Subgroups — C₁₉×#18991 #18024950

Order 4864.

840 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3531	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3172	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1663	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	2	yes	maximal, complemented
10	C₁₉×#564	C₂²	1	1	yes	characteristic
11	C₁₉×#563	—	2	2	no	—
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#563	C₂²	1	2	yes	—
14	C₁₉×#562	—	2	2	no	—
15	C₁₉×#562	C₂²	1	1	yes	characteristic
16	C₁₉×#533	—	2	2	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	2	no	—
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#501	—	2	2	no	—
23	C₁₉×#501	C₂²	1	2	yes	—
24	C₁₉×#501	C₂²	1	2	yes	—
25	C₁₉×#501	C₂²	1	2	yes	—
26	C₁₉×#497	C₂²	1	2	yes	—
27	C₁₉×#491	C₂²	1	2	yes	—
28	C₁₉×#489	C₂²	1	2	yes	—
29	C₁₉×#470	—	2	2	no	—
30	C₁₉×#468	—	2	2	no	—
31	C₄×Q₁₆×C₁₉	—	2	2	no	—
32	C₄×SD₁₆×C₁₉	—	2	2	no	—
33	C₁₉×#427	—	2	2	no	—
34	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
36	C₁₉×#330	C₂²	1	1	yes	characteristic
37	C₁₉×#330	C₂²	1	2	yes	—
38	C₁₉×#330	C₂²	1	2	yes	—
39	C₁₉×#330	C₂²	1	2	yes	—
40	C₁₉×#330	C₂²	1	1	yes	characteristic
41	C₁₉×#329	C₂²	1	2	yes	—
42	C₁₉×#329	C₂²	1	2	yes	—
43	C₂×Q₁₆×C₁₉	—	2	2	no	—
44	C₂×SD₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
50	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#126	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#125	—	2	2	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	C₂³	1	2	yes	—
62	C₁₉×#125	C₂³	1	1	yes	characteristic
63	C₁₉×#125	C₂³	1	1	yes	characteristic
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	C₂³	1	2	yes	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	D₄	1	2	yes	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
85	C₄×Q₈×C₁₉	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	2	no	—
87	C₄×Q₈×C₁₉	D₄	1	2	yes	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	D₄	1	2	yes	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	D₄	1	2	yes	—
95	C₂×C₄²×C₁₉	—	2	2	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	2	no	—
98	C₁₉×#107	—	2	2	no	—
99	C₁₉×#107	—	2	2	no	—
100	C₁₉×#106	—	2	2	no	—
101	C₁₉×#106	—	2	2	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×#103	—	2	2	no	—
104	C₁₉×#103	—	2	2	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×#97	—	2	1	no	—
108	C₁₉×#97	C₂³	1	2	yes	—
109	C₁₉×#97	C₂³	1	2	yes	—
110	C₁₉×#97	C₂³	1	2	yes	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	Q₁₆×C₁₉	—	4	4	no	—
125	SD₁₆×C₁₉	—	4	4	no	—
126	M₁₆×C₁₉	—	4	4	no	—
127	C₂×C₈×C₁₉	—	2	4	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×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	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	4	2	no	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	4	1	no	—
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	2	yes	—
169	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
170	#18991	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	#120	1	1	yes	characteristic
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	8	2	no	—
177	Q₈×C₁₉	—	8	2	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	8	2	no	—
180	D₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	#120	1	2	yes	—
193	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
196	C₈×C₁₉	—	2	4	no	—
197	C₈×C₁₉	—	2	4	no	—
198	C₈×C₁₉	—	4	2	no	—
199	#3531	C₂×C₁₉	1	1	yes	characteristic
200	#3172	C₂×C₁₉	1	2	yes	complemented
201	#3162	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1664	C₂×C₁₉	1	2	yes	complemented
203	#1663	C₂×C₁₉	1	2	yes	complemented
204	#1661	C₂×C₁₉	1	2	yes	complemented
205	#1660	C₂×C₁₉	1	2	yes	complemented
206	#1526	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1524	C₂×C₁₉	1	2	yes	complemented
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	#456	1	2	yes	—
224	#564	C₂²×C₁₉	1	1	yes	characteristic
225	#563	—	2	2	no	—
