Finite Group Databasebeta

← #14324025

Subgroups — #14324025

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×AGL(1,𝔽5)×D12C211yesmaximal, characteristic, complemented
2C2×#91909C211yesmaximal, characteristic, complemented
3D5×#895C211yesmaximal, characteristic
4#11752371C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#11751934C212yesmaximal, complemented
7#11751933C212yesmaximal, complemented
8#11751857C211yesmaximal, characteristic, complemented
9#11751855C211yesmaximal, characteristic, complemented
10#11751850C212yesmaximal, complemented
11#11751849C212yesmaximal, complemented
12#10617250—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2212yes—
14C2×D5×D12C2211yescharacteristic
15C2×D5×D12C2212yes—
16C2×C4×D3×D5C2211yescharacteristic
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2212yes—
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)C2212yes—
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×(C2×D3)⋊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—
31AGL(1,𝔽5)×D12—24no—
32#91909—24no—
33#91784C411yescharacteristic, complemented
34C5×#895C411yescharacteristic, complemented
35C3×D5×C4⋊C4C2211yescharacteristic
36D5×(C2×D3)⋊C4C2212yes—
37#91466C411yescharacteristic, complemented
38#91460C411yescharacteristic, complemented
39#91420C412yescomplemented
40#91416C412yescomplemented
41#91235C2212yes—
42C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73763—51nomaximal, Hall
45C2×D4×AGL(1,𝔽5)—31no—
46C2×#4130—31no—
47D5×#121—31no—
48#65780—31no—
49#65780—32no—
50#65779—32no—
51#65765—31no—
52#65712—31no—
53C4⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
54#65700—32no—
55#65699—32no—
56C22×D3×D5C2311yescharacteristic
57C22×D3×D5C2312yes—
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2312yes—
61C22×C3×AGL(1,𝔽5)C2312yes—
62C22×C3×AGL(1,𝔽5)C2311yescharacteristic
63C22×C3×AGL(1,𝔽5)C2311yescharacteristic
64C2×D3×AGL(1,𝔽5)—24no—
65C2×D3×AGL(1,𝔽5)—42no—
66C2×D3×AGL(1,𝔽5)—42no—
67C2×D60C2×C411yescharacteristic
68C2×D60C2×C412yescomplemented
69C2×C4×D15C2×C411yescharacteristic, complemented
70C2×C5×D12C2×C411yescharacteristic
71C2×C5×D12C2×C412yescomplemented
72C2×C4×C5×D3C2×C411yescharacteristic, complemented
73C2×C3×C4×D5C2312yes—
74C2×C3×C4×D5C2311yescharacteristic
75C2×#1203C2×C412yes—
76C2×#1203C2×C412yescomplemented
77C2×#1203C2×C412yescomplemented
78C2×#1200C2×C411yescharacteristic, complemented
79C2×D3×Dic5C2×C411yescharacteristic, complemented
80C2×D5×Dic3C2311yescharacteristic
81D5×D12—22no—
82D5×D12—22no—
83D5×D12—42no—
84D5×D12—42no—
85C4×D3×D5—22no—
86C4×D3×D5—22no—
87C4⋊ΓL(1,𝔽16)—22no—
88C4⋊ΓL(1,𝔽16)—42no—
