Finite Group Databasebeta

← C2×C3×#72213713 #72217933

Subgroups — C2×C3×#72213713 #72217933

Order 25920.

1298 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 1298 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#91886—91nomaximal
2C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—41nomaximal
3C2×C3×#10587380—41no—
4C2×C3×(PSU(3,𝔽2)⋊C3)⋊C4—51nomaximal, Hall
5C2×C3×PSU(3,𝔽2)⋊AGL(1,𝔽5)—31nomaximal
6C2×#72213713C311yesmaximal, characteristic, direct product factor
7C2×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—41no—
8C2×PSU(3,𝔽2)⋊AGL(1,𝔽5)—31no—
9C2×C3×(C3⋊ΓL(1,𝔽16))⋊C3—41no—
10C2×C3×D3×ΓL(1,𝔽16)—121no—
11C2×C3×#10624306—31no—
12C2×C3×ΓL(1,𝔽16)⋊D3—61no—
13C2×C3×D5×PSU(3,𝔽2)⋊C3C211yesmaximal, characteristic
14C22×C3×PSU(3,𝔽2)⋊C3—51no—
15C2×C3×D5×(C3⋊D3)⋊C3—41no—
16C2×C3×D5×PSU(3,𝔽2)D311yescharacteristic
17C2×C3×C5⋊PSU(3,𝔽2)—31no—
18C2×D5×PSU(3,𝔽2)⋊C3—21no—
19C2×D5×PSU(3,𝔽2)⋊C3C2×C311yescharacteristic
20C2×C3×C5×PSU(3,𝔽2)⋊C3C411yescharacteristic, complemented
21C2×C3×C5×PSU(3,𝔽2)Dic311yescharacteristic, complemented
22C2×C5×PSU(3,𝔽2)⋊C3—21no—
23C2×C5×PSU(3,𝔽2)⋊C3C3×C411yescharacteristic, complemented
24C3×#72213713C212yesmaximal, direct product factor
25C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—42no—
26C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—42no—
27C3×(PSU(3,𝔽2)⋊C3)⋊C4—52no—
28C3×PSU(3,𝔽2)⋊AGL(1,𝔽5)—32no—
29C3×PSU(3,𝔽2)⋊AGL(1,𝔽5)—32no—
30C3×D5×PSU(3,𝔽2)⋊C3C411yescharacteristic, complemented
31C3×D5×PSU(3,𝔽2)⋊C3C2211yescharacteristic
32C3×C5×PSU(3,𝔽2)⋊C3C2×C411yescharacteristic, complemented
33C3×D5×PSU(3,𝔽2)—31no—
34C3×D5×PSU(3,𝔽2)—31no—
35C3×D5×PSU(3,𝔽2)Dic311yescharacteristic, complemented
36C3×D5×PSU(3,𝔽2)C2×D311yescharacteristic
37C3×#10624306—32no—
38C3×#10624306—61no—
39C2×C3×D5⋊AGL(1,𝔽9)—31no—
40C2×C3×#67195—61no—
41C2×C3×D5×#157—31no—
42C3×D5⋊AGL(1,𝔽9)—32no—
43C3×D5⋊AGL(1,𝔽9)—61no—
44#72213713C2×C312yesdirect product factor
45D5×PSU(3,𝔽2)⋊C3—21no—
46D5×PSU(3,𝔽2)⋊C3—21no—
47D5×PSU(3,𝔽2)⋊C3C3×C411yescharacteristic, complemented
48D5×PSU(3,𝔽2)⋊C3C22×C311yescharacteristic
49C2×C3×PSU(3,𝔽2)⋊C4—151no—
50C2×(PSU(3,𝔽2)⋊C3)⋊C4—51no—
51C2×C3×C5⋊((C3⋊D3)⋊C3)—41no—
52C2×C3×C5×(C3⋊D3)⋊C3—41no—
53C2×C3×D5×H(3,𝔽3)—41no—
54C3×D5×(C3⋊D3)⋊C3—41no—
55C3×D5×(C3⋊D3)⋊C3—41no—
56C3×D5×(C3⋊D3)⋊C3—41no—
57C3×D5×(C3⋊D3)⋊C3—41no—
58C3×#10587380—42no—
59C3×(C3⋊ΓL(1,𝔽16))⋊C3—42no—
60C2×D5×PSU(3,𝔽2)C3×D311yescharacteristic
61C2×D5⋊AGL(1,𝔽9)—31no—
62C2×#10624306—31no—
63PSU(3,𝔽2)⋊AGL(1,𝔽5)—32no—
64PSU(3,𝔽2)⋊AGL(1,𝔽5)—32no—
65C2×C3×D5×SL(2,𝔽3)—91no—
66C3×#91886—92no—
67C2×C3×PSU(3,𝔽2)⋊C3—51no—
68C2×C3×PSU(3,𝔽2)⋊C3—51no—
69C2×C3×PSU(3,𝔽2)⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
70C2×C3×((C3⋊D3)⋊C3)⋊C4—201no—
71C2×C3×D5×C3⋊D3S411yescharacteristic
72C2×C32×D3×D5—121no—
73C2×C3×#4379—31no—
74C2×C3×C5×#157—31no—
75C2×C3×C3⋊ΓL(1,𝔽16)—41no—
76C2×C32×ΓL(1,𝔽16)—121no—
77C2×C32×ΓL(1,𝔽16)—121no—
78C2×C32×ΓL(1,𝔽16)—241no—
79C3×C5⋊PSU(3,𝔽2)—31no—
80C3×C5⋊PSU(3,𝔽2)—31no—
81C3×C5⋊PSU(3,𝔽2)—61no—
82C3×C5×PSU(3,𝔽2)—31no—
83C3×C5×PSU(3,𝔽2)C2×Dic311yescharacteristic, complemented
84C3×D5×#157—31no—
85C3×D5×#157—31no—
86C3×D5×#157—31no—
87C3×D5×#157—31no—
88C3×ΓL(1,𝔽16)⋊D3—62no—
89C3×ΓL(1,𝔽16)⋊D3—121no—
90C3×D3×ΓL(1,𝔽16)—122no—
91C3×D3×ΓL(1,𝔽16)—122no—
92C3×#67195—62no—
93C5×PSU(3,𝔽2)⋊C3—21no—
94C5×PSU(3,𝔽2)⋊C3C2×C3×C411yescharacteristic, complemented
95C2×D5×(C3⋊D3)⋊C3—41no—
96C2×D5×(C3⋊D3)⋊C3—81no—
97C2×#10587380—41no—
98C2×(C3⋊ΓL(1,𝔽16))⋊C3—41no—
99C2×(C3⋊ΓL(1,𝔽16))⋊C3—81no—
