Finite Group Databasebeta

← #14317009

Subgroups — #14317009

Order 1920.

448 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 67 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#11756481C211yesmaximal, characteristic, complemented
2C3×C5×#456C211yesmaximal, characteristic
3#11751347C212yesmaximal
4#11746369C211yesmaximal, characteristic, complemented
5#11746299C212yesmaximal, complemented
6#10601788—31nomaximal, Hall
7C3×C5×2−1+4C2211yescharacteristic
8C3×C5×#137—21no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91840—22no—
11#91833—21no—
12#91833C2212yes—
13#91777—22no—
14#91776—22no—
15C4×Dic30—21no—
16C3×C5×#104—21no—
17C3×C5×#101C2211yescharacteristic
18#91121—22no—
19#91120C2212yes—
20#70995—51nomaximal, Hall
21#66056—31no—
22C5×#456D311yescharacteristic
23#65535—32no—
24#64768—31no—
25#64698—32no—
26C3×C5×#41—22no—
27C3×C5×#41—21no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8—41no—
30C2×C3×C5×Q8D411yescharacteristic
31C2×C3×C5×Q8C2311yescharacteristic
32C2×Dic30—21no—
33C2×Dic30—21no—
34C2×Dic30D412yes—
35C3×C5×Q16—41no—
36C3×C5×SD16—41no—
37C3×C5×M16—21no—
38C3×C5×C4⋊C4—22no—
39C3×C42×C5D411yescharacteristic
40#6718—42no—
41#6716—42no—
42C4⋊Dic15—21no—
43#6712—22no—
44#6712—22no—
45#6712—22no—
46C4×Dic15—22no—
47C4×Dic15—21no—
48C4×Dic15D412yes—
49#6710—22no—
50#5722—51no—
51C3×#456D511yescharacteristic
52#5246—52no—
53#4548—51no—
54#4478—52no—
55C5×2−1+4C2×D311yescharacteristic
56C5×#137—21no—
57C5×C4⋊Q8C2×D311yescharacteristic
58#4097—62no—
59#4090—32no—
60#4090—61no—
61#4034—62no—
62#4033—62no—
63C4×Dic10—61no—
64C5×#104—21no—
65C5×#101C2×D311yescharacteristic
66#3969—62no—
67#3968—32no—
68#2205—151noSylow
69C3×C5×Q8—22no—
70C3×C5×Q8—21no—
71C3×C5×Q8—41no—
72C3×C5×Q8—41no—
73C3×C5×D4—22no—
74C3×C5×D4—21no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C2×D412yes—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×Dic15—22no—
83C2×Dic15—22no—
84Dic30—24no—
85Dic30—42no—
86Dic30—81no—
87C3×C5×C8—41no—
88C3⋊#168—42no—
89C3×2−1+4C2×D511yescharacteristic
90C3×#137—21no—
91C3×C4⋊Q8C2×D511yescharacteristic
92#951—102no—
93#944—52no—
94#944—101no—
95#888—102no—
96#887—102no—
97C4×Dic6—101no—
98C3×#104—21no—
99C3×#101C2×D511yescharacteristic
100#837—102no—
101#836—52no—
102C5×#41—22no—
103C5×#41—21no—
104C5×#41—41no—
105C2×C5×Q8—41no—
106C2×C5×Q8#6711yescharacteristic
107C2×C5×Q8C22×D311yescharacteristic
108C2×Dic10—32no—
109C2×Dic10—61no—
110C2×Dic10—61no—
111C5×Q16—41no—
112C5×SD16—41no—
113C5×M16—21no—
114C5×C4⋊C4—22no—
115C42×C5#6711yescharacteristic
116#689—122no—
117#687—122no—
118C4⋊Dic5—61no—
119#683—62no—
120#683—62no—
121#683—62no—
122C4×Dic5—32no—
123C4×Dic5—62no—
124C4×Dic5—61no—
125#681—62no—
126Q82—151no—
127#456—152no—
128#456D1511yescharacteristic
129#356—151no—
130#356—152no—
131C22×C3×C5—41no—
132C22×C3×C5#12011yescharacteristic
133C3×C4×C5—22no—
134C3×C4×C5—22no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138Dic15—24no—
139Dic15—42no—
140C3×#41—22no—
141C3×#41—21no—
142C3×#41—41no—
143C2×C3×Q8—41no—
144C2×C3×Q8C22⋊D511yescharacteristic
145C2×C3×Q8C22×D511yescharacteristic
146C2×Dic6—52no—
147C2×Dic6—101no—
148C2×Dic6—101no—
149C3×Q16—41no—
150C3×SD16—41no—
151C3×M16—21no—
152C3×C4⋊C4—22no—
