Subgroups — C₁₉×#8698 #18014657

Order 4864.

1158 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1779	C₂	1	2	yes	maximal
3	C₁₉×#1280	C₂	1	4	yes	maximal, complemented
4	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
8	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
9	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
10	C₂×C₁₉×#95	—	2	2	no	—
11	C₂×C₁₉×#95	—	2	2	no	—
12	C₂×C₁₉×#95	C₄	1	2	yes	—
13	C₂×C₁₉×#95	C₂²	1	2	yes	—
14	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	—	2	1	no	—
16	C₂³×C₄×C₁₉	—	2	1	no	—
17	C₂³×C₄×C₁₉	—	2	1	no	—
18	C₂³×C₄×C₁₉	—	2	1	no	—
19	C₂³×C₄×C₁₉	—	2	2	no	—
20	C₂³×C₄×C₁₉	—	2	4	no	—
21	C₂³×C₄×C₁₉	—	2	4	no	—
22	C₂³×C₄×C₁₉	—	4	2	no	—
23	C₂³×C₄×C₁₉	—	4	2	no	—
24	C₂³×C₄×C₁₉	—	4	2	no	—
25	C₂³×C₄×C₁₉	—	4	2	no	—
26	C₂³×C₄×C₁₉	—	4	2	no	—
27	C₂³×C₄×C₁₉	—	4	2	no	—
28	C₂³×C₄×C₁₉	C₈	1	4	yes	complemented
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	4	no	—
36	C₁₉×C₂²⋊C₈	—	2	8	no	—
37	C₁₉×C₂²⋊C₈	—	4	4	no	—
38	C₁₉×C₂²⋊C₈	—	4	4	no	—
39	C₁₉×#95	—	2	4	no	—
40	C₁₉×#95	—	2	4	no	—
41	C₂⁴×C₁₉	—	2	2	no	—
42	C₂⁴×C₁₉	—	2	2	no	—
43	C₂⁴×C₁₉	—	2	2	no	—
44	C₂⁴×C₁₉	—	2	2	no	—
45	C₂⁴×C₁₉	—	2	2	no	—
46	C₂⁴×C₁₉	—	2	2	no	—
47	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
50	C₂⁴×C₁₉	M₁₆	1	2	yes	—
51	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	2	4	no	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	2	4	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	—	4	16	no	—
72	C₂²×C₄×C₁₉	—	4	16	no	—
73	C₂²×C₄×C₁₉	—	4	8	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	8	no	—
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
89	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	#41	1	4	yes	—
92	C₂×C₈×C₁₉	—	4	4	no	—
93	C₂×C₈×C₁₉	—	4	4	no	—
94	C₂×C₈×C₁₉	—	4	4	no	—
95	#8698	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂³×C₁₉	—	2	8	no	—
97	C₂³×C₁₉	—	2	8	no	—
98	C₂³×C₁₉	—	2	8	no	—
99	C₂³×C₁₉	—	2	8	no	—
100	C₂³×C₁₉	—	2	4	no	—
101	C₂³×C₁₉	—	2	4	no	—
102	C₂³×C₁₉	—	2	4	no	—
103	C₂³×C₁₉	—	2	4	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	—	2	1	no	—
107	C₂³×C₁₉	—	2	1	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	4	no	—
117	C₂³×C₁₉	—	2	4	no	—
118	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
119	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
120	C₂³×C₁₉	#99	1	2	yes	—
121	C₂³×C₁₉	#99	1	2	yes	—
122	C₂³×C₁₉	#100	1	2	yes	—
123	C₂³×C₁₉	#101	1	2	yes	—
124	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₉	#117	1	2	yes	—
126	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
127	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	8	no	—
138	C₂×C₄×C₁₉	—	4	8	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	8	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	8	no	—
143	C₂×C₄×C₁₉	—	4	8	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	8	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	#123	1	4	yes	—
153	C₈×C₁₉	—	8	4	no	—
154	C₂²×#95	C₂×C₁₉	1	1	yes	characteristic
155	#1779	C₂×C₁₉	1	2	yes	—
156	#1280	C₂×C₁₉	1	4	yes	complemented
157	C₂²×C₁₉	—	2	16	no	—
158	C₂²×C₁₉	—	2	16	no	—
159	C₂²×C₁₉	—	2	2	no	—
160	C₂²×C₁₉	—	2	2	no	—
161	C₂²×C₁₉	—	2	2	no	—
162	C₂²×C₁₉	—	2	2	no	—
163	C₂²×C₁₉	—	2	2	no	—
164	C₂²×C₁₉	—	2	2	no	—
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	#323	1	4	yes	—
180	C₂²×C₁₉	#324	1	4	yes	—
181	C₂²×C₁₉	#381	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
183	C₂²×C₁₉	#407	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
188	C₂²×C₁₉	#431	1	2	yes	—
189	C₂²×C₁₉	#432	1	2	yes	—
190	C₄×C₁₉	—	2	4	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	4	4	no	—
193	C₄×C₁₉	—	4	4	no	—
194	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
195	C₂⁴×C₄	C₄×C₁₉	1	1	yes	characteristic
196	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	—	2	2	no	—
