Finite Group Databasebeta

← #67×C4⋊AGL(1,𝔽5) #14327094

Subgroups — #67×C4⋊AGL(1,𝔽5) #14327094

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×AGL(1,𝔽5)×#67C212yesmaximal
3C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C4×D5×#67C211yesmaximal, characteristic
5#11752424C211yesmaximal, characteristic, complemented
6#11752027C212yesmaximal, complemented
7#11751932C212yesmaximal, complemented
8#11751860C211yesmaximal, characteristic, complemented
9#11751855C211yesmaximal, characteristic, complemented
10Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11#11751837C212yesmaximal, complemented
12D4×C4⋊AGL(1,𝔽5)—31nomaximal, Hall
13C23×C3×AGL(1,𝔽5)C2212yes—
14C22×D3×AGL(1,𝔽5)C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C2×D5×#67C2211yescharacteristic
17C2×C4×D3×D5C2211yescharacteristic
18C2×#6763C2212yes—
19C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
20C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)—24no—
22C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
25AGL(1,𝔽5)×#67—28no—
26C2×Dic3⋊AGL(1,𝔽5)C2212yes—
27C2×Dic3⋊AGL(1,𝔽5)C2212yes—
28C2×Dic3⋊AGL(1,𝔽5)C2212yes—
29C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
30C2×Dic3×AGL(1,𝔽5)C2212yes—
31D3×C4⋊AGL(1,𝔽5)—24no—
32C4×#1220C411yescharacteristic, complemented
33C4×C5×#67C411yescharacteristic, complemented
34#91552C411yescharacteristic, complemented
35Dic5×#67C411yescharacteristic, complemented
36D5×#217C2211yescharacteristic
37D5×(C2×D3)⋊C4C2211yescharacteristic
38#91444C411yescharacteristic, complemented
39C4×#1202C411yescharacteristic, complemented
40#91440C411yescharacteristic, complemented
41C4×#1201C411yescharacteristic, complemented
42D5×Dic3⋊C4C2211yescharacteristic
43C4×D5×Dic3C2211yescharacteristic
44#91235C2212yes—
45(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
46(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
47C4⋊C4×#67—51nomaximal, Hall
48C2×D4×AGL(1,𝔽5)—32no—
49C22×C4⋊AGL(1,𝔽5)—31no—
50C22×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
51C4×D4×D5—31no—
52#65765—31no—
53#65765—31no—
54#65712—32no—
55#65699—32no—
56#65699—32no—
57#65688—31no—
58C4×C4⋊AGL(1,𝔽5)—31no—
59C23×C3×D5C2311yescharacteristic
60C22×D3×D5C2311yescharacteristic
61C22×ΓL(1,𝔽16)C2312yes—
62C22×ΓL(1,𝔽16)C2312yes—
63C22×C3×AGL(1,𝔽5)—24no—
64C22×C3×AGL(1,𝔽5)—24no—
65C22×C3×AGL(1,𝔽5)—42no—
66C22×C3×AGL(1,𝔽5)C2312yes—
67C22×C3×AGL(1,𝔽5)C2312yes—
68C2×D3×AGL(1,𝔽5)—24no—
69C2×D3×AGL(1,𝔽5)—24no—
70C2×D3×AGL(1,𝔽5)—42no—
71C22×C3×C4×C5C2×C411yescharacteristic, complemented
72C2×#1220C2×C411yescharacteristic
73C2×C4×D15C2×C411yescharacteristic, complemented
74C2×C5×#67C2×C411yescharacteristic
75C2×C4×C5×D3C2×C411yescharacteristic, complemented
76C22×C3×Dic5C2×C411yescharacteristic, complemented
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5C2×C411yescharacteristic, complemented
80C2×C3×C4×D5C2×C411yescharacteristic, complemented
