Finite Group Databasebeta

← #67×C22⋊AGL(1,𝔽5) #14325994

Subgroups — #67×C22⋊AGL(1,𝔽5) #14325994

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic
2C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C2×D3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C2×AGL(1,𝔽5)×#67C212yesmaximal, complemented
5#11752459C211yesmaximal, characteristic, complemented
6#11752055C212yesmaximal, complemented
7#11752028C211yesmaximal, characteristic, complemented
8#11752025C211yesmaximal, characteristic, complemented
9#11752022C212yesmaximal, complemented
10Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11#11752019C212yesmaximal, complemented
12D4×C22⋊AGL(1,𝔽5)—31nomaximal, Hall
13C24×C3×D5C2211yescharacteristic
14C23×D3×D5C2211yescharacteristic
15C23×C3×AGL(1,𝔽5)C2212yescomplemented
16C22×D3×AGL(1,𝔽5)C2212yescomplemented
17C22×#1220C411yescharacteristic, complemented
18C22×C5×#67C411yescharacteristic, complemented
19C2×D5×#67—28no—
20C2×D5×#67C411yescharacteristic, complemented
21C2×D5×#67C411yescharacteristic, complemented
22C2×D5×#67C411yescharacteristic, complemented
23C2×D5×#67C411yescharacteristic, complemented
24C2×D5×#67C2211yescharacteristic
25C2×D5×#67C2211yescharacteristic
26C2×D5×#67C2211yescharacteristic
27C2×D5×#67C2211yescharacteristic
28C22×#1202C411yescharacteristic, complemented
29C22×#1201C411yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic
31C2×#6763C2211yescharacteristic
32C2×#6763C2211yescharacteristic
33C2×#6763C2212yescomplemented
34C2×#6763C2212yescomplemented
35C2×C3×C22⋊AGL(1,𝔽5)—24no—
36C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
37C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
38C2×C3×C22⋊AGL(1,𝔽5)C2212yescomplemented
39D3×C22⋊AGL(1,𝔽5)—24no—
40AGL(1,𝔽5)×#67—28no—
41C2×Dic3⋊AGL(1,𝔽5)C2212yescomplemented
42C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
43C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
44C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
45C2×Dic3×AGL(1,𝔽5)C2212yescomplemented
46(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
47(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
48C22⋊C4×#67—51nomaximal, Hall
49C22×D4×D5—31no—
50C22×C22⋊AGL(1,𝔽5)—31no—
51C22×C22⋊AGL(1,𝔽5)D311yescharacteristic, complemented
52C2×D4×AGL(1,𝔽5)—32no—
53#65800—31no—
54#65800—31no—
55#65780—32no—
56#65779—32no—
57#65779—32no—
58#65765—31no—
59C4×C22⋊AGL(1,𝔽5)—31no—
60C24×C3×C5C2×C411yescharacteristic, complemented
61C23×D15C2×C411yescharacteristic, complemented
62C23×C5×D3C2×C411yescharacteristic, complemented
63C23×C3×D5—22no—
64C23×C3×D5—24no—
65C23×C3×D5—22no—
66C23×C3×D5—42no—
67C23×C3×D5C2×C411yescharacteristic, complemented
68C23×C3×D5C2×C411yescharacteristic, complemented
69C23×C3×D5C2×C411yescharacteristic, complemented
70C23×C3×D5C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—22no—
74C22×D3×D5—22no—
75C22×D3×D5—24no—
76C22×D3×D5—42no—
77C22×D3×D5C2×C411yescharacteristic, complemented
78C22×D3×D5C2×C411yescharacteristic, complemented
79C22×D3×D5C2311yescharacteristic
80C22×D3×D5C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2312yes—
82C22×ΓL(1,𝔽16)C2312yes—
83C22×C3×AGL(1,𝔽5)—24no—
84C22×C3×AGL(1,𝔽5)—24no—
85C22×C3×AGL(1,𝔽5)—42no—
86C22×C3×AGL(1,𝔽5)C2312yes—
87C22×C3×AGL(1,𝔽5)C2312yes—
88C2×D3×AGL(1,𝔽5)—24no—
89C2×D3×AGL(1,𝔽5)—24no—
90C2×D3×AGL(1,𝔽5)—42no—
91C2×#1220—24no—
92C2×#1220C2×C411yescharacteristic
93C2×#1220C2×C411yescharacteristic, complemented
94C2×#1220C2×C411yescharacteristic, complemented
95C2×#1220C2×C411yescharacteristic, complemented
96C22×Dic15C2×C411yescharacteristic, complemented
