Subgroups — C₁₉×#60277 #18066236

Order 4864.

2042 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2989	C₂	1	8	yes	maximal, complemented
3	C₁₉×#2983	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2975	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2973	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2965	C₂	1	8	yes	maximal, complemented
7	C₁₉×#2920	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₉×#431	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
10	C₄×#41×C₁₉	C₄	1	4	yes	—
11	C₄×#41×C₁₉	C₄	1	4	yes	—
12	C₄×#41×C₁₉	C₂²	1	4	yes	—
13	C₄×#41×C₁₉	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₄	1	2	yes	—
21	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
24	C₁₉×#446	C₂²	1	16	yes	complemented
25	C₁₉×#436	C₂²	1	16	yes	complemented
26	C₁₉×#435	C₂²	1	32	yes	complemented
27	C₁₉×#432	C₂²	1	8	yes	—
28	C₁₉×#432	C₂²	1	8	yes	complemented
29	C₁₉×#431	C₂²	1	4	yes	—
30	C₁₉×#431	C₂²	1	4	yes	—
31	C₁₉×#431	C₂²	1	4	yes	complemented
32	C₁₉×#431	C₂²	1	4	yes	complemented
33	C₁₉×#431	C₂²	1	8	yes	complemented
34	C₁₉×#423	C₂²	1	8	yes	complemented
35	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
36	C₁₉×#407	C₂²	1	8	yes	—
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₄×M₁₆×C₁₉	C₂²	1	8	yes	complemented
39	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	complemented
40	C₂×#41×C₁₉	—	2	8	no	—
41	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₁₉	C₂³	1	16	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
54	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
56	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
58	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
59	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
60	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
61	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
62	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
63	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₁₉	C₂³	1	8	yes	—
65	C₄×D₄×C₁₉	C₂³	1	4	yes	—
66	C₁₉×#117	C₂×C₄	1	8	yes	—
67	C₁₉×#117	C₂×C₄	1	8	yes	—
68	C₁₉×#117	C₂×C₄	1	4	yes	—
69	C₁₉×#117	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
82	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	16	yes	—
95	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
96	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
97	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	—
98	C₁₉×#97	C₂³	1	16	yes	—
99	C₄×C₈×C₁₉	C₂³	1	8	yes	—
100	C₄×C₈×C₁₉	C₂³	1	8	yes	—
101	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	#41×C₁₉	—	2	16	no	—
104	#41×C₁₉	—	2	16	no	—
105	C₂×Q₈×C₁₉	—	2	4	no	—
106	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
110	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	—	2	8	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	M₁₆	1	8	yes	complemented
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
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	2	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
138	M₁₆×C₁₉	—	4	16	no	—
139	C₂×C₈×C₁₉	—	4	8	no	—
140	C₂×C₈×C₁₉	C₂⁴	1	16	yes	—
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
144	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
146	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
147	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
148	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
154	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
155	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
157	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
158	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
159	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₄²×C₁₉	C₂⁴	1	2	yes	—
162	C₄²×C₁₉	C₂⁴	1	4	yes	—
163	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
164	#60277	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
171	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
172	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
173	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	8	no	—
175	D₄×C₁₉	—	2	16	no	—
176	D₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	8	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
195	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
196	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	—
197	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	—
198	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
202	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