81C2×C3×C4×D5C2311yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83D5×#67D414yes—
84D5×#67Q814yes—
85C2×#1202C2×C411yescharacteristic
86C2×#1201C2×C411yescharacteristic
87C2×#1200C2×C411yescharacteristic, complemented
88C2×D3×Dic5C2×C411yescharacteristic, complemented
89C2×D5×Dic3C2311yescharacteristic
90C2×D5×Dic3C2311yescharacteristic
91C2×D5×Dic3C2311yescharacteristic
92C4×D3×D5—22no—
93C4×D3×D5—22no—
94#6763—24no—
95C4⋊ΓL(1,𝔽16)—22no—
96C4⋊ΓL(1,𝔽16)—22no—
97C3×C4⋊AGL(1,𝔽5)—24no—
98C3×C4⋊AGL(1,𝔽5)—22no—
99C3×C4⋊AGL(1,𝔽5)D414yescomplemented
100Dic3⋊AGL(1,𝔽5)—24no—
101Dic3⋊AGL(1,𝔽5)—24no—
102Dic3⋊AGL(1,𝔽5)—42no—
103(C2×D3)⋊AGL(1,𝔽5)—24no—
104Dic3×AGL(1,𝔽5)—24no—
105#6719C2×C411yescharacteristic, complemented
106#6714C2×C411yescharacteristic, complemented
107#6712C2×C411yescharacteristic, complemented
108C4×Dic15C2×C411yescharacteristic, complemented
109C5×#217C2×C411yescharacteristic, complemented
110C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
111C5×Dic3⋊C4C2×C411yescharacteristic, complemented
112C4×C5×Dic3C2×C411yescharacteristic, complemented
113Dic3⋊Dic5C2×C411yescharacteristic, complemented
114#6669C2×C411yescharacteristic, complemented
115#6667C2×C411yescharacteristic, complemented
116(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
117#6665C2×C411yescharacteristic, complemented
118#6665C2×C411yescharacteristic, complemented
119Dic3×Dic5C2×C411yescharacteristic, complemented
120Dic3×Dic5C2×C411yescharacteristic, complemented
121C22×C3×C4⋊C4—51no—
122C2×C4×#67—51no—
123C2×C4×#67—52no—
124C2×D3×C4⋊C4—51no—
125#5212—51no—
126#5210—52no—
127#4989—52no—
128#4987—51no—
129#4976—52no—
130#4975—51no—
131Dic3×C4⋊C4—51no—
132C23×AGL(1,𝔽5)—32no—
133C23×AGL(1,𝔽5)C2×D312yes—
134C2×D4×D5—31no—
135C22×C4×D5—31no—
136C22×C4×D5C2×D311yescharacteristic
137C2×C22⋊AGL(1,𝔽5)—32no—
138C2×C22⋊AGL(1,𝔽5)—32no—
139D4×AGL(1,𝔽5)—68no—
140C2×C4⋊AGL(1,𝔽5)—24no—
141C2×C4⋊AGL(1,𝔽5)—32no—
142C2×C4⋊AGL(1,𝔽5)—32no—
143C2×C4⋊AGL(1,𝔽5)—31no—
144C2×C4⋊AGL(1,𝔽5)—31no—
145C2×C4⋊AGL(1,𝔽5)—32no—
146C2×C4⋊AGL(1,𝔽5)—64no—
147C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
148C2×C4⋊AGL(1,𝔽5)C2×D312yes—
149C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
150C2×C4×AGL(1,𝔽5)—32no—
151C4×C5×D4—31no—
152D4×Dic5—31no—
153C4×C22⋊D5—31no—
154C4×C22⋊D5—31no—
155#4039—31no—
156D5×C4⋊C4—31no—
157#4027—31no—
158#4027—31no—
159D5×C22⋊C4—31no—
160D5×C22⋊C4—31no—
161C4×D20—31no—
162C42×D5—31no—
163(C2×AGL(1,𝔽5))⋊C4—32no—
164(C2×AGL(1,𝔽5))⋊C4—32no—
165(C2×AGL(1,𝔽5))⋊C4—32no—
166D4×C4⋊C4—151noSylow
167C23×C3×C5C22×C411yescharacteristic
168C22×D15C22×C411yescharacteristic
169C22×C5×D3C22×C411yescharacteristic
170C22×C3×D5—21no—
171C22×C3×D5—21no—
172C22×C3×D5—21no—
173C22×C3×D5—21no—
174C22×C3×D5C22×C411yescharacteristic
175C22×C3×D5C2×D412yes—
176C22×C3×D5C2×Q812yes—
177C22×C3×D5C2411yescharacteristic
178C2×D3×D5—21no—
