Subgroups — C₁₉×#13305 #18019264

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×#121	—	2	1	no	—
13	C₂×C₁₉×SD₃₂	—	2	2	no	—
14	C₂×C₁₉×SD₃₂	—	2	2	no	—
15	C₂×C₁₉×SD₃₂	—	2	2	no	—
16	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#467	—	2	2	no	—
19	C₁₉×#467	—	2	2	no	—
20	C₁₉×#466	—	2	2	no	—
21	C₁₉×#466	—	2	2	no	—
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	—	2	1	no	—
25	C₂×C₁₉×#102	—	2	1	no	—
26	C₁₉×#358	—	2	2	no	—
27	C₁₉×#357	—	2	2	no	—
28	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	4	1	no	—
32	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×Q₁₆×C₁₉	—	2	1	no	—
34	C₂×Q₁₆×C₁₉	—	2	1	no	—
35	C₂×Q₁₆×C₁₉	—	2	1	no	—
36	C₂×Q₁₆×C₁₉	—	2	1	no	—
37	C₂×Q₁₆×C₁₉	—	2	1	no	—
38	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
39	C₂×D₈×C₁₉	—	2	1	no	—
40	C₂×D₈×C₁₉	—	2	1	no	—
41	C₂×D₈×C₁₉	—	2	1	no	—
42	C₂×D₈×C₁₉	—	2	1	no	—
43	C₂×D₈×C₁₉	—	2	1	no	—
44	C₂×D₈×C₁₉	D₄	1	2	yes	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×C₂²⋊Q₈	—	2	4	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₁₉×#121	—	2	4	no	—
56	C₁₉×#121	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
62	C₁₉×SD₃₂	—	2	8	no	—
63	C₂×C₁₆×C₁₉	—	2	1	no	—
64	C₂×C₁₆×C₁₉	—	2	1	no	—
65	C₂×C₁₆×C₁₉	—	2	1	no	—
66	C₂×C₁₆×C₁₉	—	2	1	no	—
67	C₂×C₁₆×C₁₉	—	2	1	no	—
68	C₂×C₁₆×C₁₉	D₄	1	2	yes	complemented
69	C₁₉×#107	—	2	1	no	—
70	C₁₉×#107	—	2	1	no	—
71	C₁₉×#107	D₄	1	2	yes	—
72	C₁₉×#107	D₄	1	2	yes	complemented
73	C₁₉×#103	—	2	4	no	—
74	C₁₉×#102	—	2	4	no	—
75	C₂⁴×C₁₉	—	4	1	no	—
76	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	—	4	1	no	—
82	C₂×Q₈×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	4	4	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	8	2	no	—
91	C₂×D₄×C₁₉	—	8	2	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₁₉	—	2	2	no	—
104	Q₁₆×C₁₉	—	2	2	no	—
105	Q₁₆×C₁₉	—	4	1	no	—
106	Q₁₆×C₁₉	—	4	1	no	—
107	D₈×C₁₉	—	2	2	no	—
108	D₈×C₁₉	—	2	2	no	—
109	D₈×C₁₉	—	4	1	no	—
110	D₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₉	—	4	4	no	—
131	C₁₆×C₁₉	—	2	2	no	—
132	C₁₆×C₁₉	—	4	1	no	—
133	#13305	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	SD₃₂	1	2	yes	complemented
148	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	8	1	no	—
152	Q₈×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	8	8	no	—
156	D₄×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	#120	1	1	yes	characteristic
182	C₈×C₁₉	#121	1	1	yes	characteristic
183	C₈×C₁₉	#121	1	1	yes	characteristic
184	C₈×C₁₉	#127	1	1	yes	characteristic
185	C₂²×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂×#466	C₂×C₁₉	1	1	yes	characteristic
188	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
190	C₂×C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1380	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	16	1	no	—
203	C₂²×C₁₉	—	16	1	no	—
204	C₂²×C₁₉	—	16	1	no	—
205	C₂²×C₁₉	—	16	1	no	—
206	C₂²×C₁₉	#447	1	1	yes	characteristic
207	C₂²×C₁₉	#447	1	1	yes	characteristic
208	C₂²×C₁₉	#466	1	1	yes	characteristic
209	C₂²×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
210	C₂²×C₁₉	#508	1	1	yes	characteristic
211	C₂²×C₁₉	#509	1	1	yes	characteristic
212	C₂²×C₁₉	#510	1	1	yes	characteristic
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	#392	1	1	yes	characteristic
218	C₄×C₁₉	#449	1	1	yes	characteristic
219	C₄×C₁₉	#449	1	1	yes	characteristic
220	C₄×C₁₉	#469	1	1	yes	characteristic
221	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×#121	—	2	1	no	—
226	C₂×SD₃₂	—	2	2	no	—
227	C₂×SD₃₂	—	2	2	no	—
228	C₂×SD₃₂	—	2	2	no	—
229	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
231	#467	—	2	2	no	—
232	#467	—	2	2	no	—
233	#466	—	2	2	no	—
234	#466	—	2	2	no	—
235	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#103	—	2	1	no	—
238	C₂×#102	—	2	1	no	—
239	#358	—	2	2	no	—
240	#357	—	2	2	no	—
241	C₂²⋊C₁₆	—	2	2	no	—
242	C₂×C₁₉	—	4	2	no	—
243	C₂×C₁₉	—	16	2	no	—
244	C₂×C₁₉	#1999	1	1	yes	characteristic