204	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
205	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
210	C₈×C₁₉	—	2	16	no	—
211	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
212	#2989	C₂×C₁₉	1	8	yes	complemented
213	#2983	C₂×C₁₉	1	2	yes	complemented
214	#2975	C₂×C₁₉	1	2	yes	complemented
215	#2973	C₂×C₁₉	1	4	yes	complemented
216	#2965	C₂×C₁₉	1	8	yes	complemented
217	#2920	C₂×C₁₉	1	4	yes	complemented
218	C₂×#431	C₂×C₁₉	1	2	yes	complemented
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	—	2	4	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	8	no	—
228	C₂²×C₁₉	C₂²×M₁₆	1	2	yes	—
229	C₂²×C₁₉	C₂²×M₁₆	1	4	yes	—
230	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	2	no	—
233	C₄×C₁₉	—	2	4	no	—
234	C₄×C₁₉	—	2	4	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	2	4	no	—
238	C₄×C₁₉	C₂²×M₁₆	1	2	yes	—
239	C₄×C₁₉	C₂²×M₁₆	1	2	yes	—
240	C₄×C₁₉	C₂²×M₁₆	1	4	yes	—
241	C₄×C₁₉	#568	1	2	yes	—
242	C₄×C₁₉	#585	1	2	yes	—
243	C₂²×#41	C₄×C₁₉	1	1	yes	characteristic
244	C₄×#41	C₄×C₁₉	1	4	yes	—
245	C₄×#41	C₄×C₁₉	1	4	yes	—
246	C₄×#41	C₂²×C₁₉	1	4	yes	—
247	C₄×#41	C₂²×C₁₉	1	4	yes	—
248	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
251	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
253	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#117	C₄×C₁₉	1	2	yes	—
255	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
257	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
258	#446	C₂²×C₁₉	1	16	yes	complemented
259	#436	C₂²×C₁₉	1	16	yes	complemented
260	#435	C₂²×C₁₉	1	32	yes	complemented
261	#432	C₂²×C₁₉	1	8	yes	—
262	#432	C₂²×C₁₉	1	8	yes	complemented
263	#431	C₂²×C₁₉	1	4	yes	—
264	#431	C₂²×C₁₉	1	4	yes	—
265	#431	C₂²×C₁₉	1	4	yes	complemented
266	#431	C₂²×C₁₉	1	4	yes	complemented
267	#431	C₂²×C₁₉	1	8	yes	complemented
268	#423	C₂²×C₁₉	1	8	yes	complemented
269	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
270	#407	C₂²×C₁₉	1	8	yes	—
271	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
272	C₄×M₁₆	C₂²×C₁₉	1	8	yes	complemented
273	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	complemented
274	C₂×C₁₉	—	2	2	no	—
275	C₂×C₁₉	—	2	4	no	—
276	C₂×C₁₉	—	4	4	no	—
277	C₂×C₁₉	#3428	1	1	yes	characteristic
278	C₂×C₁₉	C₂³×M₁₆	1	1	yes	characteristic
279	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
280	C₂×#41	—	2	8	no	—
281	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
282	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
283	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
285	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
287	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
288	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×M₁₆	C₂³×C₁₉	1	16	yes	—
293	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
294	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
295	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
296	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
297	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
298	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
299	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
300	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
301	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
302	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
303	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
304	C₄×D₄	C₂³×C₁₉	1	8	yes	—
305	C₄×D₄	C₂³×C₁₉	1	4	yes	—
306	#117	C₂×C₄×C₁₉	1	8	yes	—
307	#117	C₂×C₄×C₁₉	1	8	yes	—
308	#117	C₂×C₄×C₁₉	1	4	yes	—
309	#117	C₂×C₄×C₁₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
317	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
318	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
319	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
320	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
322	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
323	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
324	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
327	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
329	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
333	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
334	C₄⋊C₈	C₂³×C₁₉	1	16	yes	—
335	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
336	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	—
338	#97	C₂³×C₁₉	1	16	yes	—
339	C₄×C₈	C₂³×C₁₉	1	8	yes	—
340	C₄×C₈	C₂³×C₁₉	1	8	yes	—
341	C₁₉	#60277	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
343	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
