL(1,𝔽5)—38no—
273C4⋊AGL(1,𝔽5)—34no—
274C4⋊AGL(1,𝔽5)C4×D314yescomplemented
275C4×AGL(1,𝔽5)—24no—
276C4×AGL(1,𝔽5)—34no—
277C4×AGL(1,𝔽5)—34no—
278C4×AGL(1,𝔽5)—34no—
279C4×AGL(1,𝔽5)—64no—
280C4×AGL(1,𝔽5)—64no—
281C4×AGL(1,𝔽5)—64no—
282C4×AGL(1,𝔽5)C4×D314yescomplemented
283C5×C4⋊C4—32no—
284C5×C4⋊C4—31no—
285C5×C4⋊C4C4×D311yescharacteristic, complemented
286C4⋊Dic5—31no—
287C4⋊Dic5—32no—
288C4⋊Dic5C4×D311yescharacteristic, complemented
289#683—32no—
290#683—32no—
291#683—32no—
292#683C4×D312yescomplemented
293C22×C4⋊C4—151no—
294C22×C4⋊C4—151no—
295C22×C42—151no—
296C22×C42—152no—
297C4×C4⋊C4—51no—
298C4×C4⋊C4—152no—
299C4×C4⋊C4—152no—
300C4×C4⋊C4—151no—
301C4×C4⋊C4—151no—
302C4×C4⋊C4—151no—
303C2×#95—152no—
304C22×C3×C5C23×C411yescharacteristic
305C2×D15C2×C4212yes—
306C2×D15C4×D412yes—
307C2×D15C4×Q812yes—
308C2×C5×D3C2×C4212yes—
309C2×C5×D3C4×D412yes—
310C2×C5×D3C4×Q812yes—
311C2×C3×D5C23×C411yescharacteristic
312C2×C3×D5C23×C411yescharacteristic
313C2×C3×D5C22×D411yescharacteristic
314C2×C3×D5C22×Q811yescharacteristic
315C2×C3×D5C2×#4111yescharacteristic
316C2×C3×D5C2×#4111yescharacteristic
317D3×D5C2×C4⋊C414yes—
318D3×D5#11714yes—
319D3×D5C4×D414yes—
320D3×D5C4×Q814yes—
321ΓL(1,𝔽16)—22no—
322ΓL(1,𝔽16)—24no—
323ΓL(1,𝔽16)C2×C4⋊C414yescomplemented
324C3×AGL(1,𝔽5)—22no—
325C3×AGL(1,𝔽5)—24no—
326C3×AGL(1,𝔽5)C2×C4⋊C414yescomplemented
327C3×C4×C5—22no—
328C3×C4×C5C2×C4212yescomplemented
329Dic15—22no—
330Dic15C2×C4212yescomplemented
331C3×Dic5—22no—
332C3×Dic5C2×C4212yescomplemented
333C5×Dic3—22no—
334C5×Dic3C2×C4212yescomplemented
335C23×D3—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—52no—
340C22×C3×C4—52no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—52no—
345C22×Dic3—52no—
346C2×C4×D3—54no—
347C2×C4×D3—54no—
348C2×C4×D3—54no—
349C2×C4×D3—51no—
350C2×C4×D3—51no—
351C2×C4×D3—51no—
352C2×C4×D3—54no—
353C2×C4×D3—54no—
354C2×C4×D3—54no—
355C2×C4×D3—58no—
356C2×C4×D3—52no—
357C2×C4×D3—52no—
358C2×C4×D3—52no—
359C2×C4×D3—104no—
360C2×C4×D3—104no—
361C2×C4×D3—104no—
362C2×C4×D3—102no—
363C2×C4×D3—102no—
364C2×C4×D3—104no—
365C2×C4×D3C2×AGL(1,𝔽5)12yes—
366C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
367C3×C4⋊C4—54no—
368C3×C4⋊C4—52no—
369C3×C4⋊C4—51no—
370C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
371C3×C42—54no—
372C3×C42—104no—
373C4⋊Dic3—54no—
374C4⋊Dic3—51no—
375C4⋊Dic3—52no—
376C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
377Dic3⋊C4—58no—
378Dic3⋊C4—52no—
379Dic3⋊C4—52no—
380Dic3⋊C4—52no—
381Dic3⋊C4C2×AGL(1,𝔽5)12yescomplemented
382C4×Dic3—54no—
