Finite Group Databasebeta

← C3×#11752022 #72230038

Subgroups — C3×#11752022 #72230038

Order 2880.

1380 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×C3×D5×#67C211yesmaximal, characteristic
3C2×C3×#6763C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊AGL(1,𝔽5)C212yesmaximal, complemented
5C3×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal, complemented
6C3×#65779—31nomaximal
7#11752022C311yesmaximal, characteristic, direct product factor
8C23×C32×D5C2211yescharacteristic
9C22×C3×D3×D5C2211yescharacteristic
10C22×C3×ΓL(1,𝔽16)C2212yes—
11C22×C32×AGL(1,𝔽5)—22no—
12C22×C32×AGL(1,𝔽5)—24no—
13C22×C32×AGL(1,𝔽5)C2212yes—
14C2×C3×#1220C411yescharacteristic, complemented
15C2×C3×C5×#67C411yescharacteristic, complemented
16C3×D5×#67—22no—
17C3×D5×#67—22no—
18C2×C3×#1202C411yescharacteristic, complemented
19C2×C3×#1201C411yescharacteristic, complemented
20C2×C3×D5×Dic3C2211yescharacteristic
21C3×#6763—22no—
22C3×(C2×D3)⋊AGL(1,𝔽5)—24no—
23C3×#5213—51nomaximal, Hall
24C23×C3×AGL(1,𝔽5)—21no—
25C23×C3×AGL(1,𝔽5)D311yescharacteristic, complemented
26C23×C3×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
27C2×C3×D4×D5—31no—
28C2×D5×#67C2×C311yescharacteristic
29C2×#6763C2×C311yescharacteristic, complemented
30C2×C3×C22⋊AGL(1,𝔽5)—31no—
31C2×C3×C22⋊AGL(1,𝔽5)—32no—
32C2×(C2×D3)⋊AGL(1,𝔽5)C2×C312yescomplemented
33C3×(C2×AGL(1,𝔽5))⋊C4—32no—
34(C2×AGL(1,𝔽5))⋊Dic3C2×C312yescomplemented
35C23×C32×C5C2×C411yescharacteristic
36C22×C3×D15C2×C411yescharacteristic, complemented
37C22×C3×C5×D3C2×C411yescharacteristic, complemented
38C22×C32×D5—22no—
39C22×C32×D5—22no—
40C22×C32×D5C2×C411yescharacteristic
41C22×C32×D5D412yes—
42C22×C32×D5D412yes—
43C22×C32×D5C2311yescharacteristic
44C2×C3×D3×D5—21no—
45C2×C3×D3×D5—21no—
46C2×C3×D3×D5—22no—
47C2×C3×D3×D5—22no—
48C2×C3×ΓL(1,𝔽16)—22no—
49C2×C3×ΓL(1,𝔽16)—22no—
50C2×C3×ΓL(1,𝔽16)—22no—
51C2×C32×AGL(1,𝔽5)—28no—
52C2×C32×AGL(1,𝔽5)—22no—
53C2×C32×AGL(1,𝔽5)—22no—
54C2×C32×AGL(1,𝔽5)D414yescomplemented
55C3×#1220—22no—
56C2×C3×Dic15C2×C411yescharacteristic, complemented
57C3×C5×#67—22no—
58C2×C3×C5×Dic3C2×C411yescharacteristic, complemented
59C3×#1202—22no—
60C3×#1201—22no—
61C3×D5×Dic3—21no—
62C3×D5×Dic3—21no—
63#65779—31noHall
64C23×C32×C4—51no—
65C22×C3×#67—51no—
66C2×C3×#217—51no—
67C2×C3×(C2×D3)⋊C4—52no—
68C3×C3⋊#95—52no—
69C23×C3×D5—21no—
70C23×C3×D5—31no—
71C23×C3×D5C2×D311yescharacteristic
72C23×C3×D5C22×C311yescharacteristic
