Subgroups — C₁₉×#23430 #18029389

Order 4864.

2706 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#418	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2014	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2011	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	—	2	2	no	—
10	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
14	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
15	C₂²×D₈×C₁₉	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
17	C₂×C₁₉×#127	—	2	8	no	—
18	C₂×C₁₉×#127	—	2	2	no	—
19	C₂×C₁₉×#127	C₂²	1	4	yes	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#418	—	2	8	no	—
23	C₂×C₁₉×#102	C₂²	1	8	yes	complemented
24	C₁₉×#391	C₂²	1	2	yes	complemented
25	C₁₉×#390	C₂²	1	2	yes	complemented
26	C₁₉×#386	—	2	2	no	—
27	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₁₉×#336	C₂²	1	4	yes	complemented
29	C₂⁵×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	D₄	1	4	yes	complemented
34	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	—	2	16	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	4	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	—	2	8	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	4	16	no	—
45	C₂²×D₄×C₁₉	D₄	1	8	yes	—
46	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
47	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	D₄	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×AGL(1,ℤ/8)	—	2	64	no	—
52	C₂×SD₁₆×C₁₉	—	2	8	no	—
53	C₂×SD₁₆×C₁₉	—	2	8	no	—
54	C₂×SD₁₆×C₁₉	—	2	8	no	—
55	C₂×D₈×C₁₉	—	2	8	no	—
56	C₂×D₈×C₁₉	—	2	8	no	—
57	C₂×D₈×C₁₉	—	2	8	no	—
58	C₂×M₁₆×C₁₉	—	2	4	no	—
59	C₂×M₁₆×C₁₉	—	2	4	no	—
60	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
61	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
62	C₁₉×#127	—	2	16	no	—
63	C₁₉×#127	—	2	16	no	—
64	C₁₉×#117	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄²×C₁₉	—	2	4	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₁₉×#102	—	2	16	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	8	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	—	2	4	no	—
77	C₂⁴×C₁₉	—	4	16	no	—
78	C₂⁴×C₁₉	—	4	4	no	—
79	C₂⁴×C₁₉	—	4	4	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	#41×C₁₉	—	2	16	no	—
82	#41×C₁₉	—	4	8	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	complemented
87	C₂×D₄×C₁₉	—	2	32	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	16	no	—
90	C₂×D₄×C₁₉	—	2	8	no	—
91	C₂×D₄×C₁₉	—	2	16	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	4	64	no	—
101	C₂×D₄×C₁₉	—	4	16	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	8	no	—
105	C₂×D₄×C₁₉	—	4	8	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	16	no	—
109	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
110	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	complemented
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	SD₁₆×C₁₉	—	2	32	no	—
126	D₈×C₁₉	—	2	32	no	—
127	M₁₆×C₁₉	—	2	16	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	2	4	no	—
130	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	complemented
131	C₄⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	—	4	8	no	—
134	C₄²×C₁₉	—	2	4	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	4	2	no	—
137	#23430	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	8	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	4	32	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	4	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	16	no	—
148	C₂³×C₁₉	—	4	16	no	—
149	C₂³×C₁₉	—	8	16	no	—
150	C₂³×C₁₉	—	8	16	no	—
151	C₂³×C₁₉	#120	1	2	yes	—
152	C₂³×C₁₉	#121	1	2	yes	—
153	C₂³×C₁₉	#127	1	2	yes	—
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	4	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	2	4	no	—
158	D₄×C₁₉	—	2	8	no	—
159	D₄×C₁₉	—	2	8	no	—
160	D₄×C₁₉	—	4	64	no	—
161	D₄×C₁₉	—	4	8	no	—
162	D₄×C₁₉	—	4	4	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	16	no	—
