Subgroups — C₁₉×#19501 #18025460

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3106	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1701	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1682	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#498	C₂²	1	2	yes	—
17	C₁₉×#486	C₂²	1	2	yes	—
18	C₁₉×#482	—	2	1	no	—
19	C₁₉×#481	—	2	2	no	—
20	C₁₉×#477	C₂²	1	1	yes	characteristic
21	C₁₉×#476	—	2	1	no	—
22	C₁₉×#476	—	2	1	no	—
23	C₁₉×#476	C₂²	1	1	yes	characteristic
24	C₁₉×#462	—	2	1	no	—
25	C₁₉×#462	C₂²	1	2	yes	—
26	C₁₉×#461	—	2	1	no	—
27	C₁₉×#461	C₂²	1	2	yes	—
28	C₁₉×#460	C₂²	1	1	yes	characteristic
29	C₁₉×#459	C₂²	1	1	yes	characteristic
30	C₁₉×#449	—	2	1	no	—
31	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₄×D₈×C₁₉	—	2	1	no	—
34	C₁₉×#436	—	2	2	no	—
35	C₁₉×#436	C₂²	1	2	yes	—
36	C₁₉×#431	—	2	1	no	—
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#431	C₂²	1	1	yes	characteristic
39	C₁₉×#423	—	2	1	no	—
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₁₉×#423	C₂²	1	1	yes	characteristic
42	C₁₉×#419	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₁₉×#137	—	4	4	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×D₈×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₉×#127	C₂³	1	1	yes	characteristic
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#107	—	2	1	no	—
84	C₁₉×#106	—	2	2	no	—
85	C₁₉×#106	—	2	2	no	—
86	C₁₉×#106	—	2	1	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₁₉×#103	—	2	1	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#102	—	2	1	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	1	no	—
103	C₁₉×#102	—	2	1	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×C₂²⋊C₈	—	2	2	no	—
106	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	—	2	1	no	—
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	8	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
133	Q₁₆×C₁₉	—	4	4	no	—
134	SD₁₆×C₁₉	—	4	4	no	—
135	SD₁₆×C₁₉	—	4	2	no	—
136	D₈×C₁₉	—	4	2	no	—
137	M₁₆×C₁₉	—	4	2	no	—
138	M₁₆×C₁₉	—	8	2	no	—
139	M₁₆×C₁₉	—	8	1	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	#41	1	1	yes	characteristic
167	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
168	#19501	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	#121	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	1	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	8	1	no	—
176	Q₈×C₁₉	—	8	2	no	—
177	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
178	D₄×C₁₉	—	2	1	no	—
179	D₄×C₁₉	—	2	1	no	—
180	D₄×C₁₉	—	4	2	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	8	1	no	—
186	D₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₉	—	2	2	no	—
210	C₈×C₁₉	—	2	2	no	—
211	C₈×C₁₉	—	4	2	no	—
212	C₈×C₁₉	—	4	1	no	—
213	C₈×C₁₉	—	4	1	no	—
214	C₈×C₁₉	—	4	2	no	—
215	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#3106	C₂×C₁₉	1	1	yes	characteristic
217	#3039	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1701	C₂×C₁₉	1	2	yes	complemented
220	#1691	C₂×C₁₉	1	2	yes	complemented
221	#1682	C₂×C₁₉	1	2	yes	complemented
222	#1672	C₂×C₁₉	1	2	yes	complemented
223	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	4	1	no	—
232	C₂²×C₁₉	—	8	1	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	—	8	1	no	—
235	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	4	1	no	—
241	C₄×C₁₉	—	4	1	no	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	#471	1	2	yes	—
245	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₄×C₁₉	#575	1	1	yes	characteristic
247	C₄×C₁₉	#577	1	1	yes	characteristic
248	C₄×C₁₉	#578	1	1	yes	characteristic
249	C₂×#137	—	2	1	no	—
250	#532	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
253	#498	C₂²×C₁₉	1	2	yes	—
254	#486	C₂²×C₁₉	1	2	yes	—
255	#482	—	2	1	no	—
256	#481	—	2	2	no	—
257	#477	C₂²×C₁₉	1	1	yes	characteristic
258	#476	—	2	1	no	—
259	#476	—	2	1	no	—
260	#476	C₂²×C₁₉	1	1	yes	characteristic
261	#462	—	2	1	no	—
262	#462	C₂²×C₁₉	1	2	yes	—
263	#461	—	2	1	no	—
264	#461	C₂²×C₁₉	1	2	yes	—
265	#460	C₂²×C₁₉	1	1	yes	characteristic
266	#459	C₂²×C₁₉	1	1	yes	characteristic
267	#449	—	2	1	no	—
268	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
269	C₄×SD₁₆	—	2	1	no	—
