Subgroups — C₁₉×#19676 #18025635

Order 4864.

956 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1721	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1721	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1717	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1715	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
13	C₂²×D₈×C₁₉	—	2	2	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₁₉×#532	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#496	—	2	2	no	—
20	C₁₉×#493	—	2	2	no	—
21	C₁₉×#493	C₂²	1	2	yes	—
22	C₁₉×#493	C₂²	1	2	yes	—
23	C₁₉×#493	C₂²	1	2	yes	complemented
24	C₁₉×#493	C₂²	1	2	yes	complemented
25	C₁₉×#492	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#492	C₂²	1	2	yes	complemented
27	C₁₉×#492	C₂²	1	2	yes	complemented
28	C₁₉×#490	—	2	2	no	—
29	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#486	C₂²	1	2	yes	complemented
32	C₁₉×#486	C₂²	1	2	yes	complemented
33	C₁₉×#486	C₂²	1	2	yes	complemented
34	C₁₉×#486	C₂²	1	2	yes	complemented
35	C₁₉×#465	—	2	2	no	—
36	C₁₉×#460	—	2	2	no	—
37	C₁₉×#459	—	2	2	no	—
38	C₁₉×#450	—	2	2	no	—
39	C₁₉×#447	—	2	2	no	—
40	C₄×SD₁₆×C₁₉	—	2	2	no	—
41	C₁₉×#431	C₂²	1	1	yes	characteristic
42	C₁₉×#418	—	2	2	no	—
43	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#322	C₂²	1	2	yes	complemented
46	C₁₉×#322	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₁₉×AGL(1,ℤ/8)	—	4	8	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×D₈×C₁₉	—	2	4	no	—
59	C₂×D₈×C₁₉	—	2	4	no	—
60	C₂×D₈×C₁₉	—	2	4	no	—
61	C₂×D₈×C₁₉	—	2	4	no	—
62	C₂×D₈×C₁₉	—	4	8	no	—
63	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
64	C₂²×C₈×C₁₉	D₄	1	2	yes	—
65	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	—	2	1	no	—
73	C₁₉×#127	—	2	1	no	—
74	C₁₉×#127	C₂³	1	2	yes	—
75	C₁₉×#127	C₂³	1	2	yes	—
76	C₁₉×#127	C₂³	1	1	yes	characteristic
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×#106	—	2	2	no	—
90	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#102	—	2	2	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×#102	—	2	4	no	—
97	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
98	C₁₉×#97	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	D₄	1	2	yes	—
100	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₁₉	C₂³	1	2	yes	—
103	C₄×C₈×C₁₉	C₂³	1	2	yes	—
104	C₂⁴×C₁₉	—	4	1	no	—
105	C₂⁴×C₁₉	—	4	1	no	—
106	#41×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	—	4	4	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	4	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	8	2	no	—
131	C₂×D₄×C₁₉	—	8	2	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	SD₁₆×C₁₉	—	4	8	no	—
137	SD₁₆×C₁₉	—	4	4	no	—
138	SD₁₆×C₁₉	—	8	4	no	—
139	D₈×C₁₉	—	4	8	no	—
140	D₈×C₁₉	—	4	8	no	—
141	D₈×C₁₉	—	4	8	no	—
142	D₈×C₁₉	—	8	4	no	—
143	M₁₆×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	4	no	—
145	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
165	#19676	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	8	2	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	—	8	2	no	—
172	C₂³×C₁₉	—	8	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	—	8	2	no	—
175	C₂³×C₁₉	#127	1	1	yes	characteristic
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	4	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	8	2	no	—
189	D₄×C₁₉	—	8	2	no	—
190	D₄×C₁₉	—	8	2	no	—
191	D₄×C₁₉	—	8	2	no	—
192	D₄×C₁₉	—	8	2	no	—
