Subgroups — C₁₉×#32769 #18038728

Order 4864.

820 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2620	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2072	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2071	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2015	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2012	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2000	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#124	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₉×#396	—	2	2	no	—
24	C₁₉×#396	—	2	2	no	—
25	C₁₉×#394	—	2	2	no	—
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#390	C₂²	1	2	yes	—
29	C₁₉×#384	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₁₉	—	4	1	no	—
40	C₂×Q₁₆×C₁₉	—	4	2	no	—
41	C₂×SD₁₆×C₁₉	—	4	2	no	—
42	C₂×SD₁₆×C₁₉	—	4	2	no	—
43	C₂×SD₁₆×C₁₉	—	4	2	no	—
44	C₂×D₈×C₁₉	—	4	1	no	—
45	C₂×D₈×C₁₉	—	4	2	no	—
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×#124	—	4	2	no	—
50	C₁₉×#124	—	4	2	no	—
51	C₁₉×C₂²⋊Q₈	—	4	2	no	—
52	C₁₉×C₂²⋊Q₈	—	4	2	no	—
53	C₁₉×#121	—	4	2	no	—
54	C₁₉×#121	—	4	2	no	—
55	C₁₉×#117	—	4	1	no	—
56	C₁₉×#117	—	4	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×#103	—	4	2	no	—
74	C₁₉×#102	—	4	2	no	—
75	C₁₉×#102	—	4	2	no	—
76	C₁₉×C₂²⋊C₈	—	4	1	no	—
77	C₁₉×C₂²⋊C₈	—	4	1	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	4	4	no	—
95	C₂×D₄×C₁₉	—	8	2	no	—
96	C₂×D₄×C₁₉	—	8	2	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₁₉	—	4	4	no	—
109	SD₁₆×C₁₉	—	4	8	no	—
110	D₈×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	4	no	—
125	C₄⋊C₄×C₁₉	—	8	2	no	—
126	C₄⋊C₄×C₁₉	—	8	2	no	—
127	C₂²⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	4	4	no	—
129	C₂²⋊C₄×C₁₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₉	—	4	4	no	—
131	C₂²⋊C₄×C₁₉	—	4	4	no	—
132	C₂²⋊C₄×C₁₉	—	8	2	no	—
133	C₂²⋊C₄×C₁₉	—	8	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	#32769	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	8	8	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	C₈×C₁₉	—	4	1	no	—
184	C₈×C₁₉	—	4	2	no	—
185	C₈×C₁₉	—	4	1	no	—
186	#2620	C₂×C₁₉	1	2	yes	complemented
187	#2072	C₂×C₁₉	1	2	yes	complemented
188	#2071	C₂×C₁₉	1	2	yes	complemented
189	#2015	C₂×C₁₉	1	2	yes	complemented
190	#2012	C₂×C₁₉	1	2	yes	complemented
191	#2001	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#2000	C₂×C₁₉	1	2	yes	complemented
193	#1999	C₂×C₁₉	1	1	yes	characteristic
194	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	8	2	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	#534	1	1	yes	characteristic
208	C₂²×C₁₉	#535	1	2	yes	—
209	C₂²×C₁₉	#576	1	1	yes	characteristic
210	C₂²×C₁₉	#577	1	2	yes	—
211	C₂²×C₁₉	#578	1	1	yes	characteristic
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	1	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	#560	1	1	yes	characteristic
219	C₄×C₁₉	#560	1	2	yes	—
220	C₄×C₁₉	#560	1	1	yes	characteristic
221	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
223	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#124	C₂²×C₁₉	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
226	C₂×#121	C₂²×C₁₉	1	2	yes	—
227	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₉	1	2	yes	—
