Subgroups — C₁₉×#19520 #18025479

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	1	no	—
16	C₁₉×#492	—	2	1	no	—
17	C₁₉×#492	C₂²	1	1	yes	characteristic
18	C₁₉×#492	C₂²	1	1	yes	characteristic
19	C₁₉×#491	—	2	1	no	—
20	C₁₉×#486	—	2	1	no	—
21	C₁₉×#486	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#485	—	2	2	no	—
24	C₁₉×#477	C₂²	1	2	yes	complemented
25	C₁₉×#475	C₂²	1	2	yes	complemented
26	C₁₉×#460	—	2	2	no	—
27	C₁₉×#460	C₂²	1	2	yes	—
28	C₁₉×#460	C₂²	1	2	yes	—
29	C₁₉×#450	—	2	2	no	—
30	C₁₉×#450	—	2	2	no	—
31	C₁₉×#446	—	2	2	no	—
32	C₁₉×#446	C₂²	1	2	yes	complemented
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#431	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	complemented
40	C₁₉×#334	C₂²	1	2	yes	complemented
41	C₁₉×#333	C₂²	1	2	yes	complemented
42	C₁₉×#332	C₂²	1	2	yes	complemented
43	C₁₉×#331	C₂²	1	2	yes	—
44	C₁₉×#331	C₂²	1	2	yes	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×#127	—	2	1	no	—
57	C₁₉×#127	—	2	1	no	—
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	C₂³	1	1	yes	characteristic
60	C₁₉×#127	C₂³	1	1	yes	characteristic
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
71	C₁₉×#117	—	2	1	no	—
72	C₁₉×#117	—	2	1	no	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#106	—	2	2	no	—
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
79	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₉×#103	—	2	2	no	—
83	C₁₉×#103	—	2	2	no	—
84	C₁₉×#102	—	2	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	1	no	—
89	C₁₉×C₂²⋊C₈	—	2	1	no	—
90	C₁₉×C₂²⋊C₈	—	2	1	no	—
91	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₉×#97	—	2	2	no	—
93	C₁₉×#97	—	2	1	no	—
94	C₁₉×#97	—	2	1	no	—
95	C₄×C₈×C₁₉	—	2	2	no	—
96	C₄×C₈×C₁₉	—	2	1	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₂⁴×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂×D₄×C₁₉	—	8	2	no	—
114	C₂×D₄×C₁₉	—	8	2	no	—
115	C₂×D₄×C₁₉	—	8	2	no	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	SD₁₆×C₁₉	—	8	2	no	—
120	SD₁₆×C₁₉	—	8	2	no	—
121	SD₁₆×C₁₉	—	8	2	no	—
122	SD₁₆×C₁₉	—	8	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	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	#41	1	1	yes	characteristic
147	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
148	#19520	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	8	2	no	—
152	C₂³×C₁₉	—	8	2	no	—
153	C₂³×C₁₉	—	8	2	no	—
154	C₂³×C₁₉	#121	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	2	2	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	8	1	no	—
159	Q₈×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	4	2	no	—
161	D₄×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	8	2	no	—
167	D₄×C₁₉	—	8	2	no	—
168	D₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
182	C₈×C₁₉	—	2	2	no	—
183	C₈×C₁₉	—	2	2	no	—
184	C₈×C₁₉	—	4	2	no	—
185	C₈×C₁₉	—	4	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#3208	C₂×C₁₉	1	1	yes	characteristic
189	#3208	C₂×C₁₉	1	1	yes	characteristic
190	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1698	C₂×C₁₉	1	2	yes	complemented
192	#1686	C₂×C₁₉	1	2	yes	complemented
193	#1678	C₂×C₁₉	1	2	yes	complemented
194	#1666	C₂×C₁₉	1	2	yes	complemented
195	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1555	C₂×C₁₉	1	1	yes	characteristic
197	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	16	4	no	—
208	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	#577	1	2	yes	—
218	C₄×C₁₉	#577	1	2	yes	—
219	#533	C₂²×C₁₉	1	1	yes	characteristic
220	#533	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
222	#501	—	2	1	no	—
223	#492	—	2	1	no	—
224	#492	C₂²×C₁₉	1	1	yes	characteristic
225	#492	C₂²×C₁₉	1	1	yes	characteristic
226	#491	—	2	1	no	—
227	#486	—	2	1	no	—
