Subgroups — C₁₉×#60128 #18066087

Order 4864.

2124 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#2925	C₂	1	6	yes	maximal, complemented
3	C₁₉×#2924	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2923	C₂	1	6	yes	maximal, complemented
5	C₁₉×#2920	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₉×#432	C₂	1	3	yes	maximal, complemented
7	C₁₉×#2906	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2880	C₂	1	2	yes	maximal
9	C₁₉×#2875	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	C₂²	1	4	yes	—
12	C₄×#41×C₁₉	C₄	1	1	yes	characteristic
13	C₄×#41×C₁₉	C₄	1	3	yes	—
14	C₄×#41×C₁₉	C₄	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₄	1	3	yes	—
16	C₄×#41×C₁₉	C₂²	1	3	yes	—
17	C₄×#41×C₁₉	C₂²	1	3	yes	—
18	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₄	1	3	yes	—
23	C₂×C₄×D₄×C₁₉	C₄	1	3	yes	—
24	C₂×C₁₉×#117	C₂²	1	3	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
26	C₁₉×#433	C₂²	1	24	yes	complemented
27	C₁₉×#432	C₂²	1	1	yes	characteristic
28	C₁₉×#432	C₂²	1	3	yes	—
29	C₁₉×#432	C₂²	1	6	yes	—
30	C₁₉×#432	C₂²	1	6	yes	complemented
31	C₁₉×#432	C₂²	1	6	yes	complemented
32	C₁₉×#432	C₂²	1	6	yes	complemented
33	C₁₉×#431	C₂²	1	6	yes	—
34	C₁₉×#431	C₂²	1	6	yes	complemented
35	C₁₉×#424	C₂²	1	12	yes	complemented
36	C₁₉×#423	C₂²	1	6	yes	complemented
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	6	yes	complemented
38	C₁₉×#408	C₂²	1	12	yes	—
39	C₁₉×#407	C₂²	1	6	yes	—
40	C₂×C₁₉×C₂²⋊C₈	C₂²	1	6	yes	—
41	C₁₉×#405	C₂²	1	12	yes	complemented
42	C₄×M₁₆×C₁₉	C₂²	1	6	yes	complemented
43	C₂×C₁₉×#97	C₂²	1	6	yes	complemented
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×#41×C₁₉	C₂×C₄	1	3	yes	—
47	C₂×#41×C₁₉	C₂³	1	3	yes	—
48	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
51	C₂³×C₄×C₁₉	C₂×C₄	1	3	yes	—
52	C₂³×C₄×C₁₉	C₂×C₄	1	3	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
54	C₁₉×#131	—	2	16	no	—
55	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	12	yes	—
57	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
58	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
59	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
60	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
66	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
67	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
68	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
69	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
71	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
72	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
73	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
74	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
75	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
76	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
77	C₁₉×#117	C₂×C₄	1	3	yes	—
78	C₁₉×#117	C₂×C₄	1	3	yes	—
79	C₁₉×#117	C₂×C₄	1	6	yes	—
80	C₁₉×#117	C₂³	1	3	yes	—
81	C₁₉×#117	C₂³	1	3	yes	—
82	C₁₉×#117	C₂³	1	6	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
86	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
87	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
88	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
89	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
90	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
91	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
98	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
100	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
101	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
102	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
103	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
104	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
106	C₁₉×#97	C₂³	1	2	yes	—
107	C₁₉×#97	C₂³	1	6	yes	—
108	C₁₉×#97	C₂³	1	12	yes	—
109	C₄×C₈×C₁₉	C₂³	1	12	yes	—
110	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	2	12	no	—
113	#41×C₁₉	—	2	12	no	—
114	#41×C₁₉	#41	1	8	yes	—
115	C₂×Q₈×C₁₉	—	2	4	no	—
116	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
117	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₉	—	2	12	no	—
119	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
121	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
122	C₂²×C₄×C₁₉	—	2	12	no	—
123	C₂²×C₄×C₁₉	—	4	6	no	—
124	C₂²×C₄×C₁₉	—	4	6	no	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
132	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
143	M₁₆×C₁₉	—	2	24	no	—
144	C₂×C₈×C₁₉	—	2	24	no	—
145	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
146	C₂×C₈×C₁₉	C₂⁴	1	12	yes	—
