Subgroups — C₅×#20429 #11943149

Order 1280.

1150 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₅×M₁₆	C₂	1	2	yes	maximal
3	C₂×C₅×#376	C₂	1	1	yes	maximal, characteristic
4	C₅×#1768	C₂	1	8	yes	maximal, complemented
5	C₅×#1728	C₂	1	2	yes	maximal
6	C₂²×C₅×M₁₆	C₂²	1	4	yes	—
7	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×#423	C₄	1	16	yes	complemented
11	C₂×C₅×C₄⋊C₈	C₂²	1	8	yes	—
12	C₄×C₅×M₁₆	—	2	8	no	—
13	C₂×C₅×#97	C₂²	1	4	yes	—
14	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
15	C₅×#376	C₄	1	4	yes	—
16	C₅×#376	C₂²	1	4	yes	—
17	C₂×C₅×#95	C₄	1	4	yes	—
18	C₅×#336	C₂²	1	8	yes	—
19	#20429	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
24	C₂×C₅×M₁₆	—	2	8	no	—
25	C₂×C₅×M₁₆	—	2	8	no	—
26	C₂×C₅×M₁₆	C₂×C₄	1	16	yes	—
27	C₂²×C₅×C₈	C₂³	1	8	yes	—
28	C₂×C₄²×C₅	—	2	4	no	—
29	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₅	C₂×C₄	1	8	yes	—
32	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₅	D₄	1	4	yes	—
34	C₂×C₄²×C₅	Q₈	1	4	yes	—
35	C₂×C₄²×C₅	C₂³	1	2	yes	—
36	C₂×C₄²×C₅	C₂³	1	2	yes	—
37	C₂×C₄²×C₅	C₂³	1	2	yes	—
38	C₅×C₄⋊C₈	C₂×C₄	1	32	yes	complemented
39	C₅×#97	—	2	8	no	—
40	C₄×C₅×C₈	—	2	8	no	—
41	C₅×#95	C₂×C₄	1	16	yes	—
42	C₂×#423	C₂×C₅	1	2	yes	—
43	C₂×C₄×M₁₆	C₂×C₅	1	2	yes	—
44	C₂×#376	C₂×C₅	1	1	yes	characteristic
45	#1768	C₂×C₅	1	8	yes	complemented
46	#1728	C₂×C₅	1	2	yes	—
47	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅	—	2	4	no	—
49	C₂²×C₄×C₅	—	4	4	no	—
50	C₂²×C₄×C₅	—	4	4	no	—
51	C₂²×C₄×C₅	—	4	4	no	—
52	C₂²×C₄×C₅	C₄²	1	8	yes	—
53	C₂²×C₄×C₅	C₄⋊C₄	1	8	yes	—
54	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
55	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
56	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
61	C₂²×C₄×C₅	#41	1	4	yes	—
62	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
63	C₅×M₁₆	—	2	32	no	—
64	C₂×C₅×C₈	—	2	8	no	—
65	C₂×C₅×C₈	—	2	8	no	—
66	C₂×C₅×C₈	C₂²×C₄	1	16	yes	—
67	C₄²×C₅	—	2	4	no	—
68	C₄²×C₅	—	2	4	no	—
69	C₄²×C₅	C₄²	1	8	yes	—
70	C₄²×C₅	C₄⋊C₄	1	8	yes	—
71	C₄²×C₅	C₂²×C₄	1	8	yes	—
72	C₄²×C₅	C₂×D₄	1	4	yes	—
73	C₄²×C₅	C₂×Q₈	1	4	yes	—
74	C₂²×M₁₆	C₂²×C₅	1	4	yes	—
75	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
76	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
77	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
78	#423	C₄×C₅	1	16	yes	complemented
79	C₂×C₄⋊C₈	C₂²×C₅	1	8	yes	—
80	C₄×M₁₆	—	2	8	no	—
81	C₂×#97	C₂²×C₅	1	4	yes	—
82	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
83	#376	C₄×C₅	1	4	yes	—
84	#376	C₂²×C₅	1	4	yes	—
85	C₂×#95	C₄×C₅	1	4	yes	—
86	#336	C₂²×C₅	1	8	yes	—
87	C₂³×C₅	—	2	4	no	—
88	C₂³×C₅	C₂×C₄²	1	2	yes	—
89	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
90	C₂³×C₅	#117	1	2	yes	—
91	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
92	C₂×C₄×C₅	—	2	8	no	—
93	C₂×C₄×C₅	—	2	8	no	—
94	C₂×C₄×C₅	—	2	4	no	—
95	C₂×C₄×C₅	—	2	8	no	—
96	C₂×C₄×C₅	—	4	8	no	—
97	C₂×C₄×C₅	—	4	8	no	—
98	C₂×C₄×C₅	—	4	8	no	—
99	C₂×C₄×C₅	C₂×C₄²	1	8	yes	—
100	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
101	C₂×C₄×C₅	C₂×C₄⋊C₄	1	8	yes	—
102	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
103	C₂×C₄×C₅	#117	1	2	yes	—
104	C₂×C₄×C₅	C₄×D₄	1	8	yes	—
105	C₂×C₄×C₅	C₄×Q₈	1	8	yes	—
106	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
107	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
109	C₂×C₄×C₅	C₂×#41	1	2	yes	—
110	C₅×C₈	—	2	16	no	—
111	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
112	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
113	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
114	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
115	C₂×M₁₆	—	2	8	no	—
116	C₂×M₁₆	—	2	8	no	—
117	C₂×M₁₆	C₂×C₄×C₅	1	16	yes	—
118	C₂²×C₈	C₂³×C₅	1	8	yes	—
119	C₂×C₄²	—	2	4	no	—
120	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
121	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
122	C₂×C₄²	C₂×C₄×C₅	1	8	yes	—
