Finite Group Databasebeta

← #14280287

Subgroups — #14280287

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, 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
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
8#10604345—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×#6712C411yescharacteristic, complemented
17C2×C5×Dic3⋊C4C411yescharacteristic, complemented
18C2×Dic3⋊Dic5C411yescharacteristic, complemented
19C2×#6669C411yescharacteristic, complemented
20D5×Dic3⋊C4—22no—
21D5×Dic3⋊C4—22no—
22#91235—22no—
23C3×(C2×AGL(1,𝔽5))⋊C4—22no—
24(C2×AGL(1,𝔽5))⋊Dic3—22no—
25(C2×AGL(1,𝔽5))⋊Dic3—22no—
26(C2×AGL(1,𝔽5))⋊Dic3—22no—
27(C2×AGL(1,𝔽5))⋊Dic3—22no—
28#69421—51nomaximal, Hall
29C2×D5×C4⋊C4—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))⋊C4—31no—
35C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic
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)Q812yes—
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×Dic3D412yes—
89#6712—22no—
90C5×Dic3⋊C4—22no—
91Dic3⋊Dic5—22no—
92#6669—22no—
93C22×Dic3⋊C4—51no—
94C2×C3×#95—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95—51no—
97C2×C3⋊#95—51no—
98C2×C3⋊#95—51no—
99C2×C3⋊#95—51no—
100C23×AGL(1,𝔽5)—31no—
101C23×AGL(1,𝔽5)—31no—
102C23×AGL(1,𝔽5)C2×D311yescharacteristic
103C23×AGL(1,𝔽5)C2×D311yescharacteristic
104C22×C4×D5—31no—
105C22×C4×D5—31no—
106C22×C4×D5C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108C2×C4⋊Dic5—31no—
109C2×#683—31no—
110C2×#683—31no—
111D5×C4⋊C4—62no—
112D5×C4⋊C4—62no—
113(C2×AGL(1,𝔽5))⋊C4—22no—
114(C2×AGL(1,𝔽5))⋊C4—62no—
115(C2×AGL(1,𝔽5))⋊C4—62no—
116(C2×AGL(1,𝔽5))⋊C4—62no—
117(C2×AGL(1,𝔽5))⋊C4—62no—
118(C2×AGL(1,𝔽5))⋊C4—62no—
119#1445—151noSylow
120C23×C3×C5C22×C411yescharacteristic
121C22×C3×D5C2×D411yescharacteristic
122C22×C3×D5C2×D411yescharacteristic
123C22×C3×D5C2×D411yescharacteristic
124C22×C3×D5C2×D411yescharacteristic
125C22×C3×D5C2×Q811yescharacteristic
126C22×C3×D5C2×Q811yescharacteristic
127C22×C3×D5#4111yescharacteristic
128C22×C3×D5#4111yescharacteristic
129C22×C3×D5#4111yescharacteristic
130C22×C3×D5#4111yescharacteristic
131C22×C3×D5#4111yescharacteristic
132C22×C3×D5#4111yescharacteristic
133C22×C3×D5#4111yescharacteristic
134C22×C3×D5#4111yescharacteristic
135C2×ΓL(1,𝔽16)—22no—
136C2×ΓL(1,𝔽16)—22no—
137C2×ΓL(1,𝔽16)—22no—
138C2×ΓL(1,𝔽16)—22no—
139C2×ΓL(1,𝔽16)—22no—
140C2×ΓL(1,𝔽16)—22no—
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×ΓL(1,𝔽16)—41no—
147C2×ΓL(1,𝔽16)—41no—
148C2×ΓL(1,𝔽16)—41no—
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—22no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—22no—
154C2×C3×AGL(1,𝔽5)—22no—
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×AGL(1,𝔽5)—41no—
161C2×C3×AGL(1,𝔽5)—41no—
162C2×C3×AGL(1,𝔽5)—41no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—21no—
165C2×C3×C4×C5—21no—
166C2×Dic15—21no—
167C2×Dic15—21no—
168C2×Dic15—21no—
169C2×Dic15—21no—
170C2×Dic15—21no—
171C2×Dic15C22⋊C412yes—
172C2×C5×Dic3—21no—
173C2×C5×Dic3—21no—
174C2×C5×Dic3—21no—
175C2×C5×Dic3—21no—
176C2×C5×Dic3—21no—
177C2×C5×Dic3C22⋊C412yes—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—21no—
180C2×C3×Dic5—21no—
181C3×C4×D5—41no—
182C3×C4×D5—41no—
183C3×C4×D5—41no—
184C3×C4×D5—41no—
185D5×Dic3—22no—
186D5×Dic3—22no—
187D5×Dic3—22no—
188D5×Dic3—22no—
189D5×Dic3—41no—
190D5×Dic3—41no—
