Subgroups — C₂×C₁₉×#3036 #18066369

Order 4864.

3242 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3036	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₉×#463	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	—	2	1	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
15	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	—
16	C₂²×D₈×C₁₉	C₂²	1	4	yes	—
17	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#532	—	2	4	no	—
19	C₁₉×#532	C₂²	1	8	yes	complemented
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×#124	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#121	—	2	1	no	—
24	C₂×C₁₉×#121	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	—	2	1	no	—
28	C₂×C₄×D₄×C₁₉	—	2	1	no	—
29	C₂×C₄×D₄×C₁₉	—	2	4	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
33	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#463	C₂²	1	32	yes	complemented
37	C₁₉×#461	C₂²	1	16	yes	complemented
38	C₁₉×#459	C₂²	1	16	yes	complemented
39	C₁₉×#423	C₂²	1	8	yes	complemented
40	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
41	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
42	C₁₉×#417	C₂²	1	16	yes	complemented
43	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
44	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
45	C₂⁵×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	4	no	—
47	C₂×#41×C₁₉	—	2	8	no	—
48	C₂×#41×C₁₉	—	2	8	no	—
49	C₂×#41×C₁₉	C₂³	1	8	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	4	no	—
57	C₂²×D₄×C₁₉	D₄	1	8	yes	complemented
58	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂³×C₄×C₁₉	—	2	2	no	—
63	C₂³×C₄×C₁₉	—	2	2	no	—
64	C₂³×C₄×C₁₉	—	2	2	no	—
65	C₂³×C₄×C₁₉	—	2	8	no	—
66	C₂³×C₄×C₁₉	—	4	8	no	—
67	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×AGL(1,ℤ/8)	—	2	64	no	—
71	C₂×SD₁₆×C₁₉	—	2	16	no	—
72	C₂×SD₁₆×C₁₉	C₂³	1	16	yes	—
73	C₂×D₈×C₁₉	—	2	16	no	—
74	C₂×D₈×C₁₉	C₂³	1	16	yes	—
75	C₂×M₁₆×C₁₉	—	2	8	no	—
76	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
78	C₁₉×C₄⋊Q₈	—	2	2	no	—
79	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	complemented
80	C₁₉×#127	—	2	2	no	—
81	C₁₉×#127	C₂³	1	4	yes	complemented
82	C₁₉×#124	—	2	4	no	—
83	C₁₉×#124	C₂³	1	8	yes	complemented
84	C₁₉×#121	—	2	8	no	—
85	C₁₉×#121	—	2	8	no	—
86	C₄×D₄×C₁₉	—	2	4	no	—
87	C₄×D₄×C₁₉	—	2	4	no	—
88	C₄×D₄×C₁₉	—	2	8	no	—
89	C₄×D₄×C₁₉	—	2	8	no	—
90	C₄×D₄×C₁₉	—	2	8	no	—
91	C₄×D₄×C₁₉	—	2	8	no	—
92	C₄×D₄×C₁₉	C₂³	1	8	yes	—
93	C₄×D₄×C₁₉	C₂³	1	8	yes	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	D₄	1	4	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
111	C₁₉×C₄⋊C₈	C₂³	1	8	yes	complemented
112	C₁₉×C₄⋊C₈	C₂³	1	8	yes	complemented
113	C₁₉×#103	C₂³	1	16	yes	complemented
114	C₁₉×#102	C₂³	1	16	yes	complemented
115	C₂⁴×C₁₉	—	2	8	no	—
116	C₂⁴×C₁₉	—	2	4	no	—
117	C₂⁴×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	4	4	no	—
120	C₂⁴×C₁₉	—	4	4	no	—
121	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
122	#41×C₁₉	—	2	16	no	—
123	#41×C₁₉	—	2	16	no	—
124	#41×C₁₉	—	4	16	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	2	4	no	—
128	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
129	C₂×D₄×C₁₉	—	2	8	no	—
130	C₂×D₄×C₁₉	—	2	8	no	—
131	C₂×D₄×C₁₉	—	2	16	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	8	no	—
140	C₂×D₄×C₁₉	—	2	4	no	—
141	C₂×D₄×C₁₉	—	4	4	no	—
142	C₂×D₄×C₁₉	—	4	8	no	—
143	C₂×D₄×C₁₉	—	4	4	no	—
144	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
145	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	complemented
146	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	8	no	—
154	C₂²×C₄×C₁₉	—	2	8	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	4	8	no	—
157	C₂²×C₄×C₁₉	—	4	32	no	—
158	C₂²×C₄×C₁₉	—	4	4	no	—
159	C₂²×C₄×C₁₉	—	4	8	no	—
160	C₂²×C₄×C₁₉	—	4	8	no	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	4	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	SD₁₆×C₁₉	—	2	32	no	—
174	D₈×C₁₉	—	2	32	no	—