89C4×ΓL(1,𝔽16)—22no—
90C3×C4⋊AGL(1,𝔽5)—22no—
91C3×C4×AGL(1,𝔽5)—42no—
92C3×C4×AGL(1,𝔽5)D414yescomplemented
93Dic3⋊AGL(1,𝔽5)—22no—
94Dic3⋊AGL(1,𝔽5)—22no—
95(C2×D3)⋊AGL(1,𝔽5)—22no—
96(C2×D3)⋊AGL(1,𝔽5)—22no—
97(C2×D3)⋊AGL(1,𝔽5)—24no—
98(C2×D3)⋊AGL(1,𝔽5)—42no—
99(C2×D3)⋊AGL(1,𝔽5)—42no—
100(C2×D3)⋊AGL(1,𝔽5)—42no—
101C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
102#6714C2×C412yescomplemented
103C5×(C2×D3)⋊C4C2×C412yescomplemented
104C3×C4⋊Dic5C2×C411yescharacteristic, complemented
105C3×#683C2×C412yescomplemented
106#6667C2×C412yescomplemented
107(C2×D3)⋊Dic5C2×C412yescomplemented
108C2×#895—51no—
109C2×C4×D12—51no—
110C2×#872—51no—
111C3×C4×C4⋊C4—51no—
112#4988—51no—
113#4987—51no—
114#4984—51no—
115#4940—52no—
116#4939—52no—
117#4668—52no—
118#4665—52no—
119C23×AGL(1,𝔽5)—32no—
120C2×D4×D5—31no—
121C2×D4×D5—32no—
122C22×C4×D5—31no—
123C2×C22⋊AGL(1,𝔽5)—32no—
124C2×C22⋊AGL(1,𝔽5)—31no—
125C2×C22⋊AGL(1,𝔽5)—31no—
126C2×C22⋊AGL(1,𝔽5)—32no—
127C2×C22⋊AGL(1,𝔽5)—32no—
128C2×C22⋊AGL(1,𝔽5)—32no—
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)—31no—
134C2×C4⋊AGL(1,𝔽5)—32no—
135C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
136C2×C4×AGL(1,𝔽5)—31no—
137C2×C4×AGL(1,𝔽5)C2×D312yes—
138C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
139C5×#121—31no—
140#4085—32no—
141#4084—31no—
142#4076—31no—
143#4041—31no—
144D5×C4⋊C4C2×D311yescharacteristic
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
151C22×D15C22×C412yes—
152C22×D15C22×C411yescharacteristic
153C22×C5×D3C22×C412yes—
154C22×C5×D3C22×C411yescharacteristic
155C22×C3×D5C2411yescharacteristic
156C2×D3×D5—21no—
157C2×D3×D5—22no—
158C2×D3×D5—21no—
159C2×D3×D5—22no—
160C2×D3×D5—21no—
161C2×D3×D5—22no—
162C2×D3×D5—22no—
163C2×D3×D5—21no—
164C2×D3×D5—21no—
165C2×D3×D5—22no—
166C2×D3×D5—21no—
167C2×D3×D5—22no—
168C2×ΓL(1,𝔽16)—21no—
169C2×ΓL(1,𝔽16)—21no—
170C2×ΓL(1,𝔽16)—22no—
171C2×ΓL(1,𝔽16)—21no—
172C2×ΓL(1,𝔽16)—21no—
173C2×ΓL(1,𝔽16)—22no—
174C2×ΓL(1,𝔽16)—21no—
175C2×ΓL(1,𝔽16)—22no—
176C2×ΓL(1,𝔽16)—21no—
177C2×C3×AGL(1,𝔽5)—21no—
178C2×C3×AGL(1,𝔽5)—21no—
179C2×C3×AGL(1,𝔽5)—21no—
180C2×C3×AGL(1,𝔽5)—21no—
181C2×C3×AGL(1,𝔽5)—22no—
182C2×C3×AGL(1,𝔽5)—22no—
183C2×C3×AGL(1,𝔽5)—22no—
184C2×C3×AGL(1,𝔽5)C2×D412yes—
185C2×C3×AGL(1,𝔽5)C2×D412yes—
186D3×AGL(1,𝔽5)—48no—
187C2×C3×C4×C5C22×C412yes—
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×Dic15C22×C411yescharacteristic
190D60—22no—
191D60—42no—
192C4×D15—22no—
193C2×C5×Dic3C22×C411yescharacteristic
194C5×D12—22no—
195C5×D12—42no—
196C4×C5×D3—22no—
197C2×C3×Dic5C22×C412yes—
198C2×C3×Dic5C22×C411yescharacteristic
199C3×C4×D5—22no—
200C3×C4×D5—22no—
