Finite Group Databasebeta

← #14287013

Subgroups — #14287013

Order 1920.

364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×#6653C211yesmaximal, characteristic
2#11747012C211yesmaximal, characteristic, complemented
3C3⋊C8×D20C211yesmaximal, characteristic, complemented
4#11746280C211yesmaximal, characteristic, complemented
5C5×#4455C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7#11745866C211yesmaximal, characteristic, complemented
8#10598874—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C3×C4×D20C2211yescharacteristic
11C2×#6653C411yescharacteristic
12C2×#6651—21no—
13C2×D5×C3⋊C8—21no—
14C3×C4×C5×C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C4×C5×C3⋊C8C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×C4⋊#168C2211yescharacteristic
19#90990C411yescharacteristic
20#90968C411yescharacteristic
21#90965C411yescharacteristic
22#90957—21no—
23#90955—21no—
24#68157—51nomaximal, Hall
25C4×D40—31no—
26#64977—31no—
27C8×D20—31no—
28C5×#322—31no—
29#64679—31no—
30#64679D311yescharacteristic, complemented
31#64677—31no—
32C2×D60C2×C411yescharacteristic
33C2×C4×D15—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38#6714—21no—
39C4⋊Dic15C2×C411yescharacteristic
40C2×C3⋊#168—21no—
41C2×C5×C3⋊C8C2×C411yescharacteristic
42C2×C5×C3⋊C8C2×C411yescharacteristic
43C2×C5×C3⋊C8D411yescharacteristic
44C2×C5×C3⋊C8D411yescharacteristic
45C3×#685—21no—
46C3×C4⋊Dic5C2×C411yescharacteristic
47C2×C3×#168—21no—
48#6653—22no—
49#6651—42no—
50D5×C3⋊C8—42no—
51C4×#213—51no—
52D4×C3⋊C8—51no—
53#4838—51no—
54C3×D4⋊C8—51no—
55#4480—51no—
56#4459—51no—
57#4455D511yescharacteristic, complemented
58C2×D40—31no—
59C2×#676—61no—
60C2×C8×D5—61no—
61C4×D20—31no—
62C4×D20C2×D311yescharacteristic
63C4×C5×C8—31no—
64C4×C5×C8—31no—
65C4×C5×C8C2×D311yescharacteristic
66#3953—31no—
67#3953—31no—
68#3952—61no—
69#3952—61no—
70#3950—31no—
71C4⋊#168—31no—
72C4⋊#168C2×D311yescharacteristic
73#1586—151noSylow
74C22×D15—21no—
75C22×C3×D5—21no—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—21no—
80D60—21no—
81D60—21no—
82C4×D15—41no—
83C4×D15—41no—
84C2×C3×Dic5—21no—
85C3×D20—21no—
86C3×D20M1612yescomplemented
87C3×C4×D5—41no—
88C3×C4×D5—41no—
89C3×C5×C8—22no—
90C3⋊#168—41no—
91C3×#168—41no—
92C5×C3⋊C8—21no—
93C5×C3⋊C8—21no—
94C5×C3⋊C8—21no—
95C5×C3⋊C8—21no—
96C3×C4×D4—51no—
97C2×#213—51no—
98C22×C3⋊C8—101no—
99C2×ΓL(1,𝔽25)—101no—
100C4×D12—51no—
101C3×C4⋊C8—51no—
102C3×C4×C8C2×D511yescharacteristic
103#832—51no—
104#830—101no—
105(C2×D3)⋊C8—101no—
106#809—51no—
107#807—51no—
108C4⋊(C3⋊C8)—51no—
109C4×C3⋊C8C2×D511yescharacteristic
110C4×C3⋊C8C2×D511yescharacteristic
111C2×D20—31no—
112C2×D20C4×D311yescharacteristic
113C2×C4×D5—21no—
114C2×C4×D5—61no—
115C2×C5×C8—21no—
116C2×C5×C8—31no—
117C2×C5×C8—31no—
118C2×C5×C8—31no—
119C2×C5×C8—31no—
120C42×C5C22×D311yescharacteristic
121#685—21no—
122#685—61no—
123C4⋊Dic5—31no—
124C4⋊Dic5C4×D311yescharacteristic
125C2×#168—21no—
126C2×#168—61no—
127D40—62no—
128#676—122no—
129C8×D5—122no—
130C4×D8—151no—
131#436—151no—
132C8×D4—151no—
133#334—151no—
134D4⋊C8—51no—
135D4⋊C8—151no—
136#322—31no—
137C22×C3×C5C4×D411yescharacteristic
138C2×D15—41no—
139C2×D15—41no—
140C2×D15—41no—
141C2×C3×D5—22no—
142C2×C3×D5—41no—
143C2×C3×D5—41no—
144C3×C4×C5—21no—
145C3×C4×C5C2×M1611yescharacteristic
146C3×C4×C5#13111yescharacteristic
147C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
148C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
149Dic15—41no—
150C3×Dic5—41no—
151C2×C3×D4—51no—
152C22×C3×C4—101no—
153C2×D12—51no—
154C2×C4×D3—101no—
155C2×C3×C8—21no—
156C2×C3×C8—101no—
157C3×C4⋊C4—51no—
158C3×C22⋊C4—101no—
159C3×C42C22×D511yescharacteristic
160#213—102no—
161(C2×D3)⋊C4—101no—
162C4⋊Dic3—51no—
163C2×C3⋊C8—101no—
164C2×C3⋊C8—202no—
165C2×C3⋊C8C4×D511yescharacteristic
166C2×C3⋊C8C4×D511yescharacteristic
167C2×C3⋊C8D2011yescharacteristic
168C2×C3⋊C8D2011yescharacteristic
169ΓL(1,𝔽25)—202no—
170C22×D5—21no—
171C22×D5—61no—
172C2×C4×C5C2×C4×D311yescharacteristic
