Finite Group Databasebeta

← #14280205

Subgroups — #14280205

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×#91235C211yesmaximal, characteristic
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
4C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
5C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
6C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
7D5×C3⋊#95C211yesmaximal, characteristic
8#10603802—31nomaximal, Hall
9C23×ΓL(1,𝔽16)C2211yescharacteristic
10C23×ΓL(1,𝔽16)C2211yescharacteristic
11C23×C3×AGL(1,𝔽5)C2211yescharacteristic
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×Dic3⋊AGL(1,𝔽5)—22no—
17C2×Dic3⋊AGL(1,𝔽5)—22no—
18C2×Dic3⋊AGL(1,𝔽5)—22no—
19#91235—22no—
20C3×(C2×AGL(1,𝔽5))⋊C4—22no—
21(C2×AGL(1,𝔽5))⋊Dic3—22no—
22(C2×AGL(1,𝔽5))⋊Dic3—22no—
23(C2×AGL(1,𝔽5))⋊Dic3—22no—
24#91115C411yescharacteristic, complemented
25C5×C3⋊#95C411yescharacteristic, complemented
26#90994C411yescharacteristic, complemented
27#90994C411yescharacteristic, complemented
28#69414—51nomaximal, Hall
29C22×C4⋊AGL(1,𝔽5)—31no—
30C2×(C2×AGL(1,𝔽5))⋊C4—31no—
31C2×(C2×AGL(1,𝔽5))⋊C4—31no—
32C2×(C2×AGL(1,𝔽5))⋊C4—31no—
33C2×(C2×AGL(1,𝔽5))⋊C4—31no—
34C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic
35D5×#95—31no—
36C23×C3×D5C2311yescharacteristic
37C22×ΓL(1,𝔽16)—21no—
38C22×ΓL(1,𝔽16)—21no—
39C22×ΓL(1,𝔽16)—21no—
40C22×ΓL(1,𝔽16)—21no—
41C22×ΓL(1,𝔽16)—21no—
42C22×ΓL(1,𝔽16)—21no—
43C22×ΓL(1,𝔽16)—21no—
44C22×ΓL(1,𝔽16)—21no—
45C22×ΓL(1,𝔽16)—21no—
46C22×ΓL(1,𝔽16)—21no—
47C22×ΓL(1,𝔽16)—21no—
48C22×ΓL(1,𝔽16)—21no—
49C22×ΓL(1,𝔽16)D412yes—
50C22×ΓL(1,𝔽16)D412yes—
51C22×C3×AGL(1,𝔽5)—21no—
52C22×C3×AGL(1,𝔽5)—21no—
53C22×C3×AGL(1,𝔽5)—21no—
54C22×C3×AGL(1,𝔽5)—21no—
55C22×C3×AGL(1,𝔽5)—21no—
56C22×C3×AGL(1,𝔽5)—21no—
57C22×C3×AGL(1,𝔽5)—21no—
58C22×C3×AGL(1,𝔽5)—21no—
59C22×C3×AGL(1,𝔽5)—21no—
60C22×C3×AGL(1,𝔽5)—21no—
61C22×C3×AGL(1,𝔽5)—21no—
62C22×C3×AGL(1,𝔽5)—21no—
63C22×C3×AGL(1,𝔽5)D412yes—
64C22×C3×AGL(1,𝔽5)Q812yes—
65C22×C3×C4×C5C2×C411yescharacteristic
66C22×Dic15C2×C411yescharacteristic
67C22×Dic15C2×C411yescharacteristic
68C22×C5×Dic3C2×C411yescharacteristic
69C22×C5×Dic3C2×C411yescharacteristic
70C22×C3×Dic5C2×C411yescharacteristic
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—21no—
76C2×C3×C4×D5—21no—
77C2×D5×Dic3—21no—
78C2×D5×Dic3—21no—
79C2×D5×Dic3—21no—
80C2×D5×Dic3—21no—
81C2×D5×Dic3—21no—
82C2×D5×Dic3—21no—
83C2×D5×Dic3—21no—
84C2×D5×Dic3—21no—
85C2×D5×Dic3—21no—
86C2×D5×Dic3—21no—
87C2×D5×Dic3D412yes—
88C2×D5×Dic3Q812yes—
89Dic3⋊AGL(1,𝔽5)—28no—
90C22×Dic3⋊C4—51no—
91C2×C3×#95—51no—
92C2×C3⋊#95—51no—
93C2×C3⋊#95—51no—
94C2×C3⋊#95—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95—51no—
97C23×AGL(1,𝔽5)—31no—
98C23×AGL(1,𝔽5)—31no—
99C23×AGL(1,𝔽5)C2×D311yescharacteristic
100C23×AGL(1,𝔽5)C2×D311yescharacteristic