193	D₄×C₁₉	—	8	2	no	—
194	D₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
204	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
205	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₁₉	—	2	2	no	—
209	C₈×C₁₉	—	2	4	no	—
210	C₈×C₁₉	—	2	4	no	—
211	C₈×C₁₉	AGL(1,ℤ/8)	1	4	yes	complemented
212	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#3151	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂×#493	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1721	C₂×C₁₉	1	2	yes	complemented
219	#1721	C₂×C₁₉	1	2	yes	complemented
220	#1717	C₂×C₁₉	1	2	yes	complemented
221	#1715	C₂×C₁₉	1	2	yes	complemented
222	#1451	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	2	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	—	16	4	no	—
235	C₂²×C₁₉	—	16	4	no	—
236	C₂²×C₁₉	#496	1	2	yes	—
237	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	#496	1	2	yes	—
244	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
245	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
246	C₄×C₁₉	#576	1	2	yes	—
247	C₂×AGL(1,ℤ/8)	—	2	2	no	—
248	C₂²×D₈	—	2	2	no	—
249	#533	C₂²×C₁₉	1	1	yes	characteristic
250	#532	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
253	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	#496	—	2	2	no	—
255	#493	—	2	2	no	—
256	#493	C₂²×C₁₉	1	2	yes	—
257	#493	C₂²×C₁₉	1	2	yes	—
258	#493	C₂²×C₁₉	1	2	yes	complemented
259	#493	C₂²×C₁₉	1	2	yes	complemented
260	#492	C₂²×C₁₉	1	2	yes	complemented
261	#492	C₂²×C₁₉	1	1	yes	characteristic, complemented
262	#492	C₂²×C₁₉	1	2	yes	complemented
263	#490	—	2	2	no	—
264	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
265	#486	C₂²×C₁₉	1	2	yes	complemented
266	#486	C₂²×C₁₉	1	2	yes	complemented
267	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
268	#486	C₂²×C₁₉	1	2	yes	complemented
269	#486	C₂²×C₁₉	1	2	yes	complemented
270	#465	—	2	2	no	—
271	#460	—	2	2	no	—
272	#459	—	2	2	no	—
273	#450	—	2	2	no	—
274	#447	—	2	2	no	—
275	C₄×SD₁₆	—	2	2	no	—
276	#431	C₂²×C₁₉	1	1	yes	characteristic
277	#418	—	2	2	no	—
278	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
280	#322	C₂²×C₁₉	1	2	yes	complemented
281	#322	C₂²×C₁₉	1	2	yes	complemented
282	C₂×C₁₉	—	2	2	no	—
283	C₂×C₁₉	—	16	1	no	—
284	C₂×C₁₉	—	16	2	no	—
285	C₂×C₁₉	—	16	2	no	—
286	C₂×C₁₉	C₂×#496	1	1	yes	characteristic
287	C₂×C₁₉	#3151	1	1	yes	characteristic
288	C₂×C₁₉	#3155	1	1	yes	characteristic
289	C₂×#41	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	AGL(1,ℤ/8)	—	4	8	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×D₈	—	2	4	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	—	2	4	no	—
304	C₂×D₈	—	4	8	no	—
305	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
306	C₂²×C₈	D₄×C₁₉	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
310	#127	—	2	1	no	—
311	#127	—	2	1	no	—
312	#127	—	2	1	no	—
313	#127	—	2	1	no	—
314	#127	—	2	1	no	—
315	#127	—	2	1	no	—
316	#127	C₂³×C₁₉	1	2	yes	—
317	#127	C₂³×C₁₉	1	2	yes	—
318	#127	C₂³×C₁₉	1	1	yes	characteristic
319	#125	—	2	1	no	—
320	#124	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	#117	—	2	1	no	—
330	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
331	#106	—	2	2	no	—
332	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
333	#103	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	2	2	no	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
340	#97	D₄×C₁₉	1	2	yes	—
