Finite Group Databasebeta

← #14319762

Subgroups — #14319762

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×AGL(1,𝔽5)×#67C212yesmaximal
2C4×D5×#67C211yesmaximal, characteristic
3C4×#6763C211yesmaximal, characteristic, complemented
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
5AGL(1,𝔽5)×#217C212yesmaximal, complemented
6#11751931C212yesmaximal, complemented
7D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
8#11751848C211yesmaximal, characteristic, complemented
9#11751834C211yesmaximal, characteristic, complemented
10#11751833C212yesmaximal, complemented
11#11751832C211yesmaximal, characteristic, complemented
12#10617172—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)C2212yes—
20AGL(1,𝔽5)×#67C4116yescomplemented
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C4×#1220C411yescharacteristic, complemented
27C4×C5×#67C411yescharacteristic, complemented
28#91552C411yescharacteristic, complemented
29Dic5×#67C411yescharacteristic, complemented
30D5×#217C2211yescharacteristic
31D5×(C2×D3)⋊C4C2211yescharacteristic
32#91444C411yescharacteristic, complemented
33C4×#1202C411yescharacteristic, complemented
34#91440C411yescharacteristic, complemented
35C4×#1201C411yescharacteristic, complemented
36D5×Dic3⋊C4C2211yescharacteristic
37C4×D5×Dic3C2211yescharacteristic
38#91235C2211yescharacteristic
39#91235C2211yescharacteristic
40C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
45#73322—51nomaximal, Hall
46C2×D4×AGL(1,𝔽5)—32no—
47C4×D4×D5—31no—
48C4×C22⋊AGL(1,𝔽5)—31no—
49C4×C22⋊AGL(1,𝔽5)—31no—
50C2×(C2×AGL(1,𝔽5))⋊C4—31no—
51C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic, complemented
52C4⋊C4×AGL(1,𝔽5)—32no—
53C22⋊C4×AGL(1,𝔽5)—32no—
54C22⋊C4×AGL(1,𝔽5)—32no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56#65686—31no—
57C23×C3×D5C2311yescharacteristic
58C22×D3×D5C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2312yes—
60C22×ΓL(1,𝔽16)C2312yes—
61C22×C3×AGL(1,𝔽5)—42no—
62C22×C3×AGL(1,𝔽5)—42no—
63C22×C3×AGL(1,𝔽5)C2×C418yescomplemented
64C22×C3×AGL(1,𝔽5)C2312yes—
65C22×C3×AGL(1,𝔽5)C2312yes—
66C2×D3×AGL(1,𝔽5)—42no—
67C2×D3×AGL(1,𝔽5)—42no—
68C2×D3×AGL(1,𝔽5)C2×C418yescomplemented
69C22×C3×C4×C5C2×C411yescharacteristic, complemented
70C2×#1220C2×C411yescharacteristic
71C2×C4×D15C2×C411yescharacteristic, complemented
72C2×C5×#67C2×C411yescharacteristic
73C2×C4×C5×D3C2×C411yescharacteristic, complemented
74C22×C3×Dic5C2×C411yescharacteristic, complemented
75C2×C3×C4×D5—42no—
76C2×C3×C4×D5C2×C411yescharacteristic, complemented
77C2×C3×C4×D5C2×C411yescharacteristic, complemented
78C2×C3×C4×D5C2311yescharacteristic
79C2×C3×C4×D5C2311yescharacteristic
80D5×#67C2×C418yes—
81C2×#1202C2×C411yescharacteristic
82C2×#1201C2×C411yescharacteristic
83C2×#1200C2×C411yescharacteristic, complemented
84C2×D3×Dic5C2×C411yescharacteristic, complemented
85C2×D5×Dic3C2311yescharacteristic
86C2×D5×Dic3C2311yescharacteristic
87C2×D5×Dic3C2311yescharacteristic
