Finite Group Databasebeta

← #14324021

Subgroups — #14324021

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91989C211yesmaximal, characteristic, complemented
2C2×#91921C211yesmaximal, characteristic, complemented
3D5×#930C211yesmaximal, characteristic
4C3×#65765C211yesmaximal, characteristic, complemented
5#11752055C212yesmaximal, complemented
6#11752019C212yesmaximal, complemented
7#11751934C212yesmaximal, complemented
8#11751861C211yesmaximal, characteristic, complemented
9#11751857C211yesmaximal, characteristic, complemented
10#11751846C211yesmaximal, characteristic, complemented
11#11751841C212yesmaximal, complemented
12#10617250—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×D5×#67C2212yes—
16C2×D5×D12C2211yescharacteristic
17C2×#6763C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19#91989—24no—
20C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
21C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
22C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
23C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
24C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
25C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3⋊AGL(1,𝔽5)C2212yes—
28C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
29C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
30C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
31C2×Dic3×AGL(1,𝔽5)C2212yes—
32#91921—24no—
33#91819C411yescharacteristic, complemented
34C5×#930C411yescharacteristic, complemented
35#91566C412yescomplemented
36D5×(C2×D3)⋊C4C2212yes—
37#91450C411yescharacteristic, complemented
38#91449C411yescharacteristic, complemented
39#91448C412yescomplemented
40D5×C4⋊Dic3C2211yescharacteristic
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73872—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)—31no—
46C2×#4130—31no—
47D5×#121—31no—
48#65780—32no—
49#65780—31no—
50#65779—32no—
51#65765D311yescharacteristic, complemented
52#65712—31no—
53C4⋊C4×AGL(1,𝔽5)—31no—
54#65700—32no—
55#65699—32no—
56C23×C3×D5C2311yescharacteristic
57C22×D3×D5C2312yes—
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2311yescharacteristic
61C22×ΓL(1,𝔽16)C2311yescharacteristic
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×AGL(1,𝔽5)C2312yes—
64C2×D3×AGL(1,𝔽5)—24no—
65C2×D3×AGL(1,𝔽5)—42no—
66C2×D3×AGL(1,𝔽5)—42no—
67C22×C3×C4×C5C2×C411yescharacteristic, complemented
68C2×#1220C2×C412yescomplemented
69C2×D60C2×C411yescharacteristic
70C2×C5×#67C2×C412yescomplemented
71C2×C5×D12C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic, complemented
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C411yescharacteristic, complemented
76C2×C3×C4×D5C2×C411yescharacteristic, complemented
