Subgroups — C₁₉×#21813 #18027772

Order 4864.

1442 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1983	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1788	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1786	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#535	—	2	4	no	—
15	C₁₉×#535	C₄	1	8	yes	complemented
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	—	2	2	no	—
21	C₂×C₁₉×#120	—	2	2	no	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₁₉×#433	—	2	4	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#388	—	2	2	no	—
37	C₁₉×#387	—	2	2	no	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	4	2	no	—
45	C₂×#41×C₁₉	—	4	2	no	—
46	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	4	2	no	—
54	C₂²×D₄×C₁₉	—	4	2	no	—
55	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#127	—	2	2	no	—
65	C₁₉×#127	C₂×C₄	1	4	yes	—
66	C₁₉×#127	C₂×C₄	1	4	yes	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	C₂×C₄	1	4	yes	—
70	C₁₉×#124	C₂×C₄	1	4	yes	—
71	C₁₉×#121	—	2	16	no	—
72	C₁₉×#120	—	2	16	no	—
73	C₁₉×#117	C₂×C₄	1	4	yes	—
74	C₁₉×#117	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	—	2	4	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#103	—	4	2	no	—
89	C₁₉×#102	—	4	2	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×#102	—	4	2	no	—
93	C₁₉×#102	—	4	2	no	—
94	C₁₉×#102	—	4	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₁₉×#97	—	2	2	no	—
97	C₄×C₈×C₁₉	—	2	2	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	2	no	—
100	C₁₉×#95	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	—	2	4	no	—
105	C₂⁴×C₁₉	—	4	2	no	—
106	C₂⁴×C₁₉	—	4	2	no	—
107	C₂⁴×C₁₉	—	8	2	no	—
108	C₂⁴×C₁₉	—	8	2	no	—
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	#41×C₁₉	—	4	8	no	—
111	#41×C₁₉	—	4	8	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	4	no	—
118	C₂×D₄×C₁₉	—	2	8	no	—
119	C₂×D₄×C₁₉	—	2	8	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	2	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	2	no	—
129	C₂×D₄×C₁₉	—	4	8	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	2	no	—
132	C₂×D₄×C₁₉	—	4	8	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	—	8	2	no	—
137	C₂×D₄×C₁₉	—	8	2	no	—
138	C₂×D₄×C₁₉	—	8	2	no	—
139	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
140	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	4	2	no	—
150	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	8	2	no	—
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
168	C₂²⋊C₄×C₁₉	—	2	8	no	—
169	C₂²⋊C₄×C₁₉	—	2	8	no	—
170	C₂²⋊C₄×C₁₉	—	8	2	no	—
171	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
172	C₄²×C₁₉	—	8	2	no	—
173	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
174	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
175	C₄²×C₁₉	C₂×D₄	1	2	yes	—
176	C₄²×C₁₉	C₂×D₄	1	2	yes	—
177	#21813	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	4	8	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	8	8	no	—
199	C₂³×C₁₉	—	8	4	no	—
200	C₂³×C₁₉	—	8	4	no	—
201	C₂³×C₁₉	—	8	8	no	—
202	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	4	no	—
209	D₄×C₁₉	—	4	8	no	—
210	D₄×C₁₉	—	4	8	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	8	8	no	—
215	D₄×C₁₉	—	8	8	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	4	8	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
240	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₁₉	—	4	2	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₂×#535	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#433	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2314	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1983	C₂×C₁₉	1	2	yes	complemented
