Subgroups — #18087729

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	2	yes	maximal
2	C₂×#11926309	C₂	1	4	yes	maximal
3	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₂²	1	4	yes	—
5	C₄×#64520	—	2	4	no	—
6	C₄×#64520	C₄	1	8	yes	—
7	C₂×#10597260	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926309	C₄	1	16	yes	complemented
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#97	—	2	4	no	—
13	C₂×C₁₉×#97	C₄	1	4	yes	—
14	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
15	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	4	no	—
17	C₂²×C₈×C₁₉	—	2	4	no	—
18	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	D₄	1	4	yes	—
24	C₂×#64520	—	2	4	no	—
25	C₂×#64520	—	2	8	no	—
26	C₂×#64520	C₂×C₄	1	16	yes	—
27	C₂×#64520	C₂×C₄	1	8	yes	—
28	C₂²×C₁₉⋊C₈	—	2	4	no	—
29	C₁₉×#97	—	2	8	no	—
30	#10597260	—	2	8	no	—
31	C₄×C₁₉⋊C₈	—	2	8	no	—
32	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	—	4	4	no	—
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
36	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	#41	1	4	yes	—
42	C₂×C₈×C₁₉	—	2	4	no	—
43	C₂×C₈×C₁₉	—	2	4	no	—
44	C₂×C₈×C₁₉	—	2	16	no	—
45	C₂×C₈×C₁₉	C₄²	1	8	yes	—
46	C₄²×C₁₉	C₄²	1	4	yes	—
47	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
48	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
49	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
50	#64520	—	2	8	no	—
51	#64520	—	2	16	no	—
52	#64520	C₄²	1	16	yes	—
53	C₂×C₁₉⋊C₈	—	2	8	no	—
54	C₂×C₁₉⋊C₈	—	2	16	no	—
55	#10705	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	—	2	4	no	—
57	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
58	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
60	C₂×C₄×C₁₉	—	2	8	no	—
61	C₂×C₄×C₁₉	—	4	8	no	—
62	C₂×C₄×C₁₉	#95	1	8	yes	—
63	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
64	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
68	C₂×C₄×C₁₉	#117	1	4	yes	—
69	C₂×C₄×C₁₉	#117	1	2	yes	—
70	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
71	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
72	C₈×C₁₉	—	2	8	no	—
73	C₁₉⋊C₈	—	2	16	no	—
74	C₂×C₄×M₁₆	—	19	2	no	—
75	C₂²×#97	D₁₉	1	1	yes	characteristic
76	C₂×#341	—	19	4	no	—
77	C₂²×C₁₉	—	2	4	no	—
78	C₂²×C₁₉	—	2	8	no	—
79	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
80	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
81	C₂²×C₁₉	C₄×C₄⋊C₄	1	4	yes	—
82	C₂²×C₁₉	#430	1	4	yes	—
83	C₄×C₁₉	—	2	8	no	—
84	C₄×C₁₉	C₄³	1	1	yes	characteristic
85	C₄×C₁₉	#376	1	1	yes	characteristic
86	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
87	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
88	C₂²×M₁₆	—	19	4	no	—
89	C₂³×C₈	C₂×D₁₉	1	2	yes	—
90	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
91	C₄×M₁₆	—	19	8	no	—
92	C₄×M₁₆	—	38	4	no	—
93	C₂×#97	—	2	4	no	—
94	C₂×#97	—	38	2	no	—
95	C₂×#97	Dic₁₉	1	4	yes	—
96	C₂×C₄×C₈	—	38	2	no	—
97	#341	—	19	16	no	—
98	C₂×C₁₉	—	2	4	no	—
99	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
100	C₂×C₁₉	#1738	1	2	yes	—
101	C₂×C₁₉	#1778	1	4	yes	—
102	C₂³×C₄	Dic₃₈	1	2	yes	—
103	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
104	C₂×M₁₆	—	19	16	no	—
105	C₂×M₁₆	—	19	8	no	—
106	C₂×M₁₆	—	38	8	no	—
107	C₂×M₁₆	—	38	4	no	—
108	C₂²×C₈	—	2	4	no	—
109	C₂²×C₈	—	2	4	no	—
110	C₂²×C₈	—	38	4	no	—
111	C₂²×C₈	C₄×D₁₉	1	8	yes	—
112	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
113	C₂×C₄²	C₄×D₁₉	1	4	yes	—
114	C₂×C₄²	D₇₆	1	2	yes	—
115	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
116	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
117	#97	—	2	8	no	—
118	#97	—	38	8	no	—
119	C₄×C₈	—	38	8	no	—
120	C₁₉	#10705	1	1	yes	characteristic, complemented, Sylow
121	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
122	C₂²×C₄	—	4	4	no	—
123	C₂²×C₄	Dic₁₉⋊C₄	1	8	yes	—
124	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
125	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
126	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
127	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
128	C₂²×C₄	#64541	1	4	yes	—
129	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
130	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
131	M₁₆	—	19	16	no	—
132	M₁₆	—	38	8	no	—
133	M₁₆	—	38	16	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	2	16	no	—
137	C₂×C₈	—	38	16	no	—
138	C₂×C₈	—	38	8	no	—
139	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
140	C₄²	C₄×Dic₁₉	1	4	yes	—
141	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
142	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
143	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
144	C₂³	—	2	4	no	—
145	C₂³	C₄×Dic₃₈	1	4	yes	—
146	C₂³	C₂×Dic₁₉⋊C₄	1	2	yes	—
147	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	4	8	no	—
150	C₂×C₄	C₁₉⋊#95	1	8	yes	—
151	C₂×C₄	C₄²×D₁₉	1	4	yes	—
152	C₂×C₄	#10597318	1	4	yes	—
153	C₂×C₄	C₄×D₇₆	1	4	yes	—
154	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
155	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
156	C₂×C₄	#10597372	1	2	yes	—
157	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
158	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
159	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
160	C₈	—	2	8	no	—
161	C₈	—	38	16	no	—
162	C₂²	—	2	4	no	—
163	C₂²	—	2	8	no	—
164	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
165	C₂²	C₄×C₄⋊Dic₁₉	1	2	yes	—
166	C₂²	C₄×Dic₁₉⋊C₄	1	4	yes	—
167	C₂²	#11926593	1	4	yes	—
168	C₄	—	2	8	no	—
169	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
170	C₄	#11926390	1	1	yes	characteristic
171	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
172	C₄	C₄×(C₂×D₁₉)⋊C₄	1	4	yes	—
173	C₂	—	2	4	no	—
174	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
175	C₂	#14563362	1	2	yes	—
176	C₂	#14563541	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#97	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#97	D₁₉
hypocenter	C₁₉	#10705
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
9. #11926309	C₄	semidirect
120. C₁₉	#10705	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
C₂×#11926309	2
C₂²×C₁₉×#97	2
#10705	19