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79D5×#67—42no—
80D5×#67—42no—
81C2×#1203C2×C412yes—
82C2×#1202C2×C412yescomplemented
83C2×#1201C2×C412yescomplemented
84C2×D5×Dic3C2312yes—
85D5×D12—22no—
86D5×D12—22no—
87#6763—22no—
88#6763—22no—
89C4⋊ΓL(1,𝔽16)—22no—
90C4⋊ΓL(1,𝔽16)—22no—
91C4×ΓL(1,𝔽16)—22no—
92C4×ΓL(1,𝔽16)D414yescomplemented
93C3×C22⋊AGL(1,𝔽5)—42no—
94C3×C4⋊AGL(1,𝔽5)—22no—
95C3×C4⋊AGL(1,𝔽5)—22no—
96Dic3⋊AGL(1,𝔽5)—42no—
97(C2×D3)⋊AGL(1,𝔽5)—24no—
98(C2×D3)⋊AGL(1,𝔽5)—42no—
99(C2×D3)⋊AGL(1,𝔽5)—42no—
100Dic3×AGL(1,𝔽5)—42no—
101#6714C2×C412yescomplemented
102C4⋊Dic15C2×C411yescharacteristic, complemented
103C5×(C2×D3)⋊C4C2×C412yescomplemented
104C5×C4⋊Dic3C2×C411yescharacteristic, complemented
105#6668C2×C412yescomplemented
106#6667C2×C412yescomplemented
107(C2×D3)⋊Dic5C2×C412yescomplemented
108C2×#930—51no—
109C2×#926—51no—
110C2×#893—51no—
111C3×#380—51no—
112#4988—51no—
113Dic3×C4⋊C4—51no—
114#4972—51no—
115#4957—52no—
116#4956—52no—
117#4670—52no—
118#4668—52no—
119C23×AGL(1,𝔽5)—32no—
120C2×D4×D5—32no—
121C2×D4×D5—31no—
122C22×C4×D5C2×D311yescharacteristic
123C2×C22⋊AGL(1,𝔽5)—31no—
124C2×C22⋊AGL(1,𝔽5)—31no—
125C2×C22⋊AGL(1,𝔽5)—32no—
126C2×C22⋊AGL(1,𝔽5)—32no—
127C2×C22⋊AGL(1,𝔽5)—32no—
128C2×C22⋊AGL(1,𝔽5)C2×D312yes—
129D4×AGL(1,𝔽5)—64no—
130#4130—64no—
131C2×C4⋊AGL(1,𝔽5)—31no—
132C2×C4⋊AGL(1,𝔽5)—31no—
133C2×C4⋊AGL(1,𝔽5)—32no—
134C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
135C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
136C2×C4×AGL(1,𝔽5)—31no—
137C2×C4×AGL(1,𝔽5)—31no—
138C2×C4×AGL(1,𝔽5)—32no—
139C5×#121—31no—
140#4085—32no—
141#4084—31no—
142#4076—31no—
143#4041—31no—
144D5×C4⋊C4—31no—
145#4030—32no—
146D5×C22⋊C4—32no—
147(C2×AGL(1,𝔽5))⋊C4—32no—
148(C2×AGL(1,𝔽5))⋊C4—32no—
149(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
150#2324—151noSylow
151C23×C3×C5C22×C411yescharacteristic
152C22×D15C22×C412yes—
153C22×C5×D3C22×C412yes—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—21no—
158C22×C3×D5—21no—
159C22×C3×D5—21no—
160C22×C3×D5C22×C411yescharacteristic
161C22×C3×D5C2411yescharacteristic
162C2×D3×D5—22no—
163C2×D3×D5—22no—
164C2×D3×D5—22no—
165C2×D3×D5—22no—
166C2×D3×D5—22no—
167C2×D3×D5—22no—
168C2×ΓL(1,𝔽16)—21no—
169C2×ΓL(1,𝔽16)—21no—
170C2×ΓL(1,𝔽16)—21no—
171C2×ΓL(1,𝔽16)—21no—
172C2×ΓL(1,𝔽16)—21no—
173C2×ΓL(1,𝔽16)—21no—
174C2×ΓL(1,𝔽16)—21no—
175C2×ΓL(1,𝔽16)—21no—
176C2×ΓL(1,𝔽16)—21no—
177C2×ΓL(1,𝔽16)—21no—
178C2×ΓL(1,𝔽16)C2×D412yes—
179C2×ΓL(1,𝔽16)C2×D412yes—
180C2×C3×AGL(1,𝔽5)—22no—
181C2×C3×AGL(1,𝔽5)—22no—
182C2×C3×AGL(1,𝔽5)—22no—
183C2×C3×AGL(1,𝔽5)—22no—
184C2×C3×AGL(1,𝔽5)—22no—
185C2×C3×AGL(1,𝔽5)—22no—
186D3×AGL(1,𝔽5)—48no—
187C2×C3×C4×C5—22no—
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190#1220—42no—
191C2×Dic15C22×C412yes—
