Subgroups — C₁₉×#32923 #18038882

Order 4864.

1334 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3039	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#456	C₂	1	2	yes	maximal
4	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1886	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1882	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	C₂²	1	4	yes	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₉×#520	—	2	2	no	—
14	C₁₉×#520	—	2	2	no	—
15	C₁₉×#520	C₂²	1	2	yes	—
16	C₁₉×#519	—	2	2	no	—
17	C₁₉×#519	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₉	—	2	2	no	—
19	C₄×#41×C₁₉	—	2	2	no	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#462	—	2	2	no	—
24	C₁₉×#462	—	2	2	no	—
25	C₁₉×#461	—	2	2	no	—
26	C₁₉×#461	—	2	2	no	—
27	C₁₉×#456	—	2	8	no	—
28	C₁₉×#423	C₂²	1	2	yes	—
29	C₂×C₁₉×#104	C₂²	1	4	yes	—
30	C₁₉×#419	C₂²	1	4	yes	—
31	C₂×C₁₉×#101	C₂²	1	2	yes	—
32	C₁₉×#398	—	2	2	no	—
33	C₁₉×#391	C₂²	1	2	yes	—
34	C₁₉×#389	—	2	2	no	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#343	C₂²	1	2	yes	—
37	C₁₉×#339	C₂²	1	4	yes	—
38	C₁₉×2₋¹⁺⁴	—	2	4	no	—
39	C₁₉×2₋¹⁺⁴	—	2	2	no	—
40	C₁₉×2₋¹⁺⁴	D₄	1	4	yes	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×#137	—	2	8	no	—
48	C₁₉×#137	—	2	8	no	—
49	C₂×Q₁₆×C₁₉	—	2	4	no	—
50	C₂×SD₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
52	C₁₉×C₄⋊Q₈	—	2	4	no	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	—	2	2	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	2	no	—
64	C₄×Q₈×C₁₉	D₄	1	2	yes	—
65	C₄×Q₈×C₁₉	D₄	1	2	yes	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	D₄	1	2	yes	—
74	C₄×D₄×C₁₉	D₄	1	2	yes	—
75	C₁₉×#117	—	2	4	no	—
76	C₁₉×#117	—	2	4	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	—	2	4	no	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	D₄	1	2	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×#104	—	2	8	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#101	—	2	4	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	4	no	—
102	#41×C₁₉	—	2	8	no	—
103	#41×C₁₉	—	2	8	no	—
104	#41×C₁₉	—	2	8	no	—
105	#41×C₁₉	—	2	8	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	C₂×D₄	1	4	yes	—
109	#41×C₁₉	#41	1	4	yes	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	8	no	—
112	C₂×Q₈×C₁₉	—	2	8	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	4	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₉	#41	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	4	8	no	—
138	SD₁₆×C₁₉	—	4	8	no	—
139	M₁₆×C₁₉	—	2	4	no	—
140	M₁₆×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	8	no	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	—	2	4	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	C₂×D₄	1	2	yes	—
170	C₄²×C₁₉	C₂×D₄	1	2	yes	—
171	#32923	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	8	no	—
175	Q₈×C₁₉	—	2	4	no	—
176	Q₈×C₁₉	—	2	2	no	—
177	Q₈×C₁₉	—	2	4	no	—
178	Q₈×C₁₉	—	4	4	no	—
179	Q₈×C₁₉	—	4	4	no	—
180	Q₈×C₁₉	#121	1	4	yes	—
181	D₄×C₁₉	—	2	8	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	2	4	no	—
184	D₄×C₁₉	—	2	2	no	—
185	D₄×C₁₉	#121	1	4	yes	—
186	C₂×C₄×C₁₉	—	2	16	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	—	8	4	no	—
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	2	yes	—
209	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#121	1	4	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
215	C₈×C₁₉	—	4	4	no	—
216	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
217	#3039	C₂×C₁₉	1	2	yes	complemented
218	C₂×#456	C₂×C₁₉	1	2	yes	—
219	#2546	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1886	C₂×C₁₉	1	2	yes	complemented
221	#1882	C₂×C₁₉	1	4	yes	complemented
222	#1806	C₂×C₁₉	1	2	yes	complemented
223	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
231	C₂²×C₁₉	#525	1	1	yes	characteristic
232	C₄×C₁₉	—	2	4	no	—
233	C₄×C₁₉	—	2	4	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	#456	1	2	yes	complemented
242	C₄×C₁₉	C₂×#121	1	2	yes	—
243	C₄×C₁₉	#525	1	2	yes	—
244	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#137	C₂²×C₁₉	1	4	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	#520	—	2	2	no	—
249	#520	—	2	2	no	—
250	#520	C₂²×C₁₉	1	2	yes	—
251	#519	—	2	2	no	—
252	#519	C₂²×C₁₉	1	1	yes	characteristic
253	C₄×#41	—	2	2	no	—
