Finite Group Databasebeta

← C2×D33×AGL(1,𝔽5) #72269708

Subgroups — C2×D33×AGL(1,𝔽5) #72269708

Order 8640.

12420 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#72222379C211yesmaximal, characteristic, complemented
2C2×D32×ΓL(1,𝔽16)C213yesmaximal, complemented
3C2×D3×ΓL(1,𝔽16)⋊D3C213yesmaximal, complemented
4C2×D33×D5C211yesmaximal, characteristic
5C2×#11762195C411yescharacteristic, complemented
6C2×D3×(C3⋊D3)⋊D5C413yescomplemented
7C2×D32×D15C413yescomplemented
8C2×C5×D33C411yescharacteristic, complemented
9C2×AGL(1,𝔽5)×#1113C211yesmaximal, characteristic, complemented
10C2×#11762163C2213yescomplemented
11C2×D5×#1113C2211yescharacteristic
12C2×D3×C3⋊D3×AGL(1,𝔽5)C213yesmaximal, complemented
13C2×ΓL(1,𝔽16)⋊(C3⋊D3)C2213yescomplemented
14C2×AGL(1,𝔽5)×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
15C2×D3×C3⋊ΓL(1,𝔽16)C2213yescomplemented
16C2×C3⋊D3×ΓL(1,𝔽16)C2213yescomplemented
17C2×D3×D5×C3⋊D3C2213yes—
18C22×D32×AGL(1,𝔽5)—33nomaximal
19D33×AGL(1,𝔽5)C2116yesmaximal, direct product factor
20AGL(1,𝔽5)×#1113C2218yescomplemented
21#72222379C2218yescomplemented
22D3×ΓL(1,𝔽16)⋊D3C22124yescomplemented
23D32×ΓL(1,𝔽16)C22124yescomplemented
24D33×D5C418yescomplemented
25D33×D5C2218yes—
26D3×C3⋊D3×AGL(1,𝔽5)C22124yescomplemented
27C2×C3×D32×AGL(1,𝔽5)C213yesmaximal, complemented
28C2×C3×D3×ΓL(1,𝔽16)C2216yescomplemented
29C2×C32×D3×AGL(1,𝔽5)C2213yescomplemented
30C2×C3×ΓL(1,𝔽16)⋊D3C2213yescomplemented
31C2×C3×D32×D5C2213yes—
32C3×D32×AGL(1,𝔽5)C22124yescomplemented
33C2×C3×C3⋊D3×AGL(1,𝔽5)C2213yescomplemented
34C2×C4×D33—51nomaximal, Hall
35C22×D32×D5—33no—
36C22×ΓL(1,𝔽16)⋊D3—33no—
37C22×D3×ΓL(1,𝔽16)—36no—
38C22×C3⋊D3×AGL(1,𝔽5)—33no—
39C22×C3×D3×AGL(1,𝔽5)—36no—
40C2×D32×AGL(1,𝔽5)—33no—
41C2×D32×AGL(1,𝔽5)—33no—
42C2×D32×AGL(1,𝔽5)—36no—
43C2×D32×AGL(1,𝔽5)—33no—
44C2×D32×AGL(1,𝔽5)—36no—
45C2×D32×AGL(1,𝔽5)—348no—
46C2×D32×AGL(1,𝔽5)—63no—
47C2×D32×AGL(1,𝔽5)D313yesdirect product factor
48C2×C5⋊#1113C2×C413yescomplemented
49C2×C5×#1113C2×C411yescharacteristic, complemented
50C2×D15⋊(C3⋊D3)C2×C413yescomplemented
51C2×D3×C3⋊D15C2×C413yescomplemented
52C2×C3⋊D3×D15C2×C413yescomplemented
53C2×C5×D3×C3⋊D3C2×C413yescomplemented
54C2×D5×C3⋊(C3⋊D3)C2311yescharacteristic
55C2×C3×(C3⋊D3)⋊D5C2×C413yescomplemented
56C2×C3×D3×D15C2×C416yescomplemented
57C2×C3×C5×D32C2×C413yescomplemented
58C2×C3×D5×C3⋊D3C2313yes—
59C2×C32×D3×D5C2313yes—
60C2×C3⋊(C3⋊ΓL(1,𝔽16))C2311yescharacteristic, complemented
61C2×C3×C3⋊ΓL(1,𝔽16)C2313yescomplemented
62C2×C32×ΓL(1,𝔽16)C2313yescomplemented
63C2×C33×AGL(1,𝔽5)C2311yescharacteristic, complemented
64#11762195C2×C418yescomplemented
65D3×(C3⋊D3)⋊D5C2×C4124yescomplemented
66D32×D15C2×C4124yescomplemented
67C5×D33C2×C418yescomplemented
68D5×#1113C2×C414yescomplemented
69D5×#1113C2314yes—
70D3×D5×C3⋊D3C2×C4112yescomplemented
71D3×D5×C3⋊D3C23112yes—
72C3×D32×D5C2×C4112yescomplemented
73C3×D32×D5C23112yes—
74#11762163C23112yescomplemented
75ΓL(1,𝔽16)⋊(C3⋊D3)C23112yescomplemented
76C3⋊D3×ΓL(1,𝔽16)C23112yescomplemented
77D3×C3⋊ΓL(1,𝔽16)C23112yescomplemented
78AGL(1,𝔽5)×C3⋊(C3⋊D3)C2314yescomplemented
79C3×ΓL(1,𝔽16)⋊D3C23112yescomplemented
80C3×D3×ΓL(1,𝔽16)C23124yescomplemented
81C3×C3⋊D3×AGL(1,𝔽5)C23112yescomplemented
82C32×D3×AGL(1,𝔽5)C23112yescomplemented
83C23×D3×AGL(1,𝔽5)—93no—
84C22×D33—51no—
85C2×C4×#1113—51no—
86C2×C4×D3×C3⋊D3—53no—
87C2×C3×C4×D32—53no—
88C2×#88949—51no—
89C2×D3×#624—53no—
90C2×D32×Dic3—53no—
91C4×D33—516no—
92C22×(C3⋊D3)⋊D5—33no—
93C22×D3×D15—36no—
94C22×C5×D32—33no—
95C22×D5×C3⋊D3—33no—
96C22×C3×D3×D5—36no—
97C22×C3⋊ΓL(1,𝔽16)—33no—
98C22×C3×ΓL(1,𝔽16)—36no—
99C22×C32×AGL(1,𝔽5)—33no—
100C2×D32×D5—33no—
101C2×D32×D5—36no—
102C2×D32×D5—33no—
103C2×D32×D5—33no—
104C2×D32×D5—36no—
105C2×D32×D5—324no—
106C2×D32×D5—324no—
107C2×D32×D5—63no—
108C2×D32×D5C2×D313yes—
109C2×ΓL(1,𝔽16)⋊D3—33no—
110C2×ΓL(1,𝔽16)⋊D3—36no—
111C2×ΓL(1,𝔽16)⋊D3—324no—
112C2×ΓL(1,𝔽16)⋊D3—63no—
113C2×ΓL(1,𝔽16)⋊D3C2×D313yescomplemented
114C2×D3×ΓL(1,𝔽16)—36no—
115C2×D3×ΓL(1,𝔽16)—36no—
116C2×D3×ΓL(1,𝔽16)—36no—
117C2×D3×ΓL(1,𝔽16)—348no—
118C2×D3×ΓL(1,𝔽16)—63no—
119C2×D3×ΓL(1,𝔽16)—63no—
120C2×D3×ΓL(1,𝔽16)C2×D316yescomplemented
121C2×C3⋊D3×AGL(1,𝔽5)—33no—
122C2×C3⋊D3×AGL(1,𝔽5)—33no—
123C2×C3⋊D3×AGL(1,𝔽5)—33no—
124C2×C3⋊D3×AGL(1,𝔽5)—324no—
125C2×C3⋊D3×AGL(1,𝔽5)—63no—
126C2×C3⋊D3×AGL(1,𝔽5)—121no—
127C2×C3⋊D3×AGL(1,𝔽5)C2×D313yescomplemented
128C2×C3×D3×AGL(1,𝔽5)—23no—
129C2×C3×D3×AGL(1,𝔽5)—36no—
130C2×C3×D3×AGL(1,𝔽5)—36no—
131C2×C3×D3×AGL(1,𝔽5)—36no—
132C2×C3×D3×AGL(1,𝔽5)—348no—
133C2×C3×D3×AGL(1,𝔽5)—63no—
134C2×C3×D3×AGL(1,𝔽5)C2×D316yescomplemented
135D32×AGL(1,𝔽5)—324no—
136D32×AGL(1,𝔽5)—324no—
137D32×AGL(1,𝔽5)—348no—
138D32×AGL(1,𝔽5)—324no—
139D32×AGL(1,𝔽5)—348no—
140D32×AGL(1,𝔽5)—624no—
141D32×AGL(1,𝔽5)C2×D3124yesdirect product factor
142C22×C4×D32—153no—