175	M₁₆×C₁₉	—	2	16	no	—
176	C₂×C₈×C₁₉	—	2	8	no	—
177	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
178	C₄⋊C₄×C₁₉	—	2	4	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
183	C₂²⋊C₄×C₁₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₉	—	2	8	no	—
187	C₄²×C₁₉	C₂×D₄	1	4	yes	—
188	C₄²×C₁₉	C₂×D₄	1	4	yes	—
189	C₄²×C₁₉	C₂×D₄	1	2	yes	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	C₄²×C₁₉	C₂⁴	1	2	yes	—
192	C₄²×C₁₉	C₂⁴	1	2	yes	—
193	C₂×#3036	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	8	no	—
197	C₂³×C₁₉	—	2	16	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	4	8	no	—
201	C₂³×C₁₉	—	4	32	no	—
202	C₂³×C₁₉	—	4	8	no	—
203	C₂³×C₁₉	—	4	4	no	—
204	C₂³×C₁₉	—	4	4	no	—
205	C₂³×C₁₉	—	4	4	no	—
206	C₂³×C₁₉	—	4	4	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	#121	1	4	yes	—
209	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
210	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₉	—	2	4	no	—
212	Q₈×C₁₉	—	2	4	no	—
213	Q₈×C₁₉	—	4	4	no	—
214	D₄×C₁₉	—	2	8	no	—
215	D₄×C₁₉	—	2	16	no	—
216	D₄×C₁₉	—	2	4	no	—
217	D₄×C₁₉	—	2	4	no	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	4	8	no	—
220	D₄×C₁₉	—	4	16	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	4	8	no	—
223	D₄×C₁₉	C₂²×D₄	1	8	yes	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	8	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	16	no	—
232	C₂×C₄×C₁₉	—	4	8	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	16	no	—
236	C₂×C₄×C₁₉	—	4	16	no	—
237	C₂×C₄×C₁₉	#121	1	4	yes	—
238	C₂×C₄×C₁₉	#121	1	8	yes	—
239	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	complemented
240	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
251	C₈×C₁₉	—	2	8	no	—
252	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
253	C₂×#532	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3036	C₂×C₁₉	1	16	yes	direct product factor
256	C₂×#463	C₂×C₁₉	1	4	yes	complemented
257	C₂×#461	C₂×C₁₉	1	2	yes	complemented
258	C₂×#459	C₂×C₁₉	1	2	yes	complemented
259	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂×#417	C₂×C₁₉	1	2	yes	complemented
261	C₂²×C₁₉	—	2	8	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	8	no	—
265	C₂²×C₁₉	—	4	32	no	—
266	C₂²×C₁₉	—	4	16	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	4	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	8	8	no	—
273	C₂²×C₁₉	C₂×#121	1	4	yes	—
274	C₂²×C₁₉	C₂×#121	1	2	yes	—
275	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
276	C₂²×C₁₉	#575	1	2	yes	—
277	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	4	4	no	—
282	C₄×C₁₉	—	4	4	no	—
283	C₄×C₁₉	C₂×#121	1	4	yes	—
284	C₄×C₁₉	C₂×#121	1	2	yes	—
285	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
286	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
287	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
288	C₂²×#41	C₂²×C₁₉	1	2	yes	—
289	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
290	C₂⁴×C₄	—	2	1	no	—
291	C₂×AGL(1,ℤ/8)	—	2	16	no	—
292	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	16	yes	complemented
293	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	—
294	C₂²×D₈	C₂²×C₁₉	1	4	yes	—
295	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
296	#532	—	2	4	no	—
297	#532	C₂²×C₁₉	1	8	yes	complemented
298	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₂×#124	C₂²×C₁₉	1	2	yes	complemented
301	C₂×#121	—	2	1	no	—
302	C₂×#121	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	—	2	4	no	—
306	C₂×C₄×D₄	—	2	1	no	—
307	C₂×C₄×D₄	—	2	1	no	—
308	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
311	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	—	2	1	no	—
313	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
314	#463	C₂²×C₁₉	1	32	yes	complemented
315	#461	C₂²×C₁₉	1	16	yes	complemented
316	#459	C₂²×C₁₉	1	16	yes	complemented
317	#423	C₂²×C₁₉	1	8	yes	complemented
318	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
