Finite Group Databasebeta

← #14285213

Subgroups — #14285213

Order 1920.

396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752497C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic
3C3×#65678C211yesmaximal, characteristic
4#11746511C212yesmaximal, complemented
5#11746510C212yesmaximal, complemented
6#10604445—31nomaximal, Hall
7C4×Dic30C411yescharacteristic
8C4×C5×Dic6C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91468C2211yescharacteristic
11C4×#1204—21no—
12#91378—21no—
13#91376C2211yescharacteristic
14#91360C411yescharacteristic
15#91359C411yescharacteristic
16#91357—21no—
17#91349—21no—
18#91233C2212yes—
19#91232—21no—
20#91231—21no—
21C3×#4004C2212yes—
22C3×#4003—21no—
23C3×C4×#170—21no—
24#70781—51nomaximal, Hall
25#65912—31no—
26#65684—31no—
27#65678D311yescharacteristic
28#64931—32no—
29#64873—32no—
30C2×Dic30C2×C411yescharacteristic
31C2×C5×Dic6C2×C411yescharacteristic
32C2×C3×C4×D5C2×C411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×#1204—21no—
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38C3×C42×C5C2×C411yescharacteristic
39C4⋊Dic15C2×C411yescharacteristic
40#6712—21no—
41C4×Dic15—21no—
42C5×C4⋊Dic3C2×C411yescharacteristic
43C5×Dic3⋊C4—21no—
44C4×C5×Dic3—21no—
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48Dic3⋊Dic5—21no—
49#6669—21no—
50#6668—21no—
51#6668—21no—
52#6668—21no—
53#6665—21no—
54#6665—21no—
55#5470—51no—
56C3×#431—51no—
57#4926—51no—
58#4486—52no—
59#4481—52no—
60C4×C5×Q8—31no—
61#4092—31no—
62#4090—31no—
63#4043—31no—
64#4042—61no—
65#4035—61no—
66#4034—31no—
67#4018—61no—
68C42×D5C2×D311yescharacteristic
69C4×Dic10—31no—
70C4×Dic10—61no—
71#4004—32no—
72#4004C2×D312yes—
73#4003—21no—
74#4003—61no—
75#4002—61no—
76C4×#170—21no—
77#1554—151noSylow
78C22×C3×D5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×Dic15—21no—
83C2×Dic15—21no—
84Dic30—41no—
85C2×C5×Dic3—21no—
86C2×C5×Dic3—21no—
87C5×Dic6—41no—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C2×C3×Dic5C2×D411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—41no—
94#1204—42no—
95C3⋊#170—42no—
96C3×#170—42no—
97C2×C3×C42—51no—
98#926—101no—
99#924—51no—
100#924—51no—
101#924—101no—
102#870—101no—
103#869—51no—
104#869—51no—
105C4×Dic6—51no—
106C4×Dic6—101no—
107C4×Dic6AGL(1,𝔽5)11yescharacteristic
108C3×C4⋊C8—52no—
109C3×C22⋊C8—101no—
110C3×C4×C8—101no—
111#830—101no—
112C4⋊(C3⋊C8)—52no—
113#803—101no—
114C2×C5×Q8—31no—
115C2×C4×D5C4×D311yescharacteristic
116C2×C4×D5D1211yescharacteristic
117C2×C4×D5#6711yescharacteristic
118C2×Dic10—31no—
119C2×Dic10—61no—
120C2×#170—22no—
121C2×#170—62no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—61no—
124C42×C5—61no—
125C42×C5C4×D311yescharacteristic
126#685—61no—
127#685—61no—
128C4⋊Dic5—31no—
129C4⋊Dic5—61no—
130#683—61no—
131#683—61no—
132#683—61no—
133#683—61no—
134#683—61no—
135C4×Dic5—61no—
136C4×Dic5D1211yescharacteristic
137C4×Dic5#6711yescharacteristic
138C4×Dic5C22×D311yescharacteristic
139#533—151no—
140#432—151no—
141#431—51no—
142#333—152no—
143#332—152no—
144C22×C3×C5C2×C22⋊C411yescharacteristic
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C2×C3×D5—21no—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151Dic15—41no—
152Dic15—41no—
153C3×Dic5—21no—
154C3×Dic5#13512yes—
155C3×Dic5#13712yes—
156C5×Dic3—41no—
157C5×Dic3—41no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C2×Dic6—51no—
162C2×Dic6—101no—
163C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
164C2×C3×C8—102no—
165C3×C42—51no—
166C3×C42—51no—
167C3×C42—51no—
168C3×C42C2×AGL(1,𝔽5)11yescharacteristic
169#217—101no—
170#217—101no—
171C4⋊Dic3—51no—
172C4⋊Dic3—101no—
173C4⋊Dic3—101no—
174C4⋊Dic3—101no—
175C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