192D60—22no—
193C5×#67—42no—
194C2×C5×Dic3C22×C412yes—
195C5×D12—22no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C22×C411yescharacteristic
199C3×C4×D5—21no—
200C3×C4×D5—21no—
201C3×C4×D5—22no—
202C3×C4×D5—22no—
203C3×C4×D5C2×D412yes—
204C3×C4×D5#4112yes—
205#1203—24no—
206#1202—42no—
207#1201—42no—
208D5×Dic3—22no—
209D5×Dic3—22no—
210C23×C3×C4—51no—
211C22×#67—52no—
212C22×D12—51no—
213C22×C4×D3—52no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C22⋊C4—52no—
217C2×#217—51no—
218C2×#217—51no—
219#930—51no—
220#930—52no—
221#930—51no—
222#930—52no—
223#930—51no—
224#930AGL(1,𝔽5)11yescharacteristic, complemented
225C2×(C2×D3)⋊C4—52no—
226C2×(C2×D3)⋊C4—52no—
227C2×(C2×D3)⋊C4—52no—
228C2×(C2×D3)⋊C4—52no—
229#926—104no—
230C2×C4⋊Dic3—51no—
231C2×C4⋊Dic3—51no—
232C2×C4⋊Dic3—51no—
233C2×Dic3⋊C4—52no—
234C2×C4×Dic3—51no—
235C2×C4×Dic3—51no—
236C2×C4×Dic3—52no—
237#893—104no—
238C3×#95—52no—
239C3⋊#95—52no—
240C3⋊#95—52no—
241C23×D5—32no—
242C23×D5C22×D311yescharacteristic
243C22×AGL(1,𝔽5)—31no—
244C22×AGL(1,𝔽5)—31no—
245C22×AGL(1,𝔽5)—31no—
246C22×AGL(1,𝔽5)—31no—
247C22×AGL(1,𝔽5)—64no—
248C22×AGL(1,𝔽5)—122no—
249C22×AGL(1,𝔽5)—122no—
250C22×AGL(1,𝔽5)C22×D312yes—
251C22×AGL(1,𝔽5)C22×D312yes—
252C2×C5×D4—32no—
253C2×C5×D4—31no—
254C22×C4×C5C4×D311yescharacteristic, complemented
255C2×C22⋊D5—32no—
256C2×C22⋊D5—32no—
257C2×C22⋊D5—32no—
258C22×Dic5C4×D311yescharacteristic, complemented
259D4×D5—62no—
260D4×D5—62no—
261D4×D5—122no—
262D4×D5—122no—
263C2×D20—31no—
264C2×D20—32no—
265C2×C4×D5—22no—
266C2×C4×D5—22no—
267C2×C4×D5—32no—
268C2×C4×D5C4×D311yescharacteristic, complemented
269C2×C4×D5C4×D311yescharacteristic, complemented
270C2×C4×D5C22×D311yescharacteristic
271C2×C4×D5C22×D311yescharacteristic
272C22⋊AGL(1,𝔽5)—42no—
273C22⋊AGL(1,𝔽5)—64no—
274C22⋊AGL(1,𝔽5)—62no—
275C22⋊AGL(1,𝔽5)—62no—
276C22⋊AGL(1,𝔽5)—122no—
277C22⋊AGL(1,𝔽5)—122no—
278C4⋊AGL(1,𝔽5)—22no—
279C4⋊AGL(1,𝔽5)—22no—
280C4⋊AGL(1,𝔽5)—62no—
281C4⋊AGL(1,𝔽5)—62no—
282C4⋊AGL(1,𝔽5)—122no—
283C4×AGL(1,𝔽5)—34no—
284C4×AGL(1,𝔽5)—62no—
285C4×AGL(1,𝔽5)—122no—
286C5×C4⋊C4—31no—
287C5×C22⋊C4—32no—
288C22⋊Dic5—32no—
289#685—32no—
290#685—32no—
291C4⋊Dic5—31no—
292#683—32no—
293C2×#121—151no—
294C2×C4×D4—151no—
295C2×#117—151no—
296#390—152no—
297#390—151no—
298#389—151no—
299#388—152no—
300#386—152no—
301#385—152no—
302#380—51no—
303C4×C4⋊C4—151no—
304C22×C3×C5—21no—
305C22×C3×C5—21no—
306C22×C3×C5—21no—
307C22×C3×C5C23×C411yescharacteristic
308C2×D15—22no—
309C2×D15—22no—
310C2×D15—22no—
311C2×C5×D3—22no—
312C2×C5×D3—22no—
313C2×C5×D3—22no—
314C2×C3×D5—21no—
315C2×C3×D5—21no—
316C2×C3×D5—21no—
317C2×C3×D5—41no—
318C2×C3×D5—41no—
319C2×C3×D5—41no—
320C2×C3×D5—41no—
321C2×C3×D5C22×D411yescharacteristic
