Finite Group Databasebeta

← #14292400

Subgroups — #14292400

Order 1920.

364 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750939C211yesmaximal, characteristic, complemented
2#11747079C211yesmaximal, characteristic, complemented
3#11747043C211yesmaximal, characteristic
4#11746966C211yesmaximal, characteristic, complemented
5C5×#4482C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7#11745868C211yesmaximal, characteristic, complemented
8#10599241—31nomaximal, Hall
9C2×#6705—21no—
10C4×D60C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13C2×#6655—21no—
14C2×#6655—21no—
15C2×#6653—21no—
16C3×C5×C4⋊C8C2211yescharacteristic
17#91104—21no—
18C4×C3⋊#168C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21#90988—21no—
22#90969—21no—
23#90965—21no—
24#68398—51nomaximal, Hall
25#65376—31no—
26#65374—31no—
27#65132—31no—
28#65127—31no—
29C5×#332—31no—
30#64705D311yescharacteristic, complemented
31#64699—31no—
32C2×D60D411yescharacteristic
33C2×C4×D15—21no—
34C2×C5×Dic6—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×C5×C8—21no—
39C3×C42×C5C2311yescharacteristic
40#6714—21no—
41C4⋊Dic15D411yescharacteristic
42C2×C3⋊#168D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44#6705—42no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C2×C3×#168—21no—
49#6655—42no—
50#6655—42no—
51#6653—42no—
52#5076—51no—
53#5072—51no—
54#4846—51no—
55#4838—51no—
56C3×#331—51no—
57#4482D511yescharacteristic, complemented
58#4479—51no—
59C5×C4⋊Q8—31no—
60C2×#688—61no—
61C2×#688—61no—
62C2×D40—61no—
63C2×#676—61no—
64#4020C2×D311yescharacteristic
65C4×D20—31no—
66C5×C4⋊C8—31no—
67C5×C4⋊C8C2×D311yescharacteristic
68#3953—61no—
69#3952—61no—
70#3941—61no—
71#3939—61no—
72C4⋊#168C2×D311yescharacteristic
73C4×#168—31no—
74#1685—151noSylow
75C22×D15—21no—
76C22×C3×D5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×Dic15—21no—
81D60—21no—
82D60—21no—
83C4×D15—41no—
84C4×D15—41no—
85C2×C5×Dic3—41no—
86C5×Dic6—41no—
87C5×Dic6—41no—
88C3×D20—41no—
89C3×D20—41no—
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—81no—
93C3×C5×C8—41no—
94C3⋊#168—21no—
95C3⋊#168D812yescomplemented
96C3×#168—41no—
97C5×C3⋊C8—41no—
98C3×#127—51no—
99C2×#214—101no—
100C2×#214—101no—
101C2×#213—101no—
102C2×ΓL(1,𝔽25)—101no—
103C4×D12—51no—
104#869C2×D511yescharacteristic
105C3×C4⋊C8—51no—
106C3×C4⋊C8C2×D511yescharacteristic
107#832—101no—
108#821—101no—
109(C2×D3)⋊C8—101no—
110#818—101no—
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112C4×C3⋊C8—51no—
113C2×C5×Q8—61no—
114C2×D20—21no—
115C2×D20—21no—
116C2×D20—21no—
117C2×D20—31no—
118C2×C4×D5—61no—
119C2×C5×C8—21no—
120C2×C5×C8—61no—
121C5×C4⋊C4—61no—
122C5×C4⋊C4—61no—
123C42×C5C22×D311yescharacteristic
124#688—122no—
125#688—122no—
126#685—61no—
127C4⋊Dic5—31no—
128C2×#168—21no—
129C2×#168—31no—
130C2×#168—31no—
131D40—122no—
132#676—122no—
133#492—151no—
134#474—151no—
135#459—151no—
136#436—151no—
137#335—151no—
138#332—31no—
139#331—51no—
140C22×C3×C5#12111yescharacteristic
141C2×D15—41no—
142C2×D15—41no—
143C2×D15—41no—
144C2×C3×D5—81no—
145C2×C3×D5—81no—
146C2×C3×D5—81no—
147C3×C4×C5—21no—
148C3×C4×C5C2×D811yescharacteristic
149C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5#13711yescharacteristic
152Dic15—41no—
153C5×Dic3—81no—
154C2×C3×D4—101no—
155C2×C3×D4—101no—
156C2×C3×D4—101no—
157C2×D12—51no—
158C2×C4×D3—101no—
159C2×Dic6—21no—
160C2×C3×C8—21no—
161C2×C3×C8—101no—
162C3×C42C22×D511yescharacteristic
163#214—202no—
164#214—202no—
165#213—202no—
166(C2×D3)⋊C4—101no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—51no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—51no—
172C2×C3⋊C8—51no—
173ΓL(1,𝔽25)—202no—
174C22×D5—41no—
175C22×D5—61no—
176C5×Q8—121no—
177C5×Q8—121no—
178C2×C4×C5—121no—
179C2×C4×C5#23511yescharacteristic
180C2×C4×C5D3×D411yescharacteristic
