Subgroups — C₂×C₁₉×#1797 #18026583

Order 4864.

2222 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×C₂²⋊C₈	C₂	1	2	yes	maximal
4	C₁₉×#1797	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#336	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₉	C₂²	1	4	yes	—
10	C₂²×C₄²×C₁₉	—	2	8	no	—
11	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
12	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
13	C₂²×C₄²×C₁₉	C₄	1	4	yes	—
14	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	—	2	8	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	8	yes	complemented
19	C₂×C₁₉×C₂²⋊C₈	—	2	8	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	8	yes	—
21	C₁₉×#336	C₂²	1	8	yes	complemented
22	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	4	no	—
24	C₂³×C₄×C₁₉	—	2	4	no	—
25	C₂³×C₄×C₁₉	—	2	4	no	—
26	C₂³×C₄×C₁₉	—	2	4	no	—
27	C₂³×C₄×C₁₉	—	2	4	no	—
28	C₂³×C₄×C₁₉	—	2	4	no	—
29	C₂³×C₄×C₁₉	—	2	4	no	—
30	C₂³×C₄×C₁₉	C₈	1	8	yes	complemented
31	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	4	yes	—
40	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	—	2	8	no	—
44	C₂²×C₈×C₁₉	—	2	8	no	—
45	C₂²×C₈×C₁₉	—	2	8	no	—
46	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
47	C₂×C₄²×C₁₉	—	2	4	no	—
48	C₂×C₄²×C₁₉	—	2	4	no	—
49	C₂×C₄²×C₁₉	—	2	4	no	—
50	C₂×C₄²×C₁₉	—	2	16	no	—
51	C₂×C₄²×C₁₉	—	2	16	no	—
52	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₉	D₄	1	8	yes	—
57	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
59	C₁₉×C₄⋊C₈	—	2	16	no	—
60	C₁₉×C₂²⋊C₈	—	2	16	no	—
61	C₂⁴×C₁₉	—	2	2	no	—
62	C₂⁴×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	2	2	no	—
64	C₂⁴×C₁₉	—	2	2	no	—
65	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
66	C₂⁴×C₁₉	C₂×C₈	1	4	yes	—
67	C₂⁴×C₁₉	M₁₆	1	4	yes	—
68	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
69	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	—	2	32	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	8	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	32	no	—
81	C₂²×C₄×C₁₉	—	2	8	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	8	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	16	no	—
86	C₂²×C₄×C₁₉	—	2	16	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
95	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×C₈	1	16	yes	complemented
98	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
99	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₉	—	2	8	no	—
114	C₂×C₈×C₁₉	—	2	8	no	—
115	C₂×C₈×C₁₉	—	2	8	no	—
116	C₂×C₈×C₁₉	—	4	16	no	—
117	C₄²×C₁₉	—	2	8	no	—
118	C₄²×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	—	2	8	no	—
120	C₄²×C₁₉	—	2	4	no	—
121	C₄²×C₁₉	C₂²⋊C₄	1	8	yes	—
122	C₄²×C₁₉	C₂×D₄	1	8	yes	—
123	C₂×#1797	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	8	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	8	no	—
131	C₂³×C₁₉	—	2	8	no	—
132	C₂³×C₁₉	—	2	8	no	—
133	C₂³×C₁₉	—	2	8	no	—
134	C₂³×C₁₉	C₄⋊C₈	1	16	yes	complemented
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
137	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₉	#117	1	2	yes	—
139	C₂³×C₁₉	C₂²×C₈	1	4	yes	—
140	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
141	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
142	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
143	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
144	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
145	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	—	2	32	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	8	no	—
156	C₂×C₄×C₁₉	—	2	8	no	—
157	C₂×C₄×C₁₉	—	2	8	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	16	no	—
162	C₂×C₄×C₁₉	—	2	32	no	—
163	C₂×C₄×C₁₉	C₂²⋊C₈	1	16	yes	complemented
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₉	#117	1	2	yes	—
170	C₂×C₄×C₁₉	#121	1	8	yes	—
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
172	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
173	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
174	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
180	C₈×C₁₉	—	4	8	no	—
181	C₂³×C₄²	C₂×C₁₉	1	1	yes	characteristic
182	C₂²×C₄⋊C₈	C₂×C₁₉	1	2	yes	complemented
183	C₂²×C₂²⋊C₈	C₂×C₁₉	1	2	yes	—
