Subgroups — C₁₉×#32955 #18038914

Order 4864.

1364 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1864	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1863	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1788	C₂	1	2	yes	maximal
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₄×#41×C₁₉	—	2	4	no	—
16	C₄×#41×C₁₉	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	—	2	1	no	—
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	—	2	1	no	—
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#475	—	2	4	no	—
28	C₁₉×#474	—	2	4	no	—
29	C₂×C₁₉×#107	C₂²	1	2	yes	—
30	C₂×C₁₉×#106	C₂²	1	2	yes	—
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	2	yes	—
34	C₂×C₁₉×#103	C₂²	1	2	yes	—
35	C₂×C₁₉×#102	C₂²	1	2	yes	—
36	C₂×C₁₉×#102	C₂²	1	2	yes	—
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₁₉×#391	—	2	1	no	—
39	C₁₉×#389	—	2	1	no	—
40	C₁₉×#389	C₂²	1	2	yes	—
41	C₁₉×#384	C₂²	1	1	yes	characteristic
42	C₁₉×#380	—	2	1	no	—
43	C₁₉×#380	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₁₉×#336	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	Q₈	1	4	yes	complemented
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	—	2	1	no	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
65	C₁₉×C₄⋊Q₈	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	4	4	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	D₄	1	4	yes	—
72	C₄×D₄×C₁₉	—	2	8	no	—
73	C₄×D₄×C₁₉	—	2	8	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	2	no	—
77	C₄×D₄×C₁₉	D₄	1	4	yes	—
78	C₁₉×#117	—	2	8	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	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	2	no	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄²×C₁₉	—	2	8	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	—	2	2	no	—
100	C₂×C₄²×C₁₉	—	2	2	no	—
101	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	—	2	4	no	—
106	C₁₉×#106	—	2	4	no	—
107	C₁₉×C₄⋊C₈	—	2	2	no	—
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×#103	—	2	4	no	—
110	C₁₉×#103	—	2	4	no	—
111	C₁₉×#102	—	2	4	no	—
112	C₁₉×#102	—	2	4	no	—
113	C₁₉×C₂²⋊C₈	—	2	4	no	—
114	C₁₉×#95	—	2	2	no	—
115	C₁₉×#95	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	1	no	—
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	#41×C₁₉	—	2	8	no	—
119	#41×C₁₉	—	2	8	no	—
120	#41×C₁₉	—	2	8	no	—
121	#41×C₁₉	—	2	8	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	—	4	2	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
130	C₂×Q₈×C₁₉	#41	1	2	yes	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
139	C₂×D₄×C₁₉	#41	1	2	yes	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	4	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	—	4	1	no	—
160	C₂²×C₄×C₁₉	—	4	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
170	C₂²×C₄×C₁₉	#41	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	4	2	no	—
187	C₄⋊C₄×C₁₉	—	4	4	no	—
188	C₄⋊C₄×C₁₉	—	4	2	no	—
189	C₄⋊C₄×C₁₉	—	4	2	no	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₁₉	—	2	4	no	—
193	C₂²⋊C₄×C₁₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	4	4	no	—
196	C₄²×C₁₉	—	2	4	no	—
197	C₄²×C₁₉	—	2	4	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	4	no	—
200	C₄²×C₁₉	—	2	2	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	C₂×D₄	1	2	yes	—
204	C₄²×C₁₉	C₂×D₄	1	2	yes	—
205	#32955	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	1	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	4	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	—	2	2	no	—
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	8	4	no	—
225	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	complemented
226	D₄×C₁₉	—	2	16	no	—
227	D₄×C₁₉	—	2	2	no	—
228	D₄×C₁₉	—	2	2	no	—
229	D₄×C₁₉	—	2	2	no	—
230	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	complemented
231	C₂×C₄×C₁₉	—	2	16	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	4	4	no	—
251	C₂×C₄×C₁₉	—	4	8	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	4	no	—
257	C₂×C₄×C₁₉	—	4	8	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	#120	1	2	yes	—
265	C₂×C₄×C₁₉	#120	1	2	yes	—
266	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
267	C₂×C₄×C₁₉	#135	1	2	yes	—
268	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₁₉	#137	1	2	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₈×C₁₉	—	4	2	no	—
277	C₈×C₁₉	—	4	2	no	—
278	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
279	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
280	C₂×#474	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1864	C₂×C₁₉	1	2	yes	complemented
283	#1863	C₂×C₁₉	1	2	yes	complemented
284	#1854	C₂×C₁₉	1	2	yes	complemented
285	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1788	C₂×C₁₉	1	2	yes	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	4	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
304	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂²×C₁₉	#525	1	1	yes	characteristic
306	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
307	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
308	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
309	C₂²×C₁₉	#575	1	1	yes	characteristic
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	—	2	4	no	—
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	8	2	no	—
318	C₄×C₁₉	—	8	2	no	—
319	C₄×C₁₉	#449	1	4	yes	—
320	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
321	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₄×C₁₉	#525	1	1	yes	characteristic
323	C₄×C₁₉	#525	1	1	yes	characteristic
324	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	—	2	1	no	—
327	C₄×#41	—	2	4	no	—
