Finite Group Databasebeta

← #14323683

Subgroups — #14323683

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#935C211yesmaximal, characteristic
4#11752438C211yesmaximal, characteristic
5#11752029C211yesmaximal, characteristic, complemented
6#11752027C212yesmaximal, complemented
7#11752018C212yesmaximal, complemented
8AGL(1,𝔽5)×#217C211yesmaximal, characteristic, complemented
9#11751984C211yesmaximal, characteristic, complemented
10#11751837C212yesmaximal, complemented
11#11751745C212yesmaximal, complemented
12#10617304—31nomaximal, Hall
13C23×ΓL(1,𝔽16)C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2211yescharacteristic
15C23×C3×AGL(1,𝔽5)C2211yescharacteristic
16C2×C3×D4×D5C2211yescharacteristic
17C22×D5×Dic3C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19C2×#6763C2212yes—
20C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
22C3×D4×AGL(1,𝔽5)—24no—
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)—24no—
26C2×Dic3⋊AGL(1,𝔽5)C2212yes—
27C2×Dic3⋊AGL(1,𝔽5)C2212yes—
28C2×Dic3⋊AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2212yes—
30#91824C411yescharacteristic, complemented
31C5×#935C411yescharacteristic, complemented
32#91548C412yescomplemented
33D5×#217C2211yescharacteristic
34D5×#217C2212yes—
35#91537C411yescharacteristic, complemented
36#91536C411yescharacteristic, complemented
37#91407C412yescomplemented
38D5×Dic3⋊C4C2212yes—
39#91235C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#82326—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)D311yescharacteristic
46C22×C4⋊AGL(1,𝔽5)—31no—
47D5×#123—31no—
48#65779—31no—
49#65764—31no—
50#65712—32no—
51#65711—32no—
52#65700—32no—
53#65699—32no—
54#65699—31no—
55C22⋊C4×AGL(1,𝔽5)—31no—
56C23×C3×D5C2311yescharacteristic
57C23×C3×D5C2311yescharacteristic
58C22×ΓL(1,𝔽16)—22no—
59C22×ΓL(1,𝔽16)—42no—
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×C3×AGL(1,𝔽5)—22no—
63C22×C3×AGL(1,𝔽5)—42no—
64C22×C3×AGL(1,𝔽5)—42no—
65C22×C3×AGL(1,𝔽5)D414yes—
66C22×C3×AGL(1,𝔽5)C2311yescharacteristic
67C22×C3×AGL(1,𝔽5)C2311yescharacteristic
68C22×C3×AGL(1,𝔽5)C2311yescharacteristic
69C22×C3×AGL(1,𝔽5)C2311yescharacteristic
70C2×C3×C5×D4C2×C411yescharacteristic
71C22×Dic15C2×C411yescharacteristic, complemented
72C22×C5×Dic3C2×C411yescharacteristic, complemented
73C2×C3×C22⋊D5C2×C411yescharacteristic
74C2×C3×C22⋊D5C2×C411yescharacteristic
75C3×D4×D5—22no—
76C3×D4×D5—22no—
77C2×C3×D20C2×C411yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79C2×D5×Dic3—22no—
80C2×D5×Dic3—22no—
81C2×D5×Dic3C2×C412yescomplemented
82C2×D5×Dic3C2312yes—
83C2×D5×Dic3C2312yes—
84#6763—22no—
85#6763—42no—
86C3×C22⋊AGL(1,𝔽5)—22no—
87C3×C22⋊AGL(1,𝔽5)—22no—
88C3×C4⋊AGL(1,𝔽5)—22no—
89C3×C4×AGL(1,𝔽5)—22no—
90Dic3⋊AGL(1,𝔽5)—24no—
91Dic3⋊AGL(1,𝔽5)—24no—
92Dic3⋊AGL(1,𝔽5)—42no—
93Dic3×AGL(1,𝔽5)—42no—
94#6719C2×C411yescharacteristic, complemented
