Subgroups — C₅×#12829 #11935549

Order 1280.

378 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2957	C₂	1	1	yes	maximal, characteristic
2	C₅×#2151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2148	C₂	1	1	yes	maximal, characteristic
4	C₅×#2138	C₂	1	1	yes	maximal, characteristic
5	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#135	C₂²	1	1	yes	characteristic
9	C₅×#568	—	2	1	no	—
10	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	C₅×#444	C₄	1	4	yes	complemented
13	C₅×#443	—	2	2	no	—
14	C₂×C₅×#108	C₂²	1	1	yes	characteristic
15	C₂×C₅×#108	C₂²	1	1	yes	characteristic
16	C₅×#427	C₂²	1	1	yes	characteristic
17	C₅×#421	—	2	1	no	—
18	C₅×#405	C₂²	1	1	yes	characteristic
19	C₅×C₄⋊C₁₆	—	2	2	no	—
20	C₅×#362	—	2	1	no	—
21	C₅×#361	—	2	1	no	—
22	C₅×#358	—	2	1	no	—
23	C₅×#357	—	2	1	no	—
24	C₅×#344	—	2	1	no	—
25	C₅×H(3,ℤ/4)	—	2	1	no	—
26	#12829	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×C₅×#41	—	2	1	no	—
28	C₅×#135	—	2	1	no	—
29	C₅×#135	—	2	1	no	—
30	C₅×#135	C₂×C₄	1	2	yes	—
31	C₅×#135	Q₈	1	2	yes	—
32	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
33	C₂×C₅×SD₁₆	—	2	1	no	—
34	C₂×C₅×D₈	D₄	1	1	yes	characteristic
35	C₅×#131	—	2	4	no	—
36	C₅×#131	—	4	2	no	—
37	C₂×C₅×M₁₆	—	2	1	no	—
38	C₂×C₅×M₁₆	—	2	1	no	—
39	C₂×C₅×M₁₆	—	4	2	no	—
40	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
42	C₅×#117	—	2	1	no	—
43	C₅×#117	D₄	1	1	yes	characteristic
44	C₅×M₃₂	—	2	1	no	—
45	C₅×M₃₂	—	2	1	no	—
46	C₂×C₅×C₁₆	—	2	1	no	—
47	C₂×C₅×C₁₆	—	2	1	no	—
48	C₂×C₅×C₁₆	—	2	1	no	—
49	C₂×C₅×C₁₆	—	2	1	no	—
50	C₅×#108	—	2	1	no	—
51	C₅×#108	—	2	1	no	—
52	C₅×#108	—	2	1	no	—
53	C₅×#108	C₂×C₄	1	2	yes	—
54	C₅×#107	—	2	1	no	—
55	C₅×#106	—	2	1	no	—
56	C₅×#104	—	2	4	no	—
57	C₅×#97	C₂×C₄	1	2	yes	—
58	C₄×C₅×C₈	D₄	1	2	yes	—
59	#2957	C₂×C₅	1	1	yes	characteristic
60	#2151	C₂×C₅	1	1	yes	characteristic, complemented
61	#2148	C₂×C₅	1	1	yes	characteristic
62	#2138	C₂×C₅	1	1	yes	characteristic
63	#1833	C₂×C₅	1	1	yes	characteristic, complemented
64	#1389	C₂×C₅	1	1	yes	characteristic, complemented
65	#1381	C₂×C₅	1	1	yes	characteristic, complemented
66	C₅×#41	—	2	2	no	—
67	C₅×#41	—	2	2	no	—
68	C₅×#41	—	4	1	no	—
69	C₅×#41	—	4	1	no	—
70	C₂×C₅×Q₈	—	2	1	no	—
71	C₂×C₅×D₄	—	2	1	no	—
72	C₂×C₅×D₄	—	4	1	no	—
73	C₂²×C₄×C₅	—	4	1	no	—
74	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
75	C₅×Q₁₆	—	2	1	no	—
76	C₅×Q₁₆	C₄⋊C₄	1	2	yes	—
77	C₅×SD₁₆	—	2	2	no	—
78	C₅×SD₁₆	—	2	2	no	—
79	C₅×D₈	—	2	1	no	—
80	C₅×D₈	C₄⋊C₄	1	2	yes	—
81	C₅×M₁₆	—	2	1	no	—
82	C₅×M₁₆	—	2	1	no	—
83	C₅×M₁₆	—	2	2	no	—
84	C₅×M₁₆	—	4	4	no	—
85	C₅×M₁₆	—	4	1	no	—
86	C₅×M₁₆	—	4	1	no	—
87	C₅×M₁₆	—	4	1	no	—
88	C₂×C₅×C₈	—	4	4	no	—
89	C₂×C₅×C₈	—	4	1	no	—
90	C₂×C₅×C₈	—	4	1	no	—
91	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
92	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
94	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
95	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₅×C₈	#41	1	1	yes	characteristic
97	C₂×C₅×C₈	#41	1	1	yes	characteristic
