Subgroups — C₁₉×#32861 #18038820

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2860	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2065	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#126	—	2	1	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₁₉×#391	C₂²	1	1	yes	characteristic
34	C₁₉×#391	C₂²	1	1	yes	characteristic
35	C₁₉×#391	C₂²	1	1	yes	characteristic
36	C₁₉×#390	C₂²	1	1	yes	characteristic
37	C₁₉×#390	C₂²	1	1	yes	characteristic
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#388	—	2	1	no	—
47	C₁₉×#388	—	2	1	no	—
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#387	—	2	1	no	—
50	C₁₉×#387	—	2	1	no	—
51	C₁₉×#383	—	2	1	no	—
52	C₄³×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×SD₁₆×C₁₉	—	4	1	no	—
62	C₂×SD₁₆×C₁₉	—	4	1	no	—
63	C₂×SD₁₆×C₁₉	—	4	1	no	—
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#126	—	4	4	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	4	1	no	—
95	C₁₉×#107	—	4	1	no	—
96	C₁₉×#106	—	4	1	no	—
97	C₁₉×C₄⋊C₈	—	4	1	no	—
98	C₁₉×C₄⋊C₈	—	4	1	no	—
99	C₁₉×C₄⋊C₈	—	4	1	no	—
100	C₁₉×C₄⋊C₈	—	4	1	no	—
101	C₁₉×C₄⋊C₈	—	4	1	no	—
102	C₁₉×C₄⋊C₈	—	4	1	no	—
103	C₁₉×#103	—	4	1	no	—
104	C₁₉×#103	—	4	1	no	—
105	C₁₉×#103	—	4	1	no	—
106	C₁₉×#102	—	4	1	no	—
107	C₁₉×#102	—	4	1	no	—
108	C₁₉×#102	—	4	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	SD₁₆×C₁₉	—	4	4	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	4	2	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	4	2	no	—
177	C₄⋊C₄×C₁₉	—	4	2	no	—
178	C₄⋊C₄×C₁₉	—	4	2	no	—
179	C₂²⋊C₄×C₁₉	—	4	2	no	—
180	C₂²⋊C₄×C₁₉	—	4	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	2	no	—
182	C₂²⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	2	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	#32861	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	4	1	no	—
205	Q₈×C₁₉	—	4	1	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	D₄×C₁₉	—	4	1	no	—
209	D₄×C₁₉	—	4	1	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	#135	1	2	yes	—
249	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
250	C₂×C₄×C₁₉	#137	1	2	yes	—
251	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	#2863	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2860	C₂×C₁₉	1	1	yes	characteristic
263	#2088	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#2087	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#2086	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2068	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#2068	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#2067	C₂×C₁₉	1	1	yes	characteristic
269	#2067	C₂×C₁₉	1	1	yes	characteristic
270	#2066	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#2065	C₂×C₁₉	1	1	yes	characteristic
272	#2055	C₂×C₁₉	1	1	yes	characteristic
273	#2055	C₂×C₁₉	1	1	yes	characteristic
274	#2055	C₂×C₁₉	1	1	yes	characteristic
275	#1842	C₂×C₁₉	1	1	yes	characteristic, complemented
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	—	8	1	no	—
280	C₂²×C₁₉	—	8	1	no	—
281	C₂²×C₁₉	—	8	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	#537	1	1	yes	characteristic
284	C₂²×C₁₉	#537	1	1	yes	characteristic
285	C₂²×C₁₉	#537	1	1	yes	characteristic
286	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
287	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
289	C₂²×C₁₉	#575	1	1	yes	characteristic
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	8	1	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	—	8	1	no	—
302	C₄×C₁₉	—	8	1	no	—
303	C₄×C₁₉	#560	1	1	yes	characteristic
304	C₄×C₁₉	#563	1	1	yes	characteristic
305	C₄×C₁₉	#563	1	1	yes	characteristic
306	C₄×C₁₉	#563	1	1	yes	characteristic
307	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#126	—	2	1	no	—
309	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
324	#391	C₂²×C₁₉	1	1	yes	characteristic
325	#391	C₂²×C₁₉	1	1	yes	characteristic
326	#391	C₂²×C₁₉	1	1	yes	characteristic
