Subgroups — C₁₉×#9905 #18015864

Order 4864.

506 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2868	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1296	C₂	1	4	yes	maximal
5	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₉×#97	—	2	1	no	—
11	C₁₉×#384	—	2	1	no	—
12	C₁₉×#384	—	2	1	no	—
13	C₁₉×#384	C₄	1	2	yes	—
14	C₁₉×#384	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#336	—	2	1	no	—
17	C₁₉×#336	—	2	1	no	—
18	C₁₉×#336	—	2	1	no	—
19	C₂²×Q₈×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	—	4	4	no	—
23	C₁₉×C₄⋊Q₈	—	4	4	no	—
24	C₁₉×C₄⋊Q₈	—	4	2	no	—
25	C₁₉×C₄⋊Q₈	—	4	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	4	no	—
41	C₁₉×C₄⋊C₈	Q₈	1	4	yes	complemented
42	C₁₉×#97	—	4	2	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂×Q₈×C₁₉	—	4	4	no	—
45	C₂×Q₈×C₁₉	—	4	4	no	—
46	C₂²×C₄×C₁₉	—	2	4	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	4	4	no	—
62	C₄⋊C₄×C₁₉	—	4	4	no	—
63	C₄⋊C₄×C₁₉	—	4	4	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	4	4	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	D₈	1	2	yes	—
73	C₄²×C₁₉	SD₁₆	1	2	yes	—
74	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
75	C₄²×C₁₉	#41	1	2	yes	—
76	#9905	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Q₈×C₁₉	—	8	8	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	#100	1	2	yes	—
93	C₂×C₄×C₁₉	#101	1	2	yes	—
94	C₂×C₄×C₁₉	#102	1	2	yes	—
95	C₂×C₄×C₁₉	#102	1	2	yes	—
96	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₁₉	#137	1	2	yes	—
104	C₂×C₄×C₁₉	#137	1	2	yes	—
105	C₈×C₁₉	—	4	4	no	—
106	C₈×C₁₉	—	8	2	no	—
107	#2868	C₂×C₁₉	1	1	yes	characteristic
108	#1831	C₂×C₁₉	1	1	yes	characteristic
109	#1767	C₂×C₁₉	1	1	yes	characteristic
110	#1296	C₂×C₁₉	1	4	yes	—
111	C₂²×C₁₉	#391	1	1	yes	characteristic
112	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
115	C₂²×C₁₉	#418	1	1	yes	characteristic
116	C₂²×C₁₉	#419	1	1	yes	characteristic
117	C₂²×C₁₉	#419	1	1	yes	characteristic
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	2	2	no	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	8	4	no	—
124	C₄×C₁₉	#474	1	2	yes	—
125	C₄×C₁₉	#475	1	2	yes	—
126	C₄×C₁₉	#489	1	2	yes	—
127	C₄×C₁₉	#501	1	2	yes	—
128	C₂×C₄⋊Q₈	—	2	1	no	—
129	C₂×C₄⋊Q₈	—	2	1	no	—
130	C₂×C₄⋊Q₈	C₄×C₁₉	1	2	yes	—
131	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
133	C₂×#97	—	2	1	no	—
134	#384	—	2	1	no	—
135	#384	—	2	1	no	—
136	#384	C₄×C₁₉	1	2	yes	—
137	#384	C₂²×C₁₉	1	2	yes	—
138	C₄³	C₂²×C₁₉	1	1	yes	characteristic
139	#336	—	2	1	no	—
140	#336	—	2	1	no	—
141	#336	—	2	1	no	—
142	C₂×C₁₉	#1545	1	1	yes	characteristic
143	C₂×C₁₉	#1546	1	1	yes	characteristic
144	C₂×C₁₉	#1556	1	1	yes	characteristic
145	C₂×C₁₉	#1558	1	1	yes	characteristic
146	C₂×C₁₉	#1988	1	1	yes	characteristic
147	C₂×C₁₉	#1993	1	1	yes	characteristic
148	C₂×C₁₉	#1997	1	1	yes	characteristic
149	C₂²×Q₈	—	2	2	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	—	2	2	no	—
152	C₄⋊Q₈	—	4	4	no	—
153	C₄⋊Q₈	—	4	4	no	—
154	C₄⋊Q₈	—	4	2	no	—
155	C₄⋊Q₈	—	4	2	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
162	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
163	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
164	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
165	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
166	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
167	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	4	no	—
171	C₄⋊C₈	Q₈×C₁₉	1	4	yes	complemented
172	#97	—	4	2	no	—
173	C₁₉	#9905	1	1	yes	characteristic, direct product factor, Sylow
174	C₂×Q₈	—	4	4	no	—
175	C₂×Q₈	—	4	4	no	—
176	C₂×Q₈	—	4	4	no	—
177	C₂²×C₄	—	2	4	no	—
178	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
179	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
182	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₄⋊C₄	—	4	4	no	—
192	C₄⋊C₄	—	4	4	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	4	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	D₈×C₁₉	1	2	yes	—
204	C₄²	SD₁₆×C₁₉	1	2	yes	—
205	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
206	C₄²	#41×C₁₉	1	2	yes	—
207	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
208	Q₈	—	8	8	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	C₁₉×#100	1	2	yes	—
223	C₂×C₄	C₁₉×#101	1	2	yes	—
224	C₂×C₄	C₁₉×#102	1	2	yes	—
225	C₂×C₄	C₁₉×#102	1	2	yes	—
226	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
227	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
228	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
229	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
230	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
231	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
232	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄	C₁₉×#137	1	2	yes	—
234	C₂×C₄	C₁₉×#137	1	2	yes	—
235	C₈	—	4	4	no	—
236	C₈	—	8	2	no	—
237	C₂²	C₁₉×#391	1	1	yes	characteristic
238	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
239	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
240	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
241	C₂²	C₁₉×#418	1	1	yes	characteristic
242	C₂²	C₁₉×#419	1	1	yes	characteristic
243	C₂²	C₁₉×#419	1	1	yes	characteristic
244	C₄	—	2	2	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	8	4	no	—
250	C₄	C₁₉×#474	1	2	yes	—
251	C₄	C₁₉×#475	1	2	yes	—
252	C₄	C₁₉×#489	1	2	yes	—
253	C₄	C₁₉×#501	1	2	yes	—
254	C₂	C₁₉×#1545	1	1	yes	characteristic
255	C₂	C₁₉×#1546	1	1	yes	characteristic
256	C₂	C₁₉×#1556	1	1	yes	characteristic
257	C₂	C₁₉×#1558	1	1	yes	characteristic
258	C₂	C₁₉×#1988	1	1	yes	characteristic
259	C₂	C₁₉×#1993	1	1	yes	characteristic
260	C₂	C₁₉×#1997	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
41. C₁₉×C₄⋊C₈	Q₈	semidirect
76. #9905	C₁₉	direct (N × H)
171. C₄⋊C₈	Q₈×C₁₉	semidirect
173. C₁₉	#9905	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×#2868	2
C₁₉×#1831	2
C₁₉×#1767	2
C₁₉×#1296	2
#9905	19

Subgroups — C19×#9905 #18015864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9905 #18015864