Finite Group Databasebeta

← C4×#91907 #14319542

Subgroups — C4×#91907 #14319542

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91907C212yesmaximal
2C42×D3×D5C211yesmaximal, characteristic
3C4×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5#11751848C212yesmaximal
6C4×(C2×D3)⋊AGL(1,𝔽5)C212yesmaximal
7Dic3×C4⋊AGL(1,𝔽5)C212yesmaximal, complemented
8#11751832C212yesmaximal, complemented
9C4×Dic3×AGL(1,𝔽5)C212yesmaximal, complemented
10C4×#4130—31nomaximal, Hall
11C2×C4×D3×D5C2211yescharacteristic
12C2×C4×D3×D5C2211yescharacteristic
13C2×C4×D3×D5C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2212yes—
15C2×C4×ΓL(1,𝔽16)C2212yes—
16C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
17C2×C3×C4×AGL(1,𝔽5)C2212yes—
18C2×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
19C2×Dic3×AGL(1,𝔽5)C2214yes—
20C2×Dic3×AGL(1,𝔽5)C2214yes—
21#91907C4116yesdirect product factor
22C42×D15C411yescharacteristic, complemented
23C42×C5×D3C411yescharacteristic, complemented
24C3×C42×D5C2211yescharacteristic
25C4×#1200C411yescharacteristic, complemented
26C4×#1200C411yescharacteristic, complemented
27C4×#1200C411yescharacteristic, complemented
28C4×D3×Dic5C411yescharacteristic, complemented
29C4×D3×Dic5C411yescharacteristic, complemented
30C4×D3×Dic5C411yescharacteristic, complemented
31C4×D5×Dic3C2211yescharacteristic
32C4×D5×Dic3C2211yescharacteristic
33C4×D5×Dic3C2211yescharacteristic
34#91235C2212yes—
35C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
36(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
37C4×#892—51nomaximal, Hall
38C2×#4130—32no—
39C2×C42×D5—31no—
40C4×C22⋊AGL(1,𝔽5)—32no—
41C4×C22⋊AGL(1,𝔽5)—32no—
42C4×C4⋊AGL(1,𝔽5)—31no—
43C4×C4⋊AGL(1,𝔽5)—32no—
44C4×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
45#65686—32no—
46C42×AGL(1,𝔽5)—32no—
47C22×D3×D5C2311yescharacteristic
48C22×ΓL(1,𝔽16)C2314yes—
49C22×C3×AGL(1,𝔽5)C2314yes—
50C2×C4×D15C2×C411yescharacteristic
51C2×C4×D15C2×C411yescharacteristic
52C2×C4×D15C2×C411yescharacteristic
53C2×C4×C5×D3C2×C411yescharacteristic
54C2×C4×C5×D3C2×C411yescharacteristic
55C2×C4×C5×D3C2×C411yescharacteristic
56C2×C3×C4×D5C2311yescharacteristic
57C2×C3×C4×D5C2311yescharacteristic
58C2×C3×C4×D5C2311yescharacteristic
59C2×#1200C2×C411yescharacteristic
60C2×#1200C2×C411yescharacteristic
61C2×#1200C2×C411yescharacteristic
62C2×D3×Dic5C2×C411yescharacteristic
63C2×D3×Dic5C2×C411yescharacteristic
64C2×D3×Dic5C2×C411yescharacteristic
65C2×D5×Dic3C2311yescharacteristic
66C2×D5×Dic3C2311yescharacteristic
67C2×D5×Dic3C2311yescharacteristic
68C4×D3×D5—22no—
69C4×D3×D5—22no—
70C4×D3×D5—24no—
71C4×D3×D5C2×C418yes—
72C4⋊ΓL(1,𝔽16)C2×C418yescomplemented
73C4×ΓL(1,𝔽16)—24no—
74C3×C4⋊AGL(1,𝔽5)C2×C418yescomplemented
75C3×C4×AGL(1,𝔽5)—24no—
76(C2×D3)⋊AGL(1,𝔽5)C2×C4116yes—
