Subgroups — C₁₉×#23527 #18029486

Order 4864.

1336 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#413	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2050	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#575	—	2	4	no	—
9	C₁₉×#575	—	2	2	no	—
10	C₁₉×#575	C₂²	1	4	yes	—
11	C₂×C₁₉×#137	—	2	2	no	—
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
13	C₂×C₁₉×#135	—	2	2	no	—
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₁₉×#424	—	2	2	no	—
19	C₁₉×#424	—	2	2	no	—
20	C₁₉×#423	C₂²	1	4	yes	complemented
21	C₁₉×#421	—	2	4	no	—
22	C₁₉×#421	—	2	4	no	—
23	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
24	C₁₉×#413	—	2	4	no	—
25	C₁₉×#413	C₂²	1	8	yes	complemented
26	C₂×C₁₉×#101	—	2	2	no	—
27	C₂×C₁₉×#100	—	2	2	no	—
28	C₁₉×#338	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	D₄	1	4	yes	—
40	C₂×#41×C₁₉	C₂³	1	4	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₁₉×#137	—	2	8	no	—
47	C₁₉×#137	—	2	8	no	—
48	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
49	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
50	C₁₉×#135	—	2	8	no	—
51	C₁₉×#135	—	2	8	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	4	no	—
54	C₂×D₈×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	2	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	2	no	—
71	C₂²×C₈×C₁₉	D₄	1	2	yes	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	D₄	1	2	yes	—
75	C₁₉×#117	D₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
79	C₁₉×C₄⋊C₈	—	2	8	no	—
80	C₁₉×#104	—	2	16	no	—
81	C₁₉×#101	—	2	8	no	—
82	C₁₉×#100	—	2	8	no	—
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	#41	1	1	yes	characteristic
85	#41×C₁₉	—	2	4	no	—
86	#41×C₁₉	—	2	4	no	—
87	#41×C₁₉	—	2	4	no	—
88	#41×C₁₉	—	2	4	no	—
89	#41×C₁₉	—	2	4	no	—
90	#41×C₁₉	—	2	4	no	—
91	#41×C₁₉	—	2	4	no	—
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	4	2	no	—
94	#41×C₁₉	—	4	2	no	—
95	#41×C₁₉	—	4	2	no	—
96	#41×C₁₉	—	4	2	no	—
97	#41×C₁₉	—	4	2	no	—
98	#41×C₁₉	—	4	2	no	—
99	#41×C₁₉	—	4	2	no	—
100	#41×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	#41	1	2	yes	—
135	C₂²×C₄×C₁₉	#41	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	2	8	no	—
138	SD₁₆×C₁₉	—	2	16	no	—
139	D₈×C₁₉	—	2	8	no	—
140	M₁₆×C₁₉	—	2	4	no	—
141	M₁₆×C₁₉	—	2	4	no	—
142	M₁₆×C₁₉	—	2	4	no	—
143	M₁₆×C₁₉	—	2	4	no	—
144	M₁₆×C₁₉	—	2	4	no	—
145	M₁₆×C₁₉	—	4	1	no	—
146	M₁₆×C₁₉	—	4	1	no	—
147	M₁₆×C₁₉	—	4	2	no	—
148	M₁₆×C₁₉	—	4	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	4	no	—
153	C₂×C₈×C₁₉	—	4	2	no	—
154	C₂×C₈×C₁₉	—	4	2	no	—
155	C₂×C₈×C₁₉	—	4	2	no	—
156	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	C₂×D₄	1	4	yes	—
163	#23527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	8	1	no	—
168	C₂³×C₁₉	—	8	4	no	—
169	C₂³×C₁₉	#121	1	1	yes	characteristic
170	C₂³×C₁₉	#121	1	1	yes	characteristic
171	C₂³×C₁₉	#123	1	2	yes	—
172	C₂³×C₁₉	#123	1	2	yes	—
173	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	4	no	—
175	Q₈×C₁₉	—	2	4	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	2	4	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	2	yes	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	#121	1	2	yes	—
200	C₂×C₄×C₁₉	#121	1	2	yes	—
201	C₂×C₄×C₁₉	#121	1	2	yes	—
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#123	1	2	yes	—
205	C₂×C₄×C₁₉	#123	1	2	yes	—
206	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#124	1	2	yes	—
208	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
213	C₈×C₁₉	—	2	4	no	—
214	C₈×C₁₉	—	4	2	no	—
215	C₈×C₁₉	—	4	4	no	—
216	C₂×#575	C₂×C₁₉	1	1	yes	characteristic
217	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
218	C₂×#421	C₂×C₁₉	1	2	yes	complemented
219	C₂×#413	C₂×C₁₉	1	2	yes	complemented
220	#2050	C₂×C₁₉	1	8	yes	complemented
221	C₂×#338	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	8	4	no	—
229	C₂²×C₁₉	—	8	4	no	—
230	C₂²×C₁₉	—	8	4	no	—
231	C₂²×C₁₉	#394	1	1	yes	characteristic
232	C₂²×C₁₉	#394	1	2	yes	—
233	C₂²×C₁₉	#394	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
235	C₂²×C₁₉	C₂×#123	1	2	yes	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	#394	1	1	yes	characteristic
239	C₄×C₁₉	#394	1	2	yes	—
240	C₄×C₁₉	#394	1	1	yes	characteristic
241	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₄×C₁₉	C₂×#121	1	2	yes	—
243	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
244	C₂²×#41	C₂²×C₁₉	1	2	yes	—
245	#575	—	2	4	no	—
246	#575	—	2	2	no	—
247	#575	C₂²×C₁₉	1	4	yes	—
248	C₂×#137	—	2	2	no	—
249	C₂×AGL(1,ℤ/8)	—	2	2	no	—