166	C₂×C₄×C₁₉	—	2	16	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	#120	1	8	yes	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	8	yes	—
178	C₂×C₄×C₁₉	#121	1	2	yes	—
179	C₂×C₄×C₁₉	#127	1	2	yes	—
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	8	yes	complemented
181	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₉	—	2	8	no	—
186	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
187	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂×#418	C₂×C₁₉	1	2	yes	complemented
189	#2297	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#2014	C₂×C₁₉	1	4	yes	complemented
191	#2011	C₂×C₁₉	1	4	yes	complemented
192	#1728	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	8	no	—
198	C₂²×C₁₉	—	4	16	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	8	32	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	8	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	8	no	—
205	C₂²×C₁₉	#392	1	4	yes	—
206	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
210	C₄×C₁₉	—	2	8	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	#392	1	4	yes	—
214	C₄×C₁₉	C₂×#120	1	2	yes	—
215	C₄×C₁₉	C₂×#121	1	2	yes	—
216	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
217	C₂³×D₄	—	2	2	no	—
218	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
219	C₂×AGL(1,ℤ/8)	—	2	8	no	—
220	C₂×AGL(1,ℤ/8)	—	2	8	no	—
221	C₂×AGL(1,ℤ/8)	—	2	8	no	—
222	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
223	C₂²×D₈	C₂²×C₁₉	1	4	yes	complemented
224	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
225	C₂×#127	—	2	8	no	—
226	C₂×#127	—	2	2	no	—
227	C₂×#127	C₂²×C₁₉	1	4	yes	—
228	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
230	#418	—	2	8	no	—
231	C₂×#102	C₂²×C₁₉	1	8	yes	complemented
232	#391	C₂²×C₁₉	1	2	yes	complemented
233	#390	C₂²×C₁₉	1	2	yes	complemented
234	#386	—	2	2	no	—
235	C₄×C₂²⋊C₄	—	2	2	no	—
236	#336	C₂²×C₁₉	1	4	yes	complemented
237	C₂×C₁₉	—	2	4	no	—
238	C₂×C₁₉	—	8	2	no	—
239	C₂×C₁₉	—	8	8	no	—
240	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
241	C₂×C₁₉	#3003	1	2	yes	—
242	C₂×C₁₉	#3038	1	2	yes	—
243	C₂×C₁₉	#3151	1	2	yes	—
244	C₂⁵	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	D₄×C₁₉	1	4	yes	complemented
249	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
250	C₂²×D₄	—	2	16	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	—	2	4	no	—
255	C₂²×D₄	—	2	4	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	8	no	—
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	4	16	no	—
260	C₂²×D₄	D₄×C₁₉	1	8	yes	—
261	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
262	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₁₉	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	AGL(1,ℤ/8)	—	2	64	no	—
267	C₂×SD₁₆	—	2	8	no	—
268	C₂×SD₁₆	—	2	8	no	—
269	C₂×SD₁₆	—	2	8	no	—
270	C₂×D₈	—	2	8	no	—
271	C₂×D₈	—	2	8	no	—
272	C₂×D₈	—	2	8	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂×M₁₆	—	2	4	no	—
275	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
276	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
277	#127	—	2	16	no	—
278	#127	—	2	16	no	—
279	#117	—	2	4	no	—
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	D₄×C₁₉	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
287	#102	—	2	16	no	—
288	#95	—	2	4	no	—
289	C₁₉	#23430	1	1	yes	characteristic, direct product factor, Sylow
290	C₂⁴	—	2	8	no	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	4	16	no	—
294	C₂⁴	—	4	4	no	—
295	C₂⁴	—	4	4	no	—
296	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
297	#41	—	2	16	no	—
298	#41	—	4	8	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	complemented
303	C₂×D₄	—	2	32	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	16	no	—
306	C₂×D₄	—	2	8	no	—
307	C₂×D₄	—	2	16	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	64	no	—
