Subgroups — C₁₉×#19561 #18025520

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1697	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1695	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1677	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1675	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#500	C₂²	1	2	yes	—
16	C₁₉×#498	—	2	1	no	—
17	C₁₉×#486	—	2	1	no	—
18	C₁₉×#486	C₂²	1	2	yes	—
19	C₁₉×#481	—	2	2	no	—
20	C₁₉×#480	—	2	2	no	—
21	C₁₉×#476	—	2	1	no	—
22	C₁₉×#476	C₂²	1	2	yes	—
23	C₁₉×#476	C₂²	1	2	yes	—
24	C₁₉×#476	C₂²	1	2	yes	—
25	C₁₉×#474	—	2	1	no	—
26	C₁₉×#474	—	2	1	no	—
27	C₁₉×#469	—	2	2	no	—
28	C₁₉×#459	—	2	1	no	—
29	C₁₉×#459	C₂²	1	2	yes	—
30	C₁₉×#436	—	2	1	no	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₈×D₄×C₁₉	—	2	1	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	1	yes	characteristic
42	C₁₉×#333	C₂²	1	2	yes	—
43	C₁₉×#333	C₂²	1	1	yes	characteristic
44	C₁₉×#333	C₂²	1	2	yes	—
45	C₁₉×#331	C₂²	1	1	yes	characteristic
46	C₁₉×#331	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂×D₈×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	D₄	1	1	yes	characteristic
61	C₁₉×#127	C₂³	1	1	yes	characteristic
62	C₁₉×#124	—	2	1	no	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	D₄	1	2	yes	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#107	—	2	2	no	—
76	C₁₉×#107	—	2	2	no	—
77	C₁₉×#106	—	2	2	no	—
78	C₁₉×#106	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#102	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×#102	—	2	2	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	#41×C₁₉	—	8	1	no	—
103	#41×C₁₉	—	8	1	no	—
104	#41×C₁₉	—	8	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	8	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	D₈×C₁₉	—	8	2	no	—
125	M₁₆×C₁₉	—	8	2	no	—
126	M₁₆×C₁₉	—	8	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	8	2	no	—
133	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	#41	1	1	yes	characteristic
150	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
151	#19561	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	#121	1	1	yes	characteristic
155	Q₈×C₁₉	—	8	1	no	—
156	Q₈×C₁₉	—	8	2	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	Q₈×C₁₉	—	8	2	no	—
159	D₄×C₁₉	—	2	2	no	—
160	D₄×C₁₉	—	2	2	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	4	1	no	—
164	D₄×C₁₉	—	4	1	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	8	1	no	—
167	D₄×C₁₉	—	8	1	no	—
168	D₄×C₁₉	—	8	2	no	—
169	D₄×C₁₉	—	8	2	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	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	2	2	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	4	1	no	—
192	C₈×C₁₉	—	4	1	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	4	1	no	—
195	#3253	C₂×C₁₉	1	1	yes	characteristic
196	#3227	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1697	C₂×C₁₉	1	2	yes	complemented
200	#1695	C₂×C₁₉	1	2	yes	complemented
201	#1677	C₂×C₁₉	1	2	yes	complemented
202	#1675	C₂×C₁₉	1	2	yes	complemented
203	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1543	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	#472	1	2	yes	—
223	C₄×C₁₉	#577	1	1	yes	characteristic
224	C₄×C₁₉	#577	1	1	yes	characteristic
225	C₄×C₁₉	#577	1	1	yes	characteristic
226	C₄×C₁₉	#578	1	1	yes	characteristic
227	#532	C₂²×C₁₉	1	1	yes	characteristic
228	#532	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
230	#500	C₂²×C₁₉	1	2	yes	—
231	#498	—	2	1	no	—
232	#486	—	2	1	no	—
233	#486	C₂²×C₁₉	1	2	yes	—
234	#481	—	2	2	no	—
235	#480	—	2	2	no	—
