Subgroups — #18088265

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926307	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	2	yes	maximal
4	#14561864	C₂	1	2	yes	maximal
5	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₁₉	—	2	4	no	—
10	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
11	C₂×C₁₉⋊#95	—	2	2	no	—
12	C₂×C₁₉⋊#95	—	2	2	no	—
13	#11926307	C₄	1	4	yes	complemented
14	#11926306	—	2	4	no	—
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₁₉×#340	C₄	1	4	yes	complemented
18	C₂³×C₄×C₁₉	—	2	2	no	—
19	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂³×Dic₁₉	—	2	2	no	—
21	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
22	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
34	C₂×C₄⋊Dic₁₉	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	2	no	—
38	C₂×C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
40	C₂×C₄×Dic₁₉	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	2	no	—
42	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
44	C₂²×C₁₉⋊C₈	—	2	2	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
49	C₁₉⋊#95	—	4	4	no	—
50	C₁₉⋊#95	—	4	4	no	—
51	C₈×Dic₁₉	—	2	8	no	—
52	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	—	2	4	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	2	yes	—
66	C₂²×C₄×C₁₉	#41	1	2	yes	—
67	C₂²×C₄×C₁₉	#41	1	2	yes	—
68	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂²×Dic₁₉	—	2	2	no	—
71	C₂²×Dic₁₉	—	2	2	no	—
72	C₂²×Dic₁₉	—	2	1	no	—
73	C₂²×Dic₁₉	—	2	2	no	—
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	4	no	—
76	C₂²×Dic₁₉	—	4	2	no	—
77	C₂²×Dic₁₉	—	4	2	no	—
78	C₂²×Dic₁₉	—	4	2	no	—
79	C₂²×Dic₁₉	—	4	2	no	—
80	C₂²×Dic₁₉	—	4	2	no	—
81	C₂²×Dic₁₉	—	4	2	no	—
82	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
83	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
84	C₂²×Dic₁₉	D₈	1	2	yes	—
85	C₂²×Dic₁₉	SD₁₆	1	4	yes	—
86	C₂²×Dic₁₉	Q₁₆	1	2	yes	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₂×C₈×C₁₉	—	2	2	no	—
89	C₂×C₈×C₁₉	—	2	4	no	—
90	C₂×C₈×C₁₉	—	2	4	no	—
91	C₂×C₈×C₁₉	C₄²	1	4	yes	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	2	no	—
96	C₄⋊Dic₁₉	—	2	4	no	—
97	C₄⋊Dic₁₉	—	2	4	no	—
98	C₄⋊Dic₁₉	—	4	2	no	—
99	C₄⋊Dic₁₉	—	4	2	no	—
100	C₄×Dic₁₉	—	2	2	no	—
101	C₄×Dic₁₉	—	2	2	no	—
102	C₄×Dic₁₉	—	2	4	no	—
103	C₂×C₁₉⋊C₈	—	2	2	no	—
104	C₂×C₁₉⋊C₈	—	2	2	no	—
105	C₂×C₁₉⋊C₈	—	2	4	no	—
106	C₂×C₁₉⋊C₈	—	2	4	no	—
107	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
108	#10820	—	19	1	no	maximal, Sylow
109	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
112	C₂³×C₁₉	#121	1	2	yes	—
113	C₂³×C₁₉	#124	1	2	yes	—
114	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
115	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
116	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
117	C₂³×C₁₉	#135	1	1	yes	characteristic
118	C₂³×C₁₉	#135	1	2	yes	—
