Subgroups — C₁₉×#32765 #18038724

Order 4864.

878 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2620	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2071	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2012	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2000	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1999	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#102	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#396	—	2	2	no	—
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#394	—	2	2	no	—
28	C₁₉×#392	—	2	2	no	—
29	C₁₉×#391	C₂²	1	1	yes	characteristic
30	C₁₉×#390	C₂²	1	1	yes	characteristic
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#384	C₂²	1	1	yes	characteristic
33	C₁₉×#382	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₉	—	4	2	no	—
47	C₂×SD₁₆×C₁₉	—	4	2	no	—
48	C₂×SD₁₆×C₁₉	—	4	2	no	—
49	C₂×D₈×C₁₉	—	4	2	no	—
50	C₂×D₈×C₁₉	—	4	2	no	—
51	C₂×D₈×C₁₉	—	4	2	no	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₁₉×#127	—	4	2	no	—
55	C₁₉×#124	—	4	2	no	—
56	C₁₉×C₂²⋊Q₈	—	4	2	no	—
57	C₁₉×#121	—	4	2	no	—
58	C₁₉×#121	—	4	2	no	—
59	C₁₉×#121	—	4	2	no	—
60	C₁₉×#117	—	4	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#103	—	4	2	no	—
78	C₁₉×#102	—	4	2	no	—
79	C₁₉×#102	—	4	2	no	—
80	C₁₉×#102	—	4	2	no	—
81	C₁₉×C₂²⋊C₈	—	4	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	1	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	8	2	no	—
105	C₂×D₄×C₁₉	—	8	2	no	—
106	C₂×D₄×C₁₉	—	8	2	no	—
107	C₂×D₄×C₁₉	—	8	2	no	—
108	C₂×D₄×C₁₉	—	8	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₁₉	—	4	8	no	—
122	D₈×C₁₉	—	4	8	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	4	2	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	8	2	no	—
136	C₂²⋊C₄×C₁₉	—	4	2	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	8	2	no	—
142	C₂²⋊C₄×C₁₉	—	8	2	no	—
143	C₂²⋊C₄×C₁₉	—	8	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	#32765	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	8	8	no	—
174	D₄×C₁₉	—	8	4	no	—
175	D₄×C₁₉	—	8	8	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₈×C₁₉	—	4	2	no	—
202	C₈×C₁₉	—	4	2	no	—
203	#2620	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2619	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2074	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2073	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2071	C₂×C₁₉	1	2	yes	complemented
208	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2012	C₂×C₁₉	1	2	yes	complemented
210	#2011	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2000	C₂×C₁₉	1	2	yes	complemented
212	#1999	C₂×C₁₉	1	2	yes	complemented
213	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	8	2	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	1	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	2	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	#534	1	1	yes	characteristic
232	C₂²×C₁₉	#535	1	1	yes	characteristic
233	C₂²×C₁₉	#535	1	1	yes	characteristic
234	C₂²×C₁₉	#576	1	2	yes	—
235	C₂²×C₁₉	#577	1	2	yes	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	#560	1	2	yes	—
244	C₄×C₁₉	#560	1	2	yes	—
245	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
246	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
247	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#121	C₂²×C₁₉	1	2	yes	—
251	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×#103	C₂²×C₁₉	1	2	yes	—
254	C₂×#102	C₂²×C₁₉	1	2	yes	—