100((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—42no—
101((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)—42no—
102C2×#91886—91no—
103C2×C3×#4009—271no—
104C22×C3×PSU(3,𝔽2)—51no—
105C22×C3×AGL(1,𝔽9)—151no—
106C22×PSU(3,𝔽2)⋊C3—51no—
107C22×PSU(3,𝔽2)⋊C3—101no—
108C2×C3×#3773—151no—
109C3×PSU(3,𝔽2)⋊C4—152no—
110C3×PSU(3,𝔽2)⋊C4—152no—
111(PSU(3,𝔽2)⋊C3)⋊C4—52no—
112C2×C3×C5×H(3,𝔽3)—41no—
113C3×C5⋊((C3⋊D3)⋊C3)—41no—
114C3×C5⋊((C3⋊D3)⋊C3)—41no—
115C3×C5×(C3⋊D3)⋊C3—41no—
116C3×C5×(C3⋊D3)⋊C3—41no—
117C3×D5×H(3,𝔽3)—41no—
118C3×D5×H(3,𝔽3)—41no—
119C22×C3×ΓL(1,𝔽16)—361no—
120C2×C5⋊PSU(3,𝔽2)—31no—
121C2×C5×PSU(3,𝔽2)C3×Dic311yescharacteristic, complemented
122C2×D5×#157—31no—
123C2×ΓL(1,𝔽16)⋊D3—61no—
124C2×D3×ΓL(1,𝔽16)—121no—
125C2×C3×D3×AGL(1,𝔽5)—361no—
126C2×#67195—61no—
127D5×PSU(3,𝔽2)—31no—
128D5×PSU(3,𝔽2)—31no—
129D5×PSU(3,𝔽2)C3×Dic311yescharacteristic, complemented
130D5×PSU(3,𝔽2)C2×C3×D311yescharacteristic
131D5⋊AGL(1,𝔽9)—32no—
132D5⋊AGL(1,𝔽9)—61no—
133#10624306—32no—
134#10624306—61no—
135C2×C3×C5×SL(2,𝔽3)—91no—
136C3×D5×SL(2,𝔽3)—91no—
137C3×D5×SL(2,𝔽3)—91no—
138C3×PSU(3,𝔽2)⋊C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
139C22×C3×(C3⋊D3)⋊C3—201no—
140C2×C3×#1084—201no—
141C2×C3×(C3⋊Dic3)⋊C3—201no—
142C3×((C3⋊D3)⋊C3)⋊C4—202no—
143C3×((C3⋊D3)⋊C3)⋊C4—202no—
144C2×PSU(3,𝔽2)⋊C4—151no—
145C2×C3×#859—451no—
146C2×C3×C3⋊D15#22611yescharacteristic
147C2×C3×C5×C3⋊D3SL(2,ℤ/4)11yescharacteristic
148C2×C32×D15—121no—
149C2×C32×C5×D3—121no—
150C2×C33×D5—41no—
151C2×C33×D5—81no—
152C2×C33×D5GL(2,𝔽3)11yescharacteristic
153C3×D5×C3⋊D3#22611yescharacteristic
154C3×D5×C3⋊D3GL(2,𝔽3)11yescharacteristic
155C3×D5×C3⋊D3SL(2,ℤ/4)11yescharacteristic
156C3×D5×C3⋊D3C2×S411yescharacteristic
157C32×D3×D5—121no—
158C32×D3×D5—121no—
159C32×D3×D5—121no—
160C32×D3×D5—121no—
161C3×#4379—31no—
162C3×#4379—31no—
163C3×C5×#157—31no—
164C3×C5×#157—31no—
165C3×C3⋊ΓL(1,𝔽16)—42no—
166C32×ΓL(1,𝔽16)—122no—
167C32×ΓL(1,𝔽16)—122no—
168C32×ΓL(1,𝔽16)—242no—
169C2×C5⋊((C3⋊D3)⋊C3)—41no—
170C2×C5⋊((C3⋊D3)⋊C3)—81no—
171C2×C5×(C3⋊D3)⋊C3—41no—
172C2×C5×(C3⋊D3)⋊C3—81no—
173C2×D5×H(3,𝔽3)—41no—
174C2×D5×H(3,𝔽3)—81no—
175C2×D5×H(3,𝔽3)—81no—
176C2×D5×H(3,𝔽3)—161no—
177D5×(C3⋊D3)⋊C3—41no—
178D5×(C3⋊D3)⋊C3—41no—
179D5×(C3⋊D3)⋊C3—41no—
180D5×(C3⋊D3)⋊C3—41no—
181D5×(C3⋊D3)⋊C3—81no—
182D5×(C3⋊D3)⋊C3—81no—
183D5×(C3⋊D3)⋊C3—81no—
184D5×(C3⋊D3)⋊C3—81no—
185#10587380—42no—
186(C3⋊ΓL(1,𝔽16))⋊C3—42no—
187(C3⋊ΓL(1,𝔽16))⋊C3—82no—
188C2×C3×Q8×D5—91no—
189C2×C3×C4⋊AGL(1,𝔽5)—271no—
190C2×C3×D5⋊C8—271no—
191C2×D5×SL(2,𝔽3)—91no—
192C2×D5×SL(2,𝔽3)—181no—
193#91886—92no—
194C3×#4009—272no—
195C3×#4009—272no—
196C22×C3×#157—151no—
197C2×C3×PSU(3,𝔽2)—51no—
198C2×C3×PSU(3,𝔽2)—51no—
199C2×C3×PSU(3,𝔽2)—151no—
200C2×C3×PSU(3,𝔽2)—151no—
201C2×C3×PSU(3,𝔽2)—151no—
202C2×C3×PSU(3,𝔽2)ΓL(1,𝔽16)11yescharacteristic, complemented
203C2×C3×AGL(1,𝔽9)—152no—
204C2×C3×AGL(1,𝔽9)—301no—
205C2×C3×AGL(1,𝔽9)—301no—
206C2×PSU(3,𝔽2)⋊C3—21no—
207C2×PSU(3,𝔽2)⋊C3—51no—
208C2×PSU(3,𝔽2)⋊C3—51no—
209C2×PSU(3,𝔽2)⋊C3—101no—
210C2×PSU(3,𝔽2)⋊C3—101no—
211C2×PSU(3,𝔽2)⋊C3C3×AGL(1,𝔽5)11yescharacteristic, complemented
212C2×C3×#624—301no—
213C2×C3×D3×Dic3—601no—
214C3×#3773—152no—
215C3×#3773—301no—
216C2×((C3⋊D3)⋊C3)⋊C4—201no—
217C3×C5×H(3,𝔽3)—41noHall
218C22×C32×D5—361no—
219C2×D5×C3⋊D3C3×S411yescharacteristic
220C2×C3×D3×D5—121no—
221C2×C3×D3×D5—121no—
222C2×C3×D3×D5—241no—
223C2×#4379—31no—
224C2×C5×#157—31no—
225C2×C3⋊ΓL(1,𝔽16)—41no—
226C2×C3×ΓL(1,𝔽16)—121no—
227C2×C3×ΓL(1,𝔽16)—121no—
228C2×C3×ΓL(1,𝔽16)—121no—
229C2×C3×ΓL(1,𝔽16)—121no—
