Subgroups — C₁₉×#11161 #18017120

Order 4864.

1146 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1736	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#339	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₁₉×#117	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#100	—	2	2	no	—
13	C₂×C₁₉×#100	—	2	4	no	—
14	C₁₉×#390	—	2	2	no	—
15	C₁₉×#390	—	2	4	no	—
16	C₁₉×#390	C₄	1	4	yes	complemented
17	C₁₉×#379	—	2	2	no	—
18	C₁₉×#340	—	2	4	no	—
19	C₁₉×#339	—	2	4	no	—
20	C₂⁵×C₁₉	D₄	1	2	yes	—
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	—	2	2	no	—
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×D₄×C₁₉	D₄	1	2	yes	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
38	C₂²×C₈×C₁₉	—	2	2	no	—
39	C₁₉×#117	—	2	2	no	—
40	C₁₉×#117	—	2	2	no	—
41	C₁₉×#117	—	2	2	no	—
42	C₁₉×#117	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
53	C₂×C₄²×C₁₉	—	2	2	no	—
54	C₂×C₄²×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
58	C₁₉×#100	—	2	8	no	—
59	C₂⁴×C₁₉	—	2	2	no	—
60	C₂⁴×C₁₉	—	2	4	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	4	4	no	—
64	C₂⁴×C₁₉	—	4	4	no	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	4	no	—
70	C₂×D₄×C₁₉	—	2	4	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	4	2	no	—
76	C₂×D₄×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	4	2	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	C₂²×C₄×C₁₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	M₁₆×C₁₉	—	2	4	no	—
101	M₁₆×C₁₉	—	2	4	no	—
102	M₁₆×C₁₉	—	4	2	no	—
103	M₁₆×C₁₉	—	4	2	no	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₂×C₈×C₁₉	—	4	2	no	—
106	C₂×C₈×C₁₉	—	4	2	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₉	—	4	16	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₉	—	8	4	no	—
115	C₂²⋊C₄×C₁₉	—	8	4	no	—
116	C₄²×C₁₉	—	2	4	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	2	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	2	no	—
121	#11161	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	4	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	4	4	no	—
128	C₂³×C₁₉	—	4	4	no	—
129	C₂³×C₁₉	—	4	16	no	—
130	C₂³×C₁₉	—	4	4	no	—
131	C₂³×C₁₉	—	4	4	no	—
132	C₂³×C₁₉	—	4	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	8	2	no	—
135	C₂³×C₁₉	—	8	2	no	—
136	C₂³×C₁₉	—	8	8	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₁₉	#120	1	1	yes	characteristic
139	C₂³×C₁₉	#121	1	2	yes	—
140	C₂³×C₁₉	#123	1	2	yes	—
141	C₂³×C₁₉	#123	1	1	yes	characteristic
142	D₄×C₁₉	—	4	4	no	—
143	D₄×C₁₉	—	4	4	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	8	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	4	4	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	2	yes	—
163	C₂×C₄×C₁₉	#121	1	2	yes	—
164	C₂×C₄×C₁₉	#121	1	2	yes	—
165	C₂×C₄×C₁₉	#123	1	2	yes	—
166	C₂×C₄×C₁₉	#123	1	2	yes	—
167	C₂×C₄×C₁₉	#123	1	2	yes	—
168	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#124	1	2	yes	—
170	C₂×C₄×C₁₉	#124	1	2	yes	—
171	C₂×C₄×C₁₉	#126	1	2	yes	—
172	C₂×C₄×C₁₉	#126	1	2	yes	—
173	C₈×C₁₉	—	4	4	no	—
174	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic
175	#2309	C₂×C₁₉	1	1	yes	characteristic
176	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
177	#1736	C₂×C₁₉	1	2	yes	complemented
178	C₂×#339	C₂×C₁₉	1	2	yes	complemented
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	4	8	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	—	8	8	no	—
191	C₂²×C₁₉	—	8	8	no	—
192	C₂²×C₁₉	#381	1	1	yes	characteristic
193	C₂²×C₁₉	#386	1	1	yes	characteristic
194	C₂²×C₁₉	#386	1	1	yes	characteristic
195	C₂²×C₁₉	#394	1	2	yes	—
196	C₂²×C₁₉	#397	1	2	yes	—
197	C₂²×C₁₉	#453	1	2	yes	—
198	C₂²×C₁₉	#455	1	2	yes	—
199	C₄×C₁₉	—	4	4	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	—	8	4	no	—
202	C₄×C₁₉	#388	1	2	yes	—
203	C₄×C₁₉	#388	1	2	yes	—
204	C₄×C₁₉	#394	1	2	yes	—
205	C₄×C₁₉	#397	1	2	yes	—
206	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