77Dic3×AGL(1,𝔽5)—28no—
78Dic3×AGL(1,𝔽5)C2×C4116yescomplemented
79C3×C42×C5C2×C411yescharacteristic
80C4×Dic15C2×C411yescharacteristic
81C4×Dic15C2×C411yescharacteristic
82C4×Dic15C2×C411yescharacteristic
83C4×C5×Dic3C2×C411yescharacteristic
84C4×C5×Dic3C2×C411yescharacteristic
85C4×C5×Dic3C2×C411yescharacteristic
86C3×C4×Dic5C2×C411yescharacteristic
87C3×C4×Dic5C2×C411yescharacteristic
88C3×C4×Dic5C2×C411yescharacteristic
89Dic3×Dic5C2×C411yescharacteristic
90Dic3×Dic5C2×C411yescharacteristic
91Dic3×Dic5C2×C411yescharacteristic
92Dic3×Dic5C2×C411yescharacteristic
93Dic3×Dic5C2×C411yescharacteristic
94Dic3×Dic5C2×C411yescharacteristic
95C2×#892—52no—
96C2×C42×D3—51no—
97C3×C4×C4⋊C4—51no—
98Dic3×C4⋊C4—52no—
99C4×(C2×D3)⋊C4—52no—
100C4×C4⋊Dic3—51no—
101C42×Dic3—52no—
102#4666—52no—
103#4648—52no—
104C22×C4×D5—31no—
105C22×C4×D5—31no—
106C22×C4×D5—31no—
107C2×C22⋊AGL(1,𝔽5)—34no—
108#4130—316no—
109C2×C4⋊AGL(1,𝔽5)—32no—
110C2×C4⋊AGL(1,𝔽5)C2×D312yes—
111C2×C4×AGL(1,𝔽5)—34no—
112C2×C4×AGL(1,𝔽5)—34no—
113C2×C4×AGL(1,𝔽5)—32no—
114C2×C4×AGL(1,𝔽5)C2×D312yes—
115C2×C42×C5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—31no—
119C42×D5—31no—
120C42×D5—31no—
121C42×D5—31no—
122C42×D5—31no—
123C42×D5—31no—
124C42×D5—31no—
125C42×D5—31no—
126C42×D5C2×D311yescharacteristic
127(C2×AGL(1,𝔽5))⋊C4—34no—
128(C2×AGL(1,𝔽5))⋊C4—32no—
129(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
130C4×#117—151noSylow
131C22×D15C22×C411yescharacteristic
132C22×C5×D3C22×C411yescharacteristic
133C22×C3×D5C2411yescharacteristic
134C2×D3×D5—21no—
135C2×D3×D5—21no—
136C2×D3×D5—22no—
137C2×D3×D5C22×C414yes—
138C2×ΓL(1,𝔽16)—24no—
139C2×ΓL(1,𝔽16)—24no—
140C2×ΓL(1,𝔽16)C22×C418yes—
141C2×C3×AGL(1,𝔽5)—24no—
142C2×C3×AGL(1,𝔽5)—24no—
143C2×C3×AGL(1,𝔽5)C22×C418yes—
144C2×C3×C4×C5C22×C411yescharacteristic
145C2×C3×C4×C5C22×C411yescharacteristic
146C2×C3×C4×C5C22×C411yescharacteristic
147C2×Dic15C22×C411yescharacteristic
148C2×Dic15C22×C411yescharacteristic
149C2×Dic15C22×C411yescharacteristic
150C4×D15—22no—
151C4×D15—22no—
152C4×D15C4214yescomplemented
153C2×C5×Dic3C22×C411yescharacteristic
154C2×C5×Dic3C22×C411yescharacteristic
155C2×C5×Dic3C22×C411yescharacteristic
156C4×C5×D3—22no—
157C4×C5×D3—22no—
158C4×C5×D3C4214yescomplemented
159C2×C3×Dic5C22×C411yescharacteristic
160C2×C3×Dic5C22×C411yescharacteristic
161C2×C3×Dic5C22×C411yescharacteristic
162C3×C4×D5—22no—
163C3×C4×D5C22×C414yes—
164C3×C4×D5#4112yes—
165C3×C4×D5#4112yes—
166#1200—22no—
167#1200—22no—
168#1200C4214yescomplemented
169D3×Dic5—22no—
170D3×Dic5—22no—
171D3×Dic5C4214yescomplemented
172D5×Dic3—21no—
173D5×Dic3—21no—
174D5×Dic3C22×C414yes—
175D5×Dic3#4114yes—
176C22×C4×D3—51no—
177C22×C4×D3—51no—
178C22×C4×D3—51no—
179C2×C3×C4⋊C4—52no—
180C2×C3×C42—51no—
181C2×C3×C42—52no—
182C2×(C2×D3)⋊C4—54no—
