Finite Group Databasebeta

← #14327655

Subgroups — #14327655

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D5×#67C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic, complemented
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
4#11752022C212yesmaximal
5AGL(1,𝔽5)×#217C212yesmaximal, complemented
6#11751853C211yesmaximal, characteristic, complemented
7#11751848C211yesmaximal, characteristic, complemented
8#11751845C212yesmaximal, complemented
9#11751841C212yesmaximal, complemented
10#11751832C211yesmaximal, characteristic, complemented
11#11751750C211yesmaximal, characteristic, complemented
12#10617180—31nomaximal, Hall
13C23×C3×AGL(1,𝔽5)C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×D5×#67C2211yescharacteristic
16C2×C4×D3×D5C2211yescharacteristic
17C2×#6763C2212yes—
18C2×C4⋊ΓL(1,𝔽16)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—
23C4×#1220C411yescharacteristic, complemented
24C4×C5×#67C411yescharacteristic, complemented
25#91552C411yescharacteristic, complemented
26Dic5×#67C411yescharacteristic, complemented
27D5×#217C2211yescharacteristic
28D5×(C2×D3)⋊C4C2211yescharacteristic
29#91444C411yescharacteristic, complemented
30C4×#1202C411yescharacteristic, complemented
31#91440C411yescharacteristic, complemented
32C4×#1201C411yescharacteristic, complemented
33D5×Dic3⋊C4C2211yescharacteristic
34C4×D5×Dic3C2211yescharacteristic
35#91235C2211yescharacteristic
36#91235C2211yescharacteristic
37C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
38C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73336—51nomaximal, Hall
45C4×D4×D5—31no—
46#65779—32no—
47#65765—31no—
48#65764—31no—
49C4×C22⋊AGL(1,𝔽5)—31no—
50C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic, complemented
51#65711—32no—
52#65700—32no—
53C22⋊C4×AGL(1,𝔽5)—32no—
54#65690—31no—
55#65686—31no—
56C23×C3×D5C2311yescharacteristic
57C22×D3×D5C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2312yes—
59C22×ΓL(1,𝔽16)C2312yes—
60C22×C3×AGL(1,𝔽5)—24no—
61C22×C3×AGL(1,𝔽5)—24no—
62C22×C3×AGL(1,𝔽5)—42no—
63C22×C3×AGL(1,𝔽5)C2312yes—
64C22×C3×AGL(1,𝔽5)C2312yes—
65C22×C3×C4×C5C2×C411yescharacteristic
66C2×#1220C2×C411yescharacteristic
67C2×C4×D15C2×C411yescharacteristic, complemented
68C2×C5×#67C2×C411yescharacteristic
69C2×C4×C5×D3C2×C411yescharacteristic, complemented
70C22×C3×Dic5C2×C411yescharacteristic
71C2×C3×C4×D5—42no—
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, complemented
81C2×D3×Dic5C2×C411yescharacteristic, complemented
82C2×D5×Dic3C2311yescharacteristic
83C2×D5×Dic3C2311yescharacteristic
84C2×D5×Dic3C2311yescharacteristic
85C4×D3×D5—42no—
86#6763—24no—
87C4⋊ΓL(1,𝔽16)—42no—
88(C2×D3)⋊AGL(1,𝔽5)—24no—
89(C2×D3)⋊AGL(1,𝔽5)—42no—
90Dic3×AGL(1,𝔽5)—24no—
91Dic3×AGL(1,𝔽5)—42no—
92#6719C2×C411yescharacteristic
93#6714C2×C411yescharacteristic, complemented
94#6712C2×C411yescharacteristic, complemented
95C4×Dic15C2×C411yescharacteristic, complemented
96C5×#217C2×C411yescharacteristic
97C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
98C5×Dic3⋊C4C2×C411yescharacteristic, complemented
