Finite Group Databasebeta

← #14313635

Subgroups — #14313635

Order 1920.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C3×#65811C211yesmaximal, characteristic
2#11752420C212yesmaximal, complemented
3#11746727C212yesmaximal, complemented
4#11746726C212yesmaximal, complemented
5#10604145—31nomaximal, Hall
6C2×C3×#709C411yescharacteristic
7C2×C3×#709C2211yescharacteristic
8D5⋊#208—22no—
9C2×C3×C42×C5C411yescharacteristic
10C3×#4076—22no—
11C3×#4021C411yescharacteristic
12C3×#4021C2211yescharacteristic
13C3×#4020C411yescharacteristic
14C3×C4×D20—22no—
15C3×#4015C2211yescharacteristic
16#91242—22no—
17#91234C2214yes—
18#71820—51nomaximal, Hall
19#65811D311yescharacteristic
20#65761—32no—
21#64856—32no—
22#64855—32no—
23C22×C3×C4×C5—21no—
24C22×C3×C4×C5C2×C411yescharacteristic
25C2×C3×C22⋊D5—21no—
26C2×C3×C22⋊D5D412yes—
27C3×#709—41no—
28C3×#709—41no—
29C3×#709—41no—
30C3×#709—41no—
31C2×C3×D20—22no—
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5D412yes—
36C2×C3×Dic10C2×C411yescharacteristic
37C2×C3×Dic10C2311yescharacteristic
38#6762—24no—
39#6758—42no—
40D5⋊(C3⋊C8)—42no—
41C3×C42×C5—21no—
42C3×C42×C5C2×C411yescharacteristic
43C3×C42×C5C2×C411yescharacteristic
44C3×#685—22no—
45C3×#685—22no—
46C3×C4⋊Dic5—22no—
47C3×#532—51no—
48#5237—52no—
49#4548—52no—
50#4542—52no—
51C2×#709Dic311yescharacteristic
52C2×#709C2×D311yescharacteristic
53D5⋊M16—62no—
54C2×C42×C5Dic311yescharacteristic
55#4076—22no—
56#4021Dic311yescharacteristic
57#4021C2×D311yescharacteristic
58#4020Dic311yescharacteristic
59C4×D20—22no—
60#4015C2×D311yescharacteristic
61#4013—62no—
62#4005—34no—
63#2132—151noSylow
64C23×C3×C5C22⋊C411yescharacteristic
65C22×C3×D5—21no—
66C22×C3×D5C22⋊C412yes—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5C22⋊C411yescharacteristic
73C2×C3×C4×C5C22×C411yescharacteristic
74C3×C22⋊D5—42no—
75C3×C22⋊D5—42no—
76C2×C3×Dic5—21no—
77C2×C3×Dic5C2×D412yes—
78C3×D20—41no—
79C3×D20—44no—
80C3×D20—41no—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83C3×C4×D5—41no—
84C3×C4×D5—41no—
85C3×Dic10—41no—
86C3×Dic10—41no—
87C3⋊#170—44no—
88C2×C3×#41—51no—
89C2×C3×#41—51no—
90C3×C4⋊Q8—51no—
91C3×#127—51no—
92C3×#124—51no—
93C3×#124—51no—
94C3×#121—102no—
95C3×C4×D4—102no—
96C2×C3×C42AGL(1,𝔽5)11yescharacteristic
97C2×#208—102no—
98#836—54no—
99#833—102no—
100C22×C4×C5—21no—
101C22×C4×C5C2×Dic311yescharacteristic
102C2×C22⋊D5—21no—
103C2×C22⋊D5#6712yes—
104#709—41no—
105#709—41no—
106#709—41no—
107#709—41no—
108C2×D20—22no—
109C2×D20C2×Dic311yescharacteristic
110C2×D20C2×Dic311yescharacteristic
111C2×C4×D5—21no—
112C2×C4×D5#6712yes—
113C2×Dic10C2×Dic311yescharacteristic
114C2×Dic10C22×D311yescharacteristic
115#704—64no—
116#700—122no—
117D5⋊C8—122no—
118C42×C5—21no—
119C42×C5C2×Dic311yescharacteristic
120C42×C5C2×Dic311yescharacteristic
121#685—22no—
122#685—22no—
123C4⋊Dic5—22no—
124#532—51no—
125#413—152no—
126#356—152no—
127#355—152no—
128C22×C3×C5—21no—
129C22×C3×C5—41no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C3×D5—22no—
132C2×C3×D5—42no—
133C2×C3×D5—42no—
134C2×C3×D5—41no—
135C3×C4×C5—22no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C3×C4×C5#9911yescharacteristic
139C3×C4×C5#9911yescharacteristic
140C3×Dic5—22no—
141C3×Dic5—41no—
142C3×#41—201no—
143C3×#41—201no—
144C3×#41—201no—
145C3×#41—201no—
146C2×C3×Q8—51no—
147C2×C3×Q8—51no—
148C2×C3×D4—52no—
149C2×C3×D4—51no—
150C2×C3×D4—51no—
151C2×C3×D4—102no—
152C2×C3×D4—101no—
153C22×C3×C4—21no—
154C22×C3×C4—52no—
155C22×C3×C4—101no—
156C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
157C3×C4⋊C4—102no—
158C3×C22⋊C4—102no—
159C3×C22⋊C4—102no—
160C3×C42—21no—
161C3×C42C2×AGL(1,𝔽5)11yescharacteristic
162C3×C42C2×AGL(1,𝔽5)11yescharacteristic
163#208—104no—
164#208—202no—
165C2×C3⋊C8—202no—
166C23×C5#21711yescharacteristic
167C22×D5—21no—
