Finite Group Databasebeta

← C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3 #72217649

Subgroups — C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3 #72217649

Order 25920.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×AGL(1,𝔽5)×SL(2,𝔽3)—91nomaximal
2C2×C3×C4×PSU(3,𝔽2)⋊C3—51nomaximal, Hall
3C2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3—41nomaximal
4C2×C3×(C3⋊ΓL(1,𝔽16))⋊C3—41no—
5C2×C3×AGL(1,𝔽5)×H(3,𝔽3)—41no—
6C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)C311yesmaximal, characteristic, complemented
7C2×C32×D3×AGL(1,𝔽5)—121no—
8C2×C3×#10624307—31no—
9C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C313yesmaximal, direct product factor
10C2×AGL(1,𝔽5)×(C3⋊D3)⋊C3—43no—
11C2×AGL(1,𝔽5)×PSU(3,𝔽2)C3211yescharacteristic, complemented
12C2×C3×D5×PSU(3,𝔽2)⋊C3C211yesmaximal, characteristic
13C22×C3×PSU(3,𝔽2)⋊C3—51no—
14C2×C3×D5×(C3⋊D3)⋊C3—41no—
15C2×C3×D5×PSU(3,𝔽2)C2×C311yescharacteristic
16C2×C3×C5⋊PSU(3,𝔽2)—31no—
17C2×D5×PSU(3,𝔽2)⋊C3C2×C313yes—
18C2×C3×C5×PSU(3,𝔽2)⋊C3C411yescharacteristic, complemented
19C2×C3×C5×PSU(3,𝔽2)C3×C411yescharacteristic, complemented
20C2×C5×PSU(3,𝔽2)⋊C3C3×C413yescomplemented
21C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C212yesmaximal, direct product factor
22C3×C4×PSU(3,𝔽2)⋊C3—52no—
23C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3—42no—
24C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3—42no—
25C3×AGL(1,𝔽5)×PSU(3,𝔽2)—32no—
26C3×AGL(1,𝔽5)×PSU(3,𝔽2)C2×C312yescomplemented
27C3×D5×PSU(3,𝔽2)⋊C3C411yescharacteristic, complemented
28C3×D5×PSU(3,𝔽2)⋊C3C2211yescharacteristic
29C3×C5×PSU(3,𝔽2)⋊C3C2×C411yescharacteristic, complemented
30C3×#10624307—32no—
31C3×#10624307—32no—
32C3×D5×PSU(3,𝔽2)—31no—
33C3×D5×PSU(3,𝔽2)—31no—
34C3×D5×PSU(3,𝔽2)C3×C411yescharacteristic, complemented
35C3×D5×PSU(3,𝔽2)C22×C311yescharacteristic
36C2×C3×AGL(1,𝔽5)×#157—31no—
37C2×C3×D5⋊#157—31no—
38C2×C3×C3⋊D3×AGL(1,𝔽5)A411yescharacteristic
39C2×C3×D5×#157—31no—
40C3×AGL(1,𝔽5)×#157—32no—
41C3×AGL(1,𝔽5)×#157—32no—
42AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C2×C316yesdirect product factor
43D5×PSU(3,𝔽2)⋊C3C3×C413yescomplemented
44D5×PSU(3,𝔽2)⋊C3C22×C313yes—
45C2×C3×C4×PSU(3,𝔽2)—51no—
46C2×C4×PSU(3,𝔽2)⋊C3—53no—
47C2×C3×C5⋊((C3⋊D3)⋊C3)—41no—
48C2×C3×C5×(C3⋊D3)⋊C3—41no—
49C2×C3×D5×H(3,𝔽3)—41no—
50C3×D5×(C3⋊D3)⋊C3—41no—
51C3×D5×(C3⋊D3)⋊C3—41no—
52C3×D5×(C3⋊D3)⋊C3—41no—
53C3×D5×(C3⋊D3)⋊C3—41no—
54C3×(C3⋊ΓL(1,𝔽16))⋊C3—42no—
55C3×AGL(1,𝔽5)×H(3,𝔽3)—42no—
56C2×D5×PSU(3,𝔽2)C2×C3211yescharacteristic
57C2×#10624307—31no—
58C2×AGL(1,𝔽5)×#157—31no—
59AGL(1,𝔽5)×PSU(3,𝔽2)—32no—
60AGL(1,𝔽5)×PSU(3,𝔽2)C2×C3212yescomplemented
61C2×C3×D5×SL(2,𝔽3)—91no—
62C3×AGL(1,𝔽5)×SL(2,𝔽3)—92no—
63C2×C3×PSU(3,𝔽2)⋊C3—51no—
64C2×C3×PSU(3,𝔽2)⋊C3—51no—
65C2×C3×PSU(3,𝔽2)⋊C3AGL(1,𝔽5)11yescharacteristic, direct product factor
66C2×C3×C4×(C3⋊D3)⋊C3—201no—
67C2×C3×D5×C3⋊D3C2×A411yescharacteristic
68C2×C32×D3×D5—121no—
69C2×C3×#4379—31no—
70C2×C3×#4380—61no—
71C2×C3×C5×#157—31no—
72C2×C3×C3⋊ΓL(1,𝔽16)SL(2,𝔽3)11yescharacteristic, complemented
73C2×C32×ΓL(1,𝔽16)—121no—
74C2×C33×AGL(1,𝔽5)—41no—
75C2×C33×AGL(1,𝔽5)—81no—
76C2×C33×AGL(1,𝔽5)SL(2,𝔽3)11yescharacteristic, complemented
77C3×C5⋊PSU(3,𝔽2)—32no—
78C3×C5⋊PSU(3,𝔽2)—31no—
79C3×C5⋊PSU(3,𝔽2)—31no—
80C3×C5×PSU(3,𝔽2)—31no—
81C3×C5×PSU(3,𝔽2)C2×C3×C411yescharacteristic, complemented
82C3×D5×#157—31no—
83C3×D5×#157—31no—
84C3×D5×#157—31no—
85C3×D5×#157—31no—
86C3×D5⋊#157—32no—
87C3×D5⋊#157—61no—
88C3×C3⋊D3×AGL(1,𝔽5)SL(2,𝔽3)12yescomplemented
89C3×C3⋊D3×AGL(1,𝔽5)C2×A412yes—
