Finite Group Databasebeta

← #14327762

Subgroups — #14327762

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4130C211yesmaximal, characteristic, complemented
2C2×#91907C211yesmaximal, characteristic, complemented
3C4×D5×#67C211yesmaximal, characteristic
4#11752424C211yesmaximal, characteristic, complemented
5#11752019C212yesmaximal
6#11752017C212yesmaximal, complemented
7#11751860C211yesmaximal, characteristic, complemented
8#11751855C211yesmaximal, characteristic, complemented
9#11751849C212yesmaximal, complemented
10Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
11AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal, complemented
12#10617181—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×D5×#67C2211yescharacteristic
15C2×C4×D3×D5C2211yescharacteristic
16C2×#6763C2212yes—
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
19C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
20C3×#4130—24no—
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×C4×AGL(1,𝔽5)C2212yes—
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
27C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
28C2×Dic3×AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2212yes—
30#91907—24no—
31C4×#1220C411yescharacteristic, complemented
32C4×C5×#67C411yescharacteristic, complemented
33#91552C411yescharacteristic, complemented
34Dic5×#67C411yescharacteristic, complemented
35D5×#217C2211yescharacteristic
36D5×(C2×D3)⋊C4C2211yescharacteristic
37#91444C411yescharacteristic, complemented
38C4×#1202C411yescharacteristic, complemented
39#91440C411yescharacteristic, complemented
40C4×#1201C411yescharacteristic, complemented
41D5×Dic3⋊C4C2211yescharacteristic
42C4×D5×Dic3C2211yescharacteristic
43#91235C2212yes—
44(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
45(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
46#82241—51nomaximal, Hall
47C2×#4130—31no—
48C2×#4130D311yescharacteristic, complemented
49C4×D4×D5—31no—
50#65780—32no—
51#65765—31no—
52#65765—31no—
53C4⋊C4×AGL(1,𝔽5)—32no—
54#65700—32no—
55#65700—32no—
56#65688—31no—
57C4×C4⋊AGL(1,𝔽5)—31no—
58C23×C3×D5C2311yescharacteristic
59C22×D3×D5C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×AGL(1,𝔽5)C2312yes—
64C22×C3×C4×C5C2×C411yescharacteristic
65C2×#1220C2×C411yescharacteristic
66C2×C4×D15C2×C411yescharacteristic
67C2×C5×#67C2×C411yescharacteristic
68C2×C4×C5×D3C2×C411yescharacteristic
69C22×C3×Dic5C2×C411yescharacteristic
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5C2×C411yescharacteristic
73C2×C3×C4×D5C2×C411yescharacteristic
74C2×C3×C4×D5C2311yescharacteristic
75C2×C3×C4×D5C2311yescharacteristic
76D5×#67—22no—
77D5×#67—22no—
78C2×#1202C2×C411yescharacteristic
79C2×#1201C2×C411yescharacteristic
80C2×#1200C2×C411yescharacteristic
