Finite Group Databasebeta

← #14326663

Subgroups — #14326663

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91909C212yesmaximal
2D3×D5×C4⋊C4C211yesmaximal, characteristic
3C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C3×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5#11751861C211yesmaximal, characteristic, complemented
6#11751859C211yesmaximal, characteristic, complemented
7#11751855C211yesmaximal, characteristic
8#11751853C212yesmaximal
9C4×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
10#11751747C212yesmaximal, complemented
11#11751745C212yesmaximal, complemented
12#10617103—31nomaximal, Hall
13C2×C4×D3×D5C2212yes—
14C2×C4×D3×D5C2211yescharacteristic
15C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
16C2×C4×ΓL(1,𝔽16)C2212yes—
17C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4×AGL(1,𝔽5)C2212yes—
20C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)C2212yes—
23C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
24C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
26#91909—28no—
27C4⋊C4×D15C411yescharacteristic, complemented
28C5×D3×C4⋊C4C411yescharacteristic, complemented
29C3×D5×C4⋊C4C2211yescharacteristic
30#91437C411yescharacteristic, complemented
31D3×C4⋊Dic5C411yescharacteristic, complemented
32D5×C4⋊Dic3C2211yescharacteristic
33#91404C412yescomplemented
34D3×#683C412yescomplemented
35D5×Dic3⋊C4C2212yes—
36#91235C2212yes—
37C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
38(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43#73767—51nomaximal, Hall
44C2×#4130—32no—
45C2×D5×C4⋊C4—31no—
46#65765—31no—
47#65764—32no—
48C4×C22⋊AGL(1,𝔽5)—31no—
49#65712—31no—
50#65712—31no—
51#65711—32no—
52#65711—32no—
53C4⋊C4×AGL(1,𝔽5)—31no—
54C4⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
55C22×D3×D5C2311yescharacteristic
56C22×ΓL(1,𝔽16)C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C2×C4×D15C2×C412yes—
63C2×C4×D15C2×C411yescharacteristic
64C2×C4×C5×D3C2×C412yes—
65C2×C4×C5×D3C2×C411yescharacteristic
66C2×C3×C4×D5C2312yes—
67C2×C3×C4×D5C2311yescharacteristic
68C2×#1200C2×C411yescharacteristic
69C2×#1200C2×C412yes—
70C2×D3×Dic5C2×C411yescharacteristic
71C2×D3×Dic5C2×C412yes—
72C2×D5×Dic3C2311yescharacteristic
73C2×D5×Dic3C2312yes—
74C4×D3×D5—24no—
75C4×D3×D5—24no—
76C4×D3×D5—22no—
77C4×D3×D5—22no—
78C4⋊ΓL(1,𝔽16)—22no—
79C4×ΓL(1,𝔽16)—24no—
80C4×ΓL(1,𝔽16)—22no—
81C3×C4⋊AGL(1,𝔽5)—22no—
82C3×C4×AGL(1,𝔽5)—24no—
83C3×C4×AGL(1,𝔽5)—22no—
84Dic3⋊AGL(1,𝔽5)—24no—
85Dic3⋊AGL(1,𝔽5)—24no—
86(C2×D3)⋊AGL(1,𝔽5)—24no—
87(C2×D3)⋊AGL(1,𝔽5)—22no—
88(C2×D3)⋊AGL(1,𝔽5)D414yes—
89C3×C5×C4⋊C4C2×C411yescharacteristic
90C4⋊Dic15C2×C411yescharacteristic
91#6712C2×C412yes—
92C5×C4⋊Dic3C2×C411yescharacteristic