168C22×D5#21712yes—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—42no—
174C2×C4×C5#21711yescharacteristic
175C2×C4×C5C22×Dic311yescharacteristic
176C22⋊D5—42no—
177C22⋊D5—42no—
178C2×Dic5—21no—
179C2×Dic5C2×#6712yes—
180D20—41no—
181D20—41no—
182D20—44no—
183C4×D5—22no—
184C4×D5—22no—
185C4×D5—41no—
186C4×D5—41no—
187Dic10—41no—
188Dic10—41no—
189#170—124no—
190C2×#41—51no—
191C2×#41—51no—
192C2×M16—302no—
193C4⋊Q8—51no—
194#127—51no—
195#124—51no—
196#124—51no—
197#121—102no—
198C4×D4—102no—
199C2×C42ΓL(1,𝔽16)11yescharacteristic
200#101—154no—
201#100—302no—
202C2×C3×C5—21no—
203C2×C3×C5—41no—
204C2×C3×C5C2×#9911yescharacteristic
205C3×D5—42no—
206C3×D5—81no—
207C23×C3—52no—
208C23×C3—101no—
209C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
210C3×Q8—201no—
211C3×Q8—201no—
212C3×D4—201no—
213C3×D4—201no—
214C3×D4—204no—
215C3×D4—202no—
216C3×D4—202no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—42no—
222C2×C3×C4—52no—
223C2×C3×C4—102no—
224C2×C3×C4—102no—
225C2×C3×C4—101no—
226C2×C3×C4—201no—
227C2×C3×C4—201no—
228C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
229C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
230C3⋊C8—204no—
231C22×C5—21no—
232C22×C5—41no—
233C22×C5C2×#21711yescharacteristic
234C2×D5—22no—
235C2×D5—42no—
236C2×D5—42no—
237C2×D5—41no—
238C4×C5—22no—
239C4×C5—21no—
240C4×C5—41no—
241C4×C5#83411yescharacteristic
242C4×C5#83411yescharacteristic
243Dic5—22no—
244Dic5—41no—
245#41—201no—
246#41—201no—
247#41—201no—
248#41—201no—
249C2×Q8—51no—
250C2×Q8—51no—
251C2×D4—52no—
252C2×D4—51no—
253C2×D4—51no—
254C2×D4—102no—
255C2×D4—101no—
256C22×C4—21no—
257C22×C4—52no—
258C22×C4—101no—
259C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
260M16—304no—
261M16—602no—
262C2×C8—602no—
263C4⋊C4—102no—
264C22⋊C4—102no—
265C22⋊C4—102no—
266C42—21no—
267C42C2×ΓL(1,𝔽16)11yescharacteristic
268C42C2×ΓL(1,𝔽16)11yescharacteristic
269C3×C5#213211yescharacteristic, complemented, Hall
270C22×C3—21no—
271C22×C3—41no—
272C22×C3—102no—
273C22×C3—202no—
274C22×C3—202no—
275C22×C3—201no—
276C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—102no—
281C3×C4—201no—
282C3×C4#399911yescharacteristic
283C3×C4#399911yescharacteristic
284C2×C5—21no—
285C2×C5—41no—
286C2×C5C2×#83411yescharacteristic
287D5—42no—
288D5—81no—
289C23—52no—
290C23—101no—
291C23#676311yescharacteristic
292Q8—201no—
293Q8—201no—
294D4—201no—
295D4—201no—
296D4—204no—
297D4—202no—
298D4—202no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—52no—
305C2×C4—102no—
306C2×C4—102no—
307C2×C4—101no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4#676311yescharacteristic
311C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
312C8—604no—
313C2×C3—21no—
314C2×C3—41no—
315C2×C3—202no—
316C2×C3—401no—
317C2×C3C2×#399911yescharacteristic
318C5#7182011yescharacteristic, complemented, Sylow
319C22—21no—
320C22—41no—
321C22—102no—
322C22—202no—
323C22—202no—
324C22—201no—
325C22C2×#676311yescharacteristic
326C4—22no—
327C4—21no—
328C4—41no—
329C4—102no—
330C4—201no—
331C4#9122811yescharacteristic
332C4#9122811yescharacteristic
333C3#1060414511yescharacteristic, complemented, Sylow
334C2—21no—
335C2—41no—
336C2—202no—
337C2—401no—
338C2C2×#9122811yescharacteristic
subgroupG/H
centerC4#91228
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC2×C3×C5C2×#99
prime radicalC3×#65811C2
cosocleC2×C3×Dic10C23
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5#2132
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11752420C2semidirect
3. #11746727C2semidirect
4. #11746726C2semidirect
269. C3×C5#2132semidirect
318. C5#71820semidirect
333. C3#10604145semidirect

Maximal subgroups

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

subgroupindex
C3×#658112
#117524202
#117467272
#117467262
#106041453
#718205