230C2×C3×ΓL(1,𝔽16)—241no—
231C2×C3×ΓL(1,𝔽16)—241no—
232C2×C3×ΓL(1,𝔽16)—241no—
233C2×C3×ΓL(1,𝔽16)—241no—
234C2×C3×ΓL(1,𝔽16)—242no—
235C2×C3×ΓL(1,𝔽16)—362no—
236C2×C3×ΓL(1,𝔽16)—362no—
237C2×C3×ΓL(1,𝔽16)—361no—
238C2×C32×AGL(1,𝔽5)—361no—
239C5⋊PSU(3,𝔽2)—31no—
240C5⋊PSU(3,𝔽2)—31no—
241C5⋊PSU(3,𝔽2)—61no—
242C5×PSU(3,𝔽2)—31no—
243C5×PSU(3,𝔽2)C2×C3×Dic311yescharacteristic, complemented
244D5×#157—31no—
245D5×#157—31no—
246D5×#157—31no—
247D5×#157—31no—
248ΓL(1,𝔽16)⋊D3—62no—
249ΓL(1,𝔽16)⋊D3—121no—
250D3×ΓL(1,𝔽16)—122no—
251D3×ΓL(1,𝔽16)—122no—
252C3×D3×AGL(1,𝔽5)—362no—
253C3×D3×AGL(1,𝔽5)—362no—
254#67195—62no—
255C3×C5×SL(2,𝔽3)—91no—
256C22×C3×H(3,𝔽3)—201no—
257C2×C3×(C3⋊D3)⋊C3—41no—
258C2×C3×(C3⋊D3)⋊C3—201no—
259C2×C3×(C3⋊D3)⋊C3—201no—
260C2×C3×(C3⋊D3)⋊C3—201no—
261C2×C3×(C3⋊D3)⋊C3—201no—
262C2×C3×(C3⋊D3)⋊C3—201no—
263C3×#1084—202no—
264C3×(C3⋊Dic3)⋊C3—202no—
265C2×#4009—271noHall
266C22×PSU(3,𝔽2)—51no—
267C22×AGL(1,𝔽9)—151no—
268C22×C3×SL(2,𝔽3)—451no—
269C2×#3773—151no—
270PSU(3,𝔽2)⋊C4—152no—
271PSU(3,𝔽2)⋊C4—152no—
272C3×#859—452no—
273C2×C33×C5—41no—
274C2×C33×C5—81no—
275C2×C33×C5#85911yescharacteristic, complemented
276C3×C3⋊D15#85911yescharacteristic, complemented
277C3×C3⋊D15C2×#22611yescharacteristic
278C3×C5×C3⋊D3#85911yescharacteristic, complemented
279C3×C5×C3⋊D3C2×SL(2,ℤ/4)11yescharacteristic
280C32×D15—121no—
281C32×D15—121no—
282C32×C5×D3—121no—
283C32×C5×D3—121no—
284C33×D5—41no—
285C33×D5—41no—
286C33×D5—81no—
287C33×D5—81no—
288C33×D5#85911yescharacteristic, complemented
289C33×D5C2×GL(2,𝔽3)11yescharacteristic
290C2×C5×H(3,𝔽3)—41no—
291C2×C5×H(3,𝔽3)—81no—
292C2×C5×H(3,𝔽3)—81no—
293C2×C5×H(3,𝔽3)—161no—
294C5⋊((C3⋊D3)⋊C3)—41no—
295C5⋊((C3⋊D3)⋊C3)—41no—
296C5⋊((C3⋊D3)⋊C3)—81no—
297C5⋊((C3⋊D3)⋊C3)—81no—
298C5×(C3⋊D3)⋊C3—41no—
299C5×(C3⋊D3)⋊C3—41no—
300C5×(C3⋊D3)⋊C3—81no—
301C5×(C3⋊D3)⋊C3—81no—
302D5×H(3,𝔽3)—41no—
303D5×H(3,𝔽3)—41no—
304D5×H(3,𝔽3)—81no—
305D5×H(3,𝔽3)—81no—
306D5×H(3,𝔽3)—81no—
307D5×H(3,𝔽3)—81no—
308D5×H(3,𝔽3)—161no—
309D5×H(3,𝔽3)—161no—
310C22×ΓL(1,𝔽16)—361no—
311C22×C3×AGL(1,𝔽5)—541no—
312C2×D3×AGL(1,𝔽5)—361no—
313C2×C3×C5×Q8—91no—
314C3×Q8×D5—91no—
315C3×Q8×D5—91no—
316C3×Q8×D5—271no—
317C3×Q8×D5—271no—
318C2×C3×C4×D5—271no—
319C2×C3×Dic10—271no—
320C2×C5×SL(2,𝔽3)—91no—
321C2×C5×SL(2,𝔽3)—181no—
322C2×C3×#170—541no—
323C3×C4⋊AGL(1,𝔽5)—272no—
324C3×C4⋊AGL(1,𝔽5)—541no—
325C3×D5⋊C8—272no—
326C3×D5⋊C8—541no—
327D5×SL(2,𝔽3)—91no—
328D5×SL(2,𝔽3)—91no—
329D5×SL(2,𝔽3)—181no—
330D5×SL(2,𝔽3)—181no—
331C22×C3×C3⋊D3—51no—
332C22×C32×D3—601no—
333C2×C3×#157—31no—
334C2×C3×#157—151no—
335C2×C3×#157—151no—
336C2×C3×#157—151no—
337C2×C3×#157—151no—
338C2×C3×#157—151no—
339C3×PSU(3,𝔽2)—31no—
340C3×PSU(3,𝔽2)—151no—
341C3×PSU(3,𝔽2)—151no—
342C3×PSU(3,𝔽2)—301no—
343C3×PSU(3,𝔽2)C2×ΓL(1,𝔽16)11yescharacteristic, complemented
344C3×AGL(1,𝔽9)—302no—
345PSU(3,𝔽2)⋊C3—21no—
346PSU(3,𝔽2)⋊C3C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
347C2×C3×C3⋊Dic3—201no—
348C2×C32×Dic3—601no—
349C2×C32×Dic3—601no—
350C2×C32×Dic3—1201no—
351C3×#624—302no—
352C3×#624—601no—
353C3×D3×Dic3—602no—
354C3×D3×Dic3—602no—
355C22×(C3⋊D3)⋊C3—201no—
356C22×(C3⋊D3)⋊C3—401no—
357C2×#1084—201no—
358C2×(C3⋊Dic3)⋊C3—201no—
359C2×(C3⋊Dic3)⋊C3—401no—
360((C3⋊D3)⋊C3)⋊C4—202no—
361((C3⋊D3)⋊C3)⋊C4—202no—
362C2×#859—451no—
363C2×C3×#103—1351no—
364C22×C32×C5—361no—
365C2×C3⋊D15C3×#22611yescharacteristic
366C2×C5×C3⋊D3C3×SL(2,ℤ/4)11yescharacteristic
367C2×C3×D15—121no—
368C2×C3×D15—121no—
369C2×C3×D15—241no—
370C2×C3×C5×D3—121no—
371C2×C3×C5×D3—121no—
372C2×C3×C5×D3—241no—