90C32×D3×AGL(1,𝔽5)—122no—
91C32×D3×AGL(1,𝔽5)—122no—
92C5×PSU(3,𝔽2)⋊C3C2×C3×C413yescomplemented
93C2×D5×(C3⋊D3)⋊C3—43no—
94C2×(C3⋊ΓL(1,𝔽16))⋊C3—43no—
95C2×AGL(1,𝔽5)×H(3,𝔽3)—43no—
96C2×AGL(1,𝔽5)×H(3,𝔽3)—83no—
97AGL(1,𝔽5)×(C3⋊D3)⋊C3—46no—
98AGL(1,𝔽5)×(C3⋊D3)⋊C3—46no—
99C2×C3×Q8×AGL(1,𝔽5)—91no—
100C2×AGL(1,𝔽5)×SL(2,𝔽3)—93no—
101C22×C3×PSU(3,𝔽2)—51no—
102C22×PSU(3,𝔽2)⋊C3—53no—
103C2×C3×C4×#157—151no—
104C2×C3×#3777—151no—
105C3×C4×PSU(3,𝔽2)—52no—
106C3×C4×PSU(3,𝔽2)—152no—
107C4×PSU(3,𝔽2)⋊C3—56no—
108C2×C3×C5×H(3,𝔽3)—41no—
109C3×C5⋊((C3⋊D3)⋊C3)—41no—
110C3×C5⋊((C3⋊D3)⋊C3)—41no—
111C3×C5×(C3⋊D3)⋊C3—41no—
112C3×C5×(C3⋊D3)⋊C3—41no—
113C3×D5×H(3,𝔽3)—41no—
114C3×D5×H(3,𝔽3)—41no—
115C22×C32×AGL(1,𝔽5)—361no—
116C2×C5⋊PSU(3,𝔽2)—31no—
117C2×C5×PSU(3,𝔽2)C32×C411yescharacteristic, complemented
118C2×D5×#157—31no—
119C2×D5⋊#157—31no—
120C2×C3⋊D3×AGL(1,𝔽5)C3×A411yescharacteristic
121C2×C3×D3×AGL(1,𝔽5)—121no—
122C2×C3×D3×AGL(1,𝔽5)—123no—
123D5×PSU(3,𝔽2)—31no—
124D5×PSU(3,𝔽2)—31no—
125D5×PSU(3,𝔽2)C32×C411yescharacteristic, complemented
126D5×PSU(3,𝔽2)C22×C3211yescharacteristic
127#10624307—32no—
128#10624307—32no—
129AGL(1,𝔽5)×#157—32no—
130AGL(1,𝔽5)×#157—32no—
131C2×C3×C5×SL(2,𝔽3)—91no—
132C3×D5×SL(2,𝔽3)—91no—
133C3×D5×SL(2,𝔽3)—91no—
134C3×PSU(3,𝔽2)⋊C3C2×AGL(1,𝔽5)11yescharacteristic, direct product factor
135C22×C3×(C3⋊D3)⋊C3—201no—
136C2×C3×C4×H(3,𝔽3)—201no—
137C2×C3×(C3⋊Dic3)⋊C3—201no—
138C3×C4×(C3⋊D3)⋊C3—202no—
139C3×C4×(C3⋊D3)⋊C3—202no—
140C2×C4×PSU(3,𝔽2)—51no—
141C2×C3×C4×SL(2,𝔽3)—451no—
142C2×C3×C3⋊D15#41⋊C311yescharacteristic
143C2×C3×C5×C3⋊D3C4×A411yescharacteristic
144C2×C32×D15—121no—
145C2×C32×C5×D3—121no—
146C2×C33×D5—41no—
147C2×C33×D5—81no—
148C2×C33×D5C2×SL(2,𝔽3)11yescharacteristic
149C3×D5×C3⋊D3C4×A411yescharacteristic
150C3×D5×C3⋊D3C2×SL(2,𝔽3)11yescharacteristic
151C3×D5×C3⋊D3#41⋊C311yescharacteristic
152C3×D5×C3⋊D3C22×A411yescharacteristic
153C32×D3×D5—121no—
154C32×D3×D5—121no—
155C32×D3×D5—121no—
156C32×D3×D5—121no—
157C3×#4379—31no—
158C3×#4379—31no—
159C3×#4380—62no—
160C3×C5×#157—31no—
161C3×C5×#157—31no—
162C3×C3⋊ΓL(1,𝔽16)C2×SL(2,𝔽3)12yescomplemented
163C32×ΓL(1,𝔽16)—122no—
164C33×AGL(1,𝔽5)—42no—
165C33×AGL(1,𝔽5)—82no—
166C33×AGL(1,𝔽5)C2×SL(2,𝔽3)12yescomplemented
167C2×C5⋊((C3⋊D3)⋊C3)—43no—
168C2×C5×(C3⋊D3)⋊C3—43no—
169C2×D5×H(3,𝔽3)—43no—
170C2×D5×H(3,𝔽3)—83no—
171D5×(C3⋊D3)⋊C3—43no—
172D5×(C3⋊D3)⋊C3—43no—
173D5×(C3⋊D3)⋊C3—43no—
174D5×(C3⋊D3)⋊C3—43no—
175(C3⋊ΓL(1,𝔽16))⋊C3—46no—
176AGL(1,𝔽5)×H(3,𝔽3)—46no—
177AGL(1,𝔽5)×H(3,𝔽3)—86no—
178C2×C3×Q8×D5—91no—
179C3×Q8×AGL(1,𝔽5)—92no—
180C3×Q8×AGL(1,𝔽5)—272no—
181C2×C3×C4⋊AGL(1,𝔽5)—271no—
182C2×C3×C4×AGL(1,𝔽5)—271no—
183C2×D5×SL(2,𝔽3)—93no—
184AGL(1,𝔽5)×SL(2,𝔽3)—96no—
185C22×C3×#157—151no—
186C22×C3×#157—151no—
187C2×C3×PSU(3,𝔽2)—51no—
188C2×C3×PSU(3,𝔽2)—51no—
189C2×C3×PSU(3,𝔽2)—151no—
190C2×C3×PSU(3,𝔽2)—151no—
191C2×C3×PSU(3,𝔽2)—151no—
192C2×C3×PSU(3,𝔽2)C3×AGL(1,𝔽5)11yescharacteristic, complemented
193C2×PSU(3,𝔽2)⋊C3—53no—
194C2×PSU(3,𝔽2)⋊C3—53no—
195C2×PSU(3,𝔽2)⋊C3C3×AGL(1,𝔽5)13yesdirect product factor
196C2×C3×C4×C3⋊D3—51no—
197C2×C32×C4×D3—601no—
198C3×C4×#157—152no—
199C3×C4×#157—152no—
200C3×#3777—152no—
201C3×#3777—152no—
202C2×C4×(C3⋊D3)⋊C3—203no—
203C3×C5×H(3,𝔽3)—41noHall
204C22×C32×D5—361no—
205C2×D5×C3⋊D3C2×C3×A411yescharacteristic
206C2×C3×D3×D5—121no—
207C2×C3×D3×D5—123no—
208C2×#4380—61no—
209C2×#4379—31no—
210C2×C5×#157—31no—
211C2×C3⋊ΓL(1,𝔽16)C3×SL(2,𝔽3)11yescharacteristic, complemented
212C2×C3×ΓL(1,𝔽16)—121no—
213C2×C3×ΓL(1,𝔽16)—123no—
214C2×C32×AGL(1,𝔽5)—41no—
