Subgroups — C₅×#8030 #11930750

Order 1280.

638 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	C₂×C₅×#432	C₂	1	2	yes	maximal
2	C₂×C₅×#382	C₂	1	1	yes	maximal, characteristic
3	C₅×#1295	C₂	1	4	yes	maximal, complemented
4	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
5	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₅×#432	—	2	4	no	—
7	C₅×#432	C₄	1	8	yes	complemented
8	C₂×C₅×C₄⋊C₈	—	2	2	no	—
9	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
10	C₂×C₅×#97	C₂²	1	4	yes	—
11	C₅×#382	—	2	2	no	—
12	C₅×#382	C₄	1	2	yes	—
13	C₅×#382	C₂²	1	2	yes	—
14	C₂×C₅×#95	—	2	2	no	—
15	#8030	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₄×C₅	—	2	2	no	—
17	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₅	D₄	1	2	yes	—
19	C₂²×C₅×C₈	—	2	4	no	—
20	C₂×C₅×C₄⋊C₄	—	2	2	no	—
21	C₂×C₅×C₄⋊C₄	—	4	4	no	—
22	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₅	D₄	1	2	yes	—
26	C₂×C₄²×C₅	D₄	1	2	yes	—
27	C₂×C₄²×C₅	Q₈	1	2	yes	—
28	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₅×C₄⋊C₈	—	2	8	no	—
30	C₅×C₂²⋊C₈	—	2	8	no	—
31	C₅×#97	—	2	4	no	—
32	C₅×#97	C₂×C₄	1	8	yes	complemented
33	C₅×#95	—	2	4	no	—
34	C₅×#95	—	2	4	no	—
35	C₂×#432	C₂×C₅	1	2	yes	—
36	C₂×#382	C₂×C₅	1	1	yes	characteristic
37	#1295	C₂×C₅	1	4	yes	complemented
38	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₅	—	2	2	no	—
40	C₂²×C₄×C₅	—	2	2	no	—
41	C₂²×C₄×C₅	—	2	4	no	—
42	C₂²×C₄×C₅	—	4	4	no	—
43	C₂²×C₄×C₅	—	4	8	no	—
44	C₂²×C₄×C₅	—	4	4	no	—
45	C₂²×C₄×C₅	C₄²	1	2	yes	—
46	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅	C₂²⋊C₄	1	4	yes	—
49	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
51	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
53	C₂×C₅×C₈	—	2	8	no	—
54	C₂×C₅×C₈	—	4	8	no	—
55	C₅×C₄⋊C₄	—	4	4	no	—
56	C₅×C₄⋊C₄	—	4	4	no	—
57	C₄²×C₅	C₄²	1	2	yes	—
58	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
59	C₄²×C₅	C₄⋊C₄	1	2	yes	—
60	C₄²×C₅	C₄⋊C₄	1	4	yes	—
61	C₄²×C₅	C₂²×C₄	1	2	yes	—
62	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
65	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
66	#432	—	2	4	no	—
67	#432	C₄×C₅	1	8	yes	complemented
68	C₂×C₄⋊C₈	—	2	2	no	—
69	C₂×C₂²⋊C₈	—	2	2	no	—
70	C₂×#97	C₂²×C₅	1	4	yes	—
71	#382	—	2	2	no	—
72	#382	C₄×C₅	1	2	yes	—
73	#382	C₂²×C₅	1	2	yes	—
74	C₂×#95	—	2	2	no	—
75	C₂³×C₅	—	2	4	no	—
76	C₂³×C₅	#95	1	2	yes	—
77	C₂³×C₅	#100	1	2	yes	—
78	C₂³×C₅	#101	1	2	yes	—
79	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₅	—	2	4	no	—
81	C₂×C₄×C₅	—	2	4	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	1	no	—
84	C₂×C₄×C₅	—	2	1	no	—
85	C₂×C₄×C₅	—	2	1	no	—
86	C₂×C₄×C₅	—	2	4	no	—
87	C₂×C₄×C₅	—	2	4	no	—
88	C₂×C₄×C₅	—	4	4	no	—
89	C₂×C₄×C₅	—	4	4	no	—
90	C₂×C₄×C₅	—	4	4	no	—
91	C₂×C₄×C₅	—	4	8	no	—
92	C₂×C₄×C₅	—	8	8	no	—
93	C₂×C₄×C₅	#95	1	4	yes	—
94	C₂×C₄×C₅	#95	1	2	yes	—
95	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
96	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
97	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
98	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₅×C₈	—	4	8	no	—
100	C₂³×C₄	—	2	2	no	—
101	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
102	C₂³×C₄	C₅×D₄	1	2	yes	—
103	C₂²×C₈	—	2	4	no	—
104	C₂×C₄⋊C₄	—	2	2	no	—
105	C₂×C₄⋊C₄	—	4	4	no	—
106	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
