Subgroups — C₁₉×#13012 #18018971

Order 4864.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	—	2	1	no	—
11	C₂×C₁₉×D₁₆	—	2	2	no	—
12	C₂×C₁₉×D₁₆	—	2	2	no	—
13	C₂×C₁₉×D₁₆	C₄	1	4	yes	complemented
14	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₁₉	—	2	2	no	—
17	C₄×D₈×C₁₉	—	2	2	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#102	—	2	1	no	—
21	C₂×C₁₉×#102	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#390	—	2	1	no	—
24	C₁₉×#357	—	2	2	no	—
25	C₁₉×#357	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	4	1	no	—
29	C₂×D₈×C₁₉	—	2	1	no	—
30	C₂×D₈×C₁₉	—	2	1	no	—
31	C₂×D₈×C₁₉	—	2	1	no	—
32	C₂×D₈×C₁₉	—	2	1	no	—
33	C₂×D₈×C₁₉	—	2	1	no	—
34	C₂×D₈×C₁₉	—	2	1	no	—
35	C₂×D₈×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	complemented
39	C₂×D₈×C₁₉	D₄	1	2	yes	—
40	C₂×D₈×C₁₉	D₄	1	2	yes	—
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₁₉	—	2	4	no	—
44	C₄×D₄×C₁₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₁₉×D₁₆	—	2	8	no	—
52	C₂×C₁₆×C₁₉	—	2	1	no	—
53	C₂×C₁₆×C₁₉	—	2	1	no	—
54	C₂×C₁₆×C₁₉	—	2	1	no	—
55	C₂×C₁₆×C₁₉	—	2	1	no	—
56	C₂×C₁₆×C₁₉	—	2	1	no	—
57	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
58	C₁₉×#107	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#107	D₄	1	2	yes	—
62	C₁₉×#102	—	2	4	no	—
63	C₁₉×#102	—	4	2	no	—
64	C₄×C₈×C₁₉	—	2	1	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	—	4	1	no	—
67	C₂⁴×C₁₉	—	4	1	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	4	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	8	2	no	—
84	C₂²×C₄×C₁₉	—	8	2	no	—
85	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	D₈×C₁₉	—	2	2	no	—
89	D₈×C₁₉	—	2	2	no	—
90	D₈×C₁₉	—	2	2	no	—
91	D₈×C₁₉	—	2	2	no	—
92	D₈×C₁₉	—	2	2	no	—
93	D₈×C₁₉	—	4	1	no	—
94	D₈×C₁₉	—	4	1	no	—
95	D₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
96	C₂×C₈×C₁₉	—	2	1	no	—
97	C₂×C₈×C₁₉	—	2	1	no	—
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
104	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₂²⋊C₄×C₁₉	—	4	4	no	—
110	C₂²⋊C₄×C₁₉	—	8	2	no	—
111	C₂²⋊C₄×C₁₉	—	8	2	no	—
112	C₄²×C₁₉	—	2	1	no	—
113	C₄²×C₁₉	—	2	1	no	—
114	C₁₆×C₁₉	—	2	2	no	—
115	C₁₆×C₁₉	—	4	1	no	—
116	#13012	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₁₉	—	4	2	no	—
118	C₂³×C₁₉	—	4	2	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	8	1	no	—
122	C₂³×C₁₉	—	8	1	no	—
123	C₂³×C₁₉	—	8	1	no	—
124	C₂³×C₁₉	—	8	1	no	—
125	C₂³×C₁₉	—	8	1	no	—
126	C₂³×C₁₉	—	8	1	no	—
127	C₂³×C₁₉	—	8	1	no	—
128	C₂³×C₁₉	—	8	1	no	—
129	C₂³×C₁₉	—	8	1	no	—
130	C₂³×C₁₉	—	8	1	no	—
131	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
132	D₄×C₁₉	—	2	4	no	—
133	D₄×C₁₉	—	4	2	no	—
134	D₄×C₁₉	—	4	2	no	—
135	D₄×C₁₉	—	4	2	no	—
136	D₄×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	8	1	no	—
139	D₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	8	8	no	—
147	C₂×C₄×C₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	—	8	1	no	—
152	C₂×C₄×C₁₉	D₁₆	1	2	yes	complemented
153	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₈×C₁₉	—	4	1	no	—
160	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₈×C₁₉	#121	1	1	yes	characteristic
163	C₈×C₁₉	#123	1	1	yes	characteristic
164	C₂²×D₁₆	C₂×C₁₉	1	1	yes	characteristic
165	C₂×C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
