Subgroups — C₁₉×#23906 #18029865

Order 4864.

2502 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#453	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3003	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2002	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1896	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1887	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
10	C₂³×D₄×C₁₉	—	2	2	no	—
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
14	C₁₉×#546	—	2	4	no	—
15	D₄²×C₁₉	—	2	4	no	—
16	C₁₉×#535	C₂²	1	2	yes	complemented
17	C₁₉×#534	—	2	2	no	—
18	C₂×C₁₉×#127	—	2	2	no	—
19	C₂×C₁₉×#127	—	2	8	no	—
20	C₂×C₁₉×#127	C₂²	1	2	yes	—
21	C₂×C₁₉×#127	C₂²	1	2	yes	complemented
22	C₁₉×#525	C₂²	1	2	yes	—
23	C₂×C₁₉×#120	—	2	2	no	—
24	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#453	—	2	8	no	—
27	C₁₉×#450	—	2	4	no	—
28	C₁₉×#447	—	2	4	no	—
29	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
30	C₁₉×#418	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
33	C₁₉×#407	C₂²	1	2	yes	complemented
34	C₁₉×#339	C₂²	1	4	yes	complemented
35	C₂⁵×C₁₉	—	2	1	no	—
36	C₂⁵×C₁₉	D₄	1	2	yes	—
37	C₁₉×H(5,𝔽₂)	—	2	4	no	—
38	C₁₉×H(5,𝔽₂)	—	4	2	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₉	—	2	16	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	4	no	—
51	C₂²×D₄×C₁₉	—	2	4	no	—
52	C₂²×D₄×C₁₉	—	4	2	no	—
53	C₂²×D₄×C₁₉	—	4	2	no	—
54	C₂²×D₄×C₁₉	—	4	16	no	—
55	C₂²×D₄×C₁₉	D₄	1	2	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
62	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
63	C₂×SD₁₆×C₁₉	—	2	4	no	—
64	C₂×D₈×C₁₉	—	2	4	no	—
65	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
66	C₁₉×#127	—	2	16	no	—
67	C₁₉×#127	—	2	4	no	—
68	C₁₉×#127	—	2	4	no	—
69	C₁₉×#127	—	2	2	no	—
70	C₁₉×#127	—	2	4	no	—
71	C₁₉×#127	D₄	1	8	yes	complemented
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	complemented
76	C₁₉×#121	—	2	8	no	—
77	C₁₉×#121	—	2	4	no	—
78	C₁₉×#121	D₄	1	4	yes	complemented
79	C₁₉×#120	—	2	8	no	—
80	C₁₉×#120	—	2	4	no	—
81	C₁₉×#120	—	2	2	no	—
82	C₁₉×#120	—	2	4	no	—
83	C₄×D₄×C₁₉	—	2	4	no	—
84	C₄×D₄×C₁₉	—	2	4	no	—
85	C₁₉×#117	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	4	no	—
90	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
91	C₁₉×#104	—	2	8	no	—
92	C₁₉×#102	—	2	8	no	—
93	C₁₉×#100	—	2	4	no	—
94	C₁₉×#100	—	4	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	4	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	4	8	no	—
103	C₂⁴×C₁₉	—	4	2	no	—
104	C₂⁴×C₁₉	—	4	8	no	—
105	C₂⁴×C₁₉	—	4	2	no	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
108	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
109	#41×C₁₉	—	2	4	no	—
110	#41×C₁₉	—	2	4	no	—
111	#41×C₁₉	—	4	8	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	complemented
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	16	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	—	2	16	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	4	16	no	—
131	C₂×D₄×C₁₉	—	4	16	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	16	no	—
134	C₂×D₄×C₁₉	—	4	16	no	—
135	C₂×D₄×C₁₉	—	4	64	no	—
136	C₂×D₄×C₁₉	—	4	2	no	—
137	C₂×D₄×C₁₉	—	4	8	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	8	8	no	—
142	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	complemented
144	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	complemented
