Subgroups — C₅×#21432 #11944152

Order 1280.

708 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2298	C₂	1	1	yes	maximal, characteristic
2	C₅×#1923	C₂	1	4	yes	maximal
3	C₅×#1916	C₂	1	4	yes	maximal, complemented
4	C₅×#1768	C₂	1	2	yes	maximal, complemented
5	C₅×#1750	C₂	1	2	yes	maximal
6	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#117	C₂²	1	1	yes	characteristic
9	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
10	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
11	C₂×C₅×#97	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
14	C₅×#388	C₄	1	4	yes	—
15	C₅×#387	C₄	1	4	yes	—
16	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₅×#376	C₂²	1	1	yes	characteristic
19	C₄³×C₅	C₂²	1	1	yes	characteristic
20	C₅×#336	C₂²	1	4	yes	—
21	C₅×#336	C₂²	1	4	yes	—
22	C₅×#336	C₂²	1	4	yes	—
23	#21432	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₂²×C₅×C₈	C₂³	1	4	yes	—
26	C₂²×C₅×C₈	C₂³	1	4	yes	—
27	C₅×#117	—	2	4	no	—
28	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
29	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
31	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
33	C₂×C₄²×C₅	C₂³	1	2	yes	—
34	C₂×C₄²×C₅	C₂³	1	2	yes	—
35	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
37	C₅×C₄⋊C₈	—	2	8	no	—
38	C₅×C₂²⋊C₈	—	2	8	no	—
39	C₅×#97	—	2	4	no	—
40	C₄×C₅×C₈	—	2	8	no	—
41	C₄×C₅×C₈	—	2	4	no	—
42	C₅×#95	C₂×C₄	1	4	yes	—
43	C₅×#95	C₂×C₄	1	4	yes	—
44	C₅×#95	C₂×C₄	1	4	yes	—
45	#2298	C₂×C₅	1	1	yes	characteristic
46	#1923	C₂×C₅	1	4	yes	—
47	#1916	C₂×C₅	1	4	yes	complemented
48	#1768	C₂×C₅	1	2	yes	complemented
49	#1750	C₂×C₅	1	2	yes	—
50	#1745	C₂×C₅	1	1	yes	characteristic, complemented
51	C₄²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₅	—	2	2	no	—
54	C₂²×C₄×C₅	—	2	4	no	—
55	C₂²×C₄×C₅	C₂²×C₄	1	2	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	2	yes	—
59	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
60	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
61	C₂×C₅×C₈	—	2	4	no	—
62	C₂×C₅×C₈	—	2	4	no	—
63	C₂×C₅×C₈	—	2	4	no	—
64	C₂×C₅×C₈	—	2	4	no	—
65	C₂×C₅×C₈	—	2	4	no	—
66	C₂×C₅×C₈	#41	1	8	yes	—
67	C₅×C₄⋊C₄	—	2	4	no	—
68	C₅×C₄⋊C₄	—	2	8	no	—
69	C₅×C₂²⋊C₄	—	2	4	no	—
70	C₅×C₂²⋊C₄	—	2	8	no	—
71	C₄²×C₅	—	2	8	no	—
72	C₄²×C₅	—	2	2	no	—
73	C₄²×C₅	—	2	4	no	—
74	C₄²×C₅	—	2	4	no	—
75	C₄²×C₅	#41	1	4	yes	—
76	C₂×#117	C₂²×C₅	1	1	yes	characteristic
77	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
78	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
79	C₂×#97	C₂²×C₅	1	2	yes	—
80	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
81	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
82	#388	C₄×C₅	1	4	yes	—
83	#387	C₄×C₅	1	4	yes	—
84	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
85	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
86	#376	C₂²×C₅	1	1	yes	characteristic
87	C₄³	C₂²×C₅	1	1	yes	characteristic
88	#336	C₂²×C₅	1	4	yes	—
89	#336	C₂²×C₅	1	4	yes	—
90	#336	C₂²×C₅	1	4	yes	—
91	C₂³×C₅	—	2	1	no	—
92	C₂³×C₅	—	2	2	no	—
93	C₂³×C₅	—	2	4	no	—
94	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅	—	2	4	no	—
96	C₂×C₄×C₅	—	2	4	no	—
97	C₂×C₄×C₅	—	2	4	no	—
98	C₂×C₄×C₅	—	2	2	no	—
99	C₂×C₄×C₅	—	2	1	no	—
100	C₂×C₄×C₅	—	2	4	no	—
101	C₂×C₄×C₅	—	2	2	no	—
102	C₂×C₄×C₅	—	2	4	no	—
103	C₂×C₄×C₅	—	2	4	no	—
