Subgroups — C₂×C₁₉×#3332 #18067111

Order 4864.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3332	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
13	C₂²×#41×C₁₉	—	2	1	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#550	—	2	4	no	—
19	C₁₉×#550	C₂²	1	8	yes	complemented
20	C₁₉×#547	—	2	4	no	—
21	C₁₉×#547	C₂²	1	8	yes	complemented
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	—	2	1	no	—
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#123	—	2	2	no	—
26	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₉×#121	—	2	2	no	—
28	C₂×C₁₉×#121	C₂²	1	2	yes	—
29	C₂×C₁₉×#121	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₉	—	2	1	no	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#486	C₂²	1	8	yes	complemented
36	C₁₉×#481	C₂²	1	16	yes	complemented
37	C₁₉×#475	C₂²	1	8	yes	complemented
38	C₁₉×#469	C₂²	1	16	yes	complemented
39	C₁₉×#459	C₂²	1	8	yes	complemented
40	C₁₉×#449	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	complemented
42	C₁₉×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#106	C₂²	1	2	yes	—
45	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#417	C₂²	1	16	yes	complemented
47	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#103	C₂²	1	2	yes	—
49	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#102	C₂²	1	2	yes	—
51	C₂×C₁₉×#102	C₂²	1	2	yes	—
52	C₂×C₁₉×#102	C₂²	1	2	yes	—
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₁₉	—	2	8	no	—
56	C₂×#41×C₁₉	—	2	4	no	—
57	C₂×#41×C₁₉	—	2	8	no	—
58	C₂×#41×C₁₉	—	4	4	no	—
59	C₂×#41×C₁₉	—	4	8	no	—
60	C₂×#41×C₁₉	C₂³	1	8	yes	—
61	C₂²×Q₈×C₁₉	—	2	1	no	—
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	—	2	2	no	—
64	C₂²×D₄×C₁₉	—	2	2	no	—
65	C₂²×D₄×C₁₉	—	2	2	no	—
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	—	2	2	no	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×SD₁₆×C₁₉	—	2	4	no	—
76	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
77	C₂×D₈×C₁₉	—	4	4	no	—
78	C₂×D₈×C₁₉	C₂³	1	8	yes	—
79	C₂×M₁₆×C₁₉	—	4	4	no	—
80	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
84	C₁₉×C₄⋊Q₈	—	2	2	no	—
85	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₉×#127	—	2	8	no	—
87	C₁₉×#127	—	2	2	no	—
88	C₁₉×#127	C₂³	1	4	yes	—
89	C₁₉×#123	—	2	16	no	—
90	C₁₉×C₂²⋊Q₈	—	2	8	no	—
91	C₁₉×#121	—	2	4	no	—
92	C₁₉×#121	—	2	4	no	—
93	C₁₉×#121	—	2	16	no	—
94	C₁₉×#121	C₂³	1	8	yes	—
95	C₁₉×#121	C₂³	1	8	yes	—
96	C₄×Q₈×C₁₉	—	2	2	no	—
97	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
98	C₄×D₄×C₁₉	—	2	8	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	D₄	1	4	yes	—
101	C₄×D₄×C₁₉	C₂³	1	4	yes	—
102	C₄×D₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×#106	C₂³	1	4	yes	—
119	C₁₉×#106	C₂³	1	8	yes	—
120	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₉×#103	C₂³	1	4	yes	—
122	C₁₉×#103	C₂³	1	8	yes	—
123	C₁₉×#102	C₂³	1	8	yes	—
124	C₁₉×#102	C₂³	1	8	yes	—
125	C₁₉×#102	C₂³	1	4	yes	—
126	C₁₉×#102	C₂³	1	8	yes	—
127	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₈×C₁₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₉	—	2	1	no	—
130	C₂⁴×C₁₉	—	2	2	no	—
131	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
132	#41×C₁₉	—	2	16	no	—
133	#41×C₁₉	—	4	8	no	—
134	#41×C₁₉	—	4	16	no	—
135	#41×C₁₉	—	4	32	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	4	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	4	4	no	—
140	C₂×Q₈×C₁₉	#41	1	4	yes	complemented
141	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
142	C₂×D₄×C₁₉	—	2	8	no	—
143	C₂×D₄×C₁₉	—	2	8	no	—
144	C₂×D₄×C₁₉	—	2	8	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	4	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	4	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	4	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	4	no	—
154	C₂×D₄×C₁₉	—	4	8	no	—
155	C₂×D₄×C₁₉	—	4	8	no	—
156	C₂×D₄×C₁₉	—	4	4	no	—
157	C₂×D₄×C₁₉	—	8	2	no	—
158	C₂×D₄×C₁₉	—	8	4	no	—
159	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
160	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