322C2×C3×D5C2×#4111yescharacteristic
323C2×C3×D5H(5,𝔽2)11yescharacteristic
324C2×C3×D5H(5,𝔽2)11yescharacteristic
325C2×C3×D5H(5,𝔽2)11yescharacteristic
326C2×C3×D52−1+411yescharacteristic
327D3×D5—42no—
328D3×D5—42no—
329D3×D5—42no—
330D3×D5—42no—
331ΓL(1,𝔽16)—22no—
332ΓL(1,𝔽16)—22no—
333ΓL(1,𝔽16)—41no—
334ΓL(1,𝔽16)—41no—
335C3×AGL(1,𝔽5)—42no—
336C3×AGL(1,𝔽5)—42no—
337C3×C4×C5—21no—
338C3×C4×C5C4×D412yes—
339Dic15—22no—
340C3×Dic5—21no—
341C3×Dic5C4×D412yes—
342C5×Dic3—22no—
343C24×C3—51no—
344C23×D3—52no—
345C22×C3×C4—51no—
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—52no—
351C22×C3×C4—52no—
352C22×C3×C4—102no—
353C22×C3×C4—102no—
354C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
355C2×#67—52no—
356C2×#67—52no—
357C2×#67—52no—
358C2×#67—202no—
359C2×#67—202no—
360C2×#67C2×AGL(1,𝔽5)12yescomplemented
361C22×Dic3—51no—
362C22×Dic3—51no—
363C22×Dic3—52no—
364C22×Dic3—51no—
365C22×Dic3—51no—
366C2×D12—52no—
367C2×D12—51no—
368C2×D12—102no—
369C2×D12—102no—
370C2×D12C2×AGL(1,𝔽5)11yescharacteristic
371C2×C4×D3—104no—
372C2×C4×D3—202no—
373C2×C4×D3—202no—
374C3×C4⋊C4—102no—
375C3×C4⋊C4—102no—
376C3×C22⋊C4—202no—
377#217—102no—
378#217—102no—
379(C2×D3)⋊C4—52no—
380(C2×D3)⋊C4—52no—
381(C2×D3)⋊C4—52no—
382(C2×D3)⋊C4—104no—
383(C2×D3)⋊C4—202no—
384(C2×D3)⋊C4—202no—
385(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
386C4⋊Dic3—51no—
387C4⋊Dic3—52no—
388C4⋊Dic3—102no—
389C4⋊Dic3—102no—
390C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
391Dic3⋊C4—202no—
392C4×Dic3—54no—
393C4×Dic3—102no—
394C4×Dic3—202no—
395C23×C5—32no—
396C23×C5C2×C4×D311yescharacteristic
397C22×D5—21no—
398C22×D5—21no—
399C22×D5—21no—
400C22×D5—21no—
401C22×D5—21no—
402C22×D5—21no—
403C22×D5—32no—
404C22×D5—62no—
405C22×D5—62no—
406C22×D5—62no—
407C22×D5—62no—
408C22×D5—62no—
409C22×D5—62no—
410C22×D5C2×C4×D311yescharacteristic
411C22×D5C23×D311yescharacteristic
412C2×AGL(1,𝔽5)—22no—
413C2×AGL(1,𝔽5)—22no—
414C2×AGL(1,𝔽5)—22no—
415C2×AGL(1,𝔽5)—22no—
416C2×AGL(1,𝔽5)—22no—
417C2×AGL(1,𝔽5)—22no—
418C2×AGL(1,𝔽5)—32no—
419C2×AGL(1,𝔽5)—32no—
420C2×AGL(1,𝔽5)—61no—
421C2×AGL(1,𝔽5)—61no—
422C2×AGL(1,𝔽5)—61no—
423C2×AGL(1,𝔽5)—61no—
424C2×AGL(1,𝔽5)—61no—
425C2×AGL(1,𝔽5)—61no—
426C2×AGL(1,𝔽5)—61no—
427C2×AGL(1,𝔽5)—61no—
428C2×AGL(1,𝔽5)—61no—
429C2×AGL(1,𝔽5)—61no—
430C2×AGL(1,𝔽5)—128no—
431C5×D4—62no—
432C5×D4—122no—
433C2×C4×C5—22no—
434C2×C4×C5—32no—
435C2×C4×C5C2×C4×D311yescharacteristic
436C2×C4×C5C2×C4×D311yescharacteristic
437C22⋊D5—64no—
438C22⋊D5—122no—
439C22⋊D5—122no—
440C2×Dic5—22no—
441C2×Dic5—32no—
442C2×Dic5C2×C4×D311yescharacteristic
443C2×Dic5C2×C4×D311yescharacteristic
444D20—62no—
445D20—122no—
446C4×D5—21no—
447C4×D5—21no—
448C4×D5—22no—
449C4×D5—22no—
450C4×D5—62no—
451C4×D5—62no—
