Subgroups — C₁₉×#14501 #18020460

Order 4864.

1310 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#391	C₂	1	2	yes	maximal
2	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1442	C₂	1	4	yes	maximal
4	C₁₉×#1441	C₂	1	2	yes	maximal
5	C₁₉×#1436	C₂	1	4	yes	maximal
6	C₁₉×#1434	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#391	—	2	8	no	—
14	C₁₉×#391	C₄	1	8	yes	complemented
15	C₂×C₁₉×#95	C₂²	1	4	yes	—
16	C₂×C₁₉×#95	C₂²	1	4	yes	—
17	C₂×C₁₉×#95	C₂²	1	4	yes	—
18	C₂×C₁₉×#95	C₂²	1	4	yes	—
19	C₂×C₁₉×#95	C₂²	1	2	yes	—
20	C₂×C₁₉×#95	C₂²	1	2	yes	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₉	—	4	1	no	—
24	C₂²×Q₈×C₁₉	—	4	1	no	—
25	C₂²×Q₈×C₁₉	—	4	1	no	—
26	C₂²×Q₈×C₁₉	—	4	1	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
29	C₂²×Q₈×C₁₉	Q₈	1	4	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₉	—	2	4	no	—
45	C₂×C₄²×C₁₉	—	4	1	no	—
46	C₂×C₄²×C₁₉	—	4	1	no	—
47	C₂×C₄²×C₁₉	—	4	2	no	—
48	C₂×C₄²×C₁₉	—	4	2	no	—
49	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
50	C₁₉×#95	—	2	8	no	—
51	C₁₉×#95	—	2	8	no	—
52	C₁₉×#95	—	2	8	no	—
53	C₁₉×#95	—	2	8	no	—
54	C₁₉×#95	—	4	2	no	—
55	C₁₉×#95	—	4	2	no	—
56	C₁₉×#95	—	4	2	no	—
57	C₁₉×#95	C₂×C₄	1	16	yes	—
58	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	—	4	4	no	—
60	C₂×Q₈×C₁₉	—	4	4	no	—
61	C₂×Q₈×C₁₉	—	4	4	no	—
62	C₂×Q₈×C₁₉	—	4	4	no	—
63	C₂×Q₈×C₁₉	—	4	4	no	—
64	C₂×Q₈×C₁₉	—	4	4	no	—
65	C₂×Q₈×C₁₉	C₄⋊C₄	1	16	yes	complemented
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₉	#41	1	8	yes	—
104	C₄⋊C₄×C₁₉	—	4	4	no	—
105	C₄⋊C₄×C₁₉	—	4	8	no	—
106	C₄⋊C₄×C₁₉	—	4	8	no	—
107	C₄²×C₁₉	—	4	4	no	—
108	C₄²×C₁₉	—	4	8	no	—
109	#14501	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
111	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
112	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
113	C₂³×C₁₉	C₂×#41	1	4	yes	—
114	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
115	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
116	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
117	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
118	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
119	Q₈×C₁₉	—	4	16	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	4	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	2	4	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	8	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	8	no	—
138	C₂×C₄×C₁₉	—	2	8	no	—
139	C₂×C₄×C₁₉	—	2	8	no	—
140	C₂×C₄×C₁₉	—	4	4	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	4	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	—	4	4	no	—
156	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
157	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
158	C₂×#391	C₂×C₁₉	1	2	yes	—
159	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
160	#1442	C₂×C₁₉	1	4	yes	—
161	#1441	C₂×C₁₉	1	2	yes	—
162	#1436	C₂×C₁₉	1	4	yes	—
163	#1434	C₂×C₁₉	1	2	yes	—
164	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₁₉	C₄×#41	1	2	yes	—
166	C₂²×C₁₉	#518	1	1	yes	characteristic
167	C₂²×C₁₉	#518	1	1	yes	characteristic
168	C₂²×C₁₉	#519	1	2	yes	—
169	C₂²×C₁₉	#534	1	1	yes	characteristic
170	C₂²×C₁₉	#534	1	1	yes	characteristic
171	C₂²×C₁₉	#539	1	4	yes	—
172	C₂²×C₁₉	#542	1	4	yes	—
173	C₂²×C₁₉	#543	1	1	yes	characteristic
174	C₂²×C₁₉	#543	1	1	yes	characteristic
175	C₂²×C₁₉	#548	1	4	yes	—
176	C₂²×C₁₉	#551	1	2	yes	—
177	C₂²×C₁₉	#555	1	2	yes	—
178	C₂²×C₁₉	#557	1	4	yes	—
179	C₂²×C₁₉	#563	1	2	yes	—
180	C₂²×C₁₉	#563	1	2	yes	—
181	C₄×C₁₉	—	2	4	no	—
182	C₄×C₁₉	—	2	8	no	—
183	C₄×C₁₉	—	4	4	no	—
184	C₄×C₁₉	—	4	4	no	—
185	C₄×C₁₉	—	4	8	no	—
186	C₄×C₁₉	—	8	4	no	—
187	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
190	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
191	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
192	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