147	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
148	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
153	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
154	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
155	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
156	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
157	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
160	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
161	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
162	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
163	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
164	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
165	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
166	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
167	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
168	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
169	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₄²×C₁₉	C₂⁴	1	3	yes	—
172	C₄²×C₁₉	C₂⁴	1	3	yes	—
173	#60128	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	6	no	—
175	C₂³×C₁₉	—	2	6	no	—
176	C₂³×C₁₉	—	4	3	no	—
177	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
178	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
179	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	6	no	—
181	Q₈×C₁₉	#117	1	4	yes	—
182	D₄×C₁₉	—	2	12	no	—
183	D₄×C₁₉	—	2	6	no	—
184	D₄×C₁₉	#117	1	12	yes	—
185	C₂×C₄×C₁₉	—	2	6	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	6	no	—
188	C₂×C₄×C₁₉	—	2	6	no	—
189	C₂×C₄×C₁₉	—	2	6	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	6	no	—
192	C₂×C₄×C₁₉	—	2	6	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	6	no	—
195	C₂×C₄×C₁₉	—	4	3	no	—
196	C₂×C₄×C₁₉	—	4	3	no	—
197	C₂×C₄×C₁₉	—	4	3	no	—
198	C₂×C₄×C₁₉	—	4	3	no	—
199	C₂×C₄×C₁₉	—	4	3	no	—
200	C₂×C₄×C₁₉	—	4	3	no	—
201	C₂×C₄×C₁₉	—	4	3	no	—
202	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
207	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
209	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
211	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
212	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
214	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
215	C₈×C₁₉	—	2	4	no	—
216	C₈×C₁₉	—	2	12	no	—
217	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
218	#2925	C₂×C₁₉	1	6	yes	complemented
219	#2924	C₂×C₁₉	1	6	yes	complemented
220	#2923	C₂×C₁₉	1	6	yes	complemented
221	#2920	C₂×C₁₉	1	3	yes	complemented
222	C₂×#432	C₂×C₁₉	1	3	yes	complemented
223	#2906	C₂×C₁₉	1	2	yes	complemented
224	#2880	C₂×C₁₉	1	2	yes	—
225	#2875	C₂×C₁₉	1	2	yes	complemented
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	3	no	—
229	C₂²×C₁₉	—	2	3	no	—
230	C₂²×C₁₉	—	2	3	no	—
231	C₂²×C₁₉	—	2	3	no	—
232	C₂²×C₁₉	—	2	3	no	—
233	C₂²×C₁₉	—	4	12	no	—
234	C₂²×C₁₉	C₂×#117	1	6	yes	—
235	C₂²×C₁₉	#568	1	2	yes	—
236	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	3	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	3	no	—
243	C₄×C₁₉	—	2	3	no	—
244	C₄×C₁₉	—	2	3	no	—
245	C₄×C₁₉	—	2	3	no	—
246	C₄×C₁₉	C₂×#117	1	6	yes	—
247	C₄×C₁₉	#568	1	2	yes	—
248	C₄×C₁₉	C₂²×#41	1	2	yes	—
249	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#131	C₂²×C₁₉	1	4	yes	—
251	C₄×#41	C₄×C₁₉	1	1	yes	characteristic
252	C₄×#41	C₄×C₁₉	1	3	yes	—
253	C₄×#41	C₄×C₁₉	1	1	yes	characteristic
254	C₄×#41	C₄×C₁₉	1	3	yes	—
255	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
256	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
257	C₄×#41	C₂²×C₁₉	1	3	yes	—
258	C₄×#41	C₂²×C₁₉	1	3	yes	—
259	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄×D₄	C₄×C₁₉	1	3	yes	—
262	C₂×C₄×D₄	C₄×C₁₉	1	3	yes	—
263	C₂×#117	C₂²×C₁₉	1	3	yes	—
264	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
265	#433	C₂²×C₁₉	1	24	yes	complemented
266	#432	C₂²×C₁₉	1	1	yes	characteristic
267	#432	C₂²×C₁₉	1	3	yes	—
268	#432	C₂²×C₁₉	1	6	yes	—
269	#432	C₂²×C₁₉	1	6	yes	complemented
270	#432	C₂²×C₁₉	1	6	yes	complemented
271	#432	C₂²×C₁₉	1	6	yes	complemented
272	#431	C₂²×C₁₉	1	6	yes	—
273	#431	C₂²×C₁₉	1	6	yes	complemented
274	#424	C₂²×C₁₉	1	12	yes	complemented
275	#423	C₂²×C₁₉	1	6	yes	complemented
276	C₂×C₄⋊C₈	C₂²×C₁₉	1	6	yes	complemented
277	#408	C₂²×C₁₉	1	12	yes	—
278	#407	C₂²×C₁₉	1	6	yes	—
279	C₂×C₂²⋊C₈	C₂²×C₁₉	1	6	yes	—
280	#405	C₂²×C₁₉	1	12	yes	complemented
281	C₄×M₁₆	C₂²×C₁₉	1	6	yes	complemented
282	C₂×#97	C₂²×C₁₉	1	6	yes	complemented
283	C₂×C₁₉	—	2	2	no	—
284	C₂×C₁₉	—	2	6	no	—
285	C₂×C₁₉	—	4	3	no	—
286	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
