Finite Group Databasebeta

← #14326380

Subgroups — #14326380

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4130C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4#11752423C211yesmaximal, characteristic, complemented
5#11752028C211yesmaximal, characteristic, complemented
6#11752025C211yesmaximal, characteristic
7Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8#11751932C212yesmaximal, complemented
9AGL(1,𝔽5)×(C2×D3)⋊C4C212yesmaximal, complemented
10#11751849C212yesmaximal, complemented
11#11751836C212yesmaximal, complemented
12#10617072—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C22×D3×AGL(1,𝔽5)C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2211yescharacteristic
17C2×#6763C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
20C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
21C3×#4130—24no—
22C2×C3×C4⋊AGL(1,𝔽5)C2212yescomplemented
23C2×C3×C4×AGL(1,𝔽5)C2212yescomplemented
24D3×C22⋊AGL(1,𝔽5)—24no—
25C2×Dic3⋊AGL(1,𝔽5)C2212yescomplemented
26C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
27C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
28C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2212yescomplemented
30C2×#6714C411yescharacteristic, complemented
31C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
32C2×#6667C411yescharacteristic, complemented
33C2×(C2×D3)⋊Dic5C411yescharacteristic, complemented
34D5×(C2×D3)⋊C4C411yescharacteristic, complemented
35D5×(C2×D3)⋊C4C411yescharacteristic, complemented
36D5×(C2×D3)⋊C4C411yescharacteristic, complemented
37D5×(C2×D3)⋊C4C411yescharacteristic, complemented
38D5×(C2×D3)⋊C4C2211yescharacteristic
39D5×(C2×D3)⋊C4C2211yescharacteristic
40D5×(C2×D3)⋊C4C2211yescharacteristic
41D5×(C2×D3)⋊C4C2211yescharacteristic
42#91235C2212yescomplemented
43#91235C2212yescomplemented
44(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
45(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
46#82271—51nomaximal, Hall
47C22×C22⋊AGL(1,𝔽5)—31no—
48C2×#4130D311yescharacteristic, complemented
49C2×D5×C22⋊C4—31no—
50#65800—31no—
51#65765—31no—
52#65764—31no—
53C4×C22⋊AGL(1,𝔽5)—31no—
54#65700—32no—
55#65700—32no—
56#65699—32no—
57C22⋊C4×AGL(1,𝔽5)—32no—
58C23×D15C2×C411yescharacteristic
59C23×C5×D3C2×C411yescharacteristic
60C23×C3×D5C2311yescharacteristic
61C22×D3×D5—22no—
62C22×D3×D5—22no—
63C22×D3×D5—24no—
64C22×D3×D5—42no—
65C22×D3×D5C2×C411yescharacteristic
66C22×D3×D5C2×C411yescharacteristic
67C22×D3×D5C2311yescharacteristic
68C22×D3×D5C2311yescharacteristic
69C22×ΓL(1,𝔽16)C2312yes—
70C22×ΓL(1,𝔽16)C2312yes—
71C22×C3×AGL(1,𝔽5)C2312yes—
72C22×C3×AGL(1,𝔽5)C2312yes—
73C2×D3×AGL(1,𝔽5)—24no—
74C2×D3×AGL(1,𝔽5)—24no—
75C2×D3×AGL(1,𝔽5)—42no—
76C22×C3×C4×C5C2×C411yescharacteristic, complemented