215C2×C32×AGL(1,𝔽5)—43no—
216C2×C32×AGL(1,𝔽5)—81no—
217C2×C32×AGL(1,𝔽5)—83no—
218C2×C32×AGL(1,𝔽5)—121no—
219C2×C32×AGL(1,𝔽5)—241no—
220C2×C32×AGL(1,𝔽5)—242no—
221C2×C32×AGL(1,𝔽5)—241no—
222C2×C32×AGL(1,𝔽5)—362no—
223C2×C32×AGL(1,𝔽5)—362no—
224C2×C32×AGL(1,𝔽5)—361no—
225C2×C32×AGL(1,𝔽5)C3×SL(2,𝔽3)11yescharacteristic, complemented
226C5⋊PSU(3,𝔽2)—32no—
227C5⋊PSU(3,𝔽2)—31no—
228C5⋊PSU(3,𝔽2)—31no—
229C5×PSU(3,𝔽2)—31no—
230C5×PSU(3,𝔽2)C2×C32×C411yescharacteristic, complemented
231D5⋊#157—32no—
232D5⋊#157—61no—
233D5×#157—31no—
234D5×#157—31no—
235D5×#157—31no—
236D5×#157—31no—
237C3⋊D3×AGL(1,𝔽5)C3×SL(2,𝔽3)12yescomplemented
238C3⋊D3×AGL(1,𝔽5)C2×C3×A412yes—
239C3×D3×AGL(1,𝔽5)—122no—
240C3×D3×AGL(1,𝔽5)—122no—
241C3×D3×AGL(1,𝔽5)—126no—
242C3×D3×AGL(1,𝔽5)—126no—
243C3×C5×SL(2,𝔽3)—91no—
244C22×C3×H(3,𝔽3)—201no—
245C2×C3×(C3⋊D3)⋊C3—41no—
246C2×C3×(C3⋊D3)⋊C3—201no—
247C2×C3×(C3⋊D3)⋊C3—201no—
248C2×C3×(C3⋊D3)⋊C3—201no—
249C2×C3×(C3⋊D3)⋊C3—201no—
250C2×C3×(C3⋊D3)⋊C3—201no—
251C3×C4×H(3,𝔽3)—202no—
252C3×(C3⋊Dic3)⋊C3—202no—
253C2×Q8×AGL(1,𝔽5)—91noHall
254C22×PSU(3,𝔽2)—51no—
255C22×C3×SL(2,𝔽3)—451no—
256C2×C4×#157—151no—
257C2×#3777—151no—
258C4×PSU(3,𝔽2)—52no—
259C4×PSU(3,𝔽2)—152no—
260C3×C4×SL(2,𝔽3)—452no—
261C2×C33×C5—41no—
262C2×C33×C5—81no—
263C2×C33×C5C4×SL(2,𝔽3)11yescharacteristic, complemented
264C3×C3⋊D15C4×SL(2,𝔽3)11yescharacteristic, complemented
265C3×C3⋊D15C2×#41⋊C311yescharacteristic
266C3×C5×C3⋊D3C4×SL(2,𝔽3)11yescharacteristic, complemented
267C3×C5×C3⋊D3C2×C4×A411yescharacteristic
268C32×D15—121no—
269C32×D15—121no—
270C32×C5×D3—121no—
271C32×C5×D3—121no—
272C33×D5—41no—
273C33×D5—41no—
274C33×D5—81no—
275C33×D5—81no—
276C33×D5C4×SL(2,𝔽3)11yescharacteristic, complemented
277C33×D5C22×SL(2,𝔽3)11yescharacteristic
278C2×C5×H(3,𝔽3)—43no—
279C2×C5×H(3,𝔽3)—83no—
280C5⋊((C3⋊D3)⋊C3)—43no—
281C5⋊((C3⋊D3)⋊C3)—43no—
282C5×(C3⋊D3)⋊C3—43no—
283C5×(C3⋊D3)⋊C3—43no—
284D5×H(3,𝔽3)—43no—
285D5×H(3,𝔽3)—43no—
286D5×H(3,𝔽3)—83no—
287D5×H(3,𝔽3)—83no—
288C22×C3×AGL(1,𝔽5)—91no—
289C22×C3×AGL(1,𝔽5)—271no—
290C22×C3×AGL(1,𝔽5)—363no—
291C2×D3×AGL(1,𝔽5)—121no—
292C2×C3×C5×Q8—91no—
293C3×Q8×D5—91no—
294C3×Q8×D5—91no—
295C3×Q8×D5—271no—
296C3×Q8×D5—271no—
297C2×C3×C4×D5—271no—
298C2×C3×Dic10—271no—
299C2×C5×SL(2,𝔽3)—93no—
300C3×C4⋊AGL(1,𝔽5)—272no—
301C3×C4⋊AGL(1,𝔽5)—272no—
302C3×C4×AGL(1,𝔽5)—272no—
303C3×C4×AGL(1,𝔽5)—272no—
304D5×SL(2,𝔽3)—93no—
305D5×SL(2,𝔽3)—93no—
306C22×C3×C3⋊D3—51no—
307C22×C32×D3—601no—
308C2×C3×#157—31no—
309C2×C3×#157—151no—
310C2×C3×#157—151no—
311C2×C3×#157—151no—
312C2×C3×#157—151no—
313C2×C3×#157—151no—
314C2×C3×#157—152no—
315C2×C3×#157—301no—
316C2×C3×#157—301no—
317C3×PSU(3,𝔽2)—31no—
318C3×PSU(3,𝔽2)—152no—
319C3×PSU(3,𝔽2)—151no—
320C3×PSU(3,𝔽2)—151no—
321C3×PSU(3,𝔽2)C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
322PSU(3,𝔽2)⋊C3C2×C3×AGL(1,𝔽5)13yesdirect product factor
323C2×C33×C4—51no—
324C2×C33×C4—201no—
325C2×C33×C4—401no—
326C2×C3×C3⋊Dic3—51no—
327C3×C4×C3⋊D3—52no—
328C3×C4×C3⋊D3—52no—
329C2×C32×Dic3—601no—
330C32×C4×D3—602no—
331C32×C4×D3—602no—
332C22×(C3⋊D3)⋊C3—203no—
333C2×C4×H(3,𝔽3)—203no—
334C2×C4×H(3,𝔽3)—403no—
335C2×(C3⋊Dic3)⋊C3—203no—
336C4×(C3⋊D3)⋊C3—206no—
337C4×(C3⋊D3)⋊C3—206no—
338C2×C3×C4×Q8—451no—
339C2×C4×SL(2,𝔽3)—453no—
340C22×C32×C5—361no—
341C2×C3⋊D15C3×#41⋊C311yescharacteristic
342C2×C5×C3⋊D3C3×C4×A411yescharacteristic
343C2×C3×D15—121no—
344C2×C3×D15—123no—
345C2×C3×C5×D3—121no—
346C2×C3×C5×D3—123no—
347C2×C32×D5—41no—
348C2×C32×D5—43no—
349C2×C32×D5—81no—
350C2×C32×D5—83no—
351C2×C32×D5—121no—
352C2×C32×D5—241no—
