Subgroups — C₁₉×#34185 #18040144

Order 4864.

2914 conjugacy classes of subgroups.

The subgroup lattice has 462 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
2	C₁₉×#2353	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2352	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2313	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2312	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2308	C₂	1	2	yes	maximal
7	C₁₉×#2283	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2280	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2273	C₂	1	2	yes	maximal, complemented
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₄	1	16	yes	complemented
15	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
17	C₂×C₁₉×#117	C₂²	1	4	yes	complemented
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#388	C₂²	1	16	yes	complemented
25	C₁₉×#387	C₂²	1	16	yes	complemented
26	C₁₉×#386	C₂²	1	16	yes	—
27	C₁₉×#383	C₂²	1	4	yes	complemented
28	C₁₉×#382	C₂²	1	4	yes	complemented
29	C₁₉×#381	C₂²	1	4	yes	—
30	C₁₉×#381	C₂²	1	4	yes	complemented
31	C₁₉×#380	C₂²	1	4	yes	—
32	C₁₉×#380	C₂²	1	4	yes	—
33	C₁₉×#380	C₂²	1	4	yes	complemented
34	C₁₉×#380	C₂²	1	4	yes	complemented
35	C₁₉×#380	C₂²	1	4	yes	complemented
36	C₁₉×#379	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	16	yes	complemented
41	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
42	C₁₉×#376	C₂²	1	4	yes	complemented
43	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
44	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
45	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	8	no	—
47	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
48	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₉	—	4	4	no	—
50	C₂³×C₄×C₁₉	—	4	4	no	—
51	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
52	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	complemented
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	complemented
64	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	complemented
65	C₁₉×#117	—	4	8	no	—
66	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
81	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
85	C₁₉×#95	C₂³	1	8	yes	—
86	C₁₉×#95	C₂³	1	8	yes	—
87	C₁₉×#95	C₂³	1	8	yes	—
88	C₁₉×#95	C₂³	1	8	yes	—
89	C₁₉×#95	C₂³	1	8	yes	—
90	C₁₉×#95	C₂³	1	8	yes	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	4	2	no	—
93	C₂⁴×C₁₉	—	4	2	no	—
94	C₂⁴×C₁₉	—	4	2	no	—
95	C₂⁴×C₁₉	—	4	2	no	—
96	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
97	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
98	C₂⁴×C₁₉	#41	1	8	yes	—
99	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
100	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
102	C₂×D₄×C₁₉	—	2	32	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	2	8	no	—
105	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	2	8	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	16	no	—
111	C₂²×C₄×C₁₉	—	4	16	no	—
112	C₂²×C₄×C₁₉	—	4	16	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	8	no	—
119	C₂²×C₄×C₁₉	—	4	8	no	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₁₉	—	2	16	no	—
137	C₄⋊C₄×C₁₉	—	4	8	no	—
138	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
139	C₂²⋊C₄×C₁₉	—	2	16	no	—
140	C₂²⋊C₄×C₁₉	—	2	16	no	—
141	C₂²⋊C₄×C₁₉	—	4	8	no	—
142	C₂²⋊C₄×C₁₉	—	4	8	no	—
143	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
144	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
145	C₄²×C₁₉	—	4	8	no	—
146	C₄²×C₁₉	—	4	8	no	—
147	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
148	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
149	#34185	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	8	no	—
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	16	no	—
163	C₂³×C₁₉	—	4	16	no	—
164	C₂³×C₁₉	#117	1	16	yes	complemented
165	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
166	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
167	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
168	C₂³×C₁₉	C₂×#41	1	4	yes	—
169	C₂³×C₁₉	C₂×#41	1	4	yes	—
170	C₂³×C₁₉	C₂×#41	1	4	yes	—
171	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
172	D₄×C₁₉	—	2	32	no	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	8	no	—
180	C₂×C₄×C₁₉	—	2	16	no	—
181	C₂×C₄×C₁₉	—	2	16	no	—
182	C₂×C₄×C₁₉	—	2	16	no	—
183	C₂×C₄×C₁₉	—	2	16	no	—
184	C₂×C₄×C₁₉	—	2	16	no	—
185	C₂×C₄×C₁₉	—	4	8	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	8	16	no	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
193	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