143C2×C3⋊(C3⋊D15)C22×C411yescharacteristic, complemented
144C2×C5×C3⋊(C3⋊D3)C22×C411yescharacteristic, complemented
145C2×C3×C3⋊D15C22×C413yescomplemented
146C2×C3×C5×C3⋊D3C22×C413yescomplemented
147C2×C32×D15C22×C413yescomplemented
148C2×C32×C5×D3C22×C413yescomplemented
149C2×C33×D5C2411yescharacteristic
150C5⋊#1113C22×C4112yescomplemented
151C5×#1113C22×C414yescomplemented
152D15⋊(C3⋊D3)C22×C4112yescomplemented
153D3×C3⋊D15C22×C4112yescomplemented
154C3⋊D3×D15C22×C4112yescomplemented
155C5×D3×C3⋊D3C22×C4112yescomplemented
156D5×C3⋊(C3⋊D3)C22×C412yescomplemented
157D5×C3⋊(C3⋊D3)C2412yes—
158C3×(C3⋊D3)⋊D5C22×C4112yescomplemented
159C3×D3×D15C22×C4124yescomplemented
160C3×C5×D32C22×C4112yescomplemented
161C3×D5×C3⋊D3C22×C416yescomplemented
162C3×D5×C3⋊D3C2416yes—
163C32×D3×D5C22×C416yescomplemented
164C32×D3×D5C2416yes—
165C3⋊(C3⋊ΓL(1,𝔽16))C2412yescomplemented
166C3×C3⋊ΓL(1,𝔽16)C2416yescomplemented
167C32×ΓL(1,𝔽16)C2416yescomplemented
168C33×AGL(1,𝔽5)C2412yescomplemented
169C23×D3×D5—93no—
170C23×ΓL(1,𝔽16)—93no—
171C23×C3×AGL(1,𝔽5)—93no—
172C22×D3×AGL(1,𝔽5)—36no—
173C22×D3×AGL(1,𝔽5)—93no—
174C22×D3×AGL(1,𝔽5)—93no—
175C22×D3×AGL(1,𝔽5)—93no—
176C22×D3×AGL(1,𝔽5)—948no—
177C22×D3×AGL(1,𝔽5)—96no—
178C22×D3×AGL(1,𝔽5)—96no—
179C22×D3×AGL(1,𝔽5)—96no—
180C22×D3×AGL(1,𝔽5)—93no—
181C22×D3×AGL(1,𝔽5)—183no—
182C22×#1113—51no—
183C22×D3×C3⋊D3—53no—
184C22×C3×D32—53no—
185C2×D33—51no—
186C2×D33—53no—
187C2×D33—53no—
188C2×D33—58no—
189C2×D33—58no—
190C2×D33AGL(1,𝔽5)11yescharacteristic, direct product factor
191C2×C4×C3⋊(C3⋊D3)—51no—
192C2×C3×C4×C3⋊D3—53no—
193C2×C32×C4×D3—53no—
194C2×#6294—53no—
195C4×#1113—58no—
196C2×#6289—53no—
197C2×Dic3×C3⋊D3—53no—
198C2×D3×C3⋊Dic3—53no—
199C4×D3×C3⋊D3—524no—
200C2×C3×#624—53no—
201C2×C3×D3×Dic3—56no—
202C3×C4×D32—524no—
203#88949—58no—
204D3×#624—524no—
205D32×Dic3—524no—
206C22×C3⋊D15—33no—
207C22×C5×C3⋊D3—33no—
208C22×C3×D15—36no—
209C22×C3×C5×D3—36no—
210C22×C32×D5—33no—
211C2×(C3⋊D3)⋊D5—33no—
212C2×(C3⋊D3)⋊D5—36no—
213C2×(C3⋊D3)⋊D5—324no—
214C2×(C3⋊D3)⋊D5—63no—
215C2×(C3⋊D3)⋊D5C4×D313yescomplemented
216C2×D3×D15—36no—
217C2×D3×D15—36no—
218C2×D3×D15—36no—
219C2×D3×D15—348no—
220C2×D3×D15—63no—
221C2×D3×D15—63no—
222C2×D3×D15C4×D316yescomplemented
223C2×C5×D32—33no—
224C2×C5×D32—36no—
225C2×C5×D32—324no—
226C2×C5×D32—63no—
227C2×C5×D32C4×D313yescomplemented
228C2×D5×C3⋊D3—33no—
229C2×D5×C3⋊D3—33no—
230C2×D5×C3⋊D3—33no—
231C2×D5×C3⋊D3—312no—
232C2×D5×C3⋊D3—312no—
233C2×D5×C3⋊D3—63no—
234C2×D5×C3⋊D3—121no—
235C2×D5×C3⋊D3C22×D313yes—
236C2×C3×D3×D5—23no—
237C2×C3×D3×D5—36no—
238C2×C3×D3×D5—36no—
239C2×C3×D3×D5—36no—
240C2×C3×D3×D5—324no—
241C2×C3×D3×D5—324no—
242C2×C3×D3×D5—63no—
243C2×C3×D3×D5C22×D316yes—
244C2×C3⋊ΓL(1,𝔽16)—33no—
245C2×C3⋊ΓL(1,𝔽16)—312no—
246C2×C3⋊ΓL(1,𝔽16)—63no—
247C2×C3⋊ΓL(1,𝔽16)—121no—
248C2×C3⋊ΓL(1,𝔽16)C22×D313yescomplemented
249C2×C3×ΓL(1,𝔽16)—23no—
250C2×C3×ΓL(1,𝔽16)—36no—
251C2×C3×ΓL(1,𝔽16)—324no—
252C2×C3×ΓL(1,𝔽16)—63no—
253C2×C3×ΓL(1,𝔽16)C22×D316yescomplemented
254C2×C32×AGL(1,𝔽5)—23no—
255C2×C32×AGL(1,𝔽5)—33no—
256C2×C32×AGL(1,𝔽5)—312no—
257C2×C32×AGL(1,𝔽5)—41no—
258C2×C32×AGL(1,𝔽5)C22×D313yescomplemented
259D32×D5—324no—
260D32×D5—348no—
261D32×D5—324no—
262D32×D5—312no—
263D32×D5—312no—
264D32×D5—324no—
265D32×D5—324no—
266D32×D5—612no—
267D32×D5—612no—
268D32×D5C4×D3112yescomplemented
269D32×D5C22×D3112yes—
270ΓL(1,𝔽16)⋊D3—312no—
271ΓL(1,𝔽16)⋊D3—324no—
272ΓL(1,𝔽16)⋊D3—612no—
273ΓL(1,𝔽16)⋊D3C22×D3112yescomplemented
274D3×ΓL(1,𝔽16)—324no—
275D3×ΓL(1,𝔽16)—324no—
276D3×ΓL(1,𝔽16)—324no—
277D3×ΓL(1,𝔽16)—612no—
278D3×ΓL(1,𝔽16)—612no—
279D3×ΓL(1,𝔽16)C22×D3124yescomplemented
280C3⋊D3×AGL(1,𝔽5)—312no—
281C3⋊D3×AGL(1,𝔽5)—312no—
282C3⋊D3×AGL(1,𝔽5)—312no—
283C3⋊D3×AGL(1,𝔽5)—612no—
284C3⋊D3×AGL(1,𝔽5)—124no—
285C3⋊D3×AGL(1,𝔽5)C22×D3112yescomplemented
286C3×D3×AGL(1,𝔽5)—212no—
287C3×D3×AGL(1,𝔽5)—324no—
288C3×D3×AGL(1,𝔽5)—324no—
289C3×D3×AGL(1,𝔽5)—324no—
290C3×D3×AGL(1,𝔽5)—612no—
291C3×D3×AGL(1,𝔽5)C22×D3124yescomplemented
292C24×AGL(1,𝔽5)—271noHall
293C23×D32—153no—
294C22×C4×C3⋊D3—153no—
295C22×C3×C4×D3—156no—
296C22×#624—153no—
297C22×D3×Dic3—156no—
298C2×C4×D32—53no—
299C2×C4×D32—153no—
300C2×C4×D32—1548no—
301C2×C4×D32—156no—
302C2×C4×D32—153no—
303C2×C4×D32—156no—
304C2×C4×D32—153no—
305C2×C4×D32—303no—
306C2×C33×C5C23×C411yescharacteristic, complemented
307C3⋊(C3⋊D15)C23×C412yescomplemented
308C5×C3⋊(C3⋊D3)C23×C412yescomplemented
309C3×C3⋊D15C23×C416yescomplemented
310C3×C5×C3⋊D3C23×C416yescomplemented
311C32×D15C23×C416yescomplemented
312C32×C5×D3C23×C416yescomplemented
313C33×D5C23×C411yescharacteristic, complemented
314C33×D5C2511yescharacteristic
315C23×D15—93no—
316C23×C5×D3—93no—
317C23×C3×D5—93no—
318C22×D3×D5—36no—
319C22×D3×D5—93no—
320C22×D3×D5—924no—
321C22×D3×D5—93no—
322C22×D3×D5—93no—
323C22×D3×D5—924no—
324C22×D3×D5—96no—
