Finite Group Databasebeta

← C2×#11756846 #14479114

Subgroups — C2×#11756846 #14479114

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#237C211yesmaximal, characteristic
2C2×D4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C2×#67⋊AGL(1,𝔽5)C212yesmaximal, complemented
5C2×AGL(1,𝔽5)×#67C212yesmaximal, complemented
6C22×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
7C2×#91923C212yesmaximal, complemented
8#11756846C2116yesmaximal, direct product factor
9C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10C2×#91909C211yesmaximal, characteristic, complemented
11C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
12C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic, complemented
13C2×#66266—31nomaximal, Hall
14C23×ΓL(1,𝔽16)C2212yes—
15C23×C3×AGL(1,𝔽5)C2212yes—
16C22×D3×AGL(1,𝔽5)C2212yes—
17C2×#6819C411yescharacteristic, complemented
18C2×C5×#237C411yescharacteristic, complemented
19C2×C3×D4×D5C2211yescharacteristic
20C2×D5×#67C2212yes—
21C2×#6780C412yescomplemented
22C2×#6779C412yescomplemented
23C22×D5×Dic3C2212yes—
24D5×#237C418yescomplemented
25D5×#237C2218yes—
26C2×C4×D3×D5C2211yescharacteristic
27C2×#6766C411yescharacteristic, complemented
28C2×#6765C411yescharacteristic, complemented
29C2×D5×Dic6C2211yescharacteristic
30C2×#6763C2212yes—
31D4×ΓL(1,𝔽16)C2218yescomplemented
32C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
33C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
34C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
35C3×D4×AGL(1,𝔽5)C2218yescomplemented
36C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
37C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
38#67⋊AGL(1,𝔽5)C22116yescomplemented
39AGL(1,𝔽5)×#67C22116yescomplemented
40C2×Dic3⋊AGL(1,𝔽5)C2212yes—
41C2×Dic3⋊AGL(1,𝔽5)C2212yes—
42C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
43C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
44C2×Dic3⋊AGL(1,𝔽5)C2212yes—
45C2×Dic3⋊AGL(1,𝔽5)C22116yescomplemented
46C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
47C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
48#91923C22116yescomplemented
49C2×Dic3×AGL(1,𝔽5)C2212yes—
50C2×Dic3×AGL(1,𝔽5)C2212yes—
51D3×C4⋊AGL(1,𝔽5)C2218yescomplemented
52#91909C2218yescomplemented
53ΓL(1,𝔽16)⋊Q8C2218yescomplemented
54AGL(1,𝔽5)×Dic6C2218yescomplemented
55C2×#5546—51nomaximal, Hall
56C2×D5×#41—31no—
57#66266—316no—
58C2×Q8×AGL(1,𝔽5)—31no—
59C2×Q8×AGL(1,𝔽5)—31no—
60C2×D4×AGL(1,𝔽5)—32no—
61C2×D4×AGL(1,𝔽5)—31no—
62C2×D4×AGL(1,𝔽5)—32no—
63C2×D4×AGL(1,𝔽5)D311yescharacteristic, complemented
64C2×#4130—32no—
65C2×#4130—31no—
66C22×C4⋊AGL(1,𝔽5)—32no—
67C22×C4⋊AGL(1,𝔽5)—31no—
68C23×C3×D5C2312yes—
69C22×D3×D5C2311yescharacteristic
70C22×ΓL(1,𝔽16)—44no—
71C22×ΓL(1,𝔽16)C2311yescharacteristic
72C22×ΓL(1,𝔽16)C2312yes—
73C22×ΓL(1,𝔽16)C2311yescharacteristic
74C22×ΓL(1,𝔽16)C2318yes—
75C22×C3×AGL(1,𝔽5)—44no—
76C22×C3×AGL(1,𝔽5)C2311yescharacteristic
77C22×C3×AGL(1,𝔽5)C2312yes—
