Finite Group Databasebeta

← C2×#11756845 #14479002

Subgroups — C2×#11756845 #14479002

Order 1920.

3840 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D4×D5C211yesmaximal, 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×D3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
6C2×AGL(1,𝔽5)×#67C212yesmaximal, complemented
7C22×(C2×D3)⋊AGL(1,𝔽5)C212yesmaximal, complemented
8#11756845C2116yesmaximal, direct product factor
9C2×#91921C211yesmaximal, characteristic, complemented
10C2×AGL(1,𝔽5)×D12C211yesmaximal, characteristic, complemented
11C2×#91909C211yesmaximal, characteristic, complemented
12C2×#91907C211yesmaximal, characteristic, complemented
13C2×#66258—31nomaximal, Hall
14C23×D3×D5C2212yes—
15C23×ΓL(1,𝔽16)C2212yescomplemented
16C23×C3×AGL(1,𝔽5)C2212yescomplemented
17C22×D3×AGL(1,𝔽5)C2212yescomplemented
18C22×D3×AGL(1,𝔽5)C2212yescomplemented
19C2×D4×D15C411yescharacteristic, complemented
20C2×C5×D3×D4C411yescharacteristic, complemented
21C2×C3×D4×D5C2211yescharacteristic
22C2×#6790C412yescomplemented
23C2×D3×C22⋊D5C412yescomplemented
24C2×D5×#67C2212yes—
25D3×D4×D5C418yescomplemented
26D3×D4×D5C2218yes—
27C2×#6777C411yescharacteristic, complemented
28C2×D3×D20C411yescharacteristic, complemented
29C2×D5×D12C2211yescharacteristic
30C2×C4×D3×D5C2211yescharacteristic
31C2×#6763C2212yescomplemented
32D4×ΓL(1,𝔽16)C2218yescomplemented
33C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic, complemented
34C2×C4×ΓL(1,𝔽16)C2211yescharacteristic, complemented
35C2×C3×C22⋊AGL(1,𝔽5)C2212yescomplemented
36C3×D4×AGL(1,𝔽5)C2218yescomplemented
37C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
38C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic, complemented
39#67⋊AGL(1,𝔽5)C22116yescomplemented
40D3×C22⋊AGL(1,𝔽5)C22116yescomplemented
41AGL(1,𝔽5)×#67C22116yescomplemented
42C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
43C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
44C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
45C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
46C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
47C2×(C2×D3)⋊AGL(1,𝔽5)C22116yescomplemented
48C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
49C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
50C2×Dic3×AGL(1,𝔽5)C2212yescomplemented
51#91921C2218yescomplemented
52AGL(1,𝔽5)×D12C2218yescomplemented
53#91909C2218yescomplemented
54#91907C2218yescomplemented
55C2×#5545—51nomaximal, Hall
56C22×D4×D5—31no—
57C22×C22⋊AGL(1,𝔽5)—32no—
58C22×C22⋊AGL(1,𝔽5)—32no—
59#66258—316no—
60C2×D4×AGL(1,𝔽5)—32no—
61C2×D4×AGL(1,𝔽5)—31no—
62C2×D4×AGL(1,𝔽5)—32no—
63C2×D4×AGL(1,𝔽5)—31no—
64C2×D4×AGL(1,𝔽5)—31no—
65C2×D4×AGL(1,𝔽5)D311yescharacteristic, complemented
66C2×#4130—31no—
67C2×#4130—31no—
68C23×D15C2×C412yescomplemented
69C23×C5×D3C2×C412yescomplemented
70C23×C3×D5C2312yes—
71C22×D3×D5—44no—
72C22×D3×D5—44no—
73C22×D3×D5C2×C418yescomplemented
74C22×D3×D5C2×C412yescomplemented
75C22×D3×D5C2×C412yescomplemented
76C22×D3×D5C2311yescharacteristic
77C22×D3×D5C2312yes—
78C22×D3×D5C2318yes—
79C22×ΓL(1,𝔽16)—44no—
80C22×ΓL(1,𝔽16)C2312yes—
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×ΓL(1,𝔽16)C2318yescomplemented
84C22×C3×AGL(1,𝔽5)—44no—
85C22×C3×AGL(1,𝔽5)C2312yes—
86C22×C3×AGL(1,𝔽5)C2311yescharacteristic
87C22×C3×AGL(1,𝔽5)C2311yescharacteristic
88C22×C3×AGL(1,𝔽5)C2318yescomplemented
