Subgroups — C₁₉×#24675 #18030634

Order 4864.

764 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3040	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2051	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2019	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#464	—	2	1	no	—
25	C₁₉×#464	—	2	1	no	—
26	C₁₉×#464	—	2	1	no	—
27	C₁₉×#464	—	2	1	no	—
28	C₁₉×#464	—	2	1	no	—
29	C₁₉×#464	—	2	1	no	—
30	C₁₉×#463	—	2	1	no	—
31	C₁₉×#463	—	2	1	no	—
32	C₁₉×#441	—	2	1	no	—
33	C₁₉×#440	—	2	1	no	—
34	C₄×Q₁₆×C₁₉	—	2	1	no	—
35	C₄×SD₁₆×C₁₉	—	2	1	no	—
36	C₁₉×#433	—	2	1	no	—
37	C₁₉×#433	—	2	1	no	—
38	C₁₉×#432	—	2	1	no	—
39	C₁₉×#431	—	2	1	no	—
40	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
42	C₁₉×#428	C₂²	1	1	yes	characteristic
43	C₁₉×#423	C₂²	1	1	yes	characteristic
44	C₁₉×#423	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#419	C₂²	1	1	yes	characteristic
47	C₁₉×#419	C₂²	1	1	yes	characteristic
48	C₁₉×#418	C₂²	1	1	yes	characteristic
49	C₁₉×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
58	C₁₉×#408	C₂²	1	1	yes	characteristic
59	C₁₉×#408	C₂²	1	1	yes	characteristic
60	C₁₉×#405	C₂²	1	1	yes	characteristic
61	C₁₉×#405	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#343	C₂²	1	1	yes	characteristic
65	C₁₉×#341	C₂²	1	1	yes	characteristic
66	C₁₉×#341	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#137	—	2	2	no	—
72	C₁₉×#137	—	2	2	no	—
73	C₁₉×#137	—	4	1	no	—
74	C₁₉×#137	—	4	1	no	—
75	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
76	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
77	C₂×Q₁₆×C₁₉	—	2	1	no	—
78	C₂×Q₁₆×C₁₉	—	2	1	no	—
79	C₂×Q₁₆×C₁₉	—	2	2	no	—
80	C₂×Q₁₆×C₁₉	—	2	1	no	—
81	C₂×Q₁₆×C₁₉	—	2	1	no	—
82	C₂×Q₁₆×C₁₉	—	4	1	no	—
83	C₂×SD₁₆×C₁₉	—	2	1	no	—
84	C₂×SD₁₆×C₁₉	—	2	1	no	—
85	C₂×SD₁₆×C₁₉	—	2	2	no	—
86	C₂×SD₁₆×C₁₉	—	2	1	no	—
87	C₂×SD₁₆×C₁₉	—	2	1	no	—
88	C₂×SD₁₆×C₁₉	—	2	1	no	—
89	C₂×SD₁₆×C₁₉	—	4	1	no	—
90	C₂×D₈×C₁₉	—	2	1	no	—
91	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#124	—	2	1	no	—
100	C₁₉×#124	—	2	1	no	—
101	C₁₉×#124	—	2	1	no	—
102	C₁₉×#124	—	2	1	no	—
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	—	2	1	no	—
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	—	2	1	no	—
111	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
112	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
113	C₁₉×#117	—	2	1	no	—
114	C₁₉×#117	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	—	2	1	no	—
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₁₉×#108	—	4	1	no	—
123	C₁₉×#108	—	4	1	no	—
124	C₁₉×#107	—	2	1	no	—
125	C₁₉×#106	—	2	1	no	—
126	C₁₉×C₄⋊C₈	—	2	1	no	—
127	C₁₉×C₄⋊C₈	—	2	1	no	—
128	C₁₉×C₄⋊C₈	—	2	1	no	—
129	C₁₉×C₄⋊C₈	—	2	1	no	—
130	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
131	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
132	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
133	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#103	—	2	1	no	—
140	C₁₉×#103	—	2	1	no	—
141	C₁₉×#102	—	2	1	no	—