99C4×C5×Dic3C2×C411yescharacteristic, complemented
100Dic3⋊Dic5C2×C411yescharacteristic, complemented
101#6669C2×C411yescharacteristic, complemented
102#6667C2×C411yescharacteristic, complemented
103(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
104#6665C2×C411yescharacteristic
105#6665C2×C411yescharacteristic
106Dic3×Dic5C2×C411yescharacteristic, complemented
107Dic3×Dic5C2×C411yescharacteristic, complemented
108C2×C4×#67—51no—
109C2×C3×#95—51no—
110#5213—52no—
111#5212—51no—
112C4×#217—52no—
113#4670—52no—
114#4666—51no—
115#4664—51no—
116#4655—52no—
117#4651—51no—
118#4648—51no—
119C23×AGL(1,𝔽5)C2×D312yes—
120C2×D4×D5—31no—
121C22×C4×D5—31no—
122C22×C4×D5C2×D311yescharacteristic
123C2×C22⋊AGL(1,𝔽5)—32no—
124C2×C22⋊AGL(1,𝔽5)—32no—
125C2×C22⋊AGL(1,𝔽5)—32no—
126C2×C4⋊AGL(1,𝔽5)—32no—
127C2×C4×AGL(1,𝔽5)—32no—
128C2×C4×AGL(1,𝔽5)—32no—
129C4×C5×D4—31no—
130D4×Dic5—31no—
131C4×C22⋊D5—31no—
132C4×C22⋊D5—31no—
133#4039—31no—
134D5×C4⋊C4—31no—
135#4027—31no—
136#4027—31no—
137D5×C22⋊C4—31no—
138D5×C22⋊C4—31no—
139C4×D20—31no—
140C42×D5—31no—
141(C2×AGL(1,𝔽5))⋊C4—32no—
142(C2×AGL(1,𝔽5))⋊C4—32no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4—32no—
145(C2×AGL(1,𝔽5))⋊C4—31no—
146(C2×AGL(1,𝔽5))⋊C4—31no—
147(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
148(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
149(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
150#2353—151noSylow
151C23×C3×C5C22×C411yescharacteristic
152C22×D15C22×C411yescharacteristic
153C22×C5×D3C22×C411yescharacteristic
154C22×C3×D5—22no—
155C22×C3×D5—22no—
156C22×C3×D5C22×C411yescharacteristic
157C22×C3×D5#4112yes—
158C22×C3×D5#4112yes—
159C22×C3×D5C2411yescharacteristic
160C2×D3×D5—22no—
161C2×D3×D5—21no—
162C2×D3×D5—21no—
163C2×D3×D5—22no—
164C2×ΓL(1,𝔽16)—22no—
165C2×ΓL(1,𝔽16)—22no—
166C2×ΓL(1,𝔽16)—22no—
167C2×ΓL(1,𝔽16)—22no—
168C2×ΓL(1,𝔽16)—22no—
169C2×ΓL(1,𝔽16)—22no—
170C2×C3×AGL(1,𝔽5)—22no—
171C2×C3×AGL(1,𝔽5)—22no—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—22no—
174C2×C3×AGL(1,𝔽5)—22no—
175C2×C3×AGL(1,𝔽5)—48no—
176C2×C3×AGL(1,𝔽5)#4114yes—
177C2×C3×C4×C5—41no—
178C2×C3×C4×C5C22×C411yescharacteristic
179C2×C3×C4×C5C22×C411yescharacteristic
180#1220—22no—
181C2×Dic15C22×C411yescharacteristic
182C2×Dic15C22×C411yescharacteristic
183C2×Dic15C22×C411yescharacteristic
184C4×D15—41no—
185C5×#67—22no—
186C2×C5×Dic3C22×C411yescharacteristic
187C2×C5×Dic3C22×C411yescharacteristic
188C2×C5×Dic3C22×C411yescharacteristic
189C4×C5×D3—41no—
190C2×C3×Dic5—41no—
191C2×C3×Dic5C22×C411yescharacteristic
192C2×C3×Dic5C22×C411yescharacteristic
193C3×C4×D5—22no—
194C3×C4×D5—22no—
195C3×C4×D5—41no—
196C3×C4×D5—41no—
197#1202—22no—
198#1201—22no—
199#1200—41no—
200D3×Dic5—41no—
201D5×Dic3—22no—
202D5×Dic3—21no—
203D5×Dic3—21no—
204D5×Dic3—22no—
205C23×C3×C4—51no—
206C23×C3×C4—52no—
207C22×#67—51no—
208C22×C4×D3—51no—
209C2×#217—51no—
210C2×#217—52no—
211C4×#67—51no—
212C4×#67—51no—
213C4×#67—51no—
214C4×#67—51no—
215C4×#67—51no—
216C4×#67—51no—
217C4×#67—51no—
218C4×#67AGL(1,𝔽5)11yescharacteristic, complemented
219C2×(C2×D3)⋊C4—51no—