236	#476	—	2	1	no	—
237	#476	C₂²×C₁₉	1	2	yes	—
238	#476	C₂²×C₁₉	1	2	yes	—
239	#476	C₂²×C₁₉	1	2	yes	—
240	#474	—	2	1	no	—
241	#474	—	2	1	no	—
242	#469	—	2	2	no	—
243	#459	—	2	1	no	—
244	#459	C₂²×C₁₉	1	2	yes	—
245	#436	—	2	1	no	—
246	#436	C₂²×C₁₉	1	2	yes	—
247	C₈×D₄	—	2	1	no	—
248	C₈×D₄	C₂²×C₁₉	1	2	yes	—
249	#431	C₂²×C₁₉	1	1	yes	characteristic
250	#431	C₂²×C₁₉	1	1	yes	characteristic
251	#431	C₂²×C₁₉	1	1	yes	characteristic
252	#423	C₂²×C₁₉	1	1	yes	characteristic
253	#408	—	2	2	no	—
254	#335	C₂²×C₁₉	1	2	yes	—
255	#334	C₂²×C₁₉	1	2	yes	—
256	#333	C₂²×C₁₉	1	1	yes	characteristic
257	#333	C₂²×C₁₉	1	1	yes	characteristic
258	#333	C₂²×C₁₉	1	2	yes	—
259	#333	C₂²×C₁₉	1	2	yes	—
260	#331	C₂²×C₁₉	1	1	yes	characteristic
261	#331	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₁₉	—	4	1	no	—
263	C₂×C₁₉	—	8	2	no	—
264	C₂×C₁₉	—	16	1	no	—
265	C₂×C₁₉	#3042	1	1	yes	characteristic
266	C₂×C₁₉	#3063	1	1	yes	characteristic
267	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
281	#127	D₄×C₁₉	1	1	yes	characteristic
282	#127	C₂³×C₁₉	1	1	yes	characteristic
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	D₄×C₁₉	1	2	yes	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#107	—	2	2	no	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
303	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	C₂³×C₁₉	1	2	yes	—
323	C₁₉	#19561	1	1	yes	characteristic, direct product factor, Sylow
324	#41	—	8	1	no	—
325	#41	—	8	1	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	8	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
346	D₈	—	8	2	no	—
347	M₁₆	—	8	2	no	—
348	M₁₆	—	8	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	8	2	no	—
355	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₄²	#41×C₁₉	1	1	yes	characteristic
372	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₂³	—	2	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₁₉×#121	1	1	yes	characteristic
376	Q₈	—	8	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	8	1	no	—
379	Q₈	—	8	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
404	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
405	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	C₁₉×#472	1	2	yes	—
433	C₄	C₁₉×#577	1	1	yes	characteristic
434	C₄	C₁₉×#577	1	1	yes	characteristic
435	C₄	C₁₉×#577	1	1	yes	characteristic
436	C₄	C₁₉×#578	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	1	no	—
440	C₂	C₁₉×#3042	1	1	yes	characteristic
441	C₂	C₁₉×#3063	1	1	yes	characteristic
442	C₂	C₂×C₁₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3253	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
2. C₁₉×#3227	C₂	semidirect
3. C₁₉×#3226	C₂	semidirect
4. C₁₉×#2979	C₂	semidirect
5. C₁₉×#1697	C₂	semidirect
6. C₁₉×#1695	C₂	semidirect
7. C₁₉×#1677	C₂	semidirect
8. C₁₉×#1675	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1548	C₂	semidirect
11. C₁₉×#1543	C₂	semidirect
151. #19561	C₁₉	direct (N × H)
196. #3227	C₂×C₁₉	semidirect
197. #3226	C₂×C₁₉	semidirect
198. #2979	C₂×C₁₉	semidirect
199. #1697	C₂×C₁₉	semidirect
200. #1695	C₂×C₁₉	semidirect
201. #1677	C₂×C₁₉	semidirect
202. #1675	C₂×C₁₉	semidirect
203. #1574	C₂×C₁₉	semidirect
204. #1548	C₂×C₁₉	semidirect
205. #1543	C₂×C₁₉	semidirect
323. C₁₉	#19561	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×#3253	2
C₁₉×#3227	2
C₁₉×#3226	2
C₁₉×#2979	2
C₁₉×#1697	2
C₁₉×#1695	2
C₁₉×#1677	2
C₁₉×#1675	2
C₁₉×#1574	2
C₁₉×#1548	2
C₁₉×#1543	2
#19561	19

Subgroups — C19×#19561 #18025520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19561 #18025520