98	C₅×C₄⋊C₄	—	2	1	no	—
99	C₅×C₄⋊C₄	—	4	1	no	—
100	C₅×C₂²⋊C₄	—	2	1	no	—
101	C₅×C₂²⋊C₄	—	4	1	no	—
102	C₄²×C₅	—	4	1	no	—
103	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
104	C₅×C₁₆	—	4	1	no	—
105	C₅×C₁₆	—	4	1	no	—
106	C₂×#135	C₂²×C₅	1	1	yes	characteristic
107	#568	—	2	1	no	—
108	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
110	#444	C₄×C₅	1	4	yes	complemented
111	#443	—	2	2	no	—
112	C₂×#108	C₂²×C₅	1	1	yes	characteristic
113	C₂×#108	C₂²×C₅	1	1	yes	characteristic
114	#427	C₂²×C₅	1	1	yes	characteristic
115	#421	—	2	1	no	—
116	#405	C₂²×C₅	1	1	yes	characteristic
117	C₄⋊C₁₆	—	2	2	no	—
118	#362	—	2	1	no	—
119	#361	—	2	1	no	—
120	#358	—	2	1	no	—
121	#357	—	2	1	no	—
122	#344	—	2	1	no	—
123	H(3,ℤ/4)	—	2	1	no	—
124	C₂³×C₅	—	4	1	no	—
125	C₂³×C₅	#135	1	1	yes	characteristic
126	C₅×Q₈	—	2	2	no	—
127	C₅×Q₈	—	4	1	no	—
128	C₅×D₄	—	2	2	no	—
129	C₅×D₄	—	4	2	no	—
130	C₅×D₄	—	4	2	no	—
131	C₅×D₄	—	4	1	no	—
132	C₂×C₄×C₅	—	2	2	no	—
133	C₂×C₄×C₅	—	4	1	no	—
134	C₂×C₄×C₅	—	4	2	no	—
135	C₂×C₄×C₅	—	4	2	no	—
136	C₂×C₄×C₅	—	8	1	no	—
137	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₅	#121	1	1	yes	characteristic
139	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₅	#135	1	1	yes	characteristic
141	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₅×C₈	—	2	2	no	—
144	C₅×C₈	—	4	2	no	—
145	C₅×C₈	—	8	1	no	—
146	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₅×C₈	#117	1	1	yes	characteristic
148	C₅×C₈	#121	1	1	yes	characteristic
149	C₅×C₈	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×#41	—	2	1	no	—
151	#135	—	2	1	no	—
152	#135	—	2	1	no	—
153	#135	C₂×C₄×C₅	1	2	yes	—
154	#135	C₅×Q₈	1	2	yes	—
155	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
156	C₂×SD₁₆	—	2	1	no	—
157	C₂×D₈	C₅×D₄	1	1	yes	characteristic
158	#131	—	2	4	no	—
159	#131	—	4	2	no	—
160	C₂×M₁₆	—	2	1	no	—
161	C₂×M₁₆	—	2	1	no	—
162	C₂×M₁₆	—	4	2	no	—
163	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
164	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
165	#117	—	2	1	no	—
166	#117	C₅×D₄	1	1	yes	characteristic
167	M₃₂	—	2	1	no	—
168	M₃₂	—	2	1	no	—
169	C₂×C₁₆	—	2	1	no	—
170	C₂×C₁₆	—	2	1	no	—
171	C₂×C₁₆	—	2	1	no	—
172	C₂×C₁₆	—	2	1	no	—
173	#108	—	2	1	no	—
174	#108	—	2	1	no	—
175	#108	—	2	1	no	—
176	#108	C₂×C₄×C₅	1	2	yes	—
177	#107	—	2	1	no	—
178	#106	—	2	1	no	—
179	#104	—	2	4	no	—
180	#97	C₂×C₄×C₅	1	2	yes	—
181	C₄×C₈	C₅×D₄	1	2	yes	—
182	C₂²×C₅	—	4	1	no	—
183	C₂²×C₅	—	4	2	no	—
184	C₂²×C₅	—	16	1	no	—
185	C₂²×C₅	#416	1	1	yes	characteristic
186	C₂²×C₅	#463	1	1	yes	characteristic
187	C₂²×C₅	#478	1	1	yes	characteristic
188	C₄×C₅	—	4	2	no	—
189	C₄×C₅	—	4	2	no	—
190	C₄×C₅	—	16	1	no	—
191	C₄×C₅	#380	1	1	yes	characteristic
192	C₄×C₅	#418	1	1	yes	characteristic
193	C₄×C₅	#463	1	1	yes	characteristic
194	C₄×C₅	#478	1	1	yes	characteristic
195	#41	—	2	2	no	—
196	#41	—	2	2	no	—
197	#41	—	4	1	no	—
198	#41	—	4	1	no	—
199	C₂×Q₈	—	2	1	no	—
200	C₂×D₄	—	2	1	no	—
201	C₂×D₄	—	4	1	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