179C2×D3×D5—21no—
180C2×D3×D5—21no—
181C2×D3×D5—21no—
182C2×D3×D5C2×D412yes—
183C2×D3×D5C2×Q812yes—
184C2×ΓL(1,𝔽16)—22no—
185C2×ΓL(1,𝔽16)—22no—
186C2×ΓL(1,𝔽16)—22no—
187C2×ΓL(1,𝔽16)—22no—
188C2×ΓL(1,𝔽16)—22no—
189C2×ΓL(1,𝔽16)—22no—
190C2×C3×AGL(1,𝔽5)—22no—
191C2×C3×AGL(1,𝔽5)—22no—
192C2×C3×AGL(1,𝔽5)—22no—
193C2×C3×AGL(1,𝔽5)—22no—
194C2×C3×AGL(1,𝔽5)—22no—
195C2×C3×AGL(1,𝔽5)—48no—
196C2×C3×AGL(1,𝔽5)C2×D414yes—
197D3×AGL(1,𝔽5)—48no—
198C2×C3×C4×C5—22no—
199C2×C3×C4×C5C22×C411yescharacteristic
200C2×C3×C4×C5C22×C411yescharacteristic
201#1220C4⋊C414yescomplemented
202C2×Dic15C22×C411yescharacteristic
203C2×Dic15C22×C411yescharacteristic
204C2×Dic15C22×C411yescharacteristic
205C4×D15—22no—
206C5×#67C4⋊C414yescomplemented
207C2×C5×Dic3C22×C411yescharacteristic
208C2×C5×Dic3C22×C411yescharacteristic
209C2×C5×Dic3C22×C411yescharacteristic
210C4×C5×D3—22no—
211C2×C3×Dic5—22no—
212C2×C3×Dic5C22×C411yescharacteristic
213C2×C3×Dic5C22×C411yescharacteristic
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—22no—
217C3×C4×D5—22no—
218C3×C4×D5C2×D412yes—
219C3×C4×D5#4112yes—
220#1202C4⋊C414yescomplemented
221#1201C4⋊C414yescomplemented
222#1200—22no—
223D3×Dic5—22no—
224D5×Dic3—21no—
225D5×Dic3—21no—
226D5×Dic3—21no—
227D5×Dic3—21no—
228D5×Dic3C2×D412yes—
229D5×Dic3C2×Q812yes—
230C23×C3×C4—51no—
231C23×C3×C4—52no—
232C22×#67—51no—
233C22×C4×D3—51no—
234C22×C4×D3—52no—
235C2×C3×C4⋊C4—51no—
236C2×C3×C4⋊C4—51no—
237C2×C3×C4⋊C4—52no—
238C2×C3×C4⋊C4—104no—
239C2×#217—51no—
240C2×#217—52no—
241C4×#67—51no—
242C4×#67—51no—
243C4×#67—51no—
244C4×#67—51no—
245C4×#67—51no—
246C4×#67—51no—
247C4×#67—51no—
248C4×#67—108no—
249C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—52no—
252C2×C4⋊Dic3—51no—
253C2×C4⋊Dic3—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4—52no—
256C2×Dic3⋊C4—52no—
257C2×Dic3⋊C4—52no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—52no—
260D3×C4⋊C4—104no—
261C3⋊#95—52no—
262C3⋊#95—52no—
263C3⋊#95—52no—
264C23×D5—31no—
265C23×D5C22×D311yescharacteristic
266C22×AGL(1,𝔽5)—24no—
267C22×AGL(1,𝔽5)—24no—
268C22×AGL(1,𝔽5)—32no—
269C22×AGL(1,𝔽5)—32no—
270C22×AGL(1,𝔽5)—42no—
271C22×AGL(1,𝔽5)—64no—
272C22×AGL(1,𝔽5)—64no—
273C22×AGL(1,𝔽5)—122no—
274C22×AGL(1,𝔽5)C22×D312yes—
275C22×AGL(1,𝔽5)C22×D312yes—
276C2×C5×D4—31no—
277C22×C4×C5—31no—
278C22×C4×C5C4×D311yescharacteristic, complemented
279C2×C22⋊D5—31no—
280C2×C22⋊D5—31no—
281C22×Dic5—31no—
282C22×Dic5C4×D311yescharacteristic, complemented
283D4×D5—34no—
284D4×D5—34no—
285C2×D20—31no—
286C2×C4×D5—22no—
287C2×C4×D5—22no—
288C2×C4×D5—31no—
289C2×C4×D5—31no—
290C2×C4×D5—31no—
291C2×C4×D5—31no—
292C2×C4×D5—31no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×C4×D5C4×D311yescharacteristic, complemented
296C2×C4×D5C4×D311yescharacteristic, complemented
297C2×C4×D5C22×D311yescharacteristic
298C2×C4×D5C22×D311yescharacteristic
299C22⋊AGL(1,𝔽5)—64no—
300C22⋊AGL(1,𝔽5)—64no—
