Subgroups — C₁₉×#23891 #18029850

Order 4864.

1622 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#578	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#456	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3013	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2020	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1908	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
12	C₁₉×#578	—	2	8	no	—
13	C₁₉×#578	—	2	8	no	—
14	C₂×C₁₉×#137	—	2	2	no	—
15	C₂×C₁₉×#137	—	2	2	no	—
16	C₂×C₁₉×#137	C₂²	1	2	yes	—
17	C₂×C₁₉×#137	C₂²	1	2	yes	—
18	C₂×C₁₉×#137	C₂²	1	2	yes	—
19	C₂×C₁₉×#135	—	2	2	no	—
20	C₂×C₁₉×#135	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₁₉	—	2	2	no	—
22	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
23	C₂×C₁₉×#131	C₂²	1	2	yes	—
24	C₁₉×#537	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#456	—	2	8	no	—
27	C₁₉×#452	—	2	2	no	—
28	C₁₉×#451	—	2	2	no	—
29	C₁₉×#449	—	2	2	no	—
30	C₁₉×#448	—	2	2	no	—
31	C₂×C₁₉×#104	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₁₉×#417	C₂²	1	2	yes	—
34	C₂×C₁₉×#103	C₂²	1	2	yes	—
35	C₂×C₁₉×#101	C₂²	1	2	yes	—
36	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
37	C₁₉×#408	C₂²	1	2	yes	—
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#343	C₂²	1	1	yes	characteristic
40	C₁₉×#341	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×2₋¹⁺⁴	—	2	4	no	—
43	C₁₉×2₋¹⁺⁴	—	2	4	no	—
44	C₁₉×2₋¹⁺⁴	—	2	4	no	—
45	C₁₉×2₋¹⁺⁴	—	2	4	no	—
46	C₁₉×2₋¹⁺⁴	—	4	1	no	—
47	C₁₉×2₋¹⁺⁴	—	4	2	no	—
48	C₁₉×2₋¹⁺⁴	D₄	1	4	yes	complemented
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	4	2	no	—
53	C₂×#41×C₁₉	—	4	1	no	—
54	C₂×#41×C₁₉	C₂³	1	2	yes	—
55	C₂×#41×C₁₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₉	—	2	2	no	—
57	C₂²×Q₈×C₁₉	—	2	2	no	—
58	C₂²×Q₈×C₁₉	—	2	2	no	—
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×#137	—	2	16	no	—
62	C₁₉×#137	—	2	16	no	—
63	C₁₉×#137	—	2	4	no	—
64	C₁₉×#137	—	2	4	no	—
65	C₁₉×#137	—	2	4	no	—
66	C₁₉×#137	—	2	4	no	—
67	C₁₉×#137	—	4	2	no	—
68	C₁₉×#137	D₄	1	8	yes	complemented
69	C₁₉×#135	—	2	16	no	—
70	C₁₉×#135	—	2	4	no	—
71	C₁₉×#135	—	2	4	no	—
72	C₂×Q₁₆×C₁₉	—	2	16	no	—
73	C₂×Q₁₆×C₁₉	—	2	2	no	—
74	C₂×Q₁₆×C₁₉	—	2	2	no	—
75	C₂×Q₁₆×C₁₉	—	2	4	no	—
76	C₂×Q₁₆×C₁₉	—	2	4	no	—
77	C₂×Q₁₆×C₁₉	—	2	2	no	—
78	C₂×Q₁₆×C₁₉	—	2	2	no	—
79	C₂×Q₁₆×C₁₉	—	2	2	no	—
80	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
81	C₂×SD₁₆×C₁₉	—	2	2	no	—
82	C₂×SD₁₆×C₁₉	—	2	2	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	D₄	1	2	yes	—
85	C₂×SD₁₆×C₁₉	D₄	1	2	yes	—
86	C₂×D₈×C₁₉	D₄	1	2	yes	—
87	C₁₉×#131	—	2	4	no	—
88	C₁₉×#131	—	2	4	no	—
89	C₂×M₁₆×C₁₉	—	2	2	no	—
90	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
91	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₉	—	2	2	no	—
93	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
94	C₁₉×C₄⋊Q₈	—	2	4	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	4	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#104	—	2	4	no	—
102	C₁₉×#104	—	2	4	no	—
103	C₁₉×#103	—	2	2	no	—
104	C₁₉×#103	—	2	2	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×#101	—	2	4	no	—
