Subgroups — C₁₉×#60129 #18066088

Order 4864.

2038 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3428	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	3	yes	maximal, complemented
5	C₁₉×#2922	C₂	1	3	yes	maximal, complemented
6	C₁₉×#2921	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₉×#433	C₂	1	3	yes	maximal, complemented
8	C₁₉×#2906	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2880	C₂	1	2	yes	maximal
10	C₁₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#131	C₂²	1	2	yes	—
14	C₂×C₁₉×#131	C₂²	1	2	yes	—
15	C₁₉×#520	C₄	1	6	yes	—
16	C₁₉×#520	C₄	1	2	yes	—
17	C₁₉×#519	C₄	1	2	yes	—
18	C₁₉×#518	C₄	1	6	yes	—
19	C₄×#41×C₁₉	C₂²	1	3	yes	—
20	C₄×#41×C₁₉	C₂²	1	3	yes	—
21	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	3	yes	—
24	C₂×C₁₉×#117	C₂²	1	3	yes	—
25	C₁₉×#433	C₂²	1	1	yes	characteristic
26	C₁₉×#433	C₂²	1	3	yes	—
27	C₁₉×#433	C₂²	1	6	yes	—
28	C₁₉×#433	C₂²	1	6	yes	—
29	C₁₉×#433	C₂²	1	3	yes	complemented
30	C₁₉×#433	C₂²	1	3	yes	complemented
31	C₁₉×#433	C₂²	1	6	yes	complemented
32	C₁₉×#433	C₂²	1	6	yes	complemented
33	C₁₉×#433	C₂²	1	6	yes	complemented
34	C₁₉×#432	C₂²	1	12	yes	complemented
35	C₁₉×#431	C₂²	1	12	yes	complemented
36	C₁₉×#424	C₂²	1	6	yes	complemented
37	C₁₉×#424	C₂²	1	6	yes	complemented
38	C₁₉×#423	C₂²	1	6	yes	complemented
39	C₂×C₁₉×C₄⋊C₈	C₂²	1	6	yes	complemented
40	C₁₉×#408	C₂²	1	6	yes	—
41	C₁₉×#408	C₂²	1	6	yes	—
42	C₁₉×#407	C₂²	1	6	yes	—
43	C₂×C₁₉×C₂²⋊C₈	C₂²	1	6	yes	—
44	C₁₉×#405	C₂²	1	6	yes	complemented
45	C₁₉×#405	C₂²	1	6	yes	complemented
46	C₄×M₁₆×C₁₉	C₂²	1	3	yes	complemented
47	C₄×M₁₆×C₁₉	C₂²	1	3	yes	complemented
48	C₂×C₁₉×#97	C₂²	1	3	yes	complemented
49	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
50	C₂×#41×C₁₉	—	2	8	no	—
51	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×#41×C₁₉	C₂×C₄	1	3	yes	—
53	C₂×#41×C₁₉	C₂³	1	3	yes	—
54	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
58	C₁₉×#131	—	2	8	no	—
59	C₁₉×#131	—	2	8	no	—
60	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
61	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
64	C₄×Q₈×C₁₉	C₂×C₄	1	6	yes	—
65	C₄×Q₈×C₁₉	C₂×C₄	1	6	yes	—
66	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₁₉	C₂×C₄	1	12	yes	—
69	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	12	yes	—
71	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
72	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
73	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
74	C₁₉×#117	C₂×C₄	1	6	yes	—
75	C₁₉×#117	C₂×C₄	1	6	yes	—
76	C₁₉×#117	C₂×C₄	1	6	yes	—
77	C₁₉×#117	C₂×C₄	1	6	yes	—
78	C₁₉×#117	C₂³	1	3	yes	—
79	C₁₉×#117	C₂³	1	3	yes	—
80	C₁₉×#117	C₂³	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	3	yes	—
82	C₁₉×#117	C₂³	1	3	yes	—
83	C₁₉×#117	C₂³	1	3	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
96	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
97	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
98	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
99	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
100	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
101	C₁₉×#97	C₂³	1	1	yes	characteristic
102	C₁₉×#97	C₂³	1	3	yes	—
103	C₁₉×#97	C₂³	1	6	yes	—
104	C₁₉×#97	C₂³	1	6	yes	—
105	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₁₉	C₂³	1	3	yes	—
107	C₄×C₈×C₁₉	C₂³	1	6	yes	—
108	C₄×C₈×C₁₉	C₂³	1	6	yes	—
109	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
110	#41×C₁₉	—	2	4	no	—
111	#41×C₁₉	—	2	12	no	—
112	#41×C₁₉	—	2	12	no	—
113	#41×C₁₉	#41	1	8	yes	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
116	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₁₉	—	2	12	no	—
118	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
119	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
121	C₂²×C₄×C₁₉	—	2	12	no	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
125	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
131	M₁₆×C₁₉	—	2	12	no	—
132	M₁₆×C₁₉	—	2	12	no	—
133	C₂×C₈×C₁₉	—	2	12	no	—