166	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
167	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1970	C₂×C₁₉	1	1	yes	characteristic, complemented
169	#1380	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1374	C₂×C₁₉	1	1	yes	characteristic, complemented
171	C₂²×C₁₉	—	4	4	no	—
172	C₂²×C₁₉	—	8	2	no	—
173	C₂²×C₁₉	—	8	2	no	—
174	C₂²×C₁₉	—	8	2	no	—
175	C₂²×C₁₉	—	8	2	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	2	no	—
178	C₂²×C₁₉	—	8	2	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	—	16	1	no	—
182	C₂²×C₁₉	—	16	1	no	—
183	C₂²×C₁₉	—	16	1	no	—
184	C₂²×C₁₉	—	16	1	no	—
185	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
186	C₂²×C₁₉	#447	1	1	yes	characteristic
187	C₂²×C₁₉	#459	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
189	C₂²×C₁₉	#508	1	1	yes	characteristic
190	C₂²×C₁₉	#509	1	1	yes	characteristic
191	C₂²×C₁₉	#509	1	1	yes	characteristic
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	4	1	no	—
194	C₄×C₁₉	—	8	2	no	—
195	C₄×C₁₉	—	16	1	no	—
196	C₄×C₁₉	#386	1	1	yes	characteristic
197	C₄×C₁₉	#442	1	1	yes	characteristic
198	C₄×C₁₉	#449	1	1	yes	characteristic
199	C₄×C₁₉	#463	1	1	yes	characteristic
200	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
201	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×C₄×D₄	—	2	1	no	—
203	C₂×D₁₆	—	2	2	no	—
204	C₂×D₁₆	—	2	2	no	—
205	C₂×D₁₆	C₄×C₁₉	1	4	yes	complemented
206	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
207	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
208	C₄×D₈	—	2	2	no	—
209	C₄×D₈	—	2	2	no	—
210	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#102	—	2	1	no	—
213	C₂×#102	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
215	#390	—	2	1	no	—
216	#357	—	2	2	no	—
217	#357	—	2	2	no	—
218	C₂×C₁₉	—	8	4	no	—
219	C₂×C₁₉	—	16	2	no	—
220	C₂×C₁₉	#1879	1	1	yes	characteristic
221	C₂×C₁₉	C₄×D₁₆	1	1	yes	characteristic
222	C₂×C₁₉	#2177	1	1	yes	characteristic
223	C₂×C₁₉	#2184	1	1	yes	characteristic
224	C₂×C₁₉	#2186	1	1	yes	characteristic
225	C₂×C₁₉	#2206	1	1	yes	characteristic
226	C₂×C₁₉	#2210	1	1	yes	characteristic
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂³×C₄	—	4	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
239	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	complemented
240	C₂×D₈	D₄×C₁₉	1	2	yes	—
241	C₂×D₈	D₄×C₁₉	1	2	yes	—
242	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
244	C₄×D₄	—	2	4	no	—
245	C₄×D₄	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	4	1	no	—
249	C₂×C₂²⋊C₄	—	4	1	no	—
250	C₂×C₂²⋊C₄	—	4	1	no	—
251	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
252	D₁₆	—	2	8	no	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	2	1	no	—
257	C₂×C₁₆	—	2	1	no	—
258	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	complemented
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	D₄×C₁₉	1	2	yes	—
263	#102	—	2	4	no	—
264	#102	—	4	2	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₁₉	#13012	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	—	4	1	no	—
269	C₂⁴	—	4	1	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	8	2	no	—
286	C₂²×C₄	—	8	2	no	—
287	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	D₈	—	2	2	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	2	no	—