101C22×C4×D5—31no—
102C22×C4×D5—31no—
103C22×C4×D5C2×D311yescharacteristic
104C2×C4⋊AGL(1,𝔽5)—62no—
105C2×C4⋊AGL(1,𝔽5)—62no—
106C2×C4⋊AGL(1,𝔽5)—62no—
107(C2×AGL(1,𝔽5))⋊C4—22no—
108(C2×AGL(1,𝔽5))⋊C4—62no—
109(C2×AGL(1,𝔽5))⋊C4—62no—
110(C2×AGL(1,𝔽5))⋊C4—62no—
111(C2×AGL(1,𝔽5))⋊C4—62no—
112C5×#95—31no—
113#3963—31no—
114#3963—31no—
115#3963—31no—
116#1442—151noSylow
117C23×C3×C5C22×C411yescharacteristic
118C22×C3×D5C2×D411yescharacteristic
119C22×C3×D5C2×D411yescharacteristic
120C22×C3×D5C2×D411yescharacteristic
121C22×C3×D5C2×D411yescharacteristic
122C22×C3×D5C2×Q811yescharacteristic
123C22×C3×D5C2×Q811yescharacteristic
124C22×C3×D5#4111yescharacteristic
125C22×C3×D5#4111yescharacteristic
126C22×C3×D5#4111yescharacteristic
127C22×C3×D5#4111yescharacteristic
128C22×C3×D5#4111yescharacteristic
129C22×C3×D5#4111yescharacteristic
130C22×C3×D5#4111yescharacteristic
131C22×C3×D5#4111yescharacteristic
132C2×ΓL(1,𝔽16)—22no—
133C2×ΓL(1,𝔽16)—22no—
134C2×ΓL(1,𝔽16)—22no—
135C2×ΓL(1,𝔽16)—22no—
136C2×ΓL(1,𝔽16)—22no—
137C2×ΓL(1,𝔽16)—22no—
138C2×ΓL(1,𝔽16)—41no—
139C2×ΓL(1,𝔽16)—41no—
140C2×ΓL(1,𝔽16)—41no—
141C2×ΓL(1,𝔽16)—41no—
142C2×ΓL(1,𝔽16)—41no—
143C2×ΓL(1,𝔽16)—41no—
144C2×ΓL(1,𝔽16)—41no—
145C2×ΓL(1,𝔽16)—41no—
146C2×C3×AGL(1,𝔽5)—22no—
147C2×C3×AGL(1,𝔽5)—22no—
148C2×C3×AGL(1,𝔽5)—22no—
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—22no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—41no—
153C2×C3×AGL(1,𝔽5)—41no—
154C2×C3×AGL(1,𝔽5)—41no—
155C2×C3×AGL(1,𝔽5)—41no—
156C2×C3×AGL(1,𝔽5)—41no—
157C2×C3×AGL(1,𝔽5)—41no—
158C2×C3×AGL(1,𝔽5)—41no—
159C2×C3×AGL(1,𝔽5)—41no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—21no—
163C2×Dic15—21no—
164C2×Dic15—21no—
165C2×Dic15—21no—
166C2×Dic15—21no—
167C2×Dic15—21no—
168C2×Dic15C4⋊C412yes—
169C2×C5×Dic3—21no—
170C2×C5×Dic3—21no—
171C2×C5×Dic3—21no—
172C2×C5×Dic3—21no—
173C2×C5×Dic3—21no—
174C2×C5×Dic3C4⋊C412yes—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177C2×C3×Dic5—21no—
178C3×C4×D5—41no—
179C3×C4×D5—41no—
180C3×C4×D5—41no—
181C3×C4×D5—41no—
182D5×Dic3—22no—
183D5×Dic3—22no—
184D5×Dic3—22no—
185D5×Dic3—22no—
186D5×Dic3—41no—
187D5×Dic3—41no—
188D5×Dic3—41no—
189D5×Dic3—41no—
190C23×C3×C4—51no—
191C23×C3×C4—51no—
192C23×C3×C4—51no—
193C23×Dic3—51no—
194C23×Dic3—51no—
195C23×Dic3—51no—
196C23×Dic3—51no—
197C2×Dic3⋊C4—102no—
198C2×Dic3⋊C4—102no—
199C2×Dic3⋊C4—102no—
200C3×#95—102no—
201C3⋊#95—51no—
202C3⋊#95—51no—
203C3⋊#95—51no—
204C3⋊#95—102no—
205C3⋊#95—102no—
206C3⋊#95—102no—
207C3⋊#95—102no—
208C3⋊#95AGL(1,𝔽5)11yescharacteristic, complemented
209C23×D5C22×D311yescharacteristic
210C22×AGL(1,𝔽5)—21no—
211C22×AGL(1,𝔽5)—21no—
212C22×AGL(1,𝔽5)—21no—
213C22×AGL(1,𝔽5)—21no—
214C22×AGL(1,𝔽5)—21no—
215C22×AGL(1,𝔽5)—21no—
216C22×AGL(1,𝔽5)—21no—
217C22×AGL(1,𝔽5)—21no—