325C22×D3×D5—96no—
326C22×D3×D5—96no—
327C22×D3×D5—93no—
328C22×D3×D5—183no—
329C22×ΓL(1,𝔽16)—36no—
330C22×ΓL(1,𝔽16)—93no—
331C22×ΓL(1,𝔽16)—924no—
332C22×ΓL(1,𝔽16)—96no—
333C22×ΓL(1,𝔽16)—93no—
334C22×ΓL(1,𝔽16)—183no—
335C22×C3×AGL(1,𝔽5)—36no—
336C22×C3×AGL(1,𝔽5)—63no—
337C22×C3×AGL(1,𝔽5)—93no—
338C22×C3×AGL(1,𝔽5)—924no—
339C22×C3×AGL(1,𝔽5)—96no—
340C22×C3×AGL(1,𝔽5)—93no—
341C2×D3×AGL(1,𝔽5)—36no—
342C2×D3×AGL(1,𝔽5)—36no—
343C2×D3×AGL(1,𝔽5)—36no—
344C2×D3×AGL(1,𝔽5)—348no—
345C2×D3×AGL(1,𝔽5)—63no—
346C2×D3×AGL(1,𝔽5)—924no—
347C2×D3×AGL(1,𝔽5)—924no—
348C2×D3×AGL(1,𝔽5)—924no—
349C2×D3×AGL(1,𝔽5)—948no—
350C2×D3×AGL(1,𝔽5)—948no—
351C2×D3×AGL(1,𝔽5)—948no—
352C2×D3×AGL(1,𝔽5)—96no—
353C2×D3×AGL(1,𝔽5)—96no—
354C2×D3×AGL(1,𝔽5)—96no—
355C2×D3×AGL(1,𝔽5)—93no—
356C2×D3×AGL(1,𝔽5)—93no—
357C2×D3×AGL(1,𝔽5)—93no—
358C2×D3×AGL(1,𝔽5)—924no—
359C2×D3×AGL(1,𝔽5)—1824no—
360C2×D3×AGL(1,𝔽5)—183no—
361C2×D3×AGL(1,𝔽5)—183no—
362C2×D3×AGL(1,𝔽5)—183no—
363C2×D3×AGL(1,𝔽5)—361no—
364C2×D3×AGL(1,𝔽5)D3213yesdirect product factor
365C22×C3⋊(C3⋊D3)—51no—
366C22×C3×C3⋊D3—53no—
367C22×C32×D3—53no—
368C2×#1113—53no—
369C2×#1113—54no—
370C2×#1113—54no—
371C2×#1113C2×AGL(1,𝔽5)11yescharacteristic, complemented
372C2×D3×C3⋊D3—53no—
373C2×D3×C3⋊D3—53no—
374C2×D3×C3⋊D3—53no—
375C2×D3×C3⋊D3—512no—
376C2×D3×C3⋊D3—512no—
377C2×D3×C3⋊D3C2×AGL(1,𝔽5)13yescomplemented
378C2×C3×D32—53no—
379C2×C3×D32—56no—
380C2×C3×D32—512no—
381C2×C3×D32—512no—
382C2×C3×D32C2×AGL(1,𝔽5)13yescomplemented
383D33—58no—
384D33—524no—
385D33—524no—
386D33C2×AGL(1,𝔽5)18yesdirect product factor
387C2×C33×C4—51no—
388C2×C3⋊(C3⋊Dic3)—51no—
389C4×C3⋊(C3⋊D3)—54no—
390C2×C3×C3⋊Dic3—53no—
391C3×C4×C3⋊D3—512no—
392C2×C32×Dic3—53no—
393C32×C4×D3—512no—
394#6294—512no—
395#6289—512no—
396Dic3×C3⋊D3—512no—
397D3×C3⋊Dic3—512no—
398C3×#624—512no—
399C3×D3×Dic3—524no—
400C23×C4×D3—453no—
401C22×C32×C5—33no—
402C2×C3⋊D15—33no—
403C2×C3⋊D15—312no—
404C2×C3⋊D15—63no—
405C2×C3⋊D15—121no—
406C2×C3⋊D15C2×C4×D313yescomplemented
407C2×C5×C3⋊D3—33no—
408C2×C5×C3⋊D3—312no—
409C2×C5×C3⋊D3—63no—
410C2×C5×C3⋊D3—121no—
411C2×C5×C3⋊D3C2×C4×D313yescomplemented
412C2×C3×D15—23no—
413C2×C3×D15—36no—
414C2×C3×D15—324no—
415C2×C3×D15—63no—
416C2×C3×D15C2×C4×D316yescomplemented
417C2×C3×C5×D3—23no—
418C2×C3×C5×D3—36no—
419C2×C3×C5×D3—324no—
420C2×C3×C5×D3—63no—
421C2×C3×C5×D3C2×C4×D316yescomplemented
422C2×C32×D5—23no—
423C2×C32×D5—33no—
424C2×C32×D5—36no—
425C2×C32×D5—36no—
426C2×C32×D5—41no—
427C2×C32×D5C23×D313yes—
428(C3⋊D3)⋊D5—312no—
429(C3⋊D3)⋊D5—324no—
430(C3⋊D3)⋊D5—612no—
431(C3⋊D3)⋊D5C2×C4×D3112yescomplemented
432D3×D15—324no—
433D3×D15—324no—
434D3×D15—324no—
435D3×D15—612no—
436D3×D15—612no—
437D3×D15C2×C4×D3124yescomplemented
438C5×D32—312no—
439C5×D32—324no—
440C5×D32—612no—
441C5×D32C2×C4×D3112yescomplemented
442D5×C3⋊D3—312no—
443D5×C3⋊D3—312no—
444D5×C3⋊D3—36no—
445D5×C3⋊D3—36no—
446D5×C3⋊D3—66no—
447D5×C3⋊D3—66no—
448D5×C3⋊D3—122no—
449D5×C3⋊D3—122no—
450D5×C3⋊D3C2×C4×D316yescomplemented
451D5×C3⋊D3C23×D316yes—
452C3×D3×D5—26no—
453C3×D3×D5—26no—
454C3×D3×D5—324no—
455C3×D3×D5—324no—
456C3×D3×D5—312no—
457C3×D3×D5—312no—
458C3×D3×D5—66no—
459C3×D3×D5—66no—
460C3×D3×D5C2×C4×D3112yescomplemented
461C3×D3×D5C23×D3112yes—
462C3⋊ΓL(1,𝔽16)—36no—
463C3⋊ΓL(1,𝔽16)—66no—
464C3⋊ΓL(1,𝔽16)—122no—
465C3⋊ΓL(1,𝔽16)C23×D316yescomplemented
466C3×ΓL(1,𝔽16)—26no—
467C3×ΓL(1,𝔽16)—312no—
468C3×ΓL(1,𝔽16)—66no—
469C3×ΓL(1,𝔽16)C23×D3112yescomplemented
470C32×AGL(1,𝔽5)—26no—
471C32×AGL(1,𝔽5)—36no—
472C32×AGL(1,𝔽5)—42no—
473C32×AGL(1,𝔽5)C23×D316yescomplemented
474C24×D5—271no—
475C23×AGL(1,𝔽5)—93no—
476C23×AGL(1,𝔽5)—273no—
477C23×AGL(1,𝔽5)—2716no—
478C23×AGL(1,𝔽5)—271no—
479C23×AGL(1,𝔽5)—273no—
480C23×AGL(1,𝔽5)—271no—
481C23×AGL(1,𝔽5)—273no—
482C23×C3⋊D3—153no—
483C23×C3×D3—156no—
484C22×D32—33no—
485C22×D32—53no—
486C22×D32—1524no—
487C22×D32—153no—
488C22×D32—156no—
489C22×D32—1524no—
490C22×D32—156no—
491C22×D32—153no—
492C22×D32—156no—
493C22×D32—153no—
494C22×D32—153no—
495C22×D32—303no—
496C22×C32×C4—153no—
497C22×C3⋊Dic3—153no—
498C2×C4×C3⋊D3—53no—
499C2×C4×C3⋊D3—1524no—
500C2×C4×C3⋊D3—153no—
501C2×C4×C3⋊D3—153no—
502C2×C4×C3⋊D3—153no—
503C2×C4×C3⋊D3—303no—
504C2×C4×C3⋊D3—601no—
505C22×C3×Dic3—156no—
506C2×C3×C4×D3—56no—
507C2×C3×C4×D3—103no—
508C2×C3×C4×D3—1548no—
509C2×C3×C4×D3—156no—
510C2×C3×C4×D3—156no—
511C2×C3×C4×D3—156no—
512C2×C3×C4×D3—303no—
513C2×#624—53no—
514C2×#624—1524no—
515C2×#624—156no—
516C2×#624—153no—
517C2×#624—303no—
518C2×D3×Dic3—56no—
519C2×D3×Dic3—1548no—
520C2×D3×Dic3—156no—
521C2×D3×Dic3—156no—
522C2×D3×Dic3—156no—
523C2×D3×Dic3—303no—
524C2×D3×Dic3—303no—
525C4×D32—524no—
526C4×D32—1548no—
527C4×D32—1524no—
528C4×D32—1548no—
529C4×D32—1524no—
530C4×D32—1524no—
531C4×D32—3024no—
532C33×C5C24×C411yescharacteristic, complemented, Hall
533C23×C3×C5—93no—