193	#391	—	2	8	no	—
194	#391	C₄×C₁₉	1	8	yes	complemented
195	C₂×#95	C₂²×C₁₉	1	4	yes	—
196	C₂×#95	C₂²×C₁₉	1	4	yes	—
197	C₂×#95	C₂²×C₁₉	1	4	yes	—
198	C₂×#95	C₂²×C₁₉	1	4	yes	—
199	C₂×#95	C₂²×C₁₉	1	2	yes	—
200	C₂×#95	C₂²×C₁₉	1	2	yes	—
201	C₂×#95	C₂²×C₁₉	1	2	yes	—
202	C₂×#95	C₂²×C₁₉	1	4	yes	—
203	C₂×C₁₉	#2315	1	1	yes	characteristic
204	C₂×C₁₉	#2332	1	2	yes	—
205	C₂×C₁₉	#2351	1	2	yes	—
206	C₂×C₁₉	#2372	1	1	yes	characteristic
207	C₂×C₁₉	#2381	1	1	yes	characteristic
208	C₂×C₁₉	#2728	1	2	yes	—
209	C₂×C₁₉	#2731	1	2	yes	—
210	C₂×C₁₉	#2799	1	2	yes	—
211	C₂×C₁₉	#2809	1	2	yes	—
212	C₂²×Q₈	—	4	1	no	—
213	C₂²×Q₈	—	4	1	no	—
214	C₂²×Q₈	—	4	1	no	—
215	C₂²×Q₈	—	4	1	no	—
216	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
217	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
218	C₂²×Q₈	Q₈×C₁₉	1	4	yes	—
219	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
221	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	—	4	1	no	—
228	C₂×C₄⋊C₄	—	4	1	no	—
229	C₂×C₄⋊C₄	—	4	2	no	—
230	C₂×C₄⋊C₄	—	4	2	no	—
231	C₂×C₄⋊C₄	—	4	2	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	—	4	1	no	—
235	C₂×C₄²	—	4	1	no	—
236	C₂×C₄²	—	4	2	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
239	#95	—	2	8	no	—
240	#95	—	2	8	no	—
241	#95	—	2	8	no	—
242	#95	—	2	8	no	—
243	#95	—	4	2	no	—
244	#95	—	4	2	no	—
245	#95	—	4	2	no	—
246	#95	C₂×C₄×C₁₉	1	16	yes	—
247	C₁₉	#14501	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
249	C₂×Q₈	—	4	4	no	—
250	C₂×Q₈	—	4	4	no	—
251	C₂×Q₈	—	4	4	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	—	4	4	no	—
254	C₂×Q₈	—	4	4	no	—
255	C₂×Q₈	C₄⋊C₄×C₁₉	1	16	yes	complemented
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
291	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
292	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
293	C₂²×C₄	#41×C₁₉	1	8	yes	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	8	no	—
296	C₄⋊C₄	—	4	8	no	—
297	C₄²	—	4	4	no	—
298	C₄²	—	4	8	no	—
299	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
300	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
301	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
302	C₂³	C₂×#41×C₁₉	1	4	yes	—
303	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
308	Q₈	—	4	16	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
346	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
347	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
348	C₂²	C₄×#41×C₁₉	1	2	yes	—
349	C₂²	C₁₉×#518	1	1	yes	characteristic
350	C₂²	C₁₉×#518	1	1	yes	characteristic
351	C₂²	C₁₉×#519	1	2	yes	—
352	C₂²	C₁₉×#534	1	1	yes	characteristic
353	C₂²	C₁₉×#534	1	1	yes	characteristic
354	C₂²	C₁₉×#539	1	4	yes	—
355	C₂²	C₁₉×#542	1	4	yes	—
356	C₂²	C₁₉×#543	1	1	yes	characteristic
357	C₂²	C₁₉×#543	1	1	yes	characteristic
358	C₂²	C₁₉×#548	1	4	yes	—
359	C₂²	C₁₉×#551	1	2	yes	—
360	C₂²	C₁₉×#555	1	2	yes	—
361	C₂²	C₁₉×#557	1	4	yes	—
362	C₂²	C₁₉×#563	1	2	yes	—
363	C₂²	C₁₉×#563	1	2	yes	—
364	C₄	—	2	4	no	—
365	C₄	—	2	8	no	—
366	C₄	—	4	8	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	4	no	—
370	C₂	C₁₉×#2315	1	1	yes	characteristic
371	C₂	C₁₉×#2332	1	2	yes	—
372	C₂	C₁₉×#2351	1	2	yes	—
373	C₂	C₁₉×#2372	1	1	yes	characteristic
374	C₂	C₁₉×#2381	1	1	yes	characteristic
375	C₂	C₁₉×#2728	1	2	yes	—
376	C₂	C₁₉×#2731	1	2	yes	—
377	C₂	C₁₉×#2799	1	2	yes	—
378	C₂	C₁₉×#2809	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
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
14. C₁₉×#391	C₄	semidirect
65. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
109. #14501	C₁₉	direct (N × H)
194. #391	C₄×C₁₉	semidirect
247. C₁₉	#14501	direct (N × H)
255. C₂×Q₈	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#391	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×#1434	2
#14501	19

Subgroups — C19×#14501 #18020460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14501 #18020460