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	8	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₁₉	—	4	8	no	—
157	D₈×C₁₉	—	4	8	no	—
158	M₁₆×C₁₉	—	2	4	no	—
159	M₁₆×C₁₉	—	2	4	no	—
160	C₂×C₈×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	complemented
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₄²×C₁₉	—	2	4	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	C₂×D₄	1	4	yes	complemented
172	#23906	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	4	8	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	—	4	4	no	—
186	C₂³×C₁₉	—	4	16	no	—
187	C₂³×C₁₉	—	4	16	no	—
188	C₂³×C₁₉	—	4	8	no	—
189	C₂³×C₁₉	—	4	8	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	8	no	—
194	C₂³×C₁₉	—	8	4	no	—
195	C₂³×C₁₉	—	8	8	no	—
196	C₂³×C₁₉	—	8	8	no	—
197	C₂³×C₁₉	—	8	4	no	—
198	C₂³×C₁₉	—	8	4	no	—
199	C₂³×C₁₉	—	8	4	no	—
200	C₂³×C₁₉	#120	1	2	yes	—
201	C₂³×C₁₉	#120	1	4	yes	—
202	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₉	—	2	4	no	—
204	D₄×C₁₉	—	2	8	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	2	8	no	—
207	D₄×C₁₉	—	4	8	no	—
208	D₄×C₁₉	—	4	32	no	—
209	D₄×C₁₉	—	4	32	no	—
210	D₄×C₁₉	—	4	8	no	—
211	D₄×C₁₉	—	4	8	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	8	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	4	no	—
217	D₄×C₁₉	—	8	8	no	—
218	C₂×C₄×C₁₉	—	2	16	no	—
219	C₂×C₄×C₁₉	—	2	8	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	8	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	8	4	no	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₁₉	—	4	4	no	—
234	#3484	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂×#453	C₂×C₁₉	1	2	yes	complemented
237	#3003	C₂×C₁₉	1	2	yes	complemented
238	#2002	C₂×C₁₉	1	4	yes	complemented
239	#1896	C₂×C₁₉	1	2	yes	complemented
240	#1887	C₂×C₁₉	1	2	yes	complemented
241	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	4	8	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	4	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	4	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	16	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	4	no	—
261	C₂²×C₁₉	—	8	16	no	—
262	C₂²×C₁₉	—	8	4	no	—
263	C₂²×C₁₉	—	16	4	no	—
264	C₂²×C₁₉	#453	1	4	yes	complemented
265	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
267	C₂²×C₁₉	#534	1	1	yes	characteristic
268	C₄×C₁₉	—	2	8	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	D₄²	1	4	yes	—
273	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	C₂³×D₄	—	2	2	no	—
275	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
277	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
278	#546	—	2	4	no	—
279	D₄²	—	2	4	no	—
280	#535	C₂²×C₁₉	1	2	yes	complemented
281	#534	—	2	2	no	—
282	C₂×#127	—	2	2	no	—
283	C₂×#127	—	2	8	no	—
284	C₂×#127	C₂²×C₁₉	1	2	yes	—
285	C₂×#127	C₂²×C₁₉	1	2	yes	complemented
286	#525	C₂²×C₁₉	1	2	yes	—
287	C₂×#120	—	2	2	no	—
288	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	#453	—	2	8	no	—
291	#450	—	2	4	no	—
292	#447	—	2	4	no	—
293	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
294	#418	C₂²×C₁₉	1	4	yes	complemented
295	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
296	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
297	#407	C₂²×C₁₉	1	2	yes	complemented
298	#339	C₂²×C₁₉	1	4	yes	complemented
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	2	1	no	—
301	C₂×C₁₉	—	2	4	no	—