218C22×AGL(1,𝔽5)—21no—
219C22×AGL(1,𝔽5)—21no—
220C22×AGL(1,𝔽5)—21no—
221C22×AGL(1,𝔽5)—21no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)—32no—
224C22×AGL(1,𝔽5)—61no—
225C22×AGL(1,𝔽5)—61no—
226C22×AGL(1,𝔽5)—61no—
227C22×AGL(1,𝔽5)—61no—
228C22×AGL(1,𝔽5)—61no—
229C22×AGL(1,𝔽5)—61no—
230C22×AGL(1,𝔽5)—61no—
231C22×AGL(1,𝔽5)—61no—
232C22×AGL(1,𝔽5)—61no—
233C22×AGL(1,𝔽5)—61no—
234C22×AGL(1,𝔽5)—61no—
235C22×AGL(1,𝔽5)—61no—
236C22×AGL(1,𝔽5)Dic612yes—
237C22×AGL(1,𝔽5)#6712yes—
238C22×C4×C5—31no—
239C22×C4×C5—31no—
240C22×C4×C5C4×D311yescharacteristic
241C22×Dic5—31no—
242C22×Dic5—31no—
243C22×Dic5C4×D311yescharacteristic
244C2×C4×D5—21no—
245C2×C4×D5—21no—
246C2×C4×D5—21no—
247C2×C4×D5—21no—
248C2×C4×D5—21no—
249C2×C4×D5—21no—
250C2×C4×D5—32no—
251C2×C4×D5—32no—
252C2×C4×D5—61no—
253C2×C4×D5—61no—
254C2×C4×D5—61no—
255C2×C4×D5—61no—
256C2×C4×D5—61no—
257C2×C4×D5—61no—
258C2×C4×D5—61no—
259C2×C4×D5—61no—
260C2×C4×D5—61no—
261C2×C4×D5—61no—
262C4⋊AGL(1,𝔽5)—68no—
263C22×C4⋊C4—151no—
264C2×#95—51no—
265C2×#95—151no—
266C2×#95—151no—
267C2×#95—151no—
268C2×#95—151no—
269C2×#95—151no—
270C22×C3×C5C2×C4⋊C411yescharacteristic
271C22×C3×C5#11711yescharacteristic
272C22×C3×C5#11711yescharacteristic
273C22×C3×C5C4×D411yescharacteristic
274C22×C3×C5C4×D411yescharacteristic
275C22×C3×C5C4×D411yescharacteristic
276C22×C3×C5C4×Q811yescharacteristic
277C2×C3×D5#12011yescharacteristic
278C2×C3×D5#12111yescharacteristic
279C2×C3×D5#12111yescharacteristic
280C2×C3×D5#12111yescharacteristic
281C2×C3×D5C22⋊Q811yescharacteristic
282C2×C3×D5C22⋊Q811yescharacteristic
283C2×C3×D5C22⋊Q811yescharacteristic
284C2×C3×D5C22⋊Q811yescharacteristic
285C2×C3×D5C22⋊Q811yescharacteristic
286C2×C3×D5#12311yescharacteristic
287C2×C3×D5#12311yescharacteristic
288C2×C3×D5#12311yescharacteristic
289C2×C3×D5#12311yescharacteristic
290C2×C3×D5#12311yescharacteristic
291C2×C3×D5#12411yescharacteristic
292C2×C3×D5#12411yescharacteristic
293C2×C3×D5#12411yescharacteristic
294C2×C3×D5#12411yescharacteristic
295C2×C3×D5#12511yescharacteristic
296C2×C3×D5#12511yescharacteristic
297C2×C3×D5#12511yescharacteristic
298C2×C3×D5#12511yescharacteristic
299C2×C3×D5#12511yescharacteristic
300C2×C3×D5#12611yescharacteristic
301C2×C3×D5#12611yescharacteristic
302C2×C3×D5#12611yescharacteristic
303C2×C3×D5#12611yescharacteristic
304C2×C3×D5C4⋊Q811yescharacteristic
305ΓL(1,𝔽16)—42no—
306ΓL(1,𝔽16)—42no—
307C3×AGL(1,𝔽5)—42no—
308C3×AGL(1,𝔽5)—42no—
309C3×C4×C5—41no—
310Dic15—22no—
311Dic15—41no—
312C3×Dic5—41no—
313C5×Dic3—22no—
314C5×Dic3—41no—
315C24×C3—51no—
316C22×C3×C4—52no—
317C22×C3×C4—52no—
318C22×C3×C4—51no—
319C22×C3×C4—101no—
320C22×C3×C4—101no—
321C22×C3×C4—101no—
322C22×C3×C4—101no—
323C22×C3×C4—101no—
324C22×C3×C4—101no—
325C22×C3×C4—101no—
326C22×C3×C4—101no—
327C22×C3×C4—101no—