287	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
288	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
289	C₂×#41	—	2	8	no	—
290	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
291	C₂×#41	C₂×C₄×C₁₉	1	3	yes	—
292	C₂×#41	C₂³×C₁₉	1	3	yes	—
293	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
296	C₂³×C₄	C₂×C₄×C₁₉	1	3	yes	—
297	C₂³×C₄	C₂×C₄×C₁₉	1	3	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
299	#131	—	2	16	no	—
300	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
301	C₂²×C₈	C₂³×C₁₉	1	12	yes	—
302	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
303	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
304	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
305	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
306	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
307	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
308	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
311	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
312	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
313	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
314	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
315	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
316	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
317	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
318	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
319	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
320	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
321	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
322	#117	C₂×C₄×C₁₉	1	3	yes	—
323	#117	C₂×C₄×C₁₉	1	3	yes	—
324	#117	C₂×C₄×C₁₉	1	6	yes	—
325	#117	C₂³×C₁₉	1	3	yes	—
326	#117	C₂³×C₁₉	1	3	yes	—
327	#117	C₂³×C₁₉	1	6	yes	—
328	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
329	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
331	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
332	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
333	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
334	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
335	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
336	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
339	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
340	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
341	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
342	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
343	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
345	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
346	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
347	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
348	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
349	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
350	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
351	#97	C₂³×C₁₉	1	2	yes	—
352	#97	C₂³×C₁₉	1	6	yes	—
353	#97	C₂³×C₁₉	1	12	yes	—
354	C₄×C₈	C₂³×C₁₉	1	12	yes	—
355	C₁₉	#60128	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
357	#41	—	2	4	no	—
358	#41	—	2	12	no	—
359	#41	—	2	12	no	—
360	#41	#41×C₁₉	1	8	yes	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
363	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
364	C₂×D₄	—	2	12	no	—
365	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
366	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
367	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
368	C₂²×C₄	—	2	12	no	—
369	C₂²×C₄	—	4	6	no	—
370	C₂²×C₄	—	4	6	no	—
371	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
374	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
381	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
382	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
383	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
386	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
388	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
389	M₁₆	—	2	24	no	—
390	C₂×C₈	—	2	24	no	—
391	C₂×C₈	C₂⁴×C₁₉	1	12	yes	—
392	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
393	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
394	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
395	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
396	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
397	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
398	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
399	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
