Finite Group Databasebeta

← #14313728

Subgroups — #14313728

Order 1920.

524 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C3×#66049C211yesmaximal, characteristic
2#11752436C212yesmaximal, complemented
3#11746794C212yesmaximal, complemented
4#11746727C212yesmaximal, complemented
5#10604603—31nomaximal, Hall
6C2×C3×#711C2211yescharacteristic
7C2×C3×D4×D5C411yescharacteristic
8C2×#6762—22no—
9C3×C5×#127C411yescharacteristic
10C3×#4086C411yescharacteristic
11C3×#4085—22no—
12C3×#4083—22no—
13C3×#4082C2211yescharacteristic
14C3×#4021C2211yescharacteristic
15C3×#4018C411yescharacteristic
16#91242—22no—
17#91234C2214yescomplemented
18#71862—51nomaximal, Hall
19#66049D311yescharacteristic
20#65777—32no—
21#64923—32no—
22#64856—32no—
23C23×C3×D5—21no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4C2×C411yescharacteristic
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×C3×C22⋊D5—22no—
28C2×C3×C22⋊D5—21no—
29C2×C3×C22⋊D5D412yes—
30C22×C3×Dic5D412yes—
31C3×#711—42no—
32C3×D4×D5—42no—
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×Dic10C2311yescharacteristic
36#6762—24no—
37#6762—42no—
38C2×C3⋊#170—42no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C22⋊Dic5—22no—
41C3×#685—21no—
42C3×#685—22no—
43C3×#683—21no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×#535—51no—
46#5237—52no—
47#4542—52no—
48#4542—52no—
49C2×#711C2×D311yescharacteristic
50C2×D4×D5Dic311yescharacteristic
51C2×#704—62no—
52C5×#127Dic311yescharacteristic
53#4086Dic311yescharacteristic
54#4085—22no—
55#4083—22no—
56#4082C2×D311yescharacteristic
57#4021C2×D311yescharacteristic
58#4018Dic311yescharacteristic
59#4013—62no—
60#4005—34no—
61#2134—151noSylow
62C23×C3×C5—21no—
63C23×C3×C5C22⋊C412yes—
64C22×C3×D5—21no—
65C22×C3×D5—42no—
66C22×C3×D5—82no—
67C22×C3×D5C22⋊C411yescharacteristic
68C3×C5×D4—41no—
69C3×C5×D4—41no—
70C3×C5×D4—82no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C3×C22⋊D5—42no—
74C3×C22⋊D5—42no—
75C3×C22⋊D5—82no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—22no—
78C2×C3×Dic5—21no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C2×D412yes—
81C3×D20—41no—
82C3×C4×D5—22no—
83C3×Dic10—41no—
84C3⋊#170—44no—
85C2×C3×#41—51no—
86C22×C3×D4—51no—
87C3×#127—51no—
88C3×#127AGL(1,𝔽5)11yescharacteristic
89C3×#124—51no—
90C3×#124—51no—
91C3×#121—102no—
92C3×#120—102no—
93C3×#117—51no—
94C2×#208—102no—
95#836—54no—
96#833—102no—
97C23×D5—21no—
98C2×C5×D4—22no—
99C2×C5×D4C2×Dic311yescharacteristic
100C2×C5×D4C2×Dic311yescharacteristic
101C2×C22⋊D5—22no—
102C2×C22⋊D5—21no—
103C2×C22⋊D5#6712yes—
104C22×Dic5#6712yes—
105#711—42no—
106D4×D5—42no—
107C2×D20C2×Dic311yescharacteristic
108C2×C4×D5C2×Dic311yescharacteristic
109C2×Dic10C22×D311yescharacteristic
110#704—64no—
111#704—122no—
112C2×#170—122no—
113C42×C5C2×Dic311yescharacteristic
114C22⋊Dic5—22no—
115#685—21no—
116#685—22no—
117#683—21no—
118C4×Dic5C2×Dic311yescharacteristic
119#535—51no—
120#413—152no—
121#355—152no—
122#355—152no—
123C22×C3×C5—22no—
124C22×C3×C5—42no—
125C22×C3×C5—42no—
126C22×C3×C5—41no—
127C22×C3×C5C2×C22⋊C411yescharacteristic
128C2×C3×D5—21no—
129C2×C3×D5—41no—
130C2×C3×D5—42no—
131C2×C3×D5—41no—
132C2×C3×D5—84no—
133C3×C4×C5—21no—
134C3×C4×C5—41no—
135C3×Dic5—22no—
136C3×Dic5—41no—
137C3×Dic5#9912yes—
138C24×C3—101no—
139C3×#41—202no—
140C2×C3×Q8—51no—
141C2×C3×D4—22no—
142C2×C3×D4—52no—
143C2×C3×D4—51no—
144C2×C3×D4—101no—
145C2×C3×D4—102no—
146C2×C3×D4—202no—
147C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
149C22×C3×C4—52no—
150C22×C3×C4—51no—
151C3×C4⋊C4—101no—
152C3×C22⋊C4—102no—
153C3×C22⋊C4—101no—
154C3×C22⋊C4—102no—
155C3×C42—51no—
156C3×C42C2×AGL(1,𝔽5)11yescharacteristic
157#208—104no—
158#208—202no—
159C2×C3⋊C8—202no—
160C23×C5—21no—
161C23×C5#21712yes—
162C22×D5—21no—