88C4×D3×D5—42no—
89#6763C2×C418yescomplemented
90C4×ΓL(1,𝔽16)—42no—
91Dic3⋊AGL(1,𝔽5)C2×C418yescomplemented
92(C2×D3)⋊AGL(1,𝔽5)C2×C418yescomplemented
93Dic3×AGL(1,𝔽5)—42no—
94Dic3×AGL(1,𝔽5)—42no—
95Dic3×AGL(1,𝔽5)C2×C418yescomplemented
96#6719C2×C411yescharacteristic, complemented
97#6714C2×C411yescharacteristic, complemented
98#6712C2×C411yescharacteristic, complemented
99C4×Dic15C2×C411yescharacteristic, complemented
100C5×#217C2×C411yescharacteristic, complemented
101C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
102C5×Dic3⋊C4C2×C411yescharacteristic, complemented
103C4×C5×Dic3C2×C411yescharacteristic, complemented
104Dic3⋊Dic5C2×C411yescharacteristic, complemented
105#6669C2×C411yescharacteristic, complemented
106#6667C2×C411yescharacteristic, complemented
107(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
108#6665C2×C411yescharacteristic, complemented
109#6665C2×C411yescharacteristic, complemented
110Dic3×Dic5C2×C411yescharacteristic, complemented
111Dic3×Dic5C2×C411yescharacteristic, complemented
112C2×C4×#67—52no—
113C2×C4×#67—51no—
114C2×C3×#95—51no—
115C4×#217—52no—
116C4×#217—51no—
117#4666—51no—
118#4666—52no—
119D3×#95—51no—
120#4649—52no—
121#4649—51no—
122#4648—51no—
123C23×AGL(1,𝔽5)—32no—
124C23×AGL(1,𝔽5)C2×D312yes—
125C2×D4×D5—31no—
126C22×C4×D5—31no—
127C22×C4×D5C2×D311yescharacteristic
128C2×C22⋊AGL(1,𝔽5)—32no—
129C2×C22⋊AGL(1,𝔽5)—32no—
130D4×AGL(1,𝔽5)—316no—
131C2×C4⋊AGL(1,𝔽5)—32no—
132C2×C4×AGL(1,𝔽5)—32no—
133C2×C4×AGL(1,𝔽5)—32no—
134C2×C4×AGL(1,𝔽5)—32no—
135C2×C4×AGL(1,𝔽5)—32no—
136C4×C5×D4—31no—
137D4×Dic5—31no—
138C4×C22⋊D5—31no—
139C4×C22⋊D5—31no—
140#4039—31no—
141D5×C4⋊C4—31no—
142#4027—31no—
143#4027—31no—
144D5×C22⋊C4—31no—
145D5×C22⋊C4—31no—
146C4×D20—31no—
147C42×D5—31no—
148(C2×AGL(1,𝔽5))⋊C4—32no—
149(C2×AGL(1,𝔽5))⋊C4—32no—
150(C2×AGL(1,𝔽5))⋊C4—31no—
151(C2×AGL(1,𝔽5))⋊C4—31no—
152(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
153(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
154(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
155#2275—151noSylow
156C23×C3×C5C22×C411yescharacteristic
157C22×D15C22×C411yescharacteristic
158C22×C5×D3C22×C411yescharacteristic
159C22×C3×D5—22no—
160C22×C3×D5—21no—
161C22×C3×D5—21no—
162C22×C3×D5C22×C411yescharacteristic
163C22×C3×D5C22×C414yes—
164C22×C3×D5C2411yescharacteristic
165C2×D3×D5—22no—
166C2×D3×D5—21no—
167C2×D3×D5—21no—
168C2×D3×D5C22×C414yes—
169C2×ΓL(1,𝔽16)—22no—
170C2×ΓL(1,𝔽16)—22no—
171C2×ΓL(1,𝔽16)—22no—
172C2×ΓL(1,𝔽16)—22no—
173C2×ΓL(1,𝔽16)C22×C414yes—
174C2×ΓL(1,𝔽16)C22×C414yes—
175C2×C3×AGL(1,𝔽5)—22no—
176C2×C3×AGL(1,𝔽5)—22no—
177C2×C3×AGL(1,𝔽5)—22no—
178C2×C3×AGL(1,𝔽5)—22no—
179C2×C3×AGL(1,𝔽5)—48no—
180C2×C3×AGL(1,𝔽5)C22×C414yes—
181C2×C3×AGL(1,𝔽5)C22×C414yes—
182D3×AGL(1,𝔽5)—48no—
183C2×C3×C4×C5—41no—
184C2×C3×C4×C5C22×C411yescharacteristic
185C2×C3×C4×C5C22×C411yescharacteristic
186#1220C4214yescomplemented
187C2×Dic15C22×C411yescharacteristic