198	C₂×C₂²⋊C₈	—	2	2	no	—
199	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
200	C₂×#95	—	2	2	no	—
201	C₂×#95	—	2	2	no	—
202	C₂×#95	C₄×C₁₉	1	2	yes	—
203	C₂×#95	C₂²×C₁₉	1	2	yes	—
204	C₂×C₁₉	—	2	4	no	—
205	C₂×C₁₉	—	2	4	no	—
206	C₂×C₁₉	—	2	2	no	—
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	C₂×#323	1	1	yes	characteristic
209	C₂×C₁₉	C₂×#324	1	1	yes	characteristic
210	C₂×C₁₉	#1462	1	1	yes	characteristic
211	C₂×C₁₉	#1463	1	1	yes	characteristic
212	C₂×C₁₉	#1817	1	1	yes	characteristic
213	C₂×C₁₉	#1819	1	1	yes	characteristic
214	C₂×C₁₉	#1821	1	1	yes	characteristic
215	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
216	C₂³×C₄	—	2	1	no	—
217	C₂³×C₄	—	2	1	no	—
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	—	4	2	no	—
224	C₂³×C₄	—	4	2	no	—
225	C₂³×C₄	—	4	2	no	—
226	C₂³×C₄	—	4	2	no	—
227	C₂³×C₄	—	4	2	no	—
228	C₂³×C₄	—	4	2	no	—
229	C₂³×C₄	C₈×C₁₉	1	4	yes	complemented
230	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
232	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
233	C₂³×C₄	D₄×C₁₉	1	2	yes	—
234	C₂³×C₄	D₄×C₁₉	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	—	2	4	no	—
237	C₂²⋊C₈	—	2	8	no	—
238	C₂²⋊C₈	—	4	4	no	—
239	C₂²⋊C₈	—	4	4	no	—
240	#95	—	2	4	no	—
241	#95	—	2	4	no	—
242	C₁₉	#8698	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	—	2	2	no	—
244	C₂⁴	—	2	2	no	—
245	C₂⁴	—	2	2	no	—
246	C₂⁴	—	2	2	no	—
247	C₂⁴	—	2	2	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
250	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
251	C₂⁴	C₂×C₈×C₁₉	1	2	yes	—
252	C₂⁴	M₁₆×C₁₉	1	2	yes	—
253	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	16	no	—
274	C₂²×C₄	—	4	16	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	—
291	C₂²×C₄	M₁₆×C₁₉	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
293	C₂²×C₄	#41×C₁₉	1	4	yes	—
294	C₂×C₈	—	4	4	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂³	—	2	8	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	C₁₉×C₂²⋊C₈	1	2	yes	—
320	C₂³	C₁₉×C₂²⋊C₈	1	2	yes	—
321	C₂³	C₁₉×#99	1	2	yes	—
322	C₂³	C₁₉×#99	1	2	yes	—
323	C₂³	C₁₉×#100	1	2	yes	—
324	C₂³	C₁₉×#101	1	2	yes	—
325	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
326	C₂³	C₁₉×#117	1	2	yes	—
327	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
328	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
329	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	C₁₉×#123	1	4	yes	—
354	C₈	—	8	4	no	—
355	C₂²	—	2	16	no	—
356	C₂²	—	2	16	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	C₁₉×#323	1	4	yes	—
378	C₂²	C₁₉×#324	1	4	yes	—
379	C₂²	C₁₉×#381	1	1	yes	characteristic
380	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
381	C₂²	C₁₉×#407	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
383	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
384	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
385	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
386	C₂²	C₁₉×#431	1	2	yes	—
387	C₂²	C₁₉×#432	1	2	yes	—
388	C₄	—	2	4	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₂	—	2	2	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	4	no	—
395	C₂	—	2	4	no	—
396	C₂	C₂×C₁₉×#323	1	1	yes	characteristic
397	C₂	C₂×C₁₉×#324	1	1	yes	characteristic
398	C₂	C₁₉×#1462	1	1	yes	characteristic
399	C₂	C₁₉×#1463	1	1	yes	characteristic
400	C₂	C₁₉×#1817	1	1	yes	characteristic
401	C₂	C₁₉×#1819	1	1	yes	characteristic
402	C₂	C₁₉×#1821	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1280	C₂	semidirect
28. C₂³×C₄×C₁₉	C₈	semidirect
95. #8698	C₁₉	direct (N × H)
156. #1280	C₂×C₁₉	semidirect
229. C₂³×C₄	C₈×C₁₉	semidirect
242. C₁₉	#8698	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×#95	2
C₁₉×#1779	2
C₁₉×#1280	2
#8698	19

Subgroups — C19×#8698 #18014657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8698 #18014657