93C5×Dic3⋊C4C2×C412yes—
94C3×C4⋊Dic5C2×C411yescharacteristic
95C3×#683C2×C412yes—
96Dic3⋊Dic5C2×C412yes—
97#6669C2×C412yes—
98#6668C2×C412yes—
99C2×D3×C4⋊C4—51no—
100C2×#872—52no—
101C3×C4×C4⋊C4—51no—
102#4987—51no—
103Dic3×C4⋊C4—51no—
104#4972—51no—
105C4×(C2×D3)⋊C4—51no—
106#4933—52no—
107#4928—51no—
108#4664—52no—
109#4652—52no—
110C22×C4×D5—32no—
111C22×C4×D5—31no—
112C2×C22⋊AGL(1,𝔽5)—31no—
113C2×C22⋊AGL(1,𝔽5)—32no—
114C2×C22⋊AGL(1,𝔽5)—31no—
115#4130—68no—
116C2×C4⋊AGL(1,𝔽5)—32no—
117C2×C4⋊AGL(1,𝔽5)—32no—
118C2×C4⋊AGL(1,𝔽5)—31no—
119C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)—31no—
122C2×C4×AGL(1,𝔽5)C2×D312yes—
123C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
124C2×C5×C4⋊C4—31no—
125C2×C4⋊Dic5—31no—
126C2×#683—32no—
127D5×C4⋊C4—32no—
128D5×C4⋊C4—31no—
129D5×C4⋊C4—31no—
130D5×C4⋊C4—31no—
131D5×C4⋊C4—32no—
132D5×C4⋊C4C2×D311yescharacteristic
133(C2×AGL(1,𝔽5))⋊C4—31no—
134(C2×AGL(1,𝔽5))⋊C4—31no—
135(C2×AGL(1,𝔽5))⋊C4—32no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4—32no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
140#2344—151noSylow
141C22×D15C22×C411yescharacteristic
142C22×C5×D3C22×C411yescharacteristic
143C22×C3×D5C2411yescharacteristic
144C2×D3×D5—21no—
145C2×D3×D5—21no—
146C2×D3×D5—21no—
147C2×D3×D5—21no—
148C2×D3×D5C2×D412yes—
149C2×D3×D5#4112yes—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)—21no—
152C2×ΓL(1,𝔽16)—22no—
153C2×ΓL(1,𝔽16)—21no—
154C2×ΓL(1,𝔽16)—21no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—22no—
157C2×ΓL(1,𝔽16)—21no—
158C2×ΓL(1,𝔽16)C2×D412yes—
159C2×C3×AGL(1,𝔽5)—21no—
160C2×C3×AGL(1,𝔽5)—21no—
161C2×C3×AGL(1,𝔽5)—22no—
162C2×C3×AGL(1,𝔽5)—21no—
163C2×C3×AGL(1,𝔽5)—21no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—21no—
167C2×C3×AGL(1,𝔽5)C2×D412yes—
168C2×C3×C4×C5C22×C412yes—
169C2×C3×C4×C5C22×C411yescharacteristic
170C2×Dic15C22×C412yes—
171C2×Dic15C22×C411yescharacteristic
172C4×D15—24no—
173C4×D15—22no—
174C2×C5×Dic3C22×C412yes—
175C2×C5×Dic3C22×C411yescharacteristic
176C4×C5×D3—24no—
177C4×C5×D3—22no—
178C2×C3×Dic5C22×C412yes—
179C2×C3×Dic5C22×C411yescharacteristic
180C3×C4×D5—22no—
181C3×C4×D5—22no—
182C3×C4×D5#4112yes—
183C3×C4×D5#4112yes—
184#1200—24no—
185#1200—22no—
186D3×Dic5—24no—
187D3×Dic5—22no—
188D5×Dic3—22no—
189D5×Dic3—21no—
190D5×Dic3—21no—
191D5×Dic3—22no—
192C22×C4×D3—52no—
193C22×C4×D3—51no—
194C2×C3×C4⋊C4—51no—
195C2×C3×C4⋊C4—51no—
196C2×C3×C42—51no—
197C2×C3×C42—52no—
198C2×(C2×D3)⋊C4—51no—
199C2×(C2×D3)⋊C4—51no—
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—51no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—52no—
207C2×C4×Dic3—51no—
208D3×C4⋊C4—52no—
209D3×C4⋊C4—51no—
210D3×C4⋊C4—51no—
211D3×C4⋊C4—51no—
212D3×C4⋊C4—52no—