142	C₁₉×#102	—	2	1	no	—
143	C₁₉×#102	—	2	1	no	—
144	C₁₉×#102	—	2	1	no	—
145	C₁₉×#102	—	2	1	no	—
146	C₁₉×#101	—	2	2	no	—
147	C₁₉×#101	—	4	1	no	—
148	C₁₉×#101	—	4	1	no	—
149	C₁₉×#101	—	4	1	no	—
150	C₁₉×#100	—	2	2	no	—
151	C₁₉×#100	—	4	1	no	—
152	C₁₉×C₂²⋊C₈	—	2	1	no	—
153	C₁₉×C₂²⋊C₈	—	2	1	no	—
154	C₁₉×C₂²⋊C₈	—	2	1	no	—
155	C₁₉×C₂²⋊C₈	—	2	1	no	—
156	C₁₉×#97	—	2	1	no	—
157	C₁₉×#97	—	2	1	no	—
158	C₁₉×#97	—	2	1	no	—
159	C₄×C₈×C₁₉	—	2	1	no	—
160	C₄×C₈×C₁₉	—	2	1	no	—
161	C₄×C₈×C₁₉	—	2	1	no	—
162	C₂⁴×C₁₉	—	2	1	no	—
163	#41×C₁₉	—	2	1	no	—
164	#41×C₁₉	—	2	1	no	—
165	#41×C₁₉	—	2	1	no	—
166	#41×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	2	1	no	—
171	C₂×Q₈×C₁₉	—	2	1	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₁₉	#41	1	2	yes	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
197	Q₁₆×C₁₉	—	2	4	no	—
198	Q₁₆×C₁₉	—	4	2	no	—
199	Q₁₆×C₁₉	—	4	2	no	—
200	Q₁₆×C₁₉	—	4	2	no	—
201	SD₁₆×C₁₉	—	2	4	no	—
202	SD₁₆×C₁₉	—	4	2	no	—
203	SD₁₆×C₁₉	—	4	2	no	—
204	SD₁₆×C₁₉	—	4	2	no	—
205	SD₁₆×C₁₉	—	4	2	no	—
206	D₈×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	2	1	no	—
208	M₁₆×C₁₉	—	2	1	no	—
209	M₁₆×C₁₉	—	2	1	no	—
210	M₁₆×C₁₉	—	2	1	no	—
211	M₁₆×C₁₉	—	2	1	no	—
212	M₁₆×C₁₉	—	2	1	no	—
213	M₁₆×C₁₉	—	2	1	no	—
214	M₁₆×C₁₉	—	2	1	no	—
215	M₁₆×C₁₉	—	2	1	no	—
216	M₁₆×C₁₉	—	2	1	no	—
217	M₁₆×C₁₉	—	2	1	no	—
218	M₁₆×C₁₉	#41	1	2	yes	—
219	C₂×C₈×C₁₉	—	2	1	no	—
220	C₂×C₈×C₁₉	—	2	1	no	—
221	C₂×C₈×C₁₉	—	2	1	no	—
222	C₂×C₈×C₁₉	—	2	1	no	—
223	C₂×C₈×C₁₉	—	2	1	no	—
224	C₂×C₈×C₁₉	—	2	1	no	—
225	C₂×C₈×C₁₉	—	2	1	no	—
226	C₂×C₈×C₁₉	—	2	1	no	—
227	C₂×C₈×C₁₉	—	2	1	no	—
228	C₂×C₈×C₁₉	—	2	1	no	—
229	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	4	1	no	—
238	C₄⋊C₄×C₁₉	—	4	1	no	—
239	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂²⋊C₄×C₁₉	—	2	1	no	—
242	C₂²⋊C₄×C₁₉	—	2	1	no	—
243	C₂²⋊C₄×C₁₉	—	2	1	no	—
244	C₂²⋊C₄×C₁₉	—	4	1	no	—
245	C₂²⋊C₄×C₁₉	—	4	1	no	—
246	C₂²⋊C₄×C₁₉	—	4	1	no	—
247	C₂²⋊C₄×C₁₉	—	4	1	no	—
248	C₄²×C₁₉	—	2	1	no	—
249	C₄²×C₁₉	—	2	1	no	—
250	C₄²×C₁₉	—	2	1	no	—
251	C₄²×C₁₉	—	4	1	no	—
252	C₄²×C₁₉	—	4	1	no	—
253	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
257	#24675	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₁₉	—	2	1	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	—	4	1	no	—
261	C₂³×C₁₉	—	4	1	no	—
262	C₂³×C₁₉	—	8	1	no	—
263	C₂³×C₁₉	—	8	1	no	—
264	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
265	Q₈×C₁₉	—	2	2	no	—
266	Q₈×C₁₉	—	2	1	no	—
267	Q₈×C₁₉	—	2	1	no	—
268	Q₈×C₁₉	—	2	2	no	—
269	Q₈×C₁₉	—	4	1	no	—
270	Q₈×C₁₉	—	4	1	no	—
271	Q₈×C₁₉	—	4	1	no	—
272	Q₈×C₁₉	—	4	1	no	—
273	Q₈×C₁₉	—	4	1	no	—
274	Q₈×C₁₉	—	4	1	no	—
275	D₄×C₁₉	—	2	1	no	—
276	D₄×C₁₉	—	2	1	no	—
277	D₄×C₁₉	—	4	1	no	—
278	D₄×C₁₉	—	4	1	no	—
279	D₄×C₁₉	—	4	1	no	—
280	D₄×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	2	1	no	—
284	C₂×C₄×C₁₉	—	2	1	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	2	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	8	1	no	—
299	C₂×C₄×C₁₉	—	8	1	no	—