73C22×D3×D5C22×C311yescharacteristic
74C22×ΓL(1,𝔽16)C22×C312yes—
75C22×C3×AGL(1,𝔽5)—22no—
76C22×C3×AGL(1,𝔽5)—24no—
77C22×C3×AGL(1,𝔽5)—22no—
78C22×C3×AGL(1,𝔽5)—24no—
79C22×C3×AGL(1,𝔽5)—22no—
80C22×C3×AGL(1,𝔽5)—22no—
81C22×C3×AGL(1,𝔽5)—24no—
82C22×C3×AGL(1,𝔽5)—24no—
83C22×C3×AGL(1,𝔽5)—22no—
84C22×C3×AGL(1,𝔽5)—32no—
85C22×C3×AGL(1,𝔽5)C2×D312yes—
86C22×C3×AGL(1,𝔽5)C22×C312yes—
87C2×C3×C5×D4—31no—
88C2×#1220C3×C411yescharacteristic, complemented
89C2×C5×#67C3×C411yescharacteristic, complemented
90C2×C3×C22⋊D5—31no—
91C2×C3×C22⋊D5—31no—
92C3×D4×D5—62no—
93C3×D4×D5—62no—
94C2×C3×D20—31no—
95C2×C3×C4×D5—31no—
96D5×#67—22no—
97D5×#67—22no—
98C2×#1202C3×C411yescharacteristic, complemented
99C2×#1201C3×C411yescharacteristic, complemented
100C2×D5×Dic3C22×C311yescharacteristic
101#6763—22no—
102C3×C22⋊AGL(1,𝔽5)—62no—
103C3×C22⋊AGL(1,𝔽5)—64no—
104(C2×D3)⋊AGL(1,𝔽5)—24no—
105C3×#386—151no—
106#5213—51no—
107C22×C32×C5—22no—
108C22×C32×C5C22⋊C412yescomplemented
109C22×C32×C5C22×C411yescharacteristic
110C2×C3×D15—21no—
111C2×C3×D15—22no—
112C2×C3×C5×D3—21no—
113C2×C3×C5×D3—22no—
114C2×C32×D5—22no—
115C2×C32×D5—22no—
116C2×C32×D5—24no—
117C2×C32×D5—22no—
118C2×C32×D5C22⋊C412yescomplemented
119C2×C32×D5C2×D412yes—
120C2×C32×D5C2×D411yescharacteristic
121C2×C32×D5C2×D411yescharacteristic
122C2×C32×D5#4112yes—
123C3×D3×D5—41no—
124C3×D3×D5—42no—
125C3×D3×D5—41no—
126C3×ΓL(1,𝔽16)—42no—
127C32×AGL(1,𝔽5)—24no—
128C3×Dic15—21no—
129C3×C5×Dic3—21no—
130C23×AGL(1,𝔽5)C3×D311yescharacteristic, complemented
131C2×D4×D5—31no—
132C2×C22⋊AGL(1,𝔽5)—31no—
133C2×C22⋊AGL(1,𝔽5)—32no—
134(C2×AGL(1,𝔽5))⋊C4—32no—
135C24×C32—51no—
136C23×C3×D3—51no—
137C22×C32×C4—52no—
138C22×C32×C4—104no—
139C22×C32×C4—102no—
140C2×C3×#67—51no—
141C2×C3×#67—51no—
142C2×C3×#67—51no—
143C2×C3×#67—102no—
144C2×C3×#67—102no—
145C2×C3×#67AGL(1,𝔽5)11yescharacteristic, complemented
146C22×C3×Dic3—51no—
147C22×C3×Dic3—52no—
148C3×#217—102no—
149C3×(C2×D3)⋊C4—104no—
150C23×C3×C5—21no—
151C23×C3×C5—31no—
152C23×C3×C5C4×D311yescharacteristic
153C23×C3×C5C2×C3×C411yescharacteristic
154C22×D15C2×C3×C411yescharacteristic, complemented
155C22×C5×D3C2×C3×C411yescharacteristic, complemented
156C22×C3×D5—22no—
157C22×C3×D5—22no—
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5—21no—
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5—22no—
164C22×C3×D5—22no—
165C22×C3×D5—21no—
166C22×C3×D5—22no—
167C22×C3×D5—22no—
168C22×C3×D5—31no—
