Subgroups — C₁₉×#11389 #18017348

Order 4864.

836 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#544	—	2	2	no	—
11	C₁₉×#544	—	2	2	no	—
12	C₁₉×#544	—	2	2	no	—
13	C₁₉×#543	—	2	2	no	—
14	C₁₉×#533	—	2	2	no	—
15	C₁₉×#533	—	2	2	no	—
16	C₁₉×#533	C₄	1	4	yes	complemented
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#344	—	2	2	no	—
23	C₁₉×#342	—	2	2	no	—
24	C₁₉×#339	—	2	2	no	—
25	C₁₉×H(3,ℤ/4)	—	2	2	no	—
26	C₁₉×H(3,ℤ/4)	—	2	2	no	—
27	C₁₉×H(3,ℤ/4)	—	2	2	no	—
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	Q₈	1	2	yes	complemented
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	Q₈	1	2	yes	complemented
43	C₁₉×C₄⋊Q₈	—	2	4	no	—
44	C₁₉×C₄⋊Q₈	—	2	4	no	—
45	C₁₉×C₄⋊Q₈	—	2	4	no	—
46	C₁₉×#125	—	2	4	no	—
47	C₁₉×#125	—	2	4	no	—
48	C₁₉×#125	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	2	8	no	—
50	C₁₉×C₂²⋊Q₈	—	2	8	no	—
51	C₁₉×C₂²⋊Q₈	—	2	8	no	—
52	C₄×Q₈×C₁₉	—	2	8	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	C₂×C₄	1	2	yes	—
67	C₁₉×#117	C₂×C₄	1	2	yes	—
68	C₁₉×#117	D₄	1	2	yes	—
69	C₁₉×#117	D₄	1	2	yes	—
70	C₁₉×#117	D₄	1	2	yes	—
71	C₁₉×#117	D₄	1	2	yes	—
72	C₁₉×#117	Q₈	1	2	yes	complemented
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₁₉	D₄	1	2	yes	—
87	C₂×C₄²×C₁₉	Q₈	1	2	yes	complemented
88	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	4	1	no	—
112	M₁₆×C₁₉	—	4	1	no	—
113	M₁₆×C₁₉	—	4	1	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	8	no	—
125	C₄⋊C₄×C₁₉	—	2	8	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	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	2	2	no	—
149	C₄²×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	—	4	1	no	—
154	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
155	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
156	#11389	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	8	1	no	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×C₁₉	#120	1	1	yes	characteristic
160	C₂³×C₁₉	#120	1	1	yes	characteristic
161	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	#124	1	1	yes	characteristic
164	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
165	Q₈×C₁₉	—	8	8	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	—	8	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	#3458	C₂×C₁₉	1	1	yes	characteristic
207	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
208	#1740	C₂×C₁₉	1	1	yes	characteristic
209	#1733	C₂×C₁₉	1	1	yes	characteristic
210	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
211	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
212	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	#379	1	1	yes	characteristic
221	C₂²×C₁₉	#391	1	1	yes	characteristic
222	C₂²×C₁₉	#391	1	1	yes	characteristic
223	C₂²×C₁₉	#393	1	1	yes	characteristic
224	C₂²×C₁₉	#393	1	1	yes	characteristic
225	C₂²×C₁₉	#395	1	1	yes	characteristic
226	C₂²×C₁₉	#395	1	1	yes	characteristic
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	—	8	2	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	#391	1	1	yes	characteristic
233	C₄×C₁₉	#391	1	1	yes	characteristic
234	C₄×C₁₉	#391	1	1	yes	characteristic
235	C₄×C₁₉	#391	1	1	yes	characteristic
236	C₄×C₁₉	#393	1	1	yes	characteristic
237	C₄×C₁₉	#393	1	1	yes	characteristic
238	C₄×C₁₉	#395	1	1	yes	characteristic
239	C₄×C₁₉	#395	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
242	#544	—	2	2	no	—
243	#544	—	2	2	no	—
244	#544	—	2	2	no	—
245	#543	—	2	2	no	—
246	#533	—	2	2	no	—
247	#533	—	2	2	no	—
248	#533	C₄×C₁₉	1	4	yes	complemented
249	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
254	#344	—	2	2	no	—
255	#342	—	2	2	no	—
256	#339	—	2	2	no	—
257	H(3,ℤ/4)	—	2	2	no	—
258	H(3,ℤ/4)	—	2	2	no	—
259	H(3,ℤ/4)	—	2	2	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	#1446	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	Q₈×C₁₉	1	2	yes	complemented
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	Q₈×C₁₉	1	2	yes	complemented
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	2	4	no	—
286	#125	—	2	4	no	—
