Finite Group Databasebeta

← #14282289

Subgroups — #14282289

Order 1920.

632 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×C3×D4×Dic5C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic, complemented
3C4×#6762C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#170)C214yesmaximal, complemented
5#10604924—31nomaximal, Hall
6C22×C3×C5×D4C411yescharacteristic
7C23×C3×Dic5—21no—
8C2×#6762—21no—
9C2×C3×C22⋊Dic5—21no—
10C3×D4×Dic5—21no—
11C3×D4×Dic5—21no—
12C3×D4×Dic5C412yes—
13C3×D4×Dic5C2212yes—
14C2×C3×C4⋊Dic5C411yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16#91241—21no—
17#91231—21no—
18#91231—21no—
19C4⋊(C3⋊#170)C2212yescomplemented
20C4×C3⋊#170C2212yescomplemented
21#71599—51nomaximal, Hall
22C2×D4×Dic5D311yescharacteristic
23#65759—31no—
24C4×#704—31no—
25D4⋊#170—34no—
26C24×C3×C5—21no—
27C2×C3×C5×D4—24no—
28C2×C3×C5×D4—21no—
29C2×C3×C5×D4C2×C412yes—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5—21no—
32C22×C3×Dic5—22no—
33C22×C3×Dic5—22no—
34C22×C3×Dic5—44no—
35C22×C3×Dic5D411yescharacteristic
36C22×C3×Dic5D411yescharacteristic
37#6762—24no—
38C2×C3⋊#170—22no—
39C2×C3⋊#170—22no—
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5—22no—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5C2×C412yes—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48C2×C3×C4×D4—51no—
49#4926—51no—
50C4×#208—51no—
51D4⋊(C3⋊C8)—54no—
52C22×C5×D4Dic311yescharacteristic
53C23×Dic5—21no—
54C2×#704—61no—
55C2×C22⋊Dic5—21no—
56D4×Dic5—21no—
57D4×Dic5—21no—
58D4×Dic5Dic312yes—
59D4×Dic5C2×D312yes—
60C2×C4⋊Dic5Dic311yescharacteristic
61C2×C4×Dic5C2×D311yescharacteristic
62C22⋊#170—61no—
63#4002—61no—
64#4002—61no—
65C4⋊#170—32no—
66C4×#170—32no—
67#1490—151noSylow
68C23×C3×C5—24no—
69C23×C3×C5—22no—
70C23×C3×C5—42no—
71C23×C3×C5—42no—
72C23×C3×C5C22⋊C411yescharacteristic
73C3×C5×D4—24no—
74C3×C5×D4—22no—
75C3×C5×D4M1614yescomplemented
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C2×C3×Dic5—22no—
82C2×C3×Dic5—44no—
83C2×C3×Dic5—42no—
84C2×C3×Dic5—44no—
85C2×C3×Dic5C22⋊C411yescharacteristic
86C2×C3×Dic5C22⋊C411yescharacteristic
87C2×C3×Dic5C2×D411yescharacteristic
88C2×C3×Dic5C2×D411yescharacteristic
89C3⋊#170—24no—
90C3⋊#170—42no—
91C22×C3×D4AGL(1,𝔽5)11yescharacteristic
92C23×C3×C4—101no—
93C3×C4×D4—52no—
94C3×C4×D4—52no—
95C3×C4×D4—101no—
96C3×C4×D4—101no—
97C2×C3×C4⋊C4—51no—
98C2×C3×C22⋊C4—101no—
99C2×C3×C42—51no—
100C2×#208—101no—
101#830—101no—
102C4⋊(C3⋊C8)—52no—
103#803—101no—
104#803—101no—
105C4×C3⋊C8—52no—
106C24×C5—21no—
107C2×C5×D4—24no—
108C2×C5×D4—21no—
109C2×C5×D4C2×Dic312yes—
110C22×C4×C5C2×Dic311yescharacteristic
111C22×Dic5—21no—
112C22×Dic5—22no—
113C22×Dic5—22no—
114C22×Dic5—44no—
115C22×Dic5#6711yescharacteristic
116C22×Dic5#6711yescharacteristic
117#704—64no—
118C2×#170—62no—
119C2×#170—62no—
120C22⋊Dic5—22no—
121C22⋊Dic5—22no—
122C4⋊Dic5—21no—
123C4⋊Dic5C2×Dic312yes—
124C4×Dic5C2×Dic311yescharacteristic
125C4×Dic5#6711yescharacteristic
126C4×Dic5#6711yescharacteristic
127C4×Dic5C22×D311yescharacteristic
128C2×C4×D4—51no—
129#432—151no—
130C4×M16—151no—
131D4⋊C8—154no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5—24no—
135C22×C3×C5—48no—
136C22×C3×C5—42no—
137C22×C3×C5—42no—
138C22×C3×C5#10412yes—
139C22×C3×C5C2×C22⋊C411yescharacteristic
140C3×C4×C5—21no—
141C3×C4×C5C2×M1612yes—
142C3×Dic5—21no—
143C3×Dic5—21no—
144C3×Dic5—21no—
145C3×Dic5—42no—
146C3×Dic5AGL(1,ℤ/8)12yes—
147C24×C3—21no—
148C2×C3×D4—24no—
149C2×C3×D4—21no—
150C2×C3×D4C2×AGL(1,𝔽5)12yes—
151C22×C3×C4—51no—
152C22×C3×C4—51no—
153C22×C3×C4—102no—
154C22×C3×C4—102no—
155C22×C3×C4—101no—
156C22×C3×C4—204no—
157C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
158C3×C4⋊C4—52no—
159C3×C4⋊C4—101no—
160C3×C22⋊C4—102no—
161C3×C22⋊C4—102no—
162C3×C42—51no—
163C3×C42—51no—
164C3×C42—51no—
165C3×C42—51no—
166#208—104no—
167C2×C3⋊C8—102no—
168C2×C3⋊C8—102no—
169C23×C5—24no—
170C23×C5—22no—
171C23×C5—42no—
172C23×C5—42no—
173C23×C5#21711yescharacteristic
174C5×D4—24no—
175C5×D4—22no—