201C3×C4×D5C2×D412yes—
202C3×C4×D5#4112yes—
203#1203—24no—
204#1203—42no—
205#1203—42no—
206#1200—22no—
207D3×Dic5—22no—
208D5×Dic3—21no—
209D5×Dic3—21no—
210C22×D12—51no—
211C22×D12—52no—
212C22×C4×D3—51no—
213C22×C4×D3—52no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C42—51no—
217C2×C3×C42—52no—
218C2×(C2×D3)⋊C4—52no—
219C2×(C2×D3)⋊C4—51no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—52no—
222C2×(C2×D3)⋊C4—52no—
223C2×(C2×D3)⋊C4—52no—
224C2×(C2×D3)⋊C4—52no—
225C2×C4⋊Dic3—51no—
226C2×C4⋊Dic3—52no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×C4×Dic3—51no—
230#895—51no—
231#895—52no—
232#895—51no—
233#895—51no—
234#895—52no—
235#895AGL(1,𝔽5)11yescharacteristic, complemented
236C4×D12—104no—
237#872—104no—
238C3×#95—52no—
239C3⋊#95—52no—
240C3⋊#95—52no—
241C23×D5—31no—
242C23×D5—32no—
243C22×AGL(1,𝔽5)—31no—
244C22×AGL(1,𝔽5)—31no—
245C22×AGL(1,𝔽5)—32no—
246C22×AGL(1,𝔽5)—64no—
247C22×AGL(1,𝔽5)—122no—
248C22×AGL(1,𝔽5)—122no—
249C22×AGL(1,𝔽5)C22×D312yes—
250C22×AGL(1,𝔽5)C22×D311yescharacteristic
251C22×AGL(1,𝔽5)C22×D311yescharacteristic
252C2×C5×D4—31no—
253C2×C5×D4—32no—
254C22×C4×C5—31no—
255C2×C22⋊D5—32no—
256C2×C22⋊D5—32no—
257C2×C22⋊D5—32no—
258C22×Dic5—31no—
259D4×D5—62no—
260D4×D5—62no—
261D4×D5—122no—
262D4×D5—122no—
263C2×D20—31no—
264C2×D20—32no—
265C2×C4×D5—31no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×C4×D5—62no—
269C2×C4×D5—62no—
270C2×C4×D5C22×D312yes—
271C2×C4×D5C22×D311yescharacteristic
272C22⋊AGL(1,𝔽5)—62no—
273C22⋊AGL(1,𝔽5)—62no—
274C22⋊AGL(1,𝔽5)—64no—
275C22⋊AGL(1,𝔽5)—122no—
276C22⋊AGL(1,𝔽5)—122no—
277C22⋊AGL(1,𝔽5)—122no—
278C4⋊AGL(1,𝔽5)—22no—
279C4⋊AGL(1,𝔽5)—62no—
280C4⋊AGL(1,𝔽5)—62no—
281C4⋊AGL(1,𝔽5)—62no—
282C4⋊AGL(1,𝔽5)—122no—
283C4×AGL(1,𝔽5)—42no—
284C4×AGL(1,𝔽5)—62no—
285C4×AGL(1,𝔽5)D1214yescomplemented
286C5×C4⋊C4C4×D311yescharacteristic, complemented
287C5×C22⋊C4—32no—
288C22⋊Dic5—32no—
289#685—32no—
290#685—32no—
291C4⋊Dic5C4×D311yescharacteristic, complemented
292#683C4×D312yescomplemented
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—151no—
303C4×C4⋊C4—51no—
304C22×C3×C5C23×C411yescharacteristic
305C2×D15—21no—
306C2×D15—22no—
307C2×D15—21no—
308C2×D15—22no—
309C2×D15—21no—
310C2×D15—22no—
311C2×C5×D3—21no—
312C2×C5×D3—22no—
313C2×C5×D3—21no—
314C2×C5×D3—22no—
315C2×C5×D3—21no—
316C2×C5×D3—22no—
317C2×C3×D5C22×D411yescharacteristic
318C2×C3×D5C2×#4111yescharacteristic
319C2×C3×D5H(5,𝔽2)11yescharacteristic
320C2×C3×D5H(5,𝔽2)11yescharacteristic
321C2×C3×D5H(5,𝔽2)11yescharacteristic
322C2×C3×D52−1+411yescharacteristic
323D3×D5—42no—
324D3×D5—41no—
325D3×D5—41no—
326D3×D5—42no—
327D3×D5—41no—
328D3×D5—42no—