220C2×(C2×D3)⋊C4—52no—
221C2×(C2×D3)⋊C4—52no—
222C2×C4⋊Dic3—52no—
223C2×Dic3⋊C4—51no—
224C2×C4×Dic3—51no—
225C2×C4×Dic3—52no—
226C2×C4×Dic3—52no—
227C3×#95—51no—
228C3×#95—51no—
229C3×#95—52no—
230C3⋊#95—52no—
231C3⋊#95—52no—
232C3⋊#95—52no—
233C3⋊#95—52no—
234C3⋊#95—51no—
235C3⋊#95—51no—
236C23×D5—31no—
237C23×D5C22×D311yescharacteristic
238C22×AGL(1,𝔽5)—24no—
239C22×AGL(1,𝔽5)—24no—
240C22×AGL(1,𝔽5)—32no—
241C22×AGL(1,𝔽5)—32no—
242C22×AGL(1,𝔽5)—42no—
243C22×AGL(1,𝔽5)C22×D312yes—
244C22×AGL(1,𝔽5)C22×D312yes—
245C2×C5×D4—31no—
246C22×C4×C5—31no—
247C22×C4×C5C4×D311yescharacteristic
248C2×C22⋊D5—31no—
249C2×C22⋊D5—31no—
250C22×Dic5—31no—
251C22×Dic5C4×D311yescharacteristic
252D4×D5—62no—
253D4×D5—62no—
254C2×D20—31no—
255C2×C4×D5—31no—
256C2×C4×D5—31no—
257C2×C4×D5—31no—
258C2×C4×D5—31no—
259C2×C4×D5—31no—
260C2×C4×D5—42no—
261C2×C4×D5—122no—
262C2×C4×D5C4×D311yescharacteristic
263C2×C4×D5C4×D311yescharacteristic
264C2×C4×D5C22×D311yescharacteristic
265C2×C4×D5C22×D311yescharacteristic
266C22⋊AGL(1,𝔽5)—64no—
267C22⋊AGL(1,𝔽5)—64no—
268C22⋊AGL(1,𝔽5)—122no—
269C4⋊AGL(1,𝔽5)—122no—
270C4×AGL(1,𝔽5)—64no—
271C4×AGL(1,𝔽5)—122no—
272C5×C4⋊C4—31no—
273C5×C22⋊C4—31no—
274C5×C22⋊C4—31no—
275C42×C5—31no—
276C22⋊Dic5—31no—
277C22⋊Dic5—31no—
278#685—31no—
279#685—31no—
280#685—31no—
281#685—31no—
282C4⋊Dic5—31no—
283#683—31no—
284#683—31no—
285C4×Dic5—31no—
286C4×Dic5—31no—
287C4×Dic5—31no—
288C2×C4×D4—151no—
289#388—152no—
290#387—152no—
291#386—152no—
292#383—151no—
293#381—151no—
294#380—151no—
295C4×C22⋊C4—151no—
296C4×C22⋊C4—152no—
297#376—151no—
298C2×#95—51no—
299C22×C3×C5—21no—
300C22×C3×C5—21no—
301C22×C3×C5#11712yes—
302C22×C3×C5C23×C411yescharacteristic
303C2×D15—21no—
304C2×D15—21no—
305C2×D15—21no—
306C2×C5×D3—21no—
307C2×C5×D3—21no—
308C2×C5×D3—21no—
309C2×C3×D5—21no—
310C2×C3×D5—21no—
311C2×C3×D5—24no—
312C2×C3×D5—24no—
313C2×C3×D5#11712yes—
314C2×C3×D5C2×#4112yes—
315C2×C3×D5C2×#4111yescharacteristic
316C2×C3×D5C2×#4111yescharacteristic
317C2×C3×D5H(5,𝔽2)12yes—
318D3×D5—42no—
319D3×D5—42no—
320ΓL(1,𝔽16)—42no—
321ΓL(1,𝔽16)—42no—
322C3×AGL(1,𝔽5)—24no—
323C3×AGL(1,𝔽5)—42no—
324C3×C4×C5—21no—
325C3×C4×C5—21no—
326Dic15—21no—
327Dic15—21no—
328Dic15—21no—
329C3×Dic5—21no—
330C3×Dic5—21no—
331C5×Dic3—21no—
332C5×Dic3—21no—
333C5×Dic3—21no—
334C24×C3—51no—
335C23×D3—51no—
336C22×C3×C4—52no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—52no—
343C22×C3×C4—104no—
344C22×C3×C4—104no—
345C22×C3×C4—202no—
346C22×C3×C4—202no—
347C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
348C2×#67—51no—
349C2×#67—51no—
350C2×#67—51no—
351C2×#67—102no—
352C2×#67—102no—
353C2×#67C2×AGL(1,𝔽5)11yescharacteristic
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—52no—
358C22×Dic3—52no—
359C2×C4×D3—51no—
360C2×C4×D3—51no—
361C2×C4×D3—51no—
362C2×C4×D3—202no—
363C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
364#217—51no—
365#217—51no—
366#217—51no—
367#217—104no—
368#217C2×AGL(1,𝔽5)11yescharacteristic
369(C2×D3)⋊C4—51no—
370(C2×D3)⋊C4—51no—
371(C2×D3)⋊C4—51no—
372(C2×D3)⋊C4—104no—
373(C2×D3)⋊C4—202no—
