Subgroups — C₁₉×#61698 #18067657

Order 4864.

1802 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#554	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3338	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3299	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3230	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3189	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3104	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#484	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2972	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#554	—	2	4	no	—
11	C₁₉×#554	—	2	4	no	—
12	C₁₉×#554	C₂²	1	8	yes	—
13	C₁₉×#554	C₂²	1	4	yes	—
14	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
15	C₁₉×#544	—	2	1	no	—
16	C₁₉×#543	—	2	2	no	—
17	C₁₉×#533	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₁₉×#518	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#500	C₂²	1	4	yes	complemented
29	C₁₉×#487	C₂²	1	4	yes	complemented
30	C₁₉×#484	C₂²	1	8	yes	—
31	C₁₉×#484	C₂²	1	4	yes	—
32	C₁₉×#484	C₂²	1	8	yes	complemented
33	C₁₉×#484	C₂²	1	16	yes	complemented
34	C₁₉×#477	C₂²	1	8	yes	complemented
35	C₁₉×#477	C₂²	1	4	yes	complemented
36	C₁₉×#467	C₂²	1	16	yes	complemented
37	C₁₉×#462	C₂²	1	4	yes	complemented
38	C₁₉×#451	C₂²	1	4	yes	—
39	C₁₉×#451	C₂²	1	8	yes	complemented
40	C₄×Q₁₆×C₁₉	C₂²	1	8	yes	complemented
41	C₈×D₄×C₁₉	C₂²	1	8	yes	—
42	C₁₉×#431	C₂²	1	2	yes	—
43	C₂×C₁₉×#107	C₂²	1	8	yes	complemented
44	C₂×C₁₉×#103	C₂²	1	8	yes	complemented
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
54	C₁₉×C₄⋊Q₈	—	2	4	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×#125	—	2	8	no	—
60	C₁₉×#125	—	2	4	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	16	no	—
67	C₁₉×C₂²⋊Q₈	—	2	8	no	—
68	C₁₉×C₂²⋊Q₈	—	2	8	no	—
69	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
71	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
76	C₄×D₄×C₁₉	—	2	8	no	—
77	C₄×D₄×C₁₉	—	2	4	no	—
78	C₄×D₄×C₁₉	—	2	4	no	—
79	C₄×D₄×C₁₉	D₄	1	4	yes	—
80	C₄×D₄×C₁₉	C₂³	1	4	yes	—
81	C₁₉×#117	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	C₂³	1	8	yes	—
99	C₁₉×#107	C₂³	1	16	yes	—
100	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₉×#103	C₂³	1	8	yes	—
102	C₁₉×#103	C₂³	1	16	yes	—
103	C₁₉×#103	C₂³	1	8	yes	—
104	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
106	C₄×C₈×C₁₉	C₂³	1	4	yes	—
107	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	4	2	no	—
113	C₂×Q₈×C₁₉	—	4	8	no	—
114	C₂×Q₈×C₁₉	—	8	2	no	—
115	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
116	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₉	Q₁₆	1	8	yes	complemented
118	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	4	4	no	—
126	C₂²×C₄×C₁₉	—	8	4	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	Q₁₆×C₁₉	—	4	8	no	—
134	C₂×C₈×C₁₉	—	4	8	no	—
135	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	8	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
157	C₄²×C₁₉	—	2	4	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	C₂×D₄	1	2	yes	—
160	C₄²×C₁₉	C₂⁴	1	2	yes	—
161	#61698	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	C₂×Q₁₆	1	8	yes	—
165	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	8	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	8	2	no	—