81C2×D3×Dic5C2×C411yescharacteristic
82C2×D5×Dic3C2311yescharacteristic
83C2×D5×Dic3C2311yescharacteristic
84C2×D5×Dic3C2311yescharacteristic
85C4×D3×D5—22no—
86C4×D3×D5—22no—
87#6763—42no—
88C4⋊ΓL(1,𝔽16)—22no—
89C4⋊ΓL(1,𝔽16)—22no—
90C3×C22⋊AGL(1,𝔽5)—24no—
91C3×C4⋊AGL(1,𝔽5)—22no—
92C3×C4⋊AGL(1,𝔽5)D414yescomplemented
93C3×C4×AGL(1,𝔽5)—24no—
94Dic3⋊AGL(1,𝔽5)—24no—
95Dic3⋊AGL(1,𝔽5)—42no—
96(C2×D3)⋊AGL(1,𝔽5)—24no—
97(C2×D3)⋊AGL(1,𝔽5)—42no—
98Dic3×AGL(1,𝔽5)—24no—
99Dic3×AGL(1,𝔽5)—24no—
100#6719C2×C411yescharacteristic
101#6714C2×C411yescharacteristic
102#6712C2×C411yescharacteristic
103C4×Dic15C2×C411yescharacteristic
104C5×#217C2×C411yescharacteristic
105C5×(C2×D3)⋊C4C2×C411yescharacteristic
106C5×Dic3⋊C4C2×C411yescharacteristic
107C4×C5×Dic3C2×C411yescharacteristic
108Dic3⋊Dic5C2×C411yescharacteristic
109#6669C2×C411yescharacteristic
110#6667C2×C411yescharacteristic
111(C2×D3)⋊Dic5C2×C411yescharacteristic
112#6665C2×C411yescharacteristic
113#6665C2×C411yescharacteristic
114Dic3×Dic5C2×C411yescharacteristic
115Dic3×Dic5C2×C411yescharacteristic
116C2×C3×#117—51no—
117C2×C4×#67—51no—
118C2×#892—51no—
119#5212—51no—
120#4987—51no—
121#4975—51no—
122Dic3×C4⋊C4—51no—
123#4957—52no—
124#4944—52no—
125#4940—52no—
126C4×Dic3⋊C4—52no—
127C2×D4×D5—31no—
128C22×C4×D5—31no—
129C22×C4×D5C2×D311yescharacteristic
130C2×C22⋊AGL(1,𝔽5)—32no—
131C2×C22⋊AGL(1,𝔽5)—32no—
132C2×C22⋊AGL(1,𝔽5)—32no—
133C2×C22⋊AGL(1,𝔽5)C2×D312yes—
134#4130—24no—
135#4130—64no—
136C2×C4⋊AGL(1,𝔽5)—32no—
137C2×C4⋊AGL(1,𝔽5)—31no—
138C2×C4⋊AGL(1,𝔽5)—31no—
139C2×C4⋊AGL(1,𝔽5)—32no—
140C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
141C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
142C2×C4×AGL(1,𝔽5)—32no—
143C2×C4×AGL(1,𝔽5)—32no—
144C2×C4×AGL(1,𝔽5)C2×D312yes—
145C4×C5×D4—31no—
146D4×Dic5—31no—
147C4×C22⋊D5—31no—
148C4×C22⋊D5—31no—
149#4039—31no—
150D5×C4⋊C4—31no—
151#4027—31no—
152#4027—31no—
153D5×C22⋊C4—31no—
154D5×C22⋊C4—31no—
155C4×D20—31no—
156C42×D5—31no—
157(C2×AGL(1,𝔽5))⋊C4—32no—
158(C2×AGL(1,𝔽5))⋊C4—32no—
159(C2×AGL(1,𝔽5))⋊C4—32no—
160#2354—151noSylow
161C23×C3×C5C22×C411yescharacteristic
162C22×D15C22×C411yescharacteristic
163C22×C5×D3C22×C411yescharacteristic
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5C22×C411yescharacteristic
171C22×C3×D5C2411yescharacteristic
172C2×D3×D5—21no—
173C2×D3×D5—21no—
174C2×D3×D5—21no—
175C2×D3×D5—21no—
176C2×D3×D5—21no—
177C2×D3×D5—21no—
178C2×ΓL(1,𝔽16)—22no—
179C2×ΓL(1,𝔽16)—22no—
180C2×ΓL(1,𝔽16)—22no—
181C2×ΓL(1,𝔽16)—22no—
182C2×ΓL(1,𝔽16)—22no—
183C2×ΓL(1,𝔽16)—22no—
184C2×C3×AGL(1,𝔽5)—22no—
185C2×C3×AGL(1,𝔽5)—22no—
186C2×C3×AGL(1,𝔽5)—22no—
187C2×C3×AGL(1,𝔽5)—22no—
188C2×C3×AGL(1,𝔽5)—22no—
189C2×C3×AGL(1,𝔽5)C2×D414yes—
190C2×C3×C4×C5—22no—
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×C3×C4×C5C22×C411yescharacteristic