89C2×D3×AGL(1,𝔽5)—44no—
90C2×D3×AGL(1,𝔽5)—44no—
91C2×D3×AGL(1,𝔽5)C2318yescomplemented
92C2×D3×AGL(1,𝔽5)C2318yescomplemented
93C2×C3×C5×D4C2×C411yescharacteristic, complemented
94C2×#1220C2×C412yescomplemented
95D4×D15C2×C418yescomplemented
96C2×D60C2×C411yescharacteristic, complemented
97C2×C4×D15C2×C411yescharacteristic, complemented
98C2×C5×#67C2×C412yescomplemented
99C5×D3×D4C2×C418yescomplemented
100C2×C5×D12C2×C411yescharacteristic, complemented
101C2×C4×C5×D3C2×C411yescharacteristic, complemented
102C2×C3×C22⋊D5C2×C412yescomplemented
103C3×D4×D5C2×C414yescomplemented
104C3×D4×D5C2314yes—
105C2×C3×D20C2×C411yescharacteristic, complemented
106C2×C3×C4×D5C2311yescharacteristic
107#6790C2×C4116yescomplemented
108D3×C22⋊D5C2×C4116yescomplemented
109D5×#67C2×C418yescomplemented
110D5×#67C2318yes—
111C2×#1203C2×C412yescomplemented
112C2×#1202C2×C412yescomplemented
113C2×#1201C2×C412yescomplemented
114C2×#1200C2×C411yescharacteristic, complemented
115C2×D3×Dic5C2×C411yescharacteristic, complemented
116C2×D5×Dic3C2311yescharacteristic
117#6777C2×C418yescomplemented
118D3×D20C2×C418yescomplemented
119D5×D12C2×C414yescomplemented
120D5×D12C2314yes—
121C4×D3×D5C2×C414yescomplemented
122C4×D3×D5C2314yes—
123#6763C2318yescomplemented
124C4⋊ΓL(1,𝔽16)C2314yescomplemented
125C4×ΓL(1,𝔽16)C2314yescomplemented
126C3×C22⋊AGL(1,𝔽5)C2318yescomplemented
127C3×C4⋊AGL(1,𝔽5)C2314yescomplemented
128C3×C4×AGL(1,𝔽5)C2314yescomplemented
129Dic3⋊AGL(1,𝔽5)C2314yescomplemented
130Dic3⋊AGL(1,𝔽5)C2314yescomplemented
131(C2×D3)⋊AGL(1,𝔽5)C2318yes—
132(C2×D3)⋊AGL(1,𝔽5)C2314yes—
133(C2×D3)⋊AGL(1,𝔽5)C2314yes—
134(C2×D3)⋊AGL(1,𝔽5)C2318yescomplemented
135(C2×D3)⋊AGL(1,𝔽5)C2318yescomplemented
136Dic3×AGL(1,𝔽5)C2318yescomplemented
137C22×D3×D4—51no—
138C2×C3×C4×D4—51no—
139C2×D4×Dic3—51no—
140C2×C4×#67—52no—
141C22×(C2×D3)⋊C4—52no—
142#5545—516no—
143C2×#893—51no—
144C2×#892—51no—
145C2×#67⋊C4—52no—
146C2×D3×C22⋊C4—52no—
147C2×C4×D12—51no—
148C2×#872—51no—
149C24×D5—32no—
150C23×AGL(1,𝔽5)—32no—
151C23×AGL(1,𝔽5)—32no—
152C23×AGL(1,𝔽5)—32no—
153C23×AGL(1,𝔽5)C2×D312yescomplemented
154C22×C5×D4—31no—
155C22×C22⋊D5—32no—
156C2×D4×D5—32no—
157C2×D4×D5—31no—
158C2×D4×D5—32no—
159C2×D4×D5—38no—
160C2×D4×D5—38no—
161C2×D4×D5—31no—
162C2×D4×D5—31no—
163C2×D4×D5C2×D311yescharacteristic
164C22×D20—31no—
165C22×C4×D5—31no—
166C2×C22⋊AGL(1,𝔽5)—32no—
167C2×C22⋊AGL(1,𝔽5)—32no—
168C2×C22⋊AGL(1,𝔽5)—31no—
169C2×C22⋊AGL(1,𝔽5)—31no—
170C2×C22⋊AGL(1,𝔽5)—32no—
171C2×C22⋊AGL(1,𝔽5)—32no—
172C2×C22⋊AGL(1,𝔽5)—316no—
173C2×C22⋊AGL(1,𝔽5)—316no—
174C2×C22⋊AGL(1,𝔽5)C2×D312yescomplemented
175D4×AGL(1,𝔽5)—316no—
176D4×AGL(1,𝔽5)—38no—
177D4×AGL(1,𝔽5)—316no—
178D4×AGL(1,𝔽5)—38no—
179D4×AGL(1,𝔽5)—38no—
180D4×AGL(1,𝔽5)C2×D318yescomplemented
181#4130—38no—
182#4130—38no—
183C2×C4⋊AGL(1,𝔽5)—31no—
184C2×C4⋊AGL(1,𝔽5)—31no—
185C2×C4⋊AGL(1,𝔽5)—31no—
186C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic, complemented
187C2×C4×AGL(1,𝔽5)—32no—
188C2×C4×AGL(1,𝔽5)—31no—
189C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic, complemented
190C2×#518—151noSylow
191C23×C3×C5C22×C412yes—
192C22×D15—44no—
193C22×D15C22×C411yescharacteristic
194C22×D15C22×C412yes—
195C22×D15C22×C418yescomplemented
196C22×C5×D3—44no—
197C22×C5×D3C22×C411yescharacteristic
198C22×C5×D3C22×C412yes—
199C22×C5×D3C22×C418yescomplemented
200C22×C3×D5—24no—
201C22×C3×D5—24no—