78C22×C3×AGL(1,𝔽5)C2311yescharacteristic
79C22×C3×AGL(1,𝔽5)C2318yes—
80C2×D3×AGL(1,𝔽5)—44no—
81C2×D3×AGL(1,𝔽5)C2318yes—
82C2×C3×C5×D4C2×C411yescharacteristic, complemented
83C2×#1220C2×C412yescomplemented
84C22×Dic15C2×C412yescomplemented
85#6819C2×C418yescomplemented
86C2×C4×D15C2×C411yescharacteristic, complemented
87C2×Dic30C2×C411yescharacteristic, complemented
88C2×C5×#67C2×C412yescomplemented
89C22×C5×Dic3C2×C412yescomplemented
90C5×#237C2×C418yescomplemented
91C2×C4×C5×D3C2×C411yescharacteristic, complemented
92C2×C5×Dic6C2×C411yescharacteristic, complemented
93C2×C3×C22⋊D5C2×C412yescomplemented
94C3×D4×D5C2×C414yescomplemented
95C3×D4×D5C2314yes—
96C2×C3×D20C2×C411yescharacteristic, complemented
97C2×C3×C4×D5C2311yescharacteristic
98D5×#67C2×C418yescomplemented
99D5×#67C2318yes—
100C2×#1204C2×C412yescomplemented
101C2×#1202C2×C412yescomplemented
102C2×#1201C2×C412yescomplemented
103C2×#1200C2×C411yescharacteristic, complemented
104C2×D3×Dic5C2×C411yescharacteristic, complemented
105#6780C2×C4116yescomplemented
106#6779C2×C4116yescomplemented
107C2×D5×Dic3C2×C418yescomplemented
108C2×D5×Dic3C2×C412yescomplemented
109C2×D5×Dic3C2×C412yescomplemented
110C2×D5×Dic3C2312yes—
111C2×D5×Dic3C2311yescharacteristic
112C2×D5×Dic3C2318yes—
113C4×D3×D5C2×C414yescomplemented
114C4×D3×D5C2314yes—
115#6766C2×C418yescomplemented
116#6765C2×C418yescomplemented
117D5×Dic6C2×C414yescomplemented
118D5×Dic6C2314yes—
119#6763C2318yes—
120C4⋊ΓL(1,𝔽16)C2314yes—
121C4×ΓL(1,𝔽16)C2314yes—
122C3×C22⋊AGL(1,𝔽5)C2318yes—
123C3×C4⋊AGL(1,𝔽5)C2314yes—
124C3×C4×AGL(1,𝔽5)C2314yes—
125Dic3⋊AGL(1,𝔽5)C2318yes—
126Dic3⋊AGL(1,𝔽5)C2318yes—
127Dic3⋊AGL(1,𝔽5)C2314yes—
128Dic3⋊AGL(1,𝔽5)C2314yes—
129Dic3⋊AGL(1,𝔽5)C2318yes—
130(C2×D3)⋊AGL(1,𝔽5)C2314yes—
131(C2×D3)⋊AGL(1,𝔽5)C2314yes—
132Dic3×AGL(1,𝔽5)C2318yes—
133Dic3×AGL(1,𝔽5)C2318yes—
134C22×#237—51no—
135C2×C3×C4×D4—51no—
136C2×D4×Dic3—51no—
137C2×C4×#67—52no—
138C22×Dic3⋊C4—52no—
139#5546—516no—
140C2×D3×C4⋊C4—51no—
141C2×#887—51no—
142C2×#67⋊C4—52no—
143C2×#877—52no—
144C2×#872—51no—
145C2×C4×Dic6—51no—
146C23×AGL(1,𝔽5)—32no—
147C23×AGL(1,𝔽5)—32no—
148C23×AGL(1,𝔽5)C2×D312yes—
149C2×C5×#41—31no—
150D5×#41—38no—
151D5×#41—38no—
152C2×#713—31no—
153C2×Q8×D5—31no—
154C2×#711—31no—
155C2×#711—32no—
156C2×D4×D5—32no—
157C2×D4×D5C2×D311yescharacteristic
158C2×#709—32no—
159C2×#709—31no—
160C22×C4×D5—32no—
161C22×C4×D5—31no—
162C2×C22⋊AGL(1,𝔽5)—32no—
163C2×C22⋊AGL(1,𝔽5)—31no—
164C2×C22⋊AGL(1,𝔽5)—31no—
165C2×C22⋊AGL(1,𝔽5)C2×D312yes—
166Q8×AGL(1,𝔽5)—38no—
167Q8×AGL(1,𝔽5)—38no—
168D4×AGL(1,𝔽5)—316no—
169D4×AGL(1,𝔽5)—38no—
170D4×AGL(1,𝔽5)—316no—
171D4×AGL(1,𝔽5)C2×D318yescomplemented
172#4130—316no—
173#4130—38no—
174C2×C4⋊AGL(1,𝔽5)—32no—
175C2×C4⋊AGL(1,𝔽5)—31no—
176C2×C4⋊AGL(1,𝔽5)—32no—
177C2×C4⋊AGL(1,𝔽5)—32no—
178C2×C4⋊AGL(1,𝔽5)—31no—
179C2×C4⋊AGL(1,𝔽5)—316no—
180C2×C4⋊AGL(1,𝔽5)—31no—
181C2×C4⋊AGL(1,𝔽5)—38no—
182C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
183C2×C4×AGL(1,𝔽5)—32no—
