Subgroups — C₁₉×#29468 #18035427

Order 4864.

798 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2624	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#399	—	2	1	no	—
35	C₁₉×#397	—	2	1	no	—
36	C₁₉×#394	—	2	1	no	—
37	C₁₉×#394	—	2	1	no	—
38	C₁₉×#390	—	2	1	no	—
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#386	—	2	1	no	—
47	C₁₉×#385	—	2	1	no	—
48	C₁₉×#380	C₂²	1	1	yes	characteristic
49	C₁₉×#380	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	4	1	no	—
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	4	1	no	—
75	C₁₉×#121	—	4	1	no	—
76	C₄×D₄×C₁₉	—	4	1	no	—
77	C₄×D₄×C₁₉	—	4	1	no	—
78	C₁₉×#117	—	4	1	no	—
79	C₁₉×#117	—	4	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	2	no	—
108	C₁₉×#107	—	2	2	no	—
109	C₁₉×#107	—	4	1	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	4	1	no	—
115	C₁₉×#102	—	4	1	no	—
116	C₁₉×C₂²⋊C₈	—	2	2	no	—
117	C₁₉×C₂²⋊C₈	—	2	2	no	—
118	C₁₉×#97	—	4	1	no	—
119	C₄×C₈×C₁₉	—	4	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	8	1	no	—
143	C₂×D₄×C₁₉	—	8	1	no	—
144	C₂×D₄×C₁₉	—	8	1	no	—
145	C₂×D₄×C₁₉	—	8	1	no	—
146	C₂×D₄×C₁₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	8	1	no	—
161	C₂²×C₄×C₁₉	—	8	1	no	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	D₈×C₁₉	—	4	4	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	#41	1	2	yes	—
180	C₂×C₈×C₁₉	#41	1	2	yes	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	8	1	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₄⋊C₄×C₁₉	—	8	1	no	—
197	C₄⋊C₄×C₁₉	#41	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	2	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	8	1	no	—
204	C₂²⋊C₄×C₁₉	—	8	1	no	—
205	C₂²⋊C₄×C₁₉	—	8	1	no	—
206	C₂²⋊C₄×C₁₉	—	8	1	no	—
207	C₂²⋊C₄×C₁₉	—	8	1	no	—
208	C₂²⋊C₄×C₁₉	—	8	1	no	—
209	C₂²⋊C₄×C₁₉	—	8	1	no	—
210	C₂²⋊C₄×C₁₉	—	8	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	8	1	no	—
216	#29468	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	8	4	no	—
248	D₄×C₁₉	—	8	4	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	8	4	no	—
287	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
293	C₈×C₁₉	—	2	2	no	—
294	C₈×C₁₉	—	2	2	no	—
295	C₈×C₁₉	—	4	1	no	—
296	C₈×C₁₉	—	4	1	no	—
297	#2624	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#2324	C₂×C₁₉	1	1	yes	characteristic, complemented
299	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1999	C₂×C₁₉	1	1	yes	characteristic
303	#1970	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1942	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#1936	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1862	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	1	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	1	no	—
327	C₂²×C₁₉	—	8	1	no	—
328	C₂²×C₁₉	—	8	1	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	#525	1	1	yes	characteristic
334	C₂²×C₁₉	#532	1	1	yes	characteristic
335	C₂²×C₁₉	#534	1	1	yes	characteristic
336	C₂²×C₁₉	#576	1	1	yes	characteristic
337	C₂²×C₁₉	#576	1	1	yes	characteristic
338	C₂²×C₁₉	#576	1	1	yes	characteristic
339	C₂²×C₁₉	#578	1	1	yes	characteristic
340	C₄×C₁₉	—	4	1	no	—
341	C₄×C₁₉	—	4	2	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	8	1	no	—
347	C₄×C₁₉	—	8	1	no	—
348	C₄×C₁₉	—	8	1	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	#551	1	1	yes	characteristic
352	C₄×C₁₉	#553	1	1	yes	characteristic
353	C₄×C₁₉	#553	1	1	yes	characteristic
354	C₄×C₁₉	#559	1	1	yes	characteristic
355	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
373	#399	—	2	1	no	—
374	#397	—	2	1	no	—
375	#394	—	2	1	no	—
376	#394	—	2	1	no	—
377	#390	—	2	1	no	—
378	#390	C₂²×C₁₉	1	1	yes	characteristic
379	#390	C₂²×C₁₉	1	1	yes	characteristic
380	#390	C₂²×C₁₉	1	1	yes	characteristic
381	#389	C₂²×C₁₉	1	1	yes	characteristic
382	#389	C₂²×C₁₉	1	1	yes	characteristic
383	#389	C₂²×C₁₉	1	1	yes	characteristic
384	#388	—	2	1	no	—
385	#386	—	2	1	no	—
386	#385	—	2	1	no	—
387	#380	C₂²×C₁₉	1	1	yes	characteristic
388	#380	C₂²×C₁₉	1	1	yes	characteristic
389	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
390	#340	C₂²×C₁₉	1	1	yes	characteristic
391	#340	C₂²×C₁₉	1	1	yes	characteristic
392	#340	C₂²×C₁₉	1	1	yes	characteristic
393	#340	C₂²×C₁₉	1	1	yes	characteristic
394	#340	C₂²×C₁₉	1	1	yes	characteristic
395	#340	C₂²×C₁₉	1	1	yes	characteristic
396	#336	C₂²×C₁₉	1	1	yes	characteristic
397	#336	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×C₁₉	—	8	1	no	—
