Finite Group Databasebeta

← C3×#10604818 #14301095

Subgroups — C3×#10604818 #14301095

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×C3×D5×SD16C211yesmaximal, characteristic
3C2×C3×#4009C211yesmaximal, characteristic, complemented
4C3×#65780C211yesmaximal, characteristic
5C2×C3×#4007C211yesmaximal, characteristic
6C3×#64893C211yesmaximal, characteristic, complemented
7C3×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic, complemented
8#10604818C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5C2211yescharacteristic
10C2×C3×D4×D5C2211yescharacteristic
11C2×C3×C22⋊AGL(1,𝔽5)—21no—
12C2×C3×C22⋊AGL(1,𝔽5)—21no—
13C3×Q8×AGL(1,𝔽5)—22no—
14C3×Q8×AGL(1,𝔽5)—22no—
15C2×C3×C4⋊AGL(1,𝔽5)—21no—
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4×AGL(1,𝔽5)—21no—
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×C3×D5⋊C8C2211yescharacteristic
21C2×C3×C5×SD16C411yescharacteristic, complemented
22C2×C3×#688C411yescharacteristic, complemented
23C2×C3×#687C411yescharacteristic, complemented
24C3×D5×SD16—22no—
25C3×D5×SD16—22no—
26C2×C3×#677C411yescharacteristic, complemented
27C2×C3×C8×D5C2211yescharacteristic
28C3×#4009—22no—
29C3×#4007—22no—
30C3×#1880—51nomaximal, Hall
31C2×Q8×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
32C2×D5×SD16C2×C311yescharacteristic
33C2×#4009C2×C311yescharacteristic, complemented
34#65780C2×C311yescharacteristic
35C2×#4007C2×C311yescharacteristic
36#64893C2×C311yescharacteristic, complemented
37(C2×AGL(1,𝔽5))⋊C8C2×C311yescharacteristic, complemented
38C23×C3×D5—21no—
39C22×C3×AGL(1,𝔽5)—21no—
40C22×C3×AGL(1,𝔽5)—21no—
41C22×C3×AGL(1,𝔽5)D411yescharacteristic
42C22×C3×AGL(1,𝔽5)D411yescharacteristic
43C2×C3×C5×Q8C2×C411yescharacteristic
44C2×C3×C5×D4C2×C411yescharacteristic
45C2×C3×C22⋊D5—21no—
46C3×Q8×D5—21no—
47C3×Q8×D5—21no—
48C3×Q8×D5D412yes—
49C3×Q8×D5D412yes—
50C3×D4×D5—21no—
51C3×D4×D5—21no—
52C3×D4×D5—21no—
53C3×D4×D5—21no—
54C2×C3×D20C2×C411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5C2311yescharacteristic
57C2×C3×Dic10—21no—
58C2×C3×Dic10C2×C411yescharacteristic
59C3×C22⋊AGL(1,𝔽5)—42no—
60C3×C22⋊AGL(1,𝔽5)—42no—
61C2×C3×#170—21no—
62C3×C4⋊AGL(1,𝔽5)—24no—
63C3×C4⋊AGL(1,𝔽5)—21no—
64C3×C4⋊AGL(1,𝔽5)—21no—
65C3×C4⋊AGL(1,𝔽5)—21no—
66C3×C4⋊AGL(1,𝔽5)D412yes—
67C3×C4×AGL(1,𝔽5)—24no—
68C3×C4×AGL(1,𝔽5)—21no—
69C3×C4×AGL(1,𝔽5)—21no—
70C3×D5⋊C8—21no—
71C3×D5⋊C8—21no—
72C3×C5×SD16—22no—
73C2×C3×C5×C8C2×C411yescharacteristic
74C3×#688—22no—
75C3×#687—22no—
76C2×C3×#168C2×C411yescharacteristic
77C3×#677—22no—
78C3×C8×D5—21no—
79C3×C8×D5—21no—
80C22×C3×SD16—51no—
81C2×C3×C4×Q8—51no—
82C2×C3×#103—51no—
83C2×C3×#102—51no—
84C3×#390—51no—
85C3×#340—51no—
86C3×#336—51no—
87C2×Q8×D5C22×C311yescharacteristic
88C2×D4×D5C22×C311yescharacteristic
89C2×C22⋊AGL(1,𝔽5)—21no—
90C2×C22⋊AGL(1,𝔽5)—21no—
91Q8×AGL(1,𝔽5)—22no—
92Q8×AGL(1,𝔽5)—22no—
93C2×C4⋊AGL(1,𝔽5)—21no—
94C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
95C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
96C2×C4×AGL(1,𝔽5)—21no—