287	#125	—	2	4	no	—
288	#125	—	2	4	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₄×Q₈	—	2	8	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	C₂×C₄×C₁₉	1	2	yes	—
307	#117	C₂×C₄×C₁₉	1	2	yes	—
308	#117	D₄×C₁₉	1	2	yes	—
309	#117	D₄×C₁₉	1	2	yes	—
310	#117	D₄×C₁₉	1	2	yes	—
311	#117	D₄×C₁₉	1	2	yes	—
312	#117	Q₈×C₁₉	1	2	yes	complemented
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
326	C₂×C₄²	D₄×C₁₉	1	2	yes	—
327	C₂×C₄²	Q₈×C₁₉	1	2	yes	complemented
328	C₁₉	#11389	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂×Q₈	—	2	8	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	—	4	1	no	—
355	M₁₆	—	4	1	no	—
356	M₁₆	—	4	1	no	—
357	M₁₆	—	4	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	1	no	—
395	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
396	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
397	C₂³	—	8	1	no	—
398	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂³	C₁₉×#120	1	1	yes	characteristic
400	C₂³	C₁₉×#120	1	1	yes	characteristic
401	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
402	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
403	C₂³	C₁₉×#124	1	1	yes	characteristic
404	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
405	Q₈	—	8	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
423	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
424	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
425	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
426	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
428	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
429	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
430	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
431	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
432	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
433	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
434	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
435	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
436	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
437	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
438	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
439	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
440	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
441	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
442	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
443	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
444	C₈	—	4	2	no	—
445	C₈	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	C₁₉×#379	1	1	yes	characteristic
454	C₂²	C₁₉×#391	1	1	yes	characteristic
455	C₂²	C₁₉×#391	1	1	yes	characteristic
456	C₂²	C₁₉×#393	1	1	yes	characteristic
457	C₂²	C₁₉×#393	1	1	yes	characteristic
458	C₂²	C₁₉×#395	1	1	yes	characteristic
459	C₂²	C₁₉×#395	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	8	2	no	—
464	C₄	—	8	2	no	—
465	C₄	C₁₉×#391	1	1	yes	characteristic
466	C₄	C₁₉×#391	1	1	yes	characteristic
467	C₄	C₁₉×#391	1	1	yes	characteristic
468	C₄	C₁₉×#391	1	1	yes	characteristic
469	C₄	C₁₉×#393	1	1	yes	characteristic
470	C₄	C₁₉×#393	1	1	yes	characteristic
471	C₄	C₁₉×#395	1	1	yes	characteristic
472	C₄	C₁₉×#395	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	C₁₉×#1446	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#391
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#1446
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#533	C₄	semidirect
40. C₂×M₁₆×C₁₉	Q₈	semidirect
42. C₂²×C₈×C₁₉	Q₈	semidirect
72. C₁₉×#117	Q₈	semidirect
87. C₂×C₄²×C₁₉	Q₈	semidirect
156. #11389	C₁₉	direct (N × H)
248. #533	C₄×C₁₉	semidirect
280. C₂×M₁₆	Q₈×C₁₉	semidirect
282. C₂²×C₈	Q₈×C₁₉	semidirect
312. #117	Q₈×C₁₉	semidirect
327. C₂×C₄²	Q₈×C₁₉	semidirect
328. C₁₉	#11389	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×#3458	2
C₂×C₁₉×#344	2
C₁₉×#1740	2
C₁₉×#1733	2
C₂×C₁₉×H(3,ℤ/4)	2
#11389	19

Subgroups — C19×#11389 #18017348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11389 #18017348