247	#1982	C₂×C₁₉	1	2	yes	complemented
248	#1961	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1959	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1958	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1957	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1788	C₂×C₁₉	1	2	yes	complemented
253	#1786	C₂×C₁₉	1	2	yes	complemented
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	4	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	4	no	—
263	C₂²×C₁₉	—	4	4	no	—
264	C₂²×C₁₉	—	4	4	no	—
265	C₂²×C₁₉	—	8	16	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	1	no	—
271	C₂²×C₁₉	—	8	1	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₁₉	#535	1	1	yes	characteristic
277	C₂²×C₁₉	#535	1	1	yes	characteristic
278	C₂²×C₁₉	#576	1	2	yes	—
279	C₂²×C₁₉	#577	1	2	yes	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	4	no	—
282	C₄×C₁₉	—	2	4	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	8	2	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	#518	1	2	yes	—
287	C₄×C₁₉	#535	1	2	yes	—
288	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
289	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
290	#535	—	2	4	no	—
291	#535	C₄×C₁₉	1	8	yes	complemented
292	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#121	—	2	2	no	—
297	C₂×#120	—	2	2	no	—
298	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
299	#433	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
301	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
302	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
303	C₂×#102	C₂²×C₁₉	1	2	yes	—
304	C₂×#102	C₂²×C₁₉	1	2	yes	—
305	C₂×#102	C₂²×C₁₉	1	2	yes	—
306	C₂×#102	C₂²×C₁₉	1	2	yes	—
307	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
308	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
309	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
310	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#388	—	2	2	no	—
313	#387	—	2	2	no	—
314	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#380	C₂²×C₁₉	1	2	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
318	C₂×C₁₉	—	4	2	no	—
319	C₂×C₁₉	—	8	2	no	—
320	C₂×C₁₉	—	8	2	no	—
321	C₂×C₁₉	—	8	2	no	—
322	C₂×C₁₉	#2309	1	1	yes	characteristic
323	C₂×C₁₉	#2897	1	2	yes	—
324	C₂×C₁₉	#3220	1	1	yes	characteristic
325	C₂×C₁₉	#3222	1	1	yes	characteristic
326	C₂×C₁₉	#3224	1	2	yes	—
327	C₂⁵	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	—	4	2	no	—
331	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
332	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	—	4	2	no	—
339	C₂²×D₄	—	4	2	no	—
340	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
348	#127	—	2	2	no	—
349	#127	—	2	2	no	—
350	#127	C₂×C₄×C₁₉	1	4	yes	—
351	#127	C₂×C₄×C₁₉	1	4	yes	—
352	#124	—	2	2	no	—
353	#124	—	2	2	no	—
354	#124	C₂×C₄×C₁₉	1	4	yes	—
355	#124	C₂×C₄×C₁₉	1	4	yes	—
356	#121	—	2	16	no	—
357	#120	—	2	16	no	—
358	#117	C₂×C₄×C₁₉	1	4	yes	—
359	#117	D₄×C₁₉	1	4	yes	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
371	C₄⋊C₈	—	2	4	no	—
372	#103	—	4	2	no	—
373	#103	—	4	2	no	—
374	#102	—	4	2	no	—
375	#102	—	4	2	no	—
376	#102	—	4	2	no	—
377	#102	—	4	2	no	—
378	#102	—	4	2	no	—
379	#102	—	4	2	no	—
380	C₂²⋊C₈	—	2	4	no	—
381	#97	—	2	2	no	—
382	C₄×C₈	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	—	2	2	no	—
386	C₁₉	#21813	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁴	—	2	1	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	2	1	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	—	4	2	no	—
393	C₂⁴	—	8	2	no	—
394	C₂⁴	—	8	2	no	—
395	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
396	#41	—	4	8	no	—
397	#41	—	4	8	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂×D₄	—	8	2	no	—
