Finite Group Databasebeta

← #14288404

Subgroups — #14288404

Order 1920.

508 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 92 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×#65844C211yesmaximal, characteristic
2C5×#4981C211yesmaximal, characteristic, complemented
3#11748370C212yesmaximal, complemented
4#11746349C211yesmaximal, characteristic, complemented
5#11745954C212yesmaximal, complemented
6#10600505—31nomaximal, Hall
7C2×C3×#709—21no—
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C5×C4⋊Dic3C2211yescharacteristic
10C2×C5×Dic3⋊C4—21no—
11C3×#4076—21no—
12C3×#4076C2212yes—
13C3×#4043—22no—
14C3×#4041—22no—
15#91114C2212yes—
16C5×C3⋊#95—21no—
17C5×C3⋊#95C2211yescharacteristic
18#90989—22no—
19#90964—22no—
20#71874—51nomaximal, Hall
21#65844D311yescharacteristic
22C5×#398—31no—
23#65256—32no—
24#64748—31no—
25#64671—32no—
26C22×C3×C4×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×C5×Dic3—21no—
30C22×C5×Dic3—21no—
31C2×C3×C22⋊D5—22no—
32C3×#709—42no—
33C3×#709—42no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×D20D412yes—
37C2×C3×C4×D5—22no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—22no—
40C2×C3⋊#168—22no—
41C5×C4⋊Dic3—22no—
42C5×Dic3⋊C4—42no—
43C3×#685—22no—
44C3×#685—22no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5D412yes—
47C3×#537—51no—
48#5033—52no—
49#4981D511yescharacteristic, complemented
50#4537—52no—
51#4528—51no—
52C2×#709—21no—
53C2×C5×C4⋊C4—31no—
54C2×C5×C4⋊C4—61no—
55C2×C5×C4⋊C4C2×D311yescharacteristic
56#4076—21no—
57#4076C2×D312yes—
58#4043—22no—
59#4041—22no—
60C5×#95—31no—
61C5×#95—61no—
62C22⋊#168—32no—
63#3941—62no—
64#3939—62no—
65#1610—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×C3×D5—22no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5D812yes—
74C2×C3×C4×C5C2×D412yes—
75C2×C5×Dic3—22no—
76C2×C5×Dic3—41no—
77C2×C5×Dic3—41no—
78C2×C5×Dic3—41no—
79C2×C5×Dic3—41no—
80C2×C5×Dic3—41no—
81C3×C22⋊D5—42no—
82C3×C22⋊D5—42no—
83C2×C3×Dic5—22no—
84C3×D20—42no—
85C3×D20—42no—
86C3×D20—81no—
87C3×C4×D5—44no—
88C3×Dic10—42no—
89C3⋊#168—42no—
90C2×C3×#41—101no—
91C3×C22⋊Q8—102no—
92C3×#121—52no—
93C3×#121—102no—
94C3×#121—101no—
95C2×C3×C4⋊C4C2×D511yescharacteristic
96C2×C4⋊Dic3C2×D511yescharacteristic
97C2×Dic3⋊C4—21no—
98#832—102no—
99C3⋊#95—21no—
100C3⋊#95C2×D511yescharacteristic
101#830—52no—
102#807—102no—
103C22×C4×C5—61no—
104C22×C4×C5—61no—
105C22×C4×C5#6711yescharacteristic
106C22×C4×C5#6711yescharacteristic
107C22×C4×C5C22×D311yescharacteristic
108C2×C22⋊D5—22no—
109#709—42no—
110#709—42no—
111C2×D20—21no—
112C2×D20—21no—
113C2×D20#6712yes—
114C2×C4×D5—22no—
115C2×Dic10—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—62no—
118C5×C4⋊C4—122no—
119#685—22no—
120#685—22no—
121C4⋊Dic5—21no—
122C4⋊Dic5#6712yes—
123C2×#168—62no—
124#537—51no—
125#480—152no—
126#398—31no—
127#327—152no—
128#324—151no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#12011yescharacteristic
132C22×C3×C5C2×D811yescharacteristic
133C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
134C2×C3×D5—42no—
135C2×C3×D5—42no—
136C2×C3×D5—42no—
137C3×C4×C5—22no—
138C3×C4×C5—22no—
139C3×C4×C5—41no—
140C3×Dic5—42no—
141C5×Dic3—42no—
142C5×Dic3—81no—
143C3×#41—202no—
144C3×#41—202no—
145C2×C3×Q8—101no—
146C2×C3×D4—52no—
147C2×C3×D4—101no—
148C2×C3×D4—101no—
149C2×C3×D4—102no—
150C22×C3×C4—102no—
151C22×C3×C4C22⋊D511yescharacteristic
152C22×C3×C4C22⋊D511yescharacteristic
153C22×C3×C4C22×D511yescharacteristic
154C22×Dic3—21no—
155C22×Dic3—21no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—52no—
158C3×C4⋊C4—101no—
159C3×C22⋊C4—102no—
160C3×C22⋊C4—102no—
161C4⋊Dic3—22no—
162Dic3⋊C4—42no—
163C2×C3⋊C8—102no—
164C23×C5C2×#6711yescharacteristic
165C22×D5—22no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—62no—
