Finite Group Databasebeta

← #14330208

Subgroups — #14330208

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#947C211yesmaximal, characteristic
2#11752449C211yesmaximal, characteristic, complemented
3C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic, complemented
4#11751933C212yesmaximal
5#11751931C212yesmaximal, complemented
6AGL(1,𝔽5)×(C2×D3)⋊C4C212yesmaximal, complemented
7#11751841C212yesmaximal, complemented
8#11751836C212yesmaximal, complemented
9#11751832C212yesmaximal, complemented
10#10617327—31nomaximal, Hall
11C22×D3×AGL(1,𝔽5)C2212yes—
12C2×C3×Q8×D5C2211yescharacteristic
13C2×D5×D12C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
18C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
19C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
20C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3×AGL(1,𝔽5)C2212yes—
22C2×Dic3×AGL(1,𝔽5)C2212yes—
23#91836C411yescharacteristic, complemented
24C5×#947C411yescharacteristic, complemented
25D5×(C2×D3)⋊C4C2212yes—
26D5×(C2×D3)⋊C4C2212yes—
27C4×D5×Dic3C2211yescharacteristic
28#91374C411yescharacteristic, complemented
29#91370C411yescharacteristic, complemented
30#91326C412yescomplemented
31#91326C412yescomplemented
32#91235C2212yes—
33#91235C2212yes—
34C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
35C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
36(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
38#76495—51nomaximal, Hall
39D5×#124—31no—
40(C2×AGL(1,𝔽5))⋊Q8—31no—
41(C2×AGL(1,𝔽5))⋊Q8D311yescharacteristic, complemented
42#65779—32no—
43#65700—32no—
44#65700—32no—
45C22⋊C4×AGL(1,𝔽5)—32no—
46C22⋊C4×AGL(1,𝔽5)—32no—
47#65686—32no—
48C22×D3×D5C2312yes—
49C22×ΓL(1,𝔽16)C2312yes—
50C22×ΓL(1,𝔽16)C2312yes—
51C22×C3×AGL(1,𝔽5)C2312yes—
52C22×C3×AGL(1,𝔽5)C2312yes—
53C2×D3×AGL(1,𝔽5)—24no—
54C2×D3×AGL(1,𝔽5)—24no—
55C2×D3×AGL(1,𝔽5)—42no—
56C2×C3×C5×Q8C2×C411yescharacteristic, complemented
57C2×D60C2×C411yescharacteristic
58C2×C5×D12C2×C411yescharacteristic
59C3×Q8×D5—41no—
60C3×Q8×D5—41no—
61C2×C3×C4×D5C2311yescharacteristic
62C2×C3×C4×D5C2311yescharacteristic
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×Dic10C2×C411yescharacteristic, complemented
65C2×C3×Dic10C2×C411yescharacteristic, complemented
66C2×C3×Dic10C2×C411yescharacteristic, complemented
67C2×#1203C2×C412yes—
68C2×D5×Dic3C2312yes—
69D5×D12—41no—
70D5×D12—41no—
71C4⋊ΓL(1,𝔽16)—41no—
72C4×ΓL(1,𝔽16)—41no—
73C3×C4⋊AGL(1,𝔽5)—41no—
74C3×C4×AGL(1,𝔽5)—41no—
75(C2×D3)⋊AGL(1,𝔽5)—24no—
76(C2×D3)⋊AGL(1,𝔽5)—24no—
77(C2×D3)⋊AGL(1,𝔽5)—42no—
78Dic3×AGL(1,𝔽5)—24no—
79Dic3×AGL(1,𝔽5)—24no—
80#6714C2×C412yescomplemented