184C2×C4×AGL(1,𝔽5)—32no—
185C2×C4×AGL(1,𝔽5)—31no—
186C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
187C2×#520—151noSylow
188C23×C3×C5C22×C412yes—
189C22×D15C22×C411yescharacteristic
190C22×C5×D3C22×C411yescharacteristic
191C22×C3×D5—24no—
192C22×C3×D5—24no—
193C22×C3×D5C22×C412yes—
194C22×C3×D5C22×C414yes—
195C22×C3×D5C2414yes—
196C22×C3×D5C2411yescharacteristic
197C2×D3×D5—22no—
198C2×D3×D5—22no—
199C2×D3×D5C22×C412yes—
200C2×D3×D5C2412yes—
201C2×ΓL(1,𝔽16)—24no—
202C2×ΓL(1,𝔽16)—22no—
203C2×ΓL(1,𝔽16)—22no—
204C2×ΓL(1,𝔽16)—48no—
205C2×ΓL(1,𝔽16)C2412yes—
206C2×ΓL(1,𝔽16)C2414yes—
207C2×ΓL(1,𝔽16)C2412yes—
208C2×C3×AGL(1,𝔽5)—24no—
209C2×C3×AGL(1,𝔽5)—22no—
210C2×C3×AGL(1,𝔽5)—22no—
211C2×C3×AGL(1,𝔽5)—48no—
212C2×C3×AGL(1,𝔽5)C2412yes—
213C2×C3×AGL(1,𝔽5)C2414yes—
214C2×C3×AGL(1,𝔽5)C2412yes—
215D3×AGL(1,𝔽5)—48no—
216C3×C5×D4C22×C414yescomplemented
217C2×C3×C4×C5C22×C411yescharacteristic
218#1220C22×C418yescomplemented
219C2×Dic15C22×C411yescharacteristic
220C2×Dic15C22×C412yes—
221C2×Dic15C22×C418yescomplemented
222C4×D15C22×C414yescomplemented
223Dic30C22×C414yescomplemented
224C5×#67C22×C418yescomplemented
225C2×C5×Dic3C22×C411yescharacteristic
226C2×C5×Dic3C22×C412yes—
227C2×C5×Dic3C22×C418yescomplemented
228C4×C5×D3C22×C414yescomplemented
229C5×Dic6C22×C414yescomplemented
230C3×C22⋊D5C22×C418yescomplemented
231C2×C3×Dic5C22×C411yescharacteristic
232C3×D20C22×C414yescomplemented
233C3×C4×D5C22×C412yes—
234C3×C4×D5C2412yes—
235#1204C22×C418yescomplemented
236#1202C22×C418yescomplemented
237#1201C22×C418yescomplemented
238#1200C22×C414yescomplemented
239D3×Dic5C22×C414yescomplemented
240D5×Dic3C22×C414yes—
241D5×Dic3C22×C412yes—
242D5×Dic3C22×C418yescomplemented
243D5×Dic3C22×C418yescomplemented
244D5×Dic3C2414yes—
245D5×Dic3C2412yes—
246C22×C3×D4—51no—
247C23×C3×C4—52no—
248C22×#67—52no—
249C23×Dic3—52no—
250C23×Dic3—52no—
251C2×#237—51no—
252C2×#237—52no—
253C2×#237—52no—
254C2×#237—58no—
255C2×#237—58no—
256C2×#237—51no—
257C2×#237—51no—
258C2×#237AGL(1,𝔽5)11yescharacteristic, complemented
259C22×C4×D3—51no—
260C22×C4×D3—52no—
261C22×Dic6—51no—
262C3×C4×D4—58no—
263C2×C3×C4⋊C4—51no—
264C2×C3×C22⋊C4—52no—
265C2×C3×C42—51no—
266C2×#217—52no—
267D4×Dic3—58no—
268C4×#67—516no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—52no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—52no—
276C2×Dic3⋊C4—52no—
277C2×Dic3⋊C4—516no—
278C2×C4×Dic3—52no—
279C2×C4×Dic3—52no—
280C2×C4×Dic3—51no—
281D3×C4⋊C4—58no—
282#887—58no—
283#67⋊C4—516no—
284#877—516no—
285#872—58no—
286C4×Dic6—58no—
287C23×D5—31no—
288C23×D5C22×D312yes—
289C22×AGL(1,𝔽5)—31no—
290C22×AGL(1,𝔽5)—32no—
291C22×AGL(1,𝔽5)—31no—
292C22×AGL(1,𝔽5)—38no—
293C22×AGL(1,𝔽5)—38no—
294C22×AGL(1,𝔽5)—44no—
295C22×AGL(1,𝔽5)—124no—
296C22×AGL(1,𝔽5)—124no—
297C22×AGL(1,𝔽5)C22×D311yescharacteristic
298C22×AGL(1,𝔽5)C22×D312yes—
299C22×AGL(1,𝔽5)C22×D311yescharacteristic
300C22×AGL(1,𝔽5)C22×D318yes—
301C5×#41—38no—
302C2×C5×Q8—31no—