534C22×D15—36no—
535C22×D15—93no—
536C22×D15—924no—
537C22×D15—96no—
538C22×D15—93no—
539C22×D15—183no—
540C22×C5×D3—36no—
541C22×C5×D3—93no—
542C22×C5×D3—924no—
543C22×C5×D3—96no—
544C22×C5×D3—93no—
545C22×C5×D3—183no—
546C22×C3×D5—36no—
547C22×C3×D5—63no—
548C22×C3×D5—912no—
549C22×C3×D5—93no—
550C22×C3×D5—912no—
551C22×C3×D5—96no—
552C22×C3×D5—93no—
553C2×D3×D5—36no—
554C2×D3×D5—36no—
555C2×D3×D5—36no—
556C2×D3×D5—324no—
557C2×D3×D5—324no—
558C2×D3×D5—63no—
559C2×D3×D5—912no—
560C2×D3×D5—924no—
561C2×D3×D5—912no—
562C2×D3×D5—924no—
563C2×D3×D5—924no—
564C2×D3×D5—924no—
565C2×D3×D5—948no—
566C2×D3×D5—948no—
567C2×D3×D5—96no—
568C2×D3×D5—96no—
569C2×D3×D5—96no—
570C2×D3×D5—93no—
571C2×D3×D5—93no—
572C2×D3×D5—93no—
573C2×D3×D5—912no—
574C2×D3×D5—912no—
575C2×D3×D5—1812no—
576C2×D3×D5—1812no—
577C2×D3×D5—183no—
578C2×D3×D5—183no—
579C2×D3×D5—183no—
580C2×D3×D5—361no—
581C2×D3×D5C2×D3213yes—
582C2×ΓL(1,𝔽16)—36no—
583C2×ΓL(1,𝔽16)—324no—
584C2×ΓL(1,𝔽16)—63no—
585C2×ΓL(1,𝔽16)—912no—
586C2×ΓL(1,𝔽16)—924no—
587C2×ΓL(1,𝔽16)—93no—
588C2×ΓL(1,𝔽16)—912no—
589C2×ΓL(1,𝔽16)—1812no—
590C2×ΓL(1,𝔽16)—183no—
591C2×ΓL(1,𝔽16)—361no—
592C2×ΓL(1,𝔽16)C2×D3213yescomplemented
593C2×C3×AGL(1,𝔽5)—23no—
594C2×C3×AGL(1,𝔽5)—36no—
595C2×C3×AGL(1,𝔽5)—324no—
596C2×C3×AGL(1,𝔽5)—41no—
597C2×C3×AGL(1,𝔽5)—612no—
598C2×C3×AGL(1,𝔽5)—63no—
599C2×C3×AGL(1,𝔽5)—912no—
600C2×C3×AGL(1,𝔽5)—924no—
601C2×C3×AGL(1,𝔽5)—93no—
602C2×C3×AGL(1,𝔽5)—912no—
603C2×C3×AGL(1,𝔽5)C2×D3213yescomplemented
604D3×AGL(1,𝔽5)—324no—
605D3×AGL(1,𝔽5)—324no—
606D3×AGL(1,𝔽5)—324no—
607D3×AGL(1,𝔽5)—612no—
608D3×AGL(1,𝔽5)—924no—
609D3×AGL(1,𝔽5)—924no—
610D3×AGL(1,𝔽5)—924no—
611D3×AGL(1,𝔽5)—912no—
612D3×AGL(1,𝔽5)—912no—
613D3×AGL(1,𝔽5)—912no—
614D3×AGL(1,𝔽5)—1812no—
615D3×AGL(1,𝔽5)—1812no—
616D3×AGL(1,𝔽5)—1812no—
617D3×AGL(1,𝔽5)—364no—
618D3×AGL(1,𝔽5)C2×D32112yesdirect product factor
619C22×C33—51no—
620C2×C3⋊(C3⋊D3)—51no—
621C2×C3⋊(C3⋊D3)—52no—
622C2×C3⋊(C3⋊D3)—52no—
623C2×C3⋊(C3⋊D3)C22×AGL(1,𝔽5)11yescharacteristic, complemented
624C2×C3×C3⋊D3—53no—
625C2×C3×C3⋊D3—56no—
626C2×C3×C3⋊D3—56no—
627C2×C3×C3⋊D3C22×AGL(1,𝔽5)13yescomplemented
628C2×C32×D3—53no—
629C2×C32×D3—56no—
630C2×C32×D3—56no—
631C2×C32×D3C22×AGL(1,𝔽5)13yescomplemented
632#1113—512no—
633#1113C22×AGL(1,𝔽5)14yescomplemented
634D3×C3⋊D3—512no—
635D3×C3⋊D3—512no—
636D3×C3⋊D3—512no—
637D3×C3⋊D3C22×AGL(1,𝔽5)112yescomplemented
638C3×D32—512no—
639C3×D32—524no—
640C3×D32C22×AGL(1,𝔽5)112yescomplemented
641C33×C4—52no—
642C3⋊(C3⋊Dic3)—52no—
643C3×C3⋊Dic3—56no—
644C32×Dic3—56no—
645C24×D3—453no—
646C23×C3×C4—453no—
647C23×Dic3—453no—
648C22×C4×D3—156no—
649C22×C4×D3—453no—
650C22×C4×D3—4548no—
651C22×C4×D3—453no—
652C22×C4×D3—453no—
653C22×C4×D3—453no—
654C22×C4×D3—456no—
655C22×C4×D3—456no—
656C22×C4×D3—456no—
657C22×C4×D3—903no—
658C2×C32×C5—23no—
659C2×C32×C5—36no—
660C2×C32×C5—41no—
661C2×C32×C5C22×C4×D313yescomplemented
662C3⋊D15—36no—
663C3⋊D15—66no—
664C3⋊D15—122no—
665C3⋊D15C22×C4×D316yescomplemented
666C5×C3⋊D3—36no—
667C5×C3⋊D3—66no—
668C5×C3⋊D3—122no—
669C5×C3⋊D3C22×C4×D316yescomplemented
670C3×D15—26no—
671C3×D15—312no—
672C3×D15—66no—
673C3×D15C22×C4×D3112yescomplemented
674C3×C5×D3—26no—
675C3×C5×D3—312no—
676C3×C5×D3—66no—
677C3×C5×D3C22×C4×D3112yescomplemented
678C32×D5—23no—
679C32×D5—23no—
680C32×D5—36no—
681C32×D5—41no—
682C32×D5—41no—
683C32×D5C22×C4×D313yescomplemented
684C32×D5C24×D313yes—
685C24×C5—271no—
686C23×D5—93no—
687C23×D5—273no—
688C23×D5—278no—
689C23×D5—271no—
690C23×D5—278no—
691C23×D5—271no—
692C23×D5—273no—
693C23×D5—273no—
694C22×AGL(1,𝔽5)—33no—
695C22×AGL(1,𝔽5)—93no—
696C22×AGL(1,𝔽5)—924no—
697C22×AGL(1,𝔽5)—96no—
698C22×AGL(1,𝔽5)—93no—
699C22×AGL(1,𝔽5)—273no—
700C22×AGL(1,𝔽5)—2724no—
701C22×AGL(1,𝔽5)—273no—
702C22×AGL(1,𝔽5)—278no—
703C22×AGL(1,𝔽5)—2724no—
704C22×AGL(1,𝔽5)—278no—
705C22×AGL(1,𝔽5)—2724no—
706C22×AGL(1,𝔽5)—273no—
707C22×AGL(1,𝔽5)—273no—
708C22×AGL(1,𝔽5)—271no—
709C23×C32—153no—
710C22×C3⋊D3—33no—
711C22×C3⋊D3—53no—
712C22×C3⋊D3—153no—
713C22×C3⋊D3—1512no—
714C22×C3⋊D3—1512no—
715C22×C3⋊D3—153no—
716C22×C3⋊D3—153no—
717C22×C3⋊D3—153no—
718C22×C3⋊D3—303no—
719C22×C3⋊D3—601no—
720C22×C3×D3—36no—
721C22×C3×D3—56no—
722C22×C3×D3—103no—
723C22×C3×D3—156no—
724C22×C3×D3—1524no—
725C22×C3×D3—1524no—
726C22×C3×D3—156no—
727C22×C3×D3—156no—
728C22×C3×D3—156no—
729C22×C3×D3—303no—
730C2×D32—33no—
731C2×D32—36no—
732C2×D32—324no—
733C2×D32—53no—
734C2×D32—56no—
735C2×D32—512no—
736C2×D32—512no—
737C2×D32—63no—
738C2×D32—1524no—
739C2×D32—1548no—
740C2×D32—1524no—
741C2×D32—1524no—
742C2×D32—1512no—
743C2×D32—1512no—
744C2×D32—1548no—
745C2×D32—1524no—
746C2×D32—156no—
747C2×D32—156no—
748C2×D32—156no—
749C2×D32—153no—
750C2×D32—156no—
751C2×D32—1524no—
752C2×D32—3012no—
753C2×D32—3012no—
754C2×D32—303no—
755C2×D32—303no—
756C2×D32—303no—