188C2×Dic15C22×C411yescharacteristic
189C2×Dic15C22×C411yescharacteristic
190C4×D15—41no—
191C5×#67C4214yescomplemented
192C2×C5×Dic3C22×C411yescharacteristic
193C2×C5×Dic3C22×C411yescharacteristic
194C2×C5×Dic3C22×C411yescharacteristic
195C4×C5×D3—41no—
196C2×C3×Dic5—41no—
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C22×C411yescharacteristic
199C3×C4×D5—22no—
200C3×C4×D5—22no—
201C3×C4×D5—41no—
202C3×C4×D5—41no—
203#1202C4214yescomplemented
204#1201C4214yescomplemented
205#1200—41no—
206D3×Dic5—41no—
207D5×Dic3—21no—
208D5×Dic3—22no—
209D5×Dic3—21no—
210D5×Dic3C22×C414yes—
211C23×C3×C4—52no—
212C23×C3×C4—51no—
213C22×#67—51no—
214C22×C4×D3—52no—
215C22×C4×D3—51no—
216C2×#217—52no—
217C2×#217—51no—
218C4×#67—516no—
219C4×#67—51no—
220C4×#67—51no—
221C4×#67—51no—
222C4×#67—51no—
223C4×#67—51no—
224C4×#67—51no—
225C4×#67—51no—
226C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
227C2×(C2×D3)⋊C4—52no—
228C2×(C2×D3)⋊C4—51no—
229C2×Dic3⋊C4—52no—
230C2×Dic3⋊C4—51no—
231C2×C4×Dic3—52no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—52no—
234C2×C4×Dic3—52no—
235C2×C4×Dic3—52no—
236C3×#95—51no—
237C3×#95—52no—
238C3×#95—51no—
239C3⋊#95—52no—
240C3⋊#95—52no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C23×D5—31no—
244C23×D5C22×D311yescharacteristic
245C22×AGL(1,𝔽5)—32no—
246C22×AGL(1,𝔽5)—32no—
247C22×AGL(1,𝔽5)—38no—
248C22×AGL(1,𝔽5)—42no—
249C22×AGL(1,𝔽5)—42no—
250C22×AGL(1,𝔽5)—122no—
251C22×AGL(1,𝔽5)—122no—
252C22×AGL(1,𝔽5)C4×D318yescomplemented
253C22×AGL(1,𝔽5)C22×D312yes—
254C22×AGL(1,𝔽5)C22×D312yes—
255C2×C5×D4—31no—
256C22×C4×C5—31no—
257C22×C4×C5C4×D311yescharacteristic, complemented
258C2×C22⋊D5—31no—
259C2×C22⋊D5—31no—
260C22×Dic5—31no—
261C22×Dic5C4×D311yescharacteristic, complemented
262D4×D5—38no—
263C2×D20—31no—
264C2×C4×D5—31no—
265C2×C4×D5—31no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×C4×D5—31no—
269C2×C4×D5—42no—
270C2×C4×D5—122no—
271C2×C4×D5C4×D311yescharacteristic, complemented
272C2×C4×D5C4×D311yescharacteristic, complemented
273C2×C4×D5C22×D311yescharacteristic
274C2×C4×D5C22×D311yescharacteristic
275C22⋊AGL(1,𝔽5)—38no—
276C22⋊AGL(1,𝔽5)—38no—
277C4⋊AGL(1,𝔽5)—38no—
278C4×AGL(1,𝔽5)—38no—
279C4×AGL(1,𝔽5)—122no—
280C4×AGL(1,𝔽5)—122no—
281C4×AGL(1,𝔽5)—122no—
282C5×C4⋊C4—31no—
283C5×C22⋊C4—31no—
284C5×C22⋊C4—31no—
285C42×C5—31no—
286C22⋊Dic5—31no—
287C22⋊Dic5—31no—
288#685—31no—
289#685—31no—
290#685—31no—
291#685—31no—
292C4⋊Dic5—31no—
293#683—31no—
294#683—31no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—31no—
298C2×C4×D4—151no—
299C2×C4×D4—152no—
300C4×C4⋊C4—151no—
301C4×C4⋊C4—152no—
302C4×C22⋊C4—152no—
303C4×C22⋊C4—151no—
304C4×C22⋊C4—152no—
305C4×C22⋊C4—151no—
306#376—151no—
307C2×#95—51no—
308C2×#95—151no—
309C22×C3×C5—21no—
310C22×C3×C5—21no—
311C22×C3×C5C2×C4212yes—
312C22×C3×C5C23×C411yescharacteristic
313C2×D15—21no—
314C2×D15—21no—
315C2×D15C2×C4212yes—
316C2×C5×D3—21no—
317C2×C5×D3—21no—
318C2×C5×D3C2×C4212yes—
