Finite Group Databasebeta

← #14285441

Subgroups — #14285441

Order 1920.

508 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 88 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
1#11754805C211yesmaximal, characteristic
2#11751920C212yesmaximal, complemented
3#11746796C211yesmaximal, characteristic, complemented
4C3×#64925C211yesmaximal, characteristic, complemented
5#11746511C212yesmaximal, complemented
6#10605006—31nomaximal, Hall
7C2×C5×#237C411yescharacteristic
8C2×#6765C411yescharacteristic
9C2×#6739—22no—
10#91825C411yescharacteristic
11C3×#4086C2211yescharacteristic
12#91565—22no—
13Dic3×C22⋊D5—22no—
14C4×D3×Dic5C2211yescharacteristic
15#91376C2211yescharacteristic
16#91368C411yescharacteristic
17#91233C2212yes—
18C3×#4004C2212yes—
19Dic3⋊#170—22no—
20#68389—51nomaximal, Hall
21#66166—31no—
22#65758—32no—
23#64931—32no—
24#64925—31no—
25#64925D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C2×C5×#67—21no—
29C22×C5×Dic3—21no—
30C5×#237—42no—
31C2×C4×C5×D3C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×C22⋊D5—22no—
34C2×C3×D20C2×C411yescharacteristic
35C2×#1201—21no—
36C2×D3×Dic5D412yes—
37C2×D5×Dic3—21no—
38#6765—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41#6739—44no—
42#6719—22no—
43C4×Dic15C2×C411yescharacteristic
44C3×C4×Dic5C2311yescharacteristic
45#6668—22no—
46#6665—22no—
47Dic3×Dic5D412yes—
48#5716—51no—
49#4837—52no—
50C3×#331—51no—
51#4544—51no—
52#4481—52no—
53C2×C5×#41—31no—
54C2×#709—31no—
55C2×#704—62no—
56#4093—31no—
57#4090—31no—
58#4086C2×D311yescharacteristic
59#4085—62no—
60#4082—31no—
61C4×C22⋊D5—62no—
62C2×C4×Dic5—31no—
63#4004—32no—
64#4004C2×D312yes—
65C4⋊#170—62no—
66#1560—151noSylow
67C23×C3×C5—21no—
68C22×C5×D3C22⋊C411yescharacteristic
69C22×C3×D5—21no—
70C3×C5×D4—41no—
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15—21no—
73C2×Dic15C22⋊C412yes—
74Dic30—41no—
75C5×#67—42no—
76C2×C5×Dic3—21no—
77C2×C5×Dic3—42no—
78C2×C5×Dic3C22⋊C411yescharacteristic
79C4×C5×D3—22no—
80C5×Dic6—41no—
81C3×C22⋊D5—42no—
82C3×C22⋊D5—42no—
83C2×C3×Dic5C2×D412yes—
84C3×D20—41no—
85#1201—42no—
86D3×Dic5—22no—
87D3×Dic5—22no—
88D5×Dic3—42no—
89C3⋊#170—42no—
90C3×#170—42no—
91C2×#237—51no—
92C2×#237AGL(1,𝔽5)11yescharacteristic
93C3×#127—51no—
94#938—102no—
95#936—51no—
96#936—51no—
97D4×Dic3—102no—
98C2×ΓL(1,𝔽25)—102no—
99C42×D3—51no—
100#869—51no—
101C3×C4⋊C8—52no—
102Dic3⋊C8—102no—
103C4⋊(C3⋊C8)—52no—
104C5×#41—122no—
105C2×C5×Q8—31no—
106C2×C5×D4—61no—
107C2×C5×D4C4×D311yescharacteristic
108C22×C4×C5—31no—
109C22×C4×C5—61no—
110C2×C22⋊D5—22no—
111C2×C22⋊D5—61no—
112C22×Dic5—32no—
113#709—122no—
114C2×D20C4×D311yescharacteristic
115C2×C4×D5—61no—
116C2×Dic10—31no—
117#704—124no—
118C2×#170—22no—
119C2×#170—62no—
120C22⋊Dic5—62no—
121#685—62no—
122#683—62no—
123C4×Dic5—31no—
124C4×Dic5—32no—
125C4×Dic5C22×D311yescharacteristic
126#532—151no—
127#423—152no—
128#333—152no—
129#331—51no—
130#331—151no—
131C22×C3×C5—41no—
132C22×C3×C5—42no—
133C22×C3×C5C2×C22⋊C411yescharacteristic
134C2×C5×D3—21no—
135C2×C5×D3—22no—
136C2×C3×D5—41no—
137C2×C3×D5—42no—
138C3×C4×C5—21no—
139Dic15—22no—
140Dic15—41no—
141C3×Dic5AGL(1,ℤ/8)12yes—
142C3×Dic5#13712yes—
143C5×Dic3—41no—
144C5×Dic3#10012yes—
145C2×C3×D4—51no—
146C2×C3×D4—102no—
147C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
148C2×#67—21no—
149C2×#67—101no—
150C22×Dic3—21no—
151C22×Dic3—101no—
152#237—42no—
153#237—202no—
154C2×C4×D3—52no—
155C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
156C2×Dic6—51no—
157C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
158C2×C3×C8—102no—
159C3×C42—51no—
160#217—102no—
161#217—102no—
162C4⋊Dic3—102no—
163C4×Dic3—51no—
164C4×Dic3—52no—
165C2×C3⋊C8—102no—
166ΓL(1,𝔽25)—204no—