245	C₂×C₁₉	#2185	1	1	yes	characteristic
246	C₂×C₁₉	#2186	1	1	yes	characteristic
247	C₂×C₁₉	#2187	1	1	yes	characteristic
248	C₂×C₁₉	#2189	1	1	yes	characteristic
249	C₂×C₁₉	#2217	1	1	yes	characteristic
250	C₂×C₁₉	#2220	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	4	1	no	—
254	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
255	C₂×Q₁₆	—	2	1	no	—
256	C₂×Q₁₆	—	2	1	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	D₄×C₁₉	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	4	2	no	—
277	#121	—	2	4	no	—
278	#121	—	4	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	4	1	no	—
282	C₂×C₂²⋊C₄	—	4	1	no	—
283	C₂×C₂²⋊C₄	—	4	1	no	—
284	SD₃₂	—	2	8	no	—
285	C₂×C₁₆	—	2	1	no	—
286	C₂×C₁₆	—	2	1	no	—
287	C₂×C₁₆	—	2	1	no	—
288	C₂×C₁₆	—	2	1	no	—
289	C₂×C₁₆	—	2	1	no	—
290	C₂×C₁₆	D₄×C₁₉	1	2	yes	complemented
291	#107	—	2	1	no	—
292	#107	—	2	1	no	—
293	#107	D₄×C₁₉	1	2	yes	—
294	#107	D₄×C₁₉	1	2	yes	complemented
295	#103	—	2	4	no	—
296	#102	—	2	4	no	—
297	C₁₉	#13305	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	4	1	no	—
299	C₂⁴	D₈×C₁₉	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	2	no	—
328	Q₁₆	—	4	1	no	—
329	Q₁₆	—	4	1	no	—
330	D₈	—	2	2	no	—
331	D₈	—	2	2	no	—
332	D₈	—	4	1	no	—
333	D₈	—	4	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₁₆	—	2	2	no	—
355	C₁₆	—	4	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	8	1	no	—
364	C₂³	—	8	1	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	8	1	no	—
367	C₂³	—	8	1	no	—
368	C₂³	—	8	1	no	—
369	C₂³	C₁₉×SD₃₂	1	2	yes	complemented
370	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	8	1	no	—
374	Q₈	—	8	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	8	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
400	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₈	—	4	1	no	—
403	C₈	C₁₉×#120	1	1	yes	characteristic
404	C₈	C₁₉×#121	1	1	yes	characteristic
405	C₈	C₁₉×#121	1	1	yes	characteristic
406	C₈	C₁₉×#127	1	1	yes	characteristic
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	16	1	no	—
418	C₂²	—	16	1	no	—
419	C₂²	—	16	1	no	—
420	C₂²	—	16	1	no	—
421	C₂²	C₁₉×#447	1	1	yes	characteristic
422	C₂²	C₁₉×#447	1	1	yes	characteristic
423	C₂²	C₁₉×#466	1	1	yes	characteristic
424	C₂²	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
425	C₂²	C₁₉×#508	1	1	yes	characteristic
426	C₂²	C₁₉×#509	1	1	yes	characteristic
427	C₂²	C₁₉×#510	1	1	yes	characteristic
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	C₁₉×#392	1	1	yes	characteristic
433	C₄	C₁₉×#449	1	1	yes	characteristic
434	C₄	C₁₉×#449	1	1	yes	characteristic
435	C₄	C₁₉×#469	1	1	yes	characteristic
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₁₉×#1999	1	1	yes	characteristic
439	C₂	C₁₉×#2185	1	1	yes	characteristic
440	C₂	C₁₉×#2186	1	1	yes	characteristic
441	C₂	C₁₉×#2187	1	1	yes	characteristic
442	C₂	C₁₉×#2189	1	1	yes	characteristic
443	C₂	C₁₉×#2217	1	1	yes	characteristic
444	C₂	C₁₉×#2220	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#466	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×SD₃₂	C₂	semidirect
2. C₂×C₁₉×#467	C₂	semidirect
4. C₂×C₁₉×#358	C₂	semidirect
5. C₂×C₁₉×#357	C₂	semidirect
6. C₂×C₁₉×C₂²⋊C₁₆	C₂	semidirect
7. C₁₉×#1380	C₂	semidirect
38. C₂×Q₁₆×C₁₉	D₄	semidirect
68. C₂×C₁₆×C₁₉	D₄	semidirect
72. C₁₉×#107	D₄	semidirect
133. #13305	C₁₉	direct (N × H)
147. C₂³×C₁₉	SD₃₂	semidirect
185. C₂²×SD₃₂	C₂×C₁₉	semidirect
186. C₂×#467	C₂×C₁₉	semidirect
188. C₂×#358	C₂×C₁₉	semidirect
189. C₂×#357	C₂×C₁₉	semidirect
190. C₂×C₂²⋊C₁₆	C₂×C₁₉	semidirect
191. #1380	C₂×C₁₉	semidirect
260. C₂×Q₁₆	D₄×C₁₉	semidirect
290. C₂×C₁₆	D₄×C₁₉	semidirect
294. #107	D₄×C₁₉	semidirect
297. C₁₉	#13305	direct (N × H)
369. C₂³	C₁₉×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×SD₃₂	2
C₂×C₁₉×#467	2
C₂×C₁₉×#466	2
C₂×C₁₉×#358	2
C₂×C₁₉×#357	2
C₂×C₁₉×C₂²⋊C₁₆	2
C₁₉×#1380	2
#13305	19

Subgroups — C19×#13305 #18019264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13305 #18019264