400	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
401	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
402	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
403	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
404	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
405	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
406	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
407	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
408	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
409	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
410	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
411	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
412	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
413	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
414	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
415	C₄²	C₂⁴×C₁₉	1	3	yes	—
416	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
418	C₄²	C₂⁴×C₁₉	1	3	yes	—
419	C₂³	—	2	6	no	—
420	C₂³	—	2	6	no	—
421	C₂³	—	4	3	no	—
422	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
423	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
424	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
425	Q₈	—	2	6	no	—
426	Q₈	C₁₉×#117	1	4	yes	—
427	D₄	—	2	12	no	—
428	D₄	—	2	6	no	—
429	D₄	C₁₉×#117	1	12	yes	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	6	no	—
433	C₂×C₄	—	2	6	no	—
434	C₂×C₄	—	2	6	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	6	no	—
437	C₂×C₄	—	2	6	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	6	no	—
440	C₂×C₄	—	4	3	no	—
441	C₂×C₄	—	4	3	no	—
442	C₂×C₄	—	4	3	no	—
443	C₂×C₄	—	4	3	no	—
444	C₂×C₄	—	4	3	no	—
445	C₂×C₄	—	4	3	no	—
446	C₂×C₄	—	4	3	no	—
447	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
452	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
453	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
454	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
455	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
456	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
457	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
459	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	2	12	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	3	no	—
464	C₂²	—	2	3	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	3	no	—
467	C₂²	—	2	3	no	—
468	C₂²	—	2	3	no	—
469	C₂²	—	4	12	no	—
470	C₂²	C₂×C₁₉×#117	1	6	yes	—
471	C₂²	C₁₉×#568	1	2	yes	—
472	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	3	no	—
477	C₄	—	2	3	no	—
478	C₄	—	2	3	no	—
479	C₄	—	2	3	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	3	no	—
482	C₄	C₂×C₁₉×#117	1	6	yes	—
483	C₄	C₁₉×#568	1	2	yes	—
484	C₄	C₂²×#41×C₁₉	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	2	6	no	—
487	C₂	—	4	3	no	—
488	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
489	C₂	C₂×C₁₉×#568	1	1	yes	characteristic
490	C₂	C₂×C₁₉×#568	1	1	yes	characteristic

	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	C₂²×#41×C₁₉	C₂²
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. C₁₉×#2925	C₂	semidirect
3. C₁₉×#2924	C₂	semidirect
4. C₁₉×#2923	C₂	semidirect
5. C₁₉×#2920	C₂	semidirect
6. C₂×C₁₉×#432	C₂	semidirect
7. C₁₉×#2906	C₂	semidirect
9. C₁₉×#2875	C₂	semidirect
26. C₁₉×#433	C₂²	semidirect
30. C₁₉×#432	C₂²	semidirect
31. C₁₉×#432	C₂²	semidirect
32. C₁₉×#432	C₂²	semidirect
34. C₁₉×#431	C₂²	semidirect
35. C₁₉×#424	C₂²	semidirect
36. C₁₉×#423	C₂²	semidirect
37. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
41. C₁₉×#405	C₂²	semidirect
42. C₄×M₁₆×C₁₉	C₂²	semidirect
43. C₂×C₁₉×#97	C₂²	semidirect
173. #60128	C₁₉	direct (N × H)
218. #2925	C₂×C₁₉	semidirect
219. #2924	C₂×C₁₉	semidirect
220. #2923	C₂×C₁₉	semidirect
221. #2920	C₂×C₁₉	semidirect
222. C₂×#432	C₂×C₁₉	semidirect
223. #2906	C₂×C₁₉	semidirect
225. #2875	C₂×C₁₉	semidirect
265. #433	C₂²×C₁₉	semidirect
269. #432	C₂²×C₁₉	semidirect
270. #432	C₂²×C₁₉	semidirect
271. #432	C₂²×C₁₉	semidirect
273. #431	C₂²×C₁₉	semidirect
274. #424	C₂²×C₁₉	semidirect
275. #423	C₂²×C₁₉	semidirect
276. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
280. #405	C₂²×C₁₉	semidirect
281. C₄×M₁₆	C₂²×C₁₉	semidirect
282. C₂×#97	C₂²×C₁₉	semidirect
355. C₁₉	#60128	direct (N × H)

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×#2925	2
C₁₉×#2924	2
C₁₉×#2923	2
C₁₉×#2920	2
C₂×C₁₉×#432	2
C₁₉×#2906	2
C₁₉×#2880	2
C₁₉×#2875	2
#60128	19

Subgroups — C19×#60128 #18066087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60128 #18066087