119	C₂³×C₁₉	#135	1	1	yes	characteristic
120	C₂×C₄×C₁₉	—	4	4	no	—
121	C₂×C₄×C₁₉	—	4	4	no	—
122	C₂×C₄×C₁₉	—	4	4	no	—
123	C₂×C₄×C₁₉	—	8	2	no	—
124	C₂×C₄×C₁₉	—	8	2	no	—
125	C₂×C₄×C₁₉	—	8	2	no	—
126	C₂×C₄×C₁₉	—	8	2	no	—
127	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#117	1	2	yes	—
132	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#117	1	2	yes	—
135	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₉	#123	1	2	yes	—
141	C₂×C₄×C₁₉	#123	1	2	yes	—
142	C₂×C₄×C₁₉	#125	1	2	yes	—
143	C₂×C₄×C₁₉	#126	1	2	yes	—
144	C₂×C₄×C₁₉	#126	1	2	yes	—
145	C₂×Dic₁₉	—	2	2	no	—
146	C₂×Dic₁₉	—	2	2	no	—
147	C₂×Dic₁₉	—	2	2	no	—
148	C₂×Dic₁₉	—	2	2	no	—
149	C₂×Dic₁₉	—	2	4	no	—
150	C₂×Dic₁₉	—	2	4	no	—
151	C₂×Dic₁₉	—	2	4	no	—
152	C₂×Dic₁₉	—	2	4	no	—
153	C₂×Dic₁₉	—	4	4	no	—
154	C₂×Dic₁₉	—	4	4	no	—
155	C₂×Dic₁₉	—	4	4	no	—
156	C₂×Dic₁₉	—	8	2	no	—
157	C₂×Dic₁₉	—	8	2	no	—
158	C₂×Dic₁₉	—	8	2	no	—
159	C₂×Dic₁₉	—	8	2	no	—
160	C₂×Dic₁₉	#106	1	4	yes	—
161	C₂×Dic₁₉	#107	1	4	yes	—
162	C₈×C₁₉	—	2	4	no	—
163	C₁₉⋊C₈	—	2	4	no	—
164	C₂²×C₄×C₈	—	19	1	no	—
165	C₂×#340	—	19	1	no	—
166	C₂×#340	—	19	2	no	—
167	C₂×#340	D₁₉	1	1	yes	characteristic
168	C₄⋊#95	—	19	2	no	—
169	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₁₉	#380	1	1	yes	characteristic
171	C₂²×C₁₉	#382	1	1	yes	characteristic
172	C₂²×C₁₉	#388	1	2	yes	—
173	C₂²×C₁₉	#388	1	2	yes	—
174	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
176	C₂²×C₁₉	#427	1	1	yes	characteristic
177	C₂²×C₁₉	#427	1	1	yes	characteristic
178	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
179	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
180	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
181	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
182	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
183	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
184	C₂²×C₁₉	#465	1	2	yes	—
185	C₂²×C₁₉	#465	1	2	yes	—
186	C₂²×C₁₉	#466	1	2	yes	—
187	C₂²×C₁₉	#467	1	2	yes	—
188	C₂²×C₁₉	#486	1	2	yes	—
189	C₂²×C₁₉	#487	1	2	yes	—
190	C₂²×C₁₉	#488	1	2	yes	—
191	C₂²×C₁₉	#488	1	2	yes	—
192	C₄×C₁₉	—	8	4	no	—
193	C₄×C₁₉	#376	1	1	yes	characteristic
194	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
195	C₄×C₁₉	#381	1	1	yes	characteristic
196	C₄×C₁₉	#383	1	1	yes	characteristic
197	C₄×C₁₉	#387	1	2	yes	—
198	C₄×C₁₉	#387	1	2	yes	—
199	Dic₁₉	—	2	4	no	—
200	Dic₁₉	—	2	4	no	—
201	Dic₁₉	—	8	4	no	—
202	C₂³×C₈	—	19	1	no	—
203	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	—	19	2	no	—
205	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
206	C₂²×C₄²	—	19	1	no	—
207	C₂×C₄×C₈	—	19	4	no	—
208	C₂×C₄×C₈	—	38	4	no	—
209	C₂×#95	—	38	2	no	—
210	C₂×#95	—	38	2	no	—
211	#340	—	19	4	no	—
212	#340	—	38	4	no	—
213	#340	Dic₁₉	1	4	yes	complemented
214	C₂×C₁₉	#1434	1	1	yes	characteristic
215	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
