Subgroups — C₁₉×#32723 #18038682

Order 4864.

812 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2068	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2000	C₂	1	2	yes	maximal
11	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#391	C₂²	1	2	yes	—
26	C₁₉×#390	C₂²	1	1	yes	characteristic
27	C₁₉×#390	C₂²	1	1	yes	characteristic
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#389	C₂²	1	1	yes	characteristic
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#388	—	2	1	no	—
33	C₁₉×#388	—	2	1	no	—
34	C₁₉×#386	—	2	1	no	—
35	C₁₉×#384	C₂²	1	1	yes	characteristic
36	C₁₉×#380	—	2	1	no	—
37	C₁₉×#380	—	2	1	no	—
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₉	—	4	2	no	—
50	C₂×SD₁₆×C₁₉	—	4	2	no	—
51	C₂×SD₁₆×C₁₉	—	4	2	no	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₁₉×C₄⋊Q₈	—	4	2	no	—
55	C₁₉×#123	—	4	4	no	—
56	C₁₉×C₂²⋊Q₈	—	4	2	no	—
57	C₁₉×C₂²⋊Q₈	—	4	2	no	—
58	C₁₉×#121	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	4	2	no	—
78	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#107	—	4	2	no	—
83	C₁₉×C₄⋊C₈	—	4	2	no	—
84	C₁₉×#103	—	4	2	no	—
85	C₁₉×#103	—	4	2	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×#102	—	4	2	no	—
88	C₁₉×C₂²⋊C₈	—	4	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₁₉	—	4	8	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	—	4	2	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	—	4	2	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	2	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	2	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	#32723	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	#137	1	2	yes	—
176	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	4	2	no	—
179	Q₈×C₁₉	—	4	2	no	—
180	Q₈×C₁₉	—	4	2	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	8	4	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	#135	1	2	yes	—
216	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₁₉	#137	1	2	yes	—
218	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
220	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₁₉	—	4	2	no	—
223	C₈×C₁₉	—	4	2	no	—
224	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2854	C₂×C₁₉	1	1	yes	characteristic
226	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2093	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2068	C₂×C₁₉	1	2	yes	complemented
229	#2055	C₂×C₁₉	1	2	yes	complemented
230	#2043	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2036	C₂×C₁₉	1	2	yes	complemented
232	#2013	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2000	C₂×C₁₉	1	2	yes	—
234	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	#534	1	1	yes	characteristic
250	C₂²×C₁₉	#535	1	1	yes	characteristic
251	C₂²×C₁₉	#537	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
253	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
255	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
256	C₄×C₁₉	—	2	2	no	—
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	2	2	no	—
259	C₄×C₁₉	—	4	1	no	—
260	C₄×C₁₉	—	4	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	2	no	—
263	C₄×C₁₉	—	8	1	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	#560	1	2	yes	—
267	C₄×C₁₉	#562	1	2	yes	—
268	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#123	—	2	1	no	—
271	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
272	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#107	C₂²×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
276	C₂×#103	C₂²×C₁₉	1	2	yes	—
277	C₂×#103	C₂²×C₁₉	1	2	yes	—
278	C₂×#103	C₂²×C₁₉	1	2	yes	—
279	C₂×#102	C₂²×C₁₉	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
281	#391	C₂²×C₁₉	1	2	yes	—
282	#390	C₂²×C₁₉	1	1	yes	characteristic
283	#390	C₂²×C₁₉	1	1	yes	characteristic
284	#389	—	2	1	no	—