169C22×C3×D5—61no—
170C22×C3×D5—62no—
171C22×C3×D5—62no—
172C22×C3×D5—61no—
173C22×C3×D5C4×D311yescharacteristic
174C22×C3×D5D1212yes—
175C22×C3×D5#6712yes—
176C22×C3×D5C2×C3×C411yescharacteristic
177C22×C3×D5C3×D412yes—
178C22×C3×D5C3×D412yes—
179C22×C3×D5C22×D311yescharacteristic
180C22×C3×D5C23×C311yescharacteristic
181C2×D3×D5—22no—
182C2×D3×D5—21no—
183C2×D3×D5—21no—
184C2×D3×D5—22no—
185C2×ΓL(1,𝔽16)—22no—
186C2×ΓL(1,𝔽16)—22no—
187C2×ΓL(1,𝔽16)—22no—
188C2×C3×AGL(1,𝔽5)—22no—
189C2×C3×AGL(1,𝔽5)—22no—
190C2×C3×AGL(1,𝔽5)—28no—
191C2×C3×AGL(1,𝔽5)—28no—
192C2×C3×AGL(1,𝔽5)—22no—
193C2×C3×AGL(1,𝔽5)—22no—
194C2×C3×AGL(1,𝔽5)—28no—
195C2×C3×AGL(1,𝔽5)—28no—
196C2×C3×AGL(1,𝔽5)—22no—
197C2×C3×AGL(1,𝔽5)—22no—
198C2×C3×AGL(1,𝔽5)—22no—
199C2×C3×AGL(1,𝔽5)—22no—
200C2×C3×AGL(1,𝔽5)—24no—
201C2×C3×AGL(1,𝔽5)—62no—
202C2×C3×AGL(1,𝔽5)—62no—
203C2×C3×AGL(1,𝔽5)—62no—
204C2×C3×AGL(1,𝔽5)#6714yescomplemented
205C2×C3×AGL(1,𝔽5)C3×D414yescomplemented
206C3×C5×D4—62no—
207C2×C3×C4×C5—31no—
208#1220—22no—
209C2×Dic15C2×C3×C411yescharacteristic, complemented
210C5×#67—22no—
211C2×C5×Dic3C2×C3×C411yescharacteristic, complemented
212C3×C22⋊D5—62no—
213C3×C22⋊D5—62no—
214C2×C3×Dic5—31no—
215C3×D20—62no—
216C3×C4×D5—61no—
217C3×C4×D5—61no—
218#1202—22no—
219#1201—22no—
220D5×Dic3—21no—
221D5×Dic3—21no—
222C22×C3×D4—151no—
223C23×C3×C4—51no—
224C23×C3×C4—51no—
225C23×C3×C4—101no—
226C22×#67—51no—
227C2×C3×C22⋊C4—152no—
228C2×C3×C22⋊C4—151no—
229C2×#217—51no—
230C2×(C2×D3)⋊C4—52no—
231C3×#95—152no—
232C3⋊#95—52no—
233C2×C32×C5—22no—
234C2×C32×C5C2×C22⋊C411yescharacteristic
235C2×C32×C5C4×D412yes—
236C3×D15—41no—
237C3×C5×D3—41no—
238C32×D5—22no—
239C32×D5#12011yescharacteristic
240C32×D5#12112yes—
241C32×D5#12311yescharacteristic
242C23×D5—31no—
243C23×D5C2×C3×D311yescharacteristic
244C22×AGL(1,𝔽5)—22no—
245C22×AGL(1,𝔽5)—24no—
246C22×AGL(1,𝔽5)—32no—
247C22×AGL(1,𝔽5)C2×C3×D312yes—
248C2×C5×D4—31no—
249C2×C22⋊D5—31no—
250C2×C22⋊D5—31no—
251D4×D5—62no—
252D4×D5—62no—
253C2×D20—31no—
254C2×C4×D5—31no—
255C22⋊AGL(1,𝔽5)—62no—
256C22⋊AGL(1,𝔽5)—64no—
257C23×C32—51no—
258C23×C32—52no—
259C23×C32—52no—
260C23×C32—51no—
261C23×C32—102no—
262C23×C32—102no—
263C23×C32C2×AGL(1,𝔽5)11yescharacteristic
264C22×C3×D3—51no—
265C22×C3×D3—102no—
266C22×C3×D3—102no—
267C22×C3×D3—101no—
268C22×C3×D3—101no—
269C22×C3×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
270C2×C32×C4—54no—
271C2×C32×C4—102no—
272C2×C32×C4—102no—
