Subgroups — C₁₉×#2985 #14560842

Order 2432.

322 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#446	C₂	1	2	yes	maximal, complemented
3	C₁₉×#446	C₂	1	4	yes	maximal, complemented
4	C₈×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
5	C₁₉×#433	C₂	1	4	yes	maximal
6	C₁₉×#432	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
10	C₁₉×#125	C₄	1	2	yes	—
11	C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
12	C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
13	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₁₉×#117	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
20	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
21	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₁₉×#97	C₂²	1	2	yes	—
24	C₁₉×#97	C₂²	1	4	yes	—
25	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₁₉	C₂²	1	4	yes	—
28	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂³	1	2	yes	—
34	C₂×C₈×C₁₉	C₂³	1	2	yes	—
35	C₂×C₈×C₁₉	C₂³	1	4	yes	—
36	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
39	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
43	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄²×C₁₉	C₂³	1	1	yes	characteristic
46	C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₄²×C₁₉	C₂³	1	4	yes	—
48	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	Q₈×C₁₉	—	2	4	no	—
50	Q₈×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
60	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
62	C₈×C₁₉	—	2	2	no	—
63	C₈×C₁₉	—	2	2	no	—
64	C₈×C₁₉	—	2	4	no	—
65	#2985	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	2	4	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	#131	1	2	yes	—
77	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
78	#533	C₂×C₁₉	1	1	yes	characteristic
79	#446	C₂×C₁₉	1	2	yes	complemented
80	#446	C₂×C₁₉	1	4	yes	complemented
81	C₈×Q₈	C₂×C₁₉	1	2	yes	complemented
82	#433	C₂×C₁₉	1	4	yes	—
83	#432	C₂×C₁₉	1	1	yes	characteristic
84	#431	C₂×C₁₉	1	1	yes	characteristic
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	#519	1	1	yes	characteristic
87	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
88	C₂×C₁₉	#568	1	1	yes	characteristic
89	C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
90	C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
91	#125	C₄×C₁₉	1	2	yes	—
92	C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
93	C₂²⋊Q₈	C₄×C₁₉	1	2	yes	—
94	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
95	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
96	#117	C₂²×C₁₉	1	2	yes	—
97	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
98	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
99	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
100	C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
101	C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
102	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
103	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
104	#97	C₂²×C₁₉	1	2	yes	—
105	#97	C₂²×C₁₉	1	4	yes	—
106	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
107	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
108	C₄×C₈	C₂²×C₁₉	1	4	yes	—
109	C₁₉	#2985	1	1	yes	characteristic, direct product factor, Sylow
110	C₂×Q₈	C₂×C₄×C₁₉	1	2	yes	—
111	C₂×Q₈	C₂×C₄×C₁₉	1	2	yes	—
112	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
115	C₂×C₈	C₂³×C₁₉	1	2	yes	—
116	C₂×C₈	C₂³×C₁₉	1	2	yes	—
117	C₂×C₈	C₂³×C₁₉	1	4	yes	—
118	C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
119	C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
120	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
121	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
122	C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
123	C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
124	C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
125	C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
126	C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
127	C₄²	C₂³×C₁₉	1	1	yes	characteristic
128	C₄²	C₂³×C₁₉	1	4	yes	—
129	C₄²	C₂³×C₁₉	1	1	yes	characteristic
130	C₂³	C₂²×C₄×C₁₉	1	1	yes	characteristic
131	Q₈	—	2	4	no	—
132	Q₈	—	4	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
137	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
138	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
139	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
141	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
142	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	2	2	no	—
146	C₈	—	2	4	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	C₂³×C₄×C₁₉	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	2	1	no	—
153	C₄	—	2	4	no	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	4	no	—
157	C₄	C₁₉×#131	1	2	yes	—
158	C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
159	C₂	—	4	1	no	—
160	C₂	C₁₉×#519	1	1	yes	characteristic
161	C₂	C₂×C₁₉×#131	1	1	yes	characteristic
162	C₂	C₁₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#446	C₂	semidirect
3. C₁₉×#446	C₂	semidirect
4. C₈×Q₈×C₁₉	C₂	semidirect
65. #2985	C₁₉	direct (N × H)
79. #446	C₂×C₁₉	semidirect
80. #446	C₂×C₁₉	semidirect
81. C₈×Q₈	C₂×C₁₉	semidirect
109. C₁₉	#2985	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#533	2
C₁₉×#446	2
C₈×Q₈×C₁₉	2
C₁₉×#433	2
C₁₉×#432	2
C₁₉×#431	2
#2985	19

Subgroups — C19×#2985 #14560842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2985 #14560842