Subgroups — C₁₉×#18294 #18024253

Order 4864.

1002 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3187	C₂	1	2	yes	maximal
3	C₁₉×#2618	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1611	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1599	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1520	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#544	—	2	4	no	—
9	C₁₉×#544	—	2	2	no	—
10	C₁₉×#544	C₂²	1	4	yes	—
11	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₁₉×#125	—	2	2	no	—
13	C₂×C₁₉×#123	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#483	C₂²	1	4	yes	—
20	C₁₉×#481	—	2	2	no	—
21	C₁₉×#465	—	2	4	no	—
22	C₁₉×#450	C₂²	1	4	yes	—
23	C₁₉×#448	—	2	2	no	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#398	C₂²	1	2	yes	—
26	C₁₉×#396	—	2	2	no	—
27	C₁₉×#394	C₂²	1	2	yes	—
28	C₁₉×#386	—	2	1	no	—
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#328	C₂²	1	8	yes	—
31	C₁₉×#324	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×SD₁₆×C₁₉	—	2	4	no	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₁₉×C₄⋊Q₈	—	2	8	no	—
42	C₁₉×C₄⋊Q₈	—	2	8	no	—
43	C₁₉×#125	—	2	8	no	—
44	C₁₉×#125	—	2	8	no	—
45	C₁₉×#123	—	4	4	no	—
46	C₁₉×C₂²⋊Q₈	—	2	4	no	—
47	C₁₉×C₂²⋊Q₈	—	2	4	no	—
48	C₁₉×C₂²⋊Q₈	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
51	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
52	C₁₉×#121	—	2	2	no	—
53	C₁₉×#121	—	2	2	no	—
54	C₁₉×#117	—	2	4	no	—
55	C₁₉×#117	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	—	2	2	no	—
75	C₁₉×#106	—	2	4	no	—
76	C₁₉×#103	—	2	4	no	—
77	C₁₉×#102	—	2	4	no	—
78	C₁₉×C₂²⋊C₈	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	C₂³	1	2	yes	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	8	2	no	—
87	C₂×Q₈×C₁₉	—	8	2	no	—
88	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	8	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	8	1	no	—
105	C₂²×C₄×C₁₉	—	8	1	no	—
106	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	SD₁₆×C₁₉	—	8	4	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	8	2	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	8	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	8	1	no	—
128	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₂²⋊C₄×C₁₉	—	8	2	no	—
135	C₄²×C₁₉	—	2	8	no	—
136	#18294	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	#120	1	1	yes	characteristic
145	C₂³×C₁₉	#120	1	1	yes	characteristic
146	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
147	C₂³×C₁₉	#137	1	2	yes	—
148	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₉	—	4	4	no	—
150	Q₈×C₁₉	—	8	2	no	—
151	Q₈×C₁₉	—	8	4	no	—
152	D₄×C₁₉	—	4	4	no	—
153	D₄×C₁₉	—	8	2	no	—
154	D₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	#120	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
180	C₈×C₁₉	—	4	4	no	—
181	C₂×#544	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#3187	C₂×C₁₉	1	2	yes	—
183	#2618	C₂×C₁₉	1	1	yes	characteristic
184	#1611	C₂×C₁₉	1	4	yes	complemented
185	#1599	C₂×C₁₉	1	4	yes	complemented
186	#1520	C₂×C₁₉	1	2	yes	complemented
187	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	#448	1	2	yes	—
202	C₂²×C₁₉	#448	1	2	yes	—
203	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
204	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
205	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	4	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	8	1	no	—
214	#544	—	2	4	no	—
215	#544	—	2	2	no	—
216	#544	C₂²×C₁₉	1	4	yes	—
217	C₂×C₄⋊Q₈	—	2	2	no	—
218	C₂×#125	—	2	2	no	—
219	C₂×#123	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
222	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	#483	C₂²×C₁₉	1	4	yes	—
226	#481	—	2	2	no	—
227	#465	—	2	4	no	—
228	#450	C₂²×C₁₉	1	4	yes	—
229	#448	—	2	2	no	—
230	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
231	#398	C₂²×C₁₉	1	2	yes	—
232	#396	—	2	2	no	—
233	#394	C₂²×C₁₉	1	2	yes	—
234	#386	—	2	1	no	—
235	#380	C₂²×C₁₉	1	1	yes	characteristic
236	#328	C₂²×C₁₉	1	8	yes	—
237	#324	C₂²×C₁₉	1	4	yes	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	2	2	no	—
242	C₂×C₁₉	—	16	1	no	—
243	C₂×C₁₉	C₂×#448	1	1	yes	characteristic
244	C₂×C₁₉	#3020	1	1	yes	characteristic
245	C₂×C₁₉	#3026	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
251	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
253	C₂×SD₁₆	—	2	4	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	8	no	—
256	C₄⋊Q₈	—	2	8	no	—
257	#125	—	2	8	no	—
258	#125	—	2	8	no	—
259	#123	—	4	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
265	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
266	#121	—	2	2	no	—
267	#121	—	2	2	no	—
268	#117	—	2	4	no	—
269	#117	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
280	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	#106	—	2	4	no	—
290	#103	—	2	4	no	—
291	#102	—	2	4	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
294	#95	—	2	2	no	—
295	#95	C₂³×C₁₉	1	2	yes	—
296	C₁₉	#18294	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	—	2	1	no	—
298	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	8	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	8	1	no	—
320	C₂²×C₄	—	8	1	no	—
321	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
328	SD₁₆	—	8	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	8	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	8	1	no	—
343	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₄²	—	2	8	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	C₁₉×#120	1	1	yes	characteristic
359	C₂³	C₁₉×#120	1	1	yes	characteristic
360	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
361	C₂³	C₁₉×#137	1	2	yes	—
362	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
363	Q₈	—	4	4	no	—
364	Q₈	—	8	2	no	—
365	Q₈	—	8	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₁₉×#120	1	2	yes	—
392	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
393	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
394	C₈	—	4	4	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	C₁₉×#448	1	2	yes	—
409	C₂²	C₁₉×#448	1	2	yes	—
410	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
411	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
412	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	2	no	—
424	C₂	—	2	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₂×C₁₉×#448	1	1	yes	characteristic
427	C₂	C₁₉×#3020	1	1	yes	characteristic
428	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#544	C₂	semidirect
4. C₁₉×#1611	C₂	semidirect
5. C₁₉×#1599	C₂	semidirect
6. C₁₉×#1520	C₂	semidirect
7. C₂×C₁₉×#324	C₂	semidirect
106. C₂²×C₄×C₁₉	SD₁₆	semidirect
136. #18294	C₁₉	direct (N × H)
181. C₂×#544	C₂×C₁₉	semidirect
184. #1611	C₂×C₁₉	semidirect
185. #1599	C₂×C₁₉	semidirect
186. #1520	C₂×C₁₉	semidirect
187. C₂×#324	C₂×C₁₉	semidirect
296. C₁₉	#18294	direct (N × H)
321. C₂²×C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#544	2
C₁₉×#3187	2
C₁₉×#2618	2
C₁₉×#1611	2
C₁₉×#1599	2
C₁₉×#1520	2
C₂×C₁₉×#324	2
#18294	19

Subgroups — C19×#18294 #18024253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18294 #18024253