329D3×D5—41no—
330D3×D5—42no—
331ΓL(1,𝔽16)—42no—
332ΓL(1,𝔽16)—41no—
333ΓL(1,𝔽16)—41no—
334C3×AGL(1,𝔽5)—22no—
335C3×AGL(1,𝔽5)—22no—
336C3×AGL(1,𝔽5)—42no—
337C3×C4×C5—22no—
338C3×C4×C5C4×D412yes—
339Dic15—21no—
340C3×Dic5—22no—
341C3×Dic5C4×D412yes—
342C5×Dic3—21no—
343C23×D3—52no—
344C23×D3—51no—
345C22×C3×C4—51no—
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—52no—
349C22×C3×C4—52no—
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3—52no—
353C22×Dic3—51no—
354C2×D12—52no—
355C2×D12—51no—
356C2×D12—52no—
357C2×D12—52no—
358C2×D12—52no—
359C2×D12—102no—
360C2×D12—102no—
361C2×D12—202no—
362C2×D12—202no—
363C2×D12C2×AGL(1,𝔽5)11yescharacteristic
364C2×D12C2×AGL(1,𝔽5)12yescomplemented
365C2×C4×D3—51no—
366C2×C4×D3—51no—
367C2×C4×D3—51no—
368C2×C4×D3—102no—
369C2×C4×D3—102no—
370C2×C4×D3—104no—
371C2×C4×D3—202no—
372C2×C4×D3—202no—
373C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
374C3×C4⋊C4—52no—
375C3×C4⋊C4—51no—
376C3×C4⋊C4—102no—
377C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
378C3×C42—54no—
379C3×C42—202no—
380(C2×D3)⋊C4—52no—
381(C2×D3)⋊C4—52no—
382(C2×D3)⋊C4—52no—
383(C2×D3)⋊C4—102no—
384(C2×D3)⋊C4—102no—
385(C2×D3)⋊C4—104no—
386(C2×D3)⋊C4—202no—
387(C2×D3)⋊C4—202no—
388(C2×D3)⋊C4—202no—
389(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
390C4⋊Dic3—102no—
391C4⋊Dic3—202no—
392Dic3⋊C4—102no—
393Dic3⋊C4—102no—
394C4×Dic3—102no—
395C23×C5—32no—
396C23×C5—31no—
397C22×D5—32no—
398C22×D5—31no—
399C22×D5—61no—
400C22×D5—62no—
401C22×D5—61no—
402C22×D5—62no—
403C22×D5—62no—
404C22×D5—61no—
405C22×D5—61no—
406C22×D5—62no—
407C22×D5—61no—
408C22×D5—62no—
409C22×D5—61no—
410C22×D5—62no—
411C22×D5C23×D311yescharacteristic
412C2×AGL(1,𝔽5)—21no—
413C2×AGL(1,𝔽5)—21no—
414C2×AGL(1,𝔽5)—21no—
415C2×AGL(1,𝔽5)—21no—
416C2×AGL(1,𝔽5)—22no—
417C2×AGL(1,𝔽5)—22no—
418C2×AGL(1,𝔽5)—22no—
419C2×AGL(1,𝔽5)—61no—
420C2×AGL(1,𝔽5)—61no—
421C2×AGL(1,𝔽5)—62no—
422C2×AGL(1,𝔽5)—61no—
423C2×AGL(1,𝔽5)—61no—
424C2×AGL(1,𝔽5)—61no—
425C2×AGL(1,𝔽5)—62no—
426C2×AGL(1,𝔽5)—61no—
427C2×AGL(1,𝔽5)—62no—
428C2×AGL(1,𝔽5)—128no—
429C2×AGL(1,𝔽5)C2×D1212yes—
430C2×AGL(1,𝔽5)C2×D1212yes—
431C5×D4—62no—
432C5×D4—122no—
433C2×C4×C5—31no—
434C2×C4×C5—62no—
435C2×C4×C5C2×C4×D312yes—
436C2×C4×C5C2×C4×D311yescharacteristic
437C22⋊D5—64no—
438C22⋊D5—122no—
439C22⋊D5—122no—
440C2×Dic5—31no—
441C2×Dic5—62no—
442C2×Dic5C2×C4×D312yes—
443C2×Dic5C2×C4×D311yescharacteristic
444D20—62no—
445D20—122no—
446C4×D5—22no—
447C4×D5—22no—
448C4×D5—61no—
449C4×D5—61no—
450C4×D5—62no—
451C4×D5—62no—
452C4×D5C2×D1212yes—
453C4×D5#23512yes—
454C22×D4—151no—
455C22×D4—152no—
456C23×C4—151no—