184	#1797	C₂×C₁₉	1	8	yes	direct product factor
185	C₂×#336	C₂×C₁₉	1	2	yes	complemented
186	C₂²×C₁₉	—	2	32	no	—
187	C₂²×C₁₉	—	2	4	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	#380	1	4	yes	—
194	C₂²×C₁₉	C₂×C₂²⋊C₈	1	4	yes	—
195	C₂²×C₁₉	#407	1	4	yes	—
196	C₂²×C₁₉	C₂×C₄⋊C₈	1	4	yes	—
197	C₂²×C₁₉	C₂×C₄⋊C₈	1	8	yes	complemented
198	C₂²×C₁₉	#423	1	4	yes	—
199	C₂²×C₁₉	#431	1	4	yes	—
200	C₂²×C₁₉	#432	1	4	yes	—
201	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
204	C₂²×C₁₉	C₂³×C₈	1	1	yes	characteristic
205	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
206	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
207	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
208	C₄×C₁₉	—	2	4	no	—
209	C₄×C₁₉	—	2	4	no	—
210	C₄×C₁₉	—	2	4	no	—
211	C₄×C₁₉	—	2	4	no	—
212	C₄×C₁₉	#380	1	4	yes	—
213	C₄×C₁₉	C₂×C₂²⋊C₈	1	8	yes	complemented
214	C₄×C₁₉	C₂×#121	1	2	yes	—
215	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
216	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
217	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
218	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₁₉	1	4	yes	—
220	C₂²×C₄²	—	2	8	no	—
221	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
222	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
223	C₂²×C₄²	C₄×C₁₉	1	4	yes	—
224	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
225	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	2	8	no	—
228	C₂×C₄⋊C₈	C₂²×C₁₉	1	8	yes	complemented
229	C₂×C₂²⋊C₈	—	2	8	no	—
230	C₂×C₂²⋊C₈	C₂²×C₁₉	1	8	yes	—
231	#336	C₂²×C₁₉	1	8	yes	complemented
232	C₂×C₁₉	—	2	8	no	—
233	C₂×C₁₉	#1797	1	8	yes	direct product factor
234	C₂×C₁₉	C₂×#380	1	1	yes	characteristic
235	C₂×C₁₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic
236	C₂×C₁₉	C₂×#407	1	1	yes	characteristic
237	C₂×C₁₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#423	1	1	yes	characteristic
239	C₂×C₁₉	C₂×#431	1	1	yes	characteristic
240	C₂×C₁₉	C₂×#432	1	1	yes	characteristic
241	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂³×C₄	—	2	4	no	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	C₈×C₁₉	1	8	yes	complemented
250	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
251	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
253	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
254	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
255	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
256	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₁₉	1	4	yes	—
259	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×C₈	—	2	8	no	—
263	C₂²×C₈	—	2	8	no	—
264	C₂²×C₈	—	2	8	no	—
265	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
266	C₂×C₄²	—	2	4	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	—	2	4	no	—
269	C₂×C₄²	—	2	16	no	—
270	C₂×C₄²	—	2	16	no	—
271	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
272	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
273	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
274	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
275	C₂×C₄²	D₄×C₁₉	1	8	yes	—
276	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
277	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
278	C₄⋊C₈	—	2	16	no	—
279	C₂²⋊C₈	—	2	16	no	—
280	C₁₉	C₂×#1797	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
286	C₂⁴	C₂×C₈×C₁₉	1	4	yes	—
287	C₂⁴	M₁₆×C₁₉	1	4	yes	—
288	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
289	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	—	2	32	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	16	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	32	no	—
311	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
313	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
314	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
315	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	—
316	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂×C₈×C₁₉	1	16	yes	complemented
318	C₂²×C₄	M₁₆×C₁₉	1	4	yes	—
319	C₂²×C₄	M₁₆×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