97C2×C5×#67—24no—
98C2×C5×#67C2×C411yescharacteristic
99C2×C5×#67C2×C411yescharacteristic, complemented
100C2×C5×#67C2×C411yescharacteristic, complemented
101C2×C5×#67C2×C411yescharacteristic, complemented
102C22×C5×Dic3C2×C411yescharacteristic, complemented
103D5×#67—24no—
104D5×#67—24no—
105D5×#67—24no—
106D5×#67—24no—
107D5×#67—24no—
108D5×#67—24no—
109D5×#67—24no—
110D5×#67D418yes—
111C2×#1202—24no—
112C2×#1202C2×C411yescharacteristic
113C2×#1202C2×C411yescharacteristic, complemented
114C2×#1202C2×C411yescharacteristic, complemented
115C2×#1202C2×C411yescharacteristic, complemented
116C2×#1201—24no—
117C2×#1201C2×C411yescharacteristic
118C2×#1201C2×C411yescharacteristic, complemented
119C2×#1201C2×C411yescharacteristic, complemented
120C2×#1201C2×C411yescharacteristic, complemented
121C2×D5×Dic3—24no—
122C2×D5×Dic3C2×C411yescharacteristic, complemented
123C2×D5×Dic3C2×C411yescharacteristic, complemented
124C2×D5×Dic3C2311yescharacteristic
125C2×D5×Dic3C2311yescharacteristic
126#6763—24no—
127#6763—22no—
128#6763—22no—
129#6763—42no—
130C3×C22⋊AGL(1,𝔽5)—22no—
131C3×C22⋊AGL(1,𝔽5)—24no—
132C3×C22⋊AGL(1,𝔽5)D414yescomplemented
133Dic3⋊AGL(1,𝔽5)—24no—
134(C2×D3)⋊AGL(1,𝔽5)—24no—
135(C2×D3)⋊AGL(1,𝔽5)—24no—
136(C2×D3)⋊AGL(1,𝔽5)—42no—
137Dic3×AGL(1,𝔽5)—24no—
138C23×#67—51no—
139C22×C3×C22⋊C4—51no—
140C2×C4×#67—52no—
141C2×D3×C22⋊C4—51no—
142#5247—51no—
143#5213—52no—
144#4957—52no—
145#4956—52no—
146#4955—51no—
147#4942—51no—
148Dic3×C22⋊C4—51no—
149C24×D5—31no—
150C24×D5C2×D311yescharacteristic
151C23×AGL(1,𝔽5)—32no—
152C23×AGL(1,𝔽5)C2×D312yescomplemented
153C22×C5×D4—31no—
154C22×C22⋊D5—31no—
155C22×C22⋊D5—31no—
156C2×D4×D5—31no—
157C2×D4×D5—31no—
158C2×D4×D5—31no—
159C2×D4×D5—31no—
160C2×D4×D5—31no—
161C2×D4×D5—31no—
162C2×D4×D5—31no—
163C2×D4×D5—31no—
164C2×D4×D5—68no—
165C22×D20—31no—
166C22×C4×D5—31no—
167C2×C22⋊AGL(1,𝔽5)—24no—
168C2×C22⋊AGL(1,𝔽5)—31no—
169C2×C22⋊AGL(1,𝔽5)—31no—
170C2×C22⋊AGL(1,𝔽5)—32no—
171C2×C22⋊AGL(1,𝔽5)—32no—
172C2×C22⋊AGL(1,𝔽5)—32no—
173C2×C22⋊AGL(1,𝔽5)—32no—
174C2×C22⋊AGL(1,𝔽5)—32no—
175C2×C22⋊AGL(1,𝔽5)—64no—
176C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
177C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
178C2×C22⋊AGL(1,𝔽5)C2×D312yescomplemented
179D4×AGL(1,𝔽5)—68no—
180C2×C4⋊AGL(1,𝔽5)—32no—
181C2×C4×AGL(1,𝔽5)—32no—
182(C2×AGL(1,𝔽5))⋊C4—32no—
183(C2×AGL(1,𝔽5))⋊C4—32no—
184D4×C22⋊C4—151noSylow
185C23×C3×C5—22no—
186C23×C3×C5—22no—
187C23×C3×C5—41no—
188C23×C3×C5C22×C411yescharacteristic
189C23×C3×C5C22×C411yescharacteristic
190C23×C3×C5C22×C411yescharacteristic
191C22×D15—22no—
192C22×D15—22no—
193C22×D15—41no—
194C22×D15C22×C411yescharacteristic
195C22×D15C22×C411yescharacteristic
196C22×C5×D3—22no—
197C22×C5×D3—22no—
198C22×C5×D3—41no—
199C22×C5×D3C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C3×D5—22no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—22no—
205C22×C3×D5—22no—
206C22×C3×D5—22no—
207C22×C3×D5—22no—
208C22×C3×D5—22no—
209C22×C3×D5—22no—
210C22×C3×D5—22no—
211C22×C3×D5—22no—
212C22×C3×D5—21no—
213C22×C3×D5—22no—
214C22×C3×D5—21no—
215C22×C3×D5—22no—
216C22×C3×D5—41no—
217C22×C3×D5—41no—
218C22×C3×D5—41no—
219C22×C3×D5—48no—
220C22×C3×D5—48no—
221C22×C3×D5C22×C411yescharacteristic
222C22×C3×D5C22×C411yescharacteristic
223C22×C3×D5C22×C411yescharacteristic
224C22×C3×D5C2×D414yes—
225C22×C3×D5C2×D412yes—
226C22×C3×D5#4112yes—
227C22×C3×D5C2411yescharacteristic
228C2×D3×D5—21no—
229C2×D3×D5—21no—
230C2×D3×D5—22no—
231C2×D3×D5—22no—
232C2×D3×D5—22no—
233C2×D3×D5—22no—
234C2×D3×D5—22no—
235C2×D3×D5—21no—
