Finite Group Databasebeta

← C2×C3×#65735 #14416332

Subgroups — C2×C3×#65735 #14416332

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 592 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×D4×AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×C3×D5×SD16C211yesmaximal, characteristic
4C2×C3×#4009C211yesmaximal, characteristic, complemented
5C2×C3×#4007C211yesmaximal, characteristic
6C3×#65735C218yesmaximal, direct product factor
7C2×C3×#3994C211yesmaximal, characteristic, complemented
8C2×C3×#3992C211yesmaximal, characteristic, complemented
9C2×#65735C311yesmaximal, characteristic, direct product factor, Hall
10C23×C3×AGL(1,𝔽5)—21no—
11C2×C3×Q8×D5C2211yescharacteristic
12C2×C3×D4×D5C2211yescharacteristic
13C2×C3×C22⋊AGL(1,𝔽5)—21no—
14C3×Q8×AGL(1,𝔽5)—22no—
15C3×Q8×AGL(1,𝔽5)C2214yescomplemented
16C3×D4×AGL(1,𝔽5)—22no—
17C3×D4×AGL(1,𝔽5)C2214yes—
18C2×C3×C4⋊AGL(1,𝔽5)—21no—
19C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)—21no—
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×D5⋊C8C2211yescharacteristic
24C2×C3×C5×SD16C411yescharacteristic, complemented
25C2×C3×#688C411yescharacteristic, complemented
26C2×C3×#687C411yescharacteristic, complemented
27C3×D5×SD16C414yescomplemented
28C3×D5×SD16C2214yes—
29C2×C3×#677C411yescharacteristic, complemented
30C2×C3×C8×D5C2211yescharacteristic
31C3×#4009C2214yescomplemented
32C3×#4007C2214yes—
33C3×#3994C2214yescomplemented
34C3×#3992C2214yescomplemented
35C2×C3×#440—51nomaximal, Hall
36C2×Q8×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
37C2×D4×AGL(1,𝔽5)C2×C311yescharacteristic
38C2×D5×SD16C2×C311yescharacteristic
39C2×#4009C2×C311yescharacteristic, complemented
40C2×#4007C2×C311yescharacteristic
41#65735C2×C318yesdirect product factor
42C2×#3994C2×C311yescharacteristic, complemented
43C2×#3992C2×C311yescharacteristic, complemented
44C23×C3×D5—21no—
45C22×C3×AGL(1,𝔽5)—21no—
46C22×C3×AGL(1,𝔽5)—21no—
47C22×C3×AGL(1,𝔽5)—24no—
48C22×C3×AGL(1,𝔽5)—44no—
49C22×C3×AGL(1,𝔽5)D411yescharacteristic
50C22×C3×AGL(1,𝔽5)D411yescharacteristic
51C2×C3×C5×Q8C2×C411yescharacteristic, complemented
52C2×C3×C5×D4C2×C411yescharacteristic
53C2×C3×C22⋊D5—21no—
54C3×Q8×D5—21no—
55C3×Q8×D5—21no—
56C3×Q8×D5C2×C412yescomplemented
57C3×Q8×D5C2312yes—
58C3×D4×D5—21no—
59C3×D4×D5—21no—
60C3×D4×D5C2×C412yes—
61C3×D4×D5C2312yes—
62C2×C3×D20C2×C411yescharacteristic
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5C2311yescharacteristic
65C2×C3×Dic10—21no—
66C2×C3×Dic10C2×C411yescharacteristic, complemented
67C3×C22⋊AGL(1,𝔽5)—24no—
68C2×C3×#170—21no—
69C3×C4⋊AGL(1,𝔽5)—24no—
70C3×C4⋊AGL(1,𝔽5)—21no—
71C3×C4⋊AGL(1,𝔽5)—21no—
72C3×C4⋊AGL(1,𝔽5)C2312yes—
73C3×C4⋊AGL(1,𝔽5)C2312yes—
74C3×C4×AGL(1,𝔽5)—24no—
75C3×C4×AGL(1,𝔽5)D412yes—
76C3×C4×AGL(1,𝔽5)C2312yes—
77C3×D5⋊C8—21no—
78C3×D5⋊C8C2312yes—
79C3×C5×SD16C2×C414yescomplemented