81#6714C2×C412yescomplemented
82C4×Dic15C2×C411yescharacteristic, complemented
83C5×(C2×D3)⋊C4C2×C412yescomplemented
84C5×(C2×D3)⋊C4C2×C412yescomplemented
85C4×C5×Dic3C2×C411yescharacteristic, complemented
86#6667C2×C412yescomplemented
87#6667C2×C412yescomplemented
88(C2×D3)⋊Dic5C2×C412yescomplemented
89(C2×D3)⋊Dic5C2×C412yescomplemented
90Dic3×Dic5C2×C412yescomplemented
91C2×#947—51no—
92C3×#391—51no—
93#5229—51no—
94#4990—52no—
95C4×(C2×D3)⋊C4—52no—
96#4670—52no—
97#4666—52no—
98#4665—52no—
99#4648—52no—
100C23×AGL(1,𝔽5)—32no—
101C2×Q8×D5C2×D311yescharacteristic
102C2×D4×D5—31no—
103C2×C22⋊AGL(1,𝔽5)—32no—
104C2×C22⋊AGL(1,𝔽5)—32no—
105C2×C22⋊AGL(1,𝔽5)—32no—
106C2×C4⋊AGL(1,𝔽5)—31no—
107C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
108C2×C4×AGL(1,𝔽5)—32no—
109C2×C4×AGL(1,𝔽5)—32no—
110C2×C4×AGL(1,𝔽5)—31no—
111C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
112C5×#124—31no—
113#4093—31no—
114#4082—31no—
115#4031—32no—
116#4031—32no—
117D5×C22⋊C4—32no—
118D5×C22⋊C4—32no—
119#4021—31no—
120C42×D5—31no—
121(C2×AGL(1,𝔽5))⋊C4—32no—
122(C2×AGL(1,𝔽5))⋊C4—32no—
123(C2×AGL(1,𝔽5))⋊C4—32no—
124(C2×AGL(1,𝔽5))⋊C4—32no—
125(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
126(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
127#2372—151noSylow
128C22×D15C22×C412yes—
129C22×C5×D3C22×C412yes—
130C22×C3×D5C2411yescharacteristic
131C2×D3×D5—22no—
132C2×D3×D5—22no—
133C2×D3×D5—22no—
134C2×D3×D5—22no—
135C2×D3×D5—22no—
136C2×D3×D5—22no—
137C2×ΓL(1,𝔽16)—22no—
138C2×ΓL(1,𝔽16)—22no—
139C2×ΓL(1,𝔽16)—22no—
140C2×ΓL(1,𝔽16)—22no—
141C2×ΓL(1,𝔽16)—22no—
142C2×ΓL(1,𝔽16)#4114yes—
143C2×C3×AGL(1,𝔽5)—22no—
144C2×C3×AGL(1,𝔽5)—22no—
145C2×C3×AGL(1,𝔽5)—22no—
146C2×C3×AGL(1,𝔽5)—22no—
147C2×C3×AGL(1,𝔽5)—22no—
148C2×C3×AGL(1,𝔽5)#4114yes—
149D3×AGL(1,𝔽5)—48no—
150C3×C5×Q8—41no—
151C2×C3×C4×C5C22×C411yescharacteristic
152C2×C3×C4×C5C22×C411yescharacteristic
153C2×C3×C4×C5C22×C411yescharacteristic
154C2×Dic15C22×C412yes—
155D60—41no—
156C2×C5×Dic3C22×C412yes—
157C5×D12—41no—
158C2×C3×Dic5C22×C411yescharacteristic
159C2×C3×Dic5C22×C411yescharacteristic
160C2×C3×Dic5C22×C411yescharacteristic
161C3×C4×D5—21no—
162C3×C4×D5—21no—
163C3×C4×D5—21no—
164C3×C4×D5—21no—
165C3×C4×D5—21no—
166C3×C4×D5—21no—
167C3×Dic10—41no—
168C3×Dic10—41no—
169C3×Dic10—41no—
170#1203—42no—
171D5×Dic3—22no—
172D5×Dic3—22no—
173C22×C3×Q8—51no—
174C22×D12—51no—
175C22×C4×D3—52no—
176C2×C3×C4⋊C4—51no—
177C2×C3×C42—51no—
178#947—51no—
179#947—51no—
180#947—52no—
181#947—52no—
182#947—51no—
183#947AGL(1,𝔽5)11yescharacteristic, complemented
184C2×(C2×D3)⋊C4—52no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×(C2×D3)⋊C4—52no—