273C2×C32×C4—108no—
274C3×#67—22no—
275C3×#67—102no—
276C3×#67—102no—
277C3×#67—102no—
278C2×C3×Dic3—51no—
279C2×C3×Dic3—101no—
280C2×C3×Dic3—101no—
281C2×C3×Dic3—102no—
282C2×C3×Dic3—102no—
283C2×C3×Dic3—102no—
284C2×C3×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
285#386—151noSylow
286C22×C3×C5—22no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5—22no—
290C22×C3×C5—22no—
291C22×C3×C5—21no—
292C22×C3×C5—61no—
293C22×C3×C5—62no—
294C22×C3×C5(C2×D3)⋊C412yescomplemented
295C22×C3×C5C3×C22⋊C412yescomplemented
296C22×C3×C5C2×C4×D311yescharacteristic
297C22×C3×C5C22×C3×C411yescharacteristic
298C2×D15—21no—
299C2×D15—22no—
300C2×C5×D3—21no—
301C2×C5×D3—22no—
302C2×C3×D5—22no—
303C2×C3×D5—22no—
304C2×C3×D5—22no—
305C2×C3×D5—22no—
306C2×C3×D5—24no—
307C2×C3×D5—22no—
308C2×C3×D5—22no—
309C2×C3×D5—24no—
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—24no—
314C2×C3×D5—22no—
315C2×C3×D5—22no—
316C2×C3×D5—24no—
317C2×C3×D5—22no—
318C2×C3×D5—22no—
319C2×C3×D5—21no—
320C2×C3×D5—22no—
321C2×C3×D5—21no—
322C2×C3×D5—22no—
323C2×C3×D5—61no—
324C2×C3×D5—62no—
325C2×C3×D5—121no—
326C2×C3×D5—122no—
327C2×C3×D5—121no—
328C2×C3×D5(C2×D3)⋊C412yescomplemented
329C2×C3×D5C3×C22⋊C412yescomplemented
330C2×C3×D5C2×D1211yescharacteristic
331C2×C3×D5#23512yes—
332C2×C3×D5C2×#6711yescharacteristic
333C2×C3×D5C2×#6712yes—
334C2×C3×D5C2×C3×D411yescharacteristic
335C2×C3×D5C2×C3×D412yes—
336C2×C3×D5C2×C3×D411yescharacteristic
337C2×C3×D5C3×#4112yes—
338D3×D5—41no—
339D3×D5—42no—
340D3×D5—41no—
341ΓL(1,𝔽16)—42no—
342C3×AGL(1,𝔽5)—24no—
343C3×AGL(1,𝔽5)—24no—
344C3×AGL(1,𝔽5)—24no—
345C3×AGL(1,𝔽5)—24no—
346C3×AGL(1,𝔽5)—122no—
347C3×C4×C5—61no—
348Dic15—21no—
349C3×Dic5—61no—
350C5×Dic3—21no—
351C24×C3—51no—
352C24×C3—51no—
353C24×C3—101no—
354C24×C3—151no—
355C23×D3—51no—
356C2×C3×D4—31no—
357C2×C3×D4—151no—
358C2×C3×D4—151no—
359C2×C3×D4—151no—
360C2×C3×D4—302no—
361C2×C3×D4—302no—
362C22×C3×C4—52no—
363C22×C3×C4—52no—
364C22×C3×C4—102no—
365C22×C3×C4—104no—
366C22×C3×C4—104no—
367C22×C3×C4—102no—
368C22×C3×C4—102no—
369C22×C3×C4—104no—
370C22×C3×C4—102no—
371C22×C3×C4—104no—
372C22×C3×C4—102no—
373C22×C3×C4—151no—
374C22×C3×C4—152no—
375C2×#67—51no—
376C2×#67—51no—
377C2×#67—51no—
378C2×#67—102no—
379C2×#67—102no—
380C2×#67C3×AGL(1,𝔽5)11yescharacteristic, complemented
381C22×Dic3—51no—
382C22×Dic3—52no—
383C3×C22⋊C4—304no—
384C3×C22⋊C4—302no—
385#217—102no—
386(C2×D3)⋊C4—104no—