236C2×D3×D5—22no—
237C2×D3×D5—21no—
238C2×D3×D5—22no—
239C2×D3×D5—48no—
240C2×D3×D5—48no—
241C2×D3×D5—41no—
242C2×D3×D5—41no—
243C2×D3×D5C2×D414yes—
244C2×ΓL(1,𝔽16)—22no—
245C2×ΓL(1,𝔽16)—22no—
246C2×ΓL(1,𝔽16)—22no—
247C2×ΓL(1,𝔽16)—22no—
248C2×ΓL(1,𝔽16)—22no—
249C2×ΓL(1,𝔽16)—22no—
250C2×C3×AGL(1,𝔽5)—22no—
251C2×C3×AGL(1,𝔽5)—22no—
252C2×C3×AGL(1,𝔽5)—22no—
253C2×C3×AGL(1,𝔽5)—22no—
254C2×C3×AGL(1,𝔽5)—22no—
255C2×C3×AGL(1,𝔽5)—48no—
256C2×C3×AGL(1,𝔽5)C2×D414yescomplemented
257D3×AGL(1,𝔽5)—48no—
258#1220—22no—
259#1220—22no—
260#1220—22no—
261#1220C22⋊C414yescomplemented
262C2×Dic15—22no—
263C2×Dic15C22×C411yescharacteristic
264C2×Dic15C22×C411yescharacteristic
265C5×#67—22no—
266C5×#67—22no—
267C5×#67—22no—
268C5×#67C22⋊C414yescomplemented
269C2×C5×Dic3—22no—
270C2×C5×Dic3C22×C411yescharacteristic
271C2×C5×Dic3C22×C411yescharacteristic
272#1202—22no—
273#1202—22no—
274#1202—22no—
275#1202C22⋊C414yescomplemented
276#1201—22no—
277#1201—22no—
278#1201—22no—
279#1201C22⋊C414yescomplemented
280D5×Dic3—22no—
281D5×Dic3—22no—
282D5×Dic3—22no—
283D5×Dic3C2×D414yes—
284C25×C3—51no—
285C24×D3—51no—
286C23×C3×C4—52no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67—51no—
295C22×#67—51no—
296C22×#67—51no—
297C22×#67—51no—
298C22×#67—108no—
299C22×#67AGL(1,𝔽5)11yescharacteristic, complemented
300C23×Dic3—51no—
301C22×C4×D3—52no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—52no—
305C2×C3×C22⋊C4—104no—
306C2×#217—51no—
307C2×#217—51no—
308C2×#217—52no—
309C2×#217—52no—
310C4×#67—108no—
311C2×(C2×D3)⋊C4—52no—
312C2×(C2×D3)⋊C4—52no—
313C2×(C2×D3)⋊C4—52no—
314C2×Dic3⋊C4—52no—
315C2×C4×Dic3—52no—
316D3×C22⋊C4—104no—
317C3⋊#95—52no—
318C3⋊#95—52no—
319C24×C5—31no—
320C24×C5C4×D311yescharacteristic, complemented
321C23×D5—22no—
322C23×D5—24no—
323C23×D5—22no—
324C23×D5—31no—
325C23×D5—31no—
326C23×D5—31no—
327C23×D5—31no—
328C23×D5—31no—
329C23×D5—42no—
330C23×D5—64no—
331C23×D5—62no—
332C23×D5—62no—
333C23×D5—122no—
334C23×D5C4×D311yescharacteristic, complemented
335C23×D5C4×D311yescharacteristic, complemented
336C23×D5C4×D311yescharacteristic, complemented
337C23×D5C22×D311yescharacteristic
338C23×D5C22×D311yescharacteristic
339C23×D5C22×D311yescharacteristic
340C22×AGL(1,𝔽5)—24no—
341C22×AGL(1,𝔽5)—24no—
342C22×AGL(1,𝔽5)—32no—
343C22×AGL(1,𝔽5)—32no—
344C22×AGL(1,𝔽5)—42no—
345C22×AGL(1,𝔽5)—64no—
346C22×AGL(1,𝔽5)—64no—
347C22×AGL(1,𝔽5)—122no—
348C22×AGL(1,𝔽5)C22×D312yes—
349C22×AGL(1,𝔽5)C22×D312yes—
350C2×C5×D4—31no—
351C2×C5×D4—31no—
352C2×C5×D4—31no—
353C2×C5×D4—31no—
354C2×C5×D4—64no—
355C22×C4×C5—31no—
356C2×C22⋊D5—31no—
357C2×C22⋊D5—31no—
358C2×C22⋊D5—31no—
359C2×C22⋊D5—31no—
360C2×C22⋊D5—31no—
361C2×C22⋊D5—31no—
362C2×C22⋊D5—31no—
363C2×C22⋊D5—31no—
364C2×C22⋊D5—64no—
365C2×C22⋊D5—64no—
366C22×Dic5—31no—
367D4×D5—38no—
368D4×D5—64no—
369D4×D5—64no—
370D4×D5—64no—
371D4×D5—64no—
372D4×D5—64no—
373D4×D5—64no—
374D4×D5—64no—
375C2×D20—31no—
376C2×D20—31no—
377C2×D20—31no—
378C2×D20—31no—
379C2×D20—64no—
380C2×C4×D5—31no—
381C2×C4×D5—31no—
382C2×C4×D5—31no—
383C2×C4×D5—31no—
384C2×C4×D5—64no—
385C22⋊AGL(1,𝔽5)—22no—
386C22⋊AGL(1,𝔽5)—24no—
387C22⋊AGL(1,𝔽5)—64no—
388C22⋊AGL(1,𝔽5)—62no—
389C22⋊AGL(1,𝔽5)—64no—
390C22⋊AGL(1,𝔽5)—62no—
391C22⋊AGL(1,𝔽5)—64no—
392C22⋊AGL(1,𝔽5)—122no—
393C22⋊AGL(1,𝔽5)—122no—
394C22⋊AGL(1,𝔽5)#6714yesdirect product factor
395C4⋊AGL(1,𝔽5)—64no—
396C4×AGL(1,𝔽5)—64no—
397C23×D4—151no—
398C2×C4×D4—152no—
399C22×C22⋊C4—51no—
400C22×C22⋊C4—151no—
401#390—152no—
402#386—152no—
403#386—152no—
404#380—151no—
405#379—151no—
406#379—151no—
407C4×C22⋊C4—151no—
408C22×C3×C5—21no—