757C2×D32D3×AGL(1,𝔽5)13yesdirect product factor
758C2×C32×C4—53no—
759C2×C32×C4—103no—
760C2×C32×C4—1512no—
761C2×C32×C4—153no—
762C2×C32×C4—201no—
763C2×C3⋊Dic3—53no—
764C2×C3⋊Dic3—1512no—
765C2×C3⋊Dic3—153no—
766C2×C3⋊Dic3—303no—
767C2×C3⋊Dic3—601no—
768C4×C3⋊D3—512no—
769C4×C3⋊D3—1512no—
770C4×C3⋊D3—1512no—
771C4×C3⋊D3—1512no—
772C4×C3⋊D3—3012no—
773C4×C3⋊D3—604no—
774C2×C3×Dic3—56no—
775C2×C3×Dic3—103no—
776C2×C3×Dic3—1524no—
777C2×C3×Dic3—156no—
778C2×C3×Dic3—303no—
779C3×C4×D3—524no—
780C3×C4×D3—1012no—
781C3×C4×D3—1524no—
782C3×C4×D3—1524no—
783C3×C4×D3—1524no—
784C3×C4×D3—3012no—
785#624—512no—
786#624—1524no—
787#624—1512no—
788#624—3012no—
789D3×Dic3—524no—
790D3×Dic3—1524no—
791D3×Dic3—1524no—
792D3×Dic3—1524no—
793D3×Dic3—3012no—
794D3×Dic3—3012no—
795C24×C4—1351noSylow
796C22×C3×C5—36no—
797C22×C3×C5—63no—
798C22×C3×C5—912no—
799C22×C3×C5—93no—
800C2×D15—36no—
801C2×D15—324no—
802C2×D15—63no—
803C2×D15—912no—
804C2×D15—924no—
805C2×D15—93no—
806C2×D15—912no—
807C2×D15—1812no—
808C2×D15—183no—
809C2×D15—361no—
810C2×D15C4×D3213yescomplemented
811C2×C5×D3—36no—
812C2×C5×D3—324no—
813C2×C5×D3—63no—
814C2×C5×D3—912no—
815C2×C5×D3—924no—
816C2×C5×D3—93no—
817C2×C5×D3—912no—
818C2×C5×D3—1812no—
819C2×C5×D3—183no—
820C2×C5×D3—361no—
821C2×C5×D3C4×D3213yescomplemented
822C2×C3×D5—23no—
823C2×C3×D5—36no—
824C2×C3×D5—312no—
825C2×C3×D5—312no—
826C2×C3×D5—41no—
827C2×C3×D5—66no—
828C2×C3×D5—66no—
829C2×C3×D5—63no—
830C2×C3×D5—912no—
831C2×C3×D5—924no—
832C2×C3×D5—93no—
833C2×C3×D5—96no—
834C2×C3×D5—96no—
835C2×C3×D5C22×D3213yes—
836D3×D5—324no—
837D3×D5—312no—
838D3×D5—312no—
839D3×D5—324no—
840D3×D5—66no—
841D3×D5—66no—
842D3×D5—924no—
843D3×D5—924no—
844D3×D5—924no—
845D3×D5—912no—
846D3×D5—96no—
847D3×D5—96no—
848D3×D5—912no—
849D3×D5—1812no—
850D3×D5—186no—
851D3×D5—186no—
852D3×D5—1812no—
853D3×D5—362no—
854D3×D5—362no—
855D3×D5C4×D3216yescomplemented
856D3×D5C22×D3216yes—
857ΓL(1,𝔽16)—312no—
858ΓL(1,𝔽16)—66no—
859ΓL(1,𝔽16)—96no—
860ΓL(1,𝔽16)—186no—
861ΓL(1,𝔽16)—362no—
862ΓL(1,𝔽16)C22×D3216yescomplemented
863C3×AGL(1,𝔽5)—26no—
864C3×AGL(1,𝔽5)—312no—
865C3×AGL(1,𝔽5)—42no—
866C3×AGL(1,𝔽5)—66no—
867C3×AGL(1,𝔽5)—96no—
868C3×AGL(1,𝔽5)C22×D3216yescomplemented
869C2×C33—51no—
870C2×C33—51no—
871C2×C33C23×AGL(1,𝔽5)11yescharacteristic, complemented
872C3⋊(C3⋊D3)—52no—
873C3⋊(C3⋊D3)C23×AGL(1,𝔽5)12yescomplemented
874C3×C3⋊D3—56no—
875C3×C3⋊D3C23×AGL(1,𝔽5)16yescomplemented
876C32×D3—56no—
877C32×D3C23×AGL(1,𝔽5)16yescomplemented
878C24×C3—453no—
879C23×D3—93no—
880C23×D3—156no—
881C23×D3—456no—
882C23×D3—453no—
883C23×D3—4524no—
884C23×D3—453no—
885C23×D3—4524no—
886C23×D3—453no—
887C23×D3—456no—
888C23×D3—453no—
889C23×D3—456no—
890C23×D3—453no—
891C23×D3—903no—
892C22×C3×C4—156no—
893C22×C3×C4—303no—
894C22×C3×C4—453no—
895C22×C3×C4—4524no—
896C22×C3×C4—453no—
897C22×C3×C4—456no—
898C22×Dic3—156no—
899C22×Dic3—453no—
900C22×Dic3—4524no—
901C22×Dic3—453no—
902C22×Dic3—456no—
903C22×Dic3—903no—
904C2×C4×D3—53no—
905C2×C4×D3—1548no—
906C2×C4×D3—156no—
907C2×C4×D3—156no—
908C2×C4×D3—156no—
909C2×C4×D3—303no—
910C2×C4×D3—4524no—
911C2×C4×D3—4524no—
912C2×C4×D3—4524no—
913C2×C4×D3—4524no—
914C2×C4×D3—4548no—
915C2×C4×D3—4548no—
916C2×C4×D3—4548no—
917C2×C4×D3—453no—
918C2×C4×D3—456no—
919C2×C4×D3—456no—
920C2×C4×D3—453no—
921C2×C4×D3—456no—
922C2×C4×D3—453no—
923C2×C4×D3—9024no—
924C2×C4×D3—903no—
925C2×C4×D3—903no—
926C2×C4×D3—903no—
927C2×C4×D3—1801no—
928C32×C5—23no—
929C32×C5—41no—
930C32×C5C23×C4×D313yescomplemented
931C23×C5—93no—
932C23×C5—273no—
933C23×C5—278no—
934C23×C5—271no—
935C22×D5—33no—
936C22×D5—912no—
937C22×D5—93no—
938C22×D5—912no—
939C22×D5—96no—
940C22×D5—93no—
941C22×D5—2712no—
942C22×D5—273no—
943C22×D5—2712no—
944C22×D5—273no—
945C22×D5—274no—
946C22×D5—278no—
947C22×D5—2724no—
948C22×D5—274no—
949C22×D5—2724no—
950C22×D5—273no—
951C22×D5—273no—
952C22×D5—271no—
953C2×AGL(1,𝔽5)—33no—
954C2×AGL(1,𝔽5)—312no—
955C2×AGL(1,𝔽5)—912no—
956C2×AGL(1,𝔽5)—924no—
957C2×AGL(1,𝔽5)—93no—
958C2×AGL(1,𝔽5)—912no—
959C2×AGL(1,𝔽5)—2712no—
960C2×AGL(1,𝔽5)—2712no—
961C2×AGL(1,𝔽5)—2712no—
962C2×AGL(1,𝔽5)—2712no—
963C2×AGL(1,𝔽5)—271no—
964C2×AGL(1,𝔽5)—274no—
965C2×AGL(1,𝔽5)D3311yescharacteristic, direct product factor
966C22×C32—33no—
967C22×C32—53no—
968C22×C32—103no—
969C22×C32—156no—
970C22×C32—156no—
971C22×C32—153no—
972C22×C32—201no—
973C2×C3⋊D3—33no—
974C2×C3⋊D3—312no—
975C2×C3⋊D3—53no—
976C2×C3⋊D3—56no—
977C2×C3⋊D3—56no—
978C2×C3⋊D3—63no—
979C2×C3⋊D3—121no—
980C2×C3⋊D3—1512no—
981C2×C3⋊D3—156no—
982C2×C3⋊D3—156no—
983C2×C3⋊D3—1512no—
984C2×C3⋊D3—153no—
985C2×C3⋊D3—1512no—
986C2×C3⋊D3—306no—
987C2×C3⋊D3—306no—
988C2×C3⋊D3—303no—
989C2×C3⋊D3—602no—
990C2×C3⋊D3—602no—
991C2×C3⋊D3—601no—
992C2×C3⋊D3C2×D3×AGL(1,𝔽5)13yescomplemented
993C2×C3×D3—23no—
994C2×C3×D3—36no—