383C4×Dic3—54no—
384C4×Dic3—54no—
385C4×Dic3—104no—
386C4×Dic3—104no—
387C4×Dic3—104no—
388C23×C5—31no—
389C22×D5—31no—
390C22×D5—32no—
391C22×D5—32no—
392C22×D5—32no—
393C22×D5—32no—
394C22×D5—32no—
395C22×D5—32no—
396C22×D5C23×D311yescharacteristic
397C2×AGL(1,𝔽5)—22no—
398C2×AGL(1,𝔽5)—21no—
399C2×AGL(1,𝔽5)—21no—
400C2×AGL(1,𝔽5)—22no—
401C2×AGL(1,𝔽5)—32no—
402C2×AGL(1,𝔽5)—32no—
403C2×AGL(1,𝔽5)—32no—
404C2×AGL(1,𝔽5)—316no—
405C2×AGL(1,𝔽5)—32no—
406C2×AGL(1,𝔽5)—34no—
407C2×AGL(1,𝔽5)—68no—
408C2×AGL(1,𝔽5)—616no—
409C2×AGL(1,𝔽5)—62no—
410C2×AGL(1,𝔽5)—61no—
411C2×AGL(1,𝔽5)—61no—
412C2×AGL(1,𝔽5)—62no—
413C2×AGL(1,𝔽5)C2×C4×D312yes—
414C2×AGL(1,𝔽5)C2×C4×D314yes—
415C2×AGL(1,𝔽5)C2×C4×D312yes—
416C2×AGL(1,𝔽5)D3×D412yes—
417C2×AGL(1,𝔽5)D3×Q812yes—
418C2×C4×C5—31no—
419C2×C4×C5—34no—
420C2×C4×C5—32no—
421C2×C4×C5—64no—
422C2×C4×C5C2×C4×D312yes—
423C2×C4×C5C2×C4×D311yescharacteristic
424C2×Dic5—31no—
425C2×Dic5—34no—
426C2×Dic5—32no—
427C2×Dic5—64no—
428C2×Dic5C2×C4×D312yes—
429C2×Dic5C2×C4×D311yescharacteristic
430C4×D5—22no—
431C4×D5—22no—
432C4×D5—32no—
433C4×D5—32no—
434C4×D5—34no—
435C4×D5—34no—
436C4×D5—64no—
437C4×D5—64no—
438C4×D5—62no—
439C4×D5—62no—
440C4×D5C2×C4×D312yes—
441C4×D5C2×C4×D312yes—
442C23×C4—151no—
443C23×C4—152no—
444C23×C4—151no—
445C23×C4—152no—
446C23×C4—151no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—51no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—152no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—152no—
453C2×C4⋊C4—151no—
454C2×C4⋊C4—152no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—158no—
457C2×C4⋊C4—152no—
458C2×C4⋊C4—151no—
459C2×C4⋊C4—151no—
460C2×C42—51no—
461C2×C42—52no—
462C2×C42—158no—
463C2×C42—151no—
464C2×C42—151no—
465C2×C42—151no—
466C2×C42—152no—
467C2×C42—152no—
468C2×C42—152no—
469C2×C42—308no—
470#95—52no—
471#95—152no—
472#95—152no—
473#95—152no—
474C2×C3×C5C22×C4211yescharacteristic
475C2×C3×C5C2×C4×D411yescharacteristic
476C2×C3×C5C2×C4×Q811yescharacteristic
477D15C4×C4⋊C414yescomplemented
478C3×D5C22×C4⋊C411yescharacteristic
479C3×D5C2×#11711yescharacteristic
480C3×D5C2×C4×D411yescharacteristic
481C3×D5C2×C4×Q811yescharacteristic
482C5×D3C4×C4⋊C414yescomplemented
483C23×C3—51no—
484C22×D3—51no—
485C22×D3—52no—
486C22×D3—52no—
487C22×D3—52no—
488C22×D3—52no—
489C22×D3—52no—
490C22×D3—52no—
491C22×D3C22×AGL(1,𝔽5)11yescharacteristic
492C2×C3×C4—52no—
493C2×C3×C4—52no—
494C2×C3×C4—52no—
495C2×C3×C4—51no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
498C2×C3×C4—52no—
499C2×C3×C4—54no—
500C2×C3×C4—52no—