387C32×C5#38611yescharacteristic, complemented, Hall
388C23×C5—31no—
389C23×C5C3×C4×D311yescharacteristic
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—31no—
393C22×D5—61no—
394C22×D5—62no—
395C22×D5—62no—
396C22×D5—61no—
397C22×D5C3×C4×D311yescharacteristic
398C22×D5C3×D1212yes—
399C22×D5C3×#6712yes—
400C22×D5C22×C3×D311yescharacteristic
401C2×AGL(1,𝔽5)—28no—
402C2×AGL(1,𝔽5)—22no—
403C2×AGL(1,𝔽5)—22no—
404C2×AGL(1,𝔽5)—62no—
405C2×AGL(1,𝔽5)—62no—
406C2×AGL(1,𝔽5)—62no—
407C2×AGL(1,𝔽5)C3×#6714yescomplemented
408C5×D4—62no—
409C2×C4×C5—31no—
410C22⋊D5—62no—
411C22⋊D5—62no—
412C2×Dic5—31no—
413D20—62no—
414C4×D5—61no—
415C4×D5—61no—
416C22×C32—22no—
417C22×C32—52no—
418C22×C32—52no—
419C22×C32—51no—
420C22×C32—51no—
421C22×C32—52no—
422C22×C32—102no—
423C22×C32—104no—
424C22×C32—102no—
425C22×C32—102no—
426C22×C32C22⋊AGL(1,𝔽5)12yescomplemented
427C22×C32C22×AGL(1,𝔽5)11yescharacteristic
428C2×C3×D3—22no—
429C2×C3×D3—21no—
430C2×C3×D3—102no—
431C2×C3×D3—101no—
432C2×C3×D3—201no—
433C2×C3×D3—202no—
434C2×C3×D3—201no—
435C32×C4—104no—
436C3×Dic3—21no—
437C3×Dic3—101no—
438C3×Dic3—202no—
439C22×D4—151no—
440C23×C4—51no—
441C2×C22⋊C4—152no—
442C2×C22⋊C4—151no—
443#95—152no—
444C2×C3×C5—22no—
445C2×C3×C5—22no—
446C2×C3×C5—22no—
447C2×C3×C5—22no—
448C2×C3×C5—21no—
449C2×C3×C5—22no—
450C2×C3×C5—121no—
451C2×C3×C5C2×(C2×D3)⋊C411yescharacteristic
452C2×C3×C5C4×#6712yes—
453C2×C3×C5C2×C3×C22⋊C411yescharacteristic
454C2×C3×C5C3×C4×D412yes—
455D15—41no—
456C3×D5—22no—
457C3×D5—22no—
458C3×D5—22no—
459C3×D5—22no—
460C3×D5—21no—
461C3×D5—22no—
462C3×D5—21no—
463C3×D5—121no—
464C3×D5#92911yescharacteristic
465C3×D5#93012yes—
466C3×D5#95311yescharacteristic
467C3×D5C3×#12011yescharacteristic
468C3×D5C3×#12112yes—
469C3×D5C3×#12311yescharacteristic
470C5×D3—41no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—51no—
474C23×C3—51no—
475C23×C3—52no—
476C23×C3—52no—
477C23×C3—52no—
478C23×C3—52no—
479C23×C3—51no—
480C23×C3—51no—
481C23×C3—102no—
482C23×C3—101no—
483C23×C3—102no—
484C23×C3—101no—
485C23×C3—102no—
486C23×C3—102no—
487C23×C3—102no—
488C23×C3—102no—
489C23×C3—102no—
490C23×C3—102no—
491C23×C3—102no—
492C23×C3—102no—
493C23×C3—151no—
494C23×C3—302no—
495C23×C3—301no—
496C23×C3—301no—
497C23×C3—302no—
498C23×C3D3×AGL(1,𝔽5)11yescharacteristic
499C23×C3C2×C3×AGL(1,𝔽5)11yescharacteristic
500C22×D3—51no—
501C22×D3—102no—
502C22×D3—101no—
503C22×D3—101no—
504C22×D3—102no—