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—152no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—152no—
476C2×C22⋊C4—152no—
477C2×C22⋊C4—152no—
478C2×C22⋊C4—152no—
479C2×C42—51no—
480C2×C42—52no—
481C2×C42—151no—
482#95—52no—
483#95—152no—
484#95—152no—
485C2×C3×C5C2×C4×D411yescharacteristic
486C2×C3×C5#51811yescharacteristic
487C2×C3×C5#52011yescharacteristic
488D15—42no—
489D15—41no—
490C3×D5#53511yescharacteristic
491C3×D5#53711yescharacteristic
492C3×D5#54011yescharacteristic
493C3×D5#54211yescharacteristic
494C5×D3—42no—
495C5×D3—41no—
496C23×C3—51no—
497C22×D3—52no—
498C22×D3—51no—
499C22×D3—101no—
500C22×D3—102no—
501C22×D3—101no—
502C22×D3—102no—
503C22×D3—102no—
504C22×D3—101no—
505C22×D3—102no—
506C22×D3—102no—
507C22×D3—101no—
508C22×D3—101no—
509C22×D3—101no—
510C22×D3—102no—
511C22×D3C22×AGL(1,𝔽5)12yes—
512C22×D3C22×AGL(1,𝔽5)11yescharacteristic
513C2×C3×C4—51no—
514C2×C3×C4—52no—
515C2×C3×C4—52no—
516C2×C3×C4—52no—
517C2×C3×C4—52no—
518C2×C3×C4—52no—
519C2×C3×C4—102no—
520C2×C3×C4—102no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—102no—
526C2×C3×C4—102no—
527C2×C3×C4—102no—
528C2×C3×C4C22×AGL(1,𝔽5)12yes—
529C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
530C2×Dic3—51no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—102no—
536C2×Dic3—101no—
537C2×Dic3—102no—
538C2×Dic3—101no—
539C2×Dic3—101no—
540C2×Dic3—102no—
541C2×Dic3—101no—
542C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
543D12—22no—
544D12—42no—
545D12—104no—
546D12—102no—
547D12—202no—
548D12—202no—
549D12—202no—
550C4×D3—22no—
551C4×D3—102no—
552C4×D3—102no—
553C4×D3—102no—
554C4×D3—208no—
555C22×C5—61no—
556C22×C5—62no—
557C22×C5—61no—
558C22×C5—62no—
559C22×C5—61no—
560C22×C5—62no—
561C22×C5C22×C4×D311yescharacteristic
562C2×D5—61no—
563C2×D5—62no—
564C2×D5—61no—
565C2×D5—62no—
566C2×D5—62no—
567C2×D5—61no—
568C2×D5—121no—
569C2×D5—122no—
570C2×D5—122no—
571C2×D5—121no—
572C2×D5—121no—
573C2×D5—122no—
574C2×D5—121no—
575C2×D5—122no—
576C2×D5C22×D1211yescharacteristic
577C2×D5C2×#23511yescharacteristic
578C2×D5#100411yescharacteristic
579C2×D5#100711yescharacteristic
580C2×D5#100911yescharacteristic
581C2×D5#100911yescharacteristic
582AGL(1,𝔽5)—22no—
583AGL(1,𝔽5)—22no—
584AGL(1,𝔽5)—42no—
585AGL(1,𝔽5)—121no—
586AGL(1,𝔽5)—121no—
587AGL(1,𝔽5)—122no—
588C4×C5—22no—
589C4×C5—61no—
590C4×C5C4×D1212yes—
591Dic5—22no—
592Dic5—61no—
593Dic5C4×D1212yes—
594C24—152no—
595C24—151no—
596C2×D4—31no—
597C2×D4—32no—
598C2×D4—152no—
599C2×D4—152no—
600C2×D4—152no—
601C2×D4—151no—
602C2×D4—152no—
603C2×D4—302no—
604C2×D4—302no—
605C2×D4—602no—
606C2×D4—602no—