191D5×Dic3—41no—
192D5×Dic3—41no—
193C23×C3×C4—51no—
194C23×C3×C4—51no—
195C23×C3×C4—51no—
196C23×Dic3—51no—
197C23×Dic3—51no—
198C23×Dic3—51no—
199C23×Dic3—51no—
200C2×Dic3⋊C4—51no—
201C2×Dic3⋊C4—51no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4—102no—
204C2×Dic3⋊C4—102no—
205C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
206C3×#95—102no—
207C3⋊#95—102no—
208C3⋊#95—102no—
209C3⋊#95—102no—
210C3⋊#95—102no—
211C3⋊#95—102no—
212C23×D5C22×D311yescharacteristic
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)—21no—
223C22×AGL(1,𝔽5)—21no—
224C22×AGL(1,𝔽5)—21no—
225C22×AGL(1,𝔽5)—32no—
226C22×AGL(1,𝔽5)—32no—
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)—61no—
237C22×AGL(1,𝔽5)—61no—
238C22×AGL(1,𝔽5)—61no—
239C22×AGL(1,𝔽5)Dic612yes—
240C22×AGL(1,𝔽5)#6712yes—
241C22×C4×C5—31no—
242C22×C4×C5—31no—
243C22×C4×C5C4×D311yescharacteristic
244C22×Dic5—31no—
245C22×Dic5—31no—
246C22×Dic5C4×D311yescharacteristic
247C2×C4×D5—21no—
248C2×C4×D5—21no—
249C2×C4×D5—21no—
250C2×C4×D5—21no—
251C2×C4×D5—21no—
252C2×C4×D5—21no—
253C2×C4×D5—32no—
254C2×C4×D5—32no—
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—
262C2×C4×D5—61no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C5×C4⋊C4—62no—
266C4⋊Dic5—62no—
267#683—62no—
268#683—62no—
269C22×C4⋊C4—151no—
270C2×#95—51no—
271C2×#95—151no—
272C2×#95—151no—
273C2×#95—151no—
274C2×#95—151no—
275C2×#95—151no—
276C22×C3×C5C2×C22⋊C411yescharacteristic
277C22×C3×C5#11711yescharacteristic
278C22×C3×C5#11711yescharacteristic
279C22×C3×C5C4×D411yescharacteristic
280C22×C3×C5C4×D411yescharacteristic
281C22×C3×C5C4×Q811yescharacteristic
282C22×C3×C5C4×Q811yescharacteristic
283C2×C3×D5#12111yescharacteristic
284C2×C3×D5#12111yescharacteristic
285C2×C3×D5C22⋊Q811yescharacteristic
286C2×C3×D5C22⋊Q811yescharacteristic
287C2×C3×D5C22⋊Q811yescharacteristic
288C2×C3×D5C22⋊Q811yescharacteristic
289C2×C3×D5C22⋊Q811yescharacteristic
290C2×C3×D5C22⋊Q811yescharacteristic
291C2×C3×D5#12311yescharacteristic
292C2×C3×D5#12311yescharacteristic
293C2×C3×D5#12311yescharacteristic
294C2×C3×D5#12311yescharacteristic
295C2×C3×D5#12311yescharacteristic
296C2×C3×D5#12311yescharacteristic
297C2×C3×D5#12311yescharacteristic
298C2×C3×D5#12311yescharacteristic
299C2×C3×D5#12411yescharacteristic
300C2×C3×D5#12411yescharacteristic
301C2×C3×D5#12511yescharacteristic
302C2×C3×D5#12511yescharacteristic
303C2×C3×D5#12511yescharacteristic
304C2×C3×D5#12511yescharacteristic
305C2×C3×D5#12611yescharacteristic
306C2×C3×D5#12611yescharacteristic
307C2×C3×D5#12611yescharacteristic
308C2×C3×D5#12611yescharacteristic
309C2×C3×D5#12711yescharacteristic
310C2×C3×D5C4⋊Q811yescharacteristic
311ΓL(1,𝔽16)—42no—
312ΓL(1,𝔽16)—42no—
313C3×AGL(1,𝔽5)—42no—
314C3×AGL(1,𝔽5)—42no—
315C3×C4×C5—41no—
316Dic15—22no—
317Dic15—41no—
318C3×Dic5—41no—
319C5×Dic3—22no—
320C5×Dic3—41no—
321C24×C3—51no—
322C22×C3×C4—52no—
323C22×C3×C4—52no—
324C22×C3×C4—51no—
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×C4—101no—
338C22×C3×C4—101no—
339C22×C3×C4—101no—
340C22×C3×C4—101no—
341C22×C3×C4—101no—
342C22×C3×C4—101no—
343C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
344C22×Dic3—51no—
345C22×Dic3—52no—
346C22×Dic3—52no—
347C22×Dic3—52no—
348C22×Dic3—52no—
349C22×Dic3—51no—
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×Dic3—101no—