202C22×C3×D5C22×C412yes—
203C22×C3×D5C22×C414yes—
204C22×C3×D5C2414yes—
205C22×C3×D5C2411yescharacteristic
206C2×D3×D5—24no—
207C2×D3×D5—24no—
208C2×D3×D5—22no—
209C2×D3×D5—22no—
210C2×D3×D5—416no—
211C2×D3×D5—48no—
212C2×D3×D5—48no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
215C2×D3×D5C22×C412yes—
216C2×D3×D5C22×C414yes—
217C2×D3×D5C22×C418yescomplemented
218C2×D3×D5C22×C418yescomplemented
219C2×D3×D5C2412yes—
220C2×D3×D5C2414yes—
221C2×ΓL(1,𝔽16)—22no—
222C2×ΓL(1,𝔽16)—24no—
223C2×ΓL(1,𝔽16)—22no—
224C2×ΓL(1,𝔽16)—48no—
225C2×ΓL(1,𝔽16)C2414yes—
226C2×ΓL(1,𝔽16)C2412yes—
227C2×ΓL(1,𝔽16)C2412yes—
228C2×C3×AGL(1,𝔽5)—22no—
229C2×C3×AGL(1,𝔽5)—24no—
230C2×C3×AGL(1,𝔽5)—22no—
231C2×C3×AGL(1,𝔽5)—48no—
232C2×C3×AGL(1,𝔽5)C2414yes—
233C2×C3×AGL(1,𝔽5)C2412yes—
234C2×C3×AGL(1,𝔽5)C2412yes—
235D3×AGL(1,𝔽5)—48no—
236D3×AGL(1,𝔽5)—48no—
237C3×C5×D4C22×C414yescomplemented
238C2×C3×C4×C5C22×C411yescharacteristic
239#1220C22×C418yescomplemented
240C2×Dic15C22×C411yescharacteristic
241D60C22×C414yescomplemented
242C4×D15C22×C414yescomplemented
243C5×#67C22×C418yescomplemented
244C2×C5×Dic3C22×C411yescharacteristic
245C5×D12C22×C414yescomplemented
246C4×C5×D3C22×C414yescomplemented
247C3×C22⋊D5C22×C418yescomplemented
248C2×C3×Dic5C22×C411yescharacteristic
249C3×D20C22×C414yescomplemented
250C3×C4×D5C22×C412yes—
251C3×C4×D5C2412yes—
252#1203C22×C418yescomplemented
253#1202C22×C418yescomplemented
254#1201C22×C418yescomplemented
255#1200C22×C414yescomplemented
256D3×Dic5C22×C414yescomplemented
257D5×Dic3C22×C412yes—
258D5×Dic3C2412yes—
259C24×D3—52no—
260C22×C3×D4—51no—
261C23×C3×C4—52no—
262C22×#67—52no—
263C23×Dic3—52no—
264C2×D3×D4—52no—
265C2×D3×D4—51no—
266C2×D3×D4—52no—
267C2×D3×D4—58no—
268C2×D3×D4—58no—
269C2×D3×D4—51no—
270C2×D3×D4—51no—
271C2×D3×D4AGL(1,𝔽5)11yescharacteristic, complemented
272C22×D12—51no—
273C22×C4×D3—51no—
274C22×C4×D3—52no—
275C22×C4×D3—52no—
276C3×C4×D4—58no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C22⋊C4—52no—
279C2×C3×C42—51no—
280C2×#217—52no—
281D4×Dic3—58no—
282C4×#67—516no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—52no—
286C2×(C2×D3)⋊C4—52no—
287C2×(C2×D3)⋊C4—52no—
288C2×(C2×D3)⋊C4—516no—
289C2×C4⋊Dic3—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×C4×Dic3—52no—
293C2×C4×Dic3—51no—
294#893—58no—
295#892—58no—
296#67⋊C4—516no—
297D3×C22⋊C4—516no—
298C4×D12—58no—
299#872—58no—
300C24×C5—32no—
301C23×D5—32no—
302C23×D5—31no—
303C23×D5—32no—
304C23×D5—32no—
305C23×D5—32no—
306C23×D5—38no—
307C23×D5—38no—
308C23×D5—124no—
309C23×D5—124no—
310C23×D5C22×D312yes—
311C22×AGL(1,𝔽5)—31no—
312C22×AGL(1,𝔽5)—32no—
313C22×AGL(1,𝔽5)—31no—
314C22×AGL(1,𝔽5)—38no—
315C22×AGL(1,𝔽5)—38no—
316C22×AGL(1,𝔽5)—38no—
317C22×AGL(1,𝔽5)—44no—
318C22×AGL(1,𝔽5)—124no—
319C22×AGL(1,𝔽5)—124no—
320C22×AGL(1,𝔽5)—124no—
321C22×AGL(1,𝔽5)C22×D312yes—
322C22×AGL(1,𝔽5)C22×D311yescharacteristic
323C22×AGL(1,𝔽5)C22×D311yescharacteristic
324C22×AGL(1,𝔽5)C22×D318yescomplemented
325C2×C5×D4—32no—
326C2×C5×D4—38no—
327C2×C5×D4—31no—
328C2×C5×D4C4×D311yescharacteristic, complemented
329C22×C4×C5—31no—
330C2×C22⋊D5—32no—
331C2×C22⋊D5—32no—
332C2×C22⋊D5—316no—
333C2×C22⋊D5—32no—
334C2×C22⋊D5C4×D312yescomplemented
335C22×Dic5—31no—
336D4×D5—38no—
337D4×D5—38no—
338D4×D5—38no—
339D4×D5—316no—
340D4×D5—38no—
341D4×D5—34no—
342D4×D5—34no—
343D4×D5C4×D314yescomplemented