317	C₂×D₄	—	4	16	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	8	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	8	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	16	no	—
325	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
326	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	complemented
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
339	C₂²×C₄	#41×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
341	SD₁₆	—	2	32	no	—
342	D₈	—	2	32	no	—
343	M₁₆	—	2	16	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	complemented
347	C₄⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	8	no	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	4	no	—
352	C₄²	—	4	2	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	32	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	8	16	no	—
365	C₂³	—	8	16	no	—
366	C₂³	C₁₉×#120	1	2	yes	—
367	C₂³	C₁₉×#121	1	2	yes	—
368	C₂³	C₁₉×#127	1	2	yes	—
369	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	8	no	—
375	D₄	—	4	64	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	16	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	16	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₁₉×#120	1	2	yes	—
391	C₂×C₄	C₁₉×#120	1	8	yes	—
392	C₂×C₄	C₁₉×#121	1	2	yes	—
393	C₂×C₄	C₁₉×#121	1	8	yes	—
394	C₂×C₄	C₁₉×#127	1	2	yes	—
395	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	8	yes	complemented
396	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
399	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
400	C₈	—	2	8	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	16	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	8	32	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	8	no	—
411	C₂²	—	8	8	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₁₉×#392	1	4	yes	—
414	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
415	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
416	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
418	C₄	—	2	8	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₁₉×#392	1	4	yes	—
422	C₄	C₂×C₁₉×#120	1	2	yes	—
423	C₄	C₂×C₁₉×#121	1	2	yes	—
424	C₂	—	2	4	no	—
425	C₂	—	8	8	no	—
426	C₂	—	8	2	no	—
427	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
428	C₂	C₁₉×#3003	1	2	yes	—
429	C₂	C₁₉×#3038	1	2	yes	—
430	C₂	C₁₉×#3151	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₁₉×#127	C₂	semidirect
3. C₂×C₁₉×#418	C₂	semidirect
4. C₁₉×#2297	C₂	semidirect
5. C₁₉×#2014	C₂	semidirect
6. C₁₉×#2011	C₂	semidirect
7. C₁₉×#1728	C₂	semidirect
14. C₂²×SD₁₆×C₁₉	C₂²	semidirect
15. C₂²×D₈×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#102	C₂²	semidirect
24. C₁₉×#391	C₂²	semidirect
25. C₁₉×#390	C₂²	semidirect
28. C₁₉×#336	C₂²	semidirect
33. C₂×#41×C₁₉	D₄	semidirect
60. C₂×M₁₆×C₁₉	D₄	semidirect
86. C₂×Q₈×C₁₉	C₂×D₄	semidirect
110. C₂×D₄×C₁₉	C₂×D₄	semidirect
130. C₂×C₈×C₁₉	C₂×D₄	semidirect
137. #23430	C₁₉	direct (N × H)
180. C₂×C₄×C₁₉	AGL(1,ℤ/8)	semidirect
186. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
187. C₂²×#127	C₂×C₁₉	semidirect
188. C₂×#418	C₂×C₁₉	semidirect
189. #2297	C₂×C₁₉	semidirect
190. #2014	C₂×C₁₉	semidirect
191. #2011	C₂×C₁₉	semidirect
192. #1728	C₂×C₁₉	semidirect
222. C₂²×SD₁₆	C₂²×C₁₉	semidirect
223. C₂²×D₈	C₂²×C₁₉	semidirect
231. C₂×#102	C₂²×C₁₉	semidirect
232. #391	C₂²×C₁₉	semidirect
233. #390	C₂²×C₁₉	semidirect
236. #336	C₂²×C₁₉	semidirect
248. C₂×#41	D₄×C₁₉	semidirect
275. C₂×M₁₆	D₄×C₁₉	semidirect
289. C₁₉	#23430	direct (N × H)
302. C₂×Q₈	C₂×D₄×C₁₉	semidirect
326. C₂×D₄	C₂×D₄×C₁₉	semidirect
346. C₂×C₈	C₂×D₄×C₁₉	semidirect
395. C₂×C₄	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
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂²×C₁₉×#127	2
C₂×C₁₉×#418	2
C₁₉×#2297	2
C₁₉×#2014	2
C₁₉×#2011	2
C₁₉×#1728	2
#23430	19

Subgroups — C19×#23430 #18029389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23430 #18029389