77C22×Dic15C2×C411yescharacteristic, complemented
78C22×C5×Dic3C2×C411yescharacteristic, complemented
79C22×C3×Dic5C2×C411yescharacteristic, complemented
80C2×C3×C4×D5—22no—
81C2×C3×C4×D5—22no—
82C2×C3×C4×D5C2×C411yescharacteristic, complemented
83C2×C3×C4×D5C2×C411yescharacteristic, complemented
84C2×C3×C4×D5C2311yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×D5×Dic3—42no—
87C2×D5×Dic3C2×C411yescharacteristic, complemented
88C2×D5×Dic3C2×C411yescharacteristic, complemented
89C2×D5×Dic3C2311yescharacteristic
90C2×D5×Dic3C2311yescharacteristic
91#6763—22no—
92#6763—22no—
93C3×C22⋊AGL(1,𝔽5)—22no—
94C3×C22⋊AGL(1,𝔽5)D414yes—
95C3×C4⋊AGL(1,𝔽5)—24no—
96C3×C4×AGL(1,𝔽5)—24no—
97Dic3⋊AGL(1,𝔽5)—42no—
98(C2×D3)⋊AGL(1,𝔽5)—24no—
99(C2×D3)⋊AGL(1,𝔽5)—24no—
100(C2×D3)⋊AGL(1,𝔽5)—42no—
101Dic3×AGL(1,𝔽5)—42no—
102#6714C2×C411yescharacteristic
103#6714C2×C411yescharacteristic
104#6714C2×C411yescharacteristic, complemented
105#6714C2×C411yescharacteristic, complemented
106C5×(C2×D3)⋊C4C2×C411yescharacteristic
107C5×(C2×D3)⋊C4C2×C411yescharacteristic
108C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
109C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
110#6667C2×C411yescharacteristic
111#6667C2×C411yescharacteristic
112#6667C2×C411yescharacteristic, complemented
113#6667C2×C411yescharacteristic, complemented
114(C2×D3)⋊Dic5C2×C411yescharacteristic
115(C2×D3)⋊Dic5C2×C411yescharacteristic
116(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
117(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
118C2×C3×#117—51no—
119C22×(C2×D3)⋊C4—51no—
120C2×D3×C22⋊C4—51no—
121#5211—51no—
122#4990—52no—
123#4989—52no—
124#4955—51no—
125#4942—51no—
126Dic3×C22⋊C4—51no—
127#4940—52no—
128C4×(C2×D3)⋊C4—52no—
129C24×D5—31no—
130C23×AGL(1,𝔽5)—32no—
131C22×C4×D5—31no—
132C22×C4×D5C2×D311yescharacteristic
133C2×C22⋊AGL(1,𝔽5)—31no—
134C2×C22⋊AGL(1,𝔽5)—31no—
135C2×C22⋊AGL(1,𝔽5)—32no—
136C2×C22⋊AGL(1,𝔽5)—32no—
137C2×C22⋊AGL(1,𝔽5)—32no—
138C2×C22⋊AGL(1,𝔽5)—64no—
139C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
140C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
141#4130—24no—
142C2×C4⋊AGL(1,𝔽5)—32no—
143C2×C4⋊AGL(1,𝔽5)C2×D312yescomplemented
144C2×C4×AGL(1,𝔽5)—32no—
145C2×C4×AGL(1,𝔽5)C2×D312yescomplemented
146C2×C5×C22⋊C4—31no—
147C2×C22⋊Dic5—31no—
148C2×#685—31no—
149C2×#685—31no—
150D5×C22⋊C4—31no—
151D5×C22⋊C4—31no—
152D5×C22⋊C4—31no—
153D5×C22⋊C4—31no—
154D5×C22⋊C4—31no—
155D5×C22⋊C4—31no—
156D5×C22⋊C4—31no—
157D5×C22⋊C4—31no—
158(C2×AGL(1,𝔽5))⋊C4—32no—
159(C2×AGL(1,𝔽5))⋊C4—32no—
160(C2×AGL(1,𝔽5))⋊C4—32no—
161(C2×AGL(1,𝔽5))⋊C4—32no—
162#2342—151noSylow
163C23×C3×C5C22×C411yescharacteristic
164C22×D15—22no—
165C22×D15—22no—
166C22×D15—41no—
167C22×D15C22×C411yescharacteristic