409C22×C3×C5—21no—
410C22×C3×C5—21no—
411C22×C3×C5—21no—
412C22×C3×C5—21no—
413C22×C3×C5—21no—
414C22×C3×C5—21no—
415C22×C3×C5—44no—
416C22×C3×C5C2×C22⋊C412yescomplemented
417C22×C3×C5C4×D412yescomplemented
418C22×C3×C5C23×C411yescharacteristic
419C2×D15—21no—
420C2×D15—21no—
421C2×D15—21no—
422C2×D15—21no—
423C2×D15—21no—
424C2×D15—44no—
425C2×D15C2×C22⋊C412yescomplemented
426C2×C5×D3—21no—
427C2×C5×D3—21no—
428C2×C5×D3—21no—
429C2×C5×D3—21no—
430C2×C5×D3—21no—
431C2×C5×D3—44no—
432C2×C5×D3C2×C22⋊C412yescomplemented
433C2×C3×D5—21no—
434C2×C3×D5—21no—
435C2×C3×D5—21no—
436C2×C3×D5—21no—
437C2×C3×D5—24no—
438C2×C3×D5—24no—
439C2×C3×D5—24no—
440C2×C3×D5—24no—
441C2×C3×D5—21no—
442C2×C3×D5—21no—
443C2×C3×D5—21no—
444C2×C3×D5—44no—
445C2×C3×D5—44no—
446C2×C3×D5—44no—
447C2×C3×D5—42no—
448C2×C3×D5—42no—
449C2×C3×D5C2×C22⋊C412yescomplemented
450C2×C3×D5C4×D412yescomplemented
451C2×C3×D5C22×D412yes—
452C2×C3×D5C22×D411yescharacteristic
453C2×C3×D5C2×#4111yescharacteristic
454C2×C3×D5H(5,𝔽2)12yes—
455D3×D5—24no—
456D3×D5—24no—
457D3×D5—44no—
458D3×D5—44no—
459D3×D5—42no—
460D3×D5—42no—
461ΓL(1,𝔽16)—42no—
462ΓL(1,𝔽16)—42no—
463C3×AGL(1,𝔽5)—24no—
464C3×AGL(1,𝔽5)—42no—
465Dic15—21no—
466Dic15C2×C22⋊C412yescomplemented
467C5×Dic3—21no—
468C5×Dic3C2×C22⋊C412yescomplemented
469C24×C3—51no—
470C24×C3—51no—
471C24×C3—51no—
472C24×C3—51no—
473C24×C3—51no—
474C24×C3—51no—
475C24×C3—102no—
476C24×C3—102no—
477C24×C3—104no—
478C24×C3—202no—
479C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—51no—
484C23×D3—51no—
485C23×D3—104no—
486C23×D3—102no—
487C23×D3—102no—
488C23×D3—202no—
489C23×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
490C22×C3×C4—52no—
491C22×C3×C4—52no—
492C22×C3×C4—104no—
493C22×C3×C4—104no—
494C22×C3×C4—202no—
495C2×#67—24no—
496C2×#67—51no—
497C2×#67—51no—
498C2×#67—58no—
499C2×#67—51no—
500C2×#67—51no—
501C2×#67—51no—
502C2×#67—51no—
503C2×#67—51no—
504C2×#67—51no—
505C2×#67—51no—
506C2×#67—51no—
507C2×#67—51no—
508C2×#67—51no—
509C2×#67—104no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—104no—
514C2×#67—104no—
515C2×#67—104no—
516C2×#67—104no—
517C2×#67—104no—
518C2×#67—104no—
519C2×#67C2×AGL(1,𝔽5)11yescharacteristic
520C2×#67C2×AGL(1,𝔽5)11yescharacteristic, complemented
521C2×#67C2×AGL(1,𝔽5)11yescharacteristic, complemented
522C2×#67C2×AGL(1,𝔽5)11yescharacteristic, complemented
523C22×Dic3—51no—
524C22×Dic3—51no—
525C22×Dic3—51no—
526C22×Dic3—51no—
527C22×Dic3—51no—
528C22×Dic3—52no—
529C22×Dic3—52no—
530C22×Dic3—104no—
531C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
532C2×C4×D3—104no—
533C2×C4×D3—104no—
534C2×C4×D3—202no—
535C3×C22⋊C4—54no—
536C3×C22⋊C4—104no—
537C3×C22⋊C4—102no—
538#217—102no—
539#217—104no—
540#217—102no—
541#217—202no—
542(C2×D3)⋊C4—104no—
543(C2×D3)⋊C4—104no—
544(C2×D3)⋊C4—202no—
545Dic3⋊C4—104no—
546C4×Dic3—104no—
547C23×C5—22no—
548C23×C5—22no—
549C23×C5—31no—
550C23×C5—31no—
551C23×C5—41no—
552C23×C5—62no—
553C23×C5—62no—
554C23×C5—121no—
555C23×C5C2×C4×D311yescharacteristic
556C23×C5C2×C4×D311yescharacteristic
557C23×C5C2×C4×D311yescharacteristic
558C22×D5—21no—
559C22×D5—22no—
560C22×D5—22no—
561C22×D5—22no—
562C22×D5—21no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—21no—
570C22×D5—22no—
571C22×D5—22no—
572C22×D5—21no—
573C22×D5—31no—
574C22×D5—34no—
575C22×D5—31no—
576C22×D5—41no—
577C22×D5—41no—
578C22×D5—41no—
579C22×D5—48no—
580C22×D5—48no—
581C22×D5—62no—
582C22×D5—62no—
583C22×D5—62no—
584C22×D5—61no—
585C22×D5—62no—
586C22×D5—61no—
587C22×D5—62no—
588C22×D5—62no—
589C22×D5—62no—
590C22×D5—61no—
591C22×D5—62no—
