Subgroups — C₁₉×#32902 #18038861

Order 4864.

2008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#459	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#447	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1879	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	—	2	1	no	—
11	C₂²×D₈×C₁₉	C₂²	1	4	yes	—
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	—	2	8	no	—
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#459	—	2	8	no	—
25	C₁₉×#447	—	2	8	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#102	C₂²	1	4	yes	—
28	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#390	C₂²	1	2	yes	complemented
33	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#340	C₂²	1	4	yes	complemented
35	C₁₉×#336	C₂²	1	2	yes	complemented
36	C₂⁵×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	—	2	8	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	—	2	2	no	—
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	4	4	no	—
52	C₂³×C₄×C₁₉	—	4	4	no	—
53	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×D₈×C₁₉	—	2	8	no	—
57	C₂×D₈×C₁₉	—	2	8	no	—
58	C₂×D₈×C₁₉	—	2	8	no	—
59	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
60	C₁₉×#127	—	2	4	no	—
61	C₁₉×#121	—	2	4	no	—
62	C₁₉×#121	—	2	4	no	—
63	C₁₉×#121	—	4	4	no	—
64	C₁₉×#121	—	4	4	no	—
65	C₄×D₄×C₁₉	—	2	8	no	—
66	C₄×D₄×C₁₉	—	2	8	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	4	no	—
69	C₄×D₄×C₁₉	—	2	4	no	—
70	C₄×D₄×C₁₉	D₄	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	8	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×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	4	no	—
84	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×C₄⋊C₈	—	2	4	no	—
89	C₁₉×#102	—	2	8	no	—
90	C₁₉×#102	—	2	8	no	—
91	C₁₉×C₂²⋊C₈	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	4	2	no	—
98	C₂⁴×C₁₉	—	4	2	no	—
99	C₂⁴×C₁₉	—	4	2	no	—
100	C₂⁴×C₁₉	—	4	2	no	—
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	16	no	—
105	C₂×D₄×C₁₉	—	2	16	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
124	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₁₉	#41	1	4	yes	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	8	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	8	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	4	no	—
139	C₂²×C₄×C₁₉	—	4	32	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	—	4	4	no	—
144	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	#41	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	D₈×C₁₉	—	4	16	no	—
155	C₂×C₈×C₁₉	—	2	4	no	—
156	C₂×C₈×C₁₉	—	2	4	no	—
157	C₂×C₈×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₉	—	4	4	no	—
168	C₂²⋊C₄×C₁₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₉	—	4	4	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	C₂×D₄	1	4	yes	—
174	#32902	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	16	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	4	8	no	—
184	C₂³×C₁₉	—	4	8	no	—
185	C₂³×C₁₉	—	4	8	no	—
186	C₂³×C₁₉	—	4	8	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	8	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	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	#121	1	2	yes	—
201	C₂³×C₁₉	C₂×D₈	1	2	yes	—
202	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	D₄×C₁₉	—	2	16	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	4	4	no	—
210	D₄×C₁₉	—	8	4	no	—
211	D₄×C₁₉	—	8	8	no	—
212	D₄×C₁₉	—	8	4	no	—
213	D₄×C₁₉	#121	1	8	yes	complemented
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	4	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	4	16	no	—
229	C₂×C₄×C₁₉	—	4	8	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	16	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	#120	1	2	yes	—
237	C₂×C₄×C₁₉	#120	1	2	yes	—
238	C₂×C₄×C₁₉	#121	1	2	yes	—
239	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
240	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
241	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
246	C₈×C₁₉	—	4	4	no	—
247	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
248	C₂×#459	C₂×C₁₉	1	2	yes	complemented
249	C₂×#447	C₂×C₁₉	1	2	yes	complemented
250	#2856	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1879	C₂×C₁₉	1	4	yes	complemented
252	#1874	C₂×C₁₉	1	2	yes	complemented
253	#1802	C₂×C₁₉	1	2	yes	complemented
254	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	2	2	no	—
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	2	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	2	8	no	—
262	C₂²×C₁₉	—	4	32	no	—
263	C₂²×C₁₉	—	4	4	no	—
264	C₂²×C₁₉	—	4	4	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	4	no	—
269	C₂²×C₁₉	—	8	2	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	#459	1	4	yes	complemented
277	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
279	C₂²×C₁₉	#525	1	1	yes	characteristic
280	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₁₉	#575	1	1	yes	characteristic
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	4	4	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	8	2	no	—
290	C₄×C₁₉	#447	1	4	yes	complemented
291	C₄×C₁₉	C₂×#121	1	2	yes	—
292	C₄×C₁₉	#525	1	2	yes	—
293	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
294	C₂⁴×C₄	—	2	1	no	—
295	C₂²×D₈	C₂²×C₁₉	1	4	yes	—
296	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	C₂×#121	—	2	1	no	—
298	C₂×#121	—	2	1	no	—
299	C₂×#121	C₂²×C₁₉	1	2	yes	—
300	C₂×C₄×D₄	—	2	8	no	—
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
304	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
306	C₂²×C₂²⋊C₄	—	2	1	no	—
307	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
308	#459	—	2	8	no	—
309	#447	—	2	8	no	—
310	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
311	C₂×#102	C₂²×C₁₉	1	4	yes	—
312	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
313	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