95#6719C2×C412yescomplemented
96#6712C2×C412yescomplemented
97C5×#217C2×C411yescharacteristic, complemented
98C5×#217C2×C412yescomplemented
99C5×Dic3⋊C4C2×C412yescomplemented
100Dic3⋊Dic5C2×C412yescomplemented
101#6669C2×C412yescomplemented
102#6665C2×C412yescomplemented
103#6665C2×C412yescomplemented
104#6665C2×C412yescomplemented
105C2×C3×C4×D4—51no—
106C2×#935—51no—
107C22×Dic3⋊C4—51no—
108#5220—51no—
109#5210—52no—
110C4×#217—51no—
111#4976—52no—
112#4946—51no—
113#4945—52no—
114#4943—51no—
115#4933—52no—
116C23×AGL(1,𝔽5)—31no—
117C23×AGL(1,𝔽5)C2×D311yescharacteristic
118C23×AGL(1,𝔽5)C2×D311yescharacteristic
119C2×D4×D5C2×D311yescharacteristic
120C22×C4×D5—31no—
121C2×C22⋊AGL(1,𝔽5)—31no—
122C2×C22⋊AGL(1,𝔽5)—32no—
123C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
124C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
125D4×AGL(1,𝔽5)—24no—
126C2×C4⋊AGL(1,𝔽5)—32no—
127C2×C4⋊AGL(1,𝔽5)—32no—
128C2×C4⋊AGL(1,𝔽5)—32no—
129C2×C4⋊AGL(1,𝔽5)—64no—
130C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
131C2×C4×AGL(1,𝔽5)—32no—
132C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
133C5×#123—31no—
134#4081—31no—
135#4075—31no—
136#4040—32no—
137D5×C4⋊C4—32no—
138#4032—31no—
139#4029—32no—
140D5×C22⋊C4—31no—
141D5×C22⋊C4—32no—
142(C2×AGL(1,𝔽5))⋊C4—32no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4—32no—
145(C2×AGL(1,𝔽5))⋊C4—32no—
146(C2×AGL(1,𝔽5))⋊C4—32no—
147#2322—151noSylow
148C23×C3×C5C22×C411yescharacteristic
149C23×C3×C5C22×C411yescharacteristic
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—21no—
153C22×C3×D5—21no—
154C22×C3×D5—22no—
155C22×C3×D5—22no—
156C22×C3×D5C22×C411yescharacteristic
157C22×C3×D5C22×C411yescharacteristic
158C22×C3×D5C2×D412yes—
159C22×C3×D5#4112yes—
160C22×C3×D5C2411yescharacteristic
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—22no—
164C2×ΓL(1,𝔽16)—22no—
165C2×ΓL(1,𝔽16)—22no—
166C2×ΓL(1,𝔽16)—22no—
167C2×ΓL(1,𝔽16)—44no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)—21no—
171C2×C3×AGL(1,𝔽5)—21no—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—22no—
174C2×C3×AGL(1,𝔽5)—44no—
175C2×C3×AGL(1,𝔽5)—44no—
176C2×C3×AGL(1,𝔽5)C2×D412yes—
177C2×C3×AGL(1,𝔽5)C2×D412yes—
178C3×C5×D4—22no—
179C2×C3×C4×C5C22×C411yescharacteristic
180C2×Dic15—22no—
181C2×Dic15C22×C412yes—
182C2×Dic15C22×C412yes—
183C2×C5×Dic3—22no—
184C2×C5×Dic3C22×C412yes—
185C2×C5×Dic3C22×C412yes—
186C3×C22⋊D5—22no—
187C3×C22⋊D5—22no—
188C2×C3×Dic5C22×C411yescharacteristic
189C3×D20—22no—
190C3×C4×D5—21no—
191C3×C4×D5—21no—
192D5×Dic3—24no—
193D5×Dic3—22no—
194D5×Dic3—22no—
195D5×Dic3—22no—
196D5×Dic3—22no—
197C22×C3×D4—51no—
198C23×C3×C4—51no—
199C23×C3×C4—51no—
200C23×Dic3—51no—
201C23×Dic3—51no—
202C3×C4×D4—104no—
203C2×C3×C4⋊C4—51no—
204C2×C3×C22⋊C4—51no—
205C2×C3×C22⋊C4—51no—
206C2×C3×C42—51no—
207C2×#217—52no—
208C2×#217—51no—
209C2×#217—51no—
