Subgroups — C₁₉×#24531 #18030490

Order 4864.

1224 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₁₉×#447	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#102	—	2	4	no	—
23	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#397	—	2	2	no	—
30	C₁₉×#390	C₂²	1	2	yes	—
31	C₁₉×#390	C₂²	1	2	yes	complemented
32	C₁₉×#386	—	2	2	no	—
33	C₁₉×#386	—	2	1	no	—
34	C₁₉×#386	—	2	1	no	—
35	C₁₉×#382	C₂²	1	2	yes	complemented
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#379	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	complemented
40	C₁₉×#340	C₂²	1	2	yes	complemented
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	4	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	4	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×D₈×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	2	4	no	—
59	C₂×D₈×C₁₉	—	4	2	no	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	4	2	no	—
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	4	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	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	—	4	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₁₉×C₄⋊C₈	—	4	2	no	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	2	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	D₄	1	2	yes	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	2	1	no	—
101	C₂⁴×C₁₉	—	4	4	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	4	2	no	—
104	C₂⁴×C₁₉	—	8	2	no	—
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂×D₄×C₁₉	—	4	8	no	—
119	C₂×D₄×C₁₉	—	4	4	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	2	yes	—
124	C₂×D₄×C₁₉	C₂×D₄	1	2	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	1	no	—
131	C₂²×C₄×C₁₉	—	4	4	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	8	2	no	—
135	C₂²×C₄×C₁₉	—	8	2	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	#41	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	D₈×C₁₉	—	4	4	no	—
143	D₈×C₁₉	—	4	4	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	4	4	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	4	no	—
163	C₂²⋊C₄×C₁₉	—	4	2	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	8	2	no	—
166	C₂²⋊C₄×C₁₉	—	8	2	no	—
167	C₂²⋊C₄×C₁₉	—	8	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	#24531	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	4	8	no	—
177	C₂³×C₁₉	—	4	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	8	no	—
185	C₂³×C₁₉	—	4	1	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	—	8	4	no	—
191	C₂³×C₁₉	—	8	8	no	—
192	C₂³×C₁₉	—	8	8	no	—
193	C₂³×C₁₉	#121	1	2	yes	—
194	C₂³×C₁₉	#135	1	2	yes	—
195	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
196	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	2	2	no	—
199	D₄×C₁₉	—	2	2	no	—
200	D₄×C₁₉	—	2	4	no	—
201	D₄×C₁₉	—	4	8	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	2	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	8	4	no	—
207	D₄×C₁₉	#123	1	4	yes	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	8	8	no	—
228	C₂×C₄×C₁₉	—	8	4	no	—
229	C₂×C₄×C₁₉	#121	1	2	yes	—
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
232	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
234	C₈×C₁₉	—	4	1	no	—
235	C₈×C₁₉	—	4	2	no	—
236	C₈×C₁₉	—	4	1	no	—
237	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
238	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2504	C₂×C₁₉	1	1	yes	characteristic, complemented
240	D₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2073	C₂×C₁₉	1	2	yes	complemented
242	#2054	C₂×C₁₉	1	2	yes	complemented
243	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1879	C₂×C₁₉	1	2	yes	complemented
245	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1804	C₂×C₁₉	1	2	yes	complemented
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	2	4	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	4	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	8	16	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	8	1	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	—	8	2	no	—
267	C₂²×C₁₉	—	8	2	no	—
268	C₂²×C₁₉	#463	1	4	yes	—
269	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
270	C₂²×C₁₉	#546	1	2	yes	—
271	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
272	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂²×C₁₉	#576	1	2	yes	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	2	no	—
279	C₄×C₁₉	—	8	2	no	—
280	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
281	C₄×C₁₉	#534	1	1	yes	characteristic
282	C₄×C₁₉	#551	1	2	yes	—
283	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	—	2	1	no	—
291	#447	—	2	4	no	—
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
293	C₂×#102	—	2	4	no	—
294	C₂×#102	C₂²×C₁₉	1	2	yes	—
295	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#102	C₂²×C₁₉	1	2	yes	—
297	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
299	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
300	#397	—	2	2	no	—
301	#390	C₂²×C₁₉	1	2	yes	—
302	#390	C₂²×C₁₉	1	2	yes	complemented
303	#386	—	2	1	no	—
304	#386	—	2	1	no	—