374(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
375C4⋊Dic3—202no—
376Dic3⋊C4—51no—
377Dic3⋊C4—51no—
378Dic3⋊C4—51no—
379Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
380C4×Dic3—51no—
381C4×Dic3—51no—
382C4×Dic3—51no—
383C4×Dic3—104no—
384C4×Dic3—202no—
385C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
386C23×C5—31no—
387C23×C5C2×C4×D311yescharacteristic
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—31no—
391C22×D5—62no—
392C22×D5—61no—
393C22×D5—62no—
394C22×D5—61no—
395C22×D5C2×C4×D311yescharacteristic
396C22×D5#23712yes—
397C22×D5#23912yes—
398C22×D5C23×D311yescharacteristic
399C2×AGL(1,𝔽5)—22no—
400C2×AGL(1,𝔽5)—22no—
401C2×AGL(1,𝔽5)—22no—
402C2×AGL(1,𝔽5)—22no—
403C2×AGL(1,𝔽5)—22no—
404C2×AGL(1,𝔽5)—48no—
405C2×AGL(1,𝔽5)—62no—
406C2×AGL(1,𝔽5)—62no—
407C2×AGL(1,𝔽5)—62no—
408C2×AGL(1,𝔽5)—62no—
409C2×AGL(1,𝔽5)—62no—
410C2×AGL(1,𝔽5)—62no—
411C2×AGL(1,𝔽5)#23514yes—
412C5×D4—62no—
413C2×C4×C5—31no—
414C2×C4×C5—31no—
415C2×C4×C5—31no—
416C2×C4×C5—41no—
417C2×C4×C5—121no—
418C2×C4×C5C2×C4×D311yescharacteristic
419C2×C4×C5C2×C4×D311yescharacteristic
420C22⋊D5—62no—
421C22⋊D5—62no—
422C2×Dic5—31no—
423C2×Dic5—31no—
424C2×Dic5—31no—
425C2×Dic5—41no—
426C2×Dic5—121no—
427C2×Dic5C2×C4×D311yescharacteristic
428C2×Dic5C2×C4×D311yescharacteristic
429D20—62no—
430C4×D5—22no—
431C4×D5—22no—
432C4×D5—41no—
433C4×D5—41no—
434C4×D5—62no—
435C4×D5—61no—
436C4×D5—62no—
437C4×D5—61no—
438C4×D5—121no—
439C4×D5—121no—
440C22×D4—151no—
441C23×C4—51no—
442C23×C4—52no—
443C23×C4—151no—
444C4×D4—31no—
445C4×D4—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—151no—
449C4×D4—151no—
450C4×D4—151no—
451C4×D4—151no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—152no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C22⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—152no—
459C2×C42—151no—
460C2×C42—152no—
461C2×C42—152no—
462#95—51no—
463#95—51no—
464#95—52no—
465#95—151no—
466#95—152no—
467#95—151no—
468#95—152no—
469#95—152no—
470#95—152no—
471C2×C3×C5—22no—
472C2×C3×C5C2×#11711yescharacteristic
473C2×C3×C5C4×#4111yescharacteristic
474C2×C3×C5#51811yescharacteristic
475D15—41no—
476C3×D5—22no—
477C3×D5#55112yes—
478C3×D5#55312yes—
479C5×D3—41no—
480C23×C3—51no—
481C23×C3—52no—
482C23×C3—52no—
483C23×C3—51no—
484C23×C3—102no—
485C23×C3—102no—
486C23×C3C22×AGL(1,𝔽5)11yescharacteristic
487C22×D3—51no—
488C22×D3—102no—
489C22×D3—102no—
490C22×D3—101no—
491C22×D3—101no—
492C22×D3C22×AGL(1,𝔽5)11yescharacteristic
493C2×C3×C4—41no—
494C2×C3×C4—54no—
495C2×C3×C4—51no—
496C2×C3×C4—51no—
497C2×C3×C4—102no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—102no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4—201no—
505C2×C3×C4—201no—
506C2×C3×C4—201no—
507C2×C3×C4—208no—
508C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
509C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
510#67—22no—
511#67—102no—
512#67—102no—
513#67—102no—
514C2×Dic3—51no—
515C2×Dic3—51no—
516C2×Dic3—51no—
517C2×Dic3—102no—
518C2×Dic3—102no—
519C2×Dic3—101no—
520C2×Dic3—101no—
521C2×Dic3—102no—
522C2×Dic3—102no—