285	#389	—	2	1	no	—
286	#389	C₂²×C₁₉	1	1	yes	characteristic
287	#389	C₂²×C₁₉	1	1	yes	characteristic
288	#388	—	2	1	no	—
289	#388	—	2	1	no	—
290	#386	—	2	1	no	—
291	#384	C₂²×C₁₉	1	1	yes	characteristic
292	#380	—	2	1	no	—
293	#380	—	2	1	no	—
294	#380	C₂²×C₁₉	1	1	yes	characteristic
295	#340	C₂²×C₁₉	1	2	yes	—
296	#340	C₂²×C₁₉	1	2	yes	—
297	#336	C₂²×C₁₉	1	1	yes	characteristic
298	#336	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₁₉	—	4	2	no	—
300	C₂×C₁₉	—	16	1	no	—
301	C₂×C₁₉	#2813	1	1	yes	characteristic
302	C₂×C₁₉	#3190	1	1	yes	characteristic
303	C₂×C₁₉	#3193	1	1	yes	characteristic
304	C₂×C₁₉	#3207	1	1	yes	characteristic
305	C₂×C₁₉	#3218	1	1	yes	characteristic
306	C₂×C₁₉	#3248	1	1	yes	characteristic
307	C₂×C₁₉	#3254	1	1	yes	characteristic
308	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×SD₁₆	—	4	2	no	—
315	C₂×SD₁₆	—	4	2	no	—
316	C₂×SD₁₆	—	4	2	no	—
317	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
319	C₄⋊Q₈	—	4	2	no	—
320	#123	—	4	4	no	—
321	C₂²⋊Q₈	—	4	2	no	—
322	C₂²⋊Q₈	—	4	2	no	—
323	#121	—	4	2	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₄²	—	4	2	no	—
343	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
347	#107	—	4	2	no	—
348	C₄⋊C₈	—	4	2	no	—
349	#103	—	4	2	no	—
350	#103	—	4	2	no	—
351	#103	—	4	2	no	—
352	#102	—	4	2	no	—
353	C₂²⋊C₈	—	4	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	C₁₉	#32723	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	2	1	no	—
361	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
396	SD₁₆	—	4	8	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	4	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	4	1	no	—
426	C₄²	—	4	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	C₁₉×#137	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	C₁₉×#135	1	2	yes	—
481	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
482	C₂×C₄	C₁₉×#137	1	2	yes	—
483	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
485	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
486	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	C₁₉×#534	1	1	yes	characteristic
504	C₂²	C₁₉×#535	1	1	yes	characteristic
505	C₂²	C₁₉×#537	1	1	yes	characteristic
506	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
507	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
508	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
509	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	2	no	—
520	C₄	C₁₉×#560	1	2	yes	—
521	C₄	C₁₉×#562	1	2	yes	—
522	C₂	—	4	2	no	—
523	C₂	—	16	1	no	—
524	C₂	C₁₉×#2813	1	1	yes	characteristic
525	C₂	C₁₉×#3190	1	1	yes	characteristic
526	C₂	C₁₉×#3193	1	1	yes	characteristic
527	C₂	C₁₉×#3207	1	1	yes	characteristic
528	C₂	C₁₉×#3218	1	1	yes	characteristic
529	C₂	C₁₉×#3248	1	1	yes	characteristic
530	C₂	C₁₉×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
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. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2099	C₂	semidirect
4. C₁₉×#2093	C₂	semidirect
5. C₁₉×#2068	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#2043	C₂	semidirect
8. C₁₉×#2036	C₂	semidirect
9. C₁₉×#2013	C₂	semidirect
11. C₁₉×#1797	C₂	semidirect
161. #32723	C₁₉	direct (N × H)
224. #2857	C₂×C₁₉	semidirect
226. #2099	C₂×C₁₉	semidirect
227. #2093	C₂×C₁₉	semidirect
228. #2068	C₂×C₁₉	semidirect
229. #2055	C₂×C₁₉	semidirect
230. #2043	C₂×C₁₉	semidirect
231. #2036	C₂×C₁₉	semidirect
232. #2013	C₂×C₁₉	semidirect
234. #1797	C₂×C₁₉	semidirect
359. C₁₉	#32723	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×#2857	2
C₁₉×#2854	2
C₁₉×#2099	2
C₁₉×#2093	2
C₁₉×#2068	2
C₁₉×#2055	2
C₁₉×#2043	2
C₁₉×#2036	2
C₁₉×#2013	2
C₁₉×#2000	2
C₁₉×#1797	2
#32723	19

Subgroups — C19×#32723 #18038682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32723 #18038682