188C2×(C2×D3)⋊C4—52no—
189C2×C4⋊Dic3—51no—
190C2×C4×Dic3—51no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—51no—
194C3×#95—52no—
195C3×#95—52no—
196C3⋊#95—52no—
197C3⋊#95—52no—
198C3⋊#95—52no—
199C3⋊#95—52no—
200C23×D5—32no—
201C22×AGL(1,𝔽5)—32no—
202C22×AGL(1,𝔽5)—32no—
203C22×AGL(1,𝔽5)—64no—
204C22×AGL(1,𝔽5)—64no—
205C22×AGL(1,𝔽5)—122no—
206C22×AGL(1,𝔽5)C22×D312yes—
207C22×AGL(1,𝔽5)C22×D312yes—
208C2×C5×Q8C4×D311yescharacteristic, complemented
209C2×C5×D4—31no—
210C2×C22⋊D5—32no—
211Q8×D5—41no—
212Q8×D5—41no—
213D4×D5—121no—
214D4×D5—121no—
215C2×D20—31no—
216C2×C4×D5—32no—
217C2×C4×D5C22×D311yescharacteristic
218C2×C4×D5C22×D311yescharacteristic
219C2×C4×D5C22×D311yescharacteristic
220C2×Dic10C4×D311yescharacteristic, complemented
221C2×Dic10C4×D311yescharacteristic, complemented
222C2×Dic10C4×D311yescharacteristic, complemented
223C22⋊AGL(1,𝔽5)—64no—
224C22⋊AGL(1,𝔽5)—64no—
225C22⋊AGL(1,𝔽5)—122no—
226C4⋊AGL(1,𝔽5)—41no—
227C4⋊AGL(1,𝔽5)—121no—
228C4×AGL(1,𝔽5)—41no—
229C4×AGL(1,𝔽5)—64no—
230C4×AGL(1,𝔽5)—64no—
231C4×AGL(1,𝔽5)—121no—
232C5×C22⋊C4—32no—
233C5×C22⋊C4—32no—
234C42×C5—31no—
235C22⋊Dic5—32no—
236C22⋊Dic5—32no—
237#685—32no—
238#685—32no—
239#685—32no—
240#685—32no—
241C4×Dic5—31no—
242C4×Dic5—32no—
243C2×#124—151no—
244#391—51no—
245#391—151no—
246#388—152no—
247#388—152no—
248#386—152no—
249C4×C22⋊C4—152no—
250C4×C22⋊C4—152no—
251#376—152no—
252C22×C3×C5C23×C411yescharacteristic
253C2×D15—22no—
254C2×D15—22no—
255C2×D15—22no—
256C2×C5×D3—22no—
257C2×C5×D3—22no—
258C2×C5×D3—22no—
259C2×C3×D5C2×#4112yes—
260C2×C3×D5C2×#4112yes—
261C2×C3×D5H(5,𝔽2)11yescharacteristic
262C2×C3×D5H(5,𝔽2)11yescharacteristic
263D3×D5—42no—
264D3×D5—42no—
265D3×D5—42no—
266D3×D5—42no—
267ΓL(1,𝔽16)—24no—
268ΓL(1,𝔽16)—42no—
269C3×AGL(1,𝔽5)—24no—
270C3×AGL(1,𝔽5)—42no—
271C3×C4×C5—21no—
272C3×C4×C5—21no—
273C3×C4×C5—21no—
274Dic15—22no—
275C3×Dic5—21no—
276C3×Dic5—21no—
277C3×Dic5—21no—
278C5×Dic3—22no—
279C23×D3—52no—
280C2×C3×Q8—51no—
281C2×C3×Q8—51no—
282C2×C3×Q8—51no—
283C2×C3×Q8—201no—
284C2×C3×Q8—201no—
285C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
286C22×C3×C4—52no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×Dic3—52no—
292C22×Dic3—52no—
293C22×Dic3—52no—
294C2×D12—52no—
295C2×D12—51no—
296C2×D12—201no—
297C2×D12—201no—
298C2×D12C2×AGL(1,𝔽5)11yescharacteristic
299C2×C4×D3—104no—
300C2×C4×D3—104no—
301C2×C4×D3—202no—
302C3×C4⋊C4—201no—
303C3×C42—201no—
304(C2×D3)⋊C4—52no—
305(C2×D3)⋊C4—52no—
306(C2×D3)⋊C4—52no—
307(C2×D3)⋊C4—52no—
308(C2×D3)⋊C4—52no—
309(C2×D3)⋊C4—52no—
310(C2×D3)⋊C4—104no—
311(C2×D3)⋊C4—104no—
