Subgroups — C₁₉×#32776 #18038735

Order 4864.

844 conjugacy classes of subgroups.

The subgroup lattice has 528 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
2	C₁₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2092	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2025	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	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×#390	—	2	1	no	—
26	C₁₉×#390	—	2	1	no	—
27	C₁₉×#390	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	1	yes	characteristic
29	C₁₉×#389	C₂²	1	1	yes	characteristic
30	C₁₉×#387	—	2	1	no	—
31	C₁₉×#387	—	2	1	no	—
32	C₁₉×#385	—	2	1	no	—
33	C₁₉×#385	—	2	1	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	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	2	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×#127	—	4	2	no	—
53	C₁₉×#125	—	4	2	no	—
54	C₁₉×#121	—	4	2	no	—
55	C₁₉×#121	—	4	2	no	—
56	C₁₉×#121	—	4	4	no	—
57	C₁₉×#121	—	4	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	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	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	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×C₄²×C₁₉	—	4	2	no	—
75	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	4	2	no	—
80	C₁₉×#106	—	4	2	no	—
81	C₁₉×#102	—	4	2	no	—
82	C₁₉×#102	—	4	2	no	—
83	C₁₉×#102	—	4	2	no	—
84	C₁₉×#102	—	4	2	no	—
85	C₁₉×C₂²⋊C₈	—	4	2	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	4	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	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	4	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	C₂×C₈×C₁₉	—	2	2	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	C₄⋊C₄×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	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	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	4	no	—
151	C₂²⋊C₄×C₁₉	—	4	4	no	—
152	C₂²⋊C₄×C₁₉	—	4	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	—	4	1	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	#32776	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	1	no	—
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	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	8	4	no	—
180	D₄×C₁₉	—	8	4	no	—
181	D₄×C₁₉	—	8	8	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	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	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	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	2	no	—
208	C₂×C₄×C₁₉	—	4	1	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	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	#135	1	2	yes	—
215	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
217	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
220	C₈×C₁₉	—	4	2	no	—
221	C₈×C₁₉	—	4	2	no	—
222	#2856	C₂×C₁₉	1	1	yes	characteristic
223	#2851	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2092	C₂×C₁₉	1	2	yes	complemented
225	#2084	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2083	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2034	C₂×C₁₉	1	2	yes	complemented
230	#2033	C₂×C₁₉	1	2	yes	complemented
231	#2025	C₂×C₁₉	1	2	yes	complemented
232	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	4	1	no	—
239	C₂²×C₁₉	—	4	1	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	2	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	#534	1	1	yes	characteristic
248	C₂²×C₁₉	#535	1	1	yes	characteristic
249	C₂²×C₁₉	#536	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
251	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₁₉	#575	1	1	yes	characteristic
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	4	1	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	—	8	2	no	—
264	C₄×C₁₉	#562	1	2	yes	—
265	C₄×C₁₉	#562	1	2	yes	—
266	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#121	—	2	1	no	—
269	C₂×#121	—	2	1	no	—
270	C₂×#121	C₂²×C₁₉	1	2	yes	—
271	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#107	C₂²×C₁₉	1	2	yes	—
273	C₂×#106	C₂²×C₁₉	1	2	yes	—
274	C₂×#102	C₂²×C₁₉	1	2	yes	—
275	C₂×#102	C₂²×C₁₉	1	2	yes	—
276	C₂×#102	C₂²×C₁₉	1	2	yes	—