592C22×D5—62no—
593C22×D5—61no—
594C22×D5—121no—
595C22×D5—121no—
596C22×D5—128no—
597C22×D5—128no—
598C22×D5—121no—
599C22×D5C2×C4×D311yescharacteristic
600C22×D5C2×C4×D311yescharacteristic
601C22×D5C2×C4×D311yescharacteristic
602C22×D5#23512yes—
603C22×D5D3×D414yes—
604C22×D5C2×#6712yes—
605C22×D5C23×D311yescharacteristic
606C2×AGL(1,𝔽5)—22no—
607C2×AGL(1,𝔽5)—22no—
608C2×AGL(1,𝔽5)—22no—
609C2×AGL(1,𝔽5)—22no—
610C2×AGL(1,𝔽5)—22no—
611C2×AGL(1,𝔽5)—48no—
612C2×AGL(1,𝔽5)—62no—
613C2×AGL(1,𝔽5)—62no—
614C2×AGL(1,𝔽5)—62no—
615C2×AGL(1,𝔽5)—62no—
616C2×AGL(1,𝔽5)—62no—
617C2×AGL(1,𝔽5)—62no—
618C2×AGL(1,𝔽5)—128no—
619C2×AGL(1,𝔽5)C2×#6714yescomplemented
620C5×D4—34no—
621C5×D4—62no—
622C5×D4—62no—
623C5×D4—62no—
624C2×C4×C5—31no—
625C2×C4×C5—31no—
626C2×C4×C5—62no—
627C22⋊D5—34no—
628C22⋊D5—34no—
629C22⋊D5—62no—
630C22⋊D5—62no—
631C22⋊D5—62no—
632C22⋊D5—62no—
633C22⋊D5—62no—
634C22⋊D5—62no—
635C2×Dic5—31no—
636C2×Dic5—31no—
637C2×Dic5—62no—
638D20—34no—
639D20—62no—
640D20—62no—
641D20—62no—
642C4×D5—34no—
643C4×D5—62no—
644C4×D5—62no—
645C4×D5—62no—
646C25—51no—
647C25—151no—
648C22×D4—31no—
649C22×D4—151no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—308no—
661C23×C4—52no—
662C23×C4—151no—
663C23×C4—152no—
664C4×D4—308no—
665C2×C4⋊C4—152no—
666C2×C22⋊C4—51no—
667C2×C22⋊C4—51no—
668C2×C22⋊C4—52no—
669C2×C22⋊C4—104no—
670C2×C22⋊C4—152no—
671C2×C22⋊C4—152no—
672C2×C22⋊C4—151no—
673C2×C22⋊C4—152no—
674C2×C22⋊C4—151no—
675C2×C22⋊C4—152no—
676C2×C22⋊C4—152no—
677C2×C22⋊C4—304no—
678C2×C42—152no—
679#95—152no—
680#95—152no—
681C2×C3×C5—22no—
682C2×C3×C5—22no—
683C2×C3×C5—41no—
684C2×C3×C5C22×C22⋊C411yescharacteristic
685C2×C3×C5C2×C4×D411yescharacteristic
686C2×C3×C5#51811yescharacteristic
687D15—22no—
688D15—41no—
689C3×D5—22no—
690C3×D5—22no—
691C3×D5—41no—
692C3×D5D4212yes—
693C3×D5#54612yes—
694C5×D3—22no—
695C5×D3—41no—
696C23×C3—22no—
697C23×C3—22no—
698C23×C3—41no—
699C23×C3—51no—
700C23×C3—52no—
701C23×C3—52no—
702C23×C3—54no—
703C23×C3—51no—
704C23×C3—51no—
705C23×C3—51no—
706C23×C3—102no—
707C23×C3—101no—
708C23×C3—102no—
709C23×C3—102no—
710C23×C3—101no—
711C23×C3—102no—
712C23×C3—101no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—101no—
718C23×C3—102no—
719C23×C3—102no—
720C23×C3—102no—
721C23×C3—201no—
722C23×C3—201no—
723C23×C3—201no—
724C23×C3—208no—
725C23×C3—208no—
726C23×C3C22×AGL(1,𝔽5)11yescharacteristic
727C23×C3C22×AGL(1,𝔽5)11yescharacteristic
728C23×C3C22×AGL(1,𝔽5)11yescharacteristic
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—41no—
732C22×D3—51no—
733C22×D3—54no—
734C22×D3—51no—
735C22×D3—102no—
736C22×D3—101no—
737C22×D3—102no—
738C22×D3—101no—
739C22×D3—101no—
740C22×D3—102no—
741C22×D3—102no—
742C22×D3—102no—
743C22×D3—102no—
744C22×D3—101no—
745C22×D3—102no—
746C22×D3—102no—
747C22×D3—102no—
748C22×D3—201no—
749C22×D3—201no—
750C22×D3—208no—
751C22×D3—208no—
752C22×D3—201no—
753C22×D3C22×AGL(1,𝔽5)11yescharacteristic
754C22×D3C22×AGL(1,𝔽5)11yescharacteristic
755C2×C3×C4—54no—
756C2×C3×C4—102no—
757C2×C3×C4—102no—
758C2×C3×C4—102no—
759C2×C3×C4—102no—
760C2×C3×C4—102no—
761C2×C3×C4—208no—
762#67—22no—
763#67—22no—
764#67—22no—
765#67—54no—
766#67—54no—
767#67—54no—
768#67—102no—
769#67—102no—
770#67—102no—
771#67—102no—
772#67—102no—
773#67—102no—
774#67—102no—
775#67—102no—
776#67—102no—
777#67C22⋊AGL(1,𝔽5)14yesdirect product factor
778C2×Dic3—22no—
779C2×Dic3—51no—
780C2×Dic3—54no—
781C2×Dic3—51no—
782C2×Dic3—102no—
783C2×Dic3—102no—
784C2×Dic3—102no—
785C2×Dic3—102no—
786C2×Dic3—102no—
787C2×Dic3—102no—
788C2×Dic3—102no—
789C2×Dic3—102no—
790C2×Dic3—102no—