171	Q₈×C₁₉	—	8	4	no	—
172	Q₈×C₁₉	—	8	4	no	—
173	D₄×C₁₉	C₂×Q₁₆	1	16	yes	—
174	C₂×C₄×C₁₉	—	2	8	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	4	no	—
188	C₂×C₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
196	C₈×C₁₉	—	2	8	no	—
197	#3501	C₂×C₁₉	1	1	yes	characteristic
198	C₂×#554	C₂×C₁₉	1	1	yes	characteristic
199	#3338	C₂×C₁₉	1	8	yes	complemented
200	#3299	C₂×C₁₉	1	8	yes	complemented
201	#3230	C₂×C₁₉	1	2	yes	complemented
202	#3189	C₂×C₁₉	1	4	yes	complemented
203	#3104	C₂×C₁₉	1	2	yes	complemented
204	C₂×#484	C₂×C₁₉	1	4	yes	complemented
205	#2972	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	4	8	no	—
211	C₂²×C₁₉	C₂²×Q₁₆	1	2	yes	—
212	C₂²×C₁₉	C₂²×Q₁₆	1	8	yes	—
213	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	C₂²×Q₁₆	1	4	yes	—
223	C₄×C₁₉	#585	1	2	yes	—
224	#554	—	2	4	no	—
225	#554	—	2	4	no	—
226	#554	C₂²×C₁₉	1	4	yes	—
227	#554	C₂²×C₁₉	1	8	yes	—
228	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
229	#544	—	2	1	no	—
230	#543	—	2	2	no	—
231	#533	C₂²×C₁₉	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#125	—	2	1	no	—
234	C₂×C₂²⋊Q₈	—	2	2	no	—
235	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
236	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
237	#518	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×C₄×D₄	—	2	1	no	—
240	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
242	#500	C₂²×C₁₉	1	4	yes	complemented
243	#487	C₂²×C₁₉	1	4	yes	complemented
244	#484	C₂²×C₁₉	1	4	yes	—
245	#484	C₂²×C₁₉	1	8	yes	—
246	#484	C₂²×C₁₉	1	8	yes	complemented
247	#484	C₂²×C₁₉	1	16	yes	complemented
248	#477	C₂²×C₁₉	1	4	yes	complemented
249	#477	C₂²×C₁₉	1	8	yes	complemented
250	#467	C₂²×C₁₉	1	16	yes	complemented
251	#462	C₂²×C₁₉	1	4	yes	complemented
252	#451	C₂²×C₁₉	1	4	yes	—
253	#451	C₂²×C₁₉	1	8	yes	complemented
254	C₄×Q₁₆	C₂²×C₁₉	1	8	yes	complemented
255	C₈×D₄	C₂²×C₁₉	1	8	yes	—
256	#431	C₂²×C₁₉	1	2	yes	—
257	C₂×#107	C₂²×C₁₉	1	8	yes	complemented
258	C₂×#103	C₂²×C₁₉	1	8	yes	complemented
259	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
260	C₂×C₁₉	—	2	2	no	—
261	C₂×C₁₉	—	2	8	no	—
262	C₂×C₁₉	#3485	1	1	yes	characteristic
263	C₂×C₁₉	C₂³×Q₁₆	1	1	yes	characteristic
264	C₂×C₁₉	#3585	1	1	yes	characteristic
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
268	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
272	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
277	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
278	#125	—	2	8	no	—
279	#125	—	2	4	no	—
280	#125	—	2	2	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	16	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
289	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
290	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
294	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
295	C₄×D₄	—	2	8	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	D₄×C₁₉	1	4	yes	—
299	C₄×D₄	C₂³×C₁₉	1	4	yes	—
300	#117	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	4	no	—
314	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
317	#107	C₂³×C₁₉	1	8	yes	—
318	#107	C₂³×C₁₉	1	16	yes	—
319	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
320	#103	C₂³×C₁₉	1	8	yes	—
321	#103	C₂³×C₁₉	1	16	yes	—
322	#103	C₂³×C₁₉	1	8	yes	—
