Finite Group Databasebeta

← #14292839

Subgroups — #14292839

Order 1920.

308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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#11751185C211yesmaximal, characteristic
2#11751179C211yesmaximal, characteristic, complemented
3#11750943C211yesmaximal, characteristic
4#11750939C211yesmaximal, characteristic
5C3×C5×#333C211yesmaximal, characteristic, complemented
6#11746302C211yesmaximal, characteristic, complemented
7#11746301C211yesmaximal, characteristic, complemented
8#10599294—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6705—21no—
11C4×D60C2211yescharacteristic
12#91758C2211yescharacteristic
13C3×C5×C4⋊C8C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15#91105—21no—
16#91104—21no—
17#91101—21no—
18#91093—21no—
19#91092—21no—
20#91091—21no—
21#91091—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68501—51nomaximal, Hall
25#65373—31no—
26#65367—31no—
27#65131—31no—
28#65127—31no—
29C5×#333D311yescharacteristic, complemented
30#64701—31no—
31#64700—31no—
32C2×C3×C5×Q8—21no—
33C2×D60D411yescharacteristic
34C2×C4×D15—21no—
35C2×Dic30—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15D411yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168D411yescharacteristic
47C2×C3⋊#168D411yescharacteristic
48#6705—42no—
49#5084—51no—
50#5078—51no—
51#4842—51no—
52#4838—51no—
53C3×#333D511yescharacteristic, complemented
54#4481—51no—
55#4480—51no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C2×#676—61no—
58C4×D20—31no—
59#4015—31no—
60C5×C4⋊C8C2×D311yescharacteristic
61C5×C4⋊C8C2×D311yescharacteristic
62#3953—61no—
63#3952—61no—
64#3949—61no—
65#3941—61no—
66#3940—61no—
67#3939—61no—
68#3939—61no—
69C4⋊#168—31no—
70C4×#168—31no—
71#1695—151noSylow
72C22×D15—21no—
73C3×C5×Q8—81no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×Dic15—21no—
79C2×Dic15—41no—
80D60—21no—
81D60—21no—
82C4×D15—41no—
83C4×D15—41no—
84Dic30—81no—
85C3×C5×C8—41no—
86C3×C5×C8—41no—
87C3⋊#168—21no—
88C3⋊#168—41no—
89C3⋊#168SD1612yes—
90C3×C4⋊Q8C2×D511yescharacteristic
91C2×ΓL(1,𝔽25)—101no—
92C4×D12—51no—
93#869—51no—
94C3×C4⋊C8C2×D511yescharacteristic
95C3×C4⋊C8C2×D511yescharacteristic
96#821—101no—
97(C2×D3)⋊C8—101no—
98#817—101no—
99#809—101no—
100#808—101no—
101#807—101no—
102#807—101no—
103C4⋊(C3⋊C8)—51no—
104C4×C3⋊C8—51no—
105C2×C5×Q8—21no—
106C2×D20—31no—
107C2×C4×D5—61no—
108C2×Dic10—61no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C42×C5C22×D311yescharacteristic
114#685—61no—
115C4⋊Dic5—31no—
116C4⋊Dic5—61no—
117C4⋊Dic5—61no—
118C2×#168—31no—
119C2×#168—31no—
120C2×#168—61no—
121#676—122no—
122#500—151no—
123#476—151no—
124#476—151no—
125#436—151no—
126#334—151no—
127#333—151no—
128#333D1511yescharacteristic, complemented
129C22×C3×C5#12111yescharacteristic
130C2×D15—41no—
131C2×D15—41no—
132C2×D15—41no—
133C3×C4×C5—21no—
134C3×C4×C5—81no—
135C3×C4×C5C2×SD1611yescharacteristic
136C3×C4×C5#13711yescharacteristic
137C3×C4×C5#13711yescharacteristic
138C3×C4×C5#13711yescharacteristic
139Dic15—41no—
140Dic15—81no—
141C2×C3×Q8—21no—
142C2×D12—51no—
143C2×C4×D3—101no—
144C2×Dic6—101no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C42C22×D511yescharacteristic
150(C2×D3)⋊C4—101no—
151C4⋊Dic3—51no—
152C4⋊Dic3—101no—
153C4⋊Dic3—101no—
154C2×C3⋊C8—51no—
155C2×C3⋊C8—51no—
156C2×C3⋊C8—101no—
157ΓL(1,𝔽25)—202no—
158C22×D5—61no—
159C5×Q8—81no—
160C2×C4×C5—41no—
161C2×C4×C5#23511yescharacteristic