97C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
98C2×D5⋊C8C22×C311yescharacteristic
99C2×C5×SD16C3×C411yescharacteristic, complemented
100C2×#688C3×C411yescharacteristic, complemented
101C2×#687C3×C411yescharacteristic, complemented
102D5×SD16—22no—
103D5×SD16—22no—
104C2×#677C3×C411yescharacteristic, complemented
105C2×C8×D5C22×C311yescharacteristic
106#4009—22no—
107#4007—22no—
108#1880—51noSylow
109C23×C3×C5—21no—
110C22×C3×D5—21no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C22×C3×D5—41no—
115C22×C3×D5—41no—
116C22×C3×D5—41no—
117C22×C3×D5C2×D411yescharacteristic
118C2×C3×AGL(1,𝔽5)—21no—
119C2×C3×AGL(1,𝔽5)—21no—
120C2×C3×AGL(1,𝔽5)—21no—
121C2×C3×AGL(1,𝔽5)—22no—
122C2×C3×AGL(1,𝔽5)—21no—
123C2×C3×AGL(1,𝔽5)—21no—
124C2×C3×AGL(1,𝔽5)—41no—
125C2×C3×AGL(1,𝔽5)—41no—
126C2×C3×AGL(1,𝔽5)—41no—
127C2×C3×AGL(1,𝔽5)—41no—
128C2×C3×AGL(1,𝔽5)—41no—
129C2×C3×AGL(1,𝔽5)SD1612yescomplemented
130C3×C5×Q8—21no—
131C3×C5×Q8C22⋊C412yescomplemented
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5C22×C411yescharacteristic
136C3×C22⋊D5—41no—
137C3×C22⋊D5—41no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5#4111yescharacteristic
140C3×D20—21no—
141C3×D20—21no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144C3×C4×D5C2×D411yescharacteristic
145C3×C4×D5C2×D411yescharacteristic
146C3×C4×D5C2×D411yescharacteristic
147C3×C4×D5#4111yescharacteristic
148C3×Dic10—21no—
149C3×Dic10—22no—
150C3×Dic10—22no—
151C3×Dic10C22⋊C412yescomplemented
152C3×#170—41no—
153C3×C5×C8—21no—
154C3×#168—21no—
155C22×C3×Q8—51no—
156C22×C3×D4—51no—
157C2×C3×SD16—51no—
158C2×C3×SD16—51no—
159C2×C3×SD16—51no—
160C2×C3×SD16—102no—
161C2×C3×SD16—102no—
162C2×C3×SD16AGL(1,𝔽5)11yescharacteristic, complemented
163C22×C3×C8—51no—
164C22×C3×C8—51no—
165C3×C4×Q8—102no—
166C3×C4×Q8—102no—
167C2×C3×C4⋊C4—51no—
168C2×C3×C4⋊C4—51no—
169C2×C3×C4⋊C4—101no—
170C2×C3×C22⋊C4—101no—
171C2×C3×C22⋊C4—101no—
172C2×C3×C42—51no—
173C2×C3×C42—101no—
174C3×#103—102no—
175C3×#102—102no—
176C23×D5—21no—
177C22×AGL(1,𝔽5)—21no—
178C22×AGL(1,𝔽5)—21no—
179C22×AGL(1,𝔽5)C3×D411yescharacteristic
180C22×AGL(1,𝔽5)C3×D411yescharacteristic
181C2×C5×Q8C2×C3×C411yescharacteristic
182C2×C5×D4C2×C3×C411yescharacteristic
183C2×C22⋊D5—21no—
184Q8×D5—21no—
185Q8×D5—21no—
186Q8×D5C3×D412yes—
187Q8×D5C3×D412yes—
188D4×D5—21no—
189D4×D5—21no—
190D4×D5—21no—
191D4×D5—21no—
192C2×D20C2×C3×C411yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5C23×C311yescharacteristic
195C2×Dic10—21no—
196C2×Dic10C2×C3×C411yescharacteristic
197C22⋊AGL(1,𝔽5)—42no—
198C22⋊AGL(1,𝔽5)—42no—
199C2×#170—21no—
200C4⋊AGL(1,𝔽5)—24no—
201C4⋊AGL(1,𝔽5)—21no—
202C4⋊AGL(1,𝔽5)—21no—
203C4⋊AGL(1,𝔽5)—21no—
204C4⋊AGL(1,𝔽5)C3×D412yes—
205C4×AGL(1,𝔽5)—24no—
206C4×AGL(1,𝔽5)—21no—
207C4×AGL(1,𝔽5)—21no—
208D5⋊C8—21no—
209D5⋊C8—21no—
210C5×SD16—22no—
211C2×C5×C8C2×C3×C411yescharacteristic
212#688—22no—
213#687—22no—
214C2×#168C2×C3×C411yescharacteristic
215#677—22no—
216C8×D5—21no—
217C8×D5—21no—
218C22×SD16—51no—
219C2×C4×Q8—51no—
220C2×#103—51no—