452C4×D5D3×D412yes—
453C4×D5#23712yes—
454C22×D4—151no—
455C22×D4—152no—
456C23×C4—51no—
457C23×C4—152no—
458#121—31no—
459#121—152no—
460#121—151no—
461#121—151no—
462#121—152no—
463#121—151no—
464C4×D4—304no—
465#117—304no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—152no—
472C2×C22⋊C4—52no—
473C2×C22⋊C4—152no—
474C2×C22⋊C4—152no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—152no—
478C2×C22⋊C4—152no—
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—152no—
482#95—52no—
483#95—152no—
484#95—152no—
485C2×C3×C5—41no—
486C2×C3×C5C2×C4×D411yescharacteristic
487C2×C3×C5#51811yescharacteristic
488C2×C3×C5#52011yescharacteristic
489D15—42no—
490C3×D5—41no—
491C3×D5#53511yescharacteristic
492C3×D5#53711yescharacteristic
493C3×D5#54011yescharacteristic
494C3×D5#54211yescharacteristic
495C5×D3—42no—
496C23×C3—51no—
497C23×C3—51no—
498C23×C3—101no—
499C23×C3—101no—
500C23×C3—101no—
501C23×C3—101no—
502C23×C3—101no—
503C23×C3—101no—
504C23×C3C22×AGL(1,𝔽5)11yescharacteristic
505C22×D3—52no—
506C22×D3—102no—
507C22×D3—102no—
508C22×D3—102no—
509C22×D3—102no—
510C22×D3—102no—
511C22×D3—102no—
512C22×D3C22×AGL(1,𝔽5)12yes—
513C2×C3×C4—22no—
514C2×C3×C4—51no—
515C2×C3×C4—52no—
516C2×C3×C4—52no—
517C2×C3×C4—51no—
518C2×C3×C4—102no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—102no—
522C2×C3×C4—102no—
523C2×C3×C4—102no—
524C2×C3×C4—102no—
525C2×C3×C4—102no—
526C2×C3×C4—102no—
527C2×C3×C4—102no—
528C2×C3×C4—102no—
529C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
530C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
531#67—42no—
532#67—202no—
533#67—202no—
534#67—202no—
535C2×Dic3—52no—
536C2×Dic3—52no—
537C2×Dic3—52no—
538C2×Dic3—102no—
539C2×Dic3—102no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3C22×AGL(1,𝔽5)12yes—
551D12—22no—
552D12—104no—
553D12—102no—
554C4×D3—208no—
555C22×C5—21no—
556C22×C5—21no—
557C22×C5—21no—
558C22×C5—62no—
559C22×C5—62no—
560C22×C5—62no—
561C22×C5C22×C4×D311yescharacteristic
562C2×D5—21no—
563C2×D5—21no—
564C2×D5—21no—
565C2×D5—41no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—41no—
569C2×D5—62no—
570C2×D5—62no—
571C2×D5—62no—
572C2×D5—122no—
573C2×D5—122no—
574C2×D5—122no—
575C2×D5—122no—
576C2×D5C2×D3×D411yescharacteristic
577C2×D5C2×#23711yescharacteristic
578C2×D5#100411yescharacteristic
579C2×D5#100711yescharacteristic
580C2×D5#100911yescharacteristic
581C2×D5#100911yescharacteristic
582AGL(1,𝔽5)—42no—
583AGL(1,𝔽5)—42no—
584AGL(1,𝔽5)—62no—
585AGL(1,𝔽5)—62no—
586AGL(1,𝔽5)—121no—
587AGL(1,𝔽5)—121no—
588C4×C5—21no—
589C4×C5—62no—
590C4×C5#67⋊C412yes—
591Dic5—21no—
592Dic5—62no—
593Dic5#67⋊C412yes—
594C24—51no—
595C24—152no—
596C2×D4—32no—
597C2×D4—31no—
598C2×D4—152no—
599C2×D4—152no—
600C2×D4—152no—