172C2×C4×C5—121no—
173C2×C4×C5—121no—
174C2×C4×C5—121no—
175C2×C4×C5—121no—
176C2×C4×C5—121no—
177C2×C4×C5#21312yes—
178C2×C4×C5C2×#6712yes—
179C22⋊D5—42no—
180C22⋊D5—42no—
181C2×Dic5—22no—
182D20—42no—
183D20—42no—
184D20—81no—
185C4×D5—44no—
186Dic10—42no—
187#168—122no—
188C2×#41—101no—
189C22⋊Q8—102no—
190#121—52no—
191#121—102no—
192#121—101no—
193C2×C4⋊C4—31no—
194C2×C4⋊C4—61no—
195C2×C4⋊C4D3×D511yescharacteristic
196#107—302no—
197#102—302no—
198C22⋊C8—152no—
199#95—31no—
200#95—61no—
201C2×C3×C5—21no—
202C2×C3×C5—21no—
203C2×C3×C5#44711yescharacteristic
204C2×C3×C5#45611yescharacteristic
205C2×C3×C5#45811yescharacteristic
206C3×D5—82no—
207C23×C3—102no—
208C23×C3C2×C22⋊D511yescharacteristic
209C3×Q8—202no—
210C3×D4—202no—
211C3×D4—202no—
212C3×D4—202no—
213C3×D4—202no—
214C3×D4—401no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—102no—
221C2×C3×C4—204no—
222C2×C3×C4#68612yes—
223C2×C3×C4D4×D512yes—
224C2×Dic3—22no—
225C2×Dic3—41no—
226C2×Dic3—41no—
227C2×Dic3—41no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C3⋊C8—202no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5C2×#21311yescharacteristic
234C22×C5#93211yescharacteristic
235C22×C5#95311yescharacteristic
236C2×D5—42no—
237C2×D5—42no—
238C2×D5—42no—
239C4×C5—22no—
240C4×C5—22no—
241C4×C5—41no—
242C4×C5—122no—
243C4×C5—241no—
244Dic5—42no—
245#41—202no—
246#41—202no—
247C2×Q8—101no—
248C2×D4—52no—
249C2×D4—101no—
250C2×D4—101no—
251C2×D4—102no—
252C22×C4—61no—
253C22×C4—61no—
254C22×C4—102no—
255C22×C4#120111yescharacteristic
256C22×C4#120111yescharacteristic
257C22×C4C2×D3×D511yescharacteristic
258C2×C8—302no—
259C4⋊C4—22no—
260C4⋊C4—52no—
261C4⋊C4—62no—
262C4⋊C4—101no—
263C4⋊C4—122no—
264C22⋊C4—102no—
265C22⋊C4—102no—
266C3×C5#161011yescharacteristic, complemented, Hall
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—202no—
270C22×C3—202no—
271C22×C3—202no—
272C22×C3C2×#68611yescharacteristic
273C22×C3#408311yescharacteristic
274C22×C3#409511yescharacteristic
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—202no—
279Dic3—42no—
280Dic3—81no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5#521711yescharacteristic
284C2×C5#524311yescharacteristic
285C2×C5#524611yescharacteristic
286D5—82no—
287C23—102no—
288C23C2×#120111yescharacteristic
289Q8—202no—
290D4—202no—
291D4—202no—
292D4—202no—
293D4—202no—
294D4—401no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—62no—
301C2×C4—102no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4—204no—
308C2×C4#665212yes—
309C2×C4D5×#6712yes—
310C8—602no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—402no—
314C2×C3#6532511yescharacteristic
315C2×C3#6534211yescharacteristic
316C2×C3#6538411yescharacteristic
317C5#7187411yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—202no—
321C22—202no—
322C22—202no—
323C22C2×#665211yescharacteristic
324C22#9129811yescharacteristic
325C22#9156311yescharacteristic
326C4—22no—
327C4—22no—
328C4—41no—
329C4—122no—
330C4—202no—
331C4—241no—
332C3#1060050511yescharacteristic, complemented, Sylow
333C2—21no—
334C2—21no—
335C2—402no—
336C2#1174851011yescharacteristic
337C2#1174918111yescharacteristic
338C2#1174939011yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC3×#65844C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1610
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#4981C2semidirect
3. #11748370C2semidirect
4. #11746349C2semidirect
5. #11745954C2semidirect
49. #4981D5semidirect
266. C3×C5#1610semidirect
317. C5#71874semidirect
332. C3#10600505semidirect

Maximal subgroups

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

subgroupindex
C3×#658442
C5×#49812
#117483702
#117463492
#117459542
#106005053
#718745