300	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
304	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₁₉	—	2	2	no	—
311	C₈×C₁₉	—	2	1	no	—
312	C₈×C₁₉	—	2	1	no	—
313	C₈×C₁₉	—	2	1	no	—
314	C₈×C₁₉	—	2	1	no	—
315	C₈×C₁₉	—	4	1	no	—
316	C₈×C₁₉	—	4	1	no	—
317	C₈×C₁₉	—	4	1	no	—
318	C₈×C₁₉	—	4	1	no	—
319	C₈×C₁₉	—	4	1	no	—
320	#3040	C₂×C₁₉	1	1	yes	characteristic
321	C₂×#464	C₂×C₁₉	1	1	yes	characteristic, complemented
322	C₄×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#2925	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2052	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2051	C₂×C₁₉	1	1	yes	characteristic
326	#2020	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2019	C₂×C₁₉	1	1	yes	characteristic
328	#1979	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1977	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1967	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1931	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
335	C₂²×C₁₉	—	2	1	no	—
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	16	1	no	—
344	C₂²×C₁₉	—	16	1	no	—
345	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
346	C₂²×C₁₉	#553	1	1	yes	characteristic
347	C₂²×C₁₉	#555	1	1	yes	characteristic
348	C₄×C₁₉	—	2	1	no	—
349	C₄×C₁₉	—	2	1	no	—
350	C₄×C₁₉	—	2	1	no	—
351	C₄×C₁₉	—	2	1	no	—
352	C₄×C₁₉	—	4	1	no	—
353	C₄×C₁₉	—	4	2	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	8	1	no	—
357	C₄×C₁₉	—	8	1	no	—
358	C₄×C₁₉	#525	1	1	yes	characteristic
359	C₄×C₁₉	#535	1	1	yes	characteristic
360	C₄×C₁₉	#546	1	1	yes	characteristic
361	C₄×C₁₉	#550	1	1	yes	characteristic
362	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
365	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
366	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
368	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
370	#464	—	2	1	no	—
371	#464	—	2	1	no	—
372	#464	—	2	1	no	—
373	#464	—	2	1	no	—
374	#464	—	2	1	no	—
375	#464	—	2	1	no	—
376	#463	—	2	1	no	—
377	#463	—	2	1	no	—
378	#441	—	2	1	no	—
379	#440	—	2	1	no	—
380	C₄×Q₁₆	—	2	1	no	—
381	C₄×SD₁₆	—	2	1	no	—
382	#433	—	2	1	no	—
383	#433	—	2	1	no	—
384	#432	—	2	1	no	—
385	#431	—	2	1	no	—
386	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
388	#428	C₂²×C₁₉	1	1	yes	characteristic
389	#423	C₂²×C₁₉	1	1	yes	characteristic
390	#423	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
392	#419	C₂²×C₁₉	1	1	yes	characteristic
393	#419	C₂²×C₁₉	1	1	yes	characteristic
394	#418	C₂²×C₁₉	1	1	yes	characteristic
395	#417	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
400	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
404	#408	C₂²×C₁₉	1	1	yes	characteristic
405	#408	C₂²×C₁₉	1	1	yes	characteristic
406	#405	C₂²×C₁₉	1	1	yes	characteristic
407	#405	C₂²×C₁₉	1	1	yes	characteristic
408	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
409	#343	C₂²×C₁₉	1	1	yes	characteristic
410	#343	C₂²×C₁₉	1	1	yes	characteristic