319C2×C3×D5—21no—
320C2×C3×D5—21no—
321C2×C3×D5—24no—
322C2×C3×D5—24no—
323C2×C3×D5C2×C4212yes—
324C2×C3×D5C23×C412yes—
325C2×C3×D5H(5,𝔽2)11yescharacteristic
326C2×C3×D5H(5,𝔽2)12yes—
327C2×C3×D52−1+411yescharacteristic
328D3×D5—24no—
329D3×D5—24no—
330ΓL(1,𝔽16)—24no—
331ΓL(1,𝔽16)—24no—
332C3×AGL(1,𝔽5)—24no—
333C3×AGL(1,𝔽5)—24no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336Dic15—21no—
337Dic15—21no—
338Dic15C2×C4212yes—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3C2×C4212yes—
344C24×C3—51no—
345C23×D3—51no—
346C22×C3×C4—52no—
347C22×C3×C4—52no—
348C22×C3×C4—58no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—51no—
352C22×C3×C4—51no—
353C22×C3×C4—51no—
354C22×C3×C4—202no—
355C22×C3×C4—202no—
356C22×C3×C4—202no—
357C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
358C2×#67—51no—
359C2×#67—51no—
360C2×#67—58no—
361C2×#67—51no—
362C2×#67C2×AGL(1,𝔽5)11yescharacteristic
363C22×Dic3—51no—
364C22×Dic3—52no—
365C22×Dic3—52no—
366C22×Dic3—51no—
367C22×Dic3—51no—
368C2×C4×D3—58no—
369C2×C4×D3—51no—
370C2×C4×D3—51no—
371C2×C4×D3—51no—
372C2×C4×D3—202no—
373C2×C4×D3—202no—
374C2×C4×D3—202no—
375C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
376#217—58no—
377#217—51no—
378#217—51no—
379#217—51no—
380#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
381(C2×D3)⋊C4—58no—
382(C2×D3)⋊C4—51no—
383(C2×D3)⋊C4—51no—
384(C2×D3)⋊C4—51no—
385(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
386Dic3⋊C4—58no—
387Dic3⋊C4—51no—
388Dic3⋊C4—51no—
389Dic3⋊C4—51no—
390Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
391C4×Dic3—58no—
392C4×Dic3—51no—
393C4×Dic3—51no—
394C4×Dic3—51no—
395C4×Dic3—202no—
396C4×Dic3—202no—
397C4×Dic3—202no—
398C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
399C23×C5—31no—
400C23×C5C2×C4×D311yescharacteristic
401C22×D5—22no—
402C22×D5—21no—
403C22×D5—21no—
404C22×D5—31no—
405C22×D5—34no—
406C22×D5—62no—
407C22×D5—61no—
408C22×D5—61no—
409C22×D5C2×C4×D311yescharacteristic
410C22×D5C2×C4×D314yes—
411C22×D5C23×D311yescharacteristic
412C2×AGL(1,𝔽5)—22no—
413C2×AGL(1,𝔽5)—22no—
414C2×AGL(1,𝔽5)—22no—
415C2×AGL(1,𝔽5)—22no—
416C2×AGL(1,𝔽5)—34no—
417C2×AGL(1,𝔽5)—34no—
418C2×AGL(1,𝔽5)—48no—
419C2×AGL(1,𝔽5)—62no—
420C2×AGL(1,𝔽5)—62no—
421C2×AGL(1,𝔽5)—62no—
422C2×AGL(1,𝔽5)—62no—
423C2×AGL(1,𝔽5)—128no—
424C2×AGL(1,𝔽5)C2×C4×D314yes—
425C2×AGL(1,𝔽5)C2×C4×D314yes—
426C5×D4—34no—
427C2×C4×C5—31no—
428C2×C4×C5—31no—
429C2×C4×C5—31no—
430C2×C4×C5—41no—
431C2×C4×C5—121no—
432C2×C4×C5C2×C4×D311yescharacteristic
433C2×C4×C5C2×C4×D311yescharacteristic
434C22⋊D5—34no—
435C22⋊D5—34no—
436C2×Dic5—31no—
437C2×Dic5—31no—
438C2×Dic5—31no—
439C2×Dic5—41no—
440C2×Dic5—121no—
441C2×Dic5C2×C4×D311yescharacteristic
442C2×Dic5C2×C4×D311yescharacteristic
443D20—34no—
444C4×D5—22no—
445C4×D5—22no—
446C4×D5—34no—
447C4×D5—41no—
448C4×D5—41no—
449C4×D5—61no—
450C4×D5—62no—
451C4×D5—61no—
452C4×D5—121no—
453C4×D5—121no—
454C22×D4—151no—
455C23×C4—52no—
