Subgroups — C₁₉×#19059 #18025018

Order 4864.

898 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1658	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1657	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1534	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1532	C₂	1	2	yes	maximal, complemented
9	C₁₉×#564	C₂²	1	1	yes	characteristic, complemented
10	C₁₉×#563	C₂²	1	2	yes	complemented
11	C₁₉×#562	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#554	—	2	2	no	—
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#541	—	2	2	no	—
16	C₁₉×#539	—	2	2	no	—
17	C₁₉×#539	—	2	2	no	—
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₁₉×#529	C₂²	1	2	yes	—
20	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
21	C₁₉×#496	C₂²	1	4	yes	—
22	C₁₉×#490	—	2	2	no	—
23	C₁₉×#490	C₂²	1	2	yes	—
24	C₁₉×#490	C₂²	1	2	yes	—
25	C₁₉×#490	C₂²	1	4	yes	—
26	C₁₉×#460	—	2	2	no	—
27	C₁₉×#459	—	2	2	no	—
28	C₁₉×#450	—	2	2	no	—
29	C₁₉×#447	—	2	2	no	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	—	2	2	no	—
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₁₉×#330	C₂²	1	2	yes	complemented
34	C₁₉×#330	C₂²	1	2	yes	complemented
35	C₁₉×#330	C₂²	1	4	yes	complemented
36	C₁₉×#329	C₂²	1	4	yes	complemented
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂×SD₁₆×C₁₉	—	2	4	no	—
40	C₂×D₈×C₁₉	—	2	4	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	2	no	—
43	C₁₉×#127	—	2	2	no	—
44	C₁₉×#127	—	2	1	no	—
45	C₁₉×#127	C₂³	1	2	yes	—
46	C₁₉×#126	—	2	2	no	—
47	C₁₉×#126	—	2	2	no	—
48	C₁₉×#126	—	2	2	no	—
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#125	—	2	2	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#125	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	D₄	1	2	yes	—
58	C₁₉×#125	C₂³	1	1	yes	characteristic
59	C₁₉×#125	C₂³	1	1	yes	characteristic
60	C₁₉×#125	C₂³	1	2	yes	—
61	C₁₉×#124	C₂³	1	2	yes	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	D₄	1	2	yes	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	D₄	1	2	yes	—
84	C₁₉×#117	—	2	2	no	—
85	C₁₉×#117	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×C₂²⋊C₈	—	2	2	no	—
96	C₁₉×#97	—	2	1	no	—
97	C₁₉×#97	C₂³	1	2	yes	—
98	C₁₉×#97	C₂³	1	4	yes	—
99	C₂⁴×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	8	4	no	—
110	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	SD₁₆×C₁₉	—	8	4	no	—
118	D₈×C₁₉	—	8	4	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	4	no	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
156	#19059	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	8	4	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	C₂³×C₁₉	#120	1	1	yes	characteristic
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	8	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	4	4	no	—
169	D₄×C₁₉	—	8	2	no	—
170	D₄×C₁₉	—	8	4	no	—
171	D₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	8	2	no	—
180	C₂×C₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	#120	1	2	yes	—
184	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	4	no	—
189	#3553	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#3217	C₂×C₁₉	1	2	yes	complemented
191	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1658	C₂×C₁₉	1	2	yes	complemented
193	#1657	C₂×C₁₉	1	4	yes	complemented
194	#1656	C₂×C₁₉	1	2	yes	complemented
195	#1534	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1532	C₂×C₁₉	1	2	yes	complemented
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	4	no	—
203	C₂²×C₁₉	—	16	4	no	—
204	C₂²×C₁₉	#454	1	2	yes	—
205	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	4	2	no	—
215	#564	C₂²×C₁₉	1	1	yes	characteristic, complemented
216	#563	C₂²×C₁₉	1	2	yes	complemented
217	#562	C₂²×C₁₉	1	1	yes	characteristic, complemented
218	#554	—	2	2	no	—
219	#553	—	2	2	no	—
220	#552	—	2	2	no	—
221	#541	—	2	2	no	—
222	#539	—	2	2	no	—
223	#539	—	2	2	no	—
224	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
225	#529	C₂²×C₁₉	1	2	yes	—
226	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
227	#496	C₂²×C₁₉	1	4	yes	—
228	#490	—	2	2	no	—
229	#490	C₂²×C₁₉	1	2	yes	—
