Subgroups — C₁₉×#14562 #18020521

Order 4864.

1590 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#396	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₉×#388	C₂	1	3	yes	maximal
4	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1439	C₂	1	3	yes	maximal
7	C₁₉×#1436	C₂	1	3	yes	maximal, complemented
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
15	C₁₉×#396	C₄	1	8	yes	complemented
16	C₁₉×#389	—	2	12	no	—
17	C₁₉×#388	—	2	12	no	—
18	C₂×C₁₉×#95	C₂²	1	3	yes	—
19	C₂×C₁₉×#95	C₂²	1	3	yes	—
20	C₂×C₁₉×#95	C₂²	1	3	yes	—
21	C₂×C₁₉×#95	C₂²	1	3	yes	—
22	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#95	C₂²	1	3	yes	—
24	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
28	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
29	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
31	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
37	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
46	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
47	C₂×C₄²×C₁₉	—	2	6	no	—
48	C₂×C₄²×C₁₉	—	2	6	no	—
49	C₂×C₄²×C₁₉	—	4	3	no	—
50	C₁₉×#95	—	2	6	no	—
51	C₁₉×#95	—	2	6	no	—
52	C₁₉×#95	—	2	6	no	—
53	C₁₉×#95	—	4	3	no	—
54	C₁₉×#95	C₂×C₄	1	4	yes	—
55	C₁₉×#95	D₄	1	12	yes	—
56	C₂⁴×C₁₉	—	2	3	no	—
57	C₂⁴×C₁₉	—	2	3	no	—
58	C₂⁴×C₁₉	—	2	3	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂⁴×C₁₉	—	2	1	no	—
61	C₂⁴×C₁₉	—	2	3	no	—
62	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
63	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	3	no	—
65	C₂²×C₄×C₁₉	—	2	3	no	—
66	C₂²×C₄×C₁₉	—	2	3	no	—
67	C₂²×C₄×C₁₉	—	2	3	no	—
68	C₂²×C₄×C₁₉	—	2	3	no	—
69	C₂²×C₄×C₁₉	—	2	3	no	—
70	C₂²×C₄×C₁₉	—	2	3	no	—
71	C₂²×C₄×C₁₉	—	2	3	no	—
72	C₂²×C₄×C₁₉	—	2	3	no	—
73	C₂²×C₄×C₁₉	—	2	3	no	—
74	C₂²×C₄×C₁₉	—	2	3	no	—
75	C₂²×C₄×C₁₉	—	2	3	no	—
76	C₂²×C₄×C₁₉	—	2	3	no	—
77	C₂²×C₄×C₁₉	—	2	3	no	—
78	C₂²×C₄×C₁₉	—	2	3	no	—
79	C₂²×C₄×C₁₉	—	2	3	no	—
80	C₂²×C₄×C₁₉	—	2	3	no	—
81	C₂²×C₄×C₁₉	—	2	3	no	—
82	C₂²×C₄×C₁₉	—	2	3	no	—
83	C₂²×C₄×C₁₉	—	2	3	no	—
84	C₂²×C₄×C₁₉	—	2	3	no	—
85	C₂²×C₄×C₁₉	—	2	3	no	—
86	C₂²×C₄×C₁₉	—	2	3	no	—
87	C₂²×C₄×C₁₉	—	2	3	no	—
88	C₂²×C₄×C₁₉	—	2	3	no	—
89	C₂²×C₄×C₁₉	—	2	3	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
97	C₂²×C₄×C₁₉	#41	1	6	yes	—
98	C₄⋊C₄×C₁₉	—	2	24	no	—
99	C₄⋊C₄×C₁₉	—	4	12	no	—
100	C₄⋊C₄×C₁₉	—	4	12	no	—
101	C₂²⋊C₄×C₁₉	—	2	24	no	—
102	C₂²⋊C₄×C₁₉	—	4	12	no	—
103	C₂²⋊C₄×C₁₉	—	4	4	no	—
104	C₄²×C₁₉	—	4	12	no	—
105	#14562	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₉	—	2	6	no	—
107	C₂³×C₁₉	—	2	2	no	—
108	C₂³×C₁₉	—	2	6	no	—
109	C₂³×C₁₉	—	4	3	no	—
110	C₂³×C₁₉	—	4	3	no	—
111	C₂³×C₁₉	—	4	3	no	—