195	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
198	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
199	#2353	C₂×C₁₉	1	8	yes	complemented
200	#2352	C₂×C₁₉	1	8	yes	complemented
201	#2313	C₂×C₁₉	1	2	yes	complemented
202	#2312	C₂×C₁₉	1	2	yes	complemented
203	#2308	C₂×C₁₉	1	2	yes	—
204	#2283	C₂×C₁₉	1	2	yes	complemented
205	#2280	C₂×C₁₉	1	2	yes	complemented
206	C₂×#380	C₂×C₁₉	1	2	yes	complemented
207	#2273	C₂×C₁₉	1	2	yes	complemented
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	4	no	—
212	C₂²×C₁₉	—	2	8	no	—
213	C₂²×C₁₉	—	2	8	no	—
214	C₂²×C₁₉	—	2	8	no	—
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	4	no	—
218	C₂²×C₁₉	—	4	16	no	—
219	C₂²×C₁₉	—	4	16	no	—
220	C₂²×C₁₉	—	4	8	no	—
221	C₂²×C₁₉	C₂×#117	1	4	yes	—
222	C₂²×C₁₉	C₂×#117	1	8	yes	—
223	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
224	C₂²×C₁₉	C₂²×#41	1	2	yes	—
225	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
226	C₂²×C₁₉	#585	1	2	yes	—
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	2	4	no	—
231	C₄×C₁₉	—	2	4	no	—
232	C₄×C₁₉	—	4	16	no	—
233	C₄×C₁₉	#518	1	4	yes	—
234	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
235	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×C₄×D₄	C₄×C₁₉	1	16	yes	complemented
238	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
239	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
240	C₂×#117	C₂²×C₁₉	1	4	yes	complemented
241	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
243	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
246	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
247	#388	C₂²×C₁₉	1	16	yes	complemented
248	#387	C₂²×C₁₉	1	16	yes	complemented
249	#386	C₂²×C₁₉	1	16	yes	—
250	#383	C₂²×C₁₉	1	4	yes	complemented
251	#382	C₂²×C₁₉	1	4	yes	complemented
252	#381	C₂²×C₁₉	1	4	yes	—
253	#381	C₂²×C₁₉	1	4	yes	complemented
254	#380	C₂²×C₁₉	1	4	yes	—
255	#380	C₂²×C₁₉	1	4	yes	—
256	#380	C₂²×C₁₉	1	4	yes	complemented
257	#380	C₂²×C₁₉	1	4	yes	complemented
258	#380	C₂²×C₁₉	1	4	yes	complemented
259	#379	C₂²×C₁₉	1	4	yes	—
260	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
261	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
262	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
263	C₄×C₂²⋊C₄	C₂²×C₁₉	1	16	yes	complemented
264	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
265	#376	C₂²×C₁₉	1	4	yes	complemented
266	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
267	C₂×C₁₉	—	2	4	no	—
268	C₂×C₁₉	—	2	8	no	—
269	C₂×C₁₉	—	4	4	no	—
270	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
272	C₂×C₁₉	#3428	1	1	yes	characteristic
273	C₂×C₁₉	#3505	1	4	yes	—
274	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
275	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
276	C₂²×D₄	—	2	8	no	—
277	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
278	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
279	C₂³×C₄	—	4	4	no	—
280	C₂³×C₄	—	4	4	no	—
281	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
282	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	complemented
283	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
293	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	complemented
294	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	complemented
295	#117	—	4	8	no	—
296	C₂×C₄⋊C₄	—	4	8	no	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
298	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
301	C₂×C₂²⋊C₄	—	2	16	no	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
304	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
310	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
311	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
312	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
313	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	#95	C₂³×C₁₉	1	8	yes	—
316	#95	C₂³×C₁₉	1	8	yes	—
317	#95	C₂³×C₁₉	1	8	yes	—
318	#95	C₂³×C₁₉	1	8	yes	—
319	#95	C₂³×C₁₉	1	8	yes	—
320	#95	C₂³×C₁₉	1	8	yes	—
321	C₁₉	#34185	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	4	2	no	—
324	C₂⁴	—	4	2	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
328	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
329	C₂⁴	#41×C₁₉	1	8	yes	—
330	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
331	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
332	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
333	C₂×D₄	—	2	32	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	4	16	no	—
343	C₂²×C₄	—	4	16	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	8	no	—