399	C₂×C₁₉	—	8	2	no	—
400	C₂×C₁₉	—	16	1	no	—
401	C₂×C₁₉	#2602	1	1	yes	characteristic
402	C₂×C₁₉	#3122	1	1	yes	characteristic
403	C₂×C₁₉	#3124	1	1	yes	characteristic
404	C₂×C₁₉	#3175	1	1	yes	characteristic
405	C₂×C₁₉	#3176	1	1	yes	characteristic
406	C₂×C₁₉	#3199	1	1	yes	characteristic
407	C₂×C₁₉	#3203	1	1	yes	characteristic
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	2	2	no	—
416	C₂×D₈	—	4	1	no	—
417	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
421	#121	—	2	2	no	—
422	#121	—	2	2	no	—
423	#121	—	4	1	no	—
424	#121	—	4	1	no	—
425	C₄×D₄	—	4	1	no	—
426	C₄×D₄	—	4	1	no	—
427	#117	—	4	1	no	—
428	#117	—	4	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
456	#107	—	2	2	no	—
457	#107	—	2	2	no	—
458	#107	—	4	1	no	—
459	#102	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	4	1	no	—
464	#102	—	4	1	no	—
465	C₂²⋊C₈	—	2	2	no	—
466	C₂²⋊C₈	—	2	2	no	—
467	#97	—	4	1	no	—
468	C₄×C₈	—	4	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	C₁₉	#29468	1	1	yes	characteristic, direct product factor, Sylow
476	C₂⁴	—	2	1	no	—
477	C₂⁴	—	2	1	no	—
478	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	—	8	1	no	—
495	C₂×D₄	—	8	1	no	—
496	C₂×D₄	#41×C₁₉	1	2	yes	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	8	1	no	—
511	C₂²×C₄	—	8	1	no	—
512	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
518	D₈	—	4	4	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	#41×C₁₉	1	2	yes	—
530	C₂×C₈	#41×C₁₉	1	2	yes	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	8	1	no	—
545	C₄⋊C₄	—	8	1	no	—
546	C₄⋊C₄	—	8	1	no	—
547	C₄⋊C₄	#41×C₁₉	1	2	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	8	1	no	—
554	C₂²⋊C₄	—	8	1	no	—
555	C₂²⋊C₄	—	8	1	no	—
556	C₂²⋊C₄	—	8	1	no	—
557	C₂²⋊C₄	—	8	1	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	8	1	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	8	4	no	—
597	D₄	—	8	4	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	8	4	no	—
636	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
638	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
640	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
642	C₈	—	2	2	no	—
643	C₈	—	2	2	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₁₉×#525	1	1	yes	characteristic
668	C₂²	C₁₉×#532	1	1	yes	characteristic
669	C₂²	C₁₉×#534	1	1	yes	characteristic
670	C₂²	C₁₉×#576	1	1	yes	characteristic
671	C₂²	C₁₉×#576	1	1	yes	characteristic
672	C₂²	C₁₉×#576	1	1	yes	characteristic
673	C₂²	C₁₉×#578	1	1	yes	characteristic
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	8	1	no	—
681	C₄	—	8	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	C₁₉×#551	1	1	yes	characteristic
686	C₄	C₁₉×#553	1	1	yes	characteristic
687	C₄	C₁₉×#553	1	1	yes	characteristic
688	C₄	C₁₉×#559	1	1	yes	characteristic
689	C₂	—	8	1	no	—
690	C₂	—	8	2	no	—
691	C₂	—	16	1	no	—
692	C₂	C₁₉×#2602	1	1	yes	characteristic
693	C₂	C₁₉×#3122	1	1	yes	characteristic
694	C₂	C₁₉×#3124	1	1	yes	characteristic
695	C₂	C₁₉×#3175	1	1	yes	characteristic
696	C₂	C₁₉×#3176	1	1	yes	characteristic
697	C₂	C₁₉×#3199	1	1	yes	characteristic
698	C₂	C₁₉×#3203	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1999	C₂
LCS	G ▷ C₂²×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
1. C₁₉×#2624	C₂	semidirect
2. C₁₉×#2324	C₂	semidirect
3. C₁₉×#2076	C₂	semidirect
4. C₁₉×#2033	C₂	semidirect
5. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1970	C₂	semidirect
8. C₁₉×#1942	C₂	semidirect
9. C₁₉×#1936	C₂	semidirect
10. C₁₉×#1936	C₂	semidirect
11. C₁₉×#1925	C₂	semidirect
12. C₁₉×#1921	C₂	semidirect
13. C₁₉×#1879	C₂	semidirect
14. C₁₉×#1862	C₂	semidirect
15. C₁₉×#1750	C₂	semidirect
216. #29468	C₁₉	direct (N × H)
297. #2624	C₂×C₁₉	semidirect
298. #2324	C₂×C₁₉	semidirect
299. #2076	C₂×C₁₉	semidirect
300. #2033	C₂×C₁₉	semidirect
301. #2033	C₂×C₁₉	semidirect
303. #1970	C₂×C₁₉	semidirect
304. #1942	C₂×C₁₉	semidirect
305. #1936	C₂×C₁₉	semidirect
306. #1936	C₂×C₁₉	semidirect
307. #1925	C₂×C₁₉	semidirect
308. #1921	C₂×C₁₉	semidirect
309. #1879	C₂×C₁₉	semidirect
310. #1862	C₂×C₁₉	semidirect
311. #1750	C₂×C₁₉	semidirect
475. C₁₉	#29468	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×#2624	2
C₁₉×#2324	2
C₁₉×#2076	2
C₁₉×#2033	2
C₁₉×#1999	2
C₁₉×#1970	2
C₁₉×#1942	2
C₁₉×#1936	2
C₁₉×#1925	2
C₁₉×#1921	2
C₁₉×#1879	2
C₁₉×#1862	2
C₁₉×#1750	2
#29468	19

Subgroups — C19×#29468 #18035427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29468 #18035427