193#1220—22no—
194C2×Dic15C22×C411yescharacteristic
195C2×Dic15C22×C411yescharacteristic
196C2×Dic15C22×C411yescharacteristic
197C4×D15—22no—
198C5×#67—22no—
199C2×C5×Dic3C22×C411yescharacteristic
200C2×C5×Dic3C22×C411yescharacteristic
201C2×C5×Dic3C22×C411yescharacteristic
202C4×C5×D3—22no—
203C2×C3×Dic5—22no—
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C22×C411yescharacteristic
206C3×C4×D5—21no—
207C3×C4×D5—21no—
208C3×C4×D5—22no—
209C3×C4×D5—22no—
210C3×C4×D5C2×D412yes—
211C3×C4×D5#4112yes—
212#1202—22no—
213#1201—22no—
214#1200—22no—
215D3×Dic5—22no—
216D5×Dic3—21no—
217D5×Dic3—21no—
218D5×Dic3—21no—
219D5×Dic3—21no—
220D5×Dic3#4112yes—
221D5×Dic3#4112yes—
222C23×C3×C4—51no—
223C22×#67—51no—
224C22×C4×D3—51no—
225C3×#117—104no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C22⋊C4—52no—
229C2×C3×C42—52no—
230C2×#217—51no—
231C2×#217—52no—
232C4×#67—51no—
233C4×#67—51no—
234C4×#67—51no—
235C4×#67—51no—
236C4×#67—51no—
237C4×#67—51no—
238C4×#67—51no—
239C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
240C2×(C2×D3)⋊C4—51no—
241C2×(C2×D3)⋊C4—52no—
242C2×(C2×D3)⋊C4—52no—
243C2×C4⋊Dic3—51no—
244C2×C4⋊Dic3—51no—
245C2×Dic3⋊C4—51no—
246C2×Dic3⋊C4—52no—
247C2×Dic3⋊C4—52no—
248C2×C4×Dic3—51no—
249C2×C4×Dic3—52no—
250C2×C4×Dic3—52no—
251#892—104no—
252C3⋊#95—52no—
253C3⋊#95—52no—
254C3⋊#95—52no—
255C23×D5—31no—
256C23×D5C22×D311yescharacteristic
257C22×AGL(1,𝔽5)—32no—
258C22×AGL(1,𝔽5)—32no—
259C22×AGL(1,𝔽5)C22×D312yes—
260C22×AGL(1,𝔽5)C22×D312yes—
261C2×C5×D4—31no—
262C22×C4×C5—31no—
263C22×C4×C5C4×D311yescharacteristic
264C2×C22⋊D5—31no—
265C2×C22⋊D5—31no—
266C22×Dic5—31no—
267C22×Dic5C4×D311yescharacteristic
268D4×D5—62no—
269D4×D5—62no—
270C2×D20—31no—
271C2×C4×D5—22no—
272C2×C4×D5—22no—
273C2×C4×D5—31no—
274C2×C4×D5—31no—
275C2×C4×D5—31no—
276C2×C4×D5—31no—
277C2×C4×D5—31no—
278C2×C4×D5—62no—
279C2×C4×D5—62no—
280C2×C4×D5C4×D311yescharacteristic
281C2×C4×D5C4×D311yescharacteristic
282C2×C4×D5C22×D311yescharacteristic
283C2×C4×D5C22×D311yescharacteristic
284C22⋊AGL(1,𝔽5)—24no—
285C22⋊AGL(1,𝔽5)—64no—
286C22⋊AGL(1,𝔽5)—122no—
287C22⋊AGL(1,𝔽5)—122no—
288C4⋊AGL(1,𝔽5)—22no—
289C4⋊AGL(1,𝔽5)—64no—
290C4⋊AGL(1,𝔽5)—62no—
291C4⋊AGL(1,𝔽5)—62no—
292C4⋊AGL(1,𝔽5)—122no—
293C4⋊AGL(1,𝔽5)#6714yescomplemented
294C4×AGL(1,𝔽5)—24no—
295C4×AGL(1,𝔽5)—64no—
296C4×AGL(1,𝔽5)—64no—
297C5×C4⋊C4—31no—
298C5×C22⋊C4—31no—
299C5×C22⋊C4—31no—
300C42×C5—31no—
301C22⋊Dic5—31no—
302C22⋊Dic5—31no—
303#685—31no—
304#685—31no—
305#685—31no—
306#685—31no—
307C4⋊Dic5—31no—
308#683—31no—
309#683—31no—
310C4×Dic5—31no—
311C4×Dic5—31no—
312C4×Dic5—31no—
313C2×C4×D4—151no—
314C2×#117—51no—
315C2×#117—151no—
316#390—152no—
317#388—152no—
318#388—152no—
319#384—151no—
320#380—151no—
321#380—151no—
322C4×C4⋊C4—152no—
323C4×C4⋊C4—151no—
