Subgroups — C₁₉×#23990 #18029949

Order 4864.

1260 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2901	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2031	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2002	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1914	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1911	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1910	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1904	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1827	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₁₉×#568	C₂²	1	1	yes	characteristic
15	C₁₉×#559	—	2	2	no	—
16	C₁₉×#550	—	2	2	no	—
17	C₁₉×#546	—	2	4	no	—
18	C₁₉×#540	—	2	2	no	—
19	C₁₉×#535	C₂²	1	1	yes	characteristic
20	C₁₉×#535	C₂²	1	2	yes	—
21	C₁₉×#535	C₂²	1	1	yes	characteristic
22	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#532	—	2	2	no	—
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×B(4,𝔽₂)	—	2	4	no	—
29	C₁₉×#454	—	2	2	no	—
30	C₁₉×#453	—	2	2	no	—
31	C₁₉×#421	—	2	2	no	—
32	C₁₉×#421	C₂²	1	2	yes	—
33	C₁₉×#421	C₂²	1	2	yes	—
34	C₂×C₁₉×#104	—	2	2	no	—
35	C₂×C₁₉×#104	C₂²	1	2	yes	—
36	C₁₉×#418	C₂²	1	2	yes	complemented
37	C₁₉×#413	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
39	C₁₉×#410	C₂²	1	2	yes	—
40	C₁₉×#410	C₂²	1	1	yes	characteristic
41	C₁₉×#344	C₂²	1	2	yes	complemented
42	C₁₉×#339	C₂²	1	2	yes	complemented
43	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
44	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	C₁₉×2₋¹⁺⁴	—	2	2	no	—
46	C₁₉×2₋¹⁺⁴	—	2	1	no	—
47	C₁₉×H(5,𝔽₂)	—	2	2	no	—
48	C₁₉×H(5,𝔽₂)	—	2	2	no	—
49	C₁₉×H(5,𝔽₂)	—	2	1	no	—
50	C₂×#41×C₁₉	—	2	4	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂×#41×C₁₉	—	4	2	no	—
53	C₂×#41×C₁₉	C₂³	1	2	yes	—
54	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	—	2	2	no	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
59	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₁₉×#131	—	4	2	no	—
63	C₂×M₁₆×C₁₉	—	2	2	no	—
64	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
65	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×#127	—	2	2	no	—
68	C₁₉×#127	—	2	1	no	—
69	C₁₉×#127	—	2	2	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	—	2	1	no	—
72	C₁₉×#127	D₄	1	2	yes	complemented
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#124	—	2	4	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#124	D₄	1	2	yes	complemented
78	C₁₉×#123	—	2	4	no	—
79	C₁₉×#123	—	2	4	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	4	no	—
83	C₁₉×#121	—	2	4	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	4	2	no	—
87	C₁₉×#120	—	2	2	no	—
88	C₁₉×#120	—	2	4	no	—
89	C₁₉×#120	D₄	1	4	yes	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	4	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₁₉×#117	D₄	1	2	yes	complemented
100	C₁₉×#117	C₂³	1	2	yes	—
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₁₉×#117	C₂³	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₄²×C₁₉	D₄	1	2	yes	complemented
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#104	—	2	2	no	—
109	C₁₉×#104	—	2	4	no	—
110	C₁₉×#104	—	2	2	no	—
111	C₁₉×#104	—	2	4	no	—
112	C₁₉×#102	—	4	2	no	—
113	C₁₉×#101	—	2	1	no	—
114	C₁₉×#100	—	2	1	no	—
115	C₁₉×#100	—	4	2	no	—
116	C₁₉×#99	—	2	2	no	—
117	C₁₉×#99	—	2	4	no	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	4	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	—	4	2	no	—
129	#41×C₁₉	—	4	2	no	—
130	#41×C₁₉	—	4	2	no	—
131	#41×C₁₉	—	4	2	no	—
132	#41×C₁₉	—	8	8	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	4	2	no	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₉	#41	1	2	yes	complemented
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	4	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	—	4	4	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	4	no	—
155	C₂×D₄×C₁₉	—	8	4	no	—
156	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₉	#41	1	2	yes	complemented
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	SD₁₆×C₁₉	—	4	4	no	—
169	D₈×C₁₉	—	4	4	no	—
170	M₁₆×C₁₉	—	2	2	no	—
171	M₁₆×C₁₉	—	2	2	no	—
172	M₁₆×C₁₉	—	2	2	no	—
173	M₁₆×C₁₉	—	2	2	no	—
174	M₁₆×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	4	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₂²⋊C₄×C₁₉	—	2	4	no	—
192	C₂²⋊C₄×C₁₉	—	2	4	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	4	4	no	—