108	C₁₉×#101	—	4	1	no	—
109	C₁₉×C₂²⋊C₈	—	2	2	no	—
110	C₁₉×C₂²⋊C₈	—	2	2	no	—
111	C₁₉×#95	—	4	1	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	8	no	—
115	#41×C₁₉	—	2	8	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	4	4	no	—
121	#41×C₁₉	—	4	4	no	—
122	#41×C₁₉	—	4	4	no	—
123	#41×C₁₉	—	4	8	no	—
124	#41×C₁₉	—	4	4	no	—
125	#41×C₁₉	—	4	4	no	—
126	#41×C₁₉	—	4	8	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	C₂×D₄	1	4	yes	—
129	#41×C₁₉	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	8	no	—
133	C₂×Q₈×C₁₉	—	2	8	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	2	no	—
142	C₂×Q₈×C₁₉	—	4	4	no	—
143	C₂×Q₈×C₁₉	—	4	4	no	—
144	C₂×Q₈×C₁₉	—	4	4	no	—
145	C₂×Q₈×C₁₉	—	4	4	no	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	4	1	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₉	—	2	8	no	—
168	Q₁₆×C₁₉	—	2	8	no	—
169	Q₁₆×C₁₉	—	2	8	no	—
170	Q₁₆×C₁₉	—	2	4	no	—
171	Q₁₆×C₁₉	—	2	8	no	—
172	Q₁₆×C₁₉	—	4	4	no	—
173	SD₁₆×C₁₉	—	2	8	no	—
174	SD₁₆×C₁₉	—	2	4	no	—
175	SD₁₆×C₁₉	—	2	8	no	—
176	SD₁₆×C₁₉	—	2	4	no	—
177	SD₁₆×C₁₉	—	4	4	no	—
178	D₈×C₁₉	—	2	4	no	—
179	M₁₆×C₁₉	—	2	8	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	2	2	no	—
182	M₁₆×C₁₉	—	2	2	no	—
183	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₁₉	—	2	8	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	4	4	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₂²⋊C₄×C₁₉	—	4	2	no	—
195	C₄²×C₁₉	—	2	2	no	—
196	#23891	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	Q₈×C₁₉	—	2	2	no	—
201	Q₈×C₁₉	—	2	4	no	—
202	Q₈×C₁₉	—	2	4	no	—
203	Q₈×C₁₉	—	2	2	no	—
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	2	2	no	—
206	Q₈×C₁₉	—	4	4	no	—
207	Q₈×C₁₉	—	4	8	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	#120	1	4	yes	—
212	D₄×C₁₉	—	2	4	no	—
213	D₄×C₁₉	—	2	4	no	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	—	2	2	no	—
216	D₄×C₁₉	—	2	2	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	4	8	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	16	1	no	—
222	D₄×C₁₉	#120	1	4	yes	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	4	8	no	—
231	C₂×C₄×C₁₉	—	4	8	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	8	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	8	1	no	—
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
247	C₈×C₁₉	—	2	2	no	—
248	C₈×C₁₉	—	2	4	no	—
249	C₈×C₁₉	—	2	2	no	—
250	C₈×C₁₉	—	4	2	no	—
251	C₂×#578	C₂×C₁₉	1	2	yes	complemented
252	C₂×#456	C₂×C₁₉	1	2	yes	complemented
253	#3013	C₂×C₁₉	1	2	yes	complemented
254	#2020	C₂×C₁₉	1	2	yes	complemented
255	#2016	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2007	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1908	C₂×C₁₉	1	2	yes	complemented
258	#1876	C₂×C₁₉	1	2	yes	complemented
259	#1793	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	#534	1	1	yes	characteristic
269	C₂²×C₁₉	D₄²	1	1	yes	characteristic
270	C₂²×C₁₉	D₄²	1	1	yes	characteristic
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	C₂×#120	1	2	yes	—
278	C₄×C₁₉	D₄²	1	2	yes	—
279	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
280	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