324C22×C3×C5—21no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5C23×C411yescharacteristic
328C2×D15—21no—
329C2×D15—21no—
330C2×D15—21no—
331C2×C5×D3—21no—
332C2×C5×D3—21no—
333C2×C5×D3—21no—
334C2×C3×D5—21no—
335C2×C3×D5—21no—
336C2×C3×D5—21no—
337C2×C3×D5—41no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5C22×D411yescharacteristic
342C2×C3×D5C2×#4111yescharacteristic
343C2×C3×D5C2×#4111yescharacteristic
344C2×C3×D5C2×#4111yescharacteristic
345C2×C3×D5H(5,𝔽2)11yescharacteristic
346C2×C3×D52−1+411yescharacteristic
347D3×D5—41no—
348D3×D5—41no—
349D3×D5—41no—
350D3×D5—41no—
351ΓL(1,𝔽16)—42no—
352ΓL(1,𝔽16)—42no—
353C3×AGL(1,𝔽5)—24no—
354C3×AGL(1,𝔽5)—42no—
355C3×C4×C5—21no—
356C3×C4×C5C4×D412yes—
357Dic15—21no—
358Dic15—21no—
359Dic15#11712yescomplemented
360C3×Dic5—21no—
361C3×Dic5C4×D412yes—
362C5×Dic3—21no—
363C5×Dic3—21no—
364C5×Dic3#11712yescomplemented
365C24×C3—51no—
366C23×D3—51no—
367C22×C3×C4—51no—
368C22×C3×C4—52no—
369C22×C3×C4—51no—
370C22×C3×C4—51no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—52no—
374C22×C3×C4—102no—
375C22×C3×C4—102no—
376C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
377C2×#67—51no—
378C2×#67—51no—
379C2×#67—51no—
380C2×#67—102no—
381C2×#67—102no—
382C2×#67C2×AGL(1,𝔽5)11yescharacteristic
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—52no—
387C22×Dic3—52no—
388C2×C4×D3—51no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
394C3×C4⋊C4—54no—
395C3×C4⋊C4—102no—
396C3×C22⋊C4—104no—
397C3×C42—104no—
398#217—51no—
399#217—51no—
400#217—51no—
401#217—202no—
402#217C2×AGL(1,𝔽5)11yescharacteristic
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—51no—
405(C2×D3)⋊C4—51no—
406(C2×D3)⋊C4—104no—
407(C2×D3)⋊C4—202no—
408(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
409C4⋊Dic3—102no—
410C4⋊Dic3—102no—
411Dic3⋊C4—51no—
412Dic3⋊C4—51no—
413Dic3⋊C4—51no—
414Dic3⋊C4—104no—
415Dic3⋊C4—202no—
416Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
417C4×Dic3—51no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—104no—
421C4×Dic3—104no—
422C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
423C23×C5—31no—
424C23×C5C2×C4×D311yescharacteristic
425C22×D5—21no—
426C22×D5—21no—
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—31no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
436C22×D5—61no—
437C22×D5—61no—
438C22×D5C2×C4×D311yescharacteristic
439C22×D5C23×D311yescharacteristic
440C2×AGL(1,𝔽5)—22no—
441C2×AGL(1,𝔽5)—22no—
442C2×AGL(1,𝔽5)—22no—
443C2×AGL(1,𝔽5)—22no—
444C2×AGL(1,𝔽5)—22no—
445C2×AGL(1,𝔽5)—62no—
446C2×AGL(1,𝔽5)—62no—
447C2×AGL(1,𝔽5)—62no—
448C2×AGL(1,𝔽5)—62no—
449C2×AGL(1,𝔽5)—62no—
450C2×AGL(1,𝔽5)—62no—
451C2×AGL(1,𝔽5)C2×#6714yes—
452C5×D4—62no—
453C2×C4×C5—22no—
454C2×C4×C5—31no—
455C2×C4×C5—31no—
456C2×C4×C5—31no—
457C2×C4×C5—62no—
458C2×C4×C5C2×C4×D311yescharacteristic
