Subgroups — C₁₉×#24001 #18029960

Order 4864.

1122 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3020	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2884	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2031	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2009	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1912	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1906	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1905	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1830	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₁₉×#575	C₂²	1	2	yes	—
14	C₂×C₁₉×#137	C₂²	1	2	yes	—
15	C₁₉×#557	—	2	2	no	—
16	C₁₉×#556	—	2	2	no	—
17	C₁₉×#552	—	2	4	no	—
18	C₁₉×#541	—	2	2	no	—
19	C₁₉×#536	C₂²	1	1	yes	characteristic
20	C₁₉×#536	C₂²	1	1	yes	characteristic
21	C₁₉×#533	—	2	2	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#519	C₂²	1	1	yes	characteristic
25	C₁₉×#519	C₂²	1	1	yes	characteristic
26	C₁₉×#519	C₂²	1	1	yes	characteristic
27	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#456	—	2	2	no	—
29	C₁₉×#456	—	2	2	no	—
30	C₁₉×#456	—	2	2	no	—
31	C₁₉×#454	—	2	2	no	—
32	C₁₉×#421	C₂²	1	2	yes	—
33	C₁₉×#421	C₂²	1	2	yes	—
34	C₂×C₁₉×#104	C₂²	1	2	yes	—
35	C₁₉×#419	C₂²	1	2	yes	—
36	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
38	C₁₉×#410	—	2	4	no	—
39	C₁₉×#410	C₂²	1	2	yes	—
40	C₁₉×#410	C₂²	1	2	yes	—
41	C₁₉×#344	C₂²	1	2	yes	—
42	C₁₉×#344	C₂²	1	2	yes	—
43	C₁₉×#339	C₂²	1	2	yes	—
44	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	—
45	C₁₉×2₋¹⁺⁴	—	2	2	no	—
46	C₁₉×2₋¹⁺⁴	—	2	2	no	—
47	C₁₉×2₋¹⁺⁴	—	4	2	no	—
48	C₂×#41×C₁₉	—	2	2	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×Q₈×C₁₉	—	2	2	no	—
53	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×#137	—	2	4	no	—
56	C₁₉×#137	—	2	2	no	—
57	C₁₉×#137	—	2	2	no	—
58	C₁₉×#137	—	4	2	no	—
59	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
60	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
61	C₁₉×#135	—	4	2	no	—
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×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	2	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
70	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
72	C₁₉×#126	—	2	4	no	—
73	C₁₉×#126	—	2	4	no	—
74	C₁₉×#125	—	2	4	no	—
75	C₁₉×#125	—	2	4	no	—
76	C₁₉×#125	—	2	4	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	D₄	1	2	yes	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₄×Q₈×C₁₉	—	2	4	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	—	2	2	no	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	4	2	no	—
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₁₉×#117	—	2	4	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	D₄	1	4	yes	—
101	C₁₉×#117	C₂³	1	2	yes	—
102	C₁₉×#117	C₂³	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₁₉×#117	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
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×#103	—	4	2	no	—
113	C₁₉×#101	—	2	2	no	—
114	C₁₉×#101	—	2	2	no	—
115	C₁₉×#99	—	2	4	no	—
116	C₁₉×#99	—	2	4	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	4	4	no	—
124	#41×C₁₉	—	4	4	no	—
125	#41×C₁₉	—	4	4	no	—
126	#41×C₁₉	—	4	4	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	4	4	no	—
135	C₂×Q₈×C₁₉	—	4	4	no	—
136	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₁₉	#41	1	2	yes	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₉	#41	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	1	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	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₁₉	—	4	4	no	—
155	Q₁₆×C₁₉	—	4	2	no	—
156	SD₁₆×C₁₉	—	4	4	no	—
157	SD₁₆×C₁₉	—	4	2	no	—
158	SD₁₆×C₁₉	—	4	2	no	—