168C22×D15C22×C411yescharacteristic
169C22×C5×D3—22no—
170C22×C5×D3—22no—
171C22×C5×D3—41no—
172C22×C5×D3C22×C411yescharacteristic
173C22×C5×D3C22×C411yescharacteristic
174C22×C3×D5—22no—
175C22×C3×D5—22no—
176C22×C3×D5C22×C411yescharacteristic
177C22×C3×D5C2×D412yes—
178C22×C3×D5#4112yes—
179C22×C3×D5C2411yescharacteristic
180C2×D3×D5—21no—
181C2×D3×D5—21no—
182C2×D3×D5—22no—
183C2×D3×D5—22no—
184C2×D3×D5—22no—
185C2×D3×D5—22no—
186C2×D3×D5—22no—
187C2×D3×D5—21no—
188C2×D3×D5—22no—
189C2×D3×D5—21no—
190C2×D3×D5—22no—
191C2×D3×D5—48no—
192C2×D3×D5—48no—
193C2×D3×D5—41no—
194C2×D3×D5—41no—
195C2×D3×D5#4114yes—
196C2×ΓL(1,𝔽16)—22no—
197C2×ΓL(1,𝔽16)—22no—
198C2×ΓL(1,𝔽16)—22no—
199C2×ΓL(1,𝔽16)—22no—
200C2×ΓL(1,𝔽16)—22no—
201C2×ΓL(1,𝔽16)—22no—
202C2×C3×AGL(1,𝔽5)—22no—
203C2×C3×AGL(1,𝔽5)—22no—
204C2×C3×AGL(1,𝔽5)—22no—
205C2×C3×AGL(1,𝔽5)—22no—
206C2×C3×AGL(1,𝔽5)—22no—
207C2×C3×AGL(1,𝔽5)C2×D414yes—
208D3×AGL(1,𝔽5)—48no—
209C2×C3×C4×C5—22no—
210C2×C3×C4×C5C22×C411yescharacteristic
211C2×C3×C4×C5C22×C411yescharacteristic
212C2×Dic15—41no—
213C2×Dic15C22×C411yescharacteristic
214C2×Dic15C22×C411yescharacteristic
215C2×C5×Dic3—41no—
216C2×C5×Dic3C22×C411yescharacteristic
217C2×C5×Dic3C22×C411yescharacteristic
218C2×C3×Dic5—22no—
219C2×C3×Dic5C22×C411yescharacteristic
220C2×C3×Dic5C22×C411yescharacteristic
221C3×C4×D5—22no—
222C3×C4×D5—22no—
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227D5×Dic3—22no—
228D5×Dic3—22no—
229D5×Dic3—41no—
230D5×Dic3—41no—
231C24×D3—51no—
232C23×C3×C4—51no—
233C23×Dic3—51no—
234C22×C4×D3—52no—
235C3×#117—104no—
236C2×C3×C4⋊C4—52no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C42—52no—
240C2×#217—51no—
241C2×#217—51no—
242C2×(C2×D3)⋊C4—51no—
243C2×(C2×D3)⋊C4—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—52no—
254C2×(C2×D3)⋊C4—52no—
255C2×(C2×D3)⋊C4—52no—
256C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
257C2×Dic3⋊C4—52no—
258C2×C4×Dic3—52no—
259D3×C22⋊C4—104no—
260C3⋊#95—52no—
261C3⋊#95—52no—
262C3⋊#95—52no—
263C3⋊#95—52no—
264C24×C5—31no—
265C23×D5—31no—
266C23×D5—31no—
267C23×D5—31no—
268C23×D5—31no—
269C23×D5—31no—
270C23×D5—64no—
271C23×D5—62no—
272C23×D5—62no—
273C23×D5—122no—
274C23×D5C22×D311yescharacteristic
275C22×AGL(1,𝔽5)—32no—
276C22×AGL(1,𝔽5)—32no—
277C22×AGL(1,𝔽5)—64no—
278C22×AGL(1,𝔽5)—64no—
279C22×AGL(1,𝔽5)—122no—
280C22×AGL(1,𝔽5)C22×D312yes—
281C22×AGL(1,𝔽5)C22×D312yes—
282C22×C4×C5—31no—
283C22×C4×C5C4×D311yescharacteristic, complemented
284C22×Dic5—31no—
285C22×Dic5C4×D311yescharacteristic, complemented
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—122no—
293C2×C4×D5C4×D311yescharacteristic, complemented
294C2×C4×D5C4×D311yescharacteristic, complemented
295C2×C4×D5C22×D311yescharacteristic