80C2×C3×C5×C8C2×C411yescharacteristic, complemented
81C3×#688C2×C414yescomplemented
82C3×#687C2×C414yescomplemented
83C2×C3×#168C2×C411yescharacteristic, complemented
84C3×#677C2×C414yescomplemented
85C3×C8×D5C2×C412yescomplemented
86C3×C8×D5C2312yes—
87C22×C3×SD16—51no—
88C2×C3×C4×Q8—51no—
89C2×C3×C4×D4—51no—
90C3×#440—58no—
91C2×C3×#107—51no—
92C2×C3×#103—51no—
93C2×C3×#102—51no—
94C2×C3×#97—51no—
95C23×AGL(1,𝔽5)—21no—
96C2×Q8×D5C22×C311yescharacteristic
97C2×D4×D5C22×C311yescharacteristic
98C2×C22⋊AGL(1,𝔽5)—21no—
99Q8×AGL(1,𝔽5)—22no—
100Q8×AGL(1,𝔽5)C22×C314yescomplemented
101D4×AGL(1,𝔽5)—22no—
102D4×AGL(1,𝔽5)C22×C314yes—
103C2×C4⋊AGL(1,𝔽5)—21no—
104C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
105C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
106C2×C4×AGL(1,𝔽5)—21no—
107C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
108C2×D5⋊C8C22×C311yescharacteristic
109C2×C5×SD16C3×C411yescharacteristic, complemented
110C2×#688C3×C411yescharacteristic, complemented
111C2×#687C3×C411yescharacteristic, complemented
112D5×SD16C3×C414yescomplemented
113D5×SD16C22×C314yes—
114C2×#677C3×C411yescharacteristic, complemented
115C2×C8×D5C22×C311yescharacteristic
116#4009C22×C314yescomplemented
117#4007C22×C314yes—
118#3994C22×C314yescomplemented
119#3992C22×C314yescomplemented
120C2×#440—51noSylow
121C23×C3×C5—21no—
122C22×C3×D5—21no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—42no—
126C22×C3×D5—42no—
127C22×C3×D5C2×D411yescharacteristic
128C2×C3×AGL(1,𝔽5)—22no—
129C2×C3×AGL(1,𝔽5)—22no—
130C2×C3×AGL(1,𝔽5)—22no—
131C2×C3×AGL(1,𝔽5)—22no—
132C2×C3×AGL(1,𝔽5)—48no—
133C2×C3×AGL(1,𝔽5)—42no—
134C2×C3×AGL(1,𝔽5)—42no—
135C2×C3×AGL(1,𝔽5)C2×D412yes—
136C2×C3×AGL(1,𝔽5)C2×D412yes—
137C3×C5×Q8—21no—
138C3×C5×Q8C22×C412yescomplemented
139C3×C5×D4—21no—
140C3×C5×D4C22×C412yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5C22×C411yescharacteristic
143C3×C22⋊D5—22no—
144C3×C22⋊D5—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5#4111yescharacteristic
147C3×D20—21no—
148C3×D20C22×C412yes—
149C3×C4×D5—22no—
150C3×C4×D5—22no—
151C3×C4×D5C22×C411yescharacteristic
152C3×C4×D5C2×D411yescharacteristic
153C3×C4×D5#4111yescharacteristic
154C3×C4×D5C2411yescharacteristic
155C3×Dic10—21no—
156C3×Dic10—22no—
157C3×Dic10—22no—
158C3×Dic10C22×C412yescomplemented
159C3×#170—22no—
160C3×C5×C8C22×C412yescomplemented
161C3×#168C22×C412yescomplemented
162C22×C3×Q8—51no—
163C22×C3×D4—51no—
164C23×C3×C4—101no—
165C2×C3×SD16—51no—
166C2×C3×SD16—51no—
167C2×C3×SD16—54no—
168C2×C3×SD16—54no—
169C2×C3×SD16—51no—
170C2×C3×SD16AGL(1,𝔽5)11yescharacteristic, complemented
171C22×C3×C8—51no—
172C22×C3×C8—51no—
173C3×C4×Q8—54no—
174C3×C4×Q8—102no—
175C3×C4×D4—54no—
176C3×C4×D4—102no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—101no—
180C2×C3×C22⋊C4—101no—
181C2×C3×C42—51no—
182C2×C3×C42—101no—