319	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
320	#417	C₂²×C₁₉	1	16	yes	complemented
321	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
322	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
323	C₂×C₁₉	—	2	4	no	—
324	C₂×C₁₉	—	4	8	no	—
325	C₂×C₁₉	—	8	4	no	—
326	C₂×C₁₉	#3036	1	4	yes	direct product factor
327	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
328	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
329	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
330	C₂⁵	—	2	1	no	—
331	C₂×#41	—	2	4	no	—
332	C₂×#41	—	2	8	no	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	C₂³×C₁₉	1	8	yes	—
335	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	D₄×C₁₉	1	8	yes	complemented
343	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
344	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	2	no	—
348	C₂³×C₄	—	2	2	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	4	8	no	—
352	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
355	AGL(1,ℤ/8)	—	2	64	no	—
356	C₂×SD₁₆	—	2	16	no	—
357	C₂×SD₁₆	C₂³×C₁₉	1	16	yes	—
358	C₂×D₈	—	2	16	no	—
359	C₂×D₈	C₂³×C₁₉	1	16	yes	—
360	C₂×M₁₆	—	2	8	no	—
361	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
362	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
365	#127	—	2	2	no	—
366	#127	C₂³×C₁₉	1	4	yes	complemented
367	#124	—	2	4	no	—
368	#124	C₂³×C₁₉	1	8	yes	complemented
369	#121	—	2	8	no	—
370	#121	—	2	8	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	8	no	—
374	C₄×D₄	—	2	8	no	—
375	C₄×D₄	—	2	8	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	C₂³×C₁₉	1	8	yes	—
378	C₄×D₄	C₂³×C₁₉	1	8	yes	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	8	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	D₄×C₁₉	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
396	C₄⋊C₈	C₂³×C₁₉	1	8	yes	complemented
397	C₄⋊C₈	C₂³×C₁₉	1	8	yes	complemented
398	#103	C₂³×C₁₉	1	16	yes	complemented
399	#102	C₂³×C₁₉	1	16	yes	complemented
400	C₁₉	C₂×#3036	1	1	yes	characteristic, direct product factor, Sylow
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	4	4	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
408	#41	—	2	16	no	—
409	#41	—	2	16	no	—
410	#41	—	4	16	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	16	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
431	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	complemented
432	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
433	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	8	no	—
443	C₂²×C₄	—	4	32	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	8	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	#41×C₁₉	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
459	SD₁₆	—	2	32	no	—
460	D₈	—	2	32	no	—
461	M₁₆	—	2	16	no	—
462	C₂×C₈	—	2	8	no	—
463	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₄²	C₂×D₄×C₁₉	1	4	yes	—
474	C₄²	C₂×D₄×C₁₉	1	4	yes	—
475	C₄²	C₂×D₄×C₁₉	1	2	yes	—
476	C₄²	C₂×D₄×C₁₉	1	2	yes	—
477	C₄²	C₂⁴×C₁₉	1	2	yes	—
478	C₄²	C₂⁴×C₁₉	1	2	yes	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	16	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	32	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	C₁₉×#121	1	4	yes	—
494	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
495	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
496	Q₈	—	2	4	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	4	4	no	—
499	D₄	—	2	8	no	—
500	D₄	—	2	16	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	16	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	8	no	—
508	D₄	C₂²×D₄×C₁₉	1	8	yes	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	16	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	16	no	—
521	C₂×C₄	—	4	16	no	—
522	C₂×C₄	C₁₉×#121	1	4	yes	—
523	C₂×C₄	C₁₉×#121	1	8	yes	—
524	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
525	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