221C2×#102—51no—
222#390—51no—
223#340—51no—
224#336—51no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5—41no—
228C22×C3×C5C4×D411yescharacteristic
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C2×C3×D5—41no—
232C2×C3×D5—81no—
233C2×C3×D5—81no—
234C2×C3×D5—81no—
235C2×C3×D5—81no—
236C2×C3×D5#12011yescharacteristic
237C2×C3×D5#12111yescharacteristic
238C2×C3×D5C2×SD1611yescharacteristic
239C2×C3×D5#13511yescharacteristic
240C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
241C2×C3×D5#13711yescharacteristic
242C3×AGL(1,𝔽5)—22no—
243C3×AGL(1,𝔽5)—41no—
244C3×AGL(1,𝔽5)—42no—
245C3×AGL(1,𝔽5)—81no—
246C3×C4×C5—22no—
247C3×C4×C5C2×C22⋊C411yescharacteristic
248C3×C4×C5C4×D411yescharacteristic
249C3×Dic5—22no—
250C3×Dic5#12111yescharacteristic
251C3×Dic5#12311yescharacteristic
252C24×C3—101no—
253C2×C3×Q8—52no—
254C2×C3×Q8—52no—
255C2×C3×Q8—51no—
256C2×C3×Q8—101no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
260C2×C3×D4—51no—
261C2×C3×D4—101no—
262C2×C3×D4—101no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
267C22×C3×C4—51no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—101no—
271C22×C3×C4—101no—
272C22×C3×C4—101no—
273C3×SD16—22no—
274C3×SD16—102no—
275C3×SD16—102no—
276C3×SD16—102no—
277C2×C3×C8—51no—
278C2×C3×C8—101no—
279C2×C3×C8—101no—
280C2×C3×C8—101no—
281C2×C3×C8—101no—
282C2×C3×C8—101no—
283C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
284C3×C4⋊C4—52no—
285C3×C4⋊C4—101no—
286C3×C4⋊C4—101no—
287C3×C4⋊C4—101no—
288C3×C4⋊C4—104no—
289C3×C22⋊C4—202no—
290C3×C22⋊C4—202no—
291C3×C42—101no—
292C3×C42—101no—
293C3×C42—104no—
294C23×C5—21no—
295C22×D5—21no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5—41no—
301C22×D5—41no—
302C22×D5C2×C3×D411yescharacteristic
303C2×AGL(1,𝔽5)—21no—
304C2×AGL(1,𝔽5)—21no—
305C2×AGL(1,𝔽5)—21no—
306C2×AGL(1,𝔽5)—22no—
307C2×AGL(1,𝔽5)—21no—
308C2×AGL(1,𝔽5)—21no—
309C2×AGL(1,𝔽5)—41no—
310C2×AGL(1,𝔽5)—41no—
311C2×AGL(1,𝔽5)—41no—
312C2×AGL(1,𝔽5)—41no—
313C2×AGL(1,𝔽5)—41no—
314C2×AGL(1,𝔽5)C3×SD1612yescomplemented
315C5×Q8—21no—
316C5×Q8C3×C22⋊C412yescomplemented
317C5×D4—21no—
318C5×D4—21no—
319C2×C4×C5—21no—
320C2×C4×C5C22×C3×C411yescharacteristic
321C22⋊D5—41no—
322C22⋊D5—41no—
323C2×Dic5—21no—
324C2×Dic5C3×#4111yescharacteristic
325D20—21no—
326D20—21no—
327C4×D5—22no—
328C4×D5—22no—
329C4×D5C2×C3×D411yescharacteristic
330C4×D5C2×C3×D411yescharacteristic
331C4×D5C2×C3×D411yescharacteristic
332C4×D5C3×#4111yescharacteristic
333Dic10—21no—
334Dic10—22no—
335Dic10—22no—
336Dic10C3×C22⋊C412yescomplemented
337#170—41no—
338C5×C8—21no—
339#168—21no—
340C22×Q8—51no—
341C22×D4—51no—
342C2×SD16—51no—
343C2×SD16—51no—
344C2×SD16—51no—
345C2×SD16—102no—
346C2×SD16—102no—
347C2×SD16C3×AGL(1,𝔽5)11yescharacteristic, complemented
348C22×C8—51no—
349C22×C8—51no—
350C4×Q8—102no—
351C4×Q8—102no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—101no—
355C2×C22⋊C4—101no—
356C2×C22⋊C4—101no—
357C2×C42—51no—
358C2×C42—101no—
359#103—102no—
360#102—102no—
361C2×C3×C5—81no—
