Subgroups — C₂²×C₁₉×#344 #18026318

Order 4864.

2190 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	#95
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#344	C₂	direct (N × H)
13. C₂²×M₁₆×C₁₉	C₄	semidirect
14. C₂²×M₁₆×C₁₉	C₄	semidirect
15. C₂²×M₁₆×C₁₉	C₄	semidirect
19. C₂³×C₈×C₁₉	C₄	semidirect
27. C₁₉×#344	C₂²	direct (N × H)
57. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
58. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
59. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
67. C₂²×C₈×C₁₉	C₂×C₄	semidirect
139. M₁₆×C₁₉	C₂²×C₄	semidirect
145. C₂×C₈×C₁₉	C₂²×C₄	semidirect
152. C₂²×#344	C₁₉	direct (N × H)
217. C₂×#344	C₂×C₁₉	direct (N × H)
229. C₂²×C₁₉	#344	direct (N × H)
254. C₂²×M₁₆	C₄×C₁₉	semidirect
255. C₂²×M₁₆	C₄×C₁₉	semidirect
256. C₂²×M₁₆	C₄×C₁₉	semidirect
260. C₂³×C₈	C₄×C₁₉	semidirect
268. #344	C₂²×C₁₉	direct (N × H)
275. C₂×C₁₉	C₂×#344	direct (N × H)
306. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
307. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
308. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
316. C₂²×C₈	C₂×C₄×C₁₉	semidirect
328. C₁₉	C₂²×#344	direct (N × H)
389. M₁₆	C₂²×C₄×C₁₉	semidirect
395. C₂×C₈	C₂²×C₄×C₁₉	semidirect
474. C₂²	C₁₉×#344	direct (N × H)
497. C₂	C₂×C₁₉×#344	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×M₁₆×C₁₉	2
C₂²×C₁₉×#117	2
C₂×C₁₉×#344	2
C₂²×#344	19

Subgroups — C22×C19×#344 #18026318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#344 #18026318