328C22×C3×C4—101no—
329C22×C3×C4—101no—
330C22×C3×C4—101no—
331C22×C3×C4—101no—
332C22×C3×C4—101no—
333C22×C3×C4—101no—
334C22×C3×C4—101no—
335C22×C3×C4—101no—
336C22×C3×C4—101no—
337C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
338C22×Dic3—51no—
339C22×Dic3—52no—
340C22×Dic3—52no—
341C22×Dic3—52no—
342C22×Dic3—52no—
343C22×Dic3—51no—
344C22×Dic3—101no—
345C22×Dic3—101no—
346C22×Dic3—101no—
347C22×Dic3—101no—
348C22×Dic3—101no—
349C22×Dic3—101no—
350C22×Dic3—101no—
351C22×Dic3—101no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C22×Dic3—101no—
355C22×Dic3—101no—
356C22×Dic3—101no—
357C22×Dic3—101no—
358C22×Dic3—101no—
359C22×Dic3—101no—
360C22×Dic3—101no—
361C22×Dic3—101no—
362C22×Dic3—101no—
363C22×Dic3—101no—
364C22×Dic3—101no—
365C22×Dic3—101no—
366C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
367C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
368Dic3⋊C4—108no—
369C23×C5C2×C4×D311yescharacteristic
370C22×D5C2×Dic611yescharacteristic
371C22×D5#23511yescharacteristic
372C22×D5#23511yescharacteristic
373C22×D5#23511yescharacteristic
374C22×D5#23511yescharacteristic
375C22×D5D3×D411yescharacteristic
376C22×D5D3×D411yescharacteristic
377C22×D5D3×D411yescharacteristic
378C22×D5#23711yescharacteristic
379C22×D5#23711yescharacteristic
380C22×D5#23711yescharacteristic
381C22×D5D3×Q811yescharacteristic
382C22×D5#23911yescharacteristic
383C22×D5C2×#6711yescharacteristic
384C2×AGL(1,𝔽5)—22no—
385C2×AGL(1,𝔽5)—22no—
386C2×AGL(1,𝔽5)—22no—
387C2×AGL(1,𝔽5)—22no—
388C2×AGL(1,𝔽5)—22no—
389C2×AGL(1,𝔽5)—22no—
390C2×AGL(1,𝔽5)—41no—
391C2×AGL(1,𝔽5)—41no—
392C2×AGL(1,𝔽5)—41no—
393C2×AGL(1,𝔽5)—41no—
394C2×AGL(1,𝔽5)—41no—
395C2×AGL(1,𝔽5)—41no—
396C2×AGL(1,𝔽5)—41no—
397C2×AGL(1,𝔽5)—41no—
398C2×AGL(1,𝔽5)—62no—
399C2×AGL(1,𝔽5)—62no—
400C2×AGL(1,𝔽5)—62no—
401C2×AGL(1,𝔽5)—62no—
402C2×AGL(1,𝔽5)—62no—
403C2×AGL(1,𝔽5)—62no—
404C2×AGL(1,𝔽5)—121no—
405C2×AGL(1,𝔽5)—121no—
406C2×AGL(1,𝔽5)—121no—
407C2×AGL(1,𝔽5)—121no—
408C2×AGL(1,𝔽5)—121no—
409C2×AGL(1,𝔽5)—121no—
410C2×AGL(1,𝔽5)—121no—
411C2×AGL(1,𝔽5)—121no—
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—32no—
416C2×C4×C5—61no—
417C2×C4×C5—61no—
418C2×C4×C5—61no—
419C2×C4×C5—61no—
420C2×C4×C5—61no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—32no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C4×D5—41no—
431C4×D5—41no—
432C4×D5—41no—
433C4×D5—41no—
434C4×D5—62no—
435C4×D5—62no—
436C4×D5—62no—
437C4×D5—62no—
438C4×D5—121no—
439C4×D5—121no—
440C4×D5—121no—
441C4×D5—121no—
442C23×C4—51no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—151no—
446C23×C4—151no—
447C23×C4—151no—
448C23×C4—151no—
449C2×C4⋊C4—302no—
450C2×C4⋊C4—302no—
451C2×C4⋊C4—302no—
452#95—31no—
453#95—102no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—302no—
458#95—302no—