161	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	8	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	8	no	—
170	C₂²×C₄×C₁₉	—	2	4	no	—
171	C₂²×C₄×C₁₉	—	4	8	no	—
172	C₂²×C₄×C₁₉	—	4	8	no	—
173	C₂²×C₄×C₁₉	—	4	4	no	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	SD₁₆×C₁₉	—	2	8	no	—
181	D₈×C₁₉	—	4	8	no	—
182	M₁₆×C₁₉	—	4	8	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	4	no	—
186	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
187	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
188	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	8	no	—
192	C₄⋊C₄×C₁₉	—	2	4	no	—
193	C₄⋊C₄×C₁₉	—	2	4	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
196	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
198	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
199	C₂²⋊C₄×C₁₉	—	2	8	no	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	8	no	—
202	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
203	C₄²×C₁₉	—	2	4	no	—
204	C₄²×C₁₉	C₂×D₄	1	2	yes	—
205	C₄²×C₁₉	C₂⁴	1	2	yes	—
206	C₂×#3332	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	—	2	4	no	—
209	C₂³×C₁₉	—	2	4	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	4	no	—
212	C₂³×C₁₉	—	4	4	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	4	no	—
216	C₂³×C₁₉	—	4	4	no	—
217	C₂³×C₁₉	—	4	2	no	—
218	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₉	—	2	4	no	—
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	—	4	8	no	—
223	Q₈×C₁₉	C₂×#41	1	4	yes	complemented
224	D₄×C₁₉	—	2	8	no	—
225	D₄×C₁₉	—	2	2	no	—
226	D₄×C₁₉	—	2	4	no	—
227	D₄×C₁₉	—	2	2	no	—
228	D₄×C₁₉	—	2	4	no	—
229	D₄×C₁₉	—	4	16	no	—
230	D₄×C₁₉	—	4	16	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	4	8	no	—
234	D₄×C₁₉	—	8	4	no	—
235	D₄×C₁₉	—	8	8	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	8	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	4	16	no	—
247	C₂×C₄×C₁₉	—	4	16	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	4	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	8	no	—
252	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
253	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
259	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
260	C₈×C₁₉	—	2	2	no	—
261	C₈×C₁₉	—	2	2	no	—
262	C₈×C₁₉	—	2	4	no	—
263	C₂×#550	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂×#547	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#3332	C₂×C₁₉	1	16	yes	direct product factor
266	C₂×#486	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂×#481	C₂×C₁₉	1	2	yes	complemented
268	C₂×#475	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂×#469	C₂×C₁₉	1	2	yes	complemented
270	C₂×#459	C₂×C₁₉	1	1	yes	characteristic, complemented
271	C₂×#449	C₂×C₁₉	1	2	yes	complemented
272	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂×#436	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂×#417	C₂×C₁₉	1	2	yes	complemented
275	C₂²×C₁₉	—	2	4	no	—
276	C₂²×C₁₉	—	2	4	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	—	4	8	no	—
279	C₂²×C₁₉	—	4	4	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	4	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	8	8	no	—
286	C₂²×C₁₉	—	8	4	no	—
287	C₂²×C₁₉	#546	1	2	yes	—
288	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
289	C₂²×C₁₉	#577	1	2	yes	—
290	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
291	C₄×C₁₉	—	2	4	no	—
292	C₄×C₁₉	—	2	4	no	—
293	C₄×C₁₉	—	2	2	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	4	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	#546	1	2	yes	—
298	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
299	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
300	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂²×#41	—	2	1	no	—
302	C₂²×#41	C₂²×C₁₉	1	2	yes	—
303	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
304	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
305	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
306	#550	—	2	4	no	—
307	#550	C₂²×C₁₉	1	8	yes	complemented
308	#547	—	2	4	no	—