183C2×C4⋊Dic3—52no—
184C2×C4×Dic3—54no—
185C2×C4×Dic3—51no—
186C2×C4×Dic3—51no—
187C2×C4×Dic3—51no—
188C2×C4×Dic3—54no—
189C2×C4×Dic3—52no—
190#892—516no—
191C42×D3—51no—
192C42×D3—51no—
193C42×D3—51no—
194C42×D3—51no—
195C42×D3—51no—
196C42×D3—51no—
197C42×D3—51no—
198C42×D3AGL(1,𝔽5)11yescharacteristic, complemented
199C3×#95—52no—
200C3⋊#95—54no—
201C3⋊#95—52no—
202C23×D5—31no—
203C22×AGL(1,𝔽5)—34no—
204C22×AGL(1,𝔽5)C22×D314yes—
205C22×C4×C5—31no—
206C22×C4×C5—31no—
207C22×C4×C5—31no—
208C22×Dic5—31no—
209C22×Dic5—31no—
210C22×Dic5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—31no—
214C2×C4×D5—31no—
215C2×C4×D5—38no—
216C2×C4×D5—31no—
217C2×C4×D5—31no—
218C2×C4×D5—31no—
219C2×C4×D5—31no—
220C2×C4×D5—31no—
221C2×C4×D5—64no—
222C2×C4×D5—62no—
223C2×C4×D5—62no—
224C2×C4×D5C22×D311yescharacteristic
225C2×C4×D5C22×D311yescharacteristic
226C2×C4×D5C22×D311yescharacteristic
227C22⋊AGL(1,𝔽5)—316no—
228C4⋊AGL(1,𝔽5)—38no—
229C4⋊AGL(1,𝔽5)C4×D318yescomplemented
230C4×AGL(1,𝔽5)—24no—
231C4×AGL(1,𝔽5)—316no—
232C4×AGL(1,𝔽5)—68no—
233C4×AGL(1,𝔽5)—64no—
234C42×C5—31no—
235C42×C5—31no—
236C42×C5—31no—
237C42×C5C4×D311yescharacteristic
238C4×Dic5—31no—
239C4×Dic5—31no—
240C4×Dic5—31no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245C4×Dic5—31no—
246C4×Dic5—31no—
247C4×Dic5C4×D311yescharacteristic
248C4×Dic5C4×D311yescharacteristic
249C4×Dic5C4×D311yescharacteristic
250C2×#117—152no—
251C22×C42—151no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—151no—
254C4×C4⋊C4—152no—
255C4×C22⋊C4—152no—
256C4×C22⋊C4—152no—
257#376—152no—
258C43—152no—
259C22×C3×C5C23×C411yescharacteristic
260C2×D15—21no—
261C2×D15—21no—
262C2×D15C2×C4212yes—
263C2×C5×D3—21no—
264C2×C5×D3—21no—
265C2×C5×D3C2×C4212yes—
266C2×C3×D5C23×C412yes—
267C2×C3×D5C2×#4111yescharacteristic
268C2×C3×D5C2×#4111yescharacteristic
269C2×C3×D5C2×#4112yes—
270D3×D5—24no—
271D3×D5—24no—
272ΓL(1,𝔽16)—28no—
273C3×AGL(1,𝔽5)—28no—
274C3×C4×C5—21no—
275C3×C4×C5C2×C4212yes—
276C3×C4×C5#11712yescomplemented
277Dic15—21no—
278Dic15C2×C4212yes—
279Dic15#11712yescomplemented
280C3×Dic5—21no—
281C3×Dic5C2×C4212yes—
282C3×Dic5#11712yescomplemented
283C5×Dic3—21no—
284C5×Dic3C2×C4212yes—
285C5×Dic3#11712yescomplemented
286C23×D3—51no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—54no—
290C22×C3×C4—51no—
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3—54no—
294C22×Dic3—51no—
295C2×C4×D3—51no—
296C2×C4×D3—51no—
297C2×C4×D3—51no—
298C2×C4×D3—58no—
299C2×C4×D3—51no—
300C2×C4×D3—51no—
301C2×C4×D3—51no—
302C2×C4×D3—51no—
303C2×C4×D3—51no—
304C2×C4×D3—51no—
305C2×C4×D3—104no—
306C2×C4×D3—102no—
307C2×C4×D3—102no—
308C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
309C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
310C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