456C23×C4—51no—
457C23×C4—151no—
458C23×C4—152no—
459C4×D4—31no—
460C4×D4—151no—
461C4×D4—151no—
462C4×D4—151no—
463C4×D4—151no—
464C4×D4—151no—
465C4×D4—151no—
466C4×D4—1516no—
467C4×D4—151no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—152no—
470C2×C22⋊C4—151no—
471C2×C22⋊C4—151no—
472C2×C22⋊C4—152no—
473C2×C22⋊C4—152no—
474C2×C42—151no—
475C2×C42—152no—
476C2×C42—152no—
477C2×C42—152no—
478C2×C42—152no—
479#95—51no—
480#95—52no—
481#95—51no—
482#95—152no—
483#95—151no—
484#95—152no—
485#95—151no—
486C2×C3×C5—22no—
487C2×C3×C5C22×C4211yescharacteristic
488C2×C3×C5#51811yescharacteristic
489C2×C3×C5#52011yescharacteristic
490D15—22no—
491C3×D5—22no—
492C3×D5#51812yes—
493C3×D5#52012yes—
494C5×D3—22no—
495C23×C3—51no—
496C23×C3—54no—
497C23×C3—51no—
498C23×C3—102no—
499C23×C3—101no—
500C23×C3—101no—
501C23×C3C22×AGL(1,𝔽5)11yescharacteristic
502C22×D3—51no—
503C22×D3—54no—
504C22×D3—102no—
505C22×D3—101no—
506C22×D3—101no—
507C22×D3C22×AGL(1,𝔽5)11yescharacteristic
508C2×C3×C4—41no—
509C2×C3×C4—54no—
510C2×C3×C4—54no—
511C2×C3×C4—51no—
512C2×C3×C4—51no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—102no—
516C2×C3×C4—102no—
517C2×C3×C4—102no—
518C2×C3×C4—102no—
519C2×C3×C4—201no—
520C2×C3×C4—201no—
521C2×C3×C4—201no—
522C2×C3×C4—208no—
523C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
524C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
525#67—54no—
526#67—54no—
527#67—54no—
528#67C4×AGL(1,𝔽5)14yescomplemented
529C2×Dic3—51no—
530C2×Dic3—54no—
531C2×Dic3—54no—
532C2×Dic3—54no—
533C2×Dic3—51no—
534C2×Dic3—51no—
535C2×Dic3—101no—
536C2×Dic3—102no—
537C2×Dic3—101no—
538C2×Dic3—102no—
539C2×Dic3—102no—
540C2×Dic3—102no—
541C2×Dic3—102no—
542C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
543C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
544C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
545C4×D3—41no—
546C4×D3—201no—
547C4×D3—201no—
548C4×D3—201no—
549C4×D3—208no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—32no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5C42×D312yes—
556C22×C5C22×C4×D311yescharacteristic
557C2×D5—21no—
558C2×D5—21no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—32no—
562C2×D5—61no—
563C2×D5—61no—
564C2×D5—64no—
565C2×D5—64no—
566C2×D5C42×D312yes—
567C2×D5C22×C4×D312yes—
568C2×D5#100411yescharacteristic
569C2×D5#100412yes—
570C2×D5#100711yescharacteristic
571AGL(1,𝔽5)—24no—
572AGL(1,𝔽5)—24no—
573AGL(1,𝔽5)—64no—
574AGL(1,𝔽5)—64no—
575C4×C5—21no—
576C4×C5—21no—
577C4×C5—32no—
578C4×C5—61no—
579C4×C5—61no—
580Dic5—21no—
581Dic5—21no—
582Dic5—32no—
583Dic5—61no—
584Dic5—61no—
585C24—51no—
586C24—151no—
587C2×D4—31no—
588C2×D4—151no—
589C2×D4—158no—
590C2×D4—151no—
591C2×D4—151no—
592C22×C4—31no—
593C22×C4—52no—
594C22×C4—52no—
595C22×C4—58no—
596C22×C4—51no—
597C22×C4—51no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—51no—
601C22×C4—151no—
602C22×C4—151no—
603C22×C4—151no—