159	D₈×C₁₉	—	4	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	4	no	—
183	C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂²⋊C₄×C₁₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	4	no	—
190	C₄²×C₁₉	—	2	4	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	2	no	—
195	C₄²×C₁₉	—	4	2	no	—
196	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	C₂×D₄	1	2	yes	—
199	#24001	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	2	no	—
202	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₉	—	2	4	no	—
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	2	4	no	—
206	Q₈×C₁₉	—	2	2	no	—
207	Q₈×C₁₉	—	2	2	no	—
208	Q₈×C₁₉	—	2	2	no	—
209	Q₈×C₁₉	—	4	4	no	—
210	Q₈×C₁₉	—	4	4	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	2	2	no	—
213	D₄×C₁₉	—	2	2	no	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	4	1	no	—
219	D₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
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	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	8	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	#120	1	4	yes	—
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
243	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₁₉	—	4	2	no	—
245	C₈×C₁₉	—	4	2	no	—
246	#3509	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#3020	C₂×C₁₉	1	1	yes	characteristic
248	C₂×#456	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2884	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#2031	C₂×C₁₉	1	2	yes	complemented
251	#2009	C₂×C₁₉	1	2	yes	complemented
252	#1912	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1906	C₂×C₁₉	1	2	yes	complemented
254	#1905	C₂×C₁₉	1	2	yes	complemented
255	#1886	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1830	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂²×C₁₉	—	4	1	no	—
258	C₂²×C₁₉	—	4	2	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	1	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₉	#525	1	1	yes	characteristic
264	C₂²×C₁₉	#535	1	1	yes	characteristic
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	2	4	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	8	2	no	—
275	C₄×C₁₉	#546	1	2	yes	—
276	C₄×C₁₉	#546	1	2	yes	—
277	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
278	#575	C₂²×C₁₉	1	2	yes	—
279	C₂×#137	C₂²×C₁₉	1	2	yes	—
280	#557	—	2	2	no	—
281	#556	—	2	2	no	—
282	#552	—	2	4	no	—
283	#541	—	2	2	no	—
284	#536	C₂²×C₁₉	1	1	yes	characteristic
285	#536	C₂²×C₁₉	1	1	yes	characteristic
286	#533	—	2	2	no	—
287	#533	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
289	#519	C₂²×C₁₉	1	1	yes	characteristic
290	#519	C₂²×C₁₉	1	1	yes	characteristic
291	#519	C₂²×C₁₉	1	1	yes	characteristic
292	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
293	#456	—	2	2	no	—
294	#456	—	2	2	no	—
295	#456	—	2	2	no	—
296	#454	—	2	2	no	—
297	#421	C₂²×C₁₉	1	2	yes	—
298	#421	C₂²×C₁₉	1	2	yes	—
299	C₂×#104	C₂²×C₁₉	1	2	yes	—
300	#419	C₂²×C₁₉	1	2	yes	—
301	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
303	#410	—	2	4	no	—
304	#410	C₂²×C₁₉	1	2	yes	—
305	#410	C₂²×C₁₉	1	2	yes	—
306	#344	C₂²×C₁₉	1	2	yes	—
307	#344	C₂²×C₁₉	1	2	yes	—
308	#339	C₂²×C₁₉	1	2	yes	—
309	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	—	2	1	no	—
312	C₂×C₁₉	—	2	1	no	—
313	C₂×C₁₉	—	8	1	no	—
314	C₂×C₁₉	—	8	2	no	—
315	C₂×C₁₉	#2404	1	1	yes	characteristic
316	2₋¹⁺⁴	—	2	2	no	—
317	2₋¹⁺⁴	—	2	2	no	—
318	2₋¹⁺⁴	—	4	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×#41	C₂³×C₁₉	1	2	yes	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
326	#137	—	2	4	no	—
327	#137	—	2	2	no	—
328	#137	—	2	2	no	—
329	#137	—	4	2	no	—
330	AGL(1,ℤ/8)	—	2	2	no	—
331	AGL(1,ℤ/8)	—	2	2	no	—