303C2×C5×D4—32no—
304C2×C5×D4C4×D311yescharacteristic, complemented
305C22×C4×C5—32no—
306C22×C4×C5—31no—
307C2×C22⋊D5—32no—
308C2×C22⋊D5—32no—
309C2×C22⋊D5C4×D312yescomplemented
310C22×Dic5—32no—
311C22×Dic5—31no—
312#713—38no—
313Q8×D5—34no—
314Q8×D5—34no—
315#711—38no—
316#711—316no—
317D4×D5—38no—
318D4×D5—38no—
319D4×D5C4×D314yescomplemented
320D4×D5C22×D314yes—
321#709—316no—
322#709—38no—
323C2×D20—32no—
324C2×D20C4×D311yescharacteristic, complemented
325C2×C4×D5—32no—
326C2×C4×D5—32no—
327C2×C4×D5—38no—
328C2×C4×D5—32no—
329C2×C4×D5—31no—
330C2×C4×D5—38no—
331C2×C4×D5—31no—
332C2×C4×D5—31no—
333C2×C4×D5—34no—
334C2×C4×D5—34no—
335C2×C4×D5C22×D311yescharacteristic
336C2×Dic10—31no—
337C2×Dic10—32no—
338C22⋊AGL(1,𝔽5)—38no—
339C22⋊AGL(1,𝔽5)—34no—
340C22⋊AGL(1,𝔽5)—34no—
341C22⋊AGL(1,𝔽5)C22×D318yes—
342C4⋊AGL(1,𝔽5)—38no—
343C4⋊AGL(1,𝔽5)—34no—
344C4⋊AGL(1,𝔽5)—38no—
345C4⋊AGL(1,𝔽5)—38no—
346C4⋊AGL(1,𝔽5)—34no—
347C4⋊AGL(1,𝔽5)—34no—
348C4⋊AGL(1,𝔽5)C22×D314yes—
349C4×AGL(1,𝔽5)—38no—
350C4×AGL(1,𝔽5)—38no—
351C4×AGL(1,𝔽5)—34no—
352C4×AGL(1,𝔽5)C22×D314yes—
353C22×#41—151no—
354#520—1516no—
355C2×C4×Q8—151no—
356C2×C4×Q8—151no—
357C2×C4×D4—51no—
358C2×C4×D4—152no—
359C2×C4×D4—152no—
360C2×C4×D4—151no—
361C2×#117—151no—
362C2×#117—152no—
363C22×C4⋊C4—151no—
364C22×C4⋊C4—152no—
365C22×C3×C5—24no—
366C22×C3×C5C23×C414yes—
367C22×C3×C5C23×C411yescharacteristic
368C2×D15—22no—
369C2×D15C23×C412yes—
370C2×C5×D3—22no—
371C2×C5×D3C23×C412yes—
372C2×C3×D5—24no—
373C2×C3×D5—28no—
374C2×C3×D5—24no—
375C2×C3×D5—24no—
376C2×C3×D5C23×C414yes—
377C2×C3×D5C23×C411yescharacteristic
378C2×C3×D5H(5,𝔽2)12yes—
379C2×C3×D52−1+412yes—
380C2×C3×D5C2511yescharacteristic
381D3×D5—24no—
382D3×D5—22no—
383D3×D5—22no—
384ΓL(1,𝔽16)—24no—
385ΓL(1,𝔽16)—22no—
386ΓL(1,𝔽16)—22no—
387C3×AGL(1,𝔽5)—24no—
388C3×AGL(1,𝔽5)—22no—
389C3×AGL(1,𝔽5)—22no—
390C3×C4×C5C23×C412yes—
391Dic15C23×C412yes—
392Dic15C23×C414yes—
393C3×Dic5C23×C412yes—
394C5×Dic3C23×C412yes—
395C5×Dic3C23×C414yes—
396C24×C3—52no—
397C23×D3—51no—
398C2×C3×D4—52no—
399C2×C3×D4—54no—
400C2×C3×D4—54no—
401C2×C3×D4—51no—
402C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
403C22×C3×C4—51no—
404C22×C3×C4—51no—
405C22×C3×C4—52no—
406C22×C3×C4—51no—
407C22×C3×C4—58no—
408C22×C3×C4—204no—
409C2×#67—52no—
410C2×#67—52no—
411C2×#67—58no—
412C2×#67—58no—
413C2×#67—52no—
414C2×#67C2×AGL(1,𝔽5)12yescomplemented
415C22×Dic3—52no—
416C22×Dic3—52no—
417C22×Dic3—52no—
418C22×Dic3—52no—
419C22×Dic3—51no—
420C22×Dic3—58no—
421C22×Dic3—58no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3—52no—
425C22×Dic3—58no—
426C22×Dic3—204no—
427C22×Dic3C2×AGL(1,𝔽5)12yescomplemented
428#237—58no—
429#237—516no—
430#237—516no—
431#237—58no—
432#237—58no—
433#237C2×AGL(1,𝔽5)18yescomplemented
434C2×C4×D3—51no—
435C2×C4×D3—51no—
436C2×C4×D3—51no—
437C2×C4×D3—54no—
438C2×C4×D3—54no—
439C2×C4×D3—58no—
440C2×C4×D3—204no—
441C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
