Subgroups — C₁₉×#60304 #18066263

Order 4864.

1922 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3459	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2992	C₂	1	6	yes	maximal, complemented
3	C₁₉×#2976	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2973	C₂	1	3	yes	maximal, complemented
5	C₁₉×#2966	C₂	1	6	yes	maximal, complemented
6	C₁₉×#2929	C₂	1	6	yes	maximal, complemented
7	C₂×C₈×D₄×C₁₉	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	3	yes	complemented
11	C₁₉×#543	C₄	1	1	yes	characteristic
12	C₁₉×#539	C₄	1	6	yes	—
13	C₁₉×#538	C₄	1	6	yes	—
14	C₁₉×#534	C₄	1	3	yes	—
15	C₁₉×#529	C₂²	1	6	yes	—
16	C₁₉×#525	C₂²	1	6	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
18	C₁₉×#446	C₂²	1	6	yes	complemented
19	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
20	C₁₉×#436	C₂²	1	6	yes	complemented
21	C₁₉×#435	C₂²	1	12	yes	complemented
22	C₁₉×#435	C₂²	1	12	yes	complemented
23	C₁₉×#435	C₂²	1	12	yes	complemented
24	C₈×D₄×C₁₉	C₂²	1	12	yes	complemented
25	C₈×D₄×C₁₉	C₂²	1	12	yes	complemented
26	C₈×D₄×C₁₉	C₂²	1	6	yes	complemented
27	C₁₉×#433	C₂²	1	12	yes	complemented
28	C₁₉×#432	C₂²	1	6	yes	complemented
29	C₁₉×#424	C₂²	1	6	yes	complemented
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	complemented
31	C₁₉×#408	C₂²	1	6	yes	complemented
32	C₁₉×#407	C₂²	1	6	yes	complemented
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	—
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	3	yes	complemented
35	C₁₉×#405	C₂²	1	6	yes	complemented
36	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
37	C₂×#41×C₁₉	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
41	C₁₉×#131	—	4	4	no	—
42	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
43	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
44	C₂²×C₈×C₁₉	—	4	2	no	—
45	C₂²×C₈×C₁₉	—	4	6	no	—
46	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	6	yes	—
52	C₁₉×#126	C₂×C₄	1	12	yes	—
53	C₁₉×#125	C₂×C₄	1	6	yes	—
54	C₁₉×#124	C₂×C₄	1	6	yes	—
55	C₁₉×#123	C₂×C₄	1	12	yes	—
56	C₁₉×#123	C₂×C₄	1	12	yes	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
58	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
59	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
60	C₁₉×#121	C₂×C₄	1	6	yes	—
61	C₁₉×#121	C₂×C₄	1	6	yes	—
62	C₁₉×#121	C₂×C₄	1	6	yes	—
63	C₁₉×#120	C₂×C₄	1	12	yes	—
64	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
65	C₄×D₄×C₁₉	C₂×C₄	1	12	yes	—
66	C₄×D₄×C₁₉	C₂³	1	12	yes	—
67	C₄×D₄×C₁₉	C₂³	1	6	yes	—
68	C₁₉×#117	C₂³	1	6	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
73	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
74	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
75	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
76	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
77	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
78	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
79	C₁₉×#97	C₂³	1	12	yes	—
80	C₄×C₈×C₁₉	C₂³	1	6	yes	—
81	C₄×C₈×C₁₉	C₂³	1	6	yes	—
82	C₂⁴×C₁₉	C₂²×C₄	1	3	yes	—
83	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	#41×C₁₉	—	4	2	no	—
85	#41×C₁₉	—	4	2	no	—
86	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₉	—	2	12	no	—
89	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
90	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
91	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	3	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	3	no	—
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	C₂⁴	1	3	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
103	M₁₆×C₁₉	—	4	6	no	—
104	M₁₆×C₁₉	—	4	6	no	—
105	C₂×C₈×C₁₉	—	2	6	no	—
106	C₂×C₈×C₁₉	—	2	12	no	—
107	C₂×C₈×C₁₉	—	4	3	no	—
108	C₂×C₈×C₁₉	—	4	6	no	—
109	C₂×C₈×C₁₉	—	4	3	no	—
110	C₂×C₈×C₁₉	—	4	3	no	—