501C2×C3×C4—102no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—102no—
507C2×C3×C4C22×AGL(1,𝔽5)12yes—
508C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
509C2×Dic3—52no—
510C2×Dic3—52no—
511C2×Dic3—52no—
512C2×Dic3—51no—
513C2×Dic3—52no—
514C2×Dic3—52no—
515C2×Dic3—52no—
516C2×Dic3—54no—
517C2×Dic3—52no—
518C2×Dic3—102no—
519C2×Dic3—102no—
520C2×Dic3—102no—
521C2×Dic3—101no—
522C2×Dic3—101no—
523C2×Dic3—102no—
524C2×Dic3C22×AGL(1,𝔽5)12yes—
525C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
526C4×D3—24no—
527C4×D3—516no—
528C4×D3—54no—
529C4×D3—54no—
530C4×D3—54no—
531C4×D3—104no—
532C4×D3—104no—
533C4×D3—108no—
534C4×D3—1016no—
535C4×D3—104no—
536C4×D3C4×AGL(1,𝔽5)14yescomplemented
537C22×C5—32no—
538C22×C5—32no—
539C22×C5—32no—
540C22×C5C22×C4×D311yescharacteristic
541C2×D5—32no—
542C2×D5—32no—
543C2×D5—32no—
544C2×D5—34no—
545C2×D5—34no—
546C2×D5—34no—
547C2×D5—34no—
548C2×D5C22×C4×D311yescharacteristic
549C2×D5C22×C4×D311yescharacteristic
550C2×D5C2×D3×D411yescharacteristic
551C2×D5C2×D3×Q811yescharacteristic
552C2×D5D3×#4111yescharacteristic
553C2×D5D3×#4111yescharacteristic
554AGL(1,𝔽5)—22no—
555AGL(1,𝔽5)—24no—
556AGL(1,𝔽5)—34no—
557AGL(1,𝔽5)—62no—
558AGL(1,𝔽5)—64no—
559AGL(1,𝔽5)D3×C4⋊C414yesdirect product factor
560C4×C5—22no—
561C4×C5—32no—
562C4×C5—62no—
563C4×C5C42×D312yescomplemented
564Dic5—22no—
565Dic5—32no—
566Dic5—62no—
567Dic5C42×D312yescomplemented
568C24—151no—
569C22×C4—31no—
570C22×C4—32no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—154no—
577C22×C4—151no—
578C22×C4—154no—
579C22×C4—152no—
580C22×C4—151no—
581C22×C4—152no—
582C22×C4—151no—
583C22×C4—154no—
584C22×C4—154no—
585C22×C4—154no—
586C22×C4—152no—
587C22×C4—154no—
588C22×C4—158no—
589C22×C4—151no—
590C22×C4—151no—
591C22×C4—151no—
592C22×C4—152no—
593C22×C4—152no—
594C22×C4—304no—
595C22×C4—304no—
596C22×C4—304no—
597C22×C4—304no—
598C22×C4—302no—
599C22×C4—302no—
600C4⋊C4—32no—
601C4⋊C4—31no—
602C4⋊C4—54no—
603C4⋊C4—52no—
604C4⋊C4—51no—
605C4⋊C4—152no—
606C4⋊C4—152no—
607C4⋊C4—152no—
608C4⋊C4—158no—
609C4⋊C4—154no—
610C4⋊C4—152no—
611C4⋊C4—151no—
612C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, direct product factor
613C42—54no—
614C42—104no—
615C42—154no—
616C42—154no—
617C42—154no—
618C42—304no—
619C42—304no—
620C42—304no—
621C3×C5C2×C4×C4⋊C411yescharacteristic, complemented, Hall
622C22×C3—51no—
623C22×C3—51no—
624C22×C3—51no—
625C22×C3—51no—
626C22×C3—51no—
627C22×C3—51no—
628C22×C3C23×AGL(1,𝔽5)11yescharacteristic
629C2×D3—52no—
630C2×D3—52no—
631C2×D3—52no—
