Subgroups — C₁₉×#32680 #18038639

Order 4864.

810 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2014	C₂	1	2	yes	maximal
5	C₁₉×#2013	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1973	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1928	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₂×C₁₉×#102	C₂²	1	2	yes	—
22	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
23	C₁₉×#400	—	2	1	no	—
24	C₁₉×#400	—	2	1	no	—
25	C₁₉×#394	—	2	1	no	—
26	C₁₉×#394	—	2	1	no	—
27	C₁₉×#391	—	2	1	no	—
28	C₁₉×#391	C₂²	1	2	yes	—
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#390	—	2	1	no	—
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#382	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂×SD₁₆×C₁₉	—	2	4	no	—
45	C₂×SD₁₆×C₁₉	—	4	2	no	—
46	C₂×SD₁₆×C₁₉	—	4	2	no	—
47	C₂×SD₁₆×C₁₉	—	4	2	no	—
48	C₂×SD₁₆×C₁₉	—	4	2	no	—
49	C₂×SD₁₆×C₁₉	—	4	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×C₄⋊Q₈	—	4	1	no	—
53	C₁₉×C₄⋊Q₈	—	4	1	no	—
54	C₁₉×#127	—	4	1	no	—
55	C₁₉×#127	—	4	1	no	—
56	C₁₉×#124	—	4	4	no	—
57	C₄×Q₈×C₁₉	—	4	1	no	—
58	C₄×Q₈×C₁₉	—	4	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#107	—	4	2	no	—
76	C₁₉×C₄⋊C₈	—	4	1	no	—
77	C₁₉×#103	—	2	4	no	—
78	C₁₉×#103	—	4	2	no	—
79	C₁₉×#102	—	2	4	no	—
80	C₁₉×#102	—	4	2	no	—
81	C₁₉×#97	—	4	1	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	1	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₂⁴×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	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	8	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₁₉	—	4	8	no	—
120	SD₁₆×C₁₉	—	4	8	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	#41	1	4	yes	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	8	2	no	—
139	C₂²⋊C₄×C₁₉	—	8	2	no	—
140	C₄²×C₁₉	—	2	1	no	—
141	C₄²×C₁₉	—	2	1	no	—
142	C₄²×C₁₉	—	2	1	no	—
143	C₄²×C₁₉	—	2	1	no	—
144	C₄²×C₁₉	—	2	1	no	—
145	C₄²×C₁₉	—	2	1	no	—
146	C₄²×C₁₉	—	4	2	no	—
147	C₄²×C₁₉	—	4	2	no	—
148	#32680	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₉	—	4	4	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	8	4	no	—
167	D₄×C₁₉	—	8	4	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₁₉	#137	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
196	C₈×C₁₉	—	2	4	no	—
197	C₈×C₁₉	—	4	2	no	—
198	#2568	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#2548	C₂×C₁₉	1	1	yes	characteristic
200	#2055	C₂×C₁₉	1	2	yes	complemented
201	#2014	C₂×C₁₉	1	2	yes	—
202	#2013	C₂×C₁₉	1	2	yes	complemented
203	#1985	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1973	C₂×C₁₉	1	2	yes	complemented
205	#1928	C₂×C₁₉	1	2	yes	complemented
206	#1925	C₂×C₁₉	1	2	yes	complemented
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	8	2	no	—
211	C₂²×C₁₉	—	8	2	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	#534	1	1	yes	characteristic
215	C₂²×C₁₉	#550	1	2	yes	—
216	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
218	C₂²×C₁₉	#577	1	2	yes	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	8	2	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	#538	1	2	yes	—
229	C₄×C₁₉	#555	1	1	yes	characteristic
230	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
232	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×#124	—	2	1	no	—