995C2×C3×D3—324no—
996C2×C3×D3—56no—
997C2×C3×D3—512no—
998C2×C3×D3—512no—
999C2×C3×D3—63no—
1000C2×C3×D3—106no—
1001C2×C3×D3—106no—
1002C2×C3×D3—103no—
1003C2×C3×D3—1524no—
1004C2×C3×D3—1512no—
1005C2×C3×D3—1512no—
1006C2×C3×D3—1524no—
1007C2×C3×D3—156no—
1008C2×C3×D3—1524no—
1009C2×C3×D3—306no—
1010C2×C3×D3—306no—
1011C2×C3×D3—303no—
1012C2×C3×D3C2×D3×AGL(1,𝔽5)16yescomplemented
1013D32—312no—
1014D32—324no—
1015D32—512no—
1016D32—524no—
1017D32—612no—
1018D32—1524no—
1019D32—1524no—
1020D32—1524no—
1021D32—1512no—
1022D32—1524no—
1023D32—3012no—
1024D32—3012no—
1025D32—3012no—
1026D32C2×D3×AGL(1,𝔽5)112yesdirect product factor
1027C32×C4—56no—
1028C32×C4—106no—
1029C32×C4—156no—
1030C32×C4—202no—
1031C3⋊Dic3—56no—
1032C3⋊Dic3—156no—
1033C3⋊Dic3—306no—
1034C3⋊Dic3—602no—
1035C3×Dic3—512no—
1036C3×Dic3—106no—
1037C3×Dic3—1512no—
1038C3×Dic3—306no—
1039C25—1351no—
1040C23×C4—453no—
1041C23×C4—1353no—
1042C23×C4—1351no—
1043C23×C4—13516no—
1044C23×C4—1351no—
1045C23×C4—1353no—
1046C23×C4—1353no—
1047C2×C3×C5—23no—
1048C2×C3×C5—312no—
1049C2×C3×C5—41no—
1050C2×C3×C5—66no—
1051C2×C3×C5—96no—
1052C2×C3×C5C2×C4×D3213yescomplemented
1053D15—312no—
1054D15—66no—
1055D15—96no—
1056D15—186no—
1057D15—362no—
1058D15C2×C4×D3216yescomplemented
1059C3×D5—23no—
1060C3×D5—23no—
1061C3×D5—312no—
1062C3×D5—41no—
1063C3×D5—41no—
1064C3×D5—66no—
1065C3×D5—96no—
1066C3×D5C2×C4×D3213yescomplemented
1067C3×D5C23×D3213yes—
1068C5×D3—312no—
1069C5×D3—66no—
1070C5×D3—96no—
1071C5×D3—186no—
1072C5×D3—362no—
1073C5×D3C2×C4×D3216yescomplemented
1074C33C24×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
1075C23×C3—93no—
1076C23×C3—156no—
1077C23×C3—303no—
1078C23×C3—456no—
1079C23×C3—453no—
1080C23×C3—4512no—
1081C23×C3—4512no—
1082C23×C3—453no—
1083C22×D3—36no—
1084C22×D3—53no—
1085C22×D3—93no—
1086C22×D3—924no—
1087C22×D3—96no—
1088C22×D3—93no—
1089C22×D3—1524no—
1090C22×D3—156no—
1091C22×D3—1524no—
1092C22×D3—156no—
1093C22×D3—156no—
1094C22×D3—156no—
1095C22×D3—183no—
1096C22×D3—303no—
1097C22×D3—456no—
1098C22×D3—4548no—
1099C22×D3—456no—
1100C22×D3—4512no—
1101C22×D3—453no—
1102C22×D3—4512no—
1103C22×D3—453no—
1104C22×D3—4512no—
1105C22×D3—4524no—
1106C22×D3—4512no—
1107C22×D3—4548no—
1108C22×D3—4524no—
1109C22×D3—4524no—
1110C22×D3—4524no—
1111C22×D3—456no—
1112C22×D3—453no—
1113C22×D3—4524no—
1114C22×D3—453no—
1115C22×D3—456no—
1116C22×D3—453no—
1117C22×D3—903no—
1118C22×D3—9012no—
1119C22×D3—9012no—
1120C22×D3—903no—
1121C22×D3—903no—
1122C22×D3—903no—
1123C22×D3—1801no—
1124C2×C3×C4—53no—
1125C2×C3×C4—103no—
1126C2×C3×C4—1524no—
1127C2×C3×C4—156no—
1128C2×C3×C4—201no—
1129C2×C3×C4—3012no—
1130C2×C3×C4—303no—
1131C2×C3×C4—4512no—
1132C2×C3×C4—4512no—
1133C2×C3×C4—4524no—
1134C2×C3×C4—453no—
1135C2×Dic3—53no—
1136C2×Dic3—1524no—
1137C2×Dic3—156no—
1138C2×Dic3—303no—
1139C2×Dic3—4512no—
1140C2×Dic3—4512no—
1141C2×Dic3—4524no—
1142C2×Dic3—453no—
1143C2×Dic3—9012no—
1144C2×Dic3—903no—
1145C2×Dic3—1801no—
1146C4×D3—512no—
1147C4×D3—1524no—
1148C4×D3—1524no—
1149C4×D3—1524no—
1150C4×D3—3012no—
1151C4×D3—4512no—
1152C4×D3—4524no—
1153C4×D3—4524no—
1154C4×D3—4512no—
1155C4×D3—4524no—
1156C4×D3—4512no—
1157C4×D3—9012no—
1158C4×D3—9012no—
1159C4×D3—9012no—
1160C4×D3—1804no—
1161C22×C5—33no—
1162C22×C5—912no—
1163C22×C5—93no—
1164C22×C5—2712no—
1165C22×C5—274no—
1166C22×C5—271no—
1167C2×D5—33no—
1168C2×D5—36no—
1169C2×D5—36no—
1170C2×D5—912no—
1171C2×D5—924no—
1172C2×D5—93no—
1173C2×D5—96no—
1174C2×D5—96no—
1175C2×D5—2712no—
1176C2×D5—2712no—
1177C2×D5—2712no—
1178C2×D5—2712no—
1179C2×D5—271no—
1180C2×D5—272no—
1181C2×D5—272no—
1182C2×D5C2×D3311yescharacteristic
1183AGL(1,𝔽5)—36no—
1184AGL(1,𝔽5)—96no—
1185AGL(1,𝔽5)—272no—
1186AGL(1,𝔽5)C2×D3312yesdirect product factor
1187C2×C32—23no—
1188C2×C32—36no—
1189C2×C32—41no—
1190C2×C32—53no—
1191C2×C32—53no—
1192C2×C32—103no—
1193C2×C32—103no—
1194C2×C32—156no—
1195C2×C32—201no—
1196C2×C32—201no—
1197C2×C32C22×D3×AGL(1,𝔽5)13yescomplemented
1198C3⋊D3—36no—
1199C3⋊D3—56no—
1200C3⋊D3—66no—
1201C3⋊D3—122no—
1202C3⋊D3—156no—
1203C3⋊D3—306no—
1204C3⋊D3—602no—
1205C3⋊D3C22×D3×AGL(1,𝔽5)16yescomplemented
1206C3×D3—26no—
1207C3×D3—312no—
1208C3×D3—512no—
1209C3×D3—66no—
1210C3×D3—106no—
1211C3×D3—1512no—
1212C3×D3—306no—
1213C3×D3C22×D3×AGL(1,𝔽5)112yescomplemented
1214C24—271no—
1215C24—453no—
1216C24—1353no—
1217C24—1353no—
1218C24—1351no—
1219C24—1358no—
1220C24—1353no—
1221C24—1351no—
1222C24—1358no—
1223C22×C4—153no—
1224C22×C4—453no—
1225C22×C4—4524no—
1226C22×C4—453no—
1227C22×C4—456no—
1228C22×C4—1351no—
1229C22×C4—13524no—
1230C22×C4—1353no—
1231C22×C4—1353no—
1232C22×C4—1358no—
1233C22×C4—1358no—
1234C22×C4—13524no—
1235C22×C4—13524no—
1236C22×C4—1353no—
1237C22×C4—1353no—
1238C3×C5—23no—
1239C3×C5—41no—
1240C3×C5C22×C4×D3213yescomplemented