255	C₂×#102	C₂²×C₁₉	1	2	yes	—
256	C₂×#102	C₂²×C₁₉	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
258	#396	—	2	2	no	—
259	#394	—	2	2	no	—
260	#394	—	2	2	no	—
261	#392	—	2	2	no	—
262	#391	C₂²×C₁₉	1	1	yes	characteristic
263	#390	C₂²×C₁₉	1	2	yes	—
264	#390	C₂²×C₁₉	1	1	yes	characteristic
265	#384	C₂²×C₁₉	1	1	yes	characteristic
266	#382	C₂²×C₁₉	1	1	yes	characteristic
267	#340	C₂²×C₁₉	1	2	yes	—
268	#340	C₂²×C₁₉	1	2	yes	—
269	#336	C₂²×C₁₉	1	2	yes	—
270	#336	C₂²×C₁₉	1	1	yes	characteristic
271	#336	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₁₉	—	8	1	no	—
273	C₂×C₁₉	—	16	2	no	—
274	C₂×C₁₉	—	16	1	no	—
275	C₂×C₁₉	#2815	1	1	yes	characteristic
276	C₂×C₁₉	#3198	1	2	yes	—
277	C₂×C₁₉	#3220	1	1	yes	characteristic
278	C₂×C₁₉	#3221	1	1	yes	characteristic
279	C₂×C₁₉	#3224	1	2	yes	—
280	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂×SD₁₆	—	4	2	no	—
288	C₂×SD₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	4	2	no	—
290	C₂×D₈	—	4	2	no	—
291	C₂×D₈	—	4	2	no	—
292	C₂×D₈	—	4	2	no	—
293	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
295	#127	—	4	2	no	—
296	#124	—	4	2	no	—
297	C₂²⋊Q₈	—	4	2	no	—
298	#121	—	4	2	no	—
299	#121	—	4	2	no	—
300	#121	—	4	2	no	—
301	#117	—	4	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
318	#103	—	4	2	no	—
319	#102	—	4	2	no	—
320	#102	—	4	2	no	—
321	#102	—	4	2	no	—
322	C₂²⋊C₈	—	4	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₁₉	#32765	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁴	—	2	1	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
363	SD₁₆	—	4	8	no	—
364	D₈	—	4	8	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	8	2	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	8	8	no	—
415	D₄	—	8	4	no	—
416	D₄	—	8	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
439	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₁₉×#534	1	1	yes	characteristic
462	C₂²	C₁₉×#535	1	1	yes	characteristic
463	C₂²	C₁₉×#535	1	1	yes	characteristic
464	C₂²	C₁₉×#576	1	2	yes	—
465	C₂²	C₁₉×#577	1	2	yes	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	C₁₉×#560	1	2	yes	—
474	C₄	C₁₉×#560	1	2	yes	—
475	C₂	—	8	1	no	—
476	C₂	—	16	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₁₉×#2815	1	1	yes	characteristic
479	C₂	C₁₉×#3198	1	2	yes	—
480	C₂	C₁₉×#3220	1	1	yes	characteristic
481	C₂	C₁₉×#3221	1	1	yes	characteristic
482	C₂	C₁₉×#3224	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 ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2620	C₂	semidirect
2. C₁₉×#2619	C₂	semidirect
3. C₁₉×#2074	C₂	semidirect
4. C₁₉×#2073	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2014	C₂	semidirect
7. C₁₉×#2012	C₂	semidirect
8. C₁₉×#2011	C₂	semidirect
9. C₁₉×#2000	C₂	semidirect
10. C₁₉×#1999	C₂	semidirect
11. C₁₉×#1818	C₂	semidirect
146. #32765	C₁₉	direct (N × H)
203. #2620	C₂×C₁₉	semidirect
204. #2619	C₂×C₁₉	semidirect
205. #2074	C₂×C₁₉	semidirect
206. #2073	C₂×C₁₉	semidirect
207. #2071	C₂×C₁₉	semidirect
208. #2014	C₂×C₁₉	semidirect
209. #2012	C₂×C₁₉	semidirect
210. #2011	C₂×C₁₉	semidirect
211. #2000	C₂×C₁₉	semidirect
212. #1999	C₂×C₁₉	semidirect
213. #1818	C₂×C₁₉	semidirect
325. C₁₉	#32765	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2620	2
C₁₉×#2619	2
C₁₉×#2074	2
C₁₉×#2073	2
C₁₉×#2071	2
C₁₉×#2014	2
C₁₉×#2012	2
C₁₉×#2011	2
C₁₉×#2000	2
C₁₉×#1999	2
C₁₉×#1818	2
#32765	19

Subgroups — C19×#32765 #18038724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32765 #18038724