Subgroups — C₁₉×#23998 #18029957

Order 4864.

1266 conjugacy classes of subgroups.

The subgroup lattice has 586 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×#3019	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2883	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2031	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2008	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1911	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1906	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1904	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1887	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1829	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₁₉×#575	C₂²	1	2	yes	—
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
21	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#532	—	2	2	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#518	C₂²	1	1	yes	characteristic
25	C₁₉×#518	C₂²	1	1	yes	characteristic
26	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#455	—	2	2	no	—
29	C₁₉×#453	—	2	2	no	—
30	C₁₉×#453	—	2	2	no	—
31	C₁₉×#453	—	2	2	no	—
32	C₁₉×#421	C₂²	1	2	yes	—
33	C₁₉×#421	C₂²	1	2	yes	complemented
34	C₂×C₁₉×#104	C₂²	1	2	yes	—
35	C₁₉×#418	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
38	C₁₉×#410	C₂²	1	2	yes	—
39	C₁₉×#410	C₂²	1	2	yes	—
40	C₂×C₁₉×#99	—	2	4	no	—
41	C₁₉×#344	C₂²	1	2	yes	complemented
42	C₁₉×#344	C₂²	1	2	yes	complemented
43	C₁₉×#339	C₂²	1	2	yes	complemented
44	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	C₁₉×H(5,𝔽₂)	—	2	2	no	—
46	C₁₉×H(5,𝔽₂)	—	2	2	no	—
47	C₁₉×H(5,𝔽₂)	—	4	2	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×#41×C₁₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×#137	—	2	2	no	—
58	C₁₉×#137	—	2	2	no	—
59	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
60	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
61	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
62	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
63	C₁₉×#135	—	4	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×D₈×C₁₉	—	2	2	no	—
66	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×#127	—	2	2	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	D₄	1	2	yes	—
72	C₁₉×#127	D₄	1	2	yes	—
73	C₁₉×#127	D₄	1	2	yes	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#124	—	2	4	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	D₄	1	2	yes	—
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×#120	—	2	2	no	—
87	C₁₉×#120	—	2	2	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	4	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	4	2	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	C₂³	1	2	yes	—
100	C₁₉×#117	C₂³	1	1	yes	characteristic
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₁₉×#117	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#104	—	2	2	no	—
109	C₁₉×#104	—	2	2	no	—
110	C₁₉×#104	—	2	4	no	—
111	C₁₉×#104	—	4	2	no	—
112	C₁₉×#102	—	4	2	no	—
113	C₁₉×#100	—	2	2	no	—
114	C₁₉×#100	—	2	2	no	—
115	C₁₉×#99	—	2	4	no	—
116	C₁₉×#99	—	2	4	no	—
117	C₂⁴×C₁₉	—	2	2	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	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	4	4	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	—	8	8	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₉	#41	1	2	yes	complemented
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	2	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	4	4	no	—
145	C₂×D₄×C₁₉	—	4	4	no	—
146	C₂×D₄×C₁₉	—	4	4	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	8	4	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₉	#41	1	2	yes	complemented
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	4	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	4	2	no	—
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	Q₁₆×C₁₉	—	4	2	no	—
164	SD₁₆×C₁₉	—	4	4	no	—
165	SD₁₆×C₁₉	—	4	2	no	—
166	SD₁₆×C₁₉	—	4	2	no	—
167	D₈×C₁₉	—	4	4	no	—
168	D₈×C₁₉	—	4	2	no	—
169	M₁₆×C₁₉	—	2	2	no	—
170	M₁₆×C₁₉	—	2	2	no	—
171	M₁₆×C₁₉	—	2	2	no	—