373C2×C32×D5—41no—
374C2×C32×D5—41no—
375C2×C32×D5—81no—
376C2×C32×D5—81no—
377C2×C32×D5—81no—
378C2×C32×D5—121no—
379C2×C32×D5—161no—
380C2×C32×D5—241no—
381C2×C32×D5—242no—
382C2×C32×D5—241no—
383C2×C32×D5—361no—
384C2×C32×D5—361no—
385C2×C32×D5—361no—
386C2×C32×D5—361no—
387C2×C32×D5—361no—
388C2×C32×D5C3×GL(2,𝔽3)11yescharacteristic
389D5×C3⋊D3C3×#22611yescharacteristic
390D5×C3⋊D3C3×GL(2,𝔽3)11yescharacteristic
391D5×C3⋊D3C3×SL(2,ℤ/4)11yescharacteristic
392D5×C3⋊D3C2×C3×S411yescharacteristic
393C3×D3×D5—121no—
394C3×D3×D5—121no—
395C3×D3×D5—121no—
396C3×D3×D5—121no—
397C3×D3×D5—121no—
398C3×D3×D5—121no—
399C3×D3×D5—121no—
400C3×D3×D5—121no—
401C3×D3×D5—241no—
402C3×D3×D5—241no—
403C3×D3×D5—241no—
404C3×D3×D5—241no—
405#4379—31no—
406#4379—31no—
407C5×#157—31no—
408C5×#157—31no—
409C3⋊ΓL(1,𝔽16)—42no—
410C3×ΓL(1,𝔽16)—122no—
411C3×ΓL(1,𝔽16)—122no—
412C3×ΓL(1,𝔽16)—122no—
413C3×ΓL(1,𝔽16)—122no—
414C3×ΓL(1,𝔽16)—242no—
415C3×ΓL(1,𝔽16)—242no—
416C3×ΓL(1,𝔽16)—242no—
417C3×ΓL(1,𝔽16)—242no—
418C3×ΓL(1,𝔽16)—244no—
419C3×ΓL(1,𝔽16)—362no—
420C32×AGL(1,𝔽5)—362no—
421C2×C3×H(3,𝔽3)—41no—
422C2×C3×H(3,𝔽3)—201no—
423C2×C3×H(3,𝔽3)—201no—
424C3×(C3⋊D3)⋊C3—41no—
425C3×(C3⋊D3)⋊C3—41no—
426C3×(C3⋊D3)⋊C3—201no—
427C3×(C3⋊D3)⋊C3—201no—
428C2×Q8×D5—91no—
429C2×C4⋊AGL(1,𝔽5)—271no—
430C2×D5⋊C8—271no—
431#4009—272no—
432#4009—272no—
433C22×#157—151no—
434C2×PSU(3,𝔽2)—51no—
435C2×PSU(3,𝔽2)—51no—
436C2×PSU(3,𝔽2)—151no—
437C2×PSU(3,𝔽2)—151no—
438C2×PSU(3,𝔽2)—151no—
439C2×PSU(3,𝔽2)C3×ΓL(1,𝔽16)11yescharacteristic, complemented
440C2×AGL(1,𝔽9)—152no—
441C2×AGL(1,𝔽9)—301no—
442C2×AGL(1,𝔽9)—301no—
443C22×C3×Dic3—1801no—
444C2×C3×C4×D3—1801no—
445C2×C3×SL(2,𝔽3)—91no—
446C2×C3×SL(2,𝔽3)—451no—
447C2×C3×SL(2,𝔽3)—451no—
448C2×#624—301no—
449C2×D3×Dic3—601no—
450#3773—152no—
451#3773—301no—
452C33×C5—41no—
453C33×C5—81no—
454C33×C5C2×#85911yescharacteristic, complemented
455C5×H(3,𝔽3)—41no—
456C5×H(3,𝔽3)—81no—
457C5×H(3,𝔽3)—81no—
458C5×H(3,𝔽3)—161no—
459C22×C3×D5—91no—
460C22×C3×D5—361no—
461C22×C3×D5—721no—
462C2×D3×D5—121no—
463C2×ΓL(1,𝔽16)—121no—
464C2×ΓL(1,𝔽16)—121no—
465C2×ΓL(1,𝔽16)—241no—
466C2×ΓL(1,𝔽16)—362no—
467C2×ΓL(1,𝔽16)—362no—
468C2×ΓL(1,𝔽16)—361no—
469C2×C3×AGL(1,𝔽5)—361no—
470C2×C3×AGL(1,𝔽5)—361no—
471C2×C3×AGL(1,𝔽5)—542no—
472C2×C3×AGL(1,𝔽5)—721no—
473C2×C3×AGL(1,𝔽5)—1081no—
474D3×AGL(1,𝔽5)—362no—
475D3×AGL(1,𝔽5)—362no—
476C3×C5×Q8—91no—
477C3×C5×Q8—271no—
478C2×C3×C4×C5—271no—
479C2×C3×Dic5—271no—
480C3×C4×D5—271no—
481C3×C4×D5—271no—
482C3×C4×D5—271no—
483C3×C4×D5—271no—
484C3×Dic10—271no—
485C3×Dic10—271no—
486C3×Dic10—541no—
487C5×SL(2,𝔽3)—91no—
488C5×SL(2,𝔽3)—181no—
489C3×#170—542no—
490C22×C33—51no—
491C22×C33—201no—
492C22×C33—401no—
493C2×C3×C3⋊D3—51no—
494C2×C3×C3⋊D3—51no—
495C2×C3×C3⋊D3—51no—
496C2×C3×C3⋊D3—51no—
497C2×C3×C3⋊D3—51no—
498C2×C3×C3⋊D3A4⋊AGL(1,𝔽5)11yescharacteristic
499C2×C32×D3—121no—
500C2×C32×D3—601no—
501C2×C32×D3—601no—
502C2×C32×D3—601no—
503C2×C32×D3—601no—
504C2×C32×D3—601no—
505C3×#157—31no—
506C3×#157—31no—
507C3×#157—151no—
508C3×#157—151no—
509C3×C3⋊Dic3—202no—
510C32×Dic3—602no—
511C32×Dic3—602no—
512C32×Dic3—1202no—
513C22×H(3,𝔽3)—201no—
514C22×H(3,𝔽3)—401no—
515C22×H(3,𝔽3)—401no—
516C22×H(3,𝔽3)—801no—
517C2×(C3⋊D3)⋊C3—41no—
518C2×(C3⋊D3)⋊C3—81no—
519C2×(C3⋊D3)⋊C3—201no—
520C2×(C3⋊D3)⋊C3—201no—
521C2×(C3⋊D3)⋊C3—201no—
522C2×(C3⋊D3)⋊C3—201no—
523C2×(C3⋊D3)⋊C3—201no—
524C2×(C3⋊D3)⋊C3—401no—
525C2×(C3⋊D3)⋊C3—401no—
526C2×(C3⋊D3)⋊C3—401no—
527C2×(C3⋊D3)⋊C3—401no—
528C2×(C3⋊D3)⋊C3—401no—
529#1084—202no—