296C2×C4×D5C22×D311yescharacteristic
297C22⋊AGL(1,𝔽5)—22no—
298C22⋊AGL(1,𝔽5)—64no—
299C22⋊AGL(1,𝔽5)—62no—
300C22⋊AGL(1,𝔽5)—62no—
301C22⋊AGL(1,𝔽5)—64no—
302C22⋊AGL(1,𝔽5)—122no—
303C22⋊AGL(1,𝔽5)#6714yes—
304C4⋊AGL(1,𝔽5)—24no—
305C4⋊AGL(1,𝔽5)—122no—
306C4×AGL(1,𝔽5)—24no—
307C4×AGL(1,𝔽5)—122no—
308C5×C22⋊C4—31no—
309C5×C22⋊C4—31no—
310C5×C22⋊C4—31no—
311C5×C22⋊C4—31no—
312C22⋊Dic5—31no—
313C22⋊Dic5—31no—
314C22⋊Dic5—31no—
315C22⋊Dic5—31no—
316#685—31no—
317#685—31no—
318#685—31no—
319#685—31no—
320#685—31no—
321#685—31no—
322#685—31no—
323#685—31no—
324C2×#117—51no—
325C22×C22⋊C4—151no—
326C22×C22⋊C4—151no—
327#388—152no—
328#388—152no—
329#385—152no—
330#381—151no—
331#380—151no—
332#379—151no—
333C4×C22⋊C4—152no—
334C4×C22⋊C4—151no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5C4×D412yes—
338C22×C3×C5C23×C411yescharacteristic
339C2×D15—21no—
340C2×D15—21no—
341C2×D15—21no—
342C2×D15—21no—
343C2×D15—21no—
344C2×D15—44no—
345C2×D15#11712yescomplemented
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3—21no—
351C2×C5×D3—44no—
352C2×C5×D3#11712yescomplemented
353C2×C3×D5—21no—
354C2×C3×D5—21no—
355C2×C3×D5—24no—
356C2×C3×D5—24no—
357C2×C3×D5C4×D412yes—
358C2×C3×D5C22×D411yescharacteristic
359C2×C3×D5C2×#4111yescharacteristic
360C2×C3×D5C2×#4112yes—
361C2×C3×D5H(5,𝔽2)12yes—
362D3×D5—24no—
363D3×D5—24no—
364D3×D5—44no—
365D3×D5—44no—
366D3×D5—42no—
367D3×D5—42no—
368ΓL(1,𝔽16)—42no—
369ΓL(1,𝔽16)—42no—
370C3×AGL(1,𝔽5)—24no—
371C3×AGL(1,𝔽5)—42no—
372C3×C4×C5—21no—
373C3×C4×C5—21no—
374Dic15—21no—
375Dic15—21no—
376C3×Dic5—21no—
377C3×Dic5—21no—
378C5×Dic3—21no—
379C5×Dic3—21no—
380C24×C3—51no—
381C23×D3—51no—
382C23×D3—51no—
383C23×D3—51no—
384C23×D3—51no—
385C23×D3—51no—
386C23×D3—104no—
387C23×D3—102no—
388C23×D3—102no—
389C23×D3—202no—
390C23×D3C2×AGL(1,𝔽5)11yescharacteristic
391C22×C3×C4—52no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—52no—
398C22×C3×C4—102no—
399C22×C3×C4—102no—
400C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3—52no—
407C22×Dic3—52no—
408C22×Dic3—202no—
409C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
410C2×C4×D3—104no—
411C2×C4×D3—104no—
412C2×C4×D3—202no—
413C3×C4⋊C4—104no—
414C3×C22⋊C4—54no—
415C3×C22⋊C4—102no—
416C3×C42—104no—
417#217—102no—
418#217—102no—
419(C2×D3)⋊C4—51no—
420(C2×D3)⋊C4—51no—
421(C2×D3)⋊C4—51no—
422(C2×D3)⋊C4—51no—
423(C2×D3)⋊C4—51no—
424(C2×D3)⋊C4—51no—
425(C2×D3)⋊C4—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4—51no—
430(C2×D3)⋊C4—51no—
431(C2×D3)⋊C4—104no—
432(C2×D3)⋊C4—104no—
433(C2×D3)⋊C4—202no—
434(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
435(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
436(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