604C22×C4—151no—
605C22×C4—151no—
606C22×C4—158no—
607C22×C4—152no—
608C22×C4—152no—
609C22×C4—151no—
610C22×C4—202no—
611C22×C4—202no—
612C22×C4—202no—
613C22×C4—602no—
614C22×C4—602no—
615C22×C4—602no—
616C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
617C4⋊C4—31no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—158no—
621C4⋊C4—151no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—151no—
625C22⋊C4—151no—
626C22⋊C4—151no—
627C22⋊C4—151no—
628C22⋊C4—158no—
629C22⋊C4—158no—
630C22⋊C4—151no—
631C22⋊C4—151no—
632C42—31no—
633C42—151no—
634C42—151no—
635C42—158no—
636C42—151no—
637C42—602no—
638C42—602no—
639C42—602no—
640C3×C5#227511yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—52no—
644C22×C3—52no—
645C22×C3—51no—
646C22×C3—51no—
647C22×C3—52no—
648C22×C3—104no—
649C22×C3—104no—
650C22×C3—101no—
651C22×C3—101no—
652C22×C3C2×C4×AGL(1,𝔽5)12yes—
653C22×C3C23×AGL(1,𝔽5)11yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—52no—
657C2×D3—104no—
658C2×D3—104no—
659C2×D3—101no—
660C2×D3—101no—
661C2×D3C2×C4×AGL(1,𝔽5)12yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—104no—
665C3×C4—104no—
666C3×C4—101no—
667C3×C4—101no—
668Dic3—21no—
669Dic3—21no—
670Dic3—52no—
671Dic3—104no—
672Dic3—104no—
673Dic3—101no—
674Dic3—101no—
675Dic3C2×C4×AGL(1,𝔽5)12yes—
676C2×C5—22no—
677C2×C5—62no—
678C2×C5C2×C42×D311yescharacteristic
679C2×C5#548611yescharacteristic
680C2×C5#550411yescharacteristic
681D5—22no—
682D5—62no—
683D5#548612yes—
684D5#550412yes—
685C23—31no—
686C23—51no—
687C23—54no—
688C23—51no—
689C23—101no—
690C23—102no—
691C23—101no—
692C23—154no—
693C23—151no—
694C23—301no—
695C23—302no—
696C23—301no—
697C23C2×D3×AGL(1,𝔽5)11yescharacteristic
698D4—34no—
699D4—154no—
700D4—154no—
701D4—154no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—41no—
706C2×C4—54no—
707C2×C4—54no—
708C2×C4—51no—
709C2×C4—51no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—121no—
717C2×C4—154no—
718C2×C4—151no—
719C2×C4—154no—
720C2×C4—154no—
721C2×C4—151no—
722C2×C4—151no—
723C2×C4—201no—
724C2×C4—201no—
725C2×C4—201no—
726C2×C4—208no—
727C2×C4—301no—
728C2×C4—302no—
729C2×C4—301no—
730C2×C4—302no—
731C2×C4—302no—
732C2×C4—302no—
733C2×C4—302no—
734C2×C4—601no—
735C2×C4—601no—
736C2×C4—601no—
737C2×C4—608no—
738C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
739C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
740C2×C3—22no—
741C2×C3—52no—
742C2×C3—52no—
743C2×C3—102no—
744C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
745C2×C3#6625811yescharacteristic
746C2×C3#6626611yescharacteristic
747D3—22no—
748D3—102no—
749C5#7332211yescharacteristic, complemented, Sylow
750C22—21no—
751C22—21no—
752C22—32no—
753C22—52no—
754C22—51no—
755C22—51no—
756C22—52no—
757C22—52no—
758C22—61no—
759C22—61no—
760C22—104no—
761C22—104no—
762C22—101no—
763C22—101no—
764C22—152no—
765C22—304no—
766C22—304no—
767C22—301no—
768C22—301no—
769C22C4×D3×AGL(1,𝔽5)12yes—