367C22×Dic3—101no—
368C22×Dic3—101no—
369C22×Dic3—101no—
370C22×Dic3—101no—
371C22×Dic3—101no—
372C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
373C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
374Dic3⋊C4—22no—
375Dic3⋊C4—102no—
376Dic3⋊C4—102no—
377Dic3⋊C4—102no—
378C23×C5C2×C4×D311yescharacteristic
379C22×D5C2×Dic611yescharacteristic
380C22×D5#23511yescharacteristic
381C22×D5#23511yescharacteristic
382C22×D5#23511yescharacteristic
383C22×D5#23511yescharacteristic
384C22×D5D3×D411yescharacteristic
385C22×D5D3×D411yescharacteristic
386C22×D5D3×D411yescharacteristic
387C22×D5#23711yescharacteristic
388C22×D5#23711yescharacteristic
389C22×D5#23711yescharacteristic
390C22×D5D3×Q811yescharacteristic
391C22×D5#23911yescharacteristic
392C22×D5C2×#6711yescharacteristic
393C2×AGL(1,𝔽5)—22no—
394C2×AGL(1,𝔽5)—22no—
395C2×AGL(1,𝔽5)—22no—
396C2×AGL(1,𝔽5)—22no—
397C2×AGL(1,𝔽5)—22no—
398C2×AGL(1,𝔽5)—22no—
399C2×AGL(1,𝔽5)—41no—
400C2×AGL(1,𝔽5)—41no—
401C2×AGL(1,𝔽5)—41no—
402C2×AGL(1,𝔽5)—41no—
403C2×AGL(1,𝔽5)—41no—
404C2×AGL(1,𝔽5)—41no—
405C2×AGL(1,𝔽5)—41no—
406C2×AGL(1,𝔽5)—41no—
407C2×AGL(1,𝔽5)—62no—
408C2×AGL(1,𝔽5)—62no—
409C2×AGL(1,𝔽5)—62no—
410C2×AGL(1,𝔽5)—62no—
411C2×AGL(1,𝔽5)—62no—
412C2×AGL(1,𝔽5)—62no—
413C2×AGL(1,𝔽5)—121no—
414C2×AGL(1,𝔽5)—121no—
415C2×AGL(1,𝔽5)—121no—
416C2×AGL(1,𝔽5)—121no—
417C2×AGL(1,𝔽5)—121no—
418C2×AGL(1,𝔽5)—121no—
419C2×AGL(1,𝔽5)—121no—
420C2×AGL(1,𝔽5)—121no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—32no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—32no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C4×D5—41no—
440C4×D5—41no—
441C4×D5—41no—
442C4×D5—41no—
443C4×D5—62no—
444C4×D5—62no—
445C4×D5—62no—
446C4×D5—62no—
447C4×D5—121no—
448C4×D5—121no—
449C4×D5—121no—
450C4×D5—121no—
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—51no—
454C23×C4—151no—
455C23×C4—151no—
456C23×C4—151no—
457C23×C4—151no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—151no—
460C2×C4⋊C4—151no—
461C2×C4⋊C4—151no—
462C2×C4⋊C4—302no—
463C2×C4⋊C4—302no—
464#95—102no—
465#95—302no—
466#95—302no—
467#95—302no—
468#95—302no—
469#95—302no—
470C2×C3×C5#38111yescharacteristic
471C2×C3×C5#38711yescharacteristic
472C2×C3×C5#38711yescharacteristic
473C2×C3×C5#38711yescharacteristic
474C2×C3×C5#38711yescharacteristic
475C2×C3×C5#39011yescharacteristic
476C2×C3×C5#39111yescharacteristic
477C3×D5#39711yescharacteristic
478C3×D5#39711yescharacteristic
479C3×D5#39811yescharacteristic
480C3×D5#39811yescharacteristic
481C3×D5#39911yescharacteristic
482C3×D5#39911yescharacteristic
483C3×D5#40011yescharacteristic
484C3×D5#40011yescharacteristic
485C23×C3—51no—
486C23×C3—51no—
487C23×C3—51no—
488C23×C3—51no—
489C23×C3—51no—
490C23×C3—51no—
491C23×C3—51no—
492C23×C3—51no—
493C23×C3—51no—
494C23×C3—51no—
495C23×C3—51no—
496C23×C3—51no—
497C23×C3—51no—
498C23×C3—51no—
499C23×C3C22×AGL(1,𝔽5)11yescharacteristic
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—102no—
504C2×C3×C4—102no—
505C2×C3×C4—102no—
506C2×C3×C4—102no—
507C2×C3×C4—102no—
508C2×C3×C4—102no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—201no—
513C2×C3×C4—201no—
514C2×C3×C4—201no—
515C2×C3×C4—201no—
516C2×C3×C4—201no—
517C2×C3×C4—201no—
518C2×C3×C4—201no—
519C2×C3×C4—201no—
520C2×C3×C4—201no—
521C2×C3×C4—201no—
522C2×C3×C4—201no—