459C2×C4×C5C2×C4×D311yescharacteristic
460C22⋊D5—62no—
461C22⋊D5—62no—
462C2×Dic5—22no—
463C2×Dic5—31no—
464C2×Dic5—31no—
465C2×Dic5—31no—
466C2×Dic5—62no—
467C2×Dic5C2×C4×D311yescharacteristic
468C2×Dic5C2×C4×D311yescharacteristic
469D20—62no—
470C4×D5—21no—
471C4×D5—21no—
472C4×D5—22no—
473C4×D5—22no—
474C4×D5—32no—
475C4×D5—32no—
476C4×D5—61no—
477C4×D5—61no—
478C4×D5—61no—
479C4×D5—61no—
480C4×D5—62no—
481C4×D5—62no—
482C4×D5#23512yes—
483C4×D5C2×#6712yes—
484C22×D4—151no—
485C23×C4—51no—
486C23×C4—151no—
487C4×D4—31no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—151no—
492C4×D4—151no—
493C4×D4—151no—
494C4×D4—151no—
495#117—104no—
496#117—304no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—151no—
500C2×C4⋊C4—151no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—152no—
503C2×C4⋊C4—152no—
504C2×C22⋊C4—52no—
505C2×C22⋊C4—151no—
506C2×C22⋊C4—151no—
507C2×C22⋊C4—152no—
508C2×C22⋊C4—152no—
509C2×C22⋊C4—152no—
510C2×C42—52no—
511C2×C42—151no—
512C2×C42—152no—
513C2×C42—152no—
514#95—152no—
515#95—152no—
516#95—152no—
517C2×C3×C5—41no—
518C2×C3×C5C2×#11711yescharacteristic
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#52011yescharacteristic
521D15—41no—
522C3×D5—41no—
523C3×D5#54711yescharacteristic
524C3×D5#55011yescharacteristic
525C3×D5#55511yescharacteristic
526C3×D5#55611yescharacteristic
527C5×D3—41no—
528C23×C3—51no—
529C23×C3—51no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3C22×AGL(1,𝔽5)11yescharacteristic
537C22×D3—51no—
538C22×D3—101no—
539C22×D3—101no—
540C22×D3—101no—
541C22×D3—101no—
542C22×D3—101no—
543C22×D3—101no—
544C22×D3C22×AGL(1,𝔽5)11yescharacteristic
545C2×C3×C4—22no—
546C2×C3×C4—51no—
547C2×C3×C4—52no—
548C2×C3×C4—52no—
549C2×C3×C4—54no—
550C2×C3×C4—51no—
551C2×C3×C4—102no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—102no—
555C2×C3×C4—102no—
556C2×C3×C4—102no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—102no—
560C2×C3×C4—102no—
561C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
562C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
563#67—22no—
564#67—102no—
565#67—102no—
566#67—102no—
567C2×Dic3—51no—
568C2×Dic3—52no—
569C2×Dic3—52no—
570C2×Dic3—51no—
571C2×Dic3—51no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—102no—
577C2×Dic3—102no—
578C2×Dic3—102no—
579C2×Dic3—102no—
580C2×Dic3—102no—
581C2×Dic3—102no—
582C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
583C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
584C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
585C4×D3—22no—
586C4×D3—102no—
587C4×D3—102no—
588C4×D3—102no—
589C22×C5—21no—
590C22×C5—21no—
591C22×C5—21no—
592C22×C5—61no—
593C22×C5—61no—
594C22×C5—61no—
595C22×C5C22×C4×D311yescharacteristic
596C2×D5—21no—
597C2×D5—21no—
598C2×D5—21no—