344D4×D5C22×D314yes—
345C2×D20—32no—
346C2×D20—31no—
347C2×D20—38no—
348C2×D20C4×D311yescharacteristic, complemented
349C2×C4×D5—31no—
350C2×C4×D5—31no—
351C2×C4×D5—31no—
352C2×C4×D5—34no—
353C2×C4×D5—34no—
354C2×C4×D5C22×D311yescharacteristic
355C22⋊AGL(1,𝔽5)—38no—
356C22⋊AGL(1,𝔽5)—38no—
357C22⋊AGL(1,𝔽5)—34no—
358C22⋊AGL(1,𝔽5)—34no—
359C22⋊AGL(1,𝔽5)—38no—
360C22⋊AGL(1,𝔽5)—38no—
361C22⋊AGL(1,𝔽5)C22×D318yescomplemented
362C4⋊AGL(1,𝔽5)—34no—
363C4⋊AGL(1,𝔽5)—34no—
364C4⋊AGL(1,𝔽5)—34no—
365C4⋊AGL(1,𝔽5)C22×D314yescomplemented
366C4×AGL(1,𝔽5)—38no—
367C4×AGL(1,𝔽5)—34no—
368C4×AGL(1,𝔽5)C22×D314yescomplemented
369C23×D4—151no—
370#518—1516no—
371C2×C4×D4—51no—
372C2×C4×D4—151no—
373C2×C4×D4—152no—
374C2×C4×D4—151no—
375C2×C4×D4—152no—
376C2×C4×D4—151no—
377C2×#117—151no—
378C2×#117—151no—
379C22×C22⋊C4—152no—
380C22×C22⋊C4—152no—
381C22×C3×C5—24no—
382C22×C3×C5C23×C414yes—
383C22×C3×C5C23×C411yescharacteristic
384C2×D15—22no—
385C2×D15—24no—
386C2×D15—48no—
387C2×D15C23×C412yes—
388C2×D15C23×C414yes—
389C2×C5×D3—22no—
390C2×C5×D3—24no—
391C2×C5×D3—48no—
392C2×C5×D3C23×C412yes—
393C2×C5×D3C23×C414yes—
394C2×C3×D5—24no—
395C2×C3×D5—28no—
396C2×C3×D5—24no—
397C2×C3×D5—24no—
398C2×C3×D5C23×C414yes—
399C2×C3×D5C23×C411yescharacteristic
400C2×C3×D5H(5,𝔽2)12yes—
401C2×C3×D5H(5,𝔽2)12yes—
402C2×C3×D5C2511yescharacteristic
403D3×D5—24no—
404D3×D5—28no—
405D3×D5—24no—
406D3×D5—24no—
407D3×D5—22no—
408D3×D5—22no—
409D3×D5—48no—
410D3×D5—48no—
411ΓL(1,𝔽16)—22no—
412ΓL(1,𝔽16)—24no—
413ΓL(1,𝔽16)—22no—
414C3×AGL(1,𝔽5)—22no—
415C3×AGL(1,𝔽5)—24no—
416C3×AGL(1,𝔽5)—22no—
417C3×C4×C5C23×C412yes—
418Dic15C23×C412yes—
419C3×Dic5C23×C412yes—
420C5×Dic3C23×C412yes—
421C24×C3—52no—
422C23×D3—52no—
423C23×D3—51no—
424C23×D3—52no—
425C23×D3—52no—
426C23×D3—52no—
427C23×D3—58no—
428C23×D3—58no—
429C23×D3—204no—
430C23×D3—204no—
431C23×D3C2×AGL(1,𝔽5)12yescomplemented
432C2×C3×D4—52no—
433C2×C3×D4—54no—
434C2×C3×D4—54no—
435C2×C3×D4—51no—
436C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
437C22×C3×C4—51no—
438C22×C3×C4—52no—
439C22×C3×C4—51no—
440C22×C3×C4—51no—
441C22×C3×C4—58no—
442C22×C3×C4—204no—
443C2×#67—52no—
444C2×#67—52no—
445C2×#67—58no—
446C2×#67—58no—
447C2×#67—52no—
448C2×#67C2×AGL(1,𝔽5)12yescomplemented
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—52no—
453C22×Dic3—58no—
454C22×Dic3—204no—
455D3×D4—516no—
456D3×D4—58no—
457D3×D4—516no—
458D3×D4—58no—
459D3×D4—58no—
460D3×D4C2×AGL(1,𝔽5)18yescomplemented
461C2×D12—52no—
462C2×D12—51no—
463C2×D12—54no—
464C2×D12—54no—
465C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
466C2×C4×D3—51no—
467C2×C4×D3—51no—
468C2×C4×D3—51no—
469C2×C4×D3—54no—
470C2×C4×D3—54no—
471C2×C4×D3—58no—
472C2×C4×D3—58no—
473C2×C4×D3—204no—
474C2×C4×D3—204no—
475C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
476C3×C4⋊C4—54no—
477C3×C22⋊C4—58no—
478C3×C42—54no—
479#217—58no—
480(C2×D3)⋊C4—54no—
481(C2×D3)⋊C4—54no—
482(C2×D3)⋊C4—58no—
483(C2×D3)⋊C4—58no—
484(C2×D3)⋊C4—58no—
485C4⋊Dic3—54no—
486Dic3⋊C4—54no—
487Dic3⋊C4—54no—
488C4×Dic3—58no—
489C4×Dic3—54no—
490C23×C5—31no—
491C23×C5—32no—
492C23×C5—38no—
493C23×C5—124no—
494C23×C5C2×C4×D312yes—
495C22×D5—24no—
496C22×D5—24no—
497C22×D5—31no—
498C22×D5—32no—
499C22×D5—38no—
500C22×D5—32no—
501C22×D5—34no—
502C22×D5—32no—
503C22×D5—34no—
504C22×D5—38no—
505C22×D5—38no—
506C22×D5—64no—
507C22×D5—62no—
508C22×D5—64no—