104	C₂×C₄×C₅	—	2	4	no	—
105	C₂×C₄×C₅	—	4	4	no	—
106	C₂×C₄×C₅	#117	1	4	yes	—
107	C₂×C₄×C₅	#131	1	8	yes	—
108	C₂×C₄×C₅	C₂×#41	1	2	yes	—
109	C₂×C₄×C₅	C₂×#41	1	4	yes	—
110	C₅×C₈	—	2	8	no	—
111	C₅×C₈	—	4	4	no	—
112	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₅	1	4	yes	—
114	C₂²×C₈	C₂³×C₅	1	4	yes	—
115	#117	—	2	4	no	—
116	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
117	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
118	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
119	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
120	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
121	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
122	C₂×C₄²	C₂³×C₅	1	2	yes	—
123	C₂×C₄²	C₂³×C₅	1	2	yes	—
124	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
125	C₄⋊C₈	—	2	8	no	—
126	C₂²⋊C₈	—	2	8	no	—
127	#97	—	2	4	no	—
128	C₄×C₈	—	2	8	no	—
129	C₄×C₈	—	2	4	no	—
130	#95	C₂×C₄×C₅	1	4	yes	—
131	#95	C₂×C₄×C₅	1	4	yes	—
132	#95	C₂×C₄×C₅	1	4	yes	—
133	C₂²×C₅	—	4	2	no	—
134	C₂²×C₅	—	4	4	no	—
135	C₂²×C₅	—	4	1	no	—
136	C₂²×C₅	C₂×#117	1	1	yes	characteristic
137	C₂²×C₅	C₄×#41	1	2	yes	—
138	C₂²×C₅	C₂×#131	1	4	yes	—
139	C₄×C₅	—	2	4	no	—
140	C₄×C₅	—	2	8	no	—
141	C₄×C₅	—	4	2	no	—
142	C₄×C₅	—	4	4	no	—
143	C₄×C₅	—	4	1	no	—
144	C₄×C₅	#529	1	4	yes	—
145	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
149	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
150	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
151	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
152	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
153	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	C₅×#41	1	8	yes	—
160	C₄⋊C₄	—	2	4	no	—
161	C₄⋊C₄	—	2	8	no	—
162	C₂²⋊C₄	—	2	4	no	—
163	C₂²⋊C₄	—	2	8	no	—
164	C₄²	—	2	8	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	4	no	—
167	C₄²	—	2	2	no	—
168	C₄²	C₅×#41	1	4	yes	—
169	C₂×C₅	—	8	1	no	—
170	C₂×C₅	#2298	1	1	yes	characteristic
171	C₂×C₅	#2922	1	2	yes	—
172	C₂×C₅	#2966	1	4	yes	—
173	C₂³	—	2	1	no	—
174	C₂³	—	2	2	no	—
175	C₂³	—	2	4	no	—
176	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	C₅×#117	1	4	yes	—
189	C₂×C₄	C₅×#131	1	8	yes	—
190	C₂×C₄	C₂×C₅×#41	1	2	yes	—
191	C₂×C₄	C₂×C₅×#41	1	4	yes	—
192	C₈	—	2	8	no	—
193	C₈	—	4	4	no	—
194	C₅	#21432	1	1	yes	characteristic, direct product factor, Sylow
195	C₂²	—	4	1	no	—
196	C₂²	—	4	2	no	—
197	C₂²	—	4	4	no	—
198	C₂²	C₂×C₅×#117	1	1	yes	characteristic
199	C₂²	C₄×C₅×#41	1	2	yes	—
200	C₂²	C₂×C₅×#131	1	4	yes	—
201	C₄	—	2	4	no	—
202	C₄	—	2	8	no	—
203	C₄	—	4	1	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	4	no	—
206	C₄	C₅×#529	1	4	yes	—
207	C₂	—	8	1	no	—
208	C₂	C₅×#2298	1	1	yes	characteristic
209	C₂	C₅×#2922	1	2	yes	—
210	C₂	C₅×#2966	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×#1916	C₂	semidirect
4. C₅×#1768	C₂	semidirect
6. C₅×#1745	C₂	semidirect
7. C₄²×C₅×C₈	C₂	semidirect
23. #21432	C₅	direct (N × H)
47. #1916	C₂×C₅	semidirect
48. #1768	C₂×C₅	semidirect
50. #1745	C₂×C₅	semidirect
51. C₄²×C₈	C₂×C₅	semidirect
194. C₅	#21432	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×#2298	2
C₅×#1923	2
C₅×#1916	2
C₅×#1768	2
C₅×#1750	2
C₅×#1745	2
C₄²×C₅×C₈	2
#21432	5

Subgroups — C5×#21432 #11944152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21432 #11944152