216	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
217	C₂×C₁₉	#1807	1	1	yes	characteristic
218	C₂×C₁₉	#1808	1	1	yes	characteristic
219	C₂×C₁₉	#1834	1	1	yes	characteristic
220	C₂×C₁₉	#1835	1	1	yes	characteristic
221	C₂×C₁₉	#1933	1	2	yes	—
222	C₂×C₁₉	#1933	1	2	yes	—
223	C₂×C₁₉	#1934	1	2	yes	—
224	C₂×C₁₉	#1934	1	2	yes	—
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	—	19	1	no	—
227	C₂³×C₄	—	19	1	no	—
228	C₂³×C₄	—	38	2	no	—
229	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	19	2	no	—
233	C₂²×C₈	—	19	4	no	—
234	C₂²×C₈	—	38	2	no	—
235	C₂²×C₈	—	38	1	no	—
236	C₂²×C₈	—	38	1	no	—
237	C₂²×C₈	C₄×D₁₉	1	2	yes	—
238	C₂²×C₈	C₄×D₁₉	1	2	yes	—
239	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	19	4	no	—
246	C₂×C₄⋊C₄	—	38	2	no	—
247	C₂×C₄⋊C₄	—	38	2	no	—
248	C₂×C₄⋊C₄	—	38	2	no	—
249	C₂×C₄⋊C₄	—	38	2	no	—
250	C₂×C₄⋊C₄	—	38	2	no	—
251	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
252	C₂×C₄²	—	19	2	no	—
253	C₂×C₄²	—	19	2	no	—
254	C₂×C₄²	—	38	2	no	—
255	C₂×C₄²	—	38	2	no	—
256	C₄×C₈	—	38	8	no	—
257	#95	—	76	4	no	—
258	#95	—	76	4	no	—
259	C₁₉	#10820	1	1	yes	characteristic, complemented, Sylow
260	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	19	2	no	—
269	C₂²×C₄	—	19	2	no	—
270	C₂²×C₄	—	19	2	no	—
271	C₂²×C₄	—	19	4	no	—
272	C₂²×C₄	—	19	2	no	—
273	C₂²×C₄	—	38	2	no	—
274	C₂²×C₄	—	38	2	no	—
275	C₂²×C₄	—	38	1	no	—
276	C₂²×C₄	—	38	2	no	—
277	C₂²×C₄	—	38	1	no	—
278	C₂²×C₄	—	38	4	no	—
279	C₂²×C₄	—	76	2	no	—
280	C₂²×C₄	—	76	2	no	—
281	C₂²×C₄	—	76	2	no	—
282	C₂²×C₄	—	76	2	no	—
283	C₂²×C₄	—	76	2	no	—
284	C₂²×C₄	—	76	2	no	—
285	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	#64541	1	2	yes	—
288	C₂²×C₄	#64541	1	2	yes	—
289	C₂²×C₄	D₄×D₁₉	1	2	yes	—
290	C₂²×C₄	#64543	1	2	yes	—
291	C₂²×C₄	#64543	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
293	C₂²×C₄	#64545	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	19	4	no	—
300	C₂×C₈	—	38	2	no	—
301	C₂×C₈	—	38	4	no	—
302	C₂×C₈	—	38	2	no	—
303	C₂×C₈	—	38	4	no	—
304	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	38	4	no	—
310	C₄⋊C₄	—	38	4	no	—
311	C₄⋊C₄	—	76	2	no	—
312	C₄⋊C₄	—	76	2	no	—
313	C₄²	—	38	2	no	—
314	C₄²	—	38	2	no	—
315	C₄²	—	38	4	no	—
316	C₂³	#10597330	1	2	yes	—
317	C₂³	#10597331	1	2	yes	—
318	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
319	C₂³	#10597339	1	1	yes	characteristic
320	C₂³	D₈×D₁₉	1	1	yes	characteristic
321	C₂³	#10597358	1	1	yes	characteristic
322	C₂³	SD₁₆×D₁₉	1	2	yes	—
323	C₂³	#10597362	1	2	yes	—
324	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
325	C₂³	#10597365	1	1	yes	characteristic
326	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	19	4	no	—
335	C₂×C₄	—	19	4	no	—
336	C₂×C₄	—	38	4	no	—
337	C₂×C₄	—	38	2	no	—
338	C₂×C₄	—	38	2	no	—
339	C₂×C₄	—	38	2	no	—
340	C₂×C₄	—	38	2	no	—
341	C₂×C₄	—	38	4	no	—
342	C₂×C₄	—	38	4	no	—