332	#135	—	4	2	no	—
333	C₂×Q₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
336	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
341	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
342	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
343	#126	—	2	4	no	—
344	#126	—	2	4	no	—
345	#125	—	2	4	no	—
346	#125	—	2	4	no	—
347	#125	—	2	4	no	—
348	#125	—	2	1	no	—
349	#124	—	2	1	no	—
350	#124	D₄×C₁₉	1	2	yes	—
351	#123	—	2	2	no	—
352	#123	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	4	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	4	2	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	2	no	—
367	#117	—	2	4	no	—
368	#117	—	2	2	no	—
369	#117	—	2	1	no	—
370	#117	—	2	2	no	—
371	#117	D₄×C₁₉	1	4	yes	—
372	#117	C₂³×C₁₉	1	2	yes	—
373	#117	C₂³×C₁₉	1	1	yes	characteristic
374	#117	C₂³×C₁₉	1	1	yes	characteristic
375	#117	C₂³×C₁₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	#104	—	2	2	no	—
380	#104	—	2	2	no	—
381	#104	—	2	4	no	—
382	#104	—	4	2	no	—
383	#103	—	4	2	no	—
384	#101	—	2	2	no	—
385	#101	—	2	2	no	—
386	#99	—	2	4	no	—
387	#99	—	2	4	no	—
388	C₁₉	#24001	1	1	yes	characteristic, direct product factor, Sylow
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	4	4	no	—
396	#41	—	4	4	no	—
397	#41	—	4	4	no	—
398	#41	—	4	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
411	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
412	C₂×Q₈	#41×C₁₉	1	2	yes	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂×D₄	#41×C₁₉	1	2	yes	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
426	Q₁₆	—	4	4	no	—
427	Q₁₆	—	4	2	no	—
428	SD₁₆	—	4	4	no	—
429	SD₁₆	—	4	2	no	—
430	SD₁₆	—	4	2	no	—
431	D₈	—	4	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
459	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	4	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	4	2	no	—
468	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₉	1	2	yes	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	4	4	no	—
481	Q₈	—	4	4	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	C₁₉×#120	1	4	yes	—
511	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
514	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
515	C₈	—	4	2	no	—
516	C₈	—	4	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	8	2	no	—
522	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
523	C₂²	C₁₉×#525	1	1	yes	characteristic
524	C₂²	C₁₉×#535	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	—	8	2	no	—
535	C₄	C₁₉×#546	1	2	yes	—
536	C₄	C₁₉×#546	1	2	yes	—
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	8	1	no	—
541	C₂	—	8	2	no	—
542	C₂	C₁₉×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3020	C₂
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×#3509	C₂	semidirect
3. C₂×C₁₉×#456	C₂	semidirect
4. C₁₉×#2884	C₂	semidirect
5. C₁₉×#2031	C₂	semidirect
6. C₁₉×#2009	C₂	semidirect
7. C₁₉×#1912	C₂	semidirect
8. C₁₉×#1906	C₂	semidirect
9. C₁₉×#1905	C₂	semidirect
10. C₁₉×#1886	C₂	semidirect
11. C₁₉×#1830	C₂	semidirect
199. #24001	C₁₉	direct (N × H)
246. #3509	C₂×C₁₉	semidirect
248. C₂×#456	C₂×C₁₉	semidirect
249. #2884	C₂×C₁₉	semidirect
250. #2031	C₂×C₁₉	semidirect
251. #2009	C₂×C₁₉	semidirect
252. #1912	C₂×C₁₉	semidirect
253. #1906	C₂×C₁₉	semidirect
254. #1905	C₂×C₁₉	semidirect
255. #1886	C₂×C₁₉	semidirect
256. #1830	C₂×C₁₉	semidirect
388. C₁₉	#24001	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3509	2
C₁₉×#3020	2
C₂×C₁₉×#456	2
C₁₉×#2884	2
C₁₉×#2031	2
C₁₉×#2009	2
C₁₉×#1912	2
C₁₉×#1906	2
C₁₉×#1905	2
C₁₉×#1886	2
C₁₉×#1830	2
#24001	19

Subgroups — C19×#24001 #18029960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24001 #18029960