112	C₂³×C₁₉	—	4	3	no	—
113	C₂³×C₁₉	—	4	3	no	—
114	C₂³×C₁₉	—	4	3	no	—
115	C₂³×C₁₉	—	4	3	no	—
116	C₂³×C₁₉	—	4	3	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	3	no	—
119	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
121	C₂³×C₁₉	C₂×#41	1	3	yes	—
122	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
123	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
124	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
125	C₂³×C₁₉	2₋¹⁺⁴	1	3	yes	—
126	C₂×C₄×C₁₉	—	2	6	no	—
127	C₂×C₄×C₁₉	—	2	6	no	—
128	C₂×C₄×C₁₉	—	2	6	no	—
129	C₂×C₄×C₁₉	—	2	6	no	—
130	C₂×C₄×C₁₉	—	2	6	no	—
131	C₂×C₄×C₁₉	—	2	6	no	—
132	C₂×C₄×C₁₉	—	2	6	no	—
133	C₂×C₄×C₁₉	—	2	6	no	—
134	C₂×C₄×C₁₉	—	2	6	no	—
135	C₂×C₄×C₁₉	—	2	6	no	—
136	C₂×C₄×C₁₉	—	2	6	no	—
137	C₂×C₄×C₁₉	—	2	6	no	—
138	C₂×C₄×C₁₉	—	2	6	no	—
139	C₂×C₄×C₁₉	—	2	6	no	—
140	C₂×C₄×C₁₉	—	2	6	no	—
141	C₂×C₄×C₁₉	—	4	3	no	—
142	C₂×C₄×C₁₉	—	4	3	no	—
143	C₂×C₄×C₁₉	—	4	3	no	—
144	C₂×C₄×C₁₉	—	4	3	no	—
145	C₂×C₄×C₁₉	—	4	3	no	—
146	C₂×C₄×C₁₉	—	4	3	no	—
147	C₂×C₄×C₁₉	—	4	3	no	—
148	C₂×C₄×C₁₉	—	4	3	no	—
149	C₂×C₄×C₁₉	—	4	3	no	—
150	C₂×C₄×C₁₉	—	4	3	no	—
151	C₂×C₄×C₁₉	—	4	3	no	—
152	C₂×C₄×C₁₉	—	4	3	no	—
153	C₂×C₄×C₁₉	—	4	3	no	—
154	C₂×C₄×C₁₉	—	4	3	no	—
155	C₂×C₄×C₁₉	—	4	3	no	—
156	C₂×C₄×C₁₉	—	4	3	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	C₄×D₄	1	12	yes	—
160	C₂×#396	C₂×C₁₉	1	1	yes	characteristic
161	C₂×#389	C₂×C₁₉	1	3	yes	complemented
162	C₂×#388	C₂×C₁₉	1	3	yes	—
163	#1444	C₂×C₁₉	1	1	yes	characteristic, complemented
164	#1443	C₂×C₁₉	1	1	yes	characteristic, complemented
165	#1439	C₂×C₁₉	1	3	yes	—
166	#1436	C₂×C₁₉	1	3	yes	complemented
167	C₂²×C₁₉	—	4	6	no	—
168	C₂²×C₁₉	—	4	6	no	—
169	C₂²×C₁₉	—	4	2	no	—
170	C₂²×C₁₉	—	8	3	no	—
171	C₂²×C₁₉	—	8	1	no	—
172	C₂²×C₁₉	—	8	3	no	—
173	C₂²×C₁₉	—	8	1	no	—
174	C₂²×C₁₉	C₂×C₄×D₄	1	3	yes	—
175	C₂²×C₁₉	#519	1	1	yes	characteristic
176	C₂²×C₁₉	#520	1	3	yes	—
177	C₂²×C₁₉	#536	1	3	yes	—
178	C₂²×C₁₉	#537	1	3	yes	—
179	C₂²×C₁₉	#541	1	3	yes	—
180	C₂²×C₁₉	#542	1	3	yes	—
181	C₂²×C₁₉	D₄²	1	3	yes	—
182	C₂²×C₁₉	#547	1	3	yes	—
183	C₂²×C₁₉	#548	1	3	yes	—
184	C₂²×C₁₉	#553	1	3	yes	—
185	C₂²×C₁₉	#560	1	1	yes	characteristic
186	C₂²×C₁₉	#563	1	3	yes	—
187	C₄×C₁₉	—	2	12	no	—
188	C₄×C₁₉	—	4	6	no	—
189	C₄×C₁₉	—	4	6	no	—
190	C₄×C₁₉	—	4	6	no	—
191	C₄×C₁₉	—	8	1	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
196	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
200	#396	C₄×C₁₉	1	8	yes	complemented
201	#389	—	2	12	no	—
202	#388	—	2	12	no	—
203	C₂×#95	C₂²×C₁₉	1	3	yes	—
204	C₂×#95	C₂²×C₁₉	1	3	yes	—
205	C₂×#95	C₂²×C₁₉	1	3	yes	—
206	C₂×#95	C₂²×C₁₉	1	3	yes	—