311C3×C4⋊C4—58no—
312C3×C42—51no—
313C3×C42—51no—
314C3×C42—51no—
315C3×C42—104no—
316C3×C42C2×AGL(1,𝔽5)11yescharacteristic
317(C2×D3)⋊C4—516no—
318C4⋊Dic3—58no—
319C4×Dic3—516no—
320C4×Dic3—51no—
321C4×Dic3—51no—
322C4×Dic3—51no—
323C4×Dic3—51no—
324C4×Dic3—51no—
325C4×Dic3—51no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328C4×Dic3—51no—
329C4×Dic3—108no—
330C4×Dic3—104no—
331C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
332C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
333C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
334C23×C5—31no—
335C22×D5—31no—
336C22×D5—34no—
337C22×D5—61no—
338C22×D5—61no—
339C22×D5—62no—
340C22×D5C23×D311yescharacteristic
341C2×AGL(1,𝔽5)—24no—
342C2×AGL(1,𝔽5)—24no—
343C2×AGL(1,𝔽5)—38no—
344C2×AGL(1,𝔽5)—64no—
345C2×AGL(1,𝔽5)—64no—
346C2×AGL(1,𝔽5)C2×C4×D318yes—
347C2×C4×C5—31no—
348C2×C4×C5—31no—
349C2×C4×C5—34no—
350C2×C4×C5—31no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5C2×C4×D311yescharacteristic
354C2×C4×C5C2×C4×D311yescharacteristic
355C2×C4×C5C2×C4×D311yescharacteristic
356C2×Dic5—31no—
357C2×Dic5—31no—
358C2×Dic5—34no—
359C2×Dic5—31no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5C2×C4×D311yescharacteristic
363C2×Dic5C2×C4×D311yescharacteristic
364C2×Dic5C2×C4×D311yescharacteristic
365C4×D5—22no—
366C4×D5—34no—
367C4×D5—34no—
368C4×D5—34no—
369C4×D5—34no—
370C4×D5—62no—
371C4×D5—62no—
372C4×D5—61no—
373C4×D5—61no—
374C4×D5—62no—
375C4×D5—62no—
376C4×D5C2×C4×D314yes—
377C4×D5#23712yes—
378C4×D5#23912yes—
379C23×C4—151no—
380C23×C4—151no—
381C23×C4—151no—
382#117—1516no—
383C2×C4⋊C4—52no—
384C2×C4⋊C4—152no—
385C2×C22⋊C4—154no—
386C2×C42—31no—
387C2×C42—51no—
388C2×C42—52no—
389C2×C42—151no—
390C2×C42—151no—
391C2×C42—151no—
392C2×C42—151no—
393C2×C42—151no—
394C2×C42—151no—
395C2×C42—151no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—154no—
399C2×C42—151no—
400C2×C42—152no—
401C2×C42—154no—
402#95—52no—
403#95—154no—
404#95—152no—
405C2×C3×C5C22×C4211yescharacteristic
406C2×C3×C5C2×#11711yescharacteristic
407C2×C3×C5C2×#11711yescharacteristic
408D15—22no—
409C3×D5C4×#4112yes—
410C3×D5C4×#4112yes—
411C5×D3—22no—
412C23×C3—51no—
413C22×D3—51no—
414C22×D3—54no—
415C22×D3—102no—
416C22×D3—101no—
417C22×D3—101no—
418C22×D3C22×AGL(1,𝔽5)11yescharacteristic
419C2×C3×C4—51no—
420C2×C3×C4—51no—
421C2×C3×C4—54no—
422C2×C3×C4—52no—
423C2×C3×C4—52no—
424C2×C3×C4—58no—
425C2×C3×C4—51no—
426C2×C3×C4—102no—
427C2×C3×C4—104no—
428C2×C3×C4—104no—
429C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
430C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
431C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
432C2×Dic3—51no—
433C2×Dic3—51no—
434C2×Dic3—54no—
435C2×Dic3—54no—
436C2×Dic3—58no—
437C2×Dic3—51no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3—104no—
