Subgroups — C₁₉×#32718 #18038677

Order 4864.

952 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1999	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	—	2	1	no	—
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₉×#390	—	2	1	no	—
28	C₁₉×#390	—	2	1	no	—
29	C₁₉×#390	C₂²	1	1	yes	characteristic
30	C₁₉×#390	C₂²	1	1	yes	characteristic
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#388	—	2	1	no	—
35	C₁₉×#388	—	2	1	no	—
36	C₁₉×#386	—	2	1	no	—
37	C₁₉×#384	C₂²	1	1	yes	characteristic
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×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×D₈×C₁₉	—	4	2	no	—
53	C₂×D₈×C₁₉	—	4	2	no	—
54	C₂×D₈×C₁₉	—	4	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×#127	—	4	2	no	—
58	C₁₉×#123	—	4	4	no	—
59	C₁₉×#121	—	4	2	no	—
60	C₁₉×#121	—	4	2	no	—
61	C₁₉×#121	—	4	2	no	—
62	C₁₉×#121	—	4	4	no	—
63	C₁₉×#121	—	4	4	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	4	2	no	—
82	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#107	—	4	2	no	—
87	C₁₉×C₄⋊C₈	—	4	2	no	—
88	C₁₉×#102	—	4	2	no	—
89	C₁₉×#102	—	4	2	no	—
90	C₁₉×#102	—	4	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×C₂²⋊C₈	—	4	2	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	D₈×C₁₉	—	4	8	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	—	4	2	no	—
156	C₄⋊C₄×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	2	no	—
160	C₂²⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	2	no	—
163	C₂²⋊C₄×C₁₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	4	2	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	4	1	no	—
170	C₄²×C₁₉	—	4	1	no	—
171	#32718	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	C₂×D₈	1	2	yes	—
193	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	8	4	no	—
201	D₄×C₁₉	—	8	4	no	—
202	D₄×C₁₉	—	8	4	no	—
203	D₄×C₁₉	—	8	8	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	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	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	2	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	C₂×D₈	1	2	yes	—
233	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
234	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
238	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₉	—	4	2	no	—
240	C₈×C₁₉	—	4	2	no	—
241	#2856	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2854	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#2093	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2067	C₂×C₁₉	1	2	yes	complemented
246	#2054	C₂×C₁₉	1	2	yes	complemented
247	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#2033	C₂×C₁₉	1	2	yes	complemented
249	#2011	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1999	C₂×C₁₉	1	2	yes	complemented
251	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	2	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	1	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	1	no	—
263	C₂²×C₁₉	—	8	2	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	2	no	—
269	C₂²×C₁₉	—	8	2	no	—
270	C₂²×C₁₉	—	8	1	no	—
271	C₂²×C₁₉	—	8	1	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	#534	1	1	yes	characteristic
274	C₂²×C₁₉	#535	1	1	yes	characteristic
275	C₂²×C₁₉	#537	1	1	yes	characteristic
276	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
277	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₂²×C₁₉	#575	1	1	yes	characteristic
279	C₂²×C₁₉	#575	1	1	yes	characteristic
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	2	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	#560	1	2	yes	—
290	C₄×C₁₉	#562	1	2	yes	—
291	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
292	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#123	—	2	1	no	—
294	C₂×#121	—	2	1	no	—
295	C₂×#121	—	2	1	no	—
296	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#121	C₂²×C₁₉	1	2	yes	—
298	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#107	C₂²×C₁₉	1	2	yes	—
300	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
301	C₂×#102	C₂²×C₁₉	1	2	yes	—
302	C₂×#102	C₂²×C₁₉	1	2	yes	—
303	C₂×#102	C₂²×C₁₉	1	2	yes	—
304	C₂×#102	C₂²×C₁₉	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
306	#390	—	2	1	no	—