509C22×D5—62no—
510C22×D5—128no—
511C22×D5—128no—
512C22×D5—1216no—
513C22×D5—124no—
514C22×D5—124no—
515C22×D5—124no—
516C22×D5C2×C4×D312yes—
517C22×D5C2×C4×D314yes—
518C22×D5C23×D314yes—
519C22×D5C23×D311yescharacteristic
520C2×AGL(1,𝔽5)—22no—
521C2×AGL(1,𝔽5)—24no—
522C2×AGL(1,𝔽5)—22no—
523C2×AGL(1,𝔽5)—32no—
524C2×AGL(1,𝔽5)—34no—
525C2×AGL(1,𝔽5)—32no—
526C2×AGL(1,𝔽5)—48no—
527C2×AGL(1,𝔽5)—62no—
528C2×AGL(1,𝔽5)—64no—
529C2×AGL(1,𝔽5)—62no—
530C2×AGL(1,𝔽5)—128no—
531C2×AGL(1,𝔽5)—128no—
532C2×AGL(1,𝔽5)—128no—
533C2×AGL(1,𝔽5)C23×D314yes—
534C2×AGL(1,𝔽5)C23×D312yes—
535C2×AGL(1,𝔽5)C23×D312yes—
536C5×D4—38no—
537C5×D4—34no—
538C5×D4C2×C4×D314yescomplemented
539C2×C4×C5—31no—
540C2×C4×C5—34no—
541C2×C4×C5C2×C4×D311yescharacteristic
542C22⋊D5—38no—
543C22⋊D5—38no—
544C22⋊D5—38no—
545C22⋊D5C2×C4×D318yescomplemented
546C2×Dic5—31no—
547C2×Dic5—34no—
548C2×Dic5C2×C4×D311yescharacteristic
549D20—38no—
550D20—34no—
551D20C2×C4×D314yescomplemented
552C4×D5—32no—
553C4×D5—32no—
554C4×D5—34no—
555C4×D5—34no—
556C4×D5C2×C4×D312yes—
557C4×D5C23×D312yes—
558C25—152no—
559C22×D4—31no—
560C22×D4—51no—
561C22×D4—151no—
562C22×D4—151no—
563C22×D4—158no—
564C22×D4—152no—
565C22×D4—158no—
566C22×D4—151no—
567C22×D4—152no—
568C22×D4—152no—
569C22×D4—151no—
570C23×C4—52no—
571C23×C4—151no—
572C23×C4—152no—
573C23×C4—152no—
574C23×C4—152no—
575C4×D4—58no—
576C4×D4—158no—
577C4×D4—1516no—
578C4×D4—158no—
579C4×D4—1516no—
580C4×D4—158no—
581#117—158no—
582#117—158no—
583C2×C4⋊C4—51no—
584C2×C4⋊C4—151no—
585C2×C4⋊C4—151no—
586C2×C4⋊C4—151no—
587C2×C22⋊C4—52no—
588C2×C22⋊C4—1516no—
589C2×C22⋊C4—151no—
590C2×C22⋊C4—151no—
591C2×C22⋊C4—152no—
592C2×C22⋊C4—152no—
593C2×C22⋊C4—152no—
594C2×C22⋊C4—1516no—
595C2×C22⋊C4—152no—
596C2×C42—51no—
597C2×C42—151no—
598C2×C42—152no—
599C2×C3×C5—24no—
600C2×C3×C5#51812yescomplemented
601C2×C3×C5C24×C411yescharacteristic
602D15—22no—
603D15—24no—
604C3×D5—24no—
605C3×D5#51812yescomplemented
606C3×D5C2×H(5,𝔽2)11yescharacteristic
607C3×D5C2×H(5,𝔽2)11yescharacteristic
608C5×D3—22no—
609C5×D3—24no—
610C23×C3—51no—
611C23×C3—54no—
612C23×C3—52no—
613C23×C3—54no—
614C23×C3—104no—
615C23×C3—104no—
616C23×C3C22×AGL(1,𝔽5)12yes—
617C22×D3—44no—
618C22×D3—51no—
619C22×D3—52no—
620C22×D3—58no—
621C22×D3—52no—
622C22×D3—54no—
623C22×D3—52no—
624C22×D3—54no—
625C22×D3—58no—
626C22×D3—58no—
627C22×D3—104no—
628C22×D3—104no—
629C22×D3—102no—
630C22×D3—102no—
631C22×D3—204no—
632C22×D3—204no—
633C22×D3—208no—
634C22×D3—208no—
635C22×D3—2016no—
636C22×D3—204no—
637C22×D3C22×AGL(1,𝔽5)11yescharacteristic
638C22×D3C22×AGL(1,𝔽5)12yes—
639C22×D3C22×AGL(1,𝔽5)18yescomplemented
640C3×D4—58no—
641C3×D4—54no—
642C3×D4C22×AGL(1,𝔽5)14yescomplemented
643C2×C3×C4—51no—
644C2×C3×C4—52no—
645C2×C3×C4—52no—
646C2×C3×C4—54no—
647C2×C3×C4—52no—
648C2×C3×C4—52no—
649C2×C3×C4—102no—
650C2×C3×C4—104no—
651C2×C3×C4—102no—
652C2×C3×C4—208no—
653C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
654#67—58no—
655#67—58no—
656#67—58no—
657#67C22×AGL(1,𝔽5)18yescomplemented
658C2×Dic3—51no—
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—54no—
664C2×Dic3—102no—
665C2×Dic3—104no—
666C2×Dic3—102no—
667C2×Dic3—208no—
668C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
669D12—58no—
670D12—54no—
671D12C22×AGL(1,𝔽5)14yescomplemented
672C4×D3—54no—
673C4×D3—54no—
674C4×D3—54no—
675C4×D3—208no—
676C4×D3—208no—