437(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
438Dic3⋊C4—202no—
439C4×Dic3—202no—
440C23×C5—31no—
441C23×C5—31no—
442C23×C5—62no—
443C23×C5—62no—
444C23×C5—121no—
445C23×C5C2×C4×D311yescharacteristic
446C22×D5—22no—
447C22×D5—22no—
448C22×D5—31no—
449C22×D5—34no—
450C22×D5—31no—
451C22×D5—62no—
452C22×D5—62no—
453C22×D5—62no—
454C22×D5—61no—
455C22×D5—62no—
456C22×D5—61no—
457C22×D5—62no—
458C22×D5—62no—
459C22×D5—62no—
460C22×D5—61no—
461C22×D5—62no—
462C22×D5—62no—
463C22×D5—61no—
464C22×D5—121no—
465C22×D5—121no—
466C22×D5—128no—
467C22×D5—128no—
468C22×D5—121no—
469C22×D5C2×C4×D311yescharacteristic
470C22×D5#23512yes—
471C22×D5C2×#6712yes—
472C22×D5C23×D311yescharacteristic
473C2×AGL(1,𝔽5)—22no—
474C2×AGL(1,𝔽5)—22no—
475C2×AGL(1,𝔽5)—22no—
476C2×AGL(1,𝔽5)—22no—
477C2×AGL(1,𝔽5)—22no—
478C2×AGL(1,𝔽5)—62no—
479C2×AGL(1,𝔽5)—62no—
480C2×AGL(1,𝔽5)—62no—
481C2×AGL(1,𝔽5)—62no—
482C2×AGL(1,𝔽5)—62no—
483C2×AGL(1,𝔽5)—62no—
484C2×AGL(1,𝔽5)—128no—
485C2×AGL(1,𝔽5)C2×#6714yes—
486C2×C4×C5—22no—
487C2×C4×C5—31no—
488C2×C4×C5—31no—
489C2×C4×C5—121no—
490C2×C4×C5C2×C4×D311yescharacteristic
491C2×C4×C5C2×C4×D311yescharacteristic
492C2×Dic5—22no—
493C2×Dic5—31no—
494C2×Dic5—31no—
495C2×Dic5—121no—
496C2×Dic5C2×C4×D311yescharacteristic
497C2×Dic5C2×C4×D311yescharacteristic
498C4×D5—22no—
499C4×D5—22no—
500C4×D5—21no—
501C4×D5—21no—
502C4×D5—21no—
503C4×D5—21no—
504C4×D5—62no—
505C4×D5—62no—
506C4×D5—121no—
507C4×D5—121no—
508C25—151no—
509C23×C4—51no—
510C23×C4—151no—
511C23×C4—152no—
512#117—104no—
513C2×C4⋊C4—52no—
514C2×C4⋊C4—152no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—51no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4—151no—
527C2×C22⋊C4—151no—
528C2×C22⋊C4—151no—
529C2×C22⋊C4—152no—
530C2×C22⋊C4—152no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—152no—
534C2×C22⋊C4—304no—
535C2×C42—52no—
536C2×C42—152no—
537#95—152no—
538#95—152no—
539#95—152no—
540#95—152no—
541C2×C3×C5—22no—
542C2×C3×C5C2×#11711yescharacteristic
543C2×C3×C5C2×C4×D411yescharacteristic
544C2×C3×C5#51811yescharacteristic
545D15—22no—
546D15—41no—
547C3×D5—22no—
548C3×D5#54612yes—
549C3×D5#55112yes—
550C5×D3—22no—
551C5×D3—41no—
552C23×C3—51no—
553C23×C3—52no—
554C23×C3—52no—
555C23×C3—51no—
556C23×C3—102no—
557C23×C3—102no—
558C23×C3C22×AGL(1,𝔽5)11yescharacteristic
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—41no—
562C22×D3—51no—
563C22×D3—54no—
564C22×D3—51no—
565C22×D3—102no—
566C22×D3—101no—
567C22×D3—102no—
568C22×D3—101no—
569C22×D3—101no—
570C22×D3—102no—
571C22×D3—102no—
572C22×D3—102no—
573C22×D3—102no—
574C22×D3—101no—
575C22×D3—102no—
576C22×D3—102no—
577C22×D3—102no—
578C22×D3—201no—
579C22×D3—201no—
580C22×D3—208no—
581C22×D3—208no—
582C22×D3—201no—