523C2×C3×C4—201no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—52no—
530C2×Dic3—102no—
531C2×Dic3—102no—
532C2×Dic3—102no—
533C2×Dic3—102no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—102no—
537C2×Dic3—102no—
538C2×Dic3—102no—
539C2×Dic3—102no—
540C2×Dic3—102no—
541C2×Dic3—102no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544C2×Dic3—101no—
545C2×Dic3—201no—
546C2×Dic3—201no—
547C2×Dic3—201no—
548C2×Dic3—201no—
549C2×Dic3—201no—
550C2×Dic3—201no—
551C2×Dic3—201no—
552C2×Dic3—201no—
553C2×Dic3—201no—
554C2×Dic3—201no—
555C2×Dic3—201no—
556C2×Dic3—201no—
557C2×Dic3C22⋊AGL(1,𝔽5)12yes—
558C22×C5C4×Dic611yescharacteristic
559C22×C5#87211yescharacteristic
560C22×C5D3×C22⋊C411yescharacteristic
561C22×C5#67⋊C411yescharacteristic
562C22×C5#88711yescharacteristic
563C22×C5#89211yescharacteristic
564C22×C5C4×#6711yescharacteristic
565C2×D5#87011yescharacteristic
566C2×D5#87611yescharacteristic
567C2×D5#87811yescharacteristic
568C2×D5#87811yescharacteristic
569C2×D5#87911yescharacteristic
570C2×D5#87911yescharacteristic
571C2×D5#88311yescharacteristic
572C2×D5#88311yescharacteristic
573C2×D5#88311yescharacteristic
574C2×D5#88411yescharacteristic
575C2×D5#88511yescharacteristic
576C2×D5#88511yescharacteristic
577C2×D5#88811yescharacteristic
578C2×D5#88911yescharacteristic
579C2×D5#88911yescharacteristic
580C2×D5#89011yescharacteristic
581C2×D5#89411yescharacteristic
582C2×D5#89411yescharacteristic
583C2×D5#89411yescharacteristic
584C2×D5#89611yescharacteristic
585C2×D5#89611yescharacteristic
586C2×D5#89811yescharacteristic
587C2×D5#92411yescharacteristic
588C2×D5#92911yescharacteristic
589C2×D5#93511yescharacteristic
590C2×D5#93911yescharacteristic
591C2×D5#94011yescharacteristic
592C2×D5#94611yescharacteristic
593AGL(1,𝔽5)—42no—
594AGL(1,𝔽5)—42no—
595AGL(1,𝔽5)—122no—
596AGL(1,𝔽5)—122no—
597C4×C5—41no—
598C4×C5—62no—
599C4×C5—121no—
600Dic5—41no—
601Dic5—62no—
602Dic5—121no—
603C24—51no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—52no—
607C22×C4—52no—
608C22×C4—51no—
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—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—152no—
628C22×C4—152no—
629C22×C4—151no—
630C22×C4—152no—
631C22×C4—152no—
632C22×C4—151no—
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×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4—301no—
650C22×C4—301no—
651C22×C4—301no—
652C22×C4—301no—
653C22×C4—301no—
654C22×C4—301no—
655C22×C4D3×AGL(1,𝔽5)11yescharacteristic
656C4⋊C4—62no—
657C4⋊C4—302no—
658C4⋊C4—302no—
659C4⋊C4—302no—
660C3×C5#144511yescharacteristic, complemented, Hall
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×C3—51no—
678C22×C3—51no—
679C22×C3—51no—
680C22×C3—51no—
681C22×C3—51no—
682C22×C3—51no—
683C22×C3—51no—
684C22×C3—51no—
685C22×C3—51no—
686C22×C3—51no—
687C22×C3—51no—
688C22×C3—51no—
689C22×C3#413011yescharacteristic
690C22×C3#413011yescharacteristic
691C22×C3D4×AGL(1,𝔽5)11yescharacteristic
692C22×C3D4×AGL(1,𝔽5)11yescharacteristic
693C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
694C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
695C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
696C3×C4—41no—
697C3×C4—202no—
698C3×C4—202no—
699C3×C4—201no—
700Dic3—22no—
701Dic3—41no—
702Dic3—102no—
703Dic3—202no—
704Dic3—202no—
705Dic3—201no—
706C2×C5#464611yescharacteristic