281	#578	—	2	8	no	—
282	#578	—	2	8	no	—
283	C₂×#137	—	2	2	no	—
284	C₂×#137	—	2	2	no	—
285	C₂×#137	C₂²×C₁₉	1	2	yes	—
286	C₂×#137	C₂²×C₁₉	1	2	yes	—
287	C₂×#137	C₂²×C₁₉	1	2	yes	—
288	C₂×#135	—	2	2	no	—
289	C₂×#135	C₂²×C₁₉	1	2	yes	—
290	C₂²×Q₁₆	—	2	2	no	—
291	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
292	C₂×#131	C₂²×C₁₉	1	2	yes	—
293	#537	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
295	#456	—	2	8	no	—
296	#452	—	2	2	no	—
297	#451	—	2	2	no	—
298	#449	—	2	2	no	—
299	#448	—	2	2	no	—
300	C₂×#104	C₂²×C₁₉	1	2	yes	—
301	C₂×#104	C₂²×C₁₉	1	2	yes	—
302	#417	C₂²×C₁₉	1	2	yes	—
303	C₂×#103	C₂²×C₁₉	1	2	yes	—
304	C₂×#101	C₂²×C₁₉	1	2	yes	—
305	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
306	#408	C₂²×C₁₉	1	2	yes	—
307	#391	C₂²×C₁₉	1	1	yes	characteristic
308	#343	C₂²×C₁₉	1	1	yes	characteristic
309	#341	C₂²×C₁₉	1	2	yes	—
310	#336	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×C₁₉	—	2	1	no	—
312	C₂×C₁₉	—	2	1	no	—
313	C₂×C₁₉	—	4	4	no	—
314	C₂×C₁₉	—	8	2	no	—
315	C₂×C₁₉	#2403	1	1	yes	characteristic
316	C₂×C₁₉	#3289	1	1	yes	characteristic
317	C₂×C₁₉	#3293	1	1	yes	characteristic
318	2₋¹⁺⁴	—	2	4	no	—
319	2₋¹⁺⁴	—	2	4	no	—
320	2₋¹⁺⁴	—	2	4	no	—
321	2₋¹⁺⁴	—	2	4	no	—
322	2₋¹⁺⁴	—	4	1	no	—
323	2₋¹⁺⁴	—	4	2	no	—
324	2₋¹⁺⁴	D₄×C₁₉	1	4	yes	complemented
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	4	1	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	C₂³×C₁₉	1	2	yes	—
331	C₂×#41	C₂³×C₁₉	1	2	yes	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	—	2	2	no	—
335	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
336	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
337	#137	—	2	16	no	—
338	#137	—	2	16	no	—
339	#137	—	2	4	no	—
340	#137	—	2	4	no	—
341	#137	—	2	4	no	—
342	#137	—	2	4	no	—
343	#137	—	4	2	no	—
344	#137	D₄×C₁₉	1	8	yes	complemented
345	#135	—	2	16	no	—
346	#135	—	2	4	no	—
347	#135	—	2	4	no	—
348	C₂×Q₁₆	—	2	16	no	—
349	C₂×Q₁₆	—	2	2	no	—
350	C₂×Q₁₆	—	2	2	no	—
351	C₂×Q₁₆	—	2	4	no	—
352	C₂×Q₁₆	—	2	4	no	—
353	C₂×Q₁₆	—	2	2	no	—
354	C₂×Q₁₆	—	2	2	no	—
355	C₂×Q₁₆	—	2	2	no	—
356	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	D₄×C₁₉	1	2	yes	—
361	C₂×SD₁₆	D₄×C₁₉	1	2	yes	—
362	C₂×D₈	D₄×C₁₉	1	2	yes	—
363	#131	—	2	4	no	—
364	#131	—	2	4	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
367	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
370	C₄⋊Q₈	—	2	4	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	4	1	no	—
374	C₂×C₄⋊C₄	—	4	1	no	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
377	#104	—	2	4	no	—
378	#104	—	2	4	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#102	—	2	2	no	—
383	#101	—	2	4	no	—
384	#101	—	4	1	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	#95	—	4	1	no	—
388	C₁₉	#23891	1	1	yes	characteristic, direct product factor, Sylow
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	8	no	—
392	#41	—	2	8	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	4	4	no	—
398	#41	—	4	4	no	—
399	#41	—	4	4	no	—
400	#41	—	4	8	no	—
401	#41	—	4	4	no	—
402	#41	—	4	4	no	—
403	#41	—	4	8	no	—
404	#41	—	4	4	no	—