323	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
324	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
325	C₄×C₈	C₂³×C₁₉	1	4	yes	—
326	C₁₉	#61698	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	8	no	—
334	C₂×Q₈	—	8	2	no	—
335	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
336	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
337	C₂×D₄	Q₁₆×C₁₉	1	8	yes	complemented
338	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	8	4	no	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
353	Q₁₆	—	4	8	no	—
354	C₂×C₈	—	4	8	no	—
355	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
371	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
372	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	C₂×D₄×C₁₉	1	2	yes	—
380	C₄²	C₂⁴×C₁₉	1	2	yes	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂×Q₁₆×C₁₉	1	8	yes	—
384	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
385	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	Q₈	—	2	4	no	—
387	Q₈	—	2	8	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	8	4	no	—
390	Q₈	—	8	4	no	—
391	Q₈	—	8	2	no	—
392	D₄	C₂×Q₁₆×C₁₉	1	16	yes	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	8	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	C₂×Q₁₆×C₁₉	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
414	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
415	C₈	—	2	8	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	4	8	no	—
421	C₂²	C₂²×Q₁₆×C₁₉	1	2	yes	—
422	C₂²	C₂²×Q₁₆×C₁₉	1	8	yes	—
423	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	4	no	—
432	C₄	C₂²×Q₁₆×C₁₉	1	4	yes	—
433	C₄	C₁₉×#585	1	2	yes	—
434	C₂	—	2	2	no	—
435	C₂	—	2	8	no	—
436	C₂	C₁₉×#3485	1	1	yes	characteristic
437	C₂	C₂³×Q₁₆×C₁₉	1	1	yes	characteristic
438	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3338	C₂	semidirect
4. C₁₉×#3299	C₂	semidirect
5. C₁₉×#3230	C₂	semidirect
6. C₁₉×#3189	C₂	semidirect
7. C₁₉×#3104	C₂	semidirect
8. C₂×C₁₉×#484	C₂	semidirect
28. C₁₉×#500	C₂²	semidirect
29. C₁₉×#487	C₂²	semidirect
32. C₁₉×#484	C₂²	semidirect
33. C₁₉×#484	C₂²	semidirect
34. C₁₉×#477	C₂²	semidirect
35. C₁₉×#477	C₂²	semidirect
36. C₁₉×#467	C₂²	semidirect
37. C₁₉×#462	C₂²	semidirect
39. C₁₉×#451	C₂²	semidirect
40. C₄×Q₁₆×C₁₉	C₂²	semidirect
43. C₂×C₁₉×#107	C₂²	semidirect
44. C₂×C₁₉×#103	C₂²	semidirect
117. C₂×D₄×C₁₉	Q₁₆	semidirect
161. #61698	C₁₉	direct (N × H)
199. #3338	C₂×C₁₉	semidirect
200. #3299	C₂×C₁₉	semidirect
201. #3230	C₂×C₁₉	semidirect
202. #3189	C₂×C₁₉	semidirect
203. #3104	C₂×C₁₉	semidirect
204. C₂×#484	C₂×C₁₉	semidirect
242. #500	C₂²×C₁₉	semidirect
243. #487	C₂²×C₁₉	semidirect
246. #484	C₂²×C₁₉	semidirect
247. #484	C₂²×C₁₉	semidirect
248. #477	C₂²×C₁₉	semidirect
249. #477	C₂²×C₁₉	semidirect
250. #467	C₂²×C₁₉	semidirect
251. #462	C₂²×C₁₉	semidirect
253. #451	C₂²×C₁₉	semidirect
254. C₄×Q₁₆	C₂²×C₁₉	semidirect
257. C₂×#107	C₂²×C₁₉	semidirect
258. C₂×#103	C₂²×C₁₉	semidirect
326. C₁₉	#61698	direct (N × H)
337. C₂×D₄	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3501	2
C₂×C₁₉×#554	2
C₁₉×#3338	2
C₁₉×#3299	2
C₁₉×#3230	2
C₁₉×#3189	2
C₁₉×#3104	2
C₂×C₁₉×#484	2
C₁₉×#2972	2
#61698	19

Subgroups — C19×#61698 #18067657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61698 #18067657