Subgroups — C₁₉×#3201 #14561058

Order 2432.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×#124	—	2	1	no	—
27	C₁₉×#123	—	2	1	no	—
28	C₁₉×#123	—	2	1	no	—
29	C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₉×#121	—	2	1	no	—
37	C₁₉×#121	—	2	1	no	—
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	C₂²	1	1	yes	characteristic
40	C₁₉×#121	C₂²	1	1	yes	characteristic
41	C₁₉×#117	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#107	C₂²	1	1	yes	characteristic
44	C₁₉×#107	C₂²	1	1	yes	characteristic
45	C₁₉×#106	C₂²	1	1	yes	characteristic
46	C₁₉×#106	C₂²	1	1	yes	characteristic
47	C₁₉×#103	C₂²	1	1	yes	characteristic
48	C₁₉×#103	C₂²	1	1	yes	characteristic
49	C₁₉×#103	C₂²	1	1	yes	characteristic
50	C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₁₉×#103	C₂²	1	1	yes	characteristic
52	C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₁₉×#102	C₂²	1	1	yes	characteristic
55	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	#41×C₁₉	—	4	1	no	—
60	#41×C₁₉	—	4	1	no	—
61	#41×C₁₉	—	4	1	no	—
62	#41×C₁₉	—	4	1	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
67	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	Q₁₆×C₁₉	—	4	1	no	—
84	Q₁₆×C₁₉	—	4	1	no	—
85	SD₁₆×C₁₉	—	4	1	no	—
86	SD₁₆×C₁₉	—	4	1	no	—
87	M₁₆×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₄²×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
118	Q₈×C₁₉	—	2	1	no	—
119	Q₈×C₁₉	—	2	1	no	—
120	Q₈×C₁₉	—	2	1	no	—
121	Q₈×C₁₉	—	2	1	no	—
122	Q₈×C₁₉	—	2	1	no	—
123	Q₈×C₁₉	—	2	1	no	—
124	Q₈×C₁₉	—	4	1	no	—
125	Q₈×C₁₉	—	4	2	no	—
126	D₄×C₁₉	—	2	1	no	—
127	D₄×C₁₉	—	2	1	no	—
128	D₄×C₁₉	—	4	1	no	—
129	D₄×C₁₉	—	4	1	no	—
130	D₄×C₁₉	—	4	1	no	—
131	D₄×C₁₉	—	4	2	no	—
132	D₄×C₁₉	—	8	1	no	—
133	D₄×C₁₉	—	8	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	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	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₈×C₁₉	—	2	1	no	—
155	C₈×C₁₉	—	2	1	no	—
156	C₈×C₁₉	—	2	1	no	—
157	C₈×C₁₉	—	2	1	no	—
158	#3201	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	4	1	no	—
169	C₂²×C₁₉	—	4	1	no	—
170	C₂²×C₁₉	—	4	1	no	—
171	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	4	1	no	—
176	C₄×C₁₉	—	4	1	no	—
177	C₄×C₁₉	—	4	1	no	—
178	C₄×C₁₉	—	4	1	no	—
179	C₄×C₁₉	—	4	1	no	—
180	C₄×C₁₉	—	4	1	no	—
181	C₄×C₁₉	—	4	1	no	—
182	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
184	#537	C₂×C₁₉	1	1	yes	characteristic
185	#536	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#485	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#484	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#483	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#482	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#470	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#468	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#467	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#465	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#452	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#452	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#451	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#448	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#408	C₂×C₁₉	1	1	yes	characteristic, complemented
199	C₂×C₁₉	—	4	1	no	—
200	C₂×C₁₉	—	4	1	no	—
201	C₂×C₁₉	—	4	1	no	—
202	C₂×C₁₉	—	8	1	no	—
203	C₂×C₁₉	#534	1	1	yes	characteristic
204	C₂×C₁₉	#577	1	1	yes	characteristic
205	C₂×C₁₉	#578	1	1	yes	characteristic
206	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