791C2×Dic3—102no—
792C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
793C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
794C4×D3—208no—
795C22×C5—21no—
796C22×C5—21no—
797C22×C5—21no—
798C22×C5—21no—
799C22×C5—21no—
800C22×C5—21no—
801C22×C5—21no—
802C22×C5—32no—
803C22×C5—44no—
804C22×C5—61no—
805C22×C5—61no—
806C22×C5—61no—
807C22×C5—61no—
808C22×C5—61no—
809C22×C5—124no—
810C22×C5D3×C22⋊C412yescomplemented
811C22×C5C4×#6712yescomplemented
812C22×C5C22×C4×D311yescharacteristic
813C2×D5—21no—
814C2×D5—21no—
815C2×D5—21no—
816C2×D5—21no—
817C2×D5—24no—
818C2×D5—24no—
819C2×D5—24no—
820C2×D5—24no—
821C2×D5—21no—
822C2×D5—21no—
823C2×D5—21no—
824C2×D5—32no—
825C2×D5—44no—
826C2×D5—44no—
827C2×D5—44no—
828C2×D5—42no—
829C2×D5—42no—
830C2×D5—61no—
831C2×D5—61no—
832C2×D5—64no—
833C2×D5—64no—
834C2×D5—61no—
835C2×D5—61no—
836C2×D5—61no—
837C2×D5—124no—
838C2×D5—124no—
839C2×D5—124no—
840C2×D5—122no—
841C2×D5—122no—
842C2×D5D3×C22⋊C412yescomplemented
843C2×D5C4×#6712yescomplemented
844C2×D5C2×#23511yescharacteristic
845C2×D5C2×D3×D412yes—
846C2×D5#100412yes—
847C2×D5C22×#6711yescharacteristic
848AGL(1,𝔽5)—24no—
849AGL(1,𝔽5)—42no—
850AGL(1,𝔽5)—122no—
851AGL(1,𝔽5)—122no—
852C4×C5—32no—
853C4×C5—61no—
854Dic5—32no—
855Dic5—61no—
856C24—31no—
857C24—51no—
858C24—51no—
859C24—51no—
860C24—51no—
861C24—51no—
862C24—51no—
863C24—102no—
864C24—104no—
865C24—102no—
866C24—151no—
867C24—151no—
868C24—151no—
869C24—151no—
870C24—151no—
871C24—202no—
872C24—302no—
873C24—302no—
874C24—304no—
875C24—602no—
876C24D3×AGL(1,𝔽5)11yescharacteristic, complemented
877C2×D4—31no—
878C2×D4—31no—
879C2×D4—31no—
880C2×D4—31no—
881C2×D4—64no—
882C2×D4—151no—
883C2×D4—151no—
884C2×D4—151no—
885C2×D4—151no—
886C2×D4—158no—
887C2×D4—151no—
888C2×D4—151no—
889C2×D4—151no—
890C2×D4—151no—
891C2×D4—151no—
892C2×D4—151no—
893C2×D4—151no—
894C2×D4—151no—
895C2×D4—304no—
896C2×D4—304no—
897C2×D4—304no—
898C2×D4—304no—
899C2×D4—304no—
900C2×D4—304no—
901C2×D4—304no—
902C2×D4—304no—
903C2×D4—304no—
904C2×D4—304no—
905C22×C4—31no—
906C22×C4—52no—
907C22×C4—52no—
908C22×C4—104no—
909C22×C4—104no—
910C22×C4—151no—
911C22×C4—151no—
912C22×C4—151no—
913C22×C4—151no—
914C22×C4—151no—
915C22×C4—152no—
916C22×C4—152no—
917C22×C4—202no—
918C22×C4—304no—
919C22×C4—304no—
920C22×C4—304no—
921C22×C4—602no—
922C4⋊C4—304no—
923C22⋊C4—54no—
924C22⋊C4—104no—
925C22⋊C4—102no—
926C22⋊C4—304no—
927C22⋊C4—304no—
928C22⋊C4—302no—
929C22⋊C4—304no—
930C22⋊C4—302no—
931C22⋊C4—602no—
932C22⋊C4—602no—
933C42—304no—
934C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—44no—
943C22×C3—51no—
944C22×C3—51no—
945C22×C3—52no—
946C22×C3—52no—
947C22×C3—52no—
948C22×C3—52no—
949C22×C3—104no—
950C22×C3—104no—
951C22×C3—104no—
952C22×C3—104no—
953C22×C3—101no—
954C22×C3—101no—
955C22×C3—101no—
956C22×C3—101no—
957C22×C3—101no—
958C22×C3—101no—
959C22×C3—101no—
960C22×C3—204no—
961C22×C3—204no—
962C22×C3—202no—
963C22×C3—202no—
964C22×C3—204no—
965C22×C3D4×AGL(1,𝔽5)12yescomplemented
966C22×C3C2×C22⋊AGL(1,𝔽5)12yescomplemented
967C22×C3C23×AGL(1,𝔽5)11yescharacteristic
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—21no—
973C2×D3—44no—
974C2×D3—52no—
975C2×D3—104no—
976C2×D3—104no—
977C2×D3—101no—
978C2×D3—101no—
979C2×D3—101no—
980C2×D3—101no—
981C2×D3—101no—
982C2×D3—204no—
983C2×D3—204no—
984C2×D3—202no—
985C2×D3—202no—
986C2×D3—204no—
987C2×D3C2×C22⋊AGL(1,𝔽5)12yescomplemented
988C3×C4—104no—
989C3×C4—202no—
990Dic3—21no—
991Dic3—52no—
992Dic3—101no—
993Dic3—202no—
994Dic3—202no—
995Dic3C2×C22⋊AGL(1,𝔽5)12yescomplemented
996C2×C5—22no—