423	C₂×D₄	—	8	2	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
426	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
427	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	8	2	no	—
453	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	8	2	no	—
457	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
458	C₄²	—	8	2	no	—
459	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
460	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
461	C₄²	C₂×D₄×C₁₉	1	2	yes	—
462	C₄²	C₂×D₄×C₁₉	1	2	yes	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	8	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	8	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	8	no	—
487	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	4	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	8	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	8	8	no	—
500	D₄	—	8	8	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
520	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
521	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
522	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
526	C₈	—	4	2	no	—
527	C₈	—	4	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	8	16	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
550	C₂²	C₁₉×#535	1	1	yes	characteristic
551	C₂²	C₁₉×#535	1	1	yes	characteristic
552	C₂²	C₁₉×#576	1	2	yes	—
553	C₂²	C₁₉×#577	1	2	yes	—
554	C₄	—	2	2	no	—
555	C₄	—	2	4	no	—
556	C₄	—	2	4	no	—
557	C₄	—	4	2	no	—
558	C₄	—	8	2	no	—
559	C₄	—	8	2	no	—
560	C₄	C₁₉×#518	1	2	yes	—
561	C₄	C₁₉×#535	1	2	yes	—
562	C₂	—	4	2	no	—
563	C₂	—	8	2	no	—
564	C₂	—	8	2	no	—
565	C₂	—	8	2	no	—
566	C₂	C₁₉×#2309	1	1	yes	characteristic
567	C₂	C₁₉×#2897	1	2	yes	—
568	C₂	C₁₉×#3220	1	1	yes	characteristic
569	C₂	C₁₉×#3222	1	1	yes	characteristic
570	C₂	C₁₉×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#535	C₂
LCS	G ▷ C₂×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
2. C₂×C₁₉×#433	C₂	semidirect
3. C₁₉×#2314	C₂	semidirect
4. C₁₉×#1983	C₂	semidirect
5. C₁₉×#1982	C₂	semidirect
6. C₁₉×#1961	C₂	semidirect
7. C₁₉×#1959	C₂	semidirect
8. C₁₉×#1958	C₂	semidirect
9. C₁₉×#1957	C₂	semidirect
10. C₁₉×#1788	C₂	semidirect
11. C₁₉×#1786	C₂	semidirect
15. C₁₉×#535	C₄	semidirect
24. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
25. C₂×C₁₉×#103	C₂²	semidirect
26. C₂×C₁₉×#103	C₂²	semidirect
31. C₂×C₁₉×#102	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
34. C₂×C₁₉×#97	C₂²	semidirect
35. C₂×C₄×C₈×C₁₉	C₂²	semidirect
38. C₁₉×#384	C₂²	semidirect
39. C₁₉×#382	C₂²	semidirect
41. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
177. #21813	C₁₉	direct (N × H)
244. C₂×#433	C₂×C₁₉	semidirect
245. #2314	C₂×C₁₉	semidirect
246. #1983	C₂×C₁₉	semidirect
247. #1982	C₂×C₁₉	semidirect
248. #1961	C₂×C₁₉	semidirect
249. #1959	C₂×C₁₉	semidirect
250. #1958	C₂×C₁₉	semidirect
251. #1957	C₂×C₁₉	semidirect
252. #1788	C₂×C₁₉	semidirect
253. #1786	C₂×C₁₉	semidirect
291. #535	C₄×C₁₉	semidirect
300. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
301. C₂×#103	C₂²×C₁₉	semidirect
302. C₂×#103	C₂²×C₁₉	semidirect
307. C₂×#102	C₂²×C₁₉	semidirect
308. C₂×#102	C₂²×C₁₉	semidirect
310. C₂×#97	C₂²×C₁₉	semidirect
311. C₂×C₄×C₈	C₂²×C₁₉	semidirect
314. #384	C₂²×C₁₉	semidirect
315. #382	C₂²×C₁₉	semidirect
317. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
386. C₁₉	#21813	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×#535	2
C₂×C₁₉×#433	2
C₁₉×#2314	2
C₁₉×#1983	2
C₁₉×#1982	2
C₁₉×#1961	2
C₁₉×#1959	2
C₁₉×#1958	2
C₁₉×#1957	2
C₁₉×#1788	2
C₁₉×#1786	2
#21813	19

Subgroups — C19×#21813 #18027772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21813 #18027772