Subgroups — C₁₉×#34967 #18040926

Order 4864.

2164 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2522	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2516	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2464	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2457	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2402	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2392	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#123	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₉×#121	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#123	C₂²	1	4	yes	—
13	C₂×C₁₉×#121	C₂²	1	4	yes	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
20	C₁₉×#400	C₂²	1	4	yes	—
21	C₁₉×#399	C₂²	1	4	yes	—
22	C₁₉×#398	C₂²	1	4	yes	—
23	C₁₉×#398	C₂²	1	2	yes	—
24	C₁₉×#397	C₂²	1	2	yes	—
25	C₁₉×#396	C₂²	1	4	yes	—
26	C₁₉×#394	C₂²	1	2	yes	—
27	C₁₉×#394	C₂²	1	4	yes	—
28	C₁₉×#392	C₂²	1	4	yes	—
29	C₁₉×#392	C₂²	1	2	yes	—
30	C₁₉×#390	C₂²	1	4	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#388	C₂²	1	4	yes	—
33	C₁₉×#388	C₂²	1	4	yes	—
34	C₁₉×#388	C₂²	1	4	yes	—
35	C₁₉×#388	C₂²	1	4	yes	—
36	C₁₉×#388	C₂²	1	4	yes	—
37	C₁₉×#387	C₂²	1	4	yes	—
38	C₁₉×#387	C₂²	1	4	yes	—
39	C₁₉×#387	C₂²	1	4	yes	—
40	C₁₉×#386	C₂²	1	4	yes	—
41	C₁₉×#386	C₂²	1	4	yes	—
42	C₁₉×#386	C₂²	1	4	yes	—
43	C₁₉×#385	C₂²	1	4	yes	—
44	C₁₉×#381	C₂²	1	4	yes	—
45	C₁₉×#380	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
51	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
53	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
55	C₁₉×#376	C₂²	1	1	yes	characteristic
56	C₄³×C₁₉	C₂²	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
64	C₁₉×#123	—	2	16	no	—
65	C₁₉×#121	—	2	16	no	—
66	C₄×D₄×C₁₉	—	2	16	no	—
67	C₄×D₄×C₁₉	—	2	8	no	—
68	C₄×D₄×C₁₉	—	4	8	no	—
69	C₄×D₄×C₁₉	—	4	8	no	—
70	C₁₉×#117	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₄²×C₁₉	—	4	8	no	—
91	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#95	C₂³	1	4	yes	—
100	C₁₉×#95	C₂³	1	4	yes	—
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	2	yes	—
103	C₁₉×#95	C₂³	1	2	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	4	yes	—
107	C₁₉×#95	C₂³	1	4	yes	—
108	C₁₉×#95	C₂³	1	4	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	8	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	—	2	8	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	8	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	2	8	no	—
126	C₂²×C₄×C₁₉	—	2	8	no	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	8	no	—
144	C₄⋊C₄×C₁₉	—	2	8	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	4	4	no	—
147	C₄⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	—	2	8	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	8	no	—
151	C₂²⋊C₄×C₁₉	—	2	8	no	—
152	C₂²⋊C₄×C₁₉	—	2	8	no	—
153	C₂²⋊C₄×C₁₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	4	no	—
158	C₂²⋊C₄×C₁₉	#41	1	16	yes	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	—	2	4	no	—
162	C₄²×C₁₉	—	2	8	no	—
163	C₄²×C₁₉	—	2	4	no	—
164	C₄²×C₁₉	—	4	4	no	—
165	C₄²×C₁₉	—	4	4	no	—
166	C₄²×C₁₉	#41	1	4	yes	—
167	#34967	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	C₂×#41	1	8	yes	—
178	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
179	D₄×C₁₉	—	2	16	no	—
180	D₄×C₁₉	—	4	16	no	—
181	D₄×C₁₉	—	4	16	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	4	16	no	—
201	C₂×C₄×C₁₉	—	4	16	no	—
202	C₂×C₄×C₁₉	—	4	16	no	—
203	C₂×C₄×C₁₉	—	4	4	no	—
204	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
205	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
206	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
207	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
209	#2522	C₂×C₁₉	1	4	yes	complemented
210	#2516	C₂×C₁₉	1	4	yes	complemented
211	#2464	C₂×C₁₉	1	4	yes	complemented
212	#2457	C₂×C₁₉	1	4	yes	complemented
213	#2402	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2397	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2392	C₂×C₁₉	1	2	yes	complemented
216	C₄×#123	C₂×C₁₉	1	4	yes	complemented
217	C₄×#121	C₂×C₁₉	1	4	yes	complemented
218	#2298	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₄²×D₄	C₂×C₁₉	1	2	yes	complemented
220	C₂²×C₁₉	—	2	8	no	—
221	C₂²×C₁₉	—	2	8	no	—
222	C₂²×C₁₉	—	2	8	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₁₉	C₂²×#41	1	4	yes	—
232	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
233	C₄×C₁₉	—	2	4	no	—
234	C₄×C₁₉	—	2	8	no	—
235	C₄×C₁₉	—	2	8	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	#540	1	4	yes	—
242	C₂×#123	C₂²×C₁₉	1	4	yes	—
243	C₂×#121	C₂²×C₁₉	1	4	yes	—
244	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
246	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
