Subgroups — C₁₉×#19007 #18024966

Order 4864.

862 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1534	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#563	—	2	2	no	—
11	C₁₉×#563	—	2	2	no	—
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#563	C₂²	1	4	yes	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₉×#126	—	2	1	no	—
17	C₂×C₁₉×#126	—	2	1	no	—
18	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#123	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
24	C₁₉×#501	C₂²	1	2	yes	complemented
25	C₁₉×#501	C₂²	1	2	yes	complemented
26	C₁₉×#501	C₂²	1	2	yes	complemented
27	C₁₉×#499	—	2	2	no	—
28	C₁₉×#497	C₂²	1	2	yes	—
29	C₁₉×#491	C₂²	1	2	yes	complemented
30	C₁₉×#489	C₂²	1	2	yes	—
31	C₁₉×#484	—	2	1	no	—
32	C₁₉×#483	—	2	1	no	—
33	C₁₉×#479	—	2	2	no	—
34	C₁₉×#464	—	2	2	no	—
35	C₁₉×#451	—	2	1	no	—
36	C₁₉×#450	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#428	—	2	1	no	—
40	C₁₉×#428	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	complemented
43	C₁₉×#330	C₂²	1	4	yes	complemented
44	C₁₉×#329	C₂²	1	4	yes	—
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	4	no	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×#126	—	2	4	no	—
57	C₁₉×#126	—	2	4	no	—
58	C₁₉×#126	—	2	4	no	—
59	C₁₉×#126	—	2	4	no	—
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#125	—	2	1	no	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	D₄	1	2	yes	—
66	C₁₉×#125	D₄	1	2	yes	—
67	C₁₉×#125	C₂³	1	2	yes	—
68	C₁₉×#125	C₂³	1	2	yes	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	D₄	1	2	yes	—
72	C₁₉×#124	C₂³	1	2	yes	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	4	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	—	2	4	no	—
77	C₁₉×C₂²⋊Q₈	—	2	4	no	—
78	C₁₉×C₂²⋊Q₈	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₁₉×#117	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#107	—	2	2	no	—
103	C₁₉×#107	—	2	2	no	—
104	C₁₉×#106	—	2	2	no	—
105	C₁₉×#106	—	2	2	no	—
106	C₁₉×#106	—	2	2	no	—
107	C₁₉×C₄⋊C₈	—	2	1	no	—
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₁₉×C₂²⋊C₈	—	2	1	no	—
115	C₁₉×#97	C₂³	1	2	yes	—
116	C₁₉×#97	C₂³	1	2	yes	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₄×C₈×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	8	1	no	—
125	C₂×Q₈×C₁₉	—	8	2	no	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	8	1	no	—
129	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	8	2	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₁₉	—	8	2	no	—
141	SD₁₆×C₁₉	—	8	2	no	—
142	M₁₆×C₁₉	—	2	4	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	4	1	no	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
184	#19007	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	#120	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	8	1	no	—
194	Q₈×C₁₉	—	8	4	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	8	1	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₁₉	—	2	4	no	—
220	C₈×C₁₉	—	4	2	no	—
221	C₈×C₁₉	—	4	2	no	—
222	C₂×#563	C₂×C₁₉	1	1	yes	characteristic
223	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#3215	C₂×C₁₉	1	1	yes	characteristic
225	#3166	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#1664	C₂×C₁₉	1	4	yes	complemented
227	#1660	C₂×C₁₉	1	4	yes	complemented
228	#1534	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1527	C₂×C₁₉	1	1	yes	characteristic
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	8	4	no	—
237	C₂²×C₁₉	#456	1	2	yes	—
238	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	4	2	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	—	8	1	no	—
252	#563	—	2	2	no	—
253	#563	—	2	2	no	—
254	#563	—	2	2	no	—
255	#563	C₂²×C₁₉	1	4	yes	—
256	#533	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	—	2	1	no	—
258	C₂×#126	—	2	1	no	—
259	C₂×#126	—	2	1	no	—
260	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#123	—	2	1	no	—
264	C₂×C₂²⋊Q₈	—	2	1	no	—
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	#501	C₂²×C₁₉	1	2	yes	complemented