583C22×D3C22×AGL(1,𝔽5)11yescharacteristic
584C22×D3C22×AGL(1,𝔽5)11yescharacteristic
585C2×C3×C4—22no—
586C2×C3×C4—54no—
587C2×C3×C4—51no—
588C2×C3×C4—51no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4—102no—
596C2×C3×C4—102no—
597C2×C3×C4—102no—
598C2×C3×C4—102no—
599C2×C3×C4—102no—
600C2×C3×C4—102no—
601C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
602C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
603C2×Dic3—41no—
604C2×Dic3—51no—
605C2×Dic3—51no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—102no—
610C2×Dic3—102no—
611C2×Dic3—102no—
612C2×Dic3—102no—
613C2×Dic3—102no—
614C2×Dic3—201no—
615C2×Dic3—201no—
616C2×Dic3—201no—
617C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
618C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
619C4×D3—208no—
620C22×C5—21no—
621C22×C5—21no—
622C22×C5—32no—
623C22×C5—61no—
624C22×C5—61no—
625C22×C5—61no—
626C22×C5—61no—
627C22×C5—61no—
628C22×C5—124no—
629C22×C5C4×#6712yes—
630C22×C5C22×C4×D311yescharacteristic
631C2×D5—21no—
632C2×D5—21no—
633C2×D5—24no—
634C2×D5—24no—
635C2×D5—32no—
636C2×D5—61no—
637C2×D5—61no—
638C2×D5—64no—
639C2×D5—64no—
640C2×D5—61no—
641C2×D5—61no—
642C2×D5—61no—
643C2×D5—124no—
644C2×D5—124no—
645C2×D5—124no—
646C2×D5—122no—
647C2×D5—122no—
648C2×D5C4×#6712yes—
649C2×D5C2×#23511yescharacteristic
650C2×D5D3×#4112yes—
651C2×D5#100912yes—
652C2×D5C22×#6711yescharacteristic
653AGL(1,𝔽5)—24no—
654AGL(1,𝔽5)—42no—
655AGL(1,𝔽5)—122no—
656AGL(1,𝔽5)—122no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—61no—
660C4×C5—61no—
661Dic5—21no—
662Dic5—21no—
663Dic5—61no—
664Dic5—61no—
665C24—31no—
666C24—51no—
667C24—151no—
668C24—151no—
669C24—151no—
670C24—151no—
671C24—151no—
672C24—302no—
673C24—302no—
674C24—304no—
675C24—602no—
676C22×C4—31no—
677C22×C4—52no—
678C22×C4—51no—
679C22×C4—51no—
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—52no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—151no—
687C22×C4—151no—
688C22×C4—151no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—152no—
692C22×C4—152no—
693C22×C4—304no—
694C22×C4—304no—
695C22×C4—602no—
696C22×C4—602no—
697C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
698C4⋊C4—104no—
699C4⋊C4—602no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—54no—
705C22⋊C4—102no—
706C22⋊C4—151no—
707C22⋊C4—151no—
708C22⋊C4—151no—
709C22⋊C4—151no—
710C22⋊C4—151no—
711C22⋊C4—151no—
712C22⋊C4—151no—
713C22⋊C4—151no—
714C22⋊C4—151no—
715C22⋊C4—151no—
716C22⋊C4—151no—
717C22⋊C4—151no—
718C22⋊C4—304no—
719C22⋊C4—304no—
720C22⋊C4—302no—
721C22⋊C4—302no—
722C22⋊C4—602no—
723C42—104no—
724C42—602no—
725C3×C5#234211yescharacteristic, complemented, Hall
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—52no—
729C22×C3—51no—