350	C₂²×C₄	—	4	8	no	—
351	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
361	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
367	C₄⋊C₄	—	2	16	no	—
368	C₄⋊C₄	—	4	8	no	—
369	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	2	16	no	—
372	C₂²⋊C₄	—	4	8	no	—
373	C₂²⋊C₄	—	4	8	no	—
374	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
375	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
376	C₄²	—	4	8	no	—
377	C₄²	—	4	8	no	—
378	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
379	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	16	no	—
393	C₂³	—	4	16	no	—
394	C₂³	C₁₉×#117	1	16	yes	complemented
395	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
396	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
397	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
398	C₂³	C₂×#41×C₁₉	1	4	yes	—
399	C₂³	C₂×#41×C₁₉	1	4	yes	—
400	C₂³	C₂×#41×C₁₉	1	4	yes	—
401	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
402	D₄	—	2	32	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	16	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	16	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	8	16	no	—
421	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
425	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
427	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	8	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	16	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	C₂×C₁₉×#117	1	4	yes	—
442	C₂²	C₂×C₁₉×#117	1	8	yes	—
443	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
444	C₂²	C₂²×#41×C₁₉	1	2	yes	—
445	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
446	C₂²	C₁₉×#585	1	2	yes	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	4	no	—
452	C₄	—	4	16	no	—
453	C₄	C₁₉×#518	1	4	yes	—
454	C₂	—	2	4	no	—
455	C₂	—	2	8	no	—
456	C₂	—	4	4	no	—
457	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
458	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
459	C₂	C₁₉×#3428	1	1	yes	characteristic
460	C₂	C₁₉×#3505	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2353	C₂	semidirect
3. C₁₉×#2352	C₂	semidirect
4. C₁₉×#2313	C₂	semidirect
5. C₁₉×#2312	C₂	semidirect
7. C₁₉×#2283	C₂	semidirect
8. C₁₉×#2280	C₂	semidirect
9. C₂×C₁₉×#380	C₂	semidirect
10. C₁₉×#2273	C₂	semidirect
14. C₂×C₄×D₄×C₁₉	C₄	semidirect
17. C₂×C₁₉×#117	C₂²	semidirect
19. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
24. C₁₉×#388	C₂²	semidirect
25. C₁₉×#387	C₂²	semidirect
27. C₁₉×#383	C₂²	semidirect
28. C₁₉×#382	C₂²	semidirect
30. C₁₉×#381	C₂²	semidirect
33. C₁₉×#380	C₂²	semidirect
34. C₁₉×#380	C₂²	semidirect
35. C₁₉×#380	C₂²	semidirect
37. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
42. C₁₉×#376	C₂²	semidirect
43. C₂×C₁₉×#95	C₂²	semidirect
52. C₂³×C₄×C₁₉	C₂×C₄	semidirect
63. C₄×D₄×C₁₉	C₂×C₄	semidirect
64. C₄×D₄×C₁₉	C₂×C₄	semidirect
67. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
73. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
80. C₂×C₄²×C₁₉	C₂×C₄	semidirect
149. #34185	C₁₉	direct (N × H)
164. C₂³×C₁₉	#117	semidirect
199. #2353	C₂×C₁₉	semidirect
200. #2352	C₂×C₁₉	semidirect
201. #2313	C₂×C₁₉	semidirect
202. #2312	C₂×C₁₉	semidirect
204. #2283	C₂×C₁₉	semidirect
205. #2280	C₂×C₁₉	semidirect
206. C₂×#380	C₂×C₁₉	semidirect
207. #2273	C₂×C₁₉	semidirect
237. C₂×C₄×D₄	C₄×C₁₉	semidirect
240. C₂×#117	C₂²×C₁₉	semidirect
242. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
247. #388	C₂²×C₁₉	semidirect
248. #387	C₂²×C₁₉	semidirect
250. #383	C₂²×C₁₉	semidirect
251. #382	C₂²×C₁₉	semidirect
253. #381	C₂²×C₁₉	semidirect
256. #380	C₂²×C₁₉	semidirect
257. #380	C₂²×C₁₉	semidirect
258. #380	C₂²×C₁₉	semidirect
260. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
263. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
264. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
265. #376	C₂²×C₁₉	semidirect
266. C₂×#95	C₂²×C₁₉	semidirect
282. C₂³×C₄	C₂×C₄×C₁₉	semidirect
293. C₄×D₄	C₂×C₄×C₁₉	semidirect
294. C₄×D₄	C₂×C₄×C₁₉	semidirect
297. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
303. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
310. C₂×C₄²	C₂×C₄×C₁₉	semidirect
321. C₁₉	#34185	direct (N × H)
394. C₂³	C₁₉×#117	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
C₁₉×#2353	2
C₁₉×#2352	2
C₁₉×#2313	2
C₁₉×#2312	2
C₁₉×#2308	2
C₁₉×#2283	2
C₁₉×#2280	2
C₂×C₁₉×#380	2
C₁₉×#2273	2
#34185	19

Subgroups — C19×#34185 #18040144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34185 #18040144