250	C₂×#135	—	2	2	no	—
251	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
253	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
255	#424	—	2	2	no	—
256	#424	—	2	2	no	—
257	#423	C₂²×C₁₉	1	4	yes	complemented
258	#421	—	2	4	no	—
259	#421	—	2	4	no	—
260	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
261	#413	—	2	4	no	—
262	#413	C₂²×C₁₉	1	8	yes	complemented
263	C₂×#101	—	2	2	no	—
264	C₂×#100	—	2	2	no	—
265	#338	C₂²×C₁₉	1	4	yes	complemented
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	2	no	—
269	C₂×C₁₉	—	2	2	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	8	4	no	—
272	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	D₄×C₁₉	1	4	yes	—
284	C₂×#41	C₂³×C₁₉	1	4	yes	—
285	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	D₄×C₁₉	1	2	yes	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
290	#137	—	2	8	no	—
291	#137	—	2	8	no	—
292	AGL(1,ℤ/8)	—	2	8	no	—
293	AGL(1,ℤ/8)	—	2	8	no	—
294	#135	—	2	8	no	—
295	#135	—	2	8	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
310	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
311	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	D₄×C₁₉	1	2	yes	—
316	#117	—	2	1	no	—
317	#117	—	2	1	no	—
318	#117	D₄×C₁₉	1	2	yes	—
319	#117	D₄×C₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
323	C₄⋊C₈	—	2	8	no	—
324	#104	—	2	16	no	—
325	#101	—	2	8	no	—
326	#100	—	2	8	no	—
327	C₁₉	#23527	1	1	yes	characteristic, direct product factor, Sylow
328	C₂⁴	—	2	2	no	—
329	C₂⁴	#41×C₁₉	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	2	no	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	#41×C₁₉	1	2	yes	—
380	C₂²×C₄	#41×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
382	Q₁₆	—	2	8	no	—
383	SD₁₆	—	2	16	no	—
384	D₈	—	2	8	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	4	no	—
390	M₁₆	—	4	1	no	—
391	M₁₆	—	4	1	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	4	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	—	4	2	no	—
401	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	C₂×D₄×C₁₉	1	4	yes	—
408	C₂³	—	2	4	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	8	4	no	—
413	C₂³	C₁₉×#121	1	1	yes	characteristic
414	C₂³	C₁₉×#121	1	1	yes	characteristic
415	C₂³	C₁₉×#123	1	2	yes	—
416	C₂³	C₁₉×#123	1	2	yes	—
417	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#120	1	2	yes	—
442	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
444	C₂×C₄	C₁₉×#121	1	2	yes	—
445	C₂×C₄	C₁₉×#121	1	2	yes	—
446	C₂×C₄	C₁₉×#121	1	2	yes	—
447	C₂×C₄	C₁₉×#121	1	2	yes	—
448	C₂×C₄	C₁₉×#123	1	2	yes	—
449	C₂×C₄	C₁₉×#123	1	2	yes	—
450	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#124	1	2	yes	—
452	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	4	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	8	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	4	no	—
469	C₂²	C₁₉×#394	1	1	yes	characteristic
470	C₂²	C₁₉×#394	1	2	yes	—
471	C₂²	C₁₉×#394	1	1	yes	characteristic
472	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
473	C₂²	C₂×C₁₉×#123	1	2	yes	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	C₁₉×#394	1	1	yes	characteristic
477	C₄	C₁₉×#394	1	2	yes	—
478	C₄	C₁₉×#394	1	1	yes	characteristic
479	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
480	C₄	C₂×C₁₉×#121	1	2	yes	—
481	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	2	no	—
485	C₂	—	2	2	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	4	no	—
488	C₂	C₂×C₁₉×#394	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	C₂×#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂×#394
prime radical	C₂×C₁₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2905	C₂	semidirect
3. C₂×C₁₉×#421	C₂	semidirect
4. C₂×C₁₉×#413	C₂	semidirect
5. C₁₉×#2050	C₂	semidirect
6. C₂×C₁₉×#338	C₂	semidirect
20. C₁₉×#423	C₂²	semidirect
23. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#413	C₂²	semidirect
28. C₁₉×#338	C₂²	semidirect
163. #23527	C₁₉	direct (N × H)
217. #2905	C₂×C₁₉	semidirect
218. C₂×#421	C₂×C₁₉	semidirect
219. C₂×#413	C₂×C₁₉	semidirect
220. #2050	C₂×C₁₉	semidirect
221. C₂×#338	C₂×C₁₉	semidirect
257. #423	C₂²×C₁₉	semidirect
260. C₂×#104	C₂²×C₁₉	semidirect
262. #413	C₂²×C₁₉	semidirect
265. #338	C₂²×C₁₉	semidirect
327. C₁₉	#23527	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#575	2
C₁₉×#2905	2
C₂×C₁₉×#421	2
C₂×C₁₉×#413	2
C₁₉×#2050	2
C₂×C₁₉×#338	2
#23527	19

Subgroups — C19×#23527 #18029486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23527 #18029486