204	Q₁₆	—	2	1	no	—
205	Q₁₆	C₅×C₄⋊C₄	1	2	yes	—
206	SD₁₆	—	2	2	no	—
207	SD₁₆	—	2	2	no	—
208	D₈	—	2	1	no	—
209	D₈	C₅×C₄⋊C₄	1	2	yes	—
210	M₁₆	—	2	1	no	—
211	M₁₆	—	2	1	no	—
212	M₁₆	—	2	2	no	—
213	M₁₆	—	4	4	no	—
214	M₁₆	—	4	1	no	—
215	M₁₆	—	4	1	no	—
216	M₁₆	—	4	1	no	—
217	C₂×C₈	—	4	4	no	—
218	C₂×C₈	—	4	1	no	—
219	C₂×C₈	—	4	1	no	—
220	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
221	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
222	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
223	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
225	C₂×C₈	C₅×#41	1	1	yes	characteristic
226	C₂×C₈	C₅×#41	1	1	yes	characteristic
227	C₄⋊C₄	—	2	1	no	—
228	C₄⋊C₄	—	4	1	no	—
229	C₂²⋊C₄	—	2	1	no	—
230	C₂²⋊C₄	—	4	1	no	—
231	C₄²	—	4	1	no	—
232	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
233	C₁₆	—	4	1	no	—
234	C₁₆	—	4	1	no	—
235	C₂×C₅	—	2	1	no	—
236	C₂×C₅	—	2	1	no	—
237	C₂×C₅	—	2	1	no	—
238	C₂×C₅	—	8	2	no	—
239	C₂×C₅	#1804	1	1	yes	characteristic
240	C₂³	—	4	1	no	—
241	C₂³	C₅×#135	1	1	yes	characteristic
242	Q₈	—	2	2	no	—
243	Q₈	—	4	1	no	—
244	D₄	—	2	2	no	—
245	D₄	—	4	2	no	—
246	D₄	—	4	2	no	—
247	D₄	—	4	1	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	8	1	no	—
253	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄	C₅×#121	1	1	yes	characteristic
255	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄	C₅×#135	1	1	yes	characteristic
257	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₈	—	2	2	no	—
260	C₈	—	4	2	no	—
261	C₈	—	8	1	no	—
262	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
263	C₈	C₅×#117	1	1	yes	characteristic
264	C₈	C₅×#121	1	1	yes	characteristic
265	C₈	C₅×C₂²⋊Q₈	1	1	yes	characteristic
266	C₅	#12829	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²	—	4	1	no	—
268	C₂²	—	4	2	no	—
269	C₂²	—	16	1	no	—
270	C₂²	C₅×#416	1	1	yes	characteristic
271	C₂²	C₅×#463	1	1	yes	characteristic
272	C₂²	C₅×#478	1	1	yes	characteristic
273	C₄	—	4	2	no	—
274	C₄	—	4	2	no	—
275	C₄	—	16	1	no	—
276	C₄	C₅×#380	1	1	yes	characteristic
277	C₄	C₅×#418	1	1	yes	characteristic
278	C₄	C₅×#463	1	1	yes	characteristic
279	C₄	C₅×#478	1	1	yes	characteristic
280	C₂	—	2	1	no	—
281	C₂	—	2	1	no	—
282	C₂	—	2	1	no	—
283	C₂	—	8	2	no	—
284	C₂	C₅×#1804	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#418
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂×C₅	#1804
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2151	C₂	semidirect
5. C₅×#1833	C₂	semidirect
6. C₅×#1389	C₂	semidirect
7. C₅×#1381	C₂	semidirect
12. C₅×#444	C₄	semidirect
26. #12829	C₅	direct (N × H)
60. #2151	C₂×C₅	semidirect
63. #1833	C₂×C₅	semidirect
64. #1389	C₂×C₅	semidirect
65. #1381	C₂×C₅	semidirect
110. #444	C₄×C₅	semidirect
266. C₅	#12829	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2957	2
C₅×#2151	2
C₅×#2148	2
C₅×#2138	2
C₅×#1833	2
C₅×#1389	2
C₅×#1381	2
#12829	5

Subgroups — C5×#12829 #11935549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12829 #11935549