123	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
124	C₂×C₄²	C₅×D₄	1	4	yes	—
125	C₂×C₄²	C₅×Q₈	1	4	yes	—
126	C₂×C₄²	C₂³×C₅	1	2	yes	—
127	C₂×C₄²	C₂³×C₅	1	2	yes	—
128	C₂×C₄²	C₂³×C₅	1	2	yes	—
129	C₄⋊C₈	C₂×C₄×C₅	1	32	yes	complemented
130	#97	—	2	8	no	—
131	C₄×C₈	—	2	8	no	—
132	#95	C₂×C₄×C₅	1	16	yes	—
133	C₂²×C₅	—	2	4	no	—
134	C₂²×C₅	—	2	4	no	—
135	C₂²×C₅	—	2	4	no	—
136	C₂²×C₅	C₄×C₄⋊C₄	1	4	yes	—
137	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
138	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×C₅	C₂×#117	1	1	yes	characteristic
140	C₂²×C₅	#568	1	4	yes	—
141	C₄×C₅	—	2	8	no	—
142	C₄×C₅	—	2	8	no	—
143	C₄×C₅	—	4	4	no	—
144	C₄×C₅	C₄×C₄⋊C₄	1	4	yes	—
145	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
146	C₄×C₅	C₂×C₄×Q₈	1	2	yes	—
147	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
148	C₂²×C₄	—	2	4	no	—
149	C₂²×C₄	—	4	4	no	—
150	C₂²×C₄	—	4	4	no	—
151	C₂²×C₄	—	4	4	no	—
152	C₂²×C₄	C₄²×C₅	1	8	yes	—
153	C₂²×C₄	C₅×C₄⋊C₄	1	8	yes	—
154	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
155	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
156	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
157	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
158	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
159	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
160	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
161	C₂²×C₄	C₅×#41	1	4	yes	—
162	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
163	M₁₆	—	2	32	no	—
164	C₂×C₈	—	2	8	no	—
165	C₂×C₈	—	2	8	no	—
166	C₂×C₈	C₂²×C₄×C₅	1	16	yes	—
167	C₄²	—	2	4	no	—
168	C₄²	—	2	4	no	—
169	C₄²	C₄²×C₅	1	8	yes	—
170	C₄²	C₅×C₄⋊C₄	1	8	yes	—
171	C₄²	C₂²×C₄×C₅	1	8	yes	—
172	C₄²	C₂×C₅×D₄	1	4	yes	—
173	C₄²	C₂×C₅×Q₈	1	4	yes	—
174	C₂×C₅	—	2	4	no	—
175	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₅	#2873	1	2	yes	—
177	C₂×C₅	#2905	1	2	yes	—
178	C₂×C₅	#2921	1	2	yes	—
179	C₂³	—	2	4	no	—
180	C₂³	C₂×C₄²×C₅	1	2	yes	—
181	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
182	C₂³	C₅×#117	1	2	yes	—
183	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
184	C₂×C₄	—	2	8	no	—
185	C₂×C₄	—	2	8	no	—
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	2	8	no	—
188	C₂×C₄	—	4	8	no	—
189	C₂×C₄	—	4	8	no	—
190	C₂×C₄	—	4	8	no	—
191	C₂×C₄	C₂×C₄²×C₅	1	8	yes	—
192	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
193	C₂×C₄	C₂×C₅×C₄⋊C₄	1	8	yes	—
194	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
195	C₂×C₄	C₅×#117	1	2	yes	—
196	C₂×C₄	C₄×C₅×D₄	1	8	yes	—
197	C₂×C₄	C₄×C₅×Q₈	1	8	yes	—
198	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
199	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
200	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
201	C₂×C₄	C₂×C₅×#41	1	2	yes	—
202	C₈	—	2	16	no	—
203	C₅	#20429	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²	—	2	4	no	—
205	C₂²	—	2	4	no	—
206	C₂²	—	2	4	no	—
207	C₂²	C₄×C₅×C₄⋊C₄	1	4	yes	—
208	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
209	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
210	C₂²	C₂×C₅×#117	1	1	yes	characteristic
211	C₂²	C₅×#568	1	4	yes	—
212	C₄	—	2	8	no	—
213	C₄	—	2	8	no	—
214	C₄	—	4	4	no	—
215	C₄	C₄×C₅×C₄⋊C₄	1	4	yes	—
216	C₄	C₂×C₄×C₅×D₄	1	2	yes	—
217	C₄	C₂×C₄×C₅×Q₈	1	2	yes	—
218	C₂	—	2	4	no	—
219	C₂	C₂×C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
220	C₂	C₅×#2873	1	2	yes	—
221	C₂	C₅×#2905	1	2	yes	—
222	C₂	C₅×#2921	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1768	C₂	semidirect
10. C₅×#423	C₄	semidirect
19. #20429	C₅	direct (N × H)
38. C₅×C₄⋊C₈	C₂×C₄	semidirect
45. #1768	C₂×C₅	semidirect
78. #423	C₄×C₅	semidirect
129. C₄⋊C₈	C₂×C₄×C₅	semidirect
203. C₅	#20429	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂×C₄×C₅×M₁₆	2
C₂×C₅×#376	2
C₅×#1768	2
C₅×#1728	2
#20429	5

Subgroups — C5×#20429 #11943149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20429 #11943149