277	C₂×#102	C₂²×C₁₉	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
279	#390	—	2	1	no	—
280	#390	—	2	1	no	—
281	#390	C₂²×C₁₉	1	2	yes	—
282	#389	C₂²×C₁₉	1	1	yes	characteristic
283	#389	C₂²×C₁₉	1	1	yes	characteristic
284	#387	—	2	1	no	—
285	#387	—	2	1	no	—
286	#385	—	2	1	no	—
287	#385	—	2	1	no	—
288	#384	C₂²×C₁₉	1	1	yes	characteristic
289	#382	C₂²×C₁₉	1	1	yes	characteristic
290	#380	C₂²×C₁₉	1	1	yes	characteristic
291	#380	C₂²×C₁₉	1	1	yes	characteristic
292	#340	C₂²×C₁₉	1	2	yes	—
293	#340	C₂²×C₁₉	1	2	yes	—
294	#336	C₂²×C₁₉	1	1	yes	characteristic
295	#336	C₂²×C₁₉	1	1	yes	characteristic
296	#336	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	4	2	no	—
298	C₂×C₁₉	—	16	2	no	—
299	C₂×C₁₉	#2816	1	1	yes	characteristic
300	C₂×C₁₉	#3188	1	1	yes	characteristic
301	C₂×C₁₉	#3194	1	1	yes	characteristic
302	C₂×C₁₉	#3212	1	1	yes	characteristic
303	C₂×C₁₉	#3217	1	1	yes	characteristic
304	C₂×C₁₉	#3228	1	1	yes	characteristic
305	C₂×C₁₉	#3234	1	1	yes	characteristic
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
310	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
315	#127	—	4	2	no	—
316	#125	—	4	2	no	—
317	#121	—	4	2	no	—
318	#121	—	4	2	no	—
319	#121	—	4	4	no	—
320	#121	—	4	4	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₄²	—	4	2	no	—
338	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
342	#107	—	4	2	no	—
343	#106	—	4	2	no	—
344	#102	—	4	2	no	—
345	#102	—	4	2	no	—
346	#102	—	4	2	no	—
347	#102	—	4	2	no	—
348	C₂²⋊C₈	—	4	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	C₁₉	#32776	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂⁴×C₁₉	1	1	yes	characteristic
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	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	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	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	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	4	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
437	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	4	no	—
443	D₄	—	8	4	no	—
444	D₄	—	8	8	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	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	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	C₁₉×#135	1	2	yes	—
478	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
479	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
480	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	C₁₉×#534	1	1	yes	characteristic
500	C₂²	C₁₉×#535	1	1	yes	characteristic
501	C₂²	C₁₉×#536	1	1	yes	characteristic
502	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
503	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
505	C₂²	C₁₉×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	2	no	—
515	C₄	—	8	1	no	—
516	C₄	C₁₉×#562	1	2	yes	—
517	C₄	C₁₉×#562	1	2	yes	—
518	C₂	—	4	2	no	—
519	C₂	—	16	2	no	—
520	C₂	C₁₉×#2816	1	1	yes	characteristic
521	C₂	C₁₉×#3188	1	1	yes	characteristic
522	C₂	C₁₉×#3194	1	1	yes	characteristic
523	C₂	C₁₉×#3212	1	1	yes	characteristic
524	C₂	C₁₉×#3217	1	1	yes	characteristic
525	C₂	C₁₉×#3228	1	1	yes	characteristic
526	C₂	C₁₉×#3234	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2856	C₂
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
2. C₁₉×#2851	C₂	semidirect
3. C₁₉×#2092	C₂	semidirect
4. C₁₉×#2084	C₂	semidirect
5. C₁₉×#2083	C₂	semidirect
6. C₁₉×#2041	C₂	semidirect
7. C₁₉×#2041	C₂	semidirect
8. C₁₉×#2034	C₂	semidirect
9. C₁₉×#2033	C₂	semidirect
10. C₁₉×#2025	C₂	semidirect
11. C₁₉×#1817	C₂	semidirect
159. #32776	C₁₉	direct (N × H)
223. #2851	C₂×C₁₉	semidirect
224. #2092	C₂×C₁₉	semidirect
225. #2084	C₂×C₁₉	semidirect
226. #2083	C₂×C₁₉	semidirect
227. #2041	C₂×C₁₉	semidirect
228. #2041	C₂×C₁₉	semidirect
229. #2034	C₂×C₁₉	semidirect
230. #2033	C₂×C₁₉	semidirect
231. #2025	C₂×C₁₉	semidirect
232. #1817	C₂×C₁₉	semidirect
355. C₁₉	#32776	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×#2856	2
C₁₉×#2851	2
C₁₉×#2092	2
C₁₉×#2084	2
C₁₉×#2083	2
C₁₉×#2041	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#2025	2
C₁₉×#1817	2
#32776	19

Subgroups — C19×#32776 #18038735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32776 #18038735