107	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
108	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
109	C₂×C₄²	C₅×D₄	1	2	yes	—
110	C₂×C₄²	C₅×D₄	1	2	yes	—
111	C₂×C₄²	C₅×Q₈	1	2	yes	—
112	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
113	C₄⋊C₈	—	2	8	no	—
114	C₂²⋊C₈	—	2	8	no	—
115	#97	—	2	4	no	—
116	#97	C₂×C₄×C₅	1	8	yes	complemented
117	#95	—	2	4	no	—
118	#95	—	2	4	no	—
119	C₂²×C₅	—	2	4	no	—
120	C₂²×C₅	—	2	4	no	—
121	C₂²×C₅	—	2	4	no	—
122	C₂²×C₅	#343	1	4	yes	—
123	C₂²×C₅	C₂×#95	1	1	yes	characteristic
124	C₂²×C₅	C₂×#100	1	1	yes	characteristic
125	C₂²×C₅	C₂×#101	1	1	yes	characteristic
126	C₂²×C₅	#421	1	4	yes	—
127	C₄×C₅	—	2	2	no	—
128	C₄×C₅	—	2	4	no	—
129	C₄×C₅	—	2	2	no	—
130	C₄×C₅	—	2	2	no	—
131	C₄×C₅	—	2	1	no	—
132	C₄×C₅	—	2	1	no	—
133	C₄×C₅	—	8	4	no	—
134	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	—	4	4	no	—
139	C₂²×C₄	—	4	8	no	—
140	C₂²×C₄	—	4	4	no	—
141	C₂²×C₄	C₄²×C₅	1	2	yes	—
142	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
143	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄	C₅×C₂²⋊C₄	1	4	yes	—
145	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
146	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
147	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
148	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
149	C₂×C₈	—	2	8	no	—
150	C₂×C₈	—	4	8	no	—
151	C₄⋊C₄	—	4	4	no	—
152	C₄⋊C₄	—	4	4	no	—
153	C₄²	C₄²×C₅	1	2	yes	—
154	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
155	C₄²	C₅×C₄⋊C₄	1	4	yes	—
156	C₄²	C₅×C₄⋊C₄	1	2	yes	—
157	C₄²	C₂²×C₄×C₅	1	2	yes	—
158	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
159	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
160	C₂×C₅	—	2	4	no	—
161	C₂×C₅	#1533	1	2	yes	—
162	C₂×C₅	#1534	1	2	yes	—
163	C₂×C₅	#1733	1	2	yes	—
164	C₂×C₅	C₂×#343	1	1	yes	characteristic
165	C₂³	—	2	4	no	—
166	C₂³	C₅×#95	1	2	yes	—
167	C₂³	C₅×#100	1	2	yes	—
168	C₂³	C₅×#101	1	2	yes	—
169	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	—	8	8	no	—
183	C₂×C₄	C₅×#95	1	4	yes	—
184	C₂×C₄	C₅×#95	1	2	yes	—
185	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
186	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
188	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
189	C₈	—	4	8	no	—
190	C₅	#8030	1	1	yes	characteristic, direct product factor, Sylow
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	—	2	4	no	—
194	C₂²	C₅×#343	1	4	yes	—
195	C₂²	C₂×C₅×#95	1	1	yes	characteristic
196	C₂²	C₂×C₅×#100	1	1	yes	characteristic
197	C₂²	C₂×C₅×#101	1	1	yes	characteristic
198	C₂²	C₅×#421	1	4	yes	—
199	C₄	—	2	2	no	—
200	C₄	—	2	2	no	—
201	C₄	—	2	4	no	—
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	2	2	no	—
205	C₄	—	8	4	no	—
206	C₂	—	2	4	no	—
207	C₂	C₅×#1533	1	2	yes	—
208	C₂	C₅×#1534	1	2	yes	—
209	C₂	C₅×#1733	1	2	yes	—
210	C₂	C₂×C₅×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1295	C₂	semidirect
7. C₅×#432	C₄	semidirect
15. #8030	C₅	direct (N × H)
32. C₅×#97	C₂×C₄	semidirect
37. #1295	C₂×C₅	semidirect
67. #432	C₄×C₅	semidirect
116. #97	C₂×C₄×C₅	semidirect
190. C₅	#8030	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×#432	2
C₂×C₅×#382	2
C₅×#1295	2
#8030	5

Subgroups — C5×#8030 #11930750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8030 #11930750