362C2×C3×C5#38611yescharacteristic
363C2×C3×C5C4×SD1611yescharacteristic
364C2×C3×C5#44011yescharacteristic
365C3×D5—81no—
366C3×D5#44811yescharacteristic
367C3×D5#44911yescharacteristic
368C3×D5#46011yescharacteristic
369C3×D5#46411yescharacteristic
370C23×C3—21no—
371C23×C3—51no—
372C23×C3—101no—
373C23×C3—201no—
374C23×C3—201no—
375C23×C3—201no—
376C23×C3—201no—
377C23×C3—201no—
378C23×C3—201no—
379C3×Q8—21no—
380C3×Q8—52no—
381C3×Q8—102no—
382C3×Q8—102no—
383C3×Q8—101no—
384C3×Q8C22⋊AGL(1,𝔽5)12yescomplemented
385C3×D4—21no—
386C3×D4—21no—
387C3×D4—101no—
388C3×D4—101no—
389C3×D4—201no—
390C3×D4—201no—
391C2×C3×C4—21no—
392C2×C3×C4—51no—
393C2×C3×C4—51no—
394C2×C3×C4—51no—
395C2×C3×C4—51no—
396C2×C3×C4—51no—
397C2×C3×C4—52no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—101no—
401C2×C3×C4—101no—
402C2×C3×C4—101no—
403C2×C3×C4—102no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—101no—
407C2×C3×C4—201no—
408C2×C3×C4—201no—
409C2×C3×C4—201no—
410C2×C3×C4—201no—
411C2×C3×C4—201no—
412C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
413C3×C8—21no—
414C3×C8—101no—
415C3×C8—201no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5C3×C4×D411yescharacteristic
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—81no—
424C2×D5—81no—
425C2×D5—81no—
426C2×D5—81no—
427C2×D5C3×#12011yescharacteristic
428C2×D5C3×#12111yescharacteristic
429C2×D5C2×C3×SD1611yescharacteristic
430C2×D5C3×#13511yescharacteristic
431C2×D5C3×AGL(1,ℤ/8)11yescharacteristic
432C2×D5C3×#13711yescharacteristic
433AGL(1,𝔽5)—22no—
434AGL(1,𝔽5)—41no—
435AGL(1,𝔽5)—42no—
436AGL(1,𝔽5)—81no—
437C4×C5—22no—
438C4×C5C2×C3×C22⋊C411yescharacteristic
439C4×C5C3×C4×D411yescharacteristic
440Dic5—22no—
441Dic5C3×#12111yescharacteristic
442Dic5C3×#12311yescharacteristic
443C24—101no—
444C2×Q8—52no—
445C2×Q8—52no—
446C2×Q8—51no—
447C2×Q8—101no—
448C2×Q8—101no—
449C2×Q8—101no—
450C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
451C2×D4—51no—
452C2×D4—101no—
453C2×D4—101no—
454C2×D4—101no—
455C2×D4—101no—
456C2×D4—101no—
457C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
458C22×C4—51no—
459C22×C4—51no—
460C22×C4—51no—
461C22×C4—101no—
462C22×C4—101no—
463C22×C4—101no—
464SD16—22no—
465SD16—102no—
466SD16—102no—
467SD16—102no—
468C2×C8—51no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
475C4⋊C4—52no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—104no—
480C22⋊C4—202no—
481C22⋊C4—202no—
482C42—101no—
483C42—101no—
484C42—104no—
485C3×C5#188011yescharacteristic, complemented, Hall
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—51no—
490C22×C3—51no—
491C22×C3—51no—
492C22×C3—51no—
493C22×C3—51no—
494C22×C3—51no—
495C22×C3—201no—
496C22×C3—201no—
497C22×C3—201no—
498C22×C3—401no—
499C22×C3—401no—
500C22×C3—401no—
501C22×C3—401no—
502C22×C3D4×AGL(1,𝔽5)11yescharacteristic
503C3×C4—22no—
504C3×C4—51no—
505C3×C4—51no—
506C3×C4—102no—
507C3×C4—102no—
508C3×C4—201no—
509C3×C4—202no—
510C3×C4—401no—
511C3×C4D4×AGL(1,𝔽5)11yescharacteristic