405	#41	C₂×D₄×C₁₉	1	4	yes	—
406	#41	C₂×D₄×C₁₉	1	4	yes	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	8	no	—
410	C₂×Q₈	—	2	8	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	4	1	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	4	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	—	4	4	no	—
422	C₂×Q₈	—	4	4	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
424	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
425	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
433	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
444	Q₁₆	—	2	8	no	—
445	Q₁₆	—	2	8	no	—
446	Q₁₆	—	2	8	no	—
447	Q₁₆	—	2	4	no	—
448	Q₁₆	—	2	8	no	—
449	Q₁₆	—	4	4	no	—
450	SD₁₆	—	2	8	no	—
451	SD₁₆	—	2	4	no	—
452	SD₁₆	—	2	8	no	—
453	SD₁₆	—	2	4	no	—
454	SD₁₆	—	4	4	no	—
455	D₈	—	2	4	no	—
456	M₁₆	—	2	8	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
461	C₂×C₈	—	2	8	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
467	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	4	4	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₄²	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
476	Q₈	—	2	2	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	4	4	no	—
483	Q₈	—	4	8	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	Q₈	C₁₉×#120	1	4	yes	—
488	D₄	—	2	4	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	8	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	16	1	no	—
498	D₄	C₁₉×#120	1	4	yes	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	8	1	no	—
519	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
522	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
523	C₈	—	2	2	no	—
524	C₈	—	2	4	no	—
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	C₁₉×#534	1	1	yes	characteristic
536	C₂²	D₄²×C₁₉	1	1	yes	characteristic
537	C₂²	D₄²×C₁₉	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	8	1	no	—
544	C₄	C₂×C₁₉×#120	1	2	yes	—
545	C₄	D₄²×C₁₉	1	2	yes	—
546	C₂	—	2	1	no	—
547	C₂	—	2	1	no	—
548	C₂	—	4	4	no	—
549	C₂	—	8	2	no	—
550	C₂	C₁₉×#2403	1	1	yes	characteristic
551	C₂	C₁₉×#3289	1	1	yes	characteristic
552	C₂	C₁₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#578	C₂	semidirect
2. C₂×C₁₉×#456	C₂	semidirect
3. C₁₉×#3013	C₂	semidirect
4. C₁₉×#2020	C₂	semidirect
5. C₁₉×#2016	C₂	semidirect
6. C₁₉×#2007	C₂	semidirect
7. C₁₉×#1908	C₂	semidirect
8. C₁₉×#1876	C₂	semidirect
9. C₁₉×#1793	C₂	semidirect
48. C₁₉×2₋¹⁺⁴	D₄	semidirect
68. C₁₉×#137	D₄	semidirect
196. #23891	C₁₉	direct (N × H)
251. C₂×#578	C₂×C₁₉	semidirect
252. C₂×#456	C₂×C₁₉	semidirect
253. #3013	C₂×C₁₉	semidirect
254. #2020	C₂×C₁₉	semidirect
255. #2016	C₂×C₁₉	semidirect
256. #2007	C₂×C₁₉	semidirect
257. #1908	C₂×C₁₉	semidirect
258. #1876	C₂×C₁₉	semidirect
259. #1793	C₂×C₁₉	semidirect
324. 2₋¹⁺⁴	D₄×C₁₉	semidirect
344. #137	D₄×C₁₉	semidirect
388. C₁₉	#23891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#578	2
C₂×C₁₉×#456	2
C₁₉×#3013	2
C₁₉×#2020	2
C₁₉×#2016	2
C₁₉×#2007	2
C₁₉×#1908	2
C₁₉×#1876	2
C₁₉×#1793	2
#23891	19

Subgroups — C19×#23891 #18029850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23891 #18029850