230	#490	C₂²×C₁₉	1	2	yes	—
231	#490	C₂²×C₁₉	1	4	yes	—
232	#460	—	2	2	no	—
233	#459	—	2	2	no	—
234	#450	—	2	2	no	—
235	#447	—	2	2	no	—
236	#432	C₂²×C₁₉	1	2	yes	—
237	C₂×#102	—	2	2	no	—
238	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
239	#330	C₂²×C₁₉	1	2	yes	complemented
240	#330	C₂²×C₁₉	1	2	yes	complemented
241	#330	C₂²×C₁₉	1	4	yes	complemented
242	#329	C₂²×C₁₉	1	4	yes	complemented
243	C₂×C₁₉	—	2	2	no	—
244	C₂×C₁₉	—	8	2	no	—
245	C₂×C₁₉	—	16	2	no	—
246	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
247	C₂×C₁₉	#3021	1	2	yes	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	#127	—	2	2	no	—
255	#127	—	2	1	no	—
256	#127	C₂³×C₁₉	1	2	yes	—
257	#126	—	2	2	no	—
258	#126	—	2	2	no	—
259	#126	—	2	2	no	—
260	#126	—	2	2	no	—
261	#126	—	2	2	no	—
262	#125	—	2	2	no	—
263	#125	—	2	2	no	—
264	#125	—	2	2	no	—
265	#125	—	2	2	no	—
266	#125	—	2	2	no	—
267	#125	—	2	2	no	—
268	#125	D₄×C₁₉	1	2	yes	—
269	#125	C₂³×C₁₉	1	1	yes	characteristic
270	#125	C₂³×C₁₉	1	1	yes	characteristic
271	#125	C₂³×C₁₉	1	2	yes	—
272	#124	C₂³×C₁₉	1	2	yes	—
273	#123	—	2	2	no	—
274	#123	—	2	2	no	—
275	#123	—	2	2	no	—
276	#123	—	2	2	no	—
277	#123	—	2	2	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	—	2	2	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
285	#121	—	2	2	no	—
286	#121	—	2	2	no	—
287	#121	D₄×C₁₉	1	2	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	D₄×C₁₉	1	2	yes	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	D₄×C₁₉	1	2	yes	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₄⋊C₈	—	2	2	no	—
302	#102	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	#97	—	2	1	no	—
308	#97	C₂³×C₁₉	1	2	yes	—
309	#97	C₂³×C₁₉	1	4	yes	—
310	C₁₉	#19059	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	4	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
329	SD₁₆	—	8	4	no	—
330	D₈	—	8	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	4	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
351	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₉	1	2	yes	—
367	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₂³	—	2	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	8	4	no	—
371	C₂³	—	8	2	no	—
372	C₂³	C₁₉×#120	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	4	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	4	no	—
382	D₄	—	8	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	C₁₉×#120	1	2	yes	—
395	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
398	C₈	—	4	2	no	—
399	C₈	—	4	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	4	no	—
406	C₂²	—	16	4	no	—
407	C₂²	C₁₉×#454	1	2	yes	—
408	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₂	—	2	2	no	—
419	C₂	—	8	2	no	—
420	C₂	—	16	2	no	—
421	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
422	C₂	C₁₉×#3021	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3553	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₂×C₁₉×#490	C₂	semidirect
4. C₁₉×#1658	C₂	semidirect
5. C₁₉×#1657	C₂	semidirect
6. C₁₉×#1656	C₂	semidirect
7. C₁₉×#1534	C₂	semidirect
8. C₁₉×#1532	C₂	semidirect
9. C₁₉×#564	C₂²	semidirect
10. C₁₉×#563	C₂²	semidirect
11. C₁₉×#562	C₂²	semidirect
33. C₁₉×#330	C₂²	semidirect
34. C₁₉×#330	C₂²	semidirect
35. C₁₉×#330	C₂²	semidirect
36. C₁₉×#329	C₂²	semidirect
156. #19059	C₁₉	direct (N × H)
189. #3553	C₂×C₁₉	semidirect
190. #3217	C₂×C₁₉	semidirect
191. C₂×#490	C₂×C₁₉	semidirect
192. #1658	C₂×C₁₉	semidirect
193. #1657	C₂×C₁₉	semidirect
194. #1656	C₂×C₁₉	semidirect
195. #1534	C₂×C₁₉	semidirect
196. #1532	C₂×C₁₉	semidirect
215. #564	C₂²×C₁₉	semidirect
216. #563	C₂²×C₁₉	semidirect
217. #562	C₂²×C₁₉	semidirect
239. #330	C₂²×C₁₉	semidirect
240. #330	C₂²×C₁₉	semidirect
241. #330	C₂²×C₁₉	semidirect
242. #329	C₂²×C₁₉	semidirect
310. C₁₉	#19059	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×#3553	2
C₁₉×#3217	2
C₂×C₁₉×#490	2
C₁₉×#1658	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1534	2
C₁₉×#1532	2
#19059	19

Subgroups — C19×#19059 #18025018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19059 #18025018