Subgroups — C₁₉×#18646 #18024605

Order 4864.

1024 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1628	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1625	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
11	C₁₉×#556	C₂²	1	2	yes	complemented
12	C₁₉×#555	—	2	1	no	—
13	C₁₉×#554	—	2	1	no	—
14	C₁₉×#553	—	2	2	no	—
15	C₁₉×#548	—	2	2	no	—
16	C₁₉×#547	C₂²	1	2	yes	complemented
17	C₁₉×#542	—	2	2	no	—
18	C₁₉×#537	—	2	1	no	—
19	C₁₉×#533	—	2	1	no	—
20	C₁₉×#532	—	2	1	no	—
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#520	—	2	1	no	—
25	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#493	—	2	1	no	—
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#486	—	2	2	no	—
29	C₁₉×#486	C₂²	1	4	yes	—
30	C₁₉×#460	—	2	1	no	—
31	C₁₉×#460	C₂²	1	2	yes	—
32	C₁₉×#459	—	2	1	no	—
33	C₁₉×#459	C₂²	1	4	yes	—
34	C₁₉×#459	C₂²	1	2	yes	—
35	C₁₉×#447	—	2	2	no	—
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₁₉×#418	—	2	1	no	—
39	C₂×C₁₉×#102	—	2	2	no	—
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#332	C₂²	1	4	yes	complemented
42	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
45	C₂×#41×C₁₉	—	2	2	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	4	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
61	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₉×#127	—	2	1	no	—
64	C₁₉×#127	—	2	1	no	—
65	C₁₉×#127	—	2	1	no	—
66	C₁₉×#127	D₄	1	1	yes	characteristic
67	C₁₉×#127	C₂³	1	2	yes	—
68	C₁₉×#126	—	2	4	no	—
69	C₁₉×#125	—	2	2	no	—
70	C₁₉×#124	—	2	4	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	4	no	—
76	C₁₉×C₂²⋊Q₈	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	2	no	—
80	C₁₉×#121	—	2	4	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	1	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	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	4	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	C₂³	1	2	yes	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₄⋊C₈	—	2	1	no	—
107	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₉×#102	—	2	8	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#102	—	2	4	no	—
113	C₁₉×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₉	—	2	1	no	—
115	C₄×C₈×C₁₉	—	2	1	no	—
116	C₄×C₈×C₁₉	C₂³	1	2	yes	—
117	C₂⁴×C₁₉	—	4	1	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	4	2	no	—
121	#41×C₁₉	—	4	2	no	—
122	#41×C₁₉	—	8	4	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	8	2	no	—
127	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	8	2	no	—
143	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	SD₁₆×C₁₉	—	4	4	no	—
155	D₈×C₁₉	—	4	4	no	—
156	D₈×C₁₉	—	8	4	no	—
157	M₁₆×C₁₉	—	4	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	2	4	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	1	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	4	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
190	#18646	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	8	2	no	—
195	C₂³×C₁₉	—	8	2	no	—
196	C₂³×C₁₉	—	8	2	no	—
197	C₂³×C₁₉	#120	1	1	yes	characteristic
198	Q₈×C₁₉	—	2	1	no	—
199	Q₈×C₁₉	—	2	1	no	—
200	Q₈×C₁₉	—	4	4	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	8	2	no	—
203	D₄×C₁₉	—	2	1	no	—
204	D₄×C₁₉	—	2	1	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	4	4	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	8	2	no	—
215	D₄×C₁₉	—	8	4	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	8	4	no	—
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#135	1	2	yes	—
236	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
240	C₈×C₁₉	—	4	2	no	—
241	C₈×C₁₉	—	4	2	no	—
242	C₈×C₁₉	—	4	2	no	—
243	#3511	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#3205	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#3038	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1628	C₂×C₁₉	1	4	yes	complemented
248	#1625	C₂×C₁₉	1	4	yes	complemented
249	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	1	no	—
257	C₂²×C₁₉	—	4	2	no	—
258	C₂²×C₁₉	—	4	1	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	16	4	no	—
264	C₂²×C₁₉	#449	1	2	yes	—
265	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	#449	1	2	yes	—
274	C₄×C₁₉	#454	1	2	yes	—
275	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
276	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₁₉	#576	1	2	yes	—
278	C₂×AGL(1,ℤ/8)	—	2	1	no	—
279	#556	C₂²×C₁₉	1	2	yes	complemented
280	#555	—	2	1	no	—
281	#554	—	2	1	no	—
282	#553	—	2	2	no	—
283	#548	—	2	2	no	—
284	#547	C₂²×C₁₉	1	2	yes	complemented
285	#542	—	2	2	no	—
286	#537	—	2	1	no	—
287	#533	—	2	1	no	—
288	#532	—	2	1	no	—
289	#532	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
292	#520	—	2	1	no	—
293	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
294	#493	—	2	1	no	—
295	#486	—	2	2	no	—