344	#41	—	2	16	no	—
345	#41	—	2	16	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
351	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	M₁₆×C₁₉	1	8	yes	complemented
358	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
367	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
379	M₁₆	—	4	16	no	—
380	C₂×C₈	—	4	8	no	—
381	C₂×C₈	C₂⁴×C₁₉	1	16	yes	—
382	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
383	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
384	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
385	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
386	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
387	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
388	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
389	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
390	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
392	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
393	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
394	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
395	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
396	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
397	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
398	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
399	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
400	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
401	C₄²	C₂⁴×C₁₉	1	2	yes	—
402	C₄²	C₂⁴×C₁₉	1	4	yes	—
403	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
404	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
405	C₂³	—	2	4	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
411	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
412	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
413	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
414	Q₈	—	2	8	no	—
415	D₄	—	2	16	no	—
416	D₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
435	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
436	C₂×C₄	C₂×M₁₆×C₁₉	1	8	yes	—
437	C₂×C₄	C₂×M₁₆×C₁₉	1	8	yes	—
438	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
441	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
442	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
444	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
445	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
450	C₈	—	2	16	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	8	no	—
460	C₂²	C₂²×M₁₆×C₁₉	1	2	yes	—
461	C₂²	C₂²×M₁₆×C₁₉	1	4	yes	—
462	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	C₂²×M₁₆×C₁₉	1	2	yes	—
471	C₄	C₂²×M₁₆×C₁₉	1	2	yes	—
472	C₄	C₂²×M₁₆×C₁₉	1	4	yes	—
473	C₄	C₁₉×#568	1	2	yes	—
474	C₄	C₁₉×#585	1	2	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	2	4	no	—
477	C₂	—	4	4	no	—
478	C₂	C₁₉×#3428	1	1	yes	characteristic
479	C₂	C₂³×M₁₆×C₁₉	1	1	yes	characteristic
480	C₂	C₂×C₁₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₂²×#41×C₁₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2989	C₂	semidirect
3. C₁₉×#2983	C₂	semidirect
4. C₁₉×#2975	C₂	semidirect
5. C₁₉×#2973	C₂	semidirect
6. C₁₉×#2965	C₂	semidirect
7. C₁₉×#2920	C₂	semidirect
8. C₂×C₁₉×#431	C₂	semidirect
24. C₁₉×#446	C₂²	semidirect
25. C₁₉×#436	C₂²	semidirect
26. C₁₉×#435	C₂²	semidirect
28. C₁₉×#432	C₂²	semidirect
31. C₁₉×#431	C₂²	semidirect
32. C₁₉×#431	C₂²	semidirect
33. C₁₉×#431	C₂²	semidirect
34. C₁₉×#423	C₂²	semidirect
35. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
38. C₄×M₁₆×C₁₉	C₂²	semidirect
39. C₂×C₄×C₈×C₁₉	C₂²	semidirect
116. C₂²×C₄×C₁₉	M₁₆	semidirect
164. #60277	C₁₉	direct (N × H)
212. #2989	C₂×C₁₉	semidirect
213. #2983	C₂×C₁₉	semidirect
214. #2975	C₂×C₁₉	semidirect
215. #2973	C₂×C₁₉	semidirect
216. #2965	C₂×C₁₉	semidirect
217. #2920	C₂×C₁₉	semidirect
218. C₂×#431	C₂×C₁₉	semidirect
258. #446	C₂²×C₁₉	semidirect
259. #436	C₂²×C₁₉	semidirect
260. #435	C₂²×C₁₉	semidirect
262. #432	C₂²×C₁₉	semidirect
265. #431	C₂²×C₁₉	semidirect
266. #431	C₂²×C₁₉	semidirect
267. #431	C₂²×C₁₉	semidirect
268. #423	C₂²×C₁₉	semidirect
269. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
272. C₄×M₁₆	C₂²×C₁₉	semidirect
273. C₂×C₄×C₈	C₂²×C₁₉	semidirect
341. C₁₉	#60277	direct (N × H)
357. C₂²×C₄	M₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₁₉×#2989	2
C₁₉×#2983	2
C₁₉×#2975	2
C₁₉×#2973	2
C₁₉×#2965	2
C₁₉×#2920	2
C₂×C₁₉×#431	2
#60277	19

Subgroups — C19×#60277 #18066236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60277 #18066236