327	#390	C₂²×C₁₉	1	1	yes	characteristic
328	#390	C₂²×C₁₉	1	1	yes	characteristic
329	#390	C₂²×C₁₉	1	1	yes	characteristic
330	#389	C₂²×C₁₉	1	1	yes	characteristic
331	#389	C₂²×C₁₉	1	1	yes	characteristic
332	#389	C₂²×C₁₉	1	1	yes	characteristic
333	#389	C₂²×C₁₉	1	1	yes	characteristic
334	#389	C₂²×C₁₉	1	1	yes	characteristic
335	#389	C₂²×C₁₉	1	1	yes	characteristic
336	#388	—	2	1	no	—
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#387	—	2	1	no	—
340	#387	—	2	1	no	—
341	#387	—	2	1	no	—
342	#383	—	2	1	no	—
343	C₄³	C₂²×C₁₉	1	1	yes	characteristic
344	#340	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	1	yes	characteristic
346	#340	C₂²×C₁₉	1	1	yes	characteristic
347	#340	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#340	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×C₁₉	—	16	1	no	—
351	C₂×C₁₉	#2823	1	1	yes	characteristic
352	C₂×C₁₉	#3247	1	1	yes	characteristic
353	C₂×C₁₉	#3248	1	1	yes	characteristic
354	C₂×C₁₉	#3250	1	1	yes	characteristic
355	C₂×C₁₉	#3251	1	1	yes	characteristic
356	C₂×C₁₉	#3252	1	1	yes	characteristic
357	C₂×C₁₉	#3254	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×SD₁₆	—	4	1	no	—
361	C₂×SD₁₆	—	4	1	no	—
362	C₂×SD₁₆	—	4	1	no	—
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	#126	—	4	4	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	#107	—	4	1	no	—
394	#107	—	4	1	no	—
395	#106	—	4	1	no	—
396	C₄⋊C₈	—	4	1	no	—
397	C₄⋊C₈	—	4	1	no	—
398	C₄⋊C₈	—	4	1	no	—
399	C₄⋊C₈	—	4	1	no	—
400	C₄⋊C₈	—	4	1	no	—
401	C₄⋊C₈	—	4	1	no	—
402	#103	—	4	1	no	—
403	#103	—	4	1	no	—
404	#103	—	4	1	no	—
405	#102	—	4	1	no	—
406	#102	—	4	1	no	—
407	#102	—	4	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	C₁₉	#32861	1	1	yes	characteristic, direct product factor, Sylow
421	C₂⁴	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
448	SD₁₆	—	4	4	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	4	2	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	4	2	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	C₁₉×#135	1	2	yes	—
548	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
549	C₂×C₄	C₁₉×#137	1	2	yes	—
550	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
554	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	C₁₉×#537	1	1	yes	characteristic
568	C₂²	C₁₉×#537	1	1	yes	characteristic
569	C₂²	C₁₉×#537	1	1	yes	characteristic
570	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
571	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
572	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
573	C₂²	C₁₉×#575	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	C₁₉×#560	1	1	yes	characteristic
588	C₄	C₁₉×#563	1	1	yes	characteristic
589	C₄	C₁₉×#563	1	1	yes	characteristic
590	C₄	C₁₉×#563	1	1	yes	characteristic
591	C₂	—	16	1	no	—
592	C₂	C₁₉×#2823	1	1	yes	characteristic
593	C₂	C₁₉×#3247	1	1	yes	characteristic
594	C₂	C₁₉×#3248	1	1	yes	characteristic
595	C₂	C₁₉×#3250	1	1	yes	characteristic
596	C₂	C₁₉×#3251	1	1	yes	characteristic
597	C₂	C₁₉×#3252	1	1	yes	characteristic
598	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	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2863	C₂	semidirect
3. C₁₉×#2088	C₂	semidirect
4. C₁₉×#2087	C₂	semidirect
5. C₁₉×#2086	C₂	semidirect
6. C₁₉×#2068	C₂	semidirect
7. C₁₉×#2068	C₂	semidirect
10. C₁₉×#2066	C₂	semidirect
15. C₁₉×#1842	C₂	semidirect
195. #32861	C₁₉	direct (N × H)
261. #2863	C₂×C₁₉	semidirect
263. #2088	C₂×C₁₉	semidirect
264. #2087	C₂×C₁₉	semidirect
265. #2086	C₂×C₁₉	semidirect
266. #2068	C₂×C₁₉	semidirect
267. #2068	C₂×C₁₉	semidirect
270. #2066	C₂×C₁₉	semidirect
275. #1842	C₂×C₁₉	semidirect
420. C₁₉	#32861	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×#2863	2
C₁₉×#2860	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#2068	2
C₁₉×#2067	2
C₁₉×#2066	2
C₁₉×#2065	2
C₁₉×#2055	2
C₁₉×#1842	2
#32861	19

Subgroups — C19×#32861 #18038820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32861 #18038820