1241C22×C3—36no—
1242C22×C3—53no—
1243C22×C3—63no—
1244C22×C3—912no—
1245C22×C3—93no—
1246C22×C3—103no—
1247C22×C3—1512no—
1248C22×C3—1512no—
1249C22×C3—156no—
1250C22×C3—201no—
1251C22×C3—303no—
1252C22×C3—306no—
1253C22×C3—306no—
1254C22×C3—4524no—
1255C22×C3—456no—
1256C22×C3—456no—
1257C22×C3—4512no—
1258C22×C3—453no—
1259C2×D3—36no—
1260C2×D3—324no—
1261C2×D3—53no—
1262C2×D3—56no—
1263C2×D3—56no—
1264C2×D3—63no—
1265C2×D3—912no—
1266C2×D3—924no—
1267C2×D3—93no—
1268C2×D3—912no—
1269C2×D3—1524no—
1270C2×D3—1512no—
1271C2×D3—1512no—
1272C2×D3—1524no—
1273C2×D3—156no—
1274C2×D3—1524no—
1275C2×D3—1812no—
1276C2×D3—183no—
1277C2×D3—306no—
1278C2×D3—306no—
1279C2×D3—303no—
1280C2×D3—361no—
1281C2×D3—4524no—
1282C2×D3—4524no—
1283C2×D3—4512no—
1284C2×D3—4512no—
1285C2×D3—4524no—
1286C2×D3—456no—
1287C2×D3—456no—
1288C2×D3—4512no—
1289C2×D3—4524no—
1290C2×D3—453no—
1291C2×D3—4512no—
1292C2×D3—9012no—
1293C2×D3—9012no—
1294C2×D3—906no—
1295C2×D3—906no—
1296C2×D3—9012no—
1297C2×D3—903no—
1298C2×D3—1802no—
1299C2×D3—1802no—
1300C2×D3—1801no—
1301C2×D3D32×AGL(1,𝔽5)13yesdirect product factor
1302C3×C4—56no—
1303C3×C4—106no—
1304C3×C4—1512no—
1305C3×C4—202no—
1306C3×C4—306no—
1307C3×C4—456no—
1308Dic3—56no—
1309Dic3—1512no—
1310Dic3—306no—
1311Dic3—456no—
1312Dic3—906no—
1313Dic3—1802no—
1314C2×C5—36no—
1315C2×C5—96no—
1316C2×C5—272no—
1317C2×C5C4×D3311yescharacteristic, complemented
1318D5—36no—
1319D5—96no—
1320D5—272no—
1321D5C4×D3311yescharacteristic, complemented
1322D5C22×D3311yescharacteristic
1323C32—23no—
1324C32—41no—
1325C32C23×D3×AGL(1,𝔽5)13yescomplemented
1326C23—93no—
1327C23—153no—
1328C23—273no—
1329C23—278no—
1330C23—271no—
1331C23—456no—
1332C23—453no—
1333C23—4512no—
1334C23—4512no—
1335C23—453no—
1336C23—1353no—
1337C23—1351no—
1338C23—1353no—
1339C23—13524no—
1340C23—1353no—
1341C23—13512no—
1342C23—13512no—
1343C23—1353no—
1344C23—1354no—
1345C23—13524no—
1346C23—1354no—
1347C23—1358no—
1348C2×C4—51no—
1349C2×C4—1512no—
1350C2×C4—153no—
1351C2×C4—4512no—
1352C2×C4—4512no—
1353C2×C4—4524no—
1354C2×C4—453no—
1355C2×C4—1354no—
1356C2×C4—13512no—
1357C2×C4—13512no—
1358C2×C4—13512no—
1359C2×C4—13512no—
1360C2×C4—1351no—
1361C2×C3—23no—
1362C2×C3—312no—
1363C2×C3—41no—
1364C2×C3—53no—
1365C2×C3—53no—
1366C2×C3—66no—
1367C2×C3—96no—
1368C2×C3—103no—
1369C2×C3—103no—
1370C2×C3—1512no—
1371C2×C3—201no—
1372C2×C3—201no—
1373C2×C3—306no—
1374C2×C3—456no—
1375C2×C3C2×D32×AGL(1,𝔽5)13yescomplemented
1376D3—312no—
1377D3—56no—
1378D3—66no—
1379D3—96no—
1380D3—1512no—
1381D3—186no—
1382D3—306no—
1383D3—362no—
1384D3—456no—
1385D3—906no—
1386D3—1802no—
1387D3C2×D32×AGL(1,𝔽5)16yesdirect product factor
1388C5C2×C4×D3311yescharacteristic, complemented, Sylow
1389C22—33no—
1390C22—51no—
1391C22—912no—
1392C22—93no—
1393C22—156no—
1394C22—156no—
1395C22—153no—
1396C22—2712no—
1397C22—274no—
1398C22—271no—
1399C22—4524no—
1400C22—456no—
1401C22—456no—
1402C22—4512no—
1403C22—453no—
1404C22—13512no—
1405C22—1352no—
1406C22—1352no—
1407C22—13512no—
1408C22—13512no—
1409C22—13512no—
1410C22—1351no—
1411C4—52no—
1412C4—156no—
1413C4—456no—
1414C4—1352no—
1415C3—23no—
1416C3—41no—
1417C3C22×D32×AGL(1,𝔽5)13yescomplemented
1418C2—36no—
1419C2—51no—
1420C2—51no—
1421C2—96no—
1422C2—156no—
1423C2—272no—
1424C2—456no—
1425C2—1352no—
1426C2D33×AGL(1,𝔽5)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D33×AGL(1,𝔽5)
commutator, hypocenterC33×C5C24×C4
FrattiniC1G
Fitting, socleC2×C33×C5C23×C4
prime radicalC2×D33×D5C2
cosocleC33×D5C25
LCSG ▷ C33×C5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#72222379C2semidirect
2. C2×D32×ΓL(1,𝔽16)C2semidirect
3. C2×D3×ΓL(1,𝔽16)⋊D3C2semidirect
5. C2×#11762195C4semidirect
6. C2×D3×(C3⋊D3)⋊D5C4semidirect
7. C2×D32×D15C4semidirect
8. C2×C5×D33C4semidirect
9. C2×AGL(1,𝔽5)×#1113C2semidirect
10. C2×#11762163C22semidirect
12. C2×D3×C3⋊D3×AGL(1,𝔽5)C2semidirect
13. C2×ΓL(1,𝔽16)⋊(C3⋊D3)C22semidirect
14. C2×AGL(1,𝔽5)×C3⋊(C3⋊D3)C22semidirect
15. C2×D3×C3⋊ΓL(1,𝔽16)C22semidirect
16. C2×C3⋊D3×ΓL(1,𝔽16)C22semidirect
19. D33×AGL(1,𝔽5)C2direct (N × H)
20. AGL(1,𝔽5)×#1113C22semidirect
21. #72222379C22semidirect
22. D3×ΓL(1,𝔽16)⋊D3C22semidirect
23. D32×ΓL(1,𝔽16)C22semidirect
24. D33×D5C4semidirect
26. D3×C3⋊D3×AGL(1,𝔽5)C22semidirect
27. C2×C3×D32×AGL(1,𝔽5)C2semidirect
28. C2×C3×D3×ΓL(1,𝔽16)C22semidirect
29. C2×C32×D3×AGL(1,𝔽5)C22semidirect
30. C2×C3×ΓL(1,𝔽16)⋊D3C22semidirect
32. C3×D32×AGL(1,𝔽5)C22semidirect
33. C2×C3×C3⋊D3×AGL(1,𝔽5)C22semidirect
47. C2×D32×AGL(1,𝔽5)D3direct (N × H)
48. C2×C5⋊#1113C2×C4semidirect
49. C2×C5×#1113C2×C4semidirect
50. C2×D15⋊(C3⋊D3)C2×C4semidirect
51. C2×D3×C3⋊D15C2×C4semidirect
52. C2×C3⋊D3×D15C2×C4semidirect
53. C2×C5×D3×C3⋊D3C2×C4semidirect
55. C2×C3×(C3⋊D3)⋊D5C2×C4semidirect
56. C2×C3×D3×D15C2×C4semidirect
57. C2×C3×C5×D32C2×C4semidirect