111	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
112	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
113	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
114	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
116	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
117	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
118	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
119	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
120	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
121	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
122	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
123	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
124	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
125	C₄²×C₁₉	C₂⁴	1	6	yes	—
126	#60304	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	2	6	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	3	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	3	no	—
132	C₂³×C₁₉	#131	1	4	yes	complemented
133	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
134	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	2	24	no	—
138	D₄×C₁₉	—	4	6	no	—
139	D₄×C₁₉	—	4	6	no	—
140	C₂×C₄×C₁₉	—	2	6	no	—
141	C₂×C₄×C₁₉	—	2	3	no	—
142	C₂×C₄×C₁₉	—	2	6	no	—
143	C₂×C₄×C₁₉	—	2	3	no	—
144	C₂×C₄×C₁₉	—	2	6	no	—
145	C₂×C₄×C₁₉	—	4	3	no	—
146	C₂×C₄×C₁₉	—	4	6	no	—
147	C₂×C₄×C₁₉	—	4	3	no	—
148	C₂×C₄×C₁₉	—	4	3	no	—
149	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
150	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
151	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
152	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
153	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
154	C₈×C₁₉	—	2	3	no	—
155	C₈×C₁₉	—	2	6	no	—
156	C₈×C₁₉	—	2	6	no	—
157	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
158	#3459	C₂×C₁₉	1	1	yes	characteristic
159	#2992	C₂×C₁₉	1	6	yes	complemented
160	#2976	C₂×C₁₉	1	6	yes	complemented
161	#2973	C₂×C₁₉	1	3	yes	complemented
162	#2966	C₂×C₁₉	1	6	yes	complemented
163	#2929	C₂×C₁₉	1	6	yes	complemented
164	C₂×C₈×D₄	C₂×C₁₉	1	3	yes	complemented
165	C₂²×C₁₉	—	2	3	no	—
166	C₂²×C₁₉	—	2	3	no	—
167	C₂²×C₁₉	—	2	6	no	—
168	C₂²×C₁₉	—	2	6	no	—
169	C₂²×C₁₉	—	2	6	no	—
170	C₂²×C₁₉	—	4	4	no	—
171	C₂²×C₁₉	—	4	12	no	—
172	C₂²×C₁₉	C₂×#131	1	6	yes	—
173	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
174	C₄×C₁₉	—	2	3	no	—
175	C₄×C₁₉	—	2	6	no	—
176	C₄×C₁₉	—	2	6	no	—
177	C₄×C₁₉	—	2	6	no	—
178	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
179	C₄×C₁₉	#585	1	1	yes	characteristic
180	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
181	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
182	C₂³×C₈	C₂²×C₁₉	1	3	yes	complemented
183	#543	C₄×C₁₉	1	1	yes	characteristic
184	#539	C₄×C₁₉	1	6	yes	—
185	#538	C₄×C₁₉	1	6	yes	—
186	#534	C₄×C₁₉	1	3	yes	—
187	#529	C₂²×C₁₉	1	6	yes	—
188	#525	C₂²×C₁₉	1	6	yes	—
189	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
190	#446	C₂²×C₁₉	1	6	yes	complemented
191	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
192	#436	C₂²×C₁₉	1	6	yes	complemented
193	#435	C₂²×C₁₉	1	12	yes	complemented
194	#435	C₂²×C₁₉	1	12	yes	complemented
195	#435	C₂²×C₁₉	1	12	yes	complemented
196	C₈×D₄	C₂²×C₁₉	1	12	yes	complemented
197	C₈×D₄	C₂²×C₁₉	1	12	yes	complemented
198	C₈×D₄	C₂²×C₁₉	1	6	yes	complemented
199	#433	C₂²×C₁₉	1	12	yes	complemented
200	#432	C₂²×C₁₉	1	6	yes	complemented
201	#424	C₂²×C₁₉	1	6	yes	complemented
202	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	complemented
203	#408	C₂²×C₁₉	1	6	yes	complemented
204	#407	C₂²×C₁₉	1	6	yes	complemented
205	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	—
206	C₂×C₂²⋊C₈	C₂²×C₁₉	1	3	yes	complemented
207	#405	C₂²×C₁₉	1	6	yes	complemented