210C2×#217—52no—
211#935—51no—
212#935—51no—
213#935—51no—
214#935—52no—
215#935—52no—
216#935AGL(1,𝔽5)11yescharacteristic, complemented
217C2×Dic3⋊C4—52no—
218C2×Dic3⋊C4—52no—
219C2×Dic3⋊C4—52no—
220C2×Dic3⋊C4—52no—
221C2×Dic3⋊C4—104no—
222C2×C4×Dic3—52no—
223C3⋊#95—52no—
224C3⋊#95—52no—
225C3⋊#95—52no—
226C3⋊#95—52no—
227C3⋊#95—52no—
228C23×D5C22×D311yescharacteristic
229C23×D5C22×D311yescharacteristic
230C22×AGL(1,𝔽5)—22no—
231C22×AGL(1,𝔽5)—32no—
232C22×AGL(1,𝔽5)—32no—
233C22×AGL(1,𝔽5)—42no—
234C22×AGL(1,𝔽5)—42no—
235C22×AGL(1,𝔽5)—62no—
236C22×AGL(1,𝔽5)—122no—
237C22×AGL(1,𝔽5)#6714yes—
238C22×AGL(1,𝔽5)C22×D311yescharacteristic
239C22×AGL(1,𝔽5)C22×D311yescharacteristic
240C22×AGL(1,𝔽5)C22×D311yescharacteristic
241C22×AGL(1,𝔽5)C22×D311yescharacteristic
242C2×C5×D4C4×D311yescharacteristic
243C22×C4×C5—31no—
244C2×C22⋊D5C4×D311yescharacteristic
245C2×C22⋊D5C4×D311yescharacteristic
246C22×Dic5—31no—
247D4×D5—22no—
248D4×D5—22no—
249C2×D20C4×D311yescharacteristic
250C2×C4×D5—32no—
251C2×C4×D5—32no—
252C2×C4×D5—32no—
253C2×C4×D5—62no—
254C2×C4×D5—62no—
255C2×C4×D5C22×D311yescharacteristic
256C22⋊AGL(1,𝔽5)—22no—
257C22⋊AGL(1,𝔽5)—22no—
258C22⋊AGL(1,𝔽5)—62no—
259C22⋊AGL(1,𝔽5)—122no—
260C4⋊AGL(1,𝔽5)—22no—
261C4⋊AGL(1,𝔽5)—64no—
262C4⋊AGL(1,𝔽5)—64no—
263C4⋊AGL(1,𝔽5)—122no—
264C4×AGL(1,𝔽5)—22no—
265C4×AGL(1,𝔽5)—122no—
266C5×C4⋊C4—32no—
267C5×C22⋊C4—32no—
268C5×C22⋊C4—31no—
269C22⋊Dic5—32no—
270C22⋊Dic5—31no—
271#685—32no—
272#685—32no—
273#685—32no—
274C4⋊Dic5—32no—
275#683—32no—
276#683—32no—
277C2×#123—151no—
278C2×C4×D4—51no—
279C22×C4⋊C4—151no—
280#389—152no—
281#388—152no—
282#387—152no—
283#386—151no—
284#385—151no—
285#385—152no—
286#381—151no—
287C4×C22⋊C4—151no—
288C22×C3×C5—22no—
289C22×C3×C5—21no—
290C22×C3×C5—22no—
291C22×C3×C5C4×D412yes—
292C22×C3×C5C23×C411yescharacteristic
293C2×C3×D5—22no—
294C2×C3×D5—22no—
295C2×C3×D5—22no—
296C2×C3×D5—24no—
297C2×C3×D5—21no—
298C2×C3×D5—22no—
299C2×C3×D5—41no—
300C2×C3×D5—41no—
301C2×C3×D5—42no—
302C2×C3×D5C4×D412yes—
303C2×C3×D5C22×D411yescharacteristic
304C2×C3×D5C2×#4111yescharacteristic
305C2×C3×D5H(5,𝔽2)12yes—
306C2×C3×D52−1+412yes—
307ΓL(1,𝔽16)—42no—
308ΓL(1,𝔽16)—42no—
309C3×AGL(1,𝔽5)—22no—
310C3×AGL(1,𝔽5)—22no—
311C3×AGL(1,𝔽5)—41no—
312C3×AGL(1,𝔽5)—41no—
313C3×C4×C5—21no—
314Dic15—22no—
315Dic15—22no—
316C3×Dic5—21no—
317C5×Dic3—22no—
318C5×Dic3—22no—
319C24×C3—51no—
320C24×C3—51no—
321C2×C3×D4—51no—
322C2×C3×D4—51no—
323C2×C3×D4—51no—
324C2×C3×D4—102no—
325C2×C3×D4—102no—
326C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
327C22×C3×C4—51no—
328C22×C3×C4—51no—
329C22×C3×C4—54no—
330C22×C3×C4—51no—
331C22×C3×C4—51no—
332C22×C3×C4—51no—
333C22×C3×C4—102no—
334C22×C3×C4—202no—
335C22×C3×C4—202no—
336C22×Dic3—51no—
337C22×Dic3—52no—
338C22×Dic3—52no—
339C22×Dic3—52no—
340C22×Dic3—52no—
341C22×Dic3—52no—
342C22×Dic3—102no—
343C22×Dic3—102no—