228	#486	C₂²×C₁₉	1	1	yes	characteristic
229	#486	C₂²×C₁₉	1	1	yes	characteristic
230	#485	—	2	2	no	—
231	#477	C₂²×C₁₉	1	2	yes	complemented
232	#475	C₂²×C₁₉	1	2	yes	complemented
233	#460	—	2	2	no	—
234	#460	C₂²×C₁₉	1	2	yes	—
235	#460	C₂²×C₁₉	1	2	yes	—
236	#450	—	2	2	no	—
237	#450	—	2	2	no	—
238	#446	—	2	2	no	—
239	#446	C₂²×C₁₉	1	2	yes	complemented
240	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
241	#433	—	2	2	no	—
242	#432	C₂²×C₁₉	1	1	yes	characteristic
243	#432	C₂²×C₁₉	1	1	yes	characteristic
244	#431	C₂²×C₁₉	1	1	yes	characteristic
245	#431	C₂²×C₁₉	1	1	yes	characteristic
246	#335	C₂²×C₁₉	1	2	yes	complemented
247	#334	C₂²×C₁₉	1	2	yes	complemented
248	#333	C₂²×C₁₉	1	2	yes	complemented
249	#332	C₂²×C₁₉	1	2	yes	complemented
250	#331	C₂²×C₁₉	1	2	yes	—
251	#331	C₂²×C₁₉	1	2	yes	—
252	C₂×C₁₉	—	4	1	no	—
253	C₂×C₁₉	—	16	1	no	—
254	C₂×C₁₉	—	16	1	no	—
255	C₂×C₁₉	#3043	1	1	yes	characteristic
256	C₂×C₁₉	#3057	1	1	yes	characteristic
257	C₂×C₁₉	#3068	1	1	yes	characteristic
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
266	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	C₂³×C₁₉	1	1	yes	characteristic
273	#127	C₂³×C₁₉	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#125	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
292	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
293	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
294	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
305	#97	—	2	2	no	—
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₁₉	#19520	1	1	yes	characteristic, direct product factor, Sylow
313	C₂⁴	—	4	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	—	8	2	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
333	SD₁₆	—	8	2	no	—
334	SD₁₆	—	8	2	no	—
335	SD₁₆	—	8	2	no	—
336	SD₁₆	—	8	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₄²	#41×C₁₉	1	1	yes	characteristic
361	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	8	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	C₁₉×#121	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	16	4	no	—
410	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	C₁₉×#577	1	2	yes	—
420	C₄	C₁₉×#577	1	2	yes	—
421	C₂	—	4	1	no	—
422	C₂	—	16	1	no	—
423	C₂	—	16	1	no	—
424	C₂	C₁₉×#3043	1	1	yes	characteristic
425	C₂	C₁₉×#3057	1	1	yes	characteristic
426	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
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×#3237	C₂	semidirect
4. C₁₉×#2985	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1686	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1572	C₂	semidirect
11. C₁₉×#1554	C₂	semidirect
24. C₁₉×#477	C₂²	semidirect
25. C₁₉×#475	C₂²	semidirect
32. C₁₉×#446	C₂²	semidirect
33. C₈×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#335	C₂²	semidirect
40. C₁₉×#334	C₂²	semidirect
41. C₁₉×#333	C₂²	semidirect
42. C₁₉×#332	C₂²	semidirect
148. #19520	C₁₉	direct (N × H)
187. #3237	C₂×C₁₉	semidirect
190. #2985	C₂×C₁₉	semidirect
191. #1698	C₂×C₁₉	semidirect
192. #1686	C₂×C₁₉	semidirect
193. #1678	C₂×C₁₉	semidirect
194. #1666	C₂×C₁₉	semidirect
195. #1572	C₂×C₁₉	semidirect
197. #1554	C₂×C₁₉	semidirect
231. #477	C₂²×C₁₉	semidirect
232. #475	C₂²×C₁₉	semidirect
239. #446	C₂²×C₁₉	semidirect
240. C₈×Q₈	C₂²×C₁₉	semidirect
246. #335	C₂²×C₁₉	semidirect
247. #334	C₂²×C₁₉	semidirect
248. #333	C₂²×C₁₉	semidirect
249. #332	C₂²×C₁₉	semidirect
312. C₁₉	#19520	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×#3237	2
C₁₉×#3208	2
C₁₉×#2985	2
C₁₉×#1698	2
C₁₉×#1686	2
C₁₉×#1678	2
C₁₉×#1666	2
C₁₉×#1572	2
C₁₉×#1555	2
C₁₉×#1554	2
#19520	19

Subgroups — C19×#19520 #18025479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19520 #18025479