134	C₂×C₈×C₁₉	—	2	12	no	—
135	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
136	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
137	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
138	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
144	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
145	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
147	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
148	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
149	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
150	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
151	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
153	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
154	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₄²×C₁₉	C₂⁴	1	3	yes	—
156	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₄²×C₁₉	C₂⁴	1	3	yes	—
158	#60129	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	6	no	—
160	C₂³×C₁₉	—	4	6	no	—
161	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
163	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
164	Q₈×C₁₉	—	2	6	no	—
165	Q₈×C₁₉	#117	1	4	yes	—
166	D₄×C₁₉	—	2	12	no	—
167	D₄×C₁₉	—	2	6	no	—
168	D₄×C₁₉	#117	1	12	yes	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	2	6	no	—
171	C₂×C₄×C₁₉	—	2	6	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	6	no	—
174	C₂×C₄×C₁₉	—	4	6	no	—
175	C₂×C₄×C₁₉	—	4	6	no	—
176	C₂×C₄×C₁₉	—	4	12	no	—
177	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
178	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
181	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
184	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
185	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
186	C₈×C₁₉	—	2	2	no	—
187	C₈×C₁₉	—	2	2	no	—
188	C₈×C₁₉	—	2	6	no	—
189	C₈×C₁₉	—	2	6	no	—
190	#3428	C₂×C₁₉	1	1	yes	characteristic
191	#2925	C₂×C₁₉	1	6	yes	complemented
192	#2924	C₂×C₁₉	1	6	yes	complemented
193	#2923	C₂×C₁₉	1	3	yes	complemented
194	#2922	C₂×C₁₉	1	3	yes	complemented
195	#2921	C₂×C₁₉	1	3	yes	complemented
196	C₂×#433	C₂×C₁₉	1	3	yes	complemented
197	#2906	C₂×C₁₉	1	2	yes	complemented
198	#2880	C₂×C₁₉	1	2	yes	—
199	#2875	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₄×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂²×C₁₉	—	2	6	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	3	no	—
204	C₂²×C₁₉	—	2	6	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	8	6	no	—
207	C₂²×C₁₉	C₂×#117	1	6	yes	—
208	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	3	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	6	no	—
214	C₄×C₁₉	—	2	6	no	—
215	C₄×C₁₉	C₂×#117	1	6	yes	—
216	C₄×C₁₉	C₂²×#41	1	2	yes	—
217	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×#131	C₂²×C₁₉	1	2	yes	—
219	C₂×#131	C₂²×C₁₉	1	2	yes	—
220	#520	C₄×C₁₉	1	6	yes	—
221	#520	C₄×C₁₉	1	2	yes	—
222	#519	C₄×C₁₉	1	2	yes	—
223	#518	C₄×C₁₉	1	6	yes	—
224	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
225	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
226	C₄×#41	C₂²×C₁₉	1	3	yes	—
227	C₄×#41	C₂²×C₁₉	1	3	yes	—
228	C₂×#117	C₂²×C₁₉	1	3	yes	—
229	C₂×#117	C₂²×C₁₉	1	3	yes	—
230	#433	C₂²×C₁₉	1	1	yes	characteristic
231	#433	C₂²×C₁₉	1	3	yes	—
232	#433	C₂²×C₁₉	1	6	yes	—
233	#433	C₂²×C₁₉	1	6	yes	—
234	#433	C₂²×C₁₉	1	3	yes	complemented
235	#433	C₂²×C₁₉	1	3	yes	complemented
236	#433	C₂²×C₁₉	1	6	yes	complemented
237	#433	C₂²×C₁₉	1	6	yes	complemented
238	#433	C₂²×C₁₉	1	6	yes	complemented
239	#432	C₂²×C₁₉	1	12	yes	complemented
240	#431	C₂²×C₁₉	1	12	yes	complemented
241	#424	C₂²×C₁₉	1	6	yes	complemented
242	#424	C₂²×C₁₉	1	6	yes	complemented
243	#423	C₂²×C₁₉	1	6	yes	complemented
244	C₂×C₄⋊C₈	C₂²×C₁₉	1	6	yes	complemented
245	#408	C₂²×C₁₉	1	6	yes	—
246	#408	C₂²×C₁₉	1	6	yes	—
247	#407	C₂²×C₁₉	1	6	yes	—
248	C₂×C₂²⋊C₈	C₂²×C₁₉	1	6	yes	—
249	#405	C₂²×C₁₉	1	6	yes	complemented
250	#405	C₂²×C₁₉	1	6	yes	complemented
251	C₄×M₁₆	C₂²×C₁₉	1	3	yes	complemented
252	C₄×M₁₆	C₂²×C₁₉	1	3	yes	complemented