441C2×Dic3—104no—
442C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
443C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
444C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
445C4×D3—22no—
446C4×D3—22no—
447C4×D3—54no—
448C4×D3—54no—
449C4×D3—54no—
450C4×D3—102no—
451C4×D3—102no—
452C4×D3—102no—
453C4×D3—102no—
454C4×D3—102no—
455C4×D3—102no—
456C4×D3C4×AGL(1,𝔽5)14yescomplemented
457C22×C5—32no—
458C22×C5—61no—
459C22×C5—61no—
460C22×C5C22×C4×D311yescharacteristic
461C2×D5—32no—
462C2×D5—61no—
463C2×D5—61no—
464C2×D5—64no—
465C2×D5—64no—
466C2×D5C22×C4×D312yes—
467C2×D5C2×#23711yescharacteristic
468C2×D5C2×#23911yescharacteristic
469C2×D5D3×#4112yes—
470AGL(1,𝔽5)—28no—
471AGL(1,𝔽5)—68no—
472C4×C5—21no—
473C4×C5—32no—
474C4×C5—32no—
475C4×C5—61no—
476C4×C5C42×D312yes—
477C4×C5#89212yescomplemented
478Dic5—21no—
479Dic5—32no—
480Dic5—32no—
481Dic5—61no—
482Dic5C42×D312yes—
483Dic5#89212yescomplemented
484C24—151no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—51no—
489C22×C4—51no—
490C22×C4—54no—
491C22×C4—51no—
492C22×C4—151no—
493C22×C4—158no—
494C22×C4—151no—
495C22×C4—151no—
496C22×C4—151no—
497C22×C4—151no—
498C22×C4—151no—
499C22×C4—151no—
500C22×C4—151no—
501C22×C4—151no—
502C22×C4—151no—
503C22×C4—154no—
504C22×C4—151no—
505C22×C4—151no—
506C22×C4—302no—
507C22×C4—302no—
508C22×C4—304no—
509C4⋊C4—58no—
510C4⋊C4—158no—
511C22⋊C4—1516no—
512C42—31no—
513C42—31no—
514C42—31no—
515C42—51no—
516C42—51no—
517C42—51no—
518C42—104no—
519C42—151no—
520C42—151no—
521C42—151no—
522C42—151no—
523C42—151no—
524C42—151no—
525C42—1516no—
526C42—151no—
527C42—151no—
528C42—151no—
529C42—304no—
530C42—308no—
531C42D3×AGL(1,𝔽5)11yescharacteristic
532C3×C5C4×#11711yescharacteristic, complemented, Hall
533C22×C3—52no—
534C22×C3—52no—
535C22×C3—51no—
536C22×C3—51no—
537C22×C3C23×AGL(1,𝔽5)11yescharacteristic
538C2×D3—21no—
539C2×D3—21no—
540C2×D3—52no—
541C2×D3—104no—
542C2×D3—104no—
543C2×D3—101no—
544C2×D3—101no—
545C2×D3C2×C4×AGL(1,𝔽5)12yes—
546C3×C4—21no—
547C3×C4—52no—
548C3×C4—52no—
549C3×C4—108no—
550C3×C4—101no—
551C3×C4C2×C4×AGL(1,𝔽5)12yes—
552C3×C4#413012yescomplemented
553Dic3—21no—
554Dic3—52no—
555Dic3—52no—
556Dic3—108no—
557Dic3—101no—
558Dic3C2×C4×AGL(1,𝔽5)12yes—
559Dic3#413012yescomplemented
560C2×C5—62no—
561C2×C5C2×C42×D311yescharacteristic
562C2×C5C2×#89211yescharacteristic
563C2×C5D3×#11711yescharacteristic
564D5—62no—
565D5C4×#23712yes—
566D5C4×#23912yes—
567C23—31no—
568C23—51no—
569C23—154no—
570C23—151no—
571C23—301no—
572C23—301no—
573C23—302no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—34no—
577C2×C4—31no—
578C2×C4—51no—
579C2×C4—51no—
580C2×C4—52no—
581C2×C4—52no—
582C2×C4—54no—
583C2×C4—58no—
584C2×C4—51no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—102no—