530(C3⋊Dic3)⋊C3—202no—
531(C3⋊Dic3)⋊C3—402no—
532C22×C3×Q8—451no—
533C22×SL(2,𝔽3)—451no—
534C22×SL(2,𝔽3)—901no—
535C22×C3×C8—1351no—
536C2×C3×C4⋊C4—1351no—
537#859—452no—
538C3×#103—1352no—
539C3×#103—1352no—
540C2×C32×C5—41no—
541C2×C32×C5—41no—
542C2×C32×C5—81no—
543C2×C32×C5—81no—
544C2×C32×C5—81no—
545C2×C32×C5—121no—
546C2×C32×C5—161no—
547C2×C32×C5—241no—
548C2×C32×C5—242no—
549C2×C32×C5—241no—
550C2×C32×C5—361no—
551C2×C32×C5—361no—
552C2×C32×C5C3×#85911yescharacteristic, complemented
553C3⋊D15C3×#85911yescharacteristic, complemented
554C3⋊D15C2×C3×#22611yescharacteristic
555C5×C3⋊D3C3×#85911yescharacteristic, complemented
556C5×C3⋊D3C2×C3×SL(2,ℤ/4)11yescharacteristic
557C3×D15—121no—
558C3×D15—121no—
559C3×D15—121no—
560C3×D15—121no—
561C3×D15—241no—
562C3×D15—241no—
563C3×C5×D3—121no—
564C3×C5×D3—121no—
565C3×C5×D3—121no—
566C3×C5×D3—121no—
567C3×C5×D3—241no—
568C3×C5×D3—241no—
569C32×D5—41no—
570C32×D5—41no—
571C32×D5—41no—
572C32×D5—41no—
573C32×D5—81no—
574C32×D5—81no—
575C32×D5—81no—
576C32×D5—81no—
577C32×D5—81no—
578C32×D5—81no—
579C32×D5—121no—
580C32×D5—121no—
581C32×D5—161no—
582C32×D5—161no—
583C32×D5—241no—
584C32×D5—241no—
585C32×D5—242no—
586C32×D5—242no—
587C32×D5—241no—
588C32×D5—241no—
589C32×D5—361no—
590C32×D5—361no—
591C32×D5C3×#85911yescharacteristic, complemented
592C32×D5C2×C3×GL(2,𝔽3)11yescharacteristic
593C3×H(3,𝔽3)—41noSylow
594C22×AGL(1,𝔽5)—541no—
595C2×C5×Q8—91no—
596Q8×D5—91no—
597Q8×D5—91no—
598Q8×D5—271no—
599Q8×D5—271no—
600C2×C4×D5—271no—
601C2×Dic10—271no—
602C2×#170—541no—
603C4⋊AGL(1,𝔽5)—272no—
604C4⋊AGL(1,𝔽5)—541no—
605D5⋊C8—272no—
606D5⋊C8—541no—
607C23×C32—1801no—
608C22×C3⋊D3—51no—
609C22×C3×D3—601no—
610C22×C3×D3—601no—
611C22×C3×D3—1201no—
612C2×#157—31no—
613C2×#157—151no—
614C2×#157—151no—
615C2×#157—151no—
616C2×#157—151no—
617C2×#157—151no—
618PSU(3,𝔽2)—31no—
619PSU(3,𝔽2)—151no—
620PSU(3,𝔽2)—151no—
621PSU(3,𝔽2)—301no—
622PSU(3,𝔽2)C2×C3×ΓL(1,𝔽16)11yescharacteristic, complemented
623AGL(1,𝔽9)—302no—
624C2×C32×C4—1801no—
625C2×C3⋊Dic3—201no—
626C2×C3×Dic3—601no—
627C2×C3×Dic3—601no—
628C2×C3×Dic3—601no—
629C2×C3×Dic3—601no—
630C2×C3×Dic3—1201no—
631C2×C3×Dic3—1201no—
632C2×C3×Dic3—1202no—
633C2×C3×Dic3—1201no—
634C2×C3×Dic3—1201no—
635C2×C3×Dic3—1802no—
636C2×C3×Dic3—1802no—
637C2×C3×Dic3—1801no—
638C3×C4×D3—1802no—
639C3×C4×D3—1802no—
640C3×SL(2,𝔽3)—91no—
641#624—302no—
642#624—601no—
643D3×Dic3—602no—
644D3×Dic3—602no—
645C2×#103—1351noSylow
646C22×C3×C5—91no—
647C22×C3×C5—361no—
648C22×C3×C5—721no—
649C2×D15—121no—
650C2×C5×D3—121no—
651C2×C3×D5—41no—
652C2×C3×D5—81no—
653C2×C3×D5—91no—
654C2×C3×D5—91no—
655C2×C3×D5—91no—
656C2×C3×D5—91no—
657C2×C3×D5—91no—
658C2×C3×D5—121no—
659C2×C3×D5—241no—
660C2×C3×D5—241no—
661C2×C3×D5—361no—
662C2×C3×D5—361no—
663C2×C3×D5—361no—
664C2×C3×D5—361no—
665C2×C3×D5—361no—
666C2×C3×D5—481no—
667C2×C3×D5—721no—
668C2×C3×D5—721no—
669C2×C3×D5—721no—
670C2×C3×D5—721no—
671C2×C3×D5—721no—
672C2×C3×D5AGL(2,𝔽3)11yescharacteristic
673D3×D5—121no—
674D3×D5—121no—
675D3×D5—121no—
676D3×D5—121no—
677ΓL(1,𝔽16)—122no—
678ΓL(1,𝔽16)—122no—
679ΓL(1,𝔽16)—242no—
680ΓL(1,𝔽16)—362no—
681C3×AGL(1,𝔽5)—362no—
682C3×AGL(1,𝔽5)—362no—
683C3×AGL(1,𝔽5)—722no—
684C3×C4×C5—271no—
685C3×C4×C5—271no—
686C3×Dic5—271no—
687C3×Dic5—271no—
688C2×C33—41no—
689C2×C33—51no—
690C2×C33—51no—
691C2×C33—81no—
692C2×C33—201no—
693C2×C33—201no—
694C2×C33—401no—
695C2×C33—401no—
696C2×C33#9188611yescharacteristic, complemented
697C3×C3⋊D3—51no—
698C3×C3⋊D3—51no—
699C3×C3⋊D3#9188611yescharacteristic, complemented