607C22×C4—31no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—52no—
612C22×C4—52no—
613C22×C4—151no—
614C22×C4—151no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—152no—
619C22×C4—151no—
620C22×C4—302no—
621C22×C4—302no—
622C22×C4—304no—
623C22×C4—602no—
624C22×C4—602no—
625C4⋊C4—52no—
626C4⋊C4—51no—
627C4⋊C4—102no—
628C4⋊C4—302no—
629C4⋊C4—302no—
630C4⋊C4—302no—
631C4⋊C4—602no—
632C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
633C22⋊C4—32no—
634C22⋊C4—152no—
635C22⋊C4—152no—
636C22⋊C4—152no—
637C22⋊C4—302no—
638C22⋊C4—302no—
639C22⋊C4—304no—
640C22⋊C4—602no—
641C22⋊C4—602no—
642C22⋊C4—602no—
643C42—54no—
644C42—202no—
645C42—302no—
646C3×C5#232411yescharacteristic, complemented, Hall
647C22×C3—51no—
648C22×C3—51no—
649C22×C3—51no—
650C22×C3—51no—
651C22×C3—51no—
652C22×C3—51no—
653C22×C3C23×AGL(1,𝔽5)11yescharacteristic
654C2×D3—21no—
655C2×D3—22no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—101no—
661C2×D3—102no—
662C2×D3—101no—
663C2×D3—102no—
664C2×D3—102no—
665C2×D3—101no—
666C2×D3—202no—
667C2×D3—201no—
668C2×D3—201no—
669C2×D3—202no—
670C2×D3—201no—
671C2×D3—202no—
672C2×D3—201no—
673C2×D3—202no—
674C3×C4—22no—
675C3×C4—52no—
676C3×C4—102no—
677C3×C4—102no—
678C3×C4—102no—
679C3×C4—202no—
680C3×C4D4×AGL(1,𝔽5)12yes—
681Dic3—21no—
682Dic3—101no—
683Dic3—202no—
684Dic3—201no—
685Dic3—201no—
686C2×C5—122no—
687C2×C5—121no—
688C2×C5C2×C4×D1211yescharacteristic
689C2×C5#554511yescharacteristic
690C2×C5#557411yescharacteristic
691D5—121no—
692D5—122no—
693D5#551011yescharacteristic
694D5#552511yescharacteristic
695D5#556211yescharacteristic
696D5#558211yescharacteristic
697C23—32no—
698C23—31no—
699C23—51no—
700C23—152no—
701C23—151no—
702C23—301no—
703C23—302no—
704C23—301no—
705C23—302no—
706C23—302no—
707C23—301no—
708C23—302no—
709C23—302no—
710C23—301no—
711C23—301no—
712C23—302no—
713C23—301no—
714D4—62no—
715D4—122no—
716D4—304no—
717D4—302no—
718D4—602no—
719D4—602no—
720D4—602no—
721C2×C4—31no—
722C2×C4—51no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—52no—
726C2×C4—52no—
727C2×C4—52no—
728C2×C4—62no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—151no—
739C2×C4—302no—
740C2×C4—302no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—302no—
744C2×C4—301no—
745C2×C4—301no—
746C2×C4—302no—
747C2×C4—301no—
748C2×C4—301no—
749C2×C4—302no—
750C2×C4—301no—
751C2×C4—302no—
752C2×C4—301no—
753C2×C4—608no—
754C2×C4C2×D3×AGL(1,𝔽5)12yes—
755C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
756C2×C3—51no—
757C2×C3—51no—
758C2×C3—51no—
759C2×C3—51no—
760C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
761C2×C3#6625811yescharacteristic