442C2×Dic6—51no—
443C2×Dic6—52no—
444C2×Dic6—54no—
445C2×Dic6—54no—
446C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
447C3×C4⋊C4—54no—
448C3×C22⋊C4—58no—
449C3×C42—54no—
450#217—58no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453C4⋊Dic3—54no—
454Dic3⋊C4—58no—
455Dic3⋊C4—54no—
456Dic3⋊C4—54no—
457Dic3⋊C4—58no—
458Dic3⋊C4—58no—
459C4×Dic3—58no—
460C4×Dic3—58no—
461C4×Dic3—54no—
462C23×C5—31no—
463C23×C5C2×C4×D312yes—
464C22×D5—24no—
465C22×D5—24no—
466C22×D5—31no—
467C22×D5—32no—
468C22×D5—32no—
469C22×D5—62no—
470C22×D5—62no—
471C22×D5C2×C4×D312yes—
472C22×D5C2×C4×D314yes—
473C22×D5C23×D314yes—
474C22×D5C23×D311yescharacteristic
475C2×AGL(1,𝔽5)—22no—
476C2×AGL(1,𝔽5)—24no—
477C2×AGL(1,𝔽5)—22no—
478C2×AGL(1,𝔽5)—32no—
479C2×AGL(1,𝔽5)—34no—
480C2×AGL(1,𝔽5)—32no—
481C2×AGL(1,𝔽5)—48no—
482C2×AGL(1,𝔽5)—64no—
483C2×AGL(1,𝔽5)—62no—
484C2×AGL(1,𝔽5)—62no—
485C2×AGL(1,𝔽5)—128no—
486C2×AGL(1,𝔽5)—128no—
487C2×AGL(1,𝔽5)C23×D312yes—
488C2×AGL(1,𝔽5)C23×D314yes—
489C2×AGL(1,𝔽5)C23×D312yes—
490C5×Q8—34no—
491C5×D4—38no—
492C5×D4C2×C4×D314yescomplemented
493C2×C4×C5—32no—
494C2×C4×C5—31no—
495C2×C4×C5—38no—
496C2×C4×C5—34no—
497C2×C4×C5C2×C4×D311yescharacteristic
498C22⋊D5—38no—
499C22⋊D5—38no—
500C22⋊D5C2×C4×D318yescomplemented
501C2×Dic5—32no—
502C2×Dic5—31no—
503C2×Dic5—38no—
504C2×Dic5—34no—
505C2×Dic5C2×C4×D311yescharacteristic
506D20—38no—
507D20C2×C4×D314yescomplemented
508C4×D5—32no—
509C4×D5—34no—
510C4×D5—38no—
511C4×D5—38no—
512C4×D5—34no—
513C4×D5—32no—
514C4×D5—34no—
515C4×D5—34no—
516C4×D5C2×C4×D312yes—
517C4×D5C23×D312yes—
518Dic10—34no—
519Dic10—38no—
520C2×#41—31no—
521C2×#41—152no—
522C2×#41—151no—
523C2×#41—152no—
524C2×#41—151no—
525C2×#41—158no—
526C2×#41—158no—
527C2×#41—151no—
528C22×Q8—151no—
529C22×D4—51no—
530C22×D4—152no—
531C23×C4—52no—
532C23×C4—151no—
533C23×C4—152no—
534C23×C4—152no—
535C23×C4—152no—
536C4×Q8—158no—
537C4×Q8—158no—
538C4×D4—58no—
539C4×D4—1516no—
540C4×D4—1516no—
541C4×D4—158no—
542#117—158no—
543#117—1516no—
544C2×C4⋊C4—51no—
545C2×C4⋊C4—158no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—152no—
548C2×C4⋊C4—152no—
549C2×C4⋊C4—152no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—1516no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—52no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—152no—
557C2×C42—51no—
558C2×C42—151no—
559C2×C42—152no—
560C2×C42—152no—
561C2×C3×C5—24no—
562C2×C3×C5#52012yescomplemented
563C2×C3×C5C24×C411yescharacteristic
564D15—22no—
565C3×D5—24no—
566C3×D5#52012yescomplemented
567C3×D5C2×H(5,𝔽2)11yescharacteristic
568C3×D5C2×2−1+411yescharacteristic
569C5×D3—22no—
570C23×C3—51no—
571C23×C3—54no—
572C23×C3—52no—
573C23×C3—54no—
574C23×C3—104no—
575C23×C3—104no—
576C23×C3C22×AGL(1,𝔽5)12yes—
577C22×D3—51no—
578C22×D3—52no—
579C22×D3—52no—
580C22×D3—102no—
581C22×D3—102no—
582C22×D3C22×AGL(1,𝔽5)11yescharacteristic
583C3×D4—58no—
584C3×D4—54no—
585C3×D4C22×AGL(1,𝔽5)14yescomplemented
586C2×C3×C4—51no—
