Finite Group Databasebeta

← #14284822

Subgroups — #14284822

Order 1920.

480 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 110 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
1D15×C4⋊Q8C211yesmaximal, characteristic
2#11747015C211yesmaximal, characteristic
3#11746859C211yesmaximal, characteristic
4C5×#4547C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599213—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91833—21no—
12C4⋊C4×D15—21no—
13C4⋊C4×D15C412yes—
14#91777—21no—
15#91777C412yes—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C2×#6651—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90983—21no—
24#90957—21no—
25#90951—21no—
26#68420—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65126—31no—
29#65122—31no—
30C5×#332—31no—
31#64767D311yescharacteristic, complemented
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35Q8×D15—42no—
36Q8×D15—42no—
37C2×C4×D15—22no—
38C2×C4×D15C2×C411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×Dic30—21no—
42C2×Dic30—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C412yes—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15C2×C412yes—
48#6712—22no—
49#6712—22no—
50C4×Dic15C2×C411yescharacteristic
51C4×Dic15D411yescharacteristic
52C4×Dic15D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#6651—42no—
58D3×C4⋊Q8—51no—
59#4837—51no—
60#4833—51no—
61C3×#332—51no—
62#4547D511yescharacteristic, complemented
63#4486—51no—
64#4482—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4090—61no—
68C2×#676—61no—
69D5×C4⋊C4—32no—
70D5×C4⋊C4—61no—
71#4034—32no—
72#4034—61no—
73C42×D5—31no—
74#4015—31no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3952—61no—
78#3946—61no—
79C8×Dic5—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82#1546—151noSylow
83C22×D15C22⋊C411yescharacteristic
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—22no—
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C22⋊C411yescharacteristic
93C2×Dic15C22⋊C411yescharacteristic
94C4×D15—21no—
95C4×D15—21no—
96C4×D15—22no—
97C4×D15—44no—
98C4×D15D812yes—
99C4×D15SD1612yes—
100Dic30—41no—
101Dic30—41no—
102Dic30—44no—
103C3×#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C5×C3⋊C8—41no—
107C2×D3×Q8—101no—
108C3×C4⋊Q8C2×D511yescharacteristic
109#944—101no—
110C2×ΓL(1,𝔽25)—101no—
111D3×C4⋊C4—52no—
112D3×C4⋊C4—101no—
113#888—52no—
114#888—101no—
115C42×D3—51no—
116#869—51no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8—51no—
119(C2×D3)⋊C8—101no—
120Dic3⋊C8—101no—
121C8×Dic3—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C2×C5×Q8—21no—
125Q8×D5—122no—
126Q8×D5—122no—
127C2×C4×D5—31no—
128C2×C4×D5—31no—
129C2×C4×D5—31no—
130C2×C4×D5—62no—
131C2×Dic10—62no—
132C2×Dic10—61no—
133C2×C5×C8—61no—
134C2×C5×C8—61no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4C4×D312yes—
137C42×C5C22×D311yescharacteristic
138C4⋊Dic5—32no—
139C4⋊Dic5—61no—
140#683—62no—
141#683—62no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145C2×#168—21no—
146C2×#168—21no—
147#676—122no—
148C2×C4⋊Q8—151no—
149#431—151no—
150#423—151no—
151#332—31no—
152#332—51no—
153#332—151no—
154#332—151no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×D15—21no—
157C2×D15—21no—
158C2×D15#10212yes—
159C3×C4×C5—21no—
160C3×C4×C5—42no—
161C3×C4×C5C2×D811yescharacteristic
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—21no—
166Dic15—42no—
167Dic15#10112yes—
168Dic15#10212yes—
169C2×C3×Q8—21no—
170D3×Q8—202no—
171D3×Q8—202no—
172C2×C4×D3—51no—
173C2×C4×D3—51no—
174C2×C4×D3—51no—
175C2×C4×D3—102no—
176C2×Dic6—102no—
177C2×Dic6—101no—
178C2×C3×C8—101no—
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4C4×D512yes—
182C3×C42C22×D511yescharacteristic
183C4⋊Dic3—52no—
184C4⋊Dic3—101no—
185Dic3⋊C4—102no—
186Dic3⋊C4—102no—
187C4×Dic3—51no—
188C4×Dic3—51no—
189C4×Dic3—51no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192ΓL(1,𝔽25)—202no—