533	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
534	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
535	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
536	C₈	—	2	8	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	8	no	—
541	C₂²	—	4	32	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	8	8	no	—
549	C₂²	C₂×C₁₉×#121	1	4	yes	—
550	C₂²	C₂×C₁₉×#121	1	2	yes	—
551	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
552	C₂²	C₁₉×#575	1	2	yes	—
553	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	C₂×C₁₉×#121	1	4	yes	—
560	C₄	C₂×C₁₉×#121	1	2	yes	—
561	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	complemented
562	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
563	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
564	C₂	—	2	4	no	—
565	C₂	—	4	8	no	—
566	C₂	—	8	4	no	—
567	C₂	C₁₉×#3036	1	4	yes	direct product factor
568	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
569	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
570	C₂	C₂×C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₉×#532	C₂	semidirect
3. C₂²×C₄×D₄×C₁₉	C₂	semidirect
4. C₁₉×#3036	C₂	direct (N × H)
5. C₂×C₁₉×#463	C₂	semidirect
6. C₂×C₁₉×#461	C₂	semidirect
7. C₂×C₁₉×#459	C₂	semidirect
8. C₂×C₁₉×#423	C₂	semidirect
9. C₂×C₁₉×#417	C₂	semidirect
14. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
19. C₁₉×#532	C₂²	semidirect
20. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₉×#127	C₂²	semidirect
22. C₂×C₁₉×#124	C₂²	semidirect
32. C₂×C₄×D₄×C₁₉	C₂²	semidirect
36. C₁₉×#463	C₂²	semidirect
37. C₁₉×#461	C₂²	semidirect
38. C₁₉×#459	C₂²	semidirect
39. C₁₉×#423	C₂²	semidirect
40. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
41. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
42. C₁₉×#417	C₂²	semidirect
43. C₂×C₁₉×#103	C₂²	semidirect
44. C₂×C₁₉×#102	C₂²	semidirect
57. C₂²×D₄×C₁₉	D₄	semidirect
79. C₁₉×C₄⋊Q₈	C₂³	semidirect
81. C₁₉×#127	C₂³	semidirect
83. C₁₉×#124	C₂³	semidirect
111. C₁₉×C₄⋊C₈	C₂³	semidirect
112. C₁₉×C₄⋊C₈	C₂³	semidirect
113. C₁₉×#103	C₂³	semidirect
114. C₁₉×#102	C₂³	semidirect
145. C₂×D₄×C₁₉	C₂×D₄	semidirect
193. C₂×#3036	C₁₉	direct (N × H)
239. C₂×C₄×C₁₉	AGL(1,ℤ/8)	semidirect
252. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
253. C₂×#532	C₂×C₁₉	semidirect
254. C₂²×C₄×D₄	C₂×C₁₉	semidirect
255. #3036	C₂×C₁₉	direct (N × H)
256. C₂×#463	C₂×C₁₉	semidirect
257. C₂×#461	C₂×C₁₉	semidirect
258. C₂×#459	C₂×C₁₉	semidirect
259. C₂×#423	C₂×C₁₉	semidirect
260. C₂×#417	C₂×C₁₉	semidirect
285. C₄×C₁₉	C₂×AGL(1,ℤ/8)	semidirect
292. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
297. #532	C₂²×C₁₉	semidirect
298. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
299. C₂×#127	C₂²×C₁₉	semidirect
300. C₂×#124	C₂²×C₁₉	semidirect
310. C₂×C₄×D₄	C₂²×C₁₉	semidirect
314. #463	C₂²×C₁₉	semidirect
315. #461	C₂²×C₁₉	semidirect
316. #459	C₂²×C₁₉	semidirect
317. #423	C₂²×C₁₉	semidirect
318. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
319. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
320. #417	C₂²×C₁₉	semidirect
321. C₂×#103	C₂²×C₁₉	semidirect
322. C₂×#102	C₂²×C₁₉	semidirect
326. C₂×C₁₉	#3036	direct (N × H)
342. C₂²×D₄	D₄×C₁₉	semidirect
364. C₄⋊Q₈	C₂³×C₁₉	semidirect
366. #127	C₂³×C₁₉	semidirect
368. #124	C₂³×C₁₉	semidirect
396. C₄⋊C₈	C₂³×C₁₉	semidirect
397. C₄⋊C₈	C₂³×C₁₉	semidirect
398. #103	C₂³×C₁₉	semidirect
399. #102	C₂³×C₁₉	semidirect
400. C₁₉	C₂×#3036	direct (N × H)
431. C₂×D₄	C₂×D₄×C₁₉	semidirect
524. C₂×C₄	C₁₉×AGL(1,ℤ/8)	semidirect
561. C₄	C₂×C₁₉×AGL(1,ℤ/8)	semidirect
567. C₂	C₁₉×#3036	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂×C₁₉×#532	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#3036	2
C₂×C₁₉×#463	2
C₂×C₁₉×#461	2
C₂×C₁₉×#459	2
C₂×C₁₉×#423	2
C₂×C₁₉×#417	2
C₂×#3036	19

Subgroups — C2×C19×#3036 #18066369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3036 #18066369