331	C₂²×C₄	#41×C₁₉	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	8	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	4	16	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	4	no	—
341	C₄²	C₂²⋊C₄×C₁₉	1	8	yes	—
342	C₄²	C₂×D₄×C₁₉	1	8	yes	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₁₉×C₄⋊C₈	1	16	yes	complemented
354	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
355	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
356	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
357	C₂³	C₁₉×#117	1	2	yes	—
358	C₂³	C₂²×C₈×C₁₉	1	4	yes	—
359	C₂³	C₂²×C₈×C₁₉	1	2	yes	—
360	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
361	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
362	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
363	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
364	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄	—	2	32	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	32	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	C₁₉×C₂²⋊C₈	1	16	yes	complemented
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
386	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
387	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₁₉×#117	1	2	yes	—
389	C₂×C₄	C₁₉×#121	1	8	yes	—
390	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
391	C₂×C₄	C₂²×C₈×C₁₉	1	4	yes	—
392	C₂×C₄	C₂²×C₈×C₁₉	1	4	yes	—
393	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
394	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
395	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
397	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
399	C₈	—	4	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	32	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	C₁₉×#380	1	4	yes	—
408	C₂²	C₂×C₁₉×C₂²⋊C₈	1	4	yes	—
409	C₂²	C₁₉×#407	1	4	yes	—
410	C₂²	C₂×C₁₉×C₄⋊C₈	1	4	yes	—
411	C₂²	C₂×C₁₉×C₄⋊C₈	1	8	yes	complemented
412	C₂²	C₁₉×#423	1	4	yes	—
413	C₂²	C₁₉×#431	1	4	yes	—
414	C₂²	C₁₉×#432	1	4	yes	—
415	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
416	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
417	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
418	C₂²	C₂³×C₈×C₁₉	1	1	yes	characteristic
419	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
420	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
421	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	C₁₉×#380	1	4	yes	—
427	C₄	C₂×C₁₉×C₂²⋊C₈	1	8	yes	complemented
428	C₄	C₂×C₁₉×#121	1	2	yes	—
429	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
430	C₂	—	2	8	no	—
431	C₂	C₁₉×#1797	1	8	yes	direct product factor
432	C₂	C₂×C₁₉×#380	1	1	yes	characteristic
433	C₂	C₂²×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
434	C₂	C₂×C₁₉×#407	1	1	yes	characteristic
435	C₂	C₂²×C₁₉×C₄⋊C₈	1	1	yes	characteristic
436	C₂	C₂×C₁₉×#423	1	1	yes	characteristic
437	C₂	C₂×C₁₉×#431	1	1	yes	characteristic
438	C₂	C₂×C₁₉×#432	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₉	C₂³
commutator	C₂²	C₂³×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂⁴×C₁₉	C₂²×C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×C₄⋊C₈	C₂	semidirect
4. C₁₉×#1797	C₂	direct (N × H)
5. C₂×C₁₉×#336	C₂	semidirect
18. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
21. C₁₉×#336	C₂²	semidirect
30. C₂³×C₄×C₁₉	C₈	semidirect
97. C₂²×C₄×C₁₉	C₂×C₈	semidirect
123. C₂×#1797	C₁₉	direct (N × H)
134. C₂³×C₁₉	C₄⋊C₈	semidirect
163. C₂×C₄×C₁₉	C₂²⋊C₈	semidirect
182. C₂²×C₄⋊C₈	C₂×C₁₉	semidirect
184. #1797	C₂×C₁₉	direct (N × H)
185. C₂×#336	C₂×C₁₉	semidirect
197. C₂²×C₁₉	C₂×C₄⋊C₈	semidirect
213. C₄×C₁₉	C₂×C₂²⋊C₈	semidirect
228. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
231. #336	C₂²×C₁₉	semidirect
233. C₂×C₁₉	#1797	direct (N × H)
249. C₂³×C₄	C₈×C₁₉	semidirect
280. C₁₉	C₂×#1797	direct (N × H)
317. C₂²×C₄	C₂×C₈×C₁₉	semidirect
353. C₂³	C₁₉×C₄⋊C₈	semidirect
382. C₂×C₄	C₁₉×C₂²⋊C₈	semidirect
411. C₂²	C₂×C₁₉×C₄⋊C₈	semidirect
427. C₄	C₂×C₁₉×C₂²⋊C₈	semidirect
431. C₂	C₁₉×#1797	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₉	2
C₂²×C₁₉×C₄⋊C₈	2
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#1797	2
C₂×C₁₉×#336	2
C₂×#1797	19

Subgroups — C2×C19×#1797 #18026583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1797 #18026583