213D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
214#872—108no—
215C3×#95—52no—
216C3⋊#95—51no—
217C3⋊#95—52no—
218C3⋊#95—52no—
219C3⋊#95—52no—
220C3⋊#95—51no—
221C3⋊#95—52no—
222C23×D5—31no—
223C22×AGL(1,𝔽5)—31no—
224C22×AGL(1,𝔽5)—32no—
225C22×AGL(1,𝔽5)—31no—
226C22×AGL(1,𝔽5)C22×D312yes—
227C22×AGL(1,𝔽5)C22×D311yescharacteristic
228C22×AGL(1,𝔽5)C22×D311yescharacteristic
229C22×C4×C5—32no—
230C22×C4×C5—31no—
231C22×Dic5—31no—
232C22×Dic5—32no—
233C2×C4×D5—32no—
234C2×C4×D5—31no—
235C2×C4×D5—32no—
236C2×C4×D5—31no—
237C2×C4×D5—32no—
238C2×C4×D5—31no—
239C2×C4×D5—64no—
240C2×C4×D5—64no—
241C2×C4×D5—62no—
242C2×C4×D5—62no—
243C2×C4×D5C22×D312yes—
244C2×C4×D5C22×D311yescharacteristic
245C22⋊AGL(1,𝔽5)—34no—
246C22⋊AGL(1,𝔽5)—64no—
247C22⋊AGL(1,𝔽5)—62no—
248C4⋊AGL(1,𝔽5)—22no—
249C4⋊AGL(1,𝔽5)—64no—
250C4⋊AGL(1,𝔽5)—64no—
251C4⋊AGL(1,𝔽5)—62no—
252C4×AGL(1,𝔽5)—24no—
253C4×AGL(1,𝔽5)—22no—
254C4×AGL(1,𝔽5)—64no—
255C4×AGL(1,𝔽5)—62no—
256C5×C4⋊C4—32no—
257C5×C4⋊C4—31no—
258C5×C4⋊C4C4×D311yescharacteristic
259C4⋊Dic5—31no—
260C4⋊Dic5—32no—
261C4⋊Dic5C4×D311yescharacteristic
262#683—32no—
263#683—32no—
264#683—32no—
265#683C4×D312yes—
266C2×#117—152no—
267C22×C4⋊C4—151no—
268#389—151no—
269#389—151no—
270#387—152no—
271#387—152no—
272#381—152no—
273#380—151no—
274C4×C4⋊C4—51no—
275C4×C4⋊C4—151no—
276C4×C22⋊C4—151no—
277C22×C3×C5C23×C411yescharacteristic
278C2×D15—21no—
279C2×D15—21no—
280C2×D15C4×D412yes—
281C2×C5×D3—21no—
282C2×C5×D3—21no—
283C2×C5×D3C4×D412yes—
284C2×C3×D5C22×D411yescharacteristic
285C2×C3×D5C2×#4111yescharacteristic
286C2×C3×D5C2×#4111yescharacteristic
287C2×C3×D5C2×#4111yescharacteristic
288C2×C3×D52−1+411yescharacteristic
289C2×C3×D52−1+411yescharacteristic
290D3×D5—22no—
291D3×D5—22no—
292D3×D5—22no—
293D3×D5—22no—
294ΓL(1,𝔽16)—22no—
295ΓL(1,𝔽16)—42no—
296ΓL(1,𝔽16)—41no—
297C3×AGL(1,𝔽5)—22no—
298C3×AGL(1,𝔽5)—42no—
299C3×AGL(1,𝔽5)—41no—
300C3×C4×C5—22no—
301C3×C4×C5#11712yescomplemented
302Dic15—21no—
303Dic15—22no—
304C3×Dic5—22no—
305C3×Dic5#11712yescomplemented
306C5×Dic3—21no—
307C5×Dic3—22no—
308C23×D3—51no—
309C22×C3×C4—51no—
310C22×C3×C4—51no—
311C22×C3×C4—52no—
312C22×C3×C4—51no—
313C22×C3×C4—52no—
314C22×Dic3—51no—
315C22×Dic3—51no—
316C22×Dic3—52no—
317C22×Dic3—51no—
318C22×Dic3—52no—
319C2×C4×D3—51no—
320C2×C4×D3—52no—
321C2×C4×D3—52no—
322C2×C4×D3—51no—
323C2×C4×D3—51no—
324C2×C4×D3—52no—
325C2×C4×D3—102no—
326C2×C4×D3—102no—
327C2×C4×D3—104no—
328C2×C4×D3—104no—
329C2×C4×D3C2×AGL(1,𝔽5)12yes—
330C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
331C3×C4⋊C4—52no—
332C3×C4⋊C4—51no—
333C3×C4⋊C4—102no—
334C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
335C3×C42—104no—
336C3×C42—102no—
337(C2×D3)⋊C4—54no—
338(C2×D3)⋊C4—104no—