632C2×D3—54no—
633C2×D3—54no—
634C2×D3—54no—
635C2×D3—54no—
636C2×D3C2×C4×AGL(1,𝔽5)12yes—
637C2×D3D4×AGL(1,𝔽5)12yes—
638C2×D3Q8×AGL(1,𝔽5)12yes—
639C3×C4—22no—
640C3×C4—54no—
641C3×C4—52no—
642C3×C4—104no—
643C3×C4—102no—
644C3×C4—102no—
645C3×C4C2×C4×AGL(1,𝔽5)12yescomplemented
646Dic3—22no—
647Dic3—54no—
648Dic3—52no—
649Dic3—104no—
650Dic3—102no—
651Dic3—102no—
652Dic3C2×C4×AGL(1,𝔽5)12yescomplemented
653C2×C5—34no—
654C2×C5C2×C42×D311yescharacteristic
655C2×C5C4×D3×D411yescharacteristic
656C2×C5C4×D3×Q811yescharacteristic
657D5—34no—
658D5C2×D3×C4⋊C411yescharacteristic
659D5D3×#11711yescharacteristic
660D5C4×D3×D411yescharacteristic
661D5C4×D3×Q811yescharacteristic
662C23—31no—
663C23—51no—
664C23—152no—
665C23—152no—
666C23—152no—
667C23—152no—
668C23—152no—
669C23—152no—
670C23—151no—
671C2×C4—31no—
672C2×C4—34no—
673C2×C4—32no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—52no—
677C2×C4—51no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—54no—
682C2×C4—52no—
683C2×C4—64no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—102no—
690C2×C4—154no—
691C2×C4—152no—
692C2×C4—152no—
693C2×C4—154no—
694C2×C4—1516no—
695C2×C4—152no—
696C2×C4—152no—
697C2×C4—152no—
698C2×C4—151no—
699C2×C4—154no—
700C2×C4—152no—
701C2×C4—154no—
702C2×C4—152no—
703C2×C4—304no—
704C2×C4—304no—
705C2×C4—302no—
706C2×C4—302no—
707C2×C4—304no—
708C2×C4—3016no—
709C2×C4—308no—
710C2×C4—302no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—302no—
714C2×C4C2×D3×AGL(1,𝔽5)12yes—
715C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
716C2×C3—51no—
717C2×C3—51no—
718C2×C3—51no—
719C2×C3—51no—
720C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
721C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
722C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
723D3—54no—
724D3C4⋊C4×AGL(1,𝔽5)14yesdirect product factor
725C5C4×D3×C4⋊C411yescharacteristic, complemented, Sylow
726C22—32no—
727C22—32no—
728C22—32no—
729C22—51no—
730C22—51no—
731C22—51no—
732C22—51no—
733C22—51no—
734C22—51no—
735C22—154no—
736C22—154no—
737C22—154no—
738C22—154no—
739C22—152no—
740C22—152no—
741C22—152no—
742C22C22×D3×AGL(1,𝔽5)11yescharacteristic
743C4—22no—
744C4—32no—
745C4—54no—
746C4—52no—
747C4—62no—
748C4—104no—
749C4—102no—
750C4—102no—
751C4—154no—
752C4—152no—
753C4—304no—
754C4—302no—
755C4—302no—
756C4C4×D3×AGL(1,𝔽5)12yescomplemented
757C3C2×C4⋊C4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
758C2—34no—
759C2—51no—
760C2—51no—
761C2—51no—
762C2—51no—
763C2—154no—