229	C₂×#103	C₂²×C₁₉	1	2	yes	—
230	C₂×#102	C₂²×C₁₉	1	2	yes	—
231	C₂×#102	C₂²×C₁₉	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
234	#396	—	2	2	no	—
235	#396	—	2	2	no	—
236	#394	—	2	2	no	—
237	#394	—	2	2	no	—
238	#391	C₂²×C₁₉	1	2	yes	—
239	#390	C₂²×C₁₉	1	2	yes	—
240	#384	C₂²×C₁₉	1	2	yes	—
241	#340	C₂²×C₁₉	1	1	yes	characteristic
242	#340	C₂²×C₁₉	1	2	yes	—
243	#340	C₂²×C₁₉	1	1	yes	characteristic
244	#336	C₂²×C₁₉	1	2	yes	—
245	#336	C₂²×C₁₉	1	2	yes	—
246	C₂×C₁₉	—	8	1	no	—
247	C₂×C₁₉	—	16	2	no	—
248	C₂×C₁₉	#2815	1	1	yes	characteristic
249	C₂×C₁₉	#3203	1	1	yes	characteristic
250	C₂×C₁₉	#3204	1	1	yes	characteristic
251	C₂×C₁₉	#3224	1	2	yes	—
252	C₂×C₁₉	#3225	1	2	yes	—
253	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×Q₁₆	—	4	1	no	—
258	C₂×Q₁₆	—	4	2	no	—
259	C₂×SD₁₆	—	4	2	no	—
260	C₂×SD₁₆	—	4	2	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂×D₈	—	4	1	no	—
263	C₂×D₈	—	4	2	no	—
264	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
267	#124	—	4	2	no	—
268	#124	—	4	2	no	—
269	C₂²⋊Q₈	—	4	2	no	—
270	C₂²⋊Q₈	—	4	2	no	—
271	#121	—	4	2	no	—
272	#121	—	4	2	no	—
273	#117	—	4	1	no	—
274	#117	—	4	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
290	#103	—	4	2	no	—
291	#103	—	4	2	no	—
292	#102	—	4	2	no	—
293	#102	—	4	2	no	—
294	C₂²⋊C₈	—	4	1	no	—
295	C₂²⋊C₈	—	4	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₁₉	#32769	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	2	no	—
300	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂×Q₈	—	2	2	no	—
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×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
327	Q₁₆	—	4	4	no	—
328	SD₁₆	—	4	8	no	—
329	D₈	—	4	4	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	8	2	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
401	C₈	—	4	1	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	C₁₉×#534	1	1	yes	characteristic
417	C₂²	C₁₉×#535	1	2	yes	—
418	C₂²	C₁₉×#576	1	1	yes	characteristic
419	C₂²	C₁₉×#577	1	2	yes	—
420	C₂²	C₁₉×#578	1	1	yes	characteristic
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	C₁₉×#560	1	1	yes	characteristic
428	C₄	C₁₉×#560	1	2	yes	—
429	C₄	C₁₉×#560	1	1	yes	characteristic
430	C₂	—	8	1	no	—
431	C₂	—	16	2	no	—
432	C₂	C₁₉×#2815	1	1	yes	characteristic
433	C₂	C₁₉×#3203	1	1	yes	characteristic
434	C₂	C₁₉×#3204	1	1	yes	characteristic
435	C₂	C₁₉×#3224	1	2	yes	—
436	C₂	C₁₉×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2620	C₂	semidirect
2. C₁₉×#2072	C₂	semidirect
3. C₁₉×#2071	C₂	semidirect
4. C₁₉×#2015	C₂	semidirect
5. C₁₉×#2012	C₂	semidirect
6. C₁₉×#2001	C₂	semidirect
7. C₁₉×#2000	C₂	semidirect
9. C₁₉×#1818	C₂	semidirect
136. #32769	C₁₉	direct (N × H)
186. #2620	C₂×C₁₉	semidirect
187. #2072	C₂×C₁₉	semidirect
188. #2071	C₂×C₁₉	semidirect
189. #2015	C₂×C₁₉	semidirect
190. #2012	C₂×C₁₉	semidirect
191. #2001	C₂×C₁₉	semidirect
192. #2000	C₂×C₁₉	semidirect
194. #1818	C₂×C₁₉	semidirect
298. C₁₉	#32769	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×#2620	2
C₁₉×#2072	2
C₁₉×#2071	2
C₁₉×#2015	2
C₁₉×#2012	2
C₁₉×#2001	2
C₁₉×#2000	2
C₁₉×#1999	2
C₁₉×#1818	2
#32769	19

Subgroups — C19×#32769 #18038728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32769 #18038728