253	C₂×#97	C₂²×C₁₉	1	3	yes	complemented
254	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
255	C₂×C₁₉	—	2	6	no	—
256	C₂×C₁₉	—	4	3	no	—
257	C₂×C₁₉	—	4	1	no	—
258	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
259	C₂×C₁₉	#3573	1	2	yes	—
260	C₂×#41	—	2	8	no	—
261	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×#41	C₂×C₄×C₁₉	1	3	yes	—
263	C₂×#41	C₂³×C₁₉	1	3	yes	—
264	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
267	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
268	#131	—	2	8	no	—
269	#131	—	2	8	no	—
270	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
271	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
272	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
273	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
274	C₄×Q₈	C₂×C₄×C₁₉	1	6	yes	—
275	C₄×Q₈	C₂×C₄×C₁₉	1	6	yes	—
276	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
277	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
278	C₄×D₄	C₂×C₄×C₁₉	1	12	yes	—
279	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
280	C₄×D₄	C₂×C₄×C₁₉	1	12	yes	—
281	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
282	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
283	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
284	#117	C₂×C₄×C₁₉	1	6	yes	—
285	#117	C₂×C₄×C₁₉	1	6	yes	—
286	#117	C₂×C₄×C₁₉	1	6	yes	—
287	#117	C₂×C₄×C₁₉	1	6	yes	—
288	#117	C₂³×C₁₉	1	1	yes	characteristic
289	#117	C₂³×C₁₉	1	3	yes	—
290	#117	C₂³×C₁₉	1	3	yes	—
291	#117	C₂³×C₁₉	1	3	yes	—
292	#117	C₂³×C₁₉	1	3	yes	—
293	#117	C₂³×C₁₉	1	3	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
298	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
299	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
301	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
302	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
303	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
304	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
305	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
306	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
307	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
308	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
309	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
310	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
311	#97	C₂³×C₁₉	1	1	yes	characteristic
312	#97	C₂³×C₁₉	1	3	yes	—
313	#97	C₂³×C₁₉	1	6	yes	—
314	#97	C₂³×C₁₉	1	6	yes	—
315	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₁₉	1	3	yes	—
317	C₄×C₈	C₂³×C₁₉	1	6	yes	—
318	C₄×C₈	C₂³×C₁₉	1	6	yes	—
319	C₁₉	#60129	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
321	#41	—	2	4	no	—
322	#41	—	2	12	no	—
323	#41	—	2	12	no	—
324	#41	#41×C₁₉	1	8	yes	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
327	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
328	C₂×D₄	—	2	12	no	—
329	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
330	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
331	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
332	C₂²×C₄	—	2	12	no	—
333	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
339	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
342	M₁₆	—	2	12	no	—
343	M₁₆	—	2	12	no	—
344	C₂×C₈	—	2	12	no	—
345	C₂×C₈	—	2	12	no	—
346	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
347	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
348	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
349	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
350	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
351	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
352	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
353	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
354	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
355	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
356	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
357	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