770C22C22×D3×AGL(1,𝔽5)11yescharacteristic
771C4—21no—
772C4—21no—
773C4—32no—
774C4—61no—
775C4—61no—
776C4—104no—
777C4—104no—
778C4—101no—
779C4—101no—
780C4—152no—
781C4—304no—
782C4—304no—
783C4—301no—
784C4—301no—
785C3#1061717211yescharacteristic, complemented, Sylow
786C2—22no—
787C2—52no—
788C2—52no—
789C2—62no—
790C2—102no—
791C2—302no—
792C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
793C2#1175683611yescharacteristic
794C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2275
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C4×#6763C2semidirect
4. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
5. AGL(1,𝔽5)×#217C2semidirect
6. #11751931C2semidirect
7. D3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
8. #11751848C2semidirect
9. #11751834C2semidirect
10. #11751833C2semidirect
11. #11751832C2semidirect
20. AGL(1,𝔽5)×#67C4semidirect
26. C4×#1220C4semidirect
27. C4×C5×#67C4semidirect
28. #91552C4semidirect
29. Dic5×#67C4semidirect
32. #91444C4semidirect
33. C4×#1202C4semidirect
34. #91440C4semidirect
35. C4×#1201C4semidirect
51. C2×(C2×AGL(1,𝔽5))⋊C4D3semidirect
63. C22×C3×AGL(1,𝔽5)C2×C4semidirect
68. C2×D3×AGL(1,𝔽5)C2×C4semidirect
69. C22×C3×C4×C5C2×C4semidirect
71. C2×C4×D15C2×C4semidirect
73. C2×C4×C5×D3C2×C4semidirect
74. C22×C3×Dic5C2×C4semidirect
76. C2×C3×C4×D5C2×C4semidirect
77. C2×C3×C4×D5C2×C4semidirect
83. C2×#1200C2×C4semidirect
84. C2×D3×Dic5C2×C4semidirect
89. #6763C2×C4semidirect
91. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
92. (C2×D3)⋊AGL(1,𝔽5)C2×C4semidirect
95. Dic3×AGL(1,𝔽5)C2×C4semidirect
96. #6719C2×C4semidirect
97. #6714C2×C4semidirect
98. #6712C2×C4semidirect
99. C4×Dic15C2×C4semidirect
100. C5×#217C2×C4semidirect
101. C5×(C2×D3)⋊C4C2×C4semidirect
102. C5×Dic3⋊C4C2×C4semidirect
103. C4×C5×Dic3C2×C4semidirect
104. Dic3⋊Dic5C2×C4semidirect
105. #6669C2×C4semidirect
106. #6667C2×C4semidirect
107. (C2×D3)⋊Dic5C2×C4semidirect
108. #6665C2×C4semidirect
109. #6665C2×C4semidirect
110. Dic3×Dic5C2×C4semidirect
111. Dic3×Dic5C2×C4semidirect
186. #1220C42semidirect
191. C5×#67C42semidirect
203. #1202C42semidirect
204. #1201C42semidirect
226. C4×#67AGL(1,𝔽5)semidirect
252. C22×AGL(1,𝔽5)C4×D3semidirect
257. C22×C4×C5C4×D3semidirect
261. C22×Dic5C4×D3semidirect
271. C2×C4×D5C4×D3semidirect
272. C2×C4×D5C4×D3semidirect
357. C22×C3×C4C2×AGL(1,𝔽5)semidirect
375. C2×C4×D3C2×AGL(1,𝔽5)semidirect
380. #217C2×AGL(1,𝔽5)semidirect
385. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
390. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
398. C4×Dic3C2×AGL(1,𝔽5)semidirect
528. #67C4×AGL(1,𝔽5)semidirect
616. C22×C4D3×AGL(1,𝔽5)semidirect
640. C3×C5#2275semidirect
749. C5#73322semidirect
785. C3#10617172semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,𝔽5)×#672
C4×D5×#672
C4×#67632
C2×C3×(C2×AGL(1,𝔽5))⋊C42
AGL(1,𝔽5)×#2172
#117519312
D3×(C2×AGL(1,𝔽5))⋊C42
#117518482
#117518342
#117518332
#117518322
#106171723
#733225