236	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#107	C₂²×C₁₉	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#103	C₂²×C₁₉	1	2	yes	—
240	C₂×#103	C₂²×C₁₉	1	2	yes	—
241	C₂×#102	C₂²×C₁₉	1	2	yes	—
242	C₂×#102	C₂²×C₁₉	1	2	yes	—
243	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
244	#400	—	2	1	no	—
245	#400	—	2	1	no	—
246	#394	—	2	1	no	—
247	#394	—	2	1	no	—
248	#391	—	2	1	no	—
249	#391	C₂²×C₁₉	1	2	yes	—
250	#391	C₂²×C₁₉	1	2	yes	—
251	#390	—	2	1	no	—
252	#390	C₂²×C₁₉	1	2	yes	—
253	#390	C₂²×C₁₉	1	2	yes	—
254	#382	—	2	1	no	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	#340	C₂²×C₁₉	1	2	yes	—
258	#336	C₂²×C₁₉	1	2	yes	—
259	#336	C₂²×C₁₉	1	2	yes	—
260	C₂×C₁₉	—	16	2	no	—
261	C₂×C₁₉	#2733	1	1	yes	characteristic
262	C₂×C₁₉	#3193	1	1	yes	characteristic
263	C₂×C₁₉	#3200	1	1	yes	characteristic
264	C₂×C₁₉	#3397	1	2	yes	—
265	C₂×C₁₉	#3400	1	2	yes	—
266	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	4	2	no	—
273	C₂×SD₁₆	—	4	2	no	—
274	C₂×SD₁₆	—	4	2	no	—
275	C₂×SD₁₆	—	4	2	no	—
276	C₂×SD₁₆	—	4	2	no	—
277	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
279	C₄⋊Q₈	—	4	1	no	—
280	C₄⋊Q₈	—	4	1	no	—
281	#127	—	4	1	no	—
282	#127	—	4	1	no	—
283	#124	—	4	4	no	—
284	C₄×Q₈	—	4	1	no	—
285	C₄×Q₈	—	4	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	#107	—	4	2	no	—
303	C₄⋊C₈	—	4	1	no	—
304	#103	—	2	4	no	—
305	#103	—	4	2	no	—
306	#102	—	2	4	no	—
307	#102	—	4	2	no	—
308	#97	—	4	1	no	—
309	#95	—	2	1	no	—
310	#95	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₁₉	#32680	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
347	SD₁₆	—	4	8	no	—
348	SD₁₆	—	4	8	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	#41×C₁₉	1	4	yes	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	4	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
418	C₂×C₄	C₁₉×#137	1	2	yes	—
419	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
420	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₁₉×#534	1	1	yes	characteristic
433	C₂²	C₁₉×#550	1	2	yes	—
434	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
436	C₂²	C₁₉×#577	1	2	yes	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	C₁₉×#538	1	2	yes	—
447	C₄	C₁₉×#555	1	1	yes	characteristic
448	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
449	C₂	—	16	2	no	—
450	C₂	C₁₉×#2733	1	1	yes	characteristic
451	C₂	C₁₉×#3193	1	1	yes	characteristic
452	C₂	C₁₉×#3200	1	1	yes	characteristic
453	C₂	C₁₉×#3397	1	2	yes	—
454	C₂	C₁₉×#3400	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2568	C₂	semidirect
3. C₁₉×#2055	C₂	semidirect
5. C₁₉×#2013	C₂	semidirect
6. C₁₉×#1985	C₂	semidirect
7. C₁₉×#1973	C₂	semidirect
8. C₁₉×#1928	C₂	semidirect
9. C₁₉×#1925	C₂	semidirect
148. #32680	C₁₉	direct (N × H)
198. #2568	C₂×C₁₉	semidirect
200. #2055	C₂×C₁₉	semidirect
202. #2013	C₂×C₁₉	semidirect
203. #1985	C₂×C₁₉	semidirect
204. #1973	C₂×C₁₉	semidirect
205. #1928	C₂×C₁₉	semidirect
206. #1925	C₂×C₁₉	semidirect
315. C₁₉	#32680	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×#2568	2
C₁₉×#2548	2
C₁₉×#2055	2
C₁₉×#2014	2
C₁₉×#2013	2
C₁₉×#1985	2
C₁₉×#1973	2
C₁₉×#1928	2
C₁₉×#1925	2
#32680	19

Subgroups — C19×#32680 #18038639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32680 #18038639