183C3×#107—54no—
184C3×#103—54no—
185C3×#102—54no—
186C3×#97—54no—
187C23×D5—21no—
188C22×AGL(1,𝔽5)—21no—
189C22×AGL(1,𝔽5)—21no—
190C22×AGL(1,𝔽5)—24no—
191C22×AGL(1,𝔽5)—44no—
192C22×AGL(1,𝔽5)C3×D411yescharacteristic
193C22×AGL(1,𝔽5)C3×D411yescharacteristic
194C2×C5×Q8C2×C3×C411yescharacteristic, complemented
195C2×C5×D4C2×C3×C411yescharacteristic
196C2×C22⋊D5—21no—
197Q8×D5—21no—
198Q8×D5—21no—
199Q8×D5C2×C3×C412yescomplemented
200Q8×D5C23×C312yes—
201D4×D5—21no—
202D4×D5—21no—
203D4×D5C2×C3×C412yes—
204D4×D5C23×C312yes—
205C2×D20C2×C3×C411yescharacteristic
206C2×C4×D5—21no—
207C2×C4×D5C23×C311yescharacteristic
208C2×Dic10—21no—
209C2×Dic10C2×C3×C411yescharacteristic, complemented
210C22⋊AGL(1,𝔽5)—24no—
211C2×#170—21no—
212C4⋊AGL(1,𝔽5)—24no—
213C4⋊AGL(1,𝔽5)—21no—
214C4⋊AGL(1,𝔽5)—21no—
215C4⋊AGL(1,𝔽5)C23×C312yes—
216C4⋊AGL(1,𝔽5)C23×C312yes—
217C4×AGL(1,𝔽5)—24no—
218C4×AGL(1,𝔽5)C3×D412yes—
219C4×AGL(1,𝔽5)C23×C312yes—
220D5⋊C8—21no—
221D5⋊C8C23×C312yes—
222C5×SD16C2×C3×C414yescomplemented
223C2×C5×C8C2×C3×C411yescharacteristic, complemented
224#688C2×C3×C414yescomplemented
225#687C2×C3×C414yescomplemented
226C2×#168C2×C3×C411yescharacteristic, complemented
227#677C2×C3×C414yescomplemented
228C8×D5C2×C3×C412yescomplemented
229C8×D5C23×C312yes—
230C22×SD16—51no—
231C2×C4×Q8—51no—
232C2×C4×D4—51no—
233#440—58no—
234C2×#107—51no—
235C2×#103—51no—
236C2×#102—51no—
237C2×#97—51no—
238C22×C3×C5—22no—
239C22×C3×C5—42no—
240C22×C3×C5C4×D411yescharacteristic
241C2×C3×D5—22no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—44no—
246C2×C3×D5C4×D411yescharacteristic
247C2×C3×D5AGL(1,ℤ/8)12yes—
248C2×C3×D5#13712yes—
249C2×C3×D5C22×D411yescharacteristic
250C3×AGL(1,𝔽5)—22no—
251C3×AGL(1,𝔽5)—22no—
252C3×AGL(1,𝔽5)—42no—
253C3×AGL(1,𝔽5)—42no—
254C3×C4×C5—22no—
255C3×C4×C5C4×D411yescharacteristic
256C3×C4×C5C23×C411yescharacteristic
257C3×Dic5—22no—
258C3×Dic5C4×D411yescharacteristic
259C3×Dic5C2×#4111yescharacteristic
260C24×C3—101no—
261C2×C3×Q8—52no—
262C2×C3×Q8—52no—
263C2×C3×Q8—51no—
264C2×C3×Q8—101no—
265C2×C3×Q8—101no—
266C2×C3×Q8—101no—
267C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
268C2×C3×D4—52no—
269C2×C3×D4—52no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C2×C3×D4—101no—
273C2×C3×D4—101no—
274C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4—101no—
279C22×C3×C4—104no—
280C22×C3×C4—101no—
281C22×C3×C4—101no—
282C22×C3×C4—204no—
283C3×SD16—54no—
284C3×SD16—54no—
285C3×SD16—54no—
286C3×SD16C2×AGL(1,𝔽5)14yescomplemented
287C2×C3×C8—51no—
288C2×C3×C8—52no—
289C2×C3×C8—52no—
290C2×C3×C8—52no—
291C2×C3×C8—101no—
292C2×C3×C8—101no—
293C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic, complemented
294C3×C4⋊C4—52no—
295C3×C4⋊C4—52no—
296C3×C4⋊C4—101no—
297C3×C4⋊C4—101no—
298C3×C4⋊C4—104no—
299C3×C22⋊C4—104no—
300C3×C42—52no—
301C3×C42—52no—