302	C₂×C₁₉	—	4	4	no	—
303	C₂×C₁₉	—	8	2	no	—
304	C₂×C₁₉	—	8	4	no	—
305	C₂×C₁₉	—	8	2	no	—
306	C₂×C₁₉	#2403	1	1	yes	characteristic
307	C₂×C₁₉	C₂×#453	1	2	yes	—
308	C₂⁵	—	2	1	no	—
309	C₂⁵	D₄×C₁₉	1	2	yes	—
310	H(5,𝔽₂)	—	2	4	no	—
311	H(5,𝔽₂)	—	4	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	C₂³×C₁₉	1	2	yes	—
314	C₂²×D₄	—	2	16	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	4	2	no	—
326	C₂²×D₄	—	4	2	no	—
327	C₂²×D₄	—	4	16	no	—
328	C₂²×D₄	D₄×C₁₉	1	2	yes	—
329	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
334	AGL(1,ℤ/8)	—	2	8	no	—
335	AGL(1,ℤ/8)	—	4	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×D₈	—	2	4	no	—
338	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
339	#127	—	2	16	no	—
340	#127	—	2	4	no	—
341	#127	—	2	4	no	—
342	#127	—	2	2	no	—
343	#127	—	2	4	no	—
344	#127	D₄×C₁₉	1	8	yes	complemented
345	#124	—	2	2	no	—
346	#123	—	2	4	no	—
347	#123	—	2	2	no	—
348	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	complemented
349	#121	—	2	8	no	—
350	#121	—	2	4	no	—
351	#121	D₄×C₁₉	1	4	yes	complemented
352	#120	—	2	8	no	—
353	#120	—	2	4	no	—
354	#120	—	2	2	no	—
355	#120	—	2	4	no	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	4	no	—
358	#117	C₂³×C₁₉	1	2	yes	—
359	C₂×C₂²⋊C₄	—	2	4	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	4	no	—
363	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
364	#104	—	2	8	no	—
365	#102	—	2	8	no	—
366	#100	—	2	4	no	—
367	#100	—	4	2	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	C₁₉	#23906	1	1	yes	characteristic, direct product factor, Sylow
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	4	no	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	4	2	no	—
376	C₂⁴	—	4	8	no	—
377	C₂⁴	—	4	8	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
382	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
383	#41	—	2	4	no	—
384	#41	—	2	4	no	—
385	#41	—	4	8	no	—
386	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	complemented
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	16	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	16	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	16	no	—
405	C₂×D₄	—	4	16	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	16	no	—
408	C₂×D₄	—	4	16	no	—
409	C₂×D₄	—	4	64	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	8	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	8	8	no	—
416	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
417	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	complemented
418	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	complemented
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
430	SD₁₆	—	4	8	no	—
431	D₈	—	4	8	no	—
432	M₁₆	—	2	4	no	—
433	M₁₆	—	2	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	complemented
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	C₂×D₄×C₁₉	1	4	yes	complemented
446	C₂³	—	2	4	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	16	no	—
460	C₂³	—	4	16	no	—
461	C₂³	—	4	8	no	—
462	C₂³	—	4	8	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	8	4	no	—
468	C₂³	—	8	8	no	—
469	C₂³	—	8	8	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	4	no	—
473	C₂³	C₁₉×#120	1	2	yes	—
474	C₂³	C₁₉×#120	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	D₄	—	2	8	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	8	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	32	no	—