176C5×D4#20814yescomplemented
177C2×C4×C5—22no—
178C2×C4×C5#21711yescharacteristic
179C2×C4×C5C22×Dic311yescharacteristic
180C2×Dic5—22no—
181C2×Dic5—22no—
182C2×Dic5—22no—
183C2×Dic5—44no—
184C2×Dic5—42no—
185C2×Dic5—44no—
186C2×Dic5#21711yescharacteristic
187C2×Dic5#21711yescharacteristic
188C2×Dic5C2×#6711yescharacteristic
189C2×Dic5C2×#6711yescharacteristic
190#170—64no—
191#170—122no—
192C22×D4ΓL(1,𝔽16)11yescharacteristic
193C23×C4—101no—
194C2×M16—301no—
195C4×D4—52no—
196C4×D4—52no—
197C4×D4—101no—
198C4×D4—101no—
199C2×C4⋊C4—51no—
200C2×C22⋊C4—101no—
201C2×C42—51no—
202C4⋊C8—152no—
203C22⋊C8—301no—
204#97—301no—
205#97—301no—
206C4×C8—152no—
207C2×C3×C5—22no—
208C2×C3×C5—44no—
209C2×C3×C5#40711yescharacteristic
210C2×C3×C5#41811yescharacteristic
211C2×C3×C5C2×#10411yescharacteristic
212C23×C3—24no—
213C23×C3—22no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
217C3×D4—24no—
218C3×D4—22no—
219C3×D4#70414yescomplemented
220C2×C3×C4—22no—
221C2×C3×C4—51no—
222C2×C3×C4—51no—
223C2×C3×C4—51no—
224C2×C3×C4—51no—
225C2×C3×C4—102no—
226C2×C3×C4—102no—
227C2×C3×C4—102no—
228C2×C3×C4—204no—
229C2×C3×C4—204no—
230C2×C3×C4—202no—
231C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
233C3⋊C8—104no—
234C3⋊C8—202no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—24no—
238C22×C5—48no—
239C22×C5—42no—
240C22×C5—42no—
241C22×C5#83712yes—
242C22×C5C2×#21711yescharacteristic
243C4×C5—21no—
244C4×C5C2×#20812yes—
245Dic5—21no—
246Dic5—21no—
247Dic5—21no—
248Dic5—42no—
249Dic5#93212yes—
250C24—21no—
251C2×D4—24no—
252C2×D4—21no—
253C2×D4C2×ΓL(1,𝔽16)12yes—
254C22×C4—51no—
255C22×C4—51no—
256C22×C4—102no—
257C22×C4—102no—
258C22×C4—101no—
259C22×C4—204no—
260C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
261M16—304no—
262C2×C8—302no—
263C2×C8—302no—
264C4⋊C4—52no—
265C4⋊C4—101no—
266C22⋊C4—102no—
267C22⋊C4—102no—
268C42—51no—
269C42—51no—
270C42—51no—
271C42—51no—
272C3×C5#149011yescharacteristic, complemented, Hall
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—24no—
276C22×C3—48no—
277C22×C3—42no—
278C22×C3—42no—
279C22×C3#400812yes—
280C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
281C3×C4—21no—
282C3×C4—52no—
283C3×C4—101no—
284C3×C4—101no—
285C3×C4—101no—
286C3×C4—202no—
287C3×C4C2×#70412yes—
288C2×C5—22no—
289C2×C5—44no—
290C2×C5#520711yescharacteristic
291C2×C5#521511yescharacteristic
292C2×C5C2×#83711yescharacteristic
293C23—24no—
294C23—22no—
295C23—42no—
296C23—42no—
297C23#676311yescharacteristic
298D4—24no—
299D4—22no—
300D4#676214yescomplemented
301C2×C4—22no—
302C2×C4—51no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—102no—
307C2×C4—102no—
308C2×C4—102no—
309C2×C4—204no—
310C2×C4—204no—
311C2×C4—202no—
312C2×C4#676311yescharacteristic
313C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
314C8—304no—
315C8—602no—
316C2×C3—22no—
317C2×C3—44no—
318C2×C3#6576711yescharacteristic
319C2×C3C2×#400811yescharacteristic
320C2×C3#6579811yescharacteristic
321C5#7159911yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—24no—
325C22—48no—
326C22—42no—
327C22—42no—
328C22#9123712yes—
329C22C2×#676311yescharacteristic
330C4—21no—
331C4—52no—
332C4—101no—
333C4—101no—
334C4—101no—
335C4—202no—
336C4C2×#676212yes—
337C3#1060492411yescharacteristic, complemented, Sylow
338C2—22no—
339C2—44no—
340C2#1175242611yescharacteristic
341C2C2×#9123711yescharacteristic
342C2#1175245711yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
Fitting, prime radicalC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#1490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11752418C2semidirect
3. C4×#6762C2semidirect
4. D4⋊(C3⋊#170)C2semidirect
19. C4⋊(C3⋊#170)C22semidirect
20. C4×C3⋊#170C22semidirect
75. C3×C5×D4M16semidirect
176. C5×D4#208semidirect
219. C3×D4#704semidirect
272. C3×C5#1490semidirect
300. D4#6762semidirect
321. C5#71599semidirect
337. C3#10604924semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
#117524182
C4×#67622
D4⋊(C3⋊#170)2
#106049243
#715995