358	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
359	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
360	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
361	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
362	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
363	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
364	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
365	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
366	C₄²	C₂⁴×C₁₉	1	3	yes	—
367	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₄²	C₂⁴×C₁₉	1	3	yes	—
369	C₂³	—	2	6	no	—
370	C₂³	—	4	6	no	—
371	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
372	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
373	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
374	Q₈	—	2	6	no	—
375	Q₈	C₁₉×#117	1	4	yes	—
376	D₄	—	2	12	no	—
377	D₄	—	2	6	no	—
378	D₄	C₁₉×#117	1	12	yes	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	2	6	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	4	6	no	—
385	C₂×C₄	—	4	6	no	—
386	C₂×C₄	—	4	12	no	—
387	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
388	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
389	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
390	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
391	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
394	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
395	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	6	no	—
399	C₈	—	2	6	no	—
400	C₂²	—	2	6	no	—
401	C₂²	—	2	6	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	3	no	—
405	C₂²	—	8	6	no	—
406	C₂²	C₂×C₁₉×#117	1	6	yes	—
407	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	6	no	—
411	C₄	—	2	6	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	3	no	—
414	C₄	C₂×C₁₉×#117	1	6	yes	—
415	C₄	C₂²×#41×C₁₉	1	2	yes	—
416	C₂	—	2	6	no	—
417	C₂	—	4	1	no	—
418	C₂	—	4	3	no	—
419	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
420	C₂	C₁₉×#3573	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	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×#2922	C₂	semidirect
6. C₁₉×#2921	C₂	semidirect
7. C₂×C₁₉×#433	C₂	semidirect
8. C₁₉×#2906	C₂	semidirect
10. C₁₉×#2875	C₂	semidirect
11. C₄×C₁₉×#131	C₂	semidirect
29. C₁₉×#433	C₂²	semidirect
30. C₁₉×#433	C₂²	semidirect
31. C₁₉×#433	C₂²	semidirect
32. C₁₉×#433	C₂²	semidirect
33. C₁₉×#433	C₂²	semidirect
34. C₁₉×#432	C₂²	semidirect
35. C₁₉×#431	C₂²	semidirect
36. C₁₉×#424	C₂²	semidirect
37. C₁₉×#424	C₂²	semidirect
38. C₁₉×#423	C₂²	semidirect
39. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
44. C₁₉×#405	C₂²	semidirect
45. C₁₉×#405	C₂²	semidirect
46. C₄×M₁₆×C₁₉	C₂²	semidirect
47. C₄×M₁₆×C₁₉	C₂²	semidirect
48. C₂×C₁₉×#97	C₂²	semidirect
49. C₂×C₄×C₈×C₁₉	C₂²	semidirect
158. #60129	C₁₉	direct (N × H)
191. #2925	C₂×C₁₉	semidirect
192. #2924	C₂×C₁₉	semidirect
193. #2923	C₂×C₁₉	semidirect
194. #2922	C₂×C₁₉	semidirect
195. #2921	C₂×C₁₉	semidirect
196. C₂×#433	C₂×C₁₉	semidirect
197. #2906	C₂×C₁₉	semidirect
199. #2875	C₂×C₁₉	semidirect
200. C₄×#131	C₂×C₁₉	semidirect
234. #433	C₂²×C₁₉	semidirect
235. #433	C₂²×C₁₉	semidirect
236. #433	C₂²×C₁₉	semidirect
237. #433	C₂²×C₁₉	semidirect
238. #433	C₂²×C₁₉	semidirect
239. #432	C₂²×C₁₉	semidirect
240. #431	C₂²×C₁₉	semidirect
241. #424	C₂²×C₁₉	semidirect
242. #424	C₂²×C₁₉	semidirect
243. #423	C₂²×C₁₉	semidirect
244. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
249. #405	C₂²×C₁₉	semidirect
250. #405	C₂²×C₁₉	semidirect
251. C₄×M₁₆	C₂²×C₁₉	semidirect
252. C₄×M₁₆	C₂²×C₁₉	semidirect
253. C₂×#97	C₂²×C₁₉	semidirect
254. C₂×C₄×C₈	C₂²×C₁₉	semidirect
319. C₁₉	#60129	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3428	2
C₁₉×#2925	2
C₁₉×#2924	2
C₁₉×#2923	2
C₁₉×#2922	2
C₁₉×#2921	2
C₂×C₁₉×#433	2
C₁₉×#2906	2
C₁₉×#2880	2
C₁₉×#2875	2
C₄×C₁₉×#131	2
#60129	19

Subgroups — C19×#60129 #18066088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60129 #18066088