267	#501	C₂²×C₁₉	1	2	yes	complemented
268	#501	C₂²×C₁₉	1	2	yes	complemented
269	#499	—	2	2	no	—
270	#497	C₂²×C₁₉	1	2	yes	—
271	#491	C₂²×C₁₉	1	2	yes	complemented
272	#489	C₂²×C₁₉	1	2	yes	—
273	#484	—	2	1	no	—
274	#483	—	2	1	no	—
275	#479	—	2	2	no	—
276	#464	—	2	2	no	—
277	#451	—	2	1	no	—
278	#450	—	2	1	no	—
279	#432	C₂²×C₁₉	1	1	yes	characteristic
280	#432	C₂²×C₁₉	1	1	yes	characteristic
281	#428	—	2	1	no	—
282	#428	—	2	1	no	—
283	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
284	#330	C₂²×C₁₉	1	4	yes	complemented
285	#330	C₂²×C₁₉	1	4	yes	complemented
286	#329	C₂²×C₁₉	1	4	yes	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	8	2	no	—
289	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
290	C₂×C₁₉	#3019	1	1	yes	characteristic
291	C₂×C₁₉	#3020	1	1	yes	characteristic
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
294	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	—	2	4	no	—
301	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
303	#126	—	2	4	no	—
304	#126	—	2	4	no	—
305	#126	—	2	4	no	—
306	#126	—	2	4	no	—
307	#125	—	2	1	no	—
308	#125	—	2	1	no	—
309	#125	—	2	1	no	—
310	#125	—	2	1	no	—
311	#125	—	2	1	no	—
312	#125	D₄×C₁₉	1	2	yes	—
313	#125	D₄×C₁₉	1	2	yes	—
314	#125	C₂³×C₁₉	1	2	yes	—
315	#125	C₂³×C₁₉	1	2	yes	—
316	#124	—	2	1	no	—
317	#124	—	2	1	no	—
318	#124	D₄×C₁₉	1	2	yes	—
319	#124	C₂³×C₁₉	1	2	yes	—
320	#123	—	2	4	no	—
321	#123	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	#117	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
348	#107	—	2	2	no	—
349	#107	—	2	2	no	—
350	#107	—	2	2	no	—
351	#106	—	2	2	no	—
352	#106	—	2	2	no	—
353	#106	—	2	2	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#102	—	2	2	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	#97	C₂³×C₁₉	1	2	yes	—
363	#97	C₂³×C₁₉	1	2	yes	—
364	#97	C₂³×C₁₉	1	2	yes	—
365	C₄×C₈	—	2	1	no	—
366	C₁₉	#19007	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	—	2	1	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	8	1	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	8	1	no	—
377	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	Q₁₆	—	8	2	no	—
389	SD₁₆	—	8	2	no	—
390	M₁₆	—	2	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	4	1	no	—
428	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
432	C₂³	—	2	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	C₁₉×#120	1	1	yes	characteristic
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	8	1	no	—
441	Q₈	—	8	4	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	8	4	no	—
460	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
462	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	4	no	—
475	C₂²	C₁₉×#456	1	2	yes	—
476	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₂	—	2	2	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
493	C₂	C₁₉×#3019	1	1	yes	characteristic
494	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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
2. C₁₉×#3236	C₂	semidirect
4. C₁₉×#3166	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1534	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
24. C₁₉×#501	C₂²	semidirect
25. C₁₉×#501	C₂²	semidirect
26. C₁₉×#501	C₂²	semidirect
29. C₁₉×#491	C₂²	semidirect
42. C₁₉×#330	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
184. #19007	C₁₉	direct (N × H)
223. #3236	C₂×C₁₉	semidirect
225. #3166	C₂×C₁₉	semidirect
226. #1664	C₂×C₁₉	semidirect
227. #1660	C₂×C₁₉	semidirect
228. #1534	C₂×C₁₉	semidirect
229. #1528	C₂×C₁₉	semidirect
266. #501	C₂²×C₁₉	semidirect
267. #501	C₂²×C₁₉	semidirect
268. #501	C₂²×C₁₉	semidirect
271. #491	C₂²×C₁₉	semidirect
284. #330	C₂²×C₁₉	semidirect
285. #330	C₂²×C₁₉	semidirect
366. C₁₉	#19007	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×#563	2
C₁₉×#3236	2
C₁₉×#3215	2
C₁₉×#3166	2
C₁₉×#1664	2
C₁₉×#1660	2
C₁₉×#1534	2
C₁₉×#1528	2
C₁₉×#1527	2
#19007	19

Subgroups — C19×#19007 #18024966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19007 #18024966