302C3×C42—104no—
303C23×C5—21no—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—42no—
308C22×D5—42no—
309C22×D5C2×C3×D411yescharacteristic
310C2×AGL(1,𝔽5)—22no—
311C2×AGL(1,𝔽5)—22no—
312C2×AGL(1,𝔽5)—22no—
313C2×AGL(1,𝔽5)—22no—
314C2×AGL(1,𝔽5)—48no—
315C2×AGL(1,𝔽5)—42no—
316C2×AGL(1,𝔽5)—42no—
317C2×AGL(1,𝔽5)C2×C3×D412yes—
318C2×AGL(1,𝔽5)C2×C3×D412yes—
319C5×Q8—21no—
320C5×Q8C22×C3×C412yescomplemented
321C5×D4—21no—
322C5×D4C22×C3×C412yes—
323C2×C4×C5—21no—
324C2×C4×C5C22×C3×C411yescharacteristic
325C22⋊D5—22no—
326C22⋊D5—22no—
327C2×Dic5—21no—
328C2×Dic5C3×#4111yescharacteristic
329D20—21no—
330D20C22×C3×C412yes—
331C4×D5—22no—
332C4×D5—22no—
333C4×D5C22×C3×C411yescharacteristic
334C4×D5C2×C3×D411yescharacteristic
335C4×D5C3×#4111yescharacteristic
336C4×D5C24×C311yescharacteristic
337Dic10—21no—
338Dic10—22no—
339Dic10—22no—
340Dic10C22×C3×C412yescomplemented
341#170—22no—
342C5×C8C22×C3×C412yescomplemented
343#168C22×C3×C412yescomplemented
344C22×Q8—51no—
345C22×D4—51no—
346C23×C4—101no—
347C2×SD16—51no—
348C2×SD16—51no—
349C2×SD16—54no—
350C2×SD16—54no—
351C2×SD16—51no—
352C2×SD16C3×AGL(1,𝔽5)11yescharacteristic, complemented
353C22×C8—51no—
354C22×C8—51no—
355C4×Q8—54no—
356C4×Q8—102no—
357C4×D4—54no—
358C4×D4—102no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—101no—
362C2×C22⋊C4—101no—
363C2×C42—51no—
364C2×C42—101no—
365#107—54no—
366#103—54no—
367#102—54no—
368#97—54no—
369C2×C3×C5—42no—
370C2×C3×C5#44012yescomplemented
371C2×C3×C5C2×C4×D411yescharacteristic
372C3×D5—42no—
373C3×D5#44012yescomplemented
374C3×D5C2×AGL(1,ℤ/8)11yescharacteristic
375C3×D5C2×#13711yescharacteristic
376C23×C3—21no—
377C23×C3—51no—
378C23×C3—102no—
379C23×C3—102no—
380C23×C3—101no—
381C23×C3—202no—
382C23×C3—202no—
383C3×Q8—21no—
384C3×Q8—52no—
385C3×Q8—102no—
386C3×Q8—102no—
387C3×Q8—101no—
388C3×Q8C22×AGL(1,𝔽5)12yescomplemented
389C3×D4—21no—
390C3×D4—52no—
391C3×D4—102no—
392C3×D4—102no—
393C3×D4—101no—
394C3×D4C22×AGL(1,𝔽5)12yes—
395C2×C3×C4—21no—
396C2×C3×C4—51no—
397C2×C3×C4—51no—
398C2×C3×C4—51no—
399C2×C3×C4—51no—
400C2×C3×C4—51no—
401C2×C3×C4—52no—
402C2×C3×C4—52no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—101no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4—208no—
411C2×C3×C4—202no—
412C2×C3×C4—202no—
413C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
414C3×C8—52no—
415C3×C8—102no—
416C3×C8C22×AGL(1,𝔽5)12yescomplemented
417C22×C5—22no—
418C22×C5—42no—
419C22×C5C3×C4×D411yescharacteristic
420C2×D5—22no—
421C2×D5—42no—
422C2×D5—42no—
423C2×D5—42no—
424C2×D5—44no—
425C2×D5C3×C4×D411yescharacteristic
426C2×D5C3×AGL(1,ℤ/8)12yes—
427C2×D5C3×#13712yes—
428C2×D5C22×C3×D411yescharacteristic
429AGL(1,𝔽5)—22no—
430AGL(1,𝔽5)—22no—
431AGL(1,𝔽5)—42no—
432AGL(1,𝔽5)—42no—
433C4×C5—22no—
434C4×C5C3×C4×D411yescharacteristic
435C4×C5C23×C3×C411yescharacteristic