707C2×C5#465211yescharacteristic
708C2×C5#465511yescharacteristic
709C2×C5#466411yescharacteristic
710C2×C5#493311yescharacteristic
711C2×C5#495711yescharacteristic
712C2×C5#497811yescharacteristic
713D5#465711yescharacteristic
714D5#465811yescharacteristic
715D5#466011yescharacteristic
716D5#467511yescharacteristic
717D5#494911yescharacteristic
718D5#495211yescharacteristic
719D5#498211yescharacteristic
720D5#499311yescharacteristic
721C23—51no—
722C23—51no—
723C23—51no—
724C23—51no—
725C23—51no—
726C23—51no—
727C23—51no—
728C23—51no—
729C23—51no—
730C23—51no—
731C23—51no—
732C23—51no—
733C23—51no—
734C23—51no—
735C23C2×D3×AGL(1,𝔽5)11yescharacteristic
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—32no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—152no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—201no—
758C2×C4—201no—
759C2×C4—201no—
760C2×C4—201no—
761C2×C4—201no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—201no—
767C2×C4—302no—
768C2×C4—302no—
769C2×C4—302no—
770C2×C4—302no—
771C2×C4—301no—
772C2×C4—301no—
773C2×C4—302no—
774C2×C4—302no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—301no—
780C2×C4—301no—
781C2×C4—301no—
782C2×C4—601no—
783C2×C4—601no—
784C2×C4—601no—
785C2×C4—601no—
786C2×C4—601no—
787C2×C4—601no—
788C2×C4—601no—
789C2×C4—601no—
790C2×C4—601no—
791C2×C4—601no—
792C2×C4—601no—
793C2×C4—601no—
794C2×C3—51no—
795C2×C3—51no—
796C2×C3—51no—
797C2×C3—51no—
798C2×C3—51no—
799C2×C3—51no—
800C2×C3—51no—
801C2×C3—51no—
802C2×C3#6571111yescharacteristic
803C2×C3#6571111yescharacteristic
804C2×C3#6571111yescharacteristic
805C2×C3#6571111yescharacteristic
806C2×C3#6576411yescharacteristic
807C2×C3#6578011yescharacteristic
808C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
809C5#6942111yescharacteristic, complemented, Sylow
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—
826C22—51no—
827C22—51no—
828C22—51no—
829C22—51no—
830C22—51no—
831C22—51no—
832C22—51no—
833C22—51no—
834C22—51no—
835C22—51no—
836C22—51no—
837C22—51no—
838C22AGL(1,𝔽5)×Dic611yescharacteristic
839C22#9190711yescharacteristic
840C22ΓL(1,𝔽16)⋊Q811yescharacteristic
841C22#9190911yescharacteristic
842C22AGL(1,𝔽5)×#6711yescharacteristic
843C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
844C22#67⋊AGL(1,𝔽5)11yescharacteristic
845C4—41no—
846C4—62no—
847C4—121no—
848C4—202no—
849C4—202no—
850C4—201no—
851C4—302no—
852C4—602no—
853C4—602no—
854C4—601no—
855C3#1060434511yescharacteristic, complemented, Sylow
856C2—51no—
857C2—51no—
858C2—51no—
859C2—51no—
860C2—51no—
861C2—51no—
862C2—51no—
863C2—51no—
864C2#1175174511yescharacteristic
865C2#1175174711yescharacteristic
866C2#1175183511yescharacteristic
867C2#1175184211yescharacteristic
868C2#1175184511yescharacteristic
869C2#1175185311yescharacteristic
870C2#1175201911yescharacteristic
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#1445
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
16. C2×#6712C4semidirect
17. C2×C5×Dic3⋊C4C4semidirect
18. C2×Dic3⋊Dic5C4semidirect
19. C2×#6669C4semidirect
205. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
660. C3×C5#1445semidirect
809. C5#69421semidirect
855. C3#10604345semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
C2×#912352
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
#106043453
#694215