172	M₁₆×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₉	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	2	no	—
191	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₄²×C₁₉	—	2	2	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₉	C₂×D₄	1	2	yes	—
201	#23998	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	—	8	2	no	—
211	C₂³×C₁₉	—	8	2	no	—
212	C₂³×C₁₉	—	16	2	no	—
213	C₂³×C₁₉	#120	1	4	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	4	no	—
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	2	no	—
224	D₄×C₁₉	—	2	2	no	—
225	D₄×C₁₉	—	4	8	no	—
226	D₄×C₁₉	—	4	8	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	8	4	no	—
233	D₄×C₁₉	—	8	4	no	—
234	D₄×C₁₉	—	8	4	no	—
235	C₂×C₄×C₁₉	—	2	1	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	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	8	4	no	—
250	C₂×C₄×C₁₉	—	8	4	no	—
251	C₂×C₄×C₁₉	—	16	2	no	—
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
256	C₈×C₁₉	—	4	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	#3508	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#3019	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂×#453	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2883	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#2031	C₂×C₁₉	1	2	yes	complemented
263	#2008	C₂×C₁₉	1	2	yes	complemented
264	#1911	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1906	C₂×C₁₉	1	2	yes	complemented
266	#1904	C₂×C₁₉	1	2	yes	complemented
267	#1887	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1829	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₁₉	—	2	4	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	4	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	8	2	no	—
278	C₂²×C₁₉	—	8	2	no	—
279	C₂²×C₁₉	—	8	2	no	—
280	C₂²×C₁₉	—	16	1	no	—
281	C₂²×C₁₉	—	16	1	no	—
282	C₂²×C₁₉	—	16	4	no	—
283	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
284	C₂²×C₁₉	#525	1	1	yes	characteristic
285	C₂²×C₁₉	#535	1	1	yes	characteristic
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₄×C₁₉	#546	1	2	yes	—
295	C₄×C₁₉	#546	1	2	yes	—
296	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
297	#575	C₂²×C₁₉	1	2	yes	—
298	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
299	#559	—	2	2	no	—
300	#550	—	2	2	no	—
301	#546	—	2	4	no	—
302	#540	—	2	2	no	—
303	#535	C₂²×C₁₉	1	1	yes	characteristic
304	#535	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	#532	—	2	2	no	—
307	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
308	#518	C₂²×C₁₉	1	1	yes	characteristic
309	#518	C₂²×C₁₉	1	1	yes	characteristic
310	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#455	—	2	2	no	—
313	#453	—	2	2	no	—
314	#453	—	2	2	no	—
315	#453	—	2	2	no	—
316	#421	C₂²×C₁₉	1	2	yes	—
317	#421	C₂²×C₁₉	1	2	yes	complemented
318	C₂×#104	C₂²×C₁₉	1	2	yes	—
319	#418	C₂²×C₁₉	1	2	yes	complemented
320	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
322	#410	C₂²×C₁₉	1	2	yes	—
323	#410	C₂²×C₁₉	1	2	yes	—
324	C₂×#99	—	2	4	no	—
325	#344	C₂²×C₁₉	1	2	yes	complemented
326	#344	C₂²×C₁₉	1	2	yes	complemented
327	#339	C₂²×C₁₉	1	2	yes	complemented
328	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	complemented
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	4	4	no	—
333	C₂×C₁₉	—	8	1	no	—
334	C₂×C₁₉	—	8	2	no	—
335	C₂×C₁₉	—	8	2	no	—
336	C₂×C₁₉	#2404	1	1	yes	characteristic
337	H(5,𝔽₂)	—	2	2	no	—
338	H(5,𝔽₂)	—	2	2	no	—
339	H(5,𝔽₂)	—	4	2	no	—
340	C₂×#41	—	2	4	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×#41	C₂³×C₁₉	1	2	yes	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
349	#137	—	2	2	no	—
350	#137	—	2	2	no	—
351	AGL(1,ℤ/8)	—	2	4	no	—
352	AGL(1,ℤ/8)	—	2	2	no	—
353	AGL(1,ℤ/8)	—	2	2	no	—
354	AGL(1,ℤ/8)	—	4	2	no	—
355	#135	—	4	2	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×D₈	—	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	D₄×C₁₉	1	2	yes	—
364	#127	D₄×C₁₉	1	2	yes	—
365	#127	D₄×C₁₉	1	2	yes	—
366	#125	—	2	1	no	—
367	#124	—	2	4	no	—
368	#124	—	2	1	no	—
369	#124	D₄×C₁₉	1	2	yes	—
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	#121	—	2	4	no	—
374	#121	—	2	4	no	—
375	#121	—	2	4	no	—
376	#121	—	2	2	no	—