436Dic5—22no—
437Dic5C3×C4×D411yescharacteristic
438Dic5C2×C3×#4111yescharacteristic
439C24—101no—
440C2×Q8—52no—
441C2×Q8—52no—
442C2×Q8—51no—
443C2×Q8—101no—
444C2×Q8—101no—
445C2×Q8—101no—
446C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
447C2×D4—52no—
448C2×D4—52no—
449C2×D4—51no—
450C2×D4—101no—
451C2×D4—101no—
452C2×D4—101no—
453C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
454C22×C4—51no—
455C22×C4—51no—
456C22×C4—51no—
457C22×C4—101no—
458C22×C4—104no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—204no—
462SD16—54no—
463SD16—54no—
464SD16—54no—
465SD16C2×C3×AGL(1,𝔽5)14yescomplemented
466C2×C8—51no—
467C2×C8—52no—
468C2×C8—52no—
469C2×C8—52no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
473C4⋊C4—52no—
474C4⋊C4—52no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—104no—
478C22⋊C4—104no—
479C42—52no—
480C42—52no—
481C42—104no—
482C3×C5C2×#44011yescharacteristic, complemented, Hall
483C22×C3—22no—
484C22×C3—42no—
485C22×C3—52no—
486C22×C3—52no—
487C22×C3—51no—
488C22×C3—51no—
489C22×C3—102no—
490C22×C3—202no—
491C22×C3—202no—
492C22×C3—204no—
493C22×C3—202no—
494C22×C3D4×AGL(1,𝔽5)11yescharacteristic
495C3×C4—22no—
496C3×C4—51no—
497C3×C4—51no—
498C3×C4—102no—
499C3×C4—102no—
500C3×C4—102no—
501C3×C4—202no—
502C3×C4—202no—
503C3×C4D4×AGL(1,𝔽5)11yescharacteristic
504C3×C4C23×AGL(1,𝔽5)11yescharacteristic
505C2×C5—42no—
506C2×C5C3×#44012yescomplemented
507C2×C5C2×C3×C4×D411yescharacteristic
508D5—42no—
509D5C3×#44012yescomplemented
510D5C2×C3×AGL(1,ℤ/8)11yescharacteristic
511D5C2×C3×#13711yescharacteristic
512C23—21no—
513C23—51no—
514C23—102no—
515C23—102no—
516C23—101no—
517C23—202no—
518C23—202no—
519Q8—21no—
520Q8—52no—
521Q8—102no—
522Q8—102no—
523Q8—101no—
524Q8C22×C3×AGL(1,𝔽5)12yescomplemented
525D4—21no—
526D4—52no—
527D4—102no—
528D4—102no—
529D4—101no—
530D4C22×C3×AGL(1,𝔽5)12yes—
531C2×C4—21no—
532C2×C4—51no—
533C2×C4—51no—
534C2×C4—51no—
535C2×C4—51no—
536C2×C4—51no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—101no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—208no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
550C8—52no—
551C8—102no—
552C8C22×C3×AGL(1,𝔽5)12yescomplemented
553C2×C3—42no—
554C2×C3—51no—
555C2×C3—51no—
556C2×C3—52no—
557C2×C3—202no—
558C2×C3#6573512yesdirect product factor
559C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
560C5C2×C3×#44011yescharacteristic, complemented, Sylow
561C22—22no—
562C22—42no—
563C22—52no—
564C22—52no—
565C22—51no—
566C22—51no—
567C22—102no—
568C22—202no—
569C22—202no—
570C22—204no—
571C22—202no—
572C22C3×D4×AGL(1,𝔽5)11yescharacteristic
573C4—22no—
574C4—51no—
575C4—51no—
576C4—102no—
577C4—102no—
578C4—102no—
579C4—202no—
580C4—202no—
581C4C3×D4×AGL(1,𝔽5)11yescharacteristic
582C4C23×C3×AGL(1,𝔽5)11yescharacteristic
583C3C2×#6573511yescharacteristic, direct product factor, Sylow