353C2×C32×D5—242no—
354C2×C32×D5—241no—
355C2×C32×D5—361no—
356C2×C32×D5—361no—
357C2×C32×D5—361no—
358C2×C32×D5—361no—
359C2×C32×D5—361no—
360C2×C32×D5C2×C3×SL(2,𝔽3)11yescharacteristic
361D5×C3⋊D3C3×C4×A411yescharacteristic
362D5×C3⋊D3C2×C3×SL(2,𝔽3)11yescharacteristic
363D5×C3⋊D3C3×#41⋊C311yescharacteristic
364D5×C3⋊D3C22×C3×A411yescharacteristic
365C3×D3×D5—121no—
366C3×D3×D5—121no—
367C3×D3×D5—121no—
368C3×D3×D5—121no—
369C3×D3×D5—123no—
370C3×D3×D5—123no—
371C3×D3×D5—123no—
372C3×D3×D5—123no—
373#4380—62no—
374#4379—31no—
375#4379—31no—
376C5×#157—31no—
377C5×#157—31no—
378C3⋊ΓL(1,𝔽16)C2×C3×SL(2,𝔽3)12yescomplemented
379C3×ΓL(1,𝔽16)—122no—
380C3×ΓL(1,𝔽16)—126no—
381C32×AGL(1,𝔽5)—42no—
382C32×AGL(1,𝔽5)—46no—
383C32×AGL(1,𝔽5)—82no—
384C32×AGL(1,𝔽5)—86no—
385C32×AGL(1,𝔽5)—122no—
386C32×AGL(1,𝔽5)—242no—
387C32×AGL(1,𝔽5)—244no—
388C32×AGL(1,𝔽5)—242no—
389C32×AGL(1,𝔽5)—362no—
390C32×AGL(1,𝔽5)C2×C3×SL(2,𝔽3)12yescomplemented
391C2×C3×H(3,𝔽3)—41no—
392C2×C3×H(3,𝔽3)—201no—
393C2×C3×H(3,𝔽3)—201no—
394C3×(C3⋊D3)⋊C3—41no—
395C3×(C3⋊D3)⋊C3—41no—
396C3×(C3⋊D3)⋊C3—201no—
397C3×(C3⋊D3)⋊C3—201no—
398C2×Q8×D5—91no—
399Q8×AGL(1,𝔽5)—92no—
400Q8×AGL(1,𝔽5)—272no—
401C2×C4⋊AGL(1,𝔽5)—271no—
402C2×C4×AGL(1,𝔽5)—271no—
403C22×#157—151no—
404C22×#157—151no—
405C2×PSU(3,𝔽2)—51no—
406C2×PSU(3,𝔽2)—51no—
407C2×PSU(3,𝔽2)—151no—
408C2×PSU(3,𝔽2)—151no—
409C2×PSU(3,𝔽2)—151no—
410C2×PSU(3,𝔽2)C32×AGL(1,𝔽5)11yescharacteristic, complemented
411C22×C32×C4—1801no—
412C2×C4×C3⋊D3—51no—
413C2×C3×C4×D3—601no—
414C2×C3×C4×D3—603no—
415C2×C3×SL(2,𝔽3)—91no—
416C2×C3×SL(2,𝔽3)—451no—
417C2×C3×SL(2,𝔽3)—451no—
418C4×#157—152no—
419C4×#157—152no—
420#3777—152no—
421#3777—152no—
422C33×C5—41no—
423C33×C5—81no—
424C33×C5C2×C4×SL(2,𝔽3)11yescharacteristic, complemented
425C5×H(3,𝔽3)—43no—
426C5×H(3,𝔽3)—83no—
427C22×C3×D5—91no—
428C22×C3×D5—363no—
429C2×D3×D5—121no—
430C2×ΓL(1,𝔽16)—121no—
431C2×C3×AGL(1,𝔽5)—41no—
432C2×C3×AGL(1,𝔽5)—81no—
433C2×C3×AGL(1,𝔽5)—91no—
434C2×C3×AGL(1,𝔽5)—92no—
435C2×C3×AGL(1,𝔽5)—92no—
436C2×C3×AGL(1,𝔽5)—123no—
437C2×C3×AGL(1,𝔽5)—243no—
438C2×C3×AGL(1,𝔽5)—272no—
439C2×C3×AGL(1,𝔽5)—366no—
440C2×C3×AGL(1,𝔽5)—366no—
441C2×C3×AGL(1,𝔽5)—363no—
442C2×C3×AGL(1,𝔽5)—541no—
443C2×C3×AGL(1,𝔽5)—541no—
444C2×C3×AGL(1,𝔽5)PSU(3,𝔽2)⋊C311yescharacteristic, direct product factor
445D3×AGL(1,𝔽5)—122no—
446D3×AGL(1,𝔽5)—122no—
447C3×C5×Q8—91no—
448C3×C5×Q8—271no—
449C2×C3×C4×C5—271no—
450C2×C3×Dic5—271no—
451C3×C4×D5—271no—
452C3×C4×D5—271no—
453C3×C4×D5—271no—
454C3×C4×D5—271no—
455C3×Dic10—272no—
456C3×Dic10—271no—
457C3×Dic10—271no—
458C5×SL(2,𝔽3)—93no—
459C22×C33—51no—
460C22×C33—201no—
461C22×C33—401no—
462C2×C3×C3⋊D3—51no—
463C2×C3×C3⋊D3—51no—
464C2×C3×C3⋊D3—51no—
465C2×C3×C3⋊D3—51no—
466C2×C3×C3⋊D3—51no—
467C2×C3×C3⋊D3A4×AGL(1,𝔽5)11yescharacteristic
468C2×C32×D3—121no—
469C2×C32×D3—601no—
470C2×C32×D3—601no—
471C2×C32×D3—601no—
472C2×C32×D3—601no—
473C2×C32×D3—601no—
474C3×#157—31no—
475C3×#157—31no—
476C3×#157—151no—
477C3×#157—151no—
478C3×#157—302no—
479C33×C4—52no—
480C33×C4—202no—
481C33×C4—402no—
482C3×C3⋊Dic3—52no—
483C32×Dic3—602no—
484C22×H(3,𝔽3)—203no—
485C22×H(3,𝔽3)—403no—
486C2×(C3⋊D3)⋊C3—43no—
487C2×(C3⋊D3)⋊C3—203no—
488C2×(C3⋊D3)⋊C3—203no—
489C2×(C3⋊D3)⋊C3—203no—
490C2×(C3⋊D3)⋊C3—203no—
491C2×(C3⋊D3)⋊C3—203no—
492C4×H(3,𝔽3)—206no—
493C4×H(3,𝔽3)—406no—
494(C3⋊Dic3)⋊C3—206no—
495C22×C3×Q8—451no—
496C22×SL(2,𝔽3)—453no—
497C3×C4×Q8—452no—
498C3×C4×Q8—1352no—
499C2×C3×C4⋊C4—1351no—
500C2×C3×C42—1351no—
501C4×SL(2,𝔽3)—456no—
502C2×C32×C5—41no—
503C2×C32×C5—43no—