247	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
248	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
250	#400	C₂²×C₁₉	1	4	yes	—
251	#399	C₂²×C₁₉	1	4	yes	—
252	#398	C₂²×C₁₉	1	2	yes	—
253	#398	C₂²×C₁₉	1	4	yes	—
254	#397	C₂²×C₁₉	1	2	yes	—
255	#396	C₂²×C₁₉	1	4	yes	—
256	#394	C₂²×C₁₉	1	2	yes	—
257	#394	C₂²×C₁₉	1	4	yes	—
258	#392	C₂²×C₁₉	1	2	yes	—
259	#392	C₂²×C₁₉	1	4	yes	—
260	#390	C₂²×C₁₉	1	4	yes	—
261	#389	C₂²×C₁₉	1	4	yes	—
262	#388	C₂²×C₁₉	1	4	yes	—
263	#388	C₂²×C₁₉	1	4	yes	—
264	#388	C₂²×C₁₉	1	4	yes	—
265	#388	C₂²×C₁₉	1	4	yes	—
266	#388	C₂²×C₁₉	1	4	yes	—
267	#387	C₂²×C₁₉	1	4	yes	—
268	#387	C₂²×C₁₉	1	4	yes	—
269	#387	C₂²×C₁₉	1	4	yes	—
270	#386	C₂²×C₁₉	1	4	yes	—
271	#386	C₂²×C₁₉	1	4	yes	—
272	#386	C₂²×C₁₉	1	4	yes	—
273	#385	C₂²×C₁₉	1	4	yes	—
274	#381	C₂²×C₁₉	1	4	yes	—
275	#380	C₂²×C₁₉	1	4	yes	—
276	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
277	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
278	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
280	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
281	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
283	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
285	#376	C₂²×C₁₉	1	1	yes	characteristic
286	C₄³	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₁₉	—	4	8	no	—
288	C₂×C₁₉	—	8	1	no	—
289	C₂×C₁₉	#3444	1	2	yes	—
290	C₂×C₁₉	C₂×#540	1	1	yes	characteristic
291	C₂×C₁₉	#3481	1	4	yes	—
292	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
293	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
294	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
295	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
299	#123	—	2	16	no	—
300	#121	—	2	16	no	—
301	C₄×D₄	—	2	16	no	—
302	C₄×D₄	—	2	8	no	—
303	C₄×D₄	—	4	8	no	—
304	C₄×D₄	—	4	8	no	—
305	#117	—	2	4	no	—
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₄²	—	4	8	no	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
329	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
334	#95	C₂³×C₁₉	1	4	yes	—
335	#95	C₂³×C₁₉	1	4	yes	—
336	#95	C₂³×C₁₉	1	4	yes	—
337	#95	C₂³×C₁₉	1	2	yes	—
338	#95	C₂³×C₁₉	1	2	yes	—
339	#95	C₂³×C₁₉	1	4	yes	—
340	#95	C₂³×C₁₉	1	4	yes	—
341	#95	C₂³×C₁₉	1	4	yes	—
342	#95	C₂³×C₁₉	1	4	yes	—
343	#95	C₂³×C₁₉	1	4	yes	—
344	#95	C₂³×C₁₉	1	4	yes	—
345	C₁₉	#34967	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
347	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	#41×C₁₉	1	16	yes	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	8	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	4	no	—
402	C₄²	#41×C₁₉	1	4	yes	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	4	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	2	no	—
412	C₂³	C₂×#41×C₁₉	1	8	yes	—
413	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
414	D₄	—	2	16	no	—
415	D₄	—	4	16	no	—
416	D₄	—	4	16	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	16	no	—
437	C₂×C₄	—	4	16	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
440	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
441	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
442	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
443	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
444	C₂²	—	2	8	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	4	no	—
454	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
455	C₂²	C₂²×#41×C₁₉	1	4	yes	—
456	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
457	C₄	—	2	4	no	—
458	C₄	—	2	8	no	—
459	C₄	—	2	8	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	C₁₉×#540	1	4	yes	—
466	C₂	—	4	8	no	—
467	C₂	—	8	1	no	—
468	C₂	C₁₉×#3444	1	2	yes	—
469	C₂	C₂×C₁₉×#540	1	1	yes	characteristic
470	C₂	C₁₉×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2522	C₂	semidirect
2. C₁₉×#2516	C₂	semidirect
3. C₁₉×#2464	C₂	semidirect
4. C₁₉×#2457	C₂	semidirect
5. C₁₉×#2402	C₂	semidirect
6. C₁₉×#2397	C₂	semidirect
7. C₁₉×#2392	C₂	semidirect
8. C₄×C₁₉×#123	C₂	semidirect
9. C₄×C₁₉×#121	C₂	semidirect
10. C₁₉×#2298	C₂	semidirect
11. C₄²×D₄×C₁₉	C₂	semidirect
167. #34967	C₁₉	direct (N × H)
209. #2522	C₂×C₁₉	semidirect
210. #2516	C₂×C₁₉	semidirect
211. #2464	C₂×C₁₉	semidirect
212. #2457	C₂×C₁₉	semidirect
213. #2402	C₂×C₁₉	semidirect
214. #2397	C₂×C₁₉	semidirect
215. #2392	C₂×C₁₉	semidirect
216. C₄×#123	C₂×C₁₉	semidirect
217. C₄×#121	C₂×C₁₉	semidirect
218. #2298	C₂×C₁₉	semidirect
219. C₄²×D₄	C₂×C₁₉	semidirect
345. C₁₉	#34967	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×#2522	2
C₁₉×#2516	2
C₁₉×#2464	2
C₁₉×#2457	2
C₁₉×#2402	2
C₁₉×#2397	2
C₁₉×#2392	2
C₄×C₁₉×#123	2
C₄×C₁₉×#121	2
C₁₉×#2298	2
C₄²×D₄×C₁₉	2
#34967	19

Subgroups — C19×#34967 #18040926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34967 #18040926