293	D₈	—	2	2	no	—
294	D₈	—	2	2	no	—
295	D₈	—	4	1	no	—
296	D₈	—	4	1	no	—
297	D₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
306	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	8	2	no	—
313	C₂²⋊C₄	—	8	2	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₁₆	—	2	2	no	—
317	C₁₆	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	8	1	no	—
323	C₂³	—	8	1	no	—
324	C₂³	—	8	1	no	—
325	C₂³	—	8	1	no	—
326	C₂³	—	8	1	no	—
327	C₂³	—	8	1	no	—
328	C₂³	—	8	1	no	—
329	C₂³	—	8	1	no	—
330	C₂³	—	8	1	no	—
331	C₂³	—	8	1	no	—
332	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
333	D₄	—	2	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	1	no	—
340	D₄	—	8	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	8	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	C₁₉×D₁₆	1	2	yes	complemented
354	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
356	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
357	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
358	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₈	—	4	1	no	—
361	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
363	C₈	C₁₉×#121	1	1	yes	characteristic
364	C₈	C₁₉×#123	1	1	yes	characteristic
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	16	1	no	—
376	C₂²	—	16	1	no	—
377	C₂²	—	16	1	no	—
378	C₂²	—	16	1	no	—
379	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
380	C₂²	C₁₉×#447	1	1	yes	characteristic
381	C₂²	C₁₉×#459	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
383	C₂²	C₁₉×#508	1	1	yes	characteristic
384	C₂²	C₁₉×#509	1	1	yes	characteristic
385	C₂²	C₁₉×#509	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	16	1	no	—
390	C₄	C₁₉×#386	1	1	yes	characteristic
391	C₄	C₁₉×#442	1	1	yes	characteristic
392	C₄	C₁₉×#449	1	1	yes	characteristic
393	C₄	C₁₉×#463	1	1	yes	characteristic
394	C₂	—	8	4	no	—
395	C₂	—	16	2	no	—
396	C₂	C₁₉×#1879	1	1	yes	characteristic
397	C₂	C₄×C₁₉×D₁₆	1	1	yes	characteristic
398	C₂	C₁₉×#2177	1	1	yes	characteristic
399	C₂	C₁₉×#2184	1	1	yes	characteristic
400	C₂	C₁₉×#2186	1	1	yes	characteristic
401	C₂	C₁₉×#2206	1	1	yes	characteristic
402	C₂	C₁₉×#2210	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂²×C₁₉×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₁₉	C₂	semidirect
3. C₂×C₁₉×#357	C₂	semidirect
4. C₂×C₁₉×#357	C₂	semidirect
5. C₁₉×#1970	C₂	semidirect
6. C₁₉×#1380	C₂	semidirect
7. C₁₉×#1374	C₂	semidirect
13. C₂×C₁₉×D₁₆	C₄	semidirect
38. C₂×D₈×C₁₉	C₂×C₄	semidirect
57. C₂×C₁₆×C₁₉	C₂×C₄	semidirect
95. D₈×C₁₉	C₂²⋊C₄	semidirect
116. #13012	C₁₉	direct (N × H)
152. C₂×C₄×C₁₉	D₁₆	semidirect
165. C₂×C₄×D₈	C₂×C₁₉	semidirect
166. C₂×#357	C₂×C₁₉	semidirect
167. C₂×#357	C₂×C₁₉	semidirect
168. #1970	C₂×C₁₉	semidirect
169. #1380	C₂×C₁₉	semidirect
170. #1374	C₂×C₁₉	semidirect
205. C₂×D₁₆	C₄×C₁₉	semidirect
239. C₂×D₈	C₂×C₄×C₁₉	semidirect
258. C₂×C₁₆	C₂×C₄×C₁₉	semidirect
267. C₁₉	#13012	direct (N × H)
297. D₈	C₂²⋊C₄×C₁₉	semidirect
353. C₂×C₄	C₁₉×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×D₁₆	2
C₂×C₄×D₈×C₁₉	2
C₂×C₁₉×#357	2
C₁₉×#1970	2
C₁₉×#1380	2
C₁₉×#1374	2
#13012	19

Subgroups — C19×#13012 #18018971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13012 #18018971