162C2×C4×C5D3×D411yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×Dic5—61no—
165C2×Dic5—121no—
166D20—61no—
167D20—61no—
168C4×D5—121no—
169C4×D5—121no—
170Dic10—241no—
171C5×C8—41no—
172C5×C8—41no—
173#168—32no—
174#168—61no—
175#168—121no—
176C2×M16—301no—
177C4⋊Q8—151no—
178C4⋊Q8C2×D1511yescharacteristic
179C4×D4—151no—
180#107—301no—
181#107—301no—
182#106—301no—
183#106—301no—
184C4⋊C8—151no—
185C4⋊C8C2×D1511yescharacteristic
186C4⋊C8C2×D1511yescharacteristic
187#102—301no—
188#102—301no—
189C22⋊C8—301no—
190C4×C8—151no—
191C2×C3×C5#46111yescharacteristic
192C2×C3×C5#47011yescharacteristic
193C2×C3×C5#47211yescharacteristic
194D15—81no—
195C22×D3—101no—
196C3×Q8—81no—
197C2×C3×C4—41no—
198C2×C3×C4#70911yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4D4×D511yescharacteristic
201C2×Dic3—101no—
202C2×Dic3—201no—
203D12—101no—
204D12—101no—
205C4×D3—201no—
206C4×D3—201no—
207Dic6—401no—
208C3×C8—41no—
209C3×C8—41no—
210C3⋊C8—52no—
211C3⋊C8—101no—
212C3⋊C8—201no—
213C22×C5#88411yescharacteristic
214C2×D5—121no—
215C2×D5—121no—
216C2×D5—121no—
217C4×C5—21no—
218C4×C5—81no—
219C4×C5D3×SD1611yescharacteristic
220C4×C5#91511yescharacteristic
221C4×C5#91811yescharacteristic
222C4×C5#91811yescharacteristic
223Dic5—121no—
224Dic5—241no—
225C2×Q8—21no—
226C2×Q8—301no—
227C2×D4—151no—
228C22×C4—301no—
229M16—602no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—151no—
233C2×C8—151no—
234C2×C8—301no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—151no—
238C4⋊C4—301no—
239C4⋊C4—301no—
240C22⋊C4—301no—
241C42C22×D1511yescharacteristic
242C3×C5#169511yescharacteristic, complemented, Hall
243C22×C3#403011yescharacteristic
244C2×D3—201no—
245C2×D3—201no—
246C2×D3—201no—
247C3×C4—21no—
248C3×C4—81no—
249C3×C4D5×SD1611yescharacteristic
250C3×C4#406111yescharacteristic
251C3×C4#406411yescharacteristic
252C3×C4#406411yescharacteristic
253Dic3—201no—
254Dic3—401no—
255C2×C5#474911yescharacteristic
256C2×C5#481611yescharacteristic
257C2×C5#481811yescharacteristic
258D5—241no—
259C23—301no—
260Q8—81no—
261Q8—1201no—
262D4—301no—
263D4—301no—
264C2×C4—41no—
265C2×C4—301no—
266C2×C4—601no—
267C2×C4—601no—
268C2×C4—601no—
269C2×C4#681711yescharacteristic
270C2×C4D4×D1511yescharacteristic
271C2×C4D4×D1511yescharacteristic
272C8—41no—
273C8—41no—
274C8—152no—
275C8—301no—
276C8—601no—
277C2×C3#6503811yescharacteristic
278C2×C3#6510511yescharacteristic
279C2×C3#6510711yescharacteristic
280D3—401no—
281C5#6850111yescharacteristic, complemented, Sylow
282C22—601no—
283C22—601no—
284C22—601no—
285C22#9177311yescharacteristic
286C4—21no—
287C4—81no—
288C4—601no—
289C4—1201no—
290C4SD16×D1511yescharacteristic
291C4#9180411yescharacteristic
292C4#9180711yescharacteristic
293C4#9180711yescharacteristic
294C3#1059929411yescharacteristic, complemented, Sylow
295C2—1201no—
296C2#1175085011yescharacteristic
297C2#1175091711yescharacteristic
298C2#1175091911yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenter#333D15
hypocenterC3×C5#1695
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #11751179C2semidirect
5. C3×C5×#333C2semidirect
6. #11746302C2semidirect
7. #11746301C2semidirect
29. C5×#333D3semidirect
53. C3×#333D5semidirect
128. #333D15semidirect
242. C3×C5#1695semidirect
281. C5#68501semidirect
294. C3#10599294semidirect

Maximal subgroups

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

subgroupindex
#117511852
#117511792
#117509432
#117509392
C3×C5×#3332
#117463022
#117463012
#105992943
#685015