677C4×D3C22×AGL(1,𝔽5)14yescomplemented
678C22×C5—24no—
679C22×C5—32no—
680C22×C5—34no—
681C22×C5—62no—
682C22×C5—64no—
683C22×C5—128no—
684C22×C5C22×C4×D314yes—
685C22×C5C22×C4×D311yescharacteristic
686C2×D5—24no—
687C2×D5—24no—
688C2×D5—24no—
689C2×D5—28no—
690C2×D5—32no—
691C2×D5—34no—
692C2×D5—64no—
693C2×D5—62no—
694C2×D5—64no—
695C2×D5—62no—
696C2×D5—64no—
697C2×D5—62no—
698C2×D5—68no—
699C2×D5—64no—
700C2×D5—128no—
701C2×D5—128no—
702C2×D5—128no—
703C2×D5C22×C4×D314yes—
704C2×D5C22×C4×D311yescharacteristic
705C2×D5#100412yes—
706C2×D5#100912yes—
707C2×D5C24×D311yescharacteristic
708AGL(1,𝔽5)—22no—
709AGL(1,𝔽5)—24no—
710AGL(1,𝔽5)—22no—
711AGL(1,𝔽5)—62no—
712AGL(1,𝔽5)—64no—
713AGL(1,𝔽5)—62no—
714C4×C5—32no—
715C4×C5C22×C4×D312yes—
716Dic5—32no—
717Dic5C22×C4×D312yes—
718C24—32no—
719C24—52no—
720C24—151no—
721C24—152no—
722C24—158no—
723C24—152no—
724C24—152no—
725C24—158no—
726C24—152no—
727C24—604no—
728C24—604no—
729C2×D4—32no—
730C2×D4—38no—
731C2×D4—31no—
732C2×D4—52no—
733C2×D4—54no—
734C2×D4—54no—
735C2×D4—51no—
736C2×D4—158no—
737C2×D4—152no—
738C2×D4—154no—
739C2×D4—154no—
740C2×D4—152no—
741C2×D4—1516no—
742C2×D4—158no—
743C2×D4—158no—
744C2×D4—158no—
745C2×D4—1516no—
746C2×D4—152no—
747C2×D4—152no—
748C2×D4—158no—
749C2×D4—151no—
750C2×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
751C22×C4—31no—
752C22×C4—51no—
753C22×C4—51no—
754C22×C4—51no—
755C22×C4—52no—
756C22×C4—58no—
757C22×C4—154no—
758C22×C4—151no—
759C22×C4—154no—
760C22×C4—151no—
761C22×C4—151no—
762C22×C4—158no—
763C22×C4—158no—
764C22×C4—151no—
765C22×C4—151no—
766C22×C4—152no—
767C22×C4—151no—
768C22×C4—158no—
769C22×C4—204no—
770C22×C4—604no—
771C22×C4—604no—
772C22×C4—604no—
773C4⋊C4—54no—
774C4⋊C4—154no—
775C4⋊C4—154no—
776C4⋊C4—154no—
777C22⋊C4—58no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C22⋊C4—158no—
781C22⋊C4—158no—
782C22⋊C4—158no—
783C22⋊C4—158no—
784C42—54no—
785C42—154no—
786C42—158no—
787C3×C5C2×#51811yescharacteristic, complemented, Hall
788C22×C3—24no—
789C22×C3—52no—
790C22×C3—52no—
791C22×C3—51no—
792C22×C3—51no—
793C22×C3—54no—
794C22×C3—104no—
795C22×C3—104no—
796C22×C3—108no—
797C22×C3—104no—
798C22×C3C23×AGL(1,𝔽5)14yes—
799C22×C3C23×AGL(1,𝔽5)11yescharacteristic
800C2×D3—22no—
801C2×D3—24no—
802C2×D3—48no—
803C2×D3—52no—
804C2×D3—54no—
805C2×D3—104no—
806C2×D3—104no—
807C2×D3—108no—
808C2×D3—102no—
809C2×D3—102no—
810C2×D3—104no—
811C2×D3—104no—
812C2×D3—102no—
813C2×D3—208no—
814C2×D3—208no—
815C2×D3—208no—
816C2×D3C23×AGL(1,𝔽5)12yes—
817C2×D3C23×AGL(1,𝔽5)14yes—
818C3×C4—52no—
819C3×C4—102no—
820C3×C4—104no—
821C3×C4—102no—
822C3×C4C23×AGL(1,𝔽5)12yes—
823Dic3—52no—
824Dic3—102no—
825Dic3—104no—
826Dic3—102no—
827Dic3C23×AGL(1,𝔽5)12yes—
828C2×C5—24no—
829C2×C5—62no—
830C2×C5—64no—
831C2×C5#554512yescomplemented
832C2×C5C23×C4×D311yescharacteristic
833D5—24no—
834D5—62no—
835D5—64no—
836D5#554512yescomplemented
837D5C2×#100411yescharacteristic
838D5C2×#100911yescharacteristic
839C23—31no—
840C23—32no—
841C23—38no—
842C23—51no—
843C23—54no—
844C23—54no—
845C23—52no—
846C23—104no—
847C23—104no—
848C23—124no—
849C23—152no—
850C23—154no—
851C23—152no—
852C23—154no—
853C23—158no—
854C23—158no—
855C23—151no—
856C23—152no—
857C23—158no—
858C23—304no—
859C23—304no—
860C23—302no—
861C23—302no—
862C23—604no—
863C23—604no—
864C23—604no—
865C23—608no—
866C23—608no—
867C23—6016no—