60. C2×C3⋊(C3⋊ΓL(1,𝔽16))C23semidirect
61. C2×C3×C3⋊ΓL(1,𝔽16)C23semidirect
62. C2×C32×ΓL(1,𝔽16)C23semidirect
63. C2×C33×AGL(1,𝔽5)C23semidirect
64. #11762195C2×C4semidirect
65. D3×(C3⋊D3)⋊D5C2×C4semidirect
66. D32×D15C2×C4semidirect
67. C5×D33C2×C4semidirect
68. D5×#1113C2×C4semidirect
70. D3×D5×C3⋊D3C2×C4semidirect
72. C3×D32×D5C2×C4semidirect
74. #11762163C23semidirect
75. ΓL(1,𝔽16)⋊(C3⋊D3)C23semidirect
76. C3⋊D3×ΓL(1,𝔽16)C23semidirect
77. D3×C3⋊ΓL(1,𝔽16)C23semidirect
78. AGL(1,𝔽5)×C3⋊(C3⋊D3)C23semidirect
79. C3×ΓL(1,𝔽16)⋊D3C23semidirect
80. C3×D3×ΓL(1,𝔽16)C23semidirect
81. C3×C3⋊D3×AGL(1,𝔽5)C23semidirect
82. C32×D3×AGL(1,𝔽5)C23semidirect
113. C2×ΓL(1,𝔽16)⋊D3C2×D3semidirect
120. C2×D3×ΓL(1,𝔽16)C2×D3semidirect
127. C2×C3⋊D3×AGL(1,𝔽5)C2×D3semidirect
134. C2×C3×D3×AGL(1,𝔽5)C2×D3semidirect
141. D32×AGL(1,𝔽5)C2×D3direct (N × H)
143. C2×C3⋊(C3⋊D15)C22×C4semidirect
144. C2×C5×C3⋊(C3⋊D3)C22×C4semidirect
145. C2×C3×C3⋊D15C22×C4semidirect
146. C2×C3×C5×C3⋊D3C22×C4semidirect
147. C2×C32×D15C22×C4semidirect
148. C2×C32×C5×D3C22×C4semidirect
150. C5⋊#1113C22×C4semidirect
151. C5×#1113C22×C4semidirect
152. D15⋊(C3⋊D3)C22×C4semidirect
153. D3×C3⋊D15C22×C4semidirect
154. C3⋊D3×D15C22×C4semidirect
155. C5×D3×C3⋊D3C22×C4semidirect
156. D5×C3⋊(C3⋊D3)C22×C4semidirect
158. C3×(C3⋊D3)⋊D5C22×C4semidirect
159. C3×D3×D15C22×C4semidirect
160. C3×C5×D32C22×C4semidirect
161. C3×D5×C3⋊D3C22×C4semidirect
163. C32×D3×D5C22×C4semidirect
165. C3⋊(C3⋊ΓL(1,𝔽16))C24semidirect
166. C3×C3⋊ΓL(1,𝔽16)C24semidirect
167. C32×ΓL(1,𝔽16)C24semidirect
168. C33×AGL(1,𝔽5)C24semidirect
190. C2×D33AGL(1,𝔽5)direct (N × H)
215. C2×(C3⋊D3)⋊D5C4×D3semidirect
222. C2×D3×D15C4×D3semidirect
227. C2×C5×D32C4×D3semidirect
248. C2×C3⋊ΓL(1,𝔽16)C22×D3semidirect
253. C2×C3×ΓL(1,𝔽16)C22×D3semidirect
258. C2×C32×AGL(1,𝔽5)C22×D3semidirect
268. D32×D5C4×D3semidirect
273. ΓL(1,𝔽16)⋊D3C22×D3semidirect
279. D3×ΓL(1,𝔽16)C22×D3semidirect
285. C3⋊D3×AGL(1,𝔽5)C22×D3semidirect
291. C3×D3×AGL(1,𝔽5)C22×D3semidirect
306. C2×C33×C5C23×C4semidirect
307. C3⋊(C3⋊D15)C23×C4semidirect
308. C5×C3⋊(C3⋊D3)C23×C4semidirect
309. C3×C3⋊D15C23×C4semidirect
310. C3×C5×C3⋊D3C23×C4semidirect
311. C32×D15C23×C4semidirect
312. C32×C5×D3C23×C4semidirect
313. C33×D5C23×C4semidirect
364. C2×D3×AGL(1,𝔽5)D32direct (N × H)
371. C2×#1113C2×AGL(1,𝔽5)semidirect
377. C2×D3×C3⋊D3C2×AGL(1,𝔽5)semidirect
382. C2×C3×D32C2×AGL(1,𝔽5)semidirect
386. D33C2×AGL(1,𝔽5)direct (N × H)
406. C2×C3⋊D15C2×C4×D3semidirect
411. C2×C5×C3⋊D3C2×C4×D3semidirect
416. C2×C3×D15C2×C4×D3semidirect
421. C2×C3×C5×D3C2×C4×D3semidirect
431. (C3⋊D3)⋊D5C2×C4×D3semidirect
437. D3×D15C2×C4×D3semidirect
441. C5×D32C2×C4×D3semidirect
450. D5×C3⋊D3C2×C4×D3semidirect
460. C3×D3×D5C2×C4×D3semidirect
465. C3⋊ΓL(1,𝔽16)C23×D3semidirect
469. C3×ΓL(1,𝔽16)C23×D3semidirect
473. C32×AGL(1,𝔽5)C23×D3semidirect
532. C33×C5C24×C4semidirect
592. C2×ΓL(1,𝔽16)C2×D32semidirect
603. C2×C3×AGL(1,𝔽5)C2×D32semidirect
618. D3×AGL(1,𝔽5)C2×D32direct (N × H)
623. C2×C3⋊(C3⋊D3)C22×AGL(1,𝔽5)semidirect
627. C2×C3×C3⋊D3C22×AGL(1,𝔽5)semidirect
631. C2×C32×D3C22×AGL(1,𝔽5)semidirect
633. #1113C22×AGL(1,𝔽5)semidirect
637. D3×C3⋊D3C22×AGL(1,𝔽5)semidirect
640. C3×D32C22×AGL(1,𝔽5)semidirect
661. C2×C32×C5C22×C4×D3semidirect
665. C3⋊D15C22×C4×D3semidirect
669. C5×C3⋊D3C22×C4×D3semidirect
673. C3×D15C22×C4×D3semidirect
677. C3×C5×D3C22×C4×D3semidirect
683. C32×D5C22×C4×D3semidirect
757. C2×D32D3×AGL(1,𝔽5)direct (N × H)
810. C2×D15C4×D32semidirect
821. C2×C5×D3C4×D32semidirect
855. D3×D5C4×D32semidirect
862. ΓL(1,𝔽16)C22×D32semidirect
868. C3×AGL(1,𝔽5)C22×D32semidirect
871. C2×C33C23×AGL(1,𝔽5)semidirect
873. C3⋊(C3⋊D3)C23×AGL(1,𝔽5)semidirect
875. C3×C3⋊D3C23×AGL(1,𝔽5)semidirect
877. C32×D3C23×AGL(1,𝔽5)semidirect
930. C32×C5C23×C4×D3semidirect
965. C2×AGL(1,𝔽5)D33direct (N × H)
992. C2×C3⋊D3C2×D3×AGL(1,𝔽5)semidirect
1012. C2×C3×D3C2×D3×AGL(1,𝔽5)semidirect
1026. D32C2×D3×AGL(1,𝔽5)direct (N × H)
1052. C2×C3×C5C2×C4×D32semidirect
1058. D15C2×C4×D32semidirect
1066. C3×D5C2×C4×D32semidirect
1073. C5×D3C2×C4×D32semidirect
1074. C33C24×AGL(1,𝔽5)semidirect
1186. AGL(1,𝔽5)C2×D33direct (N × H)
1197. C2×C32C22×D3×AGL(1,𝔽5)semidirect
1205. C3⋊D3C22×D3×AGL(1,𝔽5)semidirect
1213. C3×D3C22×D3×AGL(1,𝔽5)semidirect
1240. C3×C5C22×C4×D32semidirect
1301. C2×D3D32×AGL(1,𝔽5)direct (N × H)
1317. C2×C5C4×D33semidirect
1321. D5C4×D33semidirect
1325. C32C23×D3×AGL(1,𝔽5)semidirect
1375. C2×C3C2×D32×AGL(1,𝔽5)semidirect
1387. D3C2×D32×AGL(1,𝔽5)direct (N × H)
1388. C5C2×C4×D33semidirect
1417. C3C22×D32×AGL(1,𝔽5)semidirect
1426. C2D33×AGL(1,𝔽5)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#722223792
C2×D32×ΓL(1,𝔽16)2
C2×D3×ΓL(1,𝔽16)⋊D32
C2×D33×D52
C2×AGL(1,𝔽5)×#11132
C2×D3×C3⋊D3×AGL(1,𝔽5)2
C22×D32×AGL(1,𝔽5)3
D33×AGL(1,𝔽5)2
C2×C3×D32×AGL(1,𝔽5)2
C2×C4×D335