195	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₉	C₂×D₄	1	2	yes	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	2	yes	—
204	#23990	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	8	2	no	—
212	C₂³×C₁₉	—	8	2	no	—
213	C₂³×C₁₉	#120	1	2	yes	—
214	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	2	2	no	—
223	D₄×C₁₉	—	2	2	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	8	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	D₄×C₁₉	—	4	1	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	8	4	no	—
236	D₄×C₁₉	—	8	4	no	—
237	D₄×C₁₉	—	8	4	no	—
238	D₄×C₁₉	—	16	4	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	4	no	—
249	C₂×C₄×C₁₉	—	4	4	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	8	4	no	—
255	C₂×C₄×C₁₉	—	8	4	no	—
256	C₂×C₄×C₁₉	#120	1	2	yes	—
257	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
261	C₈×C₁₉	—	4	2	no	—
262	C₈×C₁₉	—	4	2	no	—
263	#3508	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#3027	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#3021	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2901	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#2031	C₂×C₁₉	1	2	yes	complemented
268	#2002	C₂×C₁₉	1	2	yes	complemented
269	#1914	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1911	C₂×C₁₉	1	2	yes	complemented
271	#1910	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1904	C₂×C₁₉	1	2	yes	complemented
273	#1827	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	8	2	no	—
283	C₂²×C₁₉	—	8	4	no	—
284	C₂²×C₁₉	—	16	2	no	—
285	C₂²×C₁₉	—	16	2	no	—
286	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
287	C₂²×C₁₉	#546	1	2	yes	—
288	C₄×C₁₉	—	2	2	no	—
289	C₄×C₁₉	—	2	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	#525	1	1	yes	characteristic
297	C₄×C₁₉	#535	1	1	yes	characteristic
298	C₄×C₁₉	#546	1	2	yes	—
299	#585	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
301	#568	C₂²×C₁₉	1	1	yes	characteristic
302	#559	—	2	2	no	—
303	#550	—	2	2	no	—
304	#546	—	2	4	no	—
305	#540	—	2	2	no	—
306	#535	C₂²×C₁₉	1	1	yes	characteristic
307	#535	C₂²×C₁₉	1	2	yes	—
308	#535	C₂²×C₁₉	1	1	yes	characteristic
309	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
310	#532	—	2	2	no	—
311	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
313	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
315	B(4,𝔽₂)	—	2	4	no	—
316	#454	—	2	2	no	—
317	#453	—	2	2	no	—
318	#421	—	2	2	no	—
319	#421	C₂²×C₁₉	1	2	yes	—
320	#421	C₂²×C₁₉	1	2	yes	—
321	C₂×#104	—	2	2	no	—
322	C₂×#104	C₂²×C₁₉	1	2	yes	—
323	#418	C₂²×C₁₉	1	2	yes	complemented
324	#413	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
326	#410	C₂²×C₁₉	1	1	yes	characteristic
327	#410	C₂²×C₁₉	1	2	yes	—
328	#344	C₂²×C₁₉	1	2	yes	complemented
329	#339	C₂²×C₁₉	1	2	yes	complemented
330	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	complemented
331	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	complemented
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	2	2	no	—
334	C₂×C₁₉	—	4	2	no	—
335	C₂×C₁₉	—	8	2	no	—
336	C₂×C₁₉	—	8	2	no	—
337	C₂×C₁₉	—	8	2	no	—
338	C₂×C₁₉	#2404	1	1	yes	characteristic
339	2₋¹⁺⁴	—	2	2	no	—
340	2₋¹⁺⁴	—	2	1	no	—
341	H(5,𝔽₂)	—	2	2	no	—
342	H(5,𝔽₂)	—	2	2	no	—
343	H(5,𝔽₂)	—	2	1	no	—
344	C₂×#41	—	2	4	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	4	2	no	—
347	C₂×#41	C₂³×C₁₉	1	2	yes	—
348	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
352	AGL(1,ℤ/8)	—	2	4	no	—
353	AGL(1,ℤ/8)	—	4	2	no	—
354	C₂×SD₁₆	—	2	2	no	—
355	C₂×D₈	—	2	2	no	—
356	#131	—	4	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
359	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
360	C₄⋊Q₈	—	2	1	no	—
361	#127	—	2	2	no	—
362	#127	—	2	1	no	—
363	#127	—	2	2	no	—
364	#127	—	2	1	no	—
365	#127	—	2	1	no	—
366	#127	D₄×C₁₉	1	2	yes	complemented
367	#125	—	2	1	no	—
368	#124	—	2	4	no	—
369	#124	—	2	1	no	—
370	#124	—	2	2	no	—
371	#124	D₄×C₁₉	1	2	yes	complemented
372	#123	—	2	4	no	—
373	#123	—	2	4	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	#121	—	2	4	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	4	2	no	—
381	#120	—	2	2	no	—
382	#120	—	2	4	no	—
383	#120	D₄×C₁₉	1	4	yes	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	#117	D₄×C₁₉	1	2	yes	complemented
394	#117	C₂³×C₁₉	1	2	yes	—
395	#117	C₂³×C₁₉	1	1	yes	characteristic
396	#117	C₂³×C₁₉	1	1	yes	characteristic