601C2×D4—152no—
602C2×D4—151no—
603C2×D4—302no—
604C2×D4—302no—
605C2×D4—602no—
606C2×D4—602no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—52no—
613C22×C4—52no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—152no—
617C22×C4—151no—
618C22×C4—151no—
619C22×C4—151no—
620C22×C4—151no—
621C22×C4—304no—
622C22×C4—602no—
623C22×C4—602no—
624C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
625C4⋊C4—31no—
626C4⋊C4—102no—
627C4⋊C4—102no—
628C4⋊C4—152no—
629C4⋊C4—151no—
630C4⋊C4—302no—
631C4⋊C4—302no—
632C4⋊C4—602no—
633C22⋊C4—32no—
634C22⋊C4—152no—
635C22⋊C4—152no—
636C22⋊C4—152no—
637C22⋊C4—202no—
638C22⋊C4—304no—
639C22⋊C4—302no—
640C22⋊C4—302no—
641C22⋊C4—602no—
642C22⋊C4—602no—
643C42—154no—
644C42—302no—
645C42—602no—
646C3×C5#232411yescharacteristic, complemented, Hall
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—51no—
651C22×C3—51no—
652C22×C3—51no—
653C22×C3—51no—
654C22×C3—51no—
655C22×C3—51no—
656C22×C3—101no—
657C22×C3—101no—
658C22×C3—101no—
659C22×C3—201no—
660C22×C3—201no—
661C22×C3—201no—
662C22×C3—201no—
663C22×C3C23×AGL(1,𝔽5)11yescharacteristic
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—102no—
668C2×D3—102no—
669C2×D3—102no—
670C2×D3—202no—
671C2×D3—202no—
672C2×D3—202no—
673C2×D3—202no—
674C3×C4—21no—
675C3×C4—52no—
676C3×C4—101no—
677C3×C4—202no—
678C3×C4—202no—
679C3×C4D4×AGL(1,𝔽5)12yes—
680Dic3—22no—
681Dic3—102no—
682Dic3—102no—
683Dic3—102no—
684Dic3—201no—
685Dic3—201no—
686C2×C5—41no—
687C2×C5—122no—
688C2×C5C2×#67⋊C411yescharacteristic
689C2×C5#550411yescharacteristic
690C2×C5#552111yescharacteristic
691D5—41no—
692D5—122no—
693D5#560711yescharacteristic
694D5#561911yescharacteristic
695D5#562911yescharacteristic
696D5#564311yescharacteristic
697C23—32no—
698C23—51no—
699C23—51no—
700C23—101no—
701C23—101no—
702C23—101no—
703C23—101no—
704C23—101no—
705C23—101no—
706C23—152no—
707C23—302no—
708C23—302no—
709C23—302no—
710C23—302no—
711C23—302no—
712C23—302no—
713C23C2×D3×AGL(1,𝔽5)11yescharacteristic
714D4—62no—
715D4—122no—
716D4—304no—
717D4—302no—
718D4—602no—
719D4—602no—
720D4—602no—
721C2×C4—22no—
722C2×C4—32no—
723C2×C4—51no—
724C2×C4—52no—
725C2×C4—52no—
726C2×C4—51no—
727C2×C4—102no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—152no—
739C2×C4—152no—
740C2×C4—152no—
741C2×C4—302no—
742C2×C4—302no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—301no—
746C2×C4—301no—
747C2×C4—301no—
748C2×C4—301no—
749C2×C4—301no—
750C2×C4—301no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—608no—
754C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
755C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
756C2×C3—41no—
757C2×C3—51no—
758C2×C3—51no—
759C2×C3—51no—
760C2×C3—51no—
761C2×C3—201no—