377	#121	—	2	2	no	—
378	#120	—	2	2	no	—
379	#120	—	2	2	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	4	2	no	—
390	#117	—	2	1	no	—
391	#117	C₂³×C₁₉	1	2	yes	—
392	#117	C₂³×C₁₉	1	1	yes	characteristic
393	#117	C₂³×C₁₉	1	1	yes	characteristic
394	#117	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	2	no	—
397	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
400	#104	—	2	2	no	—
401	#104	—	2	2	no	—
402	#104	—	2	4	no	—
403	#104	—	4	2	no	—
404	#102	—	4	2	no	—
405	#100	—	2	2	no	—
406	#100	—	2	2	no	—
407	#99	—	2	4	no	—
408	#99	—	2	4	no	—
409	C₁₉	#23998	1	1	yes	characteristic, direct product factor, Sylow
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	1	no	—
412	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	4	4	no	—
420	#41	—	4	4	no	—
421	#41	—	8	8	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×Q₈	#41×C₁₉	1	2	yes	complemented
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	8	4	no	—
442	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
446	C₂×D₄	#41×C₁₉	1	2	yes	complemented
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	Q₁₆	—	4	2	no	—
457	SD₁₆	—	4	4	no	—
458	SD₁₆	—	4	2	no	—
459	SD₁₆	—	4	2	no	—
460	D₈	—	4	4	no	—
461	D₈	—	4	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
485	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	2	no	—
491	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄²	C₂×D₄×C₁₉	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	16	2	no	—
505	C₂³	C₁₉×#120	1	4	yes	—
506	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	8	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	2	no	—
524	D₄	—	8	4	no	—
525	D₄	—	8	4	no	—
526	D₄	—	8	4	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	—	8	4	no	—
543	C₂×C₄	—	16	2	no	—
544	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
547	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
548	C₈	—	4	2	no	—
549	C₈	—	4	2	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	16	1	no	—
562	C₂²	—	16	1	no	—
563	C₂²	—	16	4	no	—
564	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
565	C₂²	C₁₉×#525	1	1	yes	characteristic
566	C₂²	C₁₉×#535	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	2	no	—
575	C₄	C₁₉×#546	1	2	yes	—
576	C₄	C₁₉×#546	1	2	yes	—
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	4	4	no	—
581	C₂	—	8	2	no	—
582	C₂	—	8	1	no	—
583	C₂	—	8	2	no	—
584	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×#3019	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#2883	C₂	semidirect
5. C₁₉×#2031	C₂	semidirect
6. C₁₉×#2008	C₂	semidirect
7. C₁₉×#1911	C₂	semidirect
8. C₁₉×#1906	C₂	semidirect
9. C₁₉×#1904	C₂	semidirect
10. C₁₉×#1887	C₂	semidirect
11. C₁₉×#1829	C₂	semidirect
20. C₁₉×#535	C₂²	semidirect
21. C₁₉×#533	C₂²	semidirect
26. C₁₉×#518	C₂²	semidirect
27. C₄×#41×C₁₉	C₂²	semidirect
33. C₁₉×#421	C₂²	semidirect
35. C₁₉×#418	C₂²	semidirect
41. C₁₉×#344	C₂²	semidirect
42. C₁₉×#344	C₂²	semidirect
43. C₁₉×#339	C₂²	semidirect
44. C₁₉×H(3,ℤ/4)	C₂²	semidirect
131. C₂×Q₈×C₁₉	#41	semidirect
153. C₂×D₄×C₁₉	#41	semidirect
201. #23998	C₁₉	direct (N × H)
258. #3508	C₂×C₁₉	semidirect
259. #3019	C₂×C₁₉	semidirect
260. C₂×#453	C₂×C₁₉	semidirect
261. #2883	C₂×C₁₉	semidirect
262. #2031	C₂×C₁₉	semidirect
263. #2008	C₂×C₁₉	semidirect
264. #1911	C₂×C₁₉	semidirect
265. #1906	C₂×C₁₉	semidirect
266. #1904	C₂×C₁₉	semidirect
267. #1887	C₂×C₁₉	semidirect
268. #1829	C₂×C₁₉	semidirect
304. #535	C₂²×C₁₉	semidirect
305. #533	C₂²×C₁₉	semidirect
310. #518	C₂²×C₁₉	semidirect
311. C₄×#41	C₂²×C₁₉	semidirect
317. #421	C₂²×C₁₉	semidirect
319. #418	C₂²×C₁₉	semidirect
325. #344	C₂²×C₁₉	semidirect
326. #344	C₂²×C₁₉	semidirect
327. #339	C₂²×C₁₉	semidirect
328. H(3,ℤ/4)	C₂²×C₁₉	semidirect
409. C₁₉	#23998	direct (N × H)
424. C₂×Q₈	#41×C₁₉	semidirect
446. 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×#3019	2
C₂×C₁₉×#453	2
C₁₉×#2883	2
C₁₉×#2031	2
C₁₉×#2008	2
C₁₉×#1911	2
C₁₉×#1906	2
C₁₉×#1904	2
C₁₉×#1887	2
C₁₉×#1829	2
#23998	19

Subgroups — C19×#23998 #18029957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23998 #18029957