208	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
209	C₂×C₁₉	—	2	6	no	—
210	C₂×C₁₉	—	4	6	no	—
211	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₁₉	C₂²×#131	1	1	yes	characteristic
213	C₂×C₁₉	#3573	1	1	yes	characteristic
214	C₂×#41	C₂³×C₁₉	1	2	yes	—
215	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
216	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
218	#131	—	4	4	no	—
219	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
220	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
221	C₂²×C₈	—	4	2	no	—
222	C₂²×C₈	—	4	6	no	—
223	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
224	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
225	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
226	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
227	C₂²×C₈	C₂³×C₁₉	1	6	yes	—
228	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
229	#126	C₂×C₄×C₁₉	1	12	yes	—
230	#125	C₂×C₄×C₁₉	1	6	yes	—
231	#124	C₂×C₄×C₁₉	1	6	yes	—
232	#123	C₂×C₄×C₁₉	1	12	yes	—
233	#123	C₂×C₄×C₁₉	1	12	yes	—
234	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
235	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
236	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
237	#121	C₂×C₄×C₁₉	1	6	yes	—
238	#121	C₂×C₄×C₁₉	1	6	yes	—
239	#121	C₂×C₄×C₁₉	1	6	yes	—
240	#120	C₂×C₄×C₁₉	1	12	yes	—
241	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
242	C₄×D₄	C₂×C₄×C₁₉	1	12	yes	—
243	C₄×D₄	C₂³×C₁₉	1	12	yes	—
244	C₄×D₄	C₂³×C₁₉	1	6	yes	—
245	#117	C₂³×C₁₉	1	6	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
249	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
250	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
251	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
252	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
253	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
254	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
255	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
256	#97	C₂³×C₁₉	1	12	yes	—
257	C₄×C₈	C₂³×C₁₉	1	6	yes	—
258	C₄×C₈	C₂³×C₁₉	1	6	yes	—
259	C₁₉	#60304	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂²×C₄×C₁₉	1	3	yes	—
261	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
262	#41	—	4	2	no	—
263	#41	—	4	2	no	—
264	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
265	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
266	C₂×D₄	—	2	12	no	—
267	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
268	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
269	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	3	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	3	no	—
274	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
279	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
280	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
281	M₁₆	—	4	6	no	—
282	M₁₆	—	4	6	no	—
283	C₂×C₈	—	2	6	no	—
284	C₂×C₈	—	2	12	no	—
285	C₂×C₈	—	4	3	no	—
286	C₂×C₈	—	4	6	no	—
287	C₂×C₈	—	4	3	no	—
288	C₂×C₈	—	4	3	no	—
289	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
290	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
291	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
292	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
293	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
294	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
295	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
296	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
297	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
298	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
299	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
300	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