341	C₄×C₈	D₄×C₁₉	1	2	yes	—
342	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₄×C₈	C₂³×C₁₉	1	2	yes	—
345	C₄×C₈	C₂³×C₁₉	1	2	yes	—
346	C₁₉	#19676	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	—	4	1	no	—
348	C₂⁴	—	4	1	no	—
349	#41	—	4	4	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	SD₁₆	—	4	8	no	—
380	SD₁₆	—	4	4	no	—
381	SD₁₆	—	8	4	no	—
382	D₈	—	4	8	no	—
383	D₈	—	4	8	no	—
384	D₈	—	4	8	no	—
385	D₈	—	8	4	no	—
386	M₁₆	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
390	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
391	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₁₉×#127	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	2	no	—
432	D₄	—	8	2	no	—
433	D₄	—	8	2	no	—
434	D₄	—	8	2	no	—
435	D₄	—	8	2	no	—
436	D₄	—	8	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
445	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
446	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	4	no	—
452	C₈	—	2	4	no	—
453	C₈	C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	16	4	no	—
466	C₂²	—	16	4	no	—
467	C₂²	C₁₉×#496	1	2	yes	—
468	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₉×#496	1	2	yes	—
475	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
476	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
477	C₄	C₁₉×#576	1	2	yes	—
478	C₂	—	2	2	no	—
479	C₂	—	16	2	no	—
480	C₂	—	16	2	no	—
481	C₂	—	16	1	no	—
482	C₂	C₂×C₁₉×#496	1	1	yes	characteristic
483	C₂	C₁₉×#3151	1	1	yes	characteristic
484	C₂	C₁₉×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3208	C₂	semidirect
2. C₁₉×#3205	C₂	semidirect
3. C₁₉×#3167	C₂	semidirect
4. C₁₉×#3151	C₂	semidirect
5. C₂×C₁₉×#493	C₂	semidirect
6. C₁₉×#3138	C₂	semidirect
7. C₁₉×#1721	C₂	semidirect
8. C₁₉×#1721	C₂	semidirect
9. C₁₉×#1717	C₂	semidirect
10. C₁₉×#1715	C₂	semidirect
11. C₁₉×#1451	C₂	semidirect
18. C₁₉×#498	C₂²	semidirect
23. C₁₉×#493	C₂²	semidirect
24. C₁₉×#493	C₂²	semidirect
25. C₁₉×#492	C₂²	semidirect
26. C₁₉×#492	C₂²	semidirect
27. C₁₉×#492	C₂²	semidirect
29. C₁₉×#487	C₂²	semidirect
30. C₁₉×#486	C₂²	semidirect
31. C₁₉×#486	C₂²	semidirect
32. C₁₉×#486	C₂²	semidirect
33. C₁₉×#486	C₂²	semidirect
34. C₁₉×#486	C₂²	semidirect
45. C₁₉×#322	C₂²	semidirect
46. C₁₉×#322	C₂²	semidirect
165. #19676	C₁₉	direct (N × H)
211. C₈×C₁₉	AGL(1,ℤ/8)	semidirect
212. #3208	C₂×C₁₉	semidirect
213. #3205	C₂×C₁₉	semidirect
214. #3167	C₂×C₁₉	semidirect
215. #3151	C₂×C₁₉	semidirect
216. C₂×#493	C₂×C₁₉	semidirect
217. #3138	C₂×C₁₉	semidirect
218. #1721	C₂×C₁₉	semidirect
219. #1721	C₂×C₁₉	semidirect
220. #1717	C₂×C₁₉	semidirect
221. #1715	C₂×C₁₉	semidirect
222. #1451	C₂×C₁₉	semidirect
253. #498	C₂²×C₁₉	semidirect
258. #493	C₂²×C₁₉	semidirect
259. #493	C₂²×C₁₉	semidirect
260. #492	C₂²×C₁₉	semidirect
261. #492	C₂²×C₁₉	semidirect
262. #492	C₂²×C₁₉	semidirect
264. #487	C₂²×C₁₉	semidirect
265. #486	C₂²×C₁₉	semidirect
266. #486	C₂²×C₁₉	semidirect
267. #486	C₂²×C₁₉	semidirect
268. #486	C₂²×C₁₉	semidirect
269. #486	C₂²×C₁₉	semidirect
280. #322	C₂²×C₁₉	semidirect
281. #322	C₂²×C₁₉	semidirect
346. C₁₉	#19676	direct (N × H)
453. C₈	C₁₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3208	2
C₁₉×#3205	2
C₁₉×#3167	2
C₁₉×#3151	2
C₂×C₁₉×#493	2
C₁₉×#3138	2
C₁₉×#1721	2
C₁₉×#1717	2
C₁₉×#1715	2
C₁₉×#1451	2
#19676	19

Subgroups — C19×#19676 #18025635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19676 #18025635