309	#547	C₂²×C₁₉	1	8	yes	complemented
310	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#127	—	2	1	no	—
312	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#123	—	2	2	no	—
314	C₂×C₂²⋊Q₈	—	2	1	no	—
315	C₂×#121	—	2	2	no	—
316	C₂×#121	C₂²×C₁₉	1	2	yes	—
317	C₂×#121	C₂²×C₁₉	1	2	yes	—
318	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄×D₄	—	2	1	no	—
320	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
323	#486	C₂²×C₁₉	1	8	yes	complemented
324	#481	C₂²×C₁₉	1	16	yes	complemented
325	#475	C₂²×C₁₉	1	8	yes	complemented
326	#469	C₂²×C₁₉	1	16	yes	complemented
327	#459	C₂²×C₁₉	1	8	yes	complemented
328	#449	C₂²×C₁₉	1	16	yes	complemented
329	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	complemented
330	#436	C₂²×C₁₉	1	8	yes	complemented
331	C₂×#106	C₂²×C₁₉	1	2	yes	—
332	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	#417	C₂²×C₁₉	1	16	yes	complemented
335	C₂×#103	C₂²×C₁₉	1	2	yes	—
336	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#102	C₂²×C₁₉	1	2	yes	—
338	C₂×#102	C₂²×C₁₉	1	2	yes	—
339	C₂×#102	C₂²×C₁₉	1	2	yes	—
340	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
342	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×C₁₉	—	4	4	no	—
344	C₂×C₁₉	—	8	4	no	—
345	C₂×C₁₉	—	8	2	no	—
346	C₂×C₁₉	#3332	1	4	yes	direct product factor
347	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
348	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
350	C₂×#41	—	2	8	no	—
351	C₂×#41	—	2	4	no	—
352	C₂×#41	—	2	8	no	—
353	C₂×#41	—	4	4	no	—
354	C₂×#41	—	4	8	no	—
355	C₂×#41	C₂³×C₁₉	1	8	yes	—
356	C₂²×Q₈	—	2	1	no	—
357	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
364	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
366	C₂³×C₄	—	2	2	no	—
367	C₂³×C₄	—	2	2	no	—
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
370	C₂×SD₁₆	—	2	4	no	—
371	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
372	C₂×D₈	—	4	4	no	—
373	C₂×D₈	C₂³×C₁₉	1	8	yes	—
374	C₂×M₁₆	—	4	4	no	—
375	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
376	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
378	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₄⋊Q₈	—	2	2	no	—
380	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
381	#127	—	2	8	no	—
382	#127	—	2	2	no	—
383	#127	C₂³×C₁₉	1	4	yes	—
384	#123	—	2	16	no	—
385	C₂²⋊Q₈	—	2	8	no	—
386	#121	—	2	4	no	—
387	#121	—	2	4	no	—
388	#121	—	2	16	no	—
389	#121	C₂³×C₁₉	1	8	yes	—
390	#121	C₂³×C₁₉	1	8	yes	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
393	C₄×D₄	—	2	8	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	D₄×C₁₉	1	4	yes	—
396	C₄×D₄	C₂³×C₁₉	1	4	yes	—
397	C₄×D₄	C₂³×C₁₉	1	4	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	4	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
413	#106	C₂³×C₁₉	1	4	yes	—
414	#106	C₂³×C₁₉	1	8	yes	—
415	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
416	#103	C₂³×C₁₉	1	4	yes	—
417	#103	C₂³×C₁₉	1	8	yes	—
418	#102	C₂³×C₁₉	1	8	yes	—
419	#102	C₂³×C₁₉	1	8	yes	—
420	#102	C₂³×C₁₉	1	4	yes	—
421	#102	C₂³×C₁₉	1	8	yes	—
422	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
423	C₄×C₈	C₂³×C₁₉	1	4	yes	—
424	C₁₉	C₂×#3332	1	1	yes	characteristic, direct product factor, Sylow
425	C₂⁴	—	2	1	no	—
426	C₂⁴	—	2	2	no	—
427	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
428	#41	—	2	16	no	—
429	#41	—	4	8	no	—
430	#41	—	4	16	no	—
431	#41	—	4	32	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	#41×C₁₉	1	4	yes	complemented
437	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	8	2	no	—
454	C₂×D₄	—	8	4	no	—
455	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
456	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
457	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	4	8	no	—
468	C₂²×C₄	—	4	8	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
476	SD₁₆	—	2	8	no	—
477	D₈	—	4	8	no	—
478	M₁₆	—	4	8	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	4	no	—
482	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
483	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