599C2×D5—41no—
600C2×D5—41no—
601C2×D5—41no—
602C2×D5—41no—
603C2×D5—61no—
604C2×D5—61no—
605C2×D5—61no—
606C2×D5—121no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5C2×#23511yescharacteristic
611C2×D5D3×#4111yescharacteristic
612C2×D5D3×#4111yescharacteristic
613C2×D5#100911yescharacteristic
614C2×D5#101011yescharacteristic
615C2×D5C22×#6711yescharacteristic
616AGL(1,𝔽5)—24no—
617AGL(1,𝔽5)—42no—
618AGL(1,𝔽5)—122no—
619AGL(1,𝔽5)—122no—
620C4×C5—21no—
621C4×C5—32no—
622C4×C5—61no—
623C4×C5—61no—
624C4×C5C4×#6712yes—
625Dic5—21no—
626Dic5—32no—
627Dic5—61no—
628Dic5—61no—
629Dic5C4×#6712yes—
630C24—51no—
631C24—151no—
632C2×D4—31no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—302no—
637C2×D4—302no—
638C22×C4—31no—
639C22×C4—51no—
640C22×C4—52no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—52no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—151no—
649C22×C4—151no—
650C22×C4—151no—
651C22×C4—151no—
652C22×C4—151no—
653C22×C4—151no—
654C22×C4—152no—
655C22×C4—152no—
656C22×C4—302no—
657C22×C4—302no—
658C22×C4D3×AGL(1,𝔽5)11yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—54no—
661C4⋊C4—102no—
662C4⋊C4—151no—
663C4⋊C4—151no—
664C4⋊C4—151no—
665C4⋊C4—302no—
666C4⋊C4—302no—
667C4⋊C4—304no—
668C4⋊C4—602no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—104no—
672C22⋊C4—151no—
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—304no—
679C22⋊C4—602no—
680C22⋊C4—602no—
681C42—31no—
682C42—104no—
683C42—151no—
684C42—151no—
685C42—151no—
686C42—304no—
687C42—304no—
688C3×C5#235411yescharacteristic, complemented, Hall
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—51no—
693C22×C3—51no—
694C22×C3—51no—
695C22×C3—51no—
696C22×C3—51no—
697C22×C3—51no—
698C22×C3—101no—
699C22×C3—101no—
700C22×C3—101no—
701C22×C3—201no—
702C22×C3—201no—
703C22×C3—201no—
704C22×C3—201no—
705C22×C3C23×AGL(1,𝔽5)11yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—101no—
710C2×D3—101no—
711C2×D3—101no—
712C2×D3—201no—
713C2×D3—201no—
714C2×D3—201no—
715C2×D3—201no—
716C3×C4—21no—
717C3×C4—52no—
718C3×C4—104no—
719C3×C4—101no—
720C3×C4—202no—
721C3×C4D4×AGL(1,𝔽5)12yes—
722Dic3—21no—
723Dic3—21no—
724Dic3—52no—
725Dic3—101no—
726Dic3—101no—
727Dic3—202no—
728Dic3—202no—
729Dic3#413012yescomplemented
730C2×C5—41no—
731C2×C5—121no—
732C2×C5D3×#11711yescharacteristic
733C2×C5#552311yescharacteristic
734C2×C5C2×C4×#6711yescharacteristic
735D5—41no—
736D5—121no—
737D5#553211yescharacteristic
738D5#553311yescharacteristic
739D5#582411yescharacteristic
740D5#583411yescharacteristic
741C23—31no—
742C23—51no—
743C23—51no—
744C23—101no—
745C23—101no—
746C23—101no—
747C23—101no—
748C23—101no—
749C23—101no—
750C23—151no—
751C23—301no—
752C23—301no—
753C23—301no—
754C23—301no—
755C23—301no—
756C23—301no—
757C23C2×D3×AGL(1,𝔽5)11yescharacteristic