584C2—42no—
585C2—51no—
586C2—51no—
587C2—52no—
588C2—202no—
589C2C3×#6573512yesdirect product factor
590C2C2×C3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D4×D5C22
cosocleC4×D5C24×C3
hypercenterC2×C3×SD16AGL(1,𝔽5)
hypocenterC5C2×C3×#440
LCSG ▷ 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
4. C2×C3×#4009C2semidirect
6. C3×#65735C2direct (N × H)
7. C2×C3×#3994C2semidirect
8. C2×C3×#3992C2semidirect
9. C2×#65735C3direct (N × H)
15. C3×Q8×AGL(1,𝔽5)C22semidirect
24. C2×C3×C5×SD16C4semidirect
25. C2×C3×#688C4semidirect
26. C2×C3×#687C4semidirect
27. C3×D5×SD16C4semidirect
29. C2×C3×#677C4semidirect
31. C3×#4009C22semidirect
33. C3×#3994C22semidirect
34. C3×#3992C22semidirect
36. C2×Q8×AGL(1,𝔽5)C2×C3semidirect
39. C2×#4009C2×C3semidirect
41. #65735C2×C3direct (N × H)
42. C2×#3994C2×C3semidirect
43. C2×#3992C2×C3semidirect
51. C2×C3×C5×Q8C2×C4semidirect
56. C3×Q8×D5C2×C4semidirect
66. C2×C3×Dic10C2×C4semidirect
79. C3×C5×SD16C2×C4semidirect
80. C2×C3×C5×C8C2×C4semidirect
81. C3×#688C2×C4semidirect
82. C3×#687C2×C4semidirect
83. C2×C3×#168C2×C4semidirect
84. C3×#677C2×C4semidirect
85. C3×C8×D5C2×C4semidirect
100. Q8×AGL(1,𝔽5)C22×C3semidirect
109. C2×C5×SD16C3×C4semidirect
110. C2×#688C3×C4semidirect
111. C2×#687C3×C4semidirect
112. D5×SD16C3×C4semidirect
114. C2×#677C3×C4semidirect
116. #4009C22×C3semidirect
118. #3994C22×C3semidirect
119. #3992C22×C3semidirect
138. C3×C5×Q8C22×C4semidirect
158. C3×Dic10C22×C4semidirect
160. C3×C5×C8C22×C4semidirect
161. C3×#168C22×C4semidirect
170. C2×C3×SD16AGL(1,𝔽5)semidirect
194. C2×C5×Q8C2×C3×C4semidirect
199. Q8×D5C2×C3×C4semidirect
209. C2×Dic10C2×C3×C4semidirect
222. C5×SD16C2×C3×C4semidirect
223. C2×C5×C8C2×C3×C4semidirect
224. #688C2×C3×C4semidirect
225. #687C2×C3×C4semidirect
226. C2×#168C2×C3×C4semidirect
227. #677C2×C3×C4semidirect
228. C8×D5C2×C3×C4semidirect
267. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
286. C3×SD16C2×AGL(1,𝔽5)semidirect
293. C2×C3×C8C2×AGL(1,𝔽5)semidirect
320. C5×Q8C22×C3×C4semidirect
340. Dic10C22×C3×C4semidirect
342. C5×C8C22×C3×C4semidirect
343. #168C22×C3×C4semidirect
352. C2×SD16C3×AGL(1,𝔽5)semidirect
370. C2×C3×C5#440semidirect
373. C3×D5#440semidirect
388. C3×Q8C22×AGL(1,𝔽5)semidirect
416. C3×C8C22×AGL(1,𝔽5)semidirect
446. C2×Q8C2×C3×AGL(1,𝔽5)semidirect
465. SD16C2×C3×AGL(1,𝔽5)semidirect
472. C2×C8C2×C3×AGL(1,𝔽5)semidirect
482. C3×C5C2×#440semidirect
506. C2×C5C3×#440semidirect
509. D5C3×#440semidirect
524. Q8C22×C3×AGL(1,𝔽5)semidirect
552. C8C22×C3×AGL(1,𝔽5)semidirect
558. C2×C3#65735direct (N × H)
560. C5C2×C3×#440semidirect
583. C3C2×#65735direct (N × H)
589. C2C3×#65735direct (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×D4×AGL(1,𝔽5)2
C2×C3×D5×SD162
C2×C3×#40092
C2×C3×#40072
C3×#657352
C2×C3×#39942
C2×C3×#39922
C2×#657353
C2×C3×#4405