314	#390	—	2	1	no	—
315	#390	—	2	1	no	—
316	#390	C₂²×C₁₉	1	2	yes	complemented
317	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
318	#340	C₂²×C₁₉	1	4	yes	complemented
319	#336	C₂²×C₁₉	1	2	yes	complemented
320	C₂×C₁₉	—	2	4	no	—
321	C₂×C₁₉	—	4	8	no	—
322	C₂×C₁₉	—	16	2	no	—
323	C₂×C₁₉	#2847	1	1	yes	characteristic
324	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
325	C₂×C₁₉	#3006	1	1	yes	characteristic
326	C₂×C₁₉	C₂×#459	1	1	yes	characteristic
327	C₂×C₁₉	#3036	1	1	yes	characteristic
328	C₂×C₁₉	#3100	1	1	yes	characteristic
329	C₂×C₁₉	#3109	1	1	yes	characteristic
330	C₂⁵	—	2	1	no	—
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
339	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
341	C₂³×C₄	—	2	8	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	4	4	no	—
346	C₂³×C₄	—	4	4	no	—
347	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×D₈	—	2	8	no	—
351	C₂×D₈	—	2	8	no	—
352	C₂×D₈	—	2	8	no	—
353	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
354	#127	—	2	4	no	—
355	#121	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	4	4	no	—
358	#121	—	4	4	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	D₄×C₁₉	1	8	yes	complemented
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₄²	—	2	4	no	—
378	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	C₄⋊C₈	—	2	4	no	—
383	#102	—	2	8	no	—
384	#102	—	2	8	no	—
385	C₂²⋊C₈	—	2	4	no	—
386	C₁₉	#32902	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	4	2	no	—
393	C₂⁴	—	4	2	no	—
394	C₂⁴	—	4	2	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	16	no	—
400	C₂×D₄	—	2	16	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
419	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
420	C₂×D₄	#41×C₁₉	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	32	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
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	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	#41×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
449	D₈	—	4	16	no	—
450	C₂×C₈	—	2	4	no	—
451	C₂×C₈	—	2	4	no	—
452	C₂×C₈	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	C₂×D₄×C₁₉	1	4	yes	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	16	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	4	8	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	C₁₉×#121	1	2	yes	—
495	C₂³	C₂×D₈×C₁₉	1	2	yes	—
496	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
497	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
498	D₄	—	2	16	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	8	no	—
506	D₄	—	8	4	no	—
507	D₄	C₁₉×#121	1	8	yes	complemented
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	16	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	16	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	C₁₉×#120	1	2	yes	—
531	C₂×C₄	C₁₉×#120	1	2	yes	—
532	C₂×C₄	C₁₉×#121	1	2	yes	—
533	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
534	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
535	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
538	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
539	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
540	C₈	—	4	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	4	32	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	C₁₉×#459	1	4	yes	complemented
563	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
564	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
565	C₂²	C₁₉×#525	1	1	yes	characteristic
566	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
568	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₁₉×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	2	no	—
576	C₄	C₁₉×#447	1	4	yes	complemented
577	C₄	C₂×C₁₉×#121	1	2	yes	—
578	C₄	C₁₉×#525	1	2	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	4	8	no	—
581	C₂	—	16	2	no	—
582	C₂	C₁₉×#2847	1	1	yes	characteristic
583	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
584	C₂	C₁₉×#3006	1	1	yes	characteristic
585	C₂	C₂×C₁₉×#459	1	1	yes	characteristic
586	C₂	C₁₉×#3036	1	1	yes	characteristic
587	C₂	C₁₉×#3100	1	1	yes	characteristic
588	C₂	C₁₉×#3109	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. C₂²×C₄×D₄×C₁₉	C₂	semidirect
2. C₂×C₁₉×#459	C₂	semidirect
3. C₂×C₁₉×#447	C₂	semidirect
4. C₁₉×#2856	C₂	semidirect
5. C₁₉×#1879	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1802	C₂	semidirect
8. C₁₉×#1797	C₂	semidirect
12. C₂×C₁₉×#127	C₂²	semidirect
26. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
28. C₂×C₁₉×#102	C₂²	semidirect
32. C₁₉×#390	C₂²	semidirect
33. C₁₉×#384	C₂²	semidirect
34. C₁₉×#340	C₂²	semidirect
35. C₁₉×#336	C₂²	semidirect
44. C₂²×D₄×C₁₉	D₄	semidirect
70. C₄×D₄×C₁₉	D₄	semidirect
145. C₂²×C₄×C₁₉	D₈	semidirect
174. #32902	C₁₉	direct (N × H)
213. D₄×C₁₉	#121	semidirect
247. C₂²×C₄×D₄	C₂×C₁₉	semidirect
248. C₂×#459	C₂×C₁₉	semidirect
249. C₂×#447	C₂×C₁₉	semidirect
250. #2856	C₂×C₁₉	semidirect
251. #1879	C₂×C₁₉	semidirect
252. #1874	C₂×C₁₉	semidirect
253. #1802	C₂×C₁₉	semidirect
254. #1797	C₂×C₁₉	semidirect
276. C₂²×C₁₉	#459	semidirect
290. C₄×C₁₉	#447	semidirect
296. C₂×#127	C₂²×C₁₉	semidirect
310. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
312. C₂×#102	C₂²×C₁₉	semidirect
316. #390	C₂²×C₁₉	semidirect
317. #384	C₂²×C₁₉	semidirect
318. #340	C₂²×C₁₉	semidirect
319. #336	C₂²×C₁₉	semidirect
338. C₂²×D₄	D₄×C₁₉	semidirect
364. C₄×D₄	D₄×C₁₉	semidirect
386. C₁₉	#32902	direct (N × H)
440. C₂²×C₄	D₈×C₁₉	semidirect
507. D₄	C₁₉×#121	semidirect
562. C₂²	C₁₉×#459	semidirect
576. C₄	C₁₉×#447	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₉	2
C₂×C₁₉×#459	2
C₂×C₁₉×#447	2
C₁₉×#2856	2
C₁₉×#1879	2
C₁₉×#1874	2
C₁₉×#1802	2
C₁₉×#1797	2
#32902	19

Subgroups — C19×#32902 #18038861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32902 #18038861