505C22×D3C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
506C3×D4—62no—
507C3×D4—302no—
508C3×D4—302no—
509C3×D4—302no—
510C2×C3×C4—31no—
511C2×C3×C4—54no—
512C2×C3×C4—54no—
513C2×C3×C4—104no—
514C2×C3×C4—102no—
515C2×C3×C4—102no—
516C2×C3×C4—102no—
517C2×C3×C4—102no—
518C2×C3×C4—102no—
519C2×C3×C4—102no—
520C2×C3×C4—102no—
521C2×C3×C4—102no—
522C2×C3×C4—108no—
523C2×C3×C4—108no—
524C2×C3×C4—108no—
525C2×C3×C4—108no—
526C2×C3×C4—151no—
527C2×C3×C4—301no—
528C2×C3×C4—301no—
529C2×C3×C4—302no—
530C2×C3×C4—302no—
531C2×C3×C4—302no—
532#67—22no—
533#67—102no—
534#67—102no—
535#67—102no—
536C2×Dic3—51no—
537C2×Dic3—101no—
538C2×Dic3—101no—
539C2×Dic3—102no—
540C2×Dic3—102no—
541C2×Dic3—102no—
542C2×Dic3C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
543C22×C5—22no—
544C22×C5—61no—
545C22×C5—62no—
546C22×C5C3×(C2×D3)⋊C412yescomplemented
547C22×C5C2×C3×C4×D311yescharacteristic
548C2×D5—22no—
549C2×D5—22no—
550C2×D5—24no—
551C2×D5—22no—
552C2×D5—61no—
553C2×D5—62no—
554C2×D5—121no—
555C2×D5—122no—
556C2×D5—121no—
557C2×D5C3×(C2×D3)⋊C412yescomplemented
558C2×D5C2×C3×D1211yescharacteristic
559C2×D5C3×#23512yes—
560C2×D5C2×C3×#6711yescharacteristic
561C2×D5C2×C3×#6712yes—
562AGL(1,𝔽5)—24no—
563AGL(1,𝔽5)—122no—
564C4×C5—61no—
565Dic5—61no—
566C2×C32—22no—
567C2×C32—51no—
568C2×C32—52no—
569C2×C32—51no—
570C2×C32—102no—
571C2×C32D4×AGL(1,𝔽5)12yes—
572C2×C32C2×C22⋊AGL(1,𝔽5)11yescharacteristic
573C3×D3—41no—
574C3×D3—201no—
575C24—51no—
576C24—151no—
577C2×D4—31no—
578C2×D4—151no—
579C2×D4—151no—
580C2×D4—151no—
581C2×D4—302no—
582C2×D4—302no—
583C22×C4—52no—
584C22×C4—104no—
585C22×C4—102no—
586C22×C4—151no—
587C22×C4—152no—
588C22⋊C4—304no—
589C22⋊C4—302no—
590C3×C5—21no—
591C3×C5#521311yescharacteristic, complemented
592C3×C5C3×#38611yescharacteristic, complemented
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—51no—
600C22×C3—51no—
601C22×C3—52no—
602C22×C3—52no—
603C22×C3—52no—
604C22×C3—52no—
605C22×C3—51no—
606C22×C3—51no—
607C22×C3—52no—
608C22×C3—52no—
609C22×C3—61no—
610C22×C3—62no—
611C22×C3—102no—
612C22×C3—101no—
613C22×C3—102no—
614C22×C3—101no—
615C22×C3—102no—
616C22×C3—102no—
617C22×C3—102no—
618C22×C3—104no—
619C22×C3—102no—
620C22×C3—104no—
621C22×C3—102no—
622C22×C3—102no—
623C22×C3—102no—
624C22×C3—102no—
625C22×C3—104no—
626C22×C3—102no—
627C22×C3—102no—
628C22×C3—104no—
629C22×C3—102no—
630C22×C3—102no—
631C22×C3—102no—
632C22×C3—301no—
633C22×C3—302no—