226	#563	—	2	2	no	—
227	#563	C₂²×C₁₉	1	2	yes	—
228	#562	—	2	2	no	—
229	#562	C₂²×C₁₉	1	1	yes	characteristic
230	#533	—	2	2	no	—
231	#533	C₂²×C₁₉	1	1	yes	characteristic
232	#533	C₂²×C₁₉	1	1	yes	characteristic
233	#529	—	2	2	no	—
234	#529	—	2	2	no	—
235	#529	C₂²×C₁₉	1	2	yes	—
236	#501	—	2	2	no	—
237	#501	C₂²×C₁₉	1	2	yes	—
238	#501	C₂²×C₁₉	1	2	yes	—
239	#501	C₂²×C₁₉	1	2	yes	—
240	#497	C₂²×C₁₉	1	2	yes	—
241	#491	C₂²×C₁₉	1	2	yes	—
242	#489	C₂²×C₁₉	1	2	yes	—
243	#470	—	2	2	no	—
244	#468	—	2	2	no	—
245	C₄×Q₁₆	—	2	2	no	—
246	C₄×SD₁₆	—	2	2	no	—
247	#427	—	2	2	no	—
248	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
249	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
250	#330	C₂²×C₁₉	1	1	yes	characteristic
251	#330	C₂²×C₁₉	1	2	yes	—
252	#330	C₂²×C₁₉	1	2	yes	—
253	#330	C₂²×C₁₉	1	2	yes	—
254	#330	C₂²×C₁₉	1	1	yes	characteristic
255	#329	C₂²×C₁₉	1	2	yes	—
256	#329	C₂²×C₁₉	1	2	yes	—
257	C₂×C₁₉	—	4	1	no	—
258	C₂×C₁₉	—	8	2	no	—
259	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
260	C₂×C₁₉	#3018	1	2	yes	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
268	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
269	#126	—	2	2	no	—
270	#126	—	2	2	no	—
271	#126	—	2	2	no	—
272	#126	—	2	2	no	—
273	#126	—	2	2	no	—
274	#125	—	2	2	no	—
275	#125	—	2	2	no	—
276	#125	—	2	2	no	—
277	#125	—	2	2	no	—
278	#125	—	2	1	no	—
279	#125	C₂³×C₁₉	1	2	yes	—
280	#125	C₂³×C₁₉	1	1	yes	characteristic
281	#125	C₂³×C₁₉	1	1	yes	characteristic
282	#124	—	2	2	no	—
283	#124	—	2	2	no	—
284	#124	C₂³×C₁₉	1	2	yes	—
285	#123	—	2	2	no	—
286	#123	—	2	2	no	—
287	#123	—	2	2	no	—
288	#123	—	2	2	no	—
289	#123	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
299	#121	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	D₄×C₁₉	1	2	yes	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	D₄×C₁₉	1	2	yes	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₁₉	1	2	yes	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	1	no	—
312	#117	D₄×C₁₉	1	2	yes	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
315	#107	—	2	2	no	—
316	#107	—	2	2	no	—
317	#107	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	2	no	—
320	#106	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	2	2	no	—
324	#102	—	2	2	no	—
325	#97	—	2	1	no	—
326	#97	C₂³×C₁₉	1	2	yes	—
327	#97	C₂³×C₁₉	1	2	yes	—
328	#97	C₂³×C₁₉	1	2	yes	—
329	C₄×C₈	—	2	2	no	—
330	C₁₉	#18991	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
343	Q₁₆	—	4	4	no	—
344	SD₁₆	—	4	4	no	—
345	M₁₆	—	4	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	C₂×D₄×C₁₉	1	2	yes	—
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
389	C₂³	—	2	2	no	—
390	C₂³	C₁₉×#120	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	2	no	—
395	Q₈	—	8	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	C₁₉×#120	1	2	yes	—
411	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	2	no	—
432	C₄	C₁₉×#456	1	2	yes	—
433	C₂	—	4	1	no	—
434	C₂	—	8	2	no	—
435	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
436	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#3531	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3172	C₂	semidirect
3. C₁₉×#3162	C₂	semidirect
4. C₁₉×#1664	C₂	semidirect
5. C₁₉×#1663	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1660	C₂	semidirect
8. C₁₉×#1526	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
170. #18991	C₁₉	direct (N × H)
200. #3172	C₂×C₁₉	semidirect
201. #3162	C₂×C₁₉	semidirect
202. #1664	C₂×C₁₉	semidirect
203. #1663	C₂×C₁₉	semidirect
204. #1661	C₂×C₁₉	semidirect
205. #1660	C₂×C₁₉	semidirect
206. #1526	C₂×C₁₉	semidirect
207. #1524	C₂×C₁₉	semidirect
330. C₁₉	#18991	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×#3531	2
C₁₉×#3172	2
C₁₉×#3162	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1526	2
C₁₉×#1524	2
#18991	19

Subgroups — C19×#18991 #18024950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18991 #18024950