523C2×Dic3—102no—
524C2×Dic3—102no—
525C2×Dic3—102no—
526C2×Dic3—102no—
527C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
528C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
529C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
530C4×D3—41no—
531C4×D3—201no—
532C4×D3—201no—
533C4×D3—201no—
534C22×C5—21no—
535C22×C5—21no—
536C22×C5—61no—
537C22×C5—61no—
538C22×C5—61no—
539C22×C5#89212yes—
540C22×C5C22×C4×D311yescharacteristic
541C2×D5—21no—
542C2×D5—21no—
543C2×D5—24no—
544C2×D5—24no—
545C2×D5—61no—
546C2×D5—61no—
547C2×D5—61no—
548C2×D5—122no—
549C2×D5—122no—
550C2×D5#89212yes—
551C2×D5C2×#23512yes—
552C2×D5C2×#23711yescharacteristic
553C2×D5#100412yes—
554C2×D5C2×#23911yescharacteristic
555AGL(1,𝔽5)—24no—
556AGL(1,𝔽5)—42no—
557AGL(1,𝔽5)—122no—
558AGL(1,𝔽5)—122no—
559C4×C5—21no—
560C4×C5—21no—
561C4×C5—61no—
562C4×C5—61no—
563C4×C5—61no—
564Dic5—21no—
565Dic5—21no—
566Dic5—61no—
567Dic5—61no—
568Dic5—61no—
569C24—51no—
570C24—151no—
571C2×D4—31no—
572C2×D4—151no—
573C2×D4—151no—
574C2×D4—151no—
575C2×D4—302no—
576C2×D4—302no—
577C22×C4—31no—
578C22×C4—52no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—51no—
582C22×C4—51no—
583C22×C4—51no—
584C22×C4—52no—
585C22×C4—104no—
586C22×C4—104no—
587C22×C4—151no—
588C22×C4—151no—
589C22×C4—151no—
590C22×C4—151no—
591C22×C4—151no—
592C22×C4—151no—
593C22×C4—152no—
594C22×C4—152no—
595C22×C4—202no—
596C22×C4—202no—
597C22×C4—602no—
598C22×C4D3×AGL(1,𝔽5)11yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—151no—
601C4⋊C4—151no—
602C4⋊C4—151no—
603C4⋊C4—602no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—151no—
607C22⋊C4—151no—
608C22⋊C4—151no—
609C22⋊C4—151no—
610C22⋊C4—151no—
611C22⋊C4—151no—
612C22⋊C4—304no—
613C22⋊C4—304no—
614C22⋊C4—602no—
615C42—31no—
616C42—151no—
617C42—151no—
618C42—151no—
619C42—304no—
620C42—602no—
621C3×C5#235311yescharacteristic, complemented, Hall
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—51no—
625C22×C3—51no—
626C22×C3—52no—
627C22×C3—52no—
628C22×C3—52no—
629C22×C3—104no—
630C22×C3—104no—
631C22×C3—101no—
632C22×C3—101no—
633C22×C3#413012yes—
634C22×C3C23×AGL(1,𝔽5)11yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—101no—
639C2×D3—101no—
640C2×D3—101no—
641C2×D3—202no—
642C2×D3—202no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—104no—
646C3×C4—101no—
647C3×C4—101no—
648C3×C4—202no—
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—101no—
653Dic3—101no—
654Dic3—101no—
655Dic3—202no—
656Dic3—202no—
657C2×C5—22no—
658C2×C5—121no—
659C2×C5C4×#23511yescharacteristic
660C2×C5#548611yescharacteristic
661C2×C5C2×#89211yescharacteristic
662D5—22no—
663D5—121no—
664D5#549512yes—
665D5#551412yes—
666C23—31no—
667C23—51no—
668C23—52no—
669C23—52no—
670C23—51no—
671C23—102no—
672C23—102no—
673C23—151no—
674C23—302no—
675C23—302no—
676C23—301no—
677C23—301no—
678C23C2×D3×AGL(1,𝔽5)11yescharacteristic
679D4—62no—
680D4—302no—
681D4—302no—
682D4—302no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—41no—
687C2×C4—54no—
688C2×C4—51no—
689C2×C4—51no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—121no—