764C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
765C2D3×D4×AGL(1,𝔽5)11yescharacteristic
766C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
5. C4⋊C4×ΓL(1,𝔽16)C2semidirect
6. C3×C4⋊C4×AGL(1,𝔽5)C2semidirect
8. #11751846C2semidirect
9. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
10. #11751833C2semidirect
11. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
29. D3×C4⋊AGL(1,𝔽5)C4semidirect
31. C4×D3×AGL(1,𝔽5)C4semidirect
32. C4⋊C4×D15C4semidirect
33. C5×D3×C4⋊C4C4semidirect
35. #91437C4semidirect
36. D3×C4⋊Dic5C4semidirect
38. #91404C4semidirect
39. D3×#683C4semidirect
56. C4⋊C4×AGL(1,𝔽5)D3direct (N × H)
89. C4⋊ΓL(1,𝔽16)C2×C4semidirect
91. C4×ΓL(1,𝔽16)C2×C4semidirect
92. C3×C4⋊AGL(1,𝔽5)C2×C4semidirect
94. C3×C4×AGL(1,𝔽5)C2×C4semidirect
95. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
98. Dic3×AGL(1,𝔽5)C2×C4semidirect
99. Dic3×AGL(1,𝔽5)C2×C4semidirect
100. C3×C5×C4⋊C4C2×C4semidirect
101. C4⋊Dic15C2×C4semidirect
102. #6712C2×C4semidirect
103. C5×C4⋊Dic3C2×C4semidirect
104. C5×Dic3⋊C4C2×C4semidirect
105. C3×C4⋊Dic5C2×C4semidirect
106. C3×#683C2×C4semidirect
107. Dic3⋊Dic5C2×C4semidirect
108. #6669C2×C4semidirect
109. #6668C2×C4semidirect
183. D3×AGL(1,𝔽5)C4⋊C4direct (N × H)
189. C4×D15C42semidirect
193. C4×C5×D3C42semidirect
201. #1200C42semidirect
203. D3×Dic5C42semidirect
233. D3×C4⋊C4AGL(1,𝔽5)direct (N × H)
274. C4⋊AGL(1,𝔽5)C4×D3semidirect
282. C4×AGL(1,𝔽5)C4×D3semidirect
285. C5×C4⋊C4C4×D3semidirect
288. C4⋊Dic5C4×D3semidirect
292. #683C4×D3semidirect
323. ΓL(1,𝔽16)C2×C4⋊C4semidirect
326. C3×AGL(1,𝔽5)C2×C4⋊C4semidirect
328. C3×C4×C5C2×C42semidirect
330. Dic15C2×C42semidirect
332. C3×Dic5C2×C42semidirect
334. C5×Dic3C2×C42semidirect
370. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
376. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
381. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
477. D15C4×C4⋊C4semidirect
482. C5×D3C4×C4⋊C4semidirect
536. C4×D3C4×AGL(1,𝔽5)semidirect
559. AGL(1,𝔽5)D3×C4⋊C4direct (N × H)
563. C4×C5C42×D3semidirect
567. Dic5C42×D3semidirect
612. C4⋊C4D3×AGL(1,𝔽5)direct (N × H)
621. C3×C5C2×C4×C4⋊C4semidirect
645. C3×C4C2×C4×AGL(1,𝔽5)semidirect
652. Dic3C2×C4×AGL(1,𝔽5)semidirect
724. D3C4⋊C4×AGL(1,𝔽5)direct (N × H)
725. C5C4×D3×C4⋊C4semidirect
756. C4C4×D3×AGL(1,𝔽5)semidirect
757. C3C2×C4⋊C4×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×D3×C4⋊AGL(1,𝔽5)2
C2×C4×D3×AGL(1,𝔽5)2
D3×D5×C4⋊C42
C4⋊C4×ΓL(1,𝔽16)2
C3×C4⋊C4×AGL(1,𝔽5)2
D3×(C2×AGL(1,𝔽5))⋊C42
#117518462
AGL(1,𝔽5)×C4⋊Dic32
#117518332
AGL(1,𝔽5)×Dic3⋊C42
C2×C4⋊C4×AGL(1,𝔽5)3
C4×D3×C4⋊C45