Subgroups — C₁₉×#11618 #18017577

Order 4864.

324 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1338	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1330	C₂	1	2	yes	maximal, complemented
6	C₁₉×#529	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₁₉	—	2	1	no	—
8	C₁₉×#446	C₂²	1	1	yes	characteristic
9	C₈×Q₈×C₁₉	C₄	1	1	yes	characteristic
10	C₁₉×#436	C₂²	1	1	yes	characteristic
11	C₁₉×#435	—	2	1	no	—
12	C₈×D₄×C₁₉	—	2	1	no	—
13	C₈×D₄×C₁₉	C₄	1	1	yes	characteristic
14	C₁₉×#433	—	2	1	no	—
15	C₁₉×#432	C₄	1	1	yes	characteristic
16	C₁₉×#405	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×C₄⋊C₁₆	C₂²	1	2	yes	—
19	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
20	C₁₉×#346	—	2	1	no	—
21	C₁₉×#346	C₂²	1	2	yes	—
22	C₄×C₁₆×C₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₁₉×#126	—	2	1	no	—
28	C₁₉×#125	C₈	1	1	yes	characteristic
29	C₁₉×#124	C₈	1	1	yes	characteristic
30	C₁₉×#123	—	2	1	no	—
31	C₁₉×C₂²⋊Q₈	C₈	1	1	yes	characteristic
32	C₁₉×#121	C₈	1	1	yes	characteristic
33	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₁₉×#117	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₆×C₁₉	—	2	4	no	—
39	C₂×C₁₆×C₁₉	—	2	2	no	—
40	C₂×C₁₆×C₁₉	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₄⋊C₈	—	2	1	no	—
43	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₁₉×C₂²⋊C₈	—	2	1	no	—
46	C₁₉×C₂²⋊C₈	—	2	1	no	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₁₉×#97	—	2	1	no	—
49	C₁₉×#97	—	2	1	no	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
53	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
54	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₁₉	C₂×C₈	1	1	yes	characteristic
56	C₂×D₄×C₁₉	—	2	1	no	—
57	C₂×D₄×C₁₉	C₂×C₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
62	M₁₆×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	1	no	—
66	C₂×C₈×C₁₉	—	2	1	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₄⋊C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
78	C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₄²×C₁₉	—	2	1	no	—
84	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
86	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
87	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₁₆×C₁₉	—	2	4	no	—
89	C₁₆×C₁₉	—	4	2	no	—
90	#11618	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂³×C₁₉	—	2	1	no	—
92	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
93	Q₈×C₁₉	—	4	1	no	—
94	D₄×C₁₉	—	4	1	no	—
95	D₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	1	no	—
113	C₈×C₁₉	—	4	1	no	—
114	C₈×C₁₉	—	4	1	no	—
115	C₈×C₁₉	#104	1	2	yes	—
116	C₈×C₁₉	#135	1	2	yes	—
117	#2966	C₂×C₁₉	1	1	yes	characteristic
118	#2162	C₂×C₁₉	1	1	yes	characteristic, complemented
119	C₂×#346	C₂×C₁₉	1	1	yes	characteristic, complemented
120	#1338	C₂×C₁₉	1	2	yes	complemented
121	#1330	C₂×C₁₉	1	2	yes	complemented
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	#350	1	2	yes	—
128	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	—	4	1	no	—
137	C₄×C₁₉	#416	1	1	yes	characteristic
138	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
139	#529	C₄×C₁₉	1	1	yes	characteristic
140	C₂²×C₁₆	—	2	1	no	—
141	#446	C₂²×C₁₉	1	1	yes	characteristic
142	C₈×Q₈	C₄×C₁₉	1	1	yes	characteristic
143	#436	C₂²×C₁₉	1	1	yes	characteristic
144	#435	—	2	1	no	—
145	C₈×D₄	—	2	1	no	—
146	C₈×D₄	C₄×C₁₉	1	1	yes	characteristic
147	#433	—	2	1	no	—
148	#432	C₄×C₁₉	1	1	yes	characteristic
149	#405	—	2	1	no	—
150	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
151	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
152	C₂²⋊C₁₆	—	2	1	no	—
153	#346	—	2	1	no	—
154	#346	C₂²×C₁₉	1	2	yes	—
155	C₄×C₁₆	—	2	1	no	—
156	C₂×C₁₉	—	2	2	no	—
157	C₂×C₁₉	—	8	1	no	—
158	C₂×C₁₉	#1476	1	1	yes	characteristic
159	C₂×C₁₉	#2115	1	1	yes	characteristic
160	C₂×C₁₉	C₂×#350	1	1	yes	characteristic
161	C₂×M₁₆	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