634C22×C3—601no—
635C22×C3—602no—
636C22×C3—601no—
637C22×C3(C2×D3)⋊AGL(1,𝔽5)12yescomplemented
638C22×C3C3×C22⋊AGL(1,𝔽5)12yescomplemented
639C22×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
640C22×C3C22×C3×AGL(1,𝔽5)11yescharacteristic
641C2×D3—22no—
642C2×D3—21no—
643C2×D3—102no—
644C2×D3—101no—
645C2×D3—202no—
646C2×D3—201no—
647C2×D3—201no—
648C3×C4—61no—
649C3×C4—104no—
650C3×C4—104no—
651C3×C4—104no—
652C3×C4—104no—
653C3×C4—301no—
654C3×C4—602no—
655Dic3—21no—
656Dic3—101no—
657Dic3—202no—
658C2×C5—22no—
659C2×C5—121no—
660C2×C5C2×C3×(C2×D3)⋊C411yescharacteristic
661C2×C5C3×C4×#6712yes—
662D5—22no—
663D5—121no—
664D5C3×#92911yescharacteristic
665D5C3×#93012yes—
666D5C3×#95311yescharacteristic
667C32#6577911yescharacteristic, complemented, Sylow
668C23—31no—
669C23—51no—
670C23—51no—
671C23—52no—
672C23—52no—
673C23—102no—
674C23—102no—
675C23—151no—
676C23—302no—
677C23—301no—
678C23—301no—
679C23—302no—
680C23C3×D3×AGL(1,𝔽5)11yescharacteristic
681D4—62no—
682D4—302no—
683D4—302no—
684D4—302no—
685C2×C4—31no—
686C2×C4—54no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—108no—
690C2×C4—151no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—302no—
694C2×C4—302no—
695C2×C4—302no—
696C2×C3—22no—
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—22no—
700C2×C3—21no—
701C2×C3—22no—
702C2×C3—51no—
703C2×C3—52no—
704C2×C3—51no—
705C2×C3—52no—
706C2×C3—51no—
707C2×C3—51no—
708C2×C3—101no—
709C2×C3—102no—
710C2×C3—101no—
711C2×C3—102no—
712C2×C3—102no—
713C2×C3—102no—
714C2×C3—102no—
715C2×C3—121no—
716C2×C3—601no—
717C2×C3C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
718C2×C3AGL(1,𝔽5)×#6712yes—
719C2×C3C3×D4×AGL(1,𝔽5)12yes—
720C2×C3C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
721D3—41no—
722D3—201no—
723C5C3×#521311yescharacteristic, complemented, Sylow
724C22—22no—
725C22—51no—
726C22—51no—
727C22—52no—
728C22—52no—
729C22—52no—
730C22—61no—
731C22—62no—
732C22—102no—
733C22—104no—
734C22—102no—
735C22—102no—
736C22—301no—
737C22—302no—
738C22—601no—
739C22—602no—
740C22—601no—
741C22C3×(C2×D3)⋊AGL(1,𝔽5)12yescomplemented
742C22C2×C3×D3×AGL(1,𝔽5)11yescharacteristic
743C4—61no—
744C4—104no—
745C4—301no—
746C4—602no—
747C3—21no—
748C3#1175202211yescharacteristic, direct product factor
749C3C3×#6577911yescharacteristic, complemented
750C2—22no—
751C2—51no—
752C2—52no—
753C2—51no—
754C2—102no—
755C2—121no—
756C2—601no—
