Subgroups — C₁₉×#60192 #18066151

Order 4864.

1882 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	Q₈×M₁₆×C₁₉	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2962	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2961	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2960	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2905	C₂	1	2	yes	maximal
7	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2873	C₂	1	2	yes	maximal
9	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₄	1	2	yes	—
14	C₁₉×#533	C₄	1	4	yes	—
15	C₁₉×#533	C₄	1	2	yes	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₁₉×#533	C₂²	1	2	yes	—
18	C₁₉×#533	C₂²	1	4	yes	—
19	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
20	C₂×C₁₉×#125	C₄	1	2	yes	—
21	C₂×C₁₉×C₂²⋊Q₈	C₄	1	4	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#446	C₂²	1	16	yes	complemented
26	C₁₉×#446	C₂²	1	32	yes	complemented
27	C₈×Q₈×C₁₉	C₂²	1	16	yes	complemented
28	C₁₉×#424	C₂²	1	8	yes	—
29	C₁₉×#424	C₂²	1	8	yes	—
30	C₁₉×#423	C₂²	1	2	yes	—
31	C₁₉×#423	C₂²	1	2	yes	—
32	C₁₉×#423	C₂²	1	4	yes	—
33	C₁₉×#423	C₂²	1	8	yes	—
34	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
35	C₁₉×#405	C₂²	1	8	yes	—
36	C₁₉×#405	C₂²	1	8	yes	—
37	C₄×M₁₆×C₁₉	C₂²	1	4	yes	—
38	C₄×M₁₆×C₁₉	C₂²	1	4	yes	—
39	C₄×M₁₆×C₁₉	C₂²	1	8	yes	—
40	C₂×C₁₉×#97	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	8	no	—
47	C₂×M₁₆×C₁₉	Q₈	1	8	yes	complemented
48	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
50	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
51	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
53	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
58	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
59	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
60	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
61	C₁₉×#125	C₂×C₄	1	4	yes	—
62	C₁₉×#125	C₂×C₄	1	4	yes	—
63	C₁₉×#125	C₂×C₄	1	8	yes	—
64	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
65	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
66	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
69	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
70	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
71	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
72	C₁₉×#117	C₂×C₄	1	4	yes	—
73	C₁₉×#117	C₂×C₄	1	4	yes	—
74	C₁₉×#117	C₂³	1	4	yes	—
75	C₁₉×#117	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	32	yes	—
93	C₁₉×#97	C₂³	1	8	yes	—
94	C₁₉×#97	C₂³	1	16	yes	—
95	C₄×C₈×C₁₉	C₂³	1	8	yes	—
96	C₄×C₈×C₁₉	C₂³	1	16	yes	—
97	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₉	—	4	8	no	—
99	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
100	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
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	2	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₉	#41	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₁₉	—	2	4	no	—
118	M₁₆×C₁₉	—	2	8	no	—
119	M₁₆×C₁₉	—	2	4	no	—
120	M₁₆×C₁₉	—	2	8	no	—
121	M₁₆×C₁₉	C₂×Q₈	1	8	yes	—
122	M₁₆×C₁₉	C₂×Q₈	1	8	yes	complemented
123	C₂×C₈×C₁₉	—	2	8	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	C₂×Q₈	1	8	yes	complemented
126	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
127	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
128	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
130	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
134	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
135	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
136	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
137	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
139	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
146	C₄²×C₁₉	C₂⁴	1	2	yes	—
147	C₄²×C₁₉	C₂⁴	1	2	yes	—
148	C₄²×C₁₉	C₂⁴	1	8	yes	—
149	#60192	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
152	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
154	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	16	no	—
156	Q₈×C₁₉	—	4	8	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	8	no	—
164	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
165	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
166	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
167	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
171	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
179	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
180	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
182	C₈×C₁₉	—	2	8	no	—
183	C₈×C₁₉	—	2	4	no	—
184	C₈×C₁₉	C₂²×Q₈	1	8	yes	—
185	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
186	Q₈×M₁₆	C₂×C₁₉	1	8	yes	complemented
187	#2962	C₂×C₁₉	1	8	yes	complemented
188	#2961	C₂×C₁₉	1	4	yes	complemented
189	#2960	C₂×C₁₉	1	4	yes	complemented
190	#2905	C₂×C₁₉	1	2	yes	—
191	C₂×#423	C₂×C₁₉	1	1	yes	characteristic
192	#2873	C₂×C₁₉	1	2	yes	—
193	C₂×C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
199	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
200	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
201	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	2	16	no	—
206	C₄×C₁₉	C₂×C₄×Q₈	1	2	yes	—
207	C₄×C₁₉	C₂×C₄×Q₈	1	2	yes	—
208	C₄×C₁₉	C₂×C₄×Q₈	1	2	yes	—
209	C₄×C₁₉	#568	1	4	yes	—
210	C₄×C₁₉	C₂³×Q₈	1	1	yes	characteristic
211	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
215	#533	C₄×C₁₉	1	2	yes	—
216	#533	C₄×C₁₉	1	4	yes	—
217	#533	C₄×C₁₉	1	2	yes	—
218	#533	C₂²×C₁₉	1	2	yes	—
219	#533	C₂²×C₁₉	1	2	yes	—
220	#533	C₂²×C₁₉	1	4	yes	—
221	C₂×C₄⋊Q₈	C₄×C₁₉	1	2	yes	—
222	C₂×#125	C₄×C₁₉	1	2	yes	—
223	C₂×C₂²⋊Q₈	C₄×C₁₉	1	4	yes	—
224	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
225	C₂×#117	C₂²×C₁₉	1	2	yes	—
226	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
227	#446	C₂²×C₁₉	1	16	yes	complemented
228	#446	C₂²×C₁₉	1	32	yes	complemented
229	C₈×Q₈	C₂²×C₁₉	1	16	yes	complemented
230	#424	C₂²×C₁₉	1	8	yes	—
231	#424	C₂²×C₁₉	1	8	yes	—
232	#423	C₂²×C₁₉	1	2	yes	—
233	#423	C₂²×C₁₉	1	2	yes	—
234	#423	C₂²×C₁₉	1	4	yes	—
235	#423	C₂²×C₁₉	1	8	yes	—
236	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
237	#405	C₂²×C₁₉	1	8	yes	—
238	#405	C₂²×C₁₉	1	8	yes	—
239	C₄×M₁₆	C₂²×C₁₉	1	4	yes	—
240	C₄×M₁₆	C₂²×C₁₉	1	4	yes	—
241	C₄×M₁₆	C₂²×C₁₉	1	8	yes	—
242	C₂×#97	C₂²×C₁₉	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