411	#341	C₂²×C₁₉	1	1	yes	characteristic
412	#341	C₂²×C₁₉	1	1	yes	characteristic
413	C₂×C₁₉	—	2	1	no	—
414	C₂×C₁₉	—	2	1	no	—
415	C₂×C₁₉	—	8	1	no	—
416	C₂×C₁₉	—	16	1	no	—
417	C₂×C₁₉	#2414	1	1	yes	characteristic
418	C₂×C₁₉	#3067	1	1	yes	characteristic
419	C₂×C₁₉	#3069	1	1	yes	characteristic
420	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	#137	—	2	2	no	—
425	#137	—	2	2	no	—
426	#137	—	4	1	no	—
427	#137	—	4	1	no	—
428	AGL(1,ℤ/8)	—	4	1	no	—
429	AGL(1,ℤ/8)	—	4	1	no	—
430	C₂×Q₁₆	—	2	1	no	—
431	C₂×Q₁₆	—	2	1	no	—
432	C₂×Q₁₆	—	2	2	no	—
433	C₂×Q₁₆	—	2	1	no	—
434	C₂×Q₁₆	—	2	1	no	—
435	C₂×Q₁₆	—	4	1	no	—
436	C₂×SD₁₆	—	2	1	no	—
437	C₂×SD₁₆	—	2	1	no	—
438	C₂×SD₁₆	—	2	2	no	—
439	C₂×SD₁₆	—	2	1	no	—
440	C₂×SD₁₆	—	2	1	no	—
441	C₂×SD₁₆	—	2	1	no	—
442	C₂×SD₁₆	—	4	1	no	—
443	C₂×D₈	—	2	1	no	—
444	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
452	#124	—	2	1	no	—
453	#124	—	2	1	no	—
454	#124	—	2	1	no	—
455	#124	—	2	1	no	—
456	C₄×Q₈	—	2	1	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×Q₈	—	2	1	no	—
459	C₄×Q₈	—	2	1	no	—
460	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
461	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
465	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
466	#117	—	2	1	no	—
467	#117	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
475	#108	—	4	1	no	—
476	#108	—	4	1	no	—
477	#107	—	2	1	no	—
478	#106	—	2	1	no	—
479	C₄⋊C₈	—	2	1	no	—
480	C₄⋊C₈	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	C₄⋊C₈	—	2	1	no	—
483	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
484	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
485	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
486	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
487	#103	—	2	1	no	—
488	#103	—	2	1	no	—
489	#103	—	2	1	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#103	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#101	—	2	2	no	—
500	#101	—	4	1	no	—
501	#101	—	4	1	no	—
502	#101	—	4	1	no	—
503	#100	—	2	2	no	—
504	#100	—	4	1	no	—
505	C₂²⋊C₈	—	2	1	no	—
506	C₂²⋊C₈	—	2	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	C₂²⋊C₈	—	2	1	no	—
509	#97	—	2	1	no	—
510	#97	—	2	1	no	—
511	#97	—	2	1	no	—
512	C₄×C₈	—	2	1	no	—
513	C₄×C₈	—	2	1	no	—
514	C₄×C₈	—	2	1	no	—
515	C₁₉	#24675	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	1	no	—
517	#41	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₂×Q₈	#41×C₁₉	1	2	yes	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
549	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
551	Q₁₆	—	2	4	no	—
552	Q₁₆	—	4	2	no	—
553	Q₁₆	—	4	2	no	—
554	Q₁₆	—	4	2	no	—
555	SD₁₆	—	2	4	no	—
556	SD₁₆	—	4	2	no	—
557	SD₁₆	—	4	2	no	—
558	SD₁₆	—	4	2	no	—
559	SD₁₆	—	4	2	no	—
560	D₈	—	4	2	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	—	2	1	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	2	1	no	—
565	M₁₆	—	2	1	no	—
566	M₁₆	—	2	1	no	—
567	M₁₆	—	2	1	no	—
568	M₁₆	—	2	1	no	—
569	M₁₆	—	2	1	no	—
570	M₁₆	—	2	1	no	—
571	M₁₆	—	2	1	no	—