301C4⋊AGL(1,𝔽5)—24no—
302C4⋊AGL(1,𝔽5)—22no—
303C4⋊AGL(1,𝔽5)—64no—
304C4⋊AGL(1,𝔽5)—64no—
305C4⋊AGL(1,𝔽5)—62no—
306C4⋊AGL(1,𝔽5)—62no—
307C4⋊AGL(1,𝔽5)—122no—
308C4⋊AGL(1,𝔽5)#6714yesdirect product factor
309C4×AGL(1,𝔽5)—64no—
310C5×C4⋊C4—31no—
311C5×C22⋊C4—31no—
312C5×C22⋊C4—31no—
313C42×C5—31no—
314C22⋊Dic5—31no—
315C22⋊Dic5—31no—
316#685—31no—
317#685—31no—
318#685—31no—
319#685—31no—
320C4⋊Dic5—31no—
321#683—31no—
322#683—31no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C2×C4×D4—151no—
327C2×C4×D4—152no—
328C22×C4⋊C4—51no—
329C22×C4⋊C4—151no—
330#389—152no—
331#385—152no—
332#385—152no—
333#384—151no—
334#380—151no—
335#380—151no—
336C4×C4⋊C4—151no—
337C22×C3×C5—21no—
338C22×C3×C5—21no—
339C22×C3×C5C2×C4⋊C412yescomplemented
340C22×C3×C5C23×C411yescharacteristic
341C2×D15—21no—
342C2×D15—21no—
343C2×D15C2×C4⋊C412yescomplemented
344C2×C5×D3—21no—
345C2×C5×D3—21no—
346C2×C5×D3C2×C4⋊C412yescomplemented
347C2×C3×D5—21no—
348C2×C3×D5—21no—
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5C2×C4⋊C412yescomplemented
354C2×C3×D5C22×D411yescharacteristic
355C2×C3×D5C22×D411yescharacteristic
356C2×C3×D5C22×Q811yescharacteristic
357C2×C3×D5C2×#4111yescharacteristic
358C2×C3×D5H(5,𝔽2)11yescharacteristic
359C2×C3×D52−1+411yescharacteristic
360D3×D5—22no—
361D3×D5—22no—
362D3×D5—22no—
363D3×D5—22no—
364ΓL(1,𝔽16)—42no—
365ΓL(1,𝔽16)—42no—
366C3×AGL(1,𝔽5)—24no—
367C3×AGL(1,𝔽5)—42no—
368C3×C4×C5—21no—
369C3×C4×C5C4×D412yescomplemented
370Dic15—21no—
371Dic15—21no—
372Dic15C2×C4⋊C412yescomplemented
373C3×Dic5—21no—
374C3×Dic5C4×D412yescomplemented
375C5×Dic3—21no—
376C5×Dic3—21no—
377C5×Dic3C2×C4⋊C412yescomplemented
378C24×C3—51no—
379C23×D3—51no—
380C22×C3×C4—51no—
381C22×C3×C4—52no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—52no—
387C22×C3×C4—102no—
388C22×C3×C4—102no—
389C22×C3×C4—104no—
390C22×C3×C4—104no—
391C22×C3×C4—202no—
392C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
393C2×#67—51no—
394C2×#67—51no—
395C2×#67—54no—
396C2×#67—54no—
397C2×#67—51no—
398C2×#67C2×AGL(1,𝔽5)11yescharacteristic
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—52no—
403C22×Dic3—52no—
404C2×C4×D3—51no—
405C2×C4×D3—51no—
406C2×C4×D3—51no—
407C2×C4×D3—102no—
408C2×C4×D3—102no—
409C2×C4×D3—104no—
410C2×C4×D3—104no—
411C2×C4×D3—202no—
412C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
413C3×C4⋊C4—54no—
414C3×C4⋊C4—102no—
415C3×C4⋊C4—104no—
416#217—51no—
417#217—51no—
418#217—51no—
419#217—104no—
420#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
421(C2×D3)⋊C4—51no—
422(C2×D3)⋊C4—51no—
423(C2×D3)⋊C4—51no—
424(C2×D3)⋊C4—104no—
425(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
426C4⋊Dic3—102no—
427C4⋊Dic3—102no—
428Dic3⋊C4—51no—
429Dic3⋊C4—51no—
430Dic3⋊C4—51no—
431Dic3⋊C4—104no—
432Dic3⋊C4—104no—
433Dic3⋊C4—202no—
434Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
435C4×Dic3—51no—
436C4×Dic3—51no—