512C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
513C2×C5—81no—
514C2×C5C3×#38611yescharacteristic
515C2×C5C3×C4×SD1611yescharacteristic
516C2×C5C3×#44011yescharacteristic
517D5—81no—
518D5C3×#44811yescharacteristic
519D5C3×#44911yescharacteristic
520D5C3×#46011yescharacteristic
521D5C3×#46411yescharacteristic
522C23—21no—
523C23—51no—
524C23—101no—
525C23—201no—
526C23—201no—
527C23—201no—
528C23—201no—
529C23—201no—
530C23—201no—
531Q8—21no—
532Q8—52no—
533Q8—102no—
534Q8—102no—
535Q8—101no—
536Q8C3×C22⋊AGL(1,𝔽5)12yescomplemented
537D4—21no—
538D4—21no—
539D4—101no—
540D4—101no—
541D4—201no—
542D4—201no—
543C2×C4—21no—
544C2×C4—51no—
545C2×C4—51no—
546C2×C4—51no—
547C2×C4—51no—
548C2×C4—51no—
549C2×C4—52no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—102no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
565C8—21no—
566C8—101no—
567C8—201no—
568C2×C3—51no—
569C2×C3—51no—
570C2×C3—51no—
571C2×C3—51no—
572C2×C3—81no—
573C2×C3—401no—
574C2×C3SD16×AGL(1,𝔽5)11yescharacteristic
575C2×C3#6573511yescharacteristic
576C2×C3#6577911yescharacteristic
577C5C3×#188011yescharacteristic, complemented, Sylow
578C22—41no—
579C22—41no—
580C22—41no—
581C22—51no—
582C22—51no—
583C22—51no—
584C22—51no—
585C22—51no—
586C22—51no—
587C22—201no—
588C22—201no—
589C22—201no—
590C22—401no—
591C22—401no—
592C22—401no—
593C22—401no—
594C22C3×D4×AGL(1,𝔽5)11yescharacteristic
595C4—22no—
596C4—51no—
597C4—51no—
598C4—102no—
599C4—102no—
600C4—201no—
601C4—202no—
602C4—401no—
603C4C3×D4×AGL(1,𝔽5)11yescharacteristic
604C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
605C3#1060481811yescharacteristic, direct product factor, Sylow
606C2—51no—
607C2—51no—
608C2—51no—
609C2—51no—
610C2—81no—
611C2—401no—
612C2C3×SD16×AGL(1,𝔽5)11yescharacteristic
613C2C3×#6573511yescharacteristic
614C2C3×#6577911yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×SD16AGL(1,𝔽5)
hypocenterC5C3×#1880
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×AGL(1,𝔽5)C2semidirect
3. C2×C3×#4009C2semidirect
6. C3×#64893C2semidirect
7. C3×(C2×AGL(1,𝔽5))⋊C8C2semidirect
8. #10604818C3direct (N × H)
21. C2×C3×C5×SD16C4semidirect
22. C2×C3×#688C4semidirect
23. C2×C3×#687C4semidirect
26. C2×C3×#677C4semidirect
31. C2×Q8×AGL(1,𝔽5)C2×C3semidirect
33. C2×#4009C2×C3semidirect
36. #64893C2×C3semidirect
37. (C2×AGL(1,𝔽5))⋊C8C2×C3semidirect
99. C2×C5×SD16C3×C4semidirect
100. C2×#688C3×C4semidirect
101. C2×#687C3×C4semidirect
104. C2×#677C3×C4semidirect
129. C2×C3×AGL(1,𝔽5)SD16semidirect
131. C3×C5×Q8C22⋊C4semidirect
151. C3×Dic10C22⋊C4semidirect
162. C2×C3×SD16AGL(1,𝔽5)semidirect
314. C2×AGL(1,𝔽5)C3×SD16semidirect
316. C5×Q8C3×C22⋊C4semidirect
336. Dic10C3×C22⋊C4semidirect
347. C2×SD16C3×AGL(1,𝔽5)semidirect
384. C3×Q8C22⋊AGL(1,𝔽5)semidirect
485. C3×C5#1880semidirect
536. Q8C3×C22⋊AGL(1,𝔽5)semidirect
577. C5C3×#1880semidirect
605. C3#10604818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×AGL(1,𝔽5)2
C2×C3×D5×SD162
C2×C3×#40092
C3×#657802
C2×C3×#40072
C3×#648932
C3×(C2×AGL(1,𝔽5))⋊C82
#106048183
C3×#18805