339(C2×D3)⋊C4—102no—
340C4⋊Dic3—51no—
341C4⋊Dic3—52no—
342C4⋊Dic3—102no—
343C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
344Dic3⋊C4—52no—
345Dic3⋊C4—52no—
346Dic3⋊C4—52no—
347Dic3⋊C4—104no—
348Dic3⋊C4—104no—
349Dic3⋊C4C2×AGL(1,𝔽5)12yes—
350C4×Dic3—104no—
351C4×Dic3—102no—
352C23×C5—31no—
353C22×D5—31no—
354C22×D5—32no—
355C22×D5—32no—
356C22×D5—61no—
357C22×D5—61no—
358C22×D5—61no—
359C22×D5—61no—
360C22×D5C23×D311yescharacteristic
361C2×AGL(1,𝔽5)—21no—
362C2×AGL(1,𝔽5)—21no—
363C2×AGL(1,𝔽5)—21no—
364C2×AGL(1,𝔽5)—22no—
365C2×AGL(1,𝔽5)—22no—
366C2×AGL(1,𝔽5)—21no—
367C2×AGL(1,𝔽5)—21no—
368C2×AGL(1,𝔽5)—22no—
369C2×AGL(1,𝔽5)—32no—
370C2×AGL(1,𝔽5)—61no—
371C2×AGL(1,𝔽5)—61no—
372C2×AGL(1,𝔽5)—61no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—62no—
375C2×AGL(1,𝔽5)—62no—
376C2×AGL(1,𝔽5)—61no—
377C2×AGL(1,𝔽5)—61no—
378C2×AGL(1,𝔽5)D3×D412yes—
379C2×C4×C5—32no—
380C2×C4×C5—31no—
381C2×C4×C5—64no—
382C2×C4×C5—62no—
383C2×C4×C5C2×C4×D312yes—
384C2×C4×C5C2×C4×D311yescharacteristic
385C2×Dic5—31no—
386C2×Dic5—32no—
387C2×Dic5—64no—
388C2×Dic5—62no—
389C2×Dic5C2×C4×D312yes—
390C2×Dic5C2×C4×D311yescharacteristic
391C4×D5—22no—
392C4×D5—22no—
393C4×D5—64no—
394C4×D5—64no—
395C4×D5—61no—
396C4×D5—61no—
397C4×D5—62no—
398C4×D5—62no—
399C4×D5—62no—
400C4×D5—62no—
401C4×D5#23512yes—
402C4×D5#23512yes—
403C23×C4—152no—
404C23×C4—151no—
405#117—308no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—51no—
408C2×C4⋊C4—51no—
409C2×C4⋊C4—152no—
410C2×C4⋊C4—151no—
411C2×C4⋊C4—152no—
412C2×C4⋊C4—151no—
413C2×C4⋊C4—152no—
414C2×C4⋊C4—151no—
415C2×C4⋊C4—151no—
416C2×C4⋊C4—152no—
417C2×C4⋊C4—152no—
418C2×C4⋊C4—151no—
419C2×C22⋊C4—151no—
420C2×C22⋊C4—152no—
421C2×C22⋊C4—151no—
422C2×C42—52no—
423C2×C42—51no—
424C2×C42—152no—
425C2×C42—151no—
426#95—52no—
427#95—151no—
428#95—151no—
429#95—152no—
430#95—152no—
431#95—152no—
432#95—152no—
433C2×C3×C5C2×#11711yescharacteristic
434C2×C3×C5C2×C4×D411yescharacteristic
435C2×C3×C5#51911yescharacteristic
436D15—22no—
437C3×D5#54711yescharacteristic
438C3×D5#54711yescharacteristic
439C3×D5#55211yescharacteristic
440C3×D5#55211yescharacteristic
441C5×D3—22no—
442C23×C3—51no—
443C22×D3—51no—
444C22×D3—52no—
445C22×D3—52no—
446C22×D3—101no—
447C22×D3—101no—
448C22×D3—101no—
449C22×D3—101no—
450C22×D3C22×AGL(1,𝔽5)11yescharacteristic
451C2×C3×C4—51no—
452C2×C3×C4—52no—
453C2×C3×C4—52no—
454C2×C3×C4—52no—
455C2×C3×C4—52no—
456C2×C3×C4—102no—
457C2×C3×C4—102no—
458C2×C3×C4—101no—
459C2×C3×C4—101no—
460C2×C3×C4—102no—
461C2×C3×C4—101no—
462C2×C3×C4—101no—
463C2×C3×C4—102no—
464C2×C3×C4—101no—
465C2×C3×C4—102no—
466C2×C3×C4C22×AGL(1,𝔽5)12yes—
467C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
468C2×Dic3—52no—
469C2×Dic3—51no—