459#95—302no—
460#95—302no—
461C2×C3×C5#38211yescharacteristic
462C2×C3×C5#38511yescharacteristic
463C2×C3×C5#38711yescharacteristic
464C2×C3×C5#38711yescharacteristic
465C2×C3×C5#38811yescharacteristic
466C2×C3×C5#38811yescharacteristic
467C2×C3×C5#38911yescharacteristic
468C3×D5#39311yescharacteristic
469C3×D5#39411yescharacteristic
470C3×D5#39711yescharacteristic
471C3×D5#39811yescharacteristic
472C3×D5#39811yescharacteristic
473C3×D5#40011yescharacteristic
474C3×D5#40011yescharacteristic
475C3×D5#40011yescharacteristic
476C23×C3—51no—
477C23×C3—51no—
478C23×C3—51no—
479C23×C3—51no—
480C23×C3—51no—
481C23×C3—51no—
482C23×C3—51no—
483C23×C3—51no—
484C23×C3—51no—
485C23×C3—51no—
486C23×C3—51no—
487C23×C3—51no—
488C23×C3—51no—
489C23×C3—51no—
490C23×C3C22×AGL(1,𝔽5)11yescharacteristic
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—102no—
495C2×C3×C4—102no—
496C2×C3×C4—102no—
497C2×C3×C4—102no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—201no—
504C2×C3×C4—201no—
505C2×C3×C4—201no—
506C2×C3×C4—201no—
507C2×C3×C4—201no—
508C2×C3×C4—201no—
509C2×C3×C4—201no—
510C2×C3×C4—201no—
511C2×C3×C4—201no—
512C2×C3×C4—201no—
513C2×C3×C4—201no—
514C2×C3×C4—201no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—52no—
521C2×Dic3—102no—
522C2×Dic3—102no—
523C2×Dic3—102no—
524C2×Dic3—102no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—102no—
528C2×Dic3—102no—
529C2×Dic3—102no—
530C2×Dic3—102no—
531C2×Dic3—102no—
532C2×Dic3—102no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—201no—
537C2×Dic3—201no—
538C2×Dic3—201no—
539C2×Dic3—201no—
540C2×Dic3—201no—
541C2×Dic3—201no—
542C2×Dic3—201no—
543C2×Dic3—201no—
544C2×Dic3—201no—
545C2×Dic3—201no—
546C2×Dic3—201no—
547C2×Dic3—201no—
548C2×Dic3C4⋊AGL(1,𝔽5)12yes—
549C22×C5C4×Dic611yescharacteristic
550C22×C5#87211yescharacteristic
551C22×C5#87711yescharacteristic
552C22×C5#67⋊C411yescharacteristic
553C22×C5D3×C4⋊C411yescharacteristic
554C22×C5#89311yescharacteristic
555C22×C5C4×#6711yescharacteristic
556C2×D5#87011yescharacteristic
557C2×D5#87611yescharacteristic
558C2×D5#87811yescharacteristic
559C2×D5#87811yescharacteristic
560C2×D5#87911yescharacteristic
561C2×D5#88311yescharacteristic
562C2×D5#88311yescharacteristic
563C2×D5#88411yescharacteristic
564C2×D5#88411yescharacteristic
565C2×D5#88511yescharacteristic
566C2×D5#88511yescharacteristic
567C2×D5#88511yescharacteristic
568C2×D5#88811yescharacteristic
569C2×D5#88911yescharacteristic
570C2×D5#88911yescharacteristic
571C2×D5#88911yescharacteristic
572C2×D5#89011yescharacteristic
573C2×D5#89411yescharacteristic
574C2×D5#89411yescharacteristic
575C2×D5#89611yescharacteristic
576C2×D5#89811yescharacteristic
577C2×D5#89811yescharacteristic
578C2×D5#92411yescharacteristic
579C2×D5#92911yescharacteristic