868C23C2×D3×AGL(1,𝔽5)12yes—
869D4—38no—
870D4—34no—
871D4—58no—
872D4—54no—
873D4—158no—
874D4—158no—
875D4—158no—
876D4—158no—
877D4—154no—
878D4C2×D3×AGL(1,𝔽5)14yescomplemented
879C2×C4—31no—
880C2×C4—34no—
881C2×C4—51no—
882C2×C4—52no—
883C2×C4—52no—
884C2×C4—52no—
885C2×C4—52no—
886C2×C4—54no—
887C2×C4—102no—
888C2×C4—104no—
889C2×C4—102no—
890C2×C4—154no—
891C2×C4—152no—
892C2×C4—152no—
893C2×C4—154no—
894C2×C4—151no—
895C2×C4—154no—
896C2×C4—152no—
897C2×C4—154no—
898C2×C4—152no—
899C2×C4—208no—
900C2×C4—302no—
901C2×C4—304no—
902C2×C4—302no—
903C2×C4—608no—
904C2×C4—608no—
905C2×C4—608no—
906C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
907C2×C3—24no—
908C2×C3—51no—
909C2×C3—51no—
910C2×C3—52no—
911C2×C3—104no—
912C2×C3#6625812yescomplemented
913C2×C3C24×AGL(1,𝔽5)11yescharacteristic
914D3—22no—
915D3—24no—
916D3—102no—
917D3—104no—
918C5C2×#554511yescharacteristic, complemented, Sylow
919C22—24no—
920C22—32no—
921C22—34no—
922C22—52no—
923C22—52no—
924C22—51no—
925C22—51no—
926C22—54no—
927C22—62no—
928C22—64no—
929C22—104no—
930C22—104no—
931C22—108no—
932C22—104no—
933C22—128no—
934C22—152no—
935C22—154no—
936C22—304no—
937C22—304no—
938C22—302no—
939C22—302no—
940C22—304no—
941C22—308no—
942C22—302no—
943C22—304no—
944C22—608no—
945C22—608no—
946C22—608no—
947C22C22×D3×AGL(1,𝔽5)14yes—
948C22C22×D3×AGL(1,𝔽5)11yescharacteristic
949C4—32no—
950C4—52no—
951C4—102no—
952C4—104no—
953C4—102no—
954C4—152no—
955C4—302no—
956C4—304no—
957C4—302no—
958C4C22×D3×AGL(1,𝔽5)12yes—
959C3C2×#6625811yescharacteristic, complemented, Sylow
960C2—24no—
961C2—51no—
962C2—51no—
963C2—52no—
964C2—62no—
965C2—64no—
966C2—104no—
967C2—302no—
968C2—304no—
969C2#1175684512yesdirect product factor
970C2C23×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×D3×D4×D5C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#518
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×D3×C22⋊AGL(1,𝔽5)C2semidirect
6. C2×AGL(1,𝔽5)×#67C2semidirect
7. C22×(C2×D3)⋊AGL(1,𝔽5)C2semidirect
8. #11756845C2direct (N × H)
9. C2×#91921C2semidirect
10. C2×AGL(1,𝔽5)×D12C2semidirect
11. C2×#91909C2semidirect
12. C2×#91907C2semidirect
15. C23×ΓL(1,𝔽16)C22semidirect
16. C23×C3×AGL(1,𝔽5)C22semidirect
17. C22×D3×AGL(1,𝔽5)C22semidirect
18. C22×D3×AGL(1,𝔽5)C22semidirect
19. C2×D4×D15C4semidirect
20. C2×C5×D3×D4C4semidirect
22. C2×#6790C4semidirect
23. C2×D3×C22⋊D5C4semidirect
25. D3×D4×D5C4semidirect
27. C2×#6777C4semidirect
28. C2×D3×D20C4semidirect
31. C2×#6763C22semidirect
32. D4×ΓL(1,𝔽16)C22semidirect
33. C2×C4⋊ΓL(1,𝔽16)C22semidirect
34. C2×C4×ΓL(1,𝔽16)C22semidirect
35. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
36. C3×D4×AGL(1,𝔽5)C22semidirect
37. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
38. C2×C3×C4×AGL(1,𝔽5)C22semidirect
39. #67⋊AGL(1,𝔽5)C22semidirect
40. D3×C22⋊AGL(1,𝔽5)C22semidirect
41. AGL(1,𝔽5)×#67C22semidirect
42. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
43. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
47. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
48. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
49. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
50. C2×Dic3×AGL(1,𝔽5)C22semidirect
51. #91921C22semidirect
52. AGL(1,𝔽5)×D12C22semidirect
53. #91909C22semidirect
54. #91907C22semidirect
65. C2×D4×AGL(1,𝔽5)D3semidirect
68. C23×D15C2×C4semidirect