167C23×C5—21no—
168C23×C5—31no—
169C22×D5—21no—
170C5×Q8—121no—
171C5×D4—41no—
172C5×D4—122no—
173C2×C4×C5—31no—
174C2×C4×C5—62no—
175C2×C4×C5—61no—
176C2×C4×C5—122no—
177C2×C4×C5C2×C4×D311yescharacteristic
178C22⋊D5—42no—
179C22⋊D5—42no—
180C22⋊D5—122no—
181C2×Dic5—32no—
182C2×Dic5—62no—
183C2×Dic5—62no—
184C2×Dic5—61no—
185C2×Dic5D3×D412yes—
186D20—41no—
187C4×D5—122no—
188Dic10—121no—
189#170—42no—
190#170—122no—
191C2×#41—31no—
192C2×#41—151no—
193C2×M16—302no—
194C4⋊Q8—151no—
195#127—51no—
196#124—151no—
197#124—151no—
198#121—302no—
199C4×D4—302no—
200C2×C42—151no—
201C4⋊C8—52no—
202C4⋊C8—152no—
203C4⋊C8—302no—
204C2×C3×C5—81no—
205C2×C3×C5C2×#10011yescharacteristic
206C2×C3×C5#41712yes—
207C3×D5—81no—
208C5×D3—41no—
209C23×C3—21no—
210C23×C3—101no—
211C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
212C3×D4—41no—
213C3×D4—201no—
214C3×D4—202no—
215C3×D4—202no—
216C2×C3×C4—52no—
217C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
218#67—42no—
219#67—202no—
220C2×Dic3—21no—
221C2×Dic3—42no—
222C2×Dic3—52no—
223C2×Dic3—101no—
224C2×Dic3—202no—
225C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
226C4×D3—22no—
227C4×D3—102no—
228C4×D3—102no—
229Dic6—41no—
230Dic6—201no—
231C3×C8—202no—
232C3⋊C8—202no—
233C22×C5—41no—
234C22×C5—42no—
235C22×C5—61no—
236C22×C5—62no—
237C22×C5D3×C22⋊C411yescharacteristic
238C2×D5—41no—
239C2×D5—42no—
240C4×C5—21no—
241C4×C5—32no—
242C4×C5—121no—
243Dic5—62no—
244Dic5—121no—
245Dic5#91112yes—
246Dic5#91512yes—
247#41—122no—
248#41—602no—
249C2×Q8—31no—
250C2×Q8—151no—
251C2×D4—51no—
252C2×D4—61no—
253C2×D4—102no—
254C2×D4—301no—
255C2×D4D3×AGL(1,𝔽5)11yescharacteristic
256C22×C4—31no—
257C22×C4—61no—
258C22×C4—152no—
259C22×C4—301no—
260M16—604no—
261C2×C8—102no—
262C2×C8—302no—
263C4⋊C4—302no—
264C22⋊C4—302no—
265C22⋊C4—302no—
266C42—51no—
267C42—152no—
268C42—151no—
269C3×C5#156011yescharacteristic, complemented, Hall
270C22×C3—42no—
271C22×C3—41no—
272C22×C3—202no—
273C22×C3—201no—
274C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
275C2×D3—22no—
276C2×D3—21no—
277C3×C4—21no—
278C3×C4—52no—
279C3×C4—52no—
280Dic3—41no—
281Dic3—102no—
282Dic3—201no—
283Dic3#401312yes—
284C2×C5—81no—
285C2×C5—121no—
286C2×C5D3×#10011yescharacteristic
287C2×C5#477112yes—
288D5—81no—
289C23—21no—
290C23—31no—
291C23—101no—
292Q8—121no—
293Q8—601no—
294D4—41no—
295D4—122no—
296D4—201no—
297D4—202no—
298D4—202no—
299D4—602no—
300C2×C4—31no—
301C2×C4—52no—
302C2×C4—62no—
303C2×C4—61no—
304C2×C4—122no—
305C2×C4—152no—
306C2×C4—302no—
307C2×C4—302no—
308C2×C4—301no—
309C2×C4—602no—
310C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
311C8—202no—
312C8—602no—
313C2×C3—81no—
314C2×C3—401no—
315C2×C3#6579312yes—
316C2×C3C2×#401311yescharacteristic
317D3—41no—
318C5#6838911yescharacteristic, complemented, Sylow
319C22—42no—
320C22—41no—
321C22—62no—
322C22—61no—
323C22—202no—
324C22—201no—
325C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
326C4—21no—
327C4—32no—
328C4—52no—
329C4—52no—
330C4—121no—
331C4—302no—
332C4—601no—
333C3#1060500611yescharacteristic, complemented, Sylow
334C2—81no—
335C2—121no—
336C2—401no—
337C2#1175193712yes—
338C2D3×#401311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754805C2
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1560
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751920C2semidirect
3. #11746796C2semidirect
4. C3×#64925C2semidirect
5. #11746511C2semidirect
25. #64925D3semidirect
269. C3×C5#1560semidirect
318. C5#68389semidirect
333. C3#10605006semidirect

Maximal subgroups

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

subgroupindex
#117548052
#117519202
#117467962
C3×#649252
#117465112
#106050063
#683895