587C2×C3×C4—52no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—54no—
591C2×C3×C4—52no—
592C2×C3×C4—104no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4—208no—
596C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
597#67—58no—
598#67—58no—
599#67—58no—
600#67C22×AGL(1,𝔽5)18yescomplemented
601C2×Dic3—52no—
602C2×Dic3—51no—
603C2×Dic3—58no—
604C2×Dic3—54no—
605C2×Dic3—52no—
606C2×Dic3—58no—
607C2×Dic3—58no—
608C2×Dic3—54no—
609C2×Dic3—52no—
610C2×Dic3—52no—
611C2×Dic3—52no—
612C2×Dic3—54no—
613C2×Dic3—104no—
614C2×Dic3—102no—
615C2×Dic3—102no—
616C2×Dic3—208no—
617C2×Dic3C22×AGL(1,𝔽5)12yes—
618C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
619C2×Dic3C22×AGL(1,𝔽5)18yescomplemented
620C4×D3—54no—
621C4×D3—54no—
622C4×D3—54no—
623C4×D3—208no—
624C4×D3C22×AGL(1,𝔽5)14yescomplemented
625Dic6—54no—
626Dic6—58no—
627Dic6C22×AGL(1,𝔽5)14yescomplemented
628C22×C5—24no—
629C22×C5—32no—
630C22×C5—62no—
631C22×C5C22×C4×D314yes—
632C22×C5C22×C4×D311yescharacteristic
633C2×D5—24no—
634C2×D5—24no—
635C2×D5—24no—
636C2×D5—28no—
637C2×D5—32no—
638C2×D5—62no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—64no—
642C2×D5C22×C4×D314yes—
643C2×D5C22×C4×D311yescharacteristic
644C2×D5#100412yes—
645C2×D5#101012yes—
646C2×D5C24×D311yescharacteristic
647AGL(1,𝔽5)—22no—
648AGL(1,𝔽5)—24no—
649AGL(1,𝔽5)—22no—
650AGL(1,𝔽5)—64no—
651AGL(1,𝔽5)—62no—
652AGL(1,𝔽5)—62no—
653C4×C5—34no—
654C4×C5—32no—
655C4×C5C22×C4×D312yes—
656Dic5—34no—
657Dic5—32no—
658Dic5C22×C4×D312yes—
659C24—52no—
660C24—151no—
661#41—38no—
662#41—1516no—
663#41—158no—
664#41—1516no—
665#41—158no—
666#41—158no—
667C2×Q8—31no—
668C2×Q8—152no—
669C2×Q8—154no—
670C2×Q8—154no—
671C2×Q8—151no—
672C2×D4—32no—
673C2×D4—52no—
674C2×D4—54no—
675C2×D4—54no—
676C2×D4—51no—
677C2×D4—152no—
678C2×D4—158no—
679C2×D4—158no—
680C2×D4—152no—
681C2×D4—152no—
682C2×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
683C22×C4—32no—
684C22×C4—31no—
685C22×C4—51no—
686C22×C4—51no—
687C22×C4—51no—
688C22×C4—52no—
689C22×C4—58no—
690C22×C4—154no—
691C22×C4—151no—
692C22×C4—154no—
693C22×C4—152no—
694C22×C4—151no—
695C22×C4—158no—
696C22×C4—158no—
697C22×C4—152no—
698C22×C4—152no—
699C22×C4—151no—
700C22×C4—158no—
701C22×C4—152no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—152no—
706C22×C4—158no—
707C22×C4—204no—
708C22×C4—604no—
709C22×C4—604no—
710C4⋊C4—54no—
711C4⋊C4—154no—
712C4⋊C4—158no—
713C4⋊C4—158no—
714C4⋊C4—158no—
715C4⋊C4—154no—
716C4⋊C4—154no—
717C22⋊C4—58no—
718C22⋊C4—154no—
719C22⋊C4—154no—
720C22⋊C4—158no—
721C42—54no—
722C42—154no—
723C42—158no—
724C42—158no—
725C3×C5C2×#52011yescharacteristic, complemented, Hall
726C22×C3—24no—
727C22×C3—52no—
728C22×C3—52no—
729C22×C3—51no—
730C22×C3—51no—
731C22×C3—54no—
732C22×C3—104no—
733C22×C3—104no—
734C22×C3—108no—
735C22×C3—104no—
736C22×C3C23×AGL(1,𝔽5)14yes—
737C22×C3C23×AGL(1,𝔽5)11yescharacteristic
738C2×D3—22no—
739C2×D3—52no—
740C2×D3—102no—
741C2×D3—102no—