208	C₂×#117	C₂²×C₁₉	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
210	C₂²×C₂²⋊C₄	—	2	2	no	—
211	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#100	—	2	2	no	—
213	C₂×#100	—	2	4	no	—
214	#390	—	2	2	no	—
215	#390	—	2	4	no	—
216	#390	C₄×C₁₉	1	4	yes	complemented
217	#379	—	2	2	no	—
218	#340	—	2	4	no	—
219	#339	—	2	4	no	—
220	C₂×C₁₉	—	2	1	no	—
221	C₂×C₁₉	—	2	1	no	—
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	—	8	4	no	—
224	C₂×C₁₉	#1440	1	1	yes	characteristic
225	C₂×C₁₉	#1885	1	1	yes	characteristic
226	C₂×C₁₉	#1887	1	1	yes	characteristic
227	C₂×C₁₉	#2037	1	4	yes	—
228	C₂⁵	D₄×C₁₉	1	2	yes	—
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	2	2	no	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
236	C₂²×D₄	D₄×C₁₉	1	2	yes	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
246	C₂²×C₈	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
255	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
256	C₂×C₂²⋊C₄	—	2	8	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	4	8	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
266	#100	—	2	8	no	—
267	C₁₉	#11161	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	—	2	2	no	—
269	C₂⁴	—	2	4	no	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	—	4	4	no	—
273	C₂⁴	—	4	4	no	—
274	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
275	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₉	1	2	yes	—
306	C₂²×C₄	#41×C₁₉	1	2	yes	—
307	C₂²×C₄	#41×C₁₉	1	2	yes	—
308	C₂²×C₄	#41×C₁₉	1	2	yes	—
309	M₁₆	—	2	4	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	4	2	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	16	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	8	4	no	—
324	C₂²⋊C₄	—	8	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	16	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	8	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	—	8	8	no	—
345	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₂³	C₁₉×#120	1	1	yes	characteristic
347	C₂³	C₁₉×#121	1	2	yes	—
348	C₂³	C₁₉×#123	1	2	yes	—
349	C₂³	C₁₉×#123	1	1	yes	characteristic
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
366	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
367	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
369	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
370	C₂×C₄	C₁₉×#121	1	2	yes	—
371	C₂×C₄	C₁₉×#121	1	2	yes	—
372	C₂×C₄	C₁₉×#121	1	2	yes	—
373	C₂×C₄	C₁₉×#123	1	2	yes	—
374	C₂×C₄	C₁₉×#123	1	2	yes	—
375	C₂×C₄	C₁₉×#123	1	2	yes	—
376	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#124	1	2	yes	—
378	C₂×C₄	C₁₉×#124	1	2	yes	—
379	C₂×C₄	C₁₉×#126	1	2	yes	—
380	C₂×C₄	C₁₉×#126	1	2	yes	—
381	C₈	—	4	4	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	8	8	no	—
394	C₂²	—	8	8	no	—
395	C₂²	C₁₉×#381	1	1	yes	characteristic
396	C₂²	C₁₉×#386	1	1	yes	characteristic
397	C₂²	C₁₉×#386	1	1	yes	characteristic
398	C₂²	C₁₉×#394	1	2	yes	—
399	C₂²	C₁₉×#397	1	2	yes	—
400	C₂²	C₁₉×#453	1	2	yes	—
401	C₂²	C₁₉×#455	1	2	yes	—
402	C₄	—	4	4	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	4	no	—
405	C₄	C₁₉×#388	1	2	yes	—
406	C₄	C₁₉×#388	1	2	yes	—
407	C₄	C₁₉×#394	1	2	yes	—
408	C₄	C₁₉×#397	1	2	yes	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	—	8	4	no	—
413	C₂	C₁₉×#1440	1	1	yes	characteristic
414	C₂	C₁₉×#1885	1	1	yes	characteristic
415	C₂	C₁₉×#1887	1	1	yes	characteristic
416	C₂	C₁₉×#2037	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1736	C₂	semidirect
5. C₂×C₁₉×#339	C₂	semidirect
16. C₁₉×#390	C₄	semidirect
121. #11161	C₁₉	direct (N × H)
177. #1736	C₂×C₁₉	semidirect
178. C₂×#339	C₂×C₁₉	semidirect
216. #390	C₄×C₁₉	semidirect
267. C₁₉	#11161	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#100	2
C₁₉×#2309	2
C₂×C₁₉×#390	2
C₁₉×#1736	2
C₂×C₁₉×#339	2
#11161	19

Subgroups — C19×#11161 #18017120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11161 #18017120