301	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
302	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
303	C₄²	C₂⁴×C₁₉	1	6	yes	—
304	C₂³	—	2	6	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	3	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	3	no	—
309	C₂³	C₁₉×#131	1	4	yes	complemented
310	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
311	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	2	24	no	—
315	D₄	—	4	6	no	—
316	D₄	—	4	6	no	—
317	C₂×C₄	—	2	6	no	—
318	C₂×C₄	—	2	3	no	—
319	C₂×C₄	—	2	6	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	4	3	no	—
323	C₂×C₄	—	4	6	no	—
324	C₂×C₄	—	4	3	no	—
325	C₂×C₄	—	4	3	no	—
326	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
327	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
328	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
329	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
330	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
331	C₈	—	2	3	no	—
332	C₈	—	2	6	no	—
333	C₈	—	2	6	no	—
334	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
335	C₂²	—	2	3	no	—
336	C₂²	—	2	3	no	—
337	C₂²	—	2	6	no	—
338	C₂²	—	2	6	no	—
339	C₂²	—	2	6	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	12	no	—
342	C₂²	C₂×C₁₉×#131	1	6	yes	—
343	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
344	C₄	—	2	3	no	—
345	C₄	—	2	6	no	—
346	C₄	—	2	6	no	—
347	C₄	—	2	6	no	—
348	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
349	C₄	C₁₉×#585	1	1	yes	characteristic
350	C₂	—	2	6	no	—
351	C₂	—	4	6	no	—
352	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂	C₂²×C₁₉×#131	1	1	yes	characteristic
354	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3459	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2992	C₂	semidirect
3. C₁₉×#2976	C₂	semidirect
4. C₁₉×#2973	C₂	semidirect
5. C₁₉×#2966	C₂	semidirect
6. C₁₉×#2929	C₂	semidirect
7. C₂×C₈×D₄×C₁₉	C₂	semidirect
8. C₂×C₁₉×#131	C₂²	semidirect
10. C₂³×C₈×C₁₉	C₂²	semidirect
18. C₁₉×#446	C₂²	semidirect
19. C₈×Q₈×C₁₉	C₂²	semidirect
20. C₁₉×#436	C₂²	semidirect
21. C₁₉×#435	C₂²	semidirect
22. C₁₉×#435	C₂²	semidirect
23. C₁₉×#435	C₂²	semidirect
24. C₈×D₄×C₁₉	C₂²	semidirect
25. C₈×D₄×C₁₉	C₂²	semidirect
26. C₈×D₄×C₁₉	C₂²	semidirect
27. C₁₉×#433	C₂²	semidirect
28. C₁₉×#432	C₂²	semidirect
29. C₁₉×#424	C₂²	semidirect
30. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
31. C₁₉×#408	C₂²	semidirect
32. C₁₉×#407	C₂²	semidirect
34. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
35. C₁₉×#405	C₂²	semidirect
36. C₂×C₄×C₈×C₁₉	C₂²	semidirect
126. #60304	C₁₉	direct (N × H)
132. C₂³×C₁₉	#131	semidirect
159. #2992	C₂×C₁₉	semidirect
160. #2976	C₂×C₁₉	semidirect
161. #2973	C₂×C₁₉	semidirect
162. #2966	C₂×C₁₉	semidirect
163. #2929	C₂×C₁₉	semidirect
164. C₂×C₈×D₄	C₂×C₁₉	semidirect
180. C₂×#131	C₂²×C₁₉	semidirect
182. C₂³×C₈	C₂²×C₁₉	semidirect
190. #446	C₂²×C₁₉	semidirect
191. C₈×Q₈	C₂²×C₁₉	semidirect
192. #436	C₂²×C₁₉	semidirect
193. #435	C₂²×C₁₉	semidirect
194. #435	C₂²×C₁₉	semidirect
195. #435	C₂²×C₁₉	semidirect
196. C₈×D₄	C₂²×C₁₉	semidirect
197. C₈×D₄	C₂²×C₁₉	semidirect
198. C₈×D₄	C₂²×C₁₉	semidirect
199. #433	C₂²×C₁₉	semidirect
200. #432	C₂²×C₁₉	semidirect
201. #424	C₂²×C₁₉	semidirect
202. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
203. #408	C₂²×C₁₉	semidirect
204. #407	C₂²×C₁₉	semidirect
206. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
207. #405	C₂²×C₁₉	semidirect
208. C₂×C₄×C₈	C₂²×C₁₉	semidirect
259. C₁₉	#60304	direct (N × H)
309. C₂³	C₁₉×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3459	2
C₁₉×#2992	2
C₁₉×#2976	2
C₁₉×#2973	2
C₁₉×#2966	2
C₁₉×#2929	2
C₂×C₈×D₄×C₁₉	2
#60304	19

Subgroups — C19×#60304 #18066263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60304 #18066263