742C2×D3—104no—
743C2×D3—102no—
744C2×D3C23×AGL(1,𝔽5)12yes—
745C3×C4—52no—
746C3×C4—104no—
747C3×C4—102no—
748C3×C4—102no—
749C3×C4C23×AGL(1,𝔽5)12yes—
750Dic3—54no—
751Dic3—52no—
752Dic3—104no—
753Dic3—102no—
754Dic3—102no—
755Dic3C23×AGL(1,𝔽5)14yes—
756Dic3C23×AGL(1,𝔽5)12yes—
757C2×C5—24no—
758C2×C5—62no—
759C2×C5#554612yescomplemented
760C2×C5C23×C4×D311yescharacteristic
761D5—24no—
762D5—62no—
763D5#554612yescomplemented
764D5C2×#100411yescharacteristic
765D5C2×#101011yescharacteristic
766C23—31no—
767C23—51no—
768C23—54no—
769C23—54no—
770C23—52no—
771C23—104no—
772C23—104no—
773C23—152no—
774C23—152no—
775C23—151no—
776C23—302no—
777C23—302no—
778C23C2×D3×AGL(1,𝔽5)12yes—
779Q8—34no—
780Q8—158no—
781Q8—154no—
782D4—38no—
783D4—58no—
784D4—54no—
785D4—158no—
786D4—158no—
787D4—158no—
788D4C2×D3×AGL(1,𝔽5)14yescomplemented
789C2×C4—38no—
790C2×C4—31no—
791C2×C4—32no—
792C2×C4—34no—
793C2×C4—51no—
794C2×C4—52no—
795C2×C4—52no—
796C2×C4—52no—
797C2×C4—52no—
798C2×C4—54no—
799C2×C4—102no—
800C2×C4—104no—
801C2×C4—102no—
802C2×C4—154no—
803C2×C4—154no—
804C2×C4—152no—
805C2×C4—152no—
806C2×C4—154no—
807C2×C4—158no—
808C2×C4—158no—
809C2×C4—154no—
810C2×C4—158no—
811C2×C4—151no—
812C2×C4—152no—
813C2×C4—154no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—154no—
817C2×C4—208no—
818C2×C4—304no—
819C2×C4—302no—
820C2×C4—302no—
821C2×C4—608no—
822C2×C4—608no—
823C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
824C2×C3—24no—
825C2×C3—51no—
826C2×C3—51no—
827C2×C3—52no—
828C2×C3—104no—
829C2×C3#6626612yescomplemented
830C2×C3C24×AGL(1,𝔽5)11yescharacteristic
831D3—22no—
832D3—102no—
833C5C2×#554611yescharacteristic, complemented, Sylow
834C22—24no—
835C22—32no—
836C22—52no—
837C22—52no—
838C22—51no—
839C22—51no—
840C22—54no—
841C22—62no—
842C22—104no—
843C22—104no—
844C22—108no—
845C22—104no—
846C22—152no—
847C22—302no—
848C22—302no—
849C22—304no—
850C22—302no—
851C22C22×D3×AGL(1,𝔽5)14yes—
852C22C22×D3×AGL(1,𝔽5)11yescharacteristic
853C4—32no—
854C4—34no—
855C4—52no—
856C4—102no—
857C4—104no—
858C4—102no—
859C4—152no—
860C4—154no—
861C4—304no—
862C4—302no—
863C4—302no—
864C4C22×D3×AGL(1,𝔽5)12yes—
865C3C2×#6626611yescharacteristic, complemented, Sylow
866C2—24no—
867C2—51no—
868C2—51no—
869C2—52no—
870C2—62no—
871C2—104no—
872C2—302no—
873C2#1175684612yesdirect product factor
874C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#237C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D4×ΓL(1,𝔽16)C2semidirect
3. C2×C3×D4×AGL(1,𝔽5)C2semidirect
4. C2×#67⋊AGL(1,𝔽5)C2semidirect
5. C2×AGL(1,𝔽5)×#67C2semidirect
6. C22×Dic3⋊AGL(1,𝔽5)C2semidirect
7. C2×#91923C2semidirect
8. #11756846C2direct (N × H)
9. C2×D3×C4⋊AGL(1,𝔽5)C2semidirect
10. C2×#91909C2semidirect
11. C2×ΓL(1,𝔽16)⋊Q8C2semidirect
12. C2×AGL(1,𝔽5)×Dic6C2semidirect
17. C2×#6819C4semidirect
18. C2×C5×#237C4semidirect
21. C2×#6780C4semidirect
22. C2×#6779C4semidirect
24. D5×#237C4semidirect
27. C2×#6766C4semidirect
28. C2×#6765C4semidirect