504C2×C32×C5—81no—
505C2×C32×C5—83no—
506C2×C32×C5—121no—
507C2×C32×C5—241no—
508C2×C32×C5—242no—
509C2×C32×C5—241no—
510C2×C32×C5—361no—
511C2×C32×C5—361no—
512C2×C32×C5C3×C4×SL(2,𝔽3)11yescharacteristic, complemented
513C3⋊D15C3×C4×SL(2,𝔽3)11yescharacteristic, complemented
514C3⋊D15C2×C3×#41⋊C311yescharacteristic
515C5×C3⋊D3C3×C4×SL(2,𝔽3)11yescharacteristic, complemented
516C5×C3⋊D3C2×C3×C4×A411yescharacteristic
517C3×D15—121no—
518C3×D15—121no—
519C3×D15—123no—
520C3×D15—123no—
521C3×C5×D3—121no—
522C3×C5×D3—121no—
523C3×C5×D3—123no—
524C3×C5×D3—123no—
525C32×D5—41no—
526C32×D5—41no—
527C32×D5—43no—
528C32×D5—43no—
529C32×D5—81no—
530C32×D5—81no—
531C32×D5—83no—
532C32×D5—83no—
533C32×D5—121no—
534C32×D5—121no—
535C32×D5—241no—
536C32×D5—241no—
537C32×D5—242no—
538C32×D5—242no—
539C32×D5—241no—
540C32×D5—241no—
541C32×D5—361no—
542C32×D5—361no—
543C32×D5C3×C4×SL(2,𝔽3)11yescharacteristic, complemented
544C32×D5C22×C3×SL(2,𝔽3)11yescharacteristic
545C3×H(3,𝔽3)—41noSylow
546C22×AGL(1,𝔽5)—91no—
547C22×AGL(1,𝔽5)—271no—
548C2×C5×Q8—91no—
549Q8×D5—91no—
550Q8×D5—91no—
551Q8×D5—271no—
552Q8×D5—271no—
553C2×C4×D5—271no—
554C2×Dic10—271no—
555C4⋊AGL(1,𝔽5)—272no—
556C4⋊AGL(1,𝔽5)—272no—
557C4×AGL(1,𝔽5)—272no—
558C4×AGL(1,𝔽5)—272no—
559C23×C32—1801no—
560C22×C3⋊D3—51no—
561C22×C3×D3—601no—
562C22×C3×D3—603no—
563C2×#157—31no—
564C2×#157—151no—
565C2×#157—151no—
566C2×#157—151no—
567C2×#157—151no—
568C2×#157—151no—
569C2×#157—152no—
570C2×#157—301no—
571C2×#157—301no—
572PSU(3,𝔽2)—31no—
573PSU(3,𝔽2)—151no—
574PSU(3,𝔽2)—151no—
575PSU(3,𝔽2)—152no—
576PSU(3,𝔽2)C2×C32×AGL(1,𝔽5)11yescharacteristic, complemented
577C2×C32×C4—51no—
578C2×C32×C4—201no—
579C2×C32×C4—203no—
580C2×C32×C4—401no—
581C2×C32×C4—403no—
582C2×C32×C4—601no—
583C2×C32×C4—1201no—
584C2×C32×C4—1201no—
585C2×C32×C4—1202no—
586C2×C32×C4—1802no—
587C2×C32×C4—1802no—
588C2×C32×C4—1801no—
589C2×C3⋊Dic3—51no—
590C4×C3⋊D3—52no—
591C4×C3⋊D3—52no—
592C2×C3×Dic3—601no—
593C2×C3×Dic3—603no—
594C3×C4×D3—602no—
595C3×C4×D3—602no—
596C3×C4×D3—606no—
597C3×C4×D3—606no—
598C3×SL(2,𝔽3)—91no—
599C2×C4×Q8—451noSylow
600C22×C3×C5—91no—
601C22×C3×C5—363no—
602C2×D15—121no—
603C2×C5×D3—121no—
604C2×C3×D5—41no—
605C2×C3×D5—81no—
606C2×C3×D5—91no—
607C2×C3×D5—91no—
608C2×C3×D5—91no—
609C2×C3×D5—91no—
610C2×C3×D5—91no—
611C2×C3×D5—123no—
612C2×C3×D5—243no—
613C2×C3×D5—363no—
614C2×C3×D5—363no—
615C2×C3×D5—363no—
616C2×C3×D5—363no—
617C2×C3×D5—363no—
618C2×C3×D5C2×PSU(3,𝔽2)⋊C311yescharacteristic
619D3×D5—121no—
620D3×D5—121no—
621D3×D5—121no—
622D3×D5—121no—
623ΓL(1,𝔽16)—122no—
624C3×AGL(1,𝔽5)—42no—
625C3×AGL(1,𝔽5)—82no—
626C3×AGL(1,𝔽5)—92no—
627C3×AGL(1,𝔽5)—126no—
628C3×AGL(1,𝔽5)—246no—
629C3×AGL(1,𝔽5)—366no—
630C3×AGL(1,𝔽5)—542no—
631C3×AGL(1,𝔽5)C2×PSU(3,𝔽2)⋊C312yesdirect product factor
632C3×C4×C5—271no—
633C3×C4×C5—271no—
634C3×Dic5—271no—
635C3×Dic5—271no—
636C2×C33—41no—
637C2×C33—51no—
638C2×C33—51no—
639C2×C33—81no—
640C2×C33—201no—
641C2×C33—201no—
642C2×C33—401no—
643C2×C33—401no—
644C2×C33AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
645C3×C3⋊D3—51no—
646C3×C3⋊D3—51no—
647C3×C3⋊D3AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
648C3×C3⋊D3C2×A4×AGL(1,𝔽5)11yescharacteristic
649C32×D3—121no—
650C32×D3—121no—
651C32×D3—601no—
652C32×D3—601no—
653C2×H(3,𝔽3)—43no—
654C2×H(3,𝔽3)—83no—
655C2×H(3,𝔽3)—203no—
656C2×H(3,𝔽3)—203no—
657C2×H(3,𝔽3)—403no—
658C2×H(3,𝔽3)—403no—
659(C3⋊D3)⋊C3—43no—
660(C3⋊D3)⋊C3—43no—
661(C3⋊D3)⋊C3—203no—
662(C3⋊D3)⋊C3—203no—
663C2×C3×Q8—91no—
664C2×C3×Q8—451no—