244	C₂×C₁₉	—	2	2	no	—
245	C₂×C₁₉	—	2	2	no	—
246	C₂×C₁₉	—	2	2	no	—
247	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
248	C₂×C₁₉	C₂×#568	1	2	yes	—
249	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
250	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	8	no	—
254	C₂×M₁₆	Q₈×C₁₉	1	8	yes	complemented
255	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
256	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
257	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
258	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
259	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
260	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
263	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
264	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
265	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
266	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
267	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
268	#125	C₂×C₄×C₁₉	1	4	yes	—
269	#125	C₂×C₄×C₁₉	1	4	yes	—
270	#125	C₂×C₄×C₁₉	1	8	yes	—
271	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
272	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
273	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
274	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
275	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
276	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
277	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
278	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
279	#117	C₂×C₄×C₁₉	1	4	yes	—
280	#117	C₂×C₄×C₁₉	1	4	yes	—
281	#117	C₂³×C₁₉	1	4	yes	—
282	#117	C₂³×C₁₉	1	4	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
285	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
287	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
291	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
293	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
297	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
298	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
299	C₄⋊C₈	C₂³×C₁₉	1	32	yes	—
300	#97	C₂³×C₁₉	1	8	yes	—
301	#97	C₂³×C₁₉	1	16	yes	—
302	C₄×C₈	C₂³×C₁₉	1	8	yes	—
303	C₄×C₈	C₂³×C₁₉	1	16	yes	—
304	C₁₉	#60192	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
308	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
321	C₂²×C₄	#41×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	8	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	8	no	—
329	M₁₆	C₂×Q₈×C₁₉	1	8	yes	—
330	M₁₆	C₂×Q₈×C₁₉	1	8	yes	complemented
331	C₂×C₈	—	2	8	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	C₂×Q₈×C₁₉	1	8	yes	complemented
334	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
335	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
336	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
337	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
338	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
339	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
340	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
341	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
342	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
343	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
344	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
345	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
346	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
347	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
348	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
349	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
350	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
351	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
353	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
354	C₄²	C₂⁴×C₁₉	1	2	yes	—
355	C₄²	C₂⁴×C₁₉	1	8	yes	—
356	C₄²	C₂⁴×C₁₉	1	2	yes	—
357	C₂³	—	4	2	no	—
358	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
359	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
360	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
361	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	2	16	no	—
363	Q₈	—	4	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
372	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
373	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
374	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
377	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
378	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
384	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
385	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
386	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
387	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
388	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
389	C₈	—	2	8	no	—
390	C₈	—	2	4	no	—
391	C₈	C₂²×Q₈×C₁₉	1	8	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
397	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
398	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
399	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	16	no	—
404	C₄	C₂×C₄×Q₈×C₁₉	1	2	yes	—
405	C₄	C₂×C₄×Q₈×C₁₉	1	2	yes	—
406	C₄	C₂×C₄×Q₈×C₁₉	1	2	yes	—
407	C₄	C₁₉×#568	1	4	yes	—
408	C₄	C₂³×Q₈×C₁₉	1	1	yes	characteristic
409	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
414	C₂	C₂×C₁₉×#568	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. Q₈×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#2962	C₂	semidirect
4. C₁₉×#2961	C₂	semidirect
5. C₁₉×#2960	C₂	semidirect
25. C₁₉×#446	C₂²	semidirect
26. C₁₉×#446	C₂²	semidirect
27. C₈×Q₈×C₁₉	C₂²	semidirect
47. C₂×M₁₆×C₁₉	Q₈	semidirect
122. M₁₆×C₁₉	C₂×Q₈	semidirect
125. C₂×C₈×C₁₉	C₂×Q₈	semidirect
149. #60192	C₁₉	direct (N × H)
186. Q₈×M₁₆	C₂×C₁₉	semidirect
187. #2962	C₂×C₁₉	semidirect
188. #2961	C₂×C₁₉	semidirect
189. #2960	C₂×C₁₉	semidirect
227. #446	C₂²×C₁₉	semidirect
228. #446	C₂²×C₁₉	semidirect
229. C₈×Q₈	C₂²×C₁₉	semidirect
254. C₂×M₁₆	Q₈×C₁₉	semidirect
304. C₁₉	#60192	direct (N × H)
330. M₁₆	C₂×Q₈×C₁₉	semidirect
333. C₂×C₈	C₂×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#533	2
Q₈×M₁₆×C₁₉	2
C₁₉×#2962	2
C₁₉×#2961	2
C₁₉×#2960	2
C₁₉×#2905	2
C₂×C₁₉×#423	2
C₁₉×#2873	2
C₂×C₄×M₁₆×C₁₉	2
#60192	19

Subgroups — C19×#60192 #18066151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60192 #18066151