31. D4×ΓL(1,𝔽16)C22semidirect
35. C3×D4×AGL(1,𝔽5)C22semidirect
38. #67⋊AGL(1,𝔽5)C22semidirect
39. AGL(1,𝔽5)×#67C22semidirect
45. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
48. #91923C22semidirect
51. D3×C4⋊AGL(1,𝔽5)C22semidirect
52. #91909C22semidirect
53. ΓL(1,𝔽16)⋊Q8C22semidirect
54. AGL(1,𝔽5)×Dic6C22semidirect
63. C2×D4×AGL(1,𝔽5)D3semidirect
82. C2×C3×C5×D4C2×C4semidirect
83. C2×#1220C2×C4semidirect
84. C22×Dic15C2×C4semidirect
85. #6819C2×C4semidirect
86. C2×C4×D15C2×C4semidirect
87. C2×Dic30C2×C4semidirect
88. C2×C5×#67C2×C4semidirect
89. C22×C5×Dic3C2×C4semidirect
90. C5×#237C2×C4semidirect
91. C2×C4×C5×D3C2×C4semidirect
92. C2×C5×Dic6C2×C4semidirect
93. C2×C3×C22⋊D5C2×C4semidirect
94. C3×D4×D5C2×C4semidirect
96. C2×C3×D20C2×C4semidirect
98. D5×#67C2×C4semidirect
100. C2×#1204C2×C4semidirect
101. C2×#1202C2×C4semidirect
102. C2×#1201C2×C4semidirect
103. C2×#1200C2×C4semidirect
104. C2×D3×Dic5C2×C4semidirect
105. #6780C2×C4semidirect
106. #6779C2×C4semidirect
107. C2×D5×Dic3C2×C4semidirect
108. C2×D5×Dic3C2×C4semidirect
109. C2×D5×Dic3C2×C4semidirect
113. C4×D3×D5C2×C4semidirect
115. #6766C2×C4semidirect
116. #6765C2×C4semidirect
117. D5×Dic6C2×C4semidirect
171. D4×AGL(1,𝔽5)C2×D3semidirect
216. C3×C5×D4C22×C4semidirect
218. #1220C22×C4semidirect
221. C2×Dic15C22×C4semidirect
222. C4×D15C22×C4semidirect
223. Dic30C22×C4semidirect
224. C5×#67C22×C4semidirect
227. C2×C5×Dic3C22×C4semidirect
228. C4×C5×D3C22×C4semidirect
229. C5×Dic6C22×C4semidirect
230. C3×C22⋊D5C22×C4semidirect
232. C3×D20C22×C4semidirect
235. #1204C22×C4semidirect
236. #1202C22×C4semidirect
237. #1201C22×C4semidirect
238. #1200C22×C4semidirect
239. D3×Dic5C22×C4semidirect
242. D5×Dic3C22×C4semidirect
243. D5×Dic3C22×C4semidirect
258. C2×#237AGL(1,𝔽5)semidirect
304. C2×C5×D4C4×D3semidirect
309. C2×C22⋊D5C4×D3semidirect
319. D4×D5C4×D3semidirect
324. C2×D20C4×D3semidirect
402. C2×C3×D4C2×AGL(1,𝔽5)semidirect
414. C2×#67C2×AGL(1,𝔽5)semidirect
427. C22×Dic3C2×AGL(1,𝔽5)semidirect
433. #237C2×AGL(1,𝔽5)semidirect
441. C2×C4×D3C2×AGL(1,𝔽5)semidirect
446. C2×Dic6C2×AGL(1,𝔽5)semidirect
492. C5×D4C2×C4×D3semidirect
500. C22⋊D5C2×C4×D3semidirect
507. D20C2×C4×D3semidirect
562. C2×C3×C5#520semidirect
566. C3×D5#520semidirect
585. C3×D4C22×AGL(1,𝔽5)semidirect
600. #67C22×AGL(1,𝔽5)semidirect
619. C2×Dic3C22×AGL(1,𝔽5)semidirect
624. C4×D3C22×AGL(1,𝔽5)semidirect
627. Dic6C22×AGL(1,𝔽5)semidirect
682. C2×D4D3×AGL(1,𝔽5)semidirect
725. C3×C5C2×#520semidirect
759. C2×C5#5546semidirect
763. D5#5546semidirect
788. D4C2×D3×AGL(1,𝔽5)semidirect
829. C2×C3#66266semidirect
833. C5C2×#5546semidirect
865. C3C2×#66266semidirect
873. C2#11756846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#2372
C2×D4×ΓL(1,𝔽16)2
C2×C3×D4×AGL(1,𝔽5)2
C2×#67⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C22×Dic3⋊AGL(1,𝔽5)2
C2×#919232
#117568462
C2×D3×C4⋊AGL(1,𝔽5)2
C2×#919092
C2×ΓL(1,𝔽16)⋊Q82
C2×AGL(1,𝔽5)×Dic62
C2×#662663
C2×#55465