254	C₄×#41	—	2	2	no	—
255	C₄×#41	C₂²×C₁₉	1	2	yes	—
256	C₂×C₄×Q₈	—	2	2	no	—
257	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
258	#462	—	2	2	no	—
259	#462	—	2	2	no	—
260	#461	—	2	2	no	—
261	#461	—	2	2	no	—
262	#456	—	2	8	no	—
263	#423	C₂²×C₁₉	1	2	yes	—
264	C₂×#104	C₂²×C₁₉	1	4	yes	—
265	#419	C₂²×C₁₉	1	4	yes	—
266	C₂×#101	C₂²×C₁₉	1	2	yes	—
267	#398	—	2	2	no	—
268	#391	C₂²×C₁₉	1	2	yes	—
269	#389	—	2	2	no	—
270	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
271	#343	C₂²×C₁₉	1	2	yes	—
272	#339	C₂²×C₁₉	1	4	yes	—
273	C₂×C₁₉	—	2	1	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	4	4	no	—
276	C₂×C₁₉	#2847	1	1	yes	characteristic
277	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
278	C₂×C₁₉	#3022	1	1	yes	characteristic
279	2₋¹⁺⁴	—	2	4	no	—
280	2₋¹⁺⁴	—	2	2	no	—
281	2₋¹⁺⁴	D₄×C₁₉	1	4	yes	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	C₂³×C₁₉	1	2	yes	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
287	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	#137	—	2	8	no	—
289	#137	—	2	8	no	—
290	C₂×Q₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
293	C₄⋊Q₈	—	2	4	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	4	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	D₄×C₁₉	1	2	yes	—
306	C₄×Q₈	D₄×C₁₉	1	2	yes	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	D₄×C₁₉	1	2	yes	—
315	C₄×D₄	D₄×C₁₉	1	2	yes	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	#117	—	2	2	no	—
321	#117	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₄²	—	2	4	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	D₄×C₁₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	#104	—	2	8	no	—
338	#103	—	2	4	no	—
339	#103	—	2	4	no	—
340	#101	—	2	4	no	—
341	#95	—	2	1	no	—
342	#95	—	2	4	no	—
343	C₁₉	#32923	1	1	yes	characteristic, direct product factor, Sylow
344	#41	—	2	8	no	—
345	#41	—	2	8	no	—
346	#41	—	2	8	no	—
347	#41	—	2	8	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	C₂×D₄×C₁₉	1	4	yes	—
351	#41	#41×C₁₉	1	4	yes	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	8	no	—
354	C₂×Q₈	—	2	8	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×Q₈	#41×C₁₉	1	2	yes	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
379	Q₁₆	—	4	8	no	—
380	SD₁₆	—	4	8	no	—
381	M₁₆	—	2	4	no	—
382	M₁₆	—	2	4	no	—
383	C₂×C₈	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	8	no	—
396	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	C₂×D₄×C₁₉	1	2	yes	—
412	C₄²	C₂×D₄×C₁₉	1	2	yes	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
415	Q₈	—	2	8	no	—
416	Q₈	—	2	4	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	C₁₉×#121	1	4	yes	—
422	D₄	—	2	8	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	2	2	no	—
426	D₄	C₁₉×#121	1	4	yes	—
427	C₂×C₄	—	2	16	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
449	C₂×C₄	C₁₉×#120	1	2	yes	—
450	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
451	C₂×C₄	C₁₉×#121	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
456	C₈	—	4	4	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
463	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
464	C₂²	C₁₉×#525	1	1	yes	characteristic
465	C₄	—	2	1	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₁₉×#456	1	2	yes	complemented
475	C₄	C₂×C₁₉×#121	1	2	yes	—
476	C₄	C₁₉×#525	1	2	yes	—
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	4	4	no	—
480	C₂	C₁₉×#2847	1	1	yes	characteristic
481	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
482	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3039	C₂	semidirect
4. C₁₉×#2546	C₂	semidirect
5. C₁₉×#1886	C₂	semidirect
6. C₁₉×#1882	C₂	semidirect
7. C₁₉×#1806	C₂	semidirect
8. C₁₉×#1801	C₂	semidirect
171. #32923	C₁₉	direct (N × H)
217. #3039	C₂×C₁₉	semidirect
219. #2546	C₂×C₁₉	semidirect
220. #1886	C₂×C₁₉	semidirect
221. #1882	C₂×C₁₉	semidirect
222. #1806	C₂×C₁₉	semidirect
223. #1801	C₂×C₁₉	semidirect
241. C₄×C₁₉	#456	semidirect
343. C₁₉	#32923	direct (N × H)
474. C₄	C₁₉×#456	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₁₉×#3039	2
C₂×C₁₉×#456	2
C₁₉×#2546	2
C₁₉×#1886	2
C₁₉×#1882	2
C₁₉×#1806	2
C₁₉×#1801	2
#32923	19

Subgroups — C19×#32923 #18038882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32923 #18038882