437C4×Dic3—51no—
438C4×Dic3—104no—
439C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
440C23×C5—31no—
441C23×C5C2×C4×D311yescharacteristic
442C22×D5—21no—
443C22×D5—21no—
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—31no—
447C22×D5—32no—
448C22×D5—32no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5C2×C4×D311yescharacteristic
454C22×D5D3×D412yes—
455C22×D5D3×Q812yes—
456C22×D5C23×D311yescharacteristic
457C2×AGL(1,𝔽5)—22no—
458C2×AGL(1,𝔽5)—22no—
459C2×AGL(1,𝔽5)—22no—
460C2×AGL(1,𝔽5)—22no—
461C2×AGL(1,𝔽5)—22no—
462C2×AGL(1,𝔽5)—48no—
463C2×AGL(1,𝔽5)—62no—
464C2×AGL(1,𝔽5)—62no—
465C2×AGL(1,𝔽5)—62no—
466C2×AGL(1,𝔽5)—62no—
467C2×AGL(1,𝔽5)—62no—
468C2×AGL(1,𝔽5)—62no—
469C2×AGL(1,𝔽5)—128no—
470C2×AGL(1,𝔽5)C2×#6714yes—
471C5×D4—34no—
472C2×C4×C5—22no—
473C2×C4×C5—31no—
474C2×C4×C5—31no—
475C2×C4×C5—31no—
476C2×C4×C5—62no—
477C2×C4×C5C2×C4×D311yescharacteristic
478C2×C4×C5C2×C4×D311yescharacteristic
479C22⋊D5—34no—
480C22⋊D5—34no—
481C2×Dic5—22no—
482C2×Dic5—31no—
483C2×Dic5—31no—
484C2×Dic5—31no—
485C2×Dic5—62no—
486C2×Dic5C2×C4×D311yescharacteristic
487C2×Dic5C2×C4×D311yescharacteristic
488D20—34no—
489C4×D5—21no—
490C4×D5—21no—
491C4×D5—22no—
492C4×D5—22no—
493C4×D5—32no—
494C4×D5—32no—
495C4×D5—61no—
496C4×D5—61no—
497C4×D5—61no—
498C4×D5—61no—
499C4×D5—62no—
500C4×D5—62no—
501C4×D5#23512yes—
502C4×D5C2×#6712yes—
503C22×D4—151no—
504C23×C4—51no—
505C23×C4—52no—
506C23×C4—151no—
507C23×C4—152no—
508C4×D4—31no—
509C4×D4—151no—
510C4×D4—151no—
511C4×D4—151no—
512C4×D4—151no—
513C4×D4—151no—
514C4×D4—151no—
515C4×D4—151no—
516C4×D4—308no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—52no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—152no—
524C2×C4⋊C4—152no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—152no—
527C2×C4⋊C4—304no—
528C2×C22⋊C4—151no—
529C2×C22⋊C4—151no—
530C2×C22⋊C4—152no—
531C2×C22⋊C4—152no—
532C2×C42—151no—
533C2×C42—152no—
534#95—152no—
535#95—152no—
536#95—152no—
537C2×C3×C5—22no—
538C2×C3×C5C22×C4⋊C411yescharacteristic
539C2×C3×C5C2×C4×D411yescharacteristic
540C2×C3×C5#52011yescharacteristic
541D15—22no—
542C3×D5—22no—
543C3×D5D4211yescharacteristic
544C3×D5#54711yescharacteristic
545C3×D5D4×Q811yescharacteristic
546C3×D5#55411yescharacteristic
547C5×D3—22no—
548C23×C3—51no—
549C23×C3—52no—
550C23×C3—52no—
551C23×C3—51no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3—101no—
555C23×C3—101no—
556C23×C3C22×AGL(1,𝔽5)11yescharacteristic
557C22×D3—51no—
558C22×D3—52no—
559C22×D3—52no—
560C22×D3—101no—
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—101no—
564C22×D3C22×AGL(1,𝔽5)11yescharacteristic
565C2×C3×C4—22no—
566C2×C3×C4—51no—
567C2×C3×C4—52no—
568C2×C3×C4—52no—
569C2×C3×C4—54no—
570C2×C3×C4—51no—
571C2×C3×C4—102no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—102no—
575C2×C3×C4—102no—
576C2×C3×C4—102no—
577C2×C3×C4—102no—
578C2×C3×C4—102no—