181C2×C4×C5D3×D411yescharacteristic
182C2×Dic5—61no—
183D20—41no—
184D20—41no—
185D20—41no—
186D20—41no—
187D20—61no—
188D20—61no—
189D20—81no—
190C4×D5—121no—
191C4×D5—121no—
192C5×C8—41no—
193C5×C8—121no—
194#168—32no—
195#168—41no—
196#168—61no—
197C2×SD16—301no—
198C2×SD16—301no—
199C2×D8—301no—
200C2×M16—301no—
201C4⋊Q8—31no—
202#127—51no—
203C4×D4—151no—
204#107—301no—
205C4⋊C8—31no—
206C4⋊C8—51no—
207C4⋊C8D3×D511yescharacteristic
208#102—301no—
209#102—301no—
210C22⋊C8—301no—
211C4×C8—151no—
212C2×C3×C5#45911yescharacteristic
213C2×C3×C5#46811yescharacteristic
214C2×C3×C5#47111yescharacteristic
215D15—81no—
216C3×D5—161no—
217C23×C3—201no—
218C22×D3—101no—
219C3×D4—201no—
220C3×D4—201no—
221C3×D4—201no—
222C3×D4—201no—
223C3×D4—401no—
224C2×C3×C4#70911yescharacteristic
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×Dic3—41no—
228C2×Dic3—101no—
229D12—101no—
230D12—101no—
231C4×D3—201no—
232C4×D3—201no—
233Dic6—41no—
234Dic6—41no—
235C3×C8—41no—
236C3×C8—201no—
237C3⋊C8—41no—
238C3⋊C8—52no—
239C3⋊C8—101no—
240C22×C5#88411yescharacteristic
241C2×D5—81no—
242C2×D5—81no—
243C2×D5—81no—
244C2×D5—121no—
245C2×D5—121no—
246C2×D5—121no—
247C4×C5—21no—
248C4×C5—241no—
249C4×C5D3×D811yescharacteristic
250C4×C5#91111yescharacteristic
251C4×C5#91411yescharacteristic
252C4×C5#91511yescharacteristic
253Dic5—121no—
254C2×Q8—61no—
255C2×D4—101no—
256C2×D4—101no—
257C2×D4—101no—
258C2×D4—151no—
259C22×C4—301no—
260SD16—602no—
261SD16—602no—
262D8—602no—
263M16—602no—
264C2×C8—21no—
265C2×C8—61no—
266C2×C8—101no—
267C2×C8—151no—
268C2×C8—151no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4—151no—
272C22⋊C4—301no—
273C42C2×D3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—401no—
276C22×C3—401no—
277C22×C3—401no—
278C22×C3#403011yescharacteristic
279C2×D3—201no—
280C2×D3—201no—
281C2×D3—201no—
282C3×C4—21no—
283C3×C4D5×D811yescharacteristic
284C3×C4#406011yescharacteristic
285C3×C4#406011yescharacteristic
286C3×C4#406411yescharacteristic
287Dic3—81no—
288Dic3—201no—
289C2×C5#474811yescharacteristic
290C2×C5#478011yescharacteristic
291C2×C5#478611yescharacteristic
292D5—161no—
293D5—241no—
294C23—201no—
295C23—301no—
296Q8—121no—
297Q8—121no—
298D4—201no—
299D4—201no—
300D4—201no—
301D4—201no—
302D4—301no—
303D4—301no—
304D4—401no—
305C2×C4—121no—
306C2×C4—301no—
307C2×C4—601no—
308C2×C4—601no—
309C2×C4#677111yescharacteristic
310C2×C4#677711yescharacteristic
311C2×C4#679011yescharacteristic
312C8—41no—
313C8—121no—
314C8—152no—
315C8—201no—
316C8—301no—
317C2×C3—801no—
318C2×C3#6504311yescharacteristic
319C2×C3#6507511yescharacteristic
320C2×C3#6510111yescharacteristic
321D3—401no—
322C5#6839811yescharacteristic, complemented, Sylow
323C22—401no—
324C22—401no—
325C22—401no—
326C22—601no—
327C22—601no—
328C22—601no—
329C22#9146111yescharacteristic
330C4—21no—
331C4—241no—
332C4—601no—
333C4#9125811yescharacteristic
334C4#9127811yescharacteristic
335C4#9148111yescharacteristic
336C4#9150611yescharacteristic
337C3#1059924111yescharacteristic, complemented, Sylow
338C2—801no—
339C2—1201no—
340C2#1174740611yescharacteristic
341C2#1174792711yescharacteristic
342C2#1174819811yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radical#11747043C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1685
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11750939C2semidirect
2. #11747079C2semidirect
4. #11746966C2semidirect
5. C5×#4482C2semidirect
6. C3×#64705C2semidirect
7. #11745868C2semidirect
30. #64705D3semidirect
57. #4482D5semidirect
95. C3⋊#168D8semidirect
274. C3×C5#1685semidirect
322. C5#68398semidirect
337. C3#10599241semidirect

Maximal subgroups

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

subgroupindex
#117509392
#117470792
#117470432
#117469662
C5×#44822
C3×#647052
#117458682
#105992413
#683985