730C22×C3—51no—
731C22×C3—52no—
732C22×C3—52no—
733C22×C3—104no—
734C22×C3—104no—
735C22×C3—101no—
736C22×C3—101no—
737C22×C3D4×AGL(1,𝔽5)12yes—
738C22×C3C23×AGL(1,𝔽5)11yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—44no—
745C2×D3—52no—
746C2×D3—104no—
747C2×D3—104no—
748C2×D3—101no—
749C2×D3—101no—
750C2×D3—101no—
751C2×D3—101no—
752C2×D3—101no—
753C2×D3—204no—
754C2×D3—204no—
755C2×D3—202no—
756C2×D3—202no—
757C2×D3—204no—
758C2×D3#413012yescomplemented
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—104no—
762C3×C4—101no—
763C3×C4—101no—
764C3×C4—202no—
765Dic3—21no—
766Dic3—21no—
767Dic3—101no—
768Dic3—101no—
769Dic3—202no—
770Dic3—202no—
771C2×C5—22no—
772C2×C5—62no—
773C2×C5—121no—
774C2×C5D3×#11711yescharacteristic
775C2×C5#552111yescharacteristic
776C2×C5C2×C4×#6711yescharacteristic
777D5—22no—
778D5—62no—
779D5—121no—
780D5#552712yes—
781D5#582912yes—
782C23—31no—
783C23—31no—
784C23—51no—
785C23—52no—
786C23—52no—
787C23—51no—
788C23—62no—
789C23—62no—
790C23—102no—
791C23—102no—
792C23—121no—
793C23—154no—
794C23—151no—
795C23—151no—
796C23—302no—
797C23—302no—
798C23—301no—
799C23—302no—
800C23—301no—
801C23—301no—
802C23—302no—
803C23—302no—
804C23—301no—
805C23—302no—
806C23—302no—
807C23—302no—
808C23—302no—
809C23—601no—
810C23—601no—
811C23—601no—
812C23—608no—
813C23—608no—
814C23C2×D3×AGL(1,𝔽5)11yescharacteristic
815C2×C4—22no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—54no—
819C2×C4—51no—
820C2×C4—51no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—121no—
834C2×C4—151no—
835C2×C4—151no—
836C2×C4—302no—
837C2×C4—302no—
838C2×C4—302no—
839C2×C4—302no—
840C2×C4—302no—
841C2×C4—302no—
842C2×C4—302no—
843C2×C4—302no—
844C2×C4—601no—
845C2×C4—601no—
846C2×C4—608no—
847C2×C4—601no—
848C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
849C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
850C2×C3—22no—
851C2×C3—52no—
852C2×C3—52no—
853C2×C3—102no—
854C2×C3C2×#413011yescharacteristic
855C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
856C2×C3#6625811yescharacteristic
857D3—22no—
858D3—41no—
859D3—102no—
860D3—201no—
861C5#8227111yescharacteristic, complemented, Sylow
862C22—21no—
863C22—21no—
864C22—32no—
865C22—52no—
866C22—52no—
867C22—51no—
868C22—51no—
869C22—52no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—104no—
876C22—104no—
877C22—101no—
878C22—101no—
879C22—124no—
880C22—152no—
881C22—304no—
882C22—304no—
883C22—301no—
884C22—301no—
885C22—301no—
886C22—301no—
887C22—301no—
888C22—604no—
889C22—602no—
890C22—602no—
891C22—604no—
892C22—604no—
893C22AGL(1,𝔽5)×#6712yes—
894C22C22×D3×AGL(1,𝔽5)11yescharacteristic
895C4—21no—
896C4—21no—
897C4—61no—
898C4—61no—
899C4—104no—
900C4—101no—
901C4—101no—