312(C2×D3)⋊C4—202no—
313(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
314(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
315C4⋊Dic3—201no—
316C4×Dic3—51no—
317C4×Dic3—52no—
318C4×Dic3—104no—
319C4×Dic3—104no—
320C4×Dic3—201no—
321C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
322C23×C5—32no—
323C22×D5—32no—
324C22×D5—62no—
325C22×D5—62no—
326C22×D5—62no—
327C22×D5—62no—
328C22×D5—62no—
329C22×D5—62no—
330C22×D5C23×D311yescharacteristic
331C2×AGL(1,𝔽5)—22no—
332C2×AGL(1,𝔽5)—22no—
333C2×AGL(1,𝔽5)—22no—
334C2×AGL(1,𝔽5)—22no—
335C2×AGL(1,𝔽5)—22no—
336C2×AGL(1,𝔽5)—34no—
337C2×AGL(1,𝔽5)—62no—
338C2×AGL(1,𝔽5)—62no—
339C2×AGL(1,𝔽5)—62no—
340C2×AGL(1,𝔽5)—62no—
341C2×AGL(1,𝔽5)—62no—
342C2×AGL(1,𝔽5)—128no—
343C2×AGL(1,𝔽5)#23914yes—
344C5×Q8—41no—
345C5×D4—121no—
346C2×C4×C5—32no—
347C2×C4×C5C2×C4×D311yescharacteristic
348C2×C4×C5C2×C4×D311yescharacteristic
349C2×C4×C5C2×C4×D311yescharacteristic
350C22⋊D5—122no—
351C2×Dic5—32no—
352C2×Dic5C2×C4×D311yescharacteristic
353C2×Dic5C2×C4×D311yescharacteristic
354C2×Dic5C2×C4×D311yescharacteristic
355D20—121no—
356C4×D5—21no—
357C4×D5—21no—
358C4×D5—21no—
359C4×D5—21no—
360C4×D5—21no—
361C4×D5—21no—
362C4×D5—62no—
363C4×D5—62no—
364Dic10—41no—
365Dic10—41no—
366Dic10—41no—
367C22×Q8—51no—
368C22×D4—151no—
369C23×C4—152no—
370#124—31no—
371#124—151no—
372#124—152no—
373#124—152no—
374#124—151no—
375#124—151no—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—151no—
378C2×C22⋊C4—152no—
379C2×C22⋊C4—152no—
380C2×C22⋊C4—152no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C42—51no—
384C2×C42—151no—
385C2×C42—152no—
386C2×C42—152no—
387C2×C42—151no—
388#95—52no—
389#95—52no—
390#95—152no—
391#95—152no—
392#95—152no—
393#95—152no—
394C2×C3×C5C4×#4112yes—
395C2×C3×C5#51811yescharacteristic
396D15—42no—
397C3×D5#55112yes—
398C3×D5#55511yescharacteristic
399C3×D5#55511yescharacteristic
400C5×D3—42no—
401C23×C3—51no—
402C22×D3—52no—
403C22×D3—102no—
404C22×D3—102no—
405C22×D3—102no—
406C22×D3—102no—
407C22×D3—102no—
408C22×D3—102no—
409C22×D3C22×AGL(1,𝔽5)12yes—
410C3×Q8—41no—
411C3×Q8—201no—
412C3×Q8—201no—
413C3×Q8—201no—
414C2×C3×C4—54no—
415C2×C3×C4—51no—
416C2×C3×C4—51no—
417C2×C3×C4—51no—
418C2×C3×C4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—101no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—101no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—102no—
427C2×C3×C4—102no—
428C2×C3×C4—102no—
429C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
430C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
431C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
432C2×Dic3—54no—