665C2×C3×Q8—451no—
666C2×C3×Q8—1351no—
667C2×C3×Q8—1351no—
668C2×C3×Q8—1351no—
669C22×C3×C4—451no—
670C22×C3×C4—1351no—
671C22×C3×C4—1351no—
672C22×C3×C4—1803no—
673C2×C4×D3—601no—
674C2×SL(2,𝔽3)—93no—
675C2×SL(2,𝔽3)—453no—
676C2×SL(2,𝔽3)—453no—
677C3×C4⋊C4—1352no—
678C3×C4⋊C4—1352no—
679C3×C42—1352no—
680C3×C42—1352no—
681C32×C5—41no—
682C32×C5—43no—
683C32×C5—81no—
684C32×C5—83no—
685C32×C5—121no—
686C32×C5—241no—
687C32×C5—242no—
688C32×C5—241no—
689C32×C5C2×C3×C4×SL(2,𝔽3)11yescharacteristic, complemented
690C22×D5—91no—
691C2×AGL(1,𝔽5)—91no—
692C2×AGL(1,𝔽5)—92no—
693C2×AGL(1,𝔽5)—92no—
694C2×AGL(1,𝔽5)—272no—
695C2×AGL(1,𝔽5)—541no—
696C2×AGL(1,𝔽5)—541no—
697C2×AGL(1,𝔽5)C3×PSU(3,𝔽2)⋊C311yescharacteristic, direct product factor
698C5×Q8—91no—
699C5×Q8—271no—
700C2×C4×C5—271no—
701C2×Dic5—271no—
702C4×D5—271no—
703C4×D5—271no—
704C4×D5—271no—
705C4×D5—271no—
706Dic10—272no—
707Dic10—271no—
708Dic10—271no—
709C22×C32—51no—
710C22×C32—201no—
711C22×C32—203no—
712C22×C32—361no—
713C22×C32—401no—
714C22×C32—403no—
715C22×C32—601no—
716C22×C32—1201no—
717C22×C32—1201no—
718C22×C32—1202no—
719C22×C32—1801no—
720C22×C32—1801no—
721C22×C32—1801no—
722C22×C32—1801no—
723C22×C32—1801no—
724C2×C3⋊D3—51no—
725C2×C3⋊D3—51no—
726C2×C3⋊D3—51no—
727C2×C3⋊D3—51no—
728C2×C3⋊D3—51no—
729C2×C3⋊D3C3×A4×AGL(1,𝔽5)11yescharacteristic
730C2×C3×D3—121no—
731C2×C3×D3—123no—
732C2×C3×D3—601no—
733C2×C3×D3—601no—
734C2×C3×D3—601no—
735C2×C3×D3—601no—
736C2×C3×D3—601no—
737C2×C3×D3—603no—
738C2×C3×D3—603no—
739C2×C3×D3—603no—
740C2×C3×D3—603no—
741C2×C3×D3—603no—
742#157—31no—
743#157—31no—
744#157—151no—
745#157—151no—
746#157—302no—
747C32×C4—52no—
748C32×C4—202no—
749C32×C4—206no—
750C32×C4—402no—
751C32×C4—406no—
752C32×C4—602no—
753C32×C4—1202no—
754C32×C4—1202no—
755C32×C4—1204no—
756C32×C4—1802no—
757C3⋊Dic3—52no—
758C3×Dic3—602no—
759C3×Dic3—606no—
760C22×Q8—451no—
761C4×Q8—452no—
762C4×Q8—1352no—
763C2×C4⋊C4—1351no—
764C2×C42—1351no—
765C2×C3×C5—41no—
766C2×C3×C5—81no—
767C2×C3×C5—91no—
768C2×C3×C5—91no—
769C2×C3×C5—123no—
770C2×C3×C5—243no—
771C2×C3×C5—363no—
772C2×C3×C5—363no—
773C2×C3×C5C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented
774D15—121no—
775D15—121no—
776C3×D5—41no—
777C3×D5—41no—
778C3×D5—81no—
779C3×D5—81no—
780C3×D5—91no—
781C3×D5—91no—
782C3×D5—123no—
783C3×D5—123no—
784C3×D5—243no—
785C3×D5—243no—
786C3×D5—363no—
787C3×D5—363no—
788C3×D5C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented
789C3×D5C22×PSU(3,𝔽2)⋊C311yescharacteristic
790C5×D3—121no—
791C5×D3—121no—
792C33—41no—
793C33—81no—
794C33C2×AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
795H(3,𝔽3)—43no—
796H(3,𝔽3)—83no—
797C23×C3—451no—
798C23×C3—1803no—
799C22×D3—601no—
800C3×Q8—91no—
801C3×Q8—271no—
802C3×Q8—1351no—
803C3×Q8—1351no—
804C3×Q8—1352no—
805C2×C3×C4—51no—
806C2×C3×C4—2701no—
807C2×C3×C4—2701no—
808C2×C3×C4—201no—
809C2×C3×C4—271no—
810C2×C3×C4—401no—
811C2×C3×C4—452no—
812C2×C3×C4—452no—
813C2×C3×C4—451no—
814C2×C3×C4—603no—
815C2×C3×C4—1203no—
816C2×C3×C4—1352no—
817C2×C3×C4—1351no—
818C2×C3×C4—1351no—
819C2×C3×C4—1351no—
820C2×C3×C4—1351no—
821C2×C3×C4—1351no—
822C2×C3×C4—1806no—
823C2×C3×C4—1806no—
824C2×C3×C4—1803no—
825C2×Dic3—601no—
826C4×D3—602no—
827C4×D3—602no—
828SL(2,𝔽3)—93no—
829C22×C5—91no—
830C2×D5—91no—
831C2×D5—91no—
832C2×D5—91no—
833C2×D5—91no—
834C2×D5—91no—
835C2×D5C2×C3×PSU(3,𝔽2)⋊C311yescharacteristic
836AGL(1,𝔽5)—92no—
837AGL(1,𝔽5)—542no—
838AGL(1,𝔽5)C2×C3×PSU(3,𝔽2)⋊C312yesdirect product factor
839C4×C5—271no—
840C4×C5—271no—