163C22×D5—42no—
164C22×D5—82no—
165C22×D5#21711yescharacteristic
166C5×D4—41no—
167C5×D4—41no—
168C5×D4—82no—
169C2×C4×C5—21no—
170C2×C4×C5C22×Dic311yescharacteristic
171C22⋊D5—42no—
172C22⋊D5—42no—
173C22⋊D5—82no—
174C2×Dic5—22no—
175C2×Dic5—22no—
176C2×Dic5—21no—
177C2×Dic5#21711yescharacteristic
178C2×Dic5C2×#6712yes—
179D20—41no—
180C4×D5—22no—
181Dic10—41no—
182#170—124no—
183C2×#41—51no—
184C22×D4—51no—
185C2×M16—302no—
186#127—51no—
187#127ΓL(1,𝔽16)11yescharacteristic
188#124—51no—
189#124—51no—
190#121—102no—
191#120—102no—
192#117—51no—
193#101—154no—
194#100—302no—
195C2×C3×C5—21no—
196C2×C3×C5—42no—
197C2×C3×C5—81no—
198C2×C3×C5C2×#9911yescharacteristic
199C3×D5—41no—
200C3×D5—81no—
201C23×C3—21no—
202C23×C3—51no—
203C23×C3—101no—
204C23×C3—202no—
205C23×C3—402no—
206C23×C3C22⋊AGL(1,𝔽5)12yes—
207C3×Q8—201no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—82no—
211C3×D4—201no—
212C3×D4—202no—
213C3×D4—202no—
214C3×D4—402no—
215C2×C3×C4—21no—
216C2×C3×C4—51no—
217C2×C3×C4—52no—
218C2×C3×C4—102no—
219C2×C3×C4—102no—
220C2×C3×C4—102no—
221C2×C3×C4—101no—
222C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
223C3⋊C8—204no—
224C22×C5—22no—
225C22×C5—42no—
226C22×C5—42no—
227C22×C5—41no—
228C22×C5C2×#21711yescharacteristic
229C2×D5—21no—
230C2×D5—41no—
231C2×D5—42no—
232C2×D5—41no—
233C2×D5—84no—
234C4×C5—21no—
235C4×C5—41no—
236Dic5—22no—
237Dic5—41no—
238Dic5#83412yes—
239C24—101no—
240#41—202no—
241C2×Q8—51no—
242C2×D4—22no—
243C2×D4—52no—
244C2×D4—51no—
245C2×D4—101no—
246C2×D4—102no—
247C2×D4—202no—
248C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
249C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
250C22×C4—52no—
251C22×C4—51no—
252M16—304no—
253M16—602no—
254C2×C8—602no—
255C4⋊C4—101no—
256C22⋊C4—102no—
257C22⋊C4—101no—
258C22⋊C4—102no—
259C42—51no—
260C42C2×ΓL(1,𝔽16)11yescharacteristic
261C3×C5#213411yescharacteristic, complemented, Hall
262C22×C3—22no—
263C22×C3—42no—
264C22×C3—42no—
265C22×C3—41no—
266C22×C3—101no—
267C22×C3—201no—
268C22×C3—202no—
269C22×C3—201no—
270C22×C3—404no—
271C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—52no—
275C3×C4—102no—
276C3×C4—201no—
277C2×C5—21no—
278C2×C5—42no—
279C2×C5—81no—
280C2×C5C2×#83411yescharacteristic
281D5—41no—
282D5—81no—
283C23—21no—
284C23—51no—
285C23—101no—
286C23—202no—
287C23—402no—
288C23#676312yes—
289Q8—201no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—201no—
294D4—202no—
295D4—202no—
296D4—402no—
297C2×C4—21no—
298C2×C4—51no—
299C2×C4—52no—
300C2×C4—102no—
301C2×C4—102no—
302C2×C4—102no—
303C2×C4—101no—
304C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
305C8—604no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3—201no—
310C2×C3—401no—
311C2×C3D5⋊#9911yescharacteristic
312C5#7186211yescharacteristic, complemented, Sylow
313C22—22no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—101no—
318C22—201no—
319C22—202no—
320C22—201no—
321C22—404no—
322C22C2×#676311yescharacteristic
323C4—21no—
324C4—41no—
325C4—52no—
326C4—102no—
327C4—201no—
328C3#1060460311yescharacteristic, complemented, Sylow
329C2—21no—
330C2—42no—
331C2—81no—
332C2—201no—
333C2—401no—
334C2D5⋊#83411yescharacteristic
subgroupG/H
centerC2D5⋊#834
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#127C4
socleC2×C3×C5C2×#99
prime radicalC3×#66049C2
cosocleC2×C3×Dic10C23
hypercenter#127ΓL(1,𝔽16)
hypocenterC3×C5#2134
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752436C2semidirect
3. #11746794C2semidirect
4. #11746727C2semidirect
17. #91234C22semidirect
261. C3×C5#2134semidirect
312. C5#71862semidirect
328. C3#10604603semidirect

Maximal subgroups

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

subgroupindex
C3×#660492
#117524362
#117467942
#117467272
#106046033
#718625