307	#390	—	2	1	no	—
308	#390	C₂²×C₁₉	1	1	yes	characteristic
309	#390	C₂²×C₁₉	1	2	yes	—
310	#390	C₂²×C₁₉	1	1	yes	characteristic
311	#389	C₂²×C₁₉	1	1	yes	characteristic
312	#389	C₂²×C₁₉	1	1	yes	characteristic
313	#388	—	2	1	no	—
314	#388	—	2	1	no	—
315	#386	—	2	1	no	—
316	#384	C₂²×C₁₉	1	1	yes	characteristic
317	#380	C₂²×C₁₉	1	1	yes	characteristic
318	#340	C₂²×C₁₉	1	2	yes	—
319	#340	C₂²×C₁₉	1	2	yes	—
320	#336	C₂²×C₁₉	1	1	yes	characteristic
321	#336	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₁₉	—	4	2	no	—
323	C₂×C₁₉	—	16	2	no	—
324	C₂×C₁₉	—	16	1	no	—
325	C₂×C₁₉	#2813	1	1	yes	characteristic
326	C₂×C₁₉	#3186	1	1	yes	characteristic
327	C₂×C₁₉	#3194	1	1	yes	characteristic
328	C₂×C₁₉	#3205	1	1	yes	characteristic
329	C₂×C₁₉	#3219	1	1	yes	characteristic
330	C₂×C₁₉	#3245	1	1	yes	characteristic
331	C₂×C₁₉	#3251	1	1	yes	characteristic
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
337	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×D₈	—	4	2	no	—
342	C₂×D₈	—	4	2	no	—
343	C₂×D₈	—	4	2	no	—
344	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
346	#127	—	4	2	no	—
347	#123	—	4	4	no	—
348	#121	—	4	2	no	—
349	#121	—	4	2	no	—
350	#121	—	4	2	no	—
351	#121	—	4	4	no	—
352	#121	—	4	4	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₄²	—	4	2	no	—
371	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
375	#107	—	4	2	no	—
376	C₄⋊C₈	—	4	2	no	—
377	#102	—	4	2	no	—
378	#102	—	4	2	no	—
379	#102	—	4	2	no	—
380	#102	—	4	2	no	—
381	C₂²⋊C₈	—	4	2	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	C₁₉	#32718	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁴	—	2	1	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
431	D₈	—	4	8	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	4	1	no	—
460	C₄²	—	4	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	C₂×D₈×C₁₉	1	2	yes	—
482	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	8	4	no	—
490	D₄	—	8	4	no	—
491	D₄	—	8	4	no	—
492	D₄	—	8	8	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
522	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
523	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
527	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
528	C₈	—	4	2	no	—
529	C₈	—	4	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	2	no	—
551	C₂²	C₁₉×#534	1	1	yes	characteristic
552	C₂²	C₁₉×#535	1	1	yes	characteristic
553	C₂²	C₁₉×#537	1	1	yes	characteristic
554	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
555	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
556	C₂²	C₁₉×#575	1	1	yes	characteristic
557	C₂²	C₁₉×#575	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	2	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₁₉×#560	1	2	yes	—
568	C₄	C₁₉×#562	1	2	yes	—
569	C₂	—	4	2	no	—
570	C₂	—	16	2	no	—
571	C₂	—	16	1	no	—
572	C₂	C₁₉×#2813	1	1	yes	characteristic
573	C₂	C₁₉×#3186	1	1	yes	characteristic
574	C₂	C₁₉×#3194	1	1	yes	characteristic
575	C₂	C₁₉×#3205	1	1	yes	characteristic
576	C₂	C₁₉×#3219	1	1	yes	characteristic
577	C₂	C₁₉×#3245	1	1	yes	characteristic
578	C₂	C₁₉×#3251	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2856	C₂	semidirect
2. C₁₉×#2854	C₂	semidirect
3. C₁₉×#2099	C₂	semidirect
4. C₁₉×#2093	C₂	semidirect
5. C₁₉×#2067	C₂	semidirect
6. C₁₉×#2054	C₂	semidirect
7. C₁₉×#2041	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#2011	C₂	semidirect
10. C₁₉×#1999	C₂	semidirect
11. C₁₉×#1797	C₂	semidirect
134. C₂²×C₄×C₁₉	D₈	semidirect
171. #32718	C₁₉	direct (N × H)
241. #2856	C₂×C₁₉	semidirect
242. #2854	C₂×C₁₉	semidirect
243. #2099	C₂×C₁₉	semidirect
244. #2093	C₂×C₁₉	semidirect
245. #2067	C₂×C₁₉	semidirect
246. #2054	C₂×C₁₉	semidirect
247. #2041	C₂×C₁₉	semidirect
248. #2033	C₂×C₁₉	semidirect
249. #2011	C₂×C₁₉	semidirect
250. #1999	C₂×C₁₉	semidirect
251. #1797	C₂×C₁₉	semidirect
385. C₁₉	#32718	direct (N × H)
424. C₂²×C₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2856	2
C₁₉×#2854	2
C₁₉×#2099	2
C₁₉×#2093	2
C₁₉×#2067	2
C₁₉×#2054	2
C₁₉×#2041	2
C₁₉×#2033	2
C₁₉×#2011	2
C₁₉×#1999	2
C₁₉×#1797	2
#32718	19

Subgroups — C19×#32718 #18038677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32718 #18038677