841Dic5—271no—
842Dic5—271no—
843C2×C32—41no—
844C2×C32—43no—
845C2×C32—51no—
846C2×C32—51no—
847C2×C32—81no—
848C2×C32—83no—
849C2×C32—121no—
850C2×C32—201no—
851C2×C32—201no—
852C2×C32—203no—
853C2×C32—203no—
854C2×C32—241no—
855C2×C32—242no—
856C2×C32—241no—
857C2×C32—361no—
858C2×C32—361no—
859C2×C32—401no—
860C2×C32—401no—
861C2×C32—403no—
862C2×C32—403no—
863C2×C32—601no—
864C2×C32—601no—
865C2×C32—1201no—
866C2×C32—1201no—
867C2×C32—1201no—
868C2×C32—1201no—
869C2×C32—1202no—
870C2×C32—1202no—
871C2×C32—1801no—
872C2×C32—1801no—
873C2×C32C3×AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
874C3⋊D3—51no—
875C3⋊D3—51no—
876C3⋊D3C3×AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
877C3⋊D3C2×C3×A4×AGL(1,𝔽5)11yescharacteristic
878C3×D3—121no—
879C3×D3—121no—
880C3×D3—123no—
881C3×D3—123no—
882C3×D3—601no—
883C3×D3—601no—
884C3×D3—603no—
885C3×D3—603no—
886C2×Q8—91no—
887C2×Q8—451no—
888C2×Q8—451no—
889C2×Q8—1351no—
890C2×Q8—1351no—
891C2×Q8—1351no—
892C22×C4—451no—
893C22×C4—1351no—
894C22×C4—1351no—
895C4⋊C4—1352no—
896C4⋊C4—1352no—
897C42—1352no—
898C42—1352no—
899C3×C5—41no—
900C3×C5—81no—
901C3×C5—123no—
902C3×C5—243no—
903C3×C5C2×C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented
904C22×C3—51no—
905C22×C3—91no—
906C22×C3—201no—
907C22×C3—363no—
908C22×C3—401no—
909C22×C3—451no—
910C22×C3—451no—
911C22×C3—451no—
912C22×C3—451no—
913C22×C3—451no—
914C22×C3—603no—
915C22×C3—1203no—
916C22×C3—1803no—
917C22×C3—1803no—
918C22×C3—1803no—
919C22×C3—1803no—
920C22×C3—1803no—
921C2×D3—121no—
922C2×D3—601no—
923C2×D3—601no—
924C2×D3—601no—
925C2×D3—601no—
926C2×D3—601no—
927C3×C4—52no—
928C3×C4—2702no—
929C3×C4—202no—
930C3×C4—271no—
931C3×C4—271no—
932C3×C4—402no—
933C3×C4—452no—
934C3×C4—606no—
935C3×C4—1206no—
936C3×C4—1351no—
937C3×C4—1351no—
938C3×C4—1806no—
939Dic3—602no—
940C2×C5—91no—
941C2×C5—91no—
942C2×C5C3×C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented
943D5—91no—
944D5—91no—
945D5C3×C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented
946D5C22×C3×PSU(3,𝔽2)⋊C311yescharacteristic
947C32—41no—
948C32—43no—
949C32—81no—
950C32—83no—
951C32—121no—
952C32—241no—
953C32—242no—
954C32—241no—
955C32C2×C3×AGL(1,𝔽5)×SL(2,𝔽3)11yescharacteristic, complemented
956C23—451no—
957Q8—91no—
958Q8—271no—
959Q8—1351no—
960Q8—1351no—
961Q8—1352no—
962C2×C4—51no—
963C2×C4—2701no—
964C2×C4—2701no—
965C2×C4—271no—
966C2×C4—452no—
967C2×C4—452no—
968C2×C4—451no—
969C2×C4—1352no—
970C2×C4—1351no—
971C2×C4—1351no—
972C2×C4—1351no—
973C2×C4—1351no—
974C2×C4—1351no—
975C2×C3—41no—
976C2×C3—51no—
977C2×C3—51no—
978C2×C3—81no—
979C2×C3—91no—
980C2×C3—91no—
981C2×C3—123no—
982C2×C3—201no—
983C2×C3—201no—
984C2×C3—243no—
985C2×C3—363no—
986C2×C3—363no—
987C2×C3—401no—
988C2×C3—401no—
989C2×C3—451no—
990C2×C3—451no—
991C2×C3—603no—
992C2×C3—603no—
993C2×C3—1203no—
994C2×C3—1203no—
995C2×C3—1803no—
996C2×C3—1803no—
997C2×C3AGL(1,𝔽5)×PSU(3,𝔽2)⋊C311yescharacteristic, direct product factor
998D3—121no—
999D3—121no—
1000D3—601no—
1001D3—601no—
1002C5C2×C3×C4×PSU(3,𝔽2)⋊C311yescharacteristic, complemented, Sylow
1003C22—51no—
1004C22—91no—
1005C22—451no—
1006C22—451no—
1007C22—451no—
1008C22—451no—
1009C22—451no—
1010C4—52no—
1011C4—2702no—
1012C4—271no—
1013C4—271no—
1014C4—452no—
1015C4—1351no—
1016C4—1351no—
1017C3—41no—
1018C3—81no—
1019C3—123no—
1020C3—243no—
1021C3C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C311yescharacteristic, direct product factor
1022C2—51no—
1023C2—51no—
1024C2—91no—
1025C2—91no—