173C2×C4×C5D3×D411yescharacteristic
174C2×C4×C5#23711yescharacteristic
175C2×Dic5—21no—
176C2×Dic5—61no—
177D20—21no—
178D20—61no—
179D20—61no—
180D20ΓL(1,𝔽25)12yescomplemented
181C4×D5—41no—
182C4×D5—41no—
183C4×D5—121no—
184C4×D5—121no—
185C5×C8—22no—
186C5×C8—61no—
187C5×C8—61no—
188C5×C8—61no—
189C5×C8—61no—
190#168—41no—
191#168—121no—
192C2×D8—151no—
193C2×M16—301no—
194C22×C8—301no—
195C4×D4—51no—
196C4×D4—151no—
197#107—151no—
198C4⋊C8—51no—
199C4⋊C8—151no—
200#102—151no—
201#102—151no—
202C22⋊C8—301no—
203C22⋊C8—301no—
204C4×C8—31no—
205C4×C8—31no—
206C4×C8D3×D511yescharacteristic
207C2×C3×C5#43511yescharacteristic
208C2×C3×C5#44211yescharacteristic
209C2×C3×C5#44311yescharacteristic
210D15—81no—
211C3×D5—42no—
212C23×C3—101no—
213C22×D3—101no—
214C3×D4—52no—
215C3×D4—101no—
216C2×C3×C4—101no—
217C2×C3×C4—201no—
218C2×C3×C4—201no—
219C2×C3×C4C2×C4×D511yescharacteristic
220C2×C3×C4C2×D2011yescharacteristic
221C2×C3×C4#70911yescharacteristic
222C2×Dic3—101no—
223D12—101no—
224D12—101no—
225C4×D3—201no—
226C4×D3—201no—
227C3×C8—22no—
228C3×C8—201no—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—21no—
233C3⋊C8—201no—
234C22×C5#67⋊C411yescharacteristic
235C2×D5—22no—
236C2×D5—41no—
237C2×D5—41no—
238C2×D5—121no—
239C2×D5—121no—
240C2×D5—121no—
241C4×C5—21no—
242C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
243C4×C5#90711yescharacteristic
244C4×C5#91111yescharacteristic
245C4×C5#91411yescharacteristic
246Dic5—41no—
247Dic5—121no—
248C2×D4—51no—
249C2×D4—151no—
250C22×C4—101no—
251C22×C4—301no—
252D8—302no—
253M16—602no—
254C2×C8—21no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—101no—
260C2×C8—301no—
261C2×C8—602no—
262C4⋊C4—51no—
263C4⋊C4—151no—
264C22⋊C4—101no—
265C22⋊C4—301no—
266C42C2×D3×D511yescharacteristic
267C3×C5#158611yescharacteristic, complemented, Hall
268C22×C3—102no—
269C22×C3—201no—
270C22×C3—201no—
271C22×C3C4×D2011yescharacteristic
272C2×D3—201no—
273C2×D3—201no—
274C2×D3—201no—
275C3×C4—21no—
276C3×C4—201no—
277C3×C4D5×M1611yescharacteristic
278C3×C4#405311yescharacteristic
279C3×C4#405411yescharacteristic
280C3×C4#405411yescharacteristic
281Dic3—201no—
282C2×C5#473011yescharacteristic
283C2×C5#478511yescharacteristic
284C2×C5#482411yescharacteristic
285D5—42no—
286D5—241no—
287C23—101no—
288C23—301no—
289D4—52no—
290D4—101no—
291D4—301no—
292D4—301no—
293C2×C4—101no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—301no—
297C2×C4—601no—
298C2×C4—601no—
299C2×C4C4×D3×D511yescharacteristic
300C2×C4D3×D2011yescharacteristic
301C2×C4#677911yescharacteristic
302C8—22no—
303C8—61no—
304C8—61no—
305C8—61no—
306C8—61no—
307C8—201no—
308C8—601no—
309C2×C3—202no—
310C2×C3#6498911yescharacteristic
311C2×C3#6499511yescharacteristic
312C2×C3#6500011yescharacteristic
313D3—401no—
314C5#6815711yescharacteristic, complemented, Sylow
315C22—102no—
316C22—201no—
317C22—201no—
318C22—601no—
319C22—601no—
320C22—601no—
321C22#9139511yescharacteristic
322C4—21no—
323C4—201no—
324C4—601no—
325C4D5×ΓL(1,𝔽25)11yescharacteristic
326C4#9125311yescharacteristic
327C4#9125411yescharacteristic
328C4#9126811yescharacteristic
329C3#1059887411yescharacteristic, complemented, Sylow
330C2—202no—
331C2—1201no—
332C2#1174701611yescharacteristic
333C2#1174774111yescharacteristic
334C2#1174804611yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C4×D4
prime radicalC2×#6653C4
cosocleC3×C42×C5C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#1586
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11747012C2semidirect
3. C3⋊C8×D20C2semidirect
4. #11746280C2semidirect
5. C5×#4455C2semidirect
6. C3×#64679C2semidirect
7. #11745866C2semidirect
30. #64679D3semidirect
57. #4455D5semidirect
86. C3×D20M16semidirect
180. D20ΓL(1,𝔽25)semidirect
267. C3×C5#1586semidirect
314. C5#68157semidirect
329. C3#10598874semidirect

Maximal subgroups

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

subgroupindex
C4×#66532
#117470122
C3⋊C8×D202
#117462802
C5×#44552
C3×#646792
#117458662
#105988743
#681575