344C22×Dic3—102no—
345C22×Dic3—202no—
346C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
347C3×C4⋊C4—102no—
348C3×C22⋊C4—102no—
349C3×C22⋊C4—102no—
350C3×C42—102no—
351#217—51no—
352#217—52no—
353#217—52no—
354#217—52no—
355#217—52no—
356#217—102no—
357#217—202no—
358#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
359#217C2×AGL(1,𝔽5)12yescomplemented
360Dic3⋊C4—52no—
361Dic3⋊C4—52no—
362Dic3⋊C4—52no—
363Dic3⋊C4—104no—
364Dic3⋊C4—104no—
365Dic3⋊C4—202no—
366Dic3⋊C4C2×AGL(1,𝔽5)12yescomplemented
367C4×Dic3—202no—
368C23×C5C2×C4×D311yescharacteristic
369C23×C5C2×C4×D311yescharacteristic
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—21no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—21no—
376C22×D5C2×C4×D311yescharacteristic
377C22×D5C2×C4×D311yescharacteristic
378C22×D5#23512yes—
379C22×D5C2×#6712yes—
380C22×D5C23×D311yescharacteristic
381C2×AGL(1,𝔽5)—22no—
382C2×AGL(1,𝔽5)—22no—
383C2×AGL(1,𝔽5)—22no—
384C2×AGL(1,𝔽5)—22no—
385C2×AGL(1,𝔽5)—21no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—44no—
388C2×AGL(1,𝔽5)—44no—
389C2×AGL(1,𝔽5)—62no—
390C2×AGL(1,𝔽5)—62no—
391C2×AGL(1,𝔽5)—62no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)—62no—
394C2×AGL(1,𝔽5)—62no—
395C2×AGL(1,𝔽5)—124no—
396C2×AGL(1,𝔽5)C2×#6712yes—
397C2×AGL(1,𝔽5)C2×#6712yes—
398C5×D4—22no—
399C2×C4×C5—32no—
400C2×C4×C5—32no—
401C2×C4×C5—62no—
402C2×C4×C5C2×C4×D311yescharacteristic
403C22⋊D5—22no—
404C22⋊D5—22no—
405C2×Dic5—32no—
406C2×Dic5—32no—
407C2×Dic5—62no—
408C2×Dic5C2×C4×D311yescharacteristic
409D20—22no—
410C4×D5—21no—
411C4×D5—21no—
412C4×D5—64no—
413C4×D5—62no—
414C4×D5—62no—
415C4×D5—62no—
416C4×D5—62no—
417C22×D4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—151no—
421C23×C4—151no—
422#123—31no—
423#123—152no—
424#123—151no—
425#123—152no—
426#123—151no—
427#123—151no—
428C4×D4—104no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—152no—
431C2×C4⋊C4—152no—
432C2×C4⋊C4—152no—
433C2×C4⋊C4—152no—
434C2×C4⋊C4—304no—
435C2×C22⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—152no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—152no—
441C2×C42—51no—
442C2×C42—152no—
443#95—152no—
444#95—152no—
445#95—152no—
446#95—152no—
447#95—152no—
448C2×C3×C5—22no—
449C2×C3×C5—41no—
450C2×C3×C5C2×C4×D411yescharacteristic
451C2×C3×C5#52012yes—
452C3×D5—22no—
453C3×D5—41no—
454C3×D5#53411yescharacteristic
455C3×D5#53611yescharacteristic
456C3×D5#53912yes—
457C23×C3—51no—
458C23×C3—52no—
459C23×C3—52no—
460C23×C3—51no—
461C23×C3—51no—
462C23×C3—102no—
463C23×C3—102no—
464C23×C3—102no—
465C23×C3—101no—
466C23×C3—101no—
467C23×C3—102no—
468C23×C3C22×AGL(1,𝔽5)11yescharacteristic
469C23×C3C22×AGL(1,𝔽5)11yescharacteristic
470C3×D4—22no—
471C3×D4—102no—
472C3×D4—102no—
473C3×D4—102no—
474C2×C3×C4—52no—
475C2×C3×C4—52no—
476C2×C3×C4—51no—
477C2×C3×C4—101no—
478C2×C3×C4—101no—