207	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#95	C₂²×C₁₉	1	3	yes	—
209	C₂×C₁₉	—	8	2	no	—
210	C₂×C₁₉	#2323	1	3	yes	—
211	C₂×C₁₉	#2361	1	3	yes	—
212	C₂×C₁₉	#2383	1	1	yes	characteristic
213	C₂×C₁₉	#2674	1	3	yes	—
214	C₂×C₁₉	#2675	1	1	yes	characteristic
215	C₂×C₁₉	#2725	1	3	yes	—
216	C₂×C₁₉	#2801	1	1	yes	characteristic
217	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
221	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
222	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
224	C₂×C₄⋊C₄	—	2	6	no	—
225	C₂×C₄⋊C₄	—	2	6	no	—
226	C₂×C₄⋊C₄	—	2	6	no	—
227	C₂×C₄⋊C₄	—	2	6	no	—
228	C₂×C₄⋊C₄	—	2	6	no	—
229	C₂×C₄⋊C₄	—	2	6	no	—
230	C₂×C₄⋊C₄	—	4	3	no	—
231	C₂×C₄⋊C₄	—	4	3	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
233	C₂×C₂²⋊C₄	—	2	6	no	—
234	C₂×C₂²⋊C₄	—	2	6	no	—
235	C₂×C₂²⋊C₄	—	2	6	no	—
236	C₂×C₂²⋊C₄	—	2	6	no	—
237	C₂×C₂²⋊C₄	—	4	3	no	—
238	C₂×C₂²⋊C₄	—	4	3	no	—
239	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
240	C₂×C₄²	—	2	6	no	—
241	C₂×C₄²	—	2	6	no	—
242	C₂×C₄²	—	4	3	no	—
243	#95	—	2	6	no	—
244	#95	—	2	6	no	—
245	#95	—	2	6	no	—
246	#95	—	4	3	no	—
247	#95	C₂×C₄×C₁₉	1	4	yes	—
248	#95	D₄×C₁₉	1	12	yes	—
249	C₁₉	#14562	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁴	—	2	3	no	—
251	C₂⁴	—	2	3	no	—
252	C₂⁴	—	2	3	no	—
253	C₂⁴	—	2	1	no	—
254	C₂⁴	—	2	1	no	—
255	C₂⁴	—	2	3	no	—
256	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
257	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
258	C₂²×C₄	—	2	3	no	—
259	C₂²×C₄	—	2	3	no	—
260	C₂²×C₄	—	2	3	no	—
261	C₂²×C₄	—	2	3	no	—
262	C₂²×C₄	—	2	3	no	—
263	C₂²×C₄	—	2	3	no	—
264	C₂²×C₄	—	2	3	no	—
265	C₂²×C₄	—	2	3	no	—
266	C₂²×C₄	—	2	3	no	—
267	C₂²×C₄	—	2	3	no	—
268	C₂²×C₄	—	2	3	no	—
269	C₂²×C₄	—	2	3	no	—
270	C₂²×C₄	—	2	3	no	—
271	C₂²×C₄	—	2	3	no	—
272	C₂²×C₄	—	2	3	no	—
273	C₂²×C₄	—	2	3	no	—
274	C₂²×C₄	—	2	3	no	—
275	C₂²×C₄	—	2	3	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	3	no	—
279	C₂²×C₄	—	2	3	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
289	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
290	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
291	C₂²×C₄	#41×C₁₉	1	6	yes	—
292	C₄⋊C₄	—	2	24	no	—
293	C₄⋊C₄	—	4	12	no	—
294	C₄⋊C₄	—	4	12	no	—
295	C₂²⋊C₄	—	2	24	no	—
296	C₂²⋊C₄	—	4	12	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₄²	—	4	12	no	—
299	C₂³	—	2	6	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	3	no	—
303	C₂³	—	4	3	no	—
304	C₂³	—	4	3	no	—
305	C₂³	—	4	3	no	—
306	C₂³	—	4	3	no	—
307	C₂³	—	4	3	no	—
308	C₂³	—	4	3	no	—
309	C₂³	—	4	3	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	3	no	—