902C4—202no—
903C4—301no—
904C4—301no—
905C4—602no—
906C4—602no—
907C3#1061707211yescharacteristic, complemented, Sylow
908C2—22no—
909C2—52no—
910C2—52no—
911C2—62no—
912C2—102no—
913C2—121no—
914C2—302no—
915C2—601no—
916C2D3×#413011yescharacteristic
917C2#1175683711yescharacteristic
918C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×D3×D5C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2342
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. C2×C3×#4130C2semidirect
4. #11752423C2semidirect
5. #11752028C2semidirect
7. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
8. #11751932C2semidirect
9. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
10. #11751849C2semidirect
11. #11751836C2semidirect
22. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
23. C2×C3×C4×AGL(1,𝔽5)C22semidirect
25. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
29. C2×Dic3×AGL(1,𝔽5)C22semidirect
30. C2×#6714C4semidirect
31. C2×C5×(C2×D3)⋊C4C4semidirect
32. C2×#6667C4semidirect
33. C2×(C2×D3)⋊Dic5C4semidirect
34. D5×(C2×D3)⋊C4C4semidirect
35. D5×(C2×D3)⋊C4C4semidirect
36. D5×(C2×D3)⋊C4C4semidirect
37. D5×(C2×D3)⋊C4C4semidirect
42. #91235C22semidirect
43. #91235C22semidirect
44. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
45. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
48. C2×#4130D3semidirect
76. C22×C3×C4×C5C2×C4semidirect
77. C22×Dic15C2×C4semidirect
78. C22×C5×Dic3C2×C4semidirect
79. C22×C3×Dic5C2×C4semidirect
82. C2×C3×C4×D5C2×C4semidirect
83. C2×C3×C4×D5C2×C4semidirect
87. C2×D5×Dic3C2×C4semidirect
88. C2×D5×Dic3C2×C4semidirect
104. #6714C2×C4semidirect
105. #6714C2×C4semidirect
108. C5×(C2×D3)⋊C4C2×C4semidirect
109. C5×(C2×D3)⋊C4C2×C4semidirect
112. #6667C2×C4semidirect
113. #6667C2×C4semidirect
116. (C2×D3)⋊Dic5C2×C4semidirect
117. (C2×D3)⋊Dic5C2×C4semidirect
143. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
145. C2×C4×AGL(1,𝔽5)C2×D3semidirect
256. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
283. C22×C4×C5C4×D3semidirect
285. C22×Dic5C4×D3semidirect
293. C2×C4×D5C4×D3semidirect
294. C2×C4×D5C4×D3semidirect
345. C2×D15#117semidirect
352. C2×C5×D3#117semidirect
400. C22×C3×C4C2×AGL(1,𝔽5)semidirect
409. C22×Dic3C2×AGL(1,𝔽5)semidirect
436. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
437. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
697. C22×C4D3×AGL(1,𝔽5)semidirect
725. C3×C5#2342semidirect
758. C2×D3#4130semidirect
861. C5#82271semidirect
907. C3#10617072semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41302
C2×D3×C22⋊AGL(1,𝔽5)2
C2×D5×(C2×D3)⋊C42
#117524232
#117520282
#117520252
Dic3×C22⋊AGL(1,𝔽5)2
#117519322
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518492
#117518362
#106170723
#822715