484	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
492	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
493	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
499	C₄²	—	2	4	no	—
500	C₄²	C₂×D₄×C₁₉	1	2	yes	—
501	C₄²	C₂⁴×C₁₉	1	2	yes	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	2	no	—
513	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
514	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	Q₈	—	2	4	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	8	no	—
518	Q₈	C₂×#41×C₁₉	1	4	yes	complemented
519	D₄	—	2	8	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	16	no	—
525	D₄	—	4	16	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	8	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	8	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	16	no	—
542	C₂×C₄	—	4	16	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
548	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
550	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
552	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
553	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
554	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	4	8	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	8	8	no	—
569	C₂²	—	8	4	no	—
570	C₂²	C₁₉×#546	1	2	yes	—
571	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
572	C₂²	C₁₉×#577	1	2	yes	—
573	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	C₁₉×#546	1	2	yes	—
581	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
582	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
583	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂	—	4	4	no	—
585	C₂	—	8	4	no	—
586	C₂	—	8	2	no	—
587	C₂	C₁₉×#3332	1	4	yes	direct product factor
588	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
589	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
590	C₂	C₂×C₁₉×#577	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 ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#550	C₂	semidirect
2. C₂×C₁₉×#547	C₂	semidirect
3. C₁₉×#3332	C₂	direct (N × H)
4. C₂×C₁₉×#486	C₂	semidirect
5. C₂×C₁₉×#481	C₂	semidirect
6. C₂×C₁₉×#475	C₂	semidirect
7. C₂×C₁₉×#469	C₂	semidirect
8. C₂×C₁₉×#459	C₂	semidirect
9. C₂×C₁₉×#449	C₂	semidirect
10. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
11. C₂×C₁₉×#436	C₂	semidirect
12. C₂×C₁₉×#417	C₂	semidirect
19. C₁₉×#550	C₂²	semidirect
21. C₁₉×#547	C₂²	semidirect
35. C₁₉×#486	C₂²	semidirect
36. C₁₉×#481	C₂²	semidirect
37. C₁₉×#475	C₂²	semidirect
38. C₁₉×#469	C₂²	semidirect
39. C₁₉×#459	C₂²	semidirect
40. C₁₉×#449	C₂²	semidirect
41. C₄×SD₁₆×C₁₉	C₂²	semidirect
42. C₁₉×#436	C₂²	semidirect
46. C₁₉×#417	C₂²	semidirect
140. C₂×Q₈×C₁₉	#41	semidirect
206. C₂×#3332	C₁₉	direct (N × H)
223. Q₈×C₁₉	C₂×#41	semidirect
263. C₂×#550	C₂×C₁₉	semidirect
264. C₂×#547	C₂×C₁₉	semidirect
265. #3332	C₂×C₁₉	direct (N × H)
266. C₂×#486	C₂×C₁₉	semidirect
267. C₂×#481	C₂×C₁₉	semidirect
268. C₂×#475	C₂×C₁₉	semidirect
269. C₂×#469	C₂×C₁₉	semidirect
270. C₂×#459	C₂×C₁₉	semidirect
271. C₂×#449	C₂×C₁₉	semidirect
272. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
273. C₂×#436	C₂×C₁₉	semidirect
274. C₂×#417	C₂×C₁₉	semidirect
307. #550	C₂²×C₁₉	semidirect
309. #547	C₂²×C₁₉	semidirect
323. #486	C₂²×C₁₉	semidirect
324. #481	C₂²×C₁₉	semidirect
325. #475	C₂²×C₁₉	semidirect
326. #469	C₂²×C₁₉	semidirect
327. #459	C₂²×C₁₉	semidirect
328. #449	C₂²×C₁₉	semidirect
329. C₄×SD₁₆	C₂²×C₁₉	semidirect
330. #436	C₂²×C₁₉	semidirect
334. #417	C₂²×C₁₉	semidirect
346. C₂×C₁₉	#3332	direct (N × H)
424. C₁₉	C₂×#3332	direct (N × H)
436. C₂×Q₈	#41×C₁₉	semidirect
518. Q₈	C₂×#41×C₁₉	semidirect
587. C₂	C₁₉×#3332	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×#550	2
C₂×C₁₉×#547	2
C₁₉×#3332	2
C₂×C₁₉×#486	2
C₂×C₁₉×#481	2
C₂×C₁₉×#475	2
C₂×C₁₉×#469	2
C₂×C₁₉×#459	2
C₂×C₁₉×#449	2
C₂×C₄×SD₁₆×C₁₉	2
C₂×C₁₉×#436	2
C₂×C₁₉×#417	2
C₂×#3332	19

Subgroups — C2×C19×#3332 #18067111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3332 #18067111