470C2×Dic3—52no—
471C2×Dic3—102no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474C2×Dic3—102no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3—102no—
478C2×Dic3—101no—
479C2×Dic3—102no—
480C2×Dic3—101no—
481C2×Dic3—101no—
482C2×Dic3—102no—
483C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
484C2×Dic3C22×AGL(1,𝔽5)12yes—
485C4×D3—24no—
486C4×D3—22no—
487C4×D3—102no—
488C4×D3—104no—
489C4×D3—104no—
490C4×D3—102no—
491C4×D3—104no—
492C4×D3—102no—
493C22×C5—32no—
494C22×C5—61no—
495C22×C5—61no—
496C22×C5C22×C4×D311yescharacteristic
497C2×D5—32no—
498C2×D5—61no—
499C2×D5—61no—
500C2×D5—62no—
501C2×D5—62no—
502C2×D5—62no—
503C2×D5—62no—
504C2×D5C2×#23511yescharacteristic
505C2×D5C2×#23511yescharacteristic
506C2×D5C2×D3×D411yescharacteristic
507C2×D5#100711yescharacteristic
508C2×D5D3×#4111yescharacteristic
509C2×D5#101011yescharacteristic
510AGL(1,𝔽5)—22no—
511AGL(1,𝔽5)—41no—
512AGL(1,𝔽5)—42no—
513AGL(1,𝔽5)—62no—
514AGL(1,𝔽5)—122no—
515AGL(1,𝔽5)—121no—
516C4×C5—22no—
517C4×C5—61no—
518C4×C5—62no—
519C4×C5#87212yescomplemented
520Dic5—22no—
521Dic5—61no—
522Dic5—62no—
523Dic5#87212yescomplemented
524C24—151no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—51no—
528C22×C4—51no—
529C22×C4—52no—
530C22×C4—51no—
531C22×C4—52no—
532C22×C4—151no—
533C22×C4—152no—
534C22×C4—151no—
535C22×C4—152no—
536C22×C4—151no—
537C22×C4—152no—
538C22×C4—151no—
539C22×C4—152no—
540C22×C4—151no—
541C22×C4—151no—
542C22×C4—152no—
543C22×C4—302no—
544C22×C4—302no—
545C22×C4—304no—
546C22×C4—304no—
547C4⋊C4—32no—
548C4⋊C4—31no—
549C4⋊C4—52no—
550C4⋊C4—51no—
551C4⋊C4—102no—
552C4⋊C4—152no—
553C4⋊C4—152no—
554C4⋊C4—152no—
555C4⋊C4—152no—
556C4⋊C4—151no—
557C4⋊C4—304no—
558C4⋊C4—302no—
559C4⋊C4—304no—
560C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
561C22⋊C4—154no—
562C22⋊C4—304no—
563C22⋊C4—302no—
564C42—104no—
565C42—102no—
566C42—302no—
567C42—304no—
568C3×C5#234411yescharacteristic, complemented, Hall
569C22×C3—51no—
570C22×C3—51no—
571C22×C3—51no—
572C22×C3—51no—
573C22×C3—51no—
574C22×C3—51no—
575C22×C3C23×AGL(1,𝔽5)11yescharacteristic
576C2×D3—21no—
577C2×D3—21no—
578C2×D3—52no—
579C2×D3—102no—
580C2×D3—102no—
581C2×D3—102no—
582C2×D3—102no—
583C2×D3—101no—
584C2×D3—101no—
585C2×D3D4×AGL(1,𝔽5)12yes—
586C3×C4—22no—
587C3×C4—52no—
588C3×C4—102no—
589C3×C4—102no—
590C3×C4—202no—
591C3×C4—201no—
592C3×C4#413012yescomplemented
593Dic3—21no—
594Dic3—22no—
595Dic3—102no—
596Dic3—101no—
597Dic3—102no—
598Dic3—202no—
599Dic3—201no—
600C2×C5—62no—
601C2×C5C2×#87211yescharacteristic
602C2×C5C4×D3×D411yescharacteristic
603C2×C5#557211yescharacteristic
604D5—62no—
605D5#550711yescharacteristic
606D5#552911yescharacteristic
607D5#555111yescharacteristic