305	#386	—	2	2	no	—
306	#382	C₂²×C₁₉	1	2	yes	complemented
307	#380	C₂²×C₁₉	1	1	yes	characteristic
308	#379	—	2	1	no	—
309	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	#340	C₂²×C₁₉	1	2	yes	complemented
311	#340	C₂²×C₁₉	1	2	yes	complemented
312	#340	C₂²×C₁₉	1	2	yes	complemented
313	#336	C₂²×C₁₉	1	2	yes	complemented
314	C₂×C₁₉	—	2	4	no	—
315	C₂×C₁₉	—	4	4	no	—
316	C₂×C₁₉	—	8	2	no	—
317	C₂×C₁₉	—	16	1	no	—
318	C₂×C₁₉	#2412	1	1	yes	characteristic
319	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
320	C₂×C₁₉	#3041	1	1	yes	characteristic
321	C₂×C₁₉	#3297	1	2	yes	—
322	C₂×C₁₉	#3318	1	2	yes	—
323	C₂⁵	—	2	1	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	4	2	no	—
329	C₂²×D₄	D₄×C₁₉	1	4	yes	—
330	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
336	C₂×D₈	—	2	2	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	2	4	no	—
339	C₂×D₈	—	4	2	no	—
340	C₂²×C₈	—	2	2	no	—
341	C₂²×C₈	—	4	2	no	—
342	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	4	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	4	4	no	—
363	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
366	C₄⋊C₈	—	4	2	no	—
367	#102	—	2	4	no	—
368	#102	—	2	4	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	4	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	#95	—	2	1	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	D₄×C₁₉	1	2	yes	—
377	C₁₉	#24531	1	1	yes	characteristic, direct product factor, Sylow
378	C₂⁴	—	2	1	no	—
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	4	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	—	4	4	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	—	8	2	no	—
386	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂×D₄	#41×C₁₉	1	4	yes	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	8	2	no	—
416	C₂²×C₄	—	8	2	no	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
421	C₂²×C₄	#41×C₁₉	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
423	D₈	—	4	4	no	—
424	D₈	—	4	4	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	4	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	8	2	no	—
447	C₂²⋊C₄	—	8	2	no	—
448	C₂²⋊C₄	—	8	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	8	no	—
472	C₂³	—	8	8	no	—
473	C₂³	C₁₉×#121	1	2	yes	—
474	C₂³	C₁₉×#135	1	2	yes	—
475	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
476	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	8	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	4	no	—
487	D₄	C₁₉×#123	1	4	yes	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	8	8	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	C₁₉×#121	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
514	C₈	—	4	1	no	—
515	C₈	—	4	2	no	—
516	C₈	—	4	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	16	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	C₁₉×#463	1	4	yes	—
538	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
539	C₂²	C₁₉×#546	1	2	yes	—
540	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
541	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
542	C₂²	C₁₉×#576	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	2	no	—
548	C₄	—	8	2	no	—
549	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
550	C₄	C₁₉×#534	1	1	yes	characteristic
551	C₄	C₁₉×#551	1	2	yes	—
552	C₂	—	2	4	no	—
553	C₂	—	4	4	no	—
554	C₂	—	8	2	no	—
555	C₂	—	16	1	no	—
556	C₂	C₁₉×#2412	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
558	C₂	C₁₉×#3041	1	1	yes	characteristic
559	C₂	C₁₉×#3297	1	2	yes	—
560	C₂	C₁₉×#3318	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#102	C₂	semidirect
3. C₁₉×#2504	C₂	semidirect
4. D₄×C₂²⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#2073	C₂	semidirect
6. C₁₉×#2054	C₂	semidirect
7. C₁₉×#1893	C₂	semidirect
8. C₁₉×#1879	C₂	semidirect
9. C₁₉×#1850	C₂	semidirect
10. C₁₉×#1824	C₂	semidirect
11. C₁₉×#1804	C₂	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
27. C₂×C₁₉×#102	C₂²	semidirect
31. C₁₉×#390	C₂²	semidirect
35. C₁₉×#382	C₂²	semidirect
39. C₁₉×#340	C₂²	semidirect
40. C₁₉×#340	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
170. #24531	C₁₉	direct (N × H)
238. C₂²×#102	C₂×C₁₉	semidirect
239. #2504	C₂×C₁₉	semidirect
240. D₄×C₂²⋊C₄	C₂×C₁₉	semidirect
241. #2073	C₂×C₁₉	semidirect
242. #2054	C₂×C₁₉	semidirect
243. #1893	C₂×C₁₉	semidirect
244. #1879	C₂×C₁₉	semidirect
245. #1850	C₂×C₁₉	semidirect
246. #1824	C₂×C₁₉	semidirect
247. #1804	C₂×C₁₉	semidirect
292. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
298. C₂×#102	C₂²×C₁₉	semidirect
302. #390	C₂²×C₁₉	semidirect
306. #382	C₂²×C₁₉	semidirect
310. #340	C₂²×C₁₉	semidirect
311. #340	C₂²×C₁₉	semidirect
312. #340	C₂²×C₁₉	semidirect
313. #336	C₂²×C₁₉	semidirect
377. C₁₉	#24531	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×#447	2
C₂²×C₁₉×#102	2
C₁₉×#2504	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#2073	2
C₁₉×#2054	2
C₁₉×#1893	2
C₁₉×#1879	2
C₁₉×#1850	2
C₁₉×#1824	2
C₁₉×#1804	2
#24531	19

Subgroups — C19×#24531 #18030490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24531 #18030490