270	C₄×D₈	—	2	1	no	—
271	#436	—	2	2	no	—
272	#436	C₂²×C₁₉	1	2	yes	—
273	#431	—	2	1	no	—
274	#431	C₂²×C₁₉	1	1	yes	characteristic
275	#431	C₂²×C₁₉	1	1	yes	characteristic
276	#423	—	2	1	no	—
277	#423	C₂²×C₁₉	1	1	yes	characteristic
278	#423	C₂²×C₁₉	1	1	yes	characteristic
279	#419	—	2	1	no	—
280	#335	C₂²×C₁₉	1	2	yes	—
281	#334	C₂²×C₁₉	1	2	yes	—
282	#333	C₂²×C₁₉	1	2	yes	—
283	#332	C₂²×C₁₉	1	2	yes	—
284	#332	C₂²×C₁₉	1	2	yes	—
285	#331	C₂²×C₁₉	1	2	yes	—
286	C₂×C₁₉	—	4	1	no	—
287	C₂×C₁₉	—	8	1	no	—
288	C₂×C₁₉	—	16	1	no	—
289	C₂×C₁₉	#3046	1	1	yes	characteristic
290	C₂×C₁₉	#3055	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
292	C₂×#41	—	2	1	no	—
293	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
294	C₂²×Q₈	—	2	1	no	—
295	#137	—	4	4	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	1	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×D₈	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
308	#127	C₂³×C₁₉	1	1	yes	characteristic
309	#124	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
313	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
319	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
320	#117	—	2	1	no	—
321	#117	D₄×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
326	#107	—	2	1	no	—
327	#106	—	2	2	no	—
328	#106	—	2	2	no	—
329	#106	—	2	1	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
334	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
335	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
336	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
337	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
339	#103	—	2	1	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#102	—	2	1	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	1	no	—
346	#102	—	2	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	C₂³×C₁₉	1	2	yes	—
353	C₁₉	#19501	1	1	yes	characteristic, direct product factor, Sylow
354	#41	—	2	2	no	—
355	#41	—	4	1	no	—
356	#41	—	8	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	SD₁₆	—	4	4	no	—
379	SD₁₆	—	4	2	no	—
380	D₈	—	4	2	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	8	2	no	—
383	M₁₆	—	8	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₄²	#41×C₁₉	1	1	yes	characteristic
411	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
412	C₂³	—	2	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	C₁₉×#121	1	1	yes	characteristic
415	Q₈	—	2	1	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	8	1	no	—
419	Q₈	—	8	2	no	—
420	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
421	D₄	—	2	1	no	—
422	D₄	—	2	1	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
447	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
448	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	8	2	no	—
475	C₄	—	8	1	no	—
476	C₄	C₁₉×#471	1	2	yes	—
477	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₄	C₁₉×#575	1	1	yes	characteristic
479	C₄	C₁₉×#577	1	1	yes	characteristic
480	C₄	C₁₉×#578	1	1	yes	characteristic
481	C₂	—	4	1	no	—
482	C₂	—	8	1	no	—
483	C₂	—	16	1	no	—
484	C₂	C₁₉×#3046	1	1	yes	characteristic
485	C₂	C₁₉×#3055	1	1	yes	characteristic
486	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3106	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3227	C₂	semidirect
3. C₁₉×#3039	C₂	semidirect
4. C₁₉×#2991	C₂	semidirect
5. C₁₉×#1701	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1672	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1560	C₂	semidirect
11. C₁₉×#1549	C₂	semidirect
168. #19501	C₁₉	direct (N × H)
215. #3227	C₂×C₁₉	semidirect
217. #3039	C₂×C₁₉	semidirect
218. #2991	C₂×C₁₉	semidirect
219. #1701	C₂×C₁₉	semidirect
220. #1691	C₂×C₁₉	semidirect
221. #1682	C₂×C₁₉	semidirect
222. #1672	C₂×C₁₉	semidirect
223. #1574	C₂×C₁₉	semidirect
224. #1560	C₂×C₁₉	semidirect
225. #1549	C₂×C₁₉	semidirect
353. C₁₉	#19501	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×#3227	2
C₁₉×#3106	2
C₁₉×#3039	2
C₁₉×#2991	2
C₁₉×#1701	2
C₁₉×#1691	2
C₁₉×#1682	2
C₁₉×#1672	2
C₁₉×#1574	2
C₁₉×#1560	2
C₁₉×#1549	2
#19501	19

Subgroups — C19×#19501 #18025460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19501 #18025460