700C3×C3⋊D3C2×A4⋊AGL(1,𝔽5)11yescharacteristic
701C32×D3—121no—
702C32×D3—121no—
703C32×D3—601no—
704C32×D3—601no—
705C2×H(3,𝔽3)—41no—
706C2×H(3,𝔽3)—81no—
707C2×H(3,𝔽3)—81no—
708C2×H(3,𝔽3)—161no—
709C2×H(3,𝔽3)—201no—
710C2×H(3,𝔽3)—201no—
711C2×H(3,𝔽3)—401no—
712C2×H(3,𝔽3)—401no—
713C2×H(3,𝔽3)—401no—
714C2×H(3,𝔽3)—401no—
715C2×H(3,𝔽3)—801no—
716C2×H(3,𝔽3)—801no—
717(C3⋊D3)⋊C3—41no—
718(C3⋊D3)⋊C3—41no—
719(C3⋊D3)⋊C3—81no—
720(C3⋊D3)⋊C3—81no—
721(C3⋊D3)⋊C3—201no—
722(C3⋊D3)⋊C3—201no—
723(C3⋊D3)⋊C3—401no—
724(C3⋊D3)⋊C3—401no—
725C2×C3×Q8—91no—
726C2×C3×Q8—451no—
727C2×C3×Q8—451no—
728C2×C3×Q8—1351no—
729C2×C3×Q8—1351no—
730C2×C3×Q8—1351no—
731C22×C3×C4—2701no—
732C22×C3×C4—1351no—
733C22×Dic3—1801no—
734C2×C4×D3—1801no—
735C2×SL(2,𝔽3)—91no—
736C2×SL(2,𝔽3)—181no—
737C2×SL(2,𝔽3)—451no—
738C2×SL(2,𝔽3)—451no—
739C2×SL(2,𝔽3)—901no—
740C2×SL(2,𝔽3)—901no—
741C2×C3×C8—2701no—
742C2×C3×C8—2701no—
743C2×C3×C8—1352no—
744C3×C4⋊C4—2701no—
745C3×C4⋊C4—1352no—
746C32×C5—41no—
747C32×C5—41no—
748C32×C5—81no—
749C32×C5—81no—
750C32×C5—81no—
751C32×C5—121no—
752C32×C5—161no—
753C32×C5—241no—
754C32×C5—242no—
755C32×C5—241no—
756C32×C5C2×C3×#85911yescharacteristic, complemented
757C22×D5—91no—
758C2×AGL(1,𝔽5)—361no—
759C2×AGL(1,𝔽5)—542no—
760C2×AGL(1,𝔽5)—1081no—
761C5×Q8—91no—
762C5×Q8—271no—
763C2×C4×C5—271no—
764C2×Dic5—271no—
765C4×D5—271no—
766C4×D5—271no—
767C4×D5—271no—
768C4×D5—271no—
769Dic10—271no—
770Dic10—271no—
771Dic10—541no—
772#170—542no—
773C22×C32—51no—
774C22×C32—201no—
775C22×C32—201no—
776C22×C32—361no—
777C22×C32—401no—
778C22×C32—401no—
779C22×C32—401no—
780C22×C32—601no—
781C22×C32—801no—
782C22×C32—1201no—
783C22×C32—1201no—
784C22×C32—1202no—
785C22×C32—1801no—
786C22×C32—1801no—
787C22×C32—1801no—
788C22×C32—1801no—
789C22×C32—1801no—
790C2×C3⋊D3—51no—
791C2×C3⋊D3—51no—
792C2×C3⋊D3—51no—
793C2×C3⋊D3—51no—
794C2×C3⋊D3—51no—
795C2×C3⋊D3C3×A4⋊AGL(1,𝔽5)11yescharacteristic
796C2×C3×D3—121no—
797C2×C3×D3—121no—
798C2×C3×D3—241no—
799C2×C3×D3—601no—
800C2×C3×D3—601no—
801C2×C3×D3—601no—
802C2×C3×D3—601no—
803C2×C3×D3—601no—
804C2×C3×D3—601no—
805C2×C3×D3—601no—
806C2×C3×D3—601no—
807C2×C3×D3—601no—
808C2×C3×D3—601no—
809C2×C3×D3—1201no—
810C2×C3×D3—1201no—
811C2×C3×D3—1201no—
812C2×C3×D3—1201no—
813C2×C3×D3—1201no—
814#157—31no—
815#157—31no—
816#157—151no—
817#157—151no—
818C32×C4—1802no—
819C3⋊Dic3—202no—
820C3×Dic3—602no—
821C3×Dic3—602no—
822C3×Dic3—602no—
823C3×Dic3—602no—
824C3×Dic3—1202no—
825C3×Dic3—1202no—
826C3×Dic3—1204no—
827C3×Dic3—1202no—
828C3×Dic3—1202no—
829C3×Dic3—1802no—
830C22×Q8—451no—
831C22×C8—1351no—
832C2×C4⋊C4—1351no—
833#103—1352no—
834#103—1352no—
835C2×C3×C5—41no—
836C2×C3×C5—81no—
837C2×C3×C5—91no—
838C2×C3×C5—91no—
839C2×C3×C5—121no—
840C2×C3×C5—241no—
841C2×C3×C5—241no—
842C2×C3×C5—361no—
843C2×C3×C5—361no—
844C2×C3×C5—481no—
845C2×C3×C5—721no—
846C2×C3×C5—721no—
847C2×C3×C5(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented
848D15—121no—
849D15—121no—
850C3×D5—41no—
851C3×D5—41no—
852C3×D5—81no—
853C3×D5—81no—
854C3×D5—91no—
855C3×D5—91no—
856C3×D5—121no—
857C3×D5—121no—
858C3×D5—241no—
859C3×D5—241no—
860C3×D5—241no—
861C3×D5—241no—
862C3×D5—361no—
863C3×D5—361no—
864C3×D5—481no—
865C3×D5—481no—
866C3×D5—721no—
867C3×D5—721no—
868C3×D5(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented
869C3×D5C2×AGL(2,𝔽3)11yescharacteristic
870C5×D3—121no—
871C5×D3—121no—
872C33—41no—
873C33—81no—
874C33C2×#9188611yescharacteristic, complemented
875H(3,𝔽3)—41no—
876H(3,𝔽3)—81no—