69. C23×C5×D3C2×C4semidirect
73. C22×D3×D5C2×C4semidirect
74. C22×D3×D5C2×C4semidirect
75. C22×D3×D5C2×C4semidirect
83. C22×ΓL(1,𝔽16)C23semidirect
88. C22×C3×AGL(1,𝔽5)C23semidirect
91. C2×D3×AGL(1,𝔽5)C23semidirect
92. C2×D3×AGL(1,𝔽5)C23semidirect
93. C2×C3×C5×D4C2×C4semidirect
94. C2×#1220C2×C4semidirect
95. D4×D15C2×C4semidirect
96. C2×D60C2×C4semidirect
97. C2×C4×D15C2×C4semidirect
98. C2×C5×#67C2×C4semidirect
99. C5×D3×D4C2×C4semidirect
100. C2×C5×D12C2×C4semidirect
101. C2×C4×C5×D3C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
103. C3×D4×D5C2×C4semidirect
105. C2×C3×D20C2×C4semidirect
107. #6790C2×C4semidirect
108. D3×C22⋊D5C2×C4semidirect
109. D5×#67C2×C4semidirect
111. C2×#1203C2×C4semidirect
112. C2×#1202C2×C4semidirect
113. C2×#1201C2×C4semidirect
114. C2×#1200C2×C4semidirect
115. C2×D3×Dic5C2×C4semidirect
117. #6777C2×C4semidirect
118. D3×D20C2×C4semidirect
119. D5×D12C2×C4semidirect
121. C4×D3×D5C2×C4semidirect
123. #6763C23semidirect
124. C4⋊ΓL(1,𝔽16)C23semidirect
125. C4×ΓL(1,𝔽16)C23semidirect
126. C3×C22⋊AGL(1,𝔽5)C23semidirect
127. C3×C4⋊AGL(1,𝔽5)C23semidirect
128. C3×C4×AGL(1,𝔽5)C23semidirect
129. Dic3⋊AGL(1,𝔽5)C23semidirect
130. Dic3⋊AGL(1,𝔽5)C23semidirect
134. (C2×D3)⋊AGL(1,𝔽5)C23semidirect
135. (C2×D3)⋊AGL(1,𝔽5)C23semidirect
136. Dic3×AGL(1,𝔽5)C23semidirect
153. C23×AGL(1,𝔽5)C2×D3semidirect
174. C2×C22⋊AGL(1,𝔽5)C2×D3semidirect
180. D4×AGL(1,𝔽5)C2×D3semidirect
186. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
189. C2×C4×AGL(1,𝔽5)C2×D3semidirect
195. C22×D15C22×C4semidirect
199. C22×C5×D3C22×C4semidirect
217. C2×D3×D5C22×C4semidirect
218. C2×D3×D5C22×C4semidirect
237. C3×C5×D4C22×C4semidirect
239. #1220C22×C4semidirect
241. D60C22×C4semidirect
242. C4×D15C22×C4semidirect
243. C5×#67C22×C4semidirect
245. C5×D12C22×C4semidirect
246. C4×C5×D3C22×C4semidirect
247. C3×C22⋊D5C22×C4semidirect
249. C3×D20C22×C4semidirect
252. #1203C22×C4semidirect
253. #1202C22×C4semidirect
254. #1201C22×C4semidirect
255. #1200C22×C4semidirect
256. D3×Dic5C22×C4semidirect
271. C2×D3×D4AGL(1,𝔽5)semidirect
324. C22×AGL(1,𝔽5)C22×D3semidirect
328. C2×C5×D4C4×D3semidirect
334. C2×C22⋊D5C4×D3semidirect
343. D4×D5C4×D3semidirect
348. C2×D20C4×D3semidirect
361. C22⋊AGL(1,𝔽5)C22×D3semidirect
365. C4⋊AGL(1,𝔽5)C22×D3semidirect
368. C4×AGL(1,𝔽5)C22×D3semidirect
431. C23×D3C2×AGL(1,𝔽5)semidirect
436. C2×C3×D4C2×AGL(1,𝔽5)semidirect
448. C2×#67C2×AGL(1,𝔽5)semidirect
460. D3×D4C2×AGL(1,𝔽5)semidirect
465. C2×D12C2×AGL(1,𝔽5)semidirect
475. C2×C4×D3C2×AGL(1,𝔽5)semidirect
538. C5×D4C2×C4×D3semidirect
545. C22⋊D5C2×C4×D3semidirect
551. D20C2×C4×D3semidirect
600. C2×C3×C5#518semidirect
605. C3×D5#518semidirect
639. C22×D3C22×AGL(1,𝔽5)semidirect
642. C3×D4C22×AGL(1,𝔽5)semidirect
657. #67C22×AGL(1,𝔽5)semidirect
671. D12C22×AGL(1,𝔽5)semidirect
677. C4×D3C22×AGL(1,𝔽5)semidirect
750. C2×D4D3×AGL(1,𝔽5)semidirect
787. C3×C5C2×#518semidirect
831. C2×C5#5545semidirect
836. D5#5545semidirect
878. D4C2×D3×AGL(1,𝔽5)semidirect
912. C2×C3#66258semidirect
918. C5C2×#5545semidirect
959. C3C2×#66258semidirect
969. C2#11756845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×D4×D52
C2×D4×ΓL(1,𝔽16)2
C2×C3×D4×AGL(1,𝔽5)2
C2×#67⋊AGL(1,𝔽5)2
C2×D3×C22⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C22×(C2×D3)⋊AGL(1,𝔽5)2
#117568452
C2×#919212
C2×AGL(1,𝔽5)×D122
C2×#919092
C2×#919072
C2×#662583
C2×#55455