588C2×C4—104no—
589C2×C4—104no—
590C2×C4—154no—
591C2×C4—154no—
592C2×C4—154no—
593C2×C4—154no—
594C2×C4—151no—
595C2×C4—151no—
596C2×C4—154no—
597C2×C4—158no—
598C2×C4—151no—
599C2×C4—302no—
600C2×C4—302no—
601C2×C4—302no—
602C2×C4—302no—
603C2×C4—301no—
604C2×C4—301no—
605C2×C4—302no—
606C2×C4—304no—
607C2×C4—304no—
608C2×C4—302no—
609C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
610C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
611C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
612C2×C3—52no—
613C2×C3—52no—
614C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
615C2×C3C2×#413011yescharacteristic
616C2×C3C2×#413011yescharacteristic
617D3—22no—
618D3—102no—
619C5C4×#89211yescharacteristic, complemented, Sylow
620C22—32no—
621C22—51no—
622C22—51no—
623C22—52no—
624C22—52no—
625C22—61no—
626C22—61no—
627C22—152no—
628C22—304no—
629C22—304no—
630C22—301no—
631C22—301no—
632C22C22×D3×AGL(1,𝔽5)11yescharacteristic
633C4—21no—
634C4—32no—
635C4—32no—
636C4—52no—
637C4—52no—
638C4—61no—
639C4—108no—
640C4—101no—
641C4—152no—
642C4—152no—
643C4—308no—
644C4—301no—
645C4#9190712yesdirect product factor
646C4C4×D3×AGL(1,𝔽5)12yes—
647C3C4×#413011yescharacteristic, complemented, Sylow
648C2—52no—
649C2—52no—
650C2—62no—
651C2—302no—
652C2C2×#9190711yescharacteristic
653C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
654C2D3×#413011yescharacteristic
subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊ΓL(1,𝔽16)C2semidirect
4. C3×C4×C4⋊AGL(1,𝔽5)C2semidirect
7. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
8. #11751832C2semidirect
9. C4×Dic3×AGL(1,𝔽5)C2semidirect
21. #91907C4direct (N × H)
22. C42×D15C4semidirect
23. C42×C5×D3C4semidirect
25. C4×#1200C4semidirect
26. C4×#1200C4semidirect
27. C4×#1200C4semidirect
28. C4×D3×Dic5C4semidirect
29. C4×D3×Dic5C4semidirect
30. C4×D3×Dic5C4semidirect
44. C4×C4⋊AGL(1,𝔽5)D3semidirect
72. C4⋊ΓL(1,𝔽16)C2×C4semidirect
74. C3×C4⋊AGL(1,𝔽5)C2×C4semidirect
78. Dic3×AGL(1,𝔽5)C2×C4semidirect
152. C4×D15C42semidirect
158. C4×C5×D3C42semidirect
168. #1200C42semidirect
171. D3×Dic5C42semidirect
198. C42×D3AGL(1,𝔽5)semidirect
229. C4⋊AGL(1,𝔽5)C4×D3semidirect
276. C3×C4×C5#117semidirect
279. Dic15#117semidirect
282. C3×Dic5#117semidirect
285. C5×Dic3#117semidirect
456. C4×D3C4×AGL(1,𝔽5)semidirect
477. C4×C5#892semidirect
483. Dic5#892semidirect
532. C3×C5C4×#117semidirect
552. C3×C4#4130semidirect
559. Dic3#4130semidirect
619. C5C4×#892semidirect
645. C4#91907direct (N × H)
647. C3C4×#4130semidirect

Maximal subgroups

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

subgroupindex
C2×#919072
C42×D3×D52
C4×C4⋊ΓL(1,𝔽16)2
C3×C4×C4⋊AGL(1,𝔽5)2
#117518482
C4×(C2×D3)⋊AGL(1,𝔽5)2
Dic3×C4⋊AGL(1,𝔽5)2
#117518322
C4×Dic3×AGL(1,𝔽5)2
C4×#41303
C4×#8925