Subgroups — C₁₉×#17408 #18023367

Order 4864.

1012 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2973	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1471	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1468	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1466	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1464	C₂	1	2	yes	maximal, complemented
7	C₁₉×#540	—	2	8	no	—
8	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
9	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
10	C₂×C₁₉×#123	C₄	1	2	yes	—
11	C₂×C₁₉×#123	C₂²	1	2	yes	—
12	C₂×C₁₉×#121	C₄	1	2	yes	—
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₁₉×#435	—	2	8	no	—
20	C₁₉×#432	C₂²	1	4	yes	—
21	C₁₉×#407	C₂²	1	4	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₁₉×#324	C₂²	1	4	yes	—
24	C₁₉×#323	C₂²	1	4	yes	—
25	C₁₉×#323	C₂²	1	8	yes	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂×M₁₆×C₁₉	—	2	4	no	—
36	C₂²×C₈×C₁₉	—	2	4	no	—
37	C₁₉×#127	—	2	4	no	—
38	C₁₉×#125	—	2	4	no	—
39	C₁₉×#123	—	2	4	no	—
40	C₁₉×#123	—	2	4	no	—
41	C₁₉×#123	—	2	8	no	—
42	C₁₉×#121	—	2	4	no	—
43	C₁₉×#121	—	2	4	no	—
44	C₁₉×#121	—	2	4	no	—
45	C₁₉×#121	—	2	4	no	—
46	C₁₉×#121	—	2	8	no	—
47	C₄×D₄×C₁₉	—	2	4	no	—
48	C₄×D₄×C₁₉	D₄	1	8	yes	—
49	C₁₉×#117	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	—	2	4	no	—
65	C₁₉×C₂²⋊C₈	—	2	4	no	—
66	C₁₉×C₂²⋊C₈	—	2	4	no	—
67	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
68	C₁₉×#97	—	2	4	no	—
69	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	4	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	8	2	no	—
80	C₂×D₄×C₁₉	—	8	2	no	—
81	C₂×D₄×C₁₉	—	8	2	no	—
82	C₂×D₄×C₁₉	—	8	2	no	—
83	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	—	8	2	no	—
88	C₂²×C₄×C₁₉	—	8	2	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	M₁₆×C₁₉	—	8	4	no	—
100	C₂×C₈×C₁₉	—	2	8	no	—
101	C₂×C₈×C₁₉	—	8	4	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
108	C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	C₂×D₄	1	4	yes	—
117	#17408	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₉	—	2	4	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	4	2	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
130	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
131	D₄×C₁₉	—	4	4	no	—
132	D₄×C₁₉	—	4	4	no	—
133	D₄×C₁₉	—	8	4	no	—
134	D₄×C₁₉	—	8	4	no	—
135	D₄×C₁₉	—	8	4	no	—
136	D₄×C₁₉	—	8	4	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	8	4	no	—
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
157	C₈×C₁₉	—	4	8	no	—
158	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
159	#2973	C₂×C₁₉	1	2	yes	complemented
160	#1471	C₂×C₁₉	1	4	yes	complemented
161	#1468	C₂×C₁₉	1	4	yes	complemented
162	#1466	C₂×C₁₉	1	2	yes	complemented
163	#1464	C₂×C₁₉	1	2	yes	complemented
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	4	no	—
167	C₂²×C₁₉	—	2	4	no	—
168	C₂²×C₁₉	—	2	4	no	—
169	C₂²×C₁₉	—	4	1	no	—
170	C₂²×C₁₉	—	4	2	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	2	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	—	8	4	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	4	no	—
178	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₁₉	#568	1	2	yes	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	4	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	—	4	2	no	—
187	C₄×C₁₉	—	4	1	no	—
188	#540	—	2	8	no	—
189	C₂×#127	C₄×C₁₉	1	1	yes	characteristic
190	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
191	C₂×#123	C₄×C₁₉	1	2	yes	—
192	C₂×#123	C₂²×C₁₉	1	2	yes	—
193	C₂×#121	C₄×C₁₉	1	2	yes	—
194	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
195	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
196	C₂×#121	C₂²×C₁₉	1	2	yes	—
197	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
200	#435	—	2	8	no	—
201	#432	C₂²×C₁₉	1	4	yes	—
202	#407	C₂²×C₁₉	1	4	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
204	#324	C₂²×C₁₉	1	4	yes	—
205	#323	C₂²×C₁₉	1	4	yes	—
206	#323	C₂²×C₁₉	1	8	yes	—
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	—	4	4	no	—
209	C₂×C₁₉	—	8	1	no	—
210	C₂×C₁₉	—	8	2	no	—
211	C₂×C₁₉	#2879	1	1	yes	characteristic
212	C₂×C₁₉	#2883	1	1	yes	characteristic
213	C₂×C₁₉	#2888	1	1	yes	characteristic
214	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
215	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
216	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
217	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
218	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
219	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
223	C₂×M₁₆	—	2	4	no	—
224	C₂²×C₈	—	2	4	no	—
225	#127	—	2	4	no	—
226	#125	—	2	4	no	—
227	#123	—	2	4	no	—
228	#123	—	2	4	no	—
229	#123	—	2	8	no	—
230	#121	—	2	4	no	—
231	#121	—	2	4	no	—
232	#121	—	2	4	no	—
233	#121	—	2	4	no	—
234	#121	—	2	8	no	—
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	D₄×C₁₉	1	8	yes	—
237	#117	—	2	4	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
250	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	C₄⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
256	#97	—	2	4	no	—
257	C₁₉	#17408	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
259	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
260	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	8	2	no	—
269	C₂×D₄	—	8	2	no	—
270	C₂×D₄	—	8	2	no	—
271	C₂×D₄	—	8	2	no	—
272	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	8	2	no	—
277	C₂²×C₄	—	8	2	no	—
278	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
288	M₁₆	—	8	4	no	—
289	C₂×C₈	—	2	8	no	—
290	C₂×C₈	—	8	4	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
304	C₄²	—	2	2	no	—
305	C₄²	C₂×D₄×C₁₉	1	4	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
318	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
319	D₄	—	4	4	no	—
320	D₄	—	4	4	no	—
321	D₄	—	8	4	no	—
322	D₄	—	8	4	no	—
323	D₄	—	8	4	no	—
324	D₄	—	8	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
344	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
345	C₈	—	4	8	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	4	no	—
360	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
361	C₂²	C₁₉×#568	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₂	—	2	2	no	—
371	C₂	—	4	4	no	—
372	C₂	—	8	1	no	—
373	C₂	—	8	2	no	—
374	C₂	C₁₉×#2879	1	1	yes	characteristic
375	C₂	C₁₉×#2883	1	1	yes	characteristic
376	C₂	C₁₉×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#540	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2973	C₂	semidirect
3. C₁₉×#1471	C₂	semidirect
4. C₁₉×#1468	C₂	semidirect
5. C₁₉×#1466	C₂	semidirect
6. C₁₉×#1464	C₂	semidirect
117. #17408	C₁₉	direct (N × H)
159. #2973	C₂×C₁₉	semidirect
160. #1471	C₂×C₁₉	semidirect
161. #1468	C₂×C₁₉	semidirect
162. #1466	C₂×C₁₉	semidirect
163. #1464	C₂×C₁₉	semidirect
257. C₁₉	#17408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#540	2
C₁₉×#2973	2
C₁₉×#1471	2
C₁₉×#1468	2
C₁₉×#1466	2
C₁₉×#1464	2
#17408	19

Subgroups — C19×#17408 #18023367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17408 #18023367