164	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
165	#126	—	2	1	no	—
166	#125	C₈×C₁₉	1	1	yes	characteristic
167	#124	C₈×C₁₉	1	1	yes	characteristic
168	#123	—	2	1	no	—
169	C₂²⋊Q₈	C₈×C₁₉	1	1	yes	characteristic
170	#121	C₈×C₁₉	1	1	yes	characteristic
171	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
172	C₄×D₄	—	2	1	no	—
173	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
174	#117	—	2	1	no	—
175	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
176	C₂×C₁₆	—	2	4	no	—
177	C₂×C₁₆	—	2	2	no	—
178	C₂×C₁₆	—	2	2	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
182	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
183	C₂²⋊C₈	—	2	1	no	—
184	C₂²⋊C₈	—	2	1	no	—
185	C₂²⋊C₈	—	2	1	no	—
186	#97	—	2	1	no	—
187	#97	—	2	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
190	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
191	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
192	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
193	C₁₉	#11618	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×Q₈	C₂×C₈×C₁₉	1	1	yes	characteristic
195	C₂×D₄	—	2	1	no	—
196	C₂×D₄	C₂×C₈×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
200	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
201	M₁₆	—	4	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	1	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
208	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
209	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
210	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	2	1	no	—
213	C₄⋊C₄	—	2	1	no	—
214	C₄⋊C₄	—	2	1	no	—
215	C₄⋊C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
216	C₄⋊C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
217	C₂²⋊C₄	—	2	1	no	—
218	C₂²⋊C₄	—	2	1	no	—
219	C₂²⋊C₄	—	2	1	no	—
220	C₂²⋊C₄	—	2	1	no	—
221	C₂²⋊C₄	—	2	1	no	—
222	C₄²	—	2	1	no	—
223	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
224	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
225	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
226	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
227	C₁₆	—	2	4	no	—
228	C₁₆	—	4	2	no	—
229	C₂³	—	2	1	no	—
230	C₂³	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
231	Q₈	—	4	1	no	—
232	D₄	—	4	1	no	—
233	D₄	—	4	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
244	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
245	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
246	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
247	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
248	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
249	C₈	—	2	1	no	—
250	C₈	—	2	1	no	—
251	C₈	—	4	1	no	—
252	C₈	—	4	1	no	—
253	C₈	C₁₉×#104	1	2	yes	—
254	C₈	C₁₉×#135	1	2	yes	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	4	1	no	—
258	C₂²	—	4	1	no	—
259	C₂²	—	4	1	no	—
260	C₂²	C₁₉×#350	1	2	yes	—
261	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	4	1	no	—
268	C₄	—	4	1	no	—
269	C₄	—	4	1	no	—
270	C₄	C₁₉×#416	1	1	yes	characteristic
271	C₄	C₂×C₁₉×#104	1	1	yes	characteristic
272	C₂	—	2	2	no	—
273	C₂	—	8	1	no	—
274	C₂	C₁₉×#1476	1	1	yes	characteristic
275	C₂	C₁₉×#2115	1	1	yes	characteristic
276	C₂	C₂×C₁₉×#350	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₁₉×#121	C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2162	C₂	semidirect
3. C₂×C₁₉×#346	C₂	semidirect
4. C₁₉×#1338	C₂	semidirect
5. C₁₉×#1330	C₂	semidirect
90. #11618	C₁₉	direct (N × H)
118. #2162	C₂×C₁₉	semidirect
119. C₂×#346	C₂×C₁₉	semidirect
120. #1338	C₂×C₁₉	semidirect
121. #1330	C₂×C₁₉	semidirect
193. C₁₉	#11618	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×#2966	2
C₁₉×#2162	2
C₂×C₁₉×#346	2
C₁₉×#1338	2
C₁₉×#1330	2
#11618	19

Subgroups — C19×#11618 #18017577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11618 #18017577