479C2×C3×C4—102no—
480C2×C3×C4—102no—
481C2×C3×C4—102no—
482C2×C3×C4—101no—
483C2×C3×C4—101no—
484C2×C3×C4—102no—
485C2×C3×C4—204no—
486C2×C3×C4—204no—
487C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
488C2×Dic3—22no—
489C2×Dic3—52no—
490C2×Dic3—52no—
491C2×Dic3—102no—
492C2×Dic3—102no—
493C2×Dic3—102no—
494C2×Dic3—102no—
495C2×Dic3—104no—
496C2×Dic3—102no—
497C2×Dic3—102no—
498C2×Dic3—102no—
499C2×Dic3—102no—
500C2×Dic3—102no—
501C2×Dic3—102no—
502C2×Dic3—102no—
503C2×Dic3—204no—
504C2×Dic3C22×AGL(1,𝔽5)12yes—
505C2×Dic3C22×AGL(1,𝔽5)12yes—
506C22×C5—22no—
507C22×C5—21no—
508C22×C5—22no—
509C22×C5C4×#6712yes—
510C22×C5C22×C4×D311yescharacteristic
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—24no—
514C2×D5—22no—
515C2×D5—21no—
516C2×D5—22no—
517C2×D5—41no—
518C2×D5—42no—
519C2×D5—41no—
520C2×D5C4×#6712yes—
521C2×D5C2×#23511yescharacteristic
522C2×D5#100412yes—
523C2×D5#101012yes—
524C2×D5C22×#6711yescharacteristic
525AGL(1,𝔽5)—22no—
526AGL(1,𝔽5)—22no—
527AGL(1,𝔽5)—41no—
528AGL(1,𝔽5)—41no—
529AGL(1,𝔽5)—122no—
530AGL(1,𝔽5)—122no—
531C4×C5—21no—
532C4×C5—62no—
533C4×C5—62no—
534Dic5—21no—
535Dic5—62no—
536Dic5—62no—
537C24—51no—
538C24—51no—
539C2×D4—51no—
540C2×D4—51no—
541C2×D4—51no—
542C2×D4—102no—
543C2×D4—102no—
544C2×D4D3×AGL(1,𝔽5)11yescharacteristic
545C22×C4—31no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—54no—
549C22×C4—51no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—102no—
553C22×C4—152no—
554C22×C4—152no—
555C22×C4—152no—
556C22×C4—151no—
557C22×C4—152no—
558C22×C4—152no—
559C22×C4—202no—
560C22×C4—202no—
561C22×C4—302no—
562C22×C4—302no—
563C22×C4—302no—
564C22×C4—602no—
565C4⋊C4—32no—
566C4⋊C4—102no—
567C4⋊C4—152no—
568C4⋊C4—152no—
569C4⋊C4—152no—
570C4⋊C4—304no—
571C4⋊C4—304no—
572C4⋊C4—602no—
573C22⋊C4—31no—
574C22⋊C4—32no—
575C22⋊C4—102no—
576C22⋊C4—102no—
577C22⋊C4—152no—
578C22⋊C4—152no—
579C22⋊C4—152no—
580C22⋊C4—151no—
581C22⋊C4—152no—
582C22⋊C4—302no—
583C22⋊C4—602no—
584C42—102no—
585C42—602no—
586C3×C5#232211yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—22no—
590C22×C3—51no—
591C22×C3—51no—
592C22×C3—52no—
593C22×C3—52no—
594C22×C3—52no—
595C22×C3—102no—
596C22×C3—104no—
597C22×C3—102no—
598C22×C3—102no—
599C22×C3—101no—
600C22×C3—102no—
601C22×C3—201no—
602C22×C3—202no—
603C22×C3—201no—
604C22×C3D4×AGL(1,𝔽5)12yes—
605C22×C3C23×AGL(1,𝔽5)11yescharacteristic
606C3×C4—21no—
607C3×C4—102no—
608C3×C4—102no—
609C3×C4—101no—
610C3×C4—201no—
611C3×C4—201no—
612Dic3—22no—
613Dic3—22no—
614Dic3—102no—
615Dic3—102no—
616Dic3—202no—
617Dic3—202no—
618C2×C5—22no—
619C2×C5—41no—
620C2×C5#554612yes—
621C2×C5C2×C4×#6711yescharacteristic
622D5—22no—
623D5—41no—
624D5#556412yes—
625D5#580411yescharacteristic
626D5#582511yescharacteristic
627C23—51no—
628C23—52no—
629C23—52no—
630C23—51no—
631C23—51no—
632C23—102no—
633C23—102no—