296	#486	—	2	1	no	—
297	#486	C₂²×C₁₉	1	4	yes	—
298	#460	—	2	1	no	—
299	#460	C₂²×C₁₉	1	2	yes	—
300	#459	—	2	1	no	—
301	#459	C₂²×C₁₉	1	2	yes	—
302	#459	C₂²×C₁₉	1	4	yes	—
303	#447	—	2	2	no	—
304	#431	C₂²×C₁₉	1	1	yes	characteristic
305	#423	C₂²×C₁₉	1	1	yes	characteristic
306	#418	—	2	1	no	—
307	C₂×#102	—	2	2	no	—
308	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
309	#332	C₂²×C₁₉	1	4	yes	complemented
310	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
311	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
312	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
313	C₂×C₁₉	—	2	2	no	—
314	C₂×C₁₉	—	8	1	no	—
315	C₂×C₁₉	—	8	2	no	—
316	C₂×C₁₉	—	16	2	no	—
317	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
318	C₂×C₁₉	#3008	1	1	yes	characteristic
319	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	AGL(1,ℤ/8)	—	4	4	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×D₈	—	2	4	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
336	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
338	#127	—	2	1	no	—
339	#127	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	D₄×C₁₉	1	1	yes	characteristic
342	#127	C₂³×C₁₉	1	2	yes	—
343	#126	—	2	4	no	—
344	#125	—	2	2	no	—
345	#124	—	2	4	no	—
346	#124	—	2	2	no	—
347	#124	—	2	1	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	4	no	—
356	#121	—	2	2	no	—
357	#121	—	2	1	no	—
358	#121	D₄×C₁₉	1	2	yes	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
362	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
370	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₄×D₄	C₂³×C₁₉	1	2	yes	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	2	1	no	—
375	#117	D₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
383	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
384	#102	—	2	8	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	4	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	C₂³×C₁₉	1	2	yes	—
392	C₁₉	#18646	1	1	yes	characteristic, direct product factor, Sylow
393	C₂⁴	—	4	1	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	#41	—	8	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	8	2	no	—
403	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	SD₁₆	—	4	4	no	—
431	D₈	—	4	4	no	—
432	D₈	—	8	4	no	—
433	M₁₆	—	4	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
448	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
466	C₂³	—	2	1	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	8	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	2	no	—
472	C₂³	C₁₉×#120	1	1	yes	characteristic
473	Q₈	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	4	no	—
477	Q₈	—	8	2	no	—
478	D₄	—	2	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	4	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	4	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
510	C₂×C₄	C₁₉×#135	1	2	yes	—
511	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₈	—	4	2	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	16	4	no	—
530	C₂²	C₁₉×#449	1	2	yes	—
531	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	1	no	—
539	C₄	C₁₉×#449	1	2	yes	—
540	C₄	C₁₉×#454	1	2	yes	—
541	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
542	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
543	C₄	C₁₉×#576	1	2	yes	—
544	C₂	—	2	2	no	—
545	C₂	—	8	1	no	—
546	C₂	—	8	2	no	—
547	C₂	—	16	2	no	—
548	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
549	C₂	C₁₉×#3008	1	1	yes	characteristic
550	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	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×#3511	C₂	semidirect
2. C₁₉×#3205	C₂	semidirect
3. C₂×C₁₉×#486	C₂	semidirect
4. C₁₉×#3038	C₂	semidirect
5. C₁₉×#1628	C₂	semidirect
6. C₁₉×#1625	C₂	semidirect
7. C₁₉×#1549	C₂	semidirect
8. C₁₉×#1492	C₂	semidirect
9. C₁₉×#1476	C₂	semidirect
11. C₁₉×#556	C₂²	semidirect
16. C₁₉×#547	C₂²	semidirect
41. C₁₉×#332	C₂²	semidirect
42. C₁₉×Q₈⋊C₈	C₂²	semidirect
43. C₁₉×D₄⋊C₈	C₂²	semidirect
44. C₁₉×D₄⋊C₈	C₂²	semidirect
190. #18646	C₁₉	direct (N × H)
243. #3511	C₂×C₁₉	semidirect
244. #3205	C₂×C₁₉	semidirect
245. C₂×#486	C₂×C₁₉	semidirect
246. #3038	C₂×C₁₉	semidirect
247. #1628	C₂×C₁₉	semidirect
248. #1625	C₂×C₁₉	semidirect
249. #1549	C₂×C₁₉	semidirect
250. #1492	C₂×C₁₉	semidirect
251. #1476	C₂×C₁₉	semidirect
279. #556	C₂²×C₁₉	semidirect
284. #547	C₂²×C₁₉	semidirect
309. #332	C₂²×C₁₉	semidirect
310. Q₈⋊C₈	C₂²×C₁₉	semidirect
311. D₄⋊C₈	C₂²×C₁₉	semidirect
312. D₄⋊C₈	C₂²×C₁₉	semidirect
392. C₁₉	#18646	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×#3511	2
C₁₉×#3205	2
C₂×C₁₉×#486	2
C₁₉×#3038	2
C₁₉×#1628	2
C₁₉×#1625	2
C₁₉×#1549	2
C₁₉×#1492	2
C₁₉×#1476	2
#18646	19

Subgroups — C19×#18646 #18024605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18646 #18024605