193C22×D5—31no—
194C5×Q8—41no—
195C5×Q8—41no—
196C2×C4×C5—22no—
197C2×C4×C5C2×C4×D311yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×Dic5—31no—
201C2×Dic5—31no—
202C2×Dic5—31no—
203C2×Dic5—62no—
204C4×D5—32no—
205C4×D5—32no—
206C4×D5—62no—
207C4×D5—61no—
208C4×D5—61no—
209C4×D5—124no—
210Dic10—124no—
211Dic10—121no—
212Dic10—121no—
213C5×C8—121no—
214C5×C8—121no—
215#168—41no—
216#168—41no—
217C22×Q8—301no—
218C2×M16—301no—
219C4⋊Q8—152no—
220C4⋊Q8—151no—
221C4⋊Q8—301no—
222C4⋊Q8—301no—
223C4⋊Q8D3×D511yescharacteristic
224C2×C4⋊C4—152no—
225C2×C4⋊C4—301no—
226C2×C42—151no—
227C4⋊C8—31no—
228C4⋊C8—31no—
229C4⋊C8—51no—
230C4⋊C8—51no—
231C4⋊C8—301no—
232C22⋊C8—301no—
233C4×C8—301no—
234C2×C3×C5C2×#10111yescharacteristic
235C2×C3×C5C2×#10211yescharacteristic
236C2×C3×C5#41911yescharacteristic
237D15—22no—
238C22×D3—51no—
239C3×Q8—41no—
240C3×Q8—41no—
241C2×C3×C4—22no—
242C2×C3×C4C2×C4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3—102no—
249C4×D3—52no—
250C4×D3—52no—
251C4×D3—102no—
252C4×D3—101no—
253C4×D3—101no—
254C4×D3—204no—
255Dic6—204no—
256Dic6—201no—
257Dic6—201no—
258C3×C8—201no—
259C3×C8—201no—
260C3⋊C8—41no—
261C3⋊C8—41no—
262C22×C5D3×C22⋊C411yescharacteristic
263C2×D5—32no—
264C2×D5—61no—
265C2×D5—61no—
266C4×C5—21no—
267C4×C5—42no—
268C4×C5D3×D811yescharacteristic
269C4×C5D3×SD1611yescharacteristic
270C4×C5#91511yescharacteristic
271C4×C5#91811yescharacteristic
272Dic5—32no—
273Dic5—32no—
274Dic5—61no—
275Dic5—122no—
276C2×Q8—21no—
277C2×Q8—302no—
278C2×Q8—301no—
279C2×Q8—602no—
280C2×Q8—602no—
281C22×C4—151no—
282C22×C4—151no—
283C22×C4—151no—
284C22×C4—302no—
285M16—602no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—101no—
289C2×C8—101no—
290C4⋊C4—21no—
291C4⋊C4—152no—
292C4⋊C4—302no—
293C4⋊C4—302no—
294C4⋊C4—301no—
295C4⋊C4#120012yes—
296C42—151no—
297C42—151no—
298C42—151no—
299C42C2×D3×D511yescharacteristic
300C3×C5#154611yescharacteristic, complemented, Hall
301C22×C3D5×C22⋊C411yescharacteristic
302C2×D3—52no—
303C2×D3—101no—
304C2×D3—101no—
305C3×C4—21no—
306C3×C4—42no—
307C3×C4D5×D811yescharacteristic
308C3×C4D5×SD1611yescharacteristic
309C3×C4#406111yescharacteristic
310C3×C4#406411yescharacteristic
311Dic3—52no—
312Dic3—52no—
313Dic3—101no—
314Dic3—202no—
315C2×C5D3×#10111yescharacteristic
316C2×C5D3×#10211yescharacteristic
317C2×C5#480211yescharacteristic
318D5—62no—
319C23—151no—
320Q8—41no—
321Q8—41no—
322Q8—604no—
323Q8—601no—
324Q8—601no—
325C2×C4—22no—
326C2×C4—151no—
327C2×C4—151no—
328C2×C4—152no—
329C2×C4—152no—
330C2×C4—151no—
331C2×C4—302no—
332C2×C4—301no—
333C2×C4—301no—
334C2×C4—302no—
335C2×C4—604no—
336C2×C4C2×#120011yescharacteristic
337C2×C4#679011yescharacteristic
338C2×C4#679011yescharacteristic
339C8—121no—
340C8—121no—
341C8—201no—
342C8—201no—
343C2×C3D5×#10111yescharacteristic
344C2×C3D5×#10211yescharacteristic
345C2×C3#6509111yescharacteristic
346D3—102no—
347C5#6842011yescharacteristic, complemented, Sylow
348C22—152no—
349C22—301no—
350C22—301no—
351C22#9156111yescharacteristic
352C4—21no—
353C4—42no—
354C4—152no—
355C4—152no—
356C4—301no—
357C4—602no—
358C4#9148111yescharacteristic
359C4#9148711yescharacteristic
360C4#9152211yescharacteristic
361C4#9152411yescharacteristic
362C3#1059921311yescharacteristic, complemented, Sylow
363C2—302no—
364C2#1174895711yescharacteristic
365C2#1174921811yescharacteristic
366C2#1174937311yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1546
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C5×#4547C2semidirect
5. C3×#64767C2semidirect
6. #11745860C2semidirect
7. #11745859C2semidirect
31. #64767D3semidirect
62. #4547D5semidirect
300. C3×C5#1546semidirect
347. C5#68420semidirect
362. C3#10599213semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
#117470152
#117468592
C5×#45472
C3×#647672
#117458602
#117458592
#105992133
#684205