634C23—101no—
635C23—102no—
636C23—101no—
637C23—102no—
638C23C2×D3×AGL(1,𝔽5)11yescharacteristic
639C23C2×D3×AGL(1,𝔽5)11yescharacteristic
640D4—22no—
641D4—102no—
642D4—102no—
643D4—102no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—52no—
647C2×C4—52no—
648C2×C4—51no—
649C2×C4—62no—
650C2×C4—101no—
651C2×C4—101no—
652C2×C4—102no—
653C2×C4—102no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—152no—
659C2×C4—152no—
660C2×C4—204no—
661C2×C4—204no—
662C2×C4—302no—
663C2×C4—302no—
664C2×C4—302no—
665C2×C4—304no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—302no—
669C2×C4—302no—
670C2×C4—302no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—302no—
674C2×C4—604no—
675C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
676C2×C3—22no—
677C2×C3—41no—
678C2×C3—51no—
679C2×C3—52no—
680C2×C3—51no—
681C2×C3—102no—
682C2×C3—201no—
683C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
684C2×C3#6626612yes—
685C5#8232611yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—21no—
689C22—52no—
690C22—52no—
691C22—51no—
692C22—51no—
693C22—52no—
694C22—102no—
695C22—102no—
696C22—104no—
697C22—102no—
698C22—102no—
699C22—101no—
700C22—201no—
701C22—201no—
702C22—202no—
703C22AGL(1,𝔽5)×#6712yes—
704C22C22×D3×AGL(1,𝔽5)11yescharacteristic
705C4—21no—
706C4—62no—
707C4—62no—
708C4—102no—
709C4—102no—
710C4—101no—
711C4—201no—
712C4—201no—
713C4—302no—
714C4—302no—
715C4—602no—
716C4—602no—
717C3#1061730411yescharacteristic, complemented, Sylow
718C2—22no—
719C2—41no—
720C2—51no—
721C2—51no—
722C2—52no—
723C2—102no—
724C2—201no—
725C2#1175684612yes—
726C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3⋊AGL(1,𝔽5)C2semidirect
5. #11752029C2semidirect
6. #11752027C2semidirect
7. #11752018C2semidirect
8. AGL(1,𝔽5)×#217C2semidirect
9. #11751984C2semidirect
10. #11751837C2semidirect
11. #11751745C2semidirect
30. #91824C4semidirect
31. C5×#935C4semidirect
32. #91548C4semidirect
35. #91537C4semidirect
36. #91536C4semidirect
37. #91407C4semidirect
71. C22×Dic15C2×C4semidirect
72. C22×C5×Dic3C2×C4semidirect
81. C2×D5×Dic3C2×C4semidirect
94. #6719C2×C4semidirect
95. #6719C2×C4semidirect
96. #6712C2×C4semidirect
97. C5×#217C2×C4semidirect
98. C5×#217C2×C4semidirect
99. C5×Dic3⋊C4C2×C4semidirect
100. Dic3⋊Dic5C2×C4semidirect
101. #6669C2×C4semidirect
102. #6665C2×C4semidirect
103. #6665C2×C4semidirect
104. #6665C2×C4semidirect
216. #935AGL(1,𝔽5)semidirect
346. C22×Dic3C2×AGL(1,𝔽5)semidirect
358. #217C2×AGL(1,𝔽5)semidirect
359. #217C2×AGL(1,𝔽5)semidirect
366. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
586. C3×C5#2322semidirect
685. C5#82326semidirect
717. C3#10617304semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×AGL(1,𝔽5)2
C22×Dic3⋊AGL(1,𝔽5)2
D5×#9352
#117524382
#117520292
#117520272
#117520182
AGL(1,𝔽5)×#2172
#117519842
#117518372
#117517452
#106173043
#823265