Subgroups — C₁₉×#32824 #18038783

Order 4864.

616 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2864	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2862	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2097	C₂	1	2	yes	maximal
4	C₁₉×#2074	C₂	1	2	yes	maximal
5	C₁₉×#2068	C₂	1	2	yes	maximal
6	C₁₉×#2066	C₂	1	2	yes	maximal
7	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2057	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₁₉×#391	—	2	1	no	—
22	C₁₉×#391	—	2	1	no	—
23	C₁₉×#391	C₂²	1	2	yes	—
24	C₁₉×#391	C₂²	1	2	yes	—
25	C₁₉×#389	C₂²	1	1	yes	characteristic
26	C₁₉×#389	C₂²	1	1	yes	characteristic
27	C₁₉×#389	C₂²	1	1	yes	characteristic
28	C₁₉×#389	C₂²	1	1	yes	characteristic
29	C₁₉×#387	—	2	1	no	—
30	C₁₉×#387	—	2	1	no	—
31	C₁₉×#387	—	2	1	no	—
32	C₁₉×#387	—	2	1	no	—
33	C₁₉×#382	—	2	1	no	—
34	C₁₉×#382	—	2	1	no	—
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#382	C₂²	1	1	yes	characteristic
37	C₄³×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₁₉×C₄⋊Q₈	—	4	2	no	—
48	C₁₉×C₄⋊Q₈	—	4	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#107	—	4	2	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×C₄⋊C₈	—	4	2	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×#103	—	4	2	no	—
74	C₁₉×#103	—	4	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	1	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂×Q₈×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	4	2	no	—
126	C₄⋊C₄×C₁₉	—	4	2	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	4	2	no	—
129	C₄⋊C₄×C₁₉	—	4	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	1	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	#32824	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₉	—	4	2	no	—
141	Q₈×C₁₉	—	4	2	no	—
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	Q₈×C₁₉	—	8	4	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	#135	1	2	yes	—
179	C₂×C₄×C₁₉	#137	1	2	yes	—
180	C₂×C₄×C₁₉	#137	1	2	yes	—
181	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
184	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₁₉	—	4	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	#2864	C₂×C₁₉	1	1	yes	characteristic
188	#2862	C₂×C₁₉	1	1	yes	characteristic
189	#2097	C₂×C₁₉	1	2	yes	—
190	#2074	C₂×C₁₉	1	2	yes	—
191	#2068	C₂×C₁₉	1	2	yes	—
192	#2066	C₂×C₁₉	1	2	yes	—
193	#2058	C₂×C₁₉	1	1	yes	characteristic
194	#2057	C₂×C₁₉	1	1	yes	characteristic
195	#2043	C₂×C₁₉	1	1	yes	characteristic
196	#2043	C₂×C₁₉	1	1	yes	characteristic
197	#1831	C₂×C₁₉	1	1	yes	characteristic
198	C₂²×C₁₉	#535	1	1	yes	characteristic
199	C₂²×C₁₉	#536	1	1	yes	characteristic
200	C₂²×C₁₉	#537	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
204	C₂²×C₁₉	#575	1	1	yes	characteristic
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	#562	1	2	yes	—
218	C₄×C₁₉	#563	1	2	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#107	C₂²×C₁₉	1	2	yes	—
222	C₂×#106	C₂²×C₁₉	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
224	C₂×#103	C₂²×C₁₉	1	2	yes	—
225	C₂×#103	C₂²×C₁₉	1	2	yes	—
226	C₂×#103	C₂²×C₁₉	1	2	yes	—
227	C₂×#103	C₂²×C₁₉	1	2	yes	—
228	#391	—	2	1	no	—
229	#391	—	2	1	no	—
230	#391	C₂²×C₁₉	1	2	yes	—
231	#391	C₂²×C₁₉	1	2	yes	—
232	#389	C₂²×C₁₉	1	1	yes	characteristic
233	#389	C₂²×C₁₉	1	1	yes	characteristic
234	#389	C₂²×C₁₉	1	1	yes	characteristic
235	#389	C₂²×C₁₉	1	1	yes	characteristic
236	#387	—	2	1	no	—
237	#387	—	2	1	no	—
238	#387	—	2	1	no	—
239	#387	—	2	1	no	—
240	#382	—	2	1	no	—
241	#382	—	2	1	no	—
242	#382	C₂²×C₁₉	1	1	yes	characteristic
243	#382	C₂²×C₁₉	1	1	yes	characteristic
244	C₄³	C₂²×C₁₉	1	1	yes	characteristic
245	#340	C₂²×C₁₉	1	2	yes	—
246	#340	C₂²×C₁₉	1	2	yes	—
247	#336	C₂²×C₁₉	1	1	yes	characteristic
248	#336	C₂²×C₁₉	1	1	yes	characteristic
249	#336	C₂²×C₁₉	1	2	yes	—
250	C₂×C₁₉	#2820	1	1	yes	characteristic
251	C₂×C₁₉	#3211	1	1	yes	characteristic
252	C₂×C₁₉	#3218	1	1	yes	characteristic
253	C₂×C₁₉	#3231	1	1	yes	characteristic
254	C₂×C₁₉	#3237	1	1	yes	characteristic
255	C₂×C₁₉	#3248	1	1	yes	characteristic
256	C₂×C₁₉	#3252	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
261	C₄⋊Q₈	—	4	2	no	—
262	C₄⋊Q₈	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
282	#107	—	4	2	no	—
283	#106	—	4	2	no	—
284	C₄⋊C₈	—	4	2	no	—
285	#103	—	4	2	no	—
286	#103	—	4	2	no	—
287	#103	—	4	2	no	—
288	#103	—	4	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	1	no	—
297	#95	—	2	1	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	C₁₉	#32824	1	1	yes	characteristic, direct product factor, Sylow
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	1	no	—
353	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	8	4	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₁₉×#135	1	2	yes	—
393	C₂×C₄	C₁₉×#137	1	2	yes	—
394	C₂×C₄	C₁₉×#137	1	2	yes	—
395	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
398	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₂²	C₁₉×#535	1	1	yes	characteristic
402	C₂²	C₁₉×#536	1	1	yes	characteristic
403	C₂²	C₁₉×#537	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
405	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
406	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
407	C₂²	C₁₉×#575	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	8	2	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₁₉×#562	1	2	yes	—
421	C₄	C₁₉×#563	1	2	yes	—
422	C₂	C₁₉×#2820	1	1	yes	characteristic
423	C₂	C₁₉×#3211	1	1	yes	characteristic
424	C₂	C₁₉×#3218	1	1	yes	characteristic
425	C₂	C₁₉×#3231	1	1	yes	characteristic
426	C₂	C₁₉×#3237	1	1	yes	characteristic
427	C₂	C₁₉×#3248	1	1	yes	characteristic
428	C₂	C₁₉×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
138. #32824	C₁₉	direct (N × H)
301. C₁₉	#32824	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×#2864	2
C₁₉×#2862	2
C₁₉×#2097	2
C₁₉×#2074	2
C₁₉×#2068	2
C₁₉×#2066	2
C₁₉×#2058	2
C₁₉×#2057	2
C₁₉×#2043	2
C₁₉×#1831	2
#32824	19

Subgroups — C19×#32824 #18038783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32824 #18038783