1026C2—451no—
1027C2—451no—
1028C2C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3
commutator, hypocenterC5×PSU(3,𝔽2)C2×C32×C4
FrattiniC1G
Fitting, socleC2×C33×C5C4×SL(2,𝔽3)
prime radicalC2×C3×D5×PSU(3,𝔽2)⋊C3C2
cosocleD5×PSU(3,𝔽2)C22×C32
LCSG ▷ C5×PSU(3,𝔽2)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
6. C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)C3semidirect
9. C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C3direct (N × H)
11. C2×AGL(1,𝔽5)×PSU(3,𝔽2)C32semidirect
18. C2×C3×C5×PSU(3,𝔽2)⋊C3C4semidirect
19. C2×C3×C5×PSU(3,𝔽2)C3×C4semidirect
20. C2×C5×PSU(3,𝔽2)⋊C3C3×C4semidirect
21. C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C2direct (N × H)
26. C3×AGL(1,𝔽5)×PSU(3,𝔽2)C2×C3semidirect
27. C3×D5×PSU(3,𝔽2)⋊C3C4semidirect
29. C3×C5×PSU(3,𝔽2)⋊C3C2×C4semidirect
34. C3×D5×PSU(3,𝔽2)C3×C4semidirect
42. AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3C2×C3direct (N × H)
43. D5×PSU(3,𝔽2)⋊C3C3×C4semidirect
60. AGL(1,𝔽5)×PSU(3,𝔽2)C2×C32semidirect
65. C2×C3×PSU(3,𝔽2)⋊C3AGL(1,𝔽5)direct (N × H)
72. C2×C3×C3⋊ΓL(1,𝔽16)SL(2,𝔽3)semidirect
76. C2×C33×AGL(1,𝔽5)SL(2,𝔽3)semidirect
81. C3×C5×PSU(3,𝔽2)C2×C3×C4semidirect
88. C3×C3⋊D3×AGL(1,𝔽5)SL(2,𝔽3)semidirect
92. C5×PSU(3,𝔽2)⋊C3C2×C3×C4semidirect
117. C2×C5×PSU(3,𝔽2)C32×C4semidirect
125. D5×PSU(3,𝔽2)C32×C4semidirect
134. C3×PSU(3,𝔽2)⋊C3C2×AGL(1,𝔽5)direct (N × H)
162. C3×C3⋊ΓL(1,𝔽16)C2×SL(2,𝔽3)semidirect
166. C33×AGL(1,𝔽5)C2×SL(2,𝔽3)semidirect
192. C2×C3×PSU(3,𝔽2)C3×AGL(1,𝔽5)semidirect
195. C2×PSU(3,𝔽2)⋊C3C3×AGL(1,𝔽5)direct (N × H)
211. C2×C3⋊ΓL(1,𝔽16)C3×SL(2,𝔽3)semidirect
225. C2×C32×AGL(1,𝔽5)C3×SL(2,𝔽3)semidirect
230. C5×PSU(3,𝔽2)C2×C32×C4semidirect
237. C3⋊D3×AGL(1,𝔽5)C3×SL(2,𝔽3)semidirect
263. C2×C33×C5C4×SL(2,𝔽3)semidirect
264. C3×C3⋊D15C4×SL(2,𝔽3)semidirect
266. C3×C5×C3⋊D3C4×SL(2,𝔽3)semidirect
276. C33×D5C4×SL(2,𝔽3)semidirect
321. C3×PSU(3,𝔽2)C2×C3×AGL(1,𝔽5)semidirect
322. PSU(3,𝔽2)⋊C3C2×C3×AGL(1,𝔽5)direct (N × H)
378. C3⋊ΓL(1,𝔽16)C2×C3×SL(2,𝔽3)semidirect
390. C32×AGL(1,𝔽5)C2×C3×SL(2,𝔽3)semidirect
410. C2×PSU(3,𝔽2)C32×AGL(1,𝔽5)semidirect
424. C33×C5C2×C4×SL(2,𝔽3)semidirect
444. C2×C3×AGL(1,𝔽5)PSU(3,𝔽2)⋊C3direct (N × H)
512. C2×C32×C5C3×C4×SL(2,𝔽3)semidirect
513. C3⋊D15C3×C4×SL(2,𝔽3)semidirect
515. C5×C3⋊D3C3×C4×SL(2,𝔽3)semidirect
543. C32×D5C3×C4×SL(2,𝔽3)semidirect
576. PSU(3,𝔽2)C2×C32×AGL(1,𝔽5)semidirect
631. C3×AGL(1,𝔽5)C2×PSU(3,𝔽2)⋊C3direct (N × H)
644. C2×C33AGL(1,𝔽5)×SL(2,𝔽3)semidirect
647. C3×C3⋊D3AGL(1,𝔽5)×SL(2,𝔽3)semidirect
689. C32×C5C2×C3×C4×SL(2,𝔽3)semidirect
697. C2×AGL(1,𝔽5)C3×PSU(3,𝔽2)⋊C3direct (N × H)
773. C2×C3×C5C4×PSU(3,𝔽2)⋊C3semidirect
788. C3×D5C4×PSU(3,𝔽2)⋊C3semidirect
794. C33C2×AGL(1,𝔽5)×SL(2,𝔽3)semidirect
838. AGL(1,𝔽5)C2×C3×PSU(3,𝔽2)⋊C3direct (N × H)
873. C2×C32C3×AGL(1,𝔽5)×SL(2,𝔽3)semidirect
876. C3⋊D3C3×AGL(1,𝔽5)×SL(2,𝔽3)semidirect
903. C3×C5C2×C4×PSU(3,𝔽2)⋊C3semidirect
942. C2×C5C3×C4×PSU(3,𝔽2)⋊C3semidirect
945. D5C3×C4×PSU(3,𝔽2)⋊C3semidirect
955. C32C2×C3×AGL(1,𝔽5)×SL(2,𝔽3)semidirect
997. C2×C3AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3direct (N × H)
1002. C5C2×C3×C4×PSU(3,𝔽2)⋊C3semidirect
1021. C3C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3direct (N × H)
1028. C2C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×AGL(1,𝔽5)×SL(2,𝔽3)9
C2×C3×C4×PSU(3,𝔽2)⋊C35
C2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C34
C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)3
C2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C33
C2×C3×D5×PSU(3,𝔽2)⋊C32
C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C32