608D5#558111yescharacteristic
609C23—31no—
610C23—51no—
611C23—152no—
612C23—152no—
613C23—151no—
614C23—301no—
615C23—301no—
616C23—301no—
617C23—301no—
618C2×C4—31no—
619C2×C4—32no—
620C2×C4—51no—
621C2×C4—52no—
622C2×C4—52no—
623C2×C4—52no—
624C2×C4—52no—
625C2×C4—64no—
626C2×C4—62no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—102no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—102no—
635C2×C4—101no—
636C2×C4—102no—
637C2×C4—152no—
638C2×C4—151no—
639C2×C4—152no—
640C2×C4—304no—
641C2×C4—302no—
642C2×C4—302no—
643C2×C4—304no—
644C2×C4—302no—
645C2×C4—301no—
646C2×C4—301no—
647C2×C4—302no—
648C2×C4—304no—
649C2×C4—301no—
650C2×C4—301no—
651C2×C4—302no—
652C2×C4—302no—
653C2×C4—301no—
654C2×C4—301no—
655C2×C4—302no—
656C2×C4—301no—
657C2×C4—302no—
658C2×C4C2×D3×AGL(1,𝔽5)12yes—
659C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
660C2×C3—51no—
661C2×C3—51no—
662C2×C3—51no—
663C2×C3—51no—
664C2×C3C2×#413011yescharacteristic
665C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
666C2×C3#6626211yescharacteristic
667D3—22no—
668D3—102no—
669C5#7376711yescharacteristic, complemented, Sylow
670C22—32no—
671C22—51no—
672C22—51no—
673C22—51no—
674C22—51no—
675C22—51no—
676C22—51no—
677C22—61no—
678C22—61no—
679C22—152no—
680C22—302no—
681C22—302no—
682C22—302no—
683C22—302no—
684C22—301no—
685C22—301no—
686C22C22×D3×AGL(1,𝔽5)11yescharacteristic
687C4—22no—
688C4—52no—
689C4—61no—
690C4—62no—
691C4—102no—
692C4—102no—
693C4—202no—
694C4—201no—
695C4—302no—
696C4—301no—
697C4—302no—
698C4—602no—
699C4—601no—
700C4#9190912yescomplemented
701C3#1061710311yescharacteristic, complemented, Sylow
702C2—51no—
703C2—51no—
704C2—51no—
705C2—51no—
706C2—62no—
707C2—302no—
708C2C2×#9190911yescharacteristic
709C2D3×D4×AGL(1,𝔽5)11yescharacteristic
710C2#1175684711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×ΓL(1,𝔽16)C2semidirect
4. C3×C4⋊C4×AGL(1,𝔽5)C2semidirect
5. #11751861C2semidirect
6. #11751859C2semidirect
10. #11751747C2semidirect
11. #11751745C2semidirect
27. C4⋊C4×D15C4semidirect
28. C5×D3×C4⋊C4C4semidirect
30. #91437C4semidirect
31. D3×C4⋊Dic5C4semidirect
33. #91404C4semidirect
34. D3×#683C4semidirect
54. C4⋊C4×AGL(1,𝔽5)D3semidirect
213. D3×C4⋊C4AGL(1,𝔽5)semidirect
301. C3×C4×C5#117semidirect
305. C3×Dic5#117semidirect
519. C4×C5#872semidirect
523. Dic5#872semidirect
568. C3×C5#2344semidirect
592. C3×C4#4130semidirect
669. C5#73767semidirect
700. C4#91909semidirect
701. C3#10617103semidirect

Maximal subgroups

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

subgroupindex
C2×#919092
D3×D5×C4⋊C42
C4⋊C4×ΓL(1,𝔽16)2
C3×C4⋊C4×AGL(1,𝔽5)2
#117518612
#117518592
#117518552
#117518532
C4×(C2×D3)⋊AGL(1,𝔽5)2
#117517472
#117517452
#106171033
#737675