758D4—62no—
759D4—302no—
760D4—302no—
761D4—302no—
762C2×C4—22no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—51no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—54no—
770C2×C4—51no—
771C2×C4—62no—
772C2×C4—102no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—152no—
783C2×C4—152no—
784C2×C4—151no—
785C2×C4—151no—
786C2×C4—151no—
787C2×C4—302no—
788C2×C4—302no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—302no—
794C2×C4—302no—
795C2×C4—302no—
796C2×C4—302no—
797C2×C4—302no—
798C2×C4—302no—
799C2×C4—302no—
800C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
801C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
802C2×C3—41no—
803C2×C3—51no—
804C2×C3—51no—
805C2×C3—51no—
806C2×C3—51no—
807C2×C3—201no—
808C2×C3C2×#413011yescharacteristic
809C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
810C2×C3#6626611yescharacteristic
811D3—41no—
812D3—201no—
813C5#8224111yescharacteristic, complemented, Sylow
814C22—21no—
815C22—21no—
816C22—21no—
817C22—51no—
818C22—51no—
819C22—51no—
820C22—51no—
821C22—51no—
822C22—51no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—101no—
827C22—101no—
828C22—101no—
829C22—201no—
830C22—201no—
831C22—201no—
832C22—201no—
833C22—301no—
834C22—301no—
835C22—301no—
836C22—601no—
837C22—601no—
838C22—601no—
839C22—601no—
840C22C22×D3×AGL(1,𝔽5)11yescharacteristic
841C4—21no—
842C4—32no—
843C4—52no—
844C4—61no—
845C4—61no—
846C4—104no—
847C4—101no—
848C4—152no—
849C4—202no—
850C4—301no—
851C4—301no—
852C4—602no—
853C4—602no—
854C4AGL(1,𝔽5)×#6712yes—
855C3#1061718111yescharacteristic, complemented, Sylow
856C2—41no—
857C2—51no—
858C2—51no—
859C2—51no—
860C2—51no—
861C2—121no—
862C2—201no—
863C2—601no—
864C2D3×#413011yescharacteristic
865C2#1175683811yescharacteristic
866C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4130C2semidirect
2. C2×#91907C2semidirect
4. #11752424C2semidirect
6. #11752017C2semidirect
7. #11751860C2semidirect
8. #11751855C2semidirect
9. #11751849C2semidirect
10. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
11. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
31. C4×#1220C4semidirect
32. C4×C5×#67C4semidirect
33. #91552C4semidirect
34. Dic5×#67C4semidirect
37. #91444C4semidirect
38. C4×#1202C4semidirect
39. #91440C4semidirect
40. C4×#1201C4semidirect
48. C2×#4130D3semidirect
92. C3×C4⋊AGL(1,𝔽5)D4semidirect
239. C4×#67AGL(1,𝔽5)semidirect
293. C4⋊AGL(1,𝔽5)#67semidirect
359. Dic15#117semidirect
364. C5×Dic3#117semidirect
688. C3×C5#2354semidirect
729. Dic3#4130semidirect
813. C5#82241semidirect
855. C3#10617181semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41302
C2×#919072
C4×D5×#672
#117524242
#117520192
#117520172
#117518602
#117518552
#117518492
Dic3×C4⋊AGL(1,𝔽5)2
AGL(1,𝔽5)×Dic3⋊C42
#106171813
#822415