397	#117	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₄²	D₄×C₁₉	1	2	yes	complemented
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	#104	—	2	2	no	—
403	#104	—	2	4	no	—
404	#104	—	2	2	no	—
405	#104	—	2	4	no	—
406	#102	—	4	2	no	—
407	#101	—	2	1	no	—
408	#100	—	2	1	no	—
409	#100	—	4	2	no	—
410	#99	—	2	2	no	—
411	#99	—	2	4	no	—
412	C₁₉	#23990	1	1	yes	characteristic, direct product factor, Sylow
413	C₂⁴	—	2	1	no	—
414	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	4	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	4	4	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	4	2	no	—
427	#41	—	8	8	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×Q₈	#41×C₁₉	1	2	yes	complemented
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	8	4	no	—
451	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
452	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂×D₄	#41×C₁₉	1	2	yes	complemented
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
463	SD₁₆	—	4	4	no	—
464	D₈	—	4	4	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	4	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	4	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	2	no	—
495	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₉	1	2	yes	—
497	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₁₉	1	2	yes	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	8	2	no	—
506	C₂³	—	8	2	no	—
507	C₂³	C₁₉×#120	1	2	yes	—
508	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
509	Q₈	—	2	2	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	4	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	8	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	D₄	—	16	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	8	4	no	—
549	C₂×C₄	—	8	4	no	—
550	C₂×C₄	C₁₉×#120	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
554	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	4	no	—
567	C₂²	—	16	2	no	—
568	C₂²	—	16	2	no	—
569	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
570	C₂²	C₁₉×#546	1	2	yes	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	2	no	—
579	C₄	C₁₉×#525	1	1	yes	characteristic
580	C₄	C₁₉×#535	1	1	yes	characteristic
581	C₄	C₁₉×#546	1	2	yes	—
582	C₂	—	2	1	no	—
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	2	no	—
586	C₂	—	8	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₁₉×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3508	C₂	semidirect
2. C₁₉×#3027	C₂	semidirect
3. C₁₉×#3021	C₂	semidirect
4. C₁₉×#2901	C₂	semidirect
5. C₁₉×#2031	C₂	semidirect
6. C₁₉×#2002	C₂	semidirect
7. C₁₉×#1914	C₂	semidirect
8. C₁₉×#1911	C₂	semidirect
9. C₁₉×#1910	C₂	semidirect
10. C₁₉×#1904	C₂	semidirect
11. C₁₉×#1827	C₂	semidirect
22. C₁₉×#533	C₂²	semidirect
24. C₂×C₁₉×#127	C₂²	semidirect
25. C₁₉×#518	C₂²	semidirect
26. C₁₉×#518	C₂²	semidirect
36. C₁₉×#418	C₂²	semidirect
38. C₂×C₁₉×#100	C₂²	semidirect
41. C₁₉×#344	C₂²	semidirect
42. C₁₉×#339	C₂²	semidirect
43. C₁₉×H(3,ℤ/4)	C₂²	semidirect
44. C₁₉×H(3,ℤ/4)	C₂²	semidirect
72. C₁₉×#127	D₄	semidirect
77. C₁₉×#124	D₄	semidirect
99. C₁₉×#117	D₄	semidirect
106. C₂×C₄²×C₁₉	D₄	semidirect
137. C₂×Q₈×C₁₉	#41	semidirect
159. C₂×D₄×C₁₉	#41	semidirect
204. #23990	C₁₉	direct (N × H)
263. #3508	C₂×C₁₉	semidirect
264. #3027	C₂×C₁₉	semidirect
265. #3021	C₂×C₁₉	semidirect
266. #2901	C₂×C₁₉	semidirect
267. #2031	C₂×C₁₉	semidirect
268. #2002	C₂×C₁₉	semidirect
269. #1914	C₂×C₁₉	semidirect
270. #1911	C₂×C₁₉	semidirect
271. #1910	C₂×C₁₉	semidirect
272. #1904	C₂×C₁₉	semidirect
273. #1827	C₂×C₁₉	semidirect
309. #533	C₂²×C₁₉	semidirect
311. C₂×#127	C₂²×C₁₉	semidirect
312. #518	C₂²×C₁₉	semidirect
313. #518	C₂²×C₁₉	semidirect
323. #418	C₂²×C₁₉	semidirect
325. C₂×#100	C₂²×C₁₉	semidirect
328. #344	C₂²×C₁₉	semidirect
329. #339	C₂²×C₁₉	semidirect
330. H(3,ℤ/4)	C₂²×C₁₉	semidirect
331. H(3,ℤ/4)	C₂²×C₁₉	semidirect
366. #127	D₄×C₁₉	semidirect
371. #124	D₄×C₁₉	semidirect
393. #117	D₄×C₁₉	semidirect
400. C₂×C₄²	D₄×C₁₉	semidirect
412. C₁₉	#23990	direct (N × H)
432. C₂×Q₈	#41×C₁₉	semidirect
454. C₂×D₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3508	2
C₁₉×#3027	2
C₁₉×#3021	2
C₁₉×#2901	2
C₁₉×#2031	2
C₁₉×#2002	2
C₁₉×#1914	2
C₁₉×#1911	2
C₁₉×#1910	2
C₁₉×#1904	2
C₁₉×#1827	2
#23990	19

Subgroups — C19×#23990 #18029949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23990 #18029949