579C2×C3×C4—102no—
580C2×C3×C4—102no—
581C2×C3×C4—208no—
582C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
583C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
584#67—54no—
585#67—54no—
586#67—54no—
587#67C4⋊AGL(1,𝔽5)14yesdirect product factor
588C2×Dic3—51no—
589C2×Dic3—52no—
590C2×Dic3—52no—
591C2×Dic3—51no—
592C2×Dic3—51no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—102no—
598C2×Dic3—102no—
599C2×Dic3—102no—
600C2×Dic3—102no—
601C2×Dic3—102no—
602C2×Dic3—102no—
603C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
604C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
605C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
606C4×D3—22no—
607C4×D3—102no—
608C4×D3—102no—
609C4×D3—102no—
610C4×D3—208no—
611C22×C5—21no—
612C22×C5—21no—
613C22×C5—32no—
614C22×C5—61no—
615C22×C5—61no—
616C22×C5D3×C4⋊C412yescomplemented
617C22×C5C22×C4×D311yescharacteristic
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—32no—
625C2×D5—61no—
626C2×D5—61no—
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—62no—
630C2×D5—62no—
631C2×D5D3×C4⋊C412yescomplemented
632C2×D5C2×#23511yescharacteristic
633C2×D5C2×D3×D411yescharacteristic
634C2×D5#100411yescharacteristic
635C2×D5C2×D3×Q811yescharacteristic
636C2×D5#100711yescharacteristic
637C2×D5C22×#6711yescharacteristic
638AGL(1,𝔽5)—24no—
639AGL(1,𝔽5)—42no—
640AGL(1,𝔽5)—122no—
641AGL(1,𝔽5)—122no—
642C4×C5—21no—
643C4×C5—32no—
644C4×C5—61no—
645C4×C5—61no—
646C4×C5C4×#6712yescomplemented
647Dic5—21no—
648Dic5—32no—
649Dic5—61no—
650Dic5—61no—
651Dic5C4×#6712yescomplemented
652C24—51no—
653C24—151no—
654C2×D4—31no—
655C2×D4—151no—
656C2×D4—154no—
657C2×D4—154no—
658C2×D4—151no—
659C2×D4—151no—
660C22×C4—31no—
661C22×C4—51no—
662C22×C4—52no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—52no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—104no—
671C22×C4—104no—
672C22×C4—151no—
673C22×C4—151no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—152no—
679C22×C4—152no—
680C22×C4—202no—
681C22×C4—302no—
682C22×C4—302no—
683C22×C4—304no—
684C22×C4—304no—
685C22×C4—602no—
686C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
687C4⋊C4—31no—
688C4⋊C4—54no—
689C4⋊C4—102no—
690C4⋊C4—104no—
691C4⋊C4—151no—
692C4⋊C4—151no—
693C4⋊C4—151no—
694C4⋊C4—304no—
695C4⋊C4—302no—
696C4⋊C4—302no—
697C4⋊C4—304no—
698C4⋊C4—602no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—151no—
702C22⋊C4—151no—
703C22⋊C4—151no—
704C22⋊C4—151no—
705C22⋊C4—151no—
706C22⋊C4—151no—
707C22⋊C4—304no—
708C22⋊C4—304no—
709C42—31no—
710C42—151no—
711C42—151no—
712C42—151no—
713C42—304no—
714C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—51no—
718C22×C3—51no—
719C22×C3—51no—
720C22×C3—51no—
721C22×C3—51no—
722C22×C3—51no—
723C22×C3—52no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—102no—
727C22×C3—102no—
728C22×C3—101no—
729C22×C3—101no—
730C22×C3C2×C4⋊AGL(1,𝔽5)12yescomplemented