877H(3,𝔽3)—81no—
878H(3,𝔽3)—161no—
879C23×C3—451no—
880C23×C3—3601no—
881C23×C3—1801no—
882C22×D3—601no—
883C3×Q8—91no—
884C3×Q8—2701no—
885C3×Q8—271no—
886C3×Q8—1351no—
887C3×Q8—1351no—
888C2×C3×C4—2702no—
889C2×C3×C4—271no—
890C2×C3×C4—5401no—
891C2×C3×C4—3601no—
892C2×C3×C4—1351no—
893C2×C3×C4—1351no—
894C2×C3×C4—1351no—
895C2×C3×C4—1351no—
896C2×C3×C4—1351no—
897C2×C3×C4—1801no—
898C2×C3×C4—1801no—
899C2×Dic3—601no—
900C2×Dic3—601no—
901C2×Dic3—1201no—
902C2×Dic3—1802no—
903C2×Dic3—1802no—
904C2×Dic3—1801no—
905C4×D3—1802no—
906C4×D3—1802no—
907SL(2,𝔽3)—91no—
908SL(2,𝔽3)—181no—
909C3×C8—2702no—
910C22×C5—91no—
911C2×D5—91no—
912C2×D5—91no—
913C2×D5—91no—
914C2×D5—91no—
915C2×D5—91no—
916C2×D5C3×AGL(2,𝔽3)11yescharacteristic
917AGL(1,𝔽5)—362no—
918C4×C5—271no—
919C4×C5—271no—
920Dic5—271no—
921Dic5—271no—
922C2×C32—41no—
923C2×C32—41no—
924C2×C32—51no—
925C2×C32—51no—
926C2×C32—81no—
927C2×C32—81no—
928C2×C32—81no—
929C2×C32—121no—
930C2×C32—161no—
931C2×C32—201no—
932C2×C32—201no—
933C2×C32—201no—
934C2×C32—201no—
935C2×C32—241no—
936C2×C32—242no—
937C2×C32—241no—
938C2×C32—361no—
939C2×C32—361no—
940C2×C32—401no—
941C2×C32—401no—
942C2×C32—401no—
943C2×C32—401no—
944C2×C32—401no—
945C2×C32—401no—
946C2×C32—601no—
947C2×C32—601no—
948C2×C32—801no—
949C2×C32—801no—
950C2×C32—1201no—
951C2×C32—1201no—
952C2×C32—1201no—
953C2×C32—1201no—
954C2×C32—1202no—
955C2×C32—1202no—
956C2×C32—1801no—
957C2×C32—1801no—
958C2×C32C3×#9188611yescharacteristic, complemented
959C3⋊D3—51no—
960C3⋊D3—51no—
961C3⋊D3C3×#9188611yescharacteristic, complemented
962C3⋊D3C2×C3×A4⋊AGL(1,𝔽5)11yescharacteristic
963C3×D3—121no—
964C3×D3—121no—
965C3×D3—121no—
966C3×D3—121no—
967C3×D3—241no—
968C3×D3—241no—
969C3×D3—601no—
970C3×D3—601no—
971C3×D3—601no—
972C3×D3—601no—
973C3×D3—1201no—
974C3×D3—1201no—
975C2×Q8—91no—
976C2×Q8—451no—
977C2×Q8—451no—
978C2×Q8—1351no—
979C2×Q8—1351no—
980C2×Q8—1351no—
981C22×C4—2701no—
982C22×C4—1351no—
983C2×C8—2701no—
984C2×C8—2701no—
985C2×C8—1352no—
986C4⋊C4—2701no—
987C4⋊C4—1352no—
988C3×C5—41no—
989C3×C5—81no—
990C3×C5—121no—
991C3×C5—241no—
992C3×C5—241no—
993C3×C5—481no—
994C3×C5C2×(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented
995C22×C3—51no—
996C22×C3—91no—
997C22×C3—201no—
998C22×C3—361no—
999C22×C3—401no—
1000C22×C3—451no—
1001C22×C3—451no—
1002C22×C3—451no—
1003C22×C3—451no—
1004C22×C3—451no—
1005C22×C3—601no—
1006C22×C3—721no—
1007C22×C3—3601no—
1008C22×C3—3601no—
1009C22×C3—3601no—
1010C22×C3—3601no—
1011C22×C3—3601no—
1012C22×C3—1201no—
1013C22×C3—1201no—
1014C22×C3—1801no—
1015C22×C3—1801no—
1016C22×C3—1801no—
1017C22×C3—1801no—
1018C22×C3—1801no—
1019C22×C3—2401no—
1020C2×D3—121no—
1021C2×D3—601no—
1022C2×D3—601no—
1023C2×D3—601no—
1024C2×D3—601no—
1025C2×D3—601no—
1026C3×C4—271no—
1027C3×C4—271no—
1028C3×C4—3602no—
1029C3×C4—1351no—
1030C3×C4—1351no—
1031C3×C4—1802no—
1032C3×C4—1802no—
1033Dic3—602no—
1034Dic3—602no—
1035Dic3—1202no—
1036Dic3—1802no—
1037C2×C5—91no—
1038C2×C5—91no—
1039C2×C5C3×(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented
1040D5—91no—
1041D5—91no—
1042D5C2×C3×AGL(2,𝔽3)11yescharacteristic
1043D5C3×(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented
1044C32—41no—
1045C32—41no—
1046C32—81no—
1047C32—81no—
1048C32—81no—
1049C32—121no—
1050C32—161no—
1051C32—241no—
1052C32—242no—
1053C32—241no—
1054C32C2×C3×#9188611yescharacteristic, complemented
1055C23—451no—
1056Q8—91no—
1057Q8—2701no—
1058Q8—271no—
1059Q8—1351no—
1060Q8—1351no—
1061C2×C4—2702no—
1062C2×C4—271no—