433C2×Dic3—52no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—102no—
438C2×Dic3—102no—
439C2×Dic3—102no—
440C2×Dic3—102no—
441C2×Dic3C22×AGL(1,𝔽5)12yes—
442D12—41no—
443D12—201no—
444D12—202no—
445C4×D3—208no—
446C22×C5—62no—
447C22×C5—62no—
448C22×C5—62no—
449C22×C5C22×C4×D311yescharacteristic
450C2×D5—62no—
451C2×D5—62no—
452C2×D5—62no—
453C2×D5—122no—
454C2×D5—122no—
455C2×D5—122no—
456C2×D5—122no—
457C2×D5#100411yescharacteristic
458C2×D5#100411yescharacteristic
459C2×D5C2×#23912yes—
460C2×D5D3×#4112yes—
461AGL(1,𝔽5)—24no—
462AGL(1,𝔽5)—42no—
463AGL(1,𝔽5)—64no—
464AGL(1,𝔽5)—122no—
465C4×C5—21no—
466C4×C5—21no—
467C4×C5—21no—
468C4×C5—62no—
469Dic5—21no—
470Dic5—21no—
471Dic5—21no—
472Dic5—62no—
473C24—152no—
474C2×Q8—51no—
475C2×Q8—51no—
476C2×Q8—51no—
477C2×Q8—201no—
478C2×Q8—201no—
479C2×Q8D3×AGL(1,𝔽5)11yescharacteristic, complemented
480C2×D4—31no—
481C2×D4—152no—
482C2×D4—151no—
483C2×D4—601no—
484C2×D4—601no—
485C22×C4—52no—
486C22×C4—51no—
487C22×C4—51no—
488C22×C4—51no—
489C22×C4—52no—
490C22×C4—152no—
491C22×C4—152no—
492C22×C4—152no—
493C22×C4—304no—
494C22×C4—304no—
495C22×C4—602no—
496C4⋊C4—201no—
497C4⋊C4—601no—
498C22⋊C4—32no—
499C22⋊C4—32no—
500C22⋊C4—152no—
501C22⋊C4—152no—
502C22⋊C4—152no—
503C22⋊C4—152no—
504C22⋊C4—152no—
505C22⋊C4—152no—
506C22⋊C4—304no—
507C22⋊C4—304no—
508C22⋊C4—602no—
509C42—31no—
510C42—152no—
511C42—151no—
512C42—201no—
513C42—304no—
514C42—304no—
515C42—601no—
516C3×C5#237211yescharacteristic, complemented, Hall
517C22×C3—51no—
518C22×C3—51no—
519C22×C3—52no—
520C22×C3—52no—
521C22×C3C23×AGL(1,𝔽5)11yescharacteristic
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—102no—
526C2×D3—102no—
527C2×D3—102no—
528C2×D3—202no—
529C2×D3—202no—
530C2×D3—202no—
531C2×D3—202no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—104no—
536C3×C4—101no—
537C3×C4—101no—
538C3×C4—101no—
539C3×C4—202no—
540Dic3—22no—
541Dic3—104no—
542Dic3—102no—
543Dic3—202no—
544C2×C5—122no—
545C2×C5#548611yescharacteristic
546C2×C5C4×#23912yes—
547D5—122no—
548D5#563712yes—
549D5#567011yescharacteristic
550D5#573411yescharacteristic
551C23—32no—
552C23—51no—
553C23—152no—
554C23—302no—
555C23—302no—
556C23—302no—
557C23—302no—
558C23—302no—
559C23—302no—
560Q8—41no—
561Q8—201no—
562Q8—201no—
563Q8—201no—
564D4—121no—
565D4—601no—
566D4—602no—
567C2×C4—32no—
568C2×C4—54no—
569C2×C4—51no—
570C2×C4—51no—
571C2×C4—51no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—154no—
584C2×C4—152no—
585C2×C4—302no—
586C2×C4—302no—
587C2×C4—302no—
588C2×C4—302no—
589C2×C4—302no—
590C2×C4—302no—
591C2×C4—302no—
592C2×C4—608no—