997C2×C5—22no—
998C2×C5—41no—
999C2×C5—62no—
1000C2×C5—121no—
1001C2×C5C2×D3×C22⋊C411yescharacteristic
1002C2×C5#548611yescharacteristic
1003C2×C5C2×C4×#6711yescharacteristic
1004D5—22no—
1005D5—22no—
1006D5—41no—
1007D5—62no—
1008D5—121no—
1009D5#549012yes—
1010D5D4×#6712yes—
1011C23—22no—
1012C23—22no—
1013C23—31no—
1014C23—31no—
1015C23—41no—
1016C23—51no—
1017C23—52no—
1018C23—52no—
1019C23—54no—
1020C23—51no—
1021C23—51no—
1022C23—51no—
1023C23—62no—
1024C23—62no—
1025C23—101no—
1026C23—102no—
1027C23—102no—
1028C23—101no—
1029C23—102no—
1030C23—101no—
1031C23—102no—
1032C23—102no—
1033C23—102no—
1034C23—102no—
1035C23—102no—
1036C23—101no—
1037C23—102no—
1038C23—102no—
1039C23—102no—
1040C23—121no—
1041C23—154no—
1042C23—151no—
1043C23—151no—
1044C23—201no—
1045C23—201no—
1046C23—201no—
1047C23—208no—
1048C23—208no—
1049C23—302no—
1050C23—302no—
1051C23—301no—
1052C23—302no—
1053C23—301no—
1054C23—301no—
1055C23—302no—
1056C23—302no—
1057C23—301no—
1058C23—302no—
1059C23—302no—
1060C23—302no—
1061C23—302no—
1062C23—601no—
1063C23—601no—
1064C23—601no—
1065C23—608no—
1066C23—608no—
1067C23C2×D3×AGL(1,𝔽5)11yescharacteristic
1068C23C2×D3×AGL(1,𝔽5)11yescharacteristic
1069C23C2×D3×AGL(1,𝔽5)11yescharacteristic
1070D4—34no—
1071D4—62no—
1072D4—62no—
1073D4—62no—
1074D4—154no—
1075D4—154no—
1076D4—154no—
1077D4—302no—
1078D4—302no—
1079D4—302no—
1080D4—302no—
1081D4—302no—
1082D4—302no—
1083D4—302no—
1084D4—302no—
1085D4—302no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—54no—
1089C2×C4—62no—
1090C2×C4—102no—
1091C2×C4—102no—
1092C2×C4—102no—
1093C2×C4—102no—
1094C2×C4—102no—
1095C2×C4—154no—
1096C2×C4—151no—
1097C2×C4—151no—
1098C2×C4—208no—
1099C2×C4—302no—
1100C2×C4—302no—
1101C2×C4—302no—
1102C2×C4—302no—
1103C2×C4—302no—
1104C2×C4—302no—
1105C2×C4—302no—
1106C2×C4—302no—
1107C2×C4—302no—
1108C2×C4—302no—
1109C2×C4—608no—
1110C2×C3—22no—
1111C2×C3—22no—
1112C2×C3—41no—
1113C2×C3—52no—
1114C2×C3—52no—
1115C2×C3—102no—
1116C2×C3—102no—
1117C2×C3—201no—
1118C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
1119C2×C3#6625811yescharacteristic
1120C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
1121D3—22no—
1122D3—41no—
1123D3—102no—
1124D3—201no—
1125C5C22⋊C4×#6711yescharacteristic, complemented, Sylow
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—32no—
1134C22—44no—
1135C22—51no—
1136C22—51no—
1137C22—52no—
1138C22—52no—
1139C22—52no—
1140C22—52no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—61no—
1145C22—61no—
1146C22—104no—
1147C22—104no—
1148C22—104no—
1149C22—104no—
1150C22—101no—
1151C22—101no—
1152C22—101no—
1153C22—101no—
1154C22—101no—
1155C22—101no—
1156C22—101no—
1157C22—124no—
1158C22—152no—
1159C22—204no—
1160C22—204no—
1161C22—202no—
1162C22—202no—
1163C22—204no—
1164C22—304no—
1165C22—304no—
1166C22—301no—
1167C22—301no—
1168C22—301no—
1169C22—301no—
1170C22—301no—
1171C22—604no—
1172C22—602no—
1173C22—602no—
1174C22—604no—
1175C22—604no—
1176C22AGL(1,𝔽5)×#6712yescomplemented
1177C22D3×C22⋊AGL(1,𝔽5)12yescomplemented
1178C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1179C4—32no—
1180C4—61no—
1181C4—104no—
1182C4—152no—
1183C4—202no—
1184C4—301no—
1185C4—602no—
1186C4—602no—
1187C3D4×C22⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
1188C2—22no—
1189C2—22no—
1190C2—41no—
1191C2—52no—
1192C2—52no—
1193C2—62no—
1194C2—102no—
1195C2—102no—
1196C2—121no—
1197C2—201no—
1198C2—302no—
1199C2—601no—
1200C2C2×AGL(1,𝔽5)×#6711yescharacteristic
1201C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