731C22×C3C23×AGL(1,𝔽5)11yescharacteristic
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—52no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3—102no—
738C2×D3—102no—
739C2×D3—101no—
740C2×D3—101no—
741C2×D3C2×C4⋊AGL(1,𝔽5)12yescomplemented
742C3×C4—21no—
743C3×C4—52no—
744C3×C4—104no—
745C3×C4—101no—
746C3×C4—202no—
747C3×C4D4×AGL(1,𝔽5)12yescomplemented
748Dic3—21no—
749Dic3—21no—
750Dic3—52no—
751Dic3—101no—
752Dic3—101no—
753Dic3—202no—
754Dic3—202no—
755Dic3C2×C4⋊AGL(1,𝔽5)12yescomplemented
756C2×C5—22no—
757C2×C5—62no—
758C2×C5C2×D3×C4⋊C411yescharacteristic
759C2×C5#550411yescharacteristic
760C2×C5C2×C4×#6711yescharacteristic
761D5—22no—
762D5—62no—
763D5#550711yescharacteristic
764D5#551111yescharacteristic
765D5D4×#6711yescharacteristic
766D5Q8×#6711yescharacteristic
767C23—31no—
768C23—51no—
769C23—52no—
770C23—52no—
771C23—51no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—101no—
776C23—152no—
777C23—152no—
778C23—151no—
779C23—301no—
780C23—301no—
781C23—301no—
782C23—301no—
783C23C2×D3×AGL(1,𝔽5)11yescharacteristic
784D4—34no—
785D4—154no—
786D4—154no—
787D4—154no—
788C2×C4—22no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—51no—
793C2×C4—52no—
794C2×C4—52no—
795C2×C4—54no—
796C2×C4—51no—
797C2×C4—62no—
798C2×C4—102no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—152no—
809C2×C4—152no—
810C2×C4—151no—
811C2×C4—151no—
812C2×C4—151no—
813C2×C4—208no—
814C2×C4—302no—
815C2×C4—302no—
816C2×C4—301no—
817C2×C4—301no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—302no—
821C2×C4—302no—
822C2×C4—302no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—302no—
827C2×C4—608no—
828C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
829C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
830C2×C3—22no—
831C2×C3—51no—
832C2×C3—51no—
833C2×C3—51no—
834C2×C3—51no—
835C2×C3—102no—
836C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
837C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
838C2×C3#6626611yescharacteristic
839D3—22no—
840D3—102no—
841C5C4⋊C4×#6711yescharacteristic, complemented, Sylow
842C22—21no—
843C22—21no—
844C22—32no—
845C22—51no—
846C22—51no—
847C22—51no—
848C22—51no—
849C22—51no—
850C22—51no—
851C22—52no—
852C22—61no—
853C22—61no—
854C22—102no—
855C22—102no—
856C22—102no—
857C22—102no—
858C22—101no—
859C22—101no—
860C22—152no—
861C22—302no—
862C22—302no—
863C22—302no—
864C22—302no—
865C22—301no—
866C22—301no—
867C22D3×C4⋊AGL(1,𝔽5)12yescomplemented
868C22C22×D3×AGL(1,𝔽5)11yescharacteristic
869C4—21no—
870C4—32no—
871C4—52no—
872C4—61no—
873C4—61no—
874C4—104no—
875C4—101no—
876C4—152no—
877C4—202no—
878C4—301no—
879C4—301no—
880C4—602no—
881C4—602no—
882C4AGL(1,𝔽5)×#6712yescomplemented
883C3D4×C4⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
884C2—22no—
885C2—51no—
886C2—51no—
887C2—51no—
888C2—51no—
889C2—62no—
890C2—102no—
891C2—302no—