312	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
313	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
314	C₂³	C₂×#41×C₁₉	1	3	yes	—
315	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
316	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂³	C₁₉×2₋¹⁺⁴	1	3	yes	—
319	C₂×C₄	—	2	6	no	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	2	6	no	—
323	C₂×C₄	—	2	6	no	—
324	C₂×C₄	—	2	6	no	—
325	C₂×C₄	—	2	6	no	—
326	C₂×C₄	—	2	6	no	—
327	C₂×C₄	—	2	6	no	—
328	C₂×C₄	—	2	6	no	—
329	C₂×C₄	—	2	6	no	—
330	C₂×C₄	—	2	6	no	—
331	C₂×C₄	—	2	6	no	—
332	C₂×C₄	—	2	6	no	—
333	C₂×C₄	—	2	6	no	—
334	C₂×C₄	—	4	3	no	—
335	C₂×C₄	—	4	3	no	—
336	C₂×C₄	—	4	3	no	—
337	C₂×C₄	—	4	3	no	—
338	C₂×C₄	—	4	3	no	—
339	C₂×C₄	—	4	3	no	—
340	C₂×C₄	—	4	3	no	—
341	C₂×C₄	—	4	3	no	—
342	C₂×C₄	—	4	3	no	—
343	C₂×C₄	—	4	3	no	—
344	C₂×C₄	—	4	3	no	—
345	C₂×C₄	—	4	3	no	—
346	C₂×C₄	—	4	3	no	—
347	C₂×C₄	—	4	3	no	—
348	C₂×C₄	—	4	3	no	—
349	C₂×C₄	—	4	3	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	C₄×D₄×C₁₉	1	12	yes	—
353	C₂²	—	4	6	no	—
354	C₂²	—	4	6	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	8	3	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	3	no	—
359	C₂²	—	8	1	no	—
360	C₂²	C₂×C₄×D₄×C₁₉	1	3	yes	—
361	C₂²	C₁₉×#519	1	1	yes	characteristic
362	C₂²	C₁₉×#520	1	3	yes	—
363	C₂²	C₁₉×#536	1	3	yes	—
364	C₂²	C₁₉×#537	1	3	yes	—
365	C₂²	C₁₉×#541	1	3	yes	—
366	C₂²	C₁₉×#542	1	3	yes	—
367	C₂²	D₄²×C₁₉	1	3	yes	—
368	C₂²	C₁₉×#547	1	3	yes	—
369	C₂²	C₁₉×#548	1	3	yes	—
370	C₂²	C₁₉×#553	1	3	yes	—
371	C₂²	C₁₉×#560	1	1	yes	characteristic
372	C₂²	C₁₉×#563	1	3	yes	—
373	C₄	—	2	12	no	—
374	C₄	—	4	6	no	—
375	C₄	—	4	6	no	—
376	C₄	—	4	6	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₂	—	8	2	no	—
380	C₂	C₁₉×#2323	1	3	yes	—
381	C₂	C₁₉×#2361	1	3	yes	—
382	C₂	C₁₉×#2383	1	1	yes	characteristic
383	C₂	C₁₉×#2674	1	3	yes	—
384	C₂	C₁₉×#2675	1	1	yes	characteristic
385	C₂	C₁₉×#2725	1	3	yes	—
386	C₂	C₁₉×#2801	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#389	C₂	semidirect
4. C₁₉×#1444	C₂	semidirect
5. C₁₉×#1443	C₂	semidirect
7. C₁₉×#1436	C₂	semidirect
15. C₁₉×#396	C₄	semidirect
105. #14562	C₁₉	direct (N × H)
161. C₂×#389	C₂×C₁₉	semidirect
163. #1444	C₂×C₁₉	semidirect
164. #1443	C₂×C₁₉	semidirect
166. #1436	C₂×C₁₉	semidirect
200. #396	C₄×C₁₉	semidirect
249. C₁₉	#14562	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×#396	2
C₂×C₁₉×#389	2
C₂×C₁₉×#388	2
C₁₉×#1444	2
C₁₉×#1443	2
C₁₉×#1439	2
C₁₉×#1436	2
#14562	19

Subgroups — C19×#14562 #18020521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14562 #18020521