153C3×C42C22⋊D511yescharacteristic
154#216—202no—
155#214—202no—
156C4⋊Dic3—101no—
157Dic3⋊C4—102no—
158Dic3⋊C4—102no—
159Dic3⋊C4—102no—
160C4×Dic3—52no—
161C4×Dic3—102no—
162C4×Dic3—101no—
163#208—102no—
164C5×Q8—22no—
165C5×Q8—21no—
166C5×Q8—41no—
167C5×Q8—41no—
168C5×D4—22no—
169C5×D4—21no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—42no—
174C2×C4×C5—41no—
175C2×C4×C5D3×D412yes—
176C2×C4×C5C2×#6711yescharacteristic
177C2×Dic5—62no—
178C2×Dic5—62no—
179Dic10—64no—
180Dic10—122no—
181Dic10—241no—
182C5×C8—41no—
183#168—122no—
1842−1+4C2×D1511yescharacteristic
185#137—21no—
186#137—302no—
187C4⋊Q8—152no—
188C4⋊Q8—302no—
189C4⋊Q8—301no—
190C4⋊Q8C2×D1511yescharacteristic
191C4×Q8—302no—
192C4×Q8—301no—
193#104—21no—
194#104—302no—
195#101—152no—
196#101C2×D1511yescharacteristic
197C2×C3×C5—21no—
198C2×C3×C5—81no—
199C2×C3×C5B(4,𝔽2)11yescharacteristic
200C3×Q8—22no—
201C3×Q8—21no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×D4—22no—
205C3×D4—21no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—42no—
210C2×C3×C4—41no—
211C2×C3×C4D4×D512yes—
212C2×C3×C4C2×C22⋊D511yescharacteristic
213C2×Dic3—102no—
214C2×Dic3—102no—
215Dic6—104no—
216Dic6—202no—
217Dic6—401no—
218C3×C8—41no—
219C3⋊C8—202no—
220C22×C5—41no—
221C22×C5#93711yescharacteristic
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—41no—
226C4×C5—41no—
227Dic5—64no—
228Dic5—122no—
229#41—22no—
230#41—21no—
231#41—41no—
232C2×Q8—41no—
233C2×Q8—152no—
234C2×Q8—301no—
235C2×Q8—301no—
236C2×Q8#122011yescharacteristic
237C2×Q8C22×D1511yescharacteristic
238Q16—41no—
239Q16—602no—
240SD16—41no—
241SD16—602no—
242M16—21no—
243M16—302no—
244C4⋊C4—22no—
245C4⋊C4—302no—
246C4⋊C4—301no—
247C4⋊C4—302no—
248C4⋊C4—302no—
249C42—152no—
250C42—302no—
251C42—301no—
252C42#122011yescharacteristic
253C3×C5#220511yescharacteristic, complemented, Hall
254C22×C3—41no—
255C22×C3#408311yescharacteristic
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—21no—
259C3×C4—41no—
260C3×C4—41no—
261Dic3—104no—
262Dic3—202no—
263C2×C5—21no—
264C2×C5—81no—
265C2×C5#503211yescharacteristic
266Q8—21no—
267Q8—22no—
268Q8—41no—
269Q8—41no—
270Q8—304no—
271Q8—602no—
272Q8—1201no—
273D4—21no—
274D4—22no—
275D4—41no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—302no—
281C2×C4—302no—
282C2×C4D4×D1512yes—
283C2×C4C2×#122011yescharacteristic
284C8—41no—
285C8—602no—
286C2×C3—21no—
287C2×C3—81no—
288C2×C3#6532111yescharacteristic
289C5#7099511yescharacteristic, complemented, Sylow
290C22—41no—
291C22#9182611yescharacteristic
292C4—22no—
293C4—21no—
294C4—22no—
295C4—41no—
296C4—41no—
297C4—304no—
298C4—602no—
299C3#1060178811yescharacteristic, complemented, Sylow
300C2—21no—
301C2—81no—
302C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
FittingC3×C5×#456C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×C5×2−1+4C22
hypercenter#456D15
hypocenterC3×C5#2205
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
4. #11746369C2semidirect
5. #11746299C2semidirect
253. C3×C5#2205semidirect
289. C5#70995semidirect
299. C3#10601788semidirect

Maximal subgroups

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

subgroupindex
#117564812
C3×C5×#4562
#117513472
#117463692
#117462992
#106017883
#709955