892C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
893C2#1175683611yescharacteristic
894C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊AGL(1,𝔽5)C2semidirect
3. C2×D3×C4⋊AGL(1,𝔽5)C2semidirect
5. #11752424C2semidirect
6. #11752027C2semidirect
7. #11751932C2semidirect
8. #11751860C2semidirect
9. #11751855C2semidirect
10. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
11. #11751837C2semidirect
32. C4×#1220C4semidirect
33. C4×C5×#67C4semidirect
34. #91552C4semidirect
35. Dic5×#67C4semidirect
38. #91444C4semidirect
39. C4×#1202C4semidirect
40. #91440C4semidirect
41. C4×#1201C4semidirect
50. C22×C4⋊AGL(1,𝔽5)D3semidirect
71. C22×C3×C4×C5C2×C4semidirect
73. C2×C4×D15C2×C4semidirect
75. C2×C4×C5×D3C2×C4semidirect
76. C22×C3×Dic5C2×C4semidirect
79. C2×C3×C4×D5C2×C4semidirect
80. C2×C3×C4×D5C2×C4semidirect
87. C2×#1200C2×C4semidirect
88. C2×D3×Dic5C2×C4semidirect
99. C3×C4⋊AGL(1,𝔽5)D4semidirect
105. #6719C2×C4semidirect
106. #6714C2×C4semidirect
107. #6712C2×C4semidirect
108. C4×Dic15C2×C4semidirect
109. C5×#217C2×C4semidirect
110. C5×(C2×D3)⋊C4C2×C4semidirect
111. C5×Dic3⋊C4C2×C4semidirect
112. C4×C5×Dic3C2×C4semidirect
113. Dic3⋊Dic5C2×C4semidirect
114. #6669C2×C4semidirect
115. #6667C2×C4semidirect
116. (C2×D3)⋊Dic5C2×C4semidirect
117. #6665C2×C4semidirect
118. #6665C2×C4semidirect
119. Dic3×Dic5C2×C4semidirect
120. Dic3×Dic5C2×C4semidirect
201. #1220C4⋊C4semidirect
206. C5×#67C4⋊C4semidirect
220. #1202C4⋊C4semidirect
221. #1201C4⋊C4semidirect
249. C4×#67AGL(1,𝔽5)semidirect
278. C22×C4×C5C4×D3semidirect
282. C22×Dic5C4×D3semidirect
295. C2×C4×D5C4×D3semidirect
296. C2×C4×D5C4×D3semidirect
308. C4⋊AGL(1,𝔽5)#67direct (N × H)
339. C22×C3×C5C2×C4⋊C4semidirect
343. C2×D15C2×C4⋊C4semidirect
346. C2×C5×D3C2×C4⋊C4semidirect
353. C2×C3×D5C2×C4⋊C4semidirect
369. C3×C4×C5C4×D4semidirect
372. Dic15C2×C4⋊C4semidirect
374. C3×Dic5C4×D4semidirect
377. C5×Dic3C2×C4⋊C4semidirect
392. C22×C3×C4C2×AGL(1,𝔽5)semidirect
412. C2×C4×D3C2×AGL(1,𝔽5)semidirect
420. #217C2×AGL(1,𝔽5)semidirect
425. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
434. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
439. C4×Dic3C2×AGL(1,𝔽5)semidirect
587. #67C4⋊AGL(1,𝔽5)direct (N × H)
616. C22×C5D3×C4⋊C4semidirect
631. C2×D5D3×C4⋊C4semidirect
646. C4×C5C4×#67semidirect
651. Dic5C4×#67semidirect
686. C22×C4D3×AGL(1,𝔽5)semidirect
714. C3×C5D4×C4⋊C4semidirect
730. C22×C3C2×C4⋊AGL(1,𝔽5)semidirect
741. C2×D3C2×C4⋊AGL(1,𝔽5)semidirect
747. C3×C4D4×AGL(1,𝔽5)semidirect
755. Dic3C2×C4⋊AGL(1,𝔽5)semidirect
841. C5C4⋊C4×#67semidirect
867. C22D3×C4⋊AGL(1,𝔽5)semidirect
882. C4AGL(1,𝔽5)×#67semidirect
883. C3D4×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
C22×C3×C4⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C2×D3×C4⋊AGL(1,𝔽5)2
C4×D5×#672
#117524242
#117520272
#117519322
#117518602
#117518552
Dic3×C4⋊AGL(1,𝔽5)2
#117518372
D4×C4⋊AGL(1,𝔽5)3
C4⋊C4×#675