1063C2×C4—5401no—
1064C2×C4—1351no—
1065C2×C4—1351no—
1066C2×C4—1351no—
1067C2×C4—1351no—
1068C2×C4—1351no—
1069C2×C4—1801no—
1070C8—2702no—
1071C2×C3—41no—
1072C2×C3—51no—
1073C2×C3—51no—
1074C2×C3—81no—
1075C2×C3—91no—
1076C2×C3—91no—
1077C2×C3—121no—
1078C2×C3—201no—
1079C2×C3—201no—
1080C2×C3—241no—
1081C2×C3—241no—
1082C2×C3—361no—
1083C2×C3—361no—
1084C2×C3—401no—
1085C2×C3—401no—
1086C2×C3—451no—
1087C2×C3—451no—
1088C2×C3—481no—
1089C2×C3—601no—
1090C2×C3—601no—
1091C2×C3—721no—
1092C2×C3—721no—
1093C2×C3—3601no—
1094C2×C3—3601no—
1095C2×C3—1201no—
1096C2×C3—1201no—
1097C2×C3—1201no—
1098C2×C3—1201no—
1099C2×C3—1801no—
1100C2×C3—1801no—
1101C2×C3—2401no—
1102C2×C3—2401no—
1103C2×C3#7221371311yescharacteristic, direct product factor
1104D3—121no—
1105D3—121no—
1106D3—601no—
1107D3—601no—
1108C5C2×C3×(PSU(3,𝔽2)⋊C3)⋊C411yescharacteristic, complemented, Sylow
1109C22—51no—
1110C22—91no—
1111C22—451no—
1112C22—451no—
1113C22—451no—
1114C22—451no—
1115C22—451no—
1116C4—271no—
1117C4—271no—
1118C4—1351no—
1119C4—1351no—
1120C4—1802no—
1121C3—41no—
1122C3—81no—
1123C3—121no—
1124C3—241no—
1125C3—241no—
1126C3—481no—
1127C3C2×#7221371311yescharacteristic, direct product factor
1128C2—51no—
1129C2—51no—
1130C2—91no—
1131C2—91no—
1132C2—451no—
1133C2—451no—
1134C2C3×#7221371311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#72213713
commutator, hypocenterC5×PSU(3,𝔽2)⋊C3C2×C3×C4
FrattiniC1G
Fitting, socleC2×C33×C5#859
prime radicalC2×C3×D5×PSU(3,𝔽2)⋊C3C2
cosocleD5×PSU(3,𝔽2)⋊C3C22×C3
LCSG ▷ C5×PSU(3,𝔽2)⋊C3
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
6. C2×#72213713C3direct (N × H)
20. C2×C3×C5×PSU(3,𝔽2)⋊C3C4semidirect
21. C2×C3×C5×PSU(3,𝔽2)Dic3semidirect
23. C2×C5×PSU(3,𝔽2)⋊C3C3×C4semidirect
24. C3×#72213713C2direct (N × H)
30. C3×D5×PSU(3,𝔽2)⋊C3C4semidirect
32. C3×C5×PSU(3,𝔽2)⋊C3C2×C4semidirect
35. C3×D5×PSU(3,𝔽2)Dic3semidirect
44. #72213713C2×C3direct (N × H)
47. D5×PSU(3,𝔽2)⋊C3C3×C4semidirect
69. C2×C3×PSU(3,𝔽2)⋊C3AGL(1,𝔽5)semidirect
83. C3×C5×PSU(3,𝔽2)C2×Dic3semidirect
94. C5×PSU(3,𝔽2)⋊C3C2×C3×C4semidirect
121. C2×C5×PSU(3,𝔽2)C3×Dic3semidirect
129. D5×PSU(3,𝔽2)C3×Dic3semidirect
138. C3×PSU(3,𝔽2)⋊C3C2×AGL(1,𝔽5)semidirect
202. C2×C3×PSU(3,𝔽2)ΓL(1,𝔽16)semidirect
211. C2×PSU(3,𝔽2)⋊C3C3×AGL(1,𝔽5)semidirect
243. C5×PSU(3,𝔽2)C2×C3×Dic3semidirect
275. C2×C33×C5#859semidirect
276. C3×C3⋊D15#859semidirect
278. C3×C5×C3⋊D3#859semidirect
288. C33×D5#859semidirect
343. C3×PSU(3,𝔽2)C2×ΓL(1,𝔽16)semidirect
346. PSU(3,𝔽2)⋊C3C2×C3×AGL(1,𝔽5)semidirect
439. C2×PSU(3,𝔽2)C3×ΓL(1,𝔽16)semidirect
454. C33×C5C2×#859semidirect
552. C2×C32×C5C3×#859semidirect
553. C3⋊D15C3×#859semidirect
555. C5×C3⋊D3C3×#859semidirect
591. C32×D5C3×#859semidirect
622. PSU(3,𝔽2)C2×C3×ΓL(1,𝔽16)semidirect
696. C2×C33#91886semidirect
699. C3×C3⋊D3#91886semidirect
756. C32×C5C2×C3×#859semidirect
847. C2×C3×C5(PSU(3,𝔽2)⋊C3)⋊C4semidirect
868. C3×D5(PSU(3,𝔽2)⋊C3)⋊C4semidirect
874. C33C2×#91886semidirect
958. C2×C32C3×#91886semidirect
961. C3⋊D3C3×#91886semidirect
994. C3×C5C2×(PSU(3,𝔽2)⋊C3)⋊C4semidirect
1039. C2×C5C3×(PSU(3,𝔽2)⋊C3)⋊C4semidirect
1043. D5C3×(PSU(3,𝔽2)⋊C3)⋊C4semidirect
1054. C32C2×C3×#91886semidirect
1103. C2×C3#72213713direct (N × H)
1108. C5C2×C3×(PSU(3,𝔽2)⋊C3)⋊C4semidirect
1127. C3C2×#72213713direct (N × H)
1134. C2C3×#72213713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#918869
C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)4
C2×C3×(PSU(3,𝔽2)⋊C3)⋊C45
C2×C3×PSU(3,𝔽2)⋊AGL(1,𝔽5)3
C2×#722137133
C2×C3×D5×PSU(3,𝔽2)⋊C32
C3×#722137132