482	D₄	—	4	32	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	4	no	—
490	D₄	—	8	8	no	—
491	C₂×C₄	—	2	16	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₁₉×#120	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
505	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
506	C₈	—	4	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	16	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	16	no	—
526	C₂²	—	8	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	16	4	no	—
529	C₂²	C₁₉×#453	1	4	yes	complemented
530	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
531	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
532	C₂²	C₁₉×#534	1	1	yes	characteristic
533	C₄	—	2	8	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	4	no	—
537	C₄	D₄²×C₁₉	1	4	yes	—
538	C₂	—	2	1	no	—
539	C₂	—	2	4	no	—
540	C₂	—	2	1	no	—
541	C₂	—	4	4	no	—
542	C₂	—	8	2	no	—
543	C₂	—	8	4	no	—
544	C₂	—	8	2	no	—
545	C₂	C₁₉×#2403	1	1	yes	characteristic
546	C₂	C₂×C₁₉×#453	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3484	C₂	semidirect
2. C₂²×C₁₉×#127	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#3003	C₂	semidirect
5. C₁₉×#2002	C₂	semidirect
6. C₁₉×#1896	C₂	semidirect
7. C₁₉×#1887	C₂	semidirect
8. C₁₉×#1783	C₂	semidirect
9. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
12. C₂³×D₄×C₁₉	C₂²	semidirect
13. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
16. C₁₉×#535	C₂²	semidirect
21. C₂×C₁₉×#127	C₂²	semidirect
24. C₁₉×#518	C₂²	semidirect
25. C₂²×C₄²×C₁₉	C₂²	semidirect
29. C₂×C₁₉×#104	C₂²	semidirect
30. C₁₉×#418	C₂²	semidirect
31. C₂×C₁₉×#100	C₂²	semidirect
32. C₂×C₁₉×#100	C₂²	semidirect
33. C₁₉×#407	C₂²	semidirect
34. C₁₉×#339	C₂²	semidirect
71. C₁₉×#127	D₄	semidirect
75. C₁₉×C₂²⋊Q₈	D₄	semidirect
78. C₁₉×#121	D₄	semidirect
112. C₂×Q₈×C₁₉	C₂×D₄	semidirect
143. C₂×D₄×C₁₉	C₂×D₄	semidirect
144. C₂×D₄×C₁₉	C₂×D₄	semidirect
162. C₄⋊C₄×C₁₉	C₂×D₄	semidirect
171. C₄²×C₁₉	C₂×D₄	semidirect
172. #23906	C₁₉	direct (N × H)
234. #3484	C₂×C₁₉	semidirect
235. C₂²×#127	C₂×C₁₉	semidirect
236. C₂×#453	C₂×C₁₉	semidirect
237. #3003	C₂×C₁₉	semidirect
238. #2002	C₂×C₁₉	semidirect
239. #1896	C₂×C₁₉	semidirect
240. #1887	C₂×C₁₉	semidirect
241. #1783	C₂×C₁₉	semidirect
264. C₂²×C₁₉	#453	semidirect
273. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
276. C₂³×D₄	C₂²×C₁₉	semidirect
277. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
280. #535	C₂²×C₁₉	semidirect
285. C₂×#127	C₂²×C₁₉	semidirect
288. #518	C₂²×C₁₉	semidirect
289. C₂²×C₄²	C₂²×C₁₉	semidirect
293. C₂×#104	C₂²×C₁₉	semidirect
294. #418	C₂²×C₁₉	semidirect
295. C₂×#100	C₂²×C₁₉	semidirect
296. C₂×#100	C₂²×C₁₉	semidirect
297. #407	C₂²×C₁₉	semidirect
298. #339	C₂²×C₁₉	semidirect
344. #127	D₄×C₁₉	semidirect
348. C₂²⋊Q₈	D₄×C₁₉	semidirect
351. #121	D₄×C₁₉	semidirect
369. C₁₉	#23906	direct (N × H)
386. C₂×Q₈	C₂×D₄×C₁₉	semidirect
417. C₂×D₄	C₂×D₄×C₁₉	semidirect
418. C₂×D₄	C₂×D₄×C₁₉	semidirect
436. C₄⋊C₄	C₂×D₄×C₁₉	semidirect
445. C₄²	C₂×D₄×C₁₉	semidirect
529. C₂²	C₁₉×#453	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3484	2
C₂²×C₁₉×#127	2
C₂×C₁₉×#453	2
C₁₉×#3003	2
C₁₉×#2002	2
C₁₉×#1896	2
C₁₉×#1887	2
C₁₉×#1783	2
#23906	19

Subgroups — C19×#23906 #18029865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23906 #18029865