1202C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC24×C3×C5C2×C4
prime radicalC22×D5×#67C2
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
3. C2×D3×C22⋊AGL(1,𝔽5)C2semidirect
4. C2×AGL(1,𝔽5)×#67C2semidirect
5. #11752459C2semidirect
6. #11752055C2semidirect
7. #11752028C2semidirect
8. #11752025C2semidirect
9. #11752022C2semidirect
10. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
11. #11752019C2semidirect
15. C23×C3×AGL(1,𝔽5)C22semidirect
16. C22×D3×AGL(1,𝔽5)C22semidirect
17. C22×#1220C4semidirect
18. C22×C5×#67C4semidirect
20. C2×D5×#67C4semidirect
21. C2×D5×#67C4semidirect
22. C2×D5×#67C4semidirect
23. C2×D5×#67C4semidirect
28. C22×#1202C4semidirect
29. C22×#1201C4semidirect
33. C2×#6763C22semidirect
34. C2×#6763C22semidirect
38. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
41. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
42. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
43. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
44. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
45. C2×Dic3×AGL(1,𝔽5)C22semidirect
46. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
47. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
51. C22×C22⋊AGL(1,𝔽5)D3semidirect
60. C24×C3×C5C2×C4semidirect
61. C23×D15C2×C4semidirect
62. C23×C5×D3C2×C4semidirect
67. C23×C3×D5C2×C4semidirect
68. C23×C3×D5C2×C4semidirect
69. C23×C3×D5C2×C4semidirect
77. C22×D3×D5C2×C4semidirect
78. C22×D3×D5C2×C4semidirect
93. C2×#1220C2×C4semidirect
94. C2×#1220C2×C4semidirect
95. C2×#1220C2×C4semidirect
96. C22×Dic15C2×C4semidirect
99. C2×C5×#67C2×C4semidirect
100. C2×C5×#67C2×C4semidirect
101. C2×C5×#67C2×C4semidirect
102. C22×C5×Dic3C2×C4semidirect
113. C2×#1202C2×C4semidirect
114. C2×#1202C2×C4semidirect
115. C2×#1202C2×C4semidirect
118. C2×#1201C2×C4semidirect
119. C2×#1201C2×C4semidirect
120. C2×#1201C2×C4semidirect
122. C2×D5×Dic3C2×C4semidirect
123. C2×D5×Dic3C2×C4semidirect
132. C3×C22⋊AGL(1,𝔽5)D4semidirect
152. C23×AGL(1,𝔽5)C2×D3semidirect
178. C2×C22⋊AGL(1,𝔽5)C2×D3semidirect
256. C2×C3×AGL(1,𝔽5)C2×D4semidirect
261. #1220C22⋊C4semidirect
268. C5×#67C22⋊C4semidirect
275. #1202C22⋊C4semidirect
279. #1201C22⋊C4semidirect
299. C22×#67AGL(1,𝔽5)semidirect
320. C24×C5C4×D3semidirect
334. C23×D5C4×D3semidirect
335. C23×D5C4×D3semidirect
336. C23×D5C4×D3semidirect
394. C22⋊AGL(1,𝔽5)#67direct (N × H)
416. C22×C3×C5C2×C22⋊C4semidirect
417. C22×C3×C5C4×D4semidirect
425. C2×D15C2×C22⋊C4semidirect
432. C2×C5×D3C2×C22⋊C4semidirect
449. C2×C3×D5C2×C22⋊C4semidirect
450. C2×C3×D5C4×D4semidirect
466. Dic15C2×C22⋊C4semidirect
468. C5×Dic3C2×C22⋊C4semidirect
479. C24×C3C2×AGL(1,𝔽5)semidirect
489. C23×D3C2×AGL(1,𝔽5)semidirect
520. C2×#67C2×AGL(1,𝔽5)semidirect
521. C2×#67C2×AGL(1,𝔽5)semidirect
522. C2×#67C2×AGL(1,𝔽5)semidirect
531. C22×Dic3C2×AGL(1,𝔽5)semidirect
619. C2×AGL(1,𝔽5)C2×#67semidirect
777. #67C22⋊AGL(1,𝔽5)direct (N × H)
810. C22×C5D3×C22⋊C4semidirect
811. C22×C5C4×#67semidirect
842. C2×D5D3×C22⋊C4semidirect
843. C2×D5C4×#67semidirect
876. C24D3×AGL(1,𝔽5)semidirect
934. C3×C5D4×C22⋊C4semidirect
965. C22×C3D4×AGL(1,𝔽5)semidirect
966. C22×C3C2×C22⋊AGL(1,𝔽5)semidirect
987. C2×D3C2×C22⋊AGL(1,𝔽5)semidirect
995. Dic3C2×C22⋊AGL(1,𝔽5)semidirect
1125. C5C22⋊C4×#67semidirect
1176. C22AGL(1,𝔽5)×#67semidirect
1177. C22D3×C22⋊AGL(1,𝔽5)semidirect
1187. C3D4×C22⋊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×D5×#672
C22×C3×C22⋊AGL(1,𝔽5)2
C2×D3×C22⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
#117524592
#117520552
#117520282
#117520252
#117520222
Dic3×C22⋊AGL(1,𝔽5)2
#117520192
D4×C22⋊AGL(1,𝔽5)3
C22⋊C4×#675