176Dic3⋊C4—21no—
177Dic3⋊C4—101no—
178Dic3⋊C4—101no—
179Dic3⋊C4—101no—
180C4×Dic3—21no—
181C4×Dic3—101no—
182C2×C3⋊C8—102no—
183C22×D5(C2×D3)⋊C411yescharacteristic
184C5×Q8—121no—
185C2×C4×C5—61no—
186C2×C4×C5—61no—
187C2×C4×C5(C2×D3)⋊C411yescharacteristic
188C2×C4×C5(C2×D3)⋊C411yescharacteristic
189C2×C4×C5C2×C4×D311yescharacteristic
190C2×Dic5—61no—
191C2×Dic5—61no—
192C2×Dic5(C2×D3)⋊C411yescharacteristic
193C2×Dic5C2×D1211yescharacteristic
194C2×Dic5C2×#6711yescharacteristic
195C4×D5—22no—
196C4×D5—22no—
197C4×D5—41no—
198Dic10—122no—
199Dic10—121no—
200#170—42no—
201#170—122no—
202C4⋊Q8—151no—
203C4⋊Q8—151no—
204#125—301no—
205C22⋊Q8—151no—
206C22⋊Q8—151no—
207C22⋊Q8—301no—
208C4×Q8—31no—
209C4×Q8—151no—
210C4×Q8—301no—
211#117—301no—
212C2×C42—51no—
213C4⋊C8—52no—
214C4⋊C8—152no—
215C22⋊C8—101no—
216C22⋊C8—301no—
217#97—301no—
218C4×C8—101no—
219C2×C3×C5#41311yescharacteristic
220C2×C3×C5#41611yescharacteristic
221C2×C3×C5#41911yescharacteristic
222C3×D5—41no—
223C23×C3—51no—
224C2×C3×C4—51no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—102no—
228C2×C3×C4—102no—
229C2×C3×C4—201no—
230C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
231C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—101no—
236C2×Dic3—101no—
237Dic6—41no—
238Dic6—202no—
239Dic6—201no—
240C3×C8—202no—
241C3⋊C8—202no—
242C22×C5C2×(C2×D3)⋊C411yescharacteristic
243C2×D5—21no—
244C2×D5—21no—
245C2×D5—21no—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—121no—
250C4×C5—121no—
251Dic5—21no—
252Dic5—121no—
253Dic5—121no—
254Dic5#90412yes—
255Dic5#95112yes—
256C2×Q8—31no—
257C2×Q8—151no—
258C2×Q8—301no—
259C22×C4—51no—
260C22×C4—51no—
261C22×C4—51no—
262C2×C8—102no—
263C2×C8—302no—
264C4⋊C4—31no—
265C4⋊C4—61no—
266C4⋊C4—151no—
267C4⋊C4—301no—
268C4⋊C4—301no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4—301no—
272C4⋊C4—301no—
273C22⋊C4—301no—
274C22⋊C4—301no—
275C42—51no—
276C42—51no—
277C42—51no—
278C42—61no—
279C42—301no—
280C42D3×AGL(1,𝔽5)11yescharacteristic
281C3×C5#155411yescharacteristic, complemented, Hall
282C22×C3—101no—
283C22×C3—101no—
284C22×C3—101no—
285C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—52no—
290C3×C4—52no—
291C3×C4—101no—
292Dic3—41no—
293Dic3—41no—
294Dic3—201no—
295Dic3—201no—
296C2×C5#500411yescharacteristic
297C2×C5#511311yescharacteristic
298C2×C5#513211yescharacteristic
299D5—41no—
300C23—51no—
301Q8—121no—
302Q8—601no—
303Q8—602no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—51no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—102no—
310C2×C4—102no—
311C2×C4—201no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
315C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
316C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
317C8—202no—
318C8—602no—
319C2×C3—201no—
320C2×C3#6576111yescharacteristic
321C2×C3#6578211yescharacteristic
322C2×C3#6579411yescharacteristic
323C5#7078111yescharacteristic, complemented, Sylow
324C22—101no—
325C22—101no—
326C22—101no—
327C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—52no—
332C4—52no—
333C4—101no—
334C4—121no—
335C4—121no—
336C4—601no—
337C4—601no—
338C3#1060444511yescharacteristic, complemented, Sylow
339C2—201no—
340C2#1175170411yescharacteristic
341C2#1175171111yescharacteristic
342C2#1175181811yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1554
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746511C2semidirect
5. #11746510C2semidirect
281. C3×C5#1554semidirect
323. C5#70781semidirect
338. C3#10604445semidirect

Maximal subgroups

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

subgroupindex
#117524972
#117523432
C3×#656782
#117465112
#117465102
#106044453
#707815