698C2×C4—151no—
699C2×C4—151no—
700C2×C4—151no—
701C2×C4—201no—
702C2×C4—201no—
703C2×C4—201no—
704C2×C4—208no—
705C2×C4—302no—
706C2×C4—302no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—302no—
710C2×C4—302no—
711C2×C4—302no—
712C2×C4—302no—
713C2×C4—302no—
714C2×C4—302no—
715C2×C4—601no—
716C2×C4—601no—
717C2×C4—601no—
718C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
719C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
720C2×C3—22no—
721C2×C3—52no—
722C2×C3—52no—
723C2×C3—102no—
724C2×C3C2×#413011yescharacteristic
725C2×C3#6625811yescharacteristic
726C2×C3#41×AGL(1,𝔽5)11yescharacteristic
727D3—41no—
728D3—201no—
729C5#7333611yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—51no—
733C22—51no—
734C22—52no—
735C22—52no—
736C22—52no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—104no—
741C22—104no—
742C22—101no—
743C22—101no—
744C22—301no—
745C22—301no—
746C22—301no—
747C22—602no—
748C22—602no—
749C22#9190712yes—
750C22C22×D3×AGL(1,𝔽5)11yescharacteristic
751C4—21no—
752C4—21no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—104no—
757C4—101no—
758C4—101no—
759C4—202no—
760C4—301no—
761C4—301no—
762C4—301no—
763C4—602no—
764C4—602no—
765C3#1061718011yescharacteristic, complemented, Sylow
766C2—22no—
767C2—52no—
768C2—52no—
769C2—102no—
770C2—121no—
771C2—601no—
772C2C2×#9190711yescharacteristic
773C2AGL(1,𝔽5)×#23511yescharacteristic
774C2#1175687111yescharacteristic
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#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752424C2semidirect
3. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
5. AGL(1,𝔽5)×#217C2semidirect
6. #11751853C2semidirect
7. #11751848C2semidirect
8. #11751845C2semidirect
9. #11751841C2semidirect
10. #11751832C2semidirect
11. #11751750C2semidirect
23. C4×#1220C4semidirect
24. C4×C5×#67C4semidirect
25. #91552C4semidirect
26. Dic5×#67C4semidirect
29. #91444C4semidirect
30. C4×#1202C4semidirect
31. #91440C4semidirect
32. C4×#1201C4semidirect
50. C2×(C2×AGL(1,𝔽5))⋊C4D3semidirect
67. C2×C4×D15C2×C4semidirect
69. C2×C4×C5×D3C2×C4semidirect
80. C2×#1200C2×C4semidirect
81. C2×D3×Dic5C2×C4semidirect
93. #6714C2×C4semidirect
94. #6712C2×C4semidirect
95. C4×Dic15C2×C4semidirect
97. C5×(C2×D3)⋊C4C2×C4semidirect
98. C5×Dic3⋊C4C2×C4semidirect
99. C4×C5×Dic3C2×C4semidirect
100. Dic3⋊Dic5C2×C4semidirect
101. #6669C2×C4semidirect
102. #6667C2×C4semidirect
103. (C2×D3)⋊Dic5C2×C4semidirect
106. Dic3×Dic5C2×C4semidirect
107. Dic3×Dic5C2×C4semidirect
218. C4×#67AGL(1,𝔽5)semidirect
363. C2×C4×D3C2×AGL(1,𝔽5)semidirect
374. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
379. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
385. C4×Dic3C2×AGL(1,𝔽5)semidirect
621. C3×C5#2353semidirect
729. C5#73336semidirect
765. C3#10617180semidirect

Maximal subgroups

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

subgroupindex
C4×D5×#672
#117524242
C2×C3×(C2×AGL(1,𝔽5))⋊C42
#117520222
AGL(1,𝔽5)×#2172
#117518532
#117518482
#117518452
#117518412
#117518322
#117517502
#106171803
#733365