343	C₂×C₄	—	38	4	no	—
344	C₂×C₄	—	76	4	no	—
345	C₂×C₄	—	76	4	no	—
346	C₂×C₄	—	76	4	no	—
347	C₂×C₄	—	152	2	no	—
348	C₂×C₄	—	152	2	no	—
349	C₂×C₄	—	152	2	no	—
350	C₂×C₄	—	152	2	no	—
351	C₂×C₄	#10597318	1	1	yes	characteristic
352	C₂×C₄	#10597318	1	1	yes	characteristic
353	C₂×C₄	#10597318	1	2	yes	—
354	C₂×C₄	#10597323	1	1	yes	characteristic
355	C₂×C₄	#10597325	1	2	yes	—
356	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
357	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
358	C₂×C₄	#10597329	1	2	yes	—
359	C₂×C₄	#10597333	1	1	yes	characteristic
360	C₂×C₄	#10597335	1	2	yes	—
361	C₂×C₄	#10597338	1	1	yes	characteristic
362	C₂×C₄	#10597340	1	2	yes	—
363	C₂×C₄	#10597342	1	2	yes	—
364	C₂×C₄	#10597344	1	2	yes	—
365	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
366	C₂×C₄	#10597372	1	2	yes	—
367	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
368	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	38	4	no	—
371	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
372	C₂²	#11926403	1	1	yes	characteristic
373	C₂²	#11926408	1	1	yes	characteristic
374	C₂²	#11926433	1	2	yes	—
375	C₂²	#11926437	1	2	yes	—
376	C₂²	#106×D₁₉	1	1	yes	characteristic
377	C₂²	#107×D₁₉	1	1	yes	characteristic
378	C₂²	#11926579	1	1	yes	characteristic
379	C₂²	#11926581	1	1	yes	characteristic
380	C₂²	#11926626	1	1	yes	characteristic
381	C₂²	D₈×Dic₁₉	1	1	yes	characteristic
382	C₂²	#11926631	1	2	yes	—
383	C₂²	SD₁₆×Dic₁₉	1	2	yes	—
384	C₂²	#11926638	1	1	yes	characteristic
385	C₂²	Q₁₆×Dic₁₉	1	1	yes	characteristic
386	C₂²	#11926772	1	2	yes	—
387	C₂²	#11926776	1	2	yes	—
388	C₂²	#11926779	1	2	yes	—
389	C₂²	#11926784	1	2	yes	—
390	C₂²	#11926889	1	2	yes	—
391	C₂²	#11926893	1	2	yes	—
392	C₂²	#11926897	1	2	yes	—
393	C₂²	#11926900	1	2	yes	—
394	C₄	—	8	4	no	—
395	C₄	—	38	4	no	—
396	C₄	—	38	4	no	—
397	C₄	—	152	4	no	—
398	C₄	#11926390	1	1	yes	characteristic
399	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
400	C₄	#11926406	1	1	yes	characteristic
401	C₄	#11926411	1	1	yes	characteristic
402	C₄	#11926426	1	2	yes	—
403	C₄	#11926430	1	2	yes	—
404	C₂	#14561860	1	1	yes	characteristic
405	C₂	#106×Dic₁₉	1	1	yes	characteristic
406	C₂	#107×Dic₁₉	1	1	yes	characteristic
407	C₂	#14563659	1	1	yes	characteristic
408	C₂	#14563663	1	1	yes	characteristic
409	C₂	#14563761	1	1	yes	characteristic
410	C₂	#14563764	1	1	yes	characteristic
411	C₂	#14564309	1	2	yes	—
412	C₂	#14564313	1	2	yes	—
413	C₂	#14564316	1	2	yes	—
414	C₂	#14564320	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	#10820
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
10. C₂×C₈×Dic₁₉	C₄	semidirect
13. #11926307	C₄	semidirect
17. C₁₉×#340	C₄	semidirect
213. #340	Dic₁₉	semidirect
259. C₁₉	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₁₉	2
C₂×#11926307	2
C₂×#11926306	2
#14561864	2
C₂×C₁₉×#340	2
#10820	19