757C2C2×C3×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
758C2C3×AGL(1,𝔽5)×#6712yes—
subgroupG/H
centerC22×C3C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×AGL(1,𝔽5)
FittingC23×C32×C5C2×C4
socleC22×C32×C5C22×C4
prime radicalC2×C3×D5×#67C2
cosocleC22×C3×D5C23×C3
hypercenterC23×C3D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C23×C32×AGL(1,𝔽5)C2semidirect
3. C2×C3×#6763C2semidirect
4. C2×C3×(C2×D3)⋊AGL(1,𝔽5)C2semidirect
5. C3×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
7. #11752022C3direct (N × H)
14. C2×C3×#1220C4semidirect
15. C2×C3×C5×#67C4semidirect
18. C2×C3×#1202C4semidirect
19. C2×C3×#1201C4semidirect
25. C23×C3×AGL(1,𝔽5)D3semidirect
26. C23×C3×AGL(1,𝔽5)C2×C3semidirect
29. C2×#6763C2×C3semidirect
32. C2×(C2×D3)⋊AGL(1,𝔽5)C2×C3semidirect
34. (C2×AGL(1,𝔽5))⋊Dic3C2×C3semidirect
36. C22×C3×D15C2×C4semidirect
37. C22×C3×C5×D3C2×C4semidirect
54. C2×C32×AGL(1,𝔽5)D4semidirect
56. C2×C3×Dic15C2×C4semidirect
58. C2×C3×C5×Dic3C2×C4semidirect
88. C2×#1220C3×C4semidirect
89. C2×C5×#67C3×C4semidirect
98. C2×#1202C3×C4semidirect
99. C2×#1201C3×C4semidirect
108. C22×C32×C5C22⋊C4semidirect
118. C2×C32×D5C22⋊C4semidirect
130. C23×AGL(1,𝔽5)C3×D3semidirect
145. C2×C3×#67AGL(1,𝔽5)semidirect
154. C22×D15C2×C3×C4semidirect
155. C22×C5×D3C2×C3×C4semidirect
204. C2×C3×AGL(1,𝔽5)#67semidirect
205. C2×C3×AGL(1,𝔽5)C3×D4semidirect
209. C2×Dic15C2×C3×C4semidirect
211. C2×C5×Dic3C2×C3×C4semidirect
269. C22×C3×D3C2×AGL(1,𝔽5)semidirect
284. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
294. C22×C3×C5(C2×D3)⋊C4semidirect
295. C22×C3×C5C3×C22⋊C4semidirect
328. C2×C3×D5(C2×D3)⋊C4semidirect
329. C2×C3×D5C3×C22⋊C4semidirect
380. C2×#67C3×AGL(1,𝔽5)semidirect
387. C32×C5#386semidirect
407. C2×AGL(1,𝔽5)C3×#67semidirect
426. C22×C32C22⋊AGL(1,𝔽5)semidirect
505. C22×D3C2×C3×AGL(1,𝔽5)semidirect
542. C2×Dic3C2×C3×AGL(1,𝔽5)semidirect
546. C22×C5C3×(C2×D3)⋊C4semidirect
557. C2×D5C3×(C2×D3)⋊C4semidirect
591. C3×C5#5213semidirect
592. C3×C5C3×#386semidirect
637. C22×C3(C2×D3)⋊AGL(1,𝔽5)semidirect
638. C22×C3C3×C22⋊AGL(1,𝔽5)semidirect
667. C32#65779semidirect
723. C5C3×#5213semidirect
741. C22C3×(C2×D3)⋊AGL(1,𝔽5)semidirect
748. C3#11752022direct (N × H)
749. C3C3×#65779semidirect

Maximal subgroups

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

subgroupindex
C23×C32×AGL(1,𝔽5)2
C2×C3×D5×#672
C2×C3×#67632
C2×C3×(C2×D3)⋊AGL(1,𝔽5)2
C3×(C2×AGL(1,𝔽5))⋊Dic32
C3×#657793
#117520223
C3×#52135