762C2×C3#6626611yescharacteristic
763D3—41no—
764D3—42no—
765D3—201no—
766D3—202no—
767C5#7376311yescharacteristic, complemented, Sylow
768C22—51no—
769C22—51no—
770C22—51no—
771C22—51no—
772C22—51no—
773C22—51no—
774C22—61no—
775C22—62no—
776C22—61no—
777C22—62no—
778C22—62no—
779C22—61no—
780C22—301no—
781C22—302no—
782C22—301no—
783C22—302no—
784C22—302no—
785C22—301no—
786C22—602no—
787C22—601no—
788C22—601no—
789C22—602no—
790C22—601no—
791C22—602no—
792C22—601no—
793C22—602no—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—22no—
796C4—52no—
797C4—61no—
798C4—102no—
799C4—102no—
800C4—102no—
801C4—202no—
802C4—301no—
803C4—602no—
804C4—601no—
805C4—601no—
806C4AGL(1,𝔽5)×D1212yes—
807C3#1061725011yescharacteristic, complemented, Sylow
808C2—51no—
809C2—51no—
810C2—51no—
811C2—51no—
812C2—121no—
813C2—122no—
814C2—601no—
815C2—602no—
816C2C2×AGL(1,𝔽5)×D1211yescharacteristic
817C2#1175684511yescharacteristic
818C2#1175685411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalD5×#895C2
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×AGL(1,𝔽5)×D12C2semidirect
2. C2×#91909C2semidirect
4. #11752371C2semidirect
5. C3×C4⋊C4×AGL(1,𝔽5)C2semidirect
6. #11751934C2semidirect
7. #11751933C2semidirect
8. #11751857C2semidirect
9. #11751855C2semidirect
10. #11751850C2semidirect
11. #11751849C2semidirect
33. #91784C4semidirect
34. C5×#895C4semidirect
37. #91466C4semidirect
38. #91460C4semidirect
39. #91420C4semidirect
40. #91416C4semidirect
53. C4⋊C4×AGL(1,𝔽5)D3semidirect
68. C2×D60C2×C4semidirect
69. C2×C4×D15C2×C4semidirect
71. C2×C5×D12C2×C4semidirect
72. C2×C4×C5×D3C2×C4semidirect
76. C2×#1203C2×C4semidirect
77. C2×#1203C2×C4semidirect
78. C2×#1200C2×C4semidirect
79. C2×D3×Dic5C2×C4semidirect
92. C3×C4×AGL(1,𝔽5)D4semidirect
101. C3×C5×C4⋊C4C2×C4semidirect
102. #6714C2×C4semidirect
103. C5×(C2×D3)⋊C4C2×C4semidirect
104. C3×C4⋊Dic5C2×C4semidirect
105. C3×#683C2×C4semidirect
106. #6667C2×C4semidirect
107. (C2×D3)⋊Dic5C2×C4semidirect
235. #895AGL(1,𝔽5)semidirect
285. C4×AGL(1,𝔽5)D12semidirect
286. C5×C4⋊C4C4×D3semidirect
291. C4⋊Dic5C4×D3semidirect
292. #683C4×D3semidirect
364. C2×D12C2×AGL(1,𝔽5)semidirect
373. C2×C4×D3C2×AGL(1,𝔽5)semidirect
377. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
389. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
632. C4⋊C4D3×AGL(1,𝔽5)semidirect
646. C3×C5#2324semidirect
767. C5#73763semidirect
807. C3#10617250semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,𝔽5)×D122
C2×#919092
D5×#8952
#117523712
C3×C4⋊C4×AGL(1,𝔽5)2
#117519342
#117519332
#117518572
#117518552
#117518502
#117518492
#106172503
#737635