328	C₄×#41	—	2	4	no	—
329	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×D₄	—	2	1	no	—
332	C₂×C₄×D₄	—	2	1	no	—
333	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#117	—	2	1	no	—
336	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
337	C₂²×C₄²	—	2	1	no	—
338	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
339	#475	—	2	4	no	—
340	#474	—	2	4	no	—
341	C₂×#107	C₂²×C₁₉	1	2	yes	—
342	C₂×#106	C₂²×C₁₉	1	2	yes	—
343	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₉	1	2	yes	—
346	C₂×#103	C₂²×C₁₉	1	2	yes	—
347	C₂×#102	C₂²×C₁₉	1	2	yes	—
348	C₂×#102	C₂²×C₁₉	1	2	yes	—
349	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
350	#391	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	C₂²×C₁₉	1	2	yes	—
353	#384	C₂²×C₁₉	1	1	yes	characteristic
354	#380	—	2	1	no	—
355	#380	C₂²×C₁₉	1	2	yes	—
356	#340	C₂²×C₁₉	1	2	yes	—
357	#340	C₂²×C₁₉	1	2	yes	—
358	#336	C₂²×C₁₉	1	2	yes	—
359	C₂×C₁₉	—	4	2	no	—
360	C₂×C₁₉	—	4	4	no	—
361	C₂×C₁₉	#2848	1	1	yes	characteristic
362	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
363	C₂×C₁₉	#3007	1	1	yes	characteristic
364	C₂×C₁₉	#3076	1	1	yes	characteristic
365	C₂×C₁₉	#3079	1	1	yes	characteristic
366	C₂×C₁₉	#3107	1	1	yes	characteristic
367	C₂×C₁₉	#3115	1	1	yes	characteristic
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	2	no	—
371	C₂×#41	—	2	2	no	—
372	C₂×#41	—	2	2	no	—
373	C₂×#41	Q₈×C₁₉	1	4	yes	complemented
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
385	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	4	4	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	D₄×C₁₉	1	4	yes	—
393	C₄×D₄	—	2	8	no	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	D₄×C₁₉	1	4	yes	—
399	#117	—	2	8	no	—
400	#117	—	2	2	no	—
401	#117	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₄²	—	2	8	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	2	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
426	#107	—	2	4	no	—
427	#106	—	2	4	no	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	#103	—	2	4	no	—
431	#103	—	2	4	no	—
432	#102	—	2	4	no	—
433	#102	—	2	4	no	—
434	C₂²⋊C₈	—	2	4	no	—
435	#95	—	2	2	no	—
436	#95	—	2	2	no	—
437	C₁₉	#32955	1	1	yes	characteristic, direct product factor, Sylow
438	C₂⁴	—	2	1	no	—
439	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
440	#41	—	2	8	no	—
441	#41	—	2	8	no	—
442	#41	—	2	8	no	—
443	#41	—	2	8	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	4	2	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
451	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
452	C₂×Q₈	#41×C₁₉	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
461	C₂×D₄	#41×C₁₉	1	2	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
492	C₂²×C₄	#41×C₁₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	C₂×D₄×C₁₉	1	2	yes	—
526	C₄²	C₂×D₄×C₁₉	1	2	yes	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
541	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	8	4	no	—
546	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	complemented
547	D₄	—	2	16	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	complemented
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	C₁₉×#120	1	2	yes	—
586	C₂×C₄	C₁₉×#120	1	2	yes	—
587	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
588	C₂×C₄	C₁₉×#135	1	2	yes	—
589	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
590	C₂×C₄	C₁₉×#137	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
597	C₈	—	4	2	no	—
598	C₈	—	4	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
614	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
615	C₂²	C₁₉×#525	1	1	yes	characteristic
616	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
617	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
618	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
619	C₂²	C₁₉×#575	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	2	no	—
628	C₄	—	8	2	no	—
629	C₄	C₁₉×#449	1	4	yes	—
630	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
631	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
632	C₄	C₁₉×#525	1	1	yes	characteristic
633	C₄	C₁₉×#525	1	1	yes	characteristic
634	C₂	—	4	2	no	—
635	C₂	—	4	4	no	—
636	C₂	C₁₉×#2848	1	1	yes	characteristic
637	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
638	C₂	C₁₉×#3007	1	1	yes	characteristic
639	C₂	C₁₉×#3076	1	1	yes	characteristic
640	C₂	C₁₉×#3079	1	1	yes	characteristic
641	C₂	C₁₉×#3107	1	1	yes	characteristic
642	C₂	C₁₉×#3115	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×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
2. C₂×C₁₉×#475	C₂	semidirect
3. C₂×C₁₉×#474	C₂	semidirect
4. C₁₉×#2857	C₂	semidirect
5. C₁₉×#1864	C₂	semidirect
6. C₁₉×#1863	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1803	C₂	semidirect
9. C₁₉×#1802	C₂	semidirect
10. C₁₉×#1797	C₂	semidirect
52. C₂×#41×C₁₉	Q₈	semidirect
205. #32955	C₁₉	direct (N × H)
225. Q₈×C₁₉	C₂²⋊Q₈	semidirect
230. D₄×C₁₉	C₂²⋊Q₈	semidirect
279. C₂×#475	C₂×C₁₉	semidirect
280. C₂×#474	C₂×C₁₉	semidirect
281. #2857	C₂×C₁₉	semidirect
282. #1864	C₂×C₁₉	semidirect
283. #1863	C₂×C₁₉	semidirect
284. #1854	C₂×C₁₉	semidirect
285. #1803	C₂×C₁₉	semidirect
286. #1802	C₂×C₁₉	semidirect
287. #1797	C₂×C₁₉	semidirect
373. C₂×#41	Q₈×C₁₉	semidirect
437. C₁₉	#32955	direct (N × H)
546. Q₈	C₁₉×C₂²⋊Q₈	semidirect
551. D₄	C₁₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂×C₁₉×#475	2
C₂×C₁₉×#474	2
C₁₉×#2857	2
C₁₉×#1864	2
C₁₉×#1863	2
C₁₉×#1854	2
C₁₉×#1803	2
C₁₉×#1802	2
C₁₉×#1797	2
C₁₉×#1788	2
#32955	19

Subgroups — C19×#32955 #18038914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32955 #18038914