762C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
763C2×C3#6625811yescharacteristic
764C2×C3#6626611yescharacteristic
765D3—42no—
766D3—202no—
767C5#7387211yescharacteristic, complemented, Sylow
768C22—21no—
769C22—21no—
770C22—21no—
771C22—51no—
772C22—51no—
773C22—51no—
774C22—51no—
775C22—51no—
776C22—51no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—101no—
781C22—101no—
782C22—101no—
783C22—201no—
784C22—201no—
785C22—201no—
786C22—201no—
787C22—302no—
788C22—302no—
789C22—302no—
790C22—602no—
791C22—602no—
792C22—602no—
793C22—602no—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—21no—
796C4—52no—
797C4—62no—
798C4—101no—
799C4—202no—
800C4—202no—
801C4—302no—
802C4—302no—
803C4—302no—
804C4—601no—
805C4—601no—
806C4#67⋊AGL(1,𝔽5)12yes—
807C3#1061725011yescharacteristic, complemented, Sylow
808C2—41no—
809C2—51no—
810C2—51no—
811C2—51no—
812C2—51no—
813C2—122no—
814C2—201no—
815C2—602no—
816C2#1175683611yescharacteristic
817C2#1175683711yescharacteristic
818C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalD5×#930C2
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2324
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×#91989C2semidirect
2. C2×#91921C2semidirect
4. C3×#65765C2semidirect
5. #11752055C2semidirect
6. #11752019C2semidirect
7. #11751934C2semidirect
8. #11751861C2semidirect
9. #11751857C2semidirect
10. #11751846C2semidirect
11. #11751841C2semidirect
33. #91819C4semidirect
34. C5×#930C4semidirect
35. #91566C4semidirect
37. #91450C4semidirect
38. #91449C4semidirect
39. #91448C4semidirect
51. #65765D3semidirect
67. C22×C3×C4×C5C2×C4semidirect
68. C2×#1220C2×C4semidirect
70. C2×C5×#67C2×C4semidirect
72. C22×C3×Dic5C2×C4semidirect
75. C2×C3×C4×D5C2×C4semidirect
76. C2×C3×C4×D5C2×C4semidirect
82. C2×#1202C2×C4semidirect
83. C2×#1201C2×C4semidirect
92. C4×ΓL(1,𝔽16)D4semidirect
101. #6714C2×C4semidirect
102. C4⋊Dic15C2×C4semidirect
103. C5×(C2×D3)⋊C4C2×C4semidirect
104. C5×C4⋊Dic3C2×C4semidirect
105. #6668C2×C4semidirect
106. #6667C2×C4semidirect
107. (C2×D3)⋊Dic5C2×C4semidirect
224. #930AGL(1,𝔽5)semidirect
254. C22×C4×C5C4×D3semidirect
258. C22×Dic5C4×D3semidirect
268. C2×C4×D5C4×D3semidirect
269. C2×C4×D5C4×D3semidirect
354. C22×C3×C4C2×AGL(1,𝔽5)semidirect
360. C2×#67C2×AGL(1,𝔽5)semidirect
385. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
390. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
624. C22×C4D3×AGL(1,𝔽5)semidirect
646. C3×C5#2324semidirect
767. C5#73872semidirect
807. C3#10617250semidirect

Maximal subgroups

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

subgroupindex
C2×#919892
C2×#919212
D5×#9302
C3×#657652
#117520552
#117520192
#117519342
#117518612
#117518572
#117518462
#117518412
#106172503
#738725