214	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₄⋊Q₈	—	2	1	no	—
216	#124	—	2	1	no	—
217	#123	—	2	1	no	—
218	#123	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
223	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	C₂²×C₁₉	1	1	yes	characteristic
230	#121	C₂²×C₁₉	1	1	yes	characteristic
231	#117	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
233	#107	C₂²×C₁₉	1	1	yes	characteristic
234	#107	C₂²×C₁₉	1	1	yes	characteristic
235	#106	C₂²×C₁₉	1	1	yes	characteristic
236	#106	C₂²×C₁₉	1	1	yes	characteristic
237	#103	C₂²×C₁₉	1	1	yes	characteristic
238	#103	C₂²×C₁₉	1	1	yes	characteristic
239	#103	C₂²×C₁₉	1	1	yes	characteristic
240	#103	C₂²×C₁₉	1	1	yes	characteristic
241	#103	C₂²×C₁₉	1	1	yes	characteristic
242	#103	C₂²×C₁₉	1	1	yes	characteristic
243	#102	C₂²×C₁₉	1	1	yes	characteristic
244	#102	C₂²×C₁₉	1	1	yes	characteristic
245	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
249	C₁₉	#3201	1	1	yes	characteristic, direct product factor, Sylow
250	#41	—	4	1	no	—
251	#41	—	4	1	no	—
252	#41	—	4	1	no	—
253	#41	—	4	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	4	1	no	—
256	C₂×Q₈	—	4	1	no	—
257	C₂×Q₈	D₄×C₁₉	1	1	yes	characteristic
258	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
259	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
266	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
267	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
274	Q₁₆	—	4	1	no	—
275	Q₁₆	—	4	1	no	—
276	SD₁₆	—	4	1	no	—
277	SD₁₆	—	4	1	no	—
278	M₁₆	—	4	1	no	—
279	C₂×C₈	—	4	1	no	—
280	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
281	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
282	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
283	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
309	Q₈	—	2	1	no	—
310	Q₈	—	2	1	no	—
311	Q₈	—	2	1	no	—
312	Q₈	—	2	1	no	—
313	Q₈	—	2	1	no	—
314	Q₈	—	2	1	no	—
315	Q₈	—	4	1	no	—
316	Q₈	—	4	2	no	—
317	D₄	—	2	1	no	—
318	D₄	—	2	1	no	—
319	D₄	—	4	1	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	2	no	—
323	D₄	—	8	1	no	—
324	D₄	—	8	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
373	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂	—	4	1	no	—
375	C₂	—	4	1	no	—
376	C₂	—	4	1	no	—
377	C₂	—	8	1	no	—
378	C₂	C₁₉×#534	1	1	yes	characteristic
379	C₂	C₁₉×#577	1	1	yes	characteristic
380	C₂	C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#536	C₂	semidirect
3. C₁₉×#485	C₂	semidirect
4. C₁₉×#484	C₂	semidirect
5. C₁₉×#483	C₂	semidirect
6. C₁₉×#482	C₂	semidirect
7. C₁₉×#470	C₂	semidirect
8. C₁₉×#468	C₂	semidirect
9. C₁₉×#467	C₂	semidirect
10. C₁₉×#465	C₂	semidirect
11. C₁₉×#452	C₂	semidirect
12. C₁₉×#452	C₂	semidirect
13. C₁₉×#451	C₂	semidirect
14. C₁₉×#448	C₂	semidirect
15. C₁₉×#408	C₂	semidirect
158. #3201	C₁₉	direct (N × H)
185. #536	C₂×C₁₉	semidirect
186. #485	C₂×C₁₉	semidirect
187. #484	C₂×C₁₉	semidirect
188. #483	C₂×C₁₉	semidirect
189. #482	C₂×C₁₉	semidirect
190. #470	C₂×C₁₉	semidirect
191. #468	C₂×C₁₉	semidirect
192. #467	C₂×C₁₉	semidirect
193. #465	C₂×C₁₉	semidirect
194. #452	C₂×C₁₉	semidirect
195. #452	C₂×C₁₉	semidirect
196. #451	C₂×C₁₉	semidirect
197. #448	C₂×C₁₉	semidirect
198. #408	C₂×C₁₉	semidirect
249. C₁₉	#3201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#537	2
C₁₉×#536	2
C₁₉×#485	2
C₁₉×#484	2
C₁₉×#483	2
C₁₉×#482	2
C₁₉×#470	2
C₁₉×#468	2
C₁₉×#467	2
C₁₉×#465	2
C₁₉×#452	2
C₁₉×#451	2
C₁₉×#448	2
C₁₉×#408	2
#3201	19

Subgroups — C19×#3201 #14561058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3201 #14561058