572	M₁₆	#41×C₁₉	1	2	yes	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
586	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	—	4	1	no	—
593	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
594	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	4	1	no	—
606	C₄²	—	4	1	no	—
607	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
608	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
609	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
610	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
611	C₂³	—	2	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	8	1	no	—
616	C₂³	—	8	1	no	—
617	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
618	Q₈	—	2	2	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	2	1	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	—	8	1	no	—
653	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
654	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
655	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
656	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
659	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
660	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
661	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
663	C₈	—	2	2	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	16	1	no	—
682	C₂²	—	16	1	no	—
683	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
684	C₂²	C₁₉×#553	1	1	yes	characteristic
685	C₂²	C₁₉×#555	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₁₉×#525	1	1	yes	characteristic
697	C₄	C₁₉×#535	1	1	yes	characteristic
698	C₄	C₁₉×#546	1	1	yes	characteristic
699	C₄	C₁₉×#550	1	1	yes	characteristic
700	C₂	—	2	1	no	—
701	C₂	—	2	1	no	—
702	C₂	—	8	1	no	—
703	C₂	—	16	1	no	—
704	C₂	C₁₉×#2414	1	1	yes	characteristic
705	C₂	C₁₉×#3067	1	1	yes	characteristic
706	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#464	C₂	semidirect
3. C₄×C₁₉×#137	C₂	semidirect
4. C₁₉×#2925	C₂	semidirect
5. C₁₉×#2052	C₂	semidirect
7. C₁₉×#2020	C₂	semidirect
9. C₁₉×#1979	C₂	semidirect
10. C₁₉×#1977	C₂	semidirect
11. C₁₉×#1967	C₂	semidirect
12. C₁₉×#1950	C₂	semidirect
13. C₁₉×#1931	C₂	semidirect
14. C₁₉×#1930	C₂	semidirect
15. C₁₉×#1801	C₂	semidirect
257. #24675	C₁₉	direct (N × H)
321. C₂×#464	C₂×C₁₉	semidirect
322. C₄×#137	C₂×C₁₉	semidirect
323. #2925	C₂×C₁₉	semidirect
324. #2052	C₂×C₁₉	semidirect
326. #2020	C₂×C₁₉	semidirect
328. #1979	C₂×C₁₉	semidirect
329. #1977	C₂×C₁₉	semidirect
330. #1967	C₂×C₁₉	semidirect
331. #1950	C₂×C₁₉	semidirect
332. #1931	C₂×C₁₉	semidirect
333. #1930	C₂×C₁₉	semidirect
334. #1801	C₂×C₁₉	semidirect
515. C₁₉	#24675	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×#3040	2
C₂×C₁₉×#464	2
C₄×C₁₉×#137	2
C₁₉×#2925	2
C₁₉×#2052	2
C₁₉×#2051	2
C₁₉×#2020	2
C₁₉×#2019	2
C₁₉×#1979	2
C₁₉×#1977	2
C₁₉×#1967	2
C₁₉×#1950	2
C₁₉×#1931	2
C₁₉×#1930	2
C₁₉×#1801	2
#24675	19

Subgroups — C19×#24675 #18030634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24675 #18030634