593C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
594C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
595C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
596C2×C3—52no—
597C2×C3—51no—
598C2×C3—51no—
599C2×C3#6625811yescharacteristic
600C2×C3#41×AGL(1,𝔽5)12yes—
601D3—42no—
602D3—202no—
603C5#7649511yescharacteristic, complemented, Sylow
604C22—52no—
605C22—52no—
606C22—51no—
607C22—51no—
608C22—62no—
609C22—62no—
610C22—62no—
611C22—302no—
612C22—302no—
613C22—302no—
614C22—602no—
615C22—602no—
616C22—602no—
617C22—602no—
618C22C22×D3×AGL(1,𝔽5)11yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—62no—
623C4—104no—
624C4—101no—
625C4—101no—
626C4—101no—
627C4—202no—
628C4—304no—
629C4—302no—
630C4—602no—
631C3#1061732711yescharacteristic, complemented, Sylow
632C2—52no—
633C2—51no—
634C2—51no—
635C2—122no—
636C2—602no—
637C2AGL(1,𝔽5)×#23912yes—
638C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radicalC2×D5×D12C22
cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2372
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11752449C2semidirect
3. C3×(C2×AGL(1,𝔽5))⋊Q8C2semidirect
5. #11751931C2semidirect
6. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
7. #11751841C2semidirect
8. #11751836C2semidirect
9. #11751832C2semidirect
23. #91836C4semidirect
24. C5×#947C4semidirect
28. #91374C4semidirect
29. #91370C4semidirect
30. #91326C4semidirect
31. #91326C4semidirect
41. (C2×AGL(1,𝔽5))⋊Q8D3semidirect
56. C2×C3×C5×Q8C2×C4semidirect
64. C2×C3×Dic10C2×C4semidirect
65. C2×C3×Dic10C2×C4semidirect
66. C2×C3×Dic10C2×C4semidirect
80. #6714C2×C4semidirect
81. #6714C2×C4semidirect
82. C4×Dic15C2×C4semidirect
83. C5×(C2×D3)⋊C4C2×C4semidirect
84. C5×(C2×D3)⋊C4C2×C4semidirect
85. C4×C5×Dic3C2×C4semidirect
86. #6667C2×C4semidirect
87. #6667C2×C4semidirect
88. (C2×D3)⋊Dic5C2×C4semidirect
89. (C2×D3)⋊Dic5C2×C4semidirect
90. Dic3×Dic5C2×C4semidirect
183. #947AGL(1,𝔽5)semidirect
208. C2×C5×Q8C4×D3semidirect
220. C2×Dic10C4×D3semidirect
221. C2×Dic10C4×D3semidirect
222. C2×Dic10C4×D3semidirect
285. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
313. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
314. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
321. C4×Dic3C2×AGL(1,𝔽5)semidirect
479. C2×Q8D3×AGL(1,𝔽5)semidirect
516. C3×C5#2372semidirect
603. C5#76495semidirect
631. C3#10617327semidirect

Maximal subgroups

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

subgroupindex
D5×#9472
#117524492
C3×(C2×AGL(1,𝔽5))⋊Q82
#117519332
#117519312
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518412
#117518362
#117518322
#106173273
#764955