580C2×D5#93611yescharacteristic
581C2×D5#93711yescharacteristic
582C2×D5#93911yescharacteristic
583C2×D5#94611yescharacteristic
584AGL(1,𝔽5)—42no—
585AGL(1,𝔽5)—42no—
586AGL(1,𝔽5)—122no—
587AGL(1,𝔽5)—122no—
588C4×C5—41no—
589C4×C5—62no—
590C4×C5—121no—
591Dic5—41no—
592Dic5—62no—
593Dic5—121no—
594C24—51no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—51no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—152no—
619C22×C4—152no—
620C22×C4—151no—
621C22×C4—152no—
622C22×C4—152no—
623C22×C4—151no—
624C22×C4—301no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4—301no—
629C22×C4—301no—
630C22×C4—301no—
631C22×C4—301no—
632C22×C4—301no—
633C22×C4—301no—
634C22×C4—301no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4—301no—
638C22×C4—301no—
639C22×C4—301no—
640C22×C4—301no—
641C22×C4—301no—
642C22×C4—301no—
643C22×C4—301no—
644C22×C4—301no—
645C22×C4—301no—
646C22×C4D3×AGL(1,𝔽5)11yescharacteristic
647C4⋊C4—308no—
648C3×C5#144211yescharacteristic, complemented, Hall
649C22×C3—51no—
650C22×C3—51no—
651C22×C3—51no—
652C22×C3—51no—
653C22×C3—51no—
654C22×C3—51no—
655C22×C3—51no—
656C22×C3—51no—
657C22×C3—51no—
658C22×C3—51no—
659C22×C3—51no—
660C22×C3—51no—
661C22×C3—51no—
662C22×C3—51no—
663C22×C3—51no—
664C22×C3—51no—
665C22×C3—51no—
666C22×C3—51no—
667C22×C3—51no—
668C22×C3—51no—
669C22×C3—51no—
670C22×C3—51no—
671C22×C3—51no—
672C22×C3—51no—
673C22×C3—51no—
674C22×C3—51no—
675C22×C3—51no—
676C22×C3—51no—
677C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
678C22×C3#413011yescharacteristic
679C22×C3#413011yescharacteristic
680C22×C3D4×AGL(1,𝔽5)11yescharacteristic
681C22×C3D4×AGL(1,𝔽5)11yescharacteristic
682C22×C3D4×AGL(1,𝔽5)11yescharacteristic
683C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
684C3×C4—41no—
685C3×C4—202no—
686C3×C4—202no—
687C3×C4—201no—
688Dic3—22no—
689Dic3—41no—
690Dic3—102no—
691Dic3—202no—
692Dic3—202no—
693Dic3—201no—
694C2×C5#464711yescharacteristic
695C2×C5#465011yescharacteristic
696C2×C5#465411yescharacteristic
697C2×C5#466911yescharacteristic
698C2×C5#493311yescharacteristic
699C2×C5#494511yescharacteristic
700C2×C5#498911yescharacteristic
701D5#465711yescharacteristic
702D5#465811yescharacteristic
703D5#466011yescharacteristic
704D5#467511yescharacteristic
705D5#494711yescharacteristic
706D5#495911yescharacteristic
707D5#498211yescharacteristic
708D5#498511yescharacteristic
709C23—51no—
710C23—51no—
711C23—51no—
712C23—51no—
713C23—51no—
714C23—51no—
715C23—51no—
716C23—51no—
717C23—51no—
718C23—51no—
719C23—51no—
720C23—51no—
721C23—51no—
722C23—51no—
723C23C2×D3×AGL(1,𝔽5)11yescharacteristic
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—32no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—101no—
740C2×C4—101no—
741C2×C4—101no—
742C2×C4—152no—
743C2×C4—201no—
744C2×C4—201no—
745C2×C4—201no—
746C2×C4—201no—
747C2×C4—201no—
748C2×C4—201no—
749C2×C4—201no—
750C2×C4—201no—
751C2×C4—201no—
752C2×C4—201no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—302no—
756C2×C4—302no—
757C2×C4—302no—
758C2×C4—302no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—302no—
762C2×C4—302no—
763C2×C4—302no—
764C2×C4—302no—
765C2×C4—302no—
766C2×C4—302no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—601no—
771C2×C4—601no—
772C2×C4—601no—
773C2×C4—601no—
774C2×C4—601no—
775C2×C4—601no—
776C2×C4—601no—
777C2×C4—601no—
778C2×C4—601no—
779C2×C4—601no—
780C2×C4—601no—
781C2×C4—601no—
782C2×C3—51no—
783C2×C3—51no—
784C2×C3—51no—
785C2×C3—51no—
786C2×C3—51no—
787C2×C3—51no—
788C2×C3—51no—
789C2×C3—51no—
790C2×C3#6568911yescharacteristic
791C2×C3#6569911yescharacteristic
792C2×C3#6570011yescharacteristic
793C2×C3#6570011yescharacteristic
794C2×C3#6571111yescharacteristic
795C2×C3#6571111yescharacteristic
796C2×C3#6571211yescharacteristic
797C5#6941411yescharacteristic, complemented, Sylow
798C22—51no—
799C22—51no—
800C22—51no—
801C22—51no—
802C22—51no—
803C22—51no—
804C22—51no—
805C22—51no—
806C22—51no—
807C22—51no—
808C22—51no—
809C22—51no—
810C22—51no—
811C22—51no—
812C22—51no—
813C22—51no—
814C22—51no—
815C22—51no—
816C22—51no—
817C22—51no—
818C22—51no—
819C22—51no—
820C22—51no—
821C22—51no—
822C22—51no—
823C22—51no—
824C22—51no—
825C22—51no—
826C22AGL(1,𝔽5)×Dic611yescharacteristic
827C22#9190911yescharacteristic
828C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
829C22#9192111yescharacteristic
830C22#9192311yescharacteristic
831C22AGL(1,𝔽5)×#6711yescharacteristic
832C22#67⋊AGL(1,𝔽5)11yescharacteristic
833C4—41no—
834C4—62no—
835C4—121no—
836C4—202no—
837C4—202no—
838C4—201no—
839C4—302no—
840C4—602no—
841C4—602no—
842C4—601no—
843C3#1060380211yescharacteristic, complemented, Sylow
844C2—51no—
845C2—51no—
846C2—51no—
847C2—51no—
848C2—51no—
849C2—51no—
850C2—51no—
851C2—51no—
852C2#1175174511yescharacteristic
853C2#1175174611yescharacteristic
854C2#1175184011yescharacteristic
855C2#1175184411yescharacteristic
856C2#1175185611yescharacteristic
857C2#1175193211yescharacteristic
858C2#1175201811yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutator, socleC23×C3×C5C22×C4
FittingC22×C3×C4×C5C2×C4
prime radical, cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1442
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
24. #91115C4semidirect
25. C5×C3⋊#95C4semidirect
26. #90994C4semidirect
27. #90994C4semidirect
208. C3⋊#95AGL(1,𝔽5)